LMFDB - Embedded newform 525.2.bm.a.131.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.7
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.505077 + 2.37620i) q^{2} +(0.0606037 - 1.73099i) q^{3} +(-3.56413 - 1.58685i) q^{4} +(2.07975 + 0.821374i) q^{5} +(4.08257 + 1.01829i) q^{6} +(-2.37564 + 1.16461i) q^{7} +(2.71505 - 3.73695i) q^{8} +(-2.99265 - 0.209809i) q^{9} +O(q^{10})$	\(q+(-0.505077 + 2.37620i) q^{2} +(0.0606037 - 1.73099i) q^{3} +(-3.56413 - 1.58685i) q^{4} +(2.07975 + 0.821374i) q^{5} +(4.08257 + 1.01829i) q^{6} +(-2.37564 + 1.16461i) q^{7} +(2.71505 - 3.73695i) q^{8} +(-2.99265 - 0.209809i) q^{9} +(-3.00218 + 4.52704i) q^{10} +(0.593611 + 0.534490i) q^{11} +(-2.96283 + 6.07331i) q^{12} +(2.43373 + 0.790766i) q^{13} +(-1.56746 - 6.23322i) q^{14} +(1.54783 - 3.55024i) q^{15} +(2.28729 + 2.54029i) q^{16} +(-0.392844 + 3.73766i) q^{17} +(2.01007 - 7.00518i) q^{18} +(2.39886 + 5.38793i) q^{19} +(-6.10909 - 6.22774i) q^{20} +(1.87195 + 4.18280i) q^{21} +(-1.56987 + 1.14058i) q^{22} +(-1.31025 + 6.16423i) q^{23} +(-6.30408 - 4.92620i) q^{24} +(3.65069 + 3.41650i) q^{25} +(-3.10824 + 5.38363i) q^{26} +(-0.544543 + 5.16754i) q^{27} +(10.3152 - 0.381014i) q^{28} +(0.634999 + 0.874001i) q^{29} +(7.65431 + 5.47110i) q^{30} +(-7.78552 - 0.818291i) q^{31} +(0.809048 - 0.467104i) q^{32} +(0.961171 - 0.995143i) q^{33} +(-8.68301 - 2.82128i) q^{34} +(-5.89732 + 0.470795i) q^{35} +(10.3333 + 5.49670i) q^{36} +(-1.53024 - 1.69951i) q^{37} +(-14.0144 + 2.97885i) q^{38} +(1.51630 - 4.16484i) q^{39} +(8.71605 - 5.54183i) q^{40} +(0.685693 - 2.11035i) q^{41} +(-10.8846 + 2.33550i) q^{42} -1.68878 q^{43} +(-1.26755 - 2.84697i) q^{44} +(-6.05163 - 2.89444i) q^{45} +(-13.9857 - 6.22682i) q^{46} +(1.06044 + 10.0894i) q^{47} +(4.53584 - 3.80532i) q^{48} +(4.28738 - 5.53339i) q^{49} +(-9.96217 + 6.94917i) q^{50} +(6.44604 + 0.906524i) q^{51} +(-7.41930 - 6.68037i) q^{52} +(-0.324710 + 0.729310i) q^{53} +(-12.0041 - 3.90395i) q^{54} +(0.795544 + 1.59918i) q^{55} +(-2.09792 + 12.0396i) q^{56} +(9.47183 - 3.82588i) q^{57} +(-2.39752 + 1.06745i) q^{58} +(0.0291985 - 0.00620634i) q^{59} +(-11.1504 + 10.1974i) q^{60} +(3.01141 - 14.1676i) q^{61} +(5.87671 - 18.0867i) q^{62} +(7.35383 - 2.98684i) q^{63} +(2.81393 + 8.66038i) q^{64} +(4.41202 + 3.64359i) q^{65} +(1.87919 + 2.78656i) q^{66} +(0.267589 - 2.54594i) q^{67} +(7.33127 - 12.6981i) q^{68} +(10.5908 + 2.64160i) q^{69} +(1.85990 - 14.2510i) q^{70} +(4.47388 + 6.15777i) q^{71} +(-8.90925 + 10.6137i) q^{72} +(9.76074 + 8.78861i) q^{73} +(4.81126 - 2.77778i) q^{74} +(6.13517 - 6.11225i) q^{75} -23.0100i q^{76} +(-2.03268 - 0.578434i) q^{77} +(9.13063 + 5.70660i) q^{78} +(-0.749797 - 7.13384i) q^{79} +(2.67045 + 7.16188i) q^{80} +(8.91196 + 1.25577i) q^{81} +(4.66828 + 2.69523i) q^{82} +(-11.2629 - 8.18295i) q^{83} +(-0.0343934 - 17.8786i) q^{84} +(-3.88703 + 7.45071i) q^{85} +(0.852965 - 4.01288i) q^{86} +(1.55137 - 1.04621i) q^{87} +(3.60904 - 0.767126i) q^{88} +(-11.7591 - 2.49948i) q^{89} +(9.93430 - 12.9180i) q^{90} +(-6.70260 + 0.955758i) q^{91} +(14.4516 - 19.8910i) q^{92} +(-1.88829 + 13.4271i) q^{93} +(-24.5100 - 2.57610i) q^{94} +(0.563516 + 13.1759i) q^{95} +(-0.759521 - 1.42876i) q^{96} +(5.54137 + 7.62704i) q^{97} +(10.9830 + 12.9825i) q^{98} +(-1.66433 - 1.72409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.505077	+	2.37620i	−0.357143	+	1.68023i	0.322409	+	0.946600i	$0.395507\pi$
$2$	−0.505077	+	2.37620i	−0.357143	+	1.68023i	−0.679552	+	0.733627i	$0.737826\pi$
$3$	0.0606037	−	1.73099i	0.0349896	−	0.999388i
$3$	0.0606037	−	1.73099i	0.0349896	−	0.999388i
$4$	−3.56413	−	1.58685i	−1.78207	−	0.793427i
$5$	2.07975	+	0.821374i	0.930091	+	0.367330i
$5$	2.07975	+	0.821374i	0.930091	+	0.367330i
$6$	4.08257	+	1.01829i	1.66670	+	0.415715i
$7$	−2.37564	+	1.16461i	−0.897909	+	0.440180i
$7$	−2.37564	+	1.16461i	−0.897909	+	0.440180i
$8$	2.71505	−	3.73695i	0.959915	−	1.32121i
$9$	−2.99265	−	0.209809i	−0.997551	−	0.0699363i
$10$	−3.00218	+	4.52704i	−0.949373	+	1.43157i
$11$	0.593611	+	0.534490i	0.178980	+	0.161155i	0.753751	−	0.657160i	$-0.228242\pi$
$11$	0.593611	+	0.534490i	0.178980	+	0.161155i	−0.574771	+	0.818314i	$0.694909\pi$
$12$	−2.96283	+	6.07331i	−0.855295	+	1.75321i
$13$	2.43373	+	0.790766i	0.674995	+	0.219319i	0.626403	−	0.779500i	$-0.284527\pi$
$13$	2.43373	+	0.790766i	0.674995	+	0.219319i	0.0485920	+	0.998819i	$0.484527\pi$
$14$	−1.56746	−	6.23322i	−0.418921	−	1.66590i
$15$	1.54783	−	3.55024i	0.399648	−	0.916669i
$16$	2.28729	+	2.54029i	0.571822	+	0.635073i
$17$	−0.392844	+	3.73766i	−0.0952786	+	0.906515i	0.837590	+	0.546299i	$0.183964\pi$
$17$	−0.392844	+	3.73766i	−0.0952786	+	0.906515i	−0.932869	+	0.360216i	$0.882703\pi$
$18$	2.01007	−	7.00518i	0.473778	−	1.65114i
$19$	2.39886	+	5.38793i	0.550336	+	1.23608i	0.947920	+	0.318510i	$0.103182\pi$
$19$	2.39886	+	5.38793i	0.550336	+	1.23608i	−0.397583	+	0.917566i	$0.630151\pi$
$20$	−6.10909	−	6.22774i	−1.36603	−	1.39257i
$21$	1.87195	+	4.18280i	0.408493	+	0.912761i
$22$	−1.56987	+	1.14058i	−0.334698	+	0.243172i
$23$	−1.31025	+	6.16423i	−0.273206	+	1.28533i	0.600794	+	0.799404i	$0.294851\pi$
$23$	−1.31025	+	6.16423i	−0.273206	+	1.28533i	−0.873999	+	0.485927i	$0.838482\pi$
$24$	−6.30408	−	4.92620i	−1.28681	−	1.00556i
$25$	3.65069	+	3.41650i	0.730138	+	0.683300i
$26$	−3.10824	+	5.38363i	−0.609576	+	1.05582i
$27$	−0.544543	+	5.16754i	−0.104797	+	0.994494i
$28$	10.3152	−	0.381014i	1.94939	−	0.0720049i
$29$	0.634999	+	0.874001i	0.117916	+	0.162298i	0.863895	−	0.503672i	$-0.168018\pi$
$29$	0.634999	+	0.874001i	0.117916	+	0.162298i	−0.745979	+	0.665970i	$0.768018\pi$
$30$	7.65431	+	5.47110i	1.39748	+	0.998882i
$31$	−7.78552	−	0.818291i	−1.39832	−	0.146969i	−0.624822	−	0.780767i	$-0.714828\pi$
$31$	−7.78552	−	0.818291i	−1.39832	−	0.146969i	−0.773499	+	0.633798i	$0.781495\pi$
$32$	0.809048	−	0.467104i	0.143021	−	0.0825731i
$33$	0.961171	−	0.995143i	0.167318	−	0.173232i
$34$	−8.68301	−	2.82128i	−1.48912	−	0.483845i
$35$	−5.89732	+	0.470795i	−0.996829	+	0.0795789i
$36$	10.3333	+	5.49670i	1.72221	+	0.916116i
$37$	−1.53024	−	1.69951i	−0.251571	−	0.279398i	0.604111	−	0.796900i	$-0.293528\pi$
$37$	−1.53024	−	1.69951i	−0.251571	−	0.279398i	−0.855682	+	0.517503i	$0.826862\pi$
$38$	−14.0144	+	2.97885i	−2.27344	+	0.483234i
$39$	1.51630	−	4.16484i	0.242803	−	0.666907i
$40$	8.71605	−	5.54183i	1.37813	−	0.876240i
$41$	0.685693	−	2.11035i	0.107087	−	0.329581i	−0.883127	−	0.469133i	$-0.844566\pi$
$41$	0.685693	−	2.11035i	0.107087	−	0.329581i	0.990215	+	0.139552i	$0.0445664\pi$
$42$	−10.8846	+	2.33550i	−1.67954	+	0.360375i
$43$	−1.68878			−0.257537			−0.128768	−	0.991675i	$-0.541102\pi$
$43$	−1.68878			−0.257537			−0.128768	+	0.991675i	$0.541102\pi$
$44$	−1.26755	−	2.84697i	−0.191091	−	0.429196i
$45$	−6.05163	−	2.89444i	−0.902124	−	0.431477i
$46$	−13.9857	−	6.22682i	−2.06207	−	0.918095i
$47$	1.06044	+	10.0894i	0.154681	+	1.47169i	0.746375	+	0.665526i	$0.231793\pi$
$47$	1.06044	+	10.0894i	0.154681	+	1.47169i	−0.591694	+	0.806162i	$0.701541\pi$
$48$	4.53584	−	3.80532i	0.654692	−	0.549251i
$49$	4.28738	−	5.53339i	0.612483	−	0.790484i
$50$	−9.96217	+	6.94917i	−1.40886	+	0.982761i
$51$	6.44604	+	0.906524i	0.902626	+	0.126939i
$52$	−7.41930	−	6.68037i	−1.02887	−	0.926400i
$53$	−0.324710	+	0.729310i	−0.0446023	+	0.100178i	−0.934472	−	0.356036i	$-0.884128\pi$
$53$	−0.324710	+	0.729310i	−0.0446023	+	0.100178i	0.889870	+	0.456214i	$0.150795\pi$
$54$	−12.0041	−	3.90395i	−1.63355	−	0.531260i
$55$	0.795544	+	1.59918i	0.107271	+	0.215633i
$56$	−2.09792	+	12.0396i	−0.280346	+	1.60886i
$57$	9.47183	−	3.82588i	1.25458	−	0.506750i
$58$	−2.39752	+	1.06745i	−0.314810	+	0.140163i
$59$	0.0291985	−	0.00620634i	0.00380133	−	0.000807997i	−0.206011	−	0.978550i	$-0.566048\pi$
$59$	0.0291985	−	0.00620634i	0.00380133	−	0.000807997i	0.209812	+	0.977742i	$0.432715\pi$
$60$	−11.1504	+	10.1974i	−1.43951	+	1.31647i
$61$	3.01141	−	14.1676i	0.385572	−	1.81397i	−0.173476	−	0.984838i	$-0.555500\pi$
$61$	3.01141	−	14.1676i	0.385572	−	1.81397i	0.559048	−	0.829135i	$-0.311167\pi$
$62$	5.87671	−	18.0867i	0.746343	−	2.29701i
$63$	7.35383	−	2.98684i	0.926495	−	0.376306i
$64$	2.81393	+	8.66038i	0.351741	+	1.08255i
$65$	4.41202	+	3.64359i	0.547244	+	0.451932i
$66$	1.87919	+	2.78656i	0.231313	+	0.343002i
$67$	0.267589	−	2.54594i	0.0326912	−	0.311036i	−0.965941	−	0.258761i	$-0.916686\pi$
$67$	0.267589	−	2.54594i	0.0326912	−	0.311036i	0.998633	−	0.0522755i	$-0.0166474\pi$
$68$	7.33127	−	12.6981i	0.889047	−	1.53987i
$69$	10.5908	+	2.64160i	1.27498	+	0.318011i
$70$	1.85990	−	14.2510i	0.222300	−	1.70332i
$71$	4.47388	+	6.15777i	0.530952	+	0.730792i	0.987275	−	0.159022i	$-0.0508339\pi$
$71$	4.47388	+	6.15777i	0.530952	+	0.730792i	−0.456323	+	0.889814i	$0.650834\pi$
$72$	−8.90925	+	10.6137i	−1.04997	+	1.25084i
$73$	9.76074	+	8.78861i	1.14241	+	1.02863i	0.999242	+	0.0389300i	$0.0123949\pi$
$73$	9.76074	+	8.78861i	1.14241	+	1.02863i	0.143166	+	0.989699i	$0.454272\pi$
$74$	4.81126	−	2.77778i	0.559298	−	0.322911i
$75$	6.13517	−	6.11225i	0.708429	−	0.705782i
$76$		−	23.0100i		−	2.63942i
$77$	−2.03268	−	0.578434i	−0.231645	−	0.0659187i
$78$	9.13063	+	5.70660i	1.03384	+	0.646145i
$79$	−0.749797	−	7.13384i	−0.0843587	−	0.802620i	−0.952138	−	0.305669i	$-0.901120\pi$
$79$	−0.749797	−	7.13384i	−0.0843587	−	0.802620i	0.867779	−	0.496950i	$-0.165547\pi$
$80$	2.67045	+	7.16188i	0.298566	+	0.800723i
$81$	8.91196	+	1.25577i	0.990218	+	0.139530i
$82$	4.66828	+	2.69523i	0.515525	+	0.297639i
$83$	−11.2629	−	8.18295i	−1.23626	−	0.898196i	−0.238917	−	0.971040i	$-0.576792\pi$
$83$	−11.2629	−	8.18295i	−1.23626	−	0.898196i	−0.997343	+	0.0728445i	$0.976792\pi$
$84$	−0.0343934	−	17.8786i	−0.00375263	−	1.95071i
$85$	−3.88703	+	7.45071i	−0.421608	+	0.808143i
$86$	0.852965	−	4.01288i	0.0919776	−	0.432720i
$87$	1.55137	−	1.04621i	0.166324	−	0.112165i
$88$	3.60904	−	0.767126i	0.384725	−	0.0817759i
$89$	−11.7591	−	2.49948i	−1.24646	−	0.264944i	−0.462988	−	0.886365i	$-0.653223\pi$
$89$	−11.7591	−	2.49948i	−1.24646	−	0.264944i	−0.783477	+	0.621420i	$0.786556\pi$
$90$	9.93430	−	12.9180i	1.04717	−	1.36167i
$91$	−6.70260	+	0.955758i	−0.702624	+	0.100191i
$92$	14.4516	−	19.8910i	1.50669	−	2.07378i
$93$	−1.88829	+	13.4271i	−0.195806	+	1.39232i
$94$	−24.5100	−	2.57610i	−2.52801	−	0.265705i
$95$	0.563516	+	13.1759i	0.0578155	+	1.35182i
$96$	−0.759521	−	1.42876i	−0.0775183	−	0.145822i
$97$	5.54137	+	7.62704i	0.562641	+	0.774409i	0.991659	−	0.128887i	$-0.0411405\pi$
$97$	5.54137	+	7.62704i	0.562641	+	0.774409i	−0.429018	+	0.903296i	$0.641140\pi$
$98$	10.9830	+	12.9825i	1.10945	+	1.31143i
$99$	−1.66433	−	1.72409i	−0.167272	−	0.173277i
$100$	−7.59006	−	17.9700i	−0.759006	−	1.79700i
$101$	−7.62875	−	13.2134i	−0.759089	−	1.31478i	−0.943316	−	0.331897i	$-0.892311\pi$
$101$	−7.62875	−	13.2134i	−0.759089	−	1.31478i	0.184227	−	0.982884i	$-0.441022\pi$
$102$	−5.40983	+	14.8592i	−0.535653	+	1.47128i
$103$	16.4650	−	1.73054i	1.62234	−	0.170515i	0.750695	−	0.660649i	$-0.229719\pi$
$103$	16.4650	−	1.73054i	1.62234	−	0.170515i	0.871647	+	0.490133i	$0.163052\pi$
$104$	9.56274	−	6.94774i	0.937704	−	0.681282i
$105$	0.457542	+	10.2367i	0.0446515	+	0.999003i
$106$	−1.56898	−	1.13993i	−0.152393	−	0.110720i
$107$	−8.08402	−	4.66731i	−0.781512	−	0.451206i	0.0554538	−	0.998461i	$-0.482339\pi$
$107$	−8.08402	−	4.66731i	−0.781512	−	0.451206i	−0.836966	+	0.547255i	$0.815673\pi$
$108$	10.1410	−	17.5537i	0.975815	−	1.68911i
$109$	1.61600	−	0.343492i	0.154785	−	0.0329006i	−0.129867	−	0.991531i	$-0.541455\pi$
$109$	1.61600	−	0.343492i	0.154785	−	0.0329006i	0.284652	+	0.958631i	$0.408122\pi$
$110$	−4.20178	+	1.08266i	−0.400624	+	0.103228i
$111$	−3.03457	+	2.54584i	−0.288029	+	0.241641i
$112$	−8.39223	−	3.37104i	−0.792991	−	0.318533i
$113$	12.0458	+	3.91390i	1.13317	+	0.368189i	0.814780	−	0.579771i	$-0.196858\pi$
$113$	12.0458	+	3.91390i	1.13317	+	0.368189i	0.318390	+	0.947960i	$0.396858\pi$
$114$	4.30704	+	24.4393i	0.403392	+	2.28895i
$115$	−7.78812	+	11.7438i	−0.726246	+	1.09512i
$116$	−0.876309	−	4.12271i	−0.0813632	−	0.382784i
$117$	−7.11740	−	2.87711i	−0.658003	−	0.265989i
$118$			0.0725163i			0.00667566i
$119$	−3.41965	−	9.33685i	−0.313479	−	0.855908i
$120$	−9.06462	−	15.4232i	−0.827483	−	1.40794i
$121$	−1.08312	−	10.3052i	−0.0984653	−	0.936835i
$122$	32.1440	+	14.3114i	2.91018	+	1.29570i
$123$	−3.61143	−	1.31482i	−0.325632	−	0.118554i
$124$	26.4501	+	15.2710i	2.37529	+	1.37138i
$125$	4.78628	+	10.1040i	0.428098	+	0.903732i
$126$	3.38307	+	18.9828i	0.301388	+	1.69112i
$127$	2.04375	+	6.29000i	0.181353	+	0.558147i	0.999866	−	0.0163401i	$-0.00520144\pi$
$127$	2.04375	+	6.29000i	0.181353	+	0.558147i	−0.818513	+	0.574487i	$0.805201\pi$
$128$	−20.1419	+	2.11700i	−1.78031	+	0.187118i
$129$	−0.102347	+	2.92326i	−0.00901111	+	0.257379i
$130$	−10.8863	+	8.64355i	−0.954793	+	0.758090i
$131$	5.40236	−	2.40528i	0.472006	−	0.210151i	−0.156927	−	0.987610i	$-0.550159\pi$
$131$	5.40236	−	2.40528i	0.472006	−	0.210151i	0.628933	+	0.777460i	$0.283492\pi$
$132$	−5.00489	+	2.02158i	−0.435620	+	0.175956i
$133$	−11.9737	−	10.0061i	−1.03825	−	0.867637i
$134$	5.91451	+	1.92174i	0.510936	+	0.166013i
$135$	−5.37700	+	10.2999i	−0.462778	+	0.886474i
$136$	12.9008	+	11.6160i	1.10624	+	0.996061i
$137$	1.88296	+	8.85864i	0.160872	+	0.756844i	0.982417	+	0.186700i	$0.0597793\pi$
$137$	1.88296	+	8.85864i	0.160872	+	0.756844i	−0.821545	+	0.570144i	$0.806887\pi$
$138$	−11.6262	+	23.8317i	−0.989684	+	2.02869i
$139$	−8.19822	+	2.66376i	−0.695364	+	0.225937i	−0.635309	−	0.772258i	$-0.719127\pi$
$139$	−8.19822	+	2.66376i	−0.695364	+	0.225937i	−0.0600543	+	0.998195i	$0.519127\pi$
$140$	21.7659	+	7.68021i	1.83956	+	0.649096i
$141$	17.5289	−	1.22415i	1.47620	−	0.103092i
$142$	−16.8917	+	7.52069i	−1.41752	+	0.631122i
$143$	1.02203	+	1.77021i	0.0854665	+	0.148032i
$144$	−6.31209	−	8.08211i	−0.526008	−	0.673509i
$145$	0.602755	+	2.33927i	0.0500561	+	0.194266i
$146$	−25.8134	+	18.7545i	−2.13633	+	1.55214i
$147$	−9.31841	−	7.75675i	−0.768570	−	0.639766i
$148$	2.75712	+	8.48555i	0.226634	+	0.697508i
$149$	19.0628	+	11.0059i	1.56169	+	0.901642i	0.997086	+	0.0762792i	$0.0243040\pi$
$149$	19.0628	+	11.0059i	1.56169	+	0.901642i	0.564603	+	0.825363i	$0.309029\pi$
$150$	11.4252	+	17.6656i	0.932864	+	1.44239i
$151$	1.95434	+	3.38501i	0.159042	+	0.275468i	0.934523	−	0.355902i	$-0.115826\pi$
$151$	1.95434	+	3.38501i	0.159042	+	0.275468i	−0.775482	+	0.631370i	$0.782493\pi$
$152$	26.6474	+	5.66409i	2.16139	+	0.459418i
$153$	1.95984	−	11.1031i	0.158444	−	0.897632i
$154$	2.40113	−	4.53790i	0.193489	−	0.365674i
$155$	−15.5198	−	8.09666i	−1.24658	−	0.650339i
$156$	−12.0133	+	12.4379i	−0.961833	+	0.995828i
$157$	21.6498	−	12.4995i	1.72784	−	0.997570i	0.829083	−	0.559126i	$-0.188863\pi$
$157$	21.6498	−	12.4995i	1.72784	−	0.997570i	0.898759	−	0.438444i	$-0.144470\pi$
$158$	17.3301	+	1.82147i	1.37871	+	0.144908i
$159$	1.24275	+	0.606268i	0.0985565	+	0.0480802i
$160$	2.06628	−	0.306927i	0.163354	−	0.0242647i
$161$	−4.06623	−	16.1699i	−0.320464	−	1.27437i
$162$	−7.48519	+	20.5423i	−0.588092	+	1.61396i
$163$	1.36352	+	1.51434i	0.106799	+	0.118612i	0.794174	−	0.607690i	$-0.207904\pi$
$163$	1.36352	+	1.51434i	0.106799	+	0.118612i	−0.687375	+	0.726302i	$0.741237\pi$
$164$	−5.79272	+	6.43346i	−0.452335	+	0.502369i
$165$	2.81638	−	1.28016i	0.219255	−	0.0996605i
$166$	25.1329	−	22.6298i	1.95069	−	1.75641i
$167$	−0.943322	−	0.685364i	−0.0729964	−	0.0530350i	0.550689	−	0.834711i	$-0.314365\pi$
$167$	−0.943322	−	0.685364i	−0.0729964	−	0.0530350i	−0.623685	+	0.781676i	$0.714365\pi$
$168$	20.7133	+	4.36112i	1.59807	+	0.336468i
$169$	−5.21950	−	3.79219i	−0.401500	−	0.291707i
$170$	−15.7411	−	12.9995i	−1.20729	−	0.997019i
$171$	−6.04853	−	16.6275i	−0.462542	−	1.27154i
$172$	6.01905	+	2.67985i	0.458948	+	0.204337i
$173$	1.53671	+	0.326638i	0.116834	+	0.0248339i	0.265958	−	0.963985i	$-0.414312\pi$
$173$	1.53671	+	0.326638i	0.116834	+	0.0248339i	−0.149124	+	0.988819i	$0.547645\pi$
$174$	1.70244	+	4.21478i	0.129062	+	0.319522i
$175$	−12.6516	−	3.86477i	−0.956373	−	0.292149i
$176$			2.73048i			0.205818i
$177$	−0.00897357	−	0.0509185i	−0.000674495	−	0.00382727i
$178$	11.8785	−	26.6796i	0.890333	−	1.99972i
$179$	2.64427	−	5.93912i	0.197642	−	0.443911i	−0.787351	−	0.616505i	$-0.788548\pi$
$179$	2.64427	−	5.93912i	0.197642	−	0.443911i	0.984993	+	0.172594i	$0.0552148\pi$
$180$	16.9758	+	19.9192i	1.26530	+	1.48469i
$181$	−4.52304	+	6.22543i	−0.336195	+	0.462732i	−0.943325	−	0.331870i	$-0.892321\pi$
$181$	−4.52304	+	6.22543i	−0.336195	+	0.462732i	0.607130	+	0.794602i	$0.292321\pi$
$182$	1.11426	−	16.4095i	0.0825943	−	1.21635i
$183$	−24.3414	−	6.07134i	−1.79937	−	0.448806i
$184$	19.4780	+	21.6325i	1.43594	+	1.59477i
$185$	−1.78659	−	4.79145i	−0.131353	−	0.352274i
$186$	−30.9517	−	11.2686i	−2.26949	−	0.826257i
$187$	−2.23094	+	2.00874i	−0.163142	+	0.146894i
$188$	12.2308	−	37.6427i	0.892026	−	2.74537i
$189$	−4.72452	−	12.9104i	−0.343658	−	0.939095i
$190$	−31.5932	−	5.31581i	−2.29201	−	0.385650i
$191$	−2.70188	+	2.43278i	−0.195501	+	0.176030i	−0.761067	−	0.648673i	$-0.775324\pi$
$191$	−2.70188	+	2.43278i	−0.195501	+	0.176030i	0.565566	+	0.824703i	$0.308658\pi$
$192$	15.1616	−	4.34603i	1.09419	−	0.313648i
$193$	4.12558	+	7.14572i	0.296966	+	0.514360i	0.975440	−	0.220264i	$-0.0706919\pi$
$193$	4.12558	+	7.14572i	0.296966	+	0.514360i	−0.678474	+	0.734624i	$0.737359\pi$
$194$	−20.9222	+	9.31516i	−1.50213	+	0.668790i
$195$	6.57441	−	7.41635i	0.470803	−	0.531096i
$196$	−24.0615	+	12.9183i	−1.71868	+	0.922735i
$197$	−8.54588	−	11.7624i	−0.608868	−	0.838036i	0.387615	−	0.921821i	$-0.373299\pi$
$197$	−8.54588	−	11.7624i	−0.608868	−	0.838036i	−0.996484	+	0.0837857i	$0.973299\pi$
$198$	4.93739	−	3.08399i	0.350885	−	0.219169i
$199$	13.8958	−	8.02275i	0.985048	−	0.568718i	0.0812579	−	0.996693i	$-0.474106\pi$
$199$	13.8958	−	8.02275i	0.985048	−	0.568718i	0.903790	+	0.427975i	$0.140773\pi$
$200$	22.6791	−	4.36646i	1.60365	−	0.308755i
$201$	−4.39078	−	0.617488i	−0.309702	−	0.0435542i
$202$	35.2507	−	11.4537i	2.48023	−	0.805877i
$203$	−2.52640	−	1.33679i	−0.177319	−	0.0938244i
$204$	−21.5360	−	13.4599i	−1.50782	−	0.942382i
$205$	3.15945	−	3.82577i	0.220666	−	0.267204i
$206$	−4.20397	+	39.9981i	−0.292905	+	2.78680i
$207$	5.21443	−	18.1725i	0.362428	−	1.26308i
$208$	3.55786	+	7.99109i	0.246693	+	0.554082i
$209$	−1.45580	+	4.48050i	−0.100700	+	0.309923i
$210$	−24.5556	−	4.08313i	−1.69450	−	0.281762i
$211$	2.23096	+	6.86618i	0.153585	+	0.472687i	0.998015	−	0.0629796i	$-0.0200603\pi$
$211$	2.23096	+	6.86618i	0.153585	+	0.472687i	−0.844429	+	0.535667i	$0.820060\pi$
$212$	2.31462	−	2.08409i	0.158969	−	0.143136i
$213$	10.9302	−	7.37106i	0.748923	−	0.505057i
$214$	15.1735	−	16.8519i	1.03724	−	1.15197i
$215$	−3.51224	−	1.38712i	−0.239533	−	0.0946009i
$216$	17.8324	+	16.0651i	1.21334	+	1.09309i
$217$	19.4486	−	7.12311i	1.32026	−	0.483548i
$218$			4.01344i			0.271824i
$219$	15.8045	−	16.3631i	1.06797	−	1.10572i
$220$	−0.297760	−	6.96210i	−0.0200750	−	0.469385i
$221$	−3.91169	+	8.78579i	−0.263129	+	0.590996i
$222$	−4.51674	−	8.49660i	−0.303144	−	0.570254i
$223$	−12.9986	+	4.22351i	−0.870452	+	0.282827i	−0.709987	−	0.704214i	$-0.751299\pi$
$223$	−12.9986	+	4.22351i	−0.870452	+	0.282827i	−0.160465	+	0.987042i	$0.551299\pi$
$224$	−1.37802	+	2.05190i	−0.0920727	+	0.137098i
$225$	−10.2084	−	10.9904i	−0.680563	−	0.732690i
$226$	−15.3843	+	26.6463i	−1.02335	+	1.77249i
$227$	3.13088	−	3.47719i	0.207804	−	0.230789i	−0.630229	−	0.776409i	$-0.717039\pi$
$227$	3.13088	−	3.47719i	0.207804	−	0.230789i	0.838033	+	0.545620i	$0.183706\pi$
$228$	−39.8300	−	1.39449i	−2.63781	−	0.0923523i
$229$	−2.81965	+	0.296357i	−0.186328	+	0.0195838i	−0.197233	−	0.980357i	$-0.563195\pi$
$229$	−2.81965	+	0.296357i	−0.186328	+	0.0195838i	0.0109050	+	0.999941i	$0.496529\pi$
$230$	−23.9721	−	24.4377i	−1.58067	−	1.61137i
$231$	−1.12445	+	3.48349i	−0.0739835	+	0.229197i
$232$	4.99015			0.327619
$233$	−6.87247	−	15.4358i	−0.450230	−	1.01123i	−0.985981	−	0.166858i	$-0.946638\pi$
$233$	−6.87247	−	15.4358i	−0.450230	−	1.01123i	0.535751	−	0.844376i	$-0.320029\pi$
$234$	10.4314	−	15.4592i	0.681923	−	1.01060i
$235$	−6.08172	+	21.8544i	−0.396728	+	1.42562i
$236$	−0.113916	−	0.0242136i	−0.00741530	−	0.00157617i
$237$	−12.3940	+	0.865553i	−0.805080	+	0.0562237i
$238$	23.9134	−	3.40994i	1.55008	−	0.221033i
$239$	20.6404	−	6.70646i	1.33511	−	0.433805i	0.447456	−	0.894306i	$-0.352330\pi$
$239$	20.6404	−	6.70646i	1.33511	−	0.433805i	0.887659	+	0.460501i	$0.152330\pi$
$240$	12.5590	−	4.18849i	0.810679	−	0.270366i
$241$	3.50699	+	16.4991i	0.225905	+	1.06280i	0.934163	+	0.356847i	$0.116148\pi$
$241$	3.50699	+	16.4991i	0.225905	+	1.06280i	−0.708258	+	0.705954i	$0.750519\pi$
$242$	25.0342	+	2.63120i	1.60926	+	0.169140i
$243$	2.71383	−	15.3504i	0.174092	−	0.984729i
$244$	−33.2150	+	45.7165i	−2.12637	+	2.92670i
$245$	13.4616	−	7.98650i	0.860033	−	0.510239i
$246$	4.94834	−	7.91740i	0.315494	−	0.504795i
$247$	1.57758	+	15.0097i	0.100379	+	0.955044i
$248$	−24.1960	+	26.8724i	−1.53645	+	1.70640i
$249$	−14.8472	+	19.0000i	−0.940902	+	1.20408i
$250$	−26.4267	+	6.26985i	−1.67137	+	0.396540i
$251$	−4.38475			−0.276763			−0.138381	−	0.990379i	$-0.544190\pi$
$251$	−4.38475			−0.276763			−0.138381	+	0.990379i	$0.544190\pi$
$252$	−30.9497	−	1.02397i	−1.94965	−	0.0645043i
$253$	−4.07249	+	2.95884i	−0.256036	+	0.186021i
$254$	−15.9786	+	1.67941i	−1.00258	+	0.105376i
$255$	12.6615	+	7.17995i	0.792896	+	0.449626i
$256$	3.23910	−	30.8180i	0.202444	−	1.92612i
$257$	−6.26906	+	10.8583i	−0.391053	+	0.677324i	−0.992589	−	0.121522i	$-0.961223\pi$
$257$	−6.26906	+	10.8583i	−0.391053	+	0.677324i	0.601536	+	0.798846i	$0.294556\pi$
$258$	−6.89457	−	1.71967i	−0.429237	−	0.107062i
$259$	5.61458	+	2.25529i	0.348873	+	0.140137i
$260$	−9.94318	−	19.9875i	−0.616650	−	1.23957i
$261$	−1.71696	−	2.74881i	−0.106277	−	0.170147i
$262$	2.98683	+	14.0519i	0.184527	+	0.868132i
$263$	−3.37978	−	15.9006i	−0.208406	−	0.980474i	−0.950631	−	0.310323i	$-0.899563\pi$
$263$	−3.37978	−	15.9006i	−0.208406	−	0.980474i	0.742225	−	0.670151i	$-0.233771\pi$
$264$	−1.10917	−	6.29371i	−0.0682644	−	0.387351i
$265$	−1.27435	+	1.25007i	−0.0782827	+	0.0767913i
$266$	29.8241	−	23.3980i	1.82863	−	1.43462i
$267$	−5.03922	+	20.2035i	−0.308395	+	1.23643i
$268$	−4.99376	+	8.64945i	−0.305043	+	0.528349i
$269$	2.01029	−	19.1267i	0.122570	−	1.16617i	−0.744372	−	0.667765i	$-0.767251\pi$
$269$	2.01029	−	19.1267i	0.122570	−	1.16617i	0.866942	−	0.498409i	$-0.166082\pi$
$270$	−21.7588	−	17.9791i	−1.32420	−	1.09417i
$271$	−1.72115	+	0.180900i	−0.104552	+	0.0109889i	−0.156660	−	0.987653i	$-0.550073\pi$
$271$	−1.72115	+	0.180900i	−0.104552	+	0.0109889i	0.0521079	+	0.998641i	$0.483406\pi$
$272$	−10.3933	+	7.55117i	−0.630186	+	0.457857i
$273$	1.24821	+	11.6601i	0.0755448	+	0.705699i
$274$	−22.0009			−1.32913
$275$	0.341005	+	3.97933i	0.0205634	+	0.239962i
$276$	−33.5553	−	26.2211i	−2.01979	−	1.57833i
$277$	18.6883	−	20.7554i	1.12287	−	1.24707i	0.157125	−	0.987579i	$-0.449777\pi$
$277$	18.6883	−	20.7554i	1.12287	−	1.24707i	0.965745	−	0.259494i	$-0.0835559\pi$
$278$	−2.18890	−	20.8260i	−0.131282	−	1.24906i
$279$	23.1277	+	4.08233i	1.38462	+	0.244403i
$280$	−14.2522	+	23.3162i	−0.851731	+	1.39341i
$281$	−8.61062	+	11.8515i	−0.513667	+	0.707002i	−0.984532	−	0.175203i	$-0.943942\pi$
$281$	−8.61062	+	11.8515i	−0.513667	+	0.707002i	0.470865	+	0.882205i	$0.343942\pi$
$282$	−5.94461	+	42.2705i	−0.353996	+	2.51717i
$283$	−14.7341	−	1.54861i	−0.875849	−	0.0920554i	−0.344075	−	0.938942i	$-0.611808\pi$
$283$	−14.7341	−	1.54861i	−0.875849	−	0.0920554i	−0.531774	+	0.846887i	$0.678474\pi$
$284$	−6.17403	−	29.0465i	−0.366361	−	1.72359i
$285$	22.8415	−	0.176932i	1.35301	−	0.0104805i
$286$	−4.72258	+	1.53446i	−0.279252	+	0.0907344i
$287$	0.828762	+	5.81200i	0.0489203	+	0.343071i
$288$	−2.51920	+	1.22814i	−0.148446	+	0.0723686i
$289$	2.81276	+	0.597870i	0.165456	+	0.0351688i
$290$	−5.86302	+	0.250754i	−0.344288	+	0.0147248i
$291$	13.5382	−	9.12983i	0.793621	−	0.535200i
$292$	−20.8423	−	46.8127i	−1.21971	−	2.73950i
$293$	−29.5945			−1.72893			−0.864464	−	0.502696i	$-0.832342\pi$
$293$	−29.5945			−1.72893			−0.864464	+	0.502696i	$0.832342\pi$
$294$	23.1381	−	18.2247i	1.34944	−	1.06288i
$295$	0.0658233	+	0.0110753i	0.00383238	+	0.000644829i
$296$	−10.5057	+	1.10419i	−0.610629	+	0.0641797i
$297$	−3.08524	+	2.77646i	−0.179024	+	0.161106i
$298$	−35.7805	+	39.7383i	−2.07271	+	2.30198i
$299$	−8.06325	+	13.9660i	−0.466310	+	0.807672i
$300$	−31.5658	+	12.0493i	−1.82245	+	0.695665i
$301$	4.01195	−	1.96677i	0.231245	−	0.113363i
$302$	−9.03055	+	2.93420i	−0.519650	+	0.168844i
$303$	−23.3346	+	12.4045i	−1.34054	+	0.712620i
$304$	−8.20003	+	18.4176i	−0.470304	+	1.05632i
$305$	17.8999	−	26.9915i	1.02494	−	1.54553i
$306$	25.3933	+	10.2649i	1.45164	+	0.586805i
$307$		−	8.67538i		−	0.495130i	−0.968871	−	0.247565i	$-0.920370\pi$
$307$		−	8.67538i		−	0.495130i	0.968871	−	0.247565i	$-0.0796304\pi$
$308$	6.32685	+	5.28718i	0.360506	+	0.301265i
$309$	−1.99771	−	28.6056i	−0.113646	−	1.62732i
$310$	27.0780	−	32.7887i	1.53793	−	1.86227i
$311$	4.35914	−	4.84131i	0.247184	−	0.274526i	−0.606766	−	0.794880i	$-0.707534\pi$
$311$	4.35914	−	4.84131i	0.247184	−	0.274526i	0.853950	+	0.520355i	$0.174200\pi$
$312$	−11.4469	−	16.9741i	−0.648055	−	0.960968i
$313$	−11.8472	+	10.6673i	−0.669643	+	0.602950i	−0.932190	−	0.361970i	$-0.882104\pi$
$313$	−11.8472	+	10.6673i	−0.669643	+	0.602950i	0.262546	+	0.964919i	$0.415438\pi$
$314$	18.7665	+	57.7575i	1.05906	+	3.25944i
$315$	17.7474	−	0.171616i	0.999953	−	0.00966948i
$316$	−8.64799	+	26.6158i	−0.486487	+	1.49725i
$317$	2.71045	+	6.08778i	0.152234	+	0.341924i	0.973523	−	0.228589i	$-0.0734112\pi$
$317$	2.71045	+	6.08778i	0.152234	+	0.341924i	−0.821289	+	0.570513i	$0.806744\pi$
$318$	−2.06830	+	2.64681i	−0.115984	+	0.148426i
$319$	−0.0902022	+	0.858217i	−0.00505035	+	0.0480509i
$320$	−1.26116	+	20.3227i	−0.0705008	+	1.13607i
$321$	−8.56900	+	13.7105i	−0.478275	+	0.765246i
$322$	40.4768	−	1.49510i	2.25568	−	0.0833187i
$323$	−21.0806	+	6.84951i	−1.17296	+	0.381117i
$324$	−29.7707	−	18.6177i	−1.65393	−	1.03432i
$325$	6.18313	+	11.2017i	0.342978	+	0.621357i
$326$	−4.28705	+	2.47513i	−0.237438	+	0.137085i
$327$	−0.496645	−	2.81810i	−0.0274646	−	0.155841i
$328$	−6.02456	−	8.29210i	−0.332651	−	0.457854i
$329$	−14.2694	−	22.7338i	−0.786697	−	1.25336i
$330$	1.61944	+	7.33886i	0.0891470	+	0.403991i
$331$	−27.4169	+	12.2068i	−1.50697	+	0.670945i	−0.983468	−	0.181081i	$-0.942040\pi$
$331$	−27.4169	+	12.2068i	−1.50697	+	0.670945i	−0.523499	+	0.852026i	$0.675374\pi$
$332$	27.1572	+	47.0377i	1.49045	+	2.58153i
$333$	4.22292	+	5.40710i	0.231415	+	0.296307i
$334$	2.10501	−	1.89536i	0.115181	−	0.103710i
$335$	2.64769	−	5.07512i	0.144659	−	0.277283i
$336$	−6.34384	+	14.3226i	−0.346085	+	0.781361i
$337$	−0.753067	+	2.31770i	−0.0410222	+	0.126253i	−0.969470	−	0.245209i	$-0.921143\pi$
$337$	−0.753067	+	2.31770i	−0.0410222	+	0.126253i	0.928448	+	0.371462i	$0.121143\pi$
$338$	11.6473	−	10.4872i	0.633527	−	0.570430i
$339$	7.50495	−	20.6139i	0.407613	−	1.11959i
$340$	25.6771	−	20.3872i	1.39254	−	1.10565i
$341$	−4.18420	−	4.64703i	−0.226587	−	0.251651i
$342$	42.5653	−	5.97433i	2.30167	−	0.323055i
$343$	−3.74106	+	18.1385i	−0.201998	+	0.979386i
$344$	−4.58513	+	6.31089i	−0.247214	+	0.340260i
$345$	19.8565	+	14.1929i	1.06904	+	0.764119i
$346$	−1.55232	+	3.48656i	−0.0834531	+	0.187439i
$347$	−11.4333	+	25.6797i	−0.613774	+	1.37856i	0.292663	+	0.956216i	$0.405459\pi$
$347$	−11.4333	+	25.6797i	−0.613774	+	1.37856i	−0.906436	+	0.422342i	$0.861208\pi$
$348$	−7.18948	+	1.26703i	−0.385396	+	0.0679199i
$349$		−	26.4748i		−	1.41716i	−0.705629	−	0.708582i	$-0.749335\pi$
$349$		−	26.4748i		−	1.41716i	0.705629	−	0.708582i	$-0.250665\pi$
$350$	15.5735	−	28.1108i	0.832439	−	1.50258i
$351$	−5.41159	+	12.1458i	−0.288849	+	0.648294i
$352$	0.729922	+	0.155150i	0.0389050	+	0.00826951i
$353$	−20.5992	−	9.17133i	−1.09638	−	0.488141i	−0.222823	−	0.974859i	$-0.571527\pi$
$353$	−20.5992	−	9.17133i	−1.09638	−	0.488141i	−0.873559	+	0.486718i	$0.838194\pi$
$354$	0.125525	+	0.00439476i	0.00667157	+	0.000233579i
$355$	4.24670	+	16.4813i	0.225392	+	0.874738i
$356$	37.9448	+	27.5685i	2.01107	+	1.46113i
$357$	−16.3692	+	5.35353i	−0.866352	+	0.283339i
$358$	12.7770	+	9.28302i	0.675285	+	0.490623i
$359$	12.9253	−	11.6380i	0.682170	−	0.614228i	−0.253404	−	0.967361i	$-0.581550\pi$
$359$	12.9253	−	11.6380i	0.682170	−	0.614228i	0.935573	+	0.353132i	$0.114883\pi$
$360$	−27.2468	+	14.7561i	−1.43603	+	0.777713i
$361$	−10.5618	+	11.7300i	−0.555883	+	0.617370i
$362$	−12.5084	−	13.8920i	−0.657426	−	0.730145i
$363$	−17.9038	+	1.25033i	−0.939706	+	0.0656256i
$364$	25.4056	+	7.22961i	1.33162	+	0.378935i
$365$	13.0811	+	26.2953i	0.684697	+	1.37636i
$366$	26.7210	−	54.7737i	1.39673	−	2.86307i
$367$	−13.9599	−	1.46724i	−0.728699	−	0.0765894i	−0.267088	−	0.963672i	$-0.586062\pi$
$367$	−13.9599	−	1.46724i	−0.728699	−	0.0765894i	−0.461611	+	0.887083i	$0.652728\pi$
$368$	−18.6559	+	10.7710i	−0.972504	+	0.561476i
$369$	−2.49481	+	6.17167i	−0.129875	+	0.321284i
$370$	12.2878	−	1.82524i	0.638813	−	0.0948897i
$371$	−0.0779649	−	2.11074i	−0.00404774	−	0.109584i
$372$	28.0369	−	44.8594i	1.45365	−	2.32585i
$373$	34.7237	+	7.38074i	1.79792	+	0.382160i	0.980910	−	0.194460i	$-0.0622955\pi$
$373$	34.7237	+	7.38074i	1.79792	+	0.382160i	0.817012	+	0.576620i	$0.195629\pi$
$374$	−3.64638	−	6.31572i	−0.188550	−	0.326578i
$375$	17.7801	−	7.67267i	0.918158	−	0.396215i
$376$	40.5826	+	23.4304i	2.09289	+	1.20833i
$377$	0.854284	+	2.62922i	0.0439979	+	0.135412i
$378$	33.0640	−	4.70564i	1.70063	−	0.242032i
$379$	28.3657	−	20.6089i	1.45705	−	1.05861i	0.472926	−	0.881102i	$-0.343198\pi$
$379$	28.3657	−	20.6089i	1.45705	−	1.05861i	0.984120	−	0.177504i	$-0.0568024\pi$
$380$	18.8998	−	47.8549i	0.969538	−	2.45490i
$381$	11.0118	−	3.15651i	0.564151	−	0.161713i
$382$	−4.41612	−	7.64894i	−0.225948	−	0.391354i
$383$	−8.23475	+	3.66635i	−0.420776	+	0.187342i	−0.606192	−	0.795319i	$-0.707304\pi$
$383$	−8.23475	+	3.66635i	−0.420776	+	0.187342i	0.185416	+	0.982660i	$0.440637\pi$
$384$	2.44383	+	34.9937i	0.124711	+	1.78576i
$385$	−3.75235	−	2.87259i	−0.191237	−	0.146401i
$386$	−19.0634	+	6.19407i	−0.970301	+	0.315270i
$387$	5.05394	+	0.354322i	0.256906	+	0.0180112i
$388$	−7.64718	−	35.9771i	−0.388227	−	1.82646i
$389$	14.6328	+	13.1754i	0.741911	+	0.668020i	0.950760	−	0.309928i	$-0.100305\pi$
$389$	14.6328	+	13.1754i	0.741911	+	0.668020i	−0.208849	+	0.977948i	$0.566972\pi$
$390$	14.3021	+	19.3679i	0.724218	+	0.980734i
$391$	−22.5251	−	7.31884i	−1.13914	−	0.370129i
$392$	−9.03753	−	31.0451i	−0.456464	−	1.56802i
$393$	−3.83612	−	9.49720i	−0.193507	−	0.479070i
$394$	32.2661	−	14.3658i	1.62554	−	0.723739i
$395$	4.30016	−	15.4524i	0.216365	−	0.777497i
$396$	3.19602	+	8.78593i	0.160606	+	0.441510i
$397$	−25.9980	+	2.73250i	−1.30480	+	0.137140i	−0.731296	−	0.682060i	$-0.761084\pi$
$397$	−25.9980	+	2.73250i	−1.30480	+	0.137140i	−0.573507	+	0.819200i	$0.694418\pi$
$398$	12.0452	+	37.0714i	0.603772	+	1.85822i
$399$	−18.0461	+	20.1199i	−0.903434	+	1.00725i
$400$	−0.328726	+	17.0883i	−0.0164363	+	0.854417i
$401$	23.1629	+	13.3731i	1.15670	+	0.667820i	0.950510	−	0.310693i	$-0.100561\pi$
$401$	23.1629	+	13.3731i	1.15670	+	0.667820i	0.206187	+	0.978513i	$0.433894\pi$
$402$	3.68496	−	10.1215i	0.183789	−	0.504814i
$403$	−18.3008	−	8.14802i	−0.911625	−	0.405882i
$404$	6.22217	+	59.2000i	0.309564	+	2.94531i
$405$	17.5032	+	9.93174i	0.869739	+	0.493512i
$406$	4.45251	−	5.32805i	0.220974	−	0.264427i
$407$		−	1.82675i		−	0.0905485i
$408$	20.8890	−	21.6272i	1.03416	−	1.07071i
$409$	2.48354	+	11.6842i	0.122803	+	0.577744i	0.995921	+	0.0902340i	$0.0287615\pi$
$409$	2.48354	+	11.6842i	0.122803	+	0.577744i	−0.873117	+	0.487510i	$0.837905\pi$
$410$	7.49504	+	9.43980i	0.370154	+	0.466199i
$411$	15.4483	−	2.72252i	0.762010	−	0.134292i
$412$	−61.4295	−	19.9597i	−3.02642	−	0.983342i
$413$	−0.0621374	+	0.0487489i	−0.00305758	+	0.00239878i
$414$	40.5478	+	21.5690i	1.99282	+	1.06006i
$415$	−16.7026	−	26.2695i	−0.819900	−	1.28952i
$416$	2.33837	−	0.497036i	0.114648	−	0.0243692i
$417$	4.11410	+	14.3525i	0.201469	+	0.702843i
$418$	−9.91127	−	5.72228i	−0.484776	−	0.279886i
$419$	4.62061	+	3.35707i	0.225731	+	0.164004i	0.694903	−	0.719104i	$-0.255447\pi$
$419$	4.62061	+	3.35707i	0.225731	+	0.164004i	−0.469171	+	0.883107i	$0.655447\pi$
$420$	14.6135	−	37.2111i	0.713064	−	1.81572i
$421$	7.19837	−	5.22992i	0.350827	−	0.254891i	−0.398389	−	0.917217i	$-0.630431\pi$
$421$	7.19837	−	5.22992i	0.350827	−	0.254891i	0.749216	+	0.662326i	$0.230431\pi$
$422$	−17.4422	+	1.83325i	−0.849074	+	0.0892413i
$423$	−1.05668	−	30.4165i	−0.0513774	−	1.47890i
$424$	1.84379	+	3.19354i	0.0895423	+	0.155092i
$425$	−14.2039	+	12.3029i	−0.688988	+	0.596777i
$426$	11.9945	+	29.6952i	0.581137	+	1.43874i
$427$	9.34563	+	37.1643i	0.452267	+	1.79850i
$428$	21.4062	+	29.4631i	1.03471	+	1.42415i
$429$	3.12615	−	1.66184i	0.150932	−	0.0802346i
$430$	5.07003	−	7.64518i	0.244499	−	0.368683i
$431$	12.9399	+	1.36004i	0.623293	+	0.0655108i	0.410910	−	0.911676i	$-0.365211\pi$
$431$	12.9399	+	1.36004i	0.623293	+	0.0655108i	0.212383	+	0.977187i	$0.431878\pi$
$432$	−14.3726	+	10.4364i	−0.691502	+	0.502120i
$433$	13.0481	−	17.9591i	0.627051	−	0.863061i	−0.370792	−	0.928716i	$-0.620914\pi$
$433$	13.0481	−	17.9591i	0.627051	−	0.863061i	0.997842	+	0.0656547i	$0.0209136\pi$
$434$	7.10288	+	49.8115i	0.340949	+	2.39103i
$435$	4.08579	−	0.901594i	0.195898	−	0.0432281i
$436$	−6.30472	−	1.34011i	−0.301941	−	0.0641796i
$437$	−36.3555	+	7.72761i	−1.73912	+	0.369662i
$438$	30.8995	+	45.8194i	1.47644	+	2.18933i
$439$	−5.19561	+	24.4434i	−0.247973	+	1.16662i	0.661203	+	0.750207i	$0.270046\pi$
$439$	−5.19561	+	24.4434i	−0.247973	+	1.16662i	−0.909176	+	0.416413i	$0.863287\pi$
$440$	8.13599	+	1.36895i	0.387868	+	0.0652620i
$441$	−13.9916	+	15.6600i	−0.666266	+	0.745714i
$442$	−18.9011	−	13.7325i	−0.899034	−	0.653186i
$443$	22.9813	+	13.2682i	1.09187	+	0.630393i	0.934074	−	0.357078i	$-0.116227\pi$
$443$	22.9813	+	13.2682i	1.09187	+	0.630393i	0.157798	+	0.987471i	$0.449560\pi$
$444$	14.8555	−	4.25830i	0.705011	−	0.202090i
$445$	−22.4030	−	14.8569i	−1.06200	−	0.704286i
$446$	−3.47060	−	33.0205i	−0.164338	−	1.56357i
$447$	20.2065	−	32.3306i	0.955733	−	1.52919i
$448$	−16.7708	−	17.2969i	−0.792347	−	0.817200i
$449$			26.3963i			1.24572i	0.782334	+	0.622859i	$0.214029\pi$
$449$			26.3963i			1.24572i	−0.782334	+	0.622859i	$0.785971\pi$
$450$	31.2713	−	18.7063i	1.47414	−	0.881824i
$451$	1.53499	−	0.886229i	0.0722800	−	0.0417309i
$452$	−36.7219	−	33.0645i	−1.72725	−	1.55523i
$453$	5.97786	−	3.17779i	0.280864	−	0.149306i
$454$	6.68117	+	9.19584i	0.313563	+	0.431582i
$455$	−14.7248	−	3.51761i	−0.690307	−	0.164908i
$456$	11.4194	−	45.7832i	0.534763	−	2.14399i
$457$	−8.73258	+	15.1253i	−0.408493	+	0.707531i	−0.994721	−	0.102615i	$-0.967279\pi$
$457$	−8.73258	+	15.1253i	−0.408493	+	0.707531i	0.586228	+	0.810146i	$0.300612\pi$
$458$	0.719936	−	6.84973i	0.0336404	−	0.320067i
$459$	−19.1006	−	4.06535i	−0.891538	−	0.189754i
$460$	46.3937	−	29.4980i	2.16312	−	1.37535i
$461$	3.49889	+	10.7685i	0.162960	+	0.501538i	0.998880	−	0.0473122i	$-0.0150656\pi$
$461$	3.49889	+	10.7685i	0.162960	+	0.501538i	−0.835920	+	0.548851i	$0.815066\pi$
$462$	−7.70954	−	4.43135i	−0.358680	−	0.206165i
$463$	−3.38704	+	10.4242i	−0.157409	+	0.484455i	−0.998397	−	0.0565988i	$-0.981974\pi$
$463$	−3.38704	+	10.4242i	−0.157409	+	0.484455i	0.840988	+	0.541054i	$0.181974\pi$
$464$	−0.767792	+	3.61218i	−0.0356438	+	0.167691i
$465$	−14.9558	+	26.3739i	−0.693559	+	1.22306i
$466$	40.1497	−	8.53409i	1.85990	−	0.395334i
$467$	3.53569	−	1.57419i	0.163612	−	0.0728449i	−0.323296	−	0.946298i	$-0.604791\pi$
$467$	3.53569	−	1.57419i	0.163612	−	0.0728449i	0.486909	+	0.873453i	$0.338124\pi$
$468$	20.8018	+	21.5487i	0.961564	+	0.996088i
$469$	2.32932	+	6.35989i	0.107558	+	0.293672i
$470$	−48.8586	−	25.4895i	−2.25368	−	1.17574i
$471$	−20.3245	−	38.2331i	−0.936502	−	1.76169i
$472$	0.0560827	−	0.125964i	0.00258142	−	0.00579796i
$473$	−1.00248	−	0.902636i	−0.0460940	−	0.0415033i
$474$	4.20322	−	29.8879i	0.193060	−	1.37280i
$475$	−9.65037	+	27.8654i	−0.442789	+	1.27855i
$476$	−2.62815	+	38.7043i	−0.120461	+	1.77401i
$477$	1.12476	−	2.11445i	0.0514992	−	0.0968138i
$478$	5.51092	+	52.4329i	0.252064	+	2.39823i
$479$	0.504235	+	0.224500i	0.0230391	+	0.0102577i	0.418224	−	0.908344i	$-0.362653\pi$
$479$	0.504235	+	0.224500i	0.0230391	+	0.0102577i	−0.395185	+	0.918602i	$0.629319\pi$
$480$	−0.406063	−	3.59531i	−0.0185342	−	0.164103i
$481$	−2.38028	−	5.34621i	−0.108532	−	0.243766i
$482$	−40.9765			−1.86643
$483$	−28.2365	+	6.05864i	−1.28480	+	0.275678i
$484$	−12.4925	+	38.4478i	−0.567839	+	1.74763i
$485$	5.25999	+	20.4138i	0.238844	+	0.926945i
$486$	35.1050	+	14.2017i	1.59239	+	0.644204i
$487$	6.36241	−	1.35237i	0.288308	−	0.0612818i	−0.0614873	−	0.998108i	$-0.519584\pi$
$487$	6.36241	−	1.35237i	0.288308	−	0.0612818i	0.349796	+	0.936826i	$0.386251\pi$
$488$	−44.7674	−	49.7192i	−2.02652	−	2.25068i
$489$	2.70394	−	2.26846i	0.122276	−	0.102583i
$490$	12.1784	+	36.0214i	0.550162	+	1.62728i
$491$	−23.1176	−	7.51135i	−1.04328	−	0.338982i	−0.263252	−	0.964727i	$-0.584795\pi$
$491$	−23.1176	−	7.51135i	−1.04328	−	0.338982i	−0.780028	+	0.625745i	$0.784795\pi$
$492$	10.7852	+	10.4170i	0.486234	+	0.469636i
$493$	−3.51617	+	2.03006i	−0.158360	+	0.0914294i
$494$	−36.4628	−	3.83240i	−1.64054	−	0.172428i
$495$	−2.04527	−	4.95270i	−0.0919279	−	0.222607i
$496$	−15.7290	−	21.6492i	−0.706255	−	0.972076i
$497$	−17.7997	−	9.41835i	−0.798427	−	0.422471i
$498$	−37.6488	−	44.8763i	−1.68708	−	2.01096i
$499$	1.21909	−	2.11152i	0.0545739	−	0.0945248i	−0.837448	−	0.546517i	$-0.815953\pi$
$499$	1.21909	−	2.11152i	0.0545739	−	0.0945248i	0.892022	+	0.451992i	$0.149287\pi$
$500$	−1.02532	−	43.6073i	−0.0458536	−	1.95018i
$501$	−1.24353	+	1.59135i	−0.0555567	+	0.0710961i
$502$	2.21464	−	10.4190i	0.0988441	−	0.465025i
$503$	26.3073	−	19.1133i	1.17298	−	0.852222i	0.181619	−	0.983369i	$-0.441866\pi$
$503$	26.3073	−	19.1133i	1.17298	−	0.852222i	0.991363	+	0.131147i	$0.0418661\pi$
$504$	8.80437	−	35.5903i	0.392178	−	1.58532i
$505$	−5.01273	−	33.7465i	−0.223064	−	1.50170i
$506$	−4.97387	−	11.1715i	−0.221116	−	0.496634i
$507$	−6.88057	+	8.80509i	−0.305577	+	0.391048i
$508$	2.69714	−	25.6615i	0.119666	−	1.13855i
$509$	−23.8015	−	26.4343i	−1.05498	−	1.17168i	−0.984719	−	0.174150i	$-0.944282\pi$
$509$	−23.8015	−	26.4343i	−1.05498	−	1.17168i	−0.0702643	−	0.997528i	$-0.522384\pi$
$510$	−23.4561	+	26.4599i	−1.03865	+	1.17166i
$511$	−33.4233	−	9.51118i	−1.47856	−	0.420750i
$512$	33.0706	+	10.7453i	1.46153	+	0.474879i
$513$	−29.1486	+	9.46225i	−1.28694	+	0.417769i
$514$	−22.6352	−	20.3808i	−0.998396	−	0.898960i
$515$	35.6644	+	9.92483i	1.57156	+	0.437340i
$516$	5.00357	−	10.2565i	0.220270	−	0.451517i
$517$	−4.76318	+	6.55596i	−0.209485	+	0.288331i
$518$	−8.19483	+	12.2023i	−0.360060	+	0.536137i
$519$	0.658539	−	2.64024i	0.0289066	−	0.115894i
$520$	25.5948	−	6.59494i	1.12241	−	0.289207i
$521$	14.1937	+	6.31943i	0.621836	+	0.276859i	0.693373	−	0.720579i	$-0.256124\pi$
$521$	14.1937	+	6.31943i	0.621836	+	0.276859i	−0.0715371	+	0.997438i	$0.522790\pi$
$522$	7.39892	−	2.69148i	0.323842	−	0.117803i
$523$	6.57906	−	30.9520i	0.287682	−	1.35344i	−0.562434	−	0.826842i	$-0.690135\pi$
$523$	6.57906	−	30.9520i	0.287682	−	1.35344i	0.850116	−	0.526596i	$-0.176532\pi$
$524$	−23.0716			−1.00789
$525$	−7.45662	+	21.6656i	−0.325433	+	0.945565i
$526$	39.4901			1.72185
$527$	6.11698	−	28.7781i	0.266460	−	1.25360i
$528$	4.72643	+	0.165477i	0.205691	+	0.00720147i
$529$	−15.2695	−	6.79840i	−0.663889	−	0.295583i
$530$	−2.32678	−	3.65949i	−0.101069	−	0.158958i
$531$	−0.0886833	+	0.0124473i	−0.00384853	+	0.000540168i
$532$	26.7976	+	54.6635i	1.16182	+	2.36996i
$533$	3.33758	−	4.59379i	0.144567	−	0.198979i
$534$	−45.4623	−	22.1785i	−1.96734	−	0.959758i
$535$	−12.9791	−	16.3468i	−0.561136	−	0.706735i
$536$	−8.78752	−	7.91232i	−0.379563	−	0.341760i
$537$	−10.1203	−	4.93713i	−0.436724	−	0.213053i
$538$	44.4335	+	14.4373i	1.91566	+	0.622437i
$539$	5.50257	−	0.993120i	0.237013	−	0.0427767i
$540$	35.5088	−	28.1777i	1.52805	−	1.21258i
$541$	16.7117	+	18.5602i	0.718491	+	0.797965i	0.986204	−	0.165534i	$-0.0529347\pi$
$541$	16.7117	+	18.5602i	0.718491	+	0.797965i	−0.267713	+	0.963499i	$0.586268\pi$
$542$	0.439457	−	4.18115i	0.0188763	−	0.179596i
$543$	10.5020	+	8.20662i	0.450686	+	0.352180i
$544$	1.42805	+	3.20744i	0.0612269	+	0.137518i
$545$	3.64301	+	0.612967i	0.156049	+	0.0262566i
$546$	−28.3371	−	2.92324i	−1.21272	−	0.125103i
$547$	−11.2835	+	8.19795i	−0.482448	+	0.350519i	−0.802273	−	0.596958i	$-0.796376\pi$
$547$	−11.2835	+	8.19795i	−0.482448	+	0.350519i	0.319825	+	0.947477i	$0.396376\pi$
$548$	7.34624	−	34.5614i	0.313816	−	1.47639i
$549$	−11.9846	+	41.7669i	−0.511491	+	1.78257i
$550$	−9.62791	−	1.19957i	−0.410536	−	0.0511498i
$551$	−3.18578	+	5.51794i	−0.135719	+	0.235072i
$552$	38.6261	−	32.4052i	1.64404	−	1.37926i
$553$	10.0894	+	16.0742i	0.429044	+	0.683547i
$554$	39.8800	+	54.8902i	1.69434	+	2.33206i
$555$	−8.40223	+	2.80219i	−0.356655	+	0.118946i
$556$	33.4465	+	3.51537i	1.41845	+	0.149085i
$557$	11.0791	−	6.39649i	0.469434	−	0.271028i	−0.246568	−	0.969125i	$-0.579303\pi$
$557$	11.0791	−	6.39649i	0.469434	−	0.271028i	0.716003	+	0.698097i	$0.245970\pi$
$558$	−21.3817	+	52.8941i	−0.905160	+	2.23919i
$559$	−4.11004	−	1.33543i	−0.173836	−	0.0564827i
$560$	−14.6848	−	13.9041i	−0.620547	−	0.587554i
$561$	3.34191	+	3.98346i	0.141096	+	0.168182i
$562$	−23.8125	−	26.4465i	−1.00447	−	1.11558i
$563$	24.1620	−	5.13579i	1.01831	−	0.216448i	0.331629	−	0.943410i	$-0.392402\pi$
$563$	24.1620	−	5.13579i	1.01831	−	0.216448i	0.686678	+	0.726962i	$0.259068\pi$
$564$	−64.4179	−	23.4528i	−2.71248	−	0.987540i
$565$	21.8373	+	18.0340i	0.918704	+	0.758696i
$566$	11.1216	−	34.2289i	0.467478	−	1.43875i
$567$	−22.6341	+	7.39567i	−0.950544	+	0.310589i
$568$	35.1581			1.47520
$569$	12.5025	+	28.0810i	0.524131	+	1.17722i	0.960711	+	0.277551i	$0.0895229\pi$
$569$	12.5025	+	28.0810i	0.524131	+	1.17722i	−0.436580	+	0.899665i	$0.643810\pi$
$570$	−11.1163	+	54.3653i	−0.465610	+	2.27711i
$571$	24.4042	+	10.8655i	1.02129	+	0.454705i	0.847904	−	0.530149i	$-0.177864\pi$
$571$	24.4042	+	10.8655i	1.02129	+	0.454705i	0.173381	+	0.984855i	$0.444531\pi$
$572$	−0.833590	−	7.93108i	−0.0348541	−	0.331615i
$573$	4.04738	+	4.82436i	0.169082	+	0.201540i
$574$	−14.2291	−	0.966201i	−0.593909	−	0.0403285i
$575$	−25.8434	+	18.0272i	−1.07774	+	0.751787i
$576$	−6.60409	−	26.5079i	−0.275170	−	1.10450i
$577$	21.7603	+	19.5930i	0.905892	+	0.815669i	0.983424	−	0.181321i	$-0.0580372\pi$
$577$	21.7603	+	19.5930i	0.905892	+	0.815669i	−0.0775315	+	0.996990i	$0.524704\pi$
$578$	−2.84132	+	6.38170i	−0.118183	+	0.265444i
$579$	12.6192	−	6.70828i	0.524436	−	0.278787i
$580$	1.56379	−	9.29396i	0.0649327	−	0.385911i
$581$	36.2865	+	6.32297i	1.50542	+	0.262321i
$582$	14.8565	+	36.7806i	0.615821	+	1.52461i
$583$	−0.582560	+	0.259372i	−0.0241272	+	0.0107421i
$584$	59.3434	−	12.6138i	2.45565	−	0.521964i
$585$	−12.4392	−	11.8297i	−0.514297	−	0.489098i
$586$	14.9475	−	70.3224i	0.617475	−	2.90499i
$587$	0.626522	−	1.92824i	0.0258593	−	0.0795868i	−0.937294	−	0.348540i	$-0.886678\pi$
$587$	0.626522	−	1.92824i	0.0258593	−	0.0795868i	0.963153	+	0.268953i	$0.0866776\pi$
$588$	20.9032	+	42.4331i	0.862034	+	1.74991i
$589$	−14.2675	−	43.9108i	−0.587881	−	1.80931i
$590$	−0.0595630	+	0.150815i	−0.00245217	+	0.00620897i
$591$	−20.8785	+	14.0800i	−0.858826	+	0.579173i
$592$	0.817137	−	7.77454i	0.0335841	−	0.319532i
$593$	−4.74514	+	8.21882i	−0.194859	+	0.337506i	−0.946854	−	0.321662i	$-0.895758\pi$
$593$	−4.74514	+	8.21882i	−0.194859	+	0.337506i	0.751995	+	0.659169i	$0.229092\pi$
$594$	−5.03913	−	8.73348i	−0.206758	−	0.358339i
$595$	0.557053	−	22.2271i	0.0228370	−	0.911222i
$596$	−50.4777	−	69.4766i	−2.06765	−	2.84587i
$597$	−13.0452	−	24.5397i	−0.533903	−	1.00434i
$598$	−29.1134	−	26.2138i	−1.19053	−	1.07196i
$599$	29.4888	−	17.0254i	1.20488	−	0.695638i	0.243244	−	0.969965i	$-0.421788\pi$
$599$	29.4888	−	17.0254i	1.20488	−	0.695638i	0.961637	+	0.274327i	$0.0884550\pi$
$600$	−6.18386	−	39.5219i	−0.252455	−	1.61347i
$601$			3.94156i			0.160780i	0.996764	+	0.0803898i	$0.0256165\pi$
$601$			3.94156i			0.160780i	−0.996764	+	0.0803898i	$0.974384\pi$
$602$	2.64709	+	10.5266i	0.107887	+	0.429030i
$603$	−1.33496	+	7.56298i	−0.0543639	+	0.307988i
$604$	−1.59400	−	15.1659i	−0.0648588	−	0.617091i
$605$	6.21180	−	22.3218i	0.252546	−	0.907511i
$606$	−17.6898	−	61.7128i	−0.718601	−	2.50691i
$607$	6.65159	+	3.84030i	0.269980	+	0.155873i	0.628878	−	0.777504i	$-0.283514\pi$
$607$	6.65159	+	3.84030i	0.269980	+	0.155873i	−0.358899	+	0.933376i	$0.616848\pi$
$608$	4.45752	+	3.23858i	0.180776	+	0.131342i
$609$	−2.46708	+	4.29216i	−0.0999712	+	0.173927i
$610$	55.0964	+	56.1664i	2.23079	+	2.27411i
$611$	−5.39753	+	25.3934i	−0.218361	+	1.02731i
$612$	−24.6041	+	36.4629i	−0.994563	+	1.47393i
$613$	4.01807	−	0.854067i	0.162288	−	0.0344954i	−0.126051	−	0.992024i	$-0.540230\pi$
$613$	4.01807	−	0.854067i	0.162288	−	0.0344954i	0.288339	+	0.957528i	$0.406897\pi$
$614$	20.6144	+	4.38173i	0.831931	+	0.176832i
$615$	−6.43090	−	5.70084i	−0.259319	−	0.229880i
$616$	−7.68040	+	6.02554i	−0.309452	+	0.242776i
$617$	−9.72972	+	13.3918i	−0.391704	+	0.539134i	−0.958638	−	0.284629i	$-0.908129\pi$
$617$	−9.72972	+	13.3918i	−0.391704	+	0.539134i	0.566934	+	0.823763i	$0.308129\pi$
$618$	68.9816	+	9.70108i	2.77485	+	0.390235i
$619$	20.3975	+	2.14386i	0.819843	+	0.0861690i	0.505158	−	0.863027i	$-0.331434\pi$
$619$	20.3975	+	2.14386i	0.819843	+	0.0861690i	0.314685	+	0.949196i	$0.398101\pi$
$620$	42.4664	+	53.4852i	1.70549	+	2.14802i
$621$	−31.1404	−	10.1274i	−1.24962	−	0.406401i
$622$	9.30223	+	12.8034i	0.372985	+	0.513370i
$623$	30.8464	−	7.75689i	1.23584	−	0.310773i
$624$	14.0481	−	5.67434i	0.562375	−	0.227155i
$625$	1.65506	+	24.9452i	0.0662024	+	0.997806i
$626$	−19.3638	−	33.5391i	−0.773934	−	1.34049i
$627$	7.66747	+	2.79152i	0.306209	+	0.111482i
$628$	−96.9977	+	10.1949i	−3.87063	+	0.406819i
$629$	6.95333	−	5.05189i	0.277247	−	0.201432i
$630$	−8.55601	+	42.2581i	−0.340880	+	1.68360i
$631$	3.82624	+	2.77992i	0.152320	+	0.110667i	0.661335	−	0.750091i	$-0.269990\pi$
$631$	3.82624	+	2.77992i	0.152320	+	0.110667i	−0.509015	+	0.860758i	$0.669990\pi$
$632$	−28.6945	−	16.5668i	−1.14141	−	0.658991i
$633$	12.0205	−	3.44565i	0.477772	−	0.136952i
$634$	−15.8348	+	3.36579i	−0.628879	+	0.133672i
$635$	−0.915973	+	14.7603i	−0.0363493	+	0.585744i
$636$	−3.46727	−	4.13288i	−0.137486	−	0.163880i
$637$	14.8099	−	10.0764i	0.586791	−	0.399243i
$638$	−1.99374	−	0.647804i	−0.0789328	−	0.0256468i
$639$	−12.0968	−	19.3667i	−0.478543	−	0.766136i
$640$	−43.6288	−	12.1412i	−1.72458	−	0.479923i
$641$	2.82434	+	13.2875i	0.111555	+	0.524823i	0.998069	+	0.0621213i	$0.0197866\pi$
$641$	2.82434	+	13.2875i	0.111555	+	0.524823i	−0.886514	+	0.462702i	$0.846880\pi$
$642$	−28.2509	−	27.2865i	−1.11497	−	1.07691i
$643$		−	45.3761i		−	1.78946i	−0.446609	−	0.894729i	$-0.647369\pi$
$643$		−	45.3761i		−	1.78946i	0.446609	−	0.894729i	$-0.352631\pi$
$644$	−11.1668	+	64.0844i	−0.440033	+	2.52528i
$645$	−2.61395	+	5.99558i	−0.102924	+	0.236076i
$646$	−5.62847	−	53.5513i	−0.221449	−	2.10695i
$647$	25.9759	+	11.5652i	1.02122	+	0.454675i	0.847881	−	0.530187i	$-0.177878\pi$
$647$	25.9759	+	11.5652i	1.02122	+	0.454675i	0.173337	+	0.984863i	$0.444545\pi$
$648$	28.8892	−	29.8940i	1.13487	−	1.17435i
$649$	0.0206498	+	0.0119222i	0.000810575	+	0.000467986i
$650$	−29.7404	+	9.03465i	−1.16651	+	0.354368i
$651$	−11.1514	−	34.0970i	−0.437057	−	1.33637i
$652$	−2.45672	−	7.56100i	−0.0962125	−	0.296112i
$653$	−17.4591	+	1.83502i	−0.683227	+	0.0718100i	−0.439782	−	0.898105i	$-0.644944\pi$
$653$	−17.4591	+	1.83502i	−0.683227	+	0.0718100i	−0.243445	+	0.969915i	$0.578278\pi$
$654$	6.94722	+	0.243229i	0.271658	+	0.00951102i
$655$	13.2112	−	0.565025i	0.516203	−	0.0220773i
$656$	6.92928	−	3.08511i	0.270543	−	0.120453i
$657$	−27.3666	−	28.3492i	−1.06767	−	1.10601i
$658$	61.2272	−	22.4246i	2.38689	−	0.874203i
$659$	−22.5062	−	7.31272i	−0.876719	−	0.284863i	−0.164125	−	0.986440i	$-0.552480\pi$
$659$	−22.5062	−	7.31272i	−0.876719	−	0.284863i	−0.712594	+	0.701576i	$0.752480\pi$
$660$	−12.0694	+	0.0934902i	−0.469800	+	0.00363910i
$661$	10.9804	+	9.88683i	0.427090	+	0.384553i	0.854455	−	0.519526i	$-0.173891\pi$
$661$	10.9804	+	9.88683i	0.427090	+	0.384553i	−0.427365	+	0.904079i	$0.640558\pi$
$662$	−15.1581	−	71.3133i	−0.589137	−	2.77167i
$663$	14.9711	+	7.30354i	0.581428	+	0.283646i
$664$	−61.1585	+	19.8716i	−2.37341	+	0.771168i
$665$	−16.6835	−	30.6450i	−0.646957	−	1.18836i
$666$	−14.9813	+	7.30350i	−0.580512	+	0.283005i
$667$	−6.21955	+	2.76912i	−0.240822	+	0.107221i
$668$	2.27455	+	3.93964i	0.0880051	+	0.152429i
$669$	6.52309	+	22.7565i	0.252197	+	0.879815i
$670$	10.7222	+	8.85476i	0.414235	+	0.342089i
$671$	9.36003	−	6.80046i	0.361340	−	0.262529i
$672$	3.46830	+	2.50969i	0.133793	+	0.0968133i
$673$	3.07071	+	9.45067i	0.118367	+	0.364297i	0.992634	−	0.121148i	$-0.0386577\pi$
$673$	3.07071	+	9.45067i	0.118367	+	0.364297i	−0.874267	+	0.485445i	$0.838658\pi$
$674$	−5.12697	−	2.96005i	−0.197483	−	0.114017i
$675$	−19.6429	+	17.0046i	−0.756054	+	0.654509i
$676$	12.5854	+	21.7985i	0.484052	+	0.838403i
$677$	40.6799	+	8.64678i	1.56346	+	0.332323i	0.906698	−	0.421780i	$-0.138594\pi$
$677$	40.6799	+	8.64678i	1.56346	+	0.332323i	0.656757	+	0.754102i	$0.271928\pi$
$678$	45.1921	+	28.2449i	1.73559	+	1.08474i
$679$	−22.0468	−	11.6656i	−0.846080	−	0.447685i
$680$	17.2894	+	34.7547i	0.663019	+	1.33278i
$681$	−5.82924	−	5.63025i	−0.223377	−	0.215752i
$682$	13.1556	−	7.59539i	0.503754	−	0.290843i
$683$	−33.6697	−	3.53883i	−1.28833	−	0.135409i	−0.564529	−	0.825413i	$-0.690942\pi$
$683$	−33.6697	−	3.53883i	−1.28833	−	0.135409i	−0.723806	+	0.690004i	$0.757609\pi$
$684$	−4.82769	+	68.8608i	−0.184592	+	2.63296i
$685$	−3.36017	+	19.9703i	−0.128386	+	0.763027i
$686$	−41.2111	−	18.0508i	−1.57345	−	0.689184i
$687$	0.342110	+	4.89874i	0.0130523	+	0.186899i
$688$	−3.86273	−	4.29000i	−0.147265	−	0.163555i
$689$	−1.36697	+	1.51817i	−0.0520773	+	0.0578378i
$690$	−43.7542	+	40.0145i	−1.66569	+	1.52332i
$691$	−4.70336	+	4.23492i	−0.178924	+	0.161104i	−0.753726	−	0.657188i	$-0.771746\pi$
$691$	−4.70336	+	4.23492i	−0.178924	+	0.161104i	0.574802	+	0.818292i	$0.305079\pi$
$692$	−4.95872	−	3.60272i	−0.188502	−	0.136955i
$693$	5.96175	+	2.15753i	0.226468	+	0.0819577i
$694$	−55.2454	−	40.1381i	−2.09709	−	1.52362i
$695$	−19.2382	−	1.19385i	−0.729745	−	0.0452855i
$696$	0.302422	−	8.63790i	0.0114633	−	0.327419i
$697$	7.61838	+	3.39192i	0.288567	+	0.128478i
$698$	62.9094	+	13.3718i	2.38116	+	0.506131i
$699$	−27.1357	+	10.9607i	−1.02637	+	0.414572i
$700$	38.9593	+	33.8508i	1.47252	+	1.27944i
$701$		−	11.7559i		−	0.444013i	−0.975045	−	0.222007i	$-0.928739\pi$
$701$		−	11.7559i		−	0.444013i	0.975045	−	0.222007i	$-0.0712607\pi$
$702$	−26.1275	−	18.9936i	−0.986120	−	0.716866i
$703$	5.48599	−	12.3217i	0.206908	−	0.464723i
$704$	−2.95850	+	6.64491i	−0.111503	+	0.250439i
$705$	37.4611	+	11.8519i	1.41087	+	0.446367i
$706$	32.1971	−	44.3155i	1.21175	−	1.66784i
$707$	33.5116	+	22.5058i	1.26033	+	0.846418i
$708$	−0.0488173	+	0.195720i	−0.00183466	+	0.00735561i
$709$	18.3972	+	20.4321i	0.690920	+	0.767345i	0.981903	−	0.189384i	$-0.0606490\pi$
$709$	18.3972	+	20.4321i	0.690920	+	0.767345i	−0.290983	+	0.956728i	$0.593982\pi$
$710$	−41.3078	+	1.76668i	−1.55026	+	0.0663024i
$711$	0.747139	+	21.5064i	0.0280199	+	0.806554i
$712$	−41.2670	+	37.1570i	−1.54655	+	1.39252i
$713$	15.2451	−	46.9196i	0.570933	−	1.75715i
$714$	−4.45332	−	41.6006i	−0.166661	−	1.55686i
$715$	0.671561	+	4.52106i	0.0251149	+	0.169078i
$716$	−18.8490	+	16.9718i	−0.704422	+	0.634264i
$717$	−10.3579	−	36.1347i	−0.386824	−	1.34948i
$718$	21.1259	+	36.5911i	0.788411	+	1.36557i
$719$	32.0821	−	14.2839i	1.19646	−	0.532699i	0.290834	−	0.956773i	$-0.406067\pi$
$719$	32.0821	−	14.2839i	1.19646	−	0.532699i	0.905627	+	0.424074i	$0.139400\pi$
$720$	−6.48911	−	21.9933i	−0.241835	−	0.819643i
$721$	−37.0996	+	23.2864i	−1.38166	+	0.867230i
$722$	−22.5384	−	31.0215i	−0.838793	−	1.15450i
$723$	28.7723	−	5.07066i	1.07005	−	0.188580i
$724$	25.9996	−	15.0109i	0.966266	−	0.557874i
$725$	−0.667841	+	5.36018i	−0.0248030	+	0.199072i
$726$	6.07176	−	43.1746i	0.225344	−	1.60236i
$727$	−39.0659	+	12.6933i	−1.44887	+	0.470767i	−0.924651	−	0.380815i	$-0.875644\pi$
$727$	−39.0659	+	12.6933i	−1.44887	+	0.470767i	−0.524222	+	0.851582i	$0.675644\pi$
$728$	−14.6263	+	27.6422i	−0.542086	+	1.02449i
$729$	−26.4069	−	5.62790i	−0.978035	−	0.208441i
$730$	−69.0899	+	17.8022i	−2.55713	+	0.658890i
$731$	0.663427	−	6.31209i	0.0245377	−	0.233461i
$732$	77.1219	+	60.2654i	2.85051	+	2.22747i
$733$	7.09555	+	15.9369i	0.262080	+	0.588641i	0.995876	−	0.0907289i	$-0.0289197\pi$
$733$	7.09555	+	15.9369i	0.262080	+	0.588641i	−0.733796	+	0.679370i	$0.762253\pi$
$734$	10.5373	−	32.4304i	0.388938	−	1.19703i
$735$	−13.0087	−	23.7860i	−0.479834	−	0.877359i
$736$	1.81928	+	5.59918i	0.0670597	+	0.206389i
$737$	1.51962	−	1.36827i	0.0559760	−	0.0504010i
$738$	−13.4051	−	9.04534i	−0.493447	−	0.332964i
$739$	7.03935	−	7.81799i	0.258947	−	0.287589i	−0.599627	−	0.800280i	$-0.704684\pi$
$739$	7.03935	−	7.81799i	0.258947	−	0.287589i	0.858574	+	0.512690i	$0.171351\pi$
$740$	−1.23570	+	19.9124i	−0.0454251	+	0.731995i
$741$	26.0772	−	1.82114i	0.957971	−	0.0669011i
$742$	5.05492	+	0.880826i	0.185572	+	0.0323361i
$743$		−	10.8599i		−	0.398411i	−0.979958	−	0.199206i	$-0.936164\pi$
$743$		−	10.8599i		−	0.398411i	0.979958	−	0.199206i	$-0.0638362\pi$
$744$	45.0494	+	43.5116i	1.65159	+	1.59521i
$745$	30.6059	+	38.5473i	1.12131	+	1.41226i
$746$	−35.0762	+	78.7825i	−1.28423	+	2.88443i
$747$	31.9890	+	26.8518i	1.17042	+	0.982456i
$748$	11.1389	−	3.61926i	0.407280	−	0.132333i
$749$	24.6404	+	1.67316i	0.900339	+	0.0611361i
$750$	9.25150	+	46.1242i	0.337817	+	1.68422i
$751$	−14.2988	+	24.7663i	−0.521771	+	0.903734i	0.477908	+	0.878410i	$0.341395\pi$
$751$	−14.2988	+	24.7663i	−0.521771	+	0.903734i	−0.999679	+	0.0253242i	$0.991938\pi$
$752$	−23.2045	+	25.7712i	−0.846180	+	0.939778i
$753$	−0.265732	+	7.58996i	−0.00968382	+	0.276593i
$754$	−6.67902	+	0.701994i	−0.243236	+	0.0255651i
$755$	1.28416	+	8.64520i	0.0467355	+	0.314631i
$756$	−3.64816	+	53.5116i	−0.132682	+	1.94620i
$757$	6.84786			0.248890			0.124445	−	0.992227i	$-0.460285\pi$
$757$	6.84786			0.248890			0.124445	+	0.992227i	$0.460285\pi$
$758$	34.6439	+	77.8116i	1.25832	+	2.82624i
$759$	4.87492	+	7.22877i	0.176948	+	0.262388i
$760$	50.7676	+	33.6674i	1.84153	+	1.22124i
$761$	24.5502	+	5.21831i	0.889945	+	0.189164i	0.630125	−	0.776493i	$-0.283003\pi$
$761$	24.5502	+	5.21831i	0.889945	+	0.189164i	0.259820	+	0.965657i	$0.416337\pi$
$762$	1.93869	+	27.7605i	0.0702313	+	1.00566i
$763$	−3.43901	+	2.69802i	−0.124501	+	0.0976750i
$764$	13.4903	−	4.38327i	0.488063	−	0.158581i
$765$	13.1958	−	21.4819i	0.477094	−	0.776678i
$766$	−4.55279	−	21.4192i	−0.164499	−	0.773907i
$767$	0.0759690	+	0.00798467i	0.00274308	+	0.000288310i
$768$	−53.1493	−	7.47454i	−1.91786	−	0.269714i
$769$	−2.19884	+	3.02644i	−0.0792920	+	0.109136i	−0.846821	−	0.531879i	$-0.821486\pi$
$769$	−2.19884	+	3.02644i	−0.0792920	+	0.109136i	0.767529	+	0.641015i	$0.221486\pi$
$770$	8.72106	−	7.46545i	0.314285	−	0.269036i
$771$	18.4157	+	11.5097i	0.663227	+	0.414513i
$772$	−3.36491	−	32.0150i	−0.121106	−	1.15224i
$773$	−27.7895	+	30.8634i	−0.999520	+	1.11008i	−0.00559845	+	0.999984i	$0.501782\pi$
$773$	−27.7895	+	30.8634i	−0.999520	+	1.11008i	−0.993921	+	0.110095i	$0.964885\pi$
$774$	−3.39457	+	11.8302i	−0.122015	+	0.425228i
$775$	−25.6268	−	29.5865i	−0.920542	−	1.06278i
$776$	43.5469			1.56324
$777$	4.24416	−	9.58210i	0.152258	−	0.343756i
$778$	−38.6981	+	28.1158i	−1.38739	+	1.00800i
$779$	13.0153	−	1.36796i	0.466321	−	0.0490123i
$780$	−35.2008	+	16.0002i	−1.26039	+	0.572900i
$781$	−0.635519	+	6.04656i	−0.0227407	+	0.216363i
$782$	28.7679	−	49.8275i	1.02874	−	1.78183i
$783$	−4.86222	+	2.80545i	−0.173762	+	0.100259i
$784$	23.8629	−	1.76527i	0.852246	−	0.0630453i
$785$	55.2928	−	8.21324i	1.97349	−	0.293143i
$786$	24.5048	−	4.31858i	0.874057	−	0.154039i
$787$	−6.14262	−	28.8988i	−0.218961	−	1.03013i	−0.941034	−	0.338313i	$-0.890144\pi$
$787$	−6.14262	−	28.8988i	−0.218961	−	1.03013i	0.722073	−	0.691817i	$-0.243190\pi$
$788$	11.7934	+	55.4838i	0.420124	+	1.97653i
$789$	−27.7286	+	4.88673i	−0.987166	+	0.173972i
$790$	34.5462	+	18.0227i	1.22910	+	0.641220i
$791$	−33.1746	+	4.73053i	−1.17955	+	0.168198i
$792$	−10.9616	+	1.53853i	−0.389502	+	0.0546694i
$793$	18.5322	−	32.0987i	0.658098	−	1.13986i
$794$	6.63803	−	63.1566i	0.235575	−	2.24135i
$795$	2.08663	+	2.28165i	0.0740052	+	0.0809217i
$796$	−62.2575	+	6.54353i	−2.20666	+	0.231929i
$797$	−20.6867	+	15.0298i	−0.732762	+	0.532382i	−0.890436	−	0.455109i	$-0.849600\pi$
$797$	−20.6867	+	15.0298i	−0.732762	+	0.532382i	0.157674	+	0.987491i	$0.449600\pi$
$798$	−38.6942	−	53.0432i	−1.36976	−	1.87771i
$799$	−38.1272			−1.34884
$800$	4.54944	+	1.05886i	0.160847	+	0.0374364i
$801$	34.6666	+	9.94725i	1.22488	+	0.351469i
$802$	−43.4761	+	48.2851i	−1.53520	+	1.70501i
$803$	1.09666	+	10.4340i	0.0387003	+	0.368209i
$804$	14.6695	+	9.16834i	0.517352	+	0.323342i
$805$	4.82486	−	36.9693i	0.170054	−	1.30300i
$806$	28.6046	−	39.3709i	1.00755	−	1.38678i
$807$	−32.9863	−	4.63895i	−1.16117	−	0.163299i
$808$	−70.0901	−	7.36677i	−2.46576	−	0.259162i
$809$	3.33097	+	15.6710i	0.117111	+	0.550963i	0.997109	+	0.0759857i	$0.0242103\pi$
$809$	3.33097	+	15.6710i	0.117111	+	0.550963i	−0.879998	+	0.474977i	$0.842456\pi$
$810$	−32.4402	+	36.5747i	−1.13983	+	1.28510i
$811$	−12.7581	+	4.14537i	−0.447999	+	0.145564i	−0.524323	−	0.851519i	$-0.675682\pi$
$811$	−12.7581	+	4.14537i	−0.447999	+	0.145564i	0.0763242	+	0.997083i	$0.475682\pi$
$812$	6.88314	+	8.77354i	0.241551	+	0.307891i
$813$	0.208828	+	2.99025i	0.00732391	+	0.104873i
$814$	4.34072	+	0.922648i	0.152142	+	0.0323388i
$815$	1.59193	+	4.26939i	0.0557628	+	0.149550i
$816$	12.4411	+	18.4483i	0.435526	+	0.645820i
$817$	−4.05115	−	9.09904i	−0.141732	−	0.318335i
$818$	−29.0183			−1.01460
$819$	20.2591	−	1.45399i	0.707910	−	0.0508064i
$820$	−17.3317	+	8.62198i	−0.605248	+	0.301093i
$821$	26.3061	−	2.76488i	0.918088	−	0.0964949i	0.366316	−	0.930490i	$-0.380619\pi$
$821$	26.3061	−	2.76488i	0.918088	−	0.0964949i	0.551771	+	0.833995i	$0.313952\pi$
$822$	−1.33334	+	38.0834i	−0.0465055	+	1.32831i
$823$	13.1234	−	14.5751i	0.457454	−	0.508055i	−0.469653	−	0.882851i	$-0.655621\pi$
$823$	13.1234	−	14.5751i	0.457454	−	0.508055i	0.927107	+	0.374797i	$0.122287\pi$
$824$	38.2363	−	66.2272i	1.33203	−	2.30714i
$825$	6.90884	−	0.349114i	0.240535	−	0.0121546i
$826$	−0.0844530	−	0.172273i	−0.00293849	−	0.00599414i
$827$	37.0048	−	12.0236i	1.28678	−	0.418102i	0.415819	−	0.909447i	$-0.363495\pi$
$827$	37.0048	−	12.0236i	1.28678	−	0.418102i	0.870965	+	0.491346i	$0.163495\pi$
$828$	−47.4221	+	56.4947i	−1.64803	+	1.96333i
$829$	3.93017	−	8.82732i	0.136501	−	0.306585i	−0.832342	−	0.554262i	$-0.813000\pi$
$829$	3.93017	−	8.82732i	0.136501	−	0.306585i	0.968843	+	0.247677i	$0.0796671\pi$
$830$	70.8577	−	26.4207i	2.45951	−	0.917076i
$831$	−34.7949	−	33.6071i	−1.20702	−	1.16582i
$832$			23.3022i			0.807857i
$833$	18.9976	+	18.1985i	0.658229	+	0.630541i
$834$	−36.1823	+	2.52683i	−1.25289	+	0.0874971i
$835$	−1.39893	−	2.20020i	−0.0484120	−	0.0761412i
$836$	12.2986	−	13.6590i	0.425355	−	0.472405i
$837$	8.46810	−	39.7864i	0.292700	−	1.37522i
$838$	−10.3108	+	9.28391i	−0.356182	+	0.320707i
$839$	−14.4716	−	44.5391i	−0.499616	−	1.53766i	−0.809638	−	0.586930i	$-0.800336\pi$
$839$	−14.4716	−	44.5391i	−0.499616	−	1.53766i	0.310022	−	0.950729i	$-0.399664\pi$
$840$	39.4964	+	26.0834i	1.36275	+	0.899964i
$841$	8.60084	−	26.4707i	0.296581	−	0.912781i
$842$	8.79161	+	19.7463i	0.302979	+	0.680502i
$843$	19.9930	+	15.6232i	0.688596	+	0.538090i
$844$	2.94420	−	28.0122i	0.101344	−	0.964219i
$845$	−7.74043	−	12.1740i	−0.266279	−	0.418797i
$846$	72.8095	+	12.8518i	2.50324	+	0.441854i
$847$	14.5746	+	23.2200i	0.500789	+	0.797850i
$848$	−2.59537	+	0.843285i	−0.0891252	+	0.0289585i
$849$	−3.57357	+	25.4107i	−0.122645	+	0.872092i
$850$	−22.0601	−	39.9651i	−0.756654	−	1.37079i
$851$	12.4812	−	7.20600i	0.427849	−	0.247019i
$852$	−50.6534	+	8.92685i	−1.73536	+	0.305829i
$853$	−24.0278	−	33.0715i	−0.822697	−	1.13234i	−0.989239	−	0.146311i	$-0.953260\pi$
$853$	−24.0278	−	33.0715i	−0.822697	−	1.13234i	0.166542	−	0.986034i	$-0.446740\pi$
$854$	−93.0300	+	3.43627i	−3.18342	+	0.117587i
$855$	1.07801	−	39.5491i	0.0368673	−	1.35255i
$856$	−39.3900	+	17.5376i	−1.34632	+	0.599422i
$857$	−8.74225	−	15.1420i	−0.298629	−	0.517241i	0.677193	−	0.735805i	$-0.263196\pi$
$857$	−8.74225	−	15.1420i	−0.298629	−	0.517241i	−0.975823	+	0.218564i	$0.929863\pi$
$858$	2.36993	+	8.26773i	0.0809079	+	0.282256i
$859$	−32.0297	+	28.8396i	−1.09284	+	0.983996i	−0.999932	−	0.0116789i	$-0.996282\pi$
$859$	−32.0297	+	28.8396i	−1.09284	+	0.983996i	−0.0929064	+	0.995675i	$0.529616\pi$
$860$	10.3169	+	10.5173i	0.351804	+	0.358637i
$861$	10.1107	−	1.08235i	0.344573	−	0.0368864i
$862$	−9.76737	+	30.0609i	−0.332678	+	1.02388i
$863$	−5.60442	+	5.04625i	−0.190777	+	0.171776i	−0.758984	−	0.651109i	$-0.774304\pi$
$863$	−5.60442	+	5.04625i	−0.190777	+	0.171776i	0.568207	+	0.822886i	$0.307637\pi$
$864$	1.97322	+	4.43515i	0.0671302	+	0.150887i
$865$	2.92768	+	1.94154i	0.0995442	+	0.0660144i
$866$	36.0842	+	40.0756i	1.22619	+	1.36182i
$867$	1.20537	−	4.83262i	0.0409365	−	0.164124i
$868$	−80.6208	−	5.47443i	−2.73645	−	0.185814i
$869$	3.36788	−	4.63548i	0.114247	−	0.157248i
$870$	0.0787312	+	10.1640i	0.00266924	+	0.344593i
$871$	2.66448	−	5.98452i	0.0902825	−	0.202778i
$872$	3.10392	−	6.97151i	0.105112	−	0.236085i
$873$	−14.9832	−	23.9877i	−0.507104	−	0.811861i
$874$		−	90.2911i		−	3.05414i
$875$	−23.1377	−	18.4295i	−0.782198	−	0.623029i
$876$	−82.2954	+	33.2409i	−2.78050	+	1.12310i
$877$	−9.87550	−	2.09910i	−0.333472	−	0.0708816i	0.0381329	−	0.999273i	$-0.487859\pi$
$877$	−9.87550	−	2.09910i	−0.333472	−	0.0708816i	−0.371605	+	0.928391i	$0.621192\pi$
$878$	−55.4583	−	24.6916i	−1.87163	−	0.833301i
$879$	−1.79354	+	51.2277i	−0.0604944	+	1.72787i
$880$	−2.24274	+	5.67870i	−0.0756029	+	0.191429i
$881$	−31.4986	−	22.8851i	−1.06122	−	0.771018i	−0.0869025	−	0.996217i	$-0.527697\pi$
$881$	−31.4986	−	22.8851i	−1.06122	−	0.771018i	−0.974313	+	0.225199i	$0.927697\pi$
$882$	−30.1444	−	41.1563i	−1.01502	−	1.38581i
$883$	23.7438	+	17.2509i	0.799044	+	0.580540i	0.910634	−	0.413215i	$-0.135594\pi$
$883$	23.7438	+	17.2509i	0.799044	+	0.580540i	−0.111589	+	0.993754i	$0.535594\pi$
$884$	27.8836	−	25.1065i	0.937825	−	0.844422i
$885$	0.0231604	−	0.113268i	0.000778528	−	0.00380747i
$886$	−43.1353	+	47.9066i	−1.44916	+	1.60945i
$887$	−6.45331	−	7.16713i	−0.216681	−	0.240649i	0.624999	−	0.780626i	$-0.285099\pi$
$887$	−6.45331	−	7.16713i	−0.216681	−	0.240649i	−0.841680	+	0.539977i	$0.818433\pi$
$888$	1.27466	+	18.2521i	0.0427748	+	0.612501i
$889$	−12.1806	−	12.5626i	−0.408524	−	0.421338i
$890$	46.6183	−	45.7301i	1.56265	−	1.53288i
$891$	4.61904	+	5.50879i	0.154744	+	0.184551i
$892$	53.0309	+	5.57378i	1.77561	+	0.186624i
$893$	−51.8171	+	29.9166i	−1.73399	+	1.00112i
$894$	66.6182	+	64.3440i	2.22805	+	2.15199i
$895$	10.3776	−	10.1799i	0.346886	−	0.340278i
$896$	45.3844	−	28.4866i	1.51619	−	0.951670i
$897$	23.6863	+	14.8038i	0.790862	+	0.494284i
$898$	−62.7229	−	13.3322i	−2.09309	−	0.444900i
$899$	−4.22861	−	7.32416i	−0.141032	−	0.244275i
$900$	18.9442	+	55.3704i	0.631472	+	1.84568i
$901$	−2.59835	−	1.50016i	−0.0865636	−	0.0499775i
$902$	1.33057	+	4.09507i	0.0443030	+	0.136351i
$903$	−3.16132	−	7.06383i	−0.105202	−	0.235070i
$904$	47.3309	−	34.3879i	1.57420	−	1.14372i
$905$	−14.5202	+	9.23220i	−0.482667	+	0.306889i
$906$	4.53179	+	15.8096i	0.150559	+	0.525239i
$907$	8.61214	+	14.9167i	0.285961	+	0.495299i	0.972842	−	0.231471i	$-0.0743538\pi$
$907$	8.61214	+	14.9167i	0.285961	+	0.495299i	−0.686881	+	0.726770i	$0.741020\pi$
$908$	−16.6767	+	7.42493i	−0.553435	+	0.246405i
$909$	20.0579	+	41.1437i	0.665279	+	1.36465i
$910$	15.7957	−	33.2123i	0.523622	−	1.10098i
$911$	−15.7313	+	5.11140i	−0.521200	+	0.169348i	−0.557790	−	0.829982i	$-0.688351\pi$
$911$	−15.7313	+	5.11140i	−0.521200	+	0.169348i	0.0365898	+	0.999330i	$0.488351\pi$
$912$	31.3837	+	15.3103i	1.03922	+	0.506976i
$913$	−2.31206	−	10.8774i	−0.0765179	−	0.359989i
$914$	−31.5301	−	28.3898i	−1.04292	−	0.939051i
$915$	−45.6372	−	32.6203i	−1.50872	−	1.07839i
$916$	10.5199	+	3.41812i	0.347587	+	0.112938i
$917$	−10.0329	+	12.0057i	−0.331315	+	0.396464i
$918$	19.3073	−	43.3335i	0.637237	−	1.43022i
$919$	1.54992	−	0.690067i	0.0511270	−	0.0227632i	−0.381014	−	0.924569i	$-0.624425\pi$
$919$	1.54992	−	0.690067i	0.0511270	−	0.0227632i	0.432141	+	0.901806i	$0.357758\pi$
$920$	22.7409	+	60.9889i	0.749746	+	2.01074i
$921$	−15.0170	−	0.525760i	−0.494827	−	0.0173244i
$922$	−27.3553	+	2.87516i	−0.900898	+	0.0946882i
$923$	6.01885	+	18.5241i	0.198113	+	0.609729i
$924$	9.53549	−	10.6313i	0.313695	−	0.349744i
$925$	0.219924	−	11.4325i	0.00723107	−	0.375897i
$926$	−23.0593	−	13.3133i	−0.757777	−	0.437503i
$927$	−49.6371	+	1.72440i	−1.63030	+	0.0566369i
$928$	0.921994	+	0.410498i	0.0302659	+	0.0134753i
$929$	3.21263	+	30.5661i	0.105403	+	1.00284i	0.911568	+	0.411150i	$0.134873\pi$
$929$	3.21263	+	30.5661i	0.105403	+	1.00284i	−0.806165	+	0.591691i	$0.798460\pi$
$930$	−55.1158	−	48.8588i	−1.80732	−	1.60214i
$931$	40.0983	+	9.82626i	1.31417	+	0.322043i
$932$			65.9209i			2.15931i
$933$	−8.11609	−	7.83903i	−0.265709	−	0.256638i
$934$	1.95480	+	9.19660i	0.0639629	+	0.300922i
$935$	−6.28971	+	2.34524i	−0.205695	+	0.0766977i
$936$	−30.0757	+	18.7858i	−0.983054	+	0.614034i
$937$	−22.1413	−	7.19416i	−0.723326	−	0.235023i	−0.0758613	−	0.997118i	$-0.524171\pi$
$937$	−22.1413	−	7.19416i	−0.723326	−	0.235023i	−0.647465	+	0.762096i	$0.724171\pi$
$938$	−16.2889	+	2.32271i	−0.531850	+	0.0758392i
$939$	17.7470	+	21.1539i	0.579150	+	0.690330i
$940$	56.3558	−	68.2411i	1.83812	−	2.22578i
$941$	16.7850	−	3.56776i	0.547175	−	0.116306i	0.0739743	−	0.997260i	$-0.476432\pi$
$941$	16.7850	−	3.56776i	0.547175	−	0.116306i	0.473201	+	0.880954i	$0.343098\pi$
$942$	101.115	−	28.9844i	3.29450	−	0.944362i
$943$	12.1102	+	6.99185i	0.394364	+	0.227686i
$944$	0.0825514	+	0.0599771i	0.00268682	+	0.00195209i
$945$	0.778493	−	30.7310i	0.0253244	−	0.999679i
$946$	2.65117	−	1.92619i	0.0861971	−	0.0626259i
$947$	23.8883	−	2.51076i	0.776266	−	0.0815889i	0.291894	−	0.956451i	$-0.405715\pi$
$947$	23.8883	−	2.51076i	0.776266	−	0.0815889i	0.484373	+	0.874862i	$0.339048\pi$
$948$	45.5476	+	16.5826i	1.47932	+	0.538578i
$949$	16.8052	+	29.1075i	0.545521	+	0.944871i
$950$	−61.3395	−	37.0054i	−1.99012	−	1.20061i
$951$	10.7022	−	4.32283i	0.347041	−	0.140177i
$952$	−44.1758	−	12.5710i	−1.43175	−	0.407428i
$953$	−25.7991	−	35.5095i	−0.835716	−	1.15026i	−0.986832	−	0.161748i	$-0.948287\pi$
$953$	−25.7991	−	35.5095i	−0.835716	−	1.15026i	0.151116	−	0.988516i	$-0.451713\pi$
$954$	4.45626	+	3.74061i	0.144277	+	0.121107i
$955$	−7.61744	+	2.84032i	−0.246495	+	0.0919104i
$956$	−84.2072	−	8.85054i	−2.72346	−	0.286247i
$957$	1.48010	+	0.208150i	0.0478448	+	0.00672854i
$958$	−0.788135	+	1.08477i	−0.0254635	+	0.0350475i
$959$	−14.7901	−	18.8521i	−0.477597	−	0.608765i
$960$	35.1019	+	3.41468i	1.13291	+	0.110208i
$961$	29.6221	+	6.29638i	0.955552	+	0.203109i
$962$	13.9059	−	2.95579i	0.448344	−	0.0952984i
$963$	23.2134	+	15.6638i	0.748043	+	0.504757i
$964$	13.6823	−	64.3701i	0.440677	−	2.07322i
$965$	2.71085	+	18.2499i	0.0872655	+	0.587486i
$966$	−0.134960	−	70.1555i	−0.00434226	−	2.25722i
$967$	−21.7389	−	15.7942i	−0.699076	−	0.507909i	0.180555	−	0.983565i	$-0.442211\pi$
$967$	−21.7389	−	15.7942i	−0.699076	−	0.507909i	−0.879631	+	0.475656i	$0.842211\pi$
$968$	−41.4506	−	23.9315i	−1.33227	−	0.769189i
$969$	10.5789	+	36.9054i	0.339842	+	1.18557i
$970$	−51.1641	+	2.18822i	−1.64278	+	0.0702595i
$971$	−2.53872	−	24.1543i	−0.0814713	−	0.775148i	−0.956629	−	0.291310i	$-0.905909\pi$
$971$	−2.53872	−	24.1543i	−0.0814713	−	0.775148i	0.875157	−	0.483838i	$-0.160758\pi$
$972$	−34.0313	+	50.4045i	−1.09156	+	1.61672i
$973$	16.3738	−	15.8759i	0.524920	−	0.508957i
$974$			15.8014i			0.506310i
$975$	19.7647	−	10.0241i	0.632977	−	0.321027i
$976$	42.8778	−	24.7555i	1.37248	−	0.792404i
$977$	−14.1252	−	12.7184i	−0.451906	−	0.406898i	0.411498	−	0.911411i	$-0.365006\pi$
$977$	−14.1252	−	12.7184i	−0.451906	−	0.406898i	−0.863405	+	0.504512i	$0.831672\pi$
$978$	4.02461	+	7.57084i	0.128693	+	0.242089i
$979$	−5.64440	−	7.76885i	−0.180396	−	0.248293i
$980$	−60.6525	+	7.10330i	−1.93747	+	0.226907i
$981$	−4.90820	+	0.688901i	−0.156707	+	0.0219949i
$982$	29.5246	−	51.1381i	0.942168	−	1.63188i
$983$	−1.07895	+	10.2655i	−0.0344131	+	0.327419i	0.963749	+	0.266812i	$0.0859702\pi$
$983$	−1.07895	+	10.2655i	−0.0344131	+	0.327419i	−0.998162	+	0.0606068i	$0.980696\pi$
$984$	−14.7186	+	9.92592i	−0.469213	+	0.316427i
$985$	−8.11193	−	31.4821i	−0.258468	−	1.00310i
$986$	−3.04790	−	9.38046i	−0.0970648	−	0.298735i
$987$	−40.2168	+	23.3224i	−1.28011	+	0.742361i
$988$	18.1955	−	56.0000i	0.578876	−	1.78160i
$989$	2.21272	−	10.4100i	0.0703605	−	0.331020i
$990$	12.8016	−	2.35847i	0.406863	−	0.0749569i
$991$	16.1557	−	3.43400i	0.513203	−	0.109085i	0.0559714	−	0.998432i	$-0.482174\pi$
$991$	16.1557	−	3.43400i	0.513203	−	0.109085i	0.457231	+	0.889348i	$0.348841\pi$
$992$	−6.68109	+	2.97461i	−0.212125	+	0.0944440i
$993$	19.4682	+	48.1981i	0.617806	+	1.52952i
$994$	31.3701	−	37.5387i	0.995000	−	1.19066i
$995$	35.4895	−	5.27163i	1.12509	−	0.167122i
$996$	83.0676	−	44.1582i	2.63210	−	1.39921i
$997$	−4.11341	+	9.23888i	−0.130273	+	0.292598i	−0.966891	−	0.255188i	$-0.917863\pi$
$997$	−4.11341	+	9.23888i	−0.130273	+	0.292598i	0.836618	+	0.547786i	$0.184529\pi$
$998$	4.40167	+	3.96328i	0.139332	+	0.125455i
$999$	9.61556	−	6.98214i	0.304223	−	0.220905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.7	✓	608
3.2	odd	2	inner	525.2.bm.a.131.70	yes	608
7.3	odd	6	inner	525.2.bm.a.206.7	yes	608
21.17	even	6	inner	525.2.bm.a.206.70	yes	608
25.21	even	5	inner	525.2.bm.a.446.70	yes	608
75.71	odd	10	inner	525.2.bm.a.446.7	yes	608
175.171	odd	30	inner	525.2.bm.a.521.70	yes	608
525.521	even	30	inner	525.2.bm.a.521.7	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.7	✓	608	1.1	even	1	trivial
525.2.bm.a.131.70	yes	608	3.2	odd	2	inner
525.2.bm.a.206.7	yes	608	7.3	odd	6	inner
525.2.bm.a.206.70	yes	608	21.17	even	6	inner
525.2.bm.a.446.7	yes	608	75.71	odd	10	inner
525.2.bm.a.446.70	yes	608	25.21	even	5	inner
525.2.bm.a.521.7	yes	608	525.521	even	30	inner
525.2.bm.a.521.70	yes	608	175.171	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.505077 + 2.37620i) q^{2} +(0.0606037 - 1.73099i) q^{3} +(-3.56413 - 1.58685i) q^{4} +(2.07975 + 0.821374i) q^{5} +(4.08257 + 1.01829i) q^{6} +(-2.37564 + 1.16461i) q^{7} +(2.71505 - 3.73695i) q^{8} +(-2.99265 - 0.209809i) q^{9} +O(q^{10})\)	\(q+(-0.505077 + 2.37620i) q^{2} +(0.0606037 - 1.73099i) q^{3} +(-3.56413 - 1.58685i) q^{4} +(2.07975 + 0.821374i) q^{5} +(4.08257 + 1.01829i) q^{6} +(-2.37564 + 1.16461i) q^{7} +(2.71505 - 3.73695i) q^{8} +(-2.99265 - 0.209809i) q^{9} +(-3.00218 + 4.52704i) q^{10} +(0.593611 + 0.534490i) q^{11} +(-2.96283 + 6.07331i) q^{12} +(2.43373 + 0.790766i) q^{13} +(-1.56746 - 6.23322i) q^{14} +(1.54783 - 3.55024i) q^{15} +(2.28729 + 2.54029i) q^{16} +(-0.392844 + 3.73766i) q^{17} +(2.01007 - 7.00518i) q^{18} +(2.39886 + 5.38793i) q^{19} +(-6.10909 - 6.22774i) q^{20} +(1.87195 + 4.18280i) q^{21} +(-1.56987 + 1.14058i) q^{22} +(-1.31025 + 6.16423i) q^{23} +(-6.30408 - 4.92620i) q^{24} +(3.65069 + 3.41650i) q^{25} +(-3.10824 + 5.38363i) q^{26} +(-0.544543 + 5.16754i) q^{27} +(10.3152 - 0.381014i) q^{28} +(0.634999 + 0.874001i) q^{29} +(7.65431 + 5.47110i) q^{30} +(-7.78552 - 0.818291i) q^{31} +(0.809048 - 0.467104i) q^{32} +(0.961171 - 0.995143i) q^{33} +(-8.68301 - 2.82128i) q^{34} +(-5.89732 + 0.470795i) q^{35} +(10.3333 + 5.49670i) q^{36} +(-1.53024 - 1.69951i) q^{37} +(-14.0144 + 2.97885i) q^{38} +(1.51630 - 4.16484i) q^{39} +(8.71605 - 5.54183i) q^{40} +(0.685693 - 2.11035i) q^{41} +(-10.8846 + 2.33550i) q^{42} -1.68878 q^{43} +(-1.26755 - 2.84697i) q^{44} +(-6.05163 - 2.89444i) q^{45} +(-13.9857 - 6.22682i) q^{46} +(1.06044 + 10.0894i) q^{47} +(4.53584 - 3.80532i) q^{48} +(4.28738 - 5.53339i) q^{49} +(-9.96217 + 6.94917i) q^{50} +(6.44604 + 0.906524i) q^{51} +(-7.41930 - 6.68037i) q^{52} +(-0.324710 + 0.729310i) q^{53} +(-12.0041 - 3.90395i) q^{54} +(0.795544 + 1.59918i) q^{55} +(-2.09792 + 12.0396i) q^{56} +(9.47183 - 3.82588i) q^{57} +(-2.39752 + 1.06745i) q^{58} +(0.0291985 - 0.00620634i) q^{59} +(-11.1504 + 10.1974i) q^{60} +(3.01141 - 14.1676i) q^{61} +(5.87671 - 18.0867i) q^{62} +(7.35383 - 2.98684i) q^{63} +(2.81393 + 8.66038i) q^{64} +(4.41202 + 3.64359i) q^{65} +(1.87919 + 2.78656i) q^{66} +(0.267589 - 2.54594i) q^{67} +(7.33127 - 12.6981i) q^{68} +(10.5908 + 2.64160i) q^{69} +(1.85990 - 14.2510i) q^{70} +(4.47388 + 6.15777i) q^{71} +(-8.90925 + 10.6137i) q^{72} +(9.76074 + 8.78861i) q^{73} +(4.81126 - 2.77778i) q^{74} +(6.13517 - 6.11225i) q^{75} -23.0100i q^{76} +(-2.03268 - 0.578434i) q^{77} +(9.13063 + 5.70660i) q^{78} +(-0.749797 - 7.13384i) q^{79} +(2.67045 + 7.16188i) q^{80} +(8.91196 + 1.25577i) q^{81} +(4.66828 + 2.69523i) q^{82} +(-11.2629 - 8.18295i) q^{83} +(-0.0343934 - 17.8786i) q^{84} +(-3.88703 + 7.45071i) q^{85} +(0.852965 - 4.01288i) q^{86} +(1.55137 - 1.04621i) q^{87} +(3.60904 - 0.767126i) q^{88} +(-11.7591 - 2.49948i) q^{89} +(9.93430 - 12.9180i) q^{90} +(-6.70260 + 0.955758i) q^{91} +(14.4516 - 19.8910i) q^{92} +(-1.88829 + 13.4271i) q^{93} +(-24.5100 - 2.57610i) q^{94} +(0.563516 + 13.1759i) q^{95} +(-0.759521 - 1.42876i) q^{96} +(5.54137 + 7.62704i) q^{97} +(10.9830 + 12.9825i) q^{98} +(-1.66433 - 1.72409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

L-functions

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