LMFDB - Embedded newform 1134.2.g.m.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.m.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.40545 + 2.24159i) q^{7} -1.00000 q^{8} +(0.794182 + 1.37556i) q^{10} +(0.794182 + 1.37556i) q^{11} -4.81089 q^{13} +(2.64400 - 0.0963576i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.69963 - 4.67589i) q^{17} +(-3.54944 + 6.14781i) q^{19} +1.58836 q^{20} +1.58836 q^{22} +(-0.150186 + 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(-2.40545 + 4.16635i) q^{26} +(1.23855 - 2.33795i) q^{28} -8.27561 q^{29} +(1.35600 + 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} -5.39926 q^{34} +(-4.19963 + 0.153051i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.54944 + 6.14781i) q^{38} +(0.794182 - 1.37556i) q^{40} -5.87636 q^{41} +1.66621 q^{43} +(0.794182 - 1.37556i) q^{44} +(0.150186 + 0.260130i) q^{46} +(-1.33310 + 2.30900i) q^{47} +(-3.04944 + 6.30087i) q^{49} +2.47710 q^{50} +(2.40545 + 4.16635i) q^{52} +(2.44437 + 4.23377i) q^{53} -2.52290 q^{55} +(-1.40545 - 2.24159i) q^{56} +(-4.13781 + 7.16689i) q^{58} +(-3.23855 - 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(5.02654 + 8.70623i) q^{67} +(-2.69963 + 4.67589i) q^{68} +(-1.96727 + 3.71351i) q^{70} +12.7207 q^{71} +(8.02654 + 13.9024i) q^{73} +(-0.500000 - 0.866025i) q^{74} +7.09888 q^{76} +(-1.96727 + 3.71351i) q^{77} +(-4.19344 + 7.26325i) q^{79} +(-0.794182 - 1.37556i) q^{80} +(-2.93818 + 5.08907i) q^{82} -2.36584 q^{83} +8.57598 q^{85} +(0.833104 - 1.44298i) q^{86} +(-0.794182 - 1.37556i) q^{88} +(1.60507 - 2.78007i) q^{89} +(-6.76145 - 10.7840i) q^{91} +0.300372 q^{92} +(1.33310 + 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} -1.42402 q^{97} +(3.93199 + 5.79133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + q^{5} + 2 q^{7} - 6 q^{8} - q^{10} - q^{11} - 16 q^{13} + 4 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} - 2 q^{20} - 2 q^{22} - 7 q^{23} + 2 q^{25} - 8 q^{26} + 2 q^{28} + 10 q^{29}+ \cdots - 12 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + q^5 + 2 * q^7 - 6 * q^8 - q^10 - q^11 - 16 * q^13 + 4 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 - 2 * q^20 - 2 * q^22 - 7 * q^23 + 2 * q^25 - 8 * q^26 + 2 * q^28 + 10 * q^29 + 20 * q^31 + 3 * q^32 - 8 * q^34 - 13 * q^35 + 3 * q^37 + 3 * q^38 - q^40 + 12 * q^43 - q^44 + 7 * q^46 - 9 * q^47 + 4 * q^50 + 8 * q^52 + 15 * q^53 - 26 * q^55 - 2 * q^56 + 5 * q^58 - 14 * q^59 + 8 * q^61 + 40 * q^62 + 6 * q^64 - 12 * q^65 + q^67 - 4 * q^68 - 23 * q^70 + 14 * q^71 + 19 * q^73 - 3 * q^74 + 6 * q^76 - 23 * q^77 + 5 * q^79 + q^80 - 4 * q^83 + 4 * q^85 + 6 * q^86 + q^88 - 9 * q^89 - 46 * q^91 + 14 * q^92 + 9 * q^94 - 4 * q^95 - 56 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	−0.987147	−	0.159816i	$-0.948910\pi$
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	0.631978	+	0.774986i	$0.282243\pi$
$6$		0			0
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.794182	+	1.37556i	0.251142	+	0.434991i
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	0.960558	−	0.278080i	$-0.0896979\pi$
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	−0.721103	+	0.692828i	$0.756365\pi$
$12$		0			0
$13$	−4.81089			−1.33430			−0.667151	−	0.744923i	$-0.732486\pi$
$13$	−4.81089			−1.33430			−0.667151	+	0.744923i	$0.732486\pi$
$14$	2.64400	−	0.0963576i	0.706638	−	0.0257526i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	−0.981955	−	0.189115i	$-0.939438\pi$
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	0.327199	−	0.944955i	$-0.393895\pi$
$18$		0			0
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	0.0955331	+	0.995426i	$0.469544\pi$
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	−0.909831	+	0.414979i	$0.863789\pi$
$20$	1.58836			0.355169
$21$		0			0
$22$	1.58836			0.338640
$23$	−0.150186	+	0.260130i	−0.0313159	+	0.0542408i	−0.881259	−	0.472634i	$-0.843303\pi$
$23$	−0.150186	+	0.260130i	−0.0313159	+	0.0542408i	0.849943	+	0.526875i	$0.176636\pi$
$24$		0			0
$25$	1.23855	+	2.14523i	0.247710	+	0.429046i
$26$	−2.40545	+	4.16635i	−0.471747	+	0.817089i
$27$		0			0
$28$	1.23855	−	2.33795i	0.234064	−	0.441830i
$29$	−8.27561			−1.53674			−0.768371	−	0.640004i	$-0.778933\pi$
$29$	−8.27561			−1.53674			−0.768371	+	0.640004i	$0.778933\pi$
$30$		0			0
$31$	1.35600	+	2.34867i	0.243545	+	0.421833i	0.961722	−	0.274028i	$-0.0883561\pi$
$31$	1.35600	+	2.34867i	0.243545	+	0.421833i	−0.718176	+	0.695861i	$0.755023\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−5.39926			−0.925965
$35$	−4.19963	+	0.153051i	−0.709867	+	0.0258703i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	3.54944	+	6.14781i	0.575796	+	0.997307i
$39$		0			0
$40$	0.794182	−	1.37556i	0.125571	−	0.217496i
$41$	−5.87636			−0.917733			−0.458866	−	0.888505i	$-0.651744\pi$
$41$	−5.87636			−0.917733			−0.458866	+	0.888505i	$0.651744\pi$
$42$		0			0
$43$	1.66621			0.254094			0.127047	−	0.991897i	$-0.459450\pi$
$43$	1.66621			0.254094			0.127047	+	0.991897i	$0.459450\pi$
$44$	0.794182	−	1.37556i	0.119727	−	0.207374i
$45$		0			0
$46$	0.150186	+	0.260130i	0.0221437	+	0.0383540i
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	−0.946721	−	0.322055i	$-0.895627\pi$
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	0.752268	+	0.658857i	$0.228960\pi$
$48$		0			0
$49$	−3.04944	+	6.30087i	−0.435635	+	0.900124i
$50$	2.47710			0.350315
$51$		0			0
$52$	2.40545	+	4.16635i	0.333575	+	0.577769i
$53$	2.44437	+	4.23377i	0.335760	+	0.581553i	0.983630	−	0.180197i	$-0.0576736\pi$
$53$	2.44437	+	4.23377i	0.335760	+	0.581553i	−0.647871	+	0.761750i	$0.724340\pi$
$54$		0			0
$55$	−2.52290			−0.340188
$56$	−1.40545	−	2.24159i	−0.187811	−	0.299545i
$57$		0			0
$58$	−4.13781	+	7.16689i	−0.543321	+	0.941059i
$59$	−3.23855	−	5.60933i	−0.421623	−	0.730273i	0.574475	−	0.818522i	$-0.305206\pi$
$59$	−3.23855	−	5.60933i	−0.421623	−	0.730273i	−0.996098	+	0.0882491i	$0.971873\pi$
$60$		0			0
$61$	2.23855	−	3.87728i	0.286617	−	0.496435i	−0.686383	−	0.727240i	$-0.740803\pi$
$61$	2.23855	−	3.87728i	0.286617	−	0.496435i	0.973000	+	0.230805i	$0.0741360\pi$
$62$	2.71201			0.344425
$63$		0			0
$64$	1.00000			0.125000
$65$	3.82072	−	6.61769i	0.473902	−	0.820823i
$66$		0			0
$67$	5.02654	+	8.70623i	0.614090	+	1.06363i	0.990543	+	0.137199i	$0.0438101\pi$
$67$	5.02654	+	8.70623i	0.614090	+	1.06363i	−0.376454	+	0.926435i	$0.622857\pi$
$68$	−2.69963	+	4.67589i	−0.327378	+	0.567035i
$69$		0			0
$70$	−1.96727	+	3.71351i	−0.235134	+	0.443849i
$71$	12.7207			1.50967			0.754833	−	0.655917i	$-0.227718\pi$
$71$	12.7207			1.50967			0.754833	+	0.655917i	$0.227718\pi$
$72$		0			0
$73$	8.02654	+	13.9024i	0.939436	+	1.62715i	0.766527	+	0.642213i	$0.221983\pi$
$73$	8.02654	+	13.9024i	0.939436	+	1.62715i	0.172909	+	0.984938i	$0.444683\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	7.09888			0.814298
$77$	−1.96727	+	3.71351i	−0.224191	+	0.423194i
$78$		0			0
$79$	−4.19344	+	7.26325i	−0.471799	+	0.817179i	−0.999479	−	0.0322635i	$-0.989728\pi$
$79$	−4.19344	+	7.26325i	−0.471799	+	0.817179i	0.527681	+	0.849443i	$0.323062\pi$
$80$	−0.794182	−	1.37556i	−0.0887922	−	0.153793i
$81$		0			0
$82$	−2.93818	+	5.08907i	−0.324467	+	0.561994i
$83$	−2.36584			−0.259684			−0.129842	−	0.991535i	$-0.541447\pi$
$83$	−2.36584			−0.259684			−0.129842	+	0.991535i	$0.541447\pi$
$84$		0			0
$85$	8.57598			0.930196
$86$	0.833104	−	1.44298i	0.0898359	−	0.155600i
$87$		0			0
$88$	−0.794182	−	1.37556i	−0.0846601	−	0.146636i
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	−0.768330	−	0.640054i	$-0.778912\pi$
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	0.938468	+	0.345367i	$0.112245\pi$
$90$		0			0
$91$	−6.76145	−	10.7840i	−0.708793	−	1.13047i
$92$	0.300372			0.0313159
$93$		0			0
$94$	1.33310	+	2.30900i	0.137499	+	0.238156i
$95$	−5.63781	−	9.76497i	−0.578427	−	1.00186i
$96$		0			0
$97$	−1.42402			−0.144587			−0.0722934	−	0.997383i	$-0.523032\pi$
$97$	−1.42402			−0.144587			−0.0722934	+	0.997383i	$0.523032\pi$
$98$	3.93199	+	5.79133i	0.397191	+	0.585012i
$99$		0			0
$100$	1.23855	−	2.14523i	0.123855	−	0.214523i
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	−0.993015	−	0.117984i	$-0.962357\pi$
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	0.394330	−	0.918969i	$-0.370977\pi$
$102$		0			0
$103$	3.04944	−	5.28179i	0.300470	−	0.520430i	−0.675772	−	0.737111i	$-0.736190\pi$
$103$	3.04944	−	5.28179i	0.300470	−	0.520430i	0.976243	+	0.216680i	$0.0695230\pi$
$104$	4.81089			0.471747
$105$		0			0
$106$	4.88874			0.474836
$107$	−1.54325	+	2.67299i	−0.149192	+	0.258408i	−0.930929	−	0.365200i	$-0.881001\pi$
$107$	−1.54325	+	2.67299i	−0.149192	+	0.258408i	0.781737	+	0.623608i	$0.214334\pi$
$108$		0			0
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	0.915598	−	0.402095i	$-0.131718\pi$
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	−0.806023	+	0.591884i	$0.798384\pi$
$110$	−1.26145	+	2.18490i	−0.120275	+	0.208322i
$111$		0			0
$112$	−2.64400	+	0.0963576i	−0.249834	+	0.00910494i
$113$	19.4647			1.83109			0.915543	−	0.402219i	$-0.131761\pi$
$113$	19.4647			1.83109			0.915543	+	0.402219i	$0.131761\pi$
$114$		0			0
$115$	−0.238550	−	0.413181i	−0.0222449	−	0.0385293i
$116$	4.13781	+	7.16689i	0.384186	+	0.665429i
$117$		0			0
$118$	−6.47710			−0.596265
$119$	6.68725	−	12.6232i	0.613019	−	1.15716i
$120$		0			0
$121$	4.23855	−	7.34138i	0.385323	−	0.667399i
$122$	−2.23855	−	3.87728i	−0.202669	−	0.351033i
$123$		0			0
$124$	1.35600	−	2.34867i	0.121773	−	0.210917i
$125$	−11.8764			−1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.82072	−	6.61769i	−0.335100	−	0.580410i
$131$	1.58836	−	2.75113i	0.138776	−	0.240367i	−0.788258	−	0.615345i	$-0.789017\pi$
$131$	1.58836	−	2.75113i	0.138776	−	0.240367i	0.927034	+	0.374978i	$0.122350\pi$
$132$		0			0
$133$	−18.7694	+	0.684031i	−1.62752	+	0.0593130i
$134$	10.0531			0.868454
$135$		0			0
$136$	2.69963	+	4.67589i	0.231491	+	0.400955i
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.816397	+	0.577491i	$0.195968\pi$
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.0919231	+	0.995766i	$0.470699\pi$
$138$		0			0
$139$	−13.0531			−1.10715			−0.553574	−	0.832800i	$-0.686736\pi$
$139$	−13.0531			−1.10715			−0.553574	+	0.832800i	$0.686736\pi$
$140$	2.23236	+	3.56046i	0.188669	+	0.300914i
$141$		0			0
$142$	6.36033	−	11.0164i	0.533747	−	0.924478i
$143$	−3.82072	−	6.61769i	−0.319505	−	0.553399i
$144$		0			0
$145$	6.57234	−	11.3836i	0.545803	−	0.945359i
$146$	16.0531			1.32856
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	0.739404	+	0.673262i	$0.235107\pi$
$150$		0			0
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	0.876468	−	0.481461i	$-0.159894\pi$
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	−0.855191	+	0.518313i	$0.826560\pi$
$152$	3.54944	−	6.14781i	0.287898	−	0.498654i
$153$		0			0
$154$	2.23236	+	3.56046i	0.179889	+	0.286910i
$155$	−4.30766			−0.345999
$156$		0			0
$157$	−4.43199	−	7.67643i	−0.353711	−	0.612646i	0.633185	−	0.774000i	$-0.281747\pi$
$157$	−4.43199	−	7.67643i	−0.353711	−	0.612646i	−0.986897	+	0.161354i	$0.948414\pi$
$158$	4.19344	+	7.26325i	0.333612	+	0.577833i
$159$		0			0
$160$	−1.58836			−0.125571
$161$	−0.794182	+	0.0289431i	−0.0625903	+	0.00228104i
$162$		0			0
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	−0.0116689	−	0.999932i	$-0.503714\pi$
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	0.871801	−	0.489860i	$-0.162952\pi$
$164$	2.93818	+	5.08907i	0.229433	+	0.397390i
$165$		0			0
$166$	−1.18292	+	2.04887i	−0.0918122	+	0.159023i
$167$	−3.30037			−0.255390			−0.127695	−	0.991813i	$-0.540758\pi$
$167$	−3.30037			−0.255390			−0.127695	+	0.991813i	$0.540758\pi$
$168$		0			0
$169$	10.1447			0.780360
$170$	4.28799	−	7.42702i	0.328874	−	0.569626i
$171$		0			0
$172$	−0.833104	−	1.44298i	−0.0635236	−	0.110026i
$173$	−9.55377	+	16.5476i	−0.726360	+	1.25809i	0.232052	+	0.972703i	$0.425456\pi$
$173$	−9.55377	+	16.5476i	−0.726360	+	1.25809i	−0.958412	+	0.285389i	$0.907877\pi$
$174$		0			0
$175$	−3.06801	+	5.79133i	−0.231920	+	0.437783i
$176$	−1.58836			−0.119727
$177$		0			0
$178$	−1.60507	−	2.78007i	−0.120305	−	0.208375i
$179$	−8.03706	−	13.9206i	−0.600718	−	1.04047i	−0.992712	−	0.120507i	$-0.961548\pi$
$179$	−8.03706	−	13.9206i	−0.600718	−	1.04047i	0.391994	−	0.919968i	$-0.371785\pi$
$180$		0			0
$181$	8.05308			0.598581			0.299291	−	0.954162i	$-0.403250\pi$
$181$	8.05308			0.598581			0.299291	+	0.954162i	$0.403250\pi$
$182$	−12.7200	+	0.463566i	−0.942868	+	0.0343618i
$183$		0			0
$184$	0.150186	−	0.260130i	0.0110719	−	0.0191770i
$185$	0.794182	+	1.37556i	0.0583894	+	0.101133i
$186$		0			0
$187$	4.28799	−	7.42702i	0.313569	−	0.543118i
$188$	2.66621			0.194453
$189$		0			0
$190$	−11.2756			−0.818019
$191$	11.9814	−	20.7524i	0.866946	−	1.50159i	0.00184390	−	0.999998i	$-0.499413\pi$
$191$	11.9814	−	20.7524i	0.866946	−	1.50159i	0.865102	−	0.501596i	$-0.167254\pi$
$192$		0			0
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	0.635051	−	0.772470i	$-0.280979\pi$
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	−0.986504	+	0.163735i	$0.947646\pi$
$194$	−0.712008	+	1.23323i	−0.0511192	+	0.0885410i
$195$		0			0
$196$	6.98143	−	0.509538i	0.498674	−	0.0363956i
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$		0			0
$199$	9.04944	+	15.6741i	0.641498	+	1.11111i	0.985098	+	0.171991i	$0.0550200\pi$
$199$	9.04944	+	15.6741i	0.641498	+	1.11111i	−0.343601	+	0.939116i	$0.611647\pi$
$200$	−1.23855	−	2.14523i	−0.0875787	−	0.151691i
$201$		0			0
$202$	−12.0334			−0.846669
$203$	−11.6309	−	18.5505i	−0.816331	−	1.30199i
$204$		0			0
$205$	4.66690	−	8.08330i	0.325950	−	0.564562i
$206$	−3.04944	−	5.28179i	−0.212465	−	0.368000i
$207$		0			0
$208$	2.40545	−	4.16635i	0.166788	−	0.288885i
$209$	−11.2756			−0.779950
$210$		0			0
$211$	−0.332415			−0.0228844			−0.0114422	−	0.999935i	$-0.503642\pi$
$211$	−0.332415			−0.0228844			−0.0114422	+	0.999935i	$0.503642\pi$
$212$	2.44437	−	4.23377i	0.167880	−	0.290776i
$213$		0			0
$214$	1.54325	+	2.67299i	0.105495	+	0.182722i
$215$	−1.32327	+	2.29197i	−0.0902464	+	0.156311i
$216$		0			0
$217$	−3.35896	+	6.34053i	−0.228021	+	0.430423i
$218$	2.28799			0.154962
$219$		0			0
$220$	1.26145	+	2.18490i	0.0850469	+	0.147306i
$221$	12.9876	+	22.4952i	0.873642	+	1.51319i
$222$		0			0
$223$	−6.33242			−0.424050			−0.212025	−	0.977264i	$-0.568006\pi$
$223$	−6.33242			−0.424050			−0.212025	+	0.977264i	$0.568006\pi$
$224$	−1.23855	+	2.33795i	−0.0827541	+	0.156211i
$225$		0			0
$226$	9.73236	−	16.8569i	0.647387	−	1.12131i
$227$	11.6545	+	20.1862i	0.773537	+	1.33981i	0.935613	+	0.353028i	$0.114848\pi$
$227$	11.6545	+	20.1862i	0.773537	+	1.33981i	−0.162075	+	0.986778i	$0.551819\pi$
$228$		0			0
$229$	2.47710	−	4.29046i	0.163691	−	0.283522i	−0.772498	−	0.635017i	$-0.780993\pi$
$229$	2.47710	−	4.29046i	0.163691	−	0.283522i	0.936190	+	0.351495i	$0.114327\pi$
$230$	−0.477100			−0.0314590
$231$		0			0
$232$	8.27561			0.543321
$233$	−7.13781	+	12.3630i	−0.467613	+	0.809930i	−0.999315	−	0.0370017i	$-0.988219\pi$
$233$	−7.13781	+	12.3630i	−0.467613	+	0.809930i	0.531702	+	0.846932i	$0.321553\pi$
$234$		0			0
$235$	−2.11745	−	3.66754i	−0.138127	−	0.239244i
$236$	−3.23855	+	5.60933i	−0.210812	+	0.365136i
$237$		0			0
$238$	−7.58836	−	12.1029i	−0.491881	−	0.784515i
$239$	−4.97524			−0.321822			−0.160911	−	0.986969i	$-0.551443\pi$
$239$	−4.97524			−0.321822			−0.160911	+	0.986969i	$0.551443\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	−4.23855	−	7.34138i	−0.272464	−	0.471922i
$243$		0			0
$244$	−4.47710			−0.286617
$245$	−6.24543	−	9.19874i	−0.399006	−	0.587686i
$246$		0			0
$247$	17.0760	−	29.5765i	1.08652	−	1.88191i
$248$	−1.35600	−	2.34867i	−0.0861063	−	0.149141i
$249$		0			0
$250$	−5.93818	+	10.2852i	−0.375563	+	0.650495i
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$	−6.71998	+	11.6393i	−0.421649	+	0.730318i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	−0.850213	−	0.526439i	$-0.823527\pi$
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	0.881016	+	0.473087i	$0.156860\pi$
$258$		0			0
$259$	2.64400	−	0.0963576i	0.164290	−	0.00598737i
$260$	−7.64145			−0.473902
$261$		0			0
$262$	−1.58836	−	2.75113i	−0.0981295	−	0.169965i
$263$	−8.59269	−	14.8830i	−0.529848	−	0.917724i	−0.999394	−	0.0348158i	$-0.988916\pi$
$263$	−8.59269	−	14.8830i	−0.529848	−	0.917724i	0.469545	−	0.882908i	$-0.344418\pi$
$264$		0			0
$265$	−7.76509			−0.477006
$266$	−8.79232	+	16.5968i	−0.539092	+	1.01762i
$267$		0			0
$268$	5.02654	−	8.70623i	0.307045	−	0.531817i
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	0.969069	+	0.246791i	$0.0793761\pi$
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	−0.270807	+	0.962634i	$0.587291\pi$
$270$		0			0
$271$	7.00364	−	12.1307i	0.425441	−	0.736885i	−0.571021	−	0.820936i	$-0.693452\pi$
$271$	7.00364	−	12.1307i	0.425441	−	0.736885i	0.996462	+	0.0840504i	$0.0267857\pi$
$272$	5.39926			0.327378
$273$		0			0
$274$	21.2632			1.28456
$275$	−1.96727	+	3.40741i	−0.118631	+	0.205474i
$276$		0			0
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	−0.881163	−	0.472813i	$-0.843239\pi$
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	0.0311139	−	0.999516i	$-0.490095\pi$
$278$	−6.52654	+	11.3043i	−0.391436	+	0.677987i
$279$		0			0
$280$	4.19963	−	0.153051i	0.250976	−	0.00914654i
$281$	17.5956			1.04967			0.524834	−	0.851204i	$-0.324127\pi$
$281$	17.5956			1.04967			0.524834	+	0.851204i	$0.324127\pi$
$282$		0			0
$283$	9.26145	+	16.0413i	0.550536	+	0.953556i	0.998236	+	0.0593725i	$0.0189100\pi$
$283$	9.26145	+	16.0413i	0.550536	+	0.953556i	−0.447700	+	0.894184i	$0.647757\pi$
$284$	−6.36033	−	11.0164i	−0.377416	−	0.653704i
$285$		0			0
$286$	−7.64145			−0.451848
$287$	−8.25890	−	13.1724i	−0.487508	−	0.777541i
$288$		0			0
$289$	−6.07598	+	10.5239i	−0.357411	+	0.619054i
$290$	−6.57234	−	11.3836i	−0.385941	−	0.668470i
$291$		0			0
$292$	8.02654	−	13.9024i	0.469718	−	0.813575i
$293$	14.0851			0.822862			0.411431	−	0.911441i	$-0.365029\pi$
$293$	14.0851			0.822862			0.411431	+	0.911441i	$0.365029\pi$
$294$		0			0
$295$	10.2880			0.598990
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$		0			0
$298$	2.60439	+	4.51093i	0.150868	+	0.261311i
$299$	0.722528	−	1.25146i	0.0417849	−	0.0723736i
$300$		0			0
$301$	2.34176	+	3.73495i	0.134977	+	0.215279i
$302$	0.522900			0.0300895
$303$		0			0
$304$	−3.54944	−	6.14781i	−0.203574	−	0.352601i
$305$	3.55563	+	6.15854i	0.203595	+	0.352637i
$306$		0			0
$307$	−5.85532			−0.334180			−0.167090	−	0.985942i	$-0.553437\pi$
$307$	−5.85532			−0.334180			−0.167090	+	0.985942i	$0.553437\pi$
$308$	4.19963	−	0.153051i	0.239296	−	0.00872089i
$309$		0			0
$310$	−2.15383	+	3.73054i	−0.122329	+	0.211880i
$311$	−0.405446	−	0.702253i	−0.0229907	−	0.0398211i	0.854301	−	0.519778i	$-0.173985\pi$
$311$	−0.405446	−	0.702253i	−0.0229907	−	0.0398211i	−0.877292	+	0.479957i	$0.840652\pi$
$312$		0			0
$313$	−5.28799	+	9.15907i	−0.298895	+	0.517701i	−0.975883	−	0.218292i	$-0.929951\pi$
$313$	−5.28799	+	9.15907i	−0.298895	+	0.517701i	0.676988	+	0.735994i	$0.263285\pi$
$314$	−8.86398			−0.500223
$315$		0			0
$316$	8.38688			0.471799
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	−0.984898	−	0.173136i	$-0.944610\pi$
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	0.642389	+	0.766379i	$0.277943\pi$
$318$		0			0
$319$	−6.57234	−	11.3836i	−0.367981	−	0.637361i
$320$	−0.794182	+	1.37556i	−0.0443961	+	0.0768963i
$321$		0			0
$322$	−0.372026	+	0.702253i	−0.0207322	+	0.0391350i
$323$	38.3287			2.13267
$324$		0			0
$325$	−5.95853	−	10.3205i	−0.330520	−	0.572477i
$326$	−10.9814	−	19.0204i	−0.608205	−	1.05344i
$327$		0			0
$328$	5.87636			0.324467
$329$	−7.04944	+	0.256909i	−0.388648	+	0.0141639i
$330$		0			0
$331$	7.83310	−	13.5673i	0.430546	−	0.745728i	−0.566374	−	0.824148i	$-0.691654\pi$
$331$	7.83310	−	13.5673i	0.430546	−	0.745728i	0.996920	+	0.0784202i	$0.0249876\pi$
$332$	1.18292	+	2.04887i	0.0649211	+	0.112447i
$333$		0			0
$334$	−1.65019	+	2.85821i	−0.0902942	+	0.156394i
$335$	−15.9680			−0.872423
$336$		0			0
$337$	8.42402			0.458885			0.229443	−	0.973322i	$-0.426310\pi$
$337$	8.42402			0.458885			0.229443	+	0.973322i	$0.426310\pi$
$338$	5.07234	−	8.78555i	0.275899	−	0.477871i
$339$		0			0
$340$	−4.28799	−	7.42702i	−0.232549	−	0.402787i
$341$	−2.15383	+	3.73054i	−0.116636	+	0.202020i
$342$		0			0
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$	−1.66621			−0.0898359
$345$		0			0
$346$	9.55377	+	16.5476i	0.513614	+	0.889606i
$347$	−0.283662	−	0.491316i	−0.0152277	−	0.0263752i	0.858311	−	0.513130i	$-0.171514\pi$
$347$	−0.283662	−	0.491316i	−0.0152277	−	0.0263752i	−0.873539	+	0.486754i	$0.838181\pi$
$348$		0			0
$349$	0.00728378			0.000389892			0.000194946	−	1.00000i	$-0.499938\pi$
$349$	0.00728378			0.000389892			0.000194946		1.00000i	$0.499938\pi$
$350$	3.48143	+	5.55264i	0.186090	+	0.296801i
$351$		0			0
$352$	−0.794182	+	1.37556i	−0.0423300	+	0.0733178i
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	0.763803	−	0.645449i	$-0.223330\pi$
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	−0.940877	+	0.338748i	$0.889996\pi$
$354$		0			0
$355$	−10.1025	+	17.4981i	−0.536186	+	0.928702i
$356$	−3.21015			−0.170138
$357$		0			0
$358$	−16.0741			−0.849544
$359$	−0.398568	+	0.690339i	−0.0210356	+	0.0364347i	−0.876352	−	0.481672i	$-0.840030\pi$
$359$	−0.398568	+	0.690339i	−0.0210356	+	0.0364347i	0.855316	+	0.518107i	$0.173363\pi$
$360$		0			0
$361$	−15.6971	−	27.1881i	−0.826162	−	1.43095i
$362$	4.02654	−	6.97418i	0.211630	−	0.366555i
$363$		0			0
$364$	−5.95853	+	11.2476i	−0.312312	+	0.589535i
$365$	−25.4981			−1.33463
$366$		0			0
$367$	7.71634	+	13.3651i	0.402790	+	0.697652i	0.994061	−	0.108820i	$-0.0347073\pi$
$367$	7.71634	+	13.3651i	0.402790	+	0.697652i	−0.591272	+	0.806472i	$0.701374\pi$
$368$	−0.150186	−	0.260130i	−0.00782898	−	0.0135602i
$369$		0			0
$370$	1.58836			0.0825751
$371$	−6.05494	+	11.4296i	−0.314357	+	0.593395i
$372$		0			0
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	−0.967606	−	0.252467i	$-0.918758\pi$
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	0.702445	+	0.711738i	$0.252092\pi$
$374$	−4.28799	−	7.42702i	−0.221727	−	0.384042i
$375$		0			0
$376$	1.33310	−	2.30900i	0.0687496	−	0.119078i
$377$	39.8131			2.05048
$378$		0			0
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	−5.63781	+	9.76497i	−0.289213	+	0.500932i
$381$		0			0
$382$	−11.9814	−	20.7524i	−0.613023	−	1.06179i
$383$	3.13348	−	5.42734i	0.160113	−	0.277324i	−0.774796	−	0.632211i	$-0.782147\pi$
$383$	3.13348	−	5.42734i	0.160113	−	0.277324i	0.934909	+	0.354887i	$0.115481\pi$
$384$		0			0
$385$	−3.54580	−	5.65531i	−0.180711	−	0.288221i
$386$	−9.76509			−0.497030
$387$		0			0
$388$	0.712008	+	1.23323i	0.0361467	+	0.0626080i
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	0.998381	+	0.0568774i	$0.0181144\pi$
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	−0.449933	+	0.893062i	$0.648552\pi$
$390$		0			0
$391$	1.62178			0.0820172
$392$	3.04944	−	6.30087i	0.154020	−	0.318242i
$393$		0			0
$394$	−9.12178	+	15.7994i	−0.459549	+	0.795962i
$395$	−6.66071	−	11.5367i	−0.335137	−	0.580473i
$396$		0			0
$397$	2.05308	−	3.55605i	0.103041	−	0.178473i	−0.809895	−	0.586575i	$-0.800476\pi$
$397$	2.05308	−	3.55605i	0.103041	−	0.178473i	0.912936	+	0.408102i	$0.133809\pi$
$398$	18.0989			0.907215
$399$		0			0
$400$	−2.47710			−0.123855
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	−0.995740	−	0.0922024i	$-0.970609\pi$
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	0.577720	+	0.816235i	$0.303943\pi$
$402$		0			0
$403$	−6.52359	−	11.2992i	−0.324963	−	0.562853i
$404$	−6.01671	+	10.4212i	−0.299343	+	0.518476i
$405$		0			0
$406$	−21.8807	+	0.797418i	−1.08592	+	0.0395752i
$407$	1.58836			0.0787323
$408$		0			0
$409$	4.38255	+	7.59079i	0.216703	+	0.375341i	0.953798	−	0.300449i	$-0.0971364\pi$
$409$	4.38255	+	7.59079i	0.216703	+	0.375341i	−0.737095	+	0.675789i	$0.763803\pi$
$410$	−4.66690	−	8.08330i	−0.230482	−	0.399206i
$411$		0			0
$412$	−6.09888			−0.300470
$413$	8.02221	−	15.1431i	0.394747	−	0.745144i
$414$		0			0
$415$	1.87890	−	3.25436i	0.0922318	−	0.159750i
$416$	−2.40545	−	4.16635i	−0.117937	−	0.204272i
$417$		0			0
$418$	−5.63781	+	9.76497i	−0.275754	+	0.477620i
$419$	0.420297			0.0205329			0.0102664	−	0.999947i	$-0.496732\pi$
$419$	0.420297			0.0205329			0.0102664	+	0.999947i	$0.496732\pi$
$420$		0			0
$421$	−6.57598			−0.320494			−0.160247	−	0.987077i	$-0.551229\pi$
$421$	−6.57598			−0.320494			−0.160247	+	0.987077i	$0.551229\pi$
$422$	−0.166208	+	0.287880i	−0.00809086	+	0.0140138i
$423$		0			0
$424$	−2.44437	−	4.23377i	−0.118709	−	0.205610i
$425$	6.68725	−	11.5827i	0.324379	−	0.561841i
$426$		0			0
$427$	11.8374	−	0.431403i	0.572854	−	0.0208770i
$428$	3.08650			0.149192
$429$		0			0
$430$	1.32327	+	2.29197i	0.0638138	+	0.110529i
$431$	11.0439	+	19.1287i	0.531968	+	0.921395i	0.999304	+	0.0373155i	$0.0118806\pi$
$431$	11.0439	+	19.1287i	0.531968	+	0.921395i	−0.467336	+	0.884080i	$0.654786\pi$
$432$		0			0
$433$	−9.43268			−0.453306			−0.226653	−	0.973976i	$-0.572778\pi$
$433$	−9.43268			−0.453306			−0.226653	+	0.973976i	$0.572778\pi$
$434$	3.81158	+	6.07921i	0.182962	+	0.291811i
$435$		0			0
$436$	1.14400	−	1.98146i	0.0547875	−	0.0948947i
$437$	−1.06615	−	1.84663i	−0.0510010	−	0.0883363i
$438$		0			0
$439$	15.6032	−	27.0256i	0.744701	−	1.28986i	−0.205634	−	0.978629i	$-0.565926\pi$
$439$	15.6032	−	27.0256i	0.744701	−	1.28986i	0.950334	−	0.311231i	$-0.100741\pi$
$440$	2.52290			0.120275
$441$		0			0
$442$	25.9752			1.23552
$443$	−6.52723	+	11.3055i	−0.310118	+	0.537140i	−0.978388	−	0.206779i	$-0.933702\pi$
$443$	−6.52723	+	11.3055i	−0.310118	+	0.537140i	0.668270	+	0.743919i	$0.267035\pi$
$444$		0			0
$445$	2.54944	+	4.41576i	0.120855	+	0.209327i
$446$	−3.16621	+	5.48403i	−0.149924	+	0.259676i
$447$		0			0
$448$	1.40545	+	2.24159i	0.0664011	+	0.105905i
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$		0			0
$451$	−4.66690	−	8.08330i	−0.219756	−	0.380628i
$452$	−9.73236	−	16.8569i	−0.457772	−	0.792884i
$453$		0			0
$454$	23.3090			1.09395
$455$	20.2040	−	0.736312i	0.947176	−	0.0345188i
$456$		0			0
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	−0.422629	−	0.906303i	$-0.638893\pi$
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	0.996196	−	0.0871436i	$-0.0277739\pi$
$458$	−2.47710	−	4.29046i	−0.115747	−	0.200480i
$459$		0			0
$460$	−0.238550	+	0.413181i	−0.0111224	+	0.0192646i
$461$	−3.51052			−0.163501			−0.0817506	−	0.996653i	$-0.526051\pi$
$461$	−3.51052			−0.163501			−0.0817506	+	0.996653i	$0.526051\pi$
$462$		0			0
$463$	−17.3883			−0.808101			−0.404050	−	0.914737i	$-0.632398\pi$
$463$	−17.3883			−0.808101			−0.404050	+	0.914737i	$0.632398\pi$
$464$	4.13781	−	7.16689i	0.192093	−	0.332715i
$465$		0			0
$466$	7.13781	+	12.3630i	0.330652	+	0.572707i
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	−0.668370	−	0.743829i	$-0.733008\pi$
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	0.978360	+	0.206911i	$0.0663410\pi$
$468$		0			0
$469$	−12.4512	+	23.5036i	−0.574945	+	1.08529i
$470$	−4.23491			−0.195342
$471$		0			0
$472$	3.23855	+	5.60933i	0.149066	+	0.258190i
$473$	1.32327	+	2.29197i	0.0608441	+	0.105385i
$474$		0			0
$475$	−17.5846			−0.806839
$476$	−14.2756	+	0.520259i	−0.654322	+	0.0238460i
$477$		0			0
$478$	−2.48762	+	4.30868i	−0.113781	+	0.197075i
$479$	−10.4029	−	18.0183i	−0.475321	−	0.823279i	0.524280	−	0.851546i	$-0.324335\pi$
$479$	−10.4029	−	18.0183i	−0.475321	−	0.823279i	−0.999600	+	0.0282667i	$0.991001\pi$
$480$		0			0
$481$	−2.40545	+	4.16635i	−0.109679	+	0.189969i
$482$	13.0000			0.592134
$483$		0			0
$484$	−8.47710			−0.385323
$485$	1.13093	−	1.95882i	0.0513528	−	0.0889456i
$486$		0			0
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	0.954181	+	0.299230i	$0.0967298\pi$
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	−0.217950	+	0.975960i	$0.569937\pi$
$488$	−2.23855	+	3.87728i	−0.101334	+	0.175516i
$489$		0			0
$490$	−11.0891	+	0.809332i	−0.500952	+	0.0365619i
$491$	19.3214			0.871963			0.435982	−	0.899956i	$-0.356401\pi$
$491$	19.3214			0.871963			0.435982	+	0.899956i	$0.356401\pi$
$492$		0			0
$493$	22.3411	+	38.6959i	1.00619	+	1.74277i
$494$	−17.0760	−	29.5765i	−0.768285	−	1.33071i
$495$		0			0
$496$	−2.71201			−0.121773
$497$	17.8782	+	28.5145i	0.801948	+	1.27905i
$498$		0			0
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	−0.713826	−	0.700323i	$-0.753039\pi$
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	0.963411	+	0.268030i	$0.0863726\pi$
$500$	5.93818	+	10.2852i	0.265563	+	0.459969i
$501$		0			0
$502$	1.21634	−	2.10676i	0.0542878	−	0.0940293i
$503$	−40.7651			−1.81763			−0.908813	−	0.417204i	$-0.863010\pi$
$503$	−40.7651			−1.81763			−0.908813	+	0.417204i	$0.863010\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$	−0.238550	+	0.413181i	−0.0106048	+	0.0183681i
$507$		0			0
$508$	6.71998	+	11.6393i	0.298151	+	0.516413i
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	−0.881594	−	0.472009i	$-0.843529\pi$
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	0.849568	+	0.527478i	$0.176862\pi$
$510$		0			0
$511$	−19.8825	+	37.5313i	−0.879552	+	1.66028i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.493810	−	0.855304i	−0.0217810	−	0.0377259i
$515$	4.84362	+	8.38940i	0.213436	+	0.369681i
$516$		0			0
$517$	−4.23491			−0.186251
$518$	1.23855	−	2.33795i	0.0544188	−	0.102723i
$519$		0			0
$520$	−3.82072	+	6.61769i	−0.167550	+	0.290205i
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	0.996177	−	0.0873630i	$-0.0278440\pi$
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	−0.573747	+	0.819033i	$0.694511\pi$
$522$		0			0
$523$	−18.3454	+	31.7752i	−0.802189	+	1.38943i	0.115984	+	0.993251i	$0.462998\pi$
$523$	−18.3454	+	31.7752i	−0.802189	+	1.38943i	−0.918173	+	0.396180i	$0.870335\pi$
$524$	−3.17673			−0.138776
$525$		0			0
$526$	−17.1854			−0.749319
$527$	7.32141	−	12.6811i	0.318926	−	0.552396i
$528$		0			0
$529$	11.4549	+	19.8404i	0.498039	+	0.862628i
$530$	−3.88255	+	6.72477i	−0.168647	+	0.292105i
$531$		0			0
$532$	9.97710	+	15.9128i	0.432562	+	0.689907i
$533$	28.2705			1.22453
$534$		0			0
$535$	−2.45125	−	4.24568i	−0.105977	−	0.183557i
$536$	−5.02654	−	8.70623i	−0.217114	−	0.376052i
$537$		0			0
$538$	22.9047			0.987491
$539$	−11.0891	+	0.809332i	−0.477639	+	0.0348604i
$540$		0			0
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	−0.898849	−	0.438258i	$-0.855596\pi$
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	0.828967	+	0.559298i	$0.188929\pi$
$542$	−7.00364	−	12.1307i	−0.300832	−	0.521057i
$543$		0			0
$544$	2.69963	−	4.67589i	0.115746	−	0.200477i
$545$	−3.63416			−0.155670
$546$		0			0
$547$	5.91706			0.252995			0.126498	−	0.991967i	$-0.459626\pi$
$547$	5.91706			0.252995			0.126498	+	0.991967i	$0.459626\pi$
$548$	10.6316	−	18.4145i	0.454160	−	0.786628i
$549$		0			0
$550$	1.96727	+	3.40741i	0.0838846	+	0.145292i
$551$	29.3738	−	50.8769i	1.25137	−	2.16743i
$552$		0			0
$553$	−22.1749	+	0.808139i	−0.942971	+	0.0343656i
$554$	−28.2953			−1.20215
$555$		0			0
$556$	6.52654	+	11.3043i	0.276787	+	0.479409i
$557$	12.8040	+	22.1772i	0.542523	+	0.939678i	0.998758	+	0.0498188i	$0.0158644\pi$
$557$	12.8040	+	22.1772i	0.542523	+	0.939678i	−0.456235	+	0.889859i	$0.650802\pi$
$558$		0			0
$559$	−8.01594			−0.339038
$560$	1.96727	−	3.71351i	0.0831322	−	0.156924i
$561$		0			0
$562$	8.79782	−	15.2383i	0.371114	−	0.642788i
$563$	23.3189	+	40.3895i	0.982773	+	1.70221i	0.651443	+	0.758698i	$0.274164\pi$
$563$	23.3189	+	40.3895i	0.982773	+	1.70221i	0.331330	+	0.943515i	$0.392503\pi$
$564$		0			0
$565$	−15.4585	+	26.7750i	−0.650345	+	1.12643i
$566$	18.5229			0.778576
$567$		0			0
$568$	−12.7207			−0.533747
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	0.328219	+	0.944602i	$0.393551\pi$
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	−0.982159	+	0.188054i	$0.939782\pi$
$570$		0			0
$571$	7.83812	+	13.5760i	0.328015	+	0.568139i	0.982118	−	0.188267i	$-0.0602869\pi$
$571$	7.83812	+	13.5760i	0.328015	+	0.568139i	−0.654103	+	0.756406i	$0.726954\pi$
$572$	−3.82072	+	6.61769i	−0.159752	+	0.276699i
$573$		0			0
$574$	−15.5371	+	0.566231i	−0.648504	+	0.0236340i
$575$	−0.744051			−0.0310291
$576$		0			0
$577$	6.99567	+	12.1169i	0.291234	+	0.504431i	0.974102	−	0.226110i	$-0.0726010\pi$
$577$	6.99567	+	12.1169i	0.291234	+	0.504431i	−0.682868	+	0.730542i	$0.739268\pi$
$578$	6.07598	+	10.5239i	0.252728	+	0.437737i
$579$		0			0
$580$	−13.1447			−0.545803
$581$	−3.32505	−	5.30323i	−0.137947	−	0.220015i
$582$		0			0
$583$	−3.88255	+	6.72477i	−0.160799	+	0.278511i
$584$	−8.02654	−	13.9024i	−0.332141	−	0.575285i
$585$		0			0
$586$	7.04256	−	12.1981i	0.290926	−	0.503898i
$587$	−2.89602			−0.119532			−0.0597658	−	0.998212i	$-0.519035\pi$
$587$	−2.89602			−0.119532			−0.0597658	+	0.998212i	$0.519035\pi$
$588$		0			0
$589$	−19.2522			−0.793274
$590$	5.14400	−	8.90966i	0.211775	−	0.366805i
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	−0.904937	−	0.425546i	$-0.860082\pi$
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	0.821002	+	0.570925i	$0.193415\pi$
$594$		0			0
$595$	12.0531	+	19.2238i	0.494128	+	0.788100i
$596$	5.20877			0.213360
$597$		0			0
$598$	−0.722528	−	1.25146i	−0.0295464	−	0.0511758i
$599$	9.88255	+	17.1171i	0.403790	+	0.699385i	0.994180	−	0.107734i	$-0.0343593\pi$
$599$	9.88255	+	17.1171i	0.403790	+	0.699385i	−0.590390	+	0.807118i	$0.701026\pi$
$600$		0			0
$601$	26.8640			1.09580			0.547902	−	0.836542i	$-0.315427\pi$
$601$	26.8640			1.09580			0.547902	+	0.836542i	$0.315427\pi$
$602$	4.40545	−	0.160552i	0.179553	−	0.00654360i
$603$		0			0
$604$	0.261450	−	0.452845i	0.0106383	−	0.0184260i
$605$	6.73236	+	11.6608i	0.273709	+	0.474079i
$606$		0			0
$607$	7.62110	−	13.2001i	0.309331	−	0.535777i	−0.668885	−	0.743366i	$-0.733228\pi$
$607$	7.62110	−	13.2001i	0.309331	−	0.535777i	0.978216	+	0.207589i	$0.0665617\pi$
$608$	−7.09888			−0.287898
$609$		0			0
$610$	7.11126			0.287927
$611$	6.41342	−	11.1084i	0.259459	−	0.449396i
$612$		0			0
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	0.837246	−	0.546827i	$-0.184165\pi$
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	−0.892189	+	0.451662i	$0.850831\pi$
$614$	−2.92766	+	5.07085i	−0.118151	+	0.204643i
$615$		0			0
$616$	1.96727	−	3.71351i	0.0792635	−	0.149622i
$617$	18.4362			0.742215			0.371108	−	0.928590i	$-0.378978\pi$
$617$	18.4362			0.742215			0.371108	+	0.928590i	$0.378978\pi$
$618$		0			0
$619$	−0.0537728	−	0.0931373i	−0.00216131	−	0.00374350i	0.864943	−	0.501871i	$-0.167355\pi$
$619$	−0.0537728	−	0.0931373i	−0.00216131	−	0.00374350i	−0.867104	+	0.498127i	$0.834021\pi$
$620$	2.15383	+	3.73054i	0.0864998	+	0.149822i
$621$		0			0
$622$	−0.810892			−0.0325138
$623$	8.48762	−	0.309322i	0.340049	−	0.0123927i
$624$		0			0
$625$	3.23924	−	5.61053i	0.129570	−	0.224421i
$626$	5.28799	+	9.15907i	0.211351	+	0.366070i
$627$		0			0
$628$	−4.43199	+	7.67643i	−0.176856	+	0.306323i
$629$	−5.39926			−0.215282
$630$		0			0
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	4.19344	−	7.26325i	0.166806	−	0.288916i
$633$		0			0
$634$	6.09820	+	10.5624i	0.242190	+	0.419486i
$635$	10.6738	−	18.4875i	0.423576	−	0.733655i
$636$		0			0
$637$	14.6705	−	30.3128i	0.581268	−	1.20104i
$638$	−13.1447			−0.520403
$639$		0			0
$640$	0.794182	+	1.37556i	0.0313928	+	0.0543739i
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	0.642880	−	0.765967i	$-0.277739\pi$
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	−0.984787	+	0.173767i	$0.944406\pi$
$642$		0			0
$643$	−28.9642			−1.14224			−0.571119	−	0.820867i	$-0.693491\pi$
$643$	−28.9642			−1.14224			−0.571119	+	0.820867i	$0.693491\pi$
$644$	0.422156	+	0.673310i	0.0166353	+	0.0265321i
$645$		0			0
$646$	19.1643	−	33.1936i	0.754011	−	1.30599i
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	0.890056	−	0.455851i	$-0.150665\pi$
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	−0.839807	+	0.542886i	$0.817332\pi$
$648$		0			0
$649$	5.14400	−	8.90966i	0.201920	−	0.349735i
$650$	−11.9171			−0.467426
$651$		0			0
$652$	−21.9629			−0.860132
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	0.408144	+	0.912918i	$0.366176\pi$
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	−0.994682	+	0.102996i	$0.967157\pi$
$654$		0			0
$655$	2.52290	+	4.36979i	0.0985779	+	0.170742i
$656$	2.93818	−	5.08907i	0.114717	−	0.198695i
$657$		0			0
$658$	−3.30223	+	6.23345i	−0.128734	+	0.243005i
$659$	15.2632			0.594571			0.297286	−	0.954789i	$-0.403919\pi$
$659$	15.2632			0.594571			0.297286	+	0.954789i	$0.403919\pi$
$660$		0			0
$661$	13.6261	+	23.6011i	0.529994	+	0.917977i	0.999388	+	0.0349881i	$0.0111393\pi$
$661$	13.6261	+	23.6011i	0.529994	+	0.917977i	−0.469393	+	0.882989i	$0.655527\pi$
$662$	−7.83310	−	13.5673i	−0.304442	−	0.527309i
$663$		0			0
$664$	2.36584			0.0918122
$665$	13.9654	−	26.3618i	0.541555	−	1.02227i
$666$		0			0
$667$	1.24288	−	2.15273i	0.0481245	−	0.0833541i
$668$	1.65019	+	2.85821i	0.0638476	+	0.110587i
$669$		0			0
$670$	−7.98398	+	13.8287i	−0.308448	+	0.534248i
$671$	7.11126			0.274527
$672$		0			0
$673$	−46.4559			−1.79074			−0.895372	−	0.445319i	$-0.853090\pi$
$673$	−46.4559			−1.79074			−0.895372	+	0.445319i	$0.853090\pi$
$674$	4.21201	−	7.29541i	0.162240	−	0.281009i
$675$		0			0
$676$	−5.07234	−	8.78555i	−0.195090	−	0.337906i
$677$	−2.54944	+	4.41576i	−0.0979830	+	0.169712i	−0.910850	−	0.412738i	$-0.864572\pi$
$677$	−2.54944	+	4.41576i	−0.0979830	+	0.169712i	0.812867	+	0.582450i	$0.197906\pi$
$678$		0			0
$679$	−2.00138	−	3.19206i	−0.0768058	−	0.122500i
$680$	−8.57598			−0.328874
$681$		0			0
$682$	2.15383	+	3.73054i	0.0824743	+	0.142850i
$683$	−7.77197	−	13.4614i	−0.297386	−	0.515088i	0.678151	−	0.734923i	$-0.262782\pi$
$683$	−7.77197	−	13.4614i	−0.297386	−	0.515088i	−0.975537	+	0.219835i	$0.929448\pi$
$684$		0			0
$685$	−33.7738			−1.29043
$686$	−7.45558	+	16.9533i	−0.284655	+	0.647280i
$687$		0			0
$688$	−0.833104	+	1.44298i	−0.0317618	+	0.0550130i
$689$	−11.7596	−	20.3682i	−0.448005	−	0.775967i
$690$		0			0
$691$	−11.6483	+	20.1755i	−0.443123	+	0.767512i	−0.997919	−	0.0644744i	$-0.979463\pi$
$691$	−11.6483	+	20.1755i	−0.443123	+	0.767512i	0.554796	+	0.831986i	$0.312796\pi$
$692$	19.1075			0.726360
$693$		0			0
$694$	−0.567323			−0.0215353
$695$	10.3665	−	17.9553i	0.393225	−	0.681085i
$696$		0			0
$697$	15.8640	+	27.4772i	0.600891	+	1.04077i
$698$	0.00364189	−	0.00630794i	0.000137848	−	0.000238759i
$699$		0			0
$700$	6.54944	−	0.238687i	0.247546	−	0.00902153i
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$		0			0
$703$	3.54944	+	6.14781i	0.133870	+	0.231869i
$704$	0.794182	+	1.37556i	0.0299319	+	0.0518435i
$705$		0			0
$706$	−6.65383			−0.250420
$707$	14.9040	−	28.1335i	0.560522	−	1.05807i
$708$		0			0
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	−0.984062	−	0.177827i	$-0.943093\pi$
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	0.646034	+	0.763309i	$0.276427\pi$
$710$	10.1025	+	17.4981i	0.379141	+	0.656692i
$711$		0			0
$712$	−1.60507	+	2.78007i	−0.0601527	+	0.104188i
$713$	−0.814611			−0.0305074
$714$		0			0
$715$	12.1374			0.453913
$716$	−8.03706	+	13.9206i	−0.300359	+	0.520237i
$717$		0			0
$718$	0.398568	+	0.690339i	0.0148744	+	0.0257632i
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	−0.284941	−	0.958545i	$-0.591974\pi$
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	0.972595	−	0.232506i	$-0.0746926\pi$
$720$		0			0
$721$	16.1254	−	0.587674i	0.600542	−	0.0218861i
$722$	−31.3942			−1.16837
$723$		0			0
$724$	−4.02654	−	6.97418i	−0.149645	−	0.259193i
$725$	−10.2498	−	17.7531i	−0.380666	−	0.659334i
$726$		0			0
$727$	−30.4858			−1.13065			−0.565327	−	0.824867i	$-0.691250\pi$
$727$	−30.4858			−1.13065			−0.565327	+	0.824867i	$0.691250\pi$
$728$	6.76145	+	10.7840i	0.250596	+	0.399683i
$729$		0			0
$730$	−12.7491	+	22.0820i	−0.471864	+	0.817293i
$731$	−4.49814	−	7.79101i	−0.166370	−	0.288161i
$732$		0			0
$733$	−3.07530	+	5.32657i	−0.113589	+	0.196741i	−0.917215	−	0.398393i	$-0.869568\pi$
$733$	−3.07530	+	5.32657i	−0.113589	+	0.196741i	0.803626	+	0.595135i	$0.202901\pi$
$734$	15.4327			0.569630
$735$		0			0
$736$	−0.300372			−0.0110719
$737$	−7.98398	+	13.8287i	−0.294094	+	0.509385i
$738$		0			0
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	−0.947772	−	0.318947i	$-0.896671\pi$
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	0.197670	−	0.980269i	$-0.436663\pi$
$740$	0.794182	−	1.37556i	0.0291947	−	0.0505667i
$741$		0			0
$742$	6.87085	+	10.9585i	0.252237	+	0.402301i
$743$	−14.5054			−0.532152			−0.266076	−	0.963952i	$-0.585727\pi$
$743$	−14.5054			−0.532152			−0.266076	+	0.963952i	$0.585727\pi$
$744$		0			0
$745$	−4.13671	−	7.16500i	−0.151557	−	0.262505i
$746$	5.12110	+	8.87000i	0.187497	+	0.324754i
$747$		0			0
$748$	−8.57598			−0.313569
$749$	−8.16071	+	0.297408i	−0.298186	+	0.0108671i
$750$		0			0
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	−0.901708	−	0.432346i	$-0.857686\pi$
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	0.825276	+	0.564729i	$0.191019\pi$
$752$	−1.33310	−	2.30900i	−0.0486133	−	0.0842007i
$753$		0			0
$754$	19.9065	−	34.4791i	0.724953	−	1.25566i
$755$	−0.830556			−0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$	12.5043	−	21.6581i	0.454178	−	0.786659i
$759$		0			0
$760$	5.63781	+	9.76497i	0.204505	+	0.354213i
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	−0.897079	−	0.441870i	$-0.854315\pi$
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	0.831210	+	0.555959i	$0.187649\pi$
$762$		0			0
$763$	−2.83379	+	5.34920i	−0.102590	+	0.193654i
$764$	−23.9629			−0.866946
$765$		0			0
$766$	−3.13348	−	5.42734i	−0.113217	−	0.196098i
$767$	15.5803	+	26.9859i	0.562573	+	0.974404i
$768$		0			0
$769$	39.9344			1.44007			0.720035	−	0.693937i	$-0.244126\pi$
$769$	39.9344			1.44007			0.720035	+	0.693937i	$0.244126\pi$
$770$	−6.67054	+	0.243101i	−0.240390	+	0.00876074i
$771$		0			0
$772$	−4.88255	+	8.45682i	−0.175727	+	0.304368i
$773$	18.0698	+	31.2978i	0.649925	+	1.12570i	0.983140	+	0.182853i	$0.0585332\pi$
$773$	18.0698	+	31.2978i	0.649925	+	1.12570i	−0.333215	+	0.942851i	$0.608133\pi$
$774$		0			0
$775$	−3.35896	+	5.81788i	−0.120657	+	0.208985i
$776$	1.42402			0.0511192
$777$		0			0
$778$	21.6342			0.775622
$779$	20.8578	−	36.1267i	0.747308	−	1.29438i
$780$		0			0
$781$	10.1025	+	17.4981i	0.361497	+	0.626131i
$782$	0.810892	−	1.40451i	0.0289974	−	0.0502251i
$783$		0			0
$784$	−3.93199	−	5.79133i	−0.140428	−	0.206833i
$785$	14.0792			0.502509
$786$		0			0
$787$	22.3189	+	38.6574i	0.795582	+	1.37799i	0.922469	+	0.386071i	$0.126168\pi$
$787$	22.3189	+	38.6574i	0.795582	+	1.37799i	−0.126888	+	0.991917i	$0.540499\pi$
$788$	9.12178	+	15.7994i	0.324950	+	0.562830i
$789$		0			0
$790$	−13.3214			−0.473955
$791$	27.3566	+	43.6319i	0.972689	+	1.55137i
$792$		0			0
$793$	−10.7694	+	18.6532i	−0.382433	+	0.662394i
$794$	−2.05308	−	3.55605i	−0.0728612	−	0.126199i
$795$		0			0
$796$	9.04944	−	15.6741i	0.320749	−	0.555554i
$797$	−52.5672			−1.86202			−0.931012	−	0.364988i	$-0.881073\pi$
$797$	−52.5672			−1.86202			−0.931012	+	0.364988i	$0.881073\pi$
$798$		0			0
$799$	14.3955			0.509278
$800$	−1.23855	+	2.14523i	−0.0437894	+	0.0758454i
$801$		0			0
$802$	8.37085	+	14.4987i	0.295585	+	0.511969i
$803$	−12.7491	+	22.0820i	−0.449905	+	0.779258i
$804$		0			0
$805$	0.590912	−	1.11543i	0.0208269	−	0.0393139i
$806$	−13.0472			−0.459567
$807$		0			0
$808$	6.01671	+	10.4212i	0.211667	+	0.366618i
$809$	7.40290	+	12.8222i	0.260272	+	0.450804i	0.966314	−	0.257365i	$-0.0828544\pi$
$809$	7.40290	+	12.8222i	0.260272	+	0.450804i	−0.706042	+	0.708170i	$0.749521\pi$
$810$		0			0
$811$	27.0704			0.950571			0.475285	−	0.879832i	$-0.342345\pi$
$811$	27.0704			0.950571			0.475285	+	0.879832i	$0.342345\pi$
$812$	−10.2498	+	19.3479i	−0.359696	+	0.678980i
$813$		0			0
$814$	0.794182	−	1.37556i	0.0278361	−	0.0482135i
$815$	17.4425	+	30.2113i	0.610984	+	1.05826i
$816$		0			0
$817$	−5.91411	+	10.2435i	−0.206908	+	0.358376i
$818$	8.76509			0.306464
$819$		0			0
$820$	−9.33379			−0.325950
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	0.175808	+	0.984424i	$0.443746\pi$
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	−0.940441	+	0.339958i	$0.889587\pi$
$822$		0			0
$823$	−15.6712	−	27.1434i	−0.546265	−	0.946158i	−0.998526	−	0.0542727i	$-0.982716\pi$
$823$	−15.6712	−	27.1434i	−0.546265	−	0.946158i	0.452262	−	0.891885i	$-0.350617\pi$
$824$	−3.04944	+	5.28179i	−0.106232	+	0.184000i
$825$		0			0
$826$	−9.10322	−	14.5190i	−0.316741	−	0.505180i
$827$	−14.7665			−0.513480			−0.256740	−	0.966480i	$-0.582648\pi$
$827$	−14.7665			−0.513480			−0.256740	+	0.966480i	$0.582648\pi$
$828$		0			0
$829$	−15.0036	−	25.9871i	−0.521098	−	0.902568i	−0.999699	−	0.0245357i	$-0.992189\pi$
$829$	−15.0036	−	25.9871i	−0.521098	−	0.902568i	0.478601	−	0.878033i	$-0.341144\pi$
$830$	−1.87890	−	3.25436i	−0.0652177	−	0.112960i
$831$		0			0
$832$	−4.81089			−0.166788
$833$	37.6945	−	2.75113i	1.30604	−	0.0953209i
$834$		0			0
$835$	2.62110	−	4.53987i	0.0907068	−	0.157109i
$836$	5.63781	+	9.76497i	0.194988	+	0.337728i
$837$		0			0
$838$	0.210149	−	0.363988i	0.00725946	−	0.0125738i
$839$	−36.0334			−1.24401			−0.622006	−	0.783013i	$-0.713682\pi$
$839$	−36.0334			−1.24401			−0.622006	+	0.783013i	$0.713682\pi$
$840$		0			0
$841$	39.4858			1.36158
$842$	−3.28799	+	5.69497i	−0.113312	+	0.196262i
$843$		0			0
$844$	0.166208	+	0.287880i	0.00572110	+	0.00990923i
$845$	−8.05673	+	13.9547i	−0.277160	+	0.480055i
$846$		0			0
$847$	22.4134	−	0.816833i	0.770134	−	0.0280667i
$848$	−4.88874			−0.167880
$849$		0			0
$850$	−6.68725	−	11.5827i	−0.229371	−	0.397282i
$851$	0.150186	+	0.260130i	0.00514831	+	0.00891713i
$852$		0			0
$853$	24.5316			0.839945			0.419972	−	0.907537i	$-0.362040\pi$
$853$	24.5316			0.839945			0.419972	+	0.907537i	$0.362040\pi$
$854$	5.54511	−	10.4672i	0.189750	−	0.358181i
$855$		0			0
$856$	1.54325	−	2.67299i	0.0527473	−	0.0913610i
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	0.503860	−	0.863785i	$-0.331913\pi$
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	−0.999990	+	0.00446273i	$0.998579\pi$
$858$		0			0
$859$	−12.6476	+	21.9064i	−0.431532	+	0.747435i	−0.997005	−	0.0773313i	$-0.975360\pi$
$859$	−12.6476	+	21.9064i	−0.431532	+	0.747435i	0.565474	+	0.824766i	$0.308693\pi$
$860$	2.64654			0.0902464
$861$		0			0
$862$	22.0879			0.752316
$863$	−1.34981	+	2.33795i	−0.0459482	+	0.0795846i	−0.888085	−	0.459680i	$-0.847964\pi$
$863$	−1.34981	+	2.33795i	−0.0459482	+	0.0795846i	0.842137	+	0.539264i	$0.181298\pi$
$864$		0			0
$865$	−15.1749	−	26.2836i	−0.515961	−	0.893671i
$866$	−4.71634	+	8.16894i	−0.160268	+	0.277592i
$867$		0			0
$868$	7.17054	−	0.261323i	0.243384	−	0.00886986i
$869$	−13.3214			−0.451898
$870$		0			0
$871$	−24.1822	−	41.8847i	−0.819381	−	1.41921i
$872$	−1.14400	−	1.98146i	−0.0387406	−	0.0671007i
$873$		0			0
$874$	−2.13231			−0.0721263
$875$	−16.6916	−	26.6219i	−0.564278	−	0.899985i
$876$		0			0
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	−0.757070	−	0.653334i	$-0.773370\pi$
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	0.944339	+	0.328975i	$0.106703\pi$
$878$	−15.6032	−	27.0256i	−0.526583	−	0.912069i
$879$		0			0
$880$	1.26145	−	2.18490i	0.0425235	−	0.0736528i
$881$	−40.3942			−1.36091			−0.680457	−	0.732788i	$-0.738219\pi$
$881$	−40.3942			−1.36091			−0.680457	+	0.732788i	$0.738219\pi$
$882$		0			0
$883$	−33.2581			−1.11923			−0.559613	−	0.828754i	$-0.689050\pi$
$883$	−33.2581			−1.11923			−0.559613	+	0.828754i	$0.689050\pi$
$884$	12.9876	−	22.4952i	0.436821	−	0.756596i
$885$		0			0
$886$	6.52723	+	11.3055i	0.219287	+	0.379816i
$887$	−20.2836	+	35.1322i	−0.681056	+	1.17962i	0.293603	+	0.955928i	$0.405146\pi$
$887$	−20.2836	+	35.1322i	−0.681056	+	1.17962i	−0.974659	+	0.223696i	$0.928188\pi$
$888$		0			0
$889$	−18.8891	−	30.1269i	−0.633521	−	1.01042i
$890$	5.09888			0.170915
$891$		0			0
$892$	3.16621	+	5.48403i	0.106012	+	0.183619i
$893$	−9.46355	−	16.3913i	−0.316686	−	0.548516i
$894$		0			0
$895$	25.5316			0.853426
$896$	2.64400	−	0.0963576i	0.0883297	−	0.00321908i
$897$		0			0
$898$	−4.95853	+	8.58843i	−0.165468	+	0.286599i
$899$	−11.2218	−	19.4367i	−0.374267	−	0.648249i
$900$		0			0
$901$	13.1978	−	22.8592i	0.439681	−	0.761551i
$902$	−9.33379			−0.310781
$903$		0			0
$904$	−19.4647			−0.647387
$905$	−6.39561	+	11.0775i	−0.212597	+	0.368230i
$906$		0			0
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	0.500050	−	0.865997i	$-0.333315\pi$
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	−1.00000		5.72941e-5i	$0.999982\pi$
$908$	11.6545	−	20.1862i	0.386769	−	0.669903i
$909$		0			0
$910$	9.46431	−	17.8653i	0.313739	−	0.592229i
$911$	−29.2225			−0.968186			−0.484093	−	0.875017i	$-0.660850\pi$
$911$	−29.2225			−0.968186			−0.484093	+	0.875017i	$0.660850\pi$
$912$		0			0
$913$	−1.87890	−	3.25436i	−0.0621826	−	0.107704i
$914$	−12.2615	−	21.2375i	−0.405573	−	0.702473i
$915$		0			0
$916$	−4.95420			−0.163691
$917$	8.39926	−	0.306102i	0.277368	−	0.0101084i
$918$		0			0
$919$	−5.52359	+	9.56714i	−0.182206	+	0.315591i	−0.942632	−	0.333835i	$-0.891657\pi$
$919$	−5.52359	+	9.56714i	−0.182206	+	0.315591i	0.760425	+	0.649426i	$0.224991\pi$
$920$	0.238550	+	0.413181i	0.00786476	+	0.0136222i
$921$		0			0
$922$	−1.75526	+	3.04020i	−0.0578064	+	0.100124i
$923$	−61.1978			−2.01435
$924$		0			0
$925$	2.47710			0.0814465
$926$	−8.69413	+	15.0587i	−0.285707	+	0.494859i
$927$		0			0
$928$	−4.13781	−	7.16689i	−0.135830	−	0.235265i
$929$	21.1669	−	36.6621i	0.694463	−	1.20285i	−0.275898	−	0.961187i	$-0.588975\pi$
$929$	21.1669	−	36.6621i	0.694463	−	1.20285i	0.970361	−	0.241659i	$-0.0776915\pi$
$930$		0			0
$931$	−27.9127	−	41.1120i	−0.914803	−	1.34739i
$932$	14.2756			0.467613
$933$		0			0
$934$	−6.69894	−	11.6029i	−0.219196	−	0.379659i
$935$	6.81089	+	11.7968i	0.222740	+	0.385797i
$936$		0			0
$937$	−11.7651			−0.384349			−0.192174	−	0.981361i	$-0.561554\pi$
$937$	−11.7651			−0.384349			−0.192174	+	0.981361i	$0.561554\pi$
$938$	14.1291	+	22.5349i	0.461330	+	0.735790i
$939$		0			0
$940$	−2.11745	+	3.66754i	−0.0690637	+	0.119622i
$941$	−7.28799	−	12.6232i	−0.237582	−	0.411504i	0.722438	−	0.691436i	$-0.243021\pi$
$941$	−7.28799	−	12.6232i	−0.237582	−	0.411504i	−0.960020	+	0.279932i	$0.909688\pi$
$942$		0			0
$943$	0.882546	−	1.52861i	0.0287397	−	0.0497785i
$944$	6.47710			0.210812
$945$		0			0
$946$	2.64654			0.0860466
$947$	−3.12178	+	5.40709i	−0.101444	+	0.175707i	−0.912280	−	0.409567i	$-0.865680\pi$
$947$	−3.12178	+	5.40709i	−0.101444	+	0.175707i	0.810836	+	0.585274i	$0.199013\pi$
$948$		0			0
$949$	−38.6148	−	66.8828i	−1.25349	−	2.17111i
$950$	−8.79232	+	15.2287i	−0.285261	+	0.494086i
$951$		0			0
$952$	−6.68725	+	12.6232i	−0.216735	+	0.409119i
$953$	28.0173			0.907570			0.453785	−	0.891111i	$-0.350073\pi$
$953$	28.0173			0.907570			0.453785	+	0.891111i	$0.350073\pi$
$954$		0			0
$955$	19.0309	+	32.9624i	0.615825	+	1.06664i
$956$	2.48762	+	4.30868i	0.0804554	+	0.139353i
$957$		0			0
$958$	−20.8058			−0.672205
$959$	−26.3356	+	49.7123i	−0.850420	+	1.60529i
$960$		0			0
$961$	11.8225	−	20.4772i	0.381371	−	0.660554i
$962$	2.40545	+	4.16635i	0.0775547	+	0.134329i
$963$		0			0
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$	15.5105			0.499301
$966$		0			0
$967$	−31.5673			−1.01514			−0.507568	−	0.861612i	$-0.669456\pi$
$967$	−31.5673			−1.01514			−0.507568	+	0.861612i	$0.669456\pi$
$968$	−4.23855	+	7.34138i	−0.136232	+	0.235961i
$969$		0			0
$970$	−1.13093	−	1.95882i	−0.0363119	−	0.0628941i
$971$	2.82141	−	4.88683i	0.0905434	−	0.156826i	−0.817196	−	0.576359i	$-0.804473\pi$
$971$	2.82141	−	4.88683i	0.0905434	−	0.156826i	0.907740	+	0.419533i	$0.137806\pi$
$972$		0			0
$973$	−18.3454	−	29.2596i	−0.588127	−	0.938021i
$974$	32.4944			1.04119
$975$		0			0
$976$	2.23855	+	3.87728i	0.0716542	+	0.124109i
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	0.809409	−	0.587246i	$-0.199788\pi$
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	−0.913274	+	0.407346i	$0.866454\pi$
$978$		0			0
$979$	5.09888			0.162961
$980$	−4.84362	+	10.0081i	−0.154724	+	0.319696i
$981$		0			0
$982$	9.66071	−	16.7328i	0.308286	−	0.533966i
$983$	15.1531	+	26.2460i	0.483310	+	0.837118i	0.999816	−	0.0191658i	$-0.00610104\pi$
$983$	15.1531	+	26.2460i	0.483310	+	0.837118i	−0.516506	+	0.856283i	$0.672768\pi$
$984$		0			0
$985$	14.4887	−	25.0952i	0.461649	−	0.799599i
$986$	44.6822			1.42297
$987$		0			0
$988$	−34.1520			−1.08652
$989$	−0.250241	+	0.433430i	−0.00795720	+	0.0137823i
$990$		0			0
$991$	11.1669	+	19.3416i	0.354728	+	0.614407i	0.987071	−	0.160281i	$-0.0512401\pi$
$991$	11.1669	+	19.3416i	0.354728	+	0.614407i	−0.632343	+	0.774688i	$0.717907\pi$
$992$	−1.35600	+	2.34867i	−0.0430532	+	0.0745703i
$993$		0			0
$994$	33.6334	−	1.22573i	1.06679	−	0.0388779i
$995$	−28.7476			−0.911361
$996$		0			0
$997$	4.38255	+	7.59079i	0.138797	+	0.240403i	0.927041	−	0.374959i	$-0.122343\pi$
$997$	4.38255	+	7.59079i	0.138797	+	0.240403i	−0.788245	+	0.615362i	$0.789010\pi$
$998$	−5.57530	−	9.65670i	−0.176483	−	0.305677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.m.163.1		6
3.2	odd	2		1134.2.g.l.163.3		6
7.2	even	3		7938.2.a.bv.1.3		3
7.4	even	3	inner	1134.2.g.m.487.1		6
7.5	odd	6		7938.2.a.bw.1.1		3
9.2	odd	6		378.2.e.d.37.3		6
9.4	even	3		126.2.h.d.79.3	yes	6
9.5	odd	6		378.2.h.c.289.1		6
9.7	even	3		126.2.e.c.121.1	yes	6
21.2	odd	6		7938.2.a.ca.1.1		3
21.5	even	6		7938.2.a.bz.1.3		3
21.11	odd	6		1134.2.g.l.487.3		6
36.7	odd	6		1008.2.q.g.625.3		6
36.11	even	6		3024.2.q.g.2305.3		6
36.23	even	6		3024.2.t.h.289.1		6
36.31	odd	6		1008.2.t.h.961.1		6
63.2	odd	6		2646.2.f.l.1765.3		6
63.4	even	3		126.2.e.c.25.1	✓	6
63.5	even	6		2646.2.f.m.883.1		6
63.11	odd	6		378.2.h.c.361.1		6
63.13	odd	6		882.2.h.p.79.1		6
63.16	even	3		882.2.f.n.589.3		6
63.20	even	6		2646.2.e.p.1549.1		6
63.23	odd	6		2646.2.f.l.883.3		6
63.25	even	3		126.2.h.d.67.3	yes	6
63.31	odd	6		882.2.e.o.655.3		6
63.32	odd	6		378.2.e.d.235.3		6
63.34	odd	6		882.2.e.o.373.3		6
63.38	even	6		2646.2.h.o.361.3		6
63.40	odd	6		882.2.f.o.295.1		6
63.41	even	6		2646.2.h.o.667.3		6
63.47	even	6		2646.2.f.m.1765.1		6
63.52	odd	6		882.2.h.p.67.1		6
63.58	even	3		882.2.f.n.295.3		6
63.59	even	6		2646.2.e.p.2125.1		6
63.61	odd	6		882.2.f.o.589.1		6
252.11	even	6		3024.2.t.h.1873.1		6
252.67	odd	6		1008.2.q.g.529.3		6
252.95	even	6		3024.2.q.g.2881.3		6
252.151	odd	6		1008.2.t.h.193.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	63.4	even	3
126.2.e.c.121.1	yes	6	9.7	even	3
126.2.h.d.67.3	yes	6	63.25	even	3
126.2.h.d.79.3	yes	6	9.4	even	3
378.2.e.d.37.3		6	9.2	odd	6
378.2.e.d.235.3		6	63.32	odd	6
378.2.h.c.289.1		6	9.5	odd	6
378.2.h.c.361.1		6	63.11	odd	6
882.2.e.o.373.3		6	63.34	odd	6
882.2.e.o.655.3		6	63.31	odd	6
882.2.f.n.295.3		6	63.58	even	3
882.2.f.n.589.3		6	63.16	even	3
882.2.f.o.295.1		6	63.40	odd	6
882.2.f.o.589.1		6	63.61	odd	6
882.2.h.p.67.1		6	63.52	odd	6
882.2.h.p.79.1		6	63.13	odd	6
1008.2.q.g.529.3		6	252.67	odd	6
1008.2.q.g.625.3		6	36.7	odd	6
1008.2.t.h.193.1		6	252.151	odd	6
1008.2.t.h.961.1		6	36.31	odd	6
1134.2.g.l.163.3		6	3.2	odd	2
1134.2.g.l.487.3		6	21.11	odd	6
1134.2.g.m.163.1		6	1.1	even	1	trivial
1134.2.g.m.487.1		6	7.4	even	3	inner
2646.2.e.p.1549.1		6	63.20	even	6
2646.2.e.p.2125.1		6	63.59	even	6
2646.2.f.l.883.3		6	63.23	odd	6
2646.2.f.l.1765.3		6	63.2	odd	6
2646.2.f.m.883.1		6	63.5	even	6
2646.2.f.m.1765.1		6	63.47	even	6
2646.2.h.o.361.3		6	63.38	even	6
2646.2.h.o.667.3		6	63.41	even	6
3024.2.q.g.2305.3		6	36.11	even	6
3024.2.q.g.2881.3		6	252.95	even	6
3024.2.t.h.289.1		6	36.23	even	6
3024.2.t.h.1873.1		6	252.11	even	6
7938.2.a.bv.1.3		3	7.2	even	3
7938.2.a.bw.1.1		3	7.5	odd	6
7938.2.a.bz.1.3		3	21.5	even	6
7938.2.a.ca.1.1		3	21.2	odd	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.40545 + 2.24159i) q^{7} -1.00000 q^{8} +(0.794182 + 1.37556i) q^{10} +(0.794182 + 1.37556i) q^{11} -4.81089 q^{13} +(2.64400 - 0.0963576i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.69963 - 4.67589i) q^{17} +(-3.54944 + 6.14781i) q^{19} +1.58836 q^{20} +1.58836 q^{22} +(-0.150186 + 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(-2.40545 + 4.16635i) q^{26} +(1.23855 - 2.33795i) q^{28} -8.27561 q^{29} +(1.35600 + 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} -5.39926 q^{34} +(-4.19963 + 0.153051i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.54944 + 6.14781i) q^{38} +(0.794182 - 1.37556i) q^{40} -5.87636 q^{41} +1.66621 q^{43} +(0.794182 - 1.37556i) q^{44} +(0.150186 + 0.260130i) q^{46} +(-1.33310 + 2.30900i) q^{47} +(-3.04944 + 6.30087i) q^{49} +2.47710 q^{50} +(2.40545 + 4.16635i) q^{52} +(2.44437 + 4.23377i) q^{53} -2.52290 q^{55} +(-1.40545 - 2.24159i) q^{56} +(-4.13781 + 7.16689i) q^{58} +(-3.23855 - 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(5.02654 + 8.70623i) q^{67} +(-2.69963 + 4.67589i) q^{68} +(-1.96727 + 3.71351i) q^{70} +12.7207 q^{71} +(8.02654 + 13.9024i) q^{73} +(-0.500000 - 0.866025i) q^{74} +7.09888 q^{76} +(-1.96727 + 3.71351i) q^{77} +(-4.19344 + 7.26325i) q^{79} +(-0.794182 - 1.37556i) q^{80} +(-2.93818 + 5.08907i) q^{82} -2.36584 q^{83} +8.57598 q^{85} +(0.833104 - 1.44298i) q^{86} +(-0.794182 - 1.37556i) q^{88} +(1.60507 - 2.78007i) q^{89} +(-6.76145 - 10.7840i) q^{91} +0.300372 q^{92} +(1.33310 + 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} -1.42402 q^{97} +(3.93199 + 5.79133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + q^{5} + 2 q^{7} - 6 q^{8} - q^{10} - q^{11} - 16 q^{13} + 4 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} - 2 q^{20} - 2 q^{22} - 7 q^{23} + 2 q^{25} - 8 q^{26} + 2 q^{28} + 10 q^{29}+ \cdots - 12 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + q^5 + 2 * q^7 - 6 * q^8 - q^10 - q^11 - 16 * q^13 + 4 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 - 2 * q^20 - 2 * q^22 - 7 * q^23 + 2 * q^25 - 8 * q^26 + 2 * q^28 + 10 * q^29 + 20 * q^31 + 3 * q^32 - 8 * q^34 - 13 * q^35 + 3 * q^37 + 3 * q^38 - q^40 + 12 * q^43 - q^44 + 7 * q^46 - 9 * q^47 + 4 * q^50 + 8 * q^52 + 15 * q^53 - 26 * q^55 - 2 * q^56 + 5 * q^58 - 14 * q^59 + 8 * q^61 + 40 * q^62 + 6 * q^64 - 12 * q^65 + q^67 - 4 * q^68 - 23 * q^70 + 14 * q^71 + 19 * q^73 - 3 * q^74 + 6 * q^76 - 23 * q^77 + 5 * q^79 + q^80 - 4 * q^83 + 4 * q^85 + 6 * q^86 + q^88 - 9 * q^89 - 46 * q^91 + 14 * q^92 + 9 * q^94 - 4 * q^95 - 56 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more