LMFDB - Embedded newform 805.2.bs.a.557.81

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(37,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 44, 126]))

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

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

chi := DirichletCharacter("805.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.bs (of order $132$, degree $40$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$3680$
Relative dimension:	$92$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			557.81
Character	$\chi$	$=$	805.557
Dual form			805.2.bs.a.198.81

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16029 - 1.90357i) q^{2} +(1.36545 + 0.663296i) q^{3} +(-1.36087 - 2.63972i) q^{4} +(-1.07746 + 1.95935i) q^{5} +(2.84695 - 1.82963i) q^{6} +(0.460985 + 2.60528i) q^{7} +(-2.15663 - 0.154245i) q^{8} +(-0.429976 - 0.546759i) q^{9} +O(q^{10})$	\(q+(1.16029 - 1.90357i) q^{2} +(1.36545 + 0.663296i) q^{3} +(-1.36087 - 2.63972i) q^{4} +(-1.07746 + 1.95935i) q^{5} +(2.84695 - 1.82963i) q^{6} +(0.460985 + 2.60528i) q^{7} +(-2.15663 - 0.154245i) q^{8} +(-0.429976 - 0.546759i) q^{9} +(2.47961 + 4.32445i) q^{10} +(4.64639 + 1.12720i) q^{11} +(-0.107288 - 4.50707i) q^{12} +(-0.856010 - 2.29505i) q^{13} +(5.49422 + 2.14536i) q^{14} +(-2.77086 + 1.96073i) q^{15} +(0.649454 - 0.912030i) q^{16} +(4.71396 + 4.28527i) q^{17} +(-1.53969 + 0.184093i) q^{18} +(0.0245530 - 0.515430i) q^{19} +(6.63844 + 0.177775i) q^{20} +(-1.09862 + 3.86316i) q^{21} +(7.53686 - 7.53686i) q^{22} +(-2.18953 + 4.26685i) q^{23} +(-2.84246 - 1.64110i) q^{24} +(-2.67814 - 4.22227i) q^{25} +(-5.36202 - 1.03344i) q^{26} +(-1.19249 - 5.48180i) q^{27} +(6.24987 - 4.76232i) q^{28} +(2.06283 + 3.20982i) q^{29} +(0.517397 + 7.54955i) q^{30} +(4.96747 - 0.957402i) q^{31} +(-2.68481 - 6.26963i) q^{32} +(5.59676 + 4.62107i) q^{33} +(13.6269 - 4.00121i) q^{34} +(-5.60137 - 1.90386i) q^{35} +(-0.858149 + 1.87908i) q^{36} +(0.645626 - 5.39981i) q^{37} +(-0.952670 - 0.644786i) q^{38} +(0.353458 - 3.70158i) q^{39} +(2.62591 - 4.05940i) q^{40} +(-0.797793 + 5.54877i) q^{41} +(6.07909 + 6.57369i) q^{42} +(-8.44462 + 0.603971i) q^{43} +(-3.34764 - 13.7991i) q^{44} +(1.53458 - 0.253363i) q^{45} +(5.58177 + 9.11870i) q^{46} +(1.34900 - 5.03453i) q^{47} +(1.49175 - 0.814554i) q^{48} +(-6.57499 + 2.40199i) q^{49} +(-11.1448 + 0.198992i) q^{50} +(3.59428 + 8.97809i) q^{51} +(-4.89338 + 5.38290i) q^{52} +(-6.21613 - 7.52860i) q^{53} +(-11.8186 - 4.09047i) q^{54} +(-7.21490 + 7.88940i) q^{55} +(-0.592320 - 5.68972i) q^{56} +(0.375409 - 0.687510i) q^{57} +(8.50360 - 0.202423i) q^{58} +(6.05692 - 4.31311i) q^{59} +(8.94656 + 4.64599i) q^{60} +(-0.597695 - 0.206864i) q^{61} +(3.94122 - 10.5668i) q^{62} +(1.22625 - 1.37226i) q^{63} +(-12.8334 - 1.84516i) q^{64} +(5.41914 + 0.795608i) q^{65} +(15.2904 - 5.29206i) q^{66} +(-0.141455 + 5.94240i) q^{67} +(4.89683 - 18.2752i) q^{68} +(-5.81988 + 4.37387i) q^{69} +(-10.1233 + 8.45358i) q^{70} +(-12.1961 - 3.58109i) q^{71} +(0.842963 + 1.24548i) q^{72} +(-1.12408 + 3.51643i) q^{73} +(-9.52982 - 7.49433i) q^{74} +(-0.856264 - 7.54171i) q^{75} +(-1.39400 + 0.636620i) q^{76} +(-0.794764 + 12.6248i) q^{77} +(-6.63611 - 4.96773i) q^{78} +(-11.3215 + 1.08107i) q^{79} +(1.08723 + 2.25519i) q^{80} +(1.51580 - 6.24821i) q^{81} +(9.63682 + 7.95683i) q^{82} +(-2.79197 + 3.72964i) q^{83} +(11.6927 - 2.35721i) q^{84} +(-13.4755 + 4.61909i) q^{85} +(-8.64849 + 16.7757i) q^{86} +(0.687631 + 5.75112i) q^{87} +(-9.84666 - 3.14763i) q^{88} +(5.28562 + 1.01872i) q^{89} +(1.29826 - 3.21516i) q^{90} +(5.58465 - 3.28813i) q^{91} +(14.2429 - 0.0268832i) q^{92} +(7.41789 + 1.98762i) q^{93} +(-8.01838 - 8.40943i) q^{94} +(0.983455 + 0.603465i) q^{95} +(0.492637 - 10.3417i) q^{96} +(6.20992 + 8.29548i) q^{97} +(-3.05652 + 15.3030i) q^{98} +(-1.38153 - 3.02512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.16029	−	1.90357i	0.820448	−	1.34603i	−0.115289	−	0.993332i	$-0.536779\pi$
$2$	1.16029	−	1.90357i	0.820448	−	1.34603i	0.935737	−	0.352698i	$-0.114736\pi$
$3$	1.36545	+	0.663296i	0.788345	+	0.382954i	0.786928	−	0.617045i	$-0.211670\pi$
$3$	1.36545	+	0.663296i	0.788345	+	0.382954i	0.00141677	+	0.999999i	$0.499549\pi$
$4$	−1.36087	−	2.63972i	−0.680435	−	1.31986i
$5$	−1.07746	+	1.95935i	−0.481857	+	0.876250i
$5$	−1.07746	+	1.95935i	−0.481857	+	0.876250i
$6$	2.84695	−	1.82963i	1.16226	−	0.746942i
$7$	0.460985	+	2.60528i	0.174236	+	0.984704i
$7$	0.460985	+	2.60528i	0.174236	+	0.984704i
$8$	−2.15663	−	0.154245i	−0.762482	−	0.0545338i
$9$	−0.429976	−	0.546759i	−0.143325	−	0.182253i
$10$	2.47961	+	4.32445i	0.784121	+	1.36751i
$11$	4.64639	+	1.12720i	1.40094	+	0.339864i	0.863887	−	0.503685i	$-0.168023\pi$
$11$	4.64639	+	1.12720i	1.40094	+	0.339864i	0.537052	+	0.843549i	$0.319538\pi$
$12$	−0.107288	−	4.50707i	−0.0309715	−	1.30108i
$13$	−0.856010	−	2.29505i	−0.237415	−	0.636533i	0.762531	−	0.646951i	$-0.223956\pi$
$13$	−0.856010	−	2.29505i	−0.237415	−	0.636533i	−0.999946	+	0.0104185i	$0.996684\pi$
$14$	5.49422	+	2.14536i	1.46839	+	0.573372i
$15$	−2.77086	+	1.96073i	−0.715433	+	0.506258i
$16$	0.649454	−	0.912030i	0.162363	−	0.228008i
$17$	4.71396	+	4.28527i	1.14330	+	1.03933i	0.998758	+	0.0498326i	$0.0158688\pi$
$17$	4.71396	+	4.28527i	1.14330	+	1.03933i	0.144545	+	0.989498i	$0.453828\pi$
$18$	−1.53969	+	0.184093i	−0.362909	+	0.0433911i
$19$	0.0245530	−	0.515430i	0.00563283	−	0.118248i	−0.994300	−	0.106622i	$-0.965996\pi$
$19$	0.0245530	−	0.515430i	0.00563283	−	0.118248i	0.999932	−	0.0116254i	$-0.00370056\pi$
$20$	6.63844	+	0.177775i	1.48440	+	0.0397518i
$21$	−1.09862	+	3.86316i	−0.239739	+	0.843011i
$22$	7.53686	−	7.53686i	1.60686	−	1.60686i
$23$	−2.18953	+	4.26685i	−0.456548	+	0.889699i
$23$	−2.18953	+	4.26685i	−0.456548	+	0.889699i
$24$	−2.84246	−	1.64110i	−0.580215	−	0.334987i
$25$	−2.67814	−	4.22227i	−0.535629	−	0.844454i
$26$	−5.36202	−	1.03344i	−1.05158	−	0.202675i
$27$	−1.19249	−	5.48180i	−0.229495	−	1.05497i
$28$	6.24987	−	4.76232i	1.18112	−	0.899994i
$29$	2.06283	+	3.20982i	0.383057	+	0.596049i	0.978224	−	0.207554i	$-0.0665502\pi$
$29$	2.06283	+	3.20982i	0.383057	+	0.596049i	−0.595166	+	0.803602i	$0.702914\pi$
$30$	0.517397	+	7.54955i	0.0944633	+	1.37835i
$31$	4.96747	−	0.957402i	0.892184	−	0.171954i	0.277498	−	0.960726i	$-0.410495\pi$
$31$	4.96747	−	0.957402i	0.892184	−	0.171954i	0.614686	+	0.788772i	$0.289283\pi$
$32$	−2.68481	−	6.26963i	−0.474612	−	1.10832i
$33$	5.59676	+	4.62107i	0.974271	+	0.804426i
$34$	13.6269	−	4.00121i	2.33699	−	0.686202i
$35$	−5.60137	−	1.90386i	−0.946804	−	0.321812i
$36$	−0.858149	+	1.87908i	−0.143025	+	0.313181i
$37$	0.645626	−	5.39981i	0.106140	−	0.887723i	−0.835126	−	0.550058i	$-0.814605\pi$
$37$	0.645626	−	5.39981i	0.106140	−	0.887723i	0.941266	−	0.337665i	$-0.109637\pi$
$38$	−0.952670	−	0.644786i	−0.154544	−	0.104598i
$39$	0.353458	−	3.70158i	0.0565985	−	0.592726i
$40$	2.62591	−	4.05940i	0.415192	−	0.641848i
$41$	−0.797793	+	5.54877i	−0.124594	+	0.866572i	0.827652	+	0.561241i	$0.189676\pi$
$41$	−0.797793	+	5.54877i	−0.124594	+	0.866572i	−0.952246	+	0.305331i	$0.901233\pi$
$42$	6.07909	+	6.57369i	0.938024	+	1.01434i
$43$	−8.44462	+	0.603971i	−1.28779	+	0.0921047i	−0.698380	−	0.715727i	$-0.746095\pi$
$43$	−8.44462	+	0.603971i	−1.28779	+	0.0921047i	−0.589413	+	0.807832i	$0.700641\pi$
$44$	−3.34764	−	13.7991i	−0.504675	−	2.08030i
$45$	1.53458	−	0.253363i	0.228761	−	0.0377691i
$46$	5.58177	+	9.11870i	0.822987	+	1.34448i
$47$	1.34900	−	5.03453i	0.196772	−	0.734362i	−0.795029	−	0.606571i	$-0.792545\pi$
$47$	1.34900	−	5.03453i	0.196772	−	0.734362i	0.991801	−	0.127791i	$-0.0407888\pi$
$48$	1.49175	−	0.814554i	0.215315	−	0.117571i
$49$	−6.57499	+	2.40199i	−0.939284	+	0.343141i
$50$	−11.1448	+	0.198992i	−1.57612	+	0.0281417i
$51$	3.59428	+	8.97809i	0.503300	+	1.25718i
$52$	−4.89338	+	5.38290i	−0.678589	+	0.746473i
$53$	−6.21613	−	7.52860i	−0.853852	−	1.03413i	−0.998999	−	0.0447222i	$-0.985760\pi$
$53$	−6.21613	−	7.52860i	−0.853852	−	1.03413i	0.145148	−	0.989410i	$-0.453634\pi$
$54$	−11.8186	−	4.09047i	−1.60831	−	0.556643i
$55$	−7.21490	+	7.88940i	−0.972857	+	1.06381i
$56$	−0.592320	−	5.68972i	−0.0791521	−	0.760321i
$57$	0.375409	−	0.687510i	0.0497241	−	0.0910629i
$58$	8.50360	−	0.202423i	1.11658	−	0.0265795i
$59$	6.05692	−	4.31311i	0.788544	−	0.561520i	−0.113310	−	0.993560i	$-0.536145\pi$
$59$	6.05692	−	4.31311i	0.788544	−	0.561520i	0.901854	+	0.432040i	$0.142206\pi$
$60$	8.94656	+	4.64599i	1.15500	+	0.599795i
$61$	−0.597695	−	0.206864i	−0.0765270	−	0.0264863i	0.288536	−	0.957469i	$-0.406831\pi$
$61$	−0.597695	−	0.206864i	−0.0765270	−	0.0264863i	−0.365063	+	0.930983i	$0.618953\pi$
$62$	3.94122	−	10.5668i	0.500535	−	1.34199i
$63$	1.22625	−	1.37226i	0.154493	−	0.172888i
$64$	−12.8334	−	1.84516i	−1.60417	−	0.230645i
$65$	5.41914	+	0.795608i	0.672162	+	0.0986831i
$66$	15.2904	−	5.29206i	1.88212	−	0.651408i
$67$	−0.141455	+	5.94240i	−0.0172815	+	0.725979i	0.922848	+	0.385163i	$0.125855\pi$
$67$	−0.141455	+	5.94240i	−0.0172815	+	0.725979i	−0.940130	+	0.340816i	$0.889297\pi$
$68$	4.89683	−	18.2752i	0.593828	−	2.21620i
$69$	−5.81988	+	4.37387i	−0.700631	+	0.526552i
$70$	−10.1233	+	8.45358i	−1.20997	+	1.01040i
$71$	−12.1961	−	3.58109i	−1.44741	−	0.424997i	−0.538724	−	0.842482i	$-0.681093\pi$
$71$	−12.1961	−	3.58109i	−1.44741	−	0.424997i	−0.908684	+	0.417485i	$0.862912\pi$
$72$	0.842963	+	1.24548i	0.0993441	+	0.146781i
$73$	−1.12408	+	3.51643i	−0.131564	+	0.411566i	−0.995804	−	0.0915125i	$-0.970830\pi$
$73$	−1.12408	+	3.51643i	−0.131564	+	0.411566i	0.864240	+	0.503079i	$0.167800\pi$
$74$	−9.52982	−	7.49433i	−1.10782	−	0.871199i
$75$	−0.856264	−	7.54171i	−0.0988729	−	0.870842i
$76$	−1.39400	+	0.636620i	−0.159903	+	0.0730254i
$77$	−0.794764	+	12.6248i	−0.0905718	+	1.43873i
$78$	−6.63611	−	4.96773i	−0.751391	−	0.562485i
$79$	−11.3215	+	1.08107i	−1.27377	+	0.121630i	−0.709940	−	0.704262i	$-0.751278\pi$
$79$	−11.3215	+	1.08107i	−1.27377	+	0.121630i	−0.563828	+	0.825892i	$0.690672\pi$
$80$	1.08723	+	2.25519i	0.121556	+	0.252138i
$81$	1.51580	−	6.24821i	0.168422	−	0.694246i
$82$	9.63682	+	7.95683i	1.06421	+	0.878685i
$83$	−2.79197	+	3.72964i	−0.306459	+	0.409381i	−0.927160	−	0.374666i	$-0.877757\pi$
$83$	−2.79197	+	3.72964i	−0.306459	+	0.409381i	0.620701	+	0.784048i	$0.286848\pi$
$84$	11.6927	−	2.35721i	1.27578	−	0.257193i
$85$	−13.4755	+	4.61909i	−1.46162	+	0.501011i
$86$	−8.64849	+	16.7757i	−0.932591	+	1.80897i
$87$	0.687631	+	5.75112i	0.0737218	+	0.616585i
$88$	−9.84666	−	3.14763i	−1.04966	−	0.335539i
$89$	5.28562	+	1.01872i	0.560274	+	0.107984i	0.461523	−	0.887128i	$-0.347303\pi$
$89$	5.28562	+	1.01872i	0.560274	+	0.107984i	0.0987512	+	0.995112i	$0.468515\pi$
$90$	1.29826	−	3.21516i	0.136849	−	0.338907i
$91$	5.58465	−	3.28813i	0.585430	−	0.344690i
$92$	14.2429	−	0.0268832i	1.48493	−	0.00280277i
$93$	7.41789	+	1.98762i	0.769200	+	0.206106i
$94$	−8.01838	−	8.40943i	−0.827033	−	0.867367i
$95$	0.983455	+	0.603465i	0.100900	+	0.0619142i
$96$	0.492637	−	10.3417i	0.0502795	−	1.05550i
$97$	6.20992	+	8.29548i	0.630521	+	0.842278i	0.996075	−	0.0885123i	$-0.0282113\pi$
$97$	6.20992	+	8.29548i	0.630521	+	0.842278i	−0.365554	+	0.930790i	$0.619120\pi$
$98$	−3.05652	+	15.3030i	−0.308755	+	1.54583i
$99$	−1.38153	−	3.02512i	−0.138849	−	0.304036i
$100$	−7.50100	+	12.8155i	−0.750100	+	1.28155i
$101$	2.01836	+	0.808028i	0.200834	+	0.0804018i	0.469899	−	0.882720i	$-0.344290\pi$
$101$	2.01836	+	0.808028i	0.200834	+	0.0804018i	−0.269065	+	0.963122i	$0.586715\pi$
$102$	21.2609	+	3.57519i	2.10514	+	0.353996i
$103$	0.0410688	+	1.72526i	0.00404663	+	0.169995i	0.998120	+	0.0612858i	$0.0195201\pi$
$103$	0.0410688	+	1.72526i	0.00404663	+	0.169995i	−0.994074	+	0.108709i	$0.965328\pi$
$104$	1.49209	+	5.08161i	0.146312	+	0.498292i
$105$	−6.38558	−	6.31500i	−0.623169	−	0.616281i
$106$	−21.5437	+	3.09752i	−2.09251	+	0.300858i
$107$	−8.92679	−	18.3766i	−0.862986	−	1.77653i	−0.573139	−	0.819458i	$-0.694275\pi$
$107$	−8.92679	−	18.3766i	−0.862986	−	1.77653i	−0.289846	−	0.957073i	$-0.593604\pi$
$108$	−12.8476	+	10.6079i	−1.23626	+	1.02074i
$109$	−0.235968	−	4.95359i	−0.0226017	−	0.474468i	−0.981587	−	0.191013i	$-0.938823\pi$
$109$	−0.235968	−	4.95359i	−0.0226017	−	0.474468i	0.958986	−	0.283454i	$-0.0914804\pi$
$110$	6.64669	+	22.8881i	0.633737	+	2.18229i
$111$	4.46324	−	6.94494i	0.423632	−	0.659185i
$112$	2.67548	+	1.27158i	0.252809	+	0.120153i
$113$	4.76851	+	8.73288i	0.448584	+	0.821521i	0.999919	−	0.0127638i	$-0.00406296\pi$
$113$	4.76851	+	8.73288i	0.448584	+	0.821521i	−0.551334	+	0.834284i	$0.685881\pi$
$114$	−0.873143	−	1.51233i	−0.0817773	−	0.141642i
$115$	−6.00113	−	8.88743i	−0.559608	−	0.828757i
$116$	5.66579	−	9.81343i	0.526055	−	0.911154i
$117$	−0.886777	+	1.45485i	−0.0819825	+	0.134501i
$118$	−1.18255	−	16.5343i	−0.108863	−	1.52210i
$119$	−8.99128	+	14.2566i	−0.824229	+	1.30690i
$120$	6.27814	−	3.80117i	0.573113	−	0.346998i
$121$	10.5412	+	5.43434i	0.958287	+	0.494031i
$122$	−1.08728	+	0.897734i	−0.0984377	+	0.0812771i
$123$	−4.76983	+	7.04741i	−0.430081	+	0.635444i
$124$	−9.28736	−	11.8098i	−0.834029	−	1.06055i
$125$	11.1585	−	0.698090i	0.998049	−	0.0624391i
$126$	−1.18939	−	3.92647i	−0.105959	−	0.349798i
$127$	−12.5990	−	6.87958i	−1.11798	−	0.610464i	−0.189514	−	0.981878i	$-0.560691\pi$
$127$	−12.5990	−	6.87958i	−1.11798	−	0.610464i	−0.928468	+	0.371414i	$0.878873\pi$
$128$	−9.71799	+	11.7698i	−0.858957	+	1.04032i
$129$	−11.9313	−	4.77659i	−1.05050	−	0.420555i
$130$	7.80227	−	9.39260i	0.684304	−	0.823786i
$131$	7.05821	−	9.91187i	0.616679	−	0.866004i	−0.381619	−	0.924320i	$-0.624634\pi$
$131$	7.05821	−	9.91187i	0.616679	−	0.866004i	0.998298	+	0.0583154i	$0.0185729\pi$
$132$	4.58188	−	21.0626i	0.398801	−	1.83326i
$133$	1.35416	−	0.173638i	0.117420	−	0.0150563i
$134$	11.1477	+	7.16417i	0.963011	+	0.618890i
$135$	12.0257	+	3.56993i	1.03500	+	0.307250i
$136$	−9.50526	−	9.96883i	−0.815069	−	0.854820i
$137$	−3.32958	−	12.4262i	−0.284465	−	1.06164i	−0.949229	−	0.314585i	$-0.898135\pi$
$137$	−3.32958	−	12.4262i	−0.284465	−	1.06164i	0.664764	−	0.747053i	$-0.268532\pi$
$138$	1.57325	+	16.1535i	0.133924	+	1.37508i
$139$		−	5.02885i		−	0.426541i	−0.976993	−	0.213271i	$-0.931588\pi$
$139$		−	5.02885i		−	0.426541i	0.976993	−	0.213271i	$-0.0684116\pi$
$140$	2.59706	+	17.3769i	0.219492	+	1.46862i
$141$	5.18138	−	5.97964i	0.436351	−	0.503576i
$142$	−20.9678	+	19.0610i	−1.75958	+	1.59957i
$143$	−1.39037	−	11.6286i	−0.116269	−	0.972432i
$144$	−0.777910	+	0.0370564i	−0.0648259	+	0.00308804i
$145$	−8.51180	+	0.583343i	−0.706866	+	0.0484440i
$146$	5.38952	+	6.21984i	0.446040	+	0.514757i
$147$	−10.5711	−	1.08136i	−0.871887	−	0.0891890i
$148$	−15.1326	+	5.64417i	−1.24389	+	0.463948i
$149$	−1.40723	−	1.34179i	−0.115285	−	0.109924i	0.630245	−	0.776397i	$-0.282955\pi$
$149$	−1.40723	−	1.34179i	−0.115285	−	0.109924i	−0.745529	+	0.666473i	$0.767803\pi$
$150$	−15.3497	−	7.12060i	−1.25330	−	0.581395i
$151$	10.6596	+	14.9693i	0.867463	+	1.21818i	0.974603	+	0.223938i	$0.0718913\pi$
$151$	10.6596	+	14.9693i	0.867463	+	1.21818i	−0.107140	+	0.994244i	$0.534169\pi$
$152$	−0.132454	+	1.10780i	−0.0107434	+	0.0898547i
$153$	0.316122	−	4.41996i	0.0255569	−	0.357333i
$154$	23.1100	+	16.1613i	1.86226	+	1.30231i
$155$	−3.47638	+	10.7646i	−0.279230	+	0.864634i
$156$	−10.2521	+	4.10433i	−0.820827	+	0.328610i
$157$	−1.38448	+	4.33102i	−0.110493	+	0.345653i	−0.991953	−	0.126606i	$-0.959592\pi$
$157$	−1.38448	+	4.33102i	−0.110493	+	0.345653i	0.881460	+	0.472259i	$0.156561\pi$
$158$	−11.0783	+	22.8057i	−0.881343	+	1.81432i
$159$	−3.49415	−	14.4031i	−0.277104	−	1.14224i
$160$	15.1772	+	1.49480i	1.19986	+	0.118174i
$161$	−12.1257	−	3.73739i	−0.955637	−	0.294547i
$162$	−10.1352	−	10.1352i	−0.796294	−	0.796294i
$163$	3.90155	+	2.37812i	0.305593	+	0.186269i	0.664864	−	0.746965i	$-0.268490\pi$
$163$	3.90155	+	2.37812i	0.305593	+	0.186269i	−0.359271	+	0.933233i	$0.616975\pi$
$164$	15.7329	−	5.44521i	1.22853	−	0.425199i
$165$	−15.0846	+	5.98700i	−1.17434	+	0.466087i
$166$	3.86015	+	9.64219i	0.299606	+	0.748379i
$167$	−19.1078	−	4.15665i	−1.47861	−	0.321651i	−0.600311	−	0.799767i	$-0.704956\pi$
$167$	−19.1078	−	4.15665i	−1.47861	−	0.321651i	−0.878297	+	0.478116i	$0.841320\pi$
$168$	2.96519	−	8.16194i	0.228769	−	0.629707i
$169$	5.29023	−	4.58401i	0.406941	−	0.352616i
$170$	−6.84268	+	31.0111i	−0.524809	+	2.37844i
$171$	−0.292373	+	0.208198i	−0.0223583	+	0.0159213i
$172$	13.0863	+	21.4695i	0.997824	+	1.63703i
$173$	−0.0716183	+	0.00170483i	−0.00544504	+	0.000129616i	−0.0265201	−	0.999648i	$-0.508443\pi$
$173$	−0.0716183	+	0.00170483i	−0.00544504	+	0.000129616i	0.0210751	+	0.999778i	$0.493291\pi$
$174$	11.7455	+	5.36401i	0.890427	+	0.406644i
$175$	9.76562	−	8.92372i	0.738211	−	0.674570i
$176$	4.04566	−	3.50558i	0.304953	−	0.264243i
$177$	11.1313	−	1.87182i	0.836681	−	0.140695i
$178$	8.07205	−	8.87956i	0.605026	−	0.665551i
$179$	15.9055	−	20.2255i	1.18883	−	1.51173i	0.378662	−	0.925535i	$-0.376384\pi$
$179$	15.9055	−	20.2255i	1.18883	−	1.51173i	0.810173	−	0.586191i	$-0.199373\pi$
$180$	−2.75717	−	3.70606i	−0.205507	−	0.276234i
$181$	−19.0260	−	16.4861i	−1.41419	−	1.22540i	−0.938265	−	0.345918i	$-0.887568\pi$
$181$	−19.0260	−	16.4861i	−1.41419	−	1.22540i	−0.475926	−	0.879485i	$-0.657887\pi$
$182$	0.220606	−	14.4460i	0.0163524	−	1.07081i
$183$	−0.678912	−	0.678912i	−0.0501866	−	0.0501866i
$184$	5.38013	−	8.86427i	0.396629	−	0.653482i
$185$	9.88450	+	7.08311i	0.726723	+	0.520761i
$186$	12.3905	−	11.8143i	0.908514	−	0.866266i
$187$	17.0725	+	25.2246i	1.24847	+	1.84461i
$188$	−15.1256	+	3.29037i	−1.10315	+	0.239975i
$189$	13.7319	−	5.63380i	0.998850	−	0.409799i
$190$	2.28983	−	1.17189i	0.166122	−	0.0850175i
$191$	−3.01697	−	2.14837i	−0.218300	−	0.155451i	0.465676	−	0.884955i	$-0.345811\pi$
$191$	−3.01697	−	2.14837i	−0.218300	−	0.155451i	−0.683976	+	0.729505i	$0.739751\pi$
$192$	−16.2995	−	11.0318i	−1.17631	−	0.796153i
$193$	19.6191	−	8.40137i	1.41221	−	0.604744i	0.454051	−	0.890976i	$-0.349978\pi$
$193$	19.6191	−	8.40137i	1.41221	−	0.604744i	0.958160	+	0.286232i	$0.0924027\pi$
$194$	22.9963	−	2.19588i	1.65104	−	0.157655i
$195$	6.87186	+	4.68086i	0.492104	+	0.335204i
$196$	15.2883	+	14.0873i	1.09202	+	1.00624i
$197$	−10.0913	+	3.76387i	−0.718976	+	0.268164i	−0.682207	−	0.731159i	$-0.738980\pi$
$197$	−10.0913	+	3.76387i	−0.718976	+	0.268164i	−0.0367697	+	0.999324i	$0.511707\pi$
$198$	−7.36152	−	0.880177i	−0.523160	−	0.0625515i
$199$	6.28479	−	1.21129i	0.445517	−	0.0858664i	0.0384415	−	0.999261i	$-0.487761\pi$
$199$	6.28479	−	1.21129i	0.445517	−	0.0858664i	0.407076	+	0.913394i	$0.366549\pi$
$200$	5.12449	+	9.51894i	0.362356	+	0.673091i
$201$	−4.13472	+	8.02024i	−0.291641	+	0.565704i
$202$	3.88002	−	2.90454i	0.272997	−	0.204363i
$203$	−7.41155	+	6.85392i	−0.520189	+	0.481051i
$204$	18.8083	−	21.7059i	1.31684	−	1.51972i
$205$	−10.0124	−	7.54176i	−0.699297	−	0.526739i
$206$	3.33180	+	1.92362i	0.232138	+	0.134025i
$207$	3.27438	−	0.637497i	0.227585	−	0.0443091i
$208$	−2.64910	−	0.709823i	−0.183682	−	0.0492174i
$209$	0.695076	−	2.36721i	0.0480794	−	0.163743i
$210$	−19.4302	+	4.82819i	−1.34081	+	0.333177i
$211$	6.34119	+	4.07523i	0.436545	+	0.280551i	0.740398	−	0.672168i	$-0.234637\pi$
$211$	6.34119	+	4.07523i	0.436545	+	0.280551i	−0.303853	+	0.952719i	$0.598273\pi$
$212$	−11.4140	+	26.6543i	−0.783919	+	1.83062i
$213$	−14.2778	−	12.9794i	−0.978302	−	0.889336i
$214$	−45.3388	−	4.32933i	−3.09930	−	0.295947i
$215$	7.91538	−	17.1968i	0.539824	−	1.17281i
$216$	1.72622	+	12.0061i	0.117454	+	0.816914i
$217$	4.78423	+	12.5003i	0.324775	+	0.848577i
$218$	−9.70331	−	5.29841i	−0.657191	−	0.358853i
$219$	−3.86731	+	4.05592i	−0.261329	+	0.274074i
$220$	30.6444	+	8.30887i	2.06604	+	0.560184i
$221$	5.79973	−	14.4870i	0.390132	−	0.974502i
$222$	−8.04156	−	16.5543i	−0.539714	−	1.11105i
$223$	9.55315	+	3.56314i	0.639726	+	0.238606i	0.648332	−	0.761357i	$-0.275467\pi$
$223$	9.55315	+	3.56314i	0.639726	+	0.238606i	−0.00860608	+	0.999963i	$0.502739\pi$
$224$	15.0965	−	9.88490i	1.00868	−	0.660463i
$225$	−1.15703	+	3.27977i	−0.0771351	+	0.218652i
$226$	22.1565	+	1.05545i	1.47383	+	0.0702072i
$227$	13.8157	+	6.71126i	0.916981	+	0.445442i	0.834411	−	0.551143i	$-0.185808\pi$
$227$	13.8157	+	6.71126i	0.916981	+	0.445442i	0.0825707	+	0.996585i	$0.473687\pi$
$228$	−2.32572	−	0.0553624i	−0.154024	−	0.00366646i
$229$	9.29742	+	16.1036i	0.614391	+	1.06416i	0.990491	+	0.137577i	$0.0439315\pi$
$229$	9.29742	+	16.1036i	0.614391	+	1.06416i	−0.376100	+	0.926579i	$0.622735\pi$
$230$	−23.8809	+	1.11160i	−1.57466	+	0.0732967i
$231$	−9.45918	+	16.7114i	−0.622368	+	1.09953i
$232$	−3.95365	−	7.24056i	−0.259570	−	0.475366i
$233$	6.72148	−	4.54923i	0.440339	−	0.298030i	−0.320167	−	0.947361i	$-0.603739\pi$
$233$	6.72148	−	4.54923i	0.440339	−	0.298030i	0.760506	+	0.649331i	$0.224951\pi$
$234$	1.74050	+	3.37609i	0.113780	+	0.220702i
$235$	8.41094	+	8.06770i	0.548669	+	0.526279i
$236$	−19.6281	−	10.1190i	−1.27768	−	0.658690i
$237$	−16.1761	−	6.03336i	−1.05075	−	0.391909i
$238$	16.7061	+	33.6574i	1.08289	+	2.18168i
$239$	22.4519	−	3.22809i	1.45229	−	0.208808i	0.629432	−	0.777055i	$-0.283288\pi$
$239$	22.4519	−	3.22809i	1.45229	−	0.208808i	0.822858	+	0.568248i	$0.192378\pi$
$240$	−0.0113003	+	3.80051i	−0.000729434	+	0.245322i
$241$	−19.2522	−	4.67054i	−1.24014	−	0.300856i	−0.438541	−	0.898711i	$-0.644504\pi$
$241$	−19.2522	−	4.67054i	−1.24014	−	0.300856i	−0.801604	+	0.597856i	$0.796020\pi$
$242$	22.5755	−	13.7605i	1.45121	−	0.884556i
$243$	−4.50134	+	5.45174i	−0.288761	+	0.349729i
$244$	0.267322	+	1.85926i	0.0171135	+	0.119027i
$245$	2.37796	−	15.4708i	0.151922	−	0.988392i
$246$	7.88089	+	17.2568i	0.502467	+	1.10025i
$247$	−1.20396	+	0.384863i	−0.0766059	+	0.0244882i
$248$	−10.8607	+	1.29855i	−0.689652	+	0.0824580i
$249$	−6.28617	+	3.24074i	−0.398370	+	0.205374i
$250$	11.6182	−	22.0511i	0.734802	−	1.39463i
$251$	1.04938	−	3.57386i	0.0662363	−	0.225580i	−0.919722	−	0.392569i	$-0.871586\pi$
$251$	1.04938	−	3.57386i	0.0662363	−	0.225580i	0.985959	+	0.166989i	$0.0534045\pi$
$252$	−5.29114	−	1.36949i	−0.333310	−	0.0862698i
$253$	−14.9830	+	17.3574i	−0.941973	+	1.09125i
$254$	−27.7143	+	16.0009i	−1.73895	+	1.00398i
$255$	−21.4640	−	2.63109i	−1.34413	−	0.164765i
$256$	2.64796	+	7.65079i	0.165498	+	0.478174i
$257$	−14.8026	+	13.4565i	−0.923363	+	0.839393i	−0.987350	−	0.158558i	$-0.949316\pi$
$257$	−14.8026	+	13.4565i	−0.923363	+	0.839393i	0.0639865	+	0.997951i	$0.479619\pi$
$258$	−22.9364	+	17.1700i	−1.42796	+	1.06896i
$259$	14.3656	−	0.807191i	0.892638	−	0.0501564i
$260$	−5.27457	−	15.3877i	−0.327115	−	0.954307i
$261$	0.868032	−	2.50801i	0.0537298	−	0.155242i
$262$	−10.6784	−	24.9365i	−0.659715	−	1.54058i
$263$	−3.44942	+	20.5129i	−0.212700	+	1.26488i	0.650300	+	0.759677i	$0.274643\pi$
$263$	−3.44942	+	20.5129i	−0.212700	+	1.26488i	−0.863000	+	0.505203i	$0.831417\pi$
$264$	−11.3573	−	10.8292i	−0.698996	−	0.666491i
$265$	21.4488	−	4.06782i	1.31759	−	0.249884i
$266$	1.24068	−	2.77921i	0.0760711	−	0.170404i
$267$	6.54155	+	4.89694i	0.400336	+	0.299688i
$268$	15.8788	−	7.71343i	0.969950	−	0.471172i
$269$	−2.00201	+	20.9660i	−0.122064	+	1.27832i	0.702146	+	0.712033i	$0.252225\pi$
$269$	−2.00201	+	20.9660i	−0.122064	+	1.27832i	−0.824210	+	0.566284i	$0.808381\pi$
$270$	20.7489	−	18.7496i	1.26274	−	1.14106i
$271$	−21.3084	+	8.53061i	−1.29440	+	0.518198i	−0.913657	−	0.406485i	$-0.866754\pi$
$271$	−21.3084	+	8.53061i	−1.29440	+	0.518198i	−0.380738	+	0.924683i	$0.624330\pi$
$272$	6.96979	−	1.51619i	0.422606	−	0.0919323i
$273$	9.80659	−	0.785513i	0.593522	−	0.0475414i
$274$	−27.5174	−	8.07983i	−1.66239	−	0.488121i
$275$	−7.68434	−	22.6371i	−0.463383	−	1.36507i
$276$	19.4659	+	9.41058i	1.17171	+	0.566450i
$277$	−8.59472	+	2.30295i	−0.516407	+	0.138371i	−0.507604	−	0.861590i	$-0.669469\pi$
$277$	−8.59472	+	2.30295i	−0.516407	+	0.138371i	−0.00880274	+	0.999961i	$0.502802\pi$
$278$	−9.57278	−	5.83492i	−0.574137	−	0.349955i
$279$	−2.65936	−	2.30435i	−0.159212	−	0.137958i
$280$	11.7864	+	4.96991i	0.704372	+	0.297009i
$281$	21.5911	+	3.10434i	1.28802	+	0.185189i	0.752083	−	0.659069i	$-0.229049\pi$
$281$	21.5911	+	3.10434i	1.28802	+	0.185189i	0.535937	+	0.844258i	$0.319958\pi$
$282$	−5.37078	−	16.8012i	−0.319825	−	1.00050i
$283$	5.37341	+	6.50795i	0.319416	+	0.386857i	0.906174	−	0.422905i	$-0.138990\pi$
$283$	5.37341	+	6.50795i	0.319416	+	0.386857i	−0.586758	+	0.809763i	$0.699596\pi$
$284$	7.14420	+	37.0676i	0.423930	+	2.19956i
$285$	0.942586	+	1.47633i	0.0558340	+	0.0874500i
$286$	−23.7491	−	10.8459i	−1.40432	−	0.641329i
$287$	−14.8239	+	0.479423i	−0.875026	+	0.0282994i
$288$	−2.27357	+	4.16374i	−0.133972	+	0.245351i
$289$	2.24189	+	23.4781i	0.131876	+	1.38107i
$290$	−8.76571	+	16.8797i	−0.514740	+	0.991209i
$291$	2.97699	+	15.4461i	0.174514	+	0.905466i
$292$	10.8121	−	1.81814i	0.632731	−	0.106399i
$293$	−23.2946	−	5.06743i	−1.36088	−	0.296042i	−0.527884	−	0.849316i	$-0.677015\pi$
$293$	−23.2946	−	5.06743i	−1.36088	−	0.296042i	−0.832999	+	0.553274i	$0.813378\pi$
$294$	−14.3239	+	18.8681i	−0.835389	+	1.10041i
$295$	1.92481	+	16.5149i	0.112067	+	0.961534i
$296$	−2.22527	+	11.5458i	−0.129341	+	0.671085i
$297$	0.638310	−	26.8148i	0.0370385	−	1.55595i
$298$	−4.18698	+	1.12190i	−0.242545	+	0.0649899i
$299$	11.6669	+	1.37262i	0.674714	+	0.0793805i
$300$	−18.7427	+	12.5236i	−1.08211	+	0.723050i
$301$	−5.46635	−	21.7222i	−0.315075	−	1.25205i
$302$	40.8633	−	2.92260i	2.35142	−	0.168177i
$303$	2.22001	+	2.44209i	0.127536	+	0.140295i
$304$	−0.454142	−	0.357141i	−0.0260468	−	0.0204834i
$305$	1.04932	−	0.948208i	0.0600836	−	0.0542942i
$306$	−8.04693	−	5.73019i	−0.460012	−	0.327573i
$307$	−0.0357159	+	0.499374i	−0.00203842	+	0.0285008i	−0.998370	−	0.0570815i	$-0.981821\pi$
$307$	−0.0357159	+	0.499374i	−0.00203842	+	0.0285008i	0.996331	+	0.0855823i	$0.0272751\pi$
$308$	34.4074	−	15.0827i	1.96055	−	0.859418i
$309$	−1.08828	+	2.38300i	−0.0619100	+	0.135564i
$310$	16.4576	+	19.1076i	0.934730	+	1.08524i
$311$	1.17146	−	4.82881i	0.0664273	−	0.273817i	−0.928906	−	0.370316i	$-0.879249\pi$
$311$	1.17146	−	4.82881i	0.0664273	−	0.273817i	0.995333	+	0.0964992i	$0.0307645\pi$
$312$	−1.33323	+	7.92840i	−0.0754790	+	0.448857i
$313$	−6.27128	−	0.749823i	−0.354474	−	0.0423825i	−0.0604244	−	0.998173i	$-0.519245\pi$
$313$	−6.27128	−	0.749823i	−0.354474	−	0.0423825i	−0.294049	+	0.955790i	$0.595003\pi$
$314$	6.63802	+	7.66068i	0.374605	+	0.432317i
$315$	1.36750	+	3.88121i	0.0770498	+	0.218682i
$316$	18.2608	+	28.4144i	1.02725	+	1.59843i
$317$	1.25238	+	0.536299i	0.0703404	+	0.0301215i	0.428532	−	0.903526i	$-0.359031\pi$
$317$	1.25238	+	0.536299i	0.0703404	+	0.0301215i	−0.358192	+	0.933648i	$0.616607\pi$
$318$	−31.4716	−	10.0604i	−1.76484	−	0.564157i
$319$	5.96658	+	17.2393i	0.334064	+	0.965215i
$320$	17.4428	−	23.1571i	0.975084	−	1.29452i
$321$		−	31.0135i		−	1.73100i
$322$	−21.1837	+	18.7457i	−1.18052	+	1.04466i
$323$	2.32450	−	2.32450i	0.129339	−	0.129339i
$324$	−18.5563	+	4.50172i	−1.03091	+	0.250096i
$325$	−7.39781	+	9.76078i	−0.410357	+	0.541431i
$326$	9.05385	−	4.66758i	0.501446	−	0.258513i
$327$	2.96349	−	6.92041i	0.163881	−	0.382699i
$328$	2.57641	−	11.8436i	0.142258	−	0.653951i
$329$	13.7382	+	1.19368i	0.757414	+	0.0658097i
$330$	−6.10584	+	35.6613i	−0.336115	+	1.96309i
$331$	−16.7453	+	13.1686i	−0.920404	+	0.723814i	−0.961345	−	0.275348i	$-0.911207\pi$
$331$	−16.7453	+	13.1686i	−0.920404	+	0.723814i	0.0409405	+	0.999162i	$0.486965\pi$
$332$	13.6447	+	2.29447i	0.748851	+	0.125926i
$333$	−3.23000	+	1.96879i	−0.177003	+	0.107889i
$334$	−30.0831	+	31.5502i	−1.64607	+	1.72635i
$335$	−11.4908	−	6.67988i	−0.627812	−	0.364961i
$336$	2.80982	+	3.51092i	0.153288	+	0.191536i
$337$	8.29764	+	0.593459i	0.452001	+	0.0323278i	0.295484	−	0.955348i	$-0.404519\pi$
$337$	8.29764	+	0.593459i	0.452001	+	0.0323278i	0.156517	+	0.987675i	$0.449973\pi$
$338$	−2.58781	−	15.3891i	−0.140758	−	0.837058i
$339$	0.718696	+	15.0873i	0.0390342	+	0.819429i
$340$	30.5315	+	29.2855i	1.65580	+	1.58823i
$341$	24.1600	+	1.15088i	1.30834	+	0.0623238i
$342$	0.0570829	+	0.798124i	0.00308669	+	0.0431576i
$343$	−9.28883	−	16.0224i	−0.501550	−	0.865129i
$344$	18.3050			0.986942
$345$	−2.29926	−	16.1159i	−0.123788	−	0.867651i
$346$	−0.0798527	+	0.138309i	−0.00429291	+	0.00743553i
$347$	−24.1316	−	0.574440i	−1.29545	−	0.0308376i	−0.629600	−	0.776919i	$-0.716781\pi$
$347$	−24.1316	−	0.574440i	−1.29545	−	0.0308376i	−0.665854	+	0.746082i	$0.731933\pi$
$348$	14.2456	−	9.64169i	0.763643	−	0.516849i
$349$	−4.72868	+	7.35796i	−0.253120	+	0.393863i	−0.944439	−	0.328687i	$-0.893394\pi$
$349$	−4.72868	+	7.35796i	−0.253120	+	0.393863i	0.691319	+	0.722550i	$0.257030\pi$
$350$	−5.65602	−	28.9437i	−0.302327	−	1.54710i
$351$	−11.5602	+	7.42931i	−0.617040	+	0.396547i
$352$	−5.40754	−	32.1575i	−0.288223	−	1.71400i
$353$	7.11867	−	10.5178i	0.378889	−	0.559807i	−0.589969	−	0.807426i	$-0.700860\pi$
$353$	7.11867	−	10.5178i	0.378889	−	0.559807i	0.968858	+	0.247618i	$0.0796479\pi$
$354$	9.35239	−	23.3611i	0.497074	−	1.24163i
$355$	20.1575	−	20.0379i	1.06985	−	1.06350i
$356$	−4.50391	−	15.3389i	−0.238707	−	0.812960i
$357$	−21.7335	+	13.5029i	−1.15026	+	0.714648i
$358$	−20.0458	−	53.7448i	−1.05945	−	2.84050i
$359$	2.35857	−	1.85480i	0.124480	−	0.0978925i	−0.553978	−	0.832531i	$-0.686891\pi$
$359$	2.35857	−	1.85480i	0.124480	−	0.0978925i	0.678458	+	0.734639i	$0.262648\pi$
$360$	−3.34859	+	0.309707i	−0.176486	+	0.0163230i
$361$	18.6489	+	1.78075i	0.981521	+	0.0937239i
$362$	−53.4582	+	17.0887i	−2.80970	+	0.898163i
$363$	10.7889	+	14.4122i	0.566269	+	0.756447i
$364$	−16.2797	−	10.2672i	−0.853290	−	0.538147i
$365$	−5.67877	−	5.99129i	−0.297240	−	0.313599i
$366$	−2.08009	+	0.504625i	−0.108728	+	0.0263772i
$367$	−0.714318	−	2.66587i	−0.0372871	−	0.139157i	0.944773	−	0.327725i	$-0.106282\pi$
$367$	−0.714318	−	2.66587i	−0.0372871	−	0.139157i	−0.982060	+	0.188568i	$0.939615\pi$
$368$	2.46950	+	4.76803i	0.128731	+	0.248551i
$369$	3.37687	−	1.94964i	0.175793	−	0.101494i
$370$	24.9521	−	10.5974i	1.29720	−	0.550934i
$371$	16.7486	−	19.6653i	0.869542	−	1.02097i
$372$	−4.84803	−	22.2860i	−0.251359	−	1.15548i
$373$	−19.4466	−	8.32752i	−1.00691	−	0.431182i	−0.174089	−	0.984730i	$-0.555698\pi$
$373$	−19.4466	−	8.32752i	−1.00691	−	0.431182i	−0.832818	+	0.553548i	$0.813274\pi$
$374$	67.8260	−	3.23095i	3.50720	−	0.167068i
$375$	15.6995	+	6.44820i	0.810718	+	0.332984i
$376$	−3.68584	+	10.6495i	−0.190083	+	0.549208i
$377$	5.60090	−	7.48193i	0.288461	−	0.385339i
$378$	5.20862	−	32.6765i	0.267903	−	1.68070i
$379$	15.6190	−	4.58616i	0.802296	−	0.235575i	0.145219	−	0.989399i	$-0.453611\pi$
$379$	15.6190	−	4.58616i	0.802296	−	0.235575i	0.657076	+	0.753824i	$0.271793\pi$
$380$	0.254624	−	3.41728i	0.0130619	−	0.175303i
$381$	−12.6402	−	17.7506i	−0.647575	−	0.909392i
$382$	−7.59014	+	3.25029i	−0.388345	+	0.166299i
$383$	7.05410	−	3.42667i	0.360448	−	0.175095i	−0.247860	−	0.968796i	$-0.579727\pi$
$383$	7.05410	−	3.42667i	0.360448	−	0.175095i	0.608308	+	0.793701i	$0.291849\pi$
$384$	−21.0764	+	9.62525i	−1.07555	+	0.491186i
$385$	−23.8801	−	15.1600i	−1.21704	−	0.772623i
$386$	6.77115	−	47.0944i	0.344642	−	2.39704i
$387$	3.96121	+	4.35748i	0.201360	+	0.221503i
$388$	13.4468	−	27.6815i	0.682660	−	1.40532i
$389$	5.71343	−	5.44775i	0.289683	−	0.276212i	−0.531277	−	0.847198i	$-0.678288\pi$
$389$	5.71343	−	5.44775i	0.289683	−	0.276212i	0.820960	+	0.570986i	$0.193439\pi$
$390$	16.8837	−	7.64994i	0.854940	−	0.387370i
$391$	−28.6059	+	10.7310i	−1.44666	+	0.542690i
$392$	14.5503	−	4.16604i	0.734900	−	0.210417i
$393$	16.2122	−	8.85251i	0.817795	−	0.446550i
$394$	−4.54404	+	23.5767i	−0.228926	+	1.18778i
$395$	10.0803	−	23.3477i	0.507195	−	1.17475i
$396$	−6.10540	+	7.76365i	−0.306808	+	0.390138i
$397$	5.85078	+	18.3028i	0.293642	+	0.918593i	0.981288	+	0.192546i	$0.0616746\pi$
$397$	5.85078	+	18.3028i	0.293642	+	0.918593i	−0.687646	+	0.726046i	$0.741356\pi$
$398$	4.98639	−	13.3690i	0.249945	−	0.670128i
$399$	1.96421	+	0.661114i	0.0983337	+	0.0330971i
$400$	−5.59017	−	0.299621i	−0.279508	−	0.0149810i
$401$	−1.60948	−	16.8552i	−0.0803736	−	0.841711i	−0.942320	−	0.334712i	$-0.891361\pi$
$401$	−1.60948	−	16.8552i	−0.0803736	−	0.841711i	0.861947	−	0.506999i	$-0.169245\pi$
$402$	10.4696	+	17.1765i	0.522178	+	0.856688i
$403$	−6.44949	−	10.5811i	−0.321272	−	0.527080i
$404$	−0.613753	−	6.42752i	−0.0305354	−	0.319781i
$405$	10.6092	+	9.70222i	0.527178	+	0.482107i
$406$	4.44740	+	22.0610i	0.220721	+	1.09487i
$407$	9.08650	−	24.3619i	0.450401	−	1.20757i
$408$	−6.36670	−	19.9168i	−0.315199	−	0.986027i
$409$	16.4875	−	20.9655i	0.815254	−	1.03668i	−0.183308	−	0.983056i	$-0.558680\pi$
$409$	16.4875	−	20.9655i	0.815254	−	1.03668i	0.998561	−	0.0536236i	$-0.0170771\pi$
$410$	−25.9736	+	10.3088i	−1.28274	+	0.509113i
$411$	3.69584	−	19.1758i	0.182302	−	0.945874i
$412$	4.49830	−	2.45626i	0.221616	−	0.121011i
$413$	14.0290	+	13.7917i	0.690323	+	0.678646i
$414$	2.58570	−	6.97271i	0.127080	−	0.342690i
$415$	−4.29944	−	9.48902i	−0.211051	−	0.465798i
$416$	−12.0909	+	11.5287i	−0.592805	+	0.565239i
$417$	3.33562	−	6.86666i	0.163346	−	0.336262i
$418$	−3.69967	−	4.06978i	−0.180957	−	0.199059i
$419$	−3.10650	+	21.6062i	−0.151762	+	1.05553i	0.761502	+	0.648163i	$0.224462\pi$
$419$	−3.10650	+	21.6062i	−0.151762	+	1.05553i	−0.913264	+	0.407368i	$0.866447\pi$
$420$	−7.97990	+	25.4500i	−0.389379	+	1.24183i
$421$	25.7763	−	11.7716i	1.25626	−	0.573714i	0.327659	−	0.944796i	$-0.393740\pi$
$421$	25.7763	−	11.7716i	1.25626	−	0.573714i	0.928600	+	0.371082i	$0.121013\pi$
$422$	15.1151	−	7.34247i	0.735792	−	0.357426i
$423$	−3.33271	+	1.42715i	−0.162042	+	0.0693905i
$424$	12.2446	+	17.1952i	0.594652	+	0.835071i
$425$	5.46891	−	31.3802i	0.265281	−	1.52216i
$426$	−41.2737	+	12.1191i	−1.99972	+	0.587170i
$427$	0.263411	−	1.65253i	0.0127474	−	0.0799713i
$428$	−36.3608	+	48.5724i	−1.75757	+	2.34783i
$429$	5.81472	−	16.8005i	0.280737	−	0.811138i
$430$	−23.5512	−	35.0207i	−1.13574	−	1.68885i
$431$	−7.71986	+	0.367742i	−0.371853	+	0.0177135i	−0.232677	−	0.972554i	$-0.574748\pi$
$431$	−7.71986	+	0.367742i	−0.371853	+	0.0177135i	−0.139176	+	0.990268i	$0.544445\pi$
$432$	−5.77404	−	2.47259i	−0.277803	−	0.118962i
$433$	−3.68493	−	16.9394i	−0.177087	−	0.814054i	−0.976882	−	0.213781i	$-0.931422\pi$
$433$	−3.68493	−	16.9394i	−0.177087	−	0.814054i	0.799795	−	0.600273i	$-0.204941\pi$
$434$	29.3464	+	5.39684i	1.40867	+	0.259057i
$435$	−12.0094	−	4.84932i	−0.575806	−	0.232507i
$436$	−12.7550	+	7.36408i	−0.610852	+	0.352675i
$437$	2.14550	+	1.23331i	0.102633	+	0.0589973i
$438$	3.23354	+	12.0677i	0.154505	+	0.576619i
$439$	−32.2087	+	7.81376i	−1.53724	+	0.372930i	−0.912887	−	0.408212i	$-0.866152\pi$
$439$	−32.2087	+	7.81376i	−1.53724	+	0.372930i	−0.624353	+	0.781143i	$0.714637\pi$
$440$	16.7768	−	15.9016i	0.799800	−	0.758081i
$441$	4.14040	+	2.56214i	0.197162	+	0.122006i
$442$	−20.8477	−	27.8493i	−0.991626	−	1.32466i
$443$	14.1988	−	4.53886i	0.674604	−	0.215648i	0.0525460	−	0.998619i	$-0.483266\pi$
$443$	14.1988	−	4.53886i	0.674604	−	0.215648i	0.622058	+	0.782971i	$0.286297\pi$
$444$	−24.4066	−	2.33055i	−1.15829	−	0.110603i
$445$	−7.69110	+	9.25877i	−0.364593	+	0.438908i
$446$	17.8671	−	14.0509i	0.846033	−	0.665327i
$447$	−1.03150	−	2.76556i	−0.0487883	−	0.130806i
$448$	−1.10883	−	34.2852i	−0.0523871	−	1.61982i
$449$	−7.38211	−	25.1412i	−0.348383	−	1.18648i	−0.928307	−	0.371814i	$-0.878736\pi$
$449$	−7.38211	−	25.1412i	−0.348383	−	1.18648i	0.579924	−	0.814671i	$-0.303082\pi$
$450$	4.90081	+	6.00797i	0.231026	+	0.283218i
$451$	−9.96144	+	24.8825i	−0.469066	+	1.17167i
$452$	16.5630	−	24.4719i	0.779060	−	1.15106i
$453$	4.62608	+	27.5103i	0.217352	+	1.29255i
$454$	28.8056	−	18.5122i	1.35191	−	0.868822i
$455$	0.425357	+	14.4852i	0.0199411	+	0.679075i
$456$	−0.915661	+	1.42480i	−0.0428798	+	0.0667222i
$457$	−20.8493	+	14.1112i	−0.975288	+	0.660094i	−0.940676	−	0.339307i	$-0.889808\pi$
$457$	−20.8493	+	14.1112i	−0.975288	+	0.660094i	−0.0346124	+	0.999401i	$0.511020\pi$
$458$	41.4421	+	0.986506i	1.93646	+	0.0460964i
$459$	17.8696	−	30.9511i	0.834083	−	1.44467i
$460$	−15.2936	+	27.9359i	−0.713067	+	1.30252i
$461$	22.7054			1.05749			0.528747	−	0.848779i	$-0.322662\pi$
$461$	22.7054			1.05749			0.528747	+	0.848779i	$0.322662\pi$
$462$	20.8360	+	37.3963i	0.969377	+	1.73983i
$463$	2.22985	+	31.1774i	0.103630	+	1.44894i	0.737421	+	0.675434i	$0.236044\pi$
$463$	2.22985	+	31.1774i	0.103630	+	1.44894i	−0.633791	+	0.773505i	$0.718502\pi$
$464$	4.26716	+	0.203270i	0.198098	+	0.00943657i
$465$	−11.8870	+	12.3927i	−0.551245	+	0.574698i
$466$	−0.860935	−	18.0733i	−0.0398821	−	0.837227i
$467$	4.12836	+	24.5504i	0.191038	+	1.13606i	0.901648	+	0.432472i	$0.142358\pi$
$467$	4.12836	+	24.5504i	0.191038	+	1.13606i	−0.710610	+	0.703586i	$0.751581\pi$
$468$	5.04718	+	0.360982i	0.233306	+	0.0166864i
$469$	−15.5468	+	2.37082i	−0.717886	+	0.109474i
$470$	25.1166	−	6.64999i	1.15854	−	0.306741i
$471$	−4.76319	+	4.99549i	−0.219476	+	0.230180i
$472$	−13.7278	+	8.36753i	−0.631873	+	0.385147i
$473$	−39.9178	−	6.71250i	−1.83542	−	0.308641i
$474$	−30.2538	+	23.7919i	−1.38960	+	1.09280i
$475$	−2.24204	+	1.27673i	−0.102872	+	0.0585802i
$476$	49.8695	+	4.33303i	2.28576	+	0.198604i
$477$	−1.44354	+	6.63584i	−0.0660951	+	0.303834i
$478$	19.9057	−	46.4843i	0.910467	−	2.12614i
$479$	−36.0407	+	18.5803i	−1.64674	+	0.848954i	−0.650769	+	0.759275i	$0.725554\pi$
$479$	−36.0407	+	18.5803i	−1.64674	+	0.848954i	−0.995971	+	0.0896781i	$0.971416\pi$
$480$	19.7323	+	12.1081i	0.900652	+	0.552656i
$481$	−12.9455	+	3.14055i	−0.590264	+	0.143197i
$482$	−31.2288	+	31.2288i	−1.42243	+	1.42243i
$483$	−14.0780	−	13.1461i	−0.640573	−	0.598170i
$484$		−	35.2211i		−	1.60096i
$485$	−22.9447	+	3.22935i	−1.04187	+	0.146637i
$486$	5.15494	+	14.8942i	0.233833	+	0.675615i
$487$	−20.1639	−	6.44569i	−0.913713	−	0.292082i	−0.189678	−	0.981846i	$-0.560745\pi$
$487$	−20.1639	−	6.44569i	−0.913713	−	0.292082i	−0.724034	+	0.689764i	$0.757714\pi$
$488$	1.25710	+	0.538320i	0.0569061	+	0.0243686i
$489$	3.74999	+	5.83509i	0.169580	+	0.263872i
$490$	−26.6907	−	22.4772i	−1.20576	−	1.01542i
$491$	−2.13241	−	2.46094i	−0.0962345	−	0.111061i	0.705589	−	0.708621i	$-0.250682\pi$
$491$	−2.13241	−	2.46094i	−0.0962345	−	0.111061i	−0.801824	+	0.597560i	$0.796137\pi$
$492$	25.0943	+	3.00039i	1.13134	+	0.135268i
$493$	−4.03087	+	23.9707i	−0.181541	+	1.07959i
$494$	−0.664322	+	2.73837i	−0.0298893	+	0.123205i
$495$	7.41584	+	0.552559i	0.333317	+	0.0248357i
$496$	2.35296	−	5.15227i	0.105651	−	0.231344i
$497$	3.70755	−	33.4250i	0.166306	−	1.49932i
$498$	−1.12477	+	15.7264i	−0.0504023	+	0.704716i
$499$	26.5025	+	18.8724i	1.18642	+	0.844844i	0.990733	−	0.135823i	$-0.0433680\pi$
$499$	26.5025	+	18.8724i	1.18642	+	0.844844i	0.195684	+	0.980667i	$0.437307\pi$
$500$	−17.0281	−	28.5054i	−0.761518	−	1.27480i
$501$	−23.3337	−	18.3499i	−1.04247	−	0.819811i
$502$	−5.58552	−	6.14428i	−0.249294	−	0.274233i
$503$	39.9743	−	2.85902i	1.78237	−	0.127477i	0.859142	−	0.511738i	$-0.170998\pi$
$503$	39.9743	−	2.85902i	1.78237	−	0.127477i	0.923225	+	0.384260i	$0.125544\pi$
$504$	−2.85622	+	2.77030i	−0.127226	+	0.123399i
$505$	−3.75792	+	3.08406i	−0.167225	+	0.137239i
$506$	15.6565	+	48.6608i	0.696015	+	2.16324i
$507$	10.2641	−	2.75026i	0.455846	−	0.122144i
$508$	−1.01455	+	42.6201i	−0.0450133	+	1.89096i
$509$	4.85558	−	25.1931i	0.215220	−	1.11667i	−0.700133	−	0.714012i	$-0.746876\pi$
$509$	4.85558	−	25.1931i	0.215220	−	1.11667i	0.915353	−	0.402653i	$-0.131912\pi$
$510$	−29.9129	+	37.8054i	−1.32456	+	1.67405i
$511$	−9.67946	−	1.30752i	−0.428194	−	0.0578415i
$512$	−12.1927	−	2.65237i	−0.538847	−	0.117219i
$513$	−2.85476	+	0.480052i	−0.126041	+	0.0211948i
$514$	8.44009	+	43.7913i	0.372276	+	1.93155i
$515$	−3.42464	−	1.77843i	−0.150908	−	0.0783671i
$516$	3.62815	+	37.9957i	0.159720	+	1.67267i
$517$	11.9429	−	21.8718i	0.525249	−	0.961921i
$518$	15.1317	−	28.2826i	0.664851	−	1.24267i
$519$	−0.0989223	−	0.0451763i	−0.00434221	−	0.00198302i
$520$	−11.5643	−	2.55170i	−0.507130	−	0.111900i
$521$	−4.54535	−	23.5835i	−0.199135	−	1.03321i	−0.934614	−	0.355664i	$-0.884255\pi$
$521$	−4.54535	−	23.5835i	−0.199135	−	1.03321i	0.735478	−	0.677548i	$-0.236957\pi$
$522$	−3.76702	−	4.56238i	−0.164878	−	0.199690i
$523$	8.35986	+	26.1519i	0.365551	+	1.14354i	0.944592	+	0.328245i	$0.106457\pi$
$523$	8.35986	+	26.1519i	0.365551	+	1.14354i	−0.579041	+	0.815298i	$0.696573\pi$
$524$	−35.7699	−	5.14293i	−1.56261	−	0.224670i
$525$	19.2536	−	5.70742i	0.840294	−	0.249092i
$526$	35.0455	+	30.3671i	1.52806	+	1.32407i
$527$	27.5192	+	16.7738i	1.19875	+	0.730679i
$528$	7.84939	−	2.10324i	0.341601	−	0.0915317i
$529$	−13.4119	−	18.6848i	−0.583128	−	0.812380i
$530$	17.1435	−	45.5493i	0.744664	−	1.97854i
$531$	−4.96257	−	1.45714i	−0.215357	−	0.0632345i
$532$	−2.30119	−	3.33830i	−0.0997692	−	0.144734i
$533$	13.4176	−	2.91883i	0.581182	−	0.126428i
$534$	16.9118	−	6.77046i	0.731845	−	0.292986i
$535$	45.6245	+	2.30935i	1.97252	+	0.0998419i
$536$	1.22165	−	12.7937i	0.0527673	−	0.552604i
$537$	35.1338	−	17.0669i	1.51613	−	0.736492i
$538$	37.5873	+	28.1375i	1.62051	+	1.21310i
$539$	−33.2575	+	3.74924i	−1.43250	+	0.161491i
$540$	−6.94176	−	36.6026i	−0.298726	−	1.57512i
$541$	−20.2617	−	19.3195i	−0.871118	−	0.830609i	0.115559	−	0.993301i	$-0.463134\pi$
$541$	−20.2617	−	19.3195i	−0.871118	−	0.830609i	−0.986677	+	0.162691i	$0.947983\pi$
$542$	−8.48529	+	50.4602i	−0.364475	+	2.16745i
$543$	−15.0439	−	35.1309i	−0.645597	−	1.50761i
$544$	14.2110	−	41.0599i	0.609291	−	1.76043i
$545$	9.96008	+	4.87497i	0.426643	+	0.208821i
$546$	9.88319	−	19.5790i	0.422961	−	0.837903i
$547$	−23.9417	+	17.9225i	−1.02367	+	0.766312i	−0.972624	−	0.232384i	$-0.925347\pi$
$547$	−23.9417	+	17.9225i	−1.02367	+	0.766312i	−0.0510486	+	0.998696i	$0.516256\pi$
$548$	−28.2705	+	25.6995i	−1.20765	+	1.09783i
$549$	0.143890	+	0.415742i	0.00614106	+	0.0177434i
$550$	−52.0075	−	11.6379i	−2.21761	−	0.496240i
$551$	1.70509	−	0.984432i	0.0726391	−	0.0419382i
$552$	13.2260	−	8.53512i	0.562934	−	0.363279i
$553$	−8.03554	−	28.9973i	−0.341706	−	1.23309i
$554$	−5.58853	+	19.0328i	−0.237434	+	0.808625i
$555$	8.79863	+	16.2280i	0.373481	+	0.688841i
$556$	−13.2747	+	6.84361i	−0.562975	+	0.290234i
$557$	11.6458	−	1.39243i	0.493450	−	0.0589991i	0.131729	−	0.991286i	$-0.457947\pi$
$557$	11.6458	−	1.39243i	0.493450	−	0.0589991i	0.361720	+	0.932287i	$0.382189\pi$
$558$	−7.47213	+	2.38858i	−0.316320	+	0.101117i
$559$	8.61482	+	18.8638i	0.364368	+	0.797855i
$560$	−5.37421	+	3.87214i	−0.227102	+	0.163628i
$561$	6.58032	+	45.7672i	0.277822	+	1.93229i
$562$	30.9613	−	37.4984i	1.30602	−	1.58177i
$563$	−35.3597	+	21.5529i	−1.49023	+	0.908345i	−0.490924	+	0.871202i	$0.663341\pi$
$563$	−35.3597	+	21.5529i	−1.49023	+	0.908345i	−0.999310	+	0.0371430i	$0.988174\pi$
$564$	−22.8358	−	5.53989i	−0.961559	−	0.233272i
$565$	−22.2487	−	0.0661538i	−0.936011	−	0.00278311i
$566$	18.6231	−	2.67759i	0.782786	−	0.112548i
$567$	16.9771	+	1.06876i	0.712972	+	0.0448835i
$568$	25.7500	+	9.60426i	1.08045	+	0.402986i
$569$	10.4317	+	5.37793i	0.437321	+	0.225455i	0.662805	−	0.748792i	$-0.269366\pi$
$569$	10.4317	+	5.37793i	0.437321	+	0.225455i	−0.225484	+	0.974247i	$0.572396\pi$
$570$	3.90397	−	0.0813180i	0.163519	−	0.00340604i
$571$	6.00037	+	11.6391i	0.251108	+	0.487081i	0.980373	−	0.197150i	$-0.0631685\pi$
$571$	6.00037	+	11.6391i	0.251108	+	0.487081i	−0.729266	+	0.684231i	$0.760138\pi$
$572$	−28.8041	+	19.4952i	−1.20436	+	0.815135i
$573$	−2.69452	−	4.93465i	−0.112565	−	0.206148i
$574$	−16.2874	+	28.7746i	−0.679821	+	1.20103i
$575$	23.8796	−	2.18245i	0.995850	−	0.0910144i
$576$	4.50919	+	7.81014i	0.187883	+	0.325423i
$577$	−8.47230	−	0.201678i	−0.352706	−	0.00839598i	−0.152929	−	0.988237i	$-0.548870\pi$
$577$	−8.47230	−	0.201678i	−0.352706	−	0.00839598i	−0.199778	+	0.979841i	$0.564022\pi$
$578$	47.2936	+	22.9738i	1.96715	+	0.955585i
$579$	32.3615	+	1.54157i	1.34490	+	0.0640654i
$580$	13.1233	+	21.6749i	0.544916	+	0.900001i
$581$	−11.0038	−	5.55457i	−0.456515	−	0.230442i
$582$	32.8570	+	12.2550i	1.36196	+	0.507987i
$583$	−20.3963	−	41.9876i	−0.844729	−	1.73895i
$584$	2.96661	−	7.41023i	0.122759	−	0.306638i
$585$	−1.89510	−	3.30506i	−0.0783526	−	0.136647i
$586$	−36.6747	+	38.4633i	−1.51502	+	1.58890i
$587$	−21.3383	−	11.6516i	−0.880725	−	0.480912i	−0.0258022	−	0.999667i	$-0.508214\pi$
$587$	−21.3383	−	11.6516i	−0.880725	−	0.480912i	−0.854923	+	0.518755i	$0.826396\pi$
$588$	11.5314	+	29.3762i	0.475546	+	1.21146i
$589$	−0.371507	−	2.58389i	−0.0153077	−	0.106467i
$590$	33.6706	+	15.4980i	1.38620	+	0.638044i
$591$	−16.2758	−	1.55415i	−0.669496	−	0.0639291i
$592$	−4.50548	−	4.09576i	−0.185174	−	0.168335i
$593$	−17.3088	+	40.4199i	−0.710787	+	1.65985i	0.0399136	+	0.999203i	$0.487292\pi$
$593$	−17.3088	+	40.4199i	−0.710787	+	1.65985i	−0.750701	+	0.660642i	$0.770284\pi$
$594$	−50.3032	−	32.3279i	−2.06397	−	1.32643i
$595$	−18.2460	−	32.9781i	−0.748014	−	1.35197i
$596$	−1.62689	+	5.54069i	−0.0666401	+	0.226955i
$597$	9.38504	+	2.51471i	0.384104	+	0.102920i
$598$	16.1498	−	20.6162i	0.660416	−	0.843057i
$599$	19.9880	+	11.5401i	0.816687	+	0.471515i	0.849273	−	0.527954i	$-0.177041\pi$
$599$	19.9880	+	11.5401i	0.816687	+	0.471515i	−0.0325855	+	0.999469i	$0.510374\pi$
$600$	0.683371	+	16.3967i	0.0278985	+	0.669394i
$601$	2.97289	−	3.43089i	0.121267	−	0.139949i	−0.691870	−	0.722022i	$-0.743213\pi$
$601$	2.97289	−	3.43089i	0.121267	−	0.139949i	0.813136	+	0.582073i	$0.197758\pi$
$602$	−47.6923	−	14.7984i	−1.94379	−	0.603138i
$603$	3.30988	−	2.47775i	0.134789	−	0.100902i
$604$	25.0084	−	48.5095i	1.01758	−	1.97382i
$605$	−22.0055	+	14.7986i	−0.894651	+	0.601647i
$606$	7.22456	−	1.39242i	0.293478	−	0.0565632i
$607$	29.9889	+	3.58562i	1.21721	+	0.145536i	0.702410	−	0.711772i	$-0.252107\pi$
$607$	29.9889	+	3.58562i	1.21721	+	0.145536i	0.514804	+	0.857308i	$0.327865\pi$
$608$	−3.29748	+	1.22989i	−0.133730	+	0.0498788i
$609$	−14.6663	+	4.44265i	−0.594309	+	0.180025i
$610$	−0.587475	−	3.09764i	−0.0237862	−	0.125420i
$611$	−12.7093	+	1.21359i	−0.514162	+	0.0490965i
$612$	−12.0977	+	5.18052i	−0.489019	+	0.209410i
$613$	19.5203	+	13.2117i	0.788417	+	0.533616i	0.887141	−	0.461499i	$-0.152688\pi$
$613$	19.5203	+	13.2117i	0.788417	+	0.533616i	−0.0987238	+	0.995115i	$0.531476\pi$
$614$	0.909154	+	0.647406i	0.0366905	+	0.0261272i
$615$	−8.66907	−	16.9391i	−0.349570	−	0.683051i
$616$	3.66132	−	27.1043i	0.147519	−	1.09206i
$617$	12.9709	−	2.82164i	0.522187	−	0.113595i	0.0562571	−	0.998416i	$-0.482083\pi$
$617$	12.9709	−	2.82164i	0.522187	−	0.113595i	0.465930	+	0.884821i	$0.345720\pi$
$618$	3.27350	+	4.83658i	0.131679	+	0.194556i
$619$	−3.27997	+	3.12744i	−0.131833	+	0.125703i	−0.753127	−	0.657875i	$-0.771456\pi$
$619$	−3.27997	+	3.12744i	−0.131833	+	0.125703i	0.621294	+	0.783577i	$0.286607\pi$
$620$	33.1465	−	5.47256i	1.33119	−	0.219783i
$621$	26.0010	+	6.91437i	1.04338	+	0.277464i
$622$	−7.83277	−	7.83277i	−0.314066	−	0.314066i
$623$	−0.217462	+	14.2401i	−0.00871245	+	0.570519i
$624$	−3.14639	−	2.72637i	−0.125957	−	0.109142i
$625$	−10.6551	+	22.6157i	−0.426204	+	0.904627i
$626$	−8.70384	+	11.0678i	−0.347875	+	0.442360i
$627$	2.51926	−	2.77128i	0.100609	−	0.110674i
$628$	13.3168	−	2.23932i	0.531397	−	0.0893588i
$629$	26.1831	−	22.6878i	1.04399	−	0.904621i
$630$	8.97487	+	1.90020i	0.357567	+	0.0757056i
$631$	−6.06581	−	2.77016i	−0.241476	−	0.110278i	0.291001	−	0.956723i	$-0.406012\pi$
$631$	−6.06581	−	2.77016i	−0.241476	−	0.110278i	−0.532477	+	0.846444i	$0.678739\pi$
$632$	24.5830	−	0.585184i	0.977859	−	0.0232774i
$633$	5.95551	+	9.77063i	0.236710	+	0.388348i
$634$	2.47400	−	1.76173i	0.0982552	−	0.0699672i
$635$	27.0545	−	17.2734i	1.07363	−	0.685476i
$636$	−33.2650	+	28.8243i	−1.31904	+	1.14296i
$637$	11.1409	+	13.0338i	0.441420	+	0.516418i
$638$	39.7392	+	8.64474i	1.57329	+	0.342248i
$639$	3.28603	+	8.20810i	0.129993	+	0.324707i
$640$	−12.5905	−	31.7226i	−0.497683	−	1.25394i
$641$	7.89667	−	2.73306i	0.311900	−	0.107949i	−0.166634	−	0.986019i	$-0.553290\pi$
$641$	7.89667	−	2.73306i	0.311900	−	0.107949i	0.478533	+	0.878069i	$0.341169\pi$
$642$	−59.0364	−	35.9846i	−2.32998	−	1.42020i
$643$	−2.89049	−	2.89049i	−0.113990	−	0.113990i	0.647811	−	0.761801i	$-0.275685\pi$
$643$	−2.89049	−	2.89049i	−0.113990	−	0.113990i	−0.761801	+	0.647811i	$0.775685\pi$
$644$	6.63581	+	37.0945i	0.261488	+	1.46173i
$645$	22.2146	−	18.2311i	0.874700	−	0.717850i
$646$	−1.72776	−	7.12194i	−0.0679780	−	0.280209i
$647$	−18.0964	+	37.2530i	−0.711442	+	1.46457i	0.166621	+	0.986021i	$0.446714\pi$
$647$	−18.0964	+	37.2530i	−0.711442	+	1.46457i	−0.878063	+	0.478545i	$0.841164\pi$
$648$	−4.23277	+	13.2413i	−0.166279	+	0.520166i
$649$	33.0046	−	13.2130i	1.29554	−	0.518657i
$650$	9.99678	+	25.4076i	0.392106	+	0.996568i
$651$	−1.75877	+	20.2420i	−0.0689317	+	0.793345i
$652$	0.968064	−	13.5353i	0.0379123	−	0.530083i
$653$	−0.481756	+	4.02925i	−0.0188526	+	0.157677i	−0.999219	−	0.0395058i	$-0.987422\pi$
$653$	−0.481756	+	4.02925i	−0.0188526	+	0.157677i	0.980367	+	0.197183i	$0.0631792\pi$
$654$	−9.73500	−	13.6709i	−0.380669	−	0.534574i
$655$	11.8159	+	24.5092i	0.461686	+	0.957655i
$656$	4.54252	+	4.33128i	0.177355	+	0.169108i
$657$	2.40596	−	0.897378i	0.0938656	−	0.0350101i
$658$	18.2126	−	24.7668i	0.710001	−	0.965509i
$659$	16.0353	+	18.5057i	0.624647	+	0.720881i	0.976583	−	0.215143i	$-0.0690218\pi$
$659$	16.0353	+	18.5057i	0.624647	+	0.720881i	−0.351936	+	0.936024i	$0.614476\pi$
$660$	36.3322	+	31.6717i	1.41423	+	1.23282i
$661$	24.6634	−	1.17486i	0.959295	−	0.0456969i	0.437911	−	0.899019i	$-0.355719\pi$
$661$	24.6634	−	1.17486i	0.959295	−	0.0456969i	0.521385	+	0.853322i	$0.325416\pi$
$662$	5.63811	+	47.1553i	0.219131	+	1.83274i
$663$	17.5284	−	15.9344i	0.680748	−	0.618841i
$664$	6.59652	−	7.61279i	0.255995	−	0.295434i
$665$	−1.11884	+	2.84037i	−0.0433867	+	0.110145i
$666$			8.43290i			0.326768i
$667$	−18.2124	+	1.77377i	−0.705188	+	0.0686807i
$668$	15.0309	+	56.0960i	0.581562	+	2.17042i
$669$	10.6810	+	11.2019i	0.412950	+	0.433089i
$670$	−26.0483	+	14.1231i	−1.00634	+	0.545623i
$671$	−2.54395	−	1.63489i	−0.0982079	−	0.0631144i
$672$	27.1702	−	3.48391i	1.04811	−	0.134395i
$673$	−0.727705	+	3.34521i	−0.0280510	+	0.128948i	−0.989043	−	0.147628i	$-0.952836\pi$
$673$	−0.727705	+	3.34521i	−0.0280510	+	0.128948i	0.960992	+	0.276576i	$0.0891998\pi$
$674$	10.7573	−	15.1066i	0.414358	−	0.581884i
$675$	−19.9520	+	19.7161i	−0.767951	+	0.758872i
$676$	−19.2998	−	7.72649i	−0.742301	−	0.297173i
$677$	22.3654	−	27.0876i	0.859572	−	1.04106i	−0.139137	−	0.990273i	$-0.544433\pi$
$677$	22.3654	−	27.0876i	0.859572	−	1.04106i	0.998709	−	0.0507878i	$-0.0161732\pi$
$678$	29.5537	+	16.1375i	1.13500	+	0.619757i
$679$	−18.7494	+	20.0027i	−0.719535	+	0.767632i
$680$	29.7741	−	7.88312i	1.14178	−	0.302304i
$681$	14.4132	+	18.3278i	0.552314	+	0.702324i
$682$	30.2234	−	44.6550i	1.15731	−	1.70993i
$683$	23.7793	−	19.6339i	0.909890	−	0.751269i	−0.0591298	−	0.998250i	$-0.518833\pi$
$683$	23.7793	−	19.6339i	0.909890	−	0.751269i	0.969020	+	0.246981i	$0.0794387\pi$
$684$	0.947466	+	0.488453i	0.0362273	+	0.0186765i
$685$	27.9348	+	6.86491i	1.06733	+	0.262295i
$686$	−41.2776	−	0.908656i	−1.57598	−	0.0346926i
$687$	2.01373	+	28.1557i	0.0768287	+	1.07421i
$688$	−4.93355	+	8.09400i	−0.188090	+	0.308581i
$689$	−11.9574	+	20.7109i	−0.455542	+	0.789023i
$690$	−33.3456	−	14.3223i	−1.26945	−	0.545240i
$691$	8.26020	+	14.3071i	0.314233	+	0.544267i	0.979274	−	0.202539i	$-0.0649194\pi$
$691$	8.26020	+	14.3071i	0.314233	+	0.544267i	−0.665041	+	0.746807i	$0.731586\pi$
$692$	0.101964	+	0.186732i	0.00387607	+	0.00709850i
$693$	7.24444	−	4.99381i	0.275193	−	0.189699i
$694$	−29.0932	+	45.2698i	−1.10436	+	1.71842i
$695$	9.85330	+	5.41840i	0.373757	+	0.205532i
$696$	−0.595881	−	12.5091i	−0.0225868	−	0.474156i
$697$	−27.5387	+	22.7379i	−1.04310	+	0.861259i
$698$	8.51980	+	17.5387i	0.322479	+	0.663851i
$699$	12.1954	−	1.75343i	0.461271	−	0.0663207i
$700$	−36.8459	−	13.6345i	−1.39264	−	0.515335i
$701$	8.81314	+	30.0148i	0.332868	+	1.13364i	0.940604	+	0.339505i	$0.110260\pi$
$701$	8.81314	+	30.0148i	0.332868	+	1.13364i	−0.607736	+	0.794139i	$0.707922\pi$
$702$	0.729032	+	30.6259i	0.0275156	+	1.15590i
$703$	−2.76737	−	0.465356i	−0.104373	−	0.0175512i
$704$	−57.5490	−	23.0391i	−2.16896	−	0.868321i
$705$	6.13347	+	16.5950i	0.231000	+	0.625004i
$706$	−11.7617	−	25.7546i	−0.442659	−	0.969288i
$707$	−1.17471	+	5.63088i	−0.0441795	+	0.211771i
$708$	−20.0894	−	26.8363i	−0.755005	−	1.00857i
$709$	−1.30858	+	27.4704i	−0.0491447	+	1.03167i	0.830792	+	0.556583i	$0.187888\pi$
$709$	−1.30858	+	27.4704i	−0.0491447	+	1.03167i	−0.879937	+	0.475091i	$0.842415\pi$
$710$	−14.7552	−	61.6210i	−0.553754	−	2.31260i
$711$	5.45906	+	5.72530i	0.204731	+	0.214715i
$712$	−11.2420	−	3.01228i	−0.421311	−	0.112890i
$713$	−6.79133	+	23.2917i	−0.254337	+	0.872281i
$714$	0.486554	+	57.0386i	0.0182088	+	2.13462i
$715$	24.2826	+	9.80517i	0.908119	+	0.366693i
$716$	−75.0351	−	14.4618i	−2.80419	−	0.540464i
$717$	32.7981	+	10.4844i	1.22487	+	0.391548i
$718$	−0.794126	−	6.64181i	−0.0296365	−	0.247870i
$719$	−2.71751	+	5.27124i	−0.101346	+	0.196584i	−0.934057	−	0.357124i	$-0.883757\pi$
$719$	−2.71751	+	5.27124i	−0.101346	+	0.196584i	0.832711	+	0.553708i	$0.186788\pi$
$720$	0.765564	−	1.56413i	0.0285309	−	0.0582917i
$721$	−4.47585	+	0.902312i	−0.166689	+	0.0336039i
$722$	25.0279	−	33.4334i	0.931442	−	1.24426i
$723$	−23.1901	−	19.1473i	−0.862447	−	0.712097i
$724$	−17.6268	+	72.6587i	−0.655096	+	2.70034i
$725$	8.02818	−	17.3062i	0.298159	−	0.642735i
$726$	39.9530	−	3.81505i	1.48279	−	0.141590i
$727$	11.7149	+	8.76963i	0.434480	+	0.325248i	0.794030	−	0.607878i	$-0.207979\pi$
$727$	11.7149	+	8.76963i	0.434480	+	0.325248i	−0.359550	+	0.933126i	$0.617070\pi$
$728$	−12.5512	+	6.22987i	−0.465178	+	0.230894i
$729$	−27.3078	+	12.4710i	−1.01140	+	0.461891i
$730$	−17.9939	+	3.85833i	−0.665983	+	0.142803i
$731$	−42.3957	−	33.3404i	−1.56806	−	1.23314i
$732$	−0.868227	+	2.71605i	−0.0320906	+	0.100388i
$733$	29.4015	+	43.4407i	1.08597	+	1.60452i	0.748440	+	0.663203i	$0.230803\pi$
$733$	29.4015	+	43.4407i	1.08597	+	1.60452i	0.337530	+	0.941315i	$0.390409\pi$
$734$	−5.90350	−	1.73342i	−0.217902	−	0.0639818i
$735$	13.5087	−	19.5473i	0.498276	−	0.721015i
$736$	32.6300	+	2.27185i	1.20276	+	0.0837415i
$737$	−7.35553	+	27.4512i	−0.270945	+	1.01118i
$738$	0.206867	−	8.69027i	0.00761488	−	0.319893i
$739$	−16.7976	+	5.81369i	−0.617908	+	0.213860i	−0.618049	−	0.786140i	$-0.712077\pi$
$739$	−16.7976	+	5.81369i	−0.617908	+	0.213860i	0.000140393		1.00000i	$0.499955\pi$
$740$	5.24590	−	35.7315i	0.192843	−	1.31352i
$741$	−1.89922	−	0.273067i	−0.0697698	−	0.0100314i
$742$	−18.0013	−	54.6996i	−0.660847	−	2.00809i
$743$	−8.77625	+	23.5300i	−0.321970	+	0.863234i	0.670629	+	0.741793i	$0.266024\pi$
$743$	−8.77625	+	23.5300i	−0.321970	+	0.863234i	−0.992599	+	0.121441i	$0.961249\pi$
$744$	−15.6910	−	5.43072i	−0.575261	−	0.199100i
$745$	4.14528	−	1.31153i	0.151871	−	0.0480507i
$746$	−38.4157	+	27.3557i	−1.40650	+	1.00156i
$747$	3.23970	−	0.0771192i	0.118534	−	0.00282164i
$748$	43.3524	−	79.3941i	1.58512	−	2.90293i
$749$	43.7611	−	31.7281i	1.59899	−	1.15932i
$750$	30.4906	−	22.4034i	1.11336	−	0.818055i
$751$	−24.3840	−	8.43939i	−0.889786	−	0.307958i	−0.156338	−	0.987704i	$-0.549969\pi$
$751$	−24.3840	−	8.43939i	−0.889786	−	0.307958i	−0.733448	+	0.679746i	$0.762090\pi$
$752$	−3.71553	−	4.50003i	−0.135492	−	0.164099i
$753$	3.80341	−	4.18389i	0.138604	−	0.152469i
$754$	−7.74374	−	19.3429i	−0.282011	−	0.704428i
$755$	−40.8154	+	4.75703i	−1.48542	+	0.173126i
$756$	−33.5590	−	28.5815i	−1.22053	−	1.03950i
$757$	−3.45049	+	1.88411i	−0.125410	+	0.0684791i	−0.540729	−	0.841197i	$-0.681852\pi$
$757$	−3.45049	+	1.88411i	−0.125410	+	0.0684791i	0.415319	+	0.909676i	$0.363670\pi$
$758$	9.39249	−	35.0532i	0.341151	−	1.27319i
$759$	−31.9717	+	13.7625i	−1.16050	+	0.499548i
$760$	−2.02786	−	1.45314i	−0.0735584	−	0.0527110i
$761$	−0.0957322	−	0.394613i	−0.00347029	−	0.0143047i	0.970050	−	0.242905i	$-0.0781003\pi$
$761$	−0.0957322	−	0.394613i	−0.00347029	−	0.0143047i	−0.973520	+	0.228600i	$0.926585\pi$
$762$	−48.4559	+	3.46563i	−1.75537	+	0.125547i
$763$	12.7967	−	2.89829i	0.463272	−	0.104925i
$764$	−1.56540	+	10.8876i	−0.0566342	+	0.393900i
$765$	8.31966	+	5.38174i	0.300798	+	0.194577i
$766$	1.66187	−	17.4039i	0.0600460	−	0.628830i
$767$	−15.0836	−	10.2089i	−0.544638	−	0.368621i
$768$	−1.45907	+	12.2032i	−0.0526496	+	0.440344i
$769$	−0.376760	+	0.824989i	−0.0135863	+	0.0297499i	−0.916304	−	0.400485i	$-0.868842\pi$
$769$	−0.376760	+	0.824989i	−0.0135863	+	0.0297499i	0.902717	+	0.430234i	$0.141569\pi$
$770$	−56.5659	+	27.8676i	−2.03849	+	1.00428i
$771$	−29.1380	+	8.55567i	−1.04938	+	0.308125i
$772$	−48.8763	−	40.3557i	−1.75910	−	1.45243i
$773$	0.900327	+	2.10246i	0.0323825	+	0.0756203i	0.934674	−	0.355507i	$-0.115692\pi$
$773$	0.900327	+	2.10246i	0.0323825	+	0.0756203i	−0.902291	+	0.431127i	$0.858116\pi$
$774$	12.8909	−	2.48452i	0.463355	−	0.0893043i
$775$	−17.3460	−	18.4099i	−0.623087	−	0.661305i
$776$	−12.1129	−	18.8481i	−0.434829	−	0.676607i
$777$	20.1510	+	8.42650i	0.722914	+	0.302299i
$778$	−3.74096	−	17.1969i	−0.134120	−	0.616539i
$779$	2.84041	+	0.547445i	0.101768	+	0.0196142i
$780$	3.00445	−	24.5098i	0.107577	−	0.877593i
$781$	−52.6311	−	30.3866i	−1.88329	−	1.08732i
$782$	−12.7639	+	66.9046i	−0.456435	+	2.39250i
$783$	15.1357	−	15.1357i	0.540905	−	0.540905i
$784$	−2.07946	+	7.55657i	−0.0742665	+	0.269877i
$785$	−6.99428	−	7.37920i	−0.249636	−	0.263375i
$786$	1.95938	−	41.1325i	0.0698889	−	1.46715i
$787$	37.6091	−	4.49672i	1.34062	−	0.160291i	0.582726	−	0.812669i	$-0.301986\pi$
$787$	37.6091	−	4.49672i	1.34062	−	0.160291i	0.757894	+	0.652378i	$0.226228\pi$
$788$	23.6685	+	21.5161i	0.843156	+	0.766480i
$789$	−18.3162	+	25.7214i	−0.652073	+	0.915708i
$790$	−32.7479	−	46.2786i	−1.16512	−	1.64652i
$791$	−20.5534	+	16.4490i	−0.730795	+	0.584861i
$792$	2.51283	+	6.73716i	0.0892895	+	0.239394i
$793$	0.0368688	+	1.54882i	0.00130925	+	0.0550002i
$794$	41.6294	+	10.0992i	1.47737	+	0.358406i
$795$	31.9856	+	8.67252i	1.13441	+	0.307583i
$796$	−11.7503	−	14.9417i	−0.416477	−	0.529594i
$797$	21.2287	+	1.51831i	0.751960	+	0.0537812i	0.442057	−	0.896987i	$-0.354249\pi$
$797$	21.2287	+	1.51831i	0.751960	+	0.0537812i	0.309903	+	0.950768i	$0.399703\pi$
$798$	3.53753	−	2.97194i	0.125227	−	0.105206i
$799$	27.9335	−	17.9517i	0.988215	−	0.635087i
$800$	−19.2818	+	28.1270i	−0.681713	+	0.994439i
$801$	−1.71570	−	3.32798i	−0.0606211	−	0.117589i
$802$	−33.9527	−	16.4932i	−1.19891	−	0.582395i
$803$	−9.18663	+	15.0716i	−0.324189	+	0.531866i
$804$	26.7980			0.945092
$805$	20.3878	−	19.7316i	0.718577	−	0.695447i
$806$	−27.6251			−0.973053
$807$	−16.6403	+	27.3001i	−0.585766	+	0.961009i
$808$	−4.22821	−	2.05394i	−0.148748	−	0.0722572i
$809$	−18.1261	−	35.1598i	−0.637280	−	1.23615i	−0.957397	−	0.288773i	$-0.906753\pi$
$809$	−18.1261	−	35.1598i	−0.637280	−	1.23615i	0.320117	−	0.947378i	$-0.396278\pi$
$810$	30.7787	−	8.93811i	1.08145	−	0.314053i
$811$	36.2815	−	23.3167i	1.27402	−	0.818761i	0.283880	−	0.958860i	$-0.408378\pi$
$811$	36.2815	−	23.3167i	1.27402	−	0.818761i	0.990138	+	0.140099i	$0.0447420\pi$
$812$	28.1786	+	10.2371i	0.988875	+	0.359253i
$813$	−34.7540	−	2.48566i	−1.21888	−	0.0871758i
$814$	−35.8316	−	45.5636i	−1.25590	−	1.59700i
$815$	−8.86335	+	5.08218i	−0.310470	+	0.178021i
$816$	10.5226	+	2.55276i	0.368365	+	0.0893644i
$817$	0.103964	+	4.36744i	0.00363725	+	0.152797i
$818$	−20.7792	−	55.7112i	−0.726528	−	1.94790i
$819$	−4.19908	−	1.63964i	−0.146728	−	0.0572937i
$820$	−6.28253	+	36.6933i	−0.219395	+	1.28139i
$821$	24.8965	−	34.9623i	0.868894	−	1.22019i	−0.105291	−	0.994441i	$-0.533577\pi$
$821$	24.8965	−	34.9623i	0.868894	−	1.22019i	0.974185	−	0.225750i	$-0.0724832\pi$
$822$	−32.2144	−	29.2848i	−1.12361	−	1.02143i
$823$	−5.44225	+	0.650701i	−0.189705	+	0.0226820i	−0.213029	−	0.977046i	$-0.568333\pi$
$823$	−5.44225	+	0.650701i	−0.189705	+	0.0226820i	0.0233236	+	0.999728i	$0.492575\pi$
$824$	0.177542	−	3.72707i	0.00618497	−	0.129839i
$825$	4.52249	−	36.0069i	0.157453	−	1.25360i
$826$	42.5313	−	10.7029i	1.47985	−	0.372402i
$827$	−6.26843	+	6.26843i	−0.217975	+	0.217975i	−0.807644	−	0.589670i	$-0.799258\pi$
$827$	−6.26843	+	6.26843i	−0.217975	+	0.217975i	0.589670	+	0.807644i	$0.299258\pi$
$828$	−6.13882	−	7.77590i	−0.213339	−	0.270231i
$829$	−4.87477	−	2.81445i	−0.169308	−	0.0977499i	0.412952	−	0.910753i	$-0.364498\pi$
$829$	−4.87477	−	2.81445i	−0.169308	−	0.0977499i	−0.582259	+	0.813003i	$0.697831\pi$
$830$	−23.0516	−	2.82571i	−0.800134	−	0.0980817i
$831$	−13.2632	−	2.55628i	−0.460096	−	0.0886763i
$832$	6.75076	+	31.0328i	0.234041	+	1.07587i
$833$	−41.2874	−	16.8527i	−1.43052	−	0.583912i
$834$	−9.20091	−	14.3169i	−0.318601	−	0.495754i
$835$	28.7323	−	32.9604i	0.994324	−	1.14064i
$836$	−7.19468	+	1.38666i	−0.248833	+	0.0479587i
$837$	−11.1720	−	26.0890i	−0.386159	−	0.901767i
$838$	37.5245	+	30.9829i	1.29626	+	1.07028i
$839$	1.79696	−	0.527635i	0.0620379	−	0.0182160i	−0.250566	−	0.968099i	$-0.580617\pi$
$839$	1.79696	−	0.527635i	0.0620379	−	0.0182160i	0.312604	+	0.949883i	$0.398799\pi$
$840$	12.7972	+	14.6040i	0.441547	+	0.503887i
$841$	5.99934	−	13.1367i	0.206874	−	0.452991i
$842$	7.49976	−	62.7255i	0.258459	−	2.16166i
$843$	27.4226	+	18.5602i	0.944485	+	0.639246i
$844$	2.12794	−	22.2848i	0.0732468	−	0.767075i
$845$	3.28167	+	15.3046i	0.112893	+	0.526493i
$846$	−1.15022	+	7.99998i	−0.0395455	+	0.275045i
$847$	−9.29868	+	29.9678i	−0.319507	+	1.02971i
$848$	−10.9034	+	0.779826i	−0.374424	+	0.0267793i
$849$	3.02045	+	12.4505i	0.103662	+	0.427299i
$850$	−53.3889	−	46.8205i	−1.83123	−	1.60593i
$851$	21.6265	+	14.5778i	0.741348	+	0.499721i
$852$	−14.8317	+	55.3528i	−0.508127	+	1.89636i
$853$	−25.6018	+	13.9796i	−0.876588	+	0.478653i	−0.853508	−	0.521080i	$-0.825529\pi$
$853$	−25.6018	+	13.9796i	−0.876588	+	0.478653i	−0.0230803	+	0.999734i	$0.507347\pi$
$854$	−2.84007	−	2.41883i	−0.0971852	−	0.0827707i
$855$	−0.0929122	−	0.797189i	−0.00317753	−	0.0272633i
$856$	16.4173	+	41.0083i	0.561130	+	1.40164i
$857$	−30.9714	+	34.0697i	−1.05796	+	1.16380i	−0.0719016	+	0.997412i	$0.522907\pi$
$857$	−30.9714	+	34.0697i	−1.05796	+	1.16380i	−0.986061	+	0.166386i	$0.946790\pi$
$858$	−25.2343	−	30.5622i	−0.861485	−	1.04338i
$859$	−30.0162	−	10.3887i	−1.02414	−	0.354458i	−0.237182	−	0.971465i	$-0.576224\pi$
$859$	−30.0162	−	10.3887i	−1.02414	−	0.354458i	−0.786958	+	0.617007i	$0.788345\pi$
$860$	−56.1664	+	2.50818i	−1.91526	+	0.0855282i
$861$	−20.5593	−	9.17799i	−0.700659	−	0.312785i
$862$	−8.25724	+	15.1220i	−0.281243	+	0.515058i
$863$	−40.3801	+	0.961226i	−1.37456	+	0.0327205i	−0.704560	−	0.709644i	$-0.748856\pi$
$863$	−40.3801	+	0.961226i	−1.37456	+	0.0327205i	−0.669996	+	0.742365i	$0.733704\pi$
$864$	−31.1672	+	22.1941i	−1.06033	+	0.755058i
$865$	0.0738258	−	0.142163i	0.00251015	−	0.00483368i
$866$	−36.5209	−	12.6400i	−1.24103	−	0.429525i
$867$	−12.5118	+	33.5453i	−0.424922	+	1.13926i
$868$	26.4866	−	29.6403i	0.899014	−	1.00606i
$869$	−53.8227	−	7.73853i	−1.82581	−	0.262512i
$870$	−23.1654	+	17.2342i	−0.785380	+	0.584293i
$871$	13.7592	−	4.76210i	0.466213	−	0.161358i
$872$	−0.255170	+	10.7194i	−0.00864115	+	0.363006i
$873$	1.86551	−	6.96218i	0.0631380	−	0.235634i
$874$	4.83710	−	2.65312i	0.163617	−	0.0897432i
$875$	6.96263	+	28.7493i	0.235380	+	0.971903i
$876$	15.9694	+	4.68904i	0.539556	+	0.158428i
$877$	−20.2639	−	29.9398i	−0.684262	−	1.01100i	−0.998106	−	0.0615215i	$-0.980405\pi$
$877$	−20.2639	−	29.9398i	−0.684262	−	1.01100i	0.313844	−	0.949475i	$-0.398383\pi$
$878$	−22.4974	+	70.3779i	−0.759250	+	2.37514i
$879$	−28.4465	−	22.3705i	−0.959475	−	0.754540i
$880$	2.50963	+	11.7040i	0.0845996	+	0.394542i
$881$	−15.4170	+	7.04072i	−0.519413	+	0.237208i	−0.657831	−	0.753166i	$-0.728526\pi$
$881$	−15.4170	+	7.04072i	−0.519413	+	0.237208i	0.138417	+	0.990374i	$0.455798\pi$
$882$	9.68127	−	4.90873i	0.325985	−	0.165286i
$883$	9.81329	+	7.34614i	0.330244	+	0.247217i	0.751513	−	0.659718i	$-0.229324\pi$
$883$	9.81329	+	7.34614i	0.330244	+	0.247217i	−0.421269	+	0.906936i	$0.638415\pi$
$884$	−46.1343	+	4.40529i	−1.55167	+	0.148166i
$885$	−8.32603	+	23.8270i	−0.279876	+	0.800937i
$886$	7.83463	−	32.2948i	0.263210	−	1.08497i
$887$	−1.86745	−	1.54189i	−0.0627027	−	0.0517718i	0.604812	−	0.796368i	$-0.293248\pi$
$887$	−1.86745	−	1.54189i	−0.0627027	−	0.0517718i	−0.667515	+	0.744596i	$0.732642\pi$
$888$	−10.6968	+	14.2892i	−0.358960	+	0.479515i
$889$	12.1153	−	35.9954i	0.406334	−	1.20725i
$890$	8.70086	+	25.3834i	0.291653	+	0.850854i
$891$	14.0860	−	27.3230i	0.471899	−	0.915355i
$892$	−3.59490	−	30.0666i	−0.120366	−	1.00670i
$893$	−2.56183	−	0.818927i	−0.0857283	−	0.0274044i
$894$	−6.46128	−	1.24531i	−0.216098	−	0.0416494i
$895$	22.4913	+	52.9568i	0.751803	+	1.77015i
$896$	−35.1436	−	19.8924i	−1.17406	−	0.664558i
$897$	15.0201	+	9.61285i	0.501508	+	0.320964i
$898$	−56.4234	−	15.1186i	−1.88287	−	0.504515i
$899$	13.3201	+	13.9697i	0.444251	+	0.465917i
$900$	10.2322	−	1.40912i	0.341075	−	0.0469707i
$901$	2.95949	−	62.1273i	0.0985948	−	2.06976i
$902$	35.8075	+	47.8332i	1.19226	+	1.59267i
$903$	6.94420	−	33.2864i	0.231088	−	1.10770i
$904$	−8.93690	−	19.5691i	−0.297237	−	0.650858i
$905$	52.8020	−	19.5155i	1.75520	−	0.648716i
$906$	57.7355	+	23.1138i	1.91813	+	0.767904i
$907$	45.4506	+	7.64289i	1.50916	+	0.253778i	0.861346	−	0.508020i	$-0.169622\pi$
$907$	45.4506	+	7.64289i	1.50916	+	0.253778i	0.647815	+	0.761797i	$0.275683\pi$
$908$	−1.08555	−	45.6028i	−0.0360252	−	1.51338i
$909$	−0.426048	−	1.45099i	−0.0141311	−	0.0481262i
$910$	28.0671	+	15.9973i	0.930415	+	0.530304i
$911$	23.4450	−	3.37088i	0.776767	−	0.111682i	0.257481	−	0.966283i	$-0.417107\pi$
$911$	23.4450	−	3.37088i	0.776767	−	0.111682i	0.519285	+	0.854601i	$0.326198\pi$
$912$	−0.383219	−	0.788890i	−0.0126896	−	0.0261228i
$913$	−17.1767	+	14.1822i	−0.568464	+	0.469364i
$914$	2.67052	+	56.0612i	0.0883331	+	1.85434i
$915$	2.06173	−	0.598727i	0.0681588	−	0.0197933i
$916$	29.8564	−	46.4575i	0.986484	−	1.53500i
$917$	29.0769	+	13.8194i	0.960205	+	0.456357i
$918$	−38.1838	−	69.9284i	−1.26025	−	2.30798i
$919$	−19.2219	−	33.2933i	−0.634071	−	1.09824i	−0.986711	−	0.162484i	$-0.948049\pi$
$919$	−19.2219	−	33.2933i	−0.634071	−	1.09824i	0.352640	−	0.935759i	$-0.385284\pi$
$920$	11.5713	+	20.0925i	0.381496	+	0.662431i
$921$	−0.380001	+	0.658181i	−0.0125215	+	0.0216878i
$922$	26.3448	−	43.2214i	0.867620	−	1.42342i
$923$	2.22118	+	31.0561i	0.0731109	+	1.02222i
$924$	56.9861	+	2.22757i	1.87470	+	0.0732817i
$925$	−24.5285	+	11.7355i	−0.806493	+	0.385859i
$926$	61.9358	+	31.9301i	2.03534	+	1.04929i
$927$	0.925641	−	0.764274i	0.0304020	−	0.0251020i
$928$	14.5861	−	21.5509i	0.478812	−	0.707444i
$929$	−6.81362	−	8.66423i	−0.223548	−	0.284264i	0.661322	−	0.750102i	$-0.269995\pi$
$929$	−6.81362	−	8.66423i	−0.223548	−	0.284264i	−0.884870	+	0.465838i	$0.845753\pi$
$930$	9.79810	+	37.0068i	0.321293	+	1.21350i
$931$	1.07662	+	3.44792i	0.0352849	+	0.113001i
$932$	−21.1558	−	11.5519i	−0.692980	−	0.378396i
$933$	4.80250	−	5.81650i	0.157227	−	0.190424i
$934$	51.5236	+	20.6269i	1.68590	+	0.674934i
$935$	−67.8190	+	6.27250i	−2.21792	+	0.205133i
$936$	2.13685	−	3.00078i	0.0698451	−	0.0980837i
$937$	−3.49453	+	16.0641i	−0.114161	+	0.524792i	0.884176	+	0.467154i	$0.154721\pi$
$937$	−3.49453	+	16.0641i	−0.114161	+	0.524792i	−0.998338	+	0.0576380i	$0.981643\pi$
$938$	−13.5258	+	32.3454i	−0.441632	+	1.05611i
$939$	−8.06579	−	5.18357i	−0.263217	−	0.169159i
$940$	9.85026	−	33.1816i	0.321280	−	1.08226i
$941$	28.7919	+	30.1961i	0.938591	+	0.984365i	0.999905	−	0.0137531i	$-0.00437788\pi$
$941$	28.7919	+	30.1961i	0.938591	+	0.984365i	−0.0613149	+	0.998118i	$0.519529\pi$
$942$	3.98260	+	14.8633i	0.129760	+	0.484272i
$943$	−21.9290	−	15.5532i	−0.714105	−	0.506483i
$944$		−	8.32526i		−	0.270964i
$945$	−3.75702	+	32.9759i	−0.122216	+	1.07271i
$946$	−59.0939	+	68.1980i	−1.92131	+	2.21731i
$947$	6.72456	−	6.11303i	0.218519	−	0.198647i	−0.556028	−	0.831164i	$-0.687675\pi$
$947$	6.72456	−	6.11303i	0.218519	−	0.198647i	0.774546	+	0.632517i	$0.217978\pi$
$948$	6.08714	+	50.9109i	0.197701	+	1.65351i
$949$	9.03260	−	0.430276i	0.293211	−	0.0139673i
$950$	−0.171072	+	5.74926i	−0.00555030	+	0.186531i
$951$	1.35434	+	1.56299i	0.0439173	+	0.0506833i
$952$	21.5898	−	29.3594i	0.699731	−	0.951542i
$953$	−3.10824	+	1.15931i	−0.100686	+	0.0375539i	−0.399302	−	0.916819i	$-0.630748\pi$
$953$	−3.10824	+	1.15931i	−0.100686	+	0.0375539i	0.298616	+	0.954373i	$0.403475\pi$
$954$	10.9569	+	10.4474i	0.354743	+	0.338246i
$955$	7.46010	−	3.59651i	0.241403	−	0.116380i
$956$	−39.0753	−	54.8736i	−1.26379	−	1.77474i
$957$	−3.28768	+	27.4971i	−0.106275	+	0.888854i
$958$	−6.44869	+	90.1645i	−0.208348	+	2.91308i
$959$	30.8388	−	14.4028i	0.995835	−	0.465089i
$960$	39.1774	−	20.0501i	1.26444	−	0.647114i
$961$	−5.02025	+	2.00980i	−0.161943	+	0.0648324i
$962$	−9.04226	+	28.2867i	−0.291534	+	0.911999i
$963$	−6.20926	+	12.7823i	−0.200090	+	0.411904i
$964$	13.8709	+	57.1765i	0.446750	+	1.84153i
$965$	−4.67756	+	47.4929i	−0.150576	+	1.52885i
$966$	−41.3592	+	11.5453i	−1.33071	+	0.371463i
$967$	41.1554	+	41.1554i	1.32347	+	1.32347i	0.910948	+	0.412521i	$0.135352\pi$
$967$	41.1554	+	41.1554i	1.32347	+	1.32347i	0.412521	+	0.910948i	$0.364648\pi$
$968$	−21.8951	−	13.3458i	−0.703735	−	0.428949i
$969$	4.71583	−	1.63216i	0.151494	−	0.0524326i
$970$	−20.4752	+	47.4240i	−0.657420	+	1.52269i
$971$	17.1050	+	42.7263i	0.548927	+	1.37115i	0.900444	+	0.434971i	$0.143241\pi$
$971$	17.1050	+	42.7263i	0.548927	+	1.37115i	−0.351518	+	0.936181i	$0.614334\pi$
$972$	20.5168	+	4.46316i	0.658077	+	0.143156i
$973$	13.1016	−	2.31822i	0.420017	−	0.0743188i
$974$	−35.6658	+	30.9046i	−1.14281	+	0.990246i
$975$	−16.5757	+	8.42095i	−0.530846	+	0.269686i
$976$	−0.576842	+	0.410767i	−0.0184643	+	0.0131483i
$977$	14.8474	+	24.3587i	0.475011	+	0.779305i	0.997298	−	0.0734648i	$-0.0234057\pi$
$977$	14.8474	+	24.3587i	0.475011	+	0.779305i	−0.522286	+	0.852770i	$0.674921\pi$
$978$	15.4586	−	0.367983i	0.494311	−	0.0117668i
$979$	23.4107	+	10.6913i	0.748210	+	0.341696i
$980$	−44.0746	+	14.7766i	−1.40791	+	0.472021i
$981$	−2.60696	+	2.25894i	−0.0832337	+	0.0721225i
$982$	−7.15879	+	1.20381i	−0.228446	+	0.0384151i
$983$	18.1527	−	19.9687i	0.578983	−	0.636902i	−0.378429	−	0.925631i	$-0.623535\pi$
$983$	18.1527	−	19.9687i	0.578983	−	0.636902i	0.957411	+	0.288728i	$0.0932324\pi$
$984$	11.3738	−	14.4629i	0.362582	−	0.461061i
$985$	3.49828	−	23.8279i	0.111464	−	0.759220i
$986$	40.9531	+	35.4860i	1.30421	+	1.13011i
$987$	17.9672	+	10.7424i	0.571901	+	0.341936i
$988$	2.65436	+	2.65436i	0.0844464	+	0.0844464i
$989$	15.9127	−	37.3543i	0.505994	−	1.18780i
$990$	9.65635	−	13.4755i	0.306899	−	0.428279i
$991$	−14.2939	+	13.6292i	−0.454060	+	0.432945i	−0.882277	−	0.470731i	$-0.843990\pi$
$991$	−14.2939	+	13.6292i	−0.454060	+	0.432945i	0.428217	+	0.903676i	$0.359142\pi$
$992$	−19.3393	−	28.5738i	−0.614023	−	0.907218i
$993$	−31.5996	+	6.87408i	−1.00278	+	0.218142i
$994$	−59.3252	−	45.8403i	−1.88168	−	1.45397i
$995$	−4.39828	+	13.6193i	−0.139435	+	0.431760i
$996$	17.1093	+	12.1835i	0.542129	+	0.386049i
$997$	−5.43812	−	3.68062i	−0.172227	−	0.116567i	0.471356	−	0.881943i	$-0.343765\pi$
$997$	−5.43812	−	3.68062i	−0.172227	−	0.116567i	−0.643583	+	0.765377i	$0.722553\pi$
$998$	66.6756	−	28.5521i	2.11058	−	0.903802i
$999$	−30.3706	+	2.90004i	−0.960882	+	0.0917531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.bs.a.557.81	yes	3680
5.3	odd	4	inner	805.2.bs.a.718.12	yes	3680
7.2	even	3	inner	805.2.bs.a.212.12	yes	3680
23.14	odd	22	inner	805.2.bs.a.382.12	yes	3680
35.23	odd	12	inner	805.2.bs.a.373.12	yes	3680
115.83	even	44	inner	805.2.bs.a.543.12	yes	3680
161.37	odd	66	inner	805.2.bs.a.37.12	✓	3680
805.198	even	132	inner	805.2.bs.a.198.81	yes	3680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.bs.a.37.12	✓	3680	161.37	odd	66	inner
805.2.bs.a.198.81	yes	3680	805.198	even	132	inner
805.2.bs.a.212.12	yes	3680	7.2	even	3	inner
805.2.bs.a.373.12	yes	3680	35.23	odd	12	inner
805.2.bs.a.382.12	yes	3680	23.14	odd	22	inner
805.2.bs.a.543.12	yes	3680	115.83	even	44	inner
805.2.bs.a.557.81	yes	3680	1.1	even	1	trivial
805.2.bs.a.718.12	yes	3680	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16029 - 1.90357i) q^{2} +(1.36545 + 0.663296i) q^{3} +(-1.36087 - 2.63972i) q^{4} +(-1.07746 + 1.95935i) q^{5} +(2.84695 - 1.82963i) q^{6} +(0.460985 + 2.60528i) q^{7} +(-2.15663 - 0.154245i) q^{8} +(-0.429976 - 0.546759i) q^{9} +O(q^{10})\)	\(q+(1.16029 - 1.90357i) q^{2} +(1.36545 + 0.663296i) q^{3} +(-1.36087 - 2.63972i) q^{4} +(-1.07746 + 1.95935i) q^{5} +(2.84695 - 1.82963i) q^{6} +(0.460985 + 2.60528i) q^{7} +(-2.15663 - 0.154245i) q^{8} +(-0.429976 - 0.546759i) q^{9} +(2.47961 + 4.32445i) q^{10} +(4.64639 + 1.12720i) q^{11} +(-0.107288 - 4.50707i) q^{12} +(-0.856010 - 2.29505i) q^{13} +(5.49422 + 2.14536i) q^{14} +(-2.77086 + 1.96073i) q^{15} +(0.649454 - 0.912030i) q^{16} +(4.71396 + 4.28527i) q^{17} +(-1.53969 + 0.184093i) q^{18} +(0.0245530 - 0.515430i) q^{19} +(6.63844 + 0.177775i) q^{20} +(-1.09862 + 3.86316i) q^{21} +(7.53686 - 7.53686i) q^{22} +(-2.18953 + 4.26685i) q^{23} +(-2.84246 - 1.64110i) q^{24} +(-2.67814 - 4.22227i) q^{25} +(-5.36202 - 1.03344i) q^{26} +(-1.19249 - 5.48180i) q^{27} +(6.24987 - 4.76232i) q^{28} +(2.06283 + 3.20982i) q^{29} +(0.517397 + 7.54955i) q^{30} +(4.96747 - 0.957402i) q^{31} +(-2.68481 - 6.26963i) q^{32} +(5.59676 + 4.62107i) q^{33} +(13.6269 - 4.00121i) q^{34} +(-5.60137 - 1.90386i) q^{35} +(-0.858149 + 1.87908i) q^{36} +(0.645626 - 5.39981i) q^{37} +(-0.952670 - 0.644786i) q^{38} +(0.353458 - 3.70158i) q^{39} +(2.62591 - 4.05940i) q^{40} +(-0.797793 + 5.54877i) q^{41} +(6.07909 + 6.57369i) q^{42} +(-8.44462 + 0.603971i) q^{43} +(-3.34764 - 13.7991i) q^{44} +(1.53458 - 0.253363i) q^{45} +(5.58177 + 9.11870i) q^{46} +(1.34900 - 5.03453i) q^{47} +(1.49175 - 0.814554i) q^{48} +(-6.57499 + 2.40199i) q^{49} +(-11.1448 + 0.198992i) q^{50} +(3.59428 + 8.97809i) q^{51} +(-4.89338 + 5.38290i) q^{52} +(-6.21613 - 7.52860i) q^{53} +(-11.8186 - 4.09047i) q^{54} +(-7.21490 + 7.88940i) q^{55} +(-0.592320 - 5.68972i) q^{56} +(0.375409 - 0.687510i) q^{57} +(8.50360 - 0.202423i) q^{58} +(6.05692 - 4.31311i) q^{59} +(8.94656 + 4.64599i) q^{60} +(-0.597695 - 0.206864i) q^{61} +(3.94122 - 10.5668i) q^{62} +(1.22625 - 1.37226i) q^{63} +(-12.8334 - 1.84516i) q^{64} +(5.41914 + 0.795608i) q^{65} +(15.2904 - 5.29206i) q^{66} +(-0.141455 + 5.94240i) q^{67} +(4.89683 - 18.2752i) q^{68} +(-5.81988 + 4.37387i) q^{69} +(-10.1233 + 8.45358i) q^{70} +(-12.1961 - 3.58109i) q^{71} +(0.842963 + 1.24548i) q^{72} +(-1.12408 + 3.51643i) q^{73} +(-9.52982 - 7.49433i) q^{74} +(-0.856264 - 7.54171i) q^{75} +(-1.39400 + 0.636620i) q^{76} +(-0.794764 + 12.6248i) q^{77} +(-6.63611 - 4.96773i) q^{78} +(-11.3215 + 1.08107i) q^{79} +(1.08723 + 2.25519i) q^{80} +(1.51580 - 6.24821i) q^{81} +(9.63682 + 7.95683i) q^{82} +(-2.79197 + 3.72964i) q^{83} +(11.6927 - 2.35721i) q^{84} +(-13.4755 + 4.61909i) q^{85} +(-8.64849 + 16.7757i) q^{86} +(0.687631 + 5.75112i) q^{87} +(-9.84666 - 3.14763i) q^{88} +(5.28562 + 1.01872i) q^{89} +(1.29826 - 3.21516i) q^{90} +(5.58465 - 3.28813i) q^{91} +(14.2429 - 0.0268832i) q^{92} +(7.41789 + 1.98762i) q^{93} +(-8.01838 - 8.40943i) q^{94} +(0.983455 + 0.603465i) q^{95} +(0.492637 - 10.3417i) q^{96} +(6.20992 + 8.29548i) q^{97} +(-3.05652 + 15.3030i) q^{98} +(-1.38153 - 3.02512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Introduction

L-functions

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