LMFDB - Embedded newform 680.2.h.b.509.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.8
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29647 + 0.564954i) q^{2} +2.10974i q^{3} +(1.36165 - 1.46489i) q^{4} +(-2.12767 - 0.687771i) q^{5} +(-1.19191 - 2.73521i) q^{6} +2.16636 q^{7} +(-0.937746 + 2.66845i) q^{8} -1.45102 q^{9} +(3.14701 - 0.310361i) q^{10} -1.85151 q^{11} +(3.09054 + 2.87274i) q^{12} +6.11522 q^{13} +(-2.80861 + 1.22389i) q^{14} +(1.45102 - 4.48884i) q^{15} +(-0.291795 - 3.98934i) q^{16} +(-0.319939 + 4.11067i) q^{17} +(1.88120 - 0.819760i) q^{18} +2.40417i q^{19} +(-3.90466 + 2.18029i) q^{20} +4.57046i q^{21} +(2.40042 - 1.04602i) q^{22} -5.17461 q^{23} +(-5.62975 - 1.97840i) q^{24} +(4.05394 + 2.92670i) q^{25} +(-7.92819 + 3.45482i) q^{26} +3.26795i q^{27} +(2.94983 - 3.17347i) q^{28} +3.36345 q^{29} +(0.654783 + 6.63939i) q^{30} +0.731556i q^{31} +(2.63210 + 5.00720i) q^{32} -3.90622i q^{33} +(-1.90755 - 5.51010i) q^{34} +(-4.60929 - 1.48996i) q^{35} +(-1.97579 + 2.12558i) q^{36} +10.8095i q^{37} +(-1.35825 - 3.11693i) q^{38} +12.9016i q^{39} +(3.83050 - 5.03262i) q^{40} -4.69931i q^{41} +(-2.58210 - 5.92545i) q^{42} -5.90331 q^{43} +(-2.52112 + 2.71226i) q^{44} +(3.08729 + 0.997971i) q^{45} +(6.70872 - 2.92342i) q^{46} -3.82883i q^{47} +(8.41649 - 0.615613i) q^{48} -2.30690 q^{49} +(-6.90925 - 1.50408i) q^{50} +(-8.67247 - 0.674989i) q^{51} +(8.32682 - 8.95812i) q^{52} +6.98932 q^{53} +(-1.84624 - 4.23679i) q^{54} +(3.93940 + 1.27342i) q^{55} +(-2.03149 + 5.78082i) q^{56} -5.07219 q^{57} +(-4.36060 + 1.90019i) q^{58} +1.35564i q^{59} +(-4.59985 - 8.23783i) q^{60} -3.71760 q^{61} +(-0.413295 - 0.948438i) q^{62} -3.14343 q^{63} +(-6.24126 - 5.00466i) q^{64} +(-13.0112 - 4.20587i) q^{65} +(2.20683 + 5.06428i) q^{66} -11.7947 q^{67} +(5.58603 + 6.06599i) q^{68} -10.9171i q^{69} +(6.81755 - 0.672353i) q^{70} +11.1457i q^{71} +(1.36069 - 3.87198i) q^{72} -4.82829 q^{73} +(-6.10685 - 14.0141i) q^{74} +(-6.17459 + 8.55278i) q^{75} +(3.52184 + 3.27365i) q^{76} -4.01103 q^{77} +(-7.28878 - 16.7264i) q^{78} +0.112435i q^{79} +(-2.12291 + 8.68868i) q^{80} -11.2476 q^{81} +(2.65489 + 6.09250i) q^{82} +10.5584 q^{83} +(6.69521 + 6.22339i) q^{84} +(3.50793 - 8.52610i) q^{85} +(7.65345 - 3.33510i) q^{86} +7.09602i q^{87} +(1.73625 - 4.94067i) q^{88} +10.0055 q^{89} +(-4.56638 + 0.450341i) q^{90} +13.2478 q^{91} +(-7.04604 + 7.58023i) q^{92} -1.54340 q^{93} +(2.16311 + 4.96396i) q^{94} +(1.65352 - 5.11528i) q^{95} +(-10.5639 + 5.55305i) q^{96} -10.8895 q^{97} +(2.99082 - 1.30329i) q^{98} +2.68658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) $ 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.29647	+	0.564954i	−0.916741	+	0.399483i
$2$	−1.29647	+	0.564954i	−0.916741	+	0.399483i
$3$			2.10974i			1.21806i	0.793147	+	0.609031i	$0.208441\pi$
$3$			2.10974i			1.21806i	−0.793147	+	0.609031i	$0.791559\pi$
$4$	1.36165	−	1.46489i	0.680827	−	0.732444i
$5$	−2.12767	−	0.687771i	−0.951522	−	0.307581i
$5$	−2.12767	−	0.687771i	−0.951522	−	0.307581i
$6$	−1.19191	−	2.73521i	−0.486594	−	1.11665i
$7$	2.16636			0.818806			0.409403	−	0.912354i	$-0.365737\pi$
$7$	2.16636			0.818806			0.409403	+	0.912354i	$0.365737\pi$
$8$	−0.937746	+	2.66845i	−0.331543	+	0.943440i
$9$	−1.45102			−0.483674
$10$	3.14701	−	0.310361i	0.995172	−	0.0981448i
$11$	−1.85151			−0.558252			−0.279126	−	0.960255i	$-0.590045\pi$
$11$	−1.85151			−0.558252			−0.279126	+	0.960255i	$0.590045\pi$
$12$	3.09054	+	2.87274i	0.892162	+	0.829289i
$13$	6.11522			1.69606			0.848029	−	0.529950i	$-0.177789\pi$
$13$	6.11522			1.69606			0.848029	+	0.529950i	$0.177789\pi$
$14$	−2.80861	+	1.22389i	−0.750633	+	0.327099i
$15$	1.45102	−	4.48884i	0.374652	−	1.15901i
$16$	−0.291795	−	3.98934i	−0.0729487	−	0.997336i
$17$	−0.319939	+	4.11067i	−0.0775965	+	0.996985i
$17$	−0.319939	+	4.11067i	−0.0775965	+	0.996985i
$18$	1.88120	−	0.819760i	0.443404	−	0.193219i
$19$			2.40417i			0.551555i	0.961222	+	0.275777i	$0.0889353\pi$
$19$			2.40417i			0.551555i	−0.961222	+	0.275777i	$0.911065\pi$
$20$	−3.90466	+	2.18029i	−0.873108	+	0.487527i
$21$			4.57046i			0.997356i
$22$	2.40042	−	1.04602i	0.511772	−	0.223012i
$23$	−5.17461			−1.07898			−0.539491	−	0.841992i	$-0.681383\pi$
$23$	−5.17461			−1.07898			−0.539491	+	0.841992i	$0.681383\pi$
$24$	−5.62975	−	1.97840i	−1.14917	−	0.403840i
$25$	4.05394	+	2.92670i	0.810788	+	0.585340i
$26$	−7.92819	+	3.45482i	−1.55485	+	0.677546i
$27$			3.26795i			0.628917i
$28$	2.94983	−	3.17347i	0.557465	−	0.599730i
$29$	3.36345			0.624577			0.312288	−	0.949987i	$-0.398904\pi$
$29$	3.36345			0.624577			0.312288	+	0.949987i	$0.398904\pi$
$30$	0.654783	+	6.63939i	0.119546	+	1.21218i
$31$			0.731556i			0.131391i	0.997840	+	0.0656957i	$0.0209266\pi$
$31$			0.731556i			0.131391i	−0.997840	+	0.0656957i	$0.979073\pi$
$32$	2.63210	+	5.00720i	0.465293	+	0.885157i
$33$		−	3.90622i		−	0.679985i
$34$	−1.90755	−	5.51010i	−0.327142	−	0.944975i
$35$	−4.60929	−	1.48996i	−0.779112	−	0.251849i
$36$	−1.97579	+	2.12558i	−0.329298	+	0.354264i
$37$			10.8095i			1.77706i	0.458814	+	0.888532i	$0.348274\pi$
$37$			10.8095i			1.77706i	−0.458814	+	0.888532i	$0.651726\pi$
$38$	−1.35825	−	3.11693i	−0.220337	−	0.505633i
$39$			12.9016i			2.06590i
$40$	3.83050	−	5.03262i	0.605655	−	0.795728i
$41$		−	4.69931i		−	0.733909i	−0.930239	−	0.366955i	$-0.880400\pi$
$41$		−	4.69931i		−	0.733909i	0.930239	−	0.366955i	$-0.119600\pi$
$42$	−2.58210	−	5.92545i	−0.398426	−	0.914317i
$43$	−5.90331			−0.900247			−0.450123	−	0.892966i	$-0.648620\pi$
$43$	−5.90331			−0.900247			−0.450123	+	0.892966i	$0.648620\pi$
$44$	−2.52112	+	2.71226i	−0.380073	+	0.408888i
$45$	3.08729	+	0.997971i	0.460226	+	0.148769i
$46$	6.70872	−	2.92342i	0.989146	−	0.431034i
$47$		−	3.82883i		−	0.558493i	−0.960219	−	0.279246i	$-0.909915\pi$
$47$		−	3.82883i		−	0.558493i	0.960219	−	0.279246i	$-0.0900846\pi$
$48$	8.41649	−	0.615613i	1.21482	−	0.0888560i
$49$	−2.30690			−0.329557
$50$	−6.90925	−	1.50408i	−0.977116	−	0.212709i
$51$	−8.67247	−	0.674989i	−1.21439	−	0.0945174i
$52$	8.32682	−	8.95812i	1.15472	−	1.24227i
$53$	6.98932			0.960056			0.480028	−	0.877253i	$-0.340626\pi$
$53$	6.98932			0.960056			0.480028	+	0.877253i	$0.340626\pi$
$54$	−1.84624	−	4.23679i	−0.251241	−	0.576554i
$55$	3.93940	+	1.27342i	0.531189	+	0.171707i
$56$	−2.03149	+	5.78082i	−0.271470	+	0.772494i
$57$	−5.07219			−0.671828
$58$	−4.36060	+	1.90019i	−0.572575	+	0.249508i
$59$			1.35564i			0.176490i	0.996099	+	0.0882449i	$0.0281258\pi$
$59$			1.35564i			0.176490i	−0.996099	+	0.0882449i	$0.971874\pi$
$60$	−4.59985	−	8.23783i	−0.593838	−	1.06350i
$61$	−3.71760			−0.475990			−0.237995	−	0.971266i	$-0.576490\pi$
$61$	−3.71760			−0.475990			−0.237995	+	0.971266i	$0.576490\pi$
$62$	−0.413295	−	0.948438i	−0.0524886	−	0.120452i
$63$	−3.14343			−0.396035
$64$	−6.24126	−	5.00466i	−0.780158	−	0.625582i
$65$	−13.0112	−	4.20587i	−1.61384	−	0.521675i
$66$	2.20683	+	5.06428i	0.271642	+	0.623370i
$67$	−11.7947			−1.44095			−0.720477	−	0.693478i	$-0.756077\pi$
$67$	−11.7947			−1.44095			−0.720477	+	0.693478i	$0.756077\pi$
$68$	5.58603	+	6.06599i	0.677406	+	0.735610i
$69$		−	10.9171i		−	1.31427i
$70$	6.81755	−	0.672353i	0.814853	−	0.0803615i
$71$			11.1457i			1.32275i	0.750057	+	0.661374i	$0.230026\pi$
$71$			11.1457i			1.32275i	−0.750057	+	0.661374i	$0.769974\pi$
$72$	1.36069	−	3.87198i	0.160359	−	0.456317i
$73$	−4.82829			−0.565109			−0.282554	−	0.959251i	$-0.591182\pi$
$73$	−4.82829			−0.565109			−0.282554	+	0.959251i	$0.591182\pi$
$74$	−6.10685	−	14.0141i	−0.709907	−	1.62911i
$75$	−6.17459	+	8.55278i	−0.712980	+	0.987590i
$76$	3.52184	+	3.27365i	0.403983	+	0.375514i
$77$	−4.01103			−0.457100
$78$	−7.28878	−	16.7264i	−0.825292	−	1.89390i
$79$			0.112435i			0.0126500i	0.999980	+	0.00632498i	$0.00201332\pi$
$79$			0.112435i			0.0126500i	−0.999980	+	0.00632498i	$0.997987\pi$
$80$	−2.12291	+	8.68868i	−0.237349	+	0.971424i
$81$	−11.2476			−1.24973
$82$	2.65489	+	6.09250i	0.293184	+	0.672804i
$83$	10.5584			1.15893			0.579465	−	0.814997i	$-0.303262\pi$
$83$	10.5584			1.15893			0.579465	+	0.814997i	$0.303262\pi$
$84$	6.69521	+	6.22339i	0.730507	+	0.679027i
$85$	3.50793	−	8.52610i	0.380488	−	0.924786i
$86$	7.65345	−	3.33510i	0.825293	−	0.359633i
$87$			7.09602i			0.760773i
$88$	1.73625	−	4.94067i	0.185085	−	0.526677i
$89$	10.0055			1.06058			0.530292	−	0.847815i	$-0.322082\pi$
$89$	10.0055			1.06058			0.530292	+	0.847815i	$0.322082\pi$
$90$	−4.56638	+	0.450341i	−0.481339	+	0.0474701i
$91$	13.2478			1.38874
$92$	−7.04604	+	7.58023i	−0.734600	+	0.790294i
$93$	−1.54340			−0.160043
$94$	2.16311	+	4.96396i	0.223108	+	0.511993i
$95$	1.65352	−	5.11528i	0.169648	−	0.524817i
$96$	−10.5639	+	5.55305i	−1.07818	+	0.566756i
$97$	−10.8895			−1.10566			−0.552831	−	0.833293i	$-0.686452\pi$
$97$	−10.8895			−1.10566			−0.552831	+	0.833293i	$0.686452\pi$
$98$	2.99082	−	1.30329i	0.302118	−	0.131652i
$99$	2.68658			0.270012
$100$	9.80735	−	1.95342i	0.980735	−	0.195342i
$101$		−	1.11209i		−	0.110657i	−0.998468	−	0.0553287i	$-0.982379\pi$
$101$		−	1.11209i		−	0.110657i	0.998468	−	0.0553287i	$-0.0176207\pi$
$102$	11.6249	−	4.02444i	1.15104	−	0.398479i
$103$			9.49791i			0.935857i	0.883766	+	0.467928i	$0.154999\pi$
$103$			9.49791i			0.935857i	−0.883766	+	0.467928i	$0.845001\pi$
$104$	−5.73453	+	16.3182i	−0.562316	+	1.60013i
$105$	3.14343	−	9.72442i	0.306767	−	0.949006i
$106$	−9.06142	+	3.94864i	−0.880123	+	0.383526i
$107$			9.77953i			0.945423i	0.881217	+	0.472712i	$0.156725\pi$
$107$			9.77953i			0.945423i	−0.881217	+	0.472712i	$0.843275\pi$
$108$	4.78718	+	4.44982i	0.460646	+	0.428184i
$109$	17.5905			1.68486			0.842430	−	0.538806i	$-0.181124\pi$
$109$	17.5905			1.68486			0.842430	+	0.538806i	$0.181124\pi$
$110$	−5.82673	+	0.574637i	−0.555557	+	0.0547895i
$111$	−22.8052			−2.16457
$112$	−0.632132	−	8.64234i	−0.0597308	−	0.816624i
$113$	12.1552			1.14346			0.571732	−	0.820441i	$-0.306272\pi$
$113$	12.1552			1.14346			0.571732	+	0.820441i	$0.306272\pi$
$114$	6.57593	−	2.86555i	0.615892	−	0.268384i
$115$	11.0099	+	3.55895i	1.02667	+	0.331874i
$116$	4.57985	−	4.92708i	0.425229	−	0.457468i
$117$	−8.87332			−0.820339
$118$	−0.765876	−	1.75755i	−0.0705046	−	0.161795i
$119$	−0.693101	+	8.90519i	−0.0635365	+	0.816337i
$120$	10.6175	+	8.08137i	0.969245	+	0.737725i
$121$	−7.57190			−0.688355
$122$	4.81975	−	2.10027i	0.436359	−	0.190150i
$123$	9.91435			0.893946
$124$	1.07165	+	0.996126i	0.0962368	+	0.0894548i
$125$	−6.61254	−	9.01523i	−0.591444	−	0.806346i
$126$	4.07536	−	1.77589i	0.363061	−	0.158209i
$127$			7.69908i			0.683183i	0.939849	+	0.341591i	$0.110966\pi$
$127$			7.69908i			0.683183i	−0.939849	+	0.341591i	$0.889034\pi$
$128$	10.9190	+	2.96235i	0.965112	+	0.261837i
$129$		−	12.4545i		−	1.09656i
$130$	19.2447	−	1.89793i	1.68787	−	0.166459i
$131$	−8.54786			−0.746830			−0.373415	−	0.927664i	$-0.621813\pi$
$131$	−8.54786			−0.746830			−0.373415	+	0.927664i	$0.621813\pi$
$132$	−5.72217	−	5.31892i	−0.498051	−	0.462952i
$133$			5.20829i			0.451616i
$134$	15.2915	−	6.66348i	1.32098	−	0.575637i
$135$	2.24760	−	6.95311i	0.193443	−	0.598428i
$136$	−10.6691	−	4.70851i	−0.914869	−	0.403751i
$137$			9.56697i			0.817361i	0.912677	+	0.408681i	$0.134011\pi$
$137$			9.56697i			0.817361i	−0.912677	+	0.408681i	$0.865989\pi$
$138$	6.16766	+	14.1537i	0.525026	+	1.20484i
$139$	7.97287			0.676250			0.338125	−	0.941101i	$-0.390207\pi$
$139$	7.97287			0.676250			0.338125	+	0.941101i	$0.390207\pi$
$140$	−8.45888	+	4.72328i	−0.714906	+	0.399190i
$141$	8.07786			0.680279
$142$	−6.29679	−	14.4500i	−0.528415	−	1.21262i
$143$	−11.3224			−0.946827
$144$	0.423401	+	5.78862i	0.0352834	+	0.482385i
$145$	−7.15630	−	2.31328i	−0.594299	−	0.192108i
$146$	6.25972	−	2.72776i	0.518058	−	0.225751i
$147$		−	4.86697i		−	0.401421i
$148$	15.8347	+	14.7188i	1.30160	+	1.20987i
$149$		−	21.9285i		−	1.79646i	−0.439530	−	0.898228i	$-0.644855\pi$
$149$		−	21.9285i		−	1.79646i	0.439530	−	0.898228i	$-0.355145\pi$
$150$	3.17322	−	14.5768i	0.259092	−	1.19019i
$151$	14.6281			1.19042			0.595209	−	0.803571i	$-0.297069\pi$
$151$	14.6281			1.19042			0.595209	+	0.803571i	$0.297069\pi$
$152$	−6.41542	−	2.25450i	−0.520359	−	0.182864i
$153$	0.464238	−	5.96468i	0.0375314	−	0.482216i
$154$	5.20017	−	2.26605i	0.419042	−	0.182603i
$155$	0.503143	−	1.55651i	0.0404134	−	0.125022i
$156$	18.8993	+	17.5675i	1.51316	+	1.40652i
$157$	−7.45137			−0.594684			−0.297342	−	0.954771i	$-0.596100\pi$
$157$	−7.45137			−0.594684			−0.297342	+	0.954771i	$0.596100\pi$
$158$	−0.0635208	−	0.145769i	−0.00505344	−	0.0115967i
$159$			14.7457i			1.16941i
$160$	−2.15642	−	12.4639i	−0.170480	−	0.985361i
$161$	−11.2101			−0.883476
$162$	14.5821	−	6.35438i	1.14568	−	0.499247i
$163$		−	13.8521i		−	1.08498i	−0.840063	−	0.542490i	$-0.817482\pi$
$163$		−	13.8521i		−	1.08498i	0.840063	−	0.542490i	$-0.182518\pi$
$164$	−6.88397	−	6.39884i	−0.537547	−	0.499665i
$165$	−2.68658	+	8.31113i	−0.209150	+	0.647021i
$166$	−13.6886	+	5.96498i	−1.06244	+	0.462972i
$167$	16.1778			1.25188			0.625938	−	0.779873i	$-0.284716\pi$
$167$	16.1778			1.25188			0.625938	+	0.779873i	$0.284716\pi$
$168$	−12.1960	−	4.28593i	−0.940946	−	0.330667i
$169$	24.3959			1.87661
$170$	0.268943	+	13.0356i	0.0206270	+	0.999787i
$171$		−	3.48851i		−	0.266773i
$172$	−8.03827	+	8.64769i	−0.612912	+	0.659380i
$173$			6.21909i			0.472829i	0.971652	+	0.236414i	$0.0759723\pi$
$173$			6.21909i			0.472829i	−0.971652	+	0.236414i	$0.924028\pi$
$174$	−4.00892	−	9.19975i	−0.303916	−	0.697432i
$175$	8.78228	+	6.34027i	0.663878	+	0.479280i
$176$	0.540262	+	7.38631i	0.0407238	+	0.556764i
$177$	−2.86006			−0.214975
$178$	−12.9718	+	5.65266i	−0.972280	+	0.423685i
$179$			14.0992i			1.05383i	0.849919	+	0.526913i	$0.176651\pi$
$179$			14.0992i			1.05383i	−0.849919	+	0.526913i	$0.823349\pi$
$180$	5.66574	−	3.16365i	0.422299	−	0.235804i
$181$	18.0233			1.33966			0.669829	−	0.742515i	$-0.266367\pi$
$181$	18.0233			1.33966			0.669829	+	0.742515i	$0.266367\pi$
$182$	−17.1753	+	7.48437i	−1.27312	+	0.554778i
$183$		−	7.84319i		−	0.579785i
$184$	4.85247	−	13.8082i	0.357729	−	1.01795i
$185$	7.43444	−	22.9989i	0.546591	−	1.69092i
$186$	2.00096	−	0.871947i	0.146718	−	0.0639343i
$187$	0.592370	−	7.61096i	0.0433184	−	0.556569i
$188$	−5.60881	−	5.21355i	−0.409065	−	0.380237i
$189$			7.07954i			0.514961i
$190$	0.746162	+	7.56596i	0.0541322	+	0.548892i
$191$	3.47978			0.251788			0.125894	−	0.992044i	$-0.459820\pi$
$191$	3.47978			0.251788			0.125894	+	0.992044i	$0.459820\pi$
$192$	10.5586	−	13.1675i	0.761998	−	0.950281i
$193$	16.2989			1.17322			0.586610	−	0.809870i	$-0.300462\pi$
$193$	16.2989			1.17322			0.586610	+	0.809870i	$0.300462\pi$
$194$	14.1179	−	6.15207i	1.01361	−	0.441693i
$195$	8.87332	−	27.4502i	0.635432	−	1.96575i
$196$	−3.14120	+	3.37935i	−0.224371	+	0.241382i
$197$		−	17.1153i		−	1.21941i	−0.792627	−	0.609707i	$-0.791287\pi$
$197$		−	17.1153i		−	1.21941i	0.792627	−	0.609707i	$-0.208713\pi$
$198$	−3.48307	+	1.51780i	−0.247531	+	0.107865i
$199$		−	19.0307i		−	1.34905i	−0.738253	−	0.674524i	$-0.764349\pi$
$199$		−	19.0307i		−	1.34905i	0.738253	−	0.674524i	$-0.235651\pi$
$200$	−11.6113	+	8.07325i	−0.821044	+	0.570865i
$201$		−	24.8839i		−	1.75517i
$202$	0.628281	+	1.44179i	0.0442057	+	0.101444i
$203$	7.28643			0.511407
$204$	−12.7977	+	11.7851i	−0.896018	+	0.825122i
$205$	−3.23205	+	9.99857i	−0.225736	+	0.698331i
$206$	−5.36588	−	12.3137i	−0.373859	−	0.857938i
$207$	7.50848			0.521875
$208$	−1.78439	−	24.3957i	−0.123725	−	1.69154i
$209$		−	4.45135i		−	0.307906i
$210$	1.41849	+	14.3833i	0.0978853	+	0.992541i
$211$	−3.28113			−0.225883			−0.112941	−	0.993602i	$-0.536027\pi$
$211$	−3.28113			−0.225883			−0.112941	+	0.993602i	$0.536027\pi$
$212$	9.51703	−	10.2386i	0.653632	−	0.703188i
$213$	−23.5145			−1.61119
$214$	−5.52499	−	12.6788i	−0.377680	−	0.866708i
$215$	12.5603	+	4.06013i	0.856604	+	0.276898i
$216$	−8.72036	−	3.06451i	−0.593345	−	0.208513i
$217$			1.58481i			0.107584i
$218$	−22.8054	+	9.93779i	−1.54458	+	0.673072i
$219$		−	10.1865i		−	0.688337i
$220$	7.22952	−	4.03683i	0.487414	−	0.272163i
$221$	−1.95650	+	25.1377i	−0.131608	+	1.69094i
$222$	29.5662	−	12.8839i	1.98435	−	0.864710i
$223$		−	29.0341i		−	1.94427i	−0.234424	−	0.972134i	$-0.575320\pi$
$223$		−	29.0341i		−	1.94427i	0.234424	−	0.972134i	$-0.424680\pi$
$224$	5.70206	+	10.8474i	0.380985	+	0.724771i
$225$	−5.88236	−	4.24670i	−0.392157	−	0.283114i
$226$	−15.7588	+	6.86712i	−1.04826	+	0.456794i
$227$		−	20.0978i		−	1.33394i	−0.745085	−	0.666970i	$-0.767591\pi$
$227$		−	20.0978i		−	1.33394i	0.745085	−	0.666970i	$-0.232409\pi$
$228$	−6.90657	+	7.43019i	−0.457399	+	0.492076i
$229$			18.7378i			1.23823i	0.785302	+	0.619113i	$0.212508\pi$
$229$			18.7378i			1.23823i	−0.785302	+	0.619113i	$0.787492\pi$
$230$	−16.2846	+	1.60600i	−1.07377	+	0.105896i
$231$		−	8.46226i		−	0.556776i
$232$	−3.15406	+	8.97520i	−0.207074	+	0.589251i
$233$	4.14371			0.271464			0.135732	−	0.990746i	$-0.456661\pi$
$233$	4.14371			0.271464			0.135732	+	0.990746i	$0.456661\pi$
$234$	11.5040	−	5.01302i	0.752038	−	0.327711i
$235$	−2.63336	+	8.14649i	−0.171782	+	0.531418i
$236$	1.98587	+	1.84592i	0.129269	+	0.120159i
$237$	−0.237210			−0.0154084
$238$	−4.13244	−	11.9369i	−0.267866	−	0.773751i
$239$	9.53014			0.616454			0.308227	−	0.951313i	$-0.400264\pi$
$239$	9.53014			0.616454			0.308227	+	0.951313i	$0.400264\pi$
$240$	−18.3309	−	4.47880i	−1.18325	−	0.289106i
$241$		−	1.10400i		−	0.0711151i	−0.999368	−	0.0355576i	$-0.988679\pi$
$241$		−	1.10400i		−	0.0711151i	0.999368	−	0.0355576i	$-0.0113207\pi$
$242$	9.81673	−	4.27778i	0.631043	−	0.274986i
$243$		−	13.9257i		−	0.893335i
$244$	−5.06209	+	5.44587i	−0.324067	+	0.348636i
$245$	4.90831	+	1.58662i	0.313581	+	0.101365i
$246$	−12.8536	+	5.60115i	−0.819517	+	0.357116i
$247$			14.7020i			0.935469i
$248$	−1.95212	−	0.686014i	−0.123960	−	0.0435619i
$249$			22.2754i			1.41165i
$250$	13.6661	+	7.95216i	0.864322	+	0.502939i
$251$			23.7570i			1.49953i	0.661706	+	0.749763i	$0.269833\pi$
$251$			23.7570i			1.49953i	−0.661706	+	0.749763i	$0.730167\pi$
$252$	−4.28027	+	4.60477i	−0.269631	+	0.290074i
$253$	9.58086			0.602343
$254$	−4.34962	−	9.98160i	−0.272920	−	0.626301i
$255$	17.9879	+	7.40083i	1.12645	+	0.463458i
$256$	−15.8297	+	2.32814i	−0.989357	+	0.145509i
$257$			9.30407i			0.580372i	0.956970	+	0.290186i	$0.0937171\pi$
$257$			9.30407i			0.580372i	−0.956970	+	0.290186i	$0.906283\pi$
$258$	7.03621	+	16.1468i	0.438055	+	1.00526i
$259$			23.4172i			1.45507i
$260$	−23.8778	+	13.3330i	−1.48084	+	0.826874i
$261$	−4.88044			−0.302092
$262$	11.0820	−	4.82915i	0.684649	−	0.298346i
$263$			5.99547i			0.369697i	0.982767	+	0.184848i	$0.0591794\pi$
$263$			5.99547i			0.369697i	−0.982767	+	0.184848i	$0.940821\pi$
$264$	10.4235	+	3.66304i	0.641525	+	0.225444i
$265$	−14.8709	−	4.80705i	−0.913515	−	0.295295i
$266$	−2.94245	−	6.75238i	−0.180413	−	0.414015i
$267$			21.1091i			1.29186i
$268$	−16.0603	+	17.2780i	−0.981041	+	1.05542i
$269$	−13.1391			−0.801106			−0.400553	−	0.916274i	$-0.631182\pi$
$269$	−13.1391			−0.801106			−0.400553	+	0.916274i	$0.631182\pi$
$270$	1.01424	+	10.2843i	0.0617249	+	0.625881i
$271$	−9.00112			−0.546779			−0.273389	−	0.961903i	$-0.588145\pi$
$271$	−9.00112			−0.546779			−0.273389	+	0.961903i	$0.588145\pi$
$272$	16.4922	+	0.0768717i	0.999989	+	0.00466103i
$273$			27.9494i			1.69157i
$274$	−5.40490	−	12.4033i	−0.326522	−	0.749309i
$275$	−7.50592	−	5.41882i	−0.452624	−	0.326767i
$276$	−15.9923	−	14.8653i	−0.962626	−	0.894788i
$277$		−	23.8779i		−	1.43468i	−0.696722	−	0.717342i	$-0.745359\pi$
$277$		−	23.8779i		−	1.43468i	0.696722	−	0.717342i	$-0.254641\pi$
$278$	−10.3366	+	4.50431i	−0.619946	+	0.270150i
$279$		−	1.06150i		−	0.0635506i
$280$	8.29822	−	10.9025i	0.495914	−	0.651546i
$281$	15.2045			0.907027			0.453513	−	0.891249i	$-0.350170\pi$
$281$	15.2045			0.907027			0.453513	+	0.891249i	$0.350170\pi$
$282$	−10.4727	+	4.56362i	−0.623639	+	0.271759i
$283$			23.8313i			1.41662i	0.705901	+	0.708310i	$0.250542\pi$
$283$			23.8313i			1.41662i	−0.705901	+	0.708310i	$0.749458\pi$
$284$	16.3272	+	15.1765i	0.968838	+	0.900562i
$285$	10.7919	+	3.48851i	0.639259	+	0.206641i
$286$	14.6791	−	6.39664i	0.867995	−	0.378241i
$287$		−	10.1804i		−	0.600929i
$288$	−3.81923	−	7.26556i	−0.225050	−	0.428127i
$289$	−16.7953	−	2.63033i	−0.987958	−	0.154725i
$290$	10.5848	−	1.04388i	0.621561	−	0.0612990i
$291$		−	22.9741i		−	1.34676i
$292$	−6.57446	+	7.07291i	−0.384741	+	0.413911i
$293$	−13.4198			−0.783996			−0.391998	−	0.919966i	$-0.628216\pi$
$293$	−13.4198			−0.783996			−0.391998	+	0.919966i	$0.628216\pi$
$294$	2.74961	+	6.30986i	0.160361	+	0.367999i
$295$	0.932373	−	2.88436i	0.0542848	−	0.167934i
$296$	−28.8445	−	10.1365i	−1.67655	−	0.589174i
$297$		−	6.05064i		−	0.351094i
$298$	12.3886	+	28.4296i	0.717653	+	1.64688i
$299$	−31.6439			−1.83001
$300$	4.12122	+	20.6910i	0.237939	+	1.19460i
$301$	−12.7887			−0.737127
$302$	−18.9649	+	8.26420i	−1.09130	+	0.475551i
$303$	2.34623			0.134788
$304$	9.59107	−	0.701525i	0.550085	−	0.0402352i
$305$	7.90982	+	2.55686i	0.452915	+	0.146405i
$306$	2.76790	+	7.99528i	0.158230	+	0.457060i
$307$	−29.0354			−1.65714			−0.828568	−	0.559888i	$-0.810844\pi$
$307$	−29.0354			−1.65714			−0.828568	+	0.559888i	$0.810844\pi$
$308$	−5.46164	+	5.87572i	−0.311206	+	0.334800i
$309$	−20.0382			−1.13993
$310$	0.227046	+	2.30221i	0.0128954	+	0.130757i
$311$			3.67913i			0.208624i	0.994545	+	0.104312i	$0.0332641\pi$
$311$			3.67913i			0.208624i	−0.994545	+	0.104312i	$0.966736\pi$
$312$	−34.4272	−	12.0984i	−1.94906	−	0.684936i
$313$	14.4341			0.815866			0.407933	−	0.913012i	$-0.366250\pi$
$313$	14.4341			0.815866			0.407933	+	0.913012i	$0.366250\pi$
$314$	9.66046	−	4.20968i	0.545171	−	0.237566i
$315$	6.68818	+	2.16196i	0.376836	+	0.121813i
$316$	0.164705	+	0.153098i	0.00926539	+	0.00861244i
$317$		−	0.137217i		−	0.00770689i	−0.999993	−	0.00385344i	$-0.998773\pi$
$317$		−	0.137217i		−	0.00770689i	0.999993	−	0.00385344i	$-0.00122659\pi$
$318$	−8.33062	−	19.1173i	−0.467158	−	1.07204i
$319$	−6.22746			−0.348671
$320$	9.83728	+	14.9408i	0.549921	+	0.835217i
$321$	−20.6323			−1.15158
$322$	14.5335	−	6.33317i	0.809919	−	0.352934i
$323$	−9.88277	−	0.769188i	−0.549892	−	0.0427988i
$324$	−15.3153	+	16.4765i	−0.850852	+	0.915360i
$325$	24.7908	+	17.8974i	1.37514	+	0.992770i
$326$	7.82579	+	17.9588i	0.433430	+	0.994645i
$327$			37.1114i			2.05226i
$328$	12.5399	+	4.40676i	0.692399	+	0.243323i
$329$		−	8.29462i		−	0.457297i
$330$	−1.21234	−	12.2929i	−0.0667370	−	0.676702i
$331$		−	22.5043i		−	1.23695i	−0.785806	−	0.618473i	$-0.787751\pi$
$331$		−	22.5043i		−	1.23695i	0.785806	−	0.618473i	$-0.212249\pi$
$332$	14.3768	−	15.4668i	0.789031	−	0.848851i
$333$		−	15.6848i		−	0.859520i
$334$	−20.9740	+	9.13971i	−1.14765	+	0.500103i
$335$	25.0953	+	8.11207i	1.37110	+	0.443210i
$336$	18.2331	−	1.33364i	0.994699	−	0.0727558i
$337$	12.8862			0.701955			0.350977	−	0.936384i	$-0.385849\pi$
$337$	12.8862			0.701955			0.350977	+	0.936384i	$0.385849\pi$
$338$	−31.6285	+	13.7826i	−1.72037	+	0.749674i
$339$			25.6443i			1.39281i
$340$	−7.71320	−	16.7483i	−0.418307	−	0.908306i
$341$		−	1.35448i		−	0.0733494i
$342$	1.97084	+	4.52273i	0.106571	+	0.244561i
$343$	−20.1621			−1.08865
$344$	5.53581	−	15.7527i	0.298471	−	0.849329i
$345$	−7.50848	+	23.2280i	−0.404243	+	1.25055i
$346$	−3.51350	−	8.06285i	−0.188887	−	0.433462i
$347$		−	17.0015i		−	0.912687i	−0.889804	−	0.456344i	$-0.849159\pi$
$347$		−	17.0015i		−	0.912687i	0.889804	−	0.456344i	$-0.150841\pi$
$348$	10.3949	+	9.66232i	0.557224	+	0.517955i
$349$		−	35.6065i		−	1.90597i	−0.303015	−	0.952986i	$-0.597993\pi$
$349$		−	35.6065i		−	1.90597i	0.303015	−	0.952986i	$-0.402007\pi$
$350$	−14.9679	−	3.25837i	−0.800068	−	0.174167i
$351$			19.9842i			1.06668i
$352$	−4.87336	−	9.27089i	−0.259751	−	0.494140i
$353$		−	23.2325i		−	1.23654i	−0.785965	−	0.618270i	$-0.787834\pi$
$353$		−	23.2325i		−	1.23654i	0.785965	−	0.618270i	$-0.212166\pi$
$354$	3.70798	−	1.61580i	0.197077	−	0.0858789i
$355$	7.66567	−	23.7143i	0.406852	−	1.25862i
$356$	13.6241	−	14.6570i	0.722074	−	0.776818i
$357$	−18.7877	−	1.46227i	−0.994349	−	0.0773914i
$358$	−7.96542	−	18.2792i	−0.420985	−	0.966085i
$359$	−14.9651			−0.789826			−0.394913	−	0.918719i	$-0.629225\pi$
$359$	−14.9651			−0.789826			−0.394913	+	0.918719i	$0.629225\pi$
$360$	−5.55813	+	7.30245i	−0.292939	+	0.384873i
$361$	13.2200			0.695787
$362$	−23.3666	+	10.1823i	−1.22812	+	0.535171i
$363$		−	15.9748i		−	0.838459i
$364$	18.0389	−	19.4065i	0.945493	−	1.01718i
$365$	10.2730	+	3.32076i	0.537713	+	0.173817i
$366$	4.43104	+	10.1684i	0.231614	+	0.531513i
$367$	−23.3931			−1.22111			−0.610556	−	0.791973i	$-0.709054\pi$
$367$	−23.3931			−1.22111			−0.610556	+	0.791973i	$0.709054\pi$
$368$	1.50993	+	20.6433i	0.0787103	+	1.07611i
$369$			6.81880i			0.354973i
$370$	3.35484	+	34.0175i	0.174410	+	1.76849i
$371$	15.1414			0.786100
$372$	−2.10157	+	2.26090i	−0.108961	+	0.117222i
$373$	32.4530			1.68035			0.840176	−	0.542313i	$-0.182451\pi$
$373$	32.4530			1.68035			0.840176	+	0.542313i	$0.182451\pi$
$374$	3.53185	+	10.2020i	0.182628	+	0.527534i
$375$	19.0198	−	13.9508i	0.982179	−	0.720415i
$376$	10.2171	+	3.59047i	0.526904	+	0.185165i
$377$	20.5682			1.05932
$378$	−3.99961	−	9.17839i	−0.205718	−	0.472086i
$379$	25.8746			1.32909			0.664545	−	0.747248i	$-0.268625\pi$
$379$	25.8746			1.32909			0.664545	+	0.747248i	$0.268625\pi$
$380$	−5.24179	−	9.38747i	−0.268898	−	0.481567i
$381$	−16.2431			−0.832158
$382$	−4.51143	+	1.96592i	−0.230825	+	0.100585i
$383$			11.3405i			0.579472i	0.957107	+	0.289736i	$0.0935675\pi$
$383$			11.3405i			0.579472i	−0.957107	+	0.289736i	$0.906433\pi$
$384$	−6.24980	+	23.0363i	−0.318934	+	1.17557i
$385$	8.53415	+	2.75867i	0.434941	+	0.140595i
$386$	−21.1310	+	9.20812i	−1.07554	+	0.468681i
$387$	8.56583			0.435426
$388$	−14.8277	+	15.9519i	−0.752765	+	0.809836i
$389$		−	14.9099i		−	0.755961i	−0.925814	−	0.377980i	$-0.876619\pi$
$389$		−	14.9099i		−	0.755961i	0.925814	−	0.377980i	$-0.123381\pi$
$390$	4.00414	+	40.6013i	0.202758	+	2.05593i
$391$	1.65556	−	21.2711i	0.0837252	−	1.07573i
$392$	2.16328	−	6.15585i	0.109262	−	0.310917i
$393$		−	18.0338i		−	0.909685i
$394$	9.66934	+	22.1894i	0.487134	+	1.11789i
$395$	0.0773298	−	0.239225i	0.00389088	−	0.0120367i
$396$	3.65820	−	3.93554i	0.183831	−	0.197769i
$397$			18.2959i			0.918247i	0.888372	+	0.459124i	$0.151836\pi$
$397$			18.2959i			0.918247i	−0.888372	+	0.459124i	$0.848164\pi$
$398$	10.7514	+	24.6726i	0.538921	+	1.23673i
$399$	−10.9882			−0.550097
$400$	10.4927	−	17.0266i	0.524634	−	0.851328i
$401$			15.9420i			0.796108i	0.917362	+	0.398054i	$0.130314\pi$
$401$			15.9420i			0.796108i	−0.917362	+	0.398054i	$0.869686\pi$
$402$	14.0582	+	32.2611i	0.701161	+	1.60904i
$403$			4.47363i			0.222847i
$404$	−1.62909	−	1.51429i	−0.0810504	−	0.0753386i
$405$	23.9312	+	7.73578i	1.18915	+	0.384394i
$406$	−9.44662	+	4.11650i	−0.468828	+	0.204298i
$407$		−	20.0138i		−	0.992049i
$408$	9.93375	−	22.5091i	0.491794	−	1.11437i
$409$	−9.75792			−0.482498			−0.241249	−	0.970463i	$-0.577557\pi$
$409$	−9.75792			−0.482498			−0.241249	+	0.970463i	$0.577557\pi$
$410$	−1.45848	−	14.7888i	−0.0720294	−	0.730366i
$411$	−20.1839			−0.995597
$412$	13.9134	+	12.9329i	0.685463	+	0.637157i
$413$			2.93681i			0.144511i
$414$	−9.73449	+	4.24194i	−0.478424	+	0.208480i
$415$	−22.4647	−	7.26173i	−1.10275	−	0.356464i
$416$	16.0959	+	30.6201i	0.789164	+	1.50128i
$417$			16.8207i			0.823715i
$418$	2.51481	+	5.77103i	0.123003	+	0.282270i
$419$	0.671116			0.0327861			0.0163931	−	0.999866i	$-0.494782\pi$
$419$	0.671116			0.0327861			0.0163931	+	0.999866i	$0.494782\pi$
$420$	−9.96492	−	17.8461i	−0.486238	−	0.870799i
$421$		−	26.6975i		−	1.30116i	−0.759440	−	0.650578i	$-0.774527\pi$
$421$		−	26.6975i		−	1.30116i	0.759440	−	0.650578i	$-0.225473\pi$
$422$	4.25388	−	1.85369i	0.207076	−	0.0902362i
$423$			5.55572i			0.270128i
$424$	−6.55420	+	18.6506i	−0.318300	+	0.905756i
$425$	−13.3277	+	15.7281i	−0.646489	+	0.762923i
$426$	30.4858	−	13.2846i	1.47704	−	0.643642i
$427$	−8.05365			−0.389743
$428$	14.3259	+	13.3163i	0.692470	+	0.643670i
$429$		−	23.8874i		−	1.15329i
$430$	−18.5778	+	1.83216i	−0.895900	+	0.0883545i
$431$		−	2.77459i		−	0.133647i	−0.997765	−	0.0668236i	$-0.978714\pi$
$431$		−	2.77459i		−	0.133647i	0.997765	−	0.0668236i	$-0.0212865\pi$
$432$	13.0370	−	0.953571i	0.627241	−	0.0458787i
$433$		−	11.7652i		−	0.565399i	−0.959208	−	0.282700i	$-0.908770\pi$
$433$		−	11.7652i		−	0.565399i	0.959208	−	0.282700i	$-0.0912300\pi$
$434$	−0.895345	−	2.05466i	−0.0429779	−	0.0986266i
$435$	4.88044	−	15.0980i	0.233999	−	0.723892i
$436$	23.9521	−	25.7680i	1.14710	−	1.23407i
$437$		−	12.4407i		−	0.595118i
$438$	5.75488	+	13.2064i	0.274979	+	0.631027i
$439$		−	31.3148i		−	1.49458i	−0.664500	−	0.747288i	$-0.731356\pi$
$439$		−	31.3148i		−	1.49458i	0.664500	−	0.747288i	$-0.268644\pi$
$440$	−7.09221	+	9.31796i	−0.338108	+	0.444216i
$441$	3.34736			0.159398
$442$	−11.6651	−	33.6955i	−0.554852	−	1.60273i
$443$	−34.7836			−1.65262			−0.826310	−	0.563215i	$-0.809564\pi$
$443$	−34.7836			−1.65262			−0.826310	+	0.563215i	$0.809564\pi$
$444$	−31.0528	+	33.4071i	−1.47370	+	1.58543i
$445$	−21.2884	−	6.88151i	−1.00917	−	0.326215i
$446$	16.4029	+	37.6418i	0.776702	+	1.78239i
$447$	46.2636			2.18819
$448$	−13.5208	−	10.8419i	−0.638798	−	0.512231i
$449$		−	19.6407i		−	0.926902i	−0.886123	−	0.463451i	$-0.846611\pi$
$449$		−	19.6407i		−	0.926902i	0.886123	−	0.463451i	$-0.153389\pi$
$450$	10.0255	+	2.18245i	0.472605	+	0.102882i
$451$			8.70083i			0.409706i
$452$	16.5512	−	17.8060i	0.778501	−	0.837523i
$453$			30.8616i			1.45000i
$454$	11.3543	+	26.0562i	0.532886	+	1.22288i
$455$	−28.1868	−	9.11143i	−1.32142	−	0.427150i
$456$	4.75642	−	13.5349i	0.222740	−	0.633829i
$457$		−	3.47599i		−	0.162600i	−0.996690	−	0.0812999i	$-0.974093\pi$
$457$		−	3.47599i		−	0.162600i	0.996690	−	0.0812999i	$-0.0259072\pi$
$458$	−10.5860	−	24.2929i	−0.494650	−	1.13513i
$459$	−13.4335	−	1.04554i	−0.627021	−	0.0488018i
$460$	20.2051	−	11.2822i	0.942067	−	0.526033i
$461$		−	4.83805i		−	0.225331i	−0.993633	−	0.112665i	$-0.964061\pi$
$461$		−	4.83805i		−	0.225331i	0.993633	−	0.112665i	$-0.0359388\pi$
$462$	4.78079	+	10.9710i	0.222422	+	0.510419i
$463$		−	29.2405i		−	1.35892i	−0.733711	−	0.679461i	$-0.762214\pi$
$463$		−	29.2405i		−	1.35892i	0.733711	−	0.679461i	$-0.237786\pi$
$464$	−0.981437	−	13.4180i	−0.0455621	−	0.622913i
$465$	3.28383	+	1.06150i	0.152284	+	0.0492260i
$466$	−5.37219	+	2.34101i	−0.248862	+	0.108445i
$467$	−3.72931			−0.172572			−0.0862860	−	0.996270i	$-0.527500\pi$
$467$	−3.72931			−0.172572			−0.0862860	+	0.996270i	$0.527500\pi$
$468$	−12.0824	+	12.9984i	−0.558509	+	0.600852i
$469$	−25.5516			−1.17986
$470$	−1.18832	−	12.0494i	−0.0548132	−	0.555796i
$471$		−	15.7205i		−	0.724362i
$472$	−3.61747	−	1.27125i	−0.166507	−	0.0585140i
$473$	10.9300			0.502564
$474$	0.307535	−	0.134013i	0.0141255	−	0.00615540i
$475$	−7.03629	+	9.74637i	−0.322847	+	0.447194i
$476$	12.1013	+	13.1411i	0.554664	+	0.602321i
$477$	−10.1416			−0.464354
$478$	−12.3555	+	5.38409i	−0.565128	+	0.246263i
$479$		−	29.8166i		−	1.36235i	−0.732118	−	0.681177i	$-0.761468\pi$
$479$		−	29.8166i		−	1.36235i	0.732118	−	0.681177i	$-0.238532\pi$
$480$	26.2957	−	4.54949i	1.20023	−	0.207655i
$481$			66.1023i			3.01400i
$482$	0.623711	+	1.43130i	0.0284093	+	0.0651941i
$483$		−	23.6504i		−	1.07613i
$484$	−10.3103	+	11.0920i	−0.468651	+	0.504182i
$485$	23.1693	+	7.48949i	1.05206	+	0.340080i
$486$	7.86739	+	18.0542i	0.356872	+	0.818957i
$487$	−17.2766			−0.782878			−0.391439	−	0.920204i	$-0.628023\pi$
$487$	−17.2766			−0.782878			−0.391439	+	0.920204i	$0.628023\pi$
$488$	3.48616	−	9.92023i	0.157811	−	0.449068i
$489$	29.2244			1.32157
$490$	−7.25983	+	0.715972i	−0.327966	+	0.0323443i
$491$			12.7948i			0.577421i	0.957416	+	0.288710i	$0.0932265\pi$
$491$			12.7948i			0.577421i	−0.957416	+	0.288710i	$0.906774\pi$
$492$	13.4999	−	14.5234i	0.608623	−	0.654766i
$493$	−1.07610	+	13.8260i	−0.0484650	+	0.622694i
$494$	−8.30598	−	19.0607i	−0.373704	−	0.857582i
$495$	−5.71616	−	1.84776i	−0.256922	−	0.0830504i
$496$	2.91843	−	0.213464i	0.131041	−	0.00958483i
$497$			24.1455i			1.08307i
$498$	−12.5846	−	28.8794i	−0.563929	−	1.29411i
$499$	−19.5725			−0.876183			−0.438092	−	0.898930i	$-0.644345\pi$
$499$	−19.5725			−0.876183			−0.438092	+	0.898930i	$0.644345\pi$
$500$	−22.2103	−	2.58899i	−0.993275	−	0.115783i
$501$			34.1310i			1.52486i
$502$	−13.4216	−	30.8001i	−0.599035	−	1.37468i
$503$	34.1869			1.52432			0.762160	−	0.647388i	$-0.224139\pi$
$503$	34.1869			1.52432			0.762160	+	0.647388i	$0.224139\pi$
$504$	2.94774	−	8.38809i	0.131303	−	0.373635i
$505$	−0.764866	+	2.36616i	−0.0340361	+	0.105293i
$506$	−12.4213	+	5.41274i	−0.552193	+	0.240626i
$507$			51.4692i			2.28583i
$508$	11.2783	+	10.4835i	0.500393	+	0.465129i
$509$		−	28.5269i		−	1.26443i	−0.774791	−	0.632217i	$-0.782145\pi$
$509$		−	28.5269i		−	1.26443i	0.774791	−	0.632217i	$-0.217855\pi$
$510$	−27.5019	+	0.567400i	−1.21780	+	0.0251249i
$511$	−10.4598			−0.462714
$512$	19.2074	−	11.9614i	0.848856	−	0.528625i
$513$	−7.85671			−0.346882
$514$	−5.25637	−	12.0624i	−0.231848	−	0.532050i
$515$	6.53239	−	20.2084i	0.287851	−	0.890488i
$516$	−18.2444	−	16.9587i	−0.803166	−	0.746565i
$517$			7.08913i			0.311780i
$518$	−13.2296	−	30.3596i	−0.581276	−	1.33392i
$519$	−13.1207			−0.575935
$520$	23.4243	−	30.7756i	1.02723	−	1.34960i
$521$			0.501445i			0.0219687i	0.999940	+	0.0109843i	$0.00349650\pi$
$521$			0.501445i			0.0219687i	−0.999940	+	0.0109843i	$0.996504\pi$
$522$	6.32733	−	2.75722i	0.276940	−	0.120680i
$523$	1.90322			0.0832220			0.0416110	−	0.999134i	$-0.486751\pi$
$523$	1.90322			0.0832220			0.0416110	+	0.999134i	$0.486751\pi$
$524$	−11.6392	+	12.5217i	−0.508462	+	0.547011i
$525$	−13.3764	+	18.5284i	−0.583792	+	0.808644i
$526$	−3.38717	−	7.77293i	−0.147687	−	0.338916i
$527$	−3.00719	−	0.234053i	−0.130995	−	0.0101955i
$528$	−15.5832	+	1.13981i	−0.678173	+	0.0496040i
$529$	3.77663			0.164201
$530$	21.9954	−	2.16921i	0.955421	−	0.0942245i
$531$		−	1.96707i		−	0.0853635i
$532$	7.62957	+	7.09190i	0.330784	+	0.307473i
$533$		−	28.7373i		−	1.24475i
$534$	−11.9257	−	27.3672i	−0.516074	−	1.18430i
$535$	6.72608	−	20.8076i	0.290794	−	0.899591i
$536$	11.0605	−	31.4736i	0.477739	−	1.35945i
$537$	−29.7458			−1.28363
$538$	17.0344	−	7.42299i	0.734406	−	0.320028i
$539$	4.27125			0.183976
$540$	−7.12507	−	12.7602i	−0.306614	−	0.549112i
$541$	3.26662			0.140443			0.0702215	−	0.997531i	$-0.477629\pi$
$541$	3.26662			0.140443			0.0702215	+	0.997531i	$0.477629\pi$
$542$	11.6697	−	5.08522i	0.501255	−	0.218429i
$543$			38.0245i			1.63179i
$544$	−21.4251	+	9.21769i	−0.918593	+	0.395205i
$545$	−37.4266	−	12.0982i	−1.60318	−	0.518230i
$546$	−15.7901	−	36.2354i	−0.675754	−	1.55073i
$547$			19.2791i			0.824315i	0.911113	+	0.412157i	$0.135225\pi$
$547$			19.2791i			0.824315i	−0.911113	+	0.412157i	$0.864775\pi$
$548$	14.0145	+	13.0269i	0.598672	+	0.556482i
$549$	5.39432			0.230224
$550$	12.7926	+	2.78482i	0.545477	+	0.118745i
$551$			8.08631i			0.344488i
$552$	29.1318	+	10.2375i	1.23993	+	0.435736i
$553$			0.243575i			0.0103579i
$554$	13.4899	+	30.9569i	0.573131	+	1.31523i
$555$	48.5219	+	15.6848i	2.05964	+	0.665781i
$556$	10.8563	−	11.6794i	0.460410	−	0.495316i
$557$	−5.98141			−0.253441			−0.126720	−	0.991938i	$-0.540445\pi$
$557$	−5.98141			−0.253441			−0.126720	+	0.991938i	$0.540445\pi$
$558$	0.599700	+	1.37620i	0.0253873	+	0.0582594i
$559$	−36.1001			−1.52687
$560$	−4.59899	+	18.8228i	−0.194343	+	0.795408i
$561$	16.0572	+	1.24975i	0.677935	+	0.0527645i
$562$	−19.7122	+	8.58986i	−0.831508	+	0.362341i
$563$	−15.0294			−0.633415			−0.316707	−	0.948523i	$-0.602577\pi$
$563$	−15.0294			−0.633415			−0.316707	+	0.948523i	$0.602577\pi$
$564$	10.9993	−	11.8332i	0.463152	−	0.498266i
$565$	−25.8622	−	8.35998i	−1.08803	−	0.351707i
$566$	−13.4636	−	30.8964i	−0.565916	−	1.29867i
$567$	−24.3663			−1.02329
$568$	−29.7417	−	10.4518i	−1.24793	−	0.438548i
$569$	4.62940			0.194075			0.0970373	−	0.995281i	$-0.469063\pi$
$569$	4.62940			0.194075			0.0970373	+	0.995281i	$0.469063\pi$
$570$	−15.9622	+	1.57421i	−0.668584	+	0.0659364i
$571$	30.2968			1.26788			0.633941	−	0.773381i	$-0.281436\pi$
$571$	30.2968			1.26788			0.633941	+	0.773381i	$0.281436\pi$
$572$	−15.4172	+	16.5861i	−0.644626	+	0.693498i
$573$			7.34145i			0.306694i
$574$	5.75145	+	13.1985i	0.240061	+	0.550896i
$575$	−20.9776	−	15.1445i	−0.874826	−	0.631571i
$576$	9.05621	+	7.26187i	0.377342	+	0.302578i
$577$			2.37981i			0.0990727i	0.998772	+	0.0495364i	$0.0157744\pi$
$577$			2.37981i			0.0990727i	−0.998772	+	0.0495364i	$0.984226\pi$
$578$	23.2605	−	6.07842i	0.967511	−	0.252829i
$579$			34.3865i			1.42905i
$580$	−13.1331	+	7.33329i	−0.545323	+	0.304498i
$581$	22.8732			0.948938
$582$	12.9793	+	29.7851i	0.538009	+	1.23463i
$583$	−12.9408			−0.535953
$584$	4.52771	−	12.8841i	0.187358	−	0.533146i
$585$	18.8795	+	6.10282i	0.780570	+	0.252320i
$586$	17.3984	−	7.58160i	0.718721	−	0.313193i
$587$	15.6420			0.645614			0.322807	−	0.946465i	$-0.395374\pi$
$587$	15.6420			0.645614			0.322807	+	0.946465i	$0.395374\pi$
$588$	−7.12956	−	6.62713i	−0.294018	−	0.273298i
$589$	−1.75879			−0.0724695
$590$	0.420739	+	4.26622i	0.0173216	+	0.175638i
$591$	36.1089			1.48532
$592$	43.1227	−	3.15415i	1.77233	−	0.129635i
$593$			19.7700i			0.811855i	0.913905	+	0.405928i	$0.133052\pi$
$593$			19.7700i			0.811855i	−0.913905	+	0.405928i	$0.866948\pi$
$594$	3.41833	+	7.84446i	0.140256	+	0.321862i
$595$	7.59942	−	18.4706i	0.311546	−	0.757220i
$596$	−32.1229	−	29.8591i	−1.31580	−	1.22308i
$597$	40.1498			1.64322
$598$	41.0253	−	17.8774i	1.67765	−	0.731059i
$599$	15.1584			0.619354			0.309677	−	0.950842i	$-0.399779\pi$
$599$	15.1584			0.619354			0.309677	+	0.950842i	$0.399779\pi$
$600$	−17.0325	−	24.4969i	−0.695348	−	1.00008i
$601$			25.8190i			1.05318i	0.850119	+	0.526590i	$0.176530\pi$
$601$			25.8190i			1.05318i	−0.850119	+	0.526590i	$0.823470\pi$
$602$	16.5801	−	7.22501i	0.675754	−	0.294470i
$603$	17.1144			0.696952
$604$	19.9184	−	21.4285i	0.810469	−	0.871914i
$605$	16.1105	+	5.20774i	0.654985	+	0.211725i
$606$	−3.04181	+	1.32551i	−0.123565	+	0.0538453i
$607$	−0.167507			−0.00679890			−0.00339945	−	0.999994i	$-0.501082\pi$
$607$	−0.167507			−0.00679890			−0.00339945	+	0.999994i	$0.501082\pi$
$608$	−12.0382	+	6.32801i	−0.488212	+	0.256635i
$609$			15.3725i			0.622925i
$610$	−11.6993	+	1.15380i	−0.473692	+	0.0467159i
$611$		−	23.4142i		−	0.947236i
$612$	−8.10545	−	8.80189i	−0.327644	−	0.355795i
$613$	15.2387			0.615485			0.307742	−	0.951470i	$-0.400427\pi$
$613$	15.2387			0.615485			0.307742	+	0.951470i	$0.400427\pi$
$614$	37.6434	−	16.4036i	1.51916	−	0.661997i
$615$	−21.0944	−	6.81880i	−0.850610	−	0.274961i
$616$	3.76133	−	10.7033i	0.151548	−	0.431246i
$617$	16.8431			0.678076			0.339038	−	0.940773i	$-0.389898\pi$
$617$	16.8431			0.678076			0.339038	+	0.940773i	$0.389898\pi$
$618$	25.9788	−	11.3206i	1.04502	−	0.455383i
$619$	46.2447			1.85873			0.929366	−	0.369159i	$-0.120354\pi$
$619$	46.2447			1.85873			0.929366	+	0.369159i	$0.120354\pi$
$620$	−1.59500	−	2.85647i	−0.0640569	−	0.114719i
$621$		−	16.9104i		−	0.678590i
$622$	−2.07854	−	4.76987i	−0.0833417	−	0.191254i
$623$	21.6755			0.868412
$624$	51.4687	−	3.76461i	2.06040	−	0.150705i
$625$	7.86888	+	23.7293i	0.314755	+	0.949173i
$626$	−18.7134	+	8.15463i	−0.747938	+	0.325924i
$627$	9.39122			0.375049
$628$	−10.1462	+	10.9154i	−0.404877	+	0.435573i
$629$	−44.4342	−	3.45837i	−1.77171	−	0.137894i
$630$	−9.89241	+	0.975599i	−0.394123	+	0.0388688i
$631$	38.9878			1.55208			0.776040	−	0.630684i	$-0.217225\pi$
$631$	38.9878			1.55208			0.776040	+	0.630684i	$0.217225\pi$
$632$	−0.300028	−	0.105436i	−0.0119345	−	0.00419401i
$633$		−	6.92236i		−	0.275139i
$634$	0.0775214	+	0.177898i	0.00307877	+	0.00706522i
$635$	5.29520	−	16.3811i	0.210134	−	0.650063i
$636$	21.6008	+	20.0785i	0.856526	+	0.796165i
$637$	−14.1072			−0.558948
$638$	8.07370	−	3.51823i	0.319641	−	0.139288i
$639$		−	16.1726i		−	0.639778i
$640$	−21.1946	−	13.8127i	−0.837789	−	0.545994i
$641$		−	44.8043i		−	1.76966i	−0.465910	−	0.884832i	$-0.654273\pi$
$641$		−	44.8043i		−	1.76966i	0.465910	−	0.884832i	$-0.345727\pi$
$642$	26.7491	−	11.6563i	1.05570	−	0.460038i
$643$		−	12.7986i		−	0.504727i	−0.967633	−	0.252363i	$-0.918792\pi$
$643$		−	12.7986i		−	0.504727i	0.967633	−	0.252363i	$-0.0812079\pi$
$644$	−15.2642	+	16.4215i	−0.601495	+	0.647097i
$645$	−8.56583	+	26.4990i	−0.337279	+	1.04340i
$646$	13.2472	−	4.58608i	0.521206	−	0.180437i
$647$			2.44724i			0.0962109i	0.998842	+	0.0481054i	$0.0153183\pi$
$647$			2.44724i			0.0962109i	−0.998842	+	0.0481054i	$0.984682\pi$
$648$	10.5474	−	30.0137i	0.414341	−	1.17905i
$649$		−	2.50999i		−	0.0985257i
$650$	−42.2516	−	9.19777i	−1.65724	−	0.360766i
$651$	−3.34355			−0.131044
$652$	−20.2918	−	18.8618i	−0.794687	−	0.738683i
$653$		−	16.4974i		−	0.645591i	−0.946469	−	0.322796i	$-0.895377\pi$
$653$		−	16.4974i		−	0.645591i	0.946469	−	0.322796i	$-0.104623\pi$
$654$	−20.9662	−	48.1137i	−0.819844	−	1.88139i
$655$	18.1870	+	5.87897i	0.710625	+	0.229710i
$656$	−18.7472	+	1.37124i	−0.731954	+	0.0535377i
$657$	7.00596			0.273328
$658$	4.68608	+	10.7537i	0.182682	+	0.419223i
$659$			47.2155i			1.83925i	0.392794	+	0.919627i	$0.371509\pi$
$659$			47.2155i			1.83925i	−0.392794	+	0.919627i	$0.628491\pi$
$660$	8.51668	+	15.2524i	0.331511	+	0.593700i
$661$			24.8352i			0.965977i	0.875627	+	0.482989i	$0.160449\pi$
$661$			24.8352i			0.965977i	−0.875627	+	0.482989i	$0.839551\pi$
$662$	12.7139	+	29.1761i	0.494139	+	1.13396i
$663$	−53.0341	−	4.12771i	−2.05967	−	0.160307i
$664$	−9.90105	+	28.1744i	−0.384235	+	1.09338i
$665$	3.58212	−	11.0815i	0.138908	−	0.429723i
$666$	8.86117	+	20.3348i	0.343363	+	0.787957i
$667$	−17.4045			−0.673907
$668$	22.0286	−	23.6987i	0.852311	−	0.916929i
$669$	61.2546			2.36824
$670$	−37.1181	+	3.66062i	−1.43400	+	0.141422i
$671$	6.88318			0.265722
$672$	−22.8852	+	12.0299i	−0.882816	+	0.464063i
$673$	−41.8116			−1.61172			−0.805859	−	0.592108i	$-0.798296\pi$
$673$	−41.8116			−1.61172			−0.805859	+	0.592108i	$0.798296\pi$
$674$	−16.7065	+	7.28009i	−0.643510	+	0.280419i
$675$	−9.56430	+	13.2481i	−0.368130	+	0.509918i
$676$	33.2188	−	35.7373i	1.27765	−	1.37451i
$677$			42.5535i			1.63547i	0.575598	+	0.817733i	$0.304769\pi$
$677$			42.5535i			1.63547i	−0.575598	+	0.817733i	$0.695231\pi$
$678$	−14.4879	−	33.2470i	−0.556403	−	1.27684i
$679$	−23.5906			−0.905322
$680$	19.4619	+	17.3561i	0.746332	+	0.665574i
$681$	42.4013			1.62482
$682$	0.765221	+	1.75604i	0.0293018	+	0.0672424i
$683$			38.1275i			1.45891i	0.684030	+	0.729454i	$0.260226\pi$
$683$			38.1275i			1.45891i	−0.684030	+	0.729454i	$0.739774\pi$
$684$	−5.11027	−	4.75014i	−0.195396	−	0.181626i
$685$	6.57989	−	20.3553i	0.251405	−	0.777737i
$686$	26.1395	−	11.3906i	0.998009	−	0.434896i
$687$	−39.5319			−1.50824
$688$	1.72256	+	23.5503i	0.0656718	+	0.897848i
$689$	42.7412			1.62831
$690$	−3.38825	−	34.3563i	−0.128988	−	1.30792i
$691$	33.7650			1.28448			0.642240	−	0.766503i	$-0.278005\pi$
$691$	33.7650			1.28448			0.642240	+	0.766503i	$0.278005\pi$
$692$	9.11028	+	8.46826i	0.346321	+	0.321915i
$693$	5.82010			0.221087
$694$	9.60505	+	22.0419i	0.364603	+	0.836698i
$695$	−16.9636	−	5.48351i	−0.643467	−	0.208002i
$696$	−18.9354	−	6.65426i	−0.717744	−	0.252229i
$697$	19.3173	+	1.50349i	0.731696	+	0.0569488i
$698$	20.1160	+	46.1626i	0.761403	+	1.74728i
$699$			8.74217i			0.330659i
$700$	21.2462	−	4.23180i	0.803032	−	0.159947i
$701$			17.0754i			0.644930i	0.946581	+	0.322465i	$0.104512\pi$
$701$			17.0754i			0.644930i	−0.946581	+	0.322465i	$0.895488\pi$
$702$	−11.2902	−	25.9089i	−0.426120	−	0.977868i
$703$	−25.9878			−0.980149
$704$	11.5558	+	9.26618i	0.435525	+	0.349232i
$705$	−17.1870	−	5.55572i	−0.647300	−	0.209241i
$706$	13.1253	+	30.1202i	0.493977	+	1.13359i
$707$		−	2.40919i		−	0.0906069i
$708$	−3.89441	+	4.18967i	−0.146361	+	0.157457i
$709$	5.77448			0.216865			0.108433	−	0.994104i	$-0.465417\pi$
$709$	5.77448			0.216865			0.108433	+	0.994104i	$0.465417\pi$
$710$	3.45918	+	35.0755i	0.129821	+	1.31636i
$711$		−	0.163146i		−	0.00611846i
$712$	−9.38264	+	26.6992i	−0.351629	+	1.00060i
$713$		−	3.78552i		−	0.141769i
$714$	25.1837	−	8.71838i	0.942477	−	0.326277i
$715$	24.0903	+	7.78723i	0.900927	+	0.291226i
$716$	20.6538	+	19.1983i	0.771869	+	0.717473i
$717$			20.1062i			0.750879i
$718$	19.4017	−	8.45457i	0.724065	−	0.315522i
$719$			1.08606i			0.0405032i	0.999795	+	0.0202516i	$0.00644672\pi$
$719$			1.08606i			0.0405032i	−0.999795	+	0.0202516i	$0.993553\pi$
$720$	3.08039	−	12.6075i	0.114799	−	0.469853i
$721$			20.5759i			0.766285i
$722$	−17.1392	+	7.46867i	−0.637856	+	0.277955i
$723$	2.32917			0.0866226
$724$	24.5415	−	26.4021i	0.912076	−	0.981225i
$725$	13.6352	+	9.84380i	0.506399	+	0.365590i
$726$	9.02502	+	20.7108i	0.334950	+	0.768649i
$727$			4.16080i			0.154315i	0.997019	+	0.0771577i	$0.0245845\pi$
$727$			4.16080i			0.154315i	−0.997019	+	0.0771577i	$0.975416\pi$
$728$	−12.4230	+	35.3510i	−0.460428	+	1.31019i
$729$	−4.36309			−0.161596
$730$	−15.1947	+	1.49851i	−0.562381	+	0.0554625i
$731$	1.88870	−	24.2666i	0.0698560	−	0.897532i
$732$	−11.4894	−	10.6797i	−0.424660	−	0.394733i
$733$	−4.33241			−0.160021			−0.0800106	−	0.996794i	$-0.525495\pi$
$733$	−4.33241			−0.160021			−0.0800106	+	0.996794i	$0.525495\pi$
$734$	30.3284	−	13.2160i	1.11944	−	0.487813i
$735$	−3.34736	+	10.3553i	−0.123469	+	0.381961i
$736$	−13.6201	−	25.9103i	−0.502043	−	0.955068i
$737$	21.8381			0.804416
$738$	−3.85231	−	8.84035i	−0.141805	−	0.325418i
$739$		−	15.8244i		−	0.582110i	−0.956706	−	0.291055i	$-0.905994\pi$
$739$		−	15.8244i		−	0.582110i	0.956706	−	0.291055i	$-0.0940062\pi$
$740$	−23.5677	−	42.2072i	−0.866368	−	1.55157i
$741$	−31.0176			−1.13946
$742$	−19.6303	+	8.55416i	−0.720650	+	0.314033i
$743$	18.2459			0.669377			0.334688	−	0.942329i	$-0.391369\pi$
$743$	18.2459			0.669377			0.334688	+	0.942329i	$0.391369\pi$
$744$	1.44731	−	4.11848i	0.0530611	−	0.150991i
$745$	−15.0818	+	46.6566i	−0.552555	+	1.70937i
$746$	−42.0742	+	18.3344i	−1.54045	+	0.671272i
$747$	−15.3204			−0.560544
$748$	−10.3426	−	11.2313i	−0.378163	−	0.410655i
$749$			21.1860i			0.774118i
$750$	−16.7770	+	28.8320i	−0.612611	+	1.05280i
$751$		−	31.8283i		−	1.16143i	−0.814106	−	0.580716i	$-0.802773\pi$
$751$		−	31.8283i		−	1.16143i	0.814106	−	0.580716i	$-0.197227\pi$
$752$	−15.2745	+	1.11723i	−0.557005	+	0.0407413i
$753$	−50.1211			−1.82652
$754$	−26.6660	+	11.6201i	−0.971120	+	0.423179i
$755$	−31.1237	−	10.0608i	−1.13271	−	0.366150i
$756$	10.3707	+	9.63989i	0.377180	+	0.350599i
$757$	−29.8842			−1.08616			−0.543079	−	0.839681i	$-0.682742\pi$
$757$	−29.8842			−1.08616			−0.543079	+	0.839681i	$0.682742\pi$
$758$	−33.5456	+	14.6180i	−1.21843	+	0.530949i
$759$			20.2132i			0.733691i
$760$	12.0993	+	9.20917i	0.438887	+	0.334052i
$761$	−22.4335			−0.813212			−0.406606	−	0.913604i	$-0.633288\pi$
$761$	−22.4335			−0.813212			−0.406606	+	0.913604i	$0.633288\pi$
$762$	21.0586	−	9.17659i	0.762874	−	0.332433i
$763$	38.1072			1.37957
$764$	4.73826	−	5.09749i	0.171424	−	0.184421i
$765$	−5.09008	+	12.3716i	−0.184032	+	0.447295i
$766$	−6.40685	−	14.7026i	−0.231489	−	0.531225i
$767$			8.29006i			0.299337i
$768$	−4.91178	−	33.3966i	−0.177239	−	1.20510i
$769$	−4.31813			−0.155716			−0.0778578	−	0.996964i	$-0.524808\pi$
$769$	−4.31813			−0.155716			−0.0778578	+	0.996964i	$0.524808\pi$
$770$	−12.6228	+	1.24487i	−0.454893	+	0.0448620i
$771$	−19.6292			−0.706929
$772$	22.1935	−	23.8761i	0.798760	−	0.859318i
$773$	−21.7080			−0.780784			−0.390392	−	0.920649i	$-0.627660\pi$
$773$	−21.7080			−0.780784			−0.390392	+	0.920649i	$0.627660\pi$
$774$	−11.1053	+	4.83930i	−0.399173	+	0.173945i
$775$	−2.14104	+	2.96568i	−0.0769085	+	0.106531i
$776$	10.2116	−	29.0581i	0.366575	−	1.04313i
$777$	−49.4042			−1.77237
$778$	8.42339	+	19.3302i	0.301993	+	0.693020i
$779$	11.2980			0.404791
$780$	−28.1291	−	50.3761i	−1.00718	−	1.80376i
$781$		−	20.6363i		−	0.738426i
$782$	9.87084	+	28.5127i	0.352980	+	1.01961i
$783$			10.9916i			0.392807i
$784$	0.673141	+	9.20301i	0.0240408	+	0.328679i
$785$	15.8540	+	5.12484i	0.565855	+	0.182913i
$786$	10.1883	+	23.3802i	0.363403	+	0.833945i
$787$		−	39.6960i		−	1.41501i	−0.706708	−	0.707505i	$-0.749821\pi$
$787$		−	39.6960i		−	1.41501i	0.706708	−	0.707505i	$-0.250179\pi$
$788$	−25.0720	−	23.3051i	−0.893152	−	0.830210i
$789$	−12.6489			−0.450313
$790$	0.0348955	+	0.353835i	0.00124153	+	0.0125889i
$791$	26.3325			0.936274
$792$	−2.51933	+	7.16902i	−0.0895206	+	0.254740i
$793$	−22.7340			−0.807306
$794$	−10.3364	−	23.7201i	−0.366824	−	0.841795i
$795$	10.1416	−	31.3739i	0.359687	−	1.11272i
$796$	−27.8778	−	25.9132i	−0.988102	−	0.918469i
$797$	39.4371			1.39693			0.698466	−	0.715643i	$-0.253866\pi$
$797$	39.4371			1.39693			0.698466	+	0.715643i	$0.253866\pi$
$798$	14.2458	−	6.20781i	0.504296	−	0.219754i
$799$	15.7391	+	1.22499i	0.556809	+	0.0433371i
$800$	−3.98420	+	28.0023i	−0.140863	+	0.990029i
$801$	−14.5182			−0.512976
$802$	−9.00652	−	20.6683i	−0.318031	−	0.729824i
$803$	8.93964			0.315473
$804$	−36.4521	−	33.8832i	−1.28557	−	1.19497i
$805$	23.8513	+	7.70996i	0.840647	+	0.271740i
$806$	−2.52739	−	5.79991i	−0.0890236	−	0.204293i
$807$		−	27.7202i		−	0.975796i
$808$	2.96757	+	1.04286i	0.104399	+	0.0366877i
$809$			16.9543i			0.596082i	0.954553	+	0.298041i	$0.0963333\pi$
$809$			16.9543i			0.596082i	−0.954553	+	0.298041i	$0.903667\pi$
$810$	−35.3963	+	3.49082i	−1.24370	+	0.122655i
$811$	0.243229			0.00854091			0.00427045	−	0.999991i	$-0.498641\pi$
$811$	0.243229			0.00854091			0.00427045	+	0.999991i	$0.498641\pi$
$812$	9.92160	−	10.6738i	0.348180	−	0.374577i
$813$		−	18.9901i		−	0.666010i
$814$	11.3069	+	25.9473i	0.396307	+	0.909452i
$815$	−9.52707	+	29.4726i	−0.333719	+	1.03238i
$816$	−0.162180	+	34.7944i	−0.00567742	+	1.21805i
$817$		−	14.1926i		−	0.496535i
$818$	12.6508	−	5.51277i	0.442326	−	0.192750i
$819$	−19.2228			−0.671698
$820$	10.2459	+	18.3492i	0.357801	+	0.640782i
$821$	12.8973			0.450119			0.225060	−	0.974345i	$-0.427742\pi$
$821$	12.8973			0.450119			0.225060	+	0.974345i	$0.427742\pi$
$822$	26.1677	−	11.4030i	0.912704	−	0.397724i
$823$	54.7637			1.90894			0.954471	−	0.298305i	$-0.0964212\pi$
$823$	54.7637			1.90894			0.954471	+	0.298305i	$0.0964212\pi$
$824$	−25.3447	−	8.90663i	−0.882925	−	0.310277i
$825$	11.4323	−	15.8356i	0.398022	−	0.551324i
$826$	−1.65916	−	3.80747i	−0.0577296	−	0.132479i
$827$			6.47155i			0.225038i	0.993650	+	0.112519i	$0.0358919\pi$
$827$			6.47155i			0.225038i	−0.993650	+	0.112519i	$0.964108\pi$
$828$	10.2240	−	10.9991i	0.355307	−	0.382244i
$829$		−	11.7897i		−	0.409472i	−0.978817	−	0.204736i	$-0.934366\pi$
$829$		−	11.7897i		−	0.409472i	0.978817	−	0.204736i	$-0.0656336\pi$
$830$	33.2272	−	3.27690i	1.15333	−	0.113743i
$831$	50.3762			1.74753
$832$	−38.1667	−	30.6046i	−1.32319	−	1.06102i
$833$	0.738066	−	9.48291i	0.0255725	−	0.328563i
$834$	−9.50293	−	21.8075i	−0.329060	−	0.755133i
$835$	−34.4210	−	11.1266i	−1.19119	−	0.385053i
$836$	−6.52073	−	6.06120i	−0.225524	−	0.209631i
$837$	−2.39069			−0.0826342
$838$	−0.870079	+	0.379149i	−0.0300564	+	0.0130975i
$839$			25.5582i			0.882366i	0.897417	+	0.441183i	$0.145441\pi$
$839$			25.5582i			0.882366i	−0.897417	+	0.441183i	$0.854559\pi$
$840$	23.0014	+	17.5071i	0.793624	+	0.604053i
$841$	−17.6872			−0.609904
$842$	15.0828	+	34.6124i	0.519789	+	1.19282i
$843$			32.0777i			1.10481i
$844$	−4.46777	+	4.80650i	−0.153787	+	0.165446i
$845$	−51.9065	−	16.7788i	−1.78564	−	0.577209i
$846$	−3.13873	−	7.20281i	−0.107912	−	0.247638i
$847$	−16.4034			−0.563629
$848$	−2.03945	−	27.8828i	−0.0700349	−	0.957498i
$849$	−50.2779			−1.72553
$850$	8.39331	−	27.9205i	0.287888	−	0.957664i
$851$		−	55.9348i		−	1.91742i
$852$	−32.0186	+	34.4461i	−1.09694	+	1.18010i
$853$			39.1503i			1.34048i	0.742144	+	0.670240i	$0.233809\pi$
$853$			39.1503i			1.34048i	−0.742144	+	0.670240i	$0.766191\pi$
$854$	10.4413	−	4.54994i	0.357294	−	0.155696i
$855$	−2.39929	+	7.42238i	−0.0820541	+	0.253840i
$856$	−26.0962	−	9.17072i	−0.891950	−	0.313449i
$857$	17.0651			0.582932			0.291466	−	0.956581i	$-0.405857\pi$
$857$	17.0651			0.582932			0.291466	+	0.956581i	$0.405857\pi$
$858$	13.4953	+	30.9692i	0.460721	+	1.05727i
$859$			21.7162i			0.740946i	0.928843	+	0.370473i	$0.120804\pi$
$859$			21.7162i			0.740946i	−0.928843	+	0.370473i	$0.879196\pi$
$860$	23.0504	−	12.8709i	0.786012	−	0.438895i
$861$	21.4780			0.731969
$862$	1.56751	+	3.59716i	0.0533897	+	0.122520i
$863$		−	6.55592i		−	0.223166i	−0.993755	−	0.111583i	$-0.964408\pi$
$863$		−	6.55592i		−	0.223166i	0.993755	−	0.111583i	$-0.0355921\pi$
$864$	−16.3633	+	8.60156i	−0.556690	+	0.292631i
$865$	4.27731	−	13.2322i	0.145433	−	0.449907i
$866$	6.64679	+	15.2532i	0.225867	+	0.518324i
$867$	5.54932	−	35.4337i	0.188465	−	1.20339i
$868$	2.32157	+	2.15796i	0.0787992	+	0.0732461i
$869$		−	0.208175i		−	0.00706186i
$870$	2.20233	+	22.3312i	0.0746659	+	0.757100i
$871$	−72.1274			−2.44394
$872$	−16.4954	+	46.9393i	−0.558604	+	1.58956i
$873$	15.8009			0.534780
$874$	7.02840	+	16.1289i	0.237739	+	0.545569i
$875$	−14.3251	−	19.5302i	−0.484278	−	0.660241i
$876$	−14.9220	−	13.8704i	−0.504169	−	0.468639i
$877$			9.71283i			0.327979i	0.986462	+	0.163990i	$0.0524363\pi$
$877$			9.71283i			0.327979i	−0.986462	+	0.163990i	$0.947564\pi$
$878$	17.6914	+	40.5987i	0.597057	+	1.37014i
$879$		−	28.3125i		−	0.954955i
$880$	3.93060	−	16.0872i	0.132500	−	0.542299i
$881$			18.1997i			0.613163i	0.951844	+	0.306581i	$0.0991851\pi$
$881$			18.1997i			0.613163i	−0.951844	+	0.306581i	$0.900815\pi$
$882$	−4.33974	+	1.89110i	−0.146127	+	0.0636768i
$883$	37.1100			1.24885			0.624426	−	0.781084i	$-0.285333\pi$
$883$	37.1100			1.24885			0.624426	+	0.781084i	$0.285333\pi$
$884$	34.1598	+	37.0949i	1.14892	+	1.24764i
$885$	6.08526	+	1.96707i	0.204554	+	0.0661223i
$886$	45.0959	−	19.6512i	1.51502	−	0.660193i
$887$	−15.0022			−0.503726			−0.251863	−	0.967763i	$-0.581043\pi$
$887$	−15.0022			−0.503726			−0.251863	+	0.967763i	$0.581043\pi$
$888$	21.3855	−	60.8546i	0.717650	−	2.04215i
$889$			16.6789i			0.559394i
$890$	31.4875	−	3.10532i	1.05546	−	0.104091i
$891$	20.8251			0.697666
$892$	−42.5317	−	39.5344i	−1.42407	−	1.32371i
$893$	9.20517			0.308039
$894$	−59.9792	+	26.1368i	−2.00601	+	0.874145i
$895$	9.69705	−	29.9985i	0.324137	−	1.00274i
$896$	23.6544	+	6.41751i	0.790239	+	0.214394i
$897$		−	66.7606i		−	2.22907i
$898$	11.0961	+	25.4635i	0.370281	+	0.849728i
$899$			2.46055i			0.0820640i
$900$	−14.2307	+	2.83445i	−0.474356	+	0.0944818i
$901$	−2.23615	+	28.7308i	−0.0744971	+	0.957162i
$902$	−4.91557	−	11.2803i	−0.163670	−	0.375594i
$903$		−	26.9808i		−	0.897866i
$904$	−11.3985	+	32.4355i	−0.379108	+	1.07879i
$905$	−38.3475	−	12.3959i	−1.27471	−	0.412053i
$906$	−17.4354	−	40.0110i	−0.579251	−	1.32928i
$907$			23.7320i			0.788009i	0.919108	+	0.394005i	$0.128911\pi$
$907$			23.7320i			0.788009i	−0.919108	+	0.394005i	$0.871089\pi$
$908$	−29.4411	−	27.3663i	−0.977036	−	0.908182i
$909$			1.61367i			0.0535221i
$910$	41.6908	−	4.11159i	1.38204	−	0.136298i
$911$		−	39.2283i		−	1.29969i	−0.760067	−	0.649845i	$-0.774834\pi$
$911$		−	39.2283i		−	1.29969i	0.760067	−	0.649845i	$-0.225166\pi$
$912$	1.48004	+	20.2347i	0.0490090	+	0.670038i
$913$	−19.5489			−0.646974
$914$	1.96377	+	4.50650i	0.0649558	+	0.149062i
$915$	−5.39432	+	16.6877i	−0.178331	+	0.551678i
$916$	27.4487	+	25.5144i	0.906931	+	0.843018i
$917$	−18.5177			−0.611509
$918$	18.0067	−	6.23378i	0.594311	−	0.205745i
$919$	−14.5875			−0.481198			−0.240599	−	0.970625i	$-0.577344\pi$
$919$	−14.5875			−0.481198			−0.240599	+	0.970625i	$0.577344\pi$
$920$	−19.8213	+	26.0419i	−0.653490	+	0.858575i
$921$		−	61.2572i		−	2.01849i
$922$	2.73328	+	6.27238i	0.0900157	+	0.206570i
$923$			68.1582i			2.24346i
$924$	−12.3963	−	11.5227i	−0.407807	−	0.379068i
$925$	−31.6360	+	43.8209i	−1.04019	+	1.44082i
$926$	16.5195	+	37.9094i	0.542866	+	1.24578i
$927$		−	13.7817i		−	0.452650i
$928$	8.85292	+	16.8415i	0.290611	+	0.552848i
$929$			18.3897i			0.603348i	0.953411	+	0.301674i	$0.0975454\pi$
$929$			18.3897i			0.603348i	−0.953411	+	0.301674i	$0.902455\pi$
$930$	−4.85708	+	0.479010i	−0.159270	+	0.0157074i
$931$		−	5.54618i		−	0.181769i
$932$	5.64230	−	6.07008i	0.184820	−	0.198832i
$933$	−7.76202			−0.254117
$934$	4.83493	−	2.10689i	0.158204	−	0.0689395i
$935$	−6.49497	+	15.7862i	−0.212408	+	0.516263i
$936$	8.32092	−	23.6780i	0.271978	−	0.773940i
$937$			31.7597i			1.03754i	0.854912	+	0.518772i	$0.173611\pi$
$937$			31.7597i			1.03754i	−0.854912	+	0.518772i	$0.826389\pi$
$938$	33.1268	−	14.4355i	1.08163	−	0.471335i
$939$			30.4524i			0.993775i
$940$	8.34796	+	14.9503i	0.272280	+	0.487624i
$941$	−4.49157			−0.146421			−0.0732105	−	0.997317i	$-0.523324\pi$
$941$	−4.49157			−0.146421			−0.0732105	+	0.997317i	$0.523324\pi$
$942$	8.88135	+	20.3811i	0.289370	+	0.664052i
$943$			24.3171i			0.791874i
$944$	5.40813	−	0.395570i	0.176020	−	0.0128747i
$945$	4.86911	−	15.0629i	0.158392	−	0.489997i
$946$	−14.1704	+	6.17497i	−0.460721	+	0.200766i
$947$		−	39.2638i		−	1.27590i	−0.770077	−	0.637951i	$-0.779782\pi$
$947$		−	39.2638i		−	1.27590i	0.770077	−	0.637951i	$-0.220218\pi$
$948$	−0.322998	+	0.347486i	−0.0104905	+	0.0112858i
$949$	−29.5261			−0.958457
$950$	3.61606	−	16.6110i	0.117321	−	0.538933i
$951$	0.289493			0.00938746
$952$	−23.1131	−	10.2003i	−0.749100	−	0.330594i
$953$			16.3843i			0.530739i	0.964147	+	0.265370i	$0.0854940\pi$
$953$			16.3843i			0.530739i	−0.964147	+	0.265370i	$0.914506\pi$
$954$	13.1483	−	5.72956i	0.425692	−	0.185501i
$955$	−7.40382	−	2.39330i	−0.239582	−	0.0774452i
$956$	12.9768	−	13.9606i	0.419698	−	0.451518i
$957$		−	13.1384i		−	0.424703i
$958$	16.8450	+	38.6562i	0.544237	+	1.24893i
$959$			20.7255i			0.669260i
$960$	−31.5213	+	20.7541i	−1.01735	+	0.669837i
$961$	30.4648			0.982736
$962$	−37.3447	−	85.6994i	−1.20404	−	2.76306i
$963$		−	14.1903i		−	0.457277i
$964$	−1.61724	−	1.50327i	−0.0520879	−	0.0484171i
$965$	−34.6786	−	11.2099i	−1.11634	−	0.360860i
$966$	13.3614	+	30.6619i	0.429895	+	0.986531i
$967$			33.3204i			1.07151i	0.844373	+	0.535756i	$0.179973\pi$
$967$			33.3204i			1.07151i	−0.844373	+	0.535756i	$0.820027\pi$
$968$	7.10052	−	20.2053i	0.228219	−	0.649422i
$969$	1.62279	−	20.8501i	0.0521315	−	0.669802i
$970$	−34.2694	+	3.37968i	−1.10032	+	0.108515i
$971$		−	55.2049i		−	1.77161i	−0.464058	−	0.885805i	$-0.653607\pi$
$971$		−	55.2049i		−	1.77161i	0.464058	−	0.885805i	$-0.346393\pi$
$972$	−20.3996	−	18.9620i	−0.654318	−	0.608207i
$973$	17.2721			0.553718
$974$	22.3986	−	9.76049i	0.717696	−	0.312746i
$975$	−37.7590	+	52.3022i	−1.20925	+	1.67501i
$976$	1.08478	+	14.8308i	0.0347229	+	0.474722i
$977$		−	30.9280i		−	0.989476i	−0.869042	−	0.494738i	$-0.835264\pi$
$977$		−	30.9280i		−	0.989476i	0.869042	−	0.494738i	$-0.164736\pi$
$978$	−37.8884	+	16.5104i	−1.21154	+	0.527945i
$979$	−18.5253			−0.592072
$980$	9.00765	−	5.02970i	0.287739	−	0.160668i
$981$	−25.5241			−0.814923
$982$	−7.22847	−	16.5880i	−0.230670	−	0.529345i
$983$	42.0498			1.34118			0.670590	−	0.741828i	$-0.266041\pi$
$983$	42.0498			1.34118			0.670590	+	0.741828i	$0.266041\pi$
$984$	−9.29714	+	26.4559i	−0.296382	+	0.843385i
$985$	−11.7714	+	36.4156i	−0.375068	+	1.16030i
$986$	−6.41595	−	18.5330i	−0.204325	−	0.590209i
$987$	17.4995			0.557016
$988$	21.5369	+	20.0191i	0.685179	+	0.636893i
$989$	30.5474			0.971349
$990$	8.45471	−	0.833811i	0.268708	−	0.0265003i
$991$		−	15.3276i		−	0.486898i	−0.969914	−	0.243449i	$-0.921721\pi$
$991$		−	15.3276i		−	0.486898i	0.969914	−	0.243449i	$-0.0782788\pi$
$992$	−3.66305	+	1.92553i	−0.116302	+	0.0611355i
$993$	47.4783			1.50668
$994$	−13.6411	−	31.3038i	−0.432669	−	0.992897i
$995$	−13.0887	+	40.4909i	−0.414941	+	1.28365i
$996$	32.6310	+	30.3314i	1.03395	+	0.961088i
$997$			17.8287i			0.564639i	0.959320	+	0.282320i	$0.0911039\pi$
$997$			17.8287i			0.564639i	−0.959320	+	0.282320i	$0.908896\pi$
$998$	25.3750	−	11.0575i	0.803233	−	0.350020i
$999$	−35.3248			−1.11763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.b.509.8	yes	40
5.4	even	2	inner	680.2.h.b.509.33	yes	40
8.5	even	2	inner	680.2.h.b.509.35	yes	40
17.16	even	2	inner	680.2.h.b.509.7	yes	40
40.29	even	2	inner	680.2.h.b.509.6	yes	40
85.84	even	2	inner	680.2.h.b.509.34	yes	40
136.101	even	2	inner	680.2.h.b.509.36	yes	40
680.509	even	2	inner	680.2.h.b.509.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.5	✓	40	680.509	even	2	inner
680.2.h.b.509.6	yes	40	40.29	even	2	inner
680.2.h.b.509.7	yes	40	17.16	even	2	inner
680.2.h.b.509.8	yes	40	1.1	even	1	trivial
680.2.h.b.509.33	yes	40	5.4	even	2	inner
680.2.h.b.509.34	yes	40	85.84	even	2	inner
680.2.h.b.509.35	yes	40	8.5	even	2	inner
680.2.h.b.509.36	yes	40	136.101	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29647 + 0.564954i) q^{2} +2.10974i q^{3} +(1.36165 - 1.46489i) q^{4} +(-2.12767 - 0.687771i) q^{5} +(-1.19191 - 2.73521i) q^{6} +2.16636 q^{7} +(-0.937746 + 2.66845i) q^{8} -1.45102 q^{9} +(3.14701 - 0.310361i) q^{10} -1.85151 q^{11} +(3.09054 + 2.87274i) q^{12} +6.11522 q^{13} +(-2.80861 + 1.22389i) q^{14} +(1.45102 - 4.48884i) q^{15} +(-0.291795 - 3.98934i) q^{16} +(-0.319939 + 4.11067i) q^{17} +(1.88120 - 0.819760i) q^{18} +2.40417i q^{19} +(-3.90466 + 2.18029i) q^{20} +4.57046i q^{21} +(2.40042 - 1.04602i) q^{22} -5.17461 q^{23} +(-5.62975 - 1.97840i) q^{24} +(4.05394 + 2.92670i) q^{25} +(-7.92819 + 3.45482i) q^{26} +3.26795i q^{27} +(2.94983 - 3.17347i) q^{28} +3.36345 q^{29} +(0.654783 + 6.63939i) q^{30} +0.731556i q^{31} +(2.63210 + 5.00720i) q^{32} -3.90622i q^{33} +(-1.90755 - 5.51010i) q^{34} +(-4.60929 - 1.48996i) q^{35} +(-1.97579 + 2.12558i) q^{36} +10.8095i q^{37} +(-1.35825 - 3.11693i) q^{38} +12.9016i q^{39} +(3.83050 - 5.03262i) q^{40} -4.69931i q^{41} +(-2.58210 - 5.92545i) q^{42} -5.90331 q^{43} +(-2.52112 + 2.71226i) q^{44} +(3.08729 + 0.997971i) q^{45} +(6.70872 - 2.92342i) q^{46} -3.82883i q^{47} +(8.41649 - 0.615613i) q^{48} -2.30690 q^{49} +(-6.90925 - 1.50408i) q^{50} +(-8.67247 - 0.674989i) q^{51} +(8.32682 - 8.95812i) q^{52} +6.98932 q^{53} +(-1.84624 - 4.23679i) q^{54} +(3.93940 + 1.27342i) q^{55} +(-2.03149 + 5.78082i) q^{56} -5.07219 q^{57} +(-4.36060 + 1.90019i) q^{58} +1.35564i q^{59} +(-4.59985 - 8.23783i) q^{60} -3.71760 q^{61} +(-0.413295 - 0.948438i) q^{62} -3.14343 q^{63} +(-6.24126 - 5.00466i) q^{64} +(-13.0112 - 4.20587i) q^{65} +(2.20683 + 5.06428i) q^{66} -11.7947 q^{67} +(5.58603 + 6.06599i) q^{68} -10.9171i q^{69} +(6.81755 - 0.672353i) q^{70} +11.1457i q^{71} +(1.36069 - 3.87198i) q^{72} -4.82829 q^{73} +(-6.10685 - 14.0141i) q^{74} +(-6.17459 + 8.55278i) q^{75} +(3.52184 + 3.27365i) q^{76} -4.01103 q^{77} +(-7.28878 - 16.7264i) q^{78} +0.112435i q^{79} +(-2.12291 + 8.68868i) q^{80} -11.2476 q^{81} +(2.65489 + 6.09250i) q^{82} +10.5584 q^{83} +(6.69521 + 6.22339i) q^{84} +(3.50793 - 8.52610i) q^{85} +(7.65345 - 3.33510i) q^{86} +7.09602i q^{87} +(1.73625 - 4.94067i) q^{88} +10.0055 q^{89} +(-4.56638 + 0.450341i) q^{90} +13.2478 q^{91} +(-7.04604 + 7.58023i) q^{92} -1.54340 q^{93} +(2.16311 + 4.96396i) q^{94} +(1.65352 - 5.11528i) q^{95} +(-10.5639 + 5.55305i) q^{96} -10.8895 q^{97} +(2.99082 - 1.30329i) q^{98} +2.68658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) \) 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more