LMFDB - Embedded newform 231.2.ba.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (of order $30$, 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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884754 - 0.0929913i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-1.18215 + 0.251275i) q^{4} +(1.63822 + 3.67950i) q^{5} +(-0.719723 - 0.522910i) q^{6} +(-1.92178 + 1.81845i) q^{7} +(-2.71472 + 0.882066i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.884754 - 0.0929913i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-1.18215 + 0.251275i) q^{4} +(1.63822 + 3.67950i) q^{5} +(-0.719723 - 0.522910i) q^{6} +(-1.92178 + 1.81845i) q^{7} +(-2.71472 + 0.882066i) q^{8} +(0.104528 + 0.994522i) q^{9} +(1.79158 + 3.10311i) q^{10} +(2.05881 + 2.60025i) q^{11} +(1.04665 + 0.604282i) q^{12} +(3.79943 - 2.76045i) q^{13} +(-1.53120 + 1.78759i) q^{14} +(1.24463 - 3.83058i) q^{15} +(-0.111677 + 0.0497219i) q^{16} +(0.219773 - 2.09100i) q^{17} +(0.184964 + 0.870187i) q^{18} +(-3.49690 - 0.743288i) q^{19} +(-2.86119 - 3.93809i) q^{20} +(2.64494 - 0.0654482i) q^{21} +(2.06334 + 2.10913i) q^{22} +(0.807895 - 1.39932i) q^{23} +(2.60765 + 1.16100i) q^{24} +(-7.50931 + 8.33994i) q^{25} +(3.10486 - 2.79563i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.81491 - 2.63258i) q^{28} +(3.59379 + 1.16769i) q^{29} +(0.744982 - 3.50486i) q^{30} +(-2.15695 + 4.84458i) q^{31} +(4.84983 - 2.80005i) q^{32} +(0.209909 - 3.30998i) q^{33} -1.87046i q^{34} +(-9.83928 - 4.09218i) q^{35} +(-0.373467 - 1.14941i) q^{36} +(6.34136 + 7.04280i) q^{37} +(-3.16301 - 0.332446i) q^{38} +(-4.67062 - 0.490902i) q^{39} +(-7.69287 - 8.54380i) q^{40} +(-1.87755 - 5.77849i) q^{41} +(2.33404 - 0.303862i) q^{42} -0.0838928i q^{43} +(-3.08721 - 2.55657i) q^{44} +(-3.48810 + 2.01386i) q^{45} +(0.584664 - 1.31318i) q^{46} +(2.08253 - 9.79755i) q^{47} +(0.116263 + 0.0377761i) q^{48} +(0.386487 - 6.98932i) q^{49} +(-5.86835 + 8.07709i) q^{50} +(-1.56248 + 1.40686i) q^{51} +(-3.79788 + 4.21797i) q^{52} +(2.93246 + 1.30562i) q^{53} +(0.444813 - 0.770440i) q^{54} +(-6.19483 + 11.8352i) q^{55} +(3.61311 - 6.63172i) q^{56} +(2.10134 + 2.89225i) q^{57} +(3.28820 + 0.698928i) q^{58} +(-1.21940 - 5.73685i) q^{59} +(-0.508819 + 4.84108i) q^{60} +(7.53212 - 3.35352i) q^{61} +(-1.45786 + 4.48684i) q^{62} +(-2.00937 - 1.72117i) q^{63} +(4.22832 - 3.07205i) q^{64} +(16.3814 + 9.45778i) q^{65} +(-0.122081 - 2.94803i) q^{66} +(-0.694852 - 1.20352i) q^{67} +(0.265610 + 2.52711i) q^{68} +(-1.53671 + 0.499307i) q^{69} +(-9.08588 - 2.70560i) q^{70} +(9.52979 + 6.92380i) q^{71} +(-1.16100 - 2.60765i) q^{72} +(6.27666 - 1.33415i) q^{73} +(6.26546 + 5.64145i) q^{74} +(11.1610 - 1.17307i) q^{75} +4.32064 q^{76} +(-8.68501 - 1.25326i) q^{77} -4.17800 q^{78} +(-12.7465 + 1.33971i) q^{79} +(-0.365903 - 0.329461i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-2.19852 - 4.93795i) q^{82} +(7.08142 + 5.14495i) q^{83} +(-3.11028 + 0.741976i) q^{84} +(8.05389 - 2.61687i) q^{85} +(-0.00780131 - 0.0742245i) q^{86} +(-1.88936 - 3.27248i) q^{87} +(-7.88269 - 5.24293i) q^{88} +(-10.6499 - 6.14870i) q^{89} +(-2.89884 + 2.10613i) q^{90} +(-2.28194 + 12.2140i) q^{91} +(-0.603444 + 1.85721i) q^{92} +(4.84458 - 2.15695i) q^{93} +(0.931442 - 8.86208i) q^{94} +(-2.99375 - 14.0845i) q^{95} +(-5.47772 - 1.16433i) q^{96} +(5.51985 + 7.59743i) q^{97} +(-0.308001 - 6.21977i) q^{98} +(-2.37080 + 2.31933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.884754	−	0.0929913i	0.625615	−	0.0657548i	0.213584	−	0.976925i	$-0.431486\pi$
$2$	0.884754	−	0.0929913i	0.625615	−	0.0657548i	0.412031	+	0.911170i	$0.364820\pi$
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$4$	−1.18215	+	0.251275i	−0.591077	+	0.125637i
$5$	1.63822	+	3.67950i	0.732634	+	1.64552i	0.763342	+	0.645994i	$0.223557\pi$
$5$	1.63822	+	3.67950i	0.732634	+	1.64552i	−0.0307081	+	0.999528i	$0.509776\pi$
$6$	−0.719723	−	0.522910i	−0.293826	−	0.213477i
$7$	−1.92178	+	1.81845i	−0.726365	+	0.687309i
$7$	−1.92178	+	1.81845i	−0.726365	+	0.687309i
$8$	−2.71472	+	0.882066i	−0.959798	+	0.311857i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	1.79158	+	3.10311i	0.566548	+	0.981290i
$11$	2.05881	+	2.60025i	0.620756	+	0.784004i
$11$	2.05881	+	2.60025i	0.620756	+	0.784004i
$12$	1.04665	+	0.604282i	0.302141	+	0.174441i
$13$	3.79943	−	2.76045i	1.05377	−	0.765610i	0.0808458	−	0.996727i	$-0.474238\pi$
$13$	3.79943	−	2.76045i	1.05377	−	0.765610i	0.972926	+	0.231117i	$0.0742379\pi$
$14$	−1.53120	+	1.78759i	−0.409231	+	0.477753i
$15$	1.24463	−	3.83058i	0.321363	−	0.989053i
$16$	−0.111677	+	0.0497219i	−0.0279193	+	0.0124305i
$17$	0.219773	−	2.09100i	0.0533029	−	0.507143i	−0.935001	−	0.354645i	$-0.884602\pi$
$17$	0.219773	−	2.09100i	0.0533029	−	0.507143i	0.988304	−	0.152498i	$-0.0487317\pi$
$18$	0.184964	+	0.870187i	0.0435964	+	0.205105i
$19$	−3.49690	−	0.743288i	−0.802243	−	0.170522i	−0.211496	−	0.977379i	$-0.567834\pi$
$19$	−3.49690	−	0.743288i	−0.802243	−	0.170522i	−0.590747	+	0.806857i	$0.701167\pi$
$20$	−2.86119	−	3.93809i	−0.639782	−	0.880584i
$21$	2.64494	−	0.0654482i	0.577174	−	0.0142820i
$22$	2.06334	+	2.10913i	0.439906	+	0.449667i
$23$	0.807895	−	1.39932i	0.168458	−	0.291777i	−0.769420	−	0.638743i	$-0.779455\pi$
$23$	0.807895	−	1.39932i	0.168458	−	0.291777i	0.937878	+	0.346966i	$0.112788\pi$
$24$	2.60765	+	1.16100i	0.532284	+	0.236988i
$25$	−7.50931	+	8.33994i	−1.50186	+	1.66799i
$26$	3.10486	−	2.79563i	0.608913	−	0.548268i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	1.81491	−	2.63258i	0.342986	−	0.497511i
$29$	3.59379	+	1.16769i	0.667349	+	0.216835i	0.623048	−	0.782183i	$-0.285894\pi$
$29$	3.59379	+	1.16769i	0.667349	+	0.216835i	0.0443009	+	0.999018i	$0.485894\pi$
$30$	0.744982	−	3.50486i	0.136014	−	0.639898i
$31$	−2.15695	+	4.84458i	−0.387399	+	0.870113i	0.609601	+	0.792709i	$0.291330\pi$
$31$	−2.15695	+	4.84458i	−0.387399	+	0.870113i	−0.997000	+	0.0774041i	$0.975337\pi$
$32$	4.84983	−	2.80005i	0.857336	−	0.494983i
$33$	0.209909	−	3.30998i	0.0365405	−	0.576193i
$34$		−	1.87046i		−	0.320781i
$35$	−9.83928	−	4.09218i	−1.66314	−	0.691704i
$36$	−0.373467	−	1.14941i	−0.0622445	−	0.191569i
$37$	6.34136	+	7.04280i	1.04251	+	1.15783i	0.987221	+	0.159359i	$0.0509426\pi$
$37$	6.34136	+	7.04280i	1.04251	+	1.15783i	0.0552929	+	0.998470i	$0.482391\pi$
$38$	−3.16301	−	0.332446i	−0.513108	−	0.0539298i
$39$	−4.67062	−	0.490902i	−0.747899	−	0.0786073i
$40$	−7.69287	−	8.54380i	−1.21635	−	1.35089i
$41$	−1.87755	−	5.77849i	−0.293223	−	0.902449i	−0.983812	−	0.179202i	$-0.942649\pi$
$41$	−1.87755	−	5.77849i	−0.293223	−	0.902449i	0.690589	−	0.723247i	$-0.257351\pi$
$42$	2.33404	−	0.303862i	0.360149	−	0.0468870i
$43$		−	0.0838928i		−	0.0127935i	−0.999980	−	0.00639677i	$-0.997964\pi$
$43$		−	0.0838928i		−	0.0127935i	0.999980	−	0.00639677i	$-0.00203617\pi$
$44$	−3.08721	−	2.55657i	−0.465414	−	0.385417i
$45$	−3.48810	+	2.01386i	−0.519976	+	0.300208i
$46$	0.584664	−	1.31318i	0.0862040	−	0.193617i
$47$	2.08253	−	9.79755i	0.303769	−	1.42912i	−0.516080	−	0.856540i	$-0.672609\pi$
$47$	2.08253	−	9.79755i	0.303769	−	1.42912i	0.819849	−	0.572580i	$-0.194057\pi$
$48$	0.116263	+	0.0377761i	0.0167811	+	0.00545250i
$49$	0.386487	−	6.98932i	0.0552124	−	0.998475i
$50$	−5.86835	+	8.07709i	−0.829910	+	1.14227i
$51$	−1.56248	+	1.40686i	−0.218791	+	0.197000i
$52$	−3.79788	+	4.21797i	−0.526671	+	0.584927i
$53$	2.93246	+	1.30562i	0.402804	+	0.179340i	0.598131	−	0.801398i	$-0.295910\pi$
$53$	2.93246	+	1.30562i	0.402804	+	0.179340i	−0.195327	+	0.980738i	$0.562577\pi$
$54$	0.444813	−	0.770440i	0.0605314	−	0.104844i
$55$	−6.19483	+	11.8352i	−0.835310	+	1.59586i
$56$	3.61311	−	6.63172i	0.482822	−	0.886200i
$57$	2.10134	+	2.89225i	0.278330	+	0.383088i
$58$	3.28820	+	0.698928i	0.431762	+	0.0917738i
$59$	−1.21940	−	5.73685i	−0.158753	−	0.746874i	−0.983433	−	0.181274i	$-0.941978\pi$
$59$	−1.21940	−	5.73685i	−0.158753	−	0.746874i	0.824680	−	0.565600i	$-0.191355\pi$
$60$	−0.508819	+	4.84108i	−0.0656882	+	0.624981i
$61$	7.53212	−	3.35352i	0.964389	−	0.429374i	0.136732	−	0.990608i	$-0.456340\pi$
$61$	7.53212	−	3.35352i	0.964389	−	0.429374i	0.827657	+	0.561234i	$0.189673\pi$
$62$	−1.45786	+	4.48684i	−0.185149	+	0.569829i
$63$	−2.00937	−	1.72117i	−0.253157	−	0.216848i
$64$	4.22832	−	3.07205i	0.528540	−	0.384007i
$65$	16.3814	+	9.45778i	2.03186	+	1.17309i
$66$	−0.122081	−	2.94803i	−0.0150272	−	0.362878i
$67$	−0.694852	−	1.20352i	−0.0848897	−	0.147033i	0.820455	−	0.571712i	$-0.193720\pi$
$67$	−0.694852	−	1.20352i	−0.0848897	−	0.147033i	−0.905344	+	0.424679i	$0.860387\pi$
$68$	0.265610	+	2.52711i	0.0322100	+	0.306457i
$69$	−1.53671	+	0.499307i	−0.184998	+	0.0601095i
$70$	−9.08588	−	2.70560i	−1.08597	−	0.323381i
$71$	9.52979	+	6.92380i	1.13098	+	0.821704i	0.985837	−	0.167707i	$-0.0536362\pi$
$71$	9.52979	+	6.92380i	1.13098	+	0.821704i	0.145142	+	0.989411i	$0.453636\pi$
$72$	−1.16100	−	2.60765i	−0.136825	−	0.307314i
$73$	6.27666	−	1.33415i	0.734628	−	0.156150i	0.174618	−	0.984636i	$-0.444131\pi$
$73$	6.27666	−	1.33415i	0.734628	−	0.156150i	0.560009	+	0.828486i	$0.310798\pi$
$74$	6.26546	+	5.64145i	0.728345	+	0.655805i
$75$	11.1610	−	1.17307i	1.28876	−	0.135454i
$76$	4.32064			0.495611
$77$	−8.68501	−	1.25326i	−0.989748	−	0.142822i
$78$	−4.17800			−0.473066
$79$	−12.7465	+	1.33971i	−1.43410	+	0.150730i	−0.789480	−	0.613776i	$-0.789650\pi$
$79$	−12.7465	+	1.33971i	−1.43410	+	0.150730i	−0.644617	+	0.764506i	$0.722983\pi$
$80$	−0.365903	−	0.329461i	−0.0409092	−	0.0368349i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−2.19852	−	4.93795i	−0.242785	−	0.545305i
$83$	7.08142	+	5.14495i	0.777287	+	0.564732i	0.904163	−	0.427187i	$-0.140495\pi$
$83$	7.08142	+	5.14495i	0.777287	+	0.564732i	−0.126877	+	0.991918i	$0.540495\pi$
$84$	−3.11028	+	0.741976i	−0.339360	+	0.0809563i
$85$	8.05389	−	2.61687i	0.873567	−	0.283839i
$86$	−0.00780131	−	0.0742245i	−0.000841237	−	0.00800383i
$87$	−1.88936	−	3.27248i	−0.202561	−	0.350846i
$88$	−7.88269	−	5.24293i	−0.840298	−	0.558899i
$89$	−10.6499	−	6.14870i	−1.12888	−	0.651761i	−0.185230	−	0.982695i	$-0.559303\pi$
$89$	−10.6499	−	6.14870i	−1.12888	−	0.651761i	−0.943654	+	0.330934i	$0.892636\pi$
$90$	−2.89884	+	2.10613i	−0.305565	+	0.222006i
$91$	−2.28194	+	12.2140i	−0.239212	+	1.28038i
$92$	−0.603444	+	1.85721i	−0.0629134	+	0.193627i
$93$	4.84458	−	2.15695i	0.502360	−	0.223665i
$94$	0.931442	−	8.86208i	0.0960709	−	0.914053i
$95$	−2.99375	−	14.0845i	−0.307153	−	1.44504i
$96$	−5.47772	−	1.16433i	−0.559068	−	0.118833i
$97$	5.51985	+	7.59743i	0.560456	+	0.771402i	0.991384	−	0.130984i	$-0.0418138\pi$
$97$	5.51985	+	7.59743i	0.560456	+	0.771402i	−0.430928	+	0.902386i	$0.641814\pi$
$98$	−0.308001	−	6.21977i	−0.0311128	−	0.628291i
$99$	−2.37080	+	2.31933i	−0.238274	+	0.233102i
$100$	6.78155	−	11.7460i	0.678155	−	1.17460i
$101$	6.35978	+	2.83156i	0.632822	+	0.281750i	0.697972	−	0.716125i	$-0.254086\pi$
$101$	6.35978	+	2.83156i	0.632822	+	0.281750i	−0.0651501	+	0.997875i	$0.520753\pi$
$102$	−1.25158	+	1.39002i	−0.123925	+	0.137633i
$103$	−5.90982	+	5.32122i	−0.582312	+	0.524316i	−0.906793	−	0.421576i	$-0.861477\pi$
$103$	−5.90982	+	5.32122i	−0.582312	+	0.524316i	0.324481	+	0.945892i	$0.394810\pi$
$104$	−7.87949	+	10.8452i	−0.772647	+	1.06346i
$105$	4.57381	+	9.62485i	0.446358	+	0.939289i
$106$	2.71592	+	0.882455i	0.263793	+	0.0857116i
$107$	0.218504	−	1.02798i	0.0211235	−	0.0993785i	−0.966323	−	0.257332i	$-0.917156\pi$
$107$	0.218504	−	1.02798i	0.0211235	−	0.0993785i	0.987446	+	0.157954i	$0.0504898\pi$
$108$	−0.491567	+	1.10408i	−0.0473011	+	0.106240i
$109$	−3.25387	+	1.87862i	−0.311664	+	0.179939i	−0.647671	−	0.761920i	$-0.724257\pi$
$109$	−3.25387	+	1.87862i	−0.311664	+	0.179939i	0.336007	+	0.941860i	$0.390923\pi$
$110$	−4.38033	+	11.0473i	−0.417648	+	1.05332i
$111$		−	9.47702i		−	0.899519i
$112$	0.124202	−	0.298634i	0.0117360	−	0.0282182i
$113$	−0.390892	−	1.20304i	−0.0367721	−	0.113173i	0.930986	−	0.365056i	$-0.118950\pi$
$113$	−0.390892	−	1.20304i	−0.0367721	−	0.113173i	−0.967758	+	0.251883i	$0.918950\pi$
$114$	2.12813	+	2.36352i	0.199317	+	0.221364i
$115$	6.47229	+	0.680265i	0.603544	+	0.0634351i
$116$	−4.54182	−	0.477364i	−0.421697	−	0.0443222i
$117$	3.14247	+	3.49007i	0.290522	+	0.322657i
$118$	−1.61235	−	4.96230i	−0.148429	−	0.456817i
$119$	3.38003	+	4.41810i	0.309847	+	0.405007i
$120$			11.4968i			1.04951i
$121$	−2.52258	+	10.7068i	−0.229325	+	0.973350i
$122$	6.35222	−	3.66746i	0.575103	−	0.332036i
$123$	−2.47128	+	5.55058i	−0.222828	+	0.500479i
$124$	1.33252	−	6.26903i	0.119664	−	0.562975i
$125$	−23.8358	−	7.74471i	−2.13194	−	0.692708i
$126$	−1.93785	−	1.33596i	−0.172637	−	0.119017i
$127$	5.71858	−	7.87095i	0.507442	−	0.698434i	−0.476043	−	0.879422i	$-0.657929\pi$
$127$	5.71858	−	7.87095i	0.507442	−	0.698434i	0.983485	+	0.180988i	$0.0579295\pi$
$128$	−4.86802	+	4.38319i	−0.430276	+	0.387423i
$129$	−0.0561353	+	0.0623445i	−0.00494243	+	0.00548913i
$130$	15.3730	+	6.84448i	1.34830	+	0.600301i
$131$	3.03678	−	5.25986i	0.265325	−	0.459556i	−0.702324	−	0.711857i	$-0.747854\pi$
$131$	3.03678	−	5.25986i	0.265325	−	0.459556i	0.967649	+	0.252302i	$0.0811875\pi$
$132$	0.583568	+	3.96564i	0.0507931	+	0.345165i
$133$	8.07190	−	4.93049i	0.699923	−	0.427528i
$134$	−0.726690	−	1.00020i	−0.0627764	−	0.0864044i
$135$	3.93970	+	0.837409i	0.339075	+	0.0720727i
$136$	1.24778	+	5.87035i	0.106996	+	0.503378i
$137$	−1.55946	+	14.8373i	−0.133234	+	1.26764i	0.699770	+	0.714369i	$0.253286\pi$
$137$	−1.55946	+	14.8373i	−0.133234	+	1.26764i	−0.833004	+	0.553268i	$0.813381\pi$
$138$	−1.31318	+	0.584664i	−0.111785	+	0.0497699i
$139$	1.91927	−	5.90690i	0.162790	−	0.501017i	−0.836076	−	0.548613i	$-0.815156\pi$
$139$	1.91927	−	5.90690i	0.162790	−	0.501017i	0.998867	+	0.0475962i	$0.0151561\pi$
$140$	12.6598	+	2.36522i	1.06995	+	0.199898i
$141$	−8.10347	+	5.88751i	−0.682435	+	0.495818i
$142$	9.07537	+	5.23967i	0.761588	+	0.439703i
$143$	15.0002	+	4.19621i	1.25438	+	0.350905i
$144$	−0.0611229	−	0.105868i	−0.00509358	−	0.00882234i
$145$	1.59089	+	15.1363i	0.132116	+	1.25700i
$146$	5.42924	−	1.76407i	0.449327	−	0.145995i
$147$	−4.96399	+	4.93547i	−0.409423	+	0.407071i
$148$	−9.26614	−	6.73225i	−0.761672	−	0.553387i
$149$	−4.68770	−	10.5288i	−0.384032	−	0.862549i	−0.997353	−	0.0727153i	$-0.976834\pi$
$149$	−4.68770	−	10.5288i	−0.384032	−	0.862549i	0.613321	−	0.789834i	$-0.289833\pi$
$150$	9.76566	−	2.07576i	0.797363	−	0.169485i
$151$	−3.04486	−	2.74160i	−0.247787	−	0.223108i	0.535873	−	0.844299i	$-0.319983\pi$
$151$	−3.04486	−	2.74160i	−0.247787	−	0.223108i	−0.783660	+	0.621190i	$0.786649\pi$
$152$	10.1487	−	1.06667i	0.823170	−	0.0865186i
$153$	2.10252			0.169979
$154$	−7.80063	−	0.301197i	−0.628593	−	0.0242711i
$155$	−21.3592			−1.71561
$156$	5.64475	−	0.593287i	0.451942	−	0.0475010i
$157$	−10.5946	−	9.53942i	−0.845541	−	0.761329i	0.127530	−	0.991835i	$-0.459295\pi$
$157$	−10.5946	−	9.53942i	−0.845541	−	0.761329i	−0.973071	+	0.230506i	$0.925962\pi$
$158$	−11.1530	+	2.37064i	−0.887282	+	0.188598i
$159$	−1.30562	−	2.93246i	−0.103542	−	0.232559i
$160$	18.2479	+	13.2578i	1.44262	+	1.04812i
$161$	0.991986	+	4.15829i	0.0781794	+	0.327719i
$162$	−0.846086	+	0.274910i	−0.0664748	+	0.0215990i
$163$	−1.12785	−	10.7308i	−0.0883402	−	0.840501i	−0.945538	−	0.325513i	$-0.894463\pi$
$163$	−1.12785	−	10.7308i	−0.0883402	−	0.840501i	0.857197	−	0.514988i	$-0.172204\pi$
$164$	3.67154	+	6.35929i	0.286699	+	0.496577i
$165$	12.5229	−	4.65011i	0.974909	−	0.362010i
$166$	6.74375	+	3.89350i	0.523416	+	0.302194i
$167$	8.53447	−	6.20066i	0.660417	−	0.479821i	−0.206387	−	0.978471i	$-0.566170\pi$
$167$	8.53447	−	6.20066i	0.660417	−	0.479821i	0.866804	+	0.498649i	$0.166170\pi$
$168$	−7.12255	+	2.51069i	−0.549516	+	0.193704i
$169$	2.79837	−	8.61250i	0.215259	−	0.662500i
$170$	6.88236	−	3.06423i	0.527853	−	0.235015i
$171$	0.373691	−	3.55543i	0.0285769	−	0.271891i
$172$	0.0210801	+	0.0991742i	0.00160735	+	0.00756196i
$173$	−0.0773665	−	0.0164448i	−0.00588206	−	0.00125027i	0.204970	−	0.978768i	$-0.434290\pi$
$173$	−0.0773665	−	0.0164448i	−0.00588206	−	0.00125027i	−0.210852	+	0.977518i	$0.567624\pi$
$174$	−1.97593	−	2.71964i	−0.149795	−	0.206175i
$175$	−0.734492	−	29.6828i	−0.0555224	−	2.24381i
$176$	−0.359212	−	0.188020i	−0.0270766	−	0.0141726i
$177$	−2.93251	+	5.07925i	−0.220421	+	0.381780i
$178$	−9.99428	−	4.44974i	−0.749103	−	0.333522i
$179$	−10.6842	+	11.8660i	−0.798577	+	0.886910i	−0.995621	−	0.0934847i	$-0.970199\pi$
$179$	−10.6842	+	11.8660i	−0.798577	+	0.886910i	0.197043	+	0.980395i	$0.436866\pi$
$180$	3.61744	−	3.25716i	0.269628	−	0.242774i
$181$	−5.42125	+	7.46170i	−0.402958	+	0.554624i	−0.961483	−	0.274863i	$-0.911367\pi$
$181$	−5.42125	+	7.46170i	−0.402958	+	0.554624i	0.558525	+	0.829487i	$0.311367\pi$
$182$	−0.883154	+	11.0186i	−0.0654638	+	0.816754i
$183$	−7.84140	−	2.54782i	−0.579653	−	0.188341i
$184$	−0.958920	+	4.51137i	−0.0706925	+	0.332582i
$185$	−15.5254	+	34.8707i	−1.14145	+	2.56374i
$186$	4.08568	−	2.35887i	0.299577	−	0.172961i
$187$	5.88960	−	3.73352i	0.430690	−	0.273022i
$188$			12.1055i			0.882884i
$189$	0.341561	+	2.62361i	0.0248449	+	0.190840i
$190$	−3.95847	−	12.1829i	−0.287178	−	0.883842i
$191$	−1.61277	−	1.79116i	−0.116696	−	0.129604i	0.681966	−	0.731384i	$-0.261125\pi$
$191$	−1.61277	−	1.79116i	−0.116696	−	0.129604i	−0.798662	+	0.601780i	$0.794458\pi$
$192$	−5.19786	−	0.546317i	−0.375123	−	0.0394270i
$193$	−26.2076	−	2.75453i	−1.88647	−	0.198276i	−0.910099	−	0.414392i	$-0.863994\pi$
$193$	−26.2076	−	2.75453i	−1.88647	−	0.198276i	−0.976368	+	0.216116i	$0.930661\pi$
$194$	5.59021	+	6.20855i	0.401353	+	0.445748i
$195$	−5.84523	−	17.9898i	−0.418586	−	1.28827i
$196$	1.29935	+	8.35957i	0.0928108	+	0.597112i
$197$		−	11.5574i		−	0.823431i	−0.911312	−	0.411716i	$-0.864930\pi$
$197$		−	11.5574i		−	0.823431i	0.911312	−	0.411716i	$-0.135070\pi$
$198$	−1.88189	+	2.27250i	−0.133740	+	0.161500i
$199$	−3.90636	+	2.25534i	−0.276914	+	0.159877i	−0.632026	−	0.774947i	$-0.717776\pi$
$199$	−3.90636	+	2.25534i	−0.276914	+	0.159877i	0.355111	+	0.934824i	$0.384443\pi$
$200$	13.0293	−	29.2643i	0.921311	−	2.06930i
$201$	−0.288936	+	1.35934i	−0.0203800	+	0.0958802i
$202$	5.89015	+	1.91383i	0.414429	+	0.134656i
$203$	−9.02986	+	4.29107i	−0.633772	+	0.301174i
$204$	1.49358	−	2.05574i	0.104572	−	0.143931i
$205$	18.1861	−	16.3749i	1.27017	−	1.14367i
$206$	−4.73390	+	5.25753i	−0.329827	+	0.366310i
$207$	1.47610	+	0.657201i	0.102596	+	0.0456786i
$208$	−0.287055	+	0.497194i	−0.0199037	+	0.0344742i
$209$	−5.26672	−	10.6231i	−0.364307	−	0.734814i
$210$	4.94172	+	8.09029i	0.341011	+	0.558283i
$211$	8.45726	+	11.6404i	0.582222	+	0.801359i	0.993937	−	0.109953i	$-0.0350701\pi$
$211$	8.45726	+	11.6404i	0.582222	+	0.801359i	−0.411715	+	0.911313i	$0.635070\pi$
$212$	−3.79469	−	0.806586i	−0.260620	−	0.0553965i
$213$	−2.44909	−	11.5221i	−0.167809	−	0.789479i
$214$	0.0977287	−	0.929827i	0.00668060	−	0.0635617i
$215$	0.308684	−	0.137435i	0.0210521	−	0.00937298i
$216$	−0.882066	+	2.71472i	−0.0600170	+	0.184713i
$217$	−4.66445	−	13.2325i	−0.316643	−	0.898282i
$218$	−2.70418	+	1.96470i	−0.183150	+	0.133066i
$219$	−5.55719	−	3.20844i	−0.375520	−	0.216807i
$220$	4.34936	−	15.5476i	0.293234	−	1.04822i
$221$	−4.93709	−	8.55130i	−0.332105	−	0.575222i
$222$	−0.881281	−	8.38483i	−0.0591477	−	0.562753i
$223$	11.8800	−	3.86004i	0.795541	−	0.258487i	0.117079	−	0.993123i	$-0.462647\pi$
$223$	11.8800	−	3.86004i	0.795541	−	0.258487i	0.678462	+	0.734635i	$0.262647\pi$
$224$	−4.22856	+	14.2002i	−0.282533	+	0.948794i
$225$	−9.07919	−	6.59641i	−0.605279	−	0.439761i
$226$	−0.457716	−	1.02805i	−0.0304468	−	0.0683846i
$227$	15.7456	−	3.34684i	1.04508	−	0.222138i	0.346779	−	0.937947i	$-0.387275\pi$
$227$	15.7456	−	3.34684i	1.04508	−	0.222138i	0.698296	+	0.715809i	$0.253942\pi$
$228$	−3.21086	−	2.89107i	−0.212644	−	0.191466i
$229$	−21.9724	+	2.30939i	−1.45197	+	0.152609i	−0.797428	−	0.603414i	$-0.793807\pi$
$229$	−21.9724	+	2.30939i	−1.45197	+	0.152609i	−0.654546	+	0.756022i	$0.727140\pi$
$230$	5.78964			0.381758
$231$	5.61562	+	6.74276i	0.369481	+	0.443641i
$232$	−10.7861			−0.708142
$233$	1.70952	−	0.179677i	0.111994	−	0.0117711i	−0.0483656	−	0.998830i	$-0.515401\pi$
$233$	1.70952	−	0.179677i	0.111994	−	0.0117711i	0.160360	+	0.987059i	$0.448735\pi$
$234$	3.10486	+	2.79563i	0.202971	+	0.182756i
$235$	39.4617	−	8.38785i	2.57420	−	0.547163i
$236$	2.88305	+	6.47543i	0.187670	+	0.421515i
$237$	10.3690	+	7.53350i	0.673537	+	0.489353i
$238$	3.40134	+	3.59462i	0.220476	+	0.233004i
$239$	20.9895	−	6.81989i	1.35770	−	0.441142i	0.462422	−	0.886660i	$-0.346980\pi$
$239$	20.9895	−	6.81989i	1.35770	−	0.441142i	0.895273	+	0.445518i	$0.146980\pi$
$240$	0.0514668	+	0.489674i	0.00332217	+	0.0316083i
$241$	0.163344	+	0.282921i	0.0105219	+	0.0182245i	0.871238	−	0.490860i	$-0.163317\pi$
$241$	0.163344	+	0.282921i	0.0105219	+	0.0182245i	−0.860716	+	0.509085i	$0.829984\pi$
$242$	−1.23621	+	9.70750i	−0.0794669	+	0.624022i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−8.06147	+	5.85700i	−0.516083	+	0.374956i
$245$	26.3504	−	10.0280i	1.68346	−	0.640663i
$246$	−1.67032	+	5.14070i	−0.106495	+	0.327759i
$247$	−15.3380	+	6.82892i	−0.975934	+	0.434514i
$248$	1.58227	−	15.0543i	0.100474	−	0.955946i
$249$	−1.81987	−	8.56184i	−0.115330	−	0.542584i
$250$	−21.8090	−	4.63564i	−1.37932	−	0.293184i
$251$	−13.1681	−	18.1243i	−0.831161	−	1.14400i	−0.987706	−	0.156324i	$-0.950036\pi$
$251$	−13.1681	−	18.1243i	−0.831161	−	1.14400i	0.156545	−	0.987671i	$-0.449964\pi$
$252$	2.80787	+	1.52979i	0.176879	+	0.0963677i
$253$	5.30187	−	0.780201i	0.333326	−	0.0490508i
$254$	4.32760	−	7.49563i	0.271538	−	0.470318i
$255$	−7.73623	−	3.44439i	−0.484462	−	0.215696i
$256$	−10.8938	+	12.0988i	−0.680863	+	0.756175i
$257$	9.10868	−	8.20149i	0.568184	−	0.511595i	−0.334215	−	0.942497i	$-0.608471\pi$
$257$	9.10868	−	8.20149i	0.568184	−	0.511595i	0.902399	+	0.430902i	$0.141804\pi$
$258$	−0.0438684	+	0.0603796i	−0.00273113	+	0.00375907i
$259$	−24.9937	−	2.00327i	−1.55303	−	0.124477i
$260$	−21.7418	−	7.06434i	−1.34837	−	0.438112i
$261$	−0.785642	+	3.69616i	−0.0486300	+	0.228786i
$262$	2.19768	−	4.93607i	0.135773	−	0.304951i
$263$	1.77944	−	1.02736i	0.109725	−	0.0633498i	−0.444133	−	0.895961i	$-0.646488\pi$
$263$	1.77944	−	1.02736i	0.109725	−	0.0633498i	0.553858	+	0.832611i	$0.313155\pi$
$264$	2.34977	+	9.17081i	0.144618	+	0.564424i
$265$			12.9289i			0.794215i
$266$	6.68315	−	5.11288i	0.409770	−	0.313491i
$267$	3.80011	+	11.6955i	0.232563	+	0.715755i
$268$	1.12384	+	1.24815i	0.0686492	+	0.0762427i
$269$	−15.0723	−	1.58416i	−0.918973	−	0.0965880i	−0.366783	−	0.930306i	$-0.619541\pi$
$269$	−15.0723	−	1.58416i	−0.918973	−	0.0965880i	−0.552190	+	0.833718i	$0.686208\pi$
$270$	3.56354	+	0.374543i	0.216870	+	0.0227939i
$271$	−11.7266	−	13.0238i	−0.712343	−	0.791137i	0.272947	−	0.962029i	$-0.412002\pi$
$271$	−11.7266	−	13.0238i	−0.712343	−	0.791137i	−0.985290	+	0.170892i	$0.945335\pi$
$272$	0.0794250	+	0.244445i	0.00481585	+	0.0148217i
$273$	9.86860	−	7.54989i	0.597275	−	0.456940i
$274$			13.2724i			0.801813i
$275$	−37.1462	−	2.35570i	−2.24000	−	0.142054i
$276$	1.69116	−	0.976393i	0.101796	−	0.0587719i
$277$	8.70671	−	19.5556i	0.523135	−	1.17498i	−0.438018	−	0.898966i	$-0.644319\pi$
$277$	8.70671	−	19.5556i	0.523135	−	1.17498i	0.961153	−	0.276015i	$-0.0890140\pi$
$278$	1.14879	−	5.40463i	0.0688998	−	0.324148i
$279$	−5.04351	−	1.63873i	−0.301947	−	0.0981085i
$280$	30.3205	+	2.43022i	1.81199	+	0.145233i
$281$	4.05488	−	5.58106i	0.241894	−	0.332938i	−0.670758	−	0.741676i	$-0.734031\pi$
$281$	4.05488	−	5.58106i	0.241894	−	0.332938i	0.912652	+	0.408738i	$0.134031\pi$
$282$	−6.62208	+	5.96255i	−0.394339	+	0.355065i
$283$	−14.8814	+	16.5275i	−0.884607	+	0.982455i	−0.999941	−	0.0108715i	$-0.996539\pi$
$283$	−14.8814	+	16.5275i	−0.884607	+	0.982455i	0.115334	+	0.993327i	$0.463206\pi$
$284$	−13.0055	−	5.79040i	−0.771732	−	0.343597i
$285$	−7.19958	+	12.4700i	−0.426466	+	0.738661i
$286$	13.6617	+	2.31773i	0.807831	+	0.137050i
$287$	14.1161	+	7.69078i	0.833249	+	0.453972i
$288$	3.29165	+	4.53057i	0.193963	+	0.266967i
$289$	12.3045	+	2.61540i	0.723795	+	0.153847i
$290$	2.81508	+	13.2439i	0.165307	+	0.777710i
$291$	0.981620	−	9.33949i	0.0575436	−	0.547491i
$292$	−7.08474	+	3.15433i	−0.414603	+	0.184593i
$293$	−2.45798	+	7.56489i	−0.143597	+	0.441946i	−0.996828	−	0.0795874i	$-0.974640\pi$
$293$	−2.45798	+	7.56489i	−0.143597	+	0.441946i	0.853231	+	0.521533i	$0.174640\pi$
$294$	−3.93295	+	4.82828i	−0.229374	+	0.281591i
$295$	19.1111	−	13.8850i	1.11269	−	0.808417i
$296$	−23.4272	−	13.5257i	−1.36168	−	0.786166i
$297$	3.31378	−	0.137227i	0.192285	−	0.00796275i
$298$	−5.12654	−	8.87943i	−0.296973	−	0.514372i
$299$	−0.793195	−	7.54675i	−0.0458717	−	0.436440i
$300$	−12.8993	+	4.19123i	−0.744740	+	0.241981i
$301$	0.152555	+	0.161224i	0.00879312	+	0.00929278i
$302$	−2.94889	−	2.14250i	−0.169690	−	0.123287i
$303$	−2.83156	−	6.35978i	−0.162669	−	0.365360i
$304$	0.427481	−	0.0908639i	0.0245177	−	0.00521140i
$305$	24.6785	+	22.2206i	1.41309	+	1.27235i
$306$	1.86021	−	0.195516i	0.106341	−	0.0111769i
$307$	−7.82465			−0.446576			−0.223288	−	0.974752i	$-0.571679\pi$
$307$	−7.82465			−0.446576			−0.223288	+	0.974752i	$0.571679\pi$
$308$	10.5819	−	0.700774i	0.602961	−	0.0399303i
$309$	7.95244			0.452399
$310$	−18.8976	+	1.98622i	−1.07331	+	0.112810i
$311$	−8.30971	−	7.48210i	−0.471200	−	0.424271i	0.399013	−	0.916945i	$-0.369353\pi$
$311$	−8.30971	−	7.48210i	−0.471200	−	0.424271i	−0.870214	+	0.492674i	$0.836019\pi$
$312$	13.1124	−	2.78714i	0.742346	−	0.157791i
$313$	11.5904	+	26.0325i	0.655130	+	1.47145i	0.869116	+	0.494609i	$0.164689\pi$
$313$	11.5904	+	26.0325i	0.655130	+	1.47145i	−0.213986	+	0.976837i	$0.568645\pi$
$314$	−10.2607	−	7.45483i	−0.579044	−	0.420700i
$315$	3.04128	−	10.2131i	0.171356	−	0.575445i
$316$	14.7317	−	4.78663i	0.828725	−	0.269269i
$317$	1.32410	+	12.5980i	0.0743688	+	0.707572i	0.966652	+	0.256095i	$0.0824360\pi$
$317$	1.32410	+	12.5980i	0.0743688	+	0.707572i	−0.892283	+	0.451477i	$0.850897\pi$
$318$	−1.42784	−	2.47309i	−0.0800694	−	0.138684i
$319$	4.36264	+	11.7488i	0.244261	+	0.657806i
$320$	18.2305	+	10.5254i	1.01912	+	0.588388i
$321$	−0.850232	+	0.617730i	−0.0474553	+	0.0344783i
$322$	1.26435	+	3.58682i	0.0704594	+	0.199886i
$323$	−2.32274	+	7.14867i	−0.129241	+	0.397763i
$324$	1.10408	−	0.491567i	0.0613377	−	0.0273093i
$325$	−5.50915	+	52.4160i	−0.305593	+	2.90752i
$326$	−1.99574	−	9.38923i	−0.110534	−	0.520022i
$327$	3.67514	+	0.781175i	0.203236	+	0.0431991i
$328$	10.1940	+	14.0309i	0.562871	+	0.774725i
$329$	13.8142	+	22.6157i	0.761600	+	1.24685i
$330$	10.6473	−	5.27872i	0.586114	−	0.290584i
$331$	−9.44406	+	16.3576i	−0.519093	+	0.899095i	0.480661	+	0.876906i	$0.340397\pi$
$331$	−9.44406	+	16.3576i	−0.519093	+	0.899095i	−0.999754	+	0.0221885i	$0.992937\pi$
$332$	−9.66412	−	4.30274i	−0.530388	−	0.236144i
$333$	−6.34136	+	7.04280i	−0.347505	+	0.385943i
$334$	6.97430	−	6.27968i	0.381617	−	0.343609i
$335$	3.29003	−	4.52834i	0.179754	−	0.247410i
$336$	−0.292125	+	0.138821i	−0.0159367	+	0.00757328i
$337$	20.4639	+	6.64912i	1.11474	+	0.362200i	0.807757	−	0.589515i	$-0.200681\pi$
$337$	20.4639	+	6.64912i	1.11474	+	0.362200i	0.306981	+	0.951716i	$0.400681\pi$
$338$	1.67498	−	7.88017i	0.0911070	−	0.428625i
$339$	−0.514503	+	1.15559i	−0.0279440	+	0.0627632i
$340$	−8.86339	+	5.11728i	−0.480685	+	0.277523i
$341$	−17.0379	+	4.36549i	−0.922652	+	0.236405i
$342$		−	3.18043i		−	0.171978i
$343$	11.9670	+	14.1348i	0.646156	+	0.763205i
$344$	0.0739990	+	0.227746i	0.00398976	+	0.0122792i
$345$	−4.35466	−	4.83634i	−0.234447	−	0.260380i
$346$	−0.0699795	−	0.00735514i	−0.00376212	−	0.000395415i
$347$	24.1450	+	2.53775i	1.29617	+	0.136233i	0.727373	−	0.686242i	$-0.240741\pi$
$347$	24.1450	+	2.53775i	1.29617	+	0.136233i	0.568801	+	0.822475i	$0.307408\pi$
$348$	3.05581	+	3.39382i	0.163809	+	0.181928i
$349$	−7.70232	−	23.7053i	−0.412296	−	1.26892i	−0.914648	−	0.404252i	$-0.867532\pi$
$349$	−7.70232	−	23.7053i	−0.412296	−	1.26892i	0.502352	−	0.864663i	$-0.332468\pi$
$350$	−3.41009	−	26.1937i	−0.182277	−	1.40011i
$351$		−	4.69635i		−	0.250673i
$352$	17.2657	+	6.84597i	0.920265	+	0.364892i
$353$	24.2019	−	13.9729i	1.28813	−	0.743705i	0.309813	−	0.950797i	$-0.399733\pi$
$353$	24.2019	−	13.9729i	1.28813	−	0.743705i	0.978321	+	0.207092i	$0.0664001\pi$
$354$	−2.12222	+	4.76658i	−0.112795	+	0.253341i
$355$	−9.86424	+	46.4076i	−0.523539	+	2.46306i
$356$	14.1348	+	4.59267i	0.749143	+	0.243411i
$357$	0.444436	−	5.54497i	0.0235220	−	0.293471i
$358$	−8.34948	+	11.4921i	−0.441284	+	0.607375i
$359$	6.87637	−	6.19152i	0.362921	−	0.326776i	−0.467415	−	0.884038i	$-0.654815\pi$
$359$	6.87637	−	6.19152i	0.362921	−	0.326776i	0.830337	+	0.557262i	$0.188148\pi$
$360$	7.69287	−	8.54380i	0.405450	−	0.450298i
$361$	−5.68156	−	2.52959i	−0.299029	−	0.133136i
$362$	−4.10259	+	7.10590i	−0.215627	+	0.373478i
$363$	9.03892	−	6.26881i	0.474420	−	0.329027i
$364$	−0.371474	−	15.0123i	−0.0194705	−	0.786857i
$365$	15.1915	+	20.9094i	0.795162	+	1.09445i
$366$	−7.17463	−	1.52501i	−0.375024	−	0.0797138i
$367$	1.78205	+	8.38387i	0.0930221	+	0.437635i	0.999869	+	0.0161748i	$0.00514882\pi$
$367$	1.78205	+	8.38387i	0.0930221	+	0.437635i	−0.906847	+	0.421460i	$0.861518\pi$
$368$	−0.0206468	+	0.196442i	−0.00107629	+	0.0102402i
$369$	5.55058	−	2.47128i	0.288952	−	0.128650i
$370$	−10.4935	+	32.2957i	−0.545532	+	1.67897i
$371$	−8.00974	+	2.82342i	−0.415845	+	0.146585i
$372$	−5.18506	+	3.76716i	−0.268833	+	0.195318i
$373$	−18.6462	−	10.7654i	−0.965464	−	0.557411i	−0.0676136	−	0.997712i	$-0.521538\pi$
$373$	−18.6462	−	10.7654i	−0.965464	−	0.557411i	−0.897850	+	0.440301i	$0.854872\pi$
$374$	4.86366	−	3.85093i	0.251494	−	0.199127i
$375$	12.5312	+	21.7047i	0.647109	+	1.12083i
$376$	2.98859	+	28.4345i	0.154125	+	1.46640i
$377$	16.8777	−	5.48389i	0.869245	−	0.282435i
$378$	0.546171	+	2.28949i	0.0280920	+	0.117759i
$379$	−24.1145	−	17.5202i	−1.23868	−	0.899953i	−0.241169	−	0.970483i	$-0.577531\pi$
$379$	−24.1145	−	17.5202i	−1.23868	−	0.899953i	−0.997510	+	0.0705304i	$0.977531\pi$
$380$	7.07815	+	15.8978i	0.363102	+	0.815540i
$381$	−9.51643	+	2.02278i	−0.487541	+	0.103630i
$382$	−1.59346	−	1.43476i	−0.0815286	−	0.0734087i
$383$	−6.71560	+	0.705838i	−0.343151	+	0.0360666i	−0.274537	−	0.961577i	$-0.588524\pi$
$383$	−6.71560	+	0.705838i	−0.343151	+	0.0360666i	−0.0686144	+	0.997643i	$0.521858\pi$
$384$	6.55057			0.334282
$385$	−9.61657	−	34.0096i	−0.490106	−	1.73329i
$386$	−23.4434			−1.19324
$387$	0.0834333	−	0.00876919i	0.00424115	−	0.000445763i
$388$	−8.43436	−	7.59433i	−0.428190	−	0.385544i
$389$	−1.39432	+	0.296372i	−0.0706949	+	0.0150267i	−0.243123	−	0.969995i	$-0.578172\pi$
$389$	−1.39432	+	0.296372i	−0.0706949	+	0.0150267i	0.172428	+	0.985022i	$0.444839\pi$
$390$	−6.84448	−	15.3730i	−0.346584	−	0.778440i
$391$	−2.74842	−	1.99685i	−0.138994	−	0.100985i
$392$	5.11584	+	19.3150i	0.258389	+	0.975553i
$393$	−5.77630	+	1.87683i	−0.291376	+	0.0946737i
$394$	−1.07474	−	10.2255i	−0.0541446	−	0.515151i
$395$	−25.8111	−	44.7061i	−1.29870	−	2.24941i
$396$	2.21986	−	3.33753i	0.111552	−	0.167717i
$397$	−17.0993	−	9.87228i	−0.858189	−	0.495475i	0.00521668	−	0.999986i	$-0.498339\pi$
$397$	−17.0993	−	9.87228i	−0.858189	−	0.495475i	−0.863405	+	0.504511i	$0.831673\pi$
$398$	−3.24644	+	2.35868i	−0.162729	+	0.118230i
$399$	−9.29773	−	1.73709i	−0.465469	−	0.0869632i
$400$	0.423941	−	1.30476i	0.0211971	−	0.0652379i
$401$	−8.18867	+	3.64583i	−0.408923	+	0.182064i	−0.600880	−	0.799339i	$-0.705183\pi$
$401$	−8.18867	+	3.64583i	−0.408923	+	0.182064i	0.191957	+	0.981403i	$0.438516\pi$
$402$	−0.129230	+	1.22955i	−0.00644543	+	0.0613242i
$403$	5.17804	+	24.3608i	0.257937	+	1.21350i
$404$	−8.22974	−	1.74928i	−0.409445	−	0.0870302i
$405$	−2.36743	−	3.25849i	−0.117639	−	0.161916i
$406$	−7.59017	+	4.63624i	−0.376694	+	0.230093i
$407$	−5.25734	+	30.9889i	−0.260597	+	1.53606i
$408$	3.00075	−	5.19745i	0.148559	−	0.257312i
$409$	−1.48518	−	0.661246i	−0.0734376	−	0.0326965i	0.369689	−	0.929155i	$-0.379464\pi$
$409$	−1.48518	−	0.661246i	−0.0734376	−	0.0326965i	−0.443127	+	0.896459i	$0.646131\pi$
$410$	14.5675	−	16.1789i	0.719439	−	0.799018i
$411$	11.0870	−	9.98278i	0.546881	−	0.492414i
$412$	5.64922	−	7.77549i	0.278317	−	0.383071i
$413$	12.7756	+	8.80754i	0.628646	+	0.433391i
$414$	1.36710	+	0.444197i	0.0671891	+	0.0218311i
$415$	−7.32994	+	34.4846i	−0.359812	+	1.69278i
$416$	10.6972	−	24.0263i	0.524473	−	1.17798i
$417$	−5.37878	+	3.10544i	−0.263400	+	0.152074i
$418$	−5.64761	−	8.90905i	−0.276233	−	0.435756i
$419$		−	8.56392i		−	0.418375i	−0.977876	−	0.209187i	$-0.932918\pi$
$419$		−	8.56392i		−	0.418375i	0.977876	−	0.209187i	$-0.0670819\pi$
$420$	−7.82543	−	10.2288i	−0.381842	−	0.499113i
$421$	−4.46363	−	13.7376i	−0.217544	−	0.669532i	−0.998963	−	0.0455254i	$-0.985504\pi$
$421$	−4.46363	−	13.7376i	−0.217544	−	0.669532i	0.781419	−	0.624007i	$-0.214496\pi$
$422$	8.56505	+	9.51245i	0.416940	+	0.463059i
$423$	9.96156	+	1.04700i	0.484348	+	0.0509070i
$424$	−9.11245	−	0.957757i	−0.442540	−	0.0465128i
$425$	15.7885	+	17.5349i	0.765855	+	0.850568i
$426$	−3.23829	−	9.96644i	−0.156896	−	0.482876i
$427$	−8.37689	+	20.1415i	−0.405386	+	0.974715i
$428$			1.27013i			0.0613942i
$429$	−8.33948	−	13.1555i	−0.402634	−	0.635152i
$430$	0.260329	−	0.150301i	0.0125542	−	0.00724815i
$431$	0.779768	−	1.75139i	0.0375601	−	0.0843613i	−0.893791	−	0.448484i	$-0.851964\pi$
$431$	0.779768	−	1.75139i	0.0375601	−	0.0843613i	0.931351	+	0.364122i	$0.118631\pi$
$432$	−0.0254163	+	0.119575i	−0.00122284	+	0.00575303i
$433$	−24.9258	−	8.09890i	−1.19786	−	0.389208i	−0.358886	−	0.933381i	$-0.616843\pi$
$433$	−24.9258	−	8.09890i	−1.19786	−	0.389208i	−0.838973	+	0.544173i	$0.816843\pi$
$434$	−5.35740	−	11.2738i	−0.257163	−	0.541158i
$435$	8.94588	−	12.3130i	0.428922	−	0.590361i
$436$	3.37452	−	3.03843i	0.161610	−	0.145515i
$437$	−3.86522	+	4.29276i	−0.184899	+	0.205351i
$438$	−5.21510	−	2.32191i	−0.249187	−	0.110945i
$439$	−4.29592	+	7.44076i	−0.205033	+	0.355128i	−0.950143	−	0.311813i	$-0.899064\pi$
$439$	−4.29592	+	7.44076i	−0.205033	+	0.355128i	0.745110	+	0.666942i	$0.232397\pi$
$440$	6.37781	−	37.5934i	0.304050	−	1.79220i
$441$	6.99143	−	0.346213i	0.332925	−	0.0164864i
$442$	−5.16331	−	7.10668i	−0.245593	−	0.338030i
$443$	15.3644	+	3.26580i	0.729984	+	0.155163i	0.557887	−	0.829917i	$-0.311612\pi$
$443$	15.3644	+	3.26580i	0.729984	+	0.155163i	0.172097	+	0.985080i	$0.444946\pi$
$444$	2.38133	+	11.2033i	0.113013	+	0.531685i
$445$	5.17734	−	49.2591i	0.245430	−	2.33511i
$446$	10.1519	−	4.51991i	0.480706	−	0.214024i
$447$	−3.56147	+	10.9611i	−0.168452	+	0.518441i
$448$	−2.53953	+	13.5928i	−0.119982	+	0.642199i
$449$	20.2628	−	14.7218i	0.956260	−	0.694764i	0.00398103	−	0.999992i	$-0.498733\pi$
$449$	20.2628	−	14.7218i	0.956260	−	0.694764i	0.952279	+	0.305228i	$0.0987328\pi$
$450$	−8.64625	−	4.99192i	−0.407588	−	0.235321i
$451$	11.1600	−	16.7789i	0.525504	−	0.790089i
$452$	0.764389	+	1.32396i	0.0359538	+	0.0622738i
$453$	0.428280	+	4.07481i	0.0201224	+	0.191451i
$454$	13.6198	−	4.42534i	0.639208	−	0.207691i
$455$	−48.6799	+	11.6129i	−2.28215	+	0.544420i
$456$	−8.25571	−	5.99813i	−0.386609	−	0.280888i
$457$	−9.74263	−	21.8823i	−0.455741	−	1.02361i	−0.984587	−	0.174893i	$-0.944042\pi$
$457$	−9.74263	−	21.8823i	−0.455741	−	1.02361i	0.528847	−	0.848717i	$-0.322625\pi$
$458$	−19.2254	+	4.08648i	−0.898342	+	0.190949i
$459$	−1.56248	−	1.40686i	−0.0729303	−	0.0656667i
$460$	−7.82218	+	0.822144i	−0.364711	+	0.0383327i
$461$	22.7005			1.05727			0.528634	−	0.848850i	$-0.322704\pi$
$461$	22.7005			1.05727			0.528634	+	0.848850i	$0.322704\pi$
$462$	5.59546	+	5.44347i	0.260324	+	0.253253i
$463$	5.13721			0.238747			0.119373	−	0.992849i	$-0.461911\pi$
$463$	5.13721			0.238747			0.119373	+	0.992849i	$0.461911\pi$
$464$	−0.459404	+	0.0482853i	−0.0213273	+	0.00224159i
$465$	15.8730	+	14.2921i	0.736092	+	0.662780i
$466$	1.49579	−	0.317940i	0.0692912	−	0.0147283i
$467$	6.78476	+	15.2388i	0.313961	+	0.705169i	0.999744	−	0.0226379i	$-0.00720647\pi$
$467$	6.78476	+	15.2388i	0.313961	+	0.705169i	−0.685782	+	0.727807i	$0.740540\pi$
$468$	−4.59185	−	3.33618i	−0.212258	−	0.154215i
$469$	3.52389	+	1.04935i	0.162718	+	0.0484544i
$470$	34.1339	−	11.0908i	1.57448	−	0.511580i
$471$	1.49020	+	14.1783i	0.0686650	+	0.653303i
$472$	8.37062	+	14.4983i	0.385289	+	0.667340i
$473$	0.218142	−	0.172720i	0.0100302	−	0.00794166i
$474$	9.87453	+	5.70106i	0.453552	+	0.261858i
$475$	32.4583	−	23.5823i	1.48929	−	1.08203i
$476$	−5.10587	−	4.37356i	−0.234027	−	0.200462i
$477$	−0.991938	+	3.05287i	−0.0454177	+	0.139781i
$478$	17.9363	−	7.98576i	0.820388	−	0.365260i
$479$	−0.0911023	+	0.866780i	−0.00416257	+	0.0396042i	−0.996406	−	0.0847056i	$-0.973005\pi$
$479$	−0.0911023	+	0.866780i	−0.00416257	+	0.0396042i	0.992243	+	0.124310i	$0.0396717\pi$
$480$	−4.68957	−	22.0627i	−0.214049	−	1.00702i
$481$	43.5348	+	9.25361i	1.98502	+	0.421928i
$482$	0.170829	+	0.235125i	0.00778103	+	0.0107097i
$483$	2.04525	−	3.75398i	0.0930622	−	0.170812i
$484$	0.291716	−	13.2910i	0.0132598	−	0.604136i
$485$	−18.9120	+	32.7566i	−0.858750	+	1.48740i
$486$	0.812715	+	0.361844i	0.0368655	+	0.0164136i
$487$	24.1572	−	26.8292i	1.09467	−	1.21575i	0.119837	−	0.992794i	$-0.461763\pi$
$487$	24.1572	−	26.8292i	1.09467	−	1.21575i	0.974829	−	0.222956i	$-0.0715705\pi$
$488$	−17.4896	+	15.7477i	−0.791716	+	0.712864i
$489$	−6.34215	+	8.72922i	−0.286802	+	0.394749i
$490$	22.3811	−	11.3226i	1.01107	−	0.511504i
$491$	−39.6460	−	12.8818i	−1.78920	−	0.581346i	−0.789715	−	0.613474i	$-0.789771\pi$
$491$	−39.6460	−	12.8818i	−1.78920	−	0.581346i	−0.999484	+	0.0321286i	$0.989771\pi$
$492$	1.52671	−	7.18261i	0.0688294	−	0.323817i
$493$	3.23147	−	7.25800i	0.145538	−	0.326884i
$494$	−12.9353	+	7.46822i	−0.581988	+	0.336011i
$495$	−12.4179	−	4.92378i	−0.558142	−	0.221307i
$496$		−	0.648277i		−	0.0291085i
$497$	−30.9048	+	4.02341i	−1.38627	+	0.180475i
$498$	−2.40632	−	7.40588i	−0.107830	−	0.331866i
$499$	13.3152	+	14.7880i	0.596069	+	0.662002i	0.963394	−	0.268091i	$-0.0863928\pi$
$499$	13.3152	+	14.7880i	0.596069	+	0.662002i	−0.367324	+	0.930093i	$0.619726\pi$
$500$	30.1236	+	3.16612i	1.34717	+	0.141593i
$501$	−10.4914	−	1.10269i	−0.468721	−	0.0492646i
$502$	−13.3359	−	14.8110i	−0.595210	−	0.661048i
$503$	9.66715	+	29.7524i	0.431037	+	1.32660i	0.897094	+	0.441840i	$0.145674\pi$
$503$	9.66715	+	29.7524i	0.431037	+	1.32660i	−0.466057	+	0.884755i	$0.654326\pi$
$504$	6.97306	+	2.90011i	0.310605	+	0.129181i
$505$			28.0395i			1.24774i
$506$	4.61830	−	1.18331i	0.205308	−	0.0526047i
$507$	−7.84248	+	4.52786i	−0.348297	+	0.201089i
$508$	−4.78247	+	10.7416i	−0.212188	+	0.476582i
$509$	7.00441	−	32.9532i	0.310465	−	1.46062i	−0.495473	−	0.868623i	$-0.665005\pi$
$509$	7.00441	−	32.9532i	0.310465	−	1.46062i	0.805938	−	0.592000i	$-0.201661\pi$
$510$	−7.16496	−	2.32804i	−0.317270	−	0.103087i
$511$	−9.63630	+	13.9777i	−0.426285	+	0.618338i
$512$	−0.812597	+	1.11844i	−0.0359120	+	0.0494287i
$513$	−2.65676	+	2.39215i	−0.117299	+	0.105616i
$514$	7.29627	−	8.10333i	0.321825	−	0.357423i
$515$	−29.2610	−	13.0278i	−1.28939	−	0.574076i
$516$	0.0506949	−	0.0878062i	0.00223172	−	0.00386545i
$517$	29.7636	−	14.7562i	1.30900	−	0.648978i
$518$	−22.2995	+	0.551795i	−0.979785	+	0.0242445i
$519$	0.0464908	+	0.0639891i	0.00204072	+	0.00280881i
$520$	−52.8132	−	11.2258i	−2.31601	−	0.492283i
$521$	−4.40311	−	20.7150i	−0.192904	−	0.907541i	−0.962977	−	0.269585i	$-0.913113\pi$
$521$	−4.40311	−	20.7150i	−0.192904	−	0.907541i	0.770073	−	0.637956i	$-0.220220\pi$
$522$	−0.351389	+	3.34324i	−0.0153799	+	0.146330i
$523$	30.4100	−	13.5394i	1.32974	−	0.592036i	0.385927	−	0.922529i	$-0.373882\pi$
$523$	30.4100	−	13.5394i	1.32974	−	0.592036i	0.943808	+	0.330493i	$0.107215\pi$
$524$	−2.26827	+	6.98102i	−0.0990899	+	0.304967i
$525$	−19.3159	+	22.5501i	−0.843013	+	0.984168i
$526$	1.47883	−	1.07443i	0.0644801	−	0.0468475i
$527$	9.65601	+	5.57490i	0.420622	+	0.242846i
$528$	0.141136	+	0.380086i	0.00614216	+	0.0165411i
$529$	10.1946	+	17.6576i	0.443244	+	0.767721i
$530$	1.20227	+	11.4389i	0.0522234	+	0.496873i
$531$	5.57796	−	1.81239i	0.242063	−	0.0786510i
$532$	−8.30332	+	7.85686i	−0.359995	+	0.340638i
$533$	−23.0848	−	16.7721i	−0.999915	−	0.726481i
$534$	4.44974	+	9.99428i	0.192559	+	0.432495i
$535$	4.14041	−	0.880070i	0.179005	−	0.0380488i
$536$	2.94791	+	2.65431i	0.127330	+	0.114649i
$537$	15.8799	−	1.66904i	0.685267	−	0.0720245i
$538$	−13.4826			−0.581275
$539$	18.9697	−	13.3847i	0.817082	−	0.576522i
$540$	−4.86775			−0.209475
$541$	−32.8188	+	3.44940i	−1.41099	+	0.148301i	−0.779170	−	0.626813i	$-0.784359\pi$
$541$	−32.8188	+	3.44940i	−1.41099	+	0.148301i	−0.631821	+	0.775114i	$0.717692\pi$
$542$	−11.5863	−	10.4323i	−0.497674	−	0.448107i
$543$	9.02163	−	1.91761i	0.387155	−	0.0822923i
$544$	−4.78905	−	10.7564i	−0.205329	−	0.461176i
$545$	−12.2429	−	8.89502i	−0.524430	−	0.381021i
$546$	8.02921	−	7.59748i	0.343618	−	0.325142i
$547$	−16.7167	+	5.43157i	−0.714752	+	0.232237i	−0.643747	−	0.765239i	$-0.722621\pi$
$547$	−16.7167	+	5.43157i	−0.714752	+	0.232237i	−0.0710058	+	0.997476i	$0.522621\pi$
$548$	−1.88471	−	17.9318i	−0.0805109	−	0.766010i
$549$	4.12247	+	7.14032i	0.175943	+	0.304741i
$550$	−33.0843	+	1.37006i	−1.41072	+	0.0584194i
$551$	−11.6992	−	6.75451i	−0.498401	−	0.287752i
$552$	3.73131	−	2.71095i	0.158815	−	0.115386i
$553$	22.0599	−	25.7536i	0.938080	−	1.09515i
$554$	5.88479	−	18.1115i	0.250021	−	0.769485i
$555$	34.8707	−	15.5254i	1.48018	−	0.659018i
$556$	−0.784617	+	7.46513i	−0.0332752	+	0.316592i
$557$	2.13693	+	10.0534i	0.0905445	+	0.425978i	0.999949	+	0.0100663i	$0.00320425\pi$
$557$	2.13693	+	10.0534i	0.0905445	+	0.425978i	−0.909405	+	0.415912i	$0.863462\pi$
$558$	−4.61465	−	0.980874i	−0.195354	−	0.0415237i
$559$	−0.231582	−	0.318745i	−0.00979486	−	0.0134815i
$560$	1.30229	−	0.0322248i	0.0550320	−	0.00136175i
$561$	−6.87504	−	1.16637i	−0.290265	−	0.0492440i
$562$	3.06858	−	5.31493i	0.129440	−	0.224197i
$563$	−2.94871	−	1.31285i	−0.124273	−	0.0553301i	0.343658	−	0.939095i	$-0.388334\pi$
$563$	−2.94871	−	1.31285i	−0.124273	−	0.0553301i	−0.467931	+	0.883765i	$0.655001\pi$
$564$	8.10016	−	8.99614i	0.341078	−	0.378806i
$565$	3.78623	−	3.40914i	0.159288	−	0.143423i
$566$	−11.6294	+	16.0066i	−0.488822	+	0.672806i
$567$	1.50171	−	2.17827i	0.0630659	−	0.0914788i
$568$	−31.9780	−	10.3903i	−1.34177	−	0.435966i
$569$	−7.21258	+	33.9325i	−0.302367	+	1.42252i	0.520291	+	0.853989i	$0.325823\pi$
$569$	−7.21258	+	33.9325i	−0.302367	+	1.42252i	−0.822658	+	0.568536i	$0.807510\pi$
$570$	−5.21025	+	11.7024i	−0.218233	+	0.490160i
$571$	−3.71250	+	2.14341i	−0.155363	+	0.0896990i	−0.575666	−	0.817685i	$-0.695257\pi$
$571$	−3.71250	+	2.14341i	−0.155363	+	0.0896990i	0.420303	+	0.907384i	$0.361924\pi$
$572$	−18.7869	−	1.19141i	−0.785520	−	0.0498154i
$573$			2.41024i			0.100689i
$574$	13.2045	+	5.49177i	0.551144	+	0.229222i
$575$	5.60346	+	17.2457i	0.233681	+	0.719195i
$576$	3.49720	+	3.88404i	0.145717	+	0.161835i
$577$	22.5078	+	2.36567i	0.937013	+	0.0984840i	0.560710	−	0.828012i	$-0.310528\pi$
$577$	22.5078	+	2.36567i	0.937013	+	0.0984840i	0.376303	+	0.926497i	$0.377195\pi$
$578$	11.1297	+	1.16978i	0.462933	+	0.0486562i
$579$	17.6329	+	19.5833i	0.732799	+	0.813856i
$580$	−5.68403	−	17.4937i	−0.236017	−	0.726384i
$581$	−22.9648	+	2.98973i	−0.952739	+	0.124035i
$582$		−	8.35443i		−	0.346302i
$583$	2.64246	+	10.3131i	0.109440	+	0.427127i
$584$	−15.8626	+	9.15826i	−0.656398	+	0.378972i
$585$	−7.69365	+	17.2802i	−0.318093	+	0.714450i
$586$	−1.47124	+	6.92164i	−0.0607763	+	0.285930i
$587$	9.48102	+	3.08057i	0.391324	+	0.127149i	0.498069	−	0.867138i	$-0.334043\pi$
$587$	9.48102	+	3.08057i	0.391324	+	0.127149i	−0.106745	+	0.994286i	$0.534043\pi$
$588$	4.62804	−	7.08181i	0.190857	−	0.292049i
$589$	11.1435	−	15.3378i	0.459162	−	0.631982i
$590$	15.6174	−	14.0620i	0.642959	−	0.578923i
$591$	−7.73341	+	8.58883i	−0.318110	+	0.353297i
$592$	−1.05837	−	0.471215i	−0.0434986	−	0.0193668i
$593$	−1.45077	+	2.51281i	−0.0595760	+	0.103189i	−0.894275	−	0.447518i	$-0.852308\pi$
$593$	−1.45077	+	2.51281i	−0.0595760	+	0.103189i	0.834699	+	0.550706i	$0.185642\pi$
$594$	2.91912	−	0.429566i	0.119773	−	0.0176253i
$595$	−10.7192	+	19.6746i	−0.439443	+	0.806582i
$596$	8.18719	+	11.2687i	0.335360	+	0.461584i
$597$	4.41211	+	0.937822i	0.180575	+	0.0383825i
$598$	−1.40356	−	6.60325i	−0.0573960	−	0.270027i
$599$	−1.92085	+	18.2756i	−0.0784837	+	0.746723i	0.882536	+	0.470244i	$0.155834\pi$
$599$	−1.92085	+	18.2756i	−0.0784837	+	0.746723i	−0.961020	+	0.276478i	$0.910833\pi$
$600$	−29.2643	+	13.0293i	−1.19471	+	0.531919i
$601$	−9.49420	+	29.2201i	−0.387276	+	1.19191i	0.547539	+	0.836780i	$0.315565\pi$
$601$	−9.49420	+	29.2201i	−0.387276	+	1.19191i	−0.934815	+	0.355134i	$0.884435\pi$
$602$	0.149966	+	0.128457i	0.00611215	+	0.00523551i
$603$	1.12429	−	0.816848i	0.0457848	−	0.0332646i
$604$	4.28838	+	2.47590i	0.174492	+	0.100743i
$605$	−43.5284	+	8.25834i	−1.76968	+	0.335749i
$606$	−3.09663	−	5.36353i	−0.125792	−	0.217878i
$607$	−2.74619	−	26.1282i	−0.111464	−	1.06051i	−0.897101	−	0.441825i	$-0.854331\pi$
$607$	−2.74619	−	26.1282i	−0.111464	−	1.06051i	0.785637	−	0.618688i	$-0.212335\pi$
$608$	−19.0406	+	6.18666i	−0.772197	+	0.250902i
$609$	9.58178	+	2.85327i	0.388273	+	0.115620i
$610$	23.9007	+	17.3649i	0.967713	+	0.703084i
$611$	−19.1332	−	42.9738i	−0.774046	−	1.73853i
$612$	−2.48551	+	0.528310i	−0.100471	+	0.0213557i
$613$	−9.81940	−	8.84142i	−0.396602	−	0.357102i	0.446568	−	0.894750i	$-0.352646\pi$
$613$	−9.81940	−	8.84142i	−0.396602	−	0.357102i	−0.843169	+	0.537648i	$0.819313\pi$
$614$	−6.92289	+	0.727625i	−0.279385	+	0.0293645i
$615$	−24.4719			−0.986801
$616$	24.6828	−	4.25849i	0.994499	−	0.171580i
$617$	36.7031			1.47761			0.738805	−	0.673919i	$-0.235391\pi$
$617$	36.7031			1.47761			0.738805	+	0.673919i	$0.235391\pi$
$618$	7.03595	−	0.739508i	0.283028	−	0.0297474i
$619$	35.2661	+	31.7537i	1.41746	+	1.27629i	0.909995	+	0.414620i	$0.136086\pi$
$619$	35.2661	+	31.7537i	1.41746	+	1.27629i	0.507469	+	0.861670i	$0.330581\pi$
$620$	25.2499	−	5.36702i	1.01406	−	0.215545i
$621$	−0.657201	−	1.47610i	−0.0263726	−	0.0592338i
$622$	−8.04782	−	5.84708i	−0.322688	−	0.234447i
$623$	31.6478	−	7.54978i	1.26794	−	0.302475i
$624$	0.546011	−	0.177410i	0.0218579	−	0.00710207i
$625$	−4.68620	−	44.5862i	−0.187448	−	1.78345i
$626$	12.6755	+	21.9546i	0.506614	+	0.877481i
$627$	−3.19430	+	11.4186i	−0.127568	+	0.456016i
$628$	14.9215	+	8.61491i	0.595431	+	0.343772i
$629$	16.1202	−	11.7120i	0.642754	−	0.466988i
$630$	1.74105	−	9.31892i	0.0693649	−	0.371275i
$631$	12.5008	−	38.4735i	0.497649	−	1.53161i	−0.315138	−	0.949046i	$-0.602051\pi$
$631$	12.5008	−	38.4735i	0.497649	−	1.53161i	0.812787	−	0.582560i	$-0.197949\pi$
$632$	33.4216	−	14.8802i	1.32944	−	0.591904i
$633$	1.50399	−	14.3095i	0.0597783	−	0.568753i
$634$	2.34300	+	11.0230i	0.0930525	+	0.437777i
$635$	38.3295	+	8.14718i	1.52106	+	0.323311i
$636$	2.28029	+	3.13855i	0.0904194	+	0.124452i
$637$	−17.8252	−	27.6223i	−0.706261	−	1.09444i
$638$	4.95240	+	9.98910i	0.196067	+	0.395472i
$639$	−5.88974	+	10.2013i	−0.232994	+	0.403558i
$640$	−24.1028	−	10.7313i	−0.952748	−	0.424191i
$641$	1.22874	−	1.36465i	0.0485321	−	0.0539004i	−0.718390	−	0.695641i	$-0.755121\pi$
$641$	1.22874	−	1.36465i	0.0485321	−	0.0539004i	0.766922	+	0.641740i	$0.221787\pi$
$642$	−0.694802	+	0.625603i	−0.0274217	+	0.0246906i
$643$	3.33939	−	4.59628i	0.131693	−	0.181260i	−0.738078	−	0.674715i	$-0.764266\pi$
$643$	3.33939	−	4.59628i	0.131693	−	0.181260i	0.869771	+	0.493456i	$0.164266\pi$
$644$	−2.21755	−	4.66648i	−0.0873838	−	0.183885i
$645$	−0.321359	−	0.104416i	−0.0126535	−	0.00411137i
$646$	−1.39029	+	6.54081i	−0.0547003	+	0.257345i
$647$	3.55990	−	7.99567i	0.139954	−	0.314342i	−0.829947	−	0.557843i	$-0.811629\pi$
$647$	3.55990	−	7.99567i	0.139954	−	0.314342i	0.969901	+	0.243501i	$0.0782958\pi$
$648$	2.47200	−	1.42721i	0.0971095	−	0.0560662i
$649$	12.4067	−	14.9819i	0.487006	−	0.588089i
$650$			46.8876i			1.83908i
$651$	−5.38793	+	12.9548i	−0.211170	+	0.507739i
$652$	4.02967	+	12.4021i	0.157814	+	0.485702i
$653$	7.98654	+	8.86995i	0.312537	+	0.347108i	0.878864	−	0.477073i	$-0.158302\pi$
$653$	7.98654	+	8.86995i	0.312537	+	0.347108i	−0.566326	+	0.824181i	$0.691636\pi$
$654$	3.32423	+	0.349391i	0.129988	+	0.0136623i
$655$	24.3286	+	2.55703i	0.950595	+	0.0999116i
$656$	0.496997	+	0.551971i	0.0194045	+	0.0215508i
$657$	1.98293	+	6.10282i	0.0773614	+	0.238094i
$658$	14.3252	+	18.7248i	0.558455	+	0.729967i
$659$			28.4212i			1.10713i	0.832805	+	0.553566i	$0.186734\pi$
$659$			28.4212i			1.10713i	−0.832805	+	0.553566i	$0.813266\pi$
$660$	−13.6356	+	8.64383i	−0.530764	+	0.336461i
$661$	1.62433	−	0.937807i	0.0631791	−	0.0364765i	−0.468078	−	0.883687i	$-0.655053\pi$
$661$	1.62433	−	0.937807i	0.0631791	−	0.0364765i	0.531257	+	0.847211i	$0.321720\pi$
$662$	−6.83455	+	15.3507i	−0.265632	+	0.596620i
$663$	−2.05296	+	9.65841i	−0.0797303	+	0.375102i
$664$	−23.7623	−	7.72082i	−0.922154	−	0.299626i
$665$	31.3653	+	21.6233i	1.21629	+	0.838517i
$666$	−4.95562	+	6.82083i	−0.192027	+	0.264302i
$667$	4.53737	−	4.08547i	0.175688	−	0.158190i
$668$	−8.53099	+	9.47462i	−0.330074	+	0.366584i
$669$	−11.4114	−	5.08068i	−0.441190	−	0.196431i
$670$	2.48977	−	4.31241i	0.0961882	−	0.166603i
$671$	24.2272	+	12.6811i	0.935281	+	0.489549i
$672$	12.6442	−	7.72338i	0.487762	−	0.297936i
$673$	5.84535	+	8.04543i	0.225322	+	0.310129i	0.906678	−	0.421823i	$-0.138610\pi$
$673$	5.84535	+	8.04543i	0.225322	+	0.310129i	−0.681357	+	0.731952i	$0.738610\pi$
$674$	18.7238	+	3.97987i	0.721214	+	0.153299i
$675$	2.33329	+	10.9773i	0.0898083	+	0.422515i
$676$	−1.14400	+	10.8845i	−0.0440001	+	0.418633i
$677$	−27.2157	+	12.1172i	−1.04599	+	0.465703i	−0.856482	−	0.516177i	$-0.827355\pi$
$677$	−27.2157	+	12.1172i	−1.04599	+	0.465703i	−0.189504	+	0.981880i	$0.560688\pi$
$678$	−0.347748	+	1.07026i	−0.0133552	+	0.0411031i
$679$	−24.4235	−	4.56302i	−0.937287	−	0.175113i
$680$	−19.5558	+	14.2081i	−0.749931	+	0.544857i
$681$	−13.9408	−	8.04871i	−0.534211	−	0.308427i
$682$	−14.6684	+	5.44676i	−0.561681	+	0.208567i
$683$	−19.2320	−	33.3108i	−0.735892	−	1.27460i	−0.954331	−	0.298751i	$-0.903430\pi$
$683$	−19.2320	−	33.3108i	−0.735892	−	1.27460i	0.218440	−	0.975850i	$-0.429903\pi$
$684$	0.451630	+	4.29697i	0.0172685	+	0.164299i
$685$	−57.1486	+	18.5687i	−2.18354	+	0.709474i
$686$	11.9022	+	11.3929i	0.454430	+	0.434985i
$687$	17.8739	+	12.9862i	0.681933	+	0.495453i
$688$	0.00417131	+	0.00936892i	0.000159030	+	0.000357187i
$689$	14.7458	−	3.13431i	0.561769	−	0.119408i
$690$	−4.30254	−	3.87403i	−0.163795	−	0.147482i
$691$	−22.6629	+	2.38197i	−0.862138	+	0.0906144i	−0.525268	−	0.850937i	$-0.676035\pi$
$691$	−22.6629	+	2.38197i	−0.862138	+	0.0906144i	−0.336870	+	0.941551i	$0.609368\pi$
$692$	0.0955912			0.00363383
$693$	0.338565	−	8.76843i	0.0128610	−	0.333085i
$694$	21.5984			0.819864
$695$	24.8786	−	2.61485i	0.943700	−	0.0991869i
$696$	8.01563	+	7.21731i	0.303832	+	0.273571i
$697$	−12.4955	+	2.65600i	−0.473301	+	0.100603i
$698$	−9.01904	−	20.2571i	−0.341376	−	0.766742i
$699$	−1.39065	−	1.01036i	−0.0525990	−	0.0382154i
$700$	8.32682	+	34.9051i	0.314724	+	1.31929i
$701$	13.2525	−	4.30601i	0.500542	−	0.162636i	−0.0478548	−	0.998854i	$-0.515238\pi$
$701$	13.2525	−	4.30601i	0.500542	−	0.162636i	0.548396	+	0.836218i	$0.315238\pi$
$702$	−0.436720	−	4.15511i	−0.0164829	−	0.156825i
$703$	−16.9403	−	29.3414i	−0.638914	−	1.10663i
$704$	16.6934	+	4.66989i	0.629157	+	0.176003i
$705$	−34.9384	−	20.1717i	−1.31585	−	0.759709i
$706$	20.1133	−	14.6132i	0.756975	−	0.549974i
$707$	−17.3712	+	6.12330i	−0.653309	+	0.230291i
$708$	2.19039	−	6.74132i	0.0823198	−	0.253354i
$709$	−3.23699	+	1.44120i	−0.121568	+	0.0541254i	−0.466619	−	0.884458i	$-0.654528\pi$
$709$	−3.23699	+	1.44120i	−0.121568	+	0.0541254i	0.345052	+	0.938584i	$0.387861\pi$
$710$	−4.41192	+	41.9766i	−0.165576	+	1.57535i
$711$	−2.66475	−	12.5367i	−0.0999360	−	0.470162i
$712$	34.3350	+	7.29812i	1.28676	+	0.273509i
$713$	5.03651	+	6.93216i	0.188619	+	0.259612i
$714$	−0.122418	−	4.94726i	−0.00458139	−	0.185147i
$715$	9.13358	+	62.0674i	0.341577	+	2.32119i
$716$	9.64878	−	16.7122i	0.360592	−	0.624563i
$717$	−20.1616	−	8.97652i	−0.752949	−	0.335234i
$718$	5.50814	−	6.11741i	0.205562	−	0.228300i
$719$	−13.3059	+	11.9807i	−0.496228	+	0.446806i	−0.878849	−	0.477099i	$-0.841688\pi$
$719$	−13.3059	+	11.9807i	−0.496228	+	0.446806i	0.382621	+	0.923905i	$0.375021\pi$
$720$	0.289409	−	0.398337i	0.0107856	−	0.0148451i
$721$	1.68100	−	20.9729i	0.0626038	−	0.781073i
$722$	−5.26201	−	1.70973i	−0.195832	−	0.0636296i
$723$	0.0679224	−	0.319550i	0.00252606	−	0.0118842i
$724$	4.53381	−	10.1831i	0.168498	−	0.378452i
$725$	−36.7253	+	21.2034i	−1.36394	+	0.787474i
$726$	7.41427	−	6.38689i	0.275169	−	0.237040i
$727$			44.3939i			1.64648i	0.567695	+	0.823239i	$0.307835\pi$
$727$			44.3939i			1.64648i	−0.567695	+	0.823239i	$0.692165\pi$
$728$	−4.57876	−	35.1705i	−0.169700	−	1.30351i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	15.3852	+	17.0870i	0.569430	+	0.632416i
$731$	−0.175420	−	0.0184374i	−0.00648816	−	0.000681933i
$732$	9.90994	+	1.04158i	0.366282	+	0.0384978i
$733$	−34.0782	−	37.8477i	−1.25871	−	1.39794i	−0.881757	−	0.471704i	$-0.843639\pi$
$733$	−34.0782	−	37.8477i	−1.25871	−	1.39794i	−0.376951	−	0.926233i	$-0.623028\pi$
$734$	2.35630	+	7.25195i	0.0869726	+	0.267674i
$735$	−26.2922	−	10.1796i	−0.969801	−	0.375481i
$736$		−	9.04858i		−	0.333535i
$737$	1.69888	−	4.28461i	0.0625790	−	0.157826i
$738$	4.68109	−	2.70263i	0.172313	−	0.0994851i
$739$	6.45799	−	14.5049i	0.237561	−	0.533571i	−0.754942	−	0.655792i	$-0.772335\pi$
$739$	6.45799	−	14.5049i	0.237561	−	0.533571i	0.992503	+	0.122221i	$0.0390017\pi$
$740$	9.59133	−	45.1237i	0.352584	−	1.65878i
$741$	15.9678	+	5.18826i	0.586592	+	0.190595i
$742$	−6.82409	+	3.24287i	−0.250520	+	0.119049i
$743$	−19.7751	+	27.2180i	−0.725477	+	0.998533i	0.273847	+	0.961773i	$0.411704\pi$
$743$	−19.7751	+	27.2180i	−0.725477	+	0.998533i	−0.999324	+	0.0367601i	$0.988296\pi$
$744$	−11.2491	+	10.1287i	−0.412413	+	0.371338i
$745$	31.0611	−	34.4968i	1.13799	−	1.26387i
$746$	−17.4984	−	7.79078i	−0.640661	−	0.285241i
$747$	−4.37656	+	7.58042i	−0.160130	+	0.277353i
$748$	−6.02428	+	5.89351i	−0.220269	+	0.215488i
$749$	1.44941	+	2.37289i	0.0529603	+	0.0867034i
$750$	13.1054	+	18.0380i	0.478541	+	0.658655i
$751$	45.5580	+	9.68365i	1.66243	+	0.353361i	0.940813	−	0.338926i	$-0.110064\pi$
$751$	45.5580	+	9.68365i	1.66243	+	0.353361i	0.721622	+	0.692288i	$0.243397\pi$
$752$	0.254581	+	1.19771i	0.00928362	+	0.0436760i
$753$	−2.34174	+	22.2801i	−0.0853376	+	0.811933i
$754$	14.4226	−	6.42137i	0.525241	−	0.233853i
$755$	5.09958	−	15.6949i	0.185593	−	0.571196i
$756$	−1.06302	−	3.01569i	−0.0386618	−	0.109679i
$757$	−13.1308	+	9.54009i	−0.477247	+	0.346740i	−0.800259	−	0.599655i	$-0.795305\pi$
$757$	−13.1308	+	9.54009i	−0.477247	+	0.346740i	0.323012	+	0.946395i	$0.395305\pi$
$758$	−22.9646	−	13.2586i	−0.834112	−	0.481575i
$759$	−4.46212	−	2.96784i	−0.161965	−	0.107726i
$760$	20.5507	+	35.5948i	0.745451	+	1.29116i
$761$	−3.28772	−	31.2806i	−0.119180	−	1.13392i	−0.876676	−	0.481080i	$-0.840245\pi$
$761$	−3.28772	−	31.2806i	−0.119180	−	1.13392i	0.757497	−	0.652839i	$-0.226422\pi$
$762$	−8.23159	+	2.67461i	−0.298199	+	0.0968908i
$763$	2.83705	−	9.52729i	0.102708	−	0.344911i
$764$	2.35661	+	1.71218i	0.0852592	+	0.0619444i
$765$	3.44439	+	7.73623i	0.124532	+	0.279704i
$766$	−5.87601	+	1.24899i	−0.212309	+	0.0451277i
$767$	−20.4693	−	18.4306i	−0.739104	−	0.665492i
$768$	16.1914	−	1.70178i	0.584255	−	0.0614077i
$769$	−15.5440			−0.560530			−0.280265	−	0.959923i	$-0.590422\pi$
$769$	−15.5440			−0.560530			−0.280265	+	0.959923i	$0.590422\pi$
$770$	−11.6709	−	29.1959i	−0.420590	−	1.05215i
$771$	−12.2569			−0.441423
$772$	31.6736	−	3.32903i	1.13996	−	0.119814i
$773$	26.9333	+	24.2508i	0.968723	+	0.872242i	0.991840	−	0.127490i	$-0.0406922\pi$
$773$	26.9333	+	24.2508i	0.968723	+	0.872242i	−0.0231165	+	0.999733i	$0.507359\pi$
$774$	0.0730024	−	0.0155171i	0.00262402	−	0.000557752i
$775$	−24.2063	−	54.3683i	−0.869517	−	1.95297i
$776$	−21.6863	−	15.7560i	−0.778492	−	0.565608i
$777$	17.2335	+	18.2128i	0.618247	+	0.653379i
$778$	−1.20607	+	0.391876i	−0.0432397	+	0.0140494i
$779$	2.27050	+	21.6023i	0.0813490	+	0.773984i
$780$	11.4303	+	19.7979i	0.409272	+	0.708879i
$781$	1.61647	+	39.0346i	0.0578418	+	1.39677i
$782$	−2.61736	−	1.51114i	−0.0935968	−	0.0540381i
$783$	3.05706	−	2.22108i	0.109250	−	0.0793750i
$784$	0.304360	+	0.799765i	0.0108700	+	0.0285630i
$785$	17.7440	−	54.6105i	0.633311	−	1.94913i
$786$	−4.93607	+	2.19768i	−0.176064	+	0.0783886i
$787$	2.68329	−	25.5298i	0.0956488	−	0.910038i	−0.836501	−	0.547965i	$-0.815403\pi$
$787$	2.68329	−	25.5298i	0.0956488	−	0.910038i	0.932150	−	0.362073i	$-0.117931\pi$
$788$	2.90408	+	13.6626i	0.103454	+	0.486711i
$789$	−2.00982	−	0.427201i	−0.0715515	−	0.0152087i
$790$	−26.9938	−	37.1537i	−0.960395	−	1.32187i
$791$	2.93888	+	1.60117i	0.104495	+	0.0569310i
$792$	4.39025	−	8.38754i	0.156001	−	0.298038i
$793$	19.3605	−	33.5335i	0.687513	−	1.19081i
$794$	−16.0467	−	7.14445i	−0.569476	−	0.253547i
$795$	8.65111	−	9.60803i	0.306823	−	0.340762i
$796$	4.05121	−	3.64772i	0.143591	−	0.129290i
$797$	−10.4980	+	14.4492i	−0.371858	+	0.511819i	−0.953405	−	0.301694i	$-0.902448\pi$
$797$	−10.4980	+	14.4492i	−0.371858	+	0.511819i	0.581547	+	0.813513i	$0.302448\pi$
$798$	−8.38774	−	0.672286i	−0.296923	−	0.0237987i
$799$	−20.0290	−	6.50783i	−0.708577	−	0.230230i
$800$	−13.0666	+	61.4737i	−0.461975	+	2.17342i
$801$	5.00181	−	11.2342i	0.176730	−	0.396942i
$802$	−6.90592	+	3.98714i	−0.243857	+	0.140791i
$803$	16.3916	+	13.5741i	0.578446	+	0.479020i
$804$		−	1.67955i		−	0.0592330i
$805$	−13.6754	+	10.4622i	−0.481993	+	0.368744i
$806$	6.84663	+	21.0718i	0.241162	+	0.742222i
$807$	10.1409	+	11.2626i	0.356976	+	0.396462i
$808$	−19.7626	−	2.07714i	−0.695247	−	0.0730734i
$809$	−28.9398	−	3.04170i	−1.01747	−	0.106940i	−0.418917	−	0.908024i	$-0.637590\pi$
$809$	−28.9398	−	3.04170i	−1.01747	−	0.106940i	−0.598552	+	0.801084i	$0.704257\pi$
$810$	−2.39760	−	2.66281i	−0.0842432	−	0.0935616i
$811$	4.49399	+	13.8311i	0.157805	+	0.485675i	0.998434	−	0.0559367i	$-0.0178145\pi$
$811$	4.49399	+	13.8311i	0.157805	+	0.485675i	−0.840629	+	0.541611i	$0.817814\pi$
$812$	9.59644	−	7.34167i	0.336769	−	0.257642i
$813$			17.5252i			0.614636i
$814$	−1.76975	+	27.9064i	−0.0620296	+	0.978120i
$815$	37.6363	−	21.7293i	1.31834	−	0.761146i
$816$	0.104541	−	0.234804i	0.00365968	−	0.00821978i
$817$	−0.0623566	+	0.293365i	−0.00218158	+	0.0102635i
$818$	−1.37551	−	0.446931i	−0.0480936	−	0.0156266i
$819$	−12.3857	−	0.992724i	−0.432790	−	0.0346886i
$820$	−17.3842	+	23.9273i	−0.607083	+	0.835579i
$821$	10.1650	−	9.15259i	0.354760	−	0.319428i	−0.472410	−	0.881379i	$-0.656616\pi$
$821$	10.1650	−	9.15259i	0.354760	−	0.319428i	0.827170	+	0.561951i	$0.189949\pi$
$822$	8.88095	−	9.86329i	0.309759	−	0.344022i
$823$	−10.5194	−	4.68355i	−0.366684	−	0.163258i	0.215119	−	0.976588i	$-0.430986\pi$
$823$	−10.5194	−	4.68355i	−0.366684	−	0.163258i	−0.581803	+	0.813330i	$0.697653\pi$
$824$	11.3498	−	19.6585i	0.395390	−	0.684835i
$825$	26.0287	+	26.6063i	0.906203	+	0.926311i
$826$	12.1223	+	6.60449i	0.421788	+	0.229799i
$827$	−14.8664	−	20.4619i	−0.516957	−	0.711530i	0.468116	−	0.883667i	$-0.344933\pi$
$827$	−14.8664	−	20.4619i	−0.516957	−	0.711530i	−0.985073	+	0.172137i	$0.944933\pi$
$828$	−1.91011	−	0.406007i	−0.0663810	−	0.0141097i
$829$	1.11755	+	5.25765i	0.0388140	+	0.182606i	0.993284	−	0.115701i	$-0.0369115\pi$
$829$	1.11755	+	5.25765i	0.0388140	+	0.182606i	−0.954470	+	0.298307i	$0.903578\pi$
$830$	−3.27841	+	31.1920i	−0.113795	+	1.08269i
$831$	−19.5556	+	8.70671i	−0.678376	+	0.302032i
$832$	7.58496	−	23.3441i	0.262961	−	0.809311i
$833$	−14.5298	−	2.34421i	−0.503427	−	0.0812222i
$834$	−4.47012	+	3.24773i	−0.154788	+	0.112460i
$835$	36.7967	+	21.2446i	1.27340	+	0.735198i
$836$	8.89539	+	11.2347i	0.307653	+	0.388561i
$837$	2.65153	+	4.59258i	0.0916502	+	0.158743i
$838$	−0.796370	−	7.57696i	−0.0275102	−	0.261742i
$839$	−16.9641	+	5.51197i	−0.585666	+	0.190294i	−0.586837	−	0.809705i	$-0.699627\pi$
$839$	−16.9641	+	5.51197i	−0.585666	+	0.190294i	0.00117125	+	0.999999i	$0.499627\pi$
$840$	−20.9064	−	22.0944i	−0.721338	−	0.762328i
$841$	−11.9097	−	8.65291i	−0.410679	−	0.298376i
$842$	−5.22670	−	11.7394i	−0.180124	−	0.404565i
$843$	−6.74782	+	1.43429i	−0.232407	+	0.0493997i
$844$	−12.9227	−	11.6357i	−0.444818	−	0.400516i
$845$	36.2741	−	3.81256i	1.24787	−	0.131156i
$846$	8.91089			0.306363
$847$	−14.6220	−	25.1634i	−0.502418	−	0.864625i
$848$	−0.392407			−0.0134753
$849$	22.1181	−	2.32470i	0.759090	−	0.0797835i
$850$	15.5995	+	14.0459i	0.535059	+	0.481770i
$851$	14.9783	−	3.18373i	0.513448	−	0.109137i
$852$	5.79040	+	13.0055i	0.198376	+	0.445560i
$853$	−0.000577889	0	0.000419861i	−1.97865e−5	0	1.43758e-5i	0.587775	−	0.809024i	$-0.300004\pi$
$853$	−0.000577889	0	0.000419861i	−1.97865e−5	0	1.43758e-5i	−0.587795	+	0.809010i	$0.700004\pi$
$854$	−5.53850	+	18.5992i	−0.189523	+	0.636453i
$855$	13.6944	−	4.44958i	0.468339	−	0.152173i
$856$	0.313569	+	2.98341i	0.0107176	+	0.101971i
$857$	−25.6757	−	44.4716i	−0.877065	−	1.51912i	−0.854547	−	0.519375i	$-0.826165\pi$
$857$	−25.6757	−	44.4716i	−0.877065	−	1.51912i	−0.0225182	−	0.999746i	$-0.507168\pi$
$858$	−8.60172	−	10.8638i	−0.293658	−	0.370885i
$859$	36.1425	+	20.8669i	1.23317	+	0.711969i	0.967689	−	0.252148i	$-0.0811369\pi$
$859$	36.1425	+	20.8669i	1.23317	+	0.711969i	0.265478	+	0.964117i	$0.414470\pi$
$860$	−0.330378	+	0.240034i	−0.0112658	+	0.00818508i
$861$	−5.34419	−	15.1609i	−0.182130	−	0.516682i
$862$	0.527038	−	1.62206i	0.0179510	−	0.0552475i
$863$	22.9740	−	10.2287i	0.782044	−	0.348189i	0.0234275	−	0.999726i	$-0.492542\pi$
$863$	22.9740	−	10.2287i	0.782044	−	0.348189i	0.758617	+	0.651537i	$0.225875\pi$
$864$	0.585370	−	5.56942i	0.0199147	−	0.189475i
$865$	−0.0662348	−	0.311610i	−0.00225205	−	0.0105951i
$866$	−22.8064	−	4.84764i	−0.774991	−	0.164730i
$867$	−7.39398	−	10.1769i	−0.251113	−	0.345627i
$868$	8.83909	+	14.4708i	0.300018	+	0.491172i
$869$	−29.7263	−	30.3859i	−1.00840	−	1.03077i
$870$	6.76990	−	11.7258i	0.229521	−	0.397542i
$871$	−5.96229	−	2.65458i	−0.202025	−	0.0899471i
$872$	7.17627	−	7.97006i	0.243019	−	0.269900i
$873$	−6.97883	+	6.28376i	−0.236197	+	0.212673i
$874$	−3.02058	+	4.15747i	−0.102173	+	0.140628i
$875$	59.8905	−	28.4605i	2.02467	−	0.962140i
$876$	7.37565	+	2.39649i	0.249200	+	0.0809700i
$877$	7.87747	−	37.0606i	0.266003	−	1.25145i	−0.618825	−	0.785529i	$-0.712391\pi$
$877$	7.87747	−	37.0606i	0.266003	−	1.25145i	0.884828	−	0.465918i	$-0.154276\pi$
$878$	−3.10891	+	6.98272i	−0.104921	+	0.235655i
$879$	6.88854	−	3.97710i	0.232345	−	0.134144i
$880$	0.103353	−	1.62974i	0.00348404	−	0.0549385i
$881$			36.5884i			1.23269i	0.787474	+	0.616347i	$0.211388\pi$
$881$			36.5884i			1.23269i	−0.787474	+	0.616347i	$0.788612\pi$
$882$	6.15350	−	0.956456i	0.207199	−	0.0322056i
$883$	6.13151	+	18.8709i	0.206342	+	0.635055i	0.999656	+	0.0262419i	$0.00835402\pi$
$883$	6.13151	+	18.8709i	0.206342	+	0.635055i	−0.793314	+	0.608813i	$0.791646\pi$
$884$	7.98513	+	8.86838i	0.268569	+	0.298276i
$885$	−23.4932	−	2.46923i	−0.789715	−	0.0830024i
$886$	13.8974	+	1.46067i	0.466892	+	0.0490723i
$887$	−20.5858	−	22.8629i	−0.691205	−	0.767661i	0.290745	−	0.956800i	$-0.406097\pi$
$887$	−20.5858	−	22.8629i	−0.691205	−	0.767661i	−0.981950	+	0.189140i	$0.939430\pi$
$888$	8.35935	+	25.7274i	0.280522	+	0.863357i
$889$	3.32306	+	25.5252i	0.111452	+	0.856087i
$890$		−	44.0636i		−	1.47702i
$891$	−2.55445	−	2.11537i	−0.0855771	−	0.0708677i
$892$	−13.0740	+	7.54829i	−0.437751	+	0.252735i
$893$	−14.5648	+	32.7131i	−0.487393	+	1.09470i
$894$	−2.13174	+	10.0290i	−0.0712959	+	0.335421i
$895$	−61.1643	−	19.8735i	−2.04450	−	0.664297i
$896$	1.38467	−	17.2758i	0.0462587	−	0.577143i
$897$	−4.46030	+	6.13908i	−0.148925	+	0.204978i
$898$	16.5586	−	14.9094i	0.552567	−	0.497533i
$899$	−13.4086	+	14.8917i	−0.447201	+	0.496667i
$900$	12.3905	+	5.51661i	0.413017	+	0.183887i
$901$	3.37453	−	5.84485i	0.112422	−	0.194720i
$902$	8.31355	−	15.8830i	0.276811	−	0.528846i
$903$	−0.00549064	−	0.221892i	−0.000182717	−	0.00738409i
$904$	2.12233	+	2.92113i	0.0705875	+	0.0971554i
$905$	−36.3365	−	7.72357i	−1.20787	−	0.256740i
$906$	0.757845	+	3.56538i	0.0251777	+	0.118452i
$907$	2.34530	−	22.3140i	0.0778743	−	0.740924i	−0.884010	−	0.467468i	$-0.845166\pi$
$907$	2.34530	−	22.3140i	0.0778743	−	0.740924i	0.961884	−	0.273456i	$-0.0881669\pi$
$908$	−17.7728	+	7.91296i	−0.589811	+	0.262601i
$909$	−2.15127	+	6.62092i	−0.0713530	+	0.219602i
$910$	−41.9898	+	14.8013i	−1.39195	+	0.490660i
$911$	−0.497597	+	0.361526i	−0.0164861	+	0.0119779i	−0.595998	−	0.802986i	$-0.703243\pi$
$911$	−0.497597	+	0.361526i	−0.0164861	+	0.0119779i	0.579512	+	0.814964i	$0.303243\pi$
$912$	−0.378480	−	0.218516i	−0.0125327	−	0.00723578i
$913$	1.20117	+	29.0059i	0.0397529	+	0.959956i
$914$	−10.6547	−	18.4545i	−0.352426	−	0.610419i
$915$	−3.47121	−	33.0263i	−0.114755	−	1.09182i
$916$	25.3944	−	8.25115i	0.839055	−	0.272626i
$917$	3.72875	+	15.6305i	0.123134	+	0.516165i
$918$	−1.51323	−	1.09943i	−0.0499442	−	0.0362866i
$919$	9.65297	+	21.6809i	0.318422	+	0.715188i	0.999861	−	0.0166875i	$-0.00531206\pi$
$919$	9.65297	+	21.6809i	0.318422	+	0.715188i	−0.681439	+	0.731875i	$0.738645\pi$
$920$	−18.1705	+	3.86226i	−0.599063	+	0.127335i
$921$	5.81485	+	5.23571i	0.191606	+	0.172523i
$922$	20.0844	−	2.11095i	0.661443	−	0.0695205i
$923$	55.3206			1.82090
$924$	−8.33281	−	6.55991i	−0.274129	−	0.215805i
$925$	−106.356			−3.49696
$926$	4.54517	−	0.477716i	0.149364	−	0.0156987i
$927$	−5.90982	−	5.32122i	−0.194104	−	0.174772i
$928$	20.6988	−	4.39967i	0.679472	−	0.144426i
$929$	1.44643	+	3.24873i	0.0474557	+	0.106587i	0.935717	−	0.352750i	$-0.114753\pi$
$929$	1.44643	+	3.24873i	0.0474557	+	0.106587i	−0.888262	+	0.459338i	$0.848087\pi$
$930$	15.3727	+	11.1689i	0.504091	+	0.366244i
$931$	−6.54659	+	24.1537i	−0.214556	+	0.791604i
$932$	−1.97576	+	0.641964i	−0.0647183	+	0.0210282i
$933$	1.16882	+	11.1206i	0.0382654	+	0.364071i
$934$	7.41992	+	12.8517i	0.242787	+	0.420520i
$935$	23.3860	+	15.5545i	0.764803	+	0.508686i
$936$	−11.6094	−	6.70269i	−0.379465	−	0.219084i
$937$	−1.57541	+	1.14460i	−0.0514664	+	0.0373925i	−0.613221	−	0.789911i	$-0.710127\pi$
$937$	−1.57541	+	1.14460i	−0.0514664	+	0.0373925i	0.561755	+	0.827304i	$0.310127\pi$
$938$	3.21536	+	0.600723i	0.104985	+	0.0196143i
$939$	8.80579	−	27.1014i	0.287366	−	0.884422i
$940$	−44.5422	+	19.8315i	−1.45281	+	0.646831i
$941$	−3.42035	+	32.5424i	−0.111500	+	1.06085i	0.785512	+	0.618847i	$0.212400\pi$
$941$	−3.42035	+	32.5424i	−0.111500	+	1.06085i	−0.897012	+	0.442006i	$0.854267\pi$
$942$	2.63693	+	12.4058i	0.0859157	+	0.404202i
$943$	−9.60279	−	2.04114i	−0.312710	−	0.0664686i
$944$	0.421427	+	0.580044i	0.0137163	+	0.0188788i
$945$	−9.09403	+	5.55483i	−0.295829	+	0.180699i
$946$	0.176941	−	0.173100i	0.00575284	−	0.00562796i
$947$	5.53443	−	9.58591i	0.179845	−	0.311500i	−0.761982	−	0.647598i	$-0.775774\pi$
$947$	5.53443	−	9.58591i	0.179845	−	0.311500i	0.941827	+	0.336097i	$0.109107\pi$
$948$	−14.1507	−	6.30029i	−0.459593	−	0.204624i
$949$	20.1649	−	22.3954i	0.654580	−	0.726985i
$950$	26.5246	−	23.8829i	0.860572	−	0.774862i
$951$	7.44568	−	10.2481i	0.241443	−	0.332317i
$952$	−13.0729	−	9.01250i	−0.423695	−	0.292097i
$953$	12.5206	+	4.06820i	0.405583	+	0.131782i	0.504702	−	0.863294i	$-0.331602\pi$
$953$	12.5206	+	4.06820i	0.405583	+	0.131782i	−0.0991191	+	0.995076i	$0.531602\pi$
$954$	−0.593730	+	2.79328i	−0.0192227	+	0.0904358i
$955$	3.94850	−	8.86848i	0.127771	−	0.286977i
$956$	−23.0991	+	13.3363i	−0.747078	+	0.431326i
$957$	4.61940	−	11.6502i	0.149324	−	0.376599i
$958$			0.775358i			0.0250507i
$959$	−23.9839	−	31.3499i	−0.774481	−	1.01234i
$960$	−6.50506	−	20.0205i	−0.209950	−	0.646159i
$961$	1.92549	+	2.13847i	0.0621125	+	0.0689829i
$962$	39.3781	+	4.13880i	1.26960	+	0.133440i
$963$	1.04519	+	0.109854i	0.0336807	+	0.00353998i
$964$	−0.264189	−	0.293411i	−0.00850895	−	0.00945015i
$965$	−32.7985	−	100.944i	−1.05582	−	3.24949i
$966$	1.46046	−	3.51154i	0.0469894	−	0.112982i
$967$			37.1660i			1.19518i	0.801803	+	0.597588i	$0.203874\pi$
$967$			37.1660i			1.19518i	−0.801803	+	0.597588i	$0.796126\pi$
$968$	−2.59606	−	31.2912i	−0.0834404	−	1.00574i
$969$	6.50953	−	3.75828i	0.209116	−	0.120733i
$970$	−13.6864	+	30.7401i	−0.439444	+	0.987006i
$971$	−6.77144	+	31.8571i	−0.217306	+	1.02234i	0.725299	+	0.688434i	$0.241702\pi$
$971$	−6.77144	+	31.8571i	−0.217306	+	1.02234i	−0.942605	+	0.333910i	$0.891632\pi$
$972$	−1.14941	−	0.373467i	−0.0368674	−	0.0119790i
$973$	7.05298	+	14.8419i	0.226108	+	0.475808i
$974$	18.8782	−	25.9837i	0.604898	−	0.832571i
$975$	39.1673	−	35.2664i	1.25436	−	1.12943i
$976$	−0.674423	+	0.749022i	−0.0215877	+	0.0239756i
$977$	4.54110	+	2.02183i	0.145283	+	0.0646840i	0.478090	−	0.878311i	$-0.341329\pi$
$977$	4.54110	+	2.02183i	0.145283	+	0.0646840i	−0.332807	+	0.942995i	$0.607996\pi$
$978$	−4.79950	+	8.31297i	−0.153471	+	0.265820i
$979$	−5.93793	−	40.3513i	−0.189777	−	1.28963i
$980$	−28.6304	+	18.4758i	−0.914565	+	0.590187i
$981$	−2.20845	−	3.03967i	−0.0705105	−	0.0970493i
$982$	−36.2748	−	7.71045i	−1.15758	−	0.246050i
$983$	−0.0907540	−	0.426964i	−0.00289460	−	0.0136180i	0.976677	−	0.214716i	$-0.0688825\pi$
$983$	−0.0907540	−	0.426964i	−0.00289460	−	0.0136180i	−0.979571	+	0.201098i	$0.935549\pi$
$984$	1.81285	−	17.2481i	0.0577915	−	0.549849i
$985$	42.5255	−	18.9336i	1.35497	−	0.603274i
$986$	2.18412	−	6.72204i	0.0695566	−	0.214073i
$987$	4.86695	−	26.0503i	0.154917	−	0.829189i
$988$	16.4160	−	11.9269i	0.522261	−	0.379445i
$989$	−0.117393	−	0.0677766i	−0.00373287	−	0.00215517i
$990$	−11.4446	−	3.20157i	−0.363734	−	0.101753i
$991$	15.4649	+	26.7860i	0.491259	+	0.850885i	0.999949	−	0.0100645i	$-0.00320369\pi$
$991$	15.4649	+	26.7860i	0.491259	+	0.850885i	−0.508691	+	0.860949i	$0.669870\pi$
$992$	3.10425	+	29.5349i	0.0985600	+	0.937735i
$993$	17.9637	−	5.83675i	0.570060	−	0.185224i
$994$	−26.9690	+	6.43360i	−0.855403	+	0.204062i
$995$	−14.6980	−	10.6787i	−0.465958	−	0.338538i
$996$	4.30274	+	9.66412i	0.136338	+	0.306219i
$997$	25.1630	−	5.34856i	0.796920	−	0.169391i	0.208581	−	0.978005i	$-0.433115\pi$
$997$	25.1630	−	5.34856i	0.796920	−	0.169391i	0.588339	+	0.808614i	$0.299782\pi$
$998$	13.1558	+	11.8455i	0.416440	+	0.374964i
$999$	9.42510	−	0.990618i	0.298197	−	0.0313418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.12	✓	128
3.2	odd	2		693.2.cg.c.19.5		128
7.3	odd	6	inner	231.2.ba.a.52.5	yes	128
11.7	odd	10	inner	231.2.ba.a.40.5	yes	128
21.17	even	6		693.2.cg.c.514.12		128
33.29	even	10		693.2.cg.c.271.12		128
77.73	even	30	inner	231.2.ba.a.73.12	yes	128
231.227	odd	30		693.2.cg.c.73.5		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.12	✓	128	1.1	even	1	trivial
231.2.ba.a.40.5	yes	128	11.7	odd	10	inner
231.2.ba.a.52.5	yes	128	7.3	odd	6	inner
231.2.ba.a.73.12	yes	128	77.73	even	30	inner
693.2.cg.c.19.5		128	3.2	odd	2
693.2.cg.c.73.5		128	231.227	odd	30
693.2.cg.c.271.12		128	33.29	even	10
693.2.cg.c.514.12		128	21.17	even	6

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.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.884754 - 0.0929913i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-1.18215 + 0.251275i) q^{4} +(1.63822 + 3.67950i) q^{5} +(-0.719723 - 0.522910i) q^{6} +(-1.92178 + 1.81845i) q^{7} +(-2.71472 + 0.882066i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.884754 - 0.0929913i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-1.18215 + 0.251275i) q^{4} +(1.63822 + 3.67950i) q^{5} +(-0.719723 - 0.522910i) q^{6} +(-1.92178 + 1.81845i) q^{7} +(-2.71472 + 0.882066i) q^{8} +(0.104528 + 0.994522i) q^{9} +(1.79158 + 3.10311i) q^{10} +(2.05881 + 2.60025i) q^{11} +(1.04665 + 0.604282i) q^{12} +(3.79943 - 2.76045i) q^{13} +(-1.53120 + 1.78759i) q^{14} +(1.24463 - 3.83058i) q^{15} +(-0.111677 + 0.0497219i) q^{16} +(0.219773 - 2.09100i) q^{17} +(0.184964 + 0.870187i) q^{18} +(-3.49690 - 0.743288i) q^{19} +(-2.86119 - 3.93809i) q^{20} +(2.64494 - 0.0654482i) q^{21} +(2.06334 + 2.10913i) q^{22} +(0.807895 - 1.39932i) q^{23} +(2.60765 + 1.16100i) q^{24} +(-7.50931 + 8.33994i) q^{25} +(3.10486 - 2.79563i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.81491 - 2.63258i) q^{28} +(3.59379 + 1.16769i) q^{29} +(0.744982 - 3.50486i) q^{30} +(-2.15695 + 4.84458i) q^{31} +(4.84983 - 2.80005i) q^{32} +(0.209909 - 3.30998i) q^{33} -1.87046i q^{34} +(-9.83928 - 4.09218i) q^{35} +(-0.373467 - 1.14941i) q^{36} +(6.34136 + 7.04280i) q^{37} +(-3.16301 - 0.332446i) q^{38} +(-4.67062 - 0.490902i) q^{39} +(-7.69287 - 8.54380i) q^{40} +(-1.87755 - 5.77849i) q^{41} +(2.33404 - 0.303862i) q^{42} -0.0838928i q^{43} +(-3.08721 - 2.55657i) q^{44} +(-3.48810 + 2.01386i) q^{45} +(0.584664 - 1.31318i) q^{46} +(2.08253 - 9.79755i) q^{47} +(0.116263 + 0.0377761i) q^{48} +(0.386487 - 6.98932i) q^{49} +(-5.86835 + 8.07709i) q^{50} +(-1.56248 + 1.40686i) q^{51} +(-3.79788 + 4.21797i) q^{52} +(2.93246 + 1.30562i) q^{53} +(0.444813 - 0.770440i) q^{54} +(-6.19483 + 11.8352i) q^{55} +(3.61311 - 6.63172i) q^{56} +(2.10134 + 2.89225i) q^{57} +(3.28820 + 0.698928i) q^{58} +(-1.21940 - 5.73685i) q^{59} +(-0.508819 + 4.84108i) q^{60} +(7.53212 - 3.35352i) q^{61} +(-1.45786 + 4.48684i) q^{62} +(-2.00937 - 1.72117i) q^{63} +(4.22832 - 3.07205i) q^{64} +(16.3814 + 9.45778i) q^{65} +(-0.122081 - 2.94803i) q^{66} +(-0.694852 - 1.20352i) q^{67} +(0.265610 + 2.52711i) q^{68} +(-1.53671 + 0.499307i) q^{69} +(-9.08588 - 2.70560i) q^{70} +(9.52979 + 6.92380i) q^{71} +(-1.16100 - 2.60765i) q^{72} +(6.27666 - 1.33415i) q^{73} +(6.26546 + 5.64145i) q^{74} +(11.1610 - 1.17307i) q^{75} +4.32064 q^{76} +(-8.68501 - 1.25326i) q^{77} -4.17800 q^{78} +(-12.7465 + 1.33971i) q^{79} +(-0.365903 - 0.329461i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-2.19852 - 4.93795i) q^{82} +(7.08142 + 5.14495i) q^{83} +(-3.11028 + 0.741976i) q^{84} +(8.05389 - 2.61687i) q^{85} +(-0.00780131 - 0.0742245i) q^{86} +(-1.88936 - 3.27248i) q^{87} +(-7.88269 - 5.24293i) q^{88} +(-10.6499 - 6.14870i) q^{89} +(-2.89884 + 2.10613i) q^{90} +(-2.28194 + 12.2140i) q^{91} +(-0.603444 + 1.85721i) q^{92} +(4.84458 - 2.15695i) q^{93} +(0.931442 - 8.86208i) q^{94} +(-2.99375 - 14.0845i) q^{95} +(-5.47772 - 1.16433i) q^{96} +(5.51985 + 7.59743i) q^{97} +(-0.308001 - 6.21977i) q^{98} +(-2.37080 + 2.31933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Introduction

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