LMFDB - Embedded newform 368.2.m.e.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			353.1
Character	$\chi$	$=$	368.353
Dual form			368.2.m.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05870 - 2.31822i) q^{3} +(-0.536040 - 0.618623i) q^{5} +(-1.79431 - 1.15313i) q^{7} +(-2.28874 + 2.64134i) q^{9} +O(q^{10})$	\(q+(-1.05870 - 2.31822i) q^{3} +(-0.536040 - 0.618623i) q^{5} +(-1.79431 - 1.15313i) q^{7} +(-2.28874 + 2.64134i) q^{9} +(-0.0754313 - 0.524636i) q^{11} +(0.858898 - 0.551980i) q^{13} +(-0.866603 + 1.89760i) q^{15} +(-7.15009 + 2.09946i) q^{17} +(-0.380104 - 0.111609i) q^{19} +(-0.773589 + 5.38043i) q^{21} +(-1.87002 + 4.41622i) q^{23} +(0.616218 - 4.28589i) q^{25} +(1.21041 + 0.355409i) q^{27} +(7.89765 - 2.31896i) q^{29} +(-3.17083 + 6.94314i) q^{31} +(-1.13637 + 0.730297i) q^{33} +(0.248467 + 1.72813i) q^{35} +(-1.14354 + 1.31971i) q^{37} +(-2.18892 - 1.40674i) q^{39} +(-5.75435 - 6.64088i) q^{41} +(-4.40901 - 9.65438i) q^{43} +2.86085 q^{45} +4.39680 q^{47} +(-1.01807 - 2.22927i) q^{49} +(12.4368 + 14.3528i) q^{51} +(-4.56587 - 2.93430i) q^{53} +(-0.284118 + 0.327890i) q^{55} +(0.143681 + 0.999325i) q^{57} +(6.57004 - 4.22231i) q^{59} +(3.25065 - 7.11792i) q^{61} +(7.15252 - 2.10017i) q^{63} +(-0.801871 - 0.235451i) q^{65} +(1.66491 - 11.5797i) q^{67} +(12.2176 - 0.340311i) q^{69} +(0.354163 - 2.46326i) q^{71} +(4.85019 + 1.42414i) q^{73} +(-10.5880 + 3.10893i) q^{75} +(-0.469628 + 1.02834i) q^{77} +(14.4756 - 9.30292i) q^{79} +(1.03463 + 7.19599i) q^{81} +(-6.31106 + 7.28335i) q^{83} +(5.13151 + 3.29782i) q^{85} +(-13.7371 - 15.8534i) q^{87} +(-0.199914 - 0.437751i) q^{89} -2.17764 q^{91} +19.4527 q^{93} +(0.134707 + 0.294968i) q^{95} +(-5.04314 - 5.82009i) q^{97} +(1.55839 + 1.00151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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
$3$	−1.05870	−	2.31822i	−0.611239	−	1.33843i	−0.921723	−	0.387848i	$-0.873219\pi$
$3$	−1.05870	−	2.31822i	−0.611239	−	1.33843i	0.310484	−	0.950578i	$-0.399509\pi$
$4$		0			0
$5$	−0.536040	−	0.618623i	−0.239724	−	0.276657i	0.623120	−	0.782126i	$-0.285865\pi$
$5$	−0.536040	−	0.618623i	−0.239724	−	0.276657i	−0.862845	+	0.505469i	$0.831319\pi$
$6$		0			0
$7$	−1.79431	−	1.15313i	−0.678186	−	0.435843i	0.155683	−	0.987807i	$-0.450242\pi$
$7$	−1.79431	−	1.15313i	−0.678186	−	0.435843i	−0.833868	+	0.551964i	$0.813879\pi$
$8$		0			0
$9$	−2.28874	+	2.64134i	−0.762912	+	0.880447i
$10$		0			0
$11$	−0.0754313	−	0.524636i	−0.0227434	−	0.158184i	0.975285	−	0.220952i	$-0.0709163\pi$
$11$	−0.0754313	−	0.524636i	−0.0227434	−	0.158184i	−0.998028	+	0.0627679i	$0.980007\pi$
$12$		0			0
$13$	0.858898	−	0.551980i	0.238215	−	0.153092i	−0.416087	−	0.909325i	$-0.636599\pi$
$13$	0.858898	−	0.551980i	0.238215	−	0.153092i	0.654302	+	0.756233i	$0.272962\pi$
$14$		0			0
$15$	−0.866603	+	1.89760i	−0.223756	+	0.489957i
$16$		0			0
$17$	−7.15009	+	2.09946i	−1.73415	+	0.509193i	−0.987715	−	0.156263i	$-0.950055\pi$
$17$	−7.15009	+	2.09946i	−1.73415	+	0.509193i	−0.746437	+	0.665456i	$0.768237\pi$
$18$		0			0
$19$	−0.380104	−	0.111609i	−0.0872018	−	0.0256048i	0.237841	−	0.971304i	$-0.423560\pi$
$19$	−0.380104	−	0.111609i	−0.0872018	−	0.0256048i	−0.325042	+	0.945699i	$0.605379\pi$
$20$		0			0
$21$	−0.773589	+	5.38043i	−0.168811	+	1.17411i
$22$		0			0
$23$	−1.87002	+	4.41622i	−0.389927	+	0.920846i
$23$	−1.87002	+	4.41622i	−0.389927	+	0.920846i
$24$		0			0
$25$	0.616218	−	4.28589i	0.123244	−	0.857179i
$26$		0			0
$27$	1.21041	+	0.355409i	0.232944	+	0.0683985i
$28$		0			0
$29$	7.89765	−	2.31896i	1.46656	−	0.430620i	0.551578	−	0.834123i	$-0.314026\pi$
$29$	7.89765	−	2.31896i	1.46656	−	0.430620i	0.914978	+	0.403503i	$0.132208\pi$
$30$		0			0
$31$	−3.17083	+	6.94314i	−0.569497	+	1.24703i	0.377567	+	0.925982i	$0.376761\pi$
$31$	−3.17083	+	6.94314i	−0.569497	+	1.24703i	−0.947065	+	0.321043i	$0.895967\pi$
$32$		0			0
$33$	−1.13637	+	0.730297i	−0.197816	+	0.127128i
$34$		0			0
$35$	0.248467	+	1.72813i	0.0419986	+	0.292107i
$36$		0			0
$37$	−1.14354	+	1.31971i	−0.187997	+	0.216960i	−0.841922	−	0.539600i	$-0.818576\pi$
$37$	−1.14354	+	1.31971i	−0.187997	+	0.216960i	0.653925	+	0.756559i	$0.273121\pi$
$38$		0			0
$39$	−2.18892	−	1.40674i	−0.350508	−	0.225258i
$40$		0			0
$41$	−5.75435	−	6.64088i	−0.898679	−	1.03713i	−0.999110	−	0.0421870i	$-0.986567\pi$
$41$	−5.75435	−	6.64088i	−0.898679	−	1.03713i	0.100431	−	0.994944i	$-0.467978\pi$
$42$		0			0
$43$	−4.40901	−	9.65438i	−0.672368	−	1.47228i	−0.870532	−	0.492111i	$-0.836225\pi$
$43$	−4.40901	−	9.65438i	−0.672368	−	1.47228i	0.198165	−	0.980169i	$-0.436502\pi$
$44$		0			0
$45$	2.86085			0.426470
$46$		0			0
$47$	4.39680			0.641339			0.320669	−	0.947191i	$-0.396092\pi$
$47$	4.39680			0.641339			0.320669	+	0.947191i	$0.396092\pi$
$48$		0			0
$49$	−1.01807	−	2.22927i	−0.145439	−	0.318467i
$50$		0			0
$51$	12.4368	+	14.3528i	1.74150	+	2.00980i
$52$		0			0
$53$	−4.56587	−	2.93430i	−0.627170	−	0.403058i	0.188091	−	0.982152i	$-0.439770\pi$
$53$	−4.56587	−	2.93430i	−0.627170	−	0.403058i	−0.815261	+	0.579094i	$0.803406\pi$
$54$		0			0
$55$	−0.284118	+	0.327890i	−0.0383105	+	0.0442126i
$56$		0			0
$57$	0.143681	+	0.999325i	0.0190310	+	0.132364i
$58$		0			0
$59$	6.57004	−	4.22231i	0.855347	−	0.549698i	−0.0378913	−	0.999282i	$-0.512064\pi$
$59$	6.57004	−	4.22231i	0.855347	−	0.549698i	0.893238	+	0.449584i	$0.148428\pi$
$60$		0			0
$61$	3.25065	−	7.11792i	0.416203	−	0.911357i	−0.579165	−	0.815211i	$-0.696621\pi$
$61$	3.25065	−	7.11792i	0.416203	−	0.911357i	0.995367	−	0.0961460i	$-0.0306516\pi$
$62$		0			0
$63$	7.15252	−	2.10017i	0.901133	−	0.264597i
$64$		0			0
$65$	−0.801871	−	0.235451i	−0.0994599	−	0.0292041i
$66$		0			0
$67$	1.66491	−	11.5797i	0.203401	−	1.41469i	−0.590696	−	0.806894i	$-0.701147\pi$
$67$	1.66491	−	11.5797i	0.203401	−	1.41469i	0.794097	−	0.607791i	$-0.207944\pi$
$68$		0			0
$69$	12.2176	−	0.340311i	1.47082	−	0.0409687i
$70$		0			0
$71$	0.354163	−	2.46326i	0.0420315	−	0.292335i	−0.957954	−	0.286922i	$-0.907368\pi$
$71$	0.354163	−	2.46326i	0.0420315	−	0.292335i	0.999985	−	0.00541300i	$-0.00172302\pi$
$72$		0			0
$73$	4.85019	+	1.42414i	0.567672	+	0.166684i	0.552959	−	0.833208i	$-0.313498\pi$
$73$	4.85019	+	1.42414i	0.567672	+	0.166684i	0.0147126	+	0.999892i	$0.495317\pi$
$74$		0			0
$75$	−10.5880	+	3.10893i	−1.22260	+	0.358988i
$76$		0			0
$77$	−0.469628	+	1.02834i	−0.0535191	+	0.117191i
$78$		0			0
$79$	14.4756	−	9.30292i	1.62863	−	1.04666i	0.678604	−	0.734505i	$-0.262585\pi$
$79$	14.4756	−	9.30292i	1.62863	−	1.04666i	0.950031	−	0.312155i	$-0.101051\pi$
$80$		0			0
$81$	1.03463	+	7.19599i	0.114959	+	0.799555i
$82$		0			0
$83$	−6.31106	+	7.28335i	−0.692728	+	0.799451i	−0.987751	−	0.156039i	$-0.950127\pi$
$83$	−6.31106	+	7.28335i	−0.692728	+	0.799451i	0.295022	+	0.955490i	$0.404673\pi$
$84$		0			0
$85$	5.13151	+	3.29782i	0.556590	+	0.357699i
$86$		0			0
$87$	−13.7371	−	15.8534i	−1.47277	−	1.69967i
$88$		0			0
$89$	−0.199914	−	0.437751i	−0.0211909	−	0.0464015i	0.898741	−	0.438481i	$-0.144483\pi$
$89$	−0.199914	−	0.437751i	−0.0211909	−	0.0464015i	−0.919932	+	0.392079i	$0.871756\pi$
$90$		0			0
$91$	−2.17764			−0.228278
$92$		0			0
$93$	19.4527			2.01715
$94$		0			0
$95$	0.134707	+	0.294968i	0.0138207	+	0.0302631i
$96$		0			0
$97$	−5.04314	−	5.82009i	−0.512053	−	0.590940i	0.439570	−	0.898208i	$-0.355131\pi$
$97$	−5.04314	−	5.82009i	−0.512053	−	0.590940i	−0.951623	+	0.307268i	$0.900585\pi$
$98$		0			0
$99$	1.55839	+	1.00151i	0.156624	+	0.100656i
$100$		0			0
$101$	−11.7333	+	13.5410i	−1.16751	+	1.34738i	−0.241263	+	0.970460i	$0.577562\pi$
$101$	−11.7333	+	13.5410i	−1.16751	+	1.34738i	−0.926246	+	0.376918i	$0.876984\pi$
$102$		0			0
$103$	0.327191	+	2.27566i	0.0322391	+	0.224228i	0.999571	−	0.0292852i	$-0.00932309\pi$
$103$	0.327191	+	2.27566i	0.0322391	+	0.224228i	−0.967332	+	0.253513i	$0.918414\pi$
$104$		0			0
$105$	3.74313	−	2.40557i	0.365293	−	0.234759i
$106$		0			0
$107$	−1.18578	+	2.59650i	−0.114634	+	0.251013i	−0.958249	−	0.285935i	$-0.907696\pi$
$107$	−1.18578	+	2.59650i	−0.114634	+	0.251013i	0.843615	+	0.536948i	$0.180423\pi$
$108$		0			0
$109$	5.86607	−	1.72243i	0.561868	−	0.164979i	0.0115481	−	0.999933i	$-0.496324\pi$
$109$	5.86607	−	1.72243i	0.561868	−	0.164979i	0.550320	+	0.834954i	$0.314506\pi$
$110$		0			0
$111$	4.27005	+	1.25380i	0.405295	+	0.119005i
$112$		0			0
$113$	−1.53224	+	10.6570i	−0.144141	+	1.00252i	0.781442	+	0.623978i	$0.214485\pi$
$113$	−1.53224	+	10.6570i	−0.144141	+	1.00252i	−0.925583	+	0.378545i	$0.876425\pi$
$114$		0			0
$115$	3.73439	−	1.21043i	0.348233	−	0.112873i
$116$		0			0
$117$	−0.507822	+	3.53198i	−0.0469481	+	0.326532i
$118$		0			0
$119$	15.2504	+	4.47793i	1.39801	+	0.410491i
$120$		0			0
$121$	10.2849	−	3.01991i	0.934988	−	0.274537i
$122$		0			0
$123$	−9.30292	+	20.3706i	−0.838816	+	1.83675i
$124$		0			0
$125$	−6.42474	+	4.12893i	−0.574646	+	0.369303i
$126$		0			0
$127$	−1.83570	−	12.7676i	−0.162892	−	1.13294i	−0.893147	−	0.449764i	$-0.851508\pi$
$127$	−1.83570	−	12.7676i	−0.162892	−	1.13294i	0.730256	−	0.683174i	$-0.239401\pi$
$128$		0			0
$129$	−17.7132	+	20.4421i	−1.55956	+	1.79983i
$130$		0			0
$131$	2.45705	+	1.57905i	0.214673	+	0.137962i	0.643559	−	0.765397i	$-0.277457\pi$
$131$	2.45705	+	1.57905i	0.214673	+	0.137962i	−0.428886	+	0.903359i	$0.641094\pi$
$132$		0			0
$133$	0.553325	+	0.638571i	0.0479793	+	0.0553711i
$134$		0			0
$135$	−0.428965	−	0.939303i	−0.0369195	−	0.0808423i
$136$		0			0
$137$	−9.20821			−0.786711			−0.393355	−	0.919386i	$-0.628686\pi$
$137$	−9.20821			−0.786711			−0.393355	+	0.919386i	$0.628686\pi$
$138$		0			0
$139$	−4.47037			−0.379172			−0.189586	−	0.981864i	$-0.560715\pi$
$139$	−4.47037			−0.379172			−0.189586	+	0.981864i	$0.560715\pi$
$140$		0			0
$141$	−4.65488	−	10.1928i	−0.392011	−	0.858385i
$142$		0			0
$143$	−0.354376	−	0.408972i	−0.0296345	−	0.0342000i
$144$		0			0
$145$	−5.66802	−	3.64262i	−0.470703	−	0.302503i
$146$		0			0
$147$	−4.09011	+	4.72023i	−0.337346	+	0.389318i
$148$		0			0
$149$	−2.04868	−	14.2489i	−0.167834	−	1.16731i	−0.883349	−	0.468715i	$-0.844717\pi$
$149$	−2.04868	−	14.2489i	−0.167834	−	1.16731i	0.715515	−	0.698597i	$-0.246192\pi$
$150$		0			0
$151$	−2.37013	+	1.52319i	−0.192878	+	0.123955i	−0.633516	−	0.773730i	$-0.718389\pi$
$151$	−2.37013	+	1.52319i	−0.192878	+	0.123955i	0.440637	+	0.897685i	$0.354752\pi$
$152$		0			0
$153$	10.8193	−	23.6909i	0.874688	−	1.91530i
$154$		0			0
$155$	5.99488	−	1.76026i	0.481520	−	0.141387i
$156$		0			0
$157$	−8.04154	−	2.36121i	−0.641785	−	0.188445i	−0.0553828	−	0.998465i	$-0.517638\pi$
$157$	−8.04154	−	2.36121i	−0.641785	−	0.188445i	−0.586402	+	0.810020i	$0.699456\pi$
$158$		0			0
$159$	−1.96850	+	13.6912i	−0.156112	+	1.08579i
$160$		0			0
$161$	8.44789	−	5.76769i	0.665787	−	0.454557i
$162$		0			0
$163$	1.71432	−	11.9233i	0.134276	−	0.933907i	−0.805617	−	0.592437i	$-0.798166\pi$
$163$	1.71432	−	11.9233i	0.134276	−	0.933907i	0.939893	−	0.341470i	$-0.110925\pi$
$164$		0			0
$165$	1.06092	+	0.311513i	0.0825922	+	0.0242513i
$166$		0			0
$167$	0.790579	−	0.232135i	0.0611769	−	0.0179631i	−0.251001	−	0.967987i	$-0.580760\pi$
$167$	0.790579	−	0.232135i	0.0611769	−	0.0179631i	0.312178	+	0.950024i	$0.398942\pi$
$168$		0			0
$169$	−4.96737	+	10.8770i	−0.382106	+	0.836694i
$170$		0			0
$171$	1.16475	−	0.748542i	0.0890709	−	0.0572424i
$172$		0			0
$173$	1.18441	+	8.23778i	0.0900493	+	0.626307i	0.984004	+	0.178148i	$0.0570107\pi$
$173$	1.18441	+	8.23778i	0.0900493	+	0.626307i	−0.893954	+	0.448158i	$0.852080\pi$
$174$		0			0
$175$	−6.04789	+	6.97964i	−0.457178	+	0.527611i
$176$		0			0
$177$	−16.7439	−	10.7607i	−1.25855	−	0.808822i
$178$		0			0
$179$	−4.96694	−	5.73215i	−0.371246	−	0.428441i	0.539130	−	0.842223i	$-0.318753\pi$
$179$	−4.96694	−	5.73215i	−0.371246	−	0.428441i	−0.910376	+	0.413782i	$0.864208\pi$
$180$		0			0
$181$	−0.116430	−	0.254947i	−0.00865420	−	0.0189501i	0.905256	−	0.424868i	$-0.139679\pi$
$181$	−0.116430	−	0.254947i	−0.00865420	−	0.0189501i	−0.913910	+	0.405917i	$0.866952\pi$
$182$		0			0
$183$	−19.9424			−1.47418
$184$		0			0
$185$	1.42939			0.105091
$186$		0			0
$187$	1.64079	+	3.59283i	0.119987	+	0.262734i
$188$		0			0
$189$	−1.76202	−	2.03348i	−0.128168	−	0.147914i
$190$		0			0
$191$	2.59473	+	1.66753i	0.187748	+	0.120658i	0.631138	−	0.775670i	$-0.282588\pi$
$191$	2.59473	+	1.66753i	0.187748	+	0.120658i	−0.443390	+	0.896329i	$0.646224\pi$
$192$		0			0
$193$	14.8573	−	17.1462i	1.06945	−	1.23421i	0.0984452	−	0.995142i	$-0.468613\pi$
$193$	14.8573	−	17.1462i	1.06945	−	1.23421i	0.971003	−	0.239067i	$-0.0768415\pi$
$194$		0			0
$195$	0.303112	+	2.10819i	0.0217063	+	0.150970i
$196$		0			0
$197$	13.4931	−	8.67150i	0.961345	−	0.617819i	0.0369748	−	0.999316i	$-0.488228\pi$
$197$	13.4931	−	8.67150i	0.961345	−	0.617819i	0.924370	+	0.381497i	$0.124592\pi$
$198$		0			0
$199$	−3.98628	+	8.72873i	−0.282580	+	0.618763i	−0.996692	−	0.0812676i	$-0.974103\pi$
$199$	−3.98628	+	8.72873i	−0.282580	+	0.618763i	0.714113	+	0.700031i	$0.246830\pi$
$200$		0			0
$201$	−28.6070	+	8.39976i	−2.01778	+	0.592474i
$202$		0			0
$203$	−16.8449	−	4.94611i	−1.18228	−	0.347149i
$204$		0			0
$205$	−1.02364	+	7.11956i	−0.0714940	+	0.497251i
$206$		0			0
$207$	−7.38476	−	15.0469i	−0.513277	−	1.04583i
$208$		0			0
$209$	−0.0298822	+	0.207835i	−0.00206699	+	0.0143762i
$210$		0			0
$211$	22.3528	+	6.56338i	1.53883	+	0.451842i	0.937740	−	0.347338i	$-0.112914\pi$
$211$	22.3528	+	6.56338i	1.53883	+	0.451842i	0.601092	+	0.799180i	$0.294733\pi$
$212$		0			0
$213$	−6.08534	+	1.78682i	−0.416960	+	0.122431i
$214$		0			0
$215$	−3.60902	+	7.90265i	−0.246133	+	0.538957i
$216$		0			0
$217$	13.6958	−	8.80177i	0.929732	−	0.597503i
$218$		0			0
$219$	−1.83340	−	12.7516i	−0.123890	−	0.861671i
$220$		0			0
$221$	−4.98234	+	5.74993i	−0.335148	+	0.386782i
$222$		0			0
$223$	13.4357	+	8.63459i	0.899720	+	0.578215i	0.906707	−	0.421761i	$-0.138588\pi$
$223$	13.4357	+	8.63459i	0.899720	+	0.578215i	−0.00698722	+	0.999976i	$0.502224\pi$
$224$		0			0
$225$	9.91015	+	11.4369i	0.660677	+	0.762461i
$226$		0			0
$227$	1.06207	+	2.32562i	0.0704923	+	0.154357i	0.941598	−	0.336739i	$-0.109324\pi$
$227$	1.06207	+	2.32562i	0.0704923	+	0.154357i	−0.871106	+	0.491095i	$0.836597\pi$
$228$		0			0
$229$	−18.7176			−1.23690			−0.618448	−	0.785826i	$-0.712238\pi$
$229$	−18.7176			−1.23690			−0.618448	+	0.785826i	$0.712238\pi$
$230$		0			0
$231$	2.88112			0.189564
$232$		0			0
$233$	5.45297	+	11.9403i	0.357236	+	0.782238i	0.999871	+	0.0160655i	$0.00511403\pi$
$233$	5.45297	+	11.9403i	0.357236	+	0.782238i	−0.642635	+	0.766173i	$0.722159\pi$
$234$		0			0
$235$	−2.35686	−	2.71996i	−0.153745	−	0.177431i
$236$		0			0
$237$	−36.8915	−	23.7087i	−2.39636	−	1.54005i
$238$		0			0
$239$	−18.3529	+	21.1803i	−1.18715	+	1.37004i	−0.274350	+	0.961630i	$0.588463\pi$
$239$	−18.3529	+	21.1803i	−1.18715	+	1.37004i	−0.912798	+	0.408411i	$0.866083\pi$
$240$		0			0
$241$	2.24306	+	15.6008i	0.144488	+	1.00494i	0.925046	+	0.379855i	$0.124026\pi$
$241$	2.24306	+	15.6008i	0.144488	+	1.00494i	−0.780558	+	0.625084i	$0.785065\pi$
$242$		0			0
$243$	18.7703	−	12.0629i	1.20412	−	0.773838i
$244$		0			0
$245$	−0.833349	+	1.82478i	−0.0532407	+	0.116581i
$246$		0			0
$247$	−0.388076	+	0.113949i	−0.0246927	+	0.00725042i
$248$		0			0
$249$	23.5659	+	6.91958i	1.49343	+	0.438510i
$250$		0			0
$251$	2.21898	−	15.4333i	0.140061	−	0.974144i	−0.791658	−	0.610964i	$-0.790782\pi$
$251$	2.21898	−	15.4333i	0.140061	−	0.974144i	0.931719	−	0.363180i	$-0.118309\pi$
$252$		0			0
$253$	2.45797	+	0.647960i	0.154531	+	0.0407369i
$254$		0			0
$255$	2.21237	−	15.3874i	0.138544	−	0.963595i
$256$		0			0
$257$	−3.64333	−	1.06978i	−0.227265	−	0.0667310i	0.166117	−	0.986106i	$-0.446877\pi$
$257$	−3.64333	−	1.06978i	−0.227265	−	0.0667310i	−0.393382	+	0.919375i	$0.628695\pi$
$258$		0			0
$259$	3.57367	−	1.04932i	0.222057	−	0.0652018i
$260$		0			0
$261$	−11.9505	+	26.1679i	−0.739716	+	1.61975i
$262$		0			0
$263$	−12.7634	+	8.20252i	−0.787023	+	0.505789i	−0.871358	−	0.490648i	$-0.836760\pi$
$263$	−12.7634	+	8.20252i	−0.787023	+	0.505789i	0.0843342	+	0.996438i	$0.473124\pi$
$264$		0			0
$265$	0.632259	+	4.39746i	0.0388394	+	0.270134i
$266$		0			0
$267$	−0.803156	+	0.926891i	−0.0491523	+	0.0567248i
$268$		0			0
$269$	−0.285644	−	0.183572i	−0.0174160	−	0.0111926i	0.531904	−	0.846805i	$-0.321477\pi$
$269$	−0.285644	−	0.183572i	−0.0174160	−	0.0111926i	−0.549320	+	0.835612i	$0.685113\pi$
$270$		0			0
$271$	8.64309	+	9.97466i	0.525030	+	0.605917i	0.954883	−	0.296982i	$-0.0959800\pi$
$271$	8.64309	+	9.97466i	0.525030	+	0.605917i	−0.429853	+	0.902899i	$0.641435\pi$
$272$		0			0
$273$	2.30546	+	5.04824i	0.139533	+	0.305534i
$274$		0			0
$275$	−2.29502			−0.138395
$276$		0			0
$277$	−11.4417			−0.687466			−0.343733	−	0.939067i	$-0.611691\pi$
$277$	−11.4417			−0.687466			−0.343733	+	0.939067i	$0.611691\pi$
$278$		0			0
$279$	−11.0820	−	24.2663i	−0.663464	−	1.45278i
$280$		0			0
$281$	19.4303	+	22.4238i	1.15911	+	1.33769i	0.931416	+	0.363957i	$0.118575\pi$
$281$	19.4303	+	22.4238i	1.15911	+	1.33769i	0.227698	+	0.973732i	$0.426880\pi$
$282$		0			0
$283$	−18.8660	−	12.1244i	−1.12147	−	0.720723i	−0.157705	−	0.987486i	$-0.550410\pi$
$283$	−18.8660	−	12.1244i	−1.12147	−	0.720723i	−0.963762	+	0.266763i	$0.914046\pi$
$284$		0			0
$285$	0.541187	−	0.624563i	0.0320571	−	0.0369959i
$286$		0			0
$287$	2.66728	+	18.5513i	0.157445	+	1.09505i
$288$		0			0
$289$	32.4148	−	20.8317i	1.90675	−	1.22540i
$290$		0			0
$291$	−8.15311	+	17.8528i	−0.477944	+	1.04655i
$292$		0			0
$293$	27.8380	−	8.17398i	1.62631	−	0.477529i	0.663609	−	0.748080i	$-0.269024\pi$
$293$	27.8380	−	8.17398i	1.62631	−	0.477529i	0.962706	+	0.270551i	$0.0872059\pi$
$294$		0			0
$295$	−6.13383	−	1.80105i	−0.357125	−	0.104861i
$296$		0			0
$297$	0.0951576	−	0.661835i	0.00552160	−	0.0384036i
$298$		0			0
$299$	0.831508	+	4.82530i	0.0480874	+	0.279054i
$300$		0			0
$301$	−3.22166	+	22.4071i	−0.185693	+	1.29153i
$302$		0			0
$303$	43.8131	+	12.8647i	2.51699	+	0.739056i
$304$		0			0
$305$	−6.14579	+	1.80457i	−0.351907	+	0.103329i
$306$		0			0
$307$	−0.237871	+	0.520866i	−0.0135760	+	0.0297274i	−0.916299	−	0.400496i	$-0.868838\pi$
$307$	−0.237871	+	0.520866i	−0.0135760	+	0.0297274i	0.902723	+	0.430223i	$0.141565\pi$
$308$		0			0
$309$	4.92910	−	3.16774i	0.280406	−	0.180206i
$310$		0			0
$311$	−3.07482	−	21.3858i	−0.174357	−	1.21268i	−0.869546	−	0.493852i	$-0.835588\pi$
$311$	−3.07482	−	21.3858i	−0.174357	−	1.21268i	0.695189	−	0.718827i	$-0.255321\pi$
$312$		0			0
$313$	−3.25576	+	3.75735i	−0.184026	+	0.212378i	−0.840265	−	0.542175i	$-0.817601\pi$
$313$	−3.25576	+	3.75735i	−0.184026	+	0.212378i	0.656239	+	0.754553i	$0.272146\pi$
$314$		0			0
$315$	−5.13325	−	3.29894i	−0.289226	−	0.185874i
$316$		0			0
$317$	18.8331	+	21.7346i	1.05778	+	1.22074i	0.974541	+	0.224207i	$0.0719793\pi$
$317$	18.8331	+	21.7346i	1.05778	+	1.22074i	0.0832336	+	0.996530i	$0.473475\pi$
$318$		0			0
$319$	−1.81234	−	3.96847i	−0.101472	−	0.222192i
$320$		0			0
$321$	7.27464			0.406031
$322$		0			0
$323$	2.95209			0.164259
$324$		0			0
$325$	−1.83646	−	4.02128i	−0.101868	−	0.223061i
$326$		0			0
$327$	−10.2034	−	11.7753i	−0.564248	−	0.651177i
$328$		0			0
$329$	−7.88922	−	5.07009i	−0.434947	−	0.279523i
$330$		0			0
$331$	10.0722	−	11.6239i	0.553618	−	0.638909i	−0.408104	−	0.912935i	$-0.633810\pi$
$331$	10.0722	−	11.6239i	0.553618	−	0.638909i	0.961722	+	0.274026i	$0.0883555\pi$
$332$		0			0
$333$	−0.868558	−	6.04095i	−0.0475967	−	0.331042i
$334$		0			0
$335$	−8.05593	+	5.17723i	−0.440143	+	0.282863i
$336$		0			0
$337$	8.05243	−	17.6324i	0.438644	−	0.960496i	−0.553201	−	0.833048i	$-0.686594\pi$
$337$	8.05243	−	17.6324i	0.438644	−	0.960496i	0.991845	−	0.127449i	$-0.0406788\pi$
$338$		0			0
$339$	26.3274	−	7.73042i	1.42991	−	0.419859i
$340$		0			0
$341$	3.88180	+	1.13980i	0.210211	+	0.0617237i
$342$		0			0
$343$	−2.86871	+	19.9523i	−0.154896	+	1.07732i
$344$		0			0
$345$	−6.75964	−	7.37566i	−0.363927	−	0.397092i
$346$		0			0
$347$	1.44238	−	10.0320i	0.0774310	−	0.538545i	−0.913775	−	0.406220i	$-0.866847\pi$
$347$	1.44238	−	10.0320i	0.0774310	−	0.538545i	0.991206	−	0.132325i	$-0.0422442\pi$
$348$		0			0
$349$	−15.9620	−	4.68688i	−0.854429	−	0.250883i	−0.174949	−	0.984577i	$-0.555976\pi$
$349$	−15.9620	−	4.68688i	−0.854429	−	0.250883i	−0.679479	+	0.733695i	$0.737794\pi$
$350$		0			0
$351$	1.23580	−	0.362863i	0.0659621	−	0.0193682i
$352$		0			0
$353$	8.24279	−	18.0492i	0.438719	−	0.960661i	−0.553112	−	0.833107i	$-0.686560\pi$
$353$	8.24279	−	18.0492i	0.438719	−	0.960661i	0.991832	−	0.127555i	$-0.0407128\pi$
$354$		0			0
$355$	−1.71368	+	1.10131i	−0.0909525	+	0.0584516i
$356$		0			0
$357$	−5.76475	−	40.0947i	−0.305103	−	2.12204i
$358$		0			0
$359$	5.84081	−	6.74065i	0.308266	−	0.355758i	−0.580385	−	0.814342i	$-0.697098\pi$
$359$	5.84081	−	6.74065i	0.308266	−	0.355758i	0.888651	+	0.458584i	$0.151643\pi$
$360$		0			0
$361$	−15.8518	−	10.1873i	−0.834305	−	0.536175i
$362$		0			0
$363$	−17.8894	−	20.6455i	−0.938949	−	1.08361i
$364$		0			0
$365$	−1.71889	−	3.76384i	−0.0899707	−	0.197008i
$366$		0			0
$367$	32.8280			1.71361			0.856804	−	0.515642i	$-0.172446\pi$
$367$	32.8280			1.71361			0.856804	+	0.515642i	$0.172446\pi$
$368$		0			0
$369$	30.7110			1.59875
$370$		0			0
$371$	4.80894	+	10.5301i	0.249668	+	0.546696i
$372$		0			0
$373$	5.89038	+	6.79786i	0.304992	+	0.351980i	0.887469	−	0.460868i	$-0.152462\pi$
$373$	5.89038	+	6.79786i	0.304992	+	0.351980i	−0.582477	+	0.812847i	$0.697916\pi$
$374$		0			0
$375$	16.3736	+	10.5227i	0.845530	+	0.543389i
$376$		0			0
$377$	5.50325	−	6.35109i	0.283432	−	0.327098i
$378$		0			0
$379$	4.40434	+	30.6329i	0.226236	+	1.57351i	0.713757	+	0.700394i	$0.246992\pi$
$379$	4.40434	+	30.6329i	0.226236	+	1.57351i	−0.487521	+	0.873111i	$0.662099\pi$
$380$		0			0
$381$	−27.6546	+	17.7725i	−1.41679	+	0.910515i
$382$		0			0
$383$	10.0291	−	21.9607i	0.512464	−	1.12214i	−0.459750	−	0.888048i	$-0.652061\pi$
$383$	10.0291	−	21.9607i	0.512464	−	1.12214i	0.972214	−	0.234092i	$-0.0752116\pi$
$384$		0			0
$385$	0.887897	−	0.260710i	0.0452514	−	0.0132870i
$386$		0			0
$387$	35.5916	+	10.4506i	1.80922	+	0.531236i
$388$		0			0
$389$	3.71423	−	25.8330i	0.188319	−	1.30979i	−0.648041	−	0.761606i	$-0.724411\pi$
$389$	3.71423	−	25.8330i	0.188319	−	1.30979i	0.836359	−	0.548181i	$-0.184680\pi$
$390$		0			0
$391$	4.09917	−	35.5024i	0.207304	−	1.79544i
$392$		0			0
$393$	1.05932	−	7.36771i	0.0534355	−	0.371652i
$394$		0			0
$395$	−13.5145	−	3.96822i	−0.679989	−	0.199663i
$396$		0			0
$397$	16.9673	−	4.98206i	0.851567	−	0.250043i	0.173310	−	0.984867i	$-0.444554\pi$
$397$	16.9673	−	4.98206i	0.851567	−	0.250043i	0.678257	+	0.734825i	$0.262736\pi$
$398$		0			0
$399$	0.894546	−	1.95878i	0.0447833	−	0.0980618i
$400$		0			0
$401$	−2.13396	+	1.37141i	−0.106565	+	0.0684851i	−0.592838	−	0.805322i	$-0.701992\pi$
$401$	−2.13396	+	1.37141i	−0.106565	+	0.0684851i	0.486273	+	0.873807i	$0.338356\pi$
$402$		0			0
$403$	1.10906	+	7.71368i	0.0552462	+	0.384246i
$404$		0			0
$405$	3.89701	−	4.49738i	0.193644	−	0.223477i
$406$		0			0
$407$	0.778628	+	0.500394i	0.0385952	+	0.0248036i
$408$		0			0
$409$	−21.1870	−	24.4511i	−1.04763	−	1.20903i	−0.977378	−	0.211501i	$-0.932165\pi$
$409$	−21.1870	−	24.4511i	−1.04763	−	1.20903i	−0.0702529	−	0.997529i	$-0.522381\pi$
$410$		0			0
$411$	9.74871	+	21.3467i	0.480868	+	1.05295i
$412$		0			0
$413$	−16.6576			−0.819666
$414$		0			0
$415$	7.88863			0.387238
$416$		0			0
$417$	4.73277	+	10.3633i	0.231765	+	0.507494i
$418$		0			0
$419$	6.23976	+	7.20107i	0.304832	+	0.351795i	0.887411	−	0.460979i	$-0.152502\pi$
$419$	6.23976	+	7.20107i	0.304832	+	0.351795i	−0.582579	+	0.812774i	$0.697956\pi$
$420$		0			0
$421$	−17.7221	−	11.3893i	−0.863725	−	0.555082i	0.0321026	−	0.999485i	$-0.489780\pi$
$421$	−17.7221	−	11.3893i	−0.863725	−	0.555082i	−0.895827	+	0.444402i	$0.853416\pi$
$422$		0			0
$423$	−10.0631	+	11.6134i	−0.489285	+	0.564665i
$424$		0			0
$425$	4.59203	+	31.9383i	0.222746	+	1.54923i
$426$		0			0
$427$	−14.0406	+	9.02333i	−0.679471	+	0.436670i
$428$		0			0
$429$	−0.572912	+	1.25450i	−0.0276604	+	0.0605679i
$430$		0			0
$431$	−13.4879	+	3.96041i	−0.649689	+	0.190766i	−0.589940	−	0.807447i	$-0.700848\pi$
$431$	−13.4879	+	3.96041i	−0.649689	+	0.190766i	−0.0597498	+	0.998213i	$0.519030\pi$
$432$		0			0
$433$	20.6156	+	6.05329i	0.990723	+	0.290902i	0.736644	−	0.676281i	$-0.236409\pi$
$433$	20.6156	+	6.05329i	0.990723	+	0.290902i	0.254079	+	0.967183i	$0.418228\pi$
$434$		0			0
$435$	−2.44368	+	16.9962i	−0.117165	+	0.814903i
$436$		0			0
$437$	1.20369	−	1.46991i	0.0575803	−	0.0703154i
$438$		0			0
$439$	1.79116	−	12.4578i	0.0854873	−	0.594577i	−0.901378	−	0.433033i	$-0.857443\pi$
$439$	1.79116	−	12.4578i	0.0854873	−	0.594577i	0.986865	−	0.161544i	$-0.0516475\pi$
$440$		0			0
$441$	8.21835	+	2.41313i	0.391350	+	0.114911i
$442$		0			0
$443$	−9.95516	+	2.92310i	−0.472984	+	0.138881i	−0.509533	−	0.860451i	$-0.670182\pi$
$443$	−9.95516	+	2.92310i	−0.472984	+	0.138881i	0.0365489	+	0.999332i	$0.488364\pi$
$444$		0			0
$445$	−0.163641	+	0.358324i	−0.00775732	+	0.0169862i
$446$		0			0
$447$	−30.8631	+	19.8345i	−1.45977	+	0.938140i
$448$		0			0
$449$	1.35165	+	9.40096i	0.0637885	+	0.443659i	0.996538	+	0.0831346i	$0.0264931\pi$
$449$	1.35165	+	9.40096i	0.0637885	+	0.443659i	−0.932750	+	0.360524i	$0.882598\pi$
$450$		0			0
$451$	−3.04999	+	3.51987i	−0.143618	+	0.165744i
$452$		0			0
$453$	6.04034	+	3.88189i	0.283800	+	0.182387i
$454$		0			0
$455$	1.16730	+	1.34714i	0.0547239	+	0.0631547i
$456$		0			0
$457$	10.8729	+	23.8084i	0.508614	+	1.11371i	0.973573	+	0.228378i	$0.0733421\pi$
$457$	10.8729	+	23.8084i	0.508614	+	1.11371i	−0.464958	+	0.885333i	$0.653931\pi$
$458$		0			0
$459$	−9.40073			−0.438788
$460$		0			0
$461$	28.4685			1.32591			0.662955	−	0.748660i	$-0.269302\pi$
$461$	28.4685			1.32591			0.662955	+	0.748660i	$0.269302\pi$
$462$		0			0
$463$	1.88083	+	4.11845i	0.0874097	+	0.191401i	0.948289	−	0.317409i	$-0.102813\pi$
$463$	1.88083	+	4.11845i	0.0874097	+	0.191401i	−0.860879	+	0.508810i	$0.830086\pi$
$464$		0			0
$465$	−10.4274	−	12.0339i	−0.483560	−	0.558058i
$466$		0			0
$467$	−18.1318	−	11.6526i	−0.839040	−	0.539218i	0.0490988	−	0.998794i	$-0.484365\pi$
$467$	−18.1318	−	11.6526i	−0.839040	−	0.539218i	−0.888139	+	0.459576i	$0.848001\pi$
$468$		0			0
$469$	−16.3403	+	18.8577i	−0.754525	+	0.870769i
$470$		0			0
$471$	3.03975	+	21.1419i	0.140064	+	0.974167i
$472$		0			0
$473$	−4.73246	+	3.04137i	−0.217599	+	0.139842i
$474$		0			0
$475$	−0.712569	+	1.56031i	−0.0326949	+	0.0715919i
$476$		0			0
$477$	18.2006	−	5.34417i	0.833347	−	0.244693i
$478$		0			0
$479$	2.24179	+	0.658249i	0.102430	+	0.0300762i	0.332546	−	0.943087i	$-0.392092\pi$
$479$	2.24179	+	0.658249i	0.102430	+	0.0300762i	−0.230116	+	0.973163i	$0.573911\pi$
$480$		0			0
$481$	−0.253727	+	1.76471i	−0.0115689	+	0.0804638i
$482$		0			0
$483$	−22.3145	−	13.4779i	−1.01535	−	0.613264i
$484$		0			0
$485$	−0.897119	+	6.23960i	−0.0407361	+	0.283326i
$486$		0			0
$487$	−23.4472	−	6.88473i	−1.06250	−	0.311977i	−0.296640	−	0.954989i	$-0.595866\pi$
$487$	−23.4472	−	6.88473i	−1.06250	−	0.311977i	−0.765856	+	0.643012i	$0.777684\pi$
$488$		0			0
$489$	−29.4559	+	8.64902i	−1.33204	+	0.391122i
$490$		0			0
$491$	−1.54637	+	3.38607i	−0.0697865	+	0.152811i	−0.941311	−	0.337541i	$-0.890405\pi$
$491$	−1.54637	+	3.38607i	−0.0697865	+	0.152811i	0.871524	+	0.490353i	$0.163132\pi$
$492$		0			0
$493$	−51.6004	+	33.1615i	−2.32396	+	1.49352i
$494$		0			0
$495$	−0.215798	−	1.50091i	−0.00969939	−	0.0674607i
$496$		0			0
$497$	−3.47595	+	4.01146i	−0.155917	+	0.179938i
$498$		0			0
$499$	−15.3920	−	9.89181i	−0.689039	−	0.442818i	0.148705	−	0.988882i	$-0.452489\pi$
$499$	−15.3920	−	9.89181i	−0.689039	−	0.442818i	−0.837744	+	0.546063i	$0.816126\pi$
$500$		0			0
$501$	−1.37512	−	1.58698i	−0.0614360	−	0.0709010i
$502$		0			0
$503$	6.75325	+	14.7876i	0.301113	+	0.659344i	0.998345	−	0.0575001i	$-0.0183130\pi$
$503$	6.75325	+	14.7876i	0.301113	+	0.659344i	−0.697233	+	0.716845i	$0.745586\pi$
$504$		0			0
$505$	14.6663			0.652642
$506$		0			0
$507$	30.4743			1.35341
$508$		0			0
$509$	−14.1951	−	31.0830i	−0.629189	−	1.37773i	−0.908644	−	0.417572i	$-0.862881\pi$
$509$	−14.1951	−	31.0830i	−0.629189	−	1.37773i	0.279455	−	0.960159i	$-0.409846\pi$
$510$		0			0
$511$	−7.06052	−	8.14827i	−0.312339	−	0.360458i
$512$		0			0
$513$	−0.420416	−	0.270185i	−0.0185618	−	0.0119290i
$514$		0			0
$515$	1.23239	−	1.42225i	0.0543056	−	0.0626720i
$516$		0			0
$517$	−0.331656	−	2.30672i	−0.0145862	−	0.101449i
$518$		0			0
$519$	17.8431	−	11.4670i	0.783224	−	0.503347i
$520$		0			0
$521$	−10.4059	+	22.7858i	−0.455892	+	0.998264i	0.532513	+	0.846422i	$0.321248\pi$
$521$	−10.4059	+	22.7858i	−0.455892	+	0.998264i	−0.988405	+	0.151842i	$0.951480\pi$
$522$		0			0
$523$	−24.2399	+	7.11747i	−1.05994	+	0.311225i	−0.764825	−	0.644238i	$-0.777175\pi$
$523$	−24.2399	+	7.11747i	−1.05994	+	0.311225i	−0.295111	+	0.955463i	$0.595357\pi$
$524$		0			0
$525$	22.5832	+	6.63104i	0.985614	+	0.289402i
$526$		0			0
$527$	8.09488	−	56.3011i	0.352619	−	2.45252i
$528$		0			0
$529$	−16.0060	−	16.5169i	−0.695914	−	0.718125i
$530$		0			0
$531$	−3.88453	+	27.0175i	−0.168574	+	1.17246i
$532$		0			0
$533$	−8.60803	−	2.52755i	−0.372855	−	0.109480i
$534$		0			0
$535$	2.24188	−	0.658275i	0.0969249	−	0.0284597i
$536$		0			0
$537$	−8.02992	+	17.5831i	−0.346517	+	0.758766i
$538$		0			0
$539$	−1.09276	+	0.702274i	−0.0470685	+	0.0302491i
$540$		0			0
$541$	3.14993	+	21.9082i	0.135426	+	0.941908i	0.938315	+	0.345780i	$0.112386\pi$
$541$	3.14993	+	21.9082i	0.135426	+	0.941908i	−0.802890	+	0.596128i	$0.796705\pi$
$542$		0			0
$543$	−0.467759	+	0.539823i	−0.0200735	+	0.0231660i
$544$		0			0
$545$	−4.20999	−	2.70560i	−0.180336	−	0.115895i
$546$		0			0
$547$	14.4660	+	16.6946i	0.618520	+	0.713810i	0.975425	−	0.220331i	$-0.0707137\pi$
$547$	14.4660	+	16.6946i	0.618520	+	0.713810i	−0.356906	+	0.934140i	$0.616168\pi$
$548$		0			0
$549$	11.3610	+	24.8771i	0.484876	+	1.06173i
$550$		0			0
$551$	−3.26074			−0.138912
$552$		0			0
$553$	−36.7013			−1.56070
$554$		0			0
$555$	−1.51329	−	3.31364i	−0.0642355	−	0.140656i
$556$		0			0
$557$	−5.40104	−	6.23313i	−0.228849	−	0.264106i	0.629699	−	0.776840i	$-0.283178\pi$
$557$	−5.40104	−	6.23313i	−0.228849	−	0.264106i	−0.858548	+	0.512733i	$0.828633\pi$
$558$		0			0
$559$	−9.11591	−	5.85844i	−0.385562	−	0.247786i
$560$		0			0
$561$	6.59189	−	7.60744i	0.278310	−	0.321187i
$562$		0			0
$563$	−2.86724	−	19.9421i	−0.120840	−	0.840458i	−0.956608	−	0.291376i	$-0.905887\pi$
$563$	−2.86724	−	19.9421i	−0.120840	−	0.840458i	0.835769	−	0.549081i	$-0.185022\pi$
$564$		0			0
$565$	7.41399	−	4.76468i	0.311909	−	0.200452i
$566$		0			0
$567$	6.44149	−	14.1049i	0.270517	−	0.592350i
$568$		0			0
$569$	4.94125	−	1.45088i	0.207148	−	0.0608241i	−0.176512	−	0.984298i	$-0.556482\pi$
$569$	4.94125	−	1.45088i	0.207148	−	0.0608241i	0.383660	+	0.923474i	$0.374663\pi$
$570$		0			0
$571$	37.2133	+	10.9268i	1.55733	+	0.457272i	0.943280	−	0.331998i	$-0.107723\pi$
$571$	37.2133	+	10.9268i	1.55733	+	0.457272i	0.614046	+	0.789270i	$0.289541\pi$
$572$		0			0
$573$	1.11868	−	7.78058i	0.0467335	−	0.325038i
$574$		0			0
$575$	17.7751	+	10.7361i	0.741273	+	0.447725i
$576$		0			0
$577$	5.63894	−	39.2197i	0.234752	−	1.63274i	−0.442347	−	0.896844i	$-0.645854\pi$
$577$	5.63894	−	39.2197i	0.234752	−	1.63274i	0.677099	−	0.735892i	$-0.263237\pi$
$578$		0			0
$579$	−55.4780	−	16.2898i	−2.30559	−	0.676981i
$580$		0			0
$581$	19.7227	−	5.79110i	0.818234	−	0.240255i
$582$		0			0
$583$	−1.19503	+	2.61676i	−0.0494932	+	0.108375i
$584$		0			0
$585$	2.45718	−	1.57913i	0.101592	−	0.0652891i
$586$		0			0
$587$	−4.32295	−	30.0668i	−0.178427	−	1.24099i	−0.860403	−	0.509614i	$-0.829788\pi$
$587$	−4.32295	−	30.0668i	−0.178427	−	1.24099i	0.681976	−	0.731374i	$-0.261121\pi$
$588$		0			0
$589$	1.98016	−	2.28522i	0.0815910	−	0.0941610i
$590$		0			0
$591$	−34.3876	−	22.0996i	−1.41452	−	0.909054i
$592$		0			0
$593$	3.46206	+	3.99542i	0.142170	+	0.164072i	0.822369	−	0.568955i	$-0.192652\pi$
$593$	3.46206	+	3.99542i	0.142170	+	0.164072i	−0.680199	+	0.733027i	$0.738107\pi$
$594$		0			0
$595$	−5.40469	−	11.8346i	−0.221571	−	0.485173i
$596$		0			0
$597$	24.4554			1.00089
$598$		0			0
$599$	−23.0512			−0.941846			−0.470923	−	0.882174i	$-0.656079\pi$
$599$	−23.0512			−0.941846			−0.470923	+	0.882174i	$0.656079\pi$
$600$		0			0
$601$	10.2970	+	22.5474i	0.420025	+	0.919726i	0.994841	+	0.101443i	$0.0323461\pi$
$601$	10.2970	+	22.5474i	0.420025	+	0.919726i	−0.574817	+	0.818282i	$0.694927\pi$
$602$		0			0
$603$	26.7754	+	30.9005i	1.09038	+	1.25836i
$604$		0			0
$605$	−7.38129	−	4.74367i	−0.300092	−	0.192858i
$606$		0			0
$607$	3.80519	−	4.39142i	0.154448	−	0.178242i	−0.673252	−	0.739413i	$-0.735103\pi$
$607$	3.80519	−	4.39142i	0.154448	−	0.178242i	0.827700	+	0.561170i	$0.189649\pi$
$608$		0			0
$609$	6.36746	+	44.2867i	0.258023	+	1.79459i
$610$		0			0
$611$	3.77640	−	2.42694i	0.152777	−	0.0981837i
$612$		0			0
$613$	−12.6203	+	27.6347i	−0.509731	+	1.11616i	0.463452	+	0.886122i	$0.346611\pi$
$613$	−12.6203	+	27.6347i	−0.509731	+	1.11616i	−0.973183	+	0.230033i	$0.926117\pi$
$614$		0			0
$615$	17.5884	−	5.16443i	0.709234	−	0.208250i
$616$		0			0
$617$	−13.3794	−	3.92855i	−0.538636	−	0.158158i	0.00108890	−	0.999999i	$-0.499653\pi$
$617$	−13.3794	−	3.92855i	−0.538636	−	0.158158i	−0.539724	+	0.841842i	$0.681472\pi$
$618$		0			0
$619$	4.61548	−	32.1013i	0.185512	−	1.29026i	−0.657946	−	0.753065i	$-0.728574\pi$
$619$	4.61548	−	32.1013i	0.185512	−	1.29026i	0.843457	−	0.537196i	$-0.180517\pi$
$620$		0			0
$621$	−3.83307	+	4.68083i	−0.153816	+	0.187835i
$622$		0			0
$623$	−0.146077	+	1.01599i	−0.00585246	+	0.0407047i
$624$		0			0
$625$	−14.7747	−	4.33824i	−0.590988	−	0.173530i
$626$		0			0
$627$	0.513444	−	0.150761i	0.0205050	−	0.00602081i
$628$		0			0
$629$	5.40572	−	11.8369i	0.215540	−	0.471967i
$630$		0			0
$631$	−40.8078	+	26.2256i	−1.62453	+	1.04402i	−0.671568	+	0.740943i	$0.734379\pi$
$631$	−40.8078	+	26.2256i	−1.62453	+	1.04402i	−0.952965	+	0.303081i	$0.901985\pi$
$632$		0			0
$633$	−8.44948	−	58.7675i	−0.335837	−	2.33580i
$634$		0			0
$635$	−6.91431	+	7.97953i	−0.274386	+	0.316658i
$636$		0			0
$637$	−2.10493	−	1.35276i	−0.0834003	−	0.0535981i
$638$		0			0
$639$	5.69573	+	6.57322i	0.225319	+	0.260032i
$640$		0			0
$641$	−17.1181	−	37.4834i	−0.676125	−	1.48051i	−0.866698	−	0.498834i	$-0.833762\pi$
$641$	−17.1181	−	37.4834i	−0.676125	−	1.48051i	0.190573	−	0.981673i	$-0.438965\pi$
$642$		0			0
$643$	−23.8211			−0.939413			−0.469706	−	0.882823i	$-0.655640\pi$
$643$	−23.8211			−0.939413			−0.469706	+	0.882823i	$0.655640\pi$
$644$		0			0
$645$	22.1410			0.871800
$646$		0			0
$647$	4.28784	+	9.38906i	0.168572	+	0.369122i	0.974998	−	0.222214i	$-0.0713282\pi$
$647$	4.28784	+	9.38906i	0.168572	+	0.369122i	−0.806426	+	0.591335i	$0.798601\pi$
$648$		0			0
$649$	−2.71076	−	3.12839i	−0.106407	−	0.122800i
$650$		0			0
$651$	−34.9042	−	22.4315i	−1.36800	−	0.879162i
$652$		0			0
$653$	−3.64745	+	4.20939i	−0.142736	+	0.164726i	−0.822616	−	0.568597i	$-0.807486\pi$
$653$	−3.64745	+	4.20939i	−0.142736	+	0.164726i	0.679880	+	0.733323i	$0.262032\pi$
$654$		0			0
$655$	−0.340240	−	2.36642i	−0.0132943	−	0.0924636i
$656$		0			0
$657$	−14.8625	+	9.55152i	−0.579840	+	0.372640i
$658$		0			0
$659$	−0.0857979	+	0.187871i	−0.00334221	+	0.00731842i	−0.911296	−	0.411752i	$-0.864917\pi$
$659$	−0.0857979	+	0.187871i	−0.00334221	+	0.00731842i	0.907954	+	0.419071i	$0.137644\pi$
$660$		0			0
$661$	14.4959	−	4.25637i	0.563824	−	0.165554i	0.0126145	−	0.999920i	$-0.495985\pi$
$661$	14.4959	−	4.25637i	0.563824	−	0.165554i	0.551210	+	0.834367i	$0.314166\pi$
$662$		0			0
$663$	18.6044	+	5.46274i	0.722535	+	0.212155i
$664$		0			0
$665$	0.0984305	−	0.684599i	0.00381697	−	0.0265476i
$666$		0			0
$667$	−4.52775	+	39.2143i	−0.175315	+	1.51838i
$668$		0			0
$669$	5.79259	−	40.2883i	0.223954	−	1.55764i
$670$		0			0
$671$	−3.97952	−	1.16849i	−0.153628	−	0.0451092i
$672$		0			0
$673$	−2.43267	+	0.714296i	−0.0937725	+	0.0275341i	−0.328282	−	0.944580i	$-0.606470\pi$
$673$	−2.43267	+	0.714296i	−0.0937725	+	0.0275341i	0.234510	+	0.972114i	$0.424652\pi$
$674$		0			0
$675$	2.26912	−	4.96869i	0.0873386	−	0.191245i
$676$		0			0
$677$	−31.0789	+	19.9732i	−1.19446	+	0.767632i	−0.977989	−	0.208658i	$-0.933090\pi$
$677$	−31.0789	+	19.9732i	−1.19446	+	0.767632i	−0.216469	+	0.976289i	$0.569454\pi$
$678$		0			0
$679$	2.33761	+	16.2585i	0.0897093	+	0.623942i
$680$		0			0
$681$	4.26688	−	4.92425i	0.163507	−	0.188698i
$682$		0			0
$683$	−6.17443	−	3.96807i	−0.236258	−	0.151834i	0.417155	−	0.908835i	$-0.363027\pi$
$683$	−6.17443	−	3.96807i	−0.236258	−	0.151834i	−0.653413	+	0.757001i	$0.726664\pi$
$684$		0			0
$685$	4.93597	+	5.69642i	0.188594	+	0.217649i
$686$		0			0
$687$	19.8163	+	43.3916i	0.756039	+	1.65549i
$688$		0			0
$689$	−5.54129			−0.211106
$690$		0			0
$691$	20.8536			0.793307			0.396654	−	0.917968i	$-0.370171\pi$
$691$	20.8536			0.793307			0.396654	+	0.917968i	$0.370171\pi$
$692$		0			0
$693$	−1.64135	−	3.59405i	−0.0623497	−	0.136527i
$694$		0			0
$695$	2.39630	+	2.76548i	0.0908968	+	0.104901i
$696$		0			0
$697$	55.0864	+	35.4019i	2.08655	+	1.34094i
$698$		0			0
$699$	21.9073	−	25.2824i	0.828612	−	0.956269i
$700$		0			0
$701$	0.110450	+	0.768198i	0.00417165	+	0.0290144i	0.991801	−	0.127792i	$-0.0407891\pi$
$701$	0.110450	+	0.768198i	0.00417165	+	0.0290144i	−0.987629	+	0.156807i	$0.949880\pi$
$702$		0			0
$703$	0.581955	−	0.373999i	0.0219488	−	0.0141057i
$704$		0			0
$705$	−3.81028	+	8.34334i	−0.143503	+	0.314229i
$706$		0			0
$707$	36.6678	−	10.7666i	1.37903	−	0.404921i
$708$		0			0
$709$	−5.67305	−	1.66576i	−0.213056	−	0.0625588i	0.173463	−	0.984840i	$-0.444504\pi$
$709$	−5.67305	−	1.66576i	−0.213056	−	0.0625588i	−0.386519	+	0.922282i	$0.626323\pi$
$710$		0			0
$711$	−8.55869	+	59.5270i	−0.320976	+	2.23244i
$712$		0			0
$713$	−24.7329	−	26.9869i	−0.926256	−	1.01067i
$714$		0			0
$715$	−0.0630398	+	0.438451i	−0.00235755	+	0.0163971i
$716$		0			0
$717$	68.5308	+	20.1225i	2.55933	+	0.751487i
$718$		0			0
$719$	25.2640	−	7.41818i	0.942188	−	0.276651i	0.225657	−	0.974207i	$-0.427547\pi$
$719$	25.2640	−	7.41818i	0.942188	−	0.276651i	0.716531	+	0.697555i	$0.245729\pi$
$720$		0			0
$721$	2.03706	−	4.46054i	0.0758641	−	0.166119i
$722$		0			0
$723$	33.7915	−	21.7165i	1.25672	−	0.807645i
$724$		0			0
$725$	−5.07213	−	35.2775i	−0.188374	−	1.31017i
$726$		0			0
$727$	5.73542	−	6.61902i	0.212715	−	0.245486i	−0.639358	−	0.768909i	$-0.720800\pi$
$727$	5.73542	−	6.61902i	0.212715	−	0.245486i	0.852073	+	0.523423i	$0.175345\pi$
$728$		0			0
$729$	−29.4890	−	18.9514i	−1.09218	−	0.701904i
$730$		0			0
$731$	51.7938	+	59.7732i	1.91566	+	2.21079i
$732$		0			0
$733$	18.2616	+	39.9873i	0.674507	+	1.47696i	0.868361	+	0.495933i	$0.165174\pi$
$733$	18.2616	+	39.9873i	0.674507	+	1.47696i	−0.193854	+	0.981030i	$0.562099\pi$
$734$		0			0
$735$	5.11251			0.188578
$736$		0			0
$737$	−6.20072			−0.228406
$738$		0			0
$739$	−3.27788	−	7.17755i	−0.120579	−	0.264030i	0.839712	−	0.543032i	$-0.182724\pi$
$739$	−3.27788	−	7.17755i	−0.120579	−	0.264030i	−0.960291	+	0.279002i	$0.909996\pi$
$740$		0			0
$741$	0.675015	+	0.779009i	0.0247973	+	0.0286176i
$742$		0			0
$743$	−28.2833	−	18.1766i	−1.03761	−	0.666834i	−0.0932182	−	0.995646i	$-0.529715\pi$
$743$	−28.2833	−	18.1766i	−1.03761	−	0.666834i	−0.944395	+	0.328812i	$0.893352\pi$
$744$		0			0
$745$	−7.71650	+	8.90532i	−0.282711	+	0.326266i
$746$		0			0
$747$	−4.79347	−	33.3393i	−0.175384	−	1.21982i
$748$		0			0
$749$	5.12177	−	3.29156i	0.187145	−	0.120271i
$750$		0			0
$751$	−16.9979	+	37.2203i	−0.620264	+	1.35819i	0.295064	+	0.955478i	$0.404659\pi$
$751$	−16.9979	+	37.2203i	−0.620264	+	1.35819i	−0.915327	+	0.402710i	$0.868068\pi$
$752$		0			0
$753$	−38.1272	+	11.1951i	−1.38943	+	0.407974i
$754$		0			0
$755$	2.21276	+	0.649726i	0.0805307	+	0.0236460i
$756$		0			0
$757$	2.54990	−	17.7349i	0.0926776	−	0.644587i	−0.889542	−	0.456853i	$-0.848977\pi$
$757$	2.54990	−	17.7349i	0.0926776	−	0.644587i	0.982220	−	0.187734i	$-0.0601143\pi$
$758$		0			0
$759$	−1.10013	−	6.38411i	−0.0399321	−	0.231729i
$760$		0			0
$761$	3.61638	−	25.1525i	0.131094	−	0.911777i	−0.813038	−	0.582210i	$-0.802188\pi$
$761$	3.61638	−	25.1525i	0.131094	−	0.911777i	0.944132	−	0.329567i	$-0.106903\pi$
$762$		0			0
$763$	−12.5118	−	3.67378i	−0.452956	−	0.133000i
$764$		0			0
$765$	−20.4553	+	6.00623i	−0.739565	+	0.217156i
$766$		0			0
$767$	3.31236	−	7.25306i	0.119603	−	0.261893i
$768$		0			0
$769$	−23.7903	+	15.2891i	−0.857902	+	0.551340i	−0.894030	−	0.448007i	$-0.852134\pi$
$769$	−23.7903	+	15.2891i	−0.857902	+	0.551340i	0.0361281	+	0.999347i	$0.488498\pi$
$770$		0			0
$771$	1.37720	+	9.57863i	0.0495986	+	0.344966i
$772$		0			0
$773$	26.3311	−	30.3877i	0.947064	−	1.09297i	−0.0484945	−	0.998823i	$-0.515442\pi$
$773$	26.3311	−	30.3877i	0.947064	−	1.09297i	0.995558	−	0.0941465i	$-0.0300122\pi$
$774$		0			0
$775$	27.8036	+	17.8683i	0.998736	+	0.641849i
$776$		0			0
$777$	−6.21600	−	7.17364i	−0.222998	−	0.257353i
$778$		0			0
$779$	1.44607	+	3.16646i	0.0518109	+	0.113450i
$780$		0			0
$781$	−1.31903			−0.0471986
$782$		0			0
$783$	10.3836			0.371079
$784$		0			0
$785$	2.84989	+	6.24039i	0.101717	+	0.222729i
$786$		0			0
$787$	25.9450	+	29.9422i	0.924840	+	1.06732i	0.997549	+	0.0699694i	$0.0222902\pi$
$787$	25.9450	+	29.9422i	0.924840	+	1.06732i	−0.0727088	+	0.997353i	$0.523164\pi$
$788$		0			0
$789$	32.5278	+	20.9044i	1.15802	+	0.744215i
$790$		0			0
$791$	15.0382	−	17.3550i	0.534697	−	0.617074i
$792$		0			0
$793$	−1.13698	−	7.90786i	−0.0403753	−	0.280816i
$794$		0			0
$795$	9.52492	−	6.12129i	0.337814	−	0.217100i
$796$		0			0
$797$	−2.53391	+	5.54849i	−0.0897558	+	0.196538i	−0.949186	−	0.314715i	$-0.898091\pi$
$797$	−2.53391	+	5.54849i	−0.0897558	+	0.196538i	0.859430	+	0.511253i	$0.170818\pi$
$798$		0			0
$799$	−31.4375	+	9.23089i	−1.11218	+	0.326565i
$800$		0			0
$801$	1.61380	+	0.473855i	0.0570208	+	0.0167428i
$802$		0			0
$803$	0.381302	−	2.65201i	0.0134558	−	0.0935875i
$804$		0			0
$805$	−8.09644	−	2.13435i	−0.285362	−	0.0752260i
$806$		0			0
$807$	−0.123151	+	0.856534i	−0.00433512	+	0.0301514i
$808$		0			0
$809$	22.3102	+	6.55085i	0.784384	+	0.230316i	0.649314	−	0.760520i	$-0.275056\pi$
$809$	22.3102	+	6.55085i	0.784384	+	0.230316i	0.135069	+	0.990836i	$0.456874\pi$
$810$		0			0
$811$	−49.4192	+	14.5108i	−1.73534	+	0.509542i	−0.987941	−	0.154831i	$-0.950517\pi$
$811$	−49.4192	+	14.5108i	−1.73534	+	0.509542i	−0.747401	+	0.664373i	$0.768699\pi$
$812$		0			0
$813$	13.9731	−	30.5967i	0.490057	−	1.07307i
$814$		0			0
$815$	−8.29499	+	5.33087i	−0.290561	+	0.186732i
$816$		0			0
$817$	0.598369	+	4.16175i	0.0209343	+	0.145601i
$818$		0			0
$819$	4.98403	−	5.75188i	0.174156	−	0.200987i
$820$		0			0
$821$	36.9545	+	23.7492i	1.28972	+	0.828853i	0.992053	−	0.125817i	$-0.0401554\pi$
$821$	36.9545	+	23.7492i	1.28972	+	0.828853i	0.297666	+	0.954670i	$0.403792\pi$
$822$		0			0
$823$	−7.89053	−	9.10616i	−0.275047	−	0.317421i	0.601373	−	0.798968i	$-0.294620\pi$
$823$	−7.89053	−	9.10616i	−0.275047	−	0.317421i	−0.876420	+	0.481547i	$0.840075\pi$
$824$		0			0
$825$	2.42973	+	5.32036i	0.0845923	+	0.185231i
$826$		0			0
$827$	30.8000			1.07102			0.535510	−	0.844529i	$-0.320119\pi$
$827$	30.8000			1.07102			0.535510	+	0.844529i	$0.320119\pi$
$828$		0			0
$829$	−28.3389			−0.984252			−0.492126	−	0.870524i	$-0.663780\pi$
$829$	−28.3389			−0.984252			−0.492126	+	0.870524i	$0.663780\pi$
$830$		0			0
$831$	12.1133	+	26.5244i	0.420206	+	0.920123i
$832$		0			0
$833$	11.9596	+	13.8021i	0.414374	+	0.478213i
$834$		0			0
$835$	−0.567386	−	0.364637i	−0.0196352	−	0.0126188i
$836$		0			0
$837$	−6.30567	+	7.27713i	−0.217956	+	0.251534i
$838$		0			0
$839$	0.633840	+	4.40845i	0.0218826	+	0.152197i	0.997833	−	0.0657953i	$-0.0209584\pi$
$839$	0.633840	+	4.40845i	0.0218826	+	0.152197i	−0.975951	+	0.217992i	$0.930049\pi$
$840$		0			0
$841$	32.5989	−	20.9501i	1.12410	−	0.722416i
$842$		0			0
$843$	31.4125	−	68.7837i	1.08190	−	2.36904i
$844$		0			0
$845$	9.39149	−	2.75759i	0.323077	−	0.0948640i
$846$		0			0
$847$	−21.9366	−	6.44117i	−0.753751	−	0.221321i
$848$		0			0
$849$	−8.13378	+	56.5717i	−0.279151	+	1.94154i
$850$		0			0
$851$	−3.68971	−	7.51801i	−0.126481	−	0.257714i
$852$		0			0
$853$	0.683372	−	4.75296i	0.0233982	−	0.162738i	−0.974772	−	0.223202i	$-0.928349\pi$
$853$	0.683372	−	4.75296i	0.0233982	−	0.162738i	0.998170	+	0.0604641i	$0.0192581\pi$
$854$		0			0
$855$	−1.08742	−	0.319295i	−0.0371890	−	0.0109197i
$856$		0			0
$857$	−7.84256	+	2.30278i	−0.267897	+	0.0786616i	−0.412922	−	0.910766i	$-0.635492\pi$
$857$	−7.84256	+	2.30278i	−0.267897	+	0.0786616i	0.145025	+	0.989428i	$0.453674\pi$
$858$		0			0
$859$	1.79138	−	3.92257i	0.0611211	−	0.133836i	−0.876607	−	0.481208i	$-0.840198\pi$
$859$	1.79138	−	3.92257i	0.0611211	−	0.133836i	0.937728	+	0.347371i	$0.112926\pi$
$860$		0			0
$861$	40.1823	−	25.8236i	1.36941	−	0.880066i
$862$		0			0
$863$	−1.08989	−	7.58037i	−0.0371004	−	0.258039i	0.962827	−	0.270120i	$-0.0870634\pi$
$863$	−1.08989	−	7.58037i	−0.0371004	−	0.258039i	−0.999927	+	0.0120814i	$0.996154\pi$
$864$		0			0
$865$	4.46119	−	5.14849i	0.151685	−	0.175054i
$866$		0			0
$867$	−82.6100	−	53.0903i	−2.80558	−	1.80304i
$868$		0			0
$869$	−5.97256	−	6.89271i	−0.202605	−	0.233819i
$870$		0			0
$871$	−4.96178	−	10.8648i	−0.168123	−	0.368139i
$872$		0			0
$873$	26.9152			0.910943
$874$		0			0
$875$	16.2892			0.550675
$876$		0			0
$877$	3.83407	+	8.39544i	0.129467	+	0.283494i	0.963254	−	0.268593i	$-0.0865588\pi$
$877$	3.83407	+	8.39544i	0.129467	+	0.283494i	−0.833786	+	0.552087i	$0.813832\pi$
$878$		0			0
$879$	−48.4211	−	55.8810i	−1.63320	−	1.88482i
$880$		0			0
$881$	−9.02837	−	5.80218i	−0.304173	−	0.195480i	0.379646	−	0.925132i	$-0.376046\pi$
$881$	−9.02837	−	5.80218i	−0.304173	−	0.195480i	−0.683819	+	0.729652i	$0.739682\pi$
$882$		0			0
$883$	19.0765	−	22.0154i	0.641975	−	0.740878i	−0.337748	−	0.941237i	$-0.609665\pi$
$883$	19.0765	−	22.0154i	0.641975	−	0.740878i	0.979723	+	0.200358i	$0.0642106\pi$
$884$		0			0
$885$	2.31862	+	16.1264i	0.0779395	+	0.542081i
$886$		0			0
$887$	18.3722	−	11.8071i	0.616877	−	0.396443i	−0.194553	−	0.980892i	$-0.562326\pi$
$887$	18.3722	−	11.8071i	0.616877	−	0.396443i	0.811430	+	0.584449i	$0.198689\pi$
$888$		0			0
$889$	−11.4289	+	25.0258i	−0.383313	+	0.839338i
$890$		0			0
$891$	3.69723	−	1.08561i	0.123862	−	0.0363692i
$892$		0			0
$893$	−1.67124	−	0.490720i	−0.0559259	−	0.0164213i
$894$		0			0
$895$	−0.883565	+	6.14533i	−0.0295343	+	0.205416i
$896$		0			0
$897$	10.3058	−	7.03615i	0.344101	−	0.234930i
$898$		0			0
$899$	−8.94122	+	62.1875i	−0.298206	+	2.07407i
$900$		0			0
$901$	38.8068	+	11.3947i	1.29284	+	0.379613i
$902$		0			0
$903$	55.3555	−	16.2538i	1.84212	−	0.540894i
$904$		0			0
$905$	−0.0953048	+	0.208688i	−0.00316804	+	0.00693704i
$906$		0			0
$907$	2.06087	−	1.32444i	0.0684301	−	0.0439774i	−0.505978	−	0.862546i	$-0.668868\pi$
$907$	2.06087	−	1.32444i	0.0684301	−	0.0439774i	0.574409	+	0.818569i	$0.305232\pi$
$908$		0			0
$909$	−8.91188	−	61.9835i	−0.295588	−	2.05586i
$910$		0			0
$911$	−19.5150	+	22.5215i	−0.646560	+	0.746171i	−0.980521	−	0.196417i	$-0.937069\pi$
$911$	−19.5150	+	22.5215i	−0.646560	+	0.746171i	0.333960	+	0.942587i	$0.391615\pi$
$912$		0			0
$913$	4.29716	+	2.76162i	0.142215	+	0.0913962i
$914$		0			0
$915$	10.6899	+	12.3368i	0.353398	+	0.407843i
$916$		0			0
$917$	−2.58785	−	5.66660i	−0.0854584	−	0.187128i
$918$		0			0
$919$	−23.8700			−0.787398			−0.393699	−	0.919239i	$-0.628805\pi$
$919$	−23.8700			−0.787398			−0.393699	+	0.919239i	$0.628805\pi$
$920$		0			0
$921$	1.45932			0.0480861
$922$		0			0
$923$	−1.05548	−	2.31118i	−0.0347415	−	0.0760734i
$924$		0			0
$925$	4.95148	+	5.71431i	0.162804	+	0.187886i
$926$		0			0
$927$	−6.75966	−	4.34417i	−0.222016	−	0.142681i
$928$		0			0
$929$	−8.40708	+	9.70228i	−0.275827	+	0.318322i	−0.876713	−	0.481013i	$-0.840269\pi$
$929$	−8.40708	+	9.70228i	−0.275827	+	0.318322i	0.600886	+	0.799335i	$0.294814\pi$
$930$		0			0
$931$	0.138168	+	0.960978i	0.00452827	+	0.0314948i
$932$		0			0
$933$	−46.3218	+	29.7692i	−1.51651	+	0.974601i
$934$		0			0
$935$	1.34308	−	2.94094i	0.0439234	−	0.0961789i
$936$		0			0
$937$	33.3091	−	9.78044i	1.08816	−	0.319513i	0.312022	−	0.950075i	$-0.398994\pi$
$937$	33.3091	−	9.78044i	1.08816	−	0.319513i	0.776139	+	0.630562i	$0.217175\pi$
$938$		0			0
$939$	12.1572	+	3.56969i	0.396736	+	0.116492i
$940$		0			0
$941$	1.00640	−	6.99964i	0.0328076	−	0.228182i	−0.966820	−	0.255457i	$-0.917774\pi$
$941$	1.00640	−	6.99964i	0.0328076	−	0.228182i	0.999628	+	0.0272753i	$0.00868309\pi$
$942$		0			0
$943$	40.0884	−	12.9939i	1.30546	−	0.423140i
$944$		0			0
$945$	−0.313445	+	2.18006i	−0.0101964	+	0.0709172i
$946$		0			0
$947$	−4.47533	−	1.31408i	−0.145429	−	0.0427017i	0.208208	−	0.978085i	$-0.433237\pi$
$947$	−4.47533	−	1.31408i	−0.145429	−	0.0427017i	−0.353637	+	0.935383i	$0.615055\pi$
$948$		0			0
$949$	4.95192	−	1.45401i	0.160746	−	0.0471993i
$950$		0			0
$951$	30.4471	−	66.6698i	0.987314	−	2.16192i
$952$		0			0
$953$	−22.0194	+	14.1510i	−0.713277	+	0.458395i	−0.846292	−	0.532719i	$-0.821170\pi$
$953$	−22.0194	+	14.1510i	−0.713277	+	0.458395i	0.133015	+	0.991114i	$0.457534\pi$
$954$		0			0
$955$	−0.359306	−	2.49903i	−0.0116269	−	0.0808666i
$956$		0			0
$957$	−7.28108	+	8.40282i	−0.235364	+	0.271625i
$958$		0			0
$959$	16.5224	+	10.6183i	0.533536	+	0.342883i
$960$		0			0
$961$	−17.8524	−	20.6028i	−0.575884	−	0.664605i
$962$		0			0
$963$	−4.14430	−	9.07475i	−0.133548	−	0.292430i
$964$		0			0
$965$	−18.5711			−0.597825
$966$		0			0
$967$	8.44710			0.271640			0.135820	−	0.990734i	$-0.456633\pi$
$967$	8.44710			0.271640			0.135820	+	0.990734i	$0.456633\pi$
$968$		0			0
$969$	−3.12537	−	6.84361i	−0.100401	−	0.219849i
$970$		0			0
$971$	−15.5276	−	17.9198i	−0.498305	−	0.575075i	0.449761	−	0.893149i	$-0.351509\pi$
$971$	−15.5276	−	17.9198i	−0.498305	−	0.575075i	−0.948066	+	0.318074i	$0.896964\pi$
$972$		0			0
$973$	8.02123	+	5.15493i	0.257149	+	0.165260i
$974$		0			0
$975$	−7.37798	+	8.51464i	−0.236284	+	0.272687i
$976$		0			0
$977$	−4.36614	−	30.3672i	−0.139685	−	0.971533i	−0.932268	−	0.361768i	$-0.882173\pi$
$977$	−4.36614	−	30.3672i	−0.139685	−	0.971533i	0.792583	−	0.609764i	$-0.208736\pi$
$978$		0			0
$979$	−0.214580	+	0.137902i	−0.00685801	+	0.00440738i
$980$		0			0
$981$	−8.87635	+	19.4365i	−0.283400	+	0.620560i
$982$		0			0
$983$	10.1230	−	2.97238i	0.322874	−	0.0948043i	−0.116279	−	0.993217i	$-0.537097\pi$
$983$	10.1230	−	2.97238i	0.322874	−	0.0948043i	0.439153	+	0.898412i	$0.355279\pi$
$984$		0			0
$985$	−12.5972	−	3.69888i	−0.401382	−	0.117856i
$986$		0			0
$987$	−3.40132	+	23.6567i	−0.108265	+	0.753000i
$988$		0			0
$989$	50.8808	−	1.41725i	1.61792	−	0.0450658i
$990$		0			0
$991$	6.24422	−	43.4295i	0.198354	−	1.37958i	−0.610706	−	0.791858i	$-0.709114\pi$
$991$	6.24422	−	43.4295i	0.198354	−	1.37958i	0.809060	−	0.587726i	$-0.199977\pi$
$992$		0			0
$993$	−37.6103	−	11.0434i	−1.19353	−	0.350451i
$994$		0			0
$995$	7.53660	−	2.21295i	0.238926	−	0.0701551i
$996$		0			0
$997$	−22.7695	+	49.8583i	−0.721118	+	1.57903i	0.0912124	+	0.995831i	$0.470926\pi$
$997$	−22.7695	+	49.8583i	−0.721118	+	1.57903i	−0.812331	+	0.583197i	$0.801802\pi$
$998$		0			0
$999$	−1.85319	+	1.19097i	−0.0586324	+	0.0376807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.353.1		30
4.3	odd	2		184.2.i.b.169.3	yes	30
23.3	even	11	inner	368.2.m.e.49.1		30
23.7	odd	22		8464.2.a.ch.1.2		15
23.16	even	11		8464.2.a.cg.1.2		15
92.3	odd	22		184.2.i.b.49.3	✓	30
92.7	even	22		4232.2.a.ba.1.14		15
92.39	odd	22		4232.2.a.bb.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.49.3	✓	30	92.3	odd	22
184.2.i.b.169.3	yes	30	4.3	odd	2
368.2.m.e.49.1		30	23.3	even	11	inner
368.2.m.e.353.1		30	1.1	even	1	trivial
4232.2.a.ba.1.14		15	92.7	even	22
4232.2.a.bb.1.14		15	92.39	odd	22
8464.2.a.cg.1.2		15	23.16	even	11
8464.2.a.ch.1.2		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05870 - 2.31822i) q^{3} +(-0.536040 - 0.618623i) q^{5} +(-1.79431 - 1.15313i) q^{7} +(-2.28874 + 2.64134i) q^{9} +O(q^{10})\)	\(q+(-1.05870 - 2.31822i) q^{3} +(-0.536040 - 0.618623i) q^{5} +(-1.79431 - 1.15313i) q^{7} +(-2.28874 + 2.64134i) q^{9} +(-0.0754313 - 0.524636i) q^{11} +(0.858898 - 0.551980i) q^{13} +(-0.866603 + 1.89760i) q^{15} +(-7.15009 + 2.09946i) q^{17} +(-0.380104 - 0.111609i) q^{19} +(-0.773589 + 5.38043i) q^{21} +(-1.87002 + 4.41622i) q^{23} +(0.616218 - 4.28589i) q^{25} +(1.21041 + 0.355409i) q^{27} +(7.89765 - 2.31896i) q^{29} +(-3.17083 + 6.94314i) q^{31} +(-1.13637 + 0.730297i) q^{33} +(0.248467 + 1.72813i) q^{35} +(-1.14354 + 1.31971i) q^{37} +(-2.18892 - 1.40674i) q^{39} +(-5.75435 - 6.64088i) q^{41} +(-4.40901 - 9.65438i) q^{43} +2.86085 q^{45} +4.39680 q^{47} +(-1.01807 - 2.22927i) q^{49} +(12.4368 + 14.3528i) q^{51} +(-4.56587 - 2.93430i) q^{53} +(-0.284118 + 0.327890i) q^{55} +(0.143681 + 0.999325i) q^{57} +(6.57004 - 4.22231i) q^{59} +(3.25065 - 7.11792i) q^{61} +(7.15252 - 2.10017i) q^{63} +(-0.801871 - 0.235451i) q^{65} +(1.66491 - 11.5797i) q^{67} +(12.2176 - 0.340311i) q^{69} +(0.354163 - 2.46326i) q^{71} +(4.85019 + 1.42414i) q^{73} +(-10.5880 + 3.10893i) q^{75} +(-0.469628 + 1.02834i) q^{77} +(14.4756 - 9.30292i) q^{79} +(1.03463 + 7.19599i) q^{81} +(-6.31106 + 7.28335i) q^{83} +(5.13151 + 3.29782i) q^{85} +(-13.7371 - 15.8534i) q^{87} +(-0.199914 - 0.437751i) q^{89} -2.17764 q^{91} +19.4527 q^{93} +(0.134707 + 0.294968i) q^{95} +(-5.04314 - 5.82009i) q^{97} +(1.55839 + 1.00151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

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