LMFDB - Embedded newform 231.2.y.b.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	231.4
Dual form			231.2.y.b.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.116737 + 1.11067i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.736325 + 0.156511i) q^{4} +(-0.640590 - 0.285209i) q^{5} +(-0.903504 + 0.656434i) q^{6} +(-1.42180 + 2.23125i) q^{7} +(-0.950004 + 2.92381i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.116737 + 1.11067i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.736325 + 0.156511i) q^{4} +(-0.640590 - 0.285209i) q^{5} +(-0.903504 + 0.656434i) q^{6} +(-1.42180 + 2.23125i) q^{7} +(-0.950004 + 2.92381i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.391555 - 0.678193i) q^{10} +(-0.368838 - 3.29605i) q^{11} +(0.376388 + 0.651923i) q^{12} +(2.89681 + 2.10465i) q^{13} +(-2.31222 - 1.83963i) q^{14} +(-0.216687 - 0.666894i) q^{15} +(-1.76111 - 0.784098i) q^{16} +(0.390027 + 3.71086i) q^{17} +(-1.09239 - 0.232194i) q^{18} +(6.33263 - 1.34604i) q^{19} +(-0.427045 - 0.310266i) q^{20} +(-2.60951 + 0.436394i) q^{21} +(3.70390 - 0.0248887i) q^{22} +(-2.77749 - 4.81076i) q^{23} +(-2.80849 + 1.25042i) q^{24} +(-3.01664 - 3.35032i) q^{25} +(-2.67575 + 2.97172i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.39612 + 1.42040i) q^{28} +(-1.13169 - 3.48298i) q^{29} +(0.765997 - 0.162818i) q^{30} +(-1.78438 + 0.794457i) q^{31} +(-1.99781 + 3.46032i) q^{32} +(2.20264 - 2.47959i) q^{33} -4.16709 q^{34} +(1.54717 - 1.02381i) q^{35} +(-0.232620 + 0.715932i) q^{36} +(1.11708 - 1.24064i) q^{37} +(0.755765 + 7.19063i) q^{38} +(0.374280 + 3.56104i) q^{39} +(1.44246 - 1.60202i) q^{40} +(1.67227 - 5.14670i) q^{41} +(-0.180066 - 2.94926i) q^{42} +12.2117 q^{43} +(0.244283 - 2.48469i) q^{44} +(0.350607 - 0.607269i) q^{45} +(5.66742 - 2.52330i) q^{46} +(8.92872 - 1.89786i) q^{47} +(-0.595716 - 1.83343i) q^{48} +(-2.95696 - 6.34479i) q^{49} +(4.07327 - 2.95940i) q^{50} +(-2.49673 + 2.77290i) q^{51} +(1.80359 + 2.00309i) q^{52} +(-6.85563 + 3.05232i) q^{53} +(-0.558396 - 0.967170i) q^{54} +(-0.703791 + 2.21662i) q^{55} +(-5.17304 - 6.27678i) q^{56} +(5.23766 + 3.80539i) q^{57} +(4.00056 - 0.850345i) q^{58} +(8.14925 + 1.73218i) q^{59} +(-0.0551760 - 0.524965i) q^{60} +(-2.96100 - 1.31832i) q^{61} +(-0.674081 - 2.07461i) q^{62} +(-2.07041 - 1.64724i) q^{63} +(-6.72928 - 4.88911i) q^{64} +(-1.25540 - 2.17442i) q^{65} +(2.49689 + 2.73588i) q^{66} +(2.88249 - 4.99261i) q^{67} +(-0.293603 + 2.79345i) q^{68} +(1.71658 - 5.28310i) q^{69} +(0.956506 + 1.83791i) q^{70} +(-1.24843 + 0.907036i) q^{71} +(-2.80849 - 1.25042i) q^{72} +(-14.4141 - 3.06381i) q^{73} +(1.24755 + 1.38554i) q^{74} +(0.471246 - 4.48360i) q^{75} +4.87355 q^{76} +(7.87873 + 3.86336i) q^{77} -3.99884 q^{78} +(0.531449 - 5.05640i) q^{79} +(0.904520 + 1.00457i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(5.52110 + 2.45815i) q^{82} +(-8.27734 + 6.01384i) q^{83} +(-1.98975 - 0.0870888i) q^{84} +(0.808525 - 2.48838i) q^{85} +(-1.42555 + 13.5632i) q^{86} +(1.83111 - 3.17157i) q^{87} +(9.98743 + 2.05285i) q^{88} +(6.65543 + 11.5275i) q^{89} +(0.633549 + 0.460300i) q^{90} +(-8.81469 + 3.47111i) q^{91} +(-1.29220 - 3.97699i) q^{92} +(-1.78438 - 0.794457i) q^{93} +(1.06559 + 10.1384i) q^{94} +(-4.44053 - 0.943864i) q^{95} +(-3.90831 + 0.830738i) q^{96} +(-2.57932 - 1.87399i) q^{97} +(7.39218 - 2.54355i) q^{98} +(3.31655 - 0.0222859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.116737	+	1.11067i	−0.0825452	+	0.785365i	0.872442	+	0.488718i	$0.162535\pi$
$2$	−0.116737	+	1.11067i	−0.0825452	+	0.785365i	−0.954987	+	0.296647i	$0.904131\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	0.736325	+	0.156511i	0.368163	+	0.0782554i
$5$	−0.640590	−	0.285209i	−0.286481	−	0.127549i	0.258465	−	0.966021i	$-0.416783\pi$
$5$	−0.640590	−	0.285209i	−0.286481	−	0.127549i	−0.544946	+	0.838471i	$0.683450\pi$
$6$	−0.903504	+	0.656434i	−0.368854	+	0.267988i
$7$	−1.42180	+	2.23125i	−0.537390	+	0.843334i
$7$	−1.42180	+	2.23125i	−0.537390	+	0.843334i
$8$	−0.950004	+	2.92381i	−0.335877	+	1.03372i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.391555	−	0.678193i	0.123821	−	0.214463i
$11$	−0.368838	−	3.29605i	−0.111209	−	0.993797i
$11$	−0.368838	−	3.29605i	−0.111209	−	0.993797i
$12$	0.376388	+	0.651923i	0.108654	+	0.188194i
$13$	2.89681	+	2.10465i	0.803430	+	0.583726i	0.911918	−	0.410372i	$-0.134601\pi$
$13$	2.89681	+	2.10465i	0.803430	+	0.583726i	−0.108489	+	0.994098i	$0.534601\pi$
$14$	−2.31222	−	1.83963i	−0.617966	−	0.491661i
$15$	−0.216687	−	0.666894i	−0.0559483	−	0.172191i
$16$	−1.76111	−	0.784098i	−0.440278	−	0.196025i
$17$	0.390027	+	3.71086i	0.0945955	+	0.900016i	0.934184	+	0.356793i	$0.116130\pi$
$17$	0.390027	+	3.71086i	0.0945955	+	0.900016i	−0.839588	+	0.543224i	$0.817204\pi$
$18$	−1.09239	−	0.232194i	−0.257478	−	0.0547287i
$19$	6.33263	−	1.34604i	1.45281	−	0.308803i	0.587164	−	0.809468i	$-0.300244\pi$
$19$	6.33263	−	1.34604i	1.45281	−	0.308803i	0.865642	+	0.500664i	$0.166911\pi$
$20$	−0.427045	−	0.310266i	−0.0954901	−	0.0693776i
$21$	−2.60951	+	0.436394i	−0.569442	+	0.0952291i
$22$	3.70390	−	0.0248887i	0.789673	−	0.00530629i
$23$	−2.77749	−	4.81076i	−0.579147	−	1.00311i	−0.995577	−	0.0939447i	$-0.970052\pi$
$23$	−2.77749	−	4.81076i	−0.579147	−	1.00311i	0.416430	−	0.909168i	$-0.363281\pi$
$24$	−2.80849	+	1.25042i	−0.573281	+	0.255241i
$25$	−3.01664	−	3.35032i	−0.603328	−	0.670064i
$26$	−2.67575	+	2.97172i	−0.524757	+	0.582802i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.39612	+	1.42040i	−0.263842	+	0.268430i
$29$	−1.13169	−	3.48298i	−0.210149	−	0.646772i	−0.999463	−	0.0327818i	$-0.989563\pi$
$29$	−1.13169	−	3.48298i	−0.210149	−	0.646772i	0.789313	−	0.613990i	$-0.210437\pi$
$30$	0.765997	−	0.162818i	0.139851	−	0.0297263i
$31$	−1.78438	+	0.794457i	−0.320484	+	0.142689i	−0.560673	−	0.828038i	$-0.689457\pi$
$31$	−1.78438	+	0.794457i	−0.320484	+	0.142689i	0.240189	+	0.970726i	$0.422791\pi$
$32$	−1.99781	+	3.46032i	−0.353167	+	0.611703i
$33$	2.20264	−	2.47959i	0.383431	−	0.431641i
$34$	−4.16709			−0.714650
$35$	1.54717	−	1.02381i	0.261519	−	0.173055i
$36$	−0.232620	+	0.715932i	−0.0387701	+	0.119322i
$37$	1.11708	−	1.24064i	0.183647	−	0.203960i	−0.644291	−	0.764781i	$-0.722847\pi$
$37$	1.11708	−	1.24064i	0.183647	−	0.203960i	0.827938	+	0.560820i	$0.189514\pi$
$38$	0.755765	+	7.19063i	0.122601	+	1.16647i
$39$	0.374280	+	3.56104i	0.0599328	+	0.570222i
$40$	1.44246	−	1.60202i	0.228073	−	0.253301i
$41$	1.67227	−	5.14670i	0.261164	−	0.803780i	−0.731388	−	0.681961i	$-0.761127\pi$
$41$	1.67227	−	5.14670i	0.261164	−	0.803780i	0.992552	−	0.121819i	$-0.0388727\pi$
$42$	−0.180066	−	2.94926i	−0.0277848	−	0.455081i
$43$	12.2117			1.86226			0.931130	−	0.364688i	$-0.118824\pi$
$43$	12.2117			1.86226			0.931130	+	0.364688i	$0.118824\pi$
$44$	0.244283	−	2.48469i	0.0368271	−	0.374582i
$45$	0.350607	−	0.607269i	0.0522654	−	0.0905263i
$46$	5.66742	−	2.52330i	0.835616	−	0.372040i
$47$	8.92872	−	1.89786i	1.30239	−	0.276831i	0.496054	−	0.868292i	$-0.334782\pi$
$47$	8.92872	−	1.89786i	1.30239	−	0.276831i	0.806334	+	0.591461i	$0.201449\pi$
$48$	−0.595716	−	1.83343i	−0.0859842	−	0.264632i
$49$	−2.95696	−	6.34479i	−0.422423	−	0.906399i
$50$	4.07327	−	2.95940i	0.576047	−	0.418522i
$51$	−2.49673	+	2.77290i	−0.349612	+	0.388283i
$52$	1.80359	+	2.00309i	0.250113	+	0.277779i
$53$	−6.85563	+	3.05232i	−0.941694	+	0.419269i	−0.819398	−	0.573225i	$-0.805692\pi$
$53$	−6.85563	+	3.05232i	−0.941694	+	0.419269i	−0.122295	+	0.992494i	$0.539026\pi$
$54$	−0.558396	−	0.967170i	−0.0759881	−	0.131615i
$55$	−0.703791	+	2.21662i	−0.0948991	+	0.298888i
$56$	−5.17304	−	6.27678i	−0.691277	−	0.838770i
$57$	5.23766	+	3.80539i	0.693746	+	0.504036i
$58$	4.00056	−	0.850345i	0.525299	−	0.111656i
$59$	8.14925	+	1.73218i	1.06094	+	0.225510i	0.705152	−	0.709056i	$-0.250879\pi$
$59$	8.14925	+	1.73218i	1.06094	+	0.225510i	0.355789	+	0.934566i	$0.384212\pi$
$60$	−0.0551760	−	0.524965i	−0.00712319	−	0.0677726i
$61$	−2.96100	−	1.31832i	−0.379118	−	0.168794i	0.208325	−	0.978060i	$-0.433199\pi$
$61$	−2.96100	−	1.31832i	−0.379118	−	0.168794i	−0.587443	+	0.809266i	$0.699865\pi$
$62$	−0.674081	−	2.07461i	−0.0856083	−	0.263475i
$63$	−2.07041	−	1.64724i	−0.260847	−	0.207533i
$64$	−6.72928	−	4.88911i	−0.841160	−	0.611138i
$65$	−1.25540	−	2.17442i	−0.155713	−	0.269703i
$66$	2.49689	+	2.73588i	0.307345	+	0.336763i
$67$	2.88249	−	4.99261i	0.352152	−	0.609945i	−0.634474	−	0.772944i	$-0.718783\pi$
$67$	2.88249	−	4.99261i	0.352152	−	0.609945i	0.986626	+	0.162999i	$0.0521167\pi$
$68$	−0.293603	+	2.79345i	−0.0356046	+	0.338755i
$69$	1.71658	−	5.28310i	0.206653	−	0.636011i
$70$	0.956506	+	1.83791i	0.114324	+	0.219673i
$71$	−1.24843	+	0.907036i	−0.148161	+	0.107645i	−0.659396	−	0.751795i	$-0.729188\pi$
$71$	−1.24843	+	0.907036i	−0.148161	+	0.107645i	0.511235	+	0.859441i	$0.329188\pi$
$72$	−2.80849	−	1.25042i	−0.330984	−	0.147364i
$73$	−14.4141	−	3.06381i	−1.68704	−	0.358592i	−0.738259	−	0.674517i	$-0.764352\pi$
$73$	−14.4141	−	3.06381i	−1.68704	−	0.358592i	−0.948784	+	0.315925i	$0.897685\pi$
$74$	1.24755	+	1.38554i	0.145024	+	0.161066i
$75$	0.471246	−	4.48360i	0.0544148	−	0.517722i
$76$	4.87355			0.559034
$77$	7.87873	+	3.86336i	0.897865	+	0.440271i
$78$	−3.99884			−0.452780
$79$	0.531449	−	5.05640i	0.0597927	−	0.568890i	−0.923081	−	0.384607i	$-0.874337\pi$
$79$	0.531449	−	5.05640i	0.0597927	−	0.568890i	0.982873	−	0.184283i	$-0.0589963\pi$
$80$	0.904520	+	1.00457i	0.101128	+	0.112315i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	5.52110	+	2.45815i	0.609703	+	0.271457i
$83$	−8.27734	+	6.01384i	−0.908556	+	0.660104i	−0.940649	−	0.339380i	$-0.889783\pi$
$83$	−8.27734	+	6.01384i	−0.908556	+	0.660104i	0.0320934	+	0.999485i	$0.489783\pi$
$84$	−1.98975	−	0.0870888i	−0.217100	−	0.00950216i
$85$	0.808525	−	2.48838i	0.0876968	−	0.269903i
$86$	−1.42555	+	13.5632i	−0.153721	+	1.46255i
$87$	1.83111	−	3.17157i	0.196315	−	0.340028i
$88$	9.98743	+	2.05285i	1.06466	+	0.218835i
$89$	6.65543	+	11.5275i	0.705474	+	1.22192i	0.966520	+	0.256591i	$0.0825993\pi$
$89$	6.65543	+	11.5275i	0.705474	+	1.22192i	−0.261046	+	0.965326i	$0.584067\pi$
$90$	0.633549	+	0.460300i	0.0667819	+	0.0485199i
$91$	−8.81469	+	3.47111i	−0.924031	+	0.363871i
$92$	−1.29220	−	3.97699i	−0.134721	−	0.414630i
$93$	−1.78438	−	0.794457i	−0.185032	−	0.0823814i
$94$	1.06559	+	10.1384i	0.109908	+	1.04570i
$95$	−4.44053	−	0.943864i	−0.455589	−	0.0968384i
$96$	−3.90831	+	0.830738i	−0.398891	+	0.0847868i
$97$	−2.57932	−	1.87399i	−0.261891	−	0.190275i	0.449089	−	0.893487i	$-0.351748\pi$
$97$	−2.57932	−	1.87399i	−0.261891	−	0.190275i	−0.710980	+	0.703212i	$0.751748\pi$
$98$	7.39218	−	2.54355i	0.746723	−	0.256938i
$99$	3.31655	−	0.0222859i	0.333326	−	0.00223981i
$100$	−1.69687	−	2.93906i	−0.169687	−	0.293906i
$101$	6.53558	−	2.90983i	0.650314	−	0.289539i	−0.0549436	−	0.998489i	$-0.517498\pi$
$101$	6.53558	−	2.90983i	0.650314	−	0.289539i	0.705258	+	0.708951i	$0.250831\pi$
$102$	−2.78833	−	3.09675i	−0.276086	−	0.306624i
$103$	−3.04865	+	3.38586i	−0.300392	+	0.333619i	−0.874377	−	0.485246i	$-0.838730\pi$
$103$	−3.04865	+	3.38586i	−0.300392	+	0.333619i	0.573986	+	0.818865i	$0.305397\pi$
$104$	−8.90559	+	6.47029i	−0.873265	+	0.634464i
$105$	1.79609	+	0.464707i	0.175281	+	0.0453508i
$106$	−2.58984	−	7.97069i	−0.251547	−	0.774182i
$107$	−5.71831	+	1.21546i	−0.552810	+	0.117503i	−0.475843	−	0.879530i	$-0.657857\pi$
$107$	−5.71831	+	1.21546i	−0.552810	+	0.117503i	−0.0769669	+	0.997034i	$0.524524\pi$
$108$	−0.687694	+	0.306181i	−0.0661734	+	0.0294623i
$109$	−10.2671	+	17.7831i	−0.983410	+	1.70332i	−0.334611	+	0.942356i	$0.608605\pi$
$109$	−10.2671	+	17.7831i	−0.983410	+	1.70332i	−0.648799	+	0.760960i	$0.724729\pi$
$110$	−2.37978	−	1.04044i	−0.226903	−	0.0992023i
$111$	1.66945			0.158457
$112$	4.25347	−	2.81465i	0.401915	−	0.265960i
$113$	3.53371	−	10.8756i	0.332423	−	1.02309i	−0.635554	−	0.772057i	$-0.719228\pi$
$113$	3.53371	−	10.8756i	0.332423	−	1.02309i	0.967977	−	0.251038i	$-0.0807718\pi$
$114$	−4.83797	+	5.37311i	−0.453117	+	0.503238i
$115$	0.407163	+	3.87389i	0.0379681	+	0.361242i
$116$	−0.288167	−	2.74172i	−0.0267556	−	0.254563i
$117$	−2.39592	+	2.66094i	−0.221503	+	0.246004i
$118$	−2.87520	+	8.84895i	−0.264683	+	0.814612i
$119$	−8.83441	−	4.40586i	−0.809849	−	0.403884i
$120$	2.15573			0.196790
$121$	−10.7279	+	2.43142i	−0.975265	+	0.221038i
$122$	1.80988	−	3.13481i	0.163859	−	0.283813i
$123$	4.94371	−	2.20108i	0.445759	−	0.198465i
$124$	−1.43823	+	0.305704i	−0.129156	+	0.0274531i
$125$	2.06032	+	6.34103i	0.184281	+	0.567159i
$126$	2.07124	−	2.10726i	0.184521	−	0.187729i
$127$	−3.71593	+	2.69978i	−0.329735	+	0.239567i	−0.740318	−	0.672257i	$-0.765325\pi$
$127$	−3.71593	+	2.69978i	−0.329735	+	0.239567i	0.410583	+	0.911823i	$0.365325\pi$
$128$	0.868562	−	0.964636i	0.0767708	−	0.0852626i
$129$	8.17119	+	9.07503i	0.719433	+	0.799012i
$130$	2.56162	−	1.14051i	0.224669	−	0.100029i
$131$	−2.32547	−	4.02783i	−0.203177	−	0.351913i	0.746373	−	0.665528i	$-0.231793\pi$
$131$	−2.32547	−	4.02783i	−0.203177	−	0.351913i	−0.949550	+	0.313615i	$0.898460\pi$
$132$	2.00994	−	1.48105i	0.174943	−	0.128909i
$133$	−6.00039	+	16.0435i	−0.520299	+	1.39115i
$134$	5.20868	+	3.78433i	0.449961	+	0.326916i
$135$	0.685890	−	0.145791i	0.0590320	−	0.0125476i
$136$	−11.2204	−	2.38497i	−0.962141	−	0.204509i
$137$	0.379954	+	3.61502i	0.0324617	+	0.308852i	0.998690	+	0.0511655i	$0.0162936\pi$
$137$	0.379954	+	3.61502i	0.0324617	+	0.308852i	−0.966229	+	0.257687i	$0.917040\pi$
$138$	5.66742	+	2.52330i	0.482443	+	0.214797i
$139$	2.15087	+	6.61968i	0.182434	+	0.561474i	0.999895	−	0.0145102i	$-0.00461890\pi$
$139$	2.15087	+	6.61968i	0.182434	+	0.561474i	−0.817461	+	0.575984i	$0.804619\pi$
$140$	1.29945	−	0.511707i	0.109824	−	0.0432472i
$141$	7.38486	+	5.36542i	0.621918	+	0.451850i
$142$	−0.861684	−	1.49248i	−0.0723109	−	0.125246i
$143$	5.86860	−	10.3243i	0.490757	−	0.863362i
$144$	0.963889	−	1.66951i	0.0803241	−	0.139125i
$145$	−0.268429	+	2.55393i	−0.0222918	+	0.212092i
$146$	5.08555	−	15.6517i	0.420883	−	1.29535i
$147$	2.73650	−	6.44295i	0.225703	−	0.531405i
$148$	1.01671	−	0.738682i	0.0835729	−	0.0607193i
$149$	−10.0579	−	4.47809i	−0.823979	−	0.366859i	−0.0489630	−	0.998801i	$-0.515592\pi$
$149$	−10.0579	−	4.47809i	−0.823979	−	0.366859i	−0.775016	+	0.631941i	$0.782258\pi$
$150$	4.92481	+	1.04680i	0.402109	+	0.0854709i
$151$	−1.63682	−	1.81787i	−0.133202	−	0.147936i	0.672853	−	0.739776i	$-0.265068\pi$
$151$	−1.63682	−	1.81787i	−0.133202	−	0.147936i	−0.806056	+	0.591840i	$0.798402\pi$
$152$	−2.08045	+	19.7942i	−0.168747	+	1.60552i
$153$	−3.73130			−0.301658
$154$	−5.21067	+	8.29971i	−0.419888	+	0.668810i
$155$	1.36964			0.110012
$156$	−0.281749	+	2.68066i	−0.0225579	+	0.214625i
$157$	−7.09312	−	7.87771i	−0.566093	−	0.628709i	0.390337	−	0.920672i	$-0.372358\pi$
$157$	−7.09312	−	7.87771i	−0.566093	−	0.628709i	−0.956430	+	0.291962i	$0.905692\pi$
$158$	5.55397	+	1.18053i	0.441851	+	0.0939182i
$159$	−6.85563	−	3.05232i	−0.543687	−	0.242065i
$160$	2.26669	−	1.64685i	0.179198	−	0.130195i
$161$	14.6831	+	0.642658i	1.15719	+	0.0506485i
$162$	0.345108	−	1.06213i	0.0271142	−	0.0834490i
$163$	2.08269	−	19.8155i	0.163129	−	1.55207i	−0.540403	−	0.841406i	$-0.681728\pi$
$163$	2.08269	−	19.8155i	0.163129	−	1.55207i	0.703532	−	0.710663i	$-0.251605\pi$
$164$	2.03685	−	3.52792i	0.159051	−	0.275484i
$165$	−2.11819	+	0.960187i	−0.164901	+	0.0747504i
$166$	−5.71315	−	9.89546i	−0.443426	−	0.768037i
$167$	5.05564	+	3.67314i	0.391217	+	0.284236i	0.765954	−	0.642895i	$-0.222267\pi$
$167$	5.05564	+	3.67314i	0.391217	+	0.284236i	−0.374737	+	0.927131i	$0.622267\pi$
$168$	1.20311	−	8.04430i	0.0928222	−	0.620631i
$169$	−0.0552958	−	0.170183i	−0.00425352	−	0.0130910i
$170$	2.66940	+	1.18849i	0.204734	+	0.0911532i
$171$	0.676729	+	6.43864i	0.0517507	+	0.492375i
$172$	8.99175	+	1.91126i	0.685615	+	0.145732i
$173$	−22.6560	+	4.81568i	−1.72250	+	0.366129i	−0.959814	−	0.280636i	$-0.909455\pi$
$173$	−22.6560	+	4.81568i	−1.72250	+	0.366129i	−0.762689	+	0.646765i	$0.776121\pi$
$174$	3.30883	+	2.40400i	0.250842	+	0.182247i
$175$	11.7645	−	1.96740i	0.889310	−	0.148721i
$176$	−1.93486	+	6.09393i	−0.145846	+	0.459347i
$177$	4.16565	+	7.21512i	0.313110	+	0.542322i
$178$	−13.5803	+	6.04633i	−1.01788	+	0.453192i
$179$	−0.984088	−	1.09294i	−0.0735542	−	0.0816902i	0.705244	−	0.708964i	$-0.250837\pi$
$179$	−0.984088	−	1.09294i	−0.0735542	−	0.0816902i	−0.778799	+	0.627274i	$0.784171\pi$
$180$	0.353205	−	0.392274i	0.0263263	−	0.0292384i
$181$	−14.9467	+	10.8594i	−1.11098	+	0.807173i	−0.982817	−	0.184581i	$-0.940907\pi$
$181$	−14.9467	+	10.8594i	−1.11098	+	0.807173i	−0.128160	+	0.991753i	$0.540907\pi$
$182$	−2.82627	−	10.1955i	−0.209497	−	0.755738i
$183$	−1.00159	−	3.08258i	−0.0740398	−	0.227871i
$184$	16.7044	−	3.55063i	1.23146	−	0.261756i
$185$	−1.06943	+	0.476143i	−0.0786263	+	0.0350067i
$186$	1.09069	−	1.88912i	0.0799730	−	0.138517i
$187$	12.0873	−	2.65426i	0.883914	−	0.194098i
$188$	6.87148			0.501154
$189$	−0.161235	−	2.64083i	−0.0117281	−	0.192092i
$190$	1.56670	−	4.82180i	0.113660	−	0.349810i
$191$	15.5356	−	17.2540i	1.12412	−	1.24846i	0.158819	−	0.987308i	$-0.449231\pi$
$191$	15.5356	−	17.2540i	1.12412	−	1.24846i	0.965298	−	0.261151i	$-0.0841019\pi$
$192$	−0.869451	−	8.27228i	−0.0627472	−	0.597000i
$193$	2.43126	+	23.1319i	0.175006	+	1.66507i	0.631523	+	0.775357i	$0.282430\pi$
$193$	2.43126	+	23.1319i	0.175006	+	1.66507i	−0.456517	+	0.889715i	$0.650903\pi$
$194$	2.38249	−	2.64603i	0.171053	−	0.189974i
$195$	0.775880	−	2.38791i	0.0555619	−	0.171002i
$196$	−1.18426	−	5.13463i	−0.0845899	−	0.366759i
$197$	10.2775			0.732241			0.366120	−	0.930567i	$-0.380686\pi$
$197$	10.2775			0.732241			0.366120	+	0.930567i	$0.380686\pi$
$198$	−0.362410	+	3.68621i	−0.0257554	+	0.261967i
$199$	−6.90174	+	11.9542i	−0.489251	+	0.847408i	−0.999924	−	0.0123674i	$-0.996063\pi$
$199$	−6.90174	+	11.9542i	−0.489251	+	0.847408i	0.510672	+	0.859775i	$0.329397\pi$
$200$	12.6615	−	5.63727i	0.895305	−	0.398615i
$201$	5.63900	−	1.19861i	0.397744	−	0.0845431i
$202$	2.46893	+	7.59858i	0.173713	+	0.534634i
$203$	9.38043	+	2.42702i	0.658377	+	0.170343i
$204$	−2.27239	+	1.65099i	−0.159099	+	0.115592i
$205$	−2.53913	+	2.81998i	−0.177340	+	0.196956i
$206$	−3.40470	−	3.78131i	−0.237217	−	0.263456i
$207$	5.07473	−	2.25942i	0.352718	−	0.157040i
$208$	−3.45135	−	5.97792i	−0.239308	−	0.414494i
$209$	−6.77234	−	20.3762i	−0.468453	−	1.40945i
$210$	−0.725808	+	1.94063i	−0.0500855	+	0.133916i
$211$	−10.5364	−	7.65517i	−0.725359	−	0.527004i	0.162733	−	0.986670i	$-0.447969\pi$
$211$	−10.5364	−	7.65517i	−0.725359	−	0.527004i	−0.888092	+	0.459666i	$0.847969\pi$
$212$	−5.52570	+	1.17452i	−0.379507	+	0.0806666i
$213$	−1.50942	−	0.320837i	−0.103424	−	0.0219834i
$214$	−0.682449	−	6.49307i	−0.0466513	−	0.443857i
$215$	−7.82267	−	3.48288i	−0.533502	−	0.237530i
$216$	−0.950004	−	2.92381i	−0.0646396	−	0.198940i
$217$	0.764400	−	5.11096i	0.0518909	−	0.346955i
$218$	−18.5527	−	13.4793i	−1.25655	−	0.912937i
$219$	−7.36806	−	12.7619i	−0.497888	−	0.862367i
$220$	−0.865143	+	1.52200i	−0.0583279	+	0.102613i
$221$	−6.68025	+	11.5705i	−0.449362	+	0.778318i
$222$	−0.194886	+	1.85421i	−0.0130799	+	0.124447i
$223$	0.937059	−	2.88397i	0.0627501	−	0.193125i	−0.914767	−	0.403983i	$-0.867626\pi$
$223$	0.937059	−	2.88397i	0.0627501	−	0.193125i	0.977517	+	0.210858i	$0.0676256\pi$
$224$	−4.88034	−	9.37750i	−0.326081	−	0.626561i
$225$	3.64729	−	2.64991i	0.243153	−	0.176661i
$226$	11.6668	+	5.19439i	0.776063	+	0.345525i
$227$	8.69241	+	1.84763i	0.576936	+	0.122631i	0.487133	−	0.873328i	$-0.338043\pi$
$227$	8.69241	+	1.84763i	0.576936	+	0.122631i	0.0898032	+	0.995960i	$0.471376\pi$
$228$	3.26104	+	3.62175i	0.215968	+	0.239856i
$229$	1.02986	−	9.79849i	0.0680553	−	0.647503i	−0.906323	−	0.422586i	$-0.861122\pi$
$229$	1.02986	−	9.79849i	0.0680553	−	0.647503i	0.974378	−	0.224916i	$-0.0722109\pi$
$230$	−4.35016			−0.286841
$231$	2.40087	+	8.44013i	0.157965	+	0.555320i
$232$	11.2587			0.739168
$233$	−2.02404	+	19.2574i	−0.132599	+	1.26160i	0.702574	+	0.711611i	$0.252034\pi$
$233$	−2.02404	+	19.2574i	−0.132599	+	1.26160i	−0.835173	+	0.549987i	$0.814633\pi$
$234$	−2.67575	−	2.97172i	−0.174919	−	0.194267i
$235$	−6.26094	−	1.33080i	−0.408419	−	0.0868121i
$236$	5.72939	+	2.55089i	0.372952	+	0.166049i
$237$	4.11325	−	2.98845i	0.267184	−	0.194121i
$238$	5.92477	−	9.29782i	0.384046	−	0.602688i
$239$	−3.04360	+	9.36722i	−0.196874	+	0.605915i	0.803076	+	0.595877i	$0.203195\pi$
$239$	−3.04360	+	9.36722i	−0.196874	+	0.605915i	−0.999950	+	0.0100384i	$0.996805\pi$
$240$	−0.141300	+	1.34438i	−0.00912087	+	0.0867793i
$241$	9.02876	−	15.6383i	0.581594	−	1.00735i	−0.413697	−	0.910415i	$-0.635763\pi$
$241$	9.02876	−	15.6383i	0.581594	−	1.00735i	0.995291	−	0.0969353i	$-0.0309040\pi$
$242$	−1.44817	−	12.1991i	−0.0930920	−	0.784185i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.97393	−	1.43414i	−0.126368	−	0.0918116i
$245$	0.0846097	+	4.90777i	0.00540551	+	0.313546i
$246$	1.86757	+	5.74780i	0.119072	+	0.366466i
$247$	21.1774	+	9.42877i	1.34748	+	0.599939i
$248$	−0.627675	−	5.97193i	−0.0398574	−	0.379218i
$249$	−10.0078	−	2.12722i	−0.634217	−	0.134807i
$250$	−7.28333	+	1.54812i	−0.460638	+	0.0979117i
$251$	0.120693	+	0.0876883i	0.00761805	+	0.00553484i	0.591588	−	0.806241i	$-0.298501\pi$
$251$	0.120693	+	0.0876883i	0.00761805	+	0.00553484i	−0.583970	+	0.811775i	$0.698501\pi$
$252$	−1.26668	−	1.53695i	−0.0797936	−	0.0968186i
$253$	−14.8321	+	10.9291i	−0.932484	+	0.687110i
$254$	−2.56479	−	4.44235i	−0.160929	−	0.278738i
$255$	2.39024	−	1.06420i	0.149682	−	0.0666429i
$256$	−10.1614	−	11.2854i	−0.635090	−	0.705339i
$257$	14.4246	−	16.0201i	0.899779	−	0.999306i	−0.100211	−	0.994966i	$-0.531952\pi$
$257$	14.4246	−	16.0201i	0.899779	−	0.999306i	0.999991	−	0.00433978i	$-0.00138140\pi$
$258$	−11.0333	+	8.01614i	−0.686902	+	0.499063i
$259$	1.17992	+	4.25643i	0.0733167	+	0.264482i
$260$	−0.584063	−	1.79756i	−0.0362221	−	0.111480i
$261$	3.58219	−	0.761418i	0.221732	−	0.0471306i
$262$	4.74507	−	2.11264i	0.293152	−	0.130519i
$263$	−7.81562	+	13.5370i	−0.481932	+	0.834730i	−0.999785	−	0.0207394i	$-0.993398\pi$
$263$	−7.81562	+	13.5370i	−0.481932	+	0.834730i	0.517853	+	0.855469i	$0.326731\pi$
$264$	5.15733	+	8.79573i	0.317412	+	0.541340i
$265$	5.26220			0.323255
$266$	−17.1186	−	8.53734i	−1.04961	−	0.523458i
$267$	−4.11328	+	12.6594i	−0.251729	+	0.774742i
$268$	2.90385	−	3.22505i	0.177381	−	0.197001i
$269$	1.14674	+	10.9105i	0.0699179	+	0.665225i	0.972212	+	0.234103i	$0.0752153\pi$
$269$	1.14674	+	10.9105i	0.0699179	+	0.665225i	−0.902294	+	0.431122i	$0.858118\pi$
$270$	0.0818573	+	0.778820i	0.00498167	+	0.0473975i
$271$	4.91605	−	5.45982i	0.298629	−	0.331661i	−0.575092	−	0.818089i	$-0.695034\pi$
$271$	4.91605	−	5.45982i	0.298629	−	0.331661i	0.873721	+	0.486428i	$0.161700\pi$
$272$	2.22280	−	6.84107i	0.134777	−	0.414801i
$273$	−8.47772	−	4.22797i	−0.513095	−	0.255888i
$274$	−4.05947			−0.245241
$275$	−9.93018	+	11.1787i	−0.598812	+	0.674103i
$276$	2.09083	−	3.62142i	0.125853	−	0.217984i
$277$	14.9908	−	6.67434i	0.900711	−	0.401022i	0.0964767	−	0.995335i	$-0.469243\pi$
$277$	14.9908	−	6.67434i	0.900711	−	0.401022i	0.804234	+	0.594313i	$0.202576\pi$
$278$	−7.60340	+	1.61615i	−0.456021	+	0.0969303i
$279$	−0.603587	−	1.85765i	−0.0361358	−	0.111215i
$280$	1.52361	+	5.49624i	0.0910529	+	0.328463i
$281$	−7.90308	+	5.74193i	−0.471458	+	0.342535i	−0.798009	−	0.602645i	$-0.794114\pi$
$281$	−7.90308	+	5.74193i	−0.471458	+	0.342535i	0.326551	+	0.945180i	$0.394114\pi$
$282$	−6.82131	+	7.57584i	−0.406203	+	0.451135i
$283$	−17.9032	−	19.8835i	−1.06423	−	1.18195i	−0.982685	−	0.185282i	$-0.940680\pi$
$283$	−17.9032	−	19.8835i	−1.06423	−	1.18195i	−0.0815486	−	0.996669i	$-0.525987\pi$
$284$	−1.06121	+	0.472481i	−0.0629712	+	0.0280366i
$285$	−2.26987	−	3.93152i	−0.134455	−	0.232883i
$286$	10.7819	+	7.72332i	0.637545	+	0.456690i
$287$	9.10596	+	11.0488i	0.537508	+	0.652192i
$288$	−3.23253	−	2.34857i	−0.190479	−	0.138391i
$289$	3.01013	−	0.639822i	0.177066	−	0.0376366i
$290$	−2.80525	−	0.596274i	−0.164730	−	0.0350144i
$291$	−0.333260	−	3.17075i	−0.0195360	−	0.185873i
$292$	−10.1340	−	4.51193i	−0.593045	−	0.264041i
$293$	2.51860	+	7.75146i	0.147138	+	0.452845i	0.997280	−	0.0737091i	$-0.0234836\pi$
$293$	2.51860	+	7.75146i	0.147138	+	0.452845i	−0.850141	+	0.526554i	$0.823484\pi$
$294$	6.83656	+	3.79149i	0.398716	+	0.221124i
$295$	−4.72630	−	3.43386i	−0.275176	−	0.199927i
$296$	2.56618	+	4.44475i	0.149156	+	0.258346i
$297$	2.23577	+	2.44976i	0.129732	+	0.142150i
$298$	6.14783	−	10.6483i	0.356134	−	0.616842i
$299$	2.07912	−	19.7815i	0.120239	−	1.14399i
$300$	1.04872	−	3.22764i	0.0605480	−	0.186348i
$301$	−17.3625	+	27.2473i	−1.00076	+	1.57051i
$302$	2.21014	−	1.60576i	0.127179	−	0.0924010i
$303$	6.53558	+	2.90983i	0.375459	+	0.167165i
$304$	−12.2079	−	2.59487i	−0.700172	−	0.148826i
$305$	1.52079	+	1.68901i	0.0870803	+	0.0967125i
$306$	0.435580	−	4.14426i	0.0249004	−	0.236912i
$307$	26.3427			1.50346			0.751729	−	0.659472i	$-0.229220\pi$
$307$	26.3427			1.50346			0.751729	+	0.659472i	$0.229220\pi$
$308$	5.19665	+	4.07780i	0.296107	+	0.232354i
$309$	−4.55613			−0.259189
$310$	−0.159887	+	1.52123i	−0.00908100	+	0.0863999i
$311$	9.29072	+	10.3184i	0.526828	+	0.585102i	0.946553	−	0.322550i	$-0.104540\pi$
$311$	9.29072	+	10.3184i	0.526828	+	0.585102i	−0.419724	+	0.907652i	$0.637873\pi$
$312$	−10.7674	−	2.28867i	−0.609582	−	0.129571i
$313$	−5.95288	−	2.65040i	−0.336477	−	0.149809i	0.231541	−	0.972825i	$-0.425623\pi$
$313$	−5.95288	−	2.65040i	−0.336477	−	0.149809i	−0.568018	+	0.823016i	$0.692290\pi$
$314$	9.57759	−	6.95853i	0.540495	−	0.392692i
$315$	0.856476	+	1.64571i	0.0482570	+	0.0927251i
$316$	1.18270	−	3.63998i	0.0665321	−	0.204765i
$317$	−0.486262	+	4.62647i	−0.0273112	+	0.259849i	0.972343	+	0.233557i	$0.0750365\pi$
$317$	−0.486262	+	4.62647i	−0.0273112	+	0.259849i	−0.999654	+	0.0262917i	$0.991630\pi$
$318$	4.19044	−	7.25806i	0.234988	−	0.407012i
$319$	−11.0627	+	5.01475i	−0.619390	+	0.280772i
$320$	2.91629	+	5.05117i	0.163026	+	0.282369i
$321$	−4.72956	−	3.43623i	−0.263978	−	0.191792i
$322$	−2.42783	+	16.2331i	−0.135298	+	0.904633i
$323$	7.46488	+	22.9745i	0.415357	+	1.27834i
$324$	−0.687694	−	0.306181i	−0.0382052	−	0.0170101i
$325$	−1.68737	−	16.0542i	−0.0935982	−	0.890528i
$326$	21.7654	+	4.62639i	1.20548	+	0.256232i
$327$	−20.0855	+	4.26930i	−1.11073	+	0.236093i
$328$	13.4593	+	9.77878i	0.743167	+	0.539943i
$329$	−8.46027	+	22.6206i	−0.466430	+	1.24711i
$330$	−0.819184	−	2.46471i	−0.0450946	−	0.135678i
$331$	−0.656522	−	1.13713i	−0.0360857	−	0.0625023i	0.847418	−	0.530926i	$-0.178156\pi$
$331$	−0.656522	−	1.13713i	−0.0360857	−	0.0625023i	−0.883504	+	0.468423i	$0.844822\pi$
$332$	−7.03604	+	3.13265i	−0.386153	+	0.171926i
$333$	1.11708	+	1.24064i	0.0612156	+	0.0679868i
$334$	−4.66984	+	5.18638i	−0.255522	+	0.283786i
$335$	−3.27043	+	2.37611i	−0.178683	+	0.129821i
$336$	4.93782	+	1.27757i	0.269380	+	0.0696974i
$337$	1.03602	+	3.18854i	0.0564356	+	0.173691i	0.975301	−	0.220881i	$-0.0708931\pi$
$337$	1.03602	+	3.18854i	0.0564356	+	0.173691i	−0.918865	+	0.394571i	$0.870893\pi$
$338$	0.195473	−	0.0415490i	0.0106323	−	0.00225997i
$339$	10.4467	−	4.65117i	0.567386	−	0.252617i
$340$	0.984796	−	1.70572i	0.0534081	−	0.0925055i
$341$	3.27672	+	5.58838i	0.177444	+	0.302628i
$342$	−7.23023			−0.390966
$343$	18.3610	+	2.42330i	0.991403	+	0.130846i
$344$	−11.6011	+	35.7046i	−0.625491	+	1.92506i
$345$	−2.60642	+	2.89472i	−0.140325	+	0.155847i
$346$	−2.70387	−	25.7256i	−0.145361	−	1.38302i
$347$	−3.32950	−	31.6781i	−0.178737	−	1.70057i	−0.605209	−	0.796067i	$-0.706910\pi$
$347$	−3.32950	−	31.6781i	−0.178737	−	1.70057i	0.426472	−	0.904501i	$-0.359756\pi$
$348$	1.84468	−	2.04872i	0.0988851	−	0.109823i
$349$	−2.20110	+	6.77428i	−0.117822	+	0.362619i	−0.992525	−	0.122040i	$-0.961056\pi$
$349$	−2.20110	+	6.77428i	−0.117822	+	0.362619i	0.874703	+	0.484659i	$0.161056\pi$
$350$	0.811793	+	13.2962i	0.0433922	+	0.710710i
$351$	−3.58065			−0.191121
$352$	12.1422	+	5.30860i	0.647184	+	0.282950i
$353$	4.80505	−	8.32260i	0.255747	−	0.442967i	−0.709351	−	0.704855i	$-0.751012\pi$
$353$	4.80505	−	8.32260i	0.255747	−	0.442967i	0.965098	+	0.261888i	$0.0843452\pi$
$354$	−8.49993	+	3.78441i	−0.451766	+	0.201139i
$355$	1.05843	−	0.224975i	0.0561754	−	0.0119405i
$356$	3.09638	+	9.52967i	0.164108	+	0.505071i
$357$	−2.63718	−	9.51334i	−0.139574	−	0.503499i
$358$	1.32878	−	0.965415i	0.0702282	−	0.0510238i
$359$	−8.53234	+	9.47613i	−0.450320	+	0.500131i	−0.924968	−	0.380045i	$-0.875909\pi$
$359$	−8.53234	+	9.47613i	−0.450320	+	0.500131i	0.474648	+	0.880176i	$0.342575\pi$
$360$	1.44246	+	1.60202i	0.0760244	+	0.0844337i
$361$	20.9331	−	9.32000i	1.10174	−	0.490526i
$362$	−10.3164	−	17.8686i	−0.542219	−	0.939152i
$363$	−8.98527	−	6.34546i	−0.471604	−	0.333050i
$364$	−7.03375	+	1.17627i	−0.368669	+	0.0616532i
$365$	8.35971	+	6.07369i	0.437567	+	0.317911i
$366$	3.54067	−	0.752592i	0.185074	−	0.0393386i
$367$	20.7073	+	4.40148i	1.08091	+	0.229755i	0.713750	−	0.700401i	$-0.246995\pi$
$367$	20.7073	+	4.40148i	1.08091	+	0.229755i	0.367164	+	0.930156i	$0.380329\pi$
$368$	1.11937	+	10.6501i	0.0583513	+	0.555176i
$369$	4.94371	+	2.20108i	0.257359	+	0.114584i
$370$	−0.403997	−	1.24338i	−0.0210028	−	0.0646400i
$371$	2.93684	−	19.6364i	0.152473	−	1.01947i
$372$	−1.18954	−	0.864254i	−0.0616749	−	0.0448095i
$373$	−9.74084	−	16.8716i	−0.504362	−	0.873580i	−0.999987	−	0.00504375i	$-0.998395\pi$
$373$	−9.74084	−	16.8716i	−0.504362	−	0.873580i	0.495626	−	0.868536i	$-0.334939\pi$
$374$	1.53698	+	13.7349i	0.0794753	+	0.710217i
$375$	−3.33367	+	5.77409i	−0.172150	+	0.298173i
$376$	−2.93334	+	27.9089i	−0.151275	+	1.43929i
$377$	4.05218	−	12.4713i	0.208698	−	0.642306i
$378$	2.95193	+	0.129202i	0.151831	+	0.00664543i
$379$	4.29651	−	3.12160i	0.220697	−	0.160346i	−0.471943	−	0.881629i	$-0.656447\pi$
$379$	4.29651	−	3.12160i	0.220697	−	0.160346i	0.692640	+	0.721283i	$0.256447\pi$
$380$	−3.12195	−	1.38998i	−0.160153	−	0.0713045i
$381$	−4.49277	−	0.954967i	−0.230171	−	0.0489245i
$382$	17.3500	+	19.2692i	0.887705	+	0.985897i
$383$	−2.03161	+	19.3294i	−0.103810	+	0.987689i	0.811340	+	0.584575i	$0.198739\pi$
$383$	−2.03161	+	19.3294i	−0.103810	+	0.987689i	−0.915150	+	0.403114i	$0.867928\pi$
$384$	1.29805			0.0662406
$385$	−3.94518	−	4.72192i	−0.201065	−	0.240651i
$386$	−25.9758			−1.32214
$387$	−1.27647	+	12.1448i	−0.0648864	+	0.617353i
$388$	−1.60592	−	1.78356i	−0.0815284	−	0.0905464i
$389$	−35.6107	−	7.56928i	−1.80553	−	0.383778i	−0.822729	−	0.568434i	$-0.807550\pi$
$389$	−35.6107	−	7.56928i	−1.80553	−	0.383778i	−0.982803	+	0.184656i	$0.940883\pi$
$390$	2.56162	+	1.14051i	0.129713	+	0.0577518i
$391$	16.7688	−	12.1832i	0.848033	−	0.616132i
$392$	21.3601	−	2.61803i	1.07885	−	0.132230i
$393$	1.43722	−	4.42330i	0.0724981	−	0.223126i
$394$	−1.19976	+	11.4149i	−0.0604430	+	0.575077i
$395$	−1.78257	+	3.08751i	−0.0896910	+	0.155349i
$396$	2.44555	+	0.502666i	0.122893	+	0.0252599i
$397$	6.79814	+	11.7747i	0.341189	+	0.590956i	0.984654	−	0.174519i	$-0.0558371\pi$
$397$	6.79814	+	11.7747i	0.341189	+	0.590956i	−0.643465	+	0.765476i	$0.722504\pi$
$398$	−12.4715	−	9.06107i	−0.625140	−	0.454190i
$399$	−15.9377	+	6.27604i	−0.797882	+	0.314195i
$400$	2.68567	+	8.26564i	0.134283	+	0.413282i
$401$	23.5530	+	10.4865i	1.17618	+	0.523669i	0.899341	−	0.437247i	$-0.144046\pi$
$401$	23.5530	+	10.4865i	1.17618	+	0.523669i	0.276839	+	0.960916i	$0.410713\pi$
$402$	0.672983	+	6.40301i	0.0335654	+	0.319353i
$403$	−6.84106	−	1.45411i	−0.340778	−	0.0724345i
$404$	5.26773	−	1.11969i	0.262079	−	0.0557067i
$405$	0.567294	+	0.412163i	0.0281891	+	0.0204805i
$406$	−3.79067	+	10.1353i	−0.188128	+	0.503005i
$407$	−4.50124	−	3.22436i	−0.223118	−	0.159825i
$408$	−5.73553	−	9.93423i	−0.283951	−	0.491818i
$409$	2.28069	−	1.01543i	0.112773	−	0.0502096i	−0.349575	−	0.936908i	$-0.613674\pi$
$409$	2.28069	−	1.01543i	0.112773	−	0.0502096i	0.462347	+	0.886699i	$0.347007\pi$
$410$	−2.83567	−	3.14934i	−0.140044	−	0.155535i
$411$	−2.43225	+	2.70128i	−0.119974	+	0.133244i
$412$	−2.77472	+	2.01595i	−0.136701	+	0.0993188i
$413$	−15.4515	+	15.7202i	−0.760320	+	0.773541i
$414$	1.91707	+	5.90013i	0.0942188	+	0.289976i
$415$	7.01759	−	1.49163i	0.344480	−	0.0732214i
$416$	−13.0700	+	5.81916i	−0.640812	+	0.285308i
$417$	−3.48017	+	6.02784i	−0.170425	+	0.295184i
$418$	23.4219	−	5.14322i	1.14560	−	0.251563i
$419$	−10.1903			−0.497831			−0.248915	−	0.968525i	$-0.580074\pi$
$419$	−10.1903			−0.497831			−0.248915	+	0.968525i	$0.580074\pi$
$420$	1.24978	+	0.623284i	0.0609829	+	0.0304131i
$421$	−8.82469	+	27.1596i	−0.430089	+	1.32368i	0.467947	+	0.883757i	$0.344994\pi$
$421$	−8.82469	+	27.1596i	−0.430089	+	1.32368i	−0.898036	+	0.439922i	$0.855006\pi$
$422$	9.73239	−	10.8089i	0.473766	−	0.526170i
$423$	0.954156	+	9.07819i	0.0463927	+	0.441397i
$424$	−2.41154	−	22.9443i	−0.117115	−	1.11427i
$425$	11.2560	−	12.5011i	0.545996	−	0.606390i
$426$	0.532550	−	1.63902i	0.0258021	−	0.0794108i
$427$	7.15147	−	4.73235i	0.346084	−	0.229014i
$428$	−4.40077			−0.212719
$429$	11.5993	−	2.54709i	0.560020	−	0.122975i
$430$	4.78153	−	8.28186i	0.230586	−	0.399387i
$431$	−2.62891	+	1.17047i	−0.126630	+	0.0563794i	−0.469074	−	0.883159i	$-0.655412\pi$
$431$	−2.62891	+	1.17047i	−0.126630	+	0.0563794i	0.342443	+	0.939538i	$0.388745\pi$
$432$	1.88565	−	0.400808i	0.0907235	−	0.0192839i
$433$	−8.03123	−	24.7176i	−0.385956	−	1.18785i	−0.935784	−	0.352574i	$-0.885307\pi$
$433$	−8.03123	−	24.7176i	−0.385956	−	1.18785i	0.549828	−	0.835278i	$-0.314693\pi$
$434$	5.58738	+	1.44564i	0.268203	+	0.0693927i
$435$	−2.07755	+	1.50943i	−0.0996110	+	0.0723716i
$436$	−10.3432	+	11.4873i	−0.495349	+	0.550140i
$437$	−24.0643	−	26.7261i	−1.15115	−	1.27849i
$438$	15.0344	−	6.69374i	0.718371	−	0.319839i
$439$	−10.2932	−	17.8283i	−0.491267	−	0.850899i	0.508683	−	0.860954i	$-0.330133\pi$
$439$	−10.2932	−	17.8283i	−0.491267	−	0.850899i	−0.999949	+	0.0100552i	$0.996799\pi$
$440$	−5.81236	−	4.16355i	−0.277094	−	0.198489i
$441$	6.61912	−	2.27755i	0.315196	−	0.108455i
$442$	−12.0713	−	8.77028i	−0.574171	−	0.417160i
$443$	12.4675	−	2.65004i	0.592347	−	0.125907i	0.0980220	−	0.995184i	$-0.468748\pi$
$443$	12.4675	−	2.65004i	0.592347	−	0.125907i	0.494325	+	0.869277i	$0.335415\pi$
$444$	1.22926	+	0.261287i	0.0583380	+	0.0124001i
$445$	−0.975643	−	9.28262i	−0.0462499	−	0.440039i
$446$	3.09376	+	1.37743i	0.146494	+	0.0652233i
$447$	−3.40221	−	10.4709i	−0.160919	−	0.495258i
$448$	20.4765	−	8.06337i	0.967424	−	0.380958i
$449$	6.71321	+	4.87743i	0.316816	+	0.230180i	0.734816	−	0.678267i	$-0.237269\pi$
$449$	6.71321	+	4.87743i	0.316816	+	0.230180i	−0.418000	+	0.908447i	$0.637269\pi$
$450$	2.51742	+	4.36029i	0.118672	+	0.205546i
$451$	−17.5806	−	3.61358i	−0.827838	−	0.170157i
$452$	4.30412	−	7.45495i	0.202449	−	0.350651i
$453$	0.255696	−	2.43278i	0.0120136	−	0.114302i
$454$	−3.06684	+	9.43875i	−0.143934	+	0.442983i
$455$	6.63660	+	0.290475i	0.311129	+	0.0136177i
$456$	−16.1020	+	11.6988i	−0.754047	+	0.547847i
$457$	2.48960	+	1.10844i	0.116459	+	0.0518508i	0.464139	−	0.885762i	$-0.346364\pi$
$457$	2.48960	+	1.10844i	0.116459	+	0.0518508i	−0.347680	+	0.937613i	$0.613031\pi$
$458$	10.7627	+	2.28768i	0.502908	+	0.106896i
$459$	−2.49673	−	2.77290i	−0.116537	−	0.129428i
$460$	−0.306502	+	2.91617i	−0.0142907	+	0.135967i
$461$	−1.65195			−0.0769390			−0.0384695	−	0.999260i	$-0.512248\pi$
$461$	−1.65195			−0.0769390			−0.0384695	+	0.999260i	$0.512248\pi$
$462$	−9.65451	+	1.68131i	−0.449168	+	0.0782215i
$463$	6.81764			0.316842			0.158421	−	0.987372i	$-0.449360\pi$
$463$	6.81764			0.316842			0.158421	+	0.987372i	$0.449360\pi$
$464$	−0.737965	+	7.02127i	−0.0342592	+	0.325954i
$465$	0.916470	+	1.01784i	0.0425003	+	0.0472014i
$466$	−21.1525	−	4.49610i	−0.979869	−	0.208278i
$467$	−31.1319	−	13.8608i	−1.44061	−	0.641403i	−0.470136	−	0.882594i	$-0.655795\pi$
$467$	−31.1319	−	13.8608i	−1.44061	−	0.641403i	−0.970478	+	0.241191i	$0.922462\pi$
$468$	−2.18065	+	1.58433i	−0.100800	+	0.0732357i
$469$	7.04145	+	13.5301i	0.325144	+	0.624760i
$470$	2.20897	−	6.79851i	0.101892	−	0.313592i
$471$	1.10805	−	10.5424i	0.0510564	−	0.485770i
$472$	−12.8064	+	22.1813i	−0.589461	+	1.02098i
$473$	−4.50412	−	40.2502i	−0.207100	−	1.85071i
$474$	2.83903	+	4.91734i	0.130401	+	0.225861i
$475$	−23.6130	−	17.1558i	−1.08344	−	0.787163i
$476$	−5.81543	−	4.62683i	−0.266550	−	0.212070i
$477$	−2.31899	−	7.13713i	−0.106179	−	0.326787i
$478$	−10.0486	−	4.47394i	−0.459614	−	0.204633i
$479$	−2.21260	−	21.0514i	−0.101096	−	0.961865i	−0.921052	−	0.389439i	$-0.872669\pi$
$479$	−2.21260	−	21.0514i	−0.101096	−	0.961865i	0.819956	−	0.572426i	$-0.193998\pi$
$480$	2.74056	+	0.582525i	0.125089	+	0.0265885i
$481$	5.84709	−	1.24284i	0.266604	−	0.0566685i
$482$	16.3150	+	11.8536i	0.743130	+	0.539916i
$483$	9.34729	+	11.3417i	0.425317	+	0.516063i
$484$	−8.27978	+	0.111279i	−0.376354	+	0.00505812i
$485$	1.11781	+	1.93611i	0.0507572	+	0.0879141i
$486$	1.02024	−	0.454240i	0.0462790	−	0.0206048i
$487$	2.05993	+	2.28778i	0.0933443	+	0.103669i	0.788007	−	0.615666i	$-0.211113\pi$
$487$	2.05993	+	2.28778i	0.0933443	+	0.103669i	−0.694663	+	0.719336i	$0.744446\pi$
$488$	6.66749	−	7.40500i	0.301823	−	0.335209i
$489$	16.1194	−	11.7114i	0.728943	−	0.529608i
$490$	−5.46081	−	0.478942i	−0.246694	−	0.0216364i
$491$	−5.20970	−	16.0338i	−0.235110	−	0.723596i	−0.997107	−	0.0760142i	$-0.975781\pi$
$491$	−5.20970	−	16.0338i	−0.235110	−	0.723596i	0.761996	−	0.647581i	$-0.224219\pi$
$492$	3.98467	−	0.846968i	0.179643	−	0.0381843i
$493$	12.4835	−	5.55799i	0.562226	−	0.250319i
$494$	−12.9445	+	22.4205i	−0.582399	+	1.00875i
$495$	−2.13091	−	0.931635i	−0.0957771	−	0.0418739i
$496$	3.76543			0.169073
$497$	−0.248809	−	4.07518i	−0.0111606	−	0.182797i
$498$	3.53092	−	10.8671i	0.158224	−	0.486964i
$499$	23.1104	−	25.6668i	1.03457	−	1.14900i	0.0458881	−	0.998947i	$-0.485388\pi$
$499$	23.1104	−	25.6668i	1.03457	−	1.14900i	0.988678	−	0.150055i	$-0.0479451\pi$
$500$	0.524630	+	4.99152i	0.0234622	+	0.223228i
$501$	0.653210	+	6.21488i	0.0291833	+	0.277660i
$502$	−0.111482	+	0.123814i	−0.00497570	+	0.00552608i
$503$	−9.04217	+	27.8289i	−0.403170	+	1.24083i	0.519243	+	0.854627i	$0.326214\pi$
$503$	−9.04217	+	27.8289i	−0.403170	+	1.24083i	−0.922413	+	0.386204i	$0.873786\pi$
$504$	6.78312	−	4.48860i	0.302144	−	0.199938i
$505$	−5.01654			−0.223233
$506$	−10.4073	−	17.7494i	−0.462660	−	0.789058i
$507$	0.0894704	−	0.154967i	0.00397352	−	0.00688234i
$508$	−3.15868	+	1.40633i	−0.140144	+	0.0623960i
$509$	27.6594	−	5.87918i	1.22598	−	0.260590i	0.450970	−	0.892539i	$-0.351078\pi$
$509$	27.6594	−	5.87918i	1.22598	−	0.260590i	0.775010	+	0.631949i	$0.217745\pi$
$510$	0.902954	+	2.77901i	0.0399835	+	0.123056i
$511$	27.3301	−	27.8054i	1.20901	−	1.23004i
$512$	15.8209	−	11.4946i	0.699193	−	0.507993i
$513$	−4.33202	+	4.81120i	−0.191264	+	0.212420i
$514$	16.1092	+	17.8911i	0.710548	+	0.789143i
$515$	2.91861	−	1.29945i	0.128609	−	0.0572606i
$516$	4.59632	+	7.96105i	0.202342	+	0.350466i
$517$	−9.54869	−	28.7295i	−0.419951	−	1.26352i
$518$	−4.86525	+	0.813626i	−0.213767	+	0.0357487i
$519$	−18.7386	−	13.6144i	−0.822532	−	0.597604i
$520$	7.55022	−	1.60485i	0.331099	−	0.0703773i
$521$	14.1659	+	3.01106i	0.620620	+	0.131917i	0.507482	−	0.861663i	$-0.330576\pi$
$521$	14.1659	+	3.01106i	0.620620	+	0.131917i	0.113138	+	0.993579i	$0.463910\pi$
$522$	0.427515	+	4.06753i	0.0187118	+	0.178031i
$523$	26.3960	+	11.7522i	1.15422	+	0.513890i	0.892408	−	0.451230i	$-0.149015\pi$
$523$	26.3960	+	11.7522i	1.15422	+	0.513890i	0.261808	+	0.965120i	$0.415681\pi$
$524$	−1.08190	−	3.32975i	−0.0472631	−	0.145461i
$525$	9.33403	+	7.42626i	0.407370	+	0.324108i
$526$	−14.1229	−	10.2609i	−0.615787	−	0.447395i
$527$	−3.64408	−	6.31173i	−0.158739	−	0.274943i
$528$	−5.82335	+	2.63975i	−0.253429	+	0.114880i
$529$	−3.92893	+	6.80511i	−0.170823	+	0.295874i
$530$	−0.614292	+	5.84460i	−0.0266831	+	0.253873i
$531$	−2.57451	+	7.92354i	−0.111724	+	0.343852i
$532$	−6.92922	+	10.8741i	−0.300420	+	0.471453i
$533$	15.6763	−	11.3895i	0.679014	−	0.493333i
$534$	−13.5803	−	6.04633i	−0.587676	−	0.261650i
$535$	4.00976	+	0.852300i	0.173357	+	0.0368481i
$536$	11.8591	+	13.1709i	0.512235	+	0.568894i
$537$	0.153730	−	1.46264i	0.00663393	−	0.0631176i
$538$	−12.2519			−0.528216
$539$	−19.8221	+	12.0865i	−0.853799	+	0.520603i
$540$	0.527856			0.0227153
$541$	2.10050	−	19.9849i	0.0903076	−	0.859219i	−0.851791	−	0.523882i	$-0.824483\pi$
$541$	2.10050	−	19.9849i	0.0903076	−	0.859219i	0.942098	−	0.335337i	$-0.108850\pi$
$542$	5.49020	+	6.09749i	0.235824	+	0.261910i
$543$	−18.0714	−	3.84119i	−0.775517	−	0.164841i
$544$	−13.6200	−	6.06400i	−0.583951	−	0.259992i
$545$	11.6489	−	8.46344i	0.498985	−	0.362534i
$546$	5.68556	−	8.92242i	0.243319	−	0.381844i
$547$	−0.352528	+	1.08497i	−0.0150730	+	0.0463900i	−0.958310	−	0.285730i	$-0.907764\pi$
$547$	−0.352528	+	1.08497i	−0.0150730	+	0.0463900i	0.943237	+	0.332120i	$0.107764\pi$
$548$	−0.286020	+	2.72130i	−0.0122182	+	0.116248i
$549$	1.62061	−	2.80698i	0.0691660	−	0.119799i
$550$	−11.2567	−	12.3342i	−0.479988	−	0.525930i
$551$	−11.8548	−	20.5331i	−0.505031	−	0.874740i
$552$	13.8160	+	10.0379i	0.588050	+	0.427243i
$553$	10.5265	+	8.37499i	0.447632	+	0.356141i
$554$	5.66304	+	17.4290i	0.240600	+	0.740489i
$555$	−1.06943	−	0.476143i	−0.0453949	−	0.0202111i
$556$	0.547685	+	5.21087i	0.0232270	+	0.220990i
$557$	31.3974	+	6.67372i	1.33035	+	0.282774i	0.817611	−	0.575771i	$-0.195298\pi$
$557$	31.3974	+	6.67372i	1.33035	+	0.282774i	0.512738	+	0.858545i	$0.328631\pi$
$558$	2.13370	−	0.453533i	0.0903269	−	0.0191996i
$559$	35.3748	+	25.7013i	1.49620	+	1.08705i
$560$	−3.52750	+	0.589911i	−0.149064	+	0.0249283i
$561$	10.0605	+	7.20660i	0.424755	+	0.304263i
$562$	−5.45483	−	9.44805i	−0.230098	−	0.398542i
$563$	−20.4569	+	9.10802i	−0.862157	+	0.383857i	−0.789684	−	0.613513i	$-0.789756\pi$
$563$	−20.4569	+	9.10802i	−0.862157	+	0.383857i	−0.0724727	+	0.997370i	$0.523089\pi$
$564$	4.59792	+	5.10650i	0.193607	+	0.215023i
$565$	−5.36549	+	5.95899i	−0.225728	+	0.250696i
$566$	24.1740	−	17.5635i	1.01611	−	0.738248i
$567$	1.85463	−	1.88688i	0.0778873	−	0.0792417i
$568$	−1.46599	−	4.51186i	−0.0615116	−	0.189313i
$569$	−8.46161	+	1.79857i	−0.354729	+	0.0754000i	−0.381830	−	0.924233i	$-0.624706\pi$
$569$	−8.46161	+	1.79857i	−0.354729	+	0.0754000i	0.0271005	+	0.999633i	$0.491373\pi$
$570$	4.63162	−	2.06213i	0.193997	−	0.0863731i
$571$	−23.3636	+	40.4670i	−0.977736	+	1.69349i	−0.307144	+	0.951663i	$0.599373\pi$
$571$	−23.3636	+	40.4670i	−0.977736	+	1.69349i	−0.670592	+	0.741826i	$0.733960\pi$
$572$	5.93706	−	6.68355i	0.248241	−	0.279453i
$573$	23.2176			0.969929
$574$	−13.3347	+	8.82395i	−0.556578	+	0.368305i
$575$	−7.73888	+	23.8178i	−0.322734	+	0.993272i
$576$	5.56572	−	6.18136i	0.231905	−	0.257557i
$577$	−1.18857	−	11.3084i	−0.0494806	−	0.470777i	−0.991004	−	0.133830i	$-0.957272\pi$
$577$	−1.18857	−	11.3084i	−0.0494806	−	0.470777i	0.941524	−	0.336947i	$-0.109394\pi$
$578$	0.359242	+	3.41796i	0.0149425	+	0.142168i
$579$	−15.5635	+	17.2850i	−0.646798	+	0.718342i
$580$	−0.597368	+	1.83851i	−0.0248044	+	0.0763400i
$581$	−1.64966	−	27.0193i	−0.0684392	−	1.12095i
$582$	3.56058			0.147591
$583$	12.5892	+	21.4707i	0.521393	+	0.889226i
$584$	22.6515	−	39.2335i	0.937325	−	1.62349i
$585$	2.29373	−	1.02123i	0.0948341	−	0.0422229i
$586$	−8.90336	+	1.89247i	−0.367795	+	0.0781771i
$587$	−2.56089	−	7.88162i	−0.105699	−	0.325309i	0.884195	−	0.467119i	$-0.154708\pi$
$587$	−2.56089	−	7.88162i	−0.105699	−	0.325309i	−0.989894	+	0.141810i	$0.954708\pi$
$588$	3.02335	−	4.31581i	0.124681	−	0.177981i
$589$	−10.2305	+	7.43286i	−0.421539	+	0.306266i
$590$	4.36563	−	4.84852i	0.179730	−	0.199610i
$591$	6.87698	+	7.63766i	0.282881	+	0.314171i
$592$	−2.94009	+	1.30901i	−0.120837	+	0.0538001i
$593$	3.34659	+	5.79646i	0.137428	+	0.238032i	0.926522	−	0.376240i	$-0.122783\pi$
$593$	3.34659	+	5.79646i	0.137428	+	0.238032i	−0.789094	+	0.614272i	$0.789450\pi$
$594$	−2.98189	+	2.19723i	−0.122348	+	0.0901535i
$595$	4.40265	+	5.34201i	0.180491	+	0.219001i
$596$	−6.70505	−	4.87151i	−0.274650	−	0.199545i
$597$	−13.5018	+	2.86990i	−0.552593	+	0.117457i
$598$	21.7281	+	4.61845i	0.888528	+	0.188862i
$599$	−3.61343	−	34.3795i	−0.147641	−	1.40471i	−0.777931	−	0.628349i	$-0.783731\pi$
$599$	−3.61343	−	34.3795i	−0.147641	−	1.40471i	0.630291	−	0.776359i	$-0.282936\pi$
$600$	12.6615	+	5.63727i	0.516905	+	0.230141i
$601$	0.373342	+	1.14903i	0.0152289	+	0.0468698i	0.958382	−	0.285488i	$-0.0921558\pi$
$601$	0.373342	+	1.14903i	0.0152289	+	0.0468698i	−0.943153	+	0.332358i	$0.892156\pi$
$602$	−28.2360	−	22.4649i	−1.15081	−	0.915600i
$603$	4.66396	+	3.38857i	0.189931	+	0.137993i
$604$	−0.920714	−	1.59472i	−0.0374633	−	0.0648884i
$605$	7.56566	+	1.50216i	0.307588	+	0.0610715i
$606$	−3.99481	+	6.91921i	−0.162278	+	0.281074i
$607$	−2.11930	+	20.1638i	−0.0860199	+	0.818424i	0.863422	+	0.504482i	$0.168317\pi$
$607$	−2.11930	+	20.1638i	−0.0860199	+	0.818424i	−0.949442	+	0.313942i	$0.898350\pi$
$608$	−7.99369	+	24.6021i	−0.324187	+	0.997745i
$609$	4.47310	+	8.59501i	0.181259	+	0.348287i
$610$	−2.05347	+	1.49194i	−0.0831427	+	0.0604067i
$611$	29.8591	+	13.2941i	1.20797	+	0.537823i
$612$	−2.74745	−	0.583989i	−0.111059	−	0.0236064i
$613$	5.51243	+	6.12217i	0.222645	+	0.247272i	0.844111	−	0.536169i	$-0.180129\pi$
$613$	5.51243	+	6.12217i	0.222645	+	0.247272i	−0.621466	+	0.783441i	$0.713462\pi$
$614$	−3.07516	+	29.2582i	−0.124103	+	1.18076i
$615$	−3.79466			−0.153016
$616$	−18.7806	+	19.3657i	−0.756691	+	0.780267i
$617$	1.43589			0.0578068			0.0289034	−	0.999582i	$-0.490798\pi$
$617$	1.43589			0.0578068			0.0289034	+	0.999582i	$0.490798\pi$
$618$	0.531867	−	5.06037i	0.0213948	−	0.203558i
$619$	25.6317	+	28.4668i	1.03022	+	1.14418i	0.989430	+	0.145011i	$0.0463218\pi$
$619$	25.6317	+	28.4668i	1.03022	+	1.14418i	0.0407933	+	0.999168i	$0.487011\pi$
$620$	1.00850	+	0.214364i	0.0405025	+	0.00860907i
$621$	5.07473	+	2.25942i	0.203642	+	0.0906672i
$622$	−12.5449	+	9.11443i	−0.503006	+	0.365455i
$623$	−35.1835	−	1.53994i	−1.40960	−	0.0616963i
$624$	2.13305	−	6.56486i	0.0853904	−	0.262805i
$625$	−1.86753	+	17.7684i	−0.0747013	+	0.710736i
$626$	3.63864	−	6.30232i	0.145429	−	0.251891i
$627$	10.6109	−	18.6672i	0.423759	−	0.745495i
$628$	−3.98990	−	6.91071i	−0.159214	−	0.275767i
$629$	5.03955	+	3.66145i	0.200940	+	0.145991i
$630$	−1.92783	+	0.759152i	−0.0768065	+	0.0302453i
$631$	−1.02994	−	3.16983i	−0.0410013	−	0.126189i	0.928461	−	0.371431i	$-0.121133\pi$
$631$	−1.02994	−	3.16983i	−0.0410013	−	0.126189i	−0.969462	+	0.245242i	$0.921133\pi$
$632$	14.2791	+	6.35746i	0.567992	+	0.252886i
$633$	−1.36135	−	12.9524i	−0.0541090	−	0.514812i
$634$	−5.08174	−	1.08016i	−0.201822	−	0.0428985i
$635$	3.15039	−	0.669636i	0.125019	−	0.0265737i
$636$	−4.57026	−	3.32048i	−0.181222	−	0.131666i
$637$	4.78783	−	24.6030i	0.189701	−	0.974807i
$638$	−4.27834	−	12.8724i	−0.169381	−	0.509624i
$639$	−0.771571	−	1.33640i	−0.0305229	−	0.0528672i
$640$	−0.831516	+	0.370215i	−0.0328686	+	0.0146340i
$641$	26.4381	+	29.3625i	1.04424	+	1.15975i	0.986890	+	0.161394i	$0.0515991\pi$
$641$	26.4381	+	29.3625i	1.04424	+	1.15975i	0.0573521	+	0.998354i	$0.481734\pi$
$642$	4.36864	−	4.85187i	0.172417	−	0.191488i
$643$	−38.3893	+	27.8914i	−1.51392	+	1.09993i	−0.549526	+	0.835477i	$0.685192\pi$
$643$	−38.3893	+	27.8914i	−1.51392	+	1.09993i	−0.964398	+	0.264454i	$0.914808\pi$
$644$	10.7109	+	2.77126i	0.422069	+	0.109203i
$645$	−2.64611	−	8.14388i	−0.104190	−	0.320665i
$646$	−26.3887	+	5.60908i	−1.03825	+	0.220686i
$647$	−34.8363	+	15.5101i	−1.36956	+	0.609766i	−0.954001	−	0.299802i	$-0.903079\pi$
$647$	−34.8363	+	15.5101i	−1.36956	+	0.609766i	−0.415555	+	0.909568i	$0.636413\pi$
$648$	1.53714	−	2.66240i	0.0603845	−	0.104589i
$649$	2.70359	−	27.4992i	0.106125	−	1.07944i
$650$	18.0280			0.707116
$651$	4.30967	−	2.85184i	0.168909	−	0.111772i
$652$	4.63488	−	14.2647i	0.181516	−	0.558648i
$653$	−23.7518	+	26.3790i	−0.929480	+	1.03229i	0.0699168	+	0.997553i	$0.477727\pi$
$653$	−23.7518	+	26.3790i	−0.929480	+	1.03229i	−0.999396	+	0.0347389i	$0.988940\pi$
$654$	−2.39709	−	22.8068i	−0.0937337	−	0.891817i
$655$	0.340899	+	3.24343i	0.0133200	+	0.126731i
$656$	−6.98057	+	7.75271i	−0.272545	+	0.302692i
$657$	4.55371	−	14.0149i	0.177657	−	0.546773i
$658$	−24.1365	−	12.0372i	−0.940938	−	0.469261i
$659$	39.1773			1.52613			0.763065	−	0.646321i	$-0.223693\pi$
$659$	39.1773			1.52613			0.763065	+	0.646321i	$0.223693\pi$
$660$	−1.70996	+	0.375490i	−0.0665601	+	0.0146159i
$661$	−7.77398	+	13.4649i	−0.302373	+	0.523725i	−0.976673	−	0.214733i	$-0.931112\pi$
$661$	−7.77398	+	13.4649i	−0.302373	+	0.523725i	0.674300	+	0.738457i	$0.264445\pi$
$662$	1.33962	−	0.596438i	0.0520659	−	0.0231812i
$663$	−13.0685	+	2.77780i	−0.507540	+	0.107881i
$664$	−9.71983	−	29.9145i	−0.377202	−	1.16091i
$665$	8.41955	−	8.56595i	0.326496	−	0.332173i
$666$	−1.50835	+	1.09588i	−0.0584475	+	0.0424646i
$667$	−13.6125	+	15.1182i	−0.527078	+	0.585379i
$668$	3.14771	+	3.49589i	0.121789	+	0.135260i
$669$	2.77022	−	1.23338i	0.107103	−	0.0476853i
$670$	−2.25730	−	3.90977i	−0.0872073	−	0.151047i
$671$	−3.25313	+	10.2459i	−0.125586	+	0.395537i
$672$	3.70326	−	9.90157i	0.142856	−	0.381961i
$673$	−18.8644	−	13.7058i	−0.727171	−	0.528321i	0.161496	−	0.986873i	$-0.448368\pi$
$673$	−18.8644	−	13.7058i	−0.727171	−	0.528321i	−0.888667	+	0.458553i	$0.848368\pi$
$674$	−3.66237	+	0.778461i	−0.141069	+	0.0299852i
$675$	4.40978	+	0.937328i	0.169733	+	0.0360778i
$676$	−0.0140802	−	0.133964i	−0.000541547	−	0.00515248i
$677$	−28.9473	−	12.8882i	−1.11254	−	0.495333i	−0.233629	−	0.972326i	$-0.575060\pi$
$677$	−28.9473	−	12.8882i	−1.11254	−	0.495333i	−0.878907	+	0.476992i	$0.841727\pi$
$678$	3.94642	+	12.1458i	0.151561	+	0.466458i
$679$	7.84863	−	3.09068i	0.301203	−	0.118609i
$680$	6.50746	+	4.72795i	0.249550	+	0.181309i
$681$	4.44330	+	7.69603i	0.170268	+	0.294912i
$682$	−6.58939	+	2.98700i	−0.252321	+	0.114378i
$683$	−3.76735	+	6.52524i	−0.144154	+	0.249681i	−0.929057	−	0.369937i	$-0.879379\pi$
$683$	−3.76735	+	6.52524i	−0.144154	+	0.249681i	0.784903	+	0.619618i	$0.212713\pi$
$684$	−0.509425	+	4.84685i	−0.0194783	+	0.185324i
$685$	0.787643	−	2.42412i	0.0300943	−	0.0926207i
$686$	−4.83490	+	20.1102i	−0.184597	+	0.767813i
$687$	7.97081	−	5.79113i	0.304105	−	0.220946i
$688$	−21.5061	−	9.57514i	−0.819913	−	0.365049i
$689$	−26.2835	−	5.58674i	−1.00132	−	0.212838i
$690$	−2.91083	−	3.23280i	−0.110813	−	0.123071i
$691$	−2.97718	+	28.3260i	−0.113257	+	1.07757i	0.779305	+	0.626645i	$0.215572\pi$
$691$	−2.97718	+	28.3260i	−0.113257	+	1.07757i	−0.892562	+	0.450925i	$0.851094\pi$
$692$	−17.4359			−0.662813
$693$	−4.66575	+	7.43174i	−0.177237	+	0.282309i
$694$	35.5727			1.35032
$695$	0.510171	−	4.85395i	0.0193519	−	0.184121i
$696$	7.53352	+	8.36682i	0.285557	+	0.317144i
$697$	19.7509	+	4.19819i	0.748120	+	0.159018i
$698$	−7.26707	−	3.23551i	−0.275063	−	0.122466i
$699$	−15.6654	+	11.3816i	−0.592521	+	0.430491i
$700$	8.97040	+	0.392622i	0.339049	+	0.0148397i
$701$	8.37757	−	25.7835i	0.316416	−	0.973830i	−0.658751	−	0.752361i	$-0.728915\pi$
$701$	8.37757	−	25.7835i	0.316416	−	0.973830i	0.975167	−	0.221469i	$-0.0710851\pi$
$702$	0.417993	−	3.97694i	0.0157761	−	0.150100i
$703$	5.40410	−	9.36018i	0.203819	−	0.353026i
$704$	−13.6327	+	23.9833i	−0.513803	+	0.903906i
$705$	−3.20041	−	5.54327i	−0.120534	−	0.208771i
$706$	8.68277	+	6.30840i	0.326780	+	0.237420i
$707$	−2.79974	+	18.7197i	−0.105295	+	0.704027i
$708$	1.93803	+	5.96465i	0.0728357	+	0.224165i
$709$	−24.7291	−	11.0101i	−0.928722	−	0.413494i	−0.114089	−	0.993470i	$-0.536395\pi$
$709$	−24.7291	−	11.0101i	−0.928722	−	0.413494i	−0.814633	+	0.579977i	$0.803062\pi$
$710$	0.126317	+	1.20183i	0.00474061	+	0.0451039i
$711$	4.97315	+	1.05708i	0.186508	+	0.0396434i
$712$	−40.0271	+	8.50801i	−1.50008	+	0.318851i
$713$	8.77804	+	6.37762i	0.328740	+	0.238844i
$714$	10.8741	−	1.81849i	0.406952	−	0.0680554i
$715$	−6.70395	+	4.93987i	−0.250714	+	0.184741i
$716$	−0.553552	−	0.958781i	−0.0206872	−	0.0358313i
$717$	−8.99777	+	4.00606i	−0.336028	+	0.149609i
$718$	−9.52886	−	10.5829i	−0.355614	−	0.394949i
$719$	31.6114	−	35.1080i	1.17891	−	1.30931i	0.237753	−	0.971326i	$-0.423589\pi$
$719$	31.6114	−	35.1080i	1.17891	−	1.30931i	0.941153	−	0.337982i	$-0.109744\pi$
$720$	−1.09362	+	0.794559i	−0.0407567	+	0.0296115i
$721$	−3.22014	−	11.6163i	−0.119924	−	0.432614i
$722$	7.90783	+	24.3378i	0.294299	+	0.905759i
$723$	17.6629	−	3.75437i	0.656891	−	0.139627i
$724$	−12.7052	+	5.65673i	−0.472186	+	0.210231i
$725$	−8.25519	+	14.2984i	−0.306590	+	0.531029i
$726$	8.09665	−	9.23896i	0.300495	−	0.342890i
$727$	−33.2506			−1.23319			−0.616597	−	0.787279i	$-0.711489\pi$
$727$	−33.2506			−1.23319			−0.616597	+	0.787279i	$0.711489\pi$
$728$	−1.77486	−	29.0701i	−0.0657809	−	1.07741i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−7.72177	+	8.57589i	−0.285796	+	0.317408i
$731$	4.76288	+	45.3158i	0.176161	+	1.67606i
$732$	−0.255040	−	2.42654i	−0.00942656	−	0.0896877i
$733$	−20.0157	+	22.2297i	−0.739297	+	0.821072i	−0.989103	−	0.147224i	$-0.952966\pi$
$733$	−20.0157	+	22.2297i	−0.739297	+	0.821072i	0.249807	+	0.968296i	$0.419633\pi$
$734$	−7.30592	+	22.4853i	−0.269666	+	0.829947i
$735$	−3.59057	+	3.34681i	−0.132440	+	0.123449i
$736$	22.1957			0.818143
$737$	−17.5191	−	7.65936i	−0.645324	−	0.282136i
$738$	−3.02180	+	5.23391i	−0.111234	+	0.192663i
$739$	−4.02323	+	1.79126i	−0.147997	+	0.0658924i	−0.479398	−	0.877597i	$-0.659145\pi$
$739$	−4.02323	+	1.79126i	−0.147997	+	0.0658924i	0.331402	+	0.943490i	$0.392478\pi$
$740$	−0.861973	+	0.183218i	−0.0316867	+	0.00673522i
$741$	7.16348	+	22.0469i	0.263157	+	0.809915i
$742$	21.4669	+	5.55417i	0.788073	+	0.203900i
$743$	25.2372	−	18.3359i	0.925862	−	0.672678i	−0.0191142	−	0.999817i	$-0.506085\pi$
$743$	25.2372	−	18.3359i	0.925862	−	0.672678i	0.944976	+	0.327139i	$0.106085\pi$
$744$	4.01801	−	4.46245i	0.147307	−	0.163602i
$745$	5.16583	+	5.73724i	0.189261	+	0.210196i
$746$	19.8760	−	8.84937i	0.727712	−	0.323998i
$747$	−5.11568	−	8.86061i	−0.187173	−	0.324193i
$748$	9.31564	−	0.0625973i	0.340613	−	0.00228878i
$749$	5.41829	−	14.4871i	0.197980	−	0.529348i
$750$	−6.02397	−	4.37667i	−0.219964	−	0.159814i
$751$	−18.8460	+	4.00584i	−0.687701	+	0.146175i	−0.538492	−	0.842630i	$-0.681006\pi$
$751$	−18.8460	+	4.00584i	−0.687701	+	0.146175i	−0.149209	+	0.988806i	$0.547673\pi$
$752$	−17.2126	−	3.65865i	−0.627679	−	0.133417i
$753$	0.0155940	+	0.148367i	0.000568277	+	0.00540679i
$754$	13.3785	+	5.95651i	0.487217	+	0.216923i
$755$	0.530056	+	1.63135i	0.0192907	+	0.0593707i
$756$	0.294597	−	1.96975i	0.0107144	−	0.0716390i
$757$	10.3603	+	7.52718i	0.376551	+	0.273580i	0.759922	−	0.650014i	$-0.225237\pi$
$757$	10.3603	+	7.52718i	0.376551	+	0.273580i	−0.383371	+	0.923594i	$0.625237\pi$
$758$	2.96552	+	5.13643i	0.107712	+	0.186563i
$759$	−18.0465	−	3.70934i	−0.655048	−	0.134641i
$760$	6.97820	−	12.0866i	0.253126	−	0.438427i
$761$	0.995749	−	9.47392i	0.0360959	−	0.343429i	−0.961538	−	0.274673i	$-0.911430\pi$
$761$	0.995749	−	9.47392i	0.0360959	−	0.343429i	0.997633	−	0.0687561i	$-0.0219030\pi$
$762$	1.58513	−	4.87852i	0.0574231	−	0.176730i
$763$	−25.0809	−	48.1926i	−0.907989	−	1.74469i
$764$	14.1397	−	10.2731i	0.511557	−	0.371668i
$765$	2.39024	+	1.06420i	0.0864192	+	0.0384763i
$766$	−21.2316	−	4.51291i	−0.767127	−	0.163058i
$767$	19.9612	+	22.1691i	0.720756	+	0.800480i
$768$	1.58737	−	15.1028i	0.0572794	−	0.544977i
$769$	−28.4799			−1.02701			−0.513505	−	0.858087i	$-0.671653\pi$
$769$	−28.4799			−1.02701			−0.513505	+	0.858087i	$0.671653\pi$
$770$	5.70506	−	3.83058i	0.205596	−	0.138045i
$771$	21.5572			0.776362
$772$	−1.83019	+	17.4131i	−0.0658701	+	0.626712i
$773$	13.4121	+	14.8957i	0.482400	+	0.535760i	0.934385	−	0.356266i	$-0.115950\pi$
$773$	13.4121	+	14.8957i	0.482400	+	0.535760i	−0.451984	+	0.892026i	$0.649284\pi$
$774$	−13.3399	−	2.83547i	−0.479491	−	0.101919i
$775$	8.04452	+	3.58165i	0.288968	+	0.128657i
$776$	7.92956	−	5.76116i	0.284655	−	0.206814i
$777$	−2.37363	+	3.72496i	−0.0851533	+	0.133632i
$778$	12.5641	−	38.6682i	0.450444	−	1.38632i
$779$	3.66216	−	34.8431i	0.131211	−	1.24838i
$780$	0.945034	−	1.63685i	0.0338377	−	0.0586086i
$781$	3.45011	+	3.78033i	0.123454	+	0.135271i
$782$	11.5741	+	20.0469i	0.413888	+	0.716874i
$783$	2.96280	+	2.15260i	0.105882	+	0.0769275i
$784$	0.232609	+	13.4924i	0.00830747	+	0.481873i
$785$	2.29699	+	7.06941i	0.0819831	+	0.252318i
$786$	4.74507	+	2.11264i	0.169251	+	0.0753555i
$787$	−0.580266	−	5.52086i	−0.0206842	−	0.196797i	0.979300	−	0.202414i	$-0.0648787\pi$
$787$	−0.580266	−	5.52086i	−0.0206842	−	0.196797i	−0.999984	+	0.00561691i	$0.998212\pi$
$788$	7.56758	+	1.60854i	0.269584	+	0.0573018i
$789$	−15.2897	+	3.24992i	−0.544326	+	0.115700i
$790$	−3.22112	−	2.34028i	−0.114602	−	0.0832636i
$791$	19.2421	+	23.3476i	0.684169	+	0.830145i
$792$	−3.08558	+	9.71814i	−0.109641	+	0.345319i
$793$	−5.80284	−	10.0508i	−0.206065	−	0.356915i
$794$	−13.8715	+	6.17598i	−0.492280	+	0.219177i
$795$	3.52110	+	3.91058i	0.124881	+	0.138694i
$796$	−6.95288	+	7.72196i	−0.246438	+	0.273697i
$797$	−27.8522	+	20.2358i	−0.986575	+	0.716789i	−0.959168	−	0.282835i	$-0.908725\pi$
$797$	−27.8522	+	20.2358i	−0.986575	+	0.716789i	−0.0274070	+	0.999624i	$0.508725\pi$
$798$	−5.11013	−	18.4342i	−0.180897	−	0.652564i
$799$	10.5251	+	32.3930i	0.372353	+	1.14598i
$800$	17.6198	−	3.74521i	0.622956	−	0.132413i
$801$	−12.1601	+	5.41401i	−0.429655	+	0.191295i
$802$	−14.3965	+	24.9355i	−0.508360	+	0.880505i
$803$	−4.78202	+	48.6397i	−0.168754	+	1.71646i
$804$	4.33973			0.153051
$805$	−9.22253	−	4.59942i	−0.325052	−	0.162108i
$806$	2.41365	−	7.42844i	0.0850171	−	0.261656i
$807$	−7.34076	+	8.15274i	−0.258407	+	0.286990i
$808$	2.29896	+	21.8731i	0.0808771	+	0.769495i
$809$	1.07938	+	10.2697i	0.0379491	+	0.361062i	0.996974	+	0.0777390i	$0.0247701\pi$
$809$	1.07938	+	10.2697i	0.0379491	+	0.361062i	−0.959025	+	0.283323i	$0.908563\pi$
$810$	−0.524003	+	0.581964i	−0.0184116	+	0.0204481i
$811$	−11.4662	+	35.2894i	−0.402633	+	1.23918i	0.520222	+	0.854031i	$0.325849\pi$
$811$	−11.4662	+	35.2894i	−0.402633	+	1.23918i	−0.922855	+	0.385147i	$0.874151\pi$
$812$	6.52719	+	3.25521i	0.229060	+	0.114236i
$813$	7.34692			0.257668
$814$	4.10667	−	4.62302i	0.143939	−	0.162037i
$815$	−6.98572	+	12.0996i	−0.244699	+	0.423831i
$816$	6.57125	−	2.92571i	0.230040	−	0.102420i
$817$	77.3319	−	16.4374i	2.70550	−	0.575072i
$818$	0.861569	+	2.65164i	0.0301240	+	0.0927123i
$819$	−2.53070	−	9.12924i	−0.0884300	−	0.319001i
$820$	−2.31098	+	1.67903i	−0.0807029	+	0.0586341i
$821$	0.696613	−	0.773667i	0.0243119	−	0.0270012i	−0.730866	−	0.682521i	$-0.760884\pi$
$821$	0.696613	−	0.773667i	0.0243119	−	0.0270012i	0.755178	+	0.655520i	$0.227550\pi$
$822$	−2.71631	−	3.01677i	−0.0947423	−	0.105222i
$823$	38.5681	−	17.1716i	1.34440	−	0.598565i	0.396764	−	0.917921i	$-0.370133\pi$
$823$	38.5681	−	17.1716i	1.34440	−	0.598565i	0.947635	+	0.319355i	$0.103466\pi$
$824$	−7.00340	−	12.1302i	−0.243975	−	0.422577i
$825$	−14.9520	+	0.100471i	−0.520562	+	0.00349797i
$826$	−15.6563	−	18.9967i	−0.544751	−	0.660981i
$827$	−9.91212	−	7.20158i	−0.344678	−	0.250423i	0.401955	−	0.915659i	$-0.368331\pi$
$827$	−9.91212	−	7.20158i	−0.344678	−	0.250423i	−0.746633	+	0.665236i	$0.768331\pi$
$828$	4.09028	−	0.869415i	0.142147	−	0.0302143i
$829$	19.2059	+	4.08234i	0.667049	+	0.141786i	0.528976	−	0.848637i	$-0.322576\pi$
$829$	19.2059	+	4.08234i	0.667049	+	0.141786i	0.138072	+	0.990422i	$0.455909\pi$
$830$	0.837510	+	7.96838i	0.0290704	+	0.276586i
$831$	14.9908	+	6.67434i	0.520025	+	0.231530i
$832$	−9.20354	−	28.3256i	−0.319075	−	0.982013i
$833$	22.3914	−	13.4475i	0.775814	−	0.465929i
$834$	−6.28870	−	4.56901i	−0.217760	−	0.158212i
$835$	−2.19098	−	3.79489i	−0.0758220	−	0.131328i
$836$	−1.79755	−	16.0635i	−0.0621695	−	0.555567i
$837$	0.976624	−	1.69156i	0.0337571	−	0.0584689i
$838$	1.18959	−	11.3182i	0.0410936	−	0.390979i
$839$	8.43938	−	25.9738i	0.291360	−	0.896714i	−0.693060	−	0.720880i	$-0.743738\pi$
$839$	8.43938	−	25.9738i	0.291360	−	0.896714i	0.984420	−	0.175834i	$-0.0562621\pi$
$840$	−3.06501	+	4.80996i	−0.105753	+	0.165960i
$841$	12.6111	−	9.16250i	0.434865	−	0.315948i
$842$	−29.1353	−	12.9719i	−1.00407	−	0.447040i
$843$	−9.55528	−	2.03104i	−0.329101	−	0.0699526i
$844$	−6.56013	−	7.28577i	−0.225809	−	0.250786i
$845$	−0.0131158	+	0.124788i	−0.000451197	+	0.00429285i
$846$	−10.1943			−0.350487
$847$	9.82786	−	27.3937i	0.337689	−	0.941258i
$848$	14.4669			0.496794
$849$	2.79675	−	26.6093i	0.0959843	−	0.913229i
$850$	12.5706	+	13.9611i	0.431169	+	0.478861i
$851$	−9.07111	−	1.92812i	−0.310954	−	0.0660953i
$852$	−1.06121	−	0.472481i	−0.0363565	−	0.0161869i
$853$	19.7645	−	14.3598i	0.676725	−	0.491669i	−0.195545	−	0.980695i	$-0.562647\pi$
$853$	19.7645	−	14.3598i	0.676725	−	0.491669i	0.872270	+	0.489025i	$0.162647\pi$
$854$	4.42126	+	8.49539i	0.151292	+	0.290706i
$855$	1.40285	−	4.31754i	0.0479766	−	0.147657i
$856$	1.87863	−	17.8740i	0.0642102	−	0.610919i
$857$	−7.06172	+	12.2313i	−0.241224	+	0.417812i	−0.961063	−	0.276329i	$-0.910882\pi$
$857$	−7.06172	+	12.2313i	−0.241224	+	0.417812i	0.719839	+	0.694141i	$0.244215\pi$
$858$	1.47492	+	13.1804i	0.0503531	+	0.449971i
$859$	10.8367	+	18.7698i	0.369745	+	0.640417i	0.989526	−	0.144358i	$-0.0461117\pi$
$859$	10.8367	+	18.7698i	0.369745	+	0.640417i	−0.619780	+	0.784775i	$0.712778\pi$
$860$	−5.21492	−	3.78886i	−0.177827	−	0.129199i
$861$	−2.11781	+	14.1602i	−0.0721747	+	0.482577i
$862$	−0.993117	−	3.05650i	−0.0338257	−	0.104105i
$863$	−19.7227	−	8.78111i	−0.671369	−	0.298913i	0.0425980	−	0.999092i	$-0.486437\pi$
$863$	−19.7227	−	8.78111i	−0.671369	−	0.298913i	−0.713967	+	0.700180i	$0.753103\pi$
$864$	−0.417657	−	3.97374i	−0.0142090	−	0.135189i
$865$	15.8867	+	3.37682i	0.540164	+	0.114815i
$866$	28.3907	−	6.03464i	0.964756	−	0.205065i
$867$	2.48965	+	1.80884i	0.0845529	+	0.0614313i
$868$	1.36277	−	3.64369i	0.0462553	−	0.123675i
$869$	−16.8622	+	0.113307i	−0.572010	+	0.00384368i
$870$	−1.43396	−	2.48369i	−0.0486158	−	0.0842050i
$871$	18.8577	−	8.39600i	0.638970	−	0.284488i
$872$	−42.2408	−	46.9131i	−1.43045	−	1.58868i
$873$	2.13334	−	2.36931i	0.0722025	−	0.0801890i
$874$	32.4932	−	23.6077i	1.09910	−	0.798543i
$875$	−17.0778	−	4.41858i	−0.577335	−	0.149375i
$876$	−3.42792	−	10.5501i	−0.115819	−	0.356454i
$877$	−39.5424	+	8.40499i	−1.33525	+	0.283816i	−0.819578	−	0.572968i	$-0.805792\pi$
$877$	−39.5424	+	8.40499i	−1.33525	+	0.283816i	−0.515674	+	0.856785i	$0.672458\pi$
$878$	21.0030	−	9.35115i	0.708818	−	0.315586i
$879$	−4.07519	+	7.05843i	−0.137453	+	0.238075i
$880$	2.97750	−	3.35187i	0.100371	−	0.112992i
$881$	5.39527			0.181771			0.0908856	−	0.995861i	$-0.471030\pi$
$881$	5.39527			0.181771			0.0908856	+	0.995861i	$0.471030\pi$
$882$	1.75693	+	7.61756i	0.0591588	+	0.256497i
$883$	5.38285	−	16.5667i	0.181147	−	0.557514i	−0.818713	−	0.574202i	$-0.805312\pi$
$883$	5.38285	−	16.5667i	0.181147	−	0.557514i	0.999861	+	0.0166883i	$0.00531229\pi$
$884$	−6.72975	+	7.47414i	−0.226346	+	0.251383i
$885$	−0.610658	−	5.81002i	−0.0205270	−	0.195302i
$886$	1.48792	+	14.1567i	0.0499878	+	0.475602i
$887$	3.38568	−	3.76017i	0.113680	−	0.126254i	−0.683619	−	0.729839i	$-0.739595\pi$
$887$	3.38568	−	3.76017i	0.113680	−	0.126254i	0.797299	+	0.603585i	$0.206262\pi$
$888$	−1.58598	+	4.88116i	−0.0532221	+	0.163801i
$889$	−0.740576	−	12.1297i	−0.0248381	−	0.406818i
$890$	10.4239			0.349409
$891$	−0.324510	+	3.30071i	−0.0108715	+	0.110578i
$892$	1.14135	−	1.97688i	0.0382153	−	0.0661909i
$893$	53.9877	−	24.0369i	1.80663	−	0.804364i
$894$	12.0270	−	2.55641i	0.402242	−	0.0854991i
$895$	0.318681	+	0.980799i	0.0106523	+	0.0327845i
$896$	0.917423	+	3.30950i	0.0306489	+	0.110563i
$897$	16.0917	−	11.6913i	0.537287	−	0.390362i
$898$	−6.20091	+	6.88681i	−0.206927	+	0.229816i
$899$	4.78644	+	5.31587i	0.159637	+	0.177294i
$900$	3.10033	−	1.38036i	0.103344	−	0.0460119i
$901$	−14.0006	−	24.2498i	−0.466429	−	0.807879i
$902$	6.06580	−	19.1045i	0.201969	−	0.636110i
$903$	−31.8665	+	5.32910i	−1.06045	+	0.177341i
$904$	28.4413	+	20.6638i	0.945943	+	0.687268i
$905$	12.6719	−	2.69350i	0.421228	−	0.0895348i
$906$	2.67218	+	0.567990i	0.0887773	+	0.0188702i
$907$	4.13623	+	39.3536i	0.137341	+	1.30671i	0.818469	+	0.574550i	$0.194823\pi$
$907$	4.13623	+	39.3536i	0.137341	+	1.30671i	−0.681128	+	0.732164i	$0.738510\pi$
$908$	6.11127	+	2.72091i	0.202810	+	0.0902967i
$909$	2.21073	+	6.80393i	0.0733254	+	0.225672i
$910$	−1.09736	+	7.33719i	−0.0363770	+	0.243226i
$911$	−22.8923	−	16.6322i	−0.758455	−	0.551050i	0.139981	−	0.990154i	$-0.455296\pi$
$911$	−22.8923	−	16.6322i	−0.758455	−	0.551050i	−0.898436	+	0.439105i	$0.855296\pi$
$912$	−6.24032	−	10.8086i	−0.206638	−	0.357907i
$913$	22.8749	+	25.0644i	0.757049	+	0.829511i
$914$	−1.52175	+	2.63574i	−0.0503349	+	0.0871826i
$915$	−0.237571	+	2.26034i	−0.00785386	+	0.0747245i
$916$	2.29188	−	7.05369i	0.0757260	−	0.233061i
$917$	12.2934	+	0.538068i	0.405965	+	0.0177686i
$918$	3.37125	−	2.44935i	0.111268	−	0.0808407i
$919$	45.3825	+	20.2056i	1.49703	+	0.666522i	0.981694	−	0.190465i	$-0.0609996\pi$
$919$	45.3825	+	20.2056i	1.49703	+	0.666522i	0.515338	+	0.856987i	$0.327666\pi$
$920$	−11.7133	−	2.48975i	−0.386177	−	0.0820845i
$921$	17.6267	+	19.5764i	0.580820	+	0.645066i
$922$	0.192843	−	1.83478i	0.00635094	−	0.0604252i
$923$	−5.52545			−0.181872
$924$	0.446846	+	6.59045i	0.0147002	+	0.216810i
$925$	−7.52638			−0.247466
$926$	−0.795867	+	7.57217i	−0.0261538	+	0.248837i
$927$	−3.04865	−	3.38586i	−0.100131	−	0.111206i
$928$	14.3131	+	3.04234i	0.469850	+	0.0998698i
$929$	−31.3093	−	13.9398i	−1.02722	−	0.457349i	−0.177245	−	0.984167i	$-0.556718\pi$
$929$	−31.3093	−	13.9398i	−1.02722	−	0.457349i	−0.849978	+	0.526817i	$0.823385\pi$
$930$	−1.23748	+	0.899081i	−0.0405785	+	0.0294820i
$931$	−27.2657	−	36.1990i	−0.893598	−	1.18638i
$932$	−4.50435	+	13.8630i	−0.147545	+	0.454097i
$933$	−1.45135	+	13.8087i	−0.0475151	+	0.452076i
$934$	19.0291	−	32.9594i	0.622651	−	1.07846i
$935$	−8.50005	−	1.74713i	−0.277981	−	0.0571373i
$936$	−5.50396	−	9.53313i	−0.179902	−	0.311600i
$937$	−1.62912	−	1.18362i	−0.0532210	−	0.0386673i	0.560857	−	0.827913i	$-0.310472\pi$
$937$	−1.62912	−	1.18362i	−0.0532210	−	0.0386673i	−0.614078	+	0.789246i	$0.710472\pi$
$938$	−15.8495	+	6.24131i	−0.517504	+	0.203786i
$939$	−2.01363	−	6.19732i	−0.0657123	−	0.202242i
$940$	−4.40180	−	1.95981i	−0.143571	−	0.0639219i
$941$	1.47705	+	14.0532i	0.0481504	+	0.458120i	0.991859	+	0.127342i	$0.0406445\pi$
$941$	1.47705	+	14.0532i	0.0481504	+	0.458120i	−0.943709	+	0.330778i	$0.892689\pi$
$942$	11.5799	+	2.46137i	0.377292	+	0.0801959i
$943$	−29.4043	+	6.25007i	−0.957534	+	0.203530i
$944$	−12.9935	−	9.44037i	−0.422904	−	0.307258i
$945$	−0.649904	+	1.73768i	−0.0211414	+	0.0565267i
$946$	45.2307	−	0.303932i	1.47058	−	0.00988168i
$947$	10.6209	+	18.3960i	0.345134	+	0.597790i	0.985378	−	0.170382i	$-0.0545000\pi$
$947$	10.6209	+	18.3960i	0.345134	+	0.597790i	−0.640244	+	0.768172i	$0.721167\pi$
$948$	3.49641	−	1.55670i	0.113558	−	0.0505594i
$949$	−35.3066	−	39.2120i	−1.14610	−	1.27287i
$950$	21.8110	−	24.2236i	0.707643	−	0.785917i
$951$	−3.76351	+	2.73435i	−0.122040	+	0.0886674i
$952$	21.2746	−	21.6446i	0.689515	−	0.701504i
$953$	−16.9739	−	52.2403i	−0.549839	−	1.69223i	−0.709199	−	0.705009i	$-0.750943\pi$
$953$	−16.9739	−	52.2403i	−0.549839	−	1.69223i	0.159360	−	0.987221i	$-0.449057\pi$
$954$	8.19774	−	1.74248i	0.265412	−	0.0564150i
$955$	−14.8730	+	6.62187i	−0.481278	+	0.214279i
$956$	−3.70715	+	6.42097i	−0.119898	+	0.207669i
$957$	−11.1291	−	4.86563i	−0.359751	−	0.157284i
$958$	23.6396			0.763760
$959$	−8.60624	−	4.29207i	−0.277910	−	0.138598i
$960$	−1.80237	+	5.54712i	−0.0581712	+	0.179032i
$961$	−18.1902	+	20.2023i	−0.586781	+	0.651686i
$962$	0.697818	+	6.63930i	0.0224986	+	0.214059i
$963$	−0.611080	−	5.81403i	−0.0196918	−	0.187355i
$964$	9.09567	−	10.1018i	0.292952	−	0.325356i
$965$	5.03999	−	15.5115i	0.162243	−	0.499333i
$966$	−13.6881	+	9.05781i	−0.440406	+	0.291430i
$967$	−34.1710			−1.09887			−0.549433	−	0.835538i	$-0.685156\pi$
$967$	−34.1710			−1.09887			−0.549433	+	0.835538i	$0.685156\pi$
$968$	3.08256	−	33.6763i	0.0990773	−	1.08240i
$969$	−12.0784	+	20.9205i	−0.388015	+	0.672062i
$970$	−2.28087	+	1.01551i	−0.0732344	+	0.0326061i
$971$	−29.5663	+	6.28452i	−0.948829	+	0.201680i	−0.656235	−	0.754557i	$-0.727852\pi$
$971$	−29.5663	+	6.28452i	−0.948829	+	0.201680i	−0.292594	+	0.956237i	$0.594518\pi$
$972$	−0.232620	−	0.715932i	−0.00746130	−	0.0229635i
$973$	−17.8283	−	4.61275i	−0.571548	−	0.147878i
$974$	−2.78145	+	2.02084i	−0.0891234	+	0.0647519i
$975$	10.8015	−	11.9963i	0.345926	−	0.384190i
$976$	4.18097	+	4.64343i	0.133829	+	0.148633i
$977$	−20.7168	+	9.22371i	−0.662789	+	0.295093i	−0.710426	−	0.703772i	$-0.751498\pi$
$977$	−20.7168	+	9.22371i	−0.662789	+	0.295093i	0.0476370	+	0.998865i	$0.484831\pi$
$978$	11.1258	+	19.2705i	0.355765	+	0.616203i
$979$	35.5406	−	26.1884i	1.13588	−	0.836986i
$980$	−0.705818	+	3.62695i	−0.0225465	+	0.115859i
$981$	−16.6125	−	12.0697i	−0.530397	−	0.385356i
$982$	18.4165	−	3.91455i	0.587694	−	0.124918i
$983$	−38.3366	−	8.14870i	−1.22275	−	0.259903i	−0.449079	−	0.893492i	$-0.648248\pi$
$983$	−38.3366	−	8.14870i	−1.22275	−	0.259903i	−0.773670	+	0.633589i	$0.781581\pi$
$984$	1.73900	+	16.5455i	0.0554374	+	0.527452i
$985$	−6.58366	−	2.93124i	−0.209773	−	0.0933969i
$986$	4.71584	+	14.5139i	0.150183	+	0.462216i
$987$	−22.4714	+	8.84893i	−0.715273	+	0.281665i
$988$	14.1177	+	10.2571i	0.449145	+	0.326323i
$989$	−33.9178	−	58.7473i	−1.07852	−	1.86806i
$990$	1.28350	−	2.25799i	0.0407922	−	0.0717635i
$991$	10.5475	−	18.2688i	0.335052	−	0.580327i	−0.648443	−	0.761263i	$-0.724579\pi$
$991$	10.5475	−	18.2688i	0.335052	−	0.580327i	0.983495	+	0.180936i	$0.0579128\pi$
$992$	0.815787	−	7.76170i	0.0259013	−	0.246434i
$993$	0.405753	−	1.24878i	0.0128762	−	0.0396288i
$994$	4.55524	+	0.199377i	0.144484	+	0.00632385i
$995$	7.83063	−	5.68928i	0.248248	−	0.180362i
$996$	−7.03604	−	3.13265i	−0.222946	−	0.0992618i
$997$	57.6136	+	12.2461i	1.82464	+	0.387839i	0.987303	−	0.158848i	$-0.0507780\pi$
$997$	57.6136	+	12.2461i	1.82464	+	0.387839i	0.837337	+	0.546687i	$0.184111\pi$
$998$	25.8096	+	28.6644i	0.816988	+	0.907357i
$999$	−0.174505	+	1.66030i	−0.00552109	+	0.0525297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.4.3	✓	64
3.2	odd	2		693.2.by.c.235.6		64
7.2	even	3	inner	231.2.y.b.37.6	yes	64
11.3	even	5	inner	231.2.y.b.25.6	yes	64
21.2	odd	6		693.2.by.c.37.3		64
33.14	odd	10		693.2.by.c.487.3		64
77.58	even	15	inner	231.2.y.b.58.3	yes	64
231.212	odd	30		693.2.by.c.289.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.3	✓	64	1.1	even	1	trivial
231.2.y.b.25.6	yes	64	11.3	even	5	inner
231.2.y.b.37.6	yes	64	7.2	even	3	inner
231.2.y.b.58.3	yes	64	77.58	even	15	inner
693.2.by.c.37.3		64	21.2	odd	6
693.2.by.c.235.6		64	3.2	odd	2
693.2.by.c.289.6		64	231.212	odd	30
693.2.by.c.487.3		64	33.14	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.116737 + 1.11067i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.736325 + 0.156511i) q^{4} +(-0.640590 - 0.285209i) q^{5} +(-0.903504 + 0.656434i) q^{6} +(-1.42180 + 2.23125i) q^{7} +(-0.950004 + 2.92381i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.116737 + 1.11067i) q^{2} +(0.669131 + 0.743145i) q^{3} +(0.736325 + 0.156511i) q^{4} +(-0.640590 - 0.285209i) q^{5} +(-0.903504 + 0.656434i) q^{6} +(-1.42180 + 2.23125i) q^{7} +(-0.950004 + 2.92381i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.391555 - 0.678193i) q^{10} +(-0.368838 - 3.29605i) q^{11} +(0.376388 + 0.651923i) q^{12} +(2.89681 + 2.10465i) q^{13} +(-2.31222 - 1.83963i) q^{14} +(-0.216687 - 0.666894i) q^{15} +(-1.76111 - 0.784098i) q^{16} +(0.390027 + 3.71086i) q^{17} +(-1.09239 - 0.232194i) q^{18} +(6.33263 - 1.34604i) q^{19} +(-0.427045 - 0.310266i) q^{20} +(-2.60951 + 0.436394i) q^{21} +(3.70390 - 0.0248887i) q^{22} +(-2.77749 - 4.81076i) q^{23} +(-2.80849 + 1.25042i) q^{24} +(-3.01664 - 3.35032i) q^{25} +(-2.67575 + 2.97172i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.39612 + 1.42040i) q^{28} +(-1.13169 - 3.48298i) q^{29} +(0.765997 - 0.162818i) q^{30} +(-1.78438 + 0.794457i) q^{31} +(-1.99781 + 3.46032i) q^{32} +(2.20264 - 2.47959i) q^{33} -4.16709 q^{34} +(1.54717 - 1.02381i) q^{35} +(-0.232620 + 0.715932i) q^{36} +(1.11708 - 1.24064i) q^{37} +(0.755765 + 7.19063i) q^{38} +(0.374280 + 3.56104i) q^{39} +(1.44246 - 1.60202i) q^{40} +(1.67227 - 5.14670i) q^{41} +(-0.180066 - 2.94926i) q^{42} +12.2117 q^{43} +(0.244283 - 2.48469i) q^{44} +(0.350607 - 0.607269i) q^{45} +(5.66742 - 2.52330i) q^{46} +(8.92872 - 1.89786i) q^{47} +(-0.595716 - 1.83343i) q^{48} +(-2.95696 - 6.34479i) q^{49} +(4.07327 - 2.95940i) q^{50} +(-2.49673 + 2.77290i) q^{51} +(1.80359 + 2.00309i) q^{52} +(-6.85563 + 3.05232i) q^{53} +(-0.558396 - 0.967170i) q^{54} +(-0.703791 + 2.21662i) q^{55} +(-5.17304 - 6.27678i) q^{56} +(5.23766 + 3.80539i) q^{57} +(4.00056 - 0.850345i) q^{58} +(8.14925 + 1.73218i) q^{59} +(-0.0551760 - 0.524965i) q^{60} +(-2.96100 - 1.31832i) q^{61} +(-0.674081 - 2.07461i) q^{62} +(-2.07041 - 1.64724i) q^{63} +(-6.72928 - 4.88911i) q^{64} +(-1.25540 - 2.17442i) q^{65} +(2.49689 + 2.73588i) q^{66} +(2.88249 - 4.99261i) q^{67} +(-0.293603 + 2.79345i) q^{68} +(1.71658 - 5.28310i) q^{69} +(0.956506 + 1.83791i) q^{70} +(-1.24843 + 0.907036i) q^{71} +(-2.80849 - 1.25042i) q^{72} +(-14.4141 - 3.06381i) q^{73} +(1.24755 + 1.38554i) q^{74} +(0.471246 - 4.48360i) q^{75} +4.87355 q^{76} +(7.87873 + 3.86336i) q^{77} -3.99884 q^{78} +(0.531449 - 5.05640i) q^{79} +(0.904520 + 1.00457i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(5.52110 + 2.45815i) q^{82} +(-8.27734 + 6.01384i) q^{83} +(-1.98975 - 0.0870888i) q^{84} +(0.808525 - 2.48838i) q^{85} +(-1.42555 + 13.5632i) q^{86} +(1.83111 - 3.17157i) q^{87} +(9.98743 + 2.05285i) q^{88} +(6.65543 + 11.5275i) q^{89} +(0.633549 + 0.460300i) q^{90} +(-8.81469 + 3.47111i) q^{91} +(-1.29220 - 3.97699i) q^{92} +(-1.78438 - 0.794457i) q^{93} +(1.06559 + 10.1384i) q^{94} +(-4.44053 - 0.943864i) q^{95} +(-3.90831 + 0.830738i) q^{96} +(-2.57932 - 1.87399i) q^{97} +(7.39218 - 2.54355i) q^{98} +(3.31655 - 0.0222859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

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