LMFDB - Embedded newform 945.2.j.g.541.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(541,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("945.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.j (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5883587346987.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 7x^{8} - 2x^{7} + 38x^{6} - 10x^{5} + 78x^{4} - 31x^{3} + 124x^{2} - 33x + 9 $ x^10 + 7x^8 - 2x^7 + 38x^6 - 10x^5 + 78x^4 - 31x^3 + 124x^2 - 33x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.5
Root			$-1.11349 - 1.92861i$ of defining polynomial
Character	$\chi$	$=$	945.541
Dual form			945.2.j.g.676.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11349 - 1.92861i) q^{2} +(-1.47970 - 2.56292i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0803747 - 2.64453i) q^{7} -2.13656 q^{8} +O(q^{10})$	\(q+(1.11349 - 1.92861i) q^{2} +(-1.47970 - 2.56292i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0803747 - 2.64453i) q^{7} -2.13656 q^{8} +(-1.11349 - 1.92861i) q^{10} +(-0.197262 - 0.341667i) q^{11} +2.66209 q^{13} +(-5.18977 - 2.78963i) q^{14} +(0.580375 - 1.00524i) q^{16} +(-2.33382 - 4.04229i) q^{17} +(-3.24524 + 5.62092i) q^{19} -2.95940 q^{20} -0.878592 q^{22} +(0.674190 - 1.16773i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.96420 - 5.13415i) q^{26} +(-6.65878 + 4.11911i) q^{28} +4.42975 q^{29} +(-1.80071 - 3.11892i) q^{31} +(-3.42904 - 5.93926i) q^{32} -10.3947 q^{34} +(-2.33042 - 1.25266i) q^{35} +(-5.26285 + 9.11553i) q^{37} +(7.22706 + 12.5176i) q^{38} +(-1.06828 + 1.85031i) q^{40} -4.54069 q^{41} +9.11198 q^{43} +(-0.583776 + 1.01113i) q^{44} +(-1.50140 - 2.60050i) q^{46} +(4.43244 - 7.67721i) q^{47} +(-6.98708 + 0.425107i) q^{49} -2.22697 q^{50} +(-3.93910 - 6.82272i) q^{52} +(-1.53978 - 2.66697i) q^{53} -0.394523 q^{55} +(0.171725 + 5.65019i) q^{56} +(4.93246 - 8.54328i) q^{58} +(2.07492 + 3.59386i) q^{59} +(-7.06219 + 12.2321i) q^{61} -8.02025 q^{62} -12.9512 q^{64} +(1.33105 - 2.30544i) q^{65} +(0.895924 + 1.55179i) q^{67} +(-6.90671 + 11.9628i) q^{68} +(-5.01078 + 3.09966i) q^{70} +13.7902 q^{71} +(1.30205 + 2.25522i) q^{73} +(11.7202 + 20.3000i) q^{74} +19.2079 q^{76} +(-0.887694 + 0.549126i) q^{77} +(4.10803 - 7.11531i) q^{79} +(-0.580375 - 1.00524i) q^{80} +(-5.05599 + 8.75723i) q^{82} -2.47133 q^{83} -4.66764 q^{85} +(10.1461 - 17.5735i) q^{86} +(0.421461 + 0.729991i) q^{88} +(2.44116 - 4.22821i) q^{89} +(-0.213965 - 7.03999i) q^{91} -3.99040 q^{92} +(-9.87091 - 17.0969i) q^{94} +(3.24524 + 5.62092i) q^{95} +14.9814 q^{97} +(-6.96015 + 13.9487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{4} + 5 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) $ 10 * q - 4 * q^4 + 5 * q^5 - 5 * q^7 - 6 * q^8	$ 10 q - 4 q^{4} + 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{11} + 12 q^{13} - 8 q^{14} + 10 q^{16} - q^{17} - 7 q^{19} - 8 q^{20} + 8 q^{22} + 4 q^{23} - 5 q^{25} + 7 q^{26} + q^{28} - 24 q^{29} - 11 q^{31} - 4 q^{32} + 16 q^{34} - q^{35} - 3 q^{38} - 3 q^{40} - 14 q^{41} + 4 q^{43} - 10 q^{44} - 14 q^{46} + 14 q^{47} - 19 q^{49} - 7 q^{52} + 2 q^{53} + 10 q^{55} - 6 q^{56} + 28 q^{58} + 2 q^{59} - 25 q^{61} + 48 q^{62} - 34 q^{64} + 6 q^{65} - 6 q^{67} - 14 q^{68} - 10 q^{70} + 30 q^{71} - 17 q^{73} + 29 q^{74} + 68 q^{76} + 14 q^{77} + 7 q^{79} - 10 q^{80} - 7 q^{82} - 4 q^{83} - 2 q^{85} + 7 q^{86} - 10 q^{88} + 15 q^{89} + 18 q^{91} - 42 q^{92} - 21 q^{94} + 7 q^{95} + 96 q^{97} - 23 q^{98}+O(q^{100}) $ 10 * q - 4 * q^4 + 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^11 + 12 * q^13 - 8 * q^14 + 10 * q^16 - q^17 - 7 * q^19 - 8 * q^20 + 8 * q^22 + 4 * q^23 - 5 * q^25 + 7 * q^26 + q^28 - 24 * q^29 - 11 * q^31 - 4 * q^32 + 16 * q^34 - q^35 - 3 * q^38 - 3 * q^40 - 14 * q^41 + 4 * q^43 - 10 * q^44 - 14 * q^46 + 14 * q^47 - 19 * q^49 - 7 * q^52 + 2 * q^53 + 10 * q^55 - 6 * q^56 + 28 * q^58 + 2 * q^59 - 25 * q^61 + 48 * q^62 - 34 * q^64 + 6 * q^65 - 6 * q^67 - 14 * q^68 - 10 * q^70 + 30 * q^71 - 17 * q^73 + 29 * q^74 + 68 * q^76 + 14 * q^77 + 7 * q^79 - 10 * q^80 - 7 * q^82 - 4 * q^83 - 2 * q^85 + 7 * q^86 - 10 * q^88 + 15 * q^89 + 18 * q^91 - 42 * q^92 - 21 * q^94 + 7 * q^95 + 96 * q^97 - 23 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.11349	−	1.92861i	0.787353	−	1.36374i	−0.140230	−	0.990119i	$-0.544784\pi$
$2$	1.11349	−	1.92861i	0.787353	−	1.36374i	0.927583	−	0.373617i	$-0.121882\pi$
$3$		0			0
$3$		0			0
$4$	−1.47970	−	2.56292i	−0.739850	−	1.28146i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.0803747	−	2.64453i	−0.0303788	−	0.999538i
$7$	−0.0803747	−	2.64453i	−0.0303788	−	0.999538i
$8$	−2.13656			−0.755387
$9$		0			0
$10$	−1.11349	−	1.92861i	−0.352115	−	0.609881i
$11$	−0.197262	−	0.341667i	−0.0594766	−	0.103016i	0.834754	−	0.550623i	$-0.185610\pi$
$11$	−0.197262	−	0.341667i	−0.0594766	−	0.103016i	−0.894231	+	0.447607i	$0.852277\pi$
$12$		0			0
$13$	2.66209			0.738332			0.369166	−	0.929363i	$-0.379643\pi$
$13$	2.66209			0.738332			0.369166	+	0.929363i	$0.379643\pi$
$14$	−5.18977	−	2.78963i	−1.38703	−	0.745561i
$15$		0			0
$16$	0.580375	−	1.00524i	0.145094	−	0.251310i
$17$	−2.33382	−	4.04229i	−0.566034	−	0.980400i	−0.996953	−	0.0780092i	$-0.975144\pi$
$17$	−2.33382	−	4.04229i	−0.566034	−	0.980400i	0.430918	−	0.902391i	$-0.358190\pi$
$18$		0			0
$19$	−3.24524	+	5.62092i	−0.744509	+	1.28953i	0.205914	+	0.978570i	$0.433983\pi$
$19$	−3.24524	+	5.62092i	−0.744509	+	1.28953i	−0.950424	+	0.310958i	$0.899350\pi$
$20$	−2.95940			−0.661742
$21$		0			0
$22$	−0.878592			−0.187316
$23$	0.674190	−	1.16773i	0.140578	−	0.243489i	−0.787136	−	0.616779i	$-0.788437\pi$
$23$	0.674190	−	1.16773i	0.140578	−	0.243489i	0.927715	+	0.373290i	$0.121770\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.96420	−	5.13415i	0.581328	−	1.00689i
$27$		0			0
$28$	−6.65878	+	4.11911i	−1.25839	+	0.778438i
$29$	4.42975			0.822584			0.411292	−	0.911504i	$-0.365078\pi$
$29$	4.42975			0.822584			0.411292	+	0.911504i	$0.365078\pi$
$30$		0			0
$31$	−1.80071	−	3.11892i	−0.323417	−	0.560174i	0.657774	−	0.753215i	$-0.271498\pi$
$31$	−1.80071	−	3.11892i	−0.323417	−	0.560174i	−0.981191	+	0.193041i	$0.938165\pi$
$32$	−3.42904	−	5.93926i	−0.606174	−	1.04992i
$33$		0			0
$34$	−10.3947			−1.78268
$35$	−2.33042	−	1.25266i	−0.393912	−	0.211738i
$36$		0			0
$37$	−5.26285	+	9.11553i	−0.865208	+	1.49858i	0.00163273	+	0.999999i	$0.499480\pi$
$37$	−5.26285	+	9.11553i	−0.865208	+	1.49858i	−0.866841	+	0.498585i	$0.833853\pi$
$38$	7.22706	+	12.5176i	1.17238	+	2.03063i
$39$		0			0
$40$	−1.06828	+	1.85031i	−0.168910	+	0.292560i
$41$	−4.54069			−0.709136			−0.354568	−	0.935030i	$-0.615372\pi$
$41$	−4.54069			−0.709136			−0.354568	+	0.935030i	$0.615372\pi$
$42$		0			0
$43$	9.11198			1.38956			0.694782	−	0.719221i	$-0.255501\pi$
$43$	9.11198			1.38956			0.694782	+	0.719221i	$0.255501\pi$
$44$	−0.583776	+	1.01113i	−0.0880075	+	0.152434i
$45$		0			0
$46$	−1.50140	−	2.60050i	−0.221370	−	0.383423i
$47$	4.43244	−	7.67721i	0.646537	−	1.11984i	−0.337407	−	0.941359i	$-0.609550\pi$
$47$	4.43244	−	7.67721i	0.646537	−	1.11984i	0.983944	−	0.178477i	$-0.0571169\pi$
$48$		0			0
$49$	−6.98708	+	0.425107i	−0.998154	+	0.0607295i
$50$	−2.22697			−0.314941
$51$		0			0
$52$	−3.93910	−	6.82272i	−0.546255	−	0.946141i
$53$	−1.53978	−	2.66697i	−0.211504	−	0.366336i	0.740681	−	0.671857i	$-0.234503\pi$
$53$	−1.53978	−	2.66697i	−0.211504	−	0.366336i	−0.952186	+	0.305520i	$0.901170\pi$
$54$		0			0
$55$	−0.394523			−0.0531975
$56$	0.171725	+	5.65019i	0.0229477	+	0.755038i
$57$		0			0
$58$	4.93246	−	8.54328i	0.647664	−	1.12179i
$59$	2.07492	+	3.59386i	0.270131	+	0.467881i	0.968895	−	0.247471i	$-0.0795996\pi$
$59$	2.07492	+	3.59386i	0.270131	+	0.467881i	−0.698764	+	0.715352i	$0.746266\pi$
$60$		0			0
$61$	−7.06219	+	12.2321i	−0.904221	+	1.56616i	−0.0822613	+	0.996611i	$0.526214\pi$
$61$	−7.06219	+	12.2321i	−0.904221	+	1.56616i	−0.821960	+	0.569546i	$0.807119\pi$
$62$	−8.02025			−1.01857
$63$		0			0
$64$	−12.9512			−1.61890
$65$	1.33105	−	2.30544i	0.165096	−	0.285955i
$66$		0			0
$67$	0.895924	+	1.55179i	0.109455	+	0.189581i	0.915549	−	0.402205i	$-0.131756\pi$
$67$	0.895924	+	1.55179i	0.109455	+	0.189581i	−0.806095	+	0.591786i	$0.798423\pi$
$68$	−6.90671	+	11.9628i	−0.837561	+	1.45070i
$69$		0			0
$70$	−5.01078	+	3.09966i	−0.598903	+	0.370480i
$71$	13.7902			1.63660			0.818298	−	0.574794i	$-0.194918\pi$
$71$	13.7902			1.63660			0.818298	+	0.574794i	$0.194918\pi$
$72$		0			0
$73$	1.30205	+	2.25522i	0.152394	+	0.263954i	0.932107	−	0.362183i	$-0.117968\pi$
$73$	1.30205	+	2.25522i	0.152394	+	0.263954i	−0.779713	+	0.626137i	$0.784635\pi$
$74$	11.7202	+	20.3000i	1.36245	+	2.35983i
$75$		0			0
$76$	19.2079			2.20330
$77$	−0.887694	+	0.549126i	−0.101162	+	0.0625787i
$78$		0			0
$79$	4.10803	−	7.11531i	0.462189	−	0.800535i	−0.536881	−	0.843658i	$-0.680397\pi$
$79$	4.10803	−	7.11531i	0.462189	−	0.800535i	0.999070	+	0.0431231i	$0.0137308\pi$
$80$	−0.580375	−	1.00524i	−0.0648879	−	0.112389i
$81$		0			0
$82$	−5.05599	+	8.75723i	−0.558340	+	0.967074i
$83$	−2.47133			−0.271264			−0.135632	−	0.990759i	$-0.543306\pi$
$83$	−2.47133			−0.271264			−0.135632	+	0.990759i	$0.543306\pi$
$84$		0			0
$85$	−4.66764			−0.506276
$86$	10.1461	−	17.5735i	1.09408	−	1.89500i
$87$		0			0
$88$	0.421461	+	0.729991i	0.0449279	+	0.0778173i
$89$	2.44116	−	4.22821i	0.258762	−	0.448189i	−0.707148	−	0.707065i	$-0.750019\pi$
$89$	2.44116	−	4.22821i	0.258762	−	0.448189i	0.965911	+	0.258876i	$0.0833521\pi$
$90$		0			0
$91$	−0.213965	−	7.03999i	−0.0224296	−	0.737991i
$92$	−3.99040			−0.416027
$93$		0			0
$94$	−9.87091	−	17.0969i	−1.01811	−	1.76341i
$95$	3.24524	+	5.62092i	0.332955	+	0.576694i
$96$		0			0
$97$	14.9814			1.52113			0.760563	−	0.649264i	$-0.224923\pi$
$97$	14.9814			1.52113			0.760563	+	0.649264i	$0.224923\pi$
$98$	−6.96015	+	13.9487i	−0.703081	+	1.40903i
$99$		0			0
$100$	−1.47970	+	2.56292i	−0.147970	+	0.256292i
$101$	3.36056	+	5.82066i	0.334388	+	0.579178i	0.983367	−	0.181629i	$-0.0581369\pi$
$101$	3.36056	+	5.82066i	0.334388	+	0.579178i	−0.648979	+	0.760807i	$0.724804\pi$
$102$		0			0
$103$	0.737947	−	1.27816i	0.0727121	−	0.125941i	−0.827377	−	0.561647i	$-0.810168\pi$
$103$	0.737947	−	1.27816i	0.0727121	−	0.125941i	0.900089	+	0.435706i	$0.143501\pi$
$104$	−5.68772			−0.557726
$105$		0			0
$106$	−6.85807			−0.666115
$107$	5.11017	−	8.85107i	0.494019	−	0.855666i	−0.505957	−	0.862558i	$-0.668861\pi$
$107$	5.11017	−	8.85107i	0.494019	−	0.855666i	0.999976	+	0.00689278i	$0.00219406\pi$
$108$		0			0
$109$	1.86836	+	3.23609i	0.178956	+	0.309961i	0.941523	−	0.336948i	$-0.109395\pi$
$109$	1.86836	+	3.23609i	0.178956	+	0.309961i	−0.762567	+	0.646909i	$0.776061\pi$
$110$	−0.439296	+	0.760883i	−0.0418852	+	0.0725473i
$111$		0			0
$112$	−2.70503	−	1.45402i	−0.255601	−	0.137392i
$113$	5.69858			0.536077			0.268039	−	0.963408i	$-0.413625\pi$
$113$	5.69858			0.536077			0.268039	+	0.963408i	$0.413625\pi$
$114$		0			0
$115$	−0.674190	−	1.16773i	−0.0628685	−	0.108891i
$116$	−6.55470	−	11.3531i	−0.608589	−	1.05411i
$117$		0			0
$118$	9.24156			0.850754
$119$	−10.5024	+	6.49675i	−0.962752	+	0.595556i
$120$		0			0
$121$	5.42218	−	9.39148i	0.492925	−	0.853771i
$122$	15.7273	+	27.2405i	1.42388	+	2.46624i
$123$		0			0
$124$	−5.32902	+	9.23013i	−0.478560	+	0.828890i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.45543			0.572826			0.286413	−	0.958106i	$-0.407537\pi$
$127$	6.45543			0.572826			0.286413	+	0.958106i	$0.407537\pi$
$128$	−7.56293	+	13.0994i	−0.668475	+	1.15783i
$129$		0			0
$130$	−2.96420	−	5.13415i	−0.259978	−	0.450295i
$131$	−4.67899	+	8.10425i	−0.408805	+	0.708072i	−0.994756	−	0.102275i	$-0.967388\pi$
$131$	−4.67899	+	8.10425i	−0.408805	+	0.708072i	0.585951	+	0.810347i	$0.300721\pi$
$132$		0			0
$133$	15.1255	+	8.13036i	1.31155	+	0.704991i
$134$	3.99040			0.344718
$135$		0			0
$136$	4.98634	+	8.63659i	0.427575	+	0.740582i
$137$	−2.84246	−	4.92328i	−0.242847	−	0.420624i	0.718677	−	0.695344i	$-0.244748\pi$
$137$	−2.84246	−	4.92328i	−0.242847	−	0.420624i	−0.961524	+	0.274720i	$0.911415\pi$
$138$		0			0
$139$	−5.50650			−0.467055			−0.233528	−	0.972350i	$-0.575027\pi$
$139$	−5.50650			−0.467055			−0.233528	+	0.972350i	$0.575027\pi$
$140$	0.237861	+	7.82622i	0.0201029	+	0.661437i
$141$		0			0
$142$	15.3552	−	26.5960i	1.28858	−	2.23188i
$143$	−0.525129	−	0.909550i	−0.0439135	−	0.0760604i
$144$		0			0
$145$	2.21488	−	3.83628i	0.183935	−	0.318585i
$146$	5.79927			0.479951
$147$		0			0
$148$	31.1498			2.56050
$149$	9.61244	−	16.6492i	0.787482	−	1.36396i	−0.140023	−	0.990148i	$-0.544718\pi$
$149$	9.61244	−	16.6492i	0.787482	−	1.36396i	0.927505	−	0.373810i	$-0.121949\pi$
$150$		0			0
$151$	4.50653	+	7.80554i	0.366736	+	0.635206i	0.989053	−	0.147560i	$-0.0471419\pi$
$151$	4.50653	+	7.80554i	0.366736	+	0.635206i	−0.622317	+	0.782765i	$0.713809\pi$
$152$	6.93364	−	12.0094i	0.562393	−	0.974093i
$153$		0			0
$154$	0.0706166	+	2.32346i	0.00569044	+	0.187230i
$155$	−3.60142			−0.289273
$156$		0			0
$157$	8.89859	+	15.4128i	0.710185	+	1.23008i	0.964788	+	0.263030i	$0.0847219\pi$
$157$	8.89859	+	15.4128i	0.710185	+	1.23008i	−0.254603	+	0.967046i	$0.581945\pi$
$158$	−9.14846	−	15.8456i	−0.727812	−	1.26061i
$159$		0			0
$160$	−6.85807			−0.542178
$161$	−3.14229	−	1.68906i	−0.247647	−	0.133117i
$162$		0			0
$163$	−3.47268	+	6.01485i	−0.272001	+	0.471120i	−0.969374	−	0.245589i	$-0.921019\pi$
$163$	−3.47268	+	6.01485i	−0.272001	+	0.471120i	0.697373	+	0.716708i	$0.254352\pi$
$164$	6.71885	+	11.6374i	0.524654	+	0.908728i
$165$		0			0
$166$	−2.75179	+	4.76624i	−0.213581	+	0.369932i
$167$	19.9707			1.54538			0.772688	−	0.634786i	$-0.218912\pi$
$167$	19.9707			1.54538			0.772688	+	0.634786i	$0.218912\pi$
$168$		0			0
$169$	−5.91326			−0.454866
$170$	−5.19735	+	9.00207i	−0.398618	+	0.690427i
$171$		0			0
$172$	−13.4830	−	23.3532i	−1.02807	−	1.78067i
$173$	−12.3094	+	21.3205i	−0.935865	+	1.62097i	−0.162780	+	0.986662i	$0.552046\pi$
$173$	−12.3094	+	21.3205i	−0.935865	+	1.62097i	−0.773084	+	0.634303i	$0.781287\pi$
$174$		0			0
$175$	−2.25004	+	1.39187i	−0.170087	+	0.105216i
$176$	−0.457943			−0.0345187
$177$		0			0
$178$	−5.43639	−	9.41610i	−0.407475	−	0.705767i
$179$	−0.637467	−	1.10413i	−0.0476466	−	0.0825263i	0.841219	−	0.540695i	$-0.181839\pi$
$179$	−0.637467	−	1.10413i	−0.0476466	−	0.0825263i	−0.888865	+	0.458169i	$0.848505\pi$
$180$		0			0
$181$	14.1119			1.04893			0.524465	−	0.851432i	$-0.324265\pi$
$181$	14.1119			1.04893			0.524465	+	0.851432i	$0.324265\pi$
$182$	−13.8157	−	7.42627i	−1.02409	−	0.550472i
$183$		0			0
$184$	−1.44045	+	2.49492i	−0.106191	+	0.183928i
$185$	5.26285	+	9.11553i	0.386933	+	0.670187i
$186$		0			0
$187$	−0.920746	+	1.59478i	−0.0673316	+	0.116622i
$188$	−26.2347			−1.91336
$189$		0			0
$190$	14.4541			1.04861
$191$	11.1688	−	19.3450i	0.808147	−	1.39975i	−0.105998	−	0.994366i	$-0.533804\pi$
$191$	11.1688	−	19.3450i	0.808147	−	1.39975i	0.914146	−	0.405386i	$-0.132863\pi$
$192$		0			0
$193$	3.57319	+	6.18895i	0.257204	+	0.445491i	0.965492	−	0.260433i	$-0.0838654\pi$
$193$	3.57319	+	6.18895i	0.257204	+	0.445491i	−0.708288	+	0.705924i	$0.750532\pi$
$194$	16.6815	−	28.8932i	1.19766	−	2.07441i
$195$		0			0
$196$	11.4283	+	17.2783i	0.816307	+	1.23416i
$197$	15.2441			1.08610			0.543050	−	0.839700i	$-0.317269\pi$
$197$	15.2441			1.08610			0.543050	+	0.839700i	$0.317269\pi$
$198$		0			0
$199$	2.16953	+	3.75774i	0.153794	+	0.266379i	0.932619	−	0.360862i	$-0.117517\pi$
$199$	2.16953	+	3.75774i	0.153794	+	0.266379i	−0.778825	+	0.627241i	$0.784184\pi$
$200$	1.06828	+	1.85031i	0.0755387	+	0.130837i
$201$		0			0
$202$	14.9677			1.05313
$203$	−0.356040	−	11.7146i	−0.0249891	−	0.822204i
$204$		0			0
$205$	−2.27034	+	3.93235i	−0.158568	+	0.274647i
$206$	−1.64339	−	2.84643i	−0.114500	−	0.198320i
$207$		0			0
$208$	1.54501	−	2.67604i	0.107127	−	0.185550i
$209$	2.56064			0.177124
$210$		0			0
$211$	−14.8790			−1.02431			−0.512157	−	0.858892i	$-0.671153\pi$
$211$	−14.8790			−1.02431			−0.512157	+	0.858892i	$0.671153\pi$
$212$	−4.55681	+	7.89263i	−0.312963	+	0.542068i
$213$		0			0
$214$	−11.3802	−	19.7111i	−0.777935	−	1.34742i
$215$	4.55599	−	7.89120i	0.310716	−	0.538176i
$216$		0			0
$217$	−8.10334	+	5.01271i	−0.550091	+	0.340285i
$218$	8.32156			0.563607
$219$		0			0
$220$	0.583776	+	1.01113i	0.0393582	+	0.0681703i
$221$	−6.21284	−	10.7610i	−0.417921	−	0.723861i
$222$		0			0
$223$	−3.17358			−0.212519			−0.106259	−	0.994338i	$-0.533887\pi$
$223$	−3.17358			−0.212519			−0.106259	+	0.994338i	$0.533887\pi$
$224$	−15.4310	+	9.54555i	−1.03102	+	0.637789i
$225$		0			0
$226$	6.34529	−	10.9904i	0.422082	−	0.731068i
$227$	−0.0424046	−	0.0734468i	−0.00281449	−	0.00487484i	0.864615	−	0.502435i	$-0.167563\pi$
$227$	−0.0424046	−	0.0734468i	−0.00281449	−	0.00487484i	−0.867429	+	0.497561i	$0.834229\pi$
$228$		0			0
$229$	−11.9826	+	20.7544i	−0.791830	+	1.37149i	0.133003	+	0.991116i	$0.457538\pi$
$229$	−11.9826	+	20.7544i	−0.791830	+	1.37149i	−0.924833	+	0.380374i	$0.875795\pi$
$230$	−3.00280			−0.197999
$231$		0			0
$232$	−9.46442			−0.621369
$233$	4.02765	−	6.97610i	0.263860	−	0.457019i	−0.703404	−	0.710790i	$-0.748338\pi$
$233$	4.02765	−	6.97610i	0.263860	−	0.457019i	0.967264	+	0.253771i	$0.0816709\pi$
$234$		0			0
$235$	−4.43244	−	7.67721i	−0.289140	−	0.500806i
$236$	6.14051	−	10.6357i	0.399713	−	0.692323i
$237$		0			0
$238$	0.835471	+	27.4891i	0.0541555	+	1.78185i
$239$	−26.6324			−1.72271			−0.861354	−	0.508005i	$-0.830383\pi$
$239$	−26.6324			−1.72271			−0.861354	+	0.508005i	$0.830383\pi$
$240$		0			0
$241$	−1.64327	−	2.84623i	−0.105853	−	0.183342i	0.808234	−	0.588862i	$-0.200424\pi$
$241$	−1.64327	−	2.84623i	−0.105853	−	0.183342i	−0.914086	+	0.405520i	$0.867090\pi$
$242$	−12.0750	−	20.9146i	−0.776212	−	1.34444i
$243$		0			0
$244$	41.7997			2.67595
$245$	−3.12539	+	6.26354i	−0.199674	+	0.400163i
$246$		0			0
$247$	−8.63913	+	14.9634i	−0.549695	+	0.952100i
$248$	3.84732	+	6.66375i	0.244305	+	0.423148i
$249$		0			0
$250$	−1.11349	+	1.92861i	−0.0704230	+	0.121976i
$251$	−25.0271			−1.57969			−0.789847	−	0.613304i	$-0.789840\pi$
$251$	−25.0271			−1.57969			−0.789847	+	0.613304i	$0.789840\pi$
$252$		0			0
$253$	−0.531967			−0.0334445
$254$	7.18802	−	12.4500i	0.451017	−	0.781184i
$255$		0			0
$256$	3.89121	+	6.73977i	0.243200	+	0.421236i
$257$	−14.2775	+	24.7294i	−0.890606	+	1.54257i	−0.0514557	+	0.998675i	$0.516386\pi$
$257$	−14.2775	+	24.7294i	−0.890606	+	1.54257i	−0.839150	+	0.543900i	$0.816947\pi$
$258$		0			0
$259$	24.5293	+	13.1851i	1.52418	+	0.819283i
$260$	−7.87820			−0.488585
$261$		0			0
$262$	10.4200	+	18.0479i	0.643749	+	1.11501i
$263$	−3.72203	−	6.44675i	−0.229510	−	0.397523i	0.728153	−	0.685415i	$-0.240379\pi$
$263$	−3.72203	−	6.44675i	−0.229510	−	0.397523i	−0.957663	+	0.287891i	$0.907046\pi$
$264$		0			0
$265$	−3.07955			−0.189175
$266$	32.5224	−	20.1183i	1.99407	−	1.23353i
$267$		0			0
$268$	2.65140	−	4.59236i	0.161960	−	0.280523i
$269$	−15.3261	−	26.5455i	−0.934446	−	1.61851i	−0.775619	−	0.631202i	$-0.782562\pi$
$269$	−15.3261	−	26.5455i	−0.934446	−	1.61851i	−0.158828	−	0.987306i	$-0.550771\pi$
$270$		0			0
$271$	12.3558	−	21.4010i	0.750564	−	1.30002i	−0.196985	−	0.980406i	$-0.563115\pi$
$271$	12.3558	−	21.4010i	0.750564	−	1.30002i	0.947550	−	0.319609i	$-0.103551\pi$
$272$	−5.41796			−0.328512
$273$		0			0
$274$	−12.6601			−0.764827
$275$	−0.197262	+	0.341667i	−0.0118953	+	0.0206033i
$276$		0			0
$277$	12.0346	+	20.8446i	0.723092	+	1.25243i	0.959755	+	0.280840i	$0.0906129\pi$
$277$	12.0346	+	20.8446i	0.723092	+	1.25243i	−0.236663	+	0.971592i	$0.576054\pi$
$278$	−6.13141	+	10.6199i	−0.367737	+	0.636940i
$279$		0			0
$280$	4.97907	+	2.67638i	0.297556	+	0.159944i
$281$	6.11439			0.364754			0.182377	−	0.983229i	$-0.441621\pi$
$281$	6.11439			0.364754			0.182377	+	0.983229i	$0.441621\pi$
$282$		0			0
$283$	−10.6053	−	18.3689i	−0.630419	−	1.09192i	−0.987466	−	0.157831i	$-0.949550\pi$
$283$	−10.6053	−	18.3689i	−0.630419	−	1.09192i	0.357047	−	0.934086i	$-0.383783\pi$
$284$	−20.4054	−	35.3431i	−1.21084	−	2.09723i
$285$		0			0
$286$	−2.33889			−0.138302
$287$	0.364956	+	12.0080i	0.0215427	+	0.708809i
$288$		0			0
$289$	−2.39342	+	4.14553i	−0.140790	+	0.243855i
$290$	−4.93246	−	8.54328i	−0.289644	−	0.501678i
$291$		0			0
$292$	3.85329	−	6.67410i	0.225497	−	0.390572i
$293$	−31.2110			−1.82336			−0.911682	−	0.410897i	$-0.865216\pi$
$293$	−31.2110			−1.82336			−0.911682	+	0.410897i	$0.865216\pi$
$294$		0			0
$295$	4.14983			0.241613
$296$	11.2444	−	19.4759i	0.653567	−	1.13201i
$297$		0			0
$298$	−21.4066	−	37.0774i	−1.24005	−	2.14783i
$299$	1.79476	−	3.10861i	0.103793	−	0.179776i
$300$		0			0
$301$	−0.732373	−	24.0969i	−0.0422132	−	1.38892i
$302$	20.0718			1.15500
$303$		0			0
$304$	3.76691	+	6.52448i	0.216047	+	0.374205i
$305$	7.06219	+	12.2321i	0.404380	+	0.700407i
$306$		0			0
$307$	21.3253			1.21710			0.608549	−	0.793516i	$-0.291752\pi$
$307$	21.3253			1.21710			0.608549	+	0.793516i	$0.291752\pi$
$308$	2.72088	+	1.46254i	0.155037	+	0.0833362i
$309$		0			0
$310$	−4.01012	+	6.94574i	−0.227760	+	0.394492i
$311$	−1.61686	−	2.80048i	−0.0916837	−	0.158801i	0.816536	−	0.577295i	$-0.195892\pi$
$311$	−1.61686	−	2.80048i	−0.0916837	−	0.158801i	−0.908220	+	0.418494i	$0.862558\pi$
$312$		0			0
$313$	−0.0515752	+	0.0893309i	−0.00291520	+	0.00504928i	−0.867479	−	0.497473i	$-0.834261\pi$
$313$	−0.0515752	+	0.0893309i	−0.00291520	+	0.00504928i	0.864564	+	0.502523i	$0.167595\pi$
$314$	39.6338			2.23666
$315$		0			0
$316$	−24.3146			−1.36780
$317$	1.44985	−	2.51122i	0.0814320	−	0.141044i	−0.822433	−	0.568862i	$-0.807384\pi$
$317$	1.44985	−	2.51122i	0.0814320	−	0.141044i	0.903865	+	0.427817i	$0.140717\pi$
$318$		0			0
$319$	−0.873819	−	1.51350i	−0.0489245	−	0.0847397i
$320$	−6.47561	+	11.2161i	−0.361998	+	0.626999i
$321$		0			0
$322$	−6.75643	+	4.17952i	−0.376521	+	0.232915i
$323$	30.2952			1.68567
$324$		0			0
$325$	−1.33105	−	2.30544i	−0.0738332	−	0.127883i
$326$	7.73355	+	13.3949i	0.428322	+	0.741875i
$327$		0			0
$328$	9.70143			0.535672
$329$	−20.6589	−	11.1047i	−1.13896	−	0.612220i
$330$		0			0
$331$	10.3903	−	17.9966i	0.571104	−	0.989182i	−0.425349	−	0.905030i	$-0.639849\pi$
$331$	10.3903	−	17.9966i	0.571104	−	0.989182i	0.996453	−	0.0841520i	$-0.0268181\pi$
$332$	3.65683	+	6.33382i	0.200695	+	0.347613i
$333$		0			0
$334$	22.2370	−	38.5157i	1.21676	−	2.10748i
$335$	1.79185			0.0978991
$336$		0			0
$337$	−33.7717			−1.83966			−0.919831	−	0.392315i	$-0.871674\pi$
$337$	−33.7717			−1.83966			−0.919831	+	0.392315i	$0.871674\pi$
$338$	−6.58433	+	11.4044i	−0.358140	+	0.620317i
$339$		0			0
$340$	6.90671	+	11.9628i	0.374569	+	0.648772i
$341$	−0.710421	+	1.23049i	−0.0384715	+	0.0666345i
$342$		0			0
$343$	1.68579	+	18.4434i	0.0910242	+	0.995849i
$344$	−19.4683			−1.04966
$345$		0			0
$346$	27.4126	+	47.4801i	1.47371	+	2.55254i
$347$	14.6727	+	25.4138i	0.787669	+	1.36428i	0.927391	+	0.374093i	$0.122046\pi$
$347$	14.6727	+	25.4138i	0.787669	+	1.36428i	−0.139722	+	0.990191i	$0.544621\pi$
$348$		0			0
$349$	−3.65107			−0.195437			−0.0977187	−	0.995214i	$-0.531155\pi$
$349$	−3.65107			−0.195437			−0.0977187	+	0.995214i	$0.531155\pi$
$350$	0.178992	+	5.88929i	0.00956754	+	0.314796i
$351$		0			0
$352$	−1.35283	+	2.34318i	−0.0721063	+	0.124892i
$353$	7.99185	+	13.8423i	0.425363	+	0.736751i	0.996454	−	0.0841359i	$-0.0268130\pi$
$353$	7.99185	+	13.8423i	0.425363	+	0.736751i	−0.571091	+	0.820887i	$0.693480\pi$
$354$		0			0
$355$	6.89510	−	11.9427i	0.365954	−	0.633851i
$356$	−14.4487			−0.765781
$357$		0			0
$358$	−2.83924			−0.150059
$359$	−12.5072	+	21.6632i	−0.660107	+	1.14334i	0.320480	+	0.947255i	$0.396156\pi$
$359$	−12.5072	+	21.6632i	−0.660107	+	1.14334i	−0.980587	+	0.196084i	$0.937178\pi$
$360$		0			0
$361$	−11.5632	−	20.0280i	−0.608588	−	1.05411i
$362$	15.7134	−	27.2164i	0.825879	−	1.43046i
$363$		0			0
$364$	−17.7263	+	10.9654i	−0.929110	+	0.574746i
$365$	2.60410			0.136305
$366$		0			0
$367$	−1.80351	−	3.12377i	−0.0941425	−	0.163060i	0.815108	−	0.579309i	$-0.196678\pi$
$367$	−1.80351	−	3.12377i	−0.0941425	−	0.163060i	−0.909250	+	0.416250i	$0.863344\pi$
$368$	−0.782565	−	1.35544i	−0.0407940	−	0.0706574i
$369$		0			0
$370$	23.4404			1.21861
$371$	−6.92912	+	4.28634i	−0.359742	+	0.222536i
$372$		0			0
$373$	−17.3361	+	30.0269i	−0.897627	+	1.55474i	−0.0671087	+	0.997746i	$0.521377\pi$
$373$	−17.3361	+	30.0269i	−0.897627	+	1.55474i	−0.830519	+	0.556991i	$0.811956\pi$
$374$	2.05047	+	3.55152i	0.106027	+	0.183645i
$375$		0			0
$376$	−9.47015	+	16.4028i	−0.488386	+	0.845909i
$377$	11.7924			0.607340
$378$		0			0
$379$	30.8892			1.58667			0.793336	−	0.608785i	$-0.208343\pi$
$379$	30.8892			1.58667			0.793336	+	0.608785i	$0.208343\pi$
$380$	9.60397	−	16.6346i	0.492673	−	0.853335i
$381$		0			0
$382$	−24.8726	−	43.0807i	−1.27259	−	2.20420i
$383$	−10.7289	+	18.5830i	−0.548222	+	0.949549i	0.450174	+	0.892941i	$0.351362\pi$
$383$	−10.7289	+	18.5830i	−0.548222	+	0.949549i	−0.998396	+	0.0566079i	$0.981971\pi$
$384$		0			0
$385$	0.0317097	+	1.04333i	0.00161608	+	0.0531729i
$386$	15.9148			0.810042
$387$		0			0
$388$	−22.1679	−	38.3959i	−1.12541	−	1.94926i
$389$	18.7079	+	32.4031i	0.948530	+	1.64290i	0.748525	+	0.663107i	$0.230763\pi$
$389$	18.7079	+	32.4031i	0.948530	+	1.64290i	0.200005	+	0.979795i	$0.435904\pi$
$390$		0			0
$391$	−6.29375			−0.318288
$392$	14.9283	−	0.908265i	0.753993	−	0.0458743i
$393$		0			0
$394$	16.9741	−	29.4001i	0.855144	−	1.48115i
$395$	−4.10803	−	7.11531i	−0.206697	−	0.358010i
$396$		0			0
$397$	−0.242663	+	0.420305i	−0.0121789	+	0.0210945i	−0.872051	−	0.489416i	$-0.837210\pi$
$397$	−0.242663	+	0.420305i	−0.0121789	+	0.0210945i	0.859872	+	0.510510i	$0.170543\pi$
$398$	9.66296			0.484361
$399$		0			0
$400$	−1.16075			−0.0580375
$401$	−7.39928	+	12.8159i	−0.369502	+	0.639997i	−0.989488	−	0.144617i	$-0.953805\pi$
$401$	−7.39928	+	12.8159i	−0.369502	+	0.639997i	0.619986	+	0.784613i	$0.287138\pi$
$402$		0			0
$403$	−4.79365	−	8.30285i	−0.238789	−	0.413595i
$404$	9.94525	−	17.2257i	0.494795	−	0.857009i
$405$		0			0
$406$	−22.9894	−	12.3574i	−1.14094	−	0.613287i
$407$	4.15264			0.205838
$408$		0			0
$409$	4.13039	+	7.15404i	0.204234	+	0.353744i	0.949889	−	0.312589i	$-0.101196\pi$
$409$	4.13039	+	7.15404i	0.204234	+	0.353744i	−0.745654	+	0.666333i	$0.767863\pi$
$410$	5.05599	+	8.75723i	0.249697	+	0.432489i
$411$		0			0
$412$	−4.36776			−0.215184
$413$	9.33730	−	5.77603i	0.459459	−	0.284220i
$414$		0			0
$415$	−1.23567	+	2.14024i	−0.0606565	+	0.105060i
$416$	−9.12841	−	15.8109i	−0.447557	−	0.775192i
$417$		0			0
$418$	2.85124	−	4.93849i	0.139459	−	0.241550i
$419$	−5.11517			−0.249892			−0.124946	−	0.992164i	$-0.539876\pi$
$419$	−5.11517			−0.249892			−0.124946	+	0.992164i	$0.539876\pi$
$420$		0			0
$421$	−34.3722			−1.67520			−0.837599	−	0.546285i	$-0.816041\pi$
$421$	−34.3722			−1.67520			−0.837599	+	0.546285i	$0.816041\pi$
$422$	−16.5676	+	28.6959i	−0.806497	+	1.39689i
$423$		0			0
$424$	3.28982	+	5.69813i	0.159768	+	0.276726i
$425$	−2.33382	+	4.04229i	−0.113207	+	0.196080i
$426$		0			0
$427$	32.9157	+	17.6930i	1.59290	+	0.856226i
$428$	−30.2461			−1.46200
$429$		0			0
$430$	−10.1461	−	17.5735i	−0.489286	−	0.847468i
$431$	11.2286	+	19.4485i	0.540864	+	0.936803i	0.998855	+	0.0478466i	$0.0152359\pi$
$431$	11.2286	+	19.4485i	0.540864	+	0.936803i	−0.457991	+	0.888957i	$0.651431\pi$
$432$		0			0
$433$	−19.1810			−0.921780			−0.460890	−	0.887457i	$-0.652470\pi$
$433$	−19.1810			−0.921780			−0.460890	+	0.887457i	$0.652470\pi$
$434$	0.644625	+	21.2098i	0.0309430	+	1.01810i
$435$		0			0
$436$	5.52922	−	9.57689i	0.264802	−	0.458650i
$437$	4.37582	+	7.57914i	0.209324	+	0.362559i
$438$		0			0
$439$	4.19669	−	7.26887i	0.200297	−	0.346924i	−0.748327	−	0.663330i	$-0.769143\pi$
$439$	4.19669	−	7.26887i	0.200297	−	0.346924i	0.948624	+	0.316405i	$0.102476\pi$
$440$	0.842921			0.0401847
$441$		0			0
$442$	−27.6717			−1.31621
$443$	−16.3634	+	28.3422i	−0.777447	+	1.34658i	0.155962	+	0.987763i	$0.450152\pi$
$443$	−16.3634	+	28.3422i	−0.777447	+	1.34658i	−0.933409	+	0.358814i	$0.883181\pi$
$444$		0			0
$445$	−2.44116	−	4.22821i	−0.115722	−	0.200436i
$446$	−3.53374	+	6.12061i	−0.167327	+	0.289819i
$447$		0			0
$448$	1.04095	+	34.2499i	0.0491803	+	1.61816i
$449$	−17.2817			−0.815575			−0.407787	−	0.913077i	$-0.633700\pi$
$449$	−17.2817			−0.815575			−0.407787	+	0.913077i	$0.633700\pi$
$450$		0			0
$451$	0.895703	+	1.55140i	0.0421770	+	0.0730527i
$452$	−8.43219	−	14.6050i	−0.396617	−	0.686960i
$453$		0			0
$454$	−0.188867			−0.00886399
$455$	−6.20379	−	3.33469i	−0.290838	−	0.156333i
$456$		0			0
$457$	8.65007	−	14.9824i	0.404633	−	0.700845i	−0.589645	−	0.807662i	$-0.700732\pi$
$457$	8.65007	−	14.9824i	0.404633	−	0.700845i	0.994279	+	0.106817i	$0.0340658\pi$
$458$	26.6848	+	46.2194i	1.24690	+	2.15969i
$459$		0			0
$460$	−1.99520	+	3.45578i	−0.0930266	+	0.161127i
$461$	17.8514			0.831424			0.415712	−	0.909496i	$-0.363532\pi$
$461$	17.8514			0.831424			0.415712	+	0.909496i	$0.363532\pi$
$462$		0			0
$463$	2.75459			0.128017			0.0640083	−	0.997949i	$-0.479612\pi$
$463$	2.75459			0.128017			0.0640083	+	0.997949i	$0.479612\pi$
$464$	2.57092	−	4.45296i	0.119352	−	0.206723i
$465$		0			0
$466$	−8.96947	−	15.5356i	−0.415503	−	0.719671i
$467$	−5.78479	+	10.0196i	−0.267688	+	0.463650i	−0.968264	−	0.249928i	$-0.919593\pi$
$467$	−5.78479	+	10.0196i	−0.267688	+	0.463650i	0.700576	+	0.713578i	$0.252926\pi$
$468$		0			0
$469$	4.03174	−	2.49402i	0.186168	−	0.115163i
$470$	−19.7418			−0.910622
$471$		0			0
$472$	−4.43318	−	7.67849i	−0.204054	−	0.353431i
$473$	−1.79744	−	3.11326i	−0.0826465	−	0.143148i
$474$		0			0
$475$	6.49048			0.297804
$476$	32.1910	+	17.3035i	1.47547	+	0.793104i
$477$		0			0
$478$	−29.6548	+	51.3636i	−1.35638	+	2.34932i
$479$	−3.67370	−	6.36304i	−0.167856	−	0.290735i	0.769810	−	0.638273i	$-0.220351\pi$
$479$	−3.67370	−	6.36304i	−0.167856	−	0.290735i	−0.937666	+	0.347538i	$0.887018\pi$
$480$		0			0
$481$	−14.0102	+	24.2664i	−0.638811	+	1.10645i
$482$	−7.31905			−0.333373
$483$		0			0
$484$	−32.0928			−1.45876
$485$	7.49068	−	12.9742i	0.340134	−	0.589130i
$486$		0			0
$487$	3.34246	+	5.78931i	0.151461	+	0.262338i	0.931765	−	0.363062i	$-0.118269\pi$
$487$	3.34246	+	5.78931i	0.151461	+	0.262338i	−0.780304	+	0.625401i	$0.784935\pi$
$488$	15.0888	−	26.1345i	0.683037	−	1.18305i
$489$		0			0
$490$	8.59988	+	13.0020i	0.388503	+	0.587372i
$491$	20.0129			0.903170			0.451585	−	0.892228i	$-0.350859\pi$
$491$	20.0129			0.903170			0.451585	+	0.892228i	$0.350859\pi$
$492$		0			0
$493$	−10.3382	−	17.9063i	−0.465611	−	0.806461i
$494$	19.2391	+	33.3231i	0.865608	+	1.49928i
$495$		0			0
$496$	−4.18034			−0.187703
$497$	−1.10838	−	36.4686i	−0.0497178	−	1.63584i
$498$		0			0
$499$	3.81519	−	6.60810i	0.170791	−	0.295819i	−0.767906	−	0.640563i	$-0.778701\pi$
$499$	3.81519	−	6.60810i	0.170791	−	0.295819i	0.938697	+	0.344744i	$0.112034\pi$
$500$	1.47970	+	2.56292i	0.0661742	+	0.114617i
$501$		0			0
$502$	−27.8673	+	48.2675i	−1.24378	+	2.15428i
$503$	−5.88626			−0.262455			−0.131228	−	0.991352i	$-0.541892\pi$
$503$	−5.88626			−0.262455			−0.131228	+	0.991352i	$0.541892\pi$
$504$		0			0
$505$	6.72112			0.299086
$506$	−0.592337	+	1.02596i	−0.0263326	+	0.0456094i
$507$		0			0
$508$	−9.55210	−	16.5447i	−0.423806	−	0.734053i
$509$	−16.9504	+	29.3590i	−0.751314	+	1.30131i	0.195872	+	0.980629i	$0.437246\pi$
$509$	−16.9504	+	29.3590i	−0.751314	+	1.30131i	−0.947186	+	0.320685i	$0.896087\pi$
$510$		0			0
$511$	5.85935	−	3.62458i	0.259202	−	0.160342i
$512$	−12.9205			−0.571012
$513$		0			0
$514$	31.7956	+	55.0716i	1.40244	+	2.42910i
$515$	−0.737947	−	1.27816i	−0.0325178	−	0.0563225i
$516$		0			0
$517$	−3.49740			−0.153815
$518$	52.7420	−	32.6261i	2.31735	−	1.43351i
$519$		0			0
$520$	−2.84386	+	4.92571i	−0.124711	+	0.216007i
$521$	1.70283	+	2.94939i	0.0746024	+	0.129215i	0.900913	−	0.433999i	$-0.142898\pi$
$521$	1.70283	+	2.94939i	0.0746024	+	0.129215i	−0.826311	+	0.563214i	$0.809565\pi$
$522$		0			0
$523$	−0.0119913	+	0.0207695i	−0.000524341	+	0.000908186i	−0.866287	−	0.499546i	$-0.833500\pi$
$523$	−0.0119913	+	0.0207695i	−0.000524341	+	0.000908186i	0.865763	+	0.500454i	$0.166834\pi$
$524$	27.6940			1.20982
$525$		0			0
$526$	−16.5777			−0.722822
$527$	−8.40505	+	14.5580i	−0.366130	+	0.634156i
$528$		0			0
$529$	10.5909	+	18.3440i	0.460475	+	0.797567i
$530$	−3.42904	+	5.93926i	−0.148948	+	0.257985i
$531$		0			0
$532$	−1.54383	−	50.7960i	−0.0669336	−	2.20228i
$533$	−12.0877			−0.523578
$534$		0			0
$535$	−5.11017	−	8.85107i	−0.220932	−	0.382665i
$536$	−1.91419	−	3.31548i	−0.0826806	−	0.143207i
$537$		0			0
$538$	−68.2614			−2.94296
$539$	1.52353	+	2.30340i	0.0656230	+	0.0992144i
$540$		0			0
$541$	−16.0043	+	27.7202i	−0.688078	+	1.19179i	0.284381	+	0.958711i	$0.408212\pi$
$541$	−16.0043	+	27.7202i	−0.688078	+	1.19179i	−0.972459	+	0.233075i	$0.925121\pi$
$542$	−27.5161	−	47.6593i	−1.18192	−	2.04714i
$543$		0			0
$544$	−16.0055	+	27.7223i	−0.686230	+	1.18859i
$545$	3.73672			0.160063
$546$		0			0
$547$	−21.2558			−0.908832			−0.454416	−	0.890790i	$-0.650152\pi$
$547$	−21.2558			−0.908832			−0.454416	+	0.890790i	$0.650152\pi$
$548$	−8.41197	+	14.5700i	−0.359341	+	0.622398i
$549$		0			0
$550$	0.439296	+	0.760883i	0.0187316	+	0.0324441i
$551$	−14.3756	+	24.8993i	−0.612421	+	1.06074i
$552$		0			0
$553$	−19.1468	−	10.2919i	−0.814206	−	0.437657i
$554$	53.6016			2.27731
$555$		0			0
$556$	8.14797	+	14.1127i	0.345551	+	0.598512i
$557$	−2.55086	−	4.41822i	−0.108084	−	0.187206i	0.806910	−	0.590674i	$-0.201138\pi$
$557$	−2.55086	−	4.41822i	−0.108084	−	0.187206i	−0.914994	+	0.403468i	$0.867805\pi$
$558$		0			0
$559$	24.2569			1.02596
$560$	−2.61174	+	1.61561i	−0.110366	+	0.0682722i
$561$		0			0
$562$	6.80828	−	11.7923i	0.287190	−	0.497428i
$563$	−18.1919	−	31.5092i	−0.766695	−	1.32796i	−0.939346	−	0.342972i	$-0.888566\pi$
$563$	−18.1919	−	31.5092i	−0.766695	−	1.32796i	0.172650	−	0.984983i	$-0.444767\pi$
$564$		0			0
$565$	2.84929	−	4.93511i	0.119871	−	0.207622i
$566$	−47.2353			−1.98545
$567$		0			0
$568$	−29.4636			−1.23626
$569$	−6.68402	+	11.5771i	−0.280209	+	0.485336i	−0.971436	−	0.237302i	$-0.923737\pi$
$569$	−6.68402	+	11.5771i	−0.280209	+	0.485336i	0.691227	+	0.722637i	$0.257070\pi$
$570$		0			0
$571$	−12.9036	−	22.3497i	−0.539999	−	0.935306i	−0.998903	−	0.0468205i	$-0.985091\pi$
$571$	−12.9036	−	22.3497i	−0.539999	−	0.935306i	0.458904	−	0.888486i	$-0.348242\pi$
$572$	−1.55407	+	2.69172i	−0.0649788	+	0.112547i
$573$		0			0
$574$	23.5651	+	12.6669i	0.983589	+	0.528704i
$575$	−1.34838			−0.0562313
$576$		0			0
$577$	0.590664	+	1.02306i	0.0245897	+	0.0425906i	0.878058	−	0.478554i	$-0.158839\pi$
$577$	0.590664	+	1.02306i	0.0245897	+	0.0425906i	−0.853469	+	0.521144i	$0.825505\pi$
$578$	5.33008	+	9.23197i	0.221702	+	0.383999i
$579$		0			0
$580$	−13.1094			−0.544338
$581$	0.198633	+	6.53551i	0.00824067	+	0.271139i
$582$		0			0
$583$	−0.607477	+	1.05218i	−0.0251591	+	0.0435769i
$584$	−2.78191	−	4.81841i	−0.115116	−	0.199387i
$585$		0			0
$586$	−34.7530	+	60.1939i	−1.43563	+	2.48659i
$587$	14.0304			0.579096			0.289548	−	0.957164i	$-0.406495\pi$
$587$	14.0304			0.579096			0.289548	+	0.957164i	$0.406495\pi$
$588$		0			0
$589$	23.3749			0.963147
$590$	4.62078	−	8.00342i	0.190234	−	0.329496i
$591$		0			0
$592$	6.10885	+	10.5808i	0.251072	+	0.434870i
$593$	0.983981	−	1.70431i	0.0404073	−	0.0699874i	−0.845114	−	0.534585i	$-0.820468\pi$
$593$	0.983981	−	1.70431i	0.0404073	−	0.0699874i	0.885522	+	0.464598i	$0.153801\pi$
$594$		0			0
$595$	0.375160	+	12.3437i	0.0153801	+	0.506043i
$596$	−56.8941			−2.33047
$597$		0			0
$598$	−3.99687	−	6.92278i	−0.163444	−	0.283094i
$599$	8.12356	+	14.0704i	0.331920	+	0.574902i	0.982888	−	0.184203i	$-0.0589704\pi$
$599$	8.12356	+	14.0704i	0.331920	+	0.574902i	−0.650969	+	0.759105i	$0.725637\pi$
$600$		0			0
$601$	4.50195			0.183638			0.0918192	−	0.995776i	$-0.470732\pi$
$601$	4.50195			0.183638			0.0918192	+	0.995776i	$0.470732\pi$
$602$	−47.2891	−	25.4191i	−1.92736	−	1.03600i
$603$		0			0
$604$	13.3366	−	23.0997i	0.542660	−	0.939914i
$605$	−5.42218	−	9.39148i	−0.220443	−	0.381818i
$606$		0			0
$607$	22.7975	−	39.4865i	0.925323	−	1.60271i	0.134282	−	0.990943i	$-0.457127\pi$
$607$	22.7975	−	39.4865i	0.925323	−	1.60271i	0.791041	−	0.611763i	$-0.209539\pi$
$608$	44.5122			1.80521
$609$		0			0
$610$	31.4546			1.27356
$611$	11.7996	−	20.4374i	0.477359	−	0.826810i
$612$		0			0
$613$	−8.30910	−	14.3918i	−0.335601	−	0.581279i	0.647999	−	0.761641i	$-0.275606\pi$
$613$	−8.30910	−	14.3918i	−0.335601	−	0.581279i	−0.983600	+	0.180363i	$0.942273\pi$
$614$	23.7454	−	41.1282i	0.958286	−	1.65980i
$615$		0			0
$616$	1.89661	−	1.17324i	0.0764166	−	0.0472711i
$617$	18.9959			0.764746			0.382373	−	0.924008i	$-0.375107\pi$
$617$	18.9959			0.764746			0.382373	+	0.924008i	$0.375107\pi$
$618$		0			0
$619$	−5.98615	−	10.3683i	−0.240604	−	0.416738i	0.720283	−	0.693681i	$-0.244012\pi$
$619$	−5.98615	−	10.3683i	−0.240604	−	0.416738i	−0.960886	+	0.276943i	$0.910679\pi$
$620$	5.32902	+	9.23013i	0.214018	+	0.370691i
$621$		0			0
$622$	−7.20140			−0.288750
$623$	−11.3778	−	6.11587i	−0.455843	−	0.245027i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.114856	+	0.198937i	0.00459059	+	0.00795113i
$627$		0			0
$628$	26.3345	−	45.6127i	1.05086	−	1.82014i
$629$	49.1302			1.95895
$630$		0			0
$631$	−40.0918			−1.59603			−0.798015	−	0.602638i	$-0.794116\pi$
$631$	−40.0918			−1.59603			−0.798015	+	0.602638i	$0.794116\pi$
$632$	−8.77704	+	15.2023i	−0.349132	+	0.604714i
$633$		0			0
$634$	−3.22879	−	5.59242i	−0.128231	−	0.222103i
$635$	3.22771	−	5.59056i	0.128088	−	0.221855i
$636$		0			0
$637$	−18.6003	+	1.13167i	−0.736969	+	0.0448386i
$638$	−3.89194			−0.154083
$639$		0			0
$640$	7.56293	+	13.0994i	0.298951	+	0.517799i
$641$	−18.2393	−	31.5913i	−0.720408	−	1.24778i	−0.960836	−	0.277116i	$-0.910621\pi$
$641$	−18.2393	−	31.5913i	−0.720408	−	1.24778i	0.240429	−	0.970667i	$-0.422712\pi$
$642$		0			0
$643$	36.7751			1.45027			0.725134	−	0.688608i	$-0.241778\pi$
$643$	36.7751			1.45027			0.725134	+	0.688608i	$0.241778\pi$
$644$	0.320727	+	10.5527i	0.0126384	+	0.415835i
$645$		0			0
$646$	33.7333	−	58.4278i	1.32722	−	2.29881i
$647$	−12.5950	−	21.8152i	−0.495161	−	0.857645i	0.504823	−	0.863223i	$-0.331558\pi$
$647$	−12.5950	−	21.8152i	−0.495161	−	0.857645i	−0.999984	+	0.00557807i	$0.998224\pi$
$648$		0			0
$649$	0.818603	−	1.41786i	0.0321330	−	0.0556559i
$650$	−5.92841			−0.232531
$651$		0			0
$652$	20.5541			0.804960
$653$	−15.8125	+	27.3881i	−0.618791	+	1.07178i	0.370916	+	0.928667i	$0.379044\pi$
$653$	−15.8125	+	27.3881i	−0.618791	+	1.07178i	−0.989707	+	0.143111i	$0.954289\pi$
$654$		0			0
$655$	4.67899	+	8.10425i	0.182823	+	0.316659i
$656$	−2.63530	+	4.56447i	−0.102891	+	0.178213i
$657$		0			0
$658$	−44.4199	+	27.4781i	−1.73167	+	1.07121i
$659$	−21.6764			−0.844392			−0.422196	−	0.906505i	$-0.638741\pi$
$659$	−21.6764			−0.844392			−0.422196	+	0.906505i	$0.638741\pi$
$660$		0			0
$661$	−13.1517	−	22.7794i	−0.511542	−	0.886017i	−0.999910	−	0.0133792i	$-0.995741\pi$
$661$	−13.1517	−	22.7794i	−0.511542	−	0.886017i	0.488369	−	0.872637i	$-0.337592\pi$
$662$	−23.1390	−	40.0779i	−0.899321	−	1.55767i
$663$		0			0
$664$	5.28014			0.204909
$665$	14.6039	−	9.03392i	0.566313	−	0.350320i
$666$		0			0
$667$	2.98649	−	5.17276i	0.115637	−	0.200290i
$668$	−29.5506	−	51.1831i	−1.14335	−	1.98033i
$669$		0			0
$670$	1.99520	−	3.45578i	0.0770812	−	0.133509i
$671$	5.57240			0.215120
$672$		0			0
$673$	40.3549			1.55557			0.777784	−	0.628532i	$-0.216344\pi$
$673$	40.3549			1.55557			0.777784	+	0.628532i	$0.216344\pi$
$674$	−37.6043	+	65.1326i	−1.44846	+	2.50881i
$675$		0			0
$676$	8.74985	+	15.1552i	0.336533	+	0.582892i
$677$	9.11985	−	15.7961i	0.350504	−	0.607092i	−0.635833	−	0.771826i	$-0.719343\pi$
$677$	9.11985	−	15.7961i	0.350504	−	0.607092i	0.986338	+	0.164735i	$0.0526768\pi$
$678$		0			0
$679$	−1.20412	−	39.6186i	−0.0462100	−	1.52042i
$680$	9.97268			0.382435
$681$		0			0
$682$	1.58209	+	2.74026i	0.0605812	+	0.104930i
$683$	−18.1083	−	31.3646i	−0.692896	−	1.20013i	−0.970885	−	0.239547i	$-0.923001\pi$
$683$	−18.1083	−	31.3646i	−0.692896	−	1.20013i	0.277988	−	0.960584i	$-0.410332\pi$
$684$		0			0
$685$	−5.68491			−0.217209
$686$	37.4473	+	17.2852i	1.42974	+	0.659952i
$687$		0			0
$688$	5.28836	−	9.15971i	0.201617	−	0.349211i
$689$	−4.09903	−	7.09972i	−0.156160	−	0.270478i
$690$		0			0
$691$	12.1607	−	21.0630i	0.462615	−	0.801273i	−0.536475	−	0.843916i	$-0.680244\pi$
$691$	12.1607	−	21.0630i	0.462615	−	0.801273i	0.999090	+	0.0426430i	$0.0135778\pi$
$692$	72.8568			2.76960
$693$		0			0
$694$	65.3512			2.48070
$695$	−2.75325	+	4.76877i	−0.104437	+	0.180890i
$696$		0			0
$697$	10.5971	+	18.3548i	0.401395	+	0.695237i
$698$	−4.06542	+	7.04151i	−0.153878	+	0.266525i
$699$		0			0
$700$	6.89664	+	3.70712i	0.260668	+	0.140116i
$701$	−34.3460			−1.29723			−0.648615	−	0.761117i	$-0.724651\pi$
$701$	−34.3460			−1.29723			−0.648615	+	0.761117i	$0.724651\pi$
$702$		0			0
$703$	−34.1585	−	59.1642i	−1.28831	−	2.23142i
$704$	2.55478	+	4.42501i	0.0962869	+	0.166774i
$705$		0			0
$706$	35.5952			1.33964
$707$	15.1228	−	9.35494i	0.568752	−	0.351829i
$708$		0			0
$709$	−15.6997	+	27.1927i	−0.589614	+	1.02124i	0.404669	+	0.914463i	$0.367387\pi$
$709$	−15.6997	+	27.1927i	−0.589614	+	1.02124i	−0.994283	+	0.106778i	$0.965947\pi$
$710$	−15.3552	−	26.5960i	−0.576270	−	0.998129i
$711$		0			0
$712$	−5.21567	+	9.03381i	−0.195466	+	0.338556i
$713$	−4.85608			−0.181861
$714$		0			0
$715$	−1.05026			−0.0392774
$716$	−1.88652	+	3.26755i	−0.0705026	+	0.122114i
$717$		0			0
$718$	27.8533	+	48.2433i	1.03947	+	1.80042i
$719$	−2.01358	+	3.48763i	−0.0750940	+	0.130067i	−0.901127	−	0.433555i	$-0.857259\pi$
$719$	−2.01358	+	3.48763i	−0.0750940	+	0.130067i	0.826033	+	0.563622i	$0.190592\pi$
$720$		0			0
$721$	−3.43945	−	1.84879i	−0.128092	−	0.0688526i
$722$	−51.5017			−1.91669
$723$		0			0
$724$	−20.8814	−	36.1677i	−0.776052	−	1.34416i
$725$	−2.21488	−	3.83628i	−0.0822584	−	0.142476i
$726$		0			0
$727$	−9.17871			−0.340419			−0.170210	−	0.985408i	$-0.554445\pi$
$727$	−9.17871			−0.340419			−0.170210	+	0.985408i	$0.554445\pi$
$728$	0.457149	+	15.0413i	0.0169431	+	0.557469i
$729$		0			0
$730$	2.89963	−	5.02231i	0.107320	−	0.185884i
$731$	−21.2657	−	36.8333i	−0.786540	−	1.36233i
$732$		0			0
$733$	−7.70407	+	13.3438i	−0.284556	+	0.492866i	−0.972501	−	0.232897i	$-0.925180\pi$
$733$	−7.70407	+	13.3438i	−0.284556	+	0.492866i	0.687945	+	0.725763i	$0.258513\pi$
$734$	−8.03273			−0.296494
$735$		0			0
$736$	−9.24728			−0.340859
$737$	0.353463	−	0.612216i	0.0130200	−	0.0225513i
$738$		0			0
$739$	−9.33980	−	16.1770i	−0.343570	−	0.595081i	0.641523	−	0.767104i	$-0.278303\pi$
$739$	−9.33980	−	16.1770i	−0.343570	−	0.595081i	−0.985093	+	0.172023i	$0.944970\pi$
$740$	15.5749	−	26.9765i	0.572544	−	0.991676i
$741$		0			0
$742$	0.551216	+	18.1364i	0.0202358	+	0.665807i
$743$	38.2524			1.40335			0.701673	−	0.712499i	$-0.252437\pi$
$743$	38.2524			1.40335			0.701673	+	0.712499i	$0.252437\pi$
$744$		0			0
$745$	−9.61244	−	16.6492i	−0.352173	−	0.609981i
$746$	38.6069	+	66.8691i	1.41350	+	2.44825i
$747$		0			0
$748$	5.44971			0.199261
$749$	−23.8177	−	12.8026i	−0.870278	−	0.467797i
$750$		0			0
$751$	14.2320	−	24.6506i	0.519335	−	0.899514i	−0.480413	−	0.877043i	$-0.659513\pi$
$751$	14.2320	−	24.6506i	0.519335	−	0.899514i	0.999747	−	0.0224716i	$-0.00715355\pi$
$752$	−5.14495	−	8.91131i	−0.187617	−	0.324962i
$753$		0			0
$754$	13.1307	−	22.7430i	0.478191	−	0.828251i
$755$	9.01306			0.328019
$756$		0			0
$757$	11.0135			0.400294			0.200147	−	0.979766i	$-0.435858\pi$
$757$	11.0135			0.400294			0.200147	+	0.979766i	$0.435858\pi$
$758$	34.3947	−	59.5733i	1.24927	−	2.16380i
$759$		0			0
$760$	−6.93364	−	12.0094i	−0.251510	−	0.435627i
$761$	−3.55298	+	6.15394i	−0.128795	+	0.223080i	−0.923210	−	0.384296i	$-0.874444\pi$
$761$	−3.55298	+	6.15394i	−0.128795	+	0.223080i	0.794415	+	0.607376i	$0.207778\pi$
$762$		0			0
$763$	8.40777	−	5.20103i	0.304382	−	0.188290i
$764$	−66.1060			−2.39163
$765$		0			0
$766$	23.8930	+	41.3839i	0.863289	+	1.49526i
$767$	5.52362	+	9.56719i	0.199446	+	0.345451i
$768$		0			0
$769$	27.8897			1.00573			0.502863	−	0.864366i	$-0.332280\pi$
$769$	27.8897			1.00573			0.502863	+	0.864366i	$0.332280\pi$
$770$	2.04749	+	1.10058i	0.0737863	+	0.0396620i
$771$		0			0
$772$	10.5745	−	18.3156i	0.380585	−	0.659193i
$773$	−7.57050	−	13.1125i	−0.272292	−	0.471624i	0.697156	−	0.716919i	$-0.254448\pi$
$773$	−7.57050	−	13.1125i	−0.272292	−	0.471624i	−0.969448	+	0.245295i	$0.921115\pi$
$774$		0			0
$775$	−1.80071	+	3.11892i	−0.0646833	+	0.112035i
$776$	−32.0085			−1.14904
$777$		0			0
$778$	83.3241			2.98731
$779$	14.7356	−	25.5228i	0.527958	−	0.914450i
$780$		0			0
$781$	−2.72028	−	4.71166i	−0.0973391	−	0.168596i
$782$	−7.00800	+	12.1382i	−0.250605	+	0.434061i
$783$		0			0
$784$	−3.62779	+	7.27040i	−0.129564	+	0.259657i
$785$	17.7972			0.635208
$786$		0			0
$787$	17.6652	+	30.5970i	0.629695	+	1.09066i	0.987613	+	0.156911i	$0.0501536\pi$
$787$	17.6652	+	30.5970i	0.629695	+	1.09066i	−0.357917	+	0.933753i	$0.616513\pi$
$788$	−22.5568	−	39.0695i	−0.803551	−	1.39179i
$789$		0			0
$790$	−18.2969			−0.650975
$791$	−0.458022	−	15.0701i	−0.0162854	−	0.535830i
$792$		0			0
$793$	−18.8002	+	32.5629i	−0.667615	+	1.15634i
$794$	0.540404	+	0.936008i	0.0191782	+	0.0332177i
$795$		0			0
$796$	6.42051	−	11.1206i	0.227569	−	0.394161i
$797$	3.50359			0.124104			0.0620518	−	0.998073i	$-0.480236\pi$
$797$	3.50359			0.124104			0.0620518	+	0.998073i	$0.480236\pi$
$798$		0			0
$799$	−41.3780			−1.46385
$800$	−3.42904	+	5.93926i	−0.121235	+	0.209985i
$801$		0			0
$802$	16.4780	+	28.5407i	0.581857	+	1.00781i
$803$	0.513690	−	0.889737i	0.0181277	−	0.0313981i
$804$		0			0
$805$	−3.03391	+	1.87677i	−0.106931	+	0.0661475i
$806$	−21.3507			−0.752045
$807$		0			0
$808$	−7.18003	−	12.4362i	−0.252593	−	0.437503i
$809$	16.2874	+	28.2107i	0.572636	+	0.991834i	0.996294	+	0.0860119i	$0.0274123\pi$
$809$	16.2874	+	28.2107i	0.572636	+	0.991834i	−0.423659	+	0.905822i	$0.639254\pi$
$810$		0			0
$811$	0.141435			0.00496647			0.00248323	−	0.999997i	$-0.499210\pi$
$811$	0.141435			0.00496647			0.00248323	+	0.999997i	$0.499210\pi$
$812$	−29.4967	+	18.2466i	−1.03513	+	0.640330i
$813$		0			0
$814$	4.62390	−	8.00883i	0.162068	−	0.280709i
$815$	3.47268	+	6.01485i	0.121643	+	0.210691i
$816$		0			0
$817$	−29.5706	+	51.2177i	−1.03454	+	1.79188i
$818$	18.3965			0.643219
$819$		0			0
$820$	13.4377			0.469265
$821$	14.1377	−	24.4872i	0.493410	−	0.854611i	−0.506561	−	0.862204i	$-0.669084\pi$
$821$	14.1377	−	24.4872i	0.493410	−	0.854611i	0.999971	+	0.00759311i	$0.00241698\pi$
$822$		0			0
$823$	−2.58497	−	4.47729i	−0.0901063	−	0.156069i	0.817449	−	0.576000i	$-0.195387\pi$
$823$	−2.58497	−	4.47729i	−0.0901063	−	0.156069i	−0.907556	+	0.419932i	$0.862054\pi$
$824$	−1.57667	+	2.73087i	−0.0549258	+	0.0951342i
$825$		0			0
$826$	−0.742788	−	24.4396i	−0.0258449	−	0.850362i
$827$	9.78331			0.340199			0.170099	−	0.985427i	$-0.445591\pi$
$827$	9.78331			0.340199			0.170099	+	0.985427i	$0.445591\pi$
$828$		0			0
$829$	−13.8393	−	23.9704i	−0.480659	−	0.832526i	0.519095	−	0.854717i	$-0.326269\pi$
$829$	−13.8393	−	23.9704i	−0.480659	−	0.832526i	−0.999754	+	0.0221908i	$0.992936\pi$
$830$	2.75179	+	4.76624i	0.0955161	+	0.165439i
$831$		0			0
$832$	−34.4774			−1.19529
$833$	18.0250	+	27.2517i	0.624529	+	0.944215i
$834$		0			0
$835$	9.98533	−	17.2951i	0.345557	−	0.598522i
$836$	−3.78899	−	6.56272i	−0.131045	−	0.226976i
$837$		0			0
$838$	−5.69567	+	9.86518i	−0.196753	+	0.340787i
$839$	−18.4377			−0.636541			−0.318270	−	0.948000i	$-0.603102\pi$
$839$	−18.4377			−0.636541			−0.318270	+	0.948000i	$0.603102\pi$
$840$		0			0
$841$	−9.37731			−0.323356
$842$	−38.2729	+	66.2907i	−1.31897	+	2.28453i
$843$		0			0
$844$	22.0165	+	38.1337i	0.757839	+	1.31262i
$845$	−2.95663	+	5.12103i	−0.101711	+	0.176169i
$846$		0			0
$847$	−25.2719	−	13.5843i	−0.868352	−	0.466761i
$848$	−3.57459			−0.122752
$849$		0			0
$850$	5.19735	+	9.00207i	0.178268	+	0.308768i
$851$	7.09632	+	12.2912i	0.243259	+	0.421337i
$852$		0			0
$853$	−25.1736			−0.861928			−0.430964	−	0.902369i	$-0.641826\pi$
$853$	−25.1736			−0.861928			−0.430964	+	0.902369i	$0.641826\pi$
$854$	70.7742	−	43.7808i	2.42184	−	1.49815i
$855$		0			0
$856$	−10.9182	+	18.9108i	−0.373175	+	0.646359i
$857$	10.1452	+	17.5720i	0.346553	+	0.600248i	0.985635	−	0.168891i	$-0.0540187\pi$
$857$	10.1452	+	17.5720i	0.346553	+	0.600248i	−0.639081	+	0.769139i	$0.720685\pi$
$858$		0			0
$859$	−16.3023	+	28.2364i	−0.556228	+	0.963415i	0.441579	+	0.897222i	$0.354418\pi$
$859$	−16.3023	+	28.2364i	−0.556228	+	0.963415i	−0.997807	+	0.0661924i	$0.978915\pi$
$860$	−26.9660			−0.919532
$861$		0			0
$862$	50.0116			1.70340
$863$	25.6593	−	44.4432i	0.873453	−	1.51287i	0.0150520	−	0.999887i	$-0.495209\pi$
$863$	25.6593	−	44.4432i	0.873453	−	1.51287i	0.858401	−	0.512979i	$-0.171458\pi$
$864$		0			0
$865$	12.3094	+	21.3205i	0.418531	+	0.724918i
$866$	−21.3578	+	36.9927i	−0.725767	+	1.25706i
$867$		0			0
$868$	24.8377	+	13.3509i	0.843045	+	0.453158i
$869$	−3.24142			−0.109958
$870$		0			0
$871$	2.38503	+	4.13100i	0.0808138	+	0.139974i
$872$	−3.99185	−	6.91409i	−0.135181	−	0.234141i
$873$		0			0
$874$	19.4896			0.659247
$875$	0.0803747	+	2.64453i	0.00271716	+	0.0894014i
$876$		0			0
$877$	2.01424	−	3.48877i	0.0680161	−	0.117807i	−0.830012	−	0.557746i	$-0.811666\pi$
$877$	2.01424	−	3.48877i	0.0680161	−	0.117807i	0.898028	+	0.439938i	$0.145000\pi$
$878$	−9.34590	−	16.1876i	−0.315409	−	0.546304i
$879$		0			0
$880$	−0.228971	+	0.396590i	−0.00771862	+	0.0133690i
$881$	12.1103			0.408005			0.204003	−	0.978970i	$-0.434605\pi$
$881$	12.1103			0.408005			0.204003	+	0.978970i	$0.434605\pi$
$882$		0			0
$883$	56.9539			1.91665			0.958326	−	0.285677i	$-0.0922184\pi$
$883$	56.9539			1.91665			0.958326	+	0.285677i	$0.0922184\pi$
$884$	−18.3863	+	31.8460i	−0.618398	+	1.07110i
$885$		0			0
$886$	36.4407	+	63.1172i	1.22425	+	2.12046i
$887$	−3.10531	+	5.37856i	−0.104266	+	0.180594i	−0.913438	−	0.406978i	$-0.866583\pi$
$887$	−3.10531	+	5.37856i	−0.104266	+	0.180594i	0.809172	+	0.587572i	$0.199916\pi$
$888$		0			0
$889$	−0.518853	−	17.0716i	−0.0174018	−	0.572562i
$890$	−10.8728			−0.364456
$891$		0			0
$892$	4.69595	+	8.13362i	0.157232	+	0.272334i
$893$	28.7686	+	49.8288i	0.962706	+	1.66746i
$894$		0			0
$895$	−1.27493			−0.0426164
$896$	35.2496	+	18.9475i	1.17761	+	0.632993i
$897$		0			0
$898$	−19.2429	+	33.3297i	−0.642145	+	1.11223i
$899$	−7.97669	−	13.8160i	−0.266037	−	0.460790i
$900$		0			0
$901$	−7.18711	+	12.4484i	−0.239437	+	0.414718i
$902$	3.98941			0.132833
$903$		0			0
$904$	−12.1753			−0.404946
$905$	7.05596	−	12.2213i	0.234548	−	0.406249i
$906$		0			0
$907$	11.7329	+	20.3220i	0.389585	+	0.674780i	0.992394	−	0.123105i	$-0.0392853\pi$
$907$	11.7329	+	20.3220i	0.389585	+	0.674780i	−0.602809	+	0.797885i	$0.705952\pi$
$908$	−0.125492	+	0.217359i	−0.00416460	+	0.00721330i
$909$		0			0
$910$	−13.3392	+	8.25158i	−0.442189	+	0.273537i
$911$	28.8860			0.957036			0.478518	−	0.878078i	$-0.341174\pi$
$911$	28.8860			0.957036			0.478518	+	0.878078i	$0.341174\pi$
$912$		0			0
$913$	0.487499	+	0.844373i	0.0161339	+	0.0279447i
$914$	−19.2635	−	33.3653i	−0.637179	−	1.10363i
$915$		0			0
$916$	70.9224			2.34334
$917$	21.8080	+	11.7224i	0.720164	+	0.387106i
$918$		0			0
$919$	−26.7089	+	46.2611i	−0.881044	+	1.52601i	−0.0308632	+	0.999524i	$0.509826\pi$
$919$	−26.7089	+	46.2611i	−0.881044	+	1.52601i	−0.850181	+	0.526490i	$0.823508\pi$
$920$	1.44045	+	2.49492i	0.0474901	+	0.0822552i
$921$		0			0
$922$	19.8773	−	34.4285i	0.654625	−	1.13384i
$923$	36.7108			1.20835
$924$		0			0
$925$	10.5257			0.346083
$926$	3.06720	−	5.31254i	0.100794	−	0.174581i
$927$		0			0
$928$	−15.1898	−	26.3095i	−0.498629	−	0.863650i
$929$	15.9572	−	27.6387i	0.523539	−	0.906797i	−0.476085	−	0.879399i	$-0.657945\pi$
$929$	15.9572	−	27.6387i	0.523539	−	0.906797i	0.999625	−	0.0273977i	$-0.00872204\pi$
$930$		0			0
$931$	20.2853	−	40.6534i	0.664823	−	1.33236i
$932$	−23.8389			−0.780868
$933$		0			0
$934$	12.8826	+	22.3133i	0.421531	+	0.730112i
$935$	0.920746	+	1.59478i	0.0301116	+	0.0521548i
$936$		0			0
$937$	9.39523			0.306929			0.153464	−	0.988154i	$-0.450957\pi$
$937$	9.39523			0.306929			0.153464	+	0.988154i	$0.450957\pi$
$938$	−0.320727	−	10.5527i	−0.0104721	−	0.344559i
$939$		0			0
$940$	−13.1174	+	22.7199i	−0.427841	+	0.741042i
$941$	−24.4391	−	42.3297i	−0.796691	−	1.37991i	−0.921760	−	0.387762i	$-0.873248\pi$
$941$	−24.4391	−	42.3297i	−0.796691	−	1.37991i	0.125068	−	0.992148i	$-0.460085\pi$
$942$		0			0
$943$	−3.06128	+	5.30230i	−0.0996891	+	0.172667i
$944$	4.81692			0.156777
$945$		0			0
$946$	−8.00571			−0.260288
$947$	−13.0712	+	22.6401i	−0.424759	+	0.735703i	−0.996398	−	0.0848017i	$-0.972974\pi$
$947$	−13.0712	+	22.6401i	−0.424759	+	0.735703i	0.571639	+	0.820505i	$0.306308\pi$
$948$		0			0
$949$	3.46619	+	6.00361i	0.112517	+	0.194885i
$950$	7.22706	−	12.5176i	0.234477	−	0.406126i
$951$		0			0
$952$	22.4389	−	13.8807i	0.727251	−	0.449876i
$953$	12.2195			0.395827			0.197913	−	0.980219i	$-0.436583\pi$
$953$	12.2195			0.395827			0.197913	+	0.980219i	$0.436583\pi$
$954$		0			0
$955$	−11.1688	−	19.3450i	−0.361414	−	0.625988i
$956$	39.4080	+	68.2567i	1.27455	+	2.20758i
$957$		0			0
$958$	−16.3625			−0.528647
$959$	−12.7913	+	7.91267i	−0.413053	+	0.255513i
$960$		0			0
$961$	9.01490	−	15.6143i	0.290803	−	0.503686i
$962$	31.2003	+	54.0406i	1.00594	+	1.74234i
$963$		0			0
$964$	−4.86311	+	8.42315i	−0.156630	+	0.271291i
$965$	7.14639			0.230050
$966$		0			0
$967$	−54.0385			−1.73776			−0.868880	−	0.495023i	$-0.835160\pi$
$967$	−54.0385			−1.73776			−0.868880	+	0.495023i	$0.835160\pi$
$968$	−11.5848	+	20.0654i	−0.372349	+	0.644928i
$969$		0			0
$970$	−16.6815	−	28.8932i	−0.535611	−	0.927706i
$971$	−26.3572	+	45.6520i	−0.845843	+	1.46504i	0.0390449	+	0.999237i	$0.487568\pi$
$971$	−26.3572	+	45.6520i	−0.845843	+	1.46504i	−0.884887	+	0.465805i	$0.845765\pi$
$972$		0			0
$973$	0.442583	+	14.5621i	0.0141886	+	0.466840i
$974$	14.8871			0.477014
$975$		0			0
$976$	8.19743	+	14.1984i	0.262393	+	0.454479i
$977$	−11.0718	−	19.1769i	−0.354218	−	0.613523i	0.632766	−	0.774343i	$-0.281920\pi$
$977$	−11.0718	−	19.1769i	−0.354218	−	0.613523i	−0.986984	+	0.160820i	$0.948586\pi$
$978$		0			0
$979$	−1.92619			−0.0615612
$980$	20.6776	−	1.25806i	0.660521	−	0.0401873i
$981$		0			0
$982$	22.2841	−	38.5972i	0.711114	−	1.23169i
$983$	−18.8128	−	32.5847i	−0.600036	−	1.03929i	−0.992815	−	0.119659i	$-0.961820\pi$
$983$	−18.8128	−	32.5847i	−0.600036	−	1.03929i	0.392779	−	0.919633i	$-0.371514\pi$
$984$		0			0
$985$	7.62207	−	13.2018i	0.242859	−	0.420645i
$986$	−46.0459			−1.46640
$987$		0			0
$988$	51.1333			1.62677
$989$	6.14320	−	10.6403i	0.195342	−	0.338343i
$990$		0			0
$991$	6.67935	+	11.5690i	0.212177	+	0.367501i	0.952395	−	0.304865i	$-0.0986115\pi$
$991$	6.67935	+	11.5690i	0.212177	+	0.367501i	−0.740219	+	0.672366i	$0.765278\pi$
$992$	−12.3494	+	21.3898i	−0.392093	+	0.679126i
$993$		0			0
$994$	−71.5680	−	38.4696i	−2.27000	−	1.22018i
$995$	4.33906			0.137557
$996$		0			0
$997$	−30.5161	−	52.8554i	−0.966454	−	1.67395i	−0.705657	−	0.708554i	$-0.749348\pi$
$997$	−30.5161	−	52.8554i	−0.966454	−	1.67395i	−0.260797	−	0.965394i	$-0.583985\pi$
$998$	−8.49631	−	14.7160i	−0.268946	−	0.465828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.j.g.541.5	yes	10
3.2	odd	2		945.2.j.e.541.1	✓	10
7.2	even	3		6615.2.a.bk.1.1		5
7.4	even	3	inner	945.2.j.g.676.5	yes	10
7.5	odd	6		6615.2.a.bo.1.1		5
21.2	odd	6		6615.2.a.br.1.5		5
21.5	even	6		6615.2.a.bn.1.5		5
21.11	odd	6		945.2.j.e.676.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.j.e.541.1	✓	10	3.2	odd	2
945.2.j.e.676.1	yes	10	21.11	odd	6
945.2.j.g.541.5	yes	10	1.1	even	1	trivial
945.2.j.g.676.5	yes	10	7.4	even	3	inner
6615.2.a.bk.1.1		5	7.2	even	3
6615.2.a.bn.1.5		5	21.5	even	6
6615.2.a.bo.1.1		5	7.5	odd	6
6615.2.a.br.1.5		5	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11349 - 1.92861i) q^{2} +(-1.47970 - 2.56292i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0803747 - 2.64453i) q^{7} -2.13656 q^{8} +O(q^{10})\)	\(q+(1.11349 - 1.92861i) q^{2} +(-1.47970 - 2.56292i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0803747 - 2.64453i) q^{7} -2.13656 q^{8} +(-1.11349 - 1.92861i) q^{10} +(-0.197262 - 0.341667i) q^{11} +2.66209 q^{13} +(-5.18977 - 2.78963i) q^{14} +(0.580375 - 1.00524i) q^{16} +(-2.33382 - 4.04229i) q^{17} +(-3.24524 + 5.62092i) q^{19} -2.95940 q^{20} -0.878592 q^{22} +(0.674190 - 1.16773i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.96420 - 5.13415i) q^{26} +(-6.65878 + 4.11911i) q^{28} +4.42975 q^{29} +(-1.80071 - 3.11892i) q^{31} +(-3.42904 - 5.93926i) q^{32} -10.3947 q^{34} +(-2.33042 - 1.25266i) q^{35} +(-5.26285 + 9.11553i) q^{37} +(7.22706 + 12.5176i) q^{38} +(-1.06828 + 1.85031i) q^{40} -4.54069 q^{41} +9.11198 q^{43} +(-0.583776 + 1.01113i) q^{44} +(-1.50140 - 2.60050i) q^{46} +(4.43244 - 7.67721i) q^{47} +(-6.98708 + 0.425107i) q^{49} -2.22697 q^{50} +(-3.93910 - 6.82272i) q^{52} +(-1.53978 - 2.66697i) q^{53} -0.394523 q^{55} +(0.171725 + 5.65019i) q^{56} +(4.93246 - 8.54328i) q^{58} +(2.07492 + 3.59386i) q^{59} +(-7.06219 + 12.2321i) q^{61} -8.02025 q^{62} -12.9512 q^{64} +(1.33105 - 2.30544i) q^{65} +(0.895924 + 1.55179i) q^{67} +(-6.90671 + 11.9628i) q^{68} +(-5.01078 + 3.09966i) q^{70} +13.7902 q^{71} +(1.30205 + 2.25522i) q^{73} +(11.7202 + 20.3000i) q^{74} +19.2079 q^{76} +(-0.887694 + 0.549126i) q^{77} +(4.10803 - 7.11531i) q^{79} +(-0.580375 - 1.00524i) q^{80} +(-5.05599 + 8.75723i) q^{82} -2.47133 q^{83} -4.66764 q^{85} +(10.1461 - 17.5735i) q^{86} +(0.421461 + 0.729991i) q^{88} +(2.44116 - 4.22821i) q^{89} +(-0.213965 - 7.03999i) q^{91} -3.99040 q^{92} +(-9.87091 - 17.0969i) q^{94} +(3.24524 + 5.62092i) q^{95} +14.9814 q^{97} +(-6.96015 + 13.9487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{4} + 5 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) 10 * q - 4 * q^4 + 5 * q^5 - 5 * q^7 - 6 * q^8	\( 10 q - 4 q^{4} + 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{11} + 12 q^{13} - 8 q^{14} + 10 q^{16} - q^{17} - 7 q^{19} - 8 q^{20} + 8 q^{22} + 4 q^{23} - 5 q^{25} + 7 q^{26} + q^{28} - 24 q^{29} - 11 q^{31} - 4 q^{32} + 16 q^{34} - q^{35} - 3 q^{38} - 3 q^{40} - 14 q^{41} + 4 q^{43} - 10 q^{44} - 14 q^{46} + 14 q^{47} - 19 q^{49} - 7 q^{52} + 2 q^{53} + 10 q^{55} - 6 q^{56} + 28 q^{58} + 2 q^{59} - 25 q^{61} + 48 q^{62} - 34 q^{64} + 6 q^{65} - 6 q^{67} - 14 q^{68} - 10 q^{70} + 30 q^{71} - 17 q^{73} + 29 q^{74} + 68 q^{76} + 14 q^{77} + 7 q^{79} - 10 q^{80} - 7 q^{82} - 4 q^{83} - 2 q^{85} + 7 q^{86} - 10 q^{88} + 15 q^{89} + 18 q^{91} - 42 q^{92} - 21 q^{94} + 7 q^{95} + 96 q^{97} - 23 q^{98}+O(q^{100}) \) 10 * q - 4 * q^4 + 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^11 + 12 * q^13 - 8 * q^14 + 10 * q^16 - q^17 - 7 * q^19 - 8 * q^20 + 8 * q^22 + 4 * q^23 - 5 * q^25 + 7 * q^26 + q^28 - 24 * q^29 - 11 * q^31 - 4 * q^32 + 16 * q^34 - q^35 - 3 * q^38 - 3 * q^40 - 14 * q^41 + 4 * q^43 - 10 * q^44 - 14 * q^46 + 14 * q^47 - 19 * q^49 - 7 * q^52 + 2 * q^53 + 10 * q^55 - 6 * q^56 + 28 * q^58 + 2 * q^59 - 25 * q^61 + 48 * q^62 - 34 * q^64 + 6 * q^65 - 6 * q^67 - 14 * q^68 - 10 * q^70 + 30 * q^71 - 17 * q^73 + 29 * q^74 + 68 * q^76 + 14 * q^77 + 7 * q^79 - 10 * q^80 - 7 * q^82 - 4 * q^83 - 2 * q^85 + 7 * q^86 - 10 * q^88 + 15 * q^89 + 18 * q^91 - 42 * q^92 - 21 * q^94 + 7 * q^95 + 96 * q^97 - 23 * q^98

Introduction

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