LMFDB - Embedded newform 668.2.e.a.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.10
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.189949 + 1.42543i) q^{3} +(2.53109 + 1.11927i) q^{5} +(0.927279 - 1.99403i) q^{7} +(0.899535 - 0.244073i) q^{9} +O(q^{10})$	\(q+(0.189949 + 1.42543i) q^{3} +(2.53109 + 1.11927i) q^{5} +(0.927279 - 1.99403i) q^{7} +(0.899535 - 0.244073i) q^{9} +(-1.13091 + 1.45001i) q^{11} +(2.39283 - 4.67431i) q^{13} +(-1.11467 + 3.82051i) q^{15} +(5.66373 + 0.429571i) q^{17} +(1.03489 - 1.55678i) q^{19} +(3.01849 + 0.943010i) q^{21} +(-3.88484 - 1.54493i) q^{23} +(1.78931 + 1.96717i) q^{25} +(2.18855 + 5.21372i) q^{27} +(-7.12459 + 2.83331i) q^{29} +(-2.93838 + 0.679028i) q^{31} +(-2.28171 - 1.33661i) q^{33} +(4.57889 - 4.00919i) q^{35} +(-4.45775 - 1.20953i) q^{37} +(7.11743 + 2.52294i) q^{39} +(-3.49204 + 1.70500i) q^{41} +(0.277331 - 2.92205i) q^{43} +(2.54999 + 0.389051i) q^{45} +(0.140827 + 7.44035i) q^{47} +(1.39448 + 1.65480i) q^{49} +(0.463497 + 8.15487i) q^{51} +(2.20354 + 12.8118i) q^{53} +(-4.48540 + 2.40432i) q^{55} +(2.41566 + 1.17945i) q^{57} +(-4.66117 + 0.353531i) q^{59} +(7.59924 - 7.74443i) q^{61} +(0.347431 - 2.02002i) q^{63} +(11.2883 - 9.15288i) q^{65} +(4.57112 - 2.02139i) q^{67} +(1.46427 - 5.83104i) q^{69} +(-13.5269 + 1.54264i) q^{71} +(1.29764 - 0.973148i) q^{73} +(-2.46419 + 2.92420i) q^{75} +(1.84269 + 3.59963i) q^{77} +(-3.94817 + 10.5026i) q^{79} +(-4.60340 + 2.69664i) q^{81} +(6.95087 - 9.64360i) q^{83} +(13.8546 + 7.42654i) q^{85} +(-5.39200 - 9.61744i) q^{87} +(-2.28824 - 7.84293i) q^{89} +(-7.10187 - 9.10576i) q^{91} +(-1.52605 - 4.05948i) q^{93} +(4.36186 - 2.78203i) q^{95} +(-12.5380 - 2.89741i) q^{97} +(-0.663384 + 1.58036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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			0
$2$		0			0
$3$	0.189949	+	1.42543i	0.109667	+	0.822974i	0.956627	+	0.291317i	$0.0940933\pi$
$3$	0.189949	+	1.42543i	0.109667	+	0.822974i	−0.846959	+	0.531658i	$0.821569\pi$
$4$		0			0
$5$	2.53109	+	1.11927i	1.13194	+	0.500553i	0.883657	−	0.468134i	$-0.155074\pi$
$5$	2.53109	+	1.11927i	1.13194	+	0.500553i	0.248282	+	0.968688i	$0.420134\pi$
$6$		0			0
$7$	0.927279	−	1.99403i	0.350478	−	0.753671i	−0.649499	−	0.760362i	$-0.725021\pi$
$7$	0.927279	−	1.99403i	0.350478	−	0.753671i	0.999978	+	0.00669110i	$0.00212986\pi$
$8$		0			0
$9$	0.899535	−	0.244073i	0.299845	−	0.0813577i
$10$		0			0
$11$	−1.13091	+	1.45001i	−0.340982	+	0.437195i	−0.928114	−	0.372297i	$-0.878570\pi$
$11$	−1.13091	+	1.45001i	−0.340982	+	0.437195i	0.587131	+	0.809492i	$0.300257\pi$
$12$		0			0
$13$	2.39283	−	4.67431i	0.663652	−	1.29642i	−0.278242	−	0.960511i	$-0.589752\pi$
$13$	2.39283	−	4.67431i	0.663652	−	1.29642i	0.941895	−	0.335909i	$-0.109043\pi$
$14$		0			0
$15$	−1.11467	+	3.82051i	−0.287806	+	0.986451i
$16$		0			0
$17$	5.66373	+	0.429571i	1.37366	+	0.104186i	0.741655	−	0.670781i	$-0.234041\pi$
$17$	5.66373	+	0.429571i	1.37366	+	0.104186i	0.632001	+	0.774967i	$0.282234\pi$
$18$		0			0
$19$	1.03489	−	1.55678i	0.237420	−	0.357150i	−0.694700	−	0.719299i	$-0.744463\pi$
$19$	1.03489	−	1.55678i	0.237420	−	0.357150i	0.932120	+	0.362149i	$0.117957\pi$
$20$		0			0
$21$	3.01849	+	0.943010i	0.658688	+	0.205782i
$22$		0			0
$23$	−3.88484	−	1.54493i	−0.810046	−	0.322139i	−0.0724415	−	0.997373i	$-0.523079\pi$
$23$	−3.88484	−	1.54493i	−0.810046	−	0.322139i	−0.737604	+	0.675233i	$0.764043\pi$
$24$		0			0
$25$	1.78931	+	1.96717i	0.357861	+	0.393434i
$26$		0			0
$27$	2.18855	+	5.21372i	0.421187	+	1.00338i
$28$		0			0
$29$	−7.12459	+	2.83331i	−1.32300	+	0.526132i	−0.921020	−	0.389515i	$-0.872643\pi$
$29$	−7.12459	+	2.83331i	−1.32300	+	0.526132i	−0.401982	+	0.915647i	$0.631679\pi$
$30$		0			0
$31$	−2.93838	+	0.679028i	−0.527748	+	0.121957i	−0.480615	−	0.876932i	$-0.659587\pi$
$31$	−2.93838	+	0.679028i	−0.527748	+	0.121957i	−0.0471325	+	0.998889i	$0.515008\pi$
$32$		0			0
$33$	−2.28171	−	1.33661i	−0.397195	−	0.232674i
$34$		0			0
$35$	4.57889	−	4.00919i	0.773973	−	0.677677i
$36$		0			0
$37$	−4.45775	−	1.20953i	−0.732850	−	0.198846i	−0.124169	−	0.992261i	$-0.539626\pi$
$37$	−4.45775	−	1.20953i	−0.732850	−	0.198846i	−0.608681	+	0.793415i	$0.708301\pi$
$38$		0			0
$39$	7.11743	+	2.52294i	1.13970	+	0.403994i
$40$		0			0
$41$	−3.49204	+	1.70500i	−0.545365	+	0.266276i	−0.690744	−	0.723100i	$-0.742717\pi$
$41$	−3.49204	+	1.70500i	−0.545365	+	0.266276i	0.145378	+	0.989376i	$0.453560\pi$
$42$		0			0
$43$	0.277331	−	2.92205i	0.0422925	−	0.445608i	−0.949127	−	0.314892i	$-0.898032\pi$
$43$	0.277331	−	2.92205i	0.0422925	−	0.445608i	0.991420	−	0.130715i	$-0.0417274\pi$
$44$		0			0
$45$	2.54999	+	0.389051i	0.380130	+	0.0579963i
$46$		0			0
$47$	0.140827	+	7.44035i	0.0205418	+	1.08529i	0.850021	+	0.526749i	$0.176589\pi$
$47$	0.140827	+	7.44035i	0.0205418	+	1.08529i	−0.829479	+	0.558538i	$0.811363\pi$
$48$		0			0
$49$	1.39448	+	1.65480i	0.199212	+	0.236400i
$50$		0			0
$51$	0.463497	+	8.15487i	0.0649026	+	1.14191i
$52$		0			0
$53$	2.20354	+	12.8118i	0.302680	+	1.75983i	0.595206	+	0.803573i	$0.297070\pi$
$53$	2.20354	+	12.8118i	0.302680	+	1.75983i	−0.292526	+	0.956257i	$0.594496\pi$
$54$		0			0
$55$	−4.48540	+	2.40432i	−0.604811	+	0.324199i
$56$		0			0
$57$	2.41566	+	1.17945i	0.319962	+	0.156223i
$58$		0			0
$59$	−4.66117	+	0.353531i	−0.606833	+	0.0460258i	−0.375459	−	0.926839i	$-0.622515\pi$
$59$	−4.66117	+	0.353531i	−0.606833	+	0.0460258i	−0.231374	+	0.972865i	$0.574322\pi$
$60$		0			0
$61$	7.59924	−	7.74443i	0.972983	−	0.991573i	−0.0269849	−	0.999636i	$-0.508591\pi$
$61$	7.59924	−	7.74443i	0.972983	−	0.991573i	0.999967	+	0.00806283i	$0.00256651\pi$
$62$		0			0
$63$	0.347431	−	2.02002i	0.0437722	−	0.254499i
$64$		0			0
$65$	11.2883	−	9.15288i	1.40014	−	1.13528i
$66$		0			0
$67$	4.57112	−	2.02139i	0.558451	−	0.246952i	−0.105894	−	0.994377i	$-0.533771\pi$
$67$	4.57112	−	2.02139i	0.558451	−	0.246952i	0.664346	+	0.747426i	$0.268710\pi$
$68$		0			0
$69$	1.46427	−	5.83104i	0.176277	−	0.701975i
$70$		0			0
$71$	−13.5269	+	1.54264i	−1.60535	+	0.183077i	−0.869453	−	0.494016i	$-0.835528\pi$
$71$	−13.5269	+	1.54264i	−1.60535	+	0.183077i	−0.735897	+	0.677094i	$0.763239\pi$
$72$		0			0
$73$	1.29764	−	0.973148i	0.151878	−	0.113898i	−0.521318	−	0.853362i	$-0.674560\pi$
$73$	1.29764	−	0.973148i	0.151878	−	0.113898i	0.673196	+	0.739464i	$0.264921\pi$
$74$		0			0
$75$	−2.46419	+	2.92420i	−0.284540	+	0.337657i
$76$		0			0
$77$	1.84269	+	3.59963i	0.209994	+	0.410216i
$78$		0			0
$79$	−3.94817	+	10.5026i	−0.444203	+	1.18163i	0.503926	+	0.863747i	$0.331889\pi$
$79$	−3.94817	+	10.5026i	−0.444203	+	1.18163i	−0.948129	+	0.317886i	$0.897027\pi$
$80$		0			0
$81$	−4.60340	+	2.69664i	−0.511489	+	0.299626i
$82$		0			0
$83$	6.95087	−	9.64360i	0.762957	−	1.05852i	−0.233327	−	0.972398i	$-0.574961\pi$
$83$	6.95087	−	9.64360i	0.762957	−	1.05852i	0.996284	−	0.0861245i	$-0.0274483\pi$
$84$		0			0
$85$	13.8546	+	7.42654i	1.50275	+	0.805521i
$86$		0			0
$87$	−5.39200	−	9.61744i	−0.578083	−	1.03110i
$88$		0			0
$89$	−2.28824	−	7.84293i	−0.242553	−	0.831349i	−0.986591	−	0.163212i	$-0.947815\pi$
$89$	−2.28824	−	7.84293i	−0.242553	−	0.831349i	0.744038	−	0.668138i	$-0.232908\pi$
$90$		0			0
$91$	−7.10187	−	9.10576i	−0.744478	−	0.954543i
$92$		0			0
$93$	−1.52605	−	4.05948i	−0.158244	−	0.420948i
$94$		0			0
$95$	4.36186	−	2.78203i	0.447517	−	0.285431i
$96$		0			0
$97$	−12.5380	−	2.89741i	−1.27304	−	0.294187i	−0.466056	−	0.884755i	$-0.654325\pi$
$97$	−12.5380	−	2.89741i	−1.27304	−	0.294187i	−0.806988	+	0.590568i	$0.798904\pi$
$98$		0			0
$99$	−0.663384	+	1.58036i	−0.0666726	+	0.158832i
$100$		0			0
$101$	0.266983	+	2.81302i	0.0265658	+	0.279906i	0.998923	+	0.0464064i	$0.0147769\pi$
$101$	0.266983	+	2.81302i	0.0265658	+	0.279906i	−0.972357	+	0.233500i	$0.924982\pi$
$102$		0			0
$103$	−4.87498	+	3.37545i	−0.480346	+	0.332593i	−0.784604	−	0.619997i	$-0.787134\pi$
$103$	−4.87498	+	3.37545i	−0.480346	+	0.332593i	0.304258	+	0.952590i	$0.401592\pi$
$104$		0			0
$105$	6.58459	+	5.76535i	0.642590	+	0.562641i
$106$		0			0
$107$	−1.82805	−	1.26574i	−0.176724	−	0.122364i	0.477603	−	0.878576i	$-0.341506\pi$
$107$	−1.82805	−	1.26574i	−0.176724	−	0.122364i	−0.654327	+	0.756212i	$0.727048\pi$
$108$		0			0
$109$	−1.60171	−	1.02159i	−0.153416	−	0.0978501i	0.458805	−	0.888537i	$-0.348278\pi$
$109$	−1.60171	−	1.02159i	−0.153416	−	0.0978501i	−0.612221	+	0.790687i	$0.709724\pi$
$110$		0			0
$111$	0.877363	−	6.58398i	0.0832756	−	0.624923i
$112$		0			0
$113$	2.48840	−	4.06934i	0.234089	−	0.382811i	−0.714341	−	0.699798i	$-0.753273\pi$
$113$	2.48840	−	4.06934i	0.234089	−	0.382811i	0.948430	+	0.316987i	$0.102671\pi$
$114$		0			0
$115$	−8.10371	−	8.25854i	−0.755675	−	0.770113i
$116$		0			0
$117$	1.01156	−	4.78873i	0.0935190	−	0.442718i
$118$		0			0
$119$	6.10843	−	10.8953i	0.559959	−	0.998770i
$120$		0			0
$121$	1.85552	+	7.38909i	0.168683	+	0.671736i
$122$		0			0
$123$	−3.09368	−	4.65381i	−0.278947	−	0.419620i
$124$		0			0
$125$	−2.04846	−	6.14582i	−0.183220	−	0.549699i
$126$		0			0
$127$	−19.6762	−	2.24391i	−1.74598	−	0.199115i	−0.818888	−	0.573953i	$-0.805409\pi$
$127$	−19.6762	−	2.24391i	−1.74598	−	0.199115i	−0.927090	+	0.374838i	$0.877698\pi$
$128$		0			0
$129$	4.21786	−	0.159724i	0.371362	−	0.0140630i
$130$		0			0
$131$	0.888945	−	15.6403i	0.0776674	−	1.36650i	−0.689143	−	0.724625i	$-0.742013\pi$
$131$	0.888945	−	15.6403i	0.0776674	−	1.36650i	0.766811	−	0.641873i	$-0.221842\pi$
$132$		0			0
$133$	−2.14463	−	3.50716i	−0.185963	−	0.304110i
$134$		0			0
$135$	−0.296140	+	15.6460i	−0.0254877	+	1.34659i
$136$		0			0
$137$	−2.20400	+	0.781259i	−0.188300	+	0.0667475i	−0.426583	−	0.904448i	$-0.640283\pi$
$137$	−2.20400	+	0.781259i	−0.188300	+	0.0667475i	0.238283	+	0.971196i	$0.423415\pi$
$138$		0			0
$139$	11.4810	+	10.8470i	0.973804	+	0.920028i	0.996818	−	0.0797074i	$-0.0253986\pi$
$139$	11.4810	+	10.8470i	0.973804	+	0.920028i	−0.0230142	+	0.999735i	$0.507326\pi$
$140$		0			0
$141$	−10.5790	+	1.61403i	−0.890910	+	0.135926i
$142$		0			0
$143$	4.07172	+	8.75586i	0.340495	+	0.732202i
$144$		0			0
$145$	−21.2042	−	0.802975i	−1.76092	−	0.0666834i
$146$		0			0
$147$	−2.09393	+	2.30207i	−0.172704	+	0.189872i
$148$		0			0
$149$	2.54595	+	2.06433i	0.208572	+	0.169117i	0.728395	−	0.685158i	$-0.240267\pi$
$149$	2.54595	+	2.06433i	0.208572	+	0.169117i	−0.519822	+	0.854275i	$0.674002\pi$
$150$		0			0
$151$	−5.96557	−	4.47378i	−0.485471	−	0.364071i	0.328948	−	0.944348i	$-0.393306\pi$
$151$	−5.96557	−	4.47378i	−0.485471	−	0.364071i	−0.814419	+	0.580277i	$0.802944\pi$
$152$		0			0
$153$	5.19957	−	0.995951i	0.420360	−	0.0805179i
$154$		0			0
$155$	−8.19732	−	1.57015i	−0.658425	−	0.126118i
$156$		0			0
$157$	−2.77631	−	13.1430i	−0.221574	−	1.04893i	−0.936754	−	0.349988i	$-0.886186\pi$
$157$	−2.77631	−	13.1430i	−0.221574	−	1.04893i	0.715180	−	0.698940i	$-0.246345\pi$
$158$		0			0
$159$	−17.8437	+	5.57459i	−1.41510	+	0.442094i
$160$		0			0
$161$	−6.68295	+	6.31390i	−0.526691	+	0.497605i
$162$		0			0
$163$	−1.52658	+	4.58006i	−0.119571	+	0.358738i	−0.991364	−	0.131135i	$-0.958138\pi$
$163$	−1.52658	+	4.58006i	−0.119571	+	0.358738i	0.871794	+	0.489874i	$0.162957\pi$
$164$		0			0
$165$	−4.27920	−	5.93694i	−0.333135	−	0.462190i
$166$		0			0
$167$	0.211440	+	12.9211i	0.0163617	+	0.999866i
$167$	0.211440	+	12.9211i	0.0163617	+	0.999866i
$168$		0			0
$169$	−8.52216	−	11.8236i	−0.655551	−	0.909508i
$170$		0			0
$171$	0.550950	−	1.65297i	0.0421322	−	0.126405i
$172$		0			0
$173$	6.76612	−	6.39247i	0.514418	−	0.486011i	−0.385111	−	0.922870i	$-0.625837\pi$
$173$	6.76612	−	6.39247i	0.514418	−	0.486011i	0.899530	+	0.436859i	$0.143909\pi$
$174$		0			0
$175$	5.58177	−	1.74381i	0.421942	−	0.131820i
$176$		0			0
$177$	−1.38932	−	6.57703i	−0.104428	−	0.494360i
$178$		0			0
$179$	17.9375	+	3.43584i	1.34071	+	0.256807i	0.807846	−	0.589393i	$-0.200633\pi$
$179$	17.9375	+	3.43584i	1.34071	+	0.256807i	0.532866	+	0.846200i	$0.321115\pi$
$180$		0			0
$181$	16.1056	−	3.08495i	1.19712	−	0.229302i	0.449409	−	0.893326i	$-0.351635\pi$
$181$	16.1056	−	3.08495i	1.19712	−	0.229302i	0.747711	+	0.664024i	$0.231153\pi$
$182$		0			0
$183$	12.4826	+	9.36116i	0.922743	+	0.691996i
$184$		0			0
$185$	−9.92919	−	8.05088i	−0.730008	−	0.591912i
$186$		0			0
$187$	−7.02806	+	7.72667i	−0.513942	+	0.565030i
$188$		0			0
$189$	12.4257	+	0.470543i	0.903836	+	0.0342270i
$190$		0			0
$191$	−5.78822	−	12.4470i	−0.418821	−	0.900636i	−0.996438	−	0.0843280i	$-0.973126\pi$
$191$	−5.78822	−	12.4470i	−0.418821	−	0.900636i	0.577617	−	0.816308i	$-0.303983\pi$
$192$		0			0
$193$	5.91490	−	0.902434i	0.425764	−	0.0649587i	0.0655964	−	0.997846i	$-0.479105\pi$
$193$	5.91490	−	0.902434i	0.425764	−	0.0649587i	0.360168	+	0.932888i	$0.382719\pi$
$194$		0			0
$195$	15.1910	+	14.3521i	1.08785	+	1.02778i
$196$		0			0
$197$	−16.4283	+	5.82339i	−1.17047	+	0.414899i	−0.847130	−	0.531385i	$-0.821672\pi$
$197$	−16.4283	+	5.82339i	−1.17047	+	0.414899i	−0.323335	+	0.946284i	$0.604804\pi$
$198$		0			0
$199$	0.423647	−	22.3826i	0.0300315	−	1.58666i	−0.593482	−	0.804848i	$-0.702247\pi$
$199$	0.423647	−	22.3826i	0.0300315	−	1.58666i	0.623513	−	0.781813i	$-0.285705\pi$
$200$		0			0
$201$	3.74964	+	6.13187i	0.264479	+	0.432508i
$202$		0			0
$203$	−0.956785	+	16.8339i	−0.0671531	+	1.18151i
$204$		0			0
$205$	−10.7470	+	0.406975i	−0.750606	+	0.0284244i
$206$		0			0
$207$	−3.87163	−	0.441528i	−0.269097	−	0.0306883i
$208$		0			0
$209$	1.08698	+	3.26118i	0.0751882	+	0.225580i
$210$		0			0
$211$	−3.68072	−	5.53690i	−0.253391	−	0.381176i	0.683984	−	0.729497i	$-0.260246\pi$
$211$	−3.68072	−	5.53690i	−0.253391	−	0.381176i	−0.937375	+	0.348321i	$0.886752\pi$
$212$		0			0
$213$	−4.76836	−	18.9887i	−0.326722	−	1.30108i
$214$		0			0
$215$	3.97251	−	7.08556i	0.270923	−	0.483231i
$216$		0			0
$217$	−1.37069	+	6.48885i	−0.0930487	+	0.440492i
$218$		0			0
$219$	1.63364	+	1.66486i	0.110391	+	0.112501i
$220$		0			0
$221$	15.5603	−	25.4461i	1.04670	−	1.71169i
$222$		0			0
$223$	−2.88819	+	21.6738i	−0.193408	+	1.45139i	0.578516	+	0.815671i	$0.303632\pi$
$223$	−2.88819	+	21.6738i	−0.193408	+	1.45139i	−0.771924	+	0.635715i	$0.780706\pi$
$224$		0			0
$225$	2.08968	+	1.33281i	0.139312	+	0.0888543i
$226$		0			0
$227$	11.2033	+	7.75720i	0.743591	+	0.514864i	0.879524	−	0.475854i	$-0.157861\pi$
$227$	11.2033	+	7.75720i	0.743591	+	0.514864i	−0.135933	+	0.990718i	$0.543403\pi$
$228$		0			0
$229$	−9.36684	−	8.20144i	−0.618978	−	0.541967i	0.290947	−	0.956739i	$-0.406030\pi$
$229$	−9.36684	−	8.20144i	−0.618978	−	0.541967i	−0.909925	+	0.414773i	$0.863861\pi$
$230$		0			0
$231$	−4.78102	+	3.31038i	−0.314568	+	0.217807i
$232$		0			0
$233$	0.567776	+	5.98227i	0.0371962	+	0.391912i	0.994648	+	0.103319i	$0.0329463\pi$
$233$	0.567776	+	5.98227i	0.0371962	+	0.391912i	−0.957452	+	0.288593i	$0.906813\pi$
$234$		0			0
$235$	−7.97132	+	18.9898i	−0.519992	+	1.23876i
$236$		0			0
$237$	−15.7207	−	3.63289i	−1.02117	−	0.235981i
$238$		0			0
$239$	8.29259	−	5.28909i	0.536403	−	0.342123i	−0.241608	−	0.970374i	$-0.577675\pi$
$239$	8.29259	−	5.28909i	0.536403	−	0.342123i	0.778011	+	0.628251i	$0.216229\pi$
$240$		0			0
$241$	−7.53353	−	20.0401i	−0.485277	−	1.29089i	−0.920560	−	0.390601i	$-0.872267\pi$
$241$	−7.53353	−	20.0401i	−0.485277	−	1.29089i	0.435283	−	0.900294i	$-0.356648\pi$
$242$		0			0
$243$	5.71411	+	7.32643i	0.366561	+	0.469990i
$244$		0			0
$245$	1.67740	+	5.74926i	0.107165	+	0.367307i
$246$		0			0
$247$	−4.80055	−	8.56250i	−0.305452	−	0.544819i
$248$		0			0
$249$	15.0666	+	8.07621i	0.954808	+	0.511809i
$250$		0			0
$251$	3.65828	−	5.07548i	0.230909	−	0.320361i	−0.679810	−	0.733388i	$-0.737938\pi$
$251$	3.65828	−	5.07548i	0.230909	−	0.320361i	0.910719	+	0.413026i	$0.135528\pi$
$252$		0			0
$253$	6.63357	−	3.88590i	0.417049	−	0.244304i
$254$		0			0
$255$	−7.95435	+	21.1595i	−0.498121	+	1.32506i
$256$		0			0
$257$	12.3000	+	24.0276i	0.767252	+	1.49880i	0.864001	+	0.503490i	$0.167951\pi$
$257$	12.3000	+	24.0276i	0.767252	+	1.49880i	−0.0967486	+	0.995309i	$0.530844\pi$
$258$		0			0
$259$	−6.54542	+	7.76730i	−0.406713	+	0.482636i
$260$		0			0
$261$	−5.71728	+	4.28758i	−0.353891	+	0.265395i
$262$		0			0
$263$	−12.6877	+	1.44693i	−0.782355	+	0.0892214i	−0.495333	−	0.868703i	$-0.664954\pi$
$263$	−12.6877	+	1.44693i	−0.782355	+	0.0892214i	−0.287021	+	0.957924i	$0.592665\pi$
$264$		0			0
$265$	−8.76246	+	34.8941i	−0.538274	+	2.14353i
$266$		0			0
$267$	10.7449	−	4.75150i	0.657579	−	0.290787i
$268$		0			0
$269$	−3.15659	+	2.55946i	−0.192461	+	0.156053i	−0.721189	−	0.692738i	$-0.756404\pi$
$269$	−3.15659	+	2.55946i	−0.192461	+	0.156053i	0.528728	+	0.848791i	$0.322669\pi$
$270$		0			0
$271$	2.85643	−	16.6077i	0.173516	−	1.00885i	−0.759897	−	0.650044i	$-0.774751\pi$
$271$	2.85643	−	16.6077i	0.173516	−	1.00885i	0.933413	−	0.358805i	$-0.116816\pi$
$272$		0			0
$273$	11.6307	−	11.8529i	0.703919	−	0.717369i
$274$		0			0
$275$	−4.87596	+	0.369822i	−0.294032	+	0.0223011i
$276$		0			0
$277$	−3.77417	−	1.84275i	−0.226768	−	0.110720i	0.321859	−	0.946788i	$-0.395692\pi$
$277$	−3.77417	−	1.84275i	−0.226768	−	0.110720i	−0.548626	+	0.836068i	$0.684849\pi$
$278$		0			0
$279$	−2.47744	+	1.32799i	−0.148320	+	0.0795046i
$280$		0			0
$281$	3.26241	+	18.9682i	0.194619	+	1.13155i	0.904259	+	0.426983i	$0.140424\pi$
$281$	3.26241	+	18.9682i	0.194619	+	1.13155i	−0.709640	+	0.704564i	$0.751143\pi$
$282$		0			0
$283$	0.0958791	+	1.68692i	0.00569942	+	0.100277i	0.999979	−	0.00653526i	$-0.00208025\pi$
$283$	0.0958791	+	1.68692i	0.00569942	+	0.100277i	−0.994279	+	0.106812i	$0.965936\pi$
$284$		0			0
$285$	4.79414	+	5.68909i	0.283980	+	0.336993i
$286$		0			0
$287$	0.161721	+	8.54423i	0.00954610	+	0.504350i
$288$		0			0
$289$	15.0878	+	2.30194i	0.887517	+	0.135408i
$290$		0			0
$291$	1.74847	−	18.4225i	0.102497	−	1.07994i
$292$		0			0
$293$	21.3428	−	10.4207i	1.24686	−	0.608784i	0.307446	−	0.951566i	$-0.400526\pi$
$293$	21.3428	−	10.4207i	1.24686	−	0.608784i	0.939415	+	0.342782i	$0.111369\pi$
$294$		0			0
$295$	−12.1936	−	4.32229i	−0.709936	−	0.251654i
$296$		0			0
$297$	−10.0350	−	2.72283i	−0.582290	−	0.157994i
$298$		0			0
$299$	−16.5172	+	14.4622i	−0.955216	+	0.836371i
$300$		0			0
$301$	−5.56947	−	3.26255i	−0.321019	−	0.188051i
$302$		0			0
$303$	−3.95906	+	0.914899i	−0.227442	+	0.0525596i
$304$		0			0
$305$	27.9025	−	11.0963i	1.59769	−	0.635371i
$306$		0			0
$307$	−7.37046	−	17.5584i	−0.420654	−	1.00211i	−0.984365	−	0.176140i	$-0.943639\pi$
$307$	−7.37046	−	17.5584i	−0.420654	−	1.00211i	0.563711	−	0.825972i	$-0.309373\pi$
$308$		0			0
$309$	−5.73747	−	6.30780i	−0.326394	−	0.358838i
$310$		0			0
$311$	17.0840	+	6.79396i	0.968744	+	0.385250i	0.799728	−	0.600363i	$-0.204977\pi$
$311$	17.0840	+	6.79396i	0.968744	+	0.385250i	0.169016	+	0.985613i	$0.445941\pi$
$312$		0			0
$313$	−24.1077	−	7.53151i	−1.36265	−	0.425706i	−0.472480	−	0.881342i	$-0.656641\pi$
$313$	−24.1077	−	7.53151i	−1.36265	−	0.425706i	−0.890167	+	0.455635i	$0.849412\pi$
$314$		0			0
$315$	3.14033	−	4.72399i	0.176938	−	0.266167i
$316$		0			0
$317$	2.80539	+	0.212778i	0.157567	+	0.0119508i	0.154176	−	0.988043i	$-0.450728\pi$
$317$	2.80539	+	0.212778i	0.157567	+	0.0119508i	0.00339097	+	0.999994i	$0.498921\pi$
$318$		0			0
$319$	3.94894	−	13.5350i	0.221098	−	0.757812i
$320$		0			0
$321$	1.45699	−	2.84618i	0.0813215	−	0.158859i
$322$		0			0
$323$	6.53008	−	8.37262i	0.363343	−	0.465865i
$324$		0			0
$325$	13.4767	−	3.65666i	0.747550	−	0.202835i
$326$		0			0
$327$	1.15196	−	2.47718i	0.0637034	−	0.136988i
$328$		0			0
$329$	14.9668	+	6.61846i	0.825149	+	0.364888i
$330$		0			0
$331$	−0.909861	−	6.82785i	−0.0500105	−	0.375293i	−0.998320	−	0.0579451i	$-0.981545\pi$
$331$	−0.909861	−	6.82785i	−0.0500105	−	0.375293i	0.948309	−	0.317348i	$-0.102792\pi$
$332$		0			0
$333$	−4.30512			−0.235919
$334$		0			0
$335$	13.8324			0.755746
$336$		0			0
$337$	2.11332	+	15.8589i	0.115120	+	0.863890i	0.949735	+	0.313056i	$0.101353\pi$
$337$	2.11332	+	15.8589i	0.115120	+	0.863890i	−0.834615	+	0.550834i	$0.814310\pi$
$338$		0			0
$339$	6.27324	+	2.77408i	0.340715	+	0.150667i
$340$		0			0
$341$	2.33844	−	5.02860i	0.126634	−	0.272314i
$342$		0			0
$343$	19.4492	−	5.27722i	1.05016	−	0.284943i
$344$		0			0
$345$	10.2327	−	13.1200i	0.550911	−	0.706357i
$346$		0			0
$347$	−7.45837	+	14.5696i	−0.400386	+	0.782139i	−0.999833	−	0.0182754i	$-0.994182\pi$
$347$	−7.45837	+	14.5696i	−0.400386	+	0.782139i	0.599447	+	0.800415i	$0.295387\pi$
$348$		0			0
$349$	−9.09744	+	31.1814i	−0.486975	+	1.66910i	0.230938	+	0.972968i	$0.425820\pi$
$349$	−9.09744	+	31.1814i	−0.486975	+	1.66910i	−0.717913	+	0.696133i	$0.754902\pi$
$350$		0			0
$351$	29.6074	+	2.24560i	1.58032	+	0.119861i
$352$		0			0
$353$	13.4630	−	20.2524i	0.716564	−	1.07793i	−0.276576	−	0.960992i	$-0.589200\pi$
$353$	13.4630	−	20.2524i	0.716564	−	1.07793i	0.993140	−	0.116933i	$-0.0373064\pi$
$354$		0			0
$355$	−35.9645	−	11.2357i	−1.90880	−	0.596330i
$356$		0			0
$357$	16.6908	+	6.63761i	0.883371	+	0.351299i
$358$		0			0
$359$	4.63201	+	5.09244i	0.244468	+	0.268769i	0.849684	−	0.527292i	$-0.176793\pi$
$359$	4.63201	+	5.09244i	0.244468	+	0.268769i	−0.605216	+	0.796061i	$0.706913\pi$
$360$		0			0
$361$	6.00139	+	14.2969i	0.315862	+	0.752470i
$362$		0			0
$363$	−10.1802	+	4.04847i	−0.534322	+	0.212489i
$364$		0			0
$365$	4.37368	−	1.01071i	0.228929	−	0.0529031i
$366$		0			0
$367$	12.2457	+	7.17345i	0.639221	+	0.374451i	0.789110	−	0.614252i	$-0.210542\pi$
$367$	12.2457	+	7.17345i	0.639221	+	0.374451i	−0.149889	+	0.988703i	$0.547891\pi$
$368$		0			0
$369$	−2.72507	+	2.38602i	−0.141861	+	0.124211i
$370$		0			0
$371$	27.5903	+	7.48615i	1.43242	+	0.388661i
$372$		0			0
$373$	−20.0442	−	7.10514i	−1.03785	−	0.367890i	−0.240017	−	0.970769i	$-0.577153\pi$
$373$	−20.0442	−	7.10514i	−1.03785	−	0.367890i	−0.797833	+	0.602878i	$0.794020\pi$
$374$		0			0
$375$	8.37135	−	4.08734i	0.432295	−	0.211069i
$376$		0			0
$377$	−3.80418	+	40.0821i	−0.195925	+	2.06433i
$378$		0			0
$379$	23.0136	+	3.51117i	1.18213	+	0.180357i	0.711960	−	0.702220i	$-0.247808\pi$
$379$	23.0136	+	3.51117i	1.18213	+	0.180357i	0.470168	+	0.882577i	$0.344193\pi$
$380$		0			0
$381$	−0.538929	−	28.4733i	−0.0276102	−	1.45873i
$382$		0			0
$383$	2.15487	+	2.55713i	0.110109	+	0.130663i	0.816950	−	0.576709i	$-0.195663\pi$
$383$	2.15487	+	2.55713i	0.110109	+	0.130663i	−0.706841	+	0.707373i	$0.749880\pi$
$384$		0			0
$385$	0.635065	+	11.1735i	0.0323659	+	0.569453i
$386$		0			0
$387$	−0.463725	−	2.69617i	−0.0235724	−	0.137054i
$388$		0			0
$389$	11.5805	−	6.20754i	0.587156	−	0.314735i	−0.151882	−	0.988399i	$-0.548533\pi$
$389$	11.5805	−	6.20754i	0.587156	−	0.314735i	0.739038	+	0.673664i	$0.235280\pi$
$390$		0			0
$391$	−21.3390	−	10.4189i	−1.07916	−	0.526904i
$392$		0			0
$393$	22.4630	−	1.70373i	1.13311	−	0.0859418i
$394$		0			0
$395$	−21.7484	+	22.1640i	−1.09428	+	1.11519i
$396$		0			0
$397$	−6.52092	+	37.9137i	−0.327276	+	1.90283i	0.0934089	+	0.995628i	$0.470224\pi$
$397$	−6.52092	+	37.9137i	−0.327276	+	1.90283i	−0.420685	+	0.907207i	$0.638210\pi$
$398$		0			0
$399$	4.59186	−	3.72321i	0.229880	−	0.186394i
$400$		0			0
$401$	13.6146	−	6.02049i	0.679880	−	0.300649i	−0.0355146	−	0.999369i	$-0.511307\pi$
$401$	13.6146	−	6.02049i	0.679880	−	0.300649i	0.715395	+	0.698720i	$0.246247\pi$
$402$		0			0
$403$	−3.85705	+	15.3597i	−0.192133	+	0.765120i
$404$		0			0
$405$	−14.6699	+	1.67299i	−0.728954	+	0.0831314i
$406$		0			0
$407$	6.79516	−	5.09592i	0.336823	−	0.252595i
$408$		0			0
$409$	13.5342	−	16.0607i	0.669221	−	0.794149i	−0.318907	−	0.947786i	$-0.603316\pi$
$409$	13.5342	−	16.0607i	0.669221	−	0.794149i	0.988127	+	0.153637i	$0.0490988\pi$
$410$		0			0
$411$	−1.53228	−	2.99325i	−0.0755818	−	0.147646i
$412$		0			0
$413$	−3.61725	+	9.62232i	−0.177993	+	0.473483i
$414$		0			0
$415$	28.3871	−	16.6290i	1.39347	−	0.816283i
$416$		0			0
$417$	−13.2808	+	18.4257i	−0.650365	+	0.902313i
$418$		0			0
$419$	24.5664	+	13.1684i	1.20015	+	0.643317i	0.946100	−	0.323875i	$-0.104986\pi$
$419$	24.5664	+	13.1684i	1.20015	+	0.643317i	0.254045	+	0.967192i	$0.418239\pi$
$420$		0			0
$421$	−11.9144	−	21.2511i	−0.580673	−	1.03572i	−0.992240	−	0.124337i	$-0.960320\pi$
$421$	−11.9144	−	21.2511i	−0.580673	−	1.03572i	0.411567	−	0.911379i	$-0.364982\pi$
$422$		0			0
$423$	1.94267	+	6.65848i	0.0944558	+	0.323746i
$424$		0			0
$425$	9.28910	+	11.9101i	0.450588	+	0.577727i
$426$		0			0
$427$	−8.39599	−	22.3343i	−0.406311	−	1.08083i
$428$		0			0
$429$	−11.7075	+	7.46714i	−0.565242	+	0.360517i
$430$		0			0
$431$	8.00984	+	1.85099i	0.385820	+	0.0891591i	0.413609	−	0.910455i	$-0.364268\pi$
$431$	8.00984	+	1.85099i	0.385820	+	0.0891591i	−0.0277884	+	0.999614i	$0.508846\pi$
$432$		0			0
$433$	−9.39191	+	22.3741i	−0.451346	+	1.07523i	0.523435	+	0.852066i	$0.324650\pi$
$433$	−9.39191	+	22.3741i	−0.451346	+	1.07523i	−0.974781	+	0.223163i	$0.928362\pi$
$434$		0			0
$435$	−2.88314	−	30.3777i	−0.138236	−	1.45650i
$436$		0			0
$437$	−6.42549	+	4.44902i	−0.307373	+	0.212825i
$438$		0			0
$439$	21.0442	+	18.4259i	1.00438	+	0.879420i	0.992712	−	0.120512i	$-0.0384537\pi$
$439$	21.0442	+	18.4259i	1.00438	+	0.879420i	0.0116707	+	0.999932i	$0.496285\pi$
$440$		0			0
$441$	1.65828	+	1.14820i	0.0789657	+	0.0546760i
$442$		0			0
$443$	−27.1480	−	17.3153i	−1.28984	−	0.822674i	−0.298556	−	0.954392i	$-0.596505\pi$
$443$	−27.1480	−	17.3153i	−1.28984	−	0.822674i	−0.991287	+	0.131718i	$0.957951\pi$
$444$		0			0
$445$	2.98661	−	22.4124i	0.141579	−	1.06245i
$446$		0			0
$447$	−2.45896	+	4.02120i	−0.116305	+	0.190196i
$448$		0			0
$449$	−5.74751	−	5.85732i	−0.271242	−	0.276424i	0.564636	−	0.825340i	$-0.309017\pi$
$449$	−5.74751	−	5.85732i	−0.271242	−	0.276424i	−0.835878	+	0.548916i	$0.815041\pi$
$450$		0			0
$451$	1.47692	−	6.99171i	0.0695452	−	0.329227i
$452$		0			0
$453$	5.24392	−	9.35331i	0.246381	−	0.439457i
$454$		0			0
$455$	−7.78369	−	30.9964i	−0.364905	−	1.45314i
$456$		0			0
$457$	20.2463	+	30.4564i	0.947080	+	1.42469i	0.904921	+	0.425580i	$0.139930\pi$
$457$	20.2463	+	30.4564i	0.947080	+	1.42469i	0.0421594	+	0.999111i	$0.486576\pi$
$458$		0			0
$459$	10.1557	+	30.4692i	0.474027	+	1.42218i
$460$		0			0
$461$	−11.8671	−	1.35335i	−0.552707	−	0.0630319i	−0.167517	−	0.985869i	$-0.553575\pi$
$461$	−11.8671	−	1.35335i	−0.552707	−	0.0630319i	−0.385190	+	0.922837i	$0.625864\pi$
$462$		0			0
$463$	−5.22490	+	0.197860i	−0.242822	+	0.00919532i	−0.158972	−	0.987283i	$-0.550818\pi$
$463$	−5.22490	+	0.197860i	−0.242822	+	0.00919532i	−0.0838497	+	0.996478i	$0.526722\pi$
$464$		0			0
$465$	0.681075	−	11.9830i	0.0315841	−	0.555698i
$466$		0			0
$467$	4.25201	+	6.95342i	0.196760	+	0.321766i	0.936207	−	0.351448i	$-0.114311\pi$
$467$	4.25201	+	6.95342i	0.196760	+	0.321766i	−0.739447	+	0.673214i	$0.764913\pi$
$468$		0			0
$469$	0.208001	−	10.9893i	0.00960458	−	0.507440i
$470$		0			0
$471$	18.2072	−	6.45396i	0.838942	−	0.297383i
$472$		0			0
$473$	3.92336	+	3.70670i	0.180396	+	0.170434i
$474$		0			0
$475$	4.91418	−	0.749754i	0.225478	−	0.0344011i
$476$		0			0
$477$	5.10917	+	10.9868i	0.233933	+	0.503051i
$478$		0			0
$479$	−18.3128	−	0.693482i	−0.836735	−	0.0316860i	−0.384002	−	0.923332i	$-0.625454\pi$
$479$	−18.3128	−	0.693482i	−0.836735	−	0.0316860i	−0.452733	+	0.891646i	$0.649551\pi$
$480$		0			0
$481$	−16.3204	+	17.9427i	−0.744145	+	0.818116i
$482$		0			0
$483$	−10.2695	−	8.32678i	−0.467277	−	0.378882i
$484$		0			0
$485$	−28.4919	−	21.3671i	−1.29375	−	0.970228i
$486$		0			0
$487$	−13.0337	+	2.49654i	−0.590613	+	0.113129i	−0.474726	−	0.880134i	$-0.657453\pi$
$487$	−13.0337	+	2.49654i	−0.590613	+	0.113129i	−0.115887	+	0.993262i	$0.536971\pi$
$488$		0			0
$489$	−6.81855	−	1.30606i	−0.308345	−	0.0590620i
$490$		0			0
$491$	−8.38280	−	39.6841i	−0.378311	−	1.79092i	−0.583410	−	0.812178i	$-0.698282\pi$
$491$	−8.38280	−	39.6841i	−0.378311	−	1.79092i	0.205099	−	0.978741i	$-0.434248\pi$
$492$		0			0
$493$	−41.5688	+	12.9866i	−1.87217	+	0.584886i
$494$		0			0
$495$	−3.44794	+	3.25754i	−0.154973	+	0.146415i
$496$		0			0
$497$	−9.46716	+	28.4035i	−0.424660	+	1.27407i
$498$		0			0
$499$	12.3356	+	17.1144i	0.552219	+	0.766146i	0.991203	−	0.132349i	$-0.0422518\pi$
$499$	12.3356	+	17.1144i	0.552219	+	0.766146i	−0.438984	+	0.898495i	$0.644661\pi$
$500$		0			0
$501$	−18.3780	+	2.75575i	−0.821070	+	0.123118i
$502$		0			0
$503$	−12.9076	−	17.9079i	−0.575519	−	0.798473i	0.418437	−	0.908246i	$-0.362578\pi$
$503$	−12.9076	−	17.9079i	−0.575519	−	0.798473i	−0.993957	+	0.109773i	$0.964988\pi$
$504$		0			0
$505$	−2.47278	+	7.41885i	−0.110037	+	0.330135i
$506$		0			0
$507$	15.2350	−	14.3937i	0.676609	−	0.639245i
$508$		0			0
$509$	−40.2782	+	12.5834i	−1.78530	+	0.557748i	−0.998250	−	0.0591414i	$-0.981164\pi$
$509$	−40.2782	+	12.5834i	−1.78530	+	0.557748i	−0.787050	+	0.616889i	$0.788393\pi$
$510$		0			0
$511$	−0.737204	−	3.48992i	−0.0326120	−	0.154385i
$512$		0			0
$513$	10.3815	+	1.98853i	0.458355	+	0.0877956i
$514$		0			0
$515$	−16.1171	+	3.08714i	−0.710203	+	0.136036i
$516$		0			0
$517$	−10.9479	−	8.21017i	−0.481486	−	0.361083i
$518$		0			0
$519$	10.3973	+	8.43040i	0.456389	+	0.370054i
$520$		0			0
$521$	−19.0304	+	20.9221i	−0.833736	+	0.916612i	−0.997556	−	0.0698784i	$-0.977739\pi$
$521$	−19.0304	+	20.9221i	−0.833736	+	0.916612i	0.163820	+	0.986490i	$0.447618\pi$
$522$		0			0
$523$	17.4862	+	0.662178i	0.764618	+	0.0289550i	0.417272	−	0.908782i	$-0.362986\pi$
$523$	17.4862	+	0.662178i	0.764618	+	0.0289550i	0.347347	+	0.937737i	$0.387083\pi$
$524$		0			0
$525$	3.54594	+	7.62521i	0.154757	+	0.332791i
$526$		0			0
$527$	−16.9339	+	2.58359i	−0.737650	+	0.112543i
$528$		0			0
$529$	−4.01332	−	3.79169i	−0.174492	−	0.164856i
$530$		0			0
$531$	−4.10660	+	1.45568i	−0.178211	+	0.0631711i
$532$		0			0
$533$	−0.386172	+	20.4027i	−0.0167270	+	0.883737i
$534$		0			0
$535$	−3.21025	−	5.24979i	−0.138791	−	0.226968i
$536$		0			0
$537$	−1.49034	+	26.2214i	−0.0643129	+	1.13153i
$538$		0			0
$539$	−3.97652	+	0.150585i	−0.171281	+	0.00648616i
$540$		0			0
$541$	12.9047	+	1.47168i	0.554818	+	0.0632727i	0.386211	−	0.922411i	$-0.373784\pi$
$541$	12.9047	+	1.47168i	0.554818	+	0.0632727i	0.168608	+	0.985683i	$0.446073\pi$
$542$		0			0
$543$	7.45663	+	22.3715i	0.319995	+	0.960052i
$544$		0			0
$545$	−2.91065	−	4.37848i	−0.124678	−	0.187553i
$546$		0			0
$547$	−5.02925	−	20.0276i	−0.215035	−	0.856320i	−0.977782	−	0.209623i	$-0.932776\pi$
$547$	−5.02925	−	20.0276i	−0.215035	−	0.856320i	0.762747	−	0.646697i	$-0.223850\pi$
$548$		0			0
$549$	4.94557	−	8.82116i	0.211072	−	0.376478i
$550$		0			0
$551$	−2.96231	+	14.0236i	−0.126199	+	0.597424i
$552$		0			0
$553$	17.2814	+	17.6116i	0.734879	+	0.748920i
$554$		0			0
$555$	9.58994	−	15.6827i	0.407070	−	0.665692i
$556$		0			0
$557$	4.70442	−	35.3033i	0.199332	−	1.49585i	−0.550843	−	0.834609i	$-0.685694\pi$
$557$	4.70442	−	35.3033i	0.199332	−	1.49585i	0.750176	−	0.661238i	$-0.229969\pi$
$558$		0			0
$559$	−12.9949	−	8.28829i	−0.549627	−	0.350557i
$560$		0			0
$561$	−12.3488	−	8.55035i	−0.521368	−	0.360996i
$562$		0			0
$563$	−6.92798	−	6.06602i	−0.291980	−	0.255652i	0.500242	−	0.865886i	$-0.333244\pi$
$563$	−6.92798	−	6.06602i	−0.291980	−	0.255652i	−0.792222	+	0.610233i	$0.791076\pi$
$564$		0			0
$565$	10.8531	−	7.51468i	0.456592	−	0.316145i
$566$		0			0
$567$	1.10853	+	11.6798i	0.0465539	+	0.490507i
$568$		0			0
$569$	0.521139	−	1.24149i	0.0218473	−	0.0520462i	−0.910768	−	0.412919i	$-0.864509\pi$
$569$	0.521139	−	1.24149i	0.0218473	−	0.0520462i	0.932615	+	0.360873i	$0.117521\pi$
$570$		0			0
$571$	18.5298	+	4.28204i	0.775448	+	0.179198i	0.594284	−	0.804255i	$-0.297435\pi$
$571$	18.5298	+	4.28204i	0.775448	+	0.179198i	0.181163	+	0.983453i	$0.442014\pi$
$572$		0			0
$573$	16.6430	−	10.6150i	0.695269	−	0.443449i
$574$		0			0
$575$	−3.91204	−	10.4065i	−0.163143	−	0.433980i
$576$		0			0
$577$	−7.08573	−	9.08506i	−0.294983	−	0.378216i	0.618025	−	0.786159i	$-0.287933\pi$
$577$	−7.08573	−	9.08506i	−0.294983	−	0.378216i	−0.913008	+	0.407942i	$0.866246\pi$
$578$		0			0
$579$	2.40989	+	8.25988i	0.100152	+	0.343269i
$580$		0			0
$581$	−12.7842	−	22.8025i	−0.530378	−	0.946008i
$582$		0			0
$583$	−21.0692	−	11.2938i	−0.872598	−	0.467741i
$584$		0			0
$585$	7.92025	−	10.9885i	0.327462	−	0.454319i
$586$		0			0
$587$	8.10822	−	4.74973i	0.334662	−	0.196042i	−0.328527	−	0.944495i	$-0.606552\pi$
$587$	8.10822	−	4.74973i	0.334662	−	0.196042i	0.663189	+	0.748452i	$0.269203\pi$
$588$		0			0
$589$	−1.98379	+	5.27712i	−0.0817408	+	0.217440i
$590$		0			0
$591$	−11.4214	−	22.3112i	−0.469813	−	0.917762i
$592$		0			0
$593$	−25.5202	+	30.2842i	−1.04799	+	1.24362i	−0.0789064	+	0.996882i	$0.525143\pi$
$593$	−25.5202	+	30.2842i	−1.04799	+	1.24362i	−0.969081	+	0.246741i	$0.920640\pi$
$594$		0			0
$595$	27.6558	−	20.7400i	1.13378	−	0.850258i
$596$		0			0
$597$	31.9854	−	3.64768i	1.30907	−	0.149290i
$598$		0			0
$599$	6.09844	−	24.2854i	0.249176	−	0.992275i	−0.708796	−	0.705413i	$-0.750761\pi$
$599$	6.09844	−	24.2854i	0.249176	−	0.992275i	0.957972	−	0.286862i	$-0.0926120\pi$
$600$		0			0
$601$	−22.5806	+	9.98535i	−0.921083	+	0.407311i	−0.809953	−	0.586495i	$-0.800507\pi$
$601$	−22.5806	+	9.98535i	−0.921083	+	0.407311i	−0.111130	+	0.993806i	$0.535447\pi$
$602$		0			0
$603$	3.61852	−	2.93400i	0.147357	−	0.119482i
$604$		0			0
$605$	−3.57391	+	20.7793i	−0.145300	+	0.844799i
$606$		0			0
$607$	11.2711	−	11.4865i	0.457481	−	0.466222i	−0.445886	−	0.895090i	$-0.647111\pi$
$607$	11.2711	−	11.4865i	0.457481	−	0.466222i	0.903367	+	0.428868i	$0.141087\pi$
$608$		0			0
$609$	−24.1773	+	1.83375i	−0.979714	+	0.0743074i
$610$		0			0
$611$	35.1155	+	17.1452i	1.42062	+	0.693622i
$612$		0			0
$613$	−12.2471	+	6.56483i	−0.494655	+	0.265151i	−0.700784	−	0.713374i	$-0.747166\pi$
$613$	−12.2471	+	6.56483i	−0.494655	+	0.265151i	0.206129	+	0.978525i	$0.433913\pi$
$614$		0			0
$615$	−2.62151	−	15.2419i	−0.105709	−	0.614612i
$616$		0			0
$617$	−2.03403	−	35.7872i	−0.0818869	−	1.44074i	−0.732210	−	0.681079i	$-0.761511\pi$
$617$	−2.03403	−	35.7872i	−0.0818869	−	1.44074i	0.650323	−	0.759658i	$-0.274633\pi$
$618$		0			0
$619$	−27.0340	−	32.0807i	−1.08659	−	1.28943i	−0.954506	−	0.298193i	$-0.903616\pi$
$619$	−27.0340	−	32.0807i	−1.08659	−	1.28943i	−0.132084	−	0.991239i	$-0.542167\pi$
$620$		0			0
$621$	−0.447364	−	23.6356i	−0.0179521	−	0.948465i
$622$		0			0
$623$	−17.7609	−	2.70977i	−0.711574	−	0.108565i
$624$		0			0
$625$	2.95027	−	31.0850i	0.118011	−	1.24340i
$626$		0			0
$627$	−4.44212	+	2.16888i	−0.177401	+	0.0866167i
$628$		0			0
$629$	−24.7279	−	8.76539i	−0.985967	−	0.349499i
$630$		0			0
$631$	−2.82771	−	0.767250i	−0.112569	−	0.0305438i	0.205134	−	0.978734i	$-0.434237\pi$
$631$	−2.82771	−	0.767250i	−0.112569	−	0.0305438i	−0.317703	+	0.948190i	$0.602912\pi$
$632$		0			0
$633$	7.19332	−	6.29835i	0.285909	−	0.250337i
$634$		0			0
$635$	−47.2907	−	27.7025i	−1.87667	−	1.09934i
$636$		0			0
$637$	11.0718	−	2.55858i	0.438681	−	0.101375i
$638$		0			0
$639$	−11.7914	+	4.68921i	−0.466461	+	0.185502i
$640$		0			0
$641$	2.59582	+	6.18395i	0.102529	+	0.244251i	0.965200	−	0.261515i	$-0.0842220\pi$
$641$	2.59582	+	6.18395i	0.102529	+	0.244251i	−0.862671	+	0.505766i	$0.831210\pi$
$642$		0			0
$643$	2.59402	+	2.85188i	0.102298	+	0.112467i	0.788767	−	0.614692i	$-0.210720\pi$
$643$	2.59402	+	2.85188i	0.102298	+	0.112467i	−0.686469	+	0.727159i	$0.740840\pi$
$644$		0			0
$645$	10.8546	+	4.31665i	0.427398	+	0.169968i
$646$		0			0
$647$	22.4266	+	7.00631i	0.881679	+	0.275447i	0.705328	−	0.708881i	$-0.250800\pi$
$647$	22.4266	+	7.00631i	0.881679	+	0.275447i	0.176351	+	0.984327i	$0.443571\pi$
$648$		0			0
$649$	4.75874	−	7.15856i	0.186797	−	0.280998i
$650$		0			0
$651$	−9.50978	−	0.721278i	−0.372718	−	0.0282691i
$652$		0			0
$653$	−3.73956	+	12.8173i	−0.146340	+	0.501580i	−0.999809	−	0.0195647i	$-0.993772\pi$
$653$	−3.73956	+	12.8173i	−0.146340	+	0.501580i	0.853468	+	0.521145i	$0.174495\pi$
$654$		0			0
$655$	19.7557	−	38.5921i	0.771920	−	1.50792i
$656$		0			0
$657$	0.929757	−	1.19210i	0.0362733	−	0.0465083i
$658$		0			0
$659$	13.6397	−	3.70089i	0.531326	−	0.144166i	0.0139150	−	0.999903i	$-0.495571\pi$
$659$	13.6397	−	3.70089i	0.531326	−	0.144166i	0.517411	+	0.855737i	$0.326896\pi$
$660$		0			0
$661$	12.3227	−	26.4989i	0.479299	−	1.03069i	−0.506420	−	0.862287i	$-0.669031\pi$
$661$	12.3227	−	26.4989i	0.479299	−	1.03069i	0.985719	−	0.168401i	$-0.0538602\pi$
$662$		0			0
$663$	39.2274	+	17.3467i	1.52347	+	0.673690i
$664$		0			0
$665$	−1.50279	−	11.2774i	−0.0582758	−	0.437318i
$666$		0			0
$667$	32.0551			1.24118
$668$		0			0
$669$	−31.4432			−1.21566
$670$		0			0
$671$	2.63546	+	19.7772i	0.101741	+	0.763492i
$672$		0			0
$673$	−13.9056	−	6.14919i	−0.536023	−	0.237034i	0.118663	−	0.992935i	$-0.462139\pi$
$673$	−13.9056	−	6.14919i	−0.536023	−	0.237034i	−0.654686	+	0.755901i	$0.727199\pi$
$674$		0			0
$675$	−6.34028	+	13.6342i	−0.244037	+	0.524780i
$676$		0			0
$677$	27.8484	−	7.55619i	1.07030	−	0.290408i	0.317232	−	0.948348i	$-0.397247\pi$
$677$	27.8484	−	7.55619i	1.07030	−	0.290408i	0.753070	+	0.657940i	$0.228572\pi$
$678$		0			0
$679$	−17.4038	+	22.3144i	−0.667895	+	0.856350i
$680$		0			0
$681$	−8.92931	+	17.4431i	−0.342172	+	0.668420i
$682$		0			0
$683$	−6.17314	+	21.1584i	−0.236209	+	0.809603i	0.752350	+	0.658764i	$0.228920\pi$
$683$	−6.17314	+	21.1584i	−0.236209	+	0.809603i	−0.988558	+	0.150839i	$0.951802\pi$
$684$		0			0
$685$	−6.45297	−	0.489431i	−0.246555	−	0.0187002i
$686$		0			0
$687$	9.91138	−	14.9097i	0.378143	−	0.568839i
$688$		0			0
$689$	65.1588	+	20.3564i	2.48235	+	0.775515i
$690$		0			0
$691$	12.7126	+	5.05554i	0.483609	+	0.192322i	0.598605	−	0.801044i	$-0.295722\pi$
$691$	12.7126	+	5.05554i	0.483609	+	0.192322i	−0.114996	+	0.993366i	$0.536686\pi$
$692$		0			0
$693$	2.53614	+	2.78824i	0.0963400	+	0.105917i
$694$		0			0
$695$	16.9187	+	40.3050i	0.641764	+	1.52886i
$696$		0			0
$697$	−20.5104	+	8.15658i	−0.776887	+	0.308953i
$698$		0			0
$699$	−8.41948	+	1.94566i	−0.318454	+	0.0735915i
$700$		0			0
$701$	−30.3323	−	17.7684i	−1.14563	−	0.671104i	−0.194812	−	0.980841i	$-0.562410\pi$
$701$	−30.3323	−	17.7684i	−1.14563	−	0.671104i	−0.950822	+	0.309737i	$0.899759\pi$
$702$		0			0
$703$	−6.49625	+	5.68800i	−0.245011	+	0.214527i
$704$		0			0
$705$	−28.5829	−	7.75548i	−1.07649	−	0.292088i
$706$		0			0
$707$	5.85681	+	2.07609i	0.220268	+	0.0780792i
$708$		0			0
$709$	−7.85215	+	3.83384i	−0.294894	+	0.143983i	−0.580249	−	0.814439i	$-0.697045\pi$
$709$	−7.85215	+	3.83384i	−0.294894	+	0.143983i	0.285356	+	0.958422i	$0.407888\pi$
$710$		0			0
$711$	−0.988113	+	10.4111i	−0.0370571	+	0.390446i
$712$		0			0
$713$	12.4642	+	1.90165i	0.466787	+	0.0712175i
$714$		0			0
$715$	0.505729	+	26.7193i	0.0189132	+	0.999244i
$716$		0			0
$717$	9.11442	+	10.8159i	0.340384	+	0.403926i
$718$		0			0
$719$	−1.25258	−	22.0382i	−0.0467134	−	0.821886i	−0.933250	−	0.359228i	$-0.883040\pi$
$719$	−1.25258	−	22.0382i	−0.0467134	−	0.821886i	0.886537	−	0.462659i	$-0.153104\pi$
$720$		0			0
$721$	2.21026	+	12.8508i	0.0823145	+	0.478590i
$722$		0			0
$723$	27.1348	−	14.5451i	1.00915	−	0.540940i
$724$		0			0
$725$	−18.3217	−	8.94561i	−0.680449	−	0.332231i
$726$		0			0
$727$	−18.4019	+	1.39571i	−0.682489	+	0.0517640i	−0.412306	−	0.911045i	$-0.635277\pi$
$727$	−18.4019	+	1.39571i	−0.682489	+	0.0517640i	−0.270182	+	0.962809i	$0.587084\pi$
$728$		0			0
$729$	−20.5678	+	20.9608i	−0.761769	+	0.776324i
$730$		0			0
$731$	2.82595	−	16.4305i	0.104522	−	0.607706i
$732$		0			0
$733$	−22.2945	+	18.0770i	−0.823466	+	0.667690i	−0.945782	−	0.324801i	$-0.894703\pi$
$733$	−22.2945	+	18.0770i	−0.823466	+	0.667690i	0.122317	+	0.992491i	$0.460968\pi$
$734$		0			0
$735$	−7.87657	+	3.48309i	−0.290532	+	0.128476i
$736$		0			0
$737$	−2.23849	+	8.91419i	−0.0824559	+	0.328358i
$738$		0			0
$739$	25.1158	−	2.86426i	0.923899	−	0.105363i	0.361633	−	0.932320i	$-0.382219\pi$
$739$	25.1158	−	2.86426i	0.923899	−	0.105363i	0.562265	+	0.826957i	$0.309930\pi$
$740$		0			0
$741$	11.2934	−	8.46931i	0.414874	−	0.311128i
$742$		0			0
$743$	4.86963	−	5.77868i	0.178649	−	0.211999i	−0.667984	−	0.744176i	$-0.732843\pi$
$743$	4.86963	−	5.77868i	0.178649	−	0.211999i	0.846634	+	0.532176i	$0.178626\pi$
$744$		0			0
$745$	4.13349	+	8.07462i	0.151439	+	0.295831i
$746$		0			0
$747$	3.89880	−	10.3713i	0.142650	−	0.379465i
$748$		0			0
$749$	−4.21903	+	2.47148i	−0.154160	+	0.0903058i
$750$		0			0
$751$	15.6400	−	21.6988i	0.570710	−	0.791801i	−0.422717	−	0.906262i	$-0.638924\pi$
$751$	15.6400	−	21.6988i	0.570710	−	0.791801i	0.993428	+	0.114461i	$0.0365140\pi$
$752$		0			0
$753$	7.92965	+	4.25055i	0.288972	+	0.154899i
$754$		0			0
$755$	−10.0920	−	18.0006i	−0.367287	−	0.655111i
$756$		0			0
$757$	3.87906	+	13.2955i	0.140987	+	0.483231i	0.999566	−	0.0294493i	$-0.00937535\pi$
$757$	3.87906	+	13.2955i	0.140987	+	0.483231i	−0.858579	+	0.512681i	$0.828652\pi$
$758$		0			0
$759$	6.79913	+	8.71759i	0.246793	+	0.316428i
$760$		0			0
$761$	3.12440	+	8.31127i	0.113259	+	0.301283i	0.980473	−	0.196653i	$-0.0630071\pi$
$761$	3.12440	+	8.31127i	0.113259	+	0.301283i	−0.867214	+	0.497936i	$0.834091\pi$
$762$		0			0
$763$	−3.52230	+	2.24656i	−0.127516	+	0.0813308i
$764$		0			0
$765$	14.2753	+	3.29888i	0.516126	+	0.119271i
$766$		0			0
$767$	−9.50089	+	22.6337i	−0.343057	+	0.817255i
$768$		0			0
$769$	2.14094	+	22.5576i	0.0772043	+	0.813449i	0.947254	+	0.320485i	$0.103846\pi$
$769$	2.14094	+	22.5576i	0.0772043	+	0.813449i	−0.870049	+	0.492965i	$0.835913\pi$
$770$		0			0
$771$	−31.9133	+	22.0968i	−1.14933	+	0.795798i
$772$		0			0
$773$	−25.2467	−	22.1056i	−0.908062	−	0.795083i	0.0712464	−	0.997459i	$-0.477302\pi$
$773$	−25.2467	−	22.1056i	−0.908062	−	0.795083i	−0.979308	+	0.202376i	$0.935134\pi$
$774$		0			0
$775$	−6.59341	−	4.56529i	−0.236842	−	0.163990i
$776$		0			0
$777$	−12.3151	−	7.85466i	−0.441800	−	0.281785i
$778$		0			0
$779$	−0.959562	+	7.20082i	−0.0343799	+	0.257996i
$780$		0			0
$781$	13.0609	−	21.3588i	0.467355	−	0.764277i
$782$		0			0
$783$	−30.3646	−	30.9447i	−1.08514	−	1.10588i
$784$		0			0
$785$	7.68352	−	36.3737i	0.274236	−	1.29823i
$786$		0			0
$787$	−6.87277	+	12.2586i	−0.244988	+	0.436972i	−0.966952	−	0.254958i	$-0.917938\pi$
$787$	−6.87277	+	12.2586i	−0.244988	+	0.436972i	0.721964	+	0.691930i	$0.243239\pi$
$788$		0			0
$789$	−4.47251	−	17.8106i	−0.159226	−	0.634073i
$790$		0			0
$791$	−5.80693	−	8.73534i	−0.206470	−	0.310593i
$792$		0			0
$793$	−18.0162	−	54.0523i	−0.639773	−	1.91945i
$794$		0			0
$795$	−51.4037	−	5.86218i	−1.82310	−	0.207910i
$796$		0			0
$797$	44.1535	−	1.67203i	1.56400	−	0.0592264i	0.758440	−	0.651743i	$-0.225962\pi$
$797$	44.1535	−	1.67203i	1.56400	−	0.0592264i	0.805559	+	0.592516i	$0.201865\pi$
$798$		0			0
$799$	−2.39855	+	42.2006i	−0.0848546	+	1.49295i
$800$		0			0
$801$	−3.97261	−	6.49649i	−0.140365	−	0.229542i
$802$		0			0
$803$	−0.0564446	+	2.98214i	−0.00199189	+	0.105238i
$804$		0			0
$805$	−23.9822	+	8.50104i	−0.845260	+	0.299622i
$806$		0			0
$807$	−4.24793	−	4.01335i	−0.149534	−	0.141276i
$808$		0			0
$809$	−22.7882	+	3.47679i	−0.801192	+	0.122237i	−0.538482	−	0.842637i	$-0.681002\pi$
$809$	−22.7882	+	3.47679i	−0.801192	+	0.122237i	−0.262710	+	0.964875i	$0.584616\pi$
$810$		0			0
$811$	−15.7744	−	33.9213i	−0.553913	−	1.19114i	−0.960693	−	0.277613i	$-0.910457\pi$
$811$	−15.7744	−	33.9213i	−0.553913	−	1.19114i	0.406780	−	0.913526i	$-0.366652\pi$
$812$		0			0
$813$	24.2158	+	0.917019i	0.849286	+	0.0321613i
$814$		0			0
$815$	−8.99025	+	9.88391i	−0.314915	+	0.346218i
$816$		0			0
$817$	−4.26197	−	3.45573i	−0.149108	−	0.120901i
$818$		0			0
$819$	−8.61085	−	6.45757i	−0.300888	−	0.225646i
$820$		0			0
$821$	2.72182	−	0.521352i	0.0949923	−	0.0181953i	−0.140409	−	0.990094i	$-0.544842\pi$
$821$	2.72182	−	0.521352i	0.0949923	−	0.0181953i	0.235401	+	0.971898i	$0.424360\pi$
$822$		0			0
$823$	55.6977	+	10.6686i	1.94150	+	0.371885i	0.999324	+	0.0367701i	$0.0117069\pi$
$823$	55.6977	+	10.6686i	1.94150	+	0.371885i	0.942177	+	0.335115i	$0.108775\pi$
$824$		0			0
$825$	−1.45334	−	6.88011i	−0.0505989	−	0.239535i
$826$		0			0
$827$	−13.5930	+	4.24662i	−0.472677	+	0.147670i	−0.525251	−	0.850947i	$-0.676028\pi$
$827$	−13.5930	+	4.24662i	−0.472677	+	0.147670i	0.0525742	+	0.998617i	$0.483257\pi$
$828$		0			0
$829$	22.4861	−	21.2444i	0.780975	−	0.737848i	−0.188756	−	0.982024i	$-0.560445\pi$
$829$	22.4861	−	21.2444i	0.780975	−	0.737848i	0.969731	+	0.244177i	$0.0785177\pi$
$830$		0			0
$831$	1.90982	−	5.72985i	0.0662508	−	0.198766i
$832$		0			0
$833$	7.18712	+	9.97138i	0.249019	+	0.345488i
$834$		0			0
$835$	−13.9271	+	32.9412i	−0.481966	+	1.13998i
$836$		0			0
$837$	−9.97104	−	13.8338i	−0.344650	−	0.478165i
$838$		0			0
$839$	−12.9977	+	38.9960i	−0.448732	+	1.34629i	0.444131	+	0.895962i	$0.353512\pi$
$839$	−12.9977	+	38.9960i	−0.448732	+	1.34629i	−0.892863	+	0.450329i	$0.851307\pi$
$840$		0			0
$841$	21.6522	−	20.4565i	0.746628	−	0.705397i
$842$		0			0
$843$	−26.4182	+	8.25335i	−0.909891	+	0.284260i
$844$		0			0
$845$	−8.33657	−	39.4653i	−0.286787	−	1.35765i
$846$		0			0
$847$	16.4546	+	3.15180i	0.565388	+	0.108297i
$848$		0			0
$849$	−2.38638	+	0.457098i	−0.0819002	+	0.0156876i
$850$		0			0
$851$	15.4490	+	11.5857i	0.529586	+	0.397154i
$852$		0			0
$853$	22.2997	+	18.0812i	0.763526	+	0.619089i	0.930255	−	0.366914i	$-0.119586\pi$
$853$	22.2997	+	18.0812i	0.763526	+	0.619089i	−0.166729	+	0.986003i	$0.553320\pi$
$854$		0			0
$855$	3.24462	−	3.56715i	0.110964	−	0.121994i
$856$		0			0
$857$	12.5731	+	0.476127i	0.429490	+	0.0162642i	0.251702	−	0.967805i	$-0.419010\pi$
$857$	12.5731	+	0.476127i	0.429490	+	0.0162642i	0.177788	+	0.984069i	$0.443106\pi$
$858$		0			0
$859$	5.33803	+	11.4789i	0.182131	+	0.391657i	0.976419	−	0.215886i	$-0.0692639\pi$
$859$	5.33803	+	11.4789i	0.182131	+	0.391657i	−0.794287	+	0.607542i	$0.792155\pi$
$860$		0			0
$861$	−12.1485	+	1.85349i	−0.414020	+	0.0631669i
$862$		0			0
$863$	−7.64996	−	7.22751i	−0.260408	−	0.246027i	0.545440	−	0.838150i	$-0.316362\pi$
$863$	−7.64996	−	7.22751i	−0.260408	−	0.246027i	−0.805848	+	0.592122i	$0.798290\pi$
$864$		0			0
$865$	24.2806	−	8.60683i	0.825565	−	0.292641i
$866$		0			0
$867$	−0.415343	+	21.9439i	−0.0141058	+	0.745253i
$868$		0			0
$869$	−10.7638	−	17.6024i	−0.365139	−	0.597120i
$870$		0			0
$871$	1.48933	−	26.2037i	0.0504642	−	0.887877i
$872$		0			0
$873$	−11.9856	+	0.453877i	−0.405650	+	0.0153614i
$874$		0			0
$875$	−14.1544	−	1.61420i	−0.478507	−	0.0545699i
$876$		0			0
$877$	11.4158	+	34.2500i	0.385486	+	1.15654i	0.944818	+	0.327595i	$0.106238\pi$
$877$	11.4158	+	34.2500i	0.385486	+	1.15654i	−0.559332	+	0.828943i	$0.688942\pi$
$878$		0			0
$879$	18.9081	+	28.4434i	0.637753	+	0.959371i
$880$		0			0
$881$	−1.30670	−	5.20360i	−0.0440240	−	0.175314i	0.943906	−	0.330214i	$-0.107121\pi$
$881$	−1.30670	−	5.20360i	−0.0440240	−	0.175314i	−0.987930	+	0.154900i	$0.950494\pi$
$882$		0			0
$883$	−0.0617439	+	0.110129i	−0.00207785	+	0.00370615i	−0.873302	−	0.487180i	$-0.838026\pi$
$883$	−0.0617439	+	0.110129i	−0.00207785	+	0.00370615i	0.871224	+	0.490886i	$0.163327\pi$
$884$		0			0
$885$	3.84498	−	18.2021i	0.129248	−	0.611857i
$886$		0			0
$887$	28.1244	+	28.6618i	0.944325	+	0.962368i	0.999348	−	0.0361173i	$-0.0114990\pi$
$887$	28.1244	+	28.6618i	0.944325	+	0.962368i	−0.0550226	+	0.998485i	$0.517523\pi$
$888$		0			0
$889$	−22.7197	+	37.1541i	−0.761995	+	1.24611i
$890$		0			0
$891$	1.29588	−	9.72464i	0.0434136	−	0.325788i
$892$		0			0
$893$	11.7287	+	7.48069i	0.392487	+	0.250332i
$894$		0			0
$895$	41.5559	+	28.7734i	1.38906	+	0.961787i
$896$		0			0
$897$	−23.7523	−	20.7971i	−0.793068	−	0.694396i
$898$		0			0
$899$	19.0108	−	13.1631i	0.634046	−	0.439015i
$900$		0			0
$901$	6.97671	+	73.5089i	0.232428	+	2.44894i
$902$		0			0
$903$	3.59264	−	8.55863i	0.119555	−	0.284813i
$904$		0			0
$905$	44.2177	+	10.2182i	1.46985	+	0.339666i
$906$		0			0
$907$	−12.2592	+	7.81905i	−0.407061	+	0.259627i	−0.725369	−	0.688360i	$-0.758331\pi$
$907$	−12.2592	+	7.81905i	−0.407061	+	0.259627i	0.318309	+	0.947987i	$0.396885\pi$
$908$		0			0
$909$	0.926745	+	2.46525i	0.0307382	+	0.0817672i
$910$		0			0
$911$	−32.9581	−	42.2576i	−1.09195	−	1.40006i	−0.908930	−	0.416948i	$-0.863100\pi$
$911$	−32.9581	−	42.2576i	−1.09195	−	1.40006i	−0.183020	−	0.983109i	$-0.558587\pi$
$912$		0			0
$913$	6.12252	+	20.9849i	0.202626	+	0.694499i
$914$		0			0
$915$	21.1171	+	37.6654i	0.698109	+	1.24518i
$916$		0			0
$917$	−30.3628	−	16.2755i	−1.00267	−	0.537464i
$918$		0			0
$919$	−3.35826	+	4.65923i	−0.110779	+	0.153694i	−0.862977	−	0.505243i	$-0.831403\pi$
$919$	−3.35826	+	4.65923i	−0.110779	+	0.153694i	0.752199	+	0.658936i	$0.228993\pi$
$920$		0			0
$921$	23.6284	−	13.8413i	0.778581	−	0.456087i
$922$		0			0
$923$	−25.1569	+	66.9202i	−0.828049	+	2.20271i
$924$		0			0
$925$	−5.59692	−	10.9334i	−0.184026	−	0.359487i
$926$		0			0
$927$	−3.56136	+	4.22619i	−0.116970	+	0.138806i
$928$		0			0
$929$	−9.33498	+	7.00061i	−0.306271	+	0.229683i	−0.742008	−	0.670391i	$-0.766126\pi$
$929$	−9.33498	+	7.00061i	−0.306271	+	0.229683i	0.435737	+	0.900074i	$0.356488\pi$
$930$		0			0
$931$	4.01930	−	0.458369i	0.131727	−	0.0150224i
$932$		0			0
$933$	−6.43925	+	25.6426i	−0.210812	+	0.839500i
$934$		0			0
$935$	−26.4369	+	11.6906i	−0.864579	+	0.382324i
$936$		0			0
$937$	−31.5621	+	25.5915i	−1.03109	+	0.836038i	−0.986631	−	0.162973i	$-0.947892\pi$
$937$	−31.5621	+	25.5915i	−1.03109	+	0.836038i	−0.0444598	+	0.999011i	$0.514157\pi$
$938$		0			0
$939$	6.15643	−	35.7945i	0.200907	−	1.16811i
$940$		0			0
$941$	−4.30658	+	4.38886i	−0.140391	+	0.143073i	−0.780367	−	0.625321i	$-0.784968\pi$
$941$	−4.30658	+	4.38886i	−0.140391	+	0.143073i	0.639977	+	0.768394i	$0.278944\pi$
$942$		0			0
$943$	16.2001	−	1.22871i	0.527549	−	0.0400125i
$944$		0			0
$945$	30.9239	+	15.0987i	1.00596	+	0.491161i
$946$		0			0
$947$	−11.0128	+	5.90324i	−0.357869	+	0.191830i	−0.641535	−	0.767093i	$-0.721702\pi$
$947$	−11.0128	+	5.90324i	−0.357869	+	0.191830i	0.283666	+	0.958923i	$0.408449\pi$
$948$		0			0
$949$	−1.44375	−	8.39417i	−0.0468660	−	0.272486i
$950$		0			0
$951$	0.229582	+	4.03932i	0.00744471	+	0.130984i
$952$		0			0
$953$	−8.87496	−	10.5317i	−0.287488	−	0.341156i	0.601679	−	0.798738i	$-0.294499\pi$
$953$	−8.87496	−	10.5317i	−0.287488	−	0.341156i	−0.889167	+	0.457582i	$0.848715\pi$
$954$		0			0
$955$	−0.718928	−	37.9832i	−0.0232640	−	1.22911i
$956$		0			0
$957$	20.0433	+	3.05799i	0.647907	+	0.0988509i
$958$		0			0
$959$	−0.485869	+	5.11928i	−0.0156895	+	0.165310i
$960$		0			0
$961$	−19.6839	+	9.61074i	−0.634965	+	0.310024i
$962$		0			0
$963$	−1.95332	−	0.692402i	−0.0629450	−	0.0223123i
$964$		0			0
$965$	15.9812	+	4.33623i	0.514454	+	0.139588i
$966$		0			0
$967$	35.5198	−	31.1005i	1.14224	−	1.00013i	0.142294	−	0.989824i	$-0.454552\pi$
$967$	35.5198	−	31.1005i	1.14224	−	1.00013i	0.999947	−	0.0103017i	$-0.00327919\pi$
$968$		0			0
$969$	13.1750	+	7.71781i	0.423242	+	0.247932i
$970$		0			0
$971$	26.3872	−	6.09781i	0.846806	−	0.195688i	0.220618	−	0.975360i	$-0.429193\pi$
$971$	26.3872	−	6.09781i	0.846806	−	0.195688i	0.626188	+	0.779672i	$0.284614\pi$
$972$		0			0
$973$	32.2752	−	12.8352i	1.03470	−	0.411478i
$974$		0			0
$975$	7.77220	+	18.5155i	0.248910	+	0.592970i
$976$		0			0
$977$	24.9152	+	27.3919i	0.797109	+	0.876345i	0.994581	−	0.103964i	$-0.0331526\pi$
$977$	24.9152	+	27.3919i	0.797109	+	0.876345i	−0.197472	+	0.980309i	$0.563273\pi$
$978$		0			0
$979$	13.9601	+	5.55168i	0.446168	+	0.177432i
$980$		0			0
$981$	−1.69014	−	0.528017i	−0.0539619	−	0.0168583i
$982$		0			0
$983$	−13.9557	+	20.9936i	−0.445119	+	0.669591i	−0.985080	−	0.172099i	$-0.944945\pi$
$983$	−13.9557	+	20.9936i	−0.445119	+	0.669591i	0.539961	+	0.841690i	$0.318439\pi$
$984$		0			0
$985$	−48.0994	−	3.64815i	−1.53258	−	0.116240i
$986$		0			0
$987$	−6.59124	+	22.5914i	−0.209801	+	0.719092i
$988$		0			0
$989$	−5.59173	+	10.9232i	−0.177807	+	0.347339i
$990$		0			0
$991$	32.4808	−	41.6457i	1.03179	−	1.32292i	0.0866519	−	0.996239i	$-0.472383\pi$
$991$	32.4808	−	41.6457i	1.03179	−	1.32292i	0.945135	−	0.326680i	$-0.105930\pi$
$992$		0			0
$993$	9.55982	−	2.59389i	0.303372	−	0.0823147i
$994$		0			0
$995$	26.1245	−	56.1783i	0.828202	−	1.78097i
$996$		0			0
$997$	56.4048	+	24.9427i	1.78636	+	0.789943i	0.980135	+	0.198333i	$0.0635529\pi$
$997$	56.4048	+	24.9427i	1.78636	+	0.789943i	0.806224	+	0.591610i	$0.201507\pi$
$998$		0			0
$999$	−3.44984	−	25.8886i	−0.109148	−	0.819079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.10	✓	1148
167.130	even	83	inner	668.2.e.a.297.10	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.10	✓	1148	1.1	even	1	trivial
668.2.e.a.297.10	yes	1148	167.130	even	83	inner

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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(0.189949 + 1.42543i) q^{3} +(2.53109 + 1.11927i) q^{5} +(0.927279 - 1.99403i) q^{7} +(0.899535 - 0.244073i) q^{9} +O(q^{10})\)	\(q+(0.189949 + 1.42543i) q^{3} +(2.53109 + 1.11927i) q^{5} +(0.927279 - 1.99403i) q^{7} +(0.899535 - 0.244073i) q^{9} +(-1.13091 + 1.45001i) q^{11} +(2.39283 - 4.67431i) q^{13} +(-1.11467 + 3.82051i) q^{15} +(5.66373 + 0.429571i) q^{17} +(1.03489 - 1.55678i) q^{19} +(3.01849 + 0.943010i) q^{21} +(-3.88484 - 1.54493i) q^{23} +(1.78931 + 1.96717i) q^{25} +(2.18855 + 5.21372i) q^{27} +(-7.12459 + 2.83331i) q^{29} +(-2.93838 + 0.679028i) q^{31} +(-2.28171 - 1.33661i) q^{33} +(4.57889 - 4.00919i) q^{35} +(-4.45775 - 1.20953i) q^{37} +(7.11743 + 2.52294i) q^{39} +(-3.49204 + 1.70500i) q^{41} +(0.277331 - 2.92205i) q^{43} +(2.54999 + 0.389051i) q^{45} +(0.140827 + 7.44035i) q^{47} +(1.39448 + 1.65480i) q^{49} +(0.463497 + 8.15487i) q^{51} +(2.20354 + 12.8118i) q^{53} +(-4.48540 + 2.40432i) q^{55} +(2.41566 + 1.17945i) q^{57} +(-4.66117 + 0.353531i) q^{59} +(7.59924 - 7.74443i) q^{61} +(0.347431 - 2.02002i) q^{63} +(11.2883 - 9.15288i) q^{65} +(4.57112 - 2.02139i) q^{67} +(1.46427 - 5.83104i) q^{69} +(-13.5269 + 1.54264i) q^{71} +(1.29764 - 0.973148i) q^{73} +(-2.46419 + 2.92420i) q^{75} +(1.84269 + 3.59963i) q^{77} +(-3.94817 + 10.5026i) q^{79} +(-4.60340 + 2.69664i) q^{81} +(6.95087 - 9.64360i) q^{83} +(13.8546 + 7.42654i) q^{85} +(-5.39200 - 9.61744i) q^{87} +(-2.28824 - 7.84293i) q^{89} +(-7.10187 - 9.10576i) q^{91} +(-1.52605 - 4.05948i) q^{93} +(4.36186 - 2.78203i) q^{95} +(-12.5380 - 2.89741i) q^{97} +(-0.663384 + 1.58036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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