LMFDB - Embedded newform 936.2.j.a.755.40

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.40
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15766 + 0.812299i) q^{2} +(0.680340 + 1.88073i) q^{4} +3.23777 q^{5} -4.33596i q^{7} +(-0.740114 + 2.72988i) q^{8} +(3.74823 + 2.63004i) q^{10} +1.18715i q^{11} +1.00000i q^{13} +(3.52210 - 5.01956i) q^{14} +(-3.07428 + 2.55907i) q^{16} +0.0944593i q^{17} +2.27921 q^{19} +(2.20279 + 6.08937i) q^{20} +(-0.964320 + 1.37431i) q^{22} +7.64873 q^{23} +5.48318 q^{25} +(-0.812299 + 1.15766i) q^{26} +(8.15477 - 2.94993i) q^{28} -4.80155 q^{29} -7.57575i q^{31} +(-5.63769 + 0.465290i) q^{32} +(-0.0767292 + 0.109351i) q^{34} -14.0389i q^{35} +11.6373i q^{37} +(2.63854 + 1.85140i) q^{38} +(-2.39632 + 8.83872i) q^{40} -3.47950i q^{41} -9.77740 q^{43} +(-2.23270 + 0.807664i) q^{44} +(8.85461 + 6.21306i) q^{46} -1.62643 q^{47} -11.8006 q^{49} +(6.34764 + 4.45398i) q^{50} +(-1.88073 + 0.680340i) q^{52} +10.5857 q^{53} +3.84372i q^{55} +(11.8366 + 3.20911i) q^{56} +(-5.55854 - 3.90029i) q^{58} -5.55495i q^{59} +8.82142i q^{61} +(6.15378 - 8.77013i) q^{62} +(-6.90446 - 4.04084i) q^{64} +3.23777i q^{65} +0.890006 q^{67} +(-0.177652 + 0.0642644i) q^{68} +(11.4038 - 16.2522i) q^{70} -5.75108 q^{71} -13.0699 q^{73} +(-9.45295 + 13.4720i) q^{74} +(1.55063 + 4.28657i) q^{76} +5.14743 q^{77} +15.1770i q^{79} +(-9.95381 + 8.28568i) q^{80} +(2.82640 - 4.02807i) q^{82} -6.08355i q^{83} +0.305838i q^{85} +(-11.3189 - 7.94217i) q^{86} +(-3.24077 - 0.878625i) q^{88} +2.52869i q^{89} +4.33596 q^{91} +(5.20374 + 14.3852i) q^{92} +(-1.88285 - 1.32115i) q^{94} +7.37955 q^{95} -17.4724 q^{97} +(-13.6610 - 9.58559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.15766	+	0.812299i	0.818587	+	0.574382i
$2$	1.15766	+	0.812299i	0.818587	+	0.574382i
$3$		0			0
$3$		0			0
$4$	0.680340	+	1.88073i	0.340170	+	0.940364i
$5$	3.23777			1.44798			0.723988	−	0.689812i	$-0.242307\pi$
$5$	3.23777			1.44798			0.723988	+	0.689812i	$0.242307\pi$
$6$		0			0
$7$		−	4.33596i		−	1.63884i	−0.573194	−	0.819420i	$-0.694296\pi$
$7$		−	4.33596i		−	1.63884i	0.573194	−	0.819420i	$-0.305704\pi$
$8$	−0.740114	+	2.72988i	−0.261670	+	0.965157i
$9$		0			0
$10$	3.74823	+	2.63004i	1.18529	+	0.831692i
$11$			1.18715i			0.357939i	0.983855	+	0.178969i	$0.0572763\pi$
$11$			1.18715i			0.357939i	−0.983855	+	0.178969i	$0.942724\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	3.52210	−	5.01956i	0.941321	−	1.34153i
$15$		0			0
$16$	−3.07428	+	2.55907i	−0.768569	+	0.639767i
$17$			0.0944593i			0.0229097i	0.999934	+	0.0114549i	$0.00364628\pi$
$17$			0.0944593i			0.0229097i	−0.999934	+	0.0114549i	$0.996354\pi$
$18$		0			0
$19$	2.27921			0.522886			0.261443	−	0.965219i	$-0.415802\pi$
$19$	2.27921			0.522886			0.261443	+	0.965219i	$0.415802\pi$
$20$	2.20279	+	6.08937i	0.492558	+	1.36162i
$21$		0			0
$22$	−0.964320	+	1.37431i	−0.205594	+	0.293004i
$23$	7.64873			1.59487			0.797436	−	0.603404i	$-0.206189\pi$
$23$	7.64873			1.59487			0.797436	+	0.603404i	$0.206189\pi$
$24$		0			0
$25$	5.48318			1.09664
$26$	−0.812299	+	1.15766i	−0.159305	+	0.227035i
$27$		0			0
$28$	8.15477	−	2.94993i	1.54111	−	0.557484i
$29$	−4.80155			−0.891625			−0.445812	−	0.895126i	$-0.647085\pi$
$29$	−4.80155			−0.891625			−0.445812	+	0.895126i	$0.647085\pi$
$30$		0			0
$31$		−	7.57575i		−	1.36065i	−0.732913	−	0.680323i	$-0.761840\pi$
$31$		−	7.57575i		−	1.36065i	0.732913	−	0.680323i	$-0.238160\pi$
$32$	−5.63769	+	0.465290i	−0.996612	+	0.0822525i
$33$		0			0
$34$	−0.0767292	+	0.109351i	−0.0131590	+	0.0187536i
$35$		−	14.0389i		−	2.37300i
$36$		0			0
$37$			11.6373i			1.91316i	0.291478	+	0.956578i	$0.405853\pi$
$37$			11.6373i			1.91316i	−0.291478	+	0.956578i	$0.594147\pi$
$38$	2.63854	+	1.85140i	0.428027	+	0.300336i
$39$		0			0
$40$	−2.39632	+	8.83872i	−0.378892	+	1.39753i
$41$		−	3.47950i		−	0.543407i	−0.962381	−	0.271703i	$-0.912413\pi$
$41$		−	3.47950i		−	0.543407i	0.962381	−	0.271703i	$-0.0875870\pi$
$42$		0			0
$43$	−9.77740			−1.49104			−0.745520	−	0.666484i	$-0.767799\pi$
$43$	−9.77740			−1.49104			−0.745520	+	0.666484i	$0.767799\pi$
$44$	−2.23270	+	0.807664i	−0.336593	+	0.121760i
$45$		0			0
$46$	8.85461	+	6.21306i	1.30554	+	0.916066i
$47$	−1.62643			−0.237239			−0.118620	−	0.992940i	$-0.537847\pi$
$47$	−1.62643			−0.237239			−0.118620	+	0.992940i	$0.537847\pi$
$48$		0			0
$49$	−11.8006			−1.68580
$50$	6.34764	+	4.45398i	0.897691	+	0.629888i
$51$		0			0
$52$	−1.88073	+	0.680340i	−0.260810	+	0.0943461i
$53$	10.5857			1.45406			0.727032	−	0.686604i	$-0.240899\pi$
$53$	10.5857			1.45406			0.727032	+	0.686604i	$0.240899\pi$
$54$		0			0
$55$			3.84372i			0.518287i
$56$	11.8366	+	3.20911i	1.58174	+	0.428835i
$57$		0			0
$58$	−5.55854	−	3.90029i	−0.729873	−	0.512134i
$59$		−	5.55495i		−	0.723193i	−0.932335	−	0.361596i	$-0.882232\pi$
$59$		−	5.55495i		−	0.723193i	0.932335	−	0.361596i	$-0.117768\pi$
$60$		0			0
$61$			8.82142i			1.12947i	0.825273	+	0.564734i	$0.191021\pi$
$61$			8.82142i			1.12947i	−0.825273	+	0.564734i	$0.808979\pi$
$62$	6.15378	−	8.77013i	0.781531	−	1.11381i
$63$		0			0
$64$	−6.90446	−	4.04084i	−0.863058	−	0.505105i
$65$			3.23777i			0.401596i
$66$		0			0
$67$	0.890006			0.108732			0.0543658	−	0.998521i	$-0.482686\pi$
$67$	0.890006			0.108732			0.0543658	+	0.998521i	$0.482686\pi$
$68$	−0.177652	+	0.0642644i	−0.0215435	+	0.00779320i
$69$		0			0
$70$	11.4038	−	16.2522i	1.36301	−	1.94251i
$71$	−5.75108			−0.682528			−0.341264	−	0.939968i	$-0.610855\pi$
$71$	−5.75108			−0.682528			−0.341264	+	0.939968i	$0.610855\pi$
$72$		0			0
$73$	−13.0699			−1.52972			−0.764859	−	0.644197i	$-0.777191\pi$
$73$	−13.0699			−1.52972			−0.764859	+	0.644197i	$0.777191\pi$
$74$	−9.45295	+	13.4720i	−1.09888	+	1.56608i
$75$		0			0
$76$	1.55063	+	4.28657i	0.177870	+	0.491703i
$77$	5.14743			0.586604
$78$		0			0
$79$			15.1770i			1.70754i	0.520646	+	0.853772i	$0.325691\pi$
$79$			15.1770i			1.70754i	−0.520646	+	0.853772i	$0.674309\pi$
$80$	−9.95381	+	8.28568i	−1.11287	+	0.926367i
$81$		0			0
$82$	2.82640	−	4.02807i	0.312123	−	0.444826i
$83$		−	6.08355i		−	0.667756i	−0.942616	−	0.333878i	$-0.891643\pi$
$83$		−	6.08355i		−	0.667756i	0.942616	−	0.333878i	$-0.108357\pi$
$84$		0			0
$85$			0.305838i			0.0331728i
$86$	−11.3189	−	7.94217i	−1.22055	−	0.856427i
$87$		0			0
$88$	−3.24077	−	0.878625i	−0.345467	−	0.0936617i
$89$			2.52869i			0.268041i	0.990979	+	0.134020i	$0.0427887\pi$
$89$			2.52869i			0.268041i	−0.990979	+	0.134020i	$0.957211\pi$
$90$		0			0
$91$	4.33596			0.454532
$92$	5.20374	+	14.3852i	0.542527	+	1.49976i
$93$		0			0
$94$	−1.88285	−	1.32115i	−0.194201	−	0.136266i
$95$	7.37955			0.757126
$96$		0			0
$97$	−17.4724			−1.77406			−0.887028	−	0.461716i	$-0.847234\pi$
$97$	−17.4724			−1.77406			−0.887028	+	0.461716i	$0.847234\pi$
$98$	−13.6610	−	9.58559i	−1.37997	−	0.968291i
$99$		0			0
$100$	3.73042	+	10.3124i	0.373042	+	1.03124i
$101$	−7.24871			−0.721273			−0.360637	−	0.932706i	$-0.617441\pi$
$101$	−7.24871			−0.721273			−0.360637	+	0.932706i	$0.617441\pi$
$102$		0			0
$103$			0.154510i			0.0152243i	0.999971	+	0.00761215i	$0.00242305\pi$
$103$			0.154510i			0.0152243i	−0.999971	+	0.00761215i	$0.997577\pi$
$104$	−2.72988	−	0.740114i	−0.267687	−	0.0725742i
$105$		0			0
$106$	12.2547	+	8.59879i	1.19028	+	0.835188i
$107$			2.14804i			0.207659i	0.994595	+	0.103829i	$0.0331096\pi$
$107$			2.14804i			0.207659i	−0.994595	+	0.103829i	$0.966890\pi$
$108$		0			0
$109$		−	12.8734i		−	1.23305i	−0.787337	−	0.616523i	$-0.788541\pi$
$109$		−	12.8734i		−	1.23305i	0.787337	−	0.616523i	$-0.211459\pi$
$110$	−3.12225	+	4.44971i	−0.297695	+	0.424263i
$111$		0			0
$112$	11.0960	+	13.3299i	1.04848	+	1.25956i
$113$		−	6.38438i		−	0.600592i	−0.953846	−	0.300296i	$-0.902915\pi$
$113$		−	6.38438i		−	0.600592i	0.953846	−	0.300296i	$-0.0970854\pi$
$114$		0			0
$115$	24.7649			2.30934
$116$	−3.26668	−	9.03040i	−0.303304	−	0.838452i
$117$		0			0
$118$	4.51228	−	6.43073i	0.415389	−	0.591996i
$119$	0.409572			0.0375454
$120$		0			0
$121$	9.59068			0.871880
$122$	−7.16563	+	10.2122i	−0.648746	+	0.924567i
$123$		0			0
$124$	14.2479	−	5.15409i	1.27950	−	0.462851i
$125$	1.56441			0.139925
$126$		0			0
$127$		−	8.10854i		−	0.719517i	−0.933045	−	0.359758i	$-0.882859\pi$
$127$		−	8.10854i		−	0.719517i	0.933045	−	0.359758i	$-0.117141\pi$
$128$	−4.71063	−	10.2864i	−0.416364	−	0.909198i
$129$		0			0
$130$	−2.63004	+	3.74823i	−0.230670	+	0.328742i
$131$		−	14.9127i		−	1.30293i	−0.758679	−	0.651465i	$-0.774155\pi$
$131$		−	14.9127i		−	1.30293i	0.758679	−	0.651465i	$-0.225845\pi$
$132$		0			0
$133$		−	9.88255i		−	0.856926i
$134$	1.03032	+	0.722951i	0.0890063	+	0.0624535i
$135$		0			0
$136$	−0.257862	−	0.0699107i	−0.0221115	−	0.00599479i
$137$			7.27430i			0.621486i	0.950494	+	0.310743i	$0.100578\pi$
$137$			7.27430i			0.621486i	−0.950494	+	0.310743i	$0.899422\pi$
$138$		0			0
$139$	0.428209			0.0363202			0.0181601	−	0.999835i	$-0.494219\pi$
$139$	0.428209			0.0363202			0.0181601	+	0.999835i	$0.494219\pi$
$140$	26.4033	−	9.55119i	2.23148	−	0.807223i
$141$		0			0
$142$	−6.65778	−	4.67160i	−0.558708	−	0.392032i
$143$	−1.18715			−0.0992743
$144$		0			0
$145$	−15.5463			−1.29105
$146$	−15.1305	−	10.6167i	−1.25221	−	0.878643i
$147$		0			0
$148$	−21.8865	+	7.91730i	−1.79906	+	0.650798i
$149$	11.5923			0.949682			0.474841	−	0.880072i	$-0.342506\pi$
$149$	11.5923			0.949682			0.474841	+	0.880072i	$0.342506\pi$
$150$		0			0
$151$		−	7.87771i		−	0.641079i	−0.947235	−	0.320540i	$-0.896136\pi$
$151$		−	7.87771i		−	0.641079i	0.947235	−	0.320540i	$-0.103864\pi$
$152$	−1.68687	+	6.22195i	−0.136823	+	0.504667i
$153$		0			0
$154$	5.95896	+	4.18125i	0.480186	+	0.336935i
$155$		−	24.5286i		−	1.97018i
$156$		0			0
$157$			3.66776i			0.292719i	0.989231	+	0.146360i	$0.0467557\pi$
$157$			3.66776i			0.292719i	−0.989231	+	0.146360i	$0.953244\pi$
$158$	−12.3283	+	17.5698i	−0.980784	+	1.39777i
$159$		0			0
$160$	−18.2535	+	1.50650i	−1.44307	+	0.119100i
$161$		−	33.1646i		−	2.61374i
$162$		0			0
$163$	−1.90387			−0.149123			−0.0745614	−	0.997216i	$-0.523756\pi$
$163$	−1.90387			−0.149123			−0.0745614	+	0.997216i	$0.523756\pi$
$164$	6.54399	−	2.36724i	0.511000	−	0.184851i
$165$		0			0
$166$	4.94166	−	7.04266i	0.383547	−	0.546617i
$167$	−19.6807			−1.52294			−0.761470	−	0.648200i	$-0.775522\pi$
$167$	−19.6807			−1.52294			−0.761470	+	0.648200i	$0.775522\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−0.248432	+	0.354055i	−0.0190539	+	0.0271548i
$171$		0			0
$172$	−6.65195	−	18.3886i	−0.507206	−	1.40212i
$173$	13.5528			1.03040			0.515202	−	0.857069i	$-0.327717\pi$
$173$	13.5528			1.03040			0.515202	+	0.857069i	$0.327717\pi$
$174$		0			0
$175$		−	23.7748i		−	1.79721i
$176$	−3.03799	−	3.64962i	−0.228997	−	0.275101i
$177$		0			0
$178$	−2.05405	+	2.92736i	−0.153958	+	0.219415i
$179$			23.1894i			1.73326i	0.498954	+	0.866629i	$0.333718\pi$
$179$			23.1894i			1.73326i	−0.498954	+	0.866629i	$0.666282\pi$
$180$		0			0
$181$		−	8.05640i		−	0.598827i	−0.954123	−	0.299414i	$-0.903209\pi$
$181$		−	8.05640i		−	0.598827i	0.954123	−	0.299414i	$-0.0967911\pi$
$182$	5.01956	+	3.52210i	0.372074	+	0.261075i
$183$		0			0
$184$	−5.66094	+	20.8801i	−0.417330	+	1.53930i
$185$			37.6788i			2.77020i
$186$		0			0
$187$	−0.112137			−0.00820028
$188$	−1.10652	−	3.05887i	−0.0807016	−	0.223091i
$189$		0			0
$190$	8.54299	+	5.99440i	0.619774	+	0.434880i
$191$	−11.0358			−0.798521			−0.399261	−	0.916838i	$-0.630733\pi$
$191$	−11.0358			−0.798521			−0.399261	+	0.916838i	$0.630733\pi$
$192$		0			0
$193$	−7.60726			−0.547583			−0.273791	−	0.961789i	$-0.588278\pi$
$193$	−7.60726			−0.547583			−0.273791	+	0.961789i	$0.588278\pi$
$194$	−20.2271	−	14.1928i	−1.45222	−	1.01899i
$195$		0			0
$196$	−8.02839	−	22.1937i	−0.573457	−	1.58526i
$197$	−3.65416			−0.260348			−0.130174	−	0.991491i	$-0.541554\pi$
$197$	−3.65416			−0.260348			−0.130174	+	0.991491i	$0.541554\pi$
$198$		0			0
$199$			5.50005i			0.389888i	0.980814	+	0.194944i	$0.0624525\pi$
$199$			5.50005i			0.389888i	−0.980814	+	0.194944i	$0.937547\pi$
$200$	−4.05818	+	14.9684i	−0.286956	+	1.05843i
$201$		0			0
$202$	−8.39152	−	5.88812i	−0.590425	−	0.414287i
$203$			20.8193i			1.46123i
$204$		0			0
$205$		−	11.2658i		−	0.786840i
$206$	−0.125508	+	0.178869i	−0.00874457	+	0.0124624i
$207$		0			0
$208$	−2.55907	−	3.07428i	−0.177439	−	0.213163i
$209$			2.70575i			0.187161i
$210$		0			0
$211$	5.48462			0.377577			0.188788	−	0.982018i	$-0.439544\pi$
$211$	5.48462			0.377577			0.188788	+	0.982018i	$0.439544\pi$
$212$	7.20190	+	19.9089i	0.494628	+	1.36735i
$213$		0			0
$214$	−1.74485	+	2.48669i	−0.119276	+	0.169987i
$215$	−31.6570			−2.15899
$216$		0			0
$217$	−32.8482			−2.22988
$218$	10.4570	−	14.9030i	0.708240	−	1.00936i
$219$		0			0
$220$	−7.22898	+	2.61503i	−0.487378	+	0.176305i
$221$	−0.0944593			−0.00635402
$222$		0			0
$223$		−	23.2910i		−	1.55968i	−0.625979	−	0.779840i	$-0.715301\pi$
$223$		−	23.2910i		−	1.55968i	0.625979	−	0.779840i	$-0.284699\pi$
$224$	2.01748	+	24.4448i	0.134799	+	1.63329i
$225$		0			0
$226$	5.18603	−	7.39092i	0.344969	−	0.491637i
$227$		−	9.24360i		−	0.613519i	−0.951787	−	0.306760i	$-0.900755\pi$
$227$		−	9.24360i		−	0.613519i	0.951787	−	0.306760i	$-0.0992448\pi$
$228$		0			0
$229$			4.11450i			0.271894i	0.990716	+	0.135947i	$0.0434077\pi$
$229$			4.11450i			0.271894i	−0.990716	+	0.135947i	$0.956592\pi$
$230$	28.6692	+	20.1165i	1.89039	+	1.32644i
$231$		0			0
$232$	3.55369	−	13.1076i	0.233311	−	0.860558i
$233$			0.938538i			0.0614857i	0.999527	+	0.0307428i	$0.00978729\pi$
$233$			0.938538i			0.0614857i	−0.999527	+	0.0307428i	$0.990213\pi$
$234$		0			0
$235$	−5.26601			−0.343517
$236$	10.4473	−	3.77925i	0.680065	−	0.246008i
$237$		0			0
$238$	0.474144	+	0.332695i	0.0307342	+	0.0215654i
$239$	23.8576			1.54322			0.771609	−	0.636098i	$-0.219452\pi$
$239$	23.8576			1.54322			0.771609	+	0.636098i	$0.219452\pi$
$240$		0			0
$241$	−6.67466			−0.429953			−0.214976	−	0.976619i	$-0.568967\pi$
$241$	−6.67466			−0.429953			−0.214976	+	0.976619i	$0.568967\pi$
$242$	11.1027	+	7.79050i	0.713710	+	0.500792i
$243$		0			0
$244$	−16.5907	+	6.00156i	−1.06211	+	0.384211i
$245$	−38.2076			−2.44099
$246$		0			0
$247$			2.27921i			0.145022i
$248$	20.6809	+	5.60692i	1.31324	+	0.356040i
$249$		0			0
$250$	1.81105	+	1.27077i	0.114541	+	0.0803706i
$251$			6.56246i			0.414219i	0.978318	+	0.207109i	$0.0664056\pi$
$251$			6.56246i			0.414219i	−0.978318	+	0.207109i	$0.933594\pi$
$252$		0			0
$253$			9.08018i			0.570866i
$254$	6.58656	−	9.38691i	0.413278	−	0.588987i
$255$		0			0
$256$	2.90235	−	15.7346i	0.181397	−	0.983410i
$257$		−	19.2751i		−	1.20235i	−0.799117	−	0.601175i	$-0.794699\pi$
$257$		−	19.2751i		−	1.20235i	0.799117	−	0.601175i	$-0.205301\pi$
$258$		0			0
$259$	50.4588			3.13535
$260$	−6.08937	+	2.20279i	−0.377647	+	0.136611i
$261$		0			0
$262$	12.1136	−	17.2638i	0.748379	−	1.06656i
$263$	−27.6440			−1.70460			−0.852302	−	0.523050i	$-0.824794\pi$
$263$	−27.6440			−1.70460			−0.852302	+	0.523050i	$0.824794\pi$
$264$		0			0
$265$	34.2742			2.10545
$266$	8.02759	−	11.4406i	0.492203	−	0.701468i
$267$		0			0
$268$	0.605507	+	1.67386i	0.0369872	+	0.102247i
$269$	24.3377			1.48390			0.741948	−	0.670457i	$-0.233902\pi$
$269$	24.3377			1.48390			0.741948	+	0.670457i	$0.233902\pi$
$270$		0			0
$271$			0.648615i			0.0394006i	0.999806	+	0.0197003i	$0.00627120\pi$
$271$			0.648615i			0.0394006i	−0.999806	+	0.0197003i	$0.993729\pi$
$272$	−0.241728	−	0.290394i	−0.0146569	−	0.0176077i
$273$		0			0
$274$	−5.90891	+	8.42115i	−0.356970	+	0.508740i
$275$			6.50934i			0.392528i
$276$		0			0
$277$		−	2.48540i		−	0.149333i	−0.997209	−	0.0746665i	$-0.976211\pi$
$277$		−	2.48540i		−	0.149333i	0.997209	−	0.0746665i	$-0.0237892\pi$
$278$	0.495719	+	0.347834i	0.0297313	+	0.0208617i
$279$		0			0
$280$	38.3244	+	10.3904i	2.29032	+	0.620943i
$281$			26.7449i			1.59547i	0.603011	+	0.797733i	$0.293968\pi$
$281$			26.7449i			1.59547i	−0.603011	+	0.797733i	$0.706032\pi$
$282$		0			0
$283$	−23.1975			−1.37895			−0.689474	−	0.724310i	$-0.742158\pi$
$283$	−23.1975			−1.37895			−0.689474	+	0.724310i	$0.742158\pi$
$284$	−3.91269	−	10.8162i	−0.232175	−	0.641824i
$285$		0			0
$286$	−1.37431	−	0.964320i	−0.0812647	−	0.0570214i
$287$	−15.0870			−0.890556
$288$		0			0
$289$	16.9911			0.999475
$290$	−17.9973	−	12.6283i	−1.05684	−	0.741557i
$291$		0			0
$292$	−8.89198	−	24.5810i	−0.520364	−	1.43849i
$293$	27.7476			1.62103			0.810516	−	0.585716i	$-0.199187\pi$
$293$	27.7476			1.62103			0.810516	+	0.585716i	$0.199187\pi$
$294$		0			0
$295$		−	17.9857i		−	1.04717i
$296$	−31.7683	−	8.61291i	−1.84650	−	0.500615i
$297$		0			0
$298$	13.4200	+	9.41645i	0.777397	+	0.545480i
$299$			7.64873i			0.442338i
$300$		0			0
$301$			42.3944i			2.44357i
$302$	6.39906	−	9.11969i	0.368225	−	0.524779i
$303$		0			0
$304$	−7.00691	+	5.83264i	−0.401874	+	0.334525i
$305$			28.5618i			1.63544i
$306$		0			0
$307$	−4.23451			−0.241676			−0.120838	−	0.992672i	$-0.538558\pi$
$307$	−4.23451			−0.241676			−0.120838	+	0.992672i	$0.538558\pi$
$308$	3.50200	+	9.68091i	0.199545	+	0.551621i
$309$		0			0
$310$	19.9245	−	28.3957i	1.13164	−	1.61277i
$311$	29.1156			1.65099			0.825496	−	0.564408i	$-0.190896\pi$
$311$	29.1156			1.65099			0.825496	+	0.564408i	$0.190896\pi$
$312$		0			0
$313$	23.2500			1.31417			0.657083	−	0.753818i	$-0.271790\pi$
$313$	23.2500			1.31417			0.657083	+	0.753818i	$0.271790\pi$
$314$	−2.97932	+	4.24601i	−0.168133	+	0.239616i
$315$		0			0
$316$	−28.5438	+	10.3255i	−1.60571	+	0.580855i
$317$	−6.81779			−0.382925			−0.191463	−	0.981500i	$-0.561323\pi$
$317$	−6.81779			−0.382925			−0.191463	+	0.981500i	$0.561323\pi$
$318$		0			0
$319$		−	5.70015i		−	0.319147i
$320$	−22.3551	−	13.0833i	−1.24969	−	0.731380i
$321$		0			0
$322$	26.9396	−	38.3933i	1.50129	−	2.13957i
$323$			0.215292i			0.0119792i
$324$		0			0
$325$			5.48318i			0.304152i
$326$	−2.20403	−	1.54651i	−0.122070	−	0.0856535i
$327$		0			0
$328$	9.49861	+	2.57523i	0.524473	+	0.142193i
$329$			7.05214i			0.388797i
$330$		0			0
$331$	−9.11133			−0.500804			−0.250402	−	0.968142i	$-0.580563\pi$
$331$	−9.11133			−0.500804			−0.250402	+	0.968142i	$0.580563\pi$
$332$	11.4415	−	4.13888i	0.627934	−	0.227151i
$333$		0			0
$334$	−22.7835	−	15.9866i	−1.24666	−	0.874750i
$335$	2.88164			0.157441
$336$		0			0
$337$	22.2228			1.21055			0.605276	−	0.796016i	$-0.293063\pi$
$337$	22.2228			1.21055			0.605276	+	0.796016i	$0.293063\pi$
$338$	−1.15766	−	0.812299i	−0.0629682	−	0.0441833i
$339$		0			0
$340$	−0.575198	+	0.208074i	−0.0311945	+	0.0112844i
$341$	8.99354			0.487028
$342$		0			0
$343$			20.8151i			1.12391i
$344$	7.23639	−	26.6911i	0.390160	−	1.43909i
$345$		0			0
$346$	15.6895	+	11.0090i	0.843475	+	0.591845i
$347$			1.21378i			0.0651593i	0.999469	+	0.0325796i	$0.0103723\pi$
$347$			1.21378i			0.0651593i	−0.999469	+	0.0325796i	$0.989628\pi$
$348$		0			0
$349$		−	3.97729i		−	0.212899i	−0.994318	−	0.106450i	$-0.966052\pi$
$349$		−	3.97729i		−	0.212899i	0.994318	−	0.106450i	$-0.0339483\pi$
$350$	19.3123	−	27.5231i	1.03229	−	1.47117i
$351$		0			0
$352$	−0.552369	−	6.69277i	−0.0294413	−	0.356726i
$353$			7.75251i			0.412625i	0.978486	+	0.206312i	$0.0661463\pi$
$353$			7.75251i			0.412625i	−0.978486	+	0.206312i	$0.933854\pi$
$354$		0			0
$355$	−18.6207			−0.988284
$356$	−4.75578	+	1.72037i	−0.252056	+	0.0911793i
$357$		0			0
$358$	−18.8367	+	26.8454i	−0.995552	+	1.41882i
$359$	22.3649			1.18037			0.590187	−	0.807267i	$-0.299054\pi$
$359$	22.3649			1.18037			0.590187	+	0.807267i	$0.299054\pi$
$360$		0			0
$361$	−13.8052			−0.726591
$362$	6.54421	−	9.32655i	0.343956	−	0.490192i
$363$		0			0
$364$	2.94993	+	8.15477i	0.154618	+	0.427426i
$365$	−42.3174			−2.21500
$366$		0			0
$367$			14.6130i			0.762793i	0.924411	+	0.381397i	$0.124557\pi$
$367$			14.6130i			0.762793i	−0.924411	+	0.381397i	$0.875443\pi$
$368$	−23.5143	+	19.5736i	−1.22577	+	1.02035i
$369$		0			0
$370$	−30.6065	+	43.6192i	−1.59116	+	2.26765i
$371$		−	45.8994i		−	2.38298i
$372$		0			0
$373$			35.5065i			1.83846i	0.393722	+	0.919229i	$0.371187\pi$
$373$			35.5065i			1.83846i	−0.393722	+	0.919229i	$0.628813\pi$
$374$	−0.129816	−	0.0910889i	−0.00671265	−	0.00471010i
$375$		0			0
$376$	1.20374	−	4.43995i	0.0620783	−	0.228973i
$377$		−	4.80155i		−	0.247292i
$378$		0			0
$379$	−2.22424			−0.114251			−0.0571257	−	0.998367i	$-0.518194\pi$
$379$	−2.22424			−0.114251			−0.0571257	+	0.998367i	$0.518194\pi$
$380$	5.02060	+	13.8789i	0.257551	+	0.711974i
$381$		0			0
$382$	−12.7756	−	8.96436i	−0.653659	−	0.458656i
$383$	37.1436			1.89795			0.948976	−	0.315349i	$-0.102121\pi$
$383$	37.1436			1.89795			0.948976	+	0.315349i	$0.102121\pi$
$384$		0			0
$385$	16.6662			0.849389
$386$	−8.80660	−	6.17937i	−0.448244	−	0.314522i
$387$		0			0
$388$	−11.8872	−	32.8609i	−0.603480	−	1.66826i
$389$	12.1794			0.617519			0.308760	−	0.951140i	$-0.400086\pi$
$389$	12.1794			0.617519			0.308760	+	0.951140i	$0.400086\pi$
$390$		0			0
$391$			0.722494i			0.0365381i
$392$	8.73377	−	32.2141i	0.441122	−	1.62706i
$393$		0			0
$394$	−4.23026	−	2.96827i	−0.213117	−	0.149539i
$395$			49.1397i			2.47248i
$396$		0			0
$397$		−	20.5977i		−	1.03377i	−0.856054	−	0.516886i	$-0.827091\pi$
$397$		−	20.5977i		−	1.03377i	0.856054	−	0.516886i	$-0.172909\pi$
$398$	−4.46768	+	6.36717i	−0.223945	+	0.319157i
$399$		0			0
$400$	−16.8568	+	14.0318i	−0.842840	+	0.701591i
$401$		−	11.1123i		−	0.554923i	−0.960737	−	0.277462i	$-0.910507\pi$
$401$		−	11.1123i		−	0.554923i	0.960737	−	0.277462i	$-0.0894931\pi$
$402$		0			0
$403$	7.57575			0.377375
$404$	−4.93158	−	13.6328i	−0.245355	−	0.678259i
$405$		0			0
$406$	−16.9115	+	24.1016i	−0.839305	+	1.19614i
$407$	−13.8152			−0.684792
$408$		0			0
$409$	−30.0867			−1.48769			−0.743846	−	0.668351i	$-0.767000\pi$
$409$	−30.0867			−1.48769			−0.743846	+	0.668351i	$0.767000\pi$
$410$	9.15123	−	13.0420i	0.451947	−	0.644097i
$411$		0			0
$412$	−0.290591	+	0.105119i	−0.0143164	+	0.00517885i
$413$	−24.0861			−1.18520
$414$		0			0
$415$		−	19.6972i		−	0.966895i
$416$	−0.465290	−	5.63769i	−0.0228127	−	0.276410i
$417$		0			0
$418$	−2.19788	+	3.13234i	−0.107502	+	0.153208i
$419$		−	16.9123i		−	0.826219i	−0.910681	−	0.413109i	$-0.864443\pi$
$419$		−	16.9123i		−	0.826219i	0.910681	−	0.413109i	$-0.135557\pi$
$420$		0			0
$421$			22.0720i			1.07572i	0.843033	+	0.537862i	$0.180768\pi$
$421$			22.0720i			1.07572i	−0.843033	+	0.537862i	$0.819232\pi$
$422$	6.34931	+	4.45515i	0.309079	+	0.216873i
$423$		0			0
$424$	−7.83466	+	28.8978i	−0.380485	+	1.40340i
$425$			0.517937i			0.0251236i
$426$		0			0
$427$	38.2494			1.85102
$428$	−4.03988	+	1.46140i	−0.195275	+	0.0706393i
$429$		0			0
$430$	−36.6479	−	25.7150i	−1.76732	−	1.24009i
$431$	−12.8351			−0.618247			−0.309123	−	0.951022i	$-0.600036\pi$
$431$	−12.8351			−0.618247			−0.309123	+	0.951022i	$0.600036\pi$
$432$		0			0
$433$	−22.3461			−1.07389			−0.536943	−	0.843618i	$-0.680421\pi$
$433$	−22.3461			−1.07389			−0.536943	+	0.843618i	$0.680421\pi$
$434$	−38.0269	−	26.6826i	−1.82535	−	1.28080i
$435$		0			0
$436$	24.2113	−	8.75828i	1.15951	−	0.419445i
$437$	17.4330			0.833935
$438$		0			0
$439$			30.4945i			1.45542i	0.685884	+	0.727711i	$0.259416\pi$
$439$			30.4945i			1.45542i	−0.685884	+	0.727711i	$0.740584\pi$
$440$	−10.4929	−	2.84479i	−0.500228	−	0.135620i
$441$		0			0
$442$	−0.109351	−	0.0767292i	−0.00520132	−	0.00364964i
$443$			2.66810i			0.126765i	0.997989	+	0.0633826i	$0.0201888\pi$
$443$			2.66810i			0.126765i	−0.997989	+	0.0633826i	$0.979811\pi$
$444$		0			0
$445$			8.18733i			0.388116i
$446$	18.9192	−	26.9630i	0.895852	−	1.27673i
$447$		0			0
$448$	−17.5209	+	29.9375i	−0.827786	+	1.41441i
$449$			38.8868i			1.83518i	0.397526	+	0.917591i	$0.369869\pi$
$449$			38.8868i			1.83518i	−0.397526	+	0.917591i	$0.630131\pi$
$450$		0			0
$451$	4.13068			0.194506
$452$	12.0073	−	4.34355i	0.564775	−	0.204303i
$453$		0			0
$454$	7.50857	−	10.7009i	0.352395	−	0.502219i
$455$	14.0389			0.658152
$456$		0			0
$457$	31.8203			1.48849			0.744246	−	0.667905i	$-0.232809\pi$
$457$	31.8203			1.48849			0.744246	+	0.667905i	$0.232809\pi$
$458$	−3.34221	+	4.76319i	−0.156171	+	0.222569i
$459$		0			0
$460$	16.8485	+	46.5760i	0.785566	+	2.17162i
$461$	25.9499			1.20861			0.604303	−	0.796755i	$-0.293452\pi$
$461$	25.9499			1.20861			0.604303	+	0.796755i	$0.293452\pi$
$462$		0			0
$463$			2.03696i			0.0946657i	0.998879	+	0.0473329i	$0.0150721\pi$
$463$			2.03696i			0.0946657i	−0.998879	+	0.0473329i	$0.984928\pi$
$464$	14.7613	−	12.2875i	0.685275	−	0.570432i
$465$		0			0
$466$	−0.762374	+	1.08651i	−0.0353163	+	0.0503314i
$467$			3.91994i			0.181393i	0.995879	+	0.0906967i	$0.0289094\pi$
$467$			3.91994i			0.181393i	−0.995879	+	0.0906967i	$0.971091\pi$
$468$		0			0
$469$		−	3.85903i		−	0.178194i
$470$	−6.09623	−	4.27758i	−0.281198	−	0.197310i
$471$		0			0
$472$	15.1643	+	4.11130i	0.697995	+	0.189238i
$473$		−	11.6072i		−	0.533700i
$474$		0			0
$475$	12.4973			0.573415
$476$	0.278648	+	0.770293i	0.0127718	+	0.0353063i
$477$		0			0
$478$	27.6189	+	19.3795i	1.26326	+	0.886397i
$479$	22.5822			1.03181			0.515904	−	0.856646i	$-0.327456\pi$
$479$	22.5822			1.03181			0.515904	+	0.856646i	$0.327456\pi$
$480$		0			0
$481$	−11.6373			−0.530614
$482$	−7.72696	−	5.42182i	−0.351954	−	0.246957i
$483$		0			0
$484$	6.52492	+	18.0375i	0.296587	+	0.819885i
$485$	−56.5717			−2.56879
$486$		0			0
$487$			10.9764i			0.497386i	0.968582	+	0.248693i	$0.0800011\pi$
$487$			10.9764i			0.497386i	−0.968582	+	0.248693i	$0.919999\pi$
$488$	−24.0814	−	6.52886i	−1.09011	−	0.295548i
$489$		0			0
$490$	−44.2313	−	31.0360i	−1.99816	−	1.40206i
$491$			2.57966i			0.116419i	0.998304	+	0.0582093i	$0.0185391\pi$
$491$			2.57966i			0.116419i	−0.998304	+	0.0582093i	$0.981461\pi$
$492$		0			0
$493$		−	0.453551i		−	0.0204269i
$494$	−1.85140	+	2.63854i	−0.0832983	+	0.118713i
$495$		0			0
$496$	19.3869	+	23.2900i	0.870496	+	1.04575i
$497$			24.9365i			1.11855i
$498$		0			0
$499$	5.21886			0.233628			0.116814	−	0.993154i	$-0.462732\pi$
$499$	5.21886			0.233628			0.116814	+	0.993154i	$0.462732\pi$
$500$	1.06433	+	2.94224i	0.0475984	+	0.131581i
$501$		0			0
$502$	−5.33068	+	7.59708i	−0.237920	+	0.339074i
$503$	−28.0588			−1.25108			−0.625539	−	0.780193i	$-0.715121\pi$
$503$	−28.0588			−1.25108			−0.625539	+	0.780193i	$0.715121\pi$
$504$		0			0
$505$	−23.4697			−1.04439
$506$	−7.37582	+	10.5117i	−0.327895	+	0.467304i
$507$		0			0
$508$	15.2500	−	5.51656i	0.676608	−	0.244758i
$509$	−9.51782			−0.421870			−0.210935	−	0.977500i	$-0.567651\pi$
$509$	−9.51782			−0.421870			−0.210935	+	0.977500i	$0.567651\pi$
$510$		0			0
$511$			56.6707i			2.50696i
$512$	16.1411	−	15.8577i	0.713342	−	0.700816i
$513$		0			0
$514$	15.6572	−	22.3140i	0.690609	−	0.984229i
$515$			0.500268i			0.0220444i
$516$		0			0
$517$		−	1.93081i		−	0.0849171i
$518$	58.4139	+	40.9876i	2.56656	+	1.80089i
$519$		0			0
$520$	−8.83872	−	2.39632i	−0.387604	−	0.105086i
$521$		−	3.21823i		−	0.140993i	−0.997512	−	0.0704966i	$-0.977542\pi$
$521$		−	3.21823i		−	0.140993i	0.997512	−	0.0704966i	$-0.0224584\pi$
$522$		0			0
$523$	−23.4163			−1.02392			−0.511962	−	0.859008i	$-0.671081\pi$
$523$	−23.4163			−1.02392			−0.511962	+	0.859008i	$0.671081\pi$
$524$	28.0467	−	10.1457i	1.22523	−	0.443217i
$525$		0			0
$526$	−32.0023	−	22.4552i	−1.39537	−	0.979094i
$527$	0.715600			0.0311720
$528$		0			0
$529$	35.5031			1.54362
$530$	39.6778	+	27.8409i	1.72349	+	1.20933i
$531$		0			0
$532$	18.5864	−	6.72349i	0.805822	−	0.291500i
$533$	3.47950			0.150714
$534$		0			0
$535$			6.95487i			0.300685i
$536$	−0.658706	+	2.42961i	−0.0284518	+	0.104943i
$537$		0			0
$538$	28.1747	+	19.7695i	1.21470	+	0.852324i
$539$		−	14.0090i		−	0.603411i
$540$		0			0
$541$		−	31.3574i		−	1.34816i	−0.738659	−	0.674079i	$-0.764541\pi$
$541$		−	31.3574i		−	1.34816i	0.738659	−	0.674079i	$-0.235459\pi$
$542$	−0.526870	+	0.750874i	−0.0226310	+	0.0322528i
$543$		0			0
$544$	−0.0439510	−	0.532532i	−0.00188438	−	0.0228321i
$545$		−	41.6811i		−	1.78542i
$546$		0			0
$547$	−20.2955			−0.867774			−0.433887	−	0.900967i	$-0.642858\pi$
$547$	−20.2955			−0.867774			−0.433887	+	0.900967i	$0.642858\pi$
$548$	−13.6810	+	4.94900i	−0.584423	+	0.211411i
$549$		0			0
$550$	−5.28753	+	7.53558i	−0.225461	+	0.321318i
$551$	−10.9437			−0.466218
$552$		0			0
$553$	65.8069			2.79839
$554$	2.01889	−	2.87724i	0.0857743	−	0.122242i
$555$		0			0
$556$	0.291328	+	0.805345i	0.0123550	+	0.0341542i
$557$	−28.5330			−1.20898			−0.604492	−	0.796611i	$-0.706624\pi$
$557$	−28.5330			−1.20898			−0.604492	+	0.796611i	$0.706624\pi$
$558$		0			0
$559$		−	9.77740i		−	0.413540i
$560$	35.9264	+	43.1593i	1.51817	+	1.82381i
$561$		0			0
$562$	−21.7249	+	30.9614i	−0.916408	+	1.30603i
$563$			22.5762i			0.951474i	0.879588	+	0.475737i	$0.157819\pi$
$563$			22.5762i			0.951474i	−0.879588	+	0.475737i	$0.842181\pi$
$564$		0			0
$565$		−	20.6712i		−	0.869643i
$566$	−26.8547	−	18.8433i	−1.12879	−	0.792043i
$567$		0			0
$568$	4.25646	−	15.6997i	0.178597	−	0.658747i
$569$			2.31847i			0.0971951i	0.998818	+	0.0485976i	$0.0154752\pi$
$569$			2.31847i			0.0971951i	−0.998818	+	0.0485976i	$0.984525\pi$
$570$		0			0
$571$	−8.29865			−0.347288			−0.173644	−	0.984809i	$-0.555554\pi$
$571$	−8.29865			−0.347288			−0.173644	+	0.984809i	$0.555554\pi$
$572$	−0.807664	−	2.23270i	−0.0337701	−	0.0933540i
$573$		0			0
$574$	−17.4656	−	12.2551i	−0.728998	−	0.511520i
$575$	41.9394			1.74899
$576$		0			0
$577$	24.1082			1.00364			0.501818	−	0.864973i	$-0.332665\pi$
$577$	24.1082			1.00364			0.501818	+	0.864973i	$0.332665\pi$
$578$	19.6698	+	13.8018i	0.818157	+	0.574081i
$579$		0			0
$580$	−10.5768	−	29.2384i	−0.439177	−	1.21406i
$581$	−26.3780			−1.09435
$582$		0			0
$583$			12.5668i			0.520465i
$584$	9.67323	−	35.6793i	0.400281	−	1.47642i
$585$		0			0
$586$	32.1222	+	22.5394i	1.32696	+	0.931092i
$587$			40.7910i			1.68362i	0.539771	+	0.841812i	$0.318511\pi$
$587$			40.7910i			1.68362i	−0.539771	+	0.841812i	$0.681489\pi$
$588$		0			0
$589$		−	17.2667i		−	0.711462i
$590$	14.6097	−	20.8212i	0.601474	−	0.857197i
$591$		0			0
$592$	−29.7806	−	35.7762i	−1.22397	−	1.47039i
$593$		−	9.44136i		−	0.387710i	−0.981030	−	0.193855i	$-0.937901\pi$
$593$		−	9.44136i		−	0.387710i	0.981030	−	0.193855i	$-0.0620992\pi$
$594$		0			0
$595$	1.32610			0.0543648
$596$	7.88673	+	21.8020i	0.323053	+	0.893046i
$597$		0			0
$598$	−6.21306	+	8.85461i	−0.254071	+	0.362092i
$599$	−41.8793			−1.71114			−0.855572	−	0.517684i	$-0.826794\pi$
$599$	−41.8793			−1.71114			−0.855572	+	0.517684i	$0.826794\pi$
$600$		0			0
$601$	−39.8407			−1.62514			−0.812568	−	0.582866i	$-0.801931\pi$
$601$	−39.8407			−1.62514			−0.812568	+	0.582866i	$0.801931\pi$
$602$	−34.4370	+	49.0782i	−1.40355	+	2.00028i
$603$		0			0
$604$	14.8158	−	5.35952i	0.602848	−	0.218076i
$605$	31.0524			1.26246
$606$		0			0
$607$		−	19.3389i		−	0.784944i	−0.919764	−	0.392472i	$-0.871620\pi$
$607$		−	19.3389i		−	0.784944i	0.919764	−	0.392472i	$-0.128380\pi$
$608$	−12.8494	+	1.06049i	−0.521114	+	0.0430086i
$609$		0			0
$610$	−23.2007	+	33.0647i	−0.939369	+	1.33875i
$611$		−	1.62643i		−	0.0657983i
$612$		0			0
$613$		−	42.2369i		−	1.70593i	−0.521967	−	0.852966i	$-0.674801\pi$
$613$		−	42.2369i		−	1.70593i	0.521967	−	0.852966i	$-0.325199\pi$
$614$	−4.90211	−	3.43969i	−0.197833	−	0.138814i
$615$		0			0
$616$	−3.80969	+	14.0519i	−0.153497	+	0.566165i
$617$		−	17.7584i		−	0.714927i	−0.933927	−	0.357464i	$-0.883642\pi$
$617$		−	17.7584i		−	0.714927i	0.933927	−	0.357464i	$-0.116358\pi$
$618$		0			0
$619$	24.6547			0.990956			0.495478	−	0.868620i	$-0.334993\pi$
$619$	24.6547			0.990956			0.495478	+	0.868620i	$0.334993\pi$
$620$	46.1316	−	16.6878i	1.85269	−	0.670197i
$621$		0			0
$622$	33.7058	+	23.6505i	1.35148	+	0.948300i
$623$	10.9643			0.439276
$624$		0			0
$625$	−22.3507			−0.894027
$626$	26.9155	+	18.8859i	1.07576	+	0.754833i
$627$		0			0
$628$	−6.89806	+	2.49532i	−0.275263	+	0.0995742i
$629$	−1.09925			−0.0438299
$630$		0			0
$631$			7.10652i			0.282906i	0.989945	+	0.141453i	$0.0451774\pi$
$631$			7.10652i			0.282906i	−0.989945	+	0.141453i	$0.954823\pi$
$632$	−41.4313	−	11.2327i	−1.64805	−	0.446813i
$633$		0			0
$634$	−7.89266	−	5.53808i	−0.313457	−	0.219945i
$635$		−	26.2536i		−	1.04184i
$636$		0			0
$637$		−	11.8006i		−	0.467555i
$638$	4.63023	−	6.59882i	0.183312	−	0.261250i
$639$		0			0
$640$	−15.2519	−	33.3050i	−0.602886	−	1.31650i
$641$			26.3422i			1.04046i	0.854028	+	0.520228i	$0.174153\pi$
$641$			26.3422i			1.04046i	−0.854028	+	0.520228i	$0.825847\pi$
$642$		0			0
$643$	15.8987			0.626983			0.313491	−	0.949591i	$-0.398501\pi$
$643$	15.8987			0.626983			0.313491	+	0.949591i	$0.398501\pi$
$644$	62.3736	−	22.5632i	2.45787	−	0.889115i
$645$		0			0
$646$	−0.174882	+	0.249234i	−0.00688063	+	0.00980600i
$647$	9.85006			0.387246			0.193623	−	0.981076i	$-0.437976\pi$
$647$	9.85006			0.387246			0.193623	+	0.981076i	$0.437976\pi$
$648$		0			0
$649$	6.59455			0.258859
$650$	−4.45398	+	6.34764i	−0.174699	+	0.248975i
$651$		0			0
$652$	−1.29528	−	3.58067i	−0.0507271	−	0.140230i
$653$	14.8492			0.581094			0.290547	−	0.956861i	$-0.406163\pi$
$653$	14.8492			0.581094			0.290547	+	0.956861i	$0.406163\pi$
$654$		0			0
$655$		−	48.2840i		−	1.88661i
$656$	8.90428	+	10.6969i	0.347654	+	0.417646i
$657$		0			0
$658$	−5.72845	+	8.16396i	−0.223318	+	0.318264i
$659$			42.2506i			1.64585i	0.568149	+	0.822925i	$0.307660\pi$
$659$			42.2506i			1.64585i	−0.568149	+	0.822925i	$0.692340\pi$
$660$		0			0
$661$			20.8921i			0.812608i	0.913738	+	0.406304i	$0.133183\pi$
$661$			20.8921i			0.812608i	−0.913738	+	0.406304i	$0.866817\pi$
$662$	−10.5478	−	7.40112i	−0.409952	−	0.287653i
$663$		0			0
$664$	16.6073	+	4.50252i	0.644490	+	0.174732i
$665$		−	31.9974i		−	1.24081i
$666$		0			0
$667$	−36.7258			−1.42203
$668$	−13.3896	−	37.0141i	−0.518058	−	1.43212i
$669$		0			0
$670$	3.33595	+	2.34075i	0.128879	+	0.0904312i
$671$	−10.4723			−0.404280
$672$		0			0
$673$	4.04031			0.155742			0.0778712	−	0.996963i	$-0.475188\pi$
$673$	4.04031			0.155742			0.0778712	+	0.996963i	$0.475188\pi$
$674$	25.7264	+	18.0516i	0.990942	+	0.695320i
$675$		0			0
$676$	−0.680340	−	1.88073i	−0.0261669	−	0.0723357i
$677$	25.6247			0.984836			0.492418	−	0.870359i	$-0.336113\pi$
$677$	25.6247			0.984836			0.492418	+	0.870359i	$0.336113\pi$
$678$		0			0
$679$			75.7597i			2.90739i
$680$	−0.834900	−	0.226355i	−0.0320169	−	0.00868031i
$681$		0			0
$682$	10.4114	+	7.30545i	0.398675	+	0.279740i
$683$		−	3.10338i		−	0.118747i	−0.998236	−	0.0593737i	$-0.981090\pi$
$683$		−	3.10338i		−	0.118747i	0.998236	−	0.0593737i	$-0.0189104\pi$
$684$		0			0
$685$			23.5525i			0.899896i
$686$	−16.9081	+	24.0967i	−0.645553	+	0.920017i
$687$		0			0
$688$	30.0584	−	25.0210i	1.14597	−	0.953917i
$689$			10.5857i			0.403285i
$690$		0			0
$691$	15.5146			0.590202			0.295101	−	0.955466i	$-0.404647\pi$
$691$	15.5146			0.590202			0.295101	+	0.955466i	$0.404647\pi$
$692$	9.22053	+	25.4892i	0.350512	+	0.968954i
$693$		0			0
$694$	−0.985955	+	1.40514i	−0.0374263	+	0.0533385i
$695$	1.38644			0.0525908
$696$		0			0
$697$	0.328671			0.0124493
$698$	3.23075	−	4.60433i	0.122286	−	0.174277i
$699$		0			0
$700$	44.7140	−	16.1750i	1.69003	−	0.611356i
$701$	9.73072			0.367524			0.183762	−	0.982971i	$-0.441172\pi$
$701$	9.73072			0.367524			0.183762	+	0.982971i	$0.441172\pi$
$702$		0			0
$703$			26.5237i			1.00036i
$704$	4.79708	−	8.19662i	0.180797	−	0.308922i
$705$		0			0
$706$	−6.29736	+	8.97475i	−0.237004	+	0.337769i
$707$			31.4301i			1.18205i
$708$		0			0
$709$			24.9061i			0.935367i	0.883896	+	0.467684i	$0.154911\pi$
$709$			24.9061i			0.935367i	−0.883896	+	0.467684i	$0.845089\pi$
$710$	−21.5564	−	15.1256i	−0.808996	−	0.567653i
$711$		0			0
$712$	−6.90301	−	1.87152i	−0.258701	−	0.0701382i
$713$		−	57.9449i		−	2.17006i
$714$		0			0
$715$	−3.84372			−0.143747
$716$	−43.6130	+	15.7767i	−1.62989	+	0.589602i
$717$		0			0
$718$	25.8909	+	18.1670i	0.966239	+	0.677986i
$719$	19.8333			0.739658			0.369829	−	0.929100i	$-0.379416\pi$
$719$	19.8333			0.739658			0.369829	+	0.929100i	$0.379416\pi$
$720$		0			0
$721$	0.669949			0.0249502
$722$	−15.9817	−	11.2140i	−0.594778	−	0.417341i
$723$		0			0
$724$	15.1519	−	5.48109i	0.563116	−	0.203703i
$725$	−26.3277			−0.977787
$726$		0			0
$727$			0.331359i			0.0122894i	0.999981	+	0.00614472i	$0.00195594\pi$
$727$			0.331359i			0.0122894i	−0.999981	+	0.00614472i	$0.998044\pi$
$728$	−3.20911	+	11.8366i	−0.118937	+	0.438695i
$729$		0			0
$730$	−48.9891	−	34.3744i	−1.81317	−	1.27225i
$731$		−	0.923566i		−	0.0341593i
$732$		0			0
$733$			9.92295i			0.366512i	0.983065	+	0.183256i	$0.0586638\pi$
$733$			9.92295i			0.366512i	−0.983065	+	0.183256i	$0.941336\pi$
$734$	−11.8701	+	16.9169i	−0.438135	+	0.624413i
$735$		0			0
$736$	−43.1212	+	3.55888i	−1.58947	+	0.131182i
$737$			1.05657i			0.0389192i
$738$		0			0
$739$	−11.4372			−0.420724			−0.210362	−	0.977624i	$-0.567464\pi$
$739$	−11.4372			−0.420724			−0.210362	+	0.977624i	$0.567464\pi$
$740$	−70.8636	+	25.6344i	−2.60500	+	0.942340i
$741$		0			0
$742$	37.2840	−	53.1357i	1.36874	−	1.95067i
$743$	−18.1594			−0.666204			−0.333102	−	0.942891i	$-0.608095\pi$
$743$	−18.1594			−0.666204			−0.333102	+	0.942891i	$0.608095\pi$
$744$		0			0
$745$	37.5334			1.37512
$746$	−28.8419	+	41.1044i	−1.05598	+	1.50494i
$747$		0			0
$748$	−0.0762914	−	0.210900i	−0.00278949	−	0.00771125i
$749$	9.31382			0.340320
$750$		0			0
$751$		−	5.84293i		−	0.213211i	−0.994301	−	0.106606i	$-0.966002\pi$
$751$		−	5.84293i		−	0.213211i	0.994301	−	0.106606i	$-0.0339983\pi$
$752$	5.00009	−	4.16214i	0.182335	−	0.151778i
$753$		0			0
$754$	3.90029	−	5.55854i	0.142040	−	0.202430i
$755$		−	25.5063i		−	0.928268i
$756$		0			0
$757$		−	41.0906i		−	1.49346i	−0.665126	−	0.746731i	$-0.731622\pi$
$757$		−	41.0906i		−	1.49346i	0.665126	−	0.746731i	$-0.268378\pi$
$758$	−2.57491	−	1.80675i	−0.0935248	−	0.0656240i
$759$		0			0
$760$	−5.46171	+	20.1453i	−0.198117	+	0.730746i
$761$		−	30.0805i		−	1.09042i	−0.838301	−	0.545208i	$-0.816451\pi$
$761$		−	30.0805i		−	1.09042i	0.838301	−	0.545208i	$-0.183549\pi$
$762$		0			0
$763$	−55.8185			−2.02077
$764$	−7.50808	−	20.7553i	−0.271633	−	0.750900i
$765$		0			0
$766$	42.9996	+	30.1718i	1.55364	+	1.09015i
$767$	5.55495			0.200578
$768$		0			0
$769$	27.7812			1.00182			0.500908	−	0.865501i	$-0.333000\pi$
$769$	27.7812			1.00182			0.500908	+	0.865501i	$0.333000\pi$
$770$	19.2938	+	13.5379i	0.695299	+	0.487874i
$771$		0			0
$772$	−5.17552	−	14.3072i	−0.186271	−	0.514927i
$773$	50.7995			1.82713			0.913566	−	0.406691i	$-0.133317\pi$
$773$	50.7995			1.82713			0.913566	+	0.406691i	$0.133317\pi$
$774$		0			0
$775$		−	41.5392i		−	1.49213i
$776$	12.9316	−	47.6976i	0.464217	−	1.71224i
$777$		0			0
$778$	14.0996	+	9.89331i	0.505493	+	0.354692i
$779$		−	7.93050i		−	0.284140i
$780$		0			0
$781$		−	6.82738i		−	0.244303i
$782$	−0.586881	+	0.836400i	−0.0209868	+	0.0299096i
$783$		0			0
$784$	36.2782	−	30.1984i	1.29565	−	1.07852i
$785$			11.8754i			0.423850i
$786$		0			0
$787$	−13.8683			−0.494352			−0.247176	−	0.968971i	$-0.579503\pi$
$787$	−13.8683			−0.494352			−0.247176	+	0.968971i	$0.579503\pi$
$788$	−2.48607	−	6.87247i	−0.0885625	−	0.244822i
$789$		0			0
$790$	−39.9161	+	56.8869i	−1.42015	+	2.02394i
$791$	−27.6824			−0.984274
$792$		0			0
$793$	−8.82142			−0.313258
$794$	16.7315	−	23.8451i	0.593780	−	0.846232i
$795$		0			0
$796$	−10.3441	+	3.74190i	−0.366637	+	0.132628i
$797$	44.5890			1.57942			0.789712	−	0.613478i	$-0.210230\pi$
$797$	44.5890			1.57942			0.789712	+	0.613478i	$0.210230\pi$
$798$		0			0
$799$		−	0.153631i		−	0.00543509i
$800$	−30.9124	+	2.55127i	−1.09292	+	0.0902010i
$801$		0			0
$802$	9.02654	−	12.8643i	0.318738	−	0.454253i
$803$		−	15.5159i		−	0.547545i
$804$		0			0
$805$		−	107.380i		−	3.78463i
$806$	8.77013	+	6.15378i	0.308915	+	0.216758i
$807$		0			0
$808$	5.36487	−	19.7881i	0.188735	−	0.696142i
$809$		−	36.1233i		−	1.27003i	−0.772501	−	0.635014i	$-0.780994\pi$
$809$		−	36.1233i		−	1.27003i	0.772501	−	0.635014i	$-0.219006\pi$
$810$		0			0
$811$	5.44424			0.191173			0.0955865	−	0.995421i	$-0.469527\pi$
$811$	5.44424			0.191173			0.0955865	+	0.995421i	$0.469527\pi$
$812$	−39.1555	+	14.1642i	−1.37409	+	0.497066i
$813$		0			0
$814$	−15.9932	−	11.2220i	−0.560562	−	0.393333i
$815$	−6.16431			−0.215926
$816$		0			0
$817$	−22.2847			−0.779643
$818$	−34.8301	−	24.4394i	−1.21781	−	0.854504i
$819$		0			0
$820$	21.1880	−	7.66459i	0.739916	−	0.267659i
$821$	41.7998			1.45882			0.729412	−	0.684075i	$-0.239794\pi$
$821$	41.7998			1.45882			0.729412	+	0.684075i	$0.239794\pi$
$822$		0			0
$823$		−	40.2621i		−	1.40345i	−0.712448	−	0.701725i	$-0.752414\pi$
$823$		−	40.2621i		−	1.40345i	0.712448	−	0.701725i	$-0.247586\pi$
$824$	−0.421793	−	0.114355i	−0.0146938	−	0.00398374i
$825$		0			0
$826$	−27.8834	−	19.5651i	−0.970187	−	0.680756i
$827$		−	0.370314i		−	0.0128771i	−0.999979	−	0.00643854i	$-0.997951\pi$
$827$		−	0.370314i		−	0.0128771i	0.999979	−	0.00643854i	$-0.00204947\pi$
$828$		0			0
$829$			24.4071i			0.847695i	0.905733	+	0.423848i	$0.139321\pi$
$829$			24.4071i			0.847695i	−0.905733	+	0.423848i	$0.860679\pi$
$830$	16.0000	−	22.8025i	0.555368	−	0.791488i
$831$		0			0
$832$	4.04084	−	6.90446i	0.140091	−	0.239369i
$833$		−	1.11467i		−	0.0386211i
$834$		0			0
$835$	−63.7217			−2.20518
$836$	−5.08879	+	1.84083i	−0.175999	+	0.0636665i
$837$		0			0
$838$	13.7378	−	19.5786i	0.474565	−	0.676332i
$839$	6.88667			0.237754			0.118877	−	0.992909i	$-0.462071\pi$
$839$	6.88667			0.237754			0.118877	+	0.992909i	$0.462071\pi$
$840$		0			0
$841$	−5.94515			−0.205005
$842$	−17.9291	+	25.5518i	−0.617877	+	0.880574i
$843$		0			0
$844$	3.73140	+	10.3151i	0.128440	+	0.355059i
$845$	−3.23777			−0.111383
$846$		0			0
$847$		−	41.5848i		−	1.42887i
$848$	−32.5435	+	27.0896i	−1.11755	+	0.930261i
$849$		0			0
$850$	−0.420720	+	0.599593i	−0.0144306	+	0.0205659i
$851$			89.0104i			3.05124i
$852$		0			0
$853$		−	1.95999i		−	0.0671087i	−0.999437	−	0.0335544i	$-0.989317\pi$
$853$		−	1.95999i		−	0.0671087i	0.999437	−	0.0335544i	$-0.0106827\pi$
$854$	44.2796	+	31.0699i	1.51522	+	1.06319i
$855$		0			0
$856$	−5.86389	−	1.58979i	−0.200423	−	0.0543381i
$857$			24.2994i			0.830050i	0.909810	+	0.415025i	$0.136227\pi$
$857$			24.2994i			0.830050i	−0.909810	+	0.415025i	$0.863773\pi$
$858$		0			0
$859$	−14.9524			−0.510171			−0.255085	−	0.966919i	$-0.582104\pi$
$859$	−14.9524			−0.510171			−0.255085	+	0.966919i	$0.582104\pi$
$860$	−21.5375	−	59.5382i	−0.734423	−	2.03024i
$861$		0			0
$862$	−14.8587	−	10.4260i	−0.506089	−	0.355110i
$863$	12.3312			0.419760			0.209880	−	0.977727i	$-0.432693\pi$
$863$	12.3312			0.419760			0.209880	+	0.977727i	$0.432693\pi$
$864$		0			0
$865$	43.8810			1.49200
$866$	−25.8691	−	18.1517i	−0.879069	−	0.616821i
$867$		0			0
$868$	−22.3479	−	61.7785i	−0.758538	−	2.09690i
$869$	−18.0173			−0.611196
$870$		0			0
$871$			0.890006i			0.0301567i
$872$	35.1428	+	9.52778i	1.19008	+	0.322651i
$873$		0			0
$874$	20.1815	+	14.1608i	0.682649	+	0.478998i
$875$		−	6.78323i		−	0.229315i
$876$		0			0
$877$		−	18.4786i		−	0.623980i	−0.950085	−	0.311990i	$-0.899005\pi$
$877$		−	18.4786i		−	0.623980i	0.950085	−	0.311990i	$-0.100995\pi$
$878$	−24.7706	+	35.3021i	−0.835968	+	1.19139i
$879$		0			0
$880$	−9.83633	−	11.8166i	−0.331583	−	0.398339i
$881$		−	28.9527i		−	0.975440i	−0.873000	−	0.487720i	$-0.837829\pi$
$881$		−	28.9527i		−	0.975440i	0.873000	−	0.487720i	$-0.162171\pi$
$882$		0			0
$883$	−33.0699			−1.11289			−0.556445	−	0.830884i	$-0.687835\pi$
$883$	−33.0699			−1.11289			−0.556445	+	0.830884i	$0.687835\pi$
$884$	−0.0642644	−	0.177652i	−0.00216145	−	0.00597509i
$885$		0			0
$886$	−2.16729	+	3.08874i	−0.0728117	+	0.103768i
$887$	25.3010			0.849523			0.424762	−	0.905305i	$-0.360358\pi$
$887$	25.3010			0.849523			0.424762	+	0.905305i	$0.360358\pi$
$888$		0			0
$889$	−35.1583			−1.17917
$890$	−6.65056	+	9.47812i	−0.222927	+	0.317707i
$891$		0			0
$892$	43.8040	−	15.8458i	1.46667	−	0.530556i
$893$	−3.70697			−0.124049
$894$		0			0
$895$			75.0820i			2.50971i
$896$	−44.6014	+	20.4251i	−1.49003	+	0.682355i
$897$		0			0
$898$	−31.5877	+	45.0176i	−1.05410	+	1.50226i
$899$			36.3753i			1.21319i
$900$		0			0
$901$			0.999922i			0.0333122i
$902$	4.78191	+	3.35535i	0.159220	+	0.111721i
$903$		0			0
$904$	17.4286	+	4.72517i	0.579666	+	0.157157i
$905$		−	26.0848i		−	0.867088i
$906$		0			0
$907$	45.0830			1.49696			0.748478	−	0.663160i	$-0.230785\pi$
$907$	45.0830			1.49696			0.748478	+	0.663160i	$0.230785\pi$
$908$	17.3847	−	6.28879i	0.576931	−	0.208701i
$909$		0			0
$910$	16.2522	+	11.4038i	0.538755	+	0.378031i
$911$	−18.9238			−0.626973			−0.313486	−	0.949593i	$-0.601497\pi$
$911$	−18.9238			−0.626973			−0.313486	+	0.949593i	$0.601497\pi$
$912$		0			0
$913$	7.22207			0.239016
$914$	36.8370	+	25.8476i	1.21846	+	0.854964i
$915$		0			0
$916$	−7.73826	+	2.79926i	−0.255679	+	0.0924902i
$917$	−64.6609			−2.13529
$918$		0			0
$919$			16.4591i			0.542937i	0.962447	+	0.271468i	$0.0875092\pi$
$919$			16.4591i			0.542937i	−0.962447	+	0.271468i	$0.912491\pi$
$920$	−18.3288	+	67.6051i	−0.604284	+	2.22887i
$921$		0			0
$922$	30.0411	+	21.0791i	0.989349	+	0.694202i
$923$		−	5.75108i		−	0.189299i
$924$		0			0
$925$			63.8092i			2.09803i
$926$	−1.65462	+	2.35810i	−0.0543743	+	0.0774921i
$927$		0			0
$928$	27.0696	−	2.23411i	0.888604	−	0.0733384i
$929$			30.3566i			0.995966i	0.867187	+	0.497983i	$0.165926\pi$
$929$			30.3566i			0.995966i	−0.867187	+	0.497983i	$0.834074\pi$
$930$		0			0
$931$	−26.8959			−0.881478
$932$	−1.76513	+	0.638525i	−0.0578189	+	0.0209156i
$933$		0			0
$934$	−3.18417	+	4.53795i	−0.104189	+	0.148486i
$935$	−0.363075			−0.0118738
$936$		0			0
$937$	−9.81295			−0.320575			−0.160288	−	0.987070i	$-0.551242\pi$
$937$	−9.81295			−0.320575			−0.160288	+	0.987070i	$0.551242\pi$
$938$	3.13469	−	4.46744i	0.102351	−	0.145867i
$939$		0			0
$940$	−3.58268	−	9.90394i	−0.116854	−	0.323031i
$941$	9.31708			0.303728			0.151864	−	0.988401i	$-0.451472\pi$
$941$	9.31708			0.303728			0.151864	+	0.988401i	$0.451472\pi$
$942$		0			0
$943$		−	26.6138i		−	0.866664i
$944$	14.2155	+	17.0774i	0.462675	+	0.555824i
$945$		0			0
$946$	9.42854	−	13.4372i	0.306548	−	0.436880i
$947$		−	56.9545i		−	1.85077i	−0.379025	−	0.925386i	$-0.623741\pi$
$947$		−	56.9545i		−	1.85077i	0.379025	−	0.925386i	$-0.376259\pi$
$948$		0			0
$949$		−	13.0699i		−	0.424268i
$950$	14.4676	+	10.1515i	0.469390	+	0.329359i
$951$		0			0
$952$	−0.303130	+	1.11808i	−0.00982450	+	0.0362372i
$953$		−	30.0413i		−	0.973133i	−0.873643	−	0.486567i	$-0.838249\pi$
$953$		−	30.0413i		−	0.973133i	0.873643	−	0.486567i	$-0.161751\pi$
$954$		0			0
$955$	−35.7314			−1.15624
$956$	16.2312	+	44.8696i	0.524956	+	1.45119i
$957$		0			0
$958$	26.1425	+	18.3435i	0.844625	+	0.592652i
$959$	31.5411			1.01852
$960$		0			0
$961$	−26.3921			−0.851357
$962$	−13.4720	−	9.45295i	−0.434354	−	0.304775i
$963$		0			0
$964$	−4.54103	−	12.5532i	−0.146257	−	0.404312i
$965$	−24.6306			−0.792887
$966$		0			0
$967$		−	25.3713i		−	0.815885i	−0.913008	−	0.407942i	$-0.866246\pi$
$967$		−	25.3713i		−	0.815885i	0.913008	−	0.407942i	$-0.133754\pi$
$968$	−7.09820	+	26.1814i	−0.228145	+	0.841501i
$969$		0			0
$970$	−65.4907	−	45.9532i	−2.10278	−	1.47547i
$971$			14.4712i			0.464404i	0.972668	+	0.232202i	$0.0745931\pi$
$971$			14.4712i			0.464404i	−0.972668	+	0.232202i	$0.925407\pi$
$972$		0			0
$973$		−	1.85670i		−	0.0595230i
$974$	−8.91609	+	12.7069i	−0.285690	+	0.407154i
$975$		0			0
$976$	−22.5746	−	27.1195i	−0.722596	−	0.868074i
$977$		−	16.5139i		−	0.528325i	−0.964478	−	0.264163i	$-0.914904\pi$
$977$		−	16.5139i		−	0.528325i	0.964478	−	0.264163i	$-0.0850955\pi$
$978$		0			0
$979$	−3.00193			−0.0959421
$980$	−25.9941	−	71.8580i	−0.830352	−	2.29542i
$981$		0			0
$982$	−2.09546	+	2.98637i	−0.0668688	+	0.0952988i
$983$	4.69363			0.149703			0.0748517	−	0.997195i	$-0.476152\pi$
$983$	4.69363			0.149703			0.0748517	+	0.997195i	$0.476152\pi$
$984$		0			0
$985$	−11.8313			−0.376977
$986$	0.368419	−	0.525056i	0.0117329	−	0.0167212i
$987$		0			0
$988$	−4.28657	+	1.55063i	−0.136374	+	0.0493322i
$989$	−74.7847			−2.37802
$990$		0			0
$991$		−	49.9083i		−	1.58539i	−0.609618	−	0.792695i	$-0.708677\pi$
$991$		−	49.9083i		−	1.58539i	0.609618	−	0.792695i	$-0.291323\pi$
$992$	3.52493	+	42.7097i	0.111916	+	1.35604i
$993$		0			0
$994$	−20.2559	+	28.8679i	−0.642477	+	0.915633i
$995$			17.8079i			0.564548i
$996$		0			0
$997$			47.8441i			1.51524i	0.652697	+	0.757619i	$0.273637\pi$
$997$			47.8441i			1.51524i	−0.652697	+	0.757619i	$0.726363\pi$
$998$	6.04166	+	4.23928i	0.191245	+	0.134192i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.40	yes	48
3.2	odd	2	inner	936.2.j.a.755.9	✓	48
4.3	odd	2		3744.2.j.a.2159.42		48
8.3	odd	2	inner	936.2.j.a.755.10	yes	48
8.5	even	2		3744.2.j.a.2159.7		48
12.11	even	2		3744.2.j.a.2159.8		48
24.5	odd	2		3744.2.j.a.2159.41		48
24.11	even	2	inner	936.2.j.a.755.39	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.9	✓	48	3.2	odd	2	inner
936.2.j.a.755.10	yes	48	8.3	odd	2	inner
936.2.j.a.755.39	yes	48	24.11	even	2	inner
936.2.j.a.755.40	yes	48	1.1	even	1	trivial
3744.2.j.a.2159.7		48	8.5	even	2
3744.2.j.a.2159.8		48	12.11	even	2
3744.2.j.a.2159.41		48	24.5	odd	2
3744.2.j.a.2159.42		48	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15766 + 0.812299i) q^{2} +(0.680340 + 1.88073i) q^{4} +3.23777 q^{5} -4.33596i q^{7} +(-0.740114 + 2.72988i) q^{8} +(3.74823 + 2.63004i) q^{10} +1.18715i q^{11} +1.00000i q^{13} +(3.52210 - 5.01956i) q^{14} +(-3.07428 + 2.55907i) q^{16} +0.0944593i q^{17} +2.27921 q^{19} +(2.20279 + 6.08937i) q^{20} +(-0.964320 + 1.37431i) q^{22} +7.64873 q^{23} +5.48318 q^{25} +(-0.812299 + 1.15766i) q^{26} +(8.15477 - 2.94993i) q^{28} -4.80155 q^{29} -7.57575i q^{31} +(-5.63769 + 0.465290i) q^{32} +(-0.0767292 + 0.109351i) q^{34} -14.0389i q^{35} +11.6373i q^{37} +(2.63854 + 1.85140i) q^{38} +(-2.39632 + 8.83872i) q^{40} -3.47950i q^{41} -9.77740 q^{43} +(-2.23270 + 0.807664i) q^{44} +(8.85461 + 6.21306i) q^{46} -1.62643 q^{47} -11.8006 q^{49} +(6.34764 + 4.45398i) q^{50} +(-1.88073 + 0.680340i) q^{52} +10.5857 q^{53} +3.84372i q^{55} +(11.8366 + 3.20911i) q^{56} +(-5.55854 - 3.90029i) q^{58} -5.55495i q^{59} +8.82142i q^{61} +(6.15378 - 8.77013i) q^{62} +(-6.90446 - 4.04084i) q^{64} +3.23777i q^{65} +0.890006 q^{67} +(-0.177652 + 0.0642644i) q^{68} +(11.4038 - 16.2522i) q^{70} -5.75108 q^{71} -13.0699 q^{73} +(-9.45295 + 13.4720i) q^{74} +(1.55063 + 4.28657i) q^{76} +5.14743 q^{77} +15.1770i q^{79} +(-9.95381 + 8.28568i) q^{80} +(2.82640 - 4.02807i) q^{82} -6.08355i q^{83} +0.305838i q^{85} +(-11.3189 - 7.94217i) q^{86} +(-3.24077 - 0.878625i) q^{88} +2.52869i q^{89} +4.33596 q^{91} +(5.20374 + 14.3852i) q^{92} +(-1.88285 - 1.32115i) q^{94} +7.37955 q^{95} -17.4724 q^{97} +(-13.6610 - 9.58559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

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