LMFDB - Embedded newform 637.2.bl.a.625.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.26
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11124 - 1.43942i) q^{2} +(1.10080 - 1.02139i) q^{3} +(1.65473 - 4.21619i) q^{4} +(1.18938 + 0.366875i) q^{5} +(0.853840 - 3.74092i) q^{6} +(-2.52250 - 0.798115i) q^{7} +(-1.43814 - 6.30090i) q^{8} +(-0.0556743 + 0.742922i) q^{9} +O(q^{10})$	\(q+(2.11124 - 1.43942i) q^{2} +(1.10080 - 1.02139i) q^{3} +(1.65473 - 4.21619i) q^{4} +(1.18938 + 0.366875i) q^{5} +(0.853840 - 3.74092i) q^{6} +(-2.52250 - 0.798115i) q^{7} +(-1.43814 - 6.30090i) q^{8} +(-0.0556743 + 0.742922i) q^{9} +(3.03916 - 0.937455i) q^{10} +(0.146357 + 1.95300i) q^{11} +(-2.48485 - 6.33130i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-6.47444 + 1.94593i) q^{14} +(1.68399 - 0.810966i) q^{15} +(-5.46551 - 5.07125i) q^{16} +(-2.84540 - 0.428874i) q^{17} +(0.951835 + 1.64863i) q^{18} +(0.682942 - 1.18289i) q^{19} +(3.51492 - 4.40757i) q^{20} +(-3.59195 + 1.69790i) q^{21} +(3.12019 + 3.91260i) q^{22} +(7.33596 - 1.10572i) q^{23} +(-8.01878 - 5.46711i) q^{24} +(-2.85117 - 1.94389i) q^{25} +(2.52671 - 0.380840i) q^{26} +(3.50634 + 4.39682i) q^{27} +(-7.53907 + 9.31467i) q^{28} +(-5.89378 + 7.39056i) q^{29} +(2.38799 - 4.13611i) q^{30} +(0.371359 + 0.643212i) q^{31} +(-6.05718 - 0.912973i) q^{32} +(2.15589 + 2.00037i) q^{33} +(-6.62465 + 3.19026i) q^{34} +(-2.70740 - 1.87470i) q^{35} +(3.04017 + 1.46407i) q^{36} +(2.72620 + 6.94624i) q^{37} +(-0.260821 - 3.48041i) q^{38} +(1.43495 - 0.442623i) q^{39} +(0.601149 - 8.02177i) q^{40} +(-1.96869 - 8.62539i) q^{41} +(-5.13949 + 8.75500i) q^{42} +(-0.267151 + 1.17046i) q^{43} +(8.47642 + 2.61463i) q^{44} +(-0.338777 + 0.863190i) q^{45} +(13.8964 - 12.8940i) q^{46} +(-0.330699 + 0.225467i) q^{47} -11.1961 q^{48} +(5.72602 + 4.02649i) q^{49} -8.81759 q^{50} +(-3.57025 + 2.43416i) q^{51} +(3.32020 - 3.08069i) q^{52} +(1.43822 - 3.66452i) q^{53} +(13.7316 + 4.23564i) q^{54} +(-0.542434 + 2.37656i) q^{55} +(-1.40114 + 17.0418i) q^{56} +(-0.456412 - 1.99967i) q^{57} +(-1.80506 + 24.0869i) q^{58} +(-5.14154 + 1.58596i) q^{59} +(-0.632636 - 8.44194i) q^{60} +(-2.46157 - 6.27197i) q^{61} +(1.70988 + 0.823436i) q^{62} +(0.733375 - 1.82959i) q^{63} +(-0.667403 + 0.321404i) q^{64} +(0.912412 + 0.846595i) q^{65} +(7.43099 + 1.12004i) q^{66} +(7.34068 + 12.7144i) q^{67} +(-6.51658 + 11.2871i) q^{68} +(6.94604 - 8.71005i) q^{69} +(-8.41447 - 0.0608646i) q^{70} +(-4.45024 - 5.58042i) q^{71} +(4.76114 - 0.717626i) q^{72} +(-6.17997 - 4.21343i) q^{73} +(15.7542 + 10.7410i) q^{74} +(-5.12404 + 0.772324i) q^{75} +(-3.85720 - 4.83678i) q^{76} +(1.18954 - 5.04326i) q^{77} +(2.39241 - 2.99998i) q^{78} +(1.46684 - 2.54065i) q^{79} +(-4.64005 - 8.03680i) q^{80} +(6.14059 + 0.925546i) q^{81} +(-16.5719 - 15.3765i) q^{82} +(-12.2530 + 5.90075i) q^{83} +(1.21493 + 17.9539i) q^{84} +(-3.22691 - 1.55400i) q^{85} +(1.12077 + 2.85568i) q^{86} +(1.06080 + 14.1554i) q^{87} +(12.0952 - 3.73087i) q^{88} +(0.894049 - 11.9303i) q^{89} +(0.527253 + 2.31005i) q^{90} +(-1.92641 - 1.81355i) q^{91} +(7.47713 - 32.7595i) q^{92} +(1.06576 + 0.328744i) q^{93} +(-0.373644 + 0.952031i) q^{94} +(1.24625 - 1.15635i) q^{95} +(-7.60024 + 5.18175i) q^{96} -1.27511 q^{97} +(17.8848 + 0.258747i) q^{98} -1.45908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	2.11124	−	1.43942i	1.49287	−	1.01782i	0.504905	−	0.863175i	$-0.331528\pi$
$2$	2.11124	−	1.43942i	1.49287	−	1.01782i	0.987969	−	0.154650i	$-0.0494249\pi$
$3$	1.10080	−	1.02139i	0.635546	−	0.589700i	−0.295169	−	0.955445i	$-0.595376\pi$
$3$	1.10080	−	1.02139i	0.635546	−	0.589700i	0.930715	+	0.365745i	$0.119186\pi$
$4$	1.65473	−	4.21619i	0.827366	−	2.10809i
$5$	1.18938	+	0.366875i	0.531906	+	0.164071i	0.549062	−	0.835781i	$-0.314985\pi$
$5$	1.18938	+	0.366875i	0.531906	+	0.164071i	−0.0171559	+	0.999853i	$0.505461\pi$
$6$	0.853840	−	3.74092i	0.348579	−	1.52722i
$7$	−2.52250	−	0.798115i	−0.953416	−	0.301659i
$7$	−2.52250	−	0.798115i	−0.953416	−	0.301659i
$8$	−1.43814	−	6.30090i	−0.508459	−	2.22770i
$9$	−0.0556743	+	0.742922i	−0.0185581	+	0.247641i
$10$	3.03916	−	0.937455i	0.961065	−	0.296449i
$11$	0.146357	+	1.95300i	0.0441284	+	0.588853i	0.974812	+	0.223028i	$0.0715941\pi$
$11$	0.146357	+	1.95300i	0.0441284	+	0.588853i	−0.930684	+	0.365825i	$0.880787\pi$
$12$	−2.48485	−	6.33130i	−0.717315	−	1.82769i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$14$	−6.47444	+	1.94593i	−1.73037	+	0.520071i
$15$	1.68399	−	0.810966i	0.434804	−	0.209391i
$16$	−5.46551	−	5.07125i	−1.36638	−	1.26781i
$17$	−2.84540	−	0.428874i	−0.690110	−	0.104017i	−0.205381	−	0.978682i	$-0.565843\pi$
$17$	−2.84540	−	0.428874i	−0.690110	−	0.104017i	−0.484728	+	0.874665i	$0.661082\pi$
$18$	0.951835	+	1.64863i	0.224350	+	0.388585i
$19$	0.682942	−	1.18289i	0.156678	−	0.271373i	−0.776991	−	0.629512i	$-0.783255\pi$
$19$	0.682942	−	1.18289i	0.156678	−	0.271373i	0.933669	+	0.358138i	$0.116588\pi$
$20$	3.51492	−	4.40757i	0.785959	−	0.985562i
$21$	−3.59195	+	1.69790i	−0.783828	+	0.370511i
$22$	3.12019	+	3.91260i	0.665227	+	0.834168i
$23$	7.33596	−	1.10572i	1.52965	−	0.230558i	0.670358	−	0.742038i	$-0.266141\pi$
$23$	7.33596	−	1.10572i	1.52965	−	0.230558i	0.859295	+	0.511480i	$0.170903\pi$
$24$	−8.01878	−	5.46711i	−1.63683	−	1.11597i
$25$	−2.85117	−	1.94389i	−0.570234	−	0.388779i
$26$	2.52671	−	0.380840i	0.495528	−	0.0746888i
$27$	3.50634	+	4.39682i	0.674796	+	0.846168i
$28$	−7.53907	+	9.31467i	−1.42475	+	1.76031i
$29$	−5.89378	+	7.39056i	−1.09445	+	1.37239i	−0.172531	+	0.985004i	$0.555194\pi$
$29$	−5.89378	+	7.39056i	−1.09445	+	1.37239i	−0.921916	+	0.387389i	$0.873377\pi$
$30$	2.38799	−	4.13611i	0.435985	−	0.755148i
$31$	0.371359	+	0.643212i	0.0666980	+	0.115524i	0.897446	−	0.441124i	$-0.145420\pi$
$31$	0.371359	+	0.643212i	0.0666980	+	0.115524i	−0.830748	+	0.556649i	$0.812087\pi$
$32$	−6.05718	−	0.912973i	−1.07077	−	0.161392i
$33$	2.15589	+	2.00037i	0.375292	+	0.348220i
$34$	−6.62465	+	3.19026i	−1.13612	+	0.547126i
$35$	−2.70740	−	1.87470i	−0.457634	−	0.316883i
$36$	3.04017	+	1.46407i	0.506695	+	0.244012i
$37$	2.72620	+	6.94624i	0.448184	+	1.14195i	0.959287	+	0.282435i	$0.0911420\pi$
$37$	2.72620	+	6.94624i	0.448184	+	1.14195i	−0.511103	+	0.859520i	$0.670763\pi$
$38$	−0.260821	−	3.48041i	−0.0423107	−	0.564597i
$39$	1.43495	−	0.442623i	0.229776	−	0.0708764i
$40$	0.601149	−	8.02177i	0.0950499	−	1.26835i
$41$	−1.96869	−	8.62539i	−0.307458	−	1.34706i	−0.858599	−	0.512648i	$-0.828665\pi$
$41$	−1.96869	−	8.62539i	−0.307458	−	1.34706i	0.551142	−	0.834412i	$-0.314192\pi$
$42$	−5.13949	+	8.75500i	−0.793041	+	1.35093i
$43$	−0.267151	+	1.17046i	−0.0407401	+	0.178494i	−0.991204	−	0.132339i	$-0.957751\pi$
$43$	−0.267151	+	1.17046i	−0.0407401	+	0.178494i	0.950464	+	0.310834i	$0.100608\pi$
$44$	8.47642	+	2.61463i	1.27787	+	0.394170i
$45$	−0.338777	+	0.863190i	−0.0505019	+	0.128677i
$46$	13.8964	−	12.8940i	2.04891	−	1.90111i
$47$	−0.330699	+	0.225467i	−0.0482374	+	0.0328877i	−0.587199	−	0.809443i	$-0.699769\pi$
$47$	−0.330699	+	0.225467i	−0.0482374	+	0.0328877i	0.538961	+	0.842331i	$0.318817\pi$
$48$	−11.1961			−1.61602
$49$	5.72602	+	4.02649i	0.818003	+	0.575213i
$50$	−8.81759			−1.24700
$51$	−3.57025	+	2.43416i	−0.499935	+	0.340850i
$52$	3.32020	−	3.08069i	0.460429	−	0.427215i
$53$	1.43822	−	3.66452i	0.197555	−	0.503361i	−0.797427	−	0.603415i	$-0.793806\pi$
$53$	1.43822	−	3.66452i	0.197555	−	0.503361i	0.994982	+	0.100054i	$0.0319016\pi$
$54$	13.7316	+	4.23564i	1.86864	+	0.576398i
$55$	−0.542434	+	2.37656i	−0.0731417	+	0.320455i
$56$	−1.40114	+	17.0418i	−0.187235	+	2.27731i
$57$	−0.456412	−	1.99967i	−0.0604533	−	0.264863i
$58$	−1.80506	+	24.0869i	−0.237017	+	3.16277i
$59$	−5.14154	+	1.58596i	−0.669372	+	0.206474i	−0.610771	−	0.791808i	$-0.709140\pi$
$59$	−5.14154	+	1.58596i	−0.669372	+	0.206474i	−0.0586013	+	0.998281i	$0.518664\pi$
$60$	−0.632636	−	8.44194i	−0.0816730	−	1.08985i
$61$	−2.46157	−	6.27197i	−0.315171	−	0.803043i	−0.997411	−	0.0719144i	$-0.977089\pi$
$61$	−2.46157	−	6.27197i	−0.315171	−	0.803043i	0.682240	−	0.731129i	$-0.261006\pi$
$62$	1.70988	+	0.823436i	0.217155	+	0.104576i
$63$	0.733375	−	1.82959i	0.0923966	−	0.230506i
$64$	−0.667403	+	0.321404i	−0.0834253	+	0.0401755i
$65$	0.912412	+	0.846595i	0.113171	+	0.105007i
$66$	7.43099	+	1.12004i	0.914692	+	0.137868i
$67$	7.34068	+	12.7144i	0.896807	+	1.55331i	0.831553	+	0.555446i	$0.187452\pi$
$67$	7.34068	+	12.7144i	0.896807	+	1.55331i	0.0652542	+	0.997869i	$0.479214\pi$
$68$	−6.51658	+	11.2871i	−0.790252	+	1.36876i
$69$	6.94604	−	8.71005i	0.836204	−	1.04857i
$70$	−8.41447	−	0.0608646i	−1.00572	−	0.00727471i
$71$	−4.45024	−	5.58042i	−0.528146	−	0.662274i	0.444170	−	0.895942i	$-0.353499\pi$
$71$	−4.45024	−	5.58042i	−0.528146	−	0.662274i	−0.972316	+	0.233668i	$0.924927\pi$
$72$	4.76114	−	0.717626i	0.561106	−	0.0845731i
$73$	−6.17997	−	4.21343i	−0.723311	−	0.493145i	0.144834	−	0.989456i	$-0.453735\pi$
$73$	−6.17997	−	4.21343i	−0.723311	−	0.493145i	−0.868145	+	0.496311i	$0.834688\pi$
$74$	15.7542	+	10.7410i	1.83139	+	1.24862i
$75$	−5.12404	+	0.772324i	−0.591673	+	0.0891803i
$76$	−3.85720	−	4.83678i	−0.442451	−	0.554816i
$77$	1.18954	−	5.04326i	0.135560	−	0.574733i
$78$	2.39241	−	2.99998i	0.270887	−	0.339681i
$79$	1.46684	−	2.54065i	0.165033	−	0.285845i	−0.771634	−	0.636067i	$-0.780560\pi$
$79$	1.46684	−	2.54065i	0.165033	−	0.285845i	0.936667	+	0.350222i	$0.113894\pi$
$80$	−4.64005	−	8.03680i	−0.518773	−	0.898541i
$81$	6.14059	+	0.925546i	0.682288	+	0.102838i
$82$	−16.5719	−	15.3765i	−1.83007	−	1.69805i
$83$	−12.2530	+	5.90075i	−1.34494	+	0.647691i	−0.961227	−	0.275759i	$-0.911071\pi$
$83$	−12.2530	+	5.90075i	−1.34494	+	0.647691i	−0.383718	+	0.923450i	$0.625357\pi$
$84$	1.21493	+	17.9539i	0.132560	+	1.95893i
$85$	−3.22691	−	1.55400i	−0.350008	−	0.168555i
$86$	1.12077	+	2.85568i	0.120856	+	0.307936i
$87$	1.06080	+	14.1554i	0.113729	+	1.51761i
$88$	12.0952	−	3.73087i	1.28935	−	0.397712i
$89$	0.894049	−	11.9303i	0.0947690	−	1.26460i	−0.723725	−	0.690089i	$-0.757571\pi$
$89$	0.894049	−	11.9303i	0.0947690	−	1.26460i	0.818494	−	0.574516i	$-0.194810\pi$
$90$	0.527253	+	2.31005i	0.0555773	+	0.243500i
$91$	−1.92641	−	1.81355i	−0.201942	−	0.190112i
$92$	7.47713	−	32.7595i	0.779545	−	3.41541i
$93$	1.06576	+	0.328744i	0.110514	+	0.0340892i
$94$	−0.373644	+	0.952031i	−0.0385385	+	0.0981945i
$95$	1.24625	−	1.15635i	0.127862	−	0.118639i
$96$	−7.60024	+	5.18175i	−0.775696	+	0.528860i
$97$	−1.27511			−0.129468			−0.0647341	−	0.997903i	$-0.520620\pi$
$97$	−1.27511			−0.129468			−0.0647341	+	0.997903i	$0.520620\pi$
$98$	17.8848	+	0.258747i	1.80664	+	0.0261374i
$99$	−1.45908			−0.146643
$100$	−12.9137	+	8.80444i	−1.29137	+	0.880444i
$101$	−5.65826	+	5.25010i	−0.563018	+	0.522404i	−0.909528	−	0.415642i	$-0.863557\pi$
$101$	−5.65826	+	5.25010i	−0.563018	+	0.522404i	0.346511	+	0.938046i	$0.387366\pi$
$102$	−4.03389	+	10.2782i	−0.399415	+	1.01769i
$103$	−11.7687	−	3.63016i	−1.15960	−	0.357690i	−0.345505	−	0.938417i	$-0.612292\pi$
$103$	−11.7687	−	3.63016i	−1.15960	−	0.357690i	−0.814098	+	0.580727i	$0.802768\pi$
$104$	1.43814	−	6.30090i	0.141021	−	0.617854i
$105$	−4.89511	+	0.701646i	−0.477713	+	0.0684736i
$106$	−2.23836	−	9.80690i	−0.217409	−	0.952530i
$107$	−0.446153	+	5.95350i	−0.0431313	+	0.575547i	0.933213	+	0.359324i	$0.116993\pi$
$107$	−0.446153	+	5.95350i	−0.0431313	+	0.575547i	−0.976344	+	0.216223i	$0.930626\pi$
$108$	24.3399	−	7.50786i	2.34211	−	0.722444i
$109$	−0.890502	−	11.8829i	−0.0852946	−	1.13818i	−0.861521	−	0.507722i	$-0.830488\pi$
$109$	−0.890502	−	11.8829i	−0.0852946	−	1.13818i	0.776226	−	0.630455i	$-0.217131\pi$
$110$	2.27566	+	5.79828i	0.216975	+	0.552844i
$111$	10.0958	+	4.86189i	0.958252	+	0.461470i
$112$	9.73931	+	17.1543i	0.920278	+	1.62093i
$113$	−1.83224	+	0.882362i	−0.172363	+	0.0830057i	−0.518076	−	0.855335i	$-0.673351\pi$
$113$	−1.83224	+	0.882362i	−0.172363	+	0.0830057i	0.345713	+	0.938340i	$0.387637\pi$
$114$	−3.84197	−	3.56483i	−0.359833	−	0.333876i
$115$	9.13089	+	1.37626i	0.851460	+	0.128337i
$116$	21.4074	+	37.0787i	1.98763	+	3.44267i
$117$	−0.372502	+	0.645193i	−0.0344379	+	0.0596481i
$118$	−8.57219	+	10.7492i	−0.789134	+	0.989543i
$119$	6.83522	+	3.35279i	0.626584	+	0.307350i
$120$	−7.53162	−	9.44435i	−0.687540	−	0.862148i
$121$	7.08433	−	1.06779i	0.644030	−	0.0970720i
$122$	−14.2250	−	9.69842i	−1.28787	−	0.878053i
$123$	−10.9770	−	7.48401i	−0.989765	−	0.674810i
$124$	3.32640	−	0.501375i	0.298720	−	0.0450248i
$125$	−6.55817	−	8.22368i	−0.586581	−	0.735549i
$126$	−1.08521	−	4.91834i	−0.0966783	−	0.438160i
$127$	−7.15603	+	8.97338i	−0.634995	+	0.796259i	−0.990367	−	0.138466i	$-0.955783\pi$
$127$	−7.15603	+	8.97338i	−0.634995	+	0.796259i	0.355372	+	0.934725i	$0.384354\pi$
$128$	5.17919	−	8.97062i	0.457780	−	0.792898i
$129$	0.901423	+	1.56131i	0.0793659	+	0.137466i
$130$	3.14493	+	0.474022i	0.275829	+	0.0415745i
$131$	7.33619	+	6.80699i	0.640965	+	0.594729i	0.932209	−	0.361920i	$-0.117879\pi$
$131$	7.33619	+	6.80699i	0.640965	+	0.594729i	−0.291244	+	0.956649i	$0.594069\pi$
$132$	12.0014	−	5.77956i	1.04459	−	0.503046i
$133$	−2.66680	+	2.43877i	−0.231241	+	0.211469i
$134$	33.7994	+	16.2769i	2.91982	+	1.40611i
$135$	2.55729	+	6.51587i	0.220097	+	0.560797i
$136$	1.38978	+	18.5453i	0.119173	+	1.59025i
$137$	20.4246	−	6.30014i	1.74499	−	0.538257i	0.752284	−	0.658839i	$-0.228952\pi$
$137$	20.4246	−	6.30014i	1.74499	−	0.538257i	0.992703	+	0.120582i	$0.0384760\pi$
$138$	2.12733	−	28.3873i	0.181091	−	2.41649i
$139$	3.19194	+	13.9848i	0.270737	+	1.18618i	0.909145	+	0.416479i	$0.136736\pi$
$139$	3.19194	+	13.9848i	0.270737	+	1.18618i	−0.638408	+	0.769698i	$0.720407\pi$
$140$	−12.3841	+	8.31278i	−1.04665	+	0.702558i
$141$	−0.133743	+	0.585966i	−0.0112632	+	0.0493473i
$142$	−17.4281	−	5.37586i	−1.46253	−	0.451132i
$143$	−0.715513	+	1.82310i	−0.0598342	+	0.152455i
$144$	4.07183	−	3.77811i	0.339319	−	0.314842i
$145$	−9.72135	+	6.62790i	−0.807314	+	0.550417i
$146$	−19.1123			−1.58175
$147$	10.4158	−	1.41615i	0.859082	−	0.116802i
$148$	33.7978			2.77816
$149$	−4.97129	+	3.38937i	−0.407264	+	0.277668i	−0.749576	−	0.661919i	$-0.769742\pi$
$149$	−4.97129	+	3.38937i	−0.407264	+	0.277668i	0.342312	+	0.939586i	$0.388790\pi$
$150$	−9.70639	+	9.00621i	−0.792523	+	0.735354i
$151$	0.287367	−	0.732200i	0.0233856	−	0.0595856i	−0.918704	−	0.394947i	$-0.870763\pi$
$151$	0.287367	−	0.732200i	0.0233856	−	0.0595856i	0.942090	+	0.335361i	$0.108858\pi$
$152$	−8.43543	−	2.60199i	−0.684204	−	0.211049i
$153$	0.477035	−	2.09003i	0.0385660	−	0.168969i
$154$	−4.74798	−	12.3598i	−0.382603	−	0.995981i
$155$	0.205708	+	0.901265i	0.0165229	+	0.0723914i
$156$	0.508274	−	6.78244i	0.0406945	−	0.543030i
$157$	6.74179	−	2.07957i	0.538054	−	0.165968i	−0.0138058	−	0.999905i	$-0.504395\pi$
$157$	6.74179	−	2.07957i	0.538054	−	0.165968i	0.551859	+	0.833937i	$0.313918\pi$
$158$	−0.560198	−	7.47532i	−0.0445670	−	0.594705i
$159$	−2.15972	−	5.50288i	−0.171277	−	0.436407i
$160$	−6.86934	−	3.30810i	−0.543069	−	0.261528i
$161$	−19.3875	−	3.06577i	−1.52795	−	0.241616i
$162$	14.2965	−	6.88485i	1.12324	−	0.540925i
$163$	−9.86953	−	9.15759i	−0.773041	−	0.717277i	0.191418	−	0.981509i	$-0.438691\pi$
$163$	−9.86953	−	9.15759i	−0.773041	−	0.717277i	−0.964459	+	0.264231i	$0.914882\pi$
$164$	−39.6239	−	5.97235i	−3.09411	−	0.466362i
$165$	1.83028	+	3.17014i	0.142487	+	0.246795i
$166$	−17.3755	+	30.0952i	−1.34860	+	2.33584i
$167$	12.7558	−	15.9953i	0.987077	−	1.23776i	0.0157827	−	0.999875i	$-0.494976\pi$
$167$	12.7558	−	15.9953i	0.987077	−	1.23776i	0.971294	−	0.237880i	$-0.0764526\pi$
$168$	15.8640	+	20.1907i	1.22393	+	1.55775i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−9.04965	+	1.36402i	−0.694076	+	0.104615i
$171$	0.840772	+	0.573228i	0.0642954	+	0.0438359i
$172$	4.49284	+	3.06317i	0.342576	+	0.233564i
$173$	−11.6904	+	1.76204i	−0.888801	+	0.133965i	−0.577543	−	0.816360i	$-0.695988\pi$
$173$	−11.6904	+	1.76204i	−0.888801	+	0.133965i	−0.311258	+	0.950325i	$0.600750\pi$
$174$	22.6151	+	28.3585i	1.71445	+	2.14985i
$175$	5.64062	+	7.17904i	0.426391	+	0.542684i
$176$	9.10426	−	11.4164i	0.686259	−	0.860542i
$177$	−4.03992	+	6.99734i	−0.303659	+	0.525952i
$178$	−15.2851	−	26.4746i	−1.14567	−	1.98435i
$179$	5.46100	+	0.823113i	0.408174	+	0.0615223i	0.349920	−	0.936779i	$-0.386209\pi$
$179$	5.46100	+	0.823113i	0.408174	+	0.0615223i	0.0582537	+	0.998302i	$0.481447\pi$
$180$	3.07879	+	2.85670i	0.229479	+	0.212926i
$181$	9.12364	−	4.39371i	0.678155	−	0.326582i	−0.0629066	−	0.998019i	$-0.520037\pi$
$181$	9.12364	−	4.39371i	0.678155	−	0.326582i	0.741061	+	0.671437i	$0.234323\pi$
$182$	−6.67757	−	1.05593i	−0.494975	−	0.0782711i
$183$	−9.11582	−	4.38995i	−0.673860	−	0.324514i
$184$	−17.5171	−	44.6329i	−1.29138	−	3.29038i
$185$	0.694082	+	9.26188i	0.0510299	+	0.680947i
$186$	2.72328	−	0.840022i	0.199681	−	0.0615934i
$187$	0.421149	−	5.61984i	0.0307974	−	0.410963i
$188$	0.403392	+	1.76738i	0.0294204	+	0.128899i
$189$	−5.33559	−	13.8894i	−0.388107	−	1.01031i
$190$	0.966660	−	4.23521i	0.0701289	−	0.307255i
$191$	3.37925	+	1.04236i	0.244514	+	0.0754225i	0.414590	−	0.910008i	$-0.363925\pi$
$191$	3.37925	+	1.04236i	0.244514	+	0.0754225i	−0.170076	+	0.985431i	$0.554401\pi$
$192$	−0.406396	+	1.03548i	−0.0293291	+	0.0747293i
$193$	−3.01073	+	2.79355i	−0.216717	+	0.201084i	−0.781059	−	0.624457i	$-0.785320\pi$
$193$	−3.01073	+	2.79355i	−0.216717	+	0.201084i	0.564342	+	0.825541i	$0.309130\pi$
$194$	−2.69208	+	1.83543i	−0.193280	+	0.131776i
$195$	1.86909			0.133848
$196$	26.4515	−	17.4792i	1.88939	−	1.24852i
$197$	−16.6882			−1.18898			−0.594492	−	0.804102i	$-0.702647\pi$
$197$	−16.6882			−1.18898			−0.594492	+	0.804102i	$0.702647\pi$
$198$	−3.08047	+	2.10023i	−0.218919	+	0.149257i
$199$	2.43112	−	2.25575i	0.172338	−	0.159906i	−0.589288	−	0.807923i	$-0.700592\pi$
$199$	2.43112	−	2.25575i	0.172338	−	0.159906i	0.761626	+	0.648017i	$0.224401\pi$
$200$	−8.14790	+	20.7605i	−0.576143	+	1.46799i
$201$	21.0670	+	6.49831i	1.48595	+	0.458356i
$202$	−4.38886	+	19.2288i	−0.308799	+	1.35294i
$203$	20.7656	−	13.9388i	1.45746	−	0.978311i
$204$	4.35505	+	19.0807i	0.304915	+	1.33592i
$205$	0.822921	−	10.9811i	0.0574753	−	0.766955i
$206$	−30.0719	+	9.27595i	−2.09521	+	0.646286i
$207$	0.413037	+	5.51160i	0.0287081	+	0.383083i
$208$	−2.72392	−	6.94043i	−0.188870	−	0.481233i
$209$	2.41014	+	1.16066i	0.166713	+	0.0802847i
$210$	−9.32480	+	8.52747i	−0.643472	+	0.588451i
$211$	−11.1718	+	5.38008i	−0.769102	+	0.370380i	−0.776928	−	0.629589i	$-0.783223\pi$
$211$	−11.1718	+	5.38008i	−0.769102	+	0.370380i	0.00782623	+	0.999969i	$0.497509\pi$
$212$	−13.0704	−	12.1276i	−0.897682	−	0.832927i
$213$	−10.5986	−	1.59748i	−0.726205	−	0.109458i
$214$	7.62766	+	13.2115i	0.521416	+	0.903119i
$215$	−0.747158	+	1.29412i	−0.0509557	+	0.0882579i
$216$	22.6613	−	28.4163i	1.54190	−	1.93349i
$217$	−0.423395	−	1.91889i	−0.0287419	−	0.130263i
$218$	−18.9846	−	23.8059i	−1.28580	−	1.61234i
$219$	−11.1065	+	1.67403i	−0.750505	+	0.113120i
$220$	9.12243	+	6.21957i	0.615034	+	0.419323i
$221$	−2.37753	−	1.62097i	−0.159930	−	0.109038i
$222$	28.3130	−	4.26750i	1.90025	−	0.286416i
$223$	−16.5859	−	20.7981i	−1.11067	−	1.39274i	−0.910764	−	0.412927i	$-0.864507\pi$
$223$	−16.5859	−	20.7981i	−1.11067	−	1.39274i	−0.199910	−	0.979814i	$-0.564065\pi$
$224$	14.5506	+	7.13731i	0.972202	+	0.476881i
$225$	1.60290	−	2.00997i	0.106860	−	0.133998i
$226$	−2.59822	+	4.50025i	−0.172831	+	0.299352i
$227$	1.48394	+	2.57026i	0.0984926	+	0.170594i	0.911061	−	0.412272i	$-0.135265\pi$
$227$	1.48394	+	2.57026i	0.0984926	+	0.170594i	−0.812568	+	0.582866i	$0.801931\pi$
$228$	−9.18624	−	1.38460i	−0.608373	−	0.0916975i
$229$	12.9154	+	11.9837i	0.853472	+	0.791906i	0.979779	−	0.200085i	$-0.0641218\pi$
$229$	12.9154	+	11.9837i	0.853472	+	0.791906i	−0.126306	+	0.991991i	$0.540312\pi$
$230$	21.2586	−	10.2376i	1.40175	−	0.675046i
$231$	−3.84171	−	6.76660i	−0.252766	−	0.445209i
$232$	55.0432	+	26.5074i	3.61377	+	1.74030i
$233$	−3.80253	−	9.68868i	−0.249112	−	0.634727i	0.750548	−	0.660816i	$-0.229790\pi$
$233$	−3.80253	−	9.68868i	−0.249112	−	0.634727i	−0.999660	+	0.0260895i	$0.991695\pi$
$234$	0.142261	+	1.89835i	0.00929992	+	0.124099i
$235$	−0.476045	+	0.146840i	−0.0310537	+	0.00957881i
$236$	−1.82119	+	24.3020i	−0.118549	+	1.58193i
$237$	−0.980296	−	4.29496i	−0.0636770	−	0.278987i
$238$	19.2569	−	2.76021i	1.24824	−	0.178918i
$239$	−2.85422	+	12.5052i	−0.184624	+	0.808891i	0.794766	+	0.606915i	$0.207593\pi$
$239$	−2.85422	+	12.5052i	−0.184624	+	0.808891i	−0.979391	+	0.201976i	$0.935264\pi$
$240$	−13.3165	−	4.10759i	−0.859574	−	0.265143i
$241$	−4.49250	+	11.4467i	−0.289387	+	0.737347i	0.710061	+	0.704140i	$0.248667\pi$
$241$	−4.49250	+	11.4467i	−0.289387	+	0.737347i	−0.999448	+	0.0332071i	$0.989428\pi$
$242$	13.4198	−	12.4517i	0.862654	−	0.800426i
$243$	−6.23476	+	4.25079i	−0.399960	+	0.272688i
$244$	−30.5170			−1.95365
$245$	5.33319	+	6.88976i	0.340725	+	0.440171i
$246$	−33.9478			−2.16443
$247$	1.12855	−	0.769429i	0.0718076	−	0.0489576i
$248$	3.51875	−	3.26492i	0.223441	−	0.207323i
$249$	−7.46114	+	19.0107i	−0.472830	+	1.20475i
$250$	−25.6832	−	7.92223i	−1.62435	−	0.501046i
$251$	4.74781	−	20.8015i	0.299679	−	1.31298i	−0.570928	−	0.821000i	$-0.693417\pi$
$251$	4.74781	−	20.8015i	0.299679	−	1.31298i	0.870607	−	0.491979i	$-0.163726\pi$
$252$	−6.50034	−	6.11952i	−0.409483	−	0.385494i
$253$	3.23314	+	14.1653i	0.203266	+	0.890566i
$254$	−2.19165	+	29.2455i	−0.137516	+	1.83503i
$255$	−5.13941	+	1.58530i	−0.321843	+	0.0992753i
$256$	−2.08869	−	27.8716i	−0.130543	−	1.74197i
$257$	4.39692	+	11.2032i	0.274272	+	0.698835i	0.999942	+	0.0107911i	$0.00343497\pi$
$257$	4.39692	+	11.2032i	0.274272	+	0.698835i	−0.725669	+	0.688044i	$0.758470\pi$
$258$	4.15051	+	1.99878i	0.258399	+	0.124439i
$259$	−1.33294	−	19.6977i	−0.0828247	−	1.22396i
$260$	5.07920	−	2.44602i	0.314999	−	0.151695i
$261$	−5.16248	−	4.79008i	−0.319549	−	0.296498i
$262$	25.2866	+	3.81134i	1.56221	+	0.235465i
$263$	13.3209	+	23.0724i	0.821399	+	1.42271i	0.904640	+	0.426176i	$0.140140\pi$
$263$	13.3209	+	23.0724i	0.821399	+	1.42271i	−0.0832410	+	0.996529i	$0.526527\pi$
$264$	9.50368	−	16.4609i	0.584911	−	1.01310i
$265$	3.05501	−	3.83086i	0.187668	−	0.235328i
$266$	−2.11985	+	8.98750i	−0.129976	+	0.551059i
$267$	−11.2013	−	14.0460i	−0.685508	−	0.859599i
$268$	65.7533	−	9.91072i	4.01652	−	0.605393i
$269$	8.47557	+	5.77855i	0.516765	+	0.352324i	0.793449	−	0.608637i	$-0.208283\pi$
$269$	8.47557	+	5.77855i	0.516765	+	0.352324i	−0.276684	+	0.960961i	$0.589236\pi$
$270$	14.7781	+	10.0756i	0.899369	+	0.613180i
$271$	6.50960	−	0.981165i	0.395430	−	0.0596015i	0.0516826	−	0.998664i	$-0.483542\pi$
$271$	6.50960	−	0.981165i	0.395430	−	0.0596015i	0.343748	+	0.939062i	$0.388303\pi$
$272$	13.3766	+	16.7737i	0.811076	+	1.01706i
$273$	−3.97293	−	0.0287374i	−0.240452	−	0.00173927i
$274$	34.0526	−	42.7007i	2.05720	−	2.57964i
$275$	3.37914	−	5.85285i	0.203770	−	0.352940i
$276$	−25.2294	−	43.6986i	−1.51863	−	2.63035i
$277$	−8.78132	−	1.32357i	−0.527618	−	0.0795257i	−0.120169	−	0.992753i	$-0.538344\pi$
$277$	−8.78132	−	1.32357i	−0.527618	−	0.0795257i	−0.407449	+	0.913228i	$0.633582\pi$
$278$	26.8690	+	24.9308i	1.61150	+	1.49525i
$279$	−0.498531	+	0.240080i	−0.0298463	+	0.0143732i
$280$	−7.91870	+	19.7551i	−0.473233	+	1.18060i
$281$	1.01082	+	0.486786i	0.0603005	+	0.0290392i	0.463791	−	0.885945i	$-0.346489\pi$
$281$	1.01082	+	0.486786i	0.0603005	+	0.0290392i	−0.403490	+	0.914984i	$0.632203\pi$
$282$	0.561088	+	1.42963i	0.0334123	+	0.0851332i
$283$	−0.251720	−	3.35897i	−0.0149632	−	0.199670i	−0.999675	−	0.0254804i	$-0.991888\pi$
$283$	−0.251720	−	3.35897i	−0.0149632	−	0.199670i	0.984712	−	0.174190i	$-0.0557306\pi$
$284$	−30.8921	+	9.52894i	−1.83311	+	0.565439i
$285$	0.190782	−	2.54581i	0.0113010	−	0.150801i
$286$	1.11358	+	4.87893i	0.0658476	+	0.288497i
$287$	−1.91804	+	23.3288i	−0.113218	+	1.37706i
$288$	1.01550	−	4.44918i	0.0598387	−	0.262171i
$289$	−8.33240	−	2.57020i	−0.490141	−	0.151188i
$290$	−10.9838	+	27.9862i	−0.644990	+	1.64341i
$291$	−1.40364	+	1.30239i	−0.0822830	+	0.0763475i
$292$	−27.9908	+	19.0838i	−1.63804	+	1.11680i
$293$	−20.7684			−1.21330			−0.606651	−	0.794968i	$-0.707487\pi$
$293$	−20.7684			−1.21330			−0.606651	+	0.794968i	$0.707487\pi$
$294$	19.9519	−	17.9826i	1.16362	−	1.04877i
$295$	−6.69709			−0.389920
$296$	39.8469	−	27.1671i	2.31605	−	1.57906i
$297$	−8.07382	+	7.49141i	−0.468491	+	0.434696i
$298$	−5.61687	+	14.3116i	−0.325377	+	0.829046i
$299$	7.08922	+	2.18674i	0.409980	+	0.126462i
$300$	−5.22264	+	22.8819i	−0.301529	+	1.32109i
$301$	1.60805	−	2.73928i	0.0926867	−	0.157890i
$302$	−0.447242	−	1.95950i	−0.0257359	−	0.112756i
$303$	−0.866196	+	11.5586i	−0.0497617	+	0.664024i
$304$	−9.73135	+	3.00172i	−0.558131	+	0.172161i
$305$	−0.626707	−	8.36283i	−0.0358852	−	0.478854i
$306$	−2.00129	−	5.09921i	−0.114406	−	0.291503i
$307$	4.06762	+	1.95886i	0.232151	+	0.111798i	0.546343	−	0.837561i	$-0.316019\pi$
$307$	4.06762	+	1.95886i	0.232151	+	0.111798i	−0.314192	+	0.949359i	$0.601734\pi$
$308$	−19.2950	−	13.3606i	−1.09943	−	0.761289i
$309$	−16.6628	+	8.02436i	−0.947911	+	0.456490i
$310$	1.73160	+	1.60669i	0.0983483	+	0.0912539i
$311$	−26.5831	−	4.00676i	−1.50739	−	0.227202i	−0.657215	−	0.753703i	$-0.728266\pi$
$311$	−26.5831	−	4.00676i	−1.50739	−	0.227202i	−0.850175	+	0.526501i	$0.823504\pi$
$312$	−4.85258	−	8.40491i	−0.274723	−	0.475835i
$313$	9.99374	−	17.3097i	0.564880	−	0.978400i	−0.432181	−	0.901787i	$-0.642256\pi$
$313$	9.99374	−	17.3097i	0.564880	−	0.978400i	0.997061	−	0.0766134i	$-0.0244107\pi$
$314$	11.2402	−	14.0948i	0.634321	−	0.795413i
$315$	1.54349	−	1.90701i	0.0869658	−	0.107448i
$316$	−8.28461	−	10.3886i	−0.466046	−	0.584403i
$317$	−32.4025	+	4.88389i	−1.81991	+	0.274307i	−0.968284	−	0.249851i	$-0.919618\pi$
$317$	−32.4025	+	4.88389i	−1.81991	+	0.274307i	−0.851621	+	0.524157i	$0.824380\pi$
$318$	−12.4807	−	8.50917i	−0.699881	−	0.477171i
$319$	−15.2964	−	10.4289i	−0.856434	−	0.583907i
$320$	−0.911710	+	0.137418i	−0.0509661	+	0.00768191i
$321$	5.58973	+	7.00930i	0.311988	+	0.391221i
$322$	−45.3446	+	21.4341i	−2.52695	+	1.19448i
$323$	−2.45055	+	3.07289i	−0.136352	+	0.170980i
$324$	14.0633	−	24.3584i	0.781295	−	1.35324i
$325$	−1.72539	−	2.98846i	−0.0957074	−	0.165770i
$326$	−34.0186	−	5.12748i	−1.88412	−	0.283985i
$327$	−13.1174	−	12.1711i	−0.725392	−	0.673065i
$328$	−51.5164	+	24.8090i	−2.84452	+	1.36985i
$329$	1.01414	−	0.304804i	0.0559112	−	0.0168044i
$330$	8.42735	+	4.05840i	0.463910	+	0.223407i
$331$	−2.69844	−	6.87551i	−0.148320	−	0.377912i	0.837334	−	0.546691i	$-0.184113\pi$
$331$	−2.69844	−	6.87551i	−0.148320	−	0.377912i	−0.985654	+	0.168779i	$0.946018\pi$
$332$	4.60319	+	61.4253i	0.252633	+	3.37115i
$333$	−5.31229	+	1.63862i	−0.291112	+	0.0897960i
$334$	3.90668	−	52.1311i	0.213764	−	2.85249i
$335$	4.06625	+	17.8154i	0.222163	+	0.973358i
$336$	28.2423	+	8.93582i	1.54074	+	0.487489i
$337$	1.79846	−	7.87958i	0.0979684	−	0.429228i	−0.902029	−	0.431676i	$-0.857922\pi$
$337$	1.79846	−	7.87958i	0.0979684	−	0.429228i	0.999997	+	0.00244855i	$0.000779398\pi$
$338$	2.44172	+	0.753172i	0.132812	+	0.0409672i
$339$	−1.11569	+	2.84274i	−0.0605961	+	0.154396i
$340$	−11.8916	+	11.0338i	−0.644914	+	0.598393i
$341$	−1.20185	+	0.819404i	−0.0650836	+	0.0443732i
$342$	2.60019			0.140602
$343$	−11.2303	−	14.7269i	−0.606379	−	0.795176i
$344$	7.75918			0.418347
$345$	11.4570	−	7.81123i	0.616822	−	0.420542i
$346$	−22.1449	+	20.5474i	−1.19052	+	1.10464i
$347$	−9.61188	+	24.4907i	−0.515993	+	1.31473i	0.401093	+	0.916037i	$0.368630\pi$
$347$	−9.61188	+	24.4907i	−0.515993	+	1.31473i	−0.917086	+	0.398690i	$0.869465\pi$
$348$	61.4370	+	18.9508i	3.29337	+	1.01587i
$349$	7.58190	−	33.2185i	0.405850	−	1.77814i	−0.197119	−	0.980380i	$-0.563158\pi$
$349$	7.58190	−	33.2185i	0.405850	−	1.77814i	0.602969	−	0.797765i	$-0.293984\pi$
$350$	22.2424	+	7.03746i	1.18891	+	0.376168i
$351$	1.25140	+	5.48274i	0.0667948	+	0.292647i
$352$	0.896527	−	11.9633i	0.0477851	−	0.637647i
$353$	15.0353	−	4.63777i	0.800248	−	0.246844i	0.132453	−	0.991189i	$-0.457715\pi$
$353$	15.0353	−	4.63777i	0.800248	−	0.246844i	0.667795	+	0.744345i	$0.267238\pi$
$354$	1.54287	+	20.5882i	0.0820029	+	1.09425i
$355$	−3.24570	−	8.26992i	−0.172264	−	0.438922i
$356$	−48.8208	−	23.5109i	−2.58750	−	1.24607i
$357$	10.9487	−	3.29069i	0.579467	−	0.174162i
$358$	12.7143	−	6.12288i	0.671971	−	0.323604i
$359$	21.5464	+	19.9921i	1.13717	+	1.05514i	0.997892	+	0.0648907i	$0.0206699\pi$
$359$	21.5464	+	19.9921i	1.13717	+	1.05514i	0.139282	+	0.990253i	$0.455521\pi$
$360$	5.92608	+	0.893212i	0.312332	+	0.0470764i
$361$	8.56718	+	14.8388i	0.450904	+	0.780989i
$362$	12.9378	−	22.4090i	0.679997	−	1.17779i
$363$	6.70779	−	8.41130i	0.352068	−	0.441479i
$364$	−10.8340	+	5.12115i	−0.567853	+	0.268421i
$365$	−5.80452	−	7.27864i	−0.303823	−	0.380981i
$366$	−25.5647	+	3.85326i	−1.33629	+	0.201413i
$367$	19.3425	+	13.1875i	1.00967	+	0.688381i	0.950775	−	0.309883i	$-0.100290\pi$
$367$	19.3425	+	13.1875i	1.00967	+	0.688381i	0.0588951	+	0.998264i	$0.481242\pi$
$368$	−45.7021	−	31.1592i	−2.38239	−	1.62428i
$369$	6.51759	−	0.982369i	0.339292	−	0.0511401i
$370$	14.7971	+	18.5550i	0.769266	+	0.964629i
$371$	−6.55262	+	8.09589i	−0.340195	+	0.420318i
$372$	3.14960	−	3.94947i	0.163299	−	0.204771i
$373$	14.1983	−	24.5922i	0.735160	−	1.27333i	−0.219493	−	0.975614i	$-0.570440\pi$
$373$	14.1983	−	24.5922i	0.735160	−	1.27333i	0.954653	−	0.297720i	$-0.0962262\pi$
$374$	−7.20017	−	12.4711i	−0.372312	−	0.644863i
$375$	−15.6188	−	2.35416i	−0.806552	−	0.121568i
$376$	1.89623	+	1.75945i	0.0977908	+	0.0907366i
$377$	−8.51676	+	4.10145i	−0.438635	+	0.211236i
$378$	−31.2575	−	21.6438i	−1.60771	−	1.11324i
$379$	−0.815272	−	0.392614i	−0.0418777	−	0.0201672i	0.412828	−	0.910809i	$-0.364541\pi$
$379$	−0.815272	−	0.392614i	−0.0418777	−	0.0201672i	−0.454705	+	0.890642i	$0.650255\pi$
$380$	−2.81318	−	7.16787i	−0.144313	−	0.367704i
$381$	1.28799	+	17.1870i	0.0659855	+	0.880516i
$382$	8.63481	−	2.66349i	0.441795	−	0.136276i
$383$	−0.0490578	+	0.654631i	−0.00250674	+	0.0334501i	−0.998317	−	0.0579945i	$-0.981529\pi$
$383$	−0.0490578	+	0.654631i	−0.00250674	+	0.0334501i	0.995810	+	0.0914446i	$0.0291484\pi$
$384$	−3.46127	−	15.1648i	−0.176632	−	0.773876i
$385$	3.26506	−	5.56194i	0.166403	−	0.283463i
$386$	−2.33529	+	10.2316i	−0.118863	+	0.520774i
$387$	−0.854690	−	0.263637i	−0.0434463	−	0.0134014i
$388$	−2.10997	+	5.37613i	−0.107118	+	0.272931i
$389$	−4.49467	+	4.17044i	−0.227889	+	0.211450i	−0.785850	−	0.618417i	$-0.787774\pi$
$389$	−4.49467	+	4.17044i	−0.227889	+	0.211450i	0.557961	+	0.829867i	$0.311584\pi$
$390$	3.94610	−	2.69040i	0.199818	−	0.136234i
$391$	−21.3479			−1.07961
$392$	17.1357	−	41.8697i	0.865484	−	2.11474i
$393$	15.0282			0.758075
$394$	−35.2328	+	24.0213i	−1.77500	+	1.21018i
$395$	2.67673	−	2.48364i	0.134681	−	0.124966i
$396$	−2.41438	+	6.15175i	−0.121327	+	0.309137i
$397$	−13.8982	−	4.28703i	−0.697531	−	0.215160i	−0.0743438	−	0.997233i	$-0.523686\pi$
$397$	−13.8982	−	4.28703i	−0.697531	−	0.215160i	−0.623187	+	0.782073i	$0.714162\pi$
$398$	1.88571	−	8.26185i	0.0945223	−	0.414129i
$399$	−0.444669	+	5.40845i	−0.0222613	+	0.270761i
$400$	5.72511	+	25.0834i	0.286256	+	1.25417i
$401$	−0.465675	+	6.21401i	−0.0232547	+	0.310313i	0.973432	+	0.228976i	$0.0735379\pi$
$401$	−0.465675	+	6.21401i	−0.0232547	+	0.310313i	−0.996687	+	0.0813364i	$0.974081\pi$
$402$	53.8314	−	16.6048i	2.68487	−	0.828171i
$403$	0.0555034	+	0.740641i	0.00276482	+	0.0368939i
$404$	12.7725	+	32.5438i	0.635455	+	1.61911i
$405$	6.96393	+	3.35365i	0.346041	+	0.166644i
$406$	23.7774	−	59.3186i	1.18005	−	2.94393i
$407$	−13.1670	+	6.34091i	−0.652665	+	0.314307i
$408$	20.4719	+	18.9951i	1.01351	+	0.940400i
$409$	0.241218	+	0.0363578i	0.0119275	+	0.00179778i	0.155003	−	0.987914i	$-0.450461\pi$
$409$	0.241218	+	0.0363578i	0.0119275	+	0.00179778i	−0.143076	+	0.989712i	$0.545699\pi$
$410$	−14.0691	−	24.3683i	−0.694822	−	1.20347i
$411$	16.0484	−	27.7966i	0.791609	−	1.37111i
$412$	−34.7795	+	43.6121i	−1.71346	+	2.14861i
$413$	14.2353	+	0.102969i	0.700474	+	0.00506676i
$414$	8.80554	+	11.0418i	0.432769	+	0.542675i
$415$	−16.7383	+	2.52290i	−0.821652	+	0.123844i
$416$	−5.06121	−	3.45067i	−0.248146	−	0.169183i
$417$	17.7977	+	12.1342i	0.871555	+	0.594216i
$418$	6.75908	−	1.01877i	0.330597	−	0.0498295i
$419$	21.6706	+	27.1740i	1.05868	+	1.32754i	0.942461	+	0.334315i	$0.108505\pi$
$419$	21.6706	+	27.1740i	1.05868	+	1.32754i	0.116216	+	0.993224i	$0.462924\pi$
$420$	−5.14182	+	21.7997i	−0.250895	+	1.06372i
$421$	16.5518	−	20.7554i	0.806688	−	1.01155i	−0.192852	−	0.981228i	$-0.561774\pi$
$421$	16.5518	−	20.7554i	0.806688	−	1.01155i	0.999540	−	0.0303267i	$-0.00965476\pi$
$422$	−15.8423	+	27.4396i	−0.771191	+	1.33574i
$423$	−0.149093	−	0.258236i	−0.00724914	−	0.0125559i
$424$	−25.1581	−	3.79198i	−1.22179	−	0.184155i
$425$	7.27902	+	6.75394i	0.353084	+	0.327614i
$426$	−24.6757	+	11.8832i	−1.19554	+	0.575742i
$427$	1.20355	+	17.7857i	0.0582438	+	0.860708i
$428$	24.3628	+	11.7325i	1.17762	+	0.567113i
$429$	1.07446	+	2.73768i	0.0518754	+	0.132176i
$430$	0.285345	+	3.80767i	0.0137606	+	0.183622i
$431$	31.0265	−	9.57040i	1.49449	−	0.460990i	0.563527	−	0.826097i	$-0.309444\pi$
$431$	31.0265	−	9.57040i	1.49449	−	0.460990i	0.930965	+	0.365107i	$0.118968\pi$
$432$	3.13341	−	41.8124i	0.150756	−	2.01170i
$433$	−7.26508	−	31.8304i	−0.349138	−	1.52967i	−0.779144	−	0.626846i	$-0.784346\pi$
$433$	−7.26508	−	31.8304i	−0.349138	−	1.52967i	0.430006	−	0.902826i	$-0.358511\pi$
$434$	−3.65598	−	3.44180i	−0.175493	−	0.165212i
$435$	−3.93156	+	17.2253i	−0.188504	+	0.825889i
$436$	−51.5742	−	15.9085i	−2.46995	−	0.761880i
$437$	3.70209	−	9.43277i	0.177095	−	0.451230i
$438$	−21.0388	+	19.5212i	−1.00527	+	0.932757i
$439$	32.1645	−	21.9294i	1.53513	−	1.04663i	0.559067	−	0.829122i	$-0.311159\pi$
$439$	32.1645	−	21.9294i	1.53513	−	1.04663i	0.976058	−	0.217509i	$-0.0697930\pi$
$440$	15.7545			0.751068
$441$	−3.31016	+	4.02981i	−0.157627	+	0.191896i
$442$	−7.35281			−0.349737
$443$	12.4763	−	8.50622i	0.592768	−	0.404143i	−0.229445	−	0.973322i	$-0.573691\pi$
$443$	12.4763	−	8.50622i	0.592768	−	0.404143i	0.822214	+	0.569179i	$0.192739\pi$
$444$	37.2045	−	34.5207i	1.76565	−	1.63828i
$445$	5.44027	−	13.8616i	0.257894	−	0.657102i
$446$	−64.9540	−	20.0357i	−3.07566	−	0.948716i
$447$	−2.01051	+	8.80864i	−0.0950940	+	0.416634i
$448$	1.94004	−	0.278078i	0.0916584	−	0.0131380i
$449$	−3.60269	−	15.7844i	−0.170021	−	0.744912i	−0.985988	−	0.166814i	$-0.946652\pi$
$449$	−3.60269	−	15.7844i	−0.170021	−	0.744912i	0.815967	−	0.578098i	$-0.196205\pi$
$450$	0.490913	−	6.55078i	0.0231419	−	0.308807i
$451$	16.5573	−	5.10725i	0.779652	−	0.240491i
$452$	0.688333	+	9.18516i	0.0323764	+	0.432034i
$453$	−0.431529	−	1.09952i	−0.0202750	−	0.0516599i
$454$	6.83265	+	3.29043i	0.320672	+	0.154428i
$455$	−1.62588	−	2.86375i	−0.0762225	−	0.134255i
$456$	−11.9433	+	5.75161i	−0.559298	+	0.269344i
$457$	−3.60699	−	3.34679i	−0.168728	−	0.156556i	0.591290	−	0.806459i	$-0.298619\pi$
$457$	−3.60699	−	3.34679i	−0.168728	−	0.156556i	−0.760017	+	0.649903i	$0.774810\pi$
$458$	44.5171	+	6.70988i	2.08015	+	0.313532i
$459$	−8.09125	−	14.0145i	−0.377667	−	0.654139i
$460$	20.9118	−	36.2202i	0.975016	−	1.68878i
$461$	4.48434	−	5.62318i	0.208856	−	0.261898i	−0.666359	−	0.745631i	$-0.732148\pi$
$461$	4.48434	−	5.62318i	0.208856	−	0.261898i	0.875215	+	0.483733i	$0.160720\pi$
$462$	−17.8508	−	8.75609i	−0.830493	−	0.407370i
$463$	0.300244	+	0.376494i	0.0139535	+	0.0174972i	0.788759	−	0.614702i	$-0.210724\pi$
$463$	0.300244	+	0.376494i	0.0139535	+	0.0174972i	−0.774806	+	0.632199i	$0.782152\pi$
$464$	69.6919	−	10.5044i	3.23536	−	0.487653i
$465$	1.14699	+	0.782003i	0.0531903	+	0.0362645i
$466$	−21.9742	−	14.9817i	−1.01793	−	0.694015i
$467$	−6.41735	+	0.967259i	−0.296959	+	0.0447594i	−0.295832	−	0.955240i	$-0.595597\pi$
$467$	−6.41735	+	0.967259i	−0.296959	+	0.0447594i	−0.00112725	+	0.999999i	$0.500359\pi$
$468$	2.10386	+	2.63816i	0.0972512	+	0.121949i
$469$	−8.36929	−	37.9309i	−0.386458	−	1.75148i
$470$	−0.793681	+	0.995244i	−0.0366098	+	0.0459072i
$471$	5.29730	−	9.17519i	0.244087	−	0.422770i
$472$	17.3872	+	30.1155i	0.800311	+	1.38618i
$473$	−2.32502	−	0.350441i	−0.106905	−	0.0161133i
$474$	−8.25189	−	7.65664i	−0.379022	−	0.351681i
$475$	−4.24659	+	2.04505i	−0.194847	+	0.0938334i
$476$	25.4465	−	23.2706i	1.16634	−	1.06661i
$477$	2.64238	+	1.27250i	0.120986	+	0.0582639i
$478$	11.9742	+	30.5098i	0.547689	+	1.39549i
$479$	−1.27144	−	16.9662i	−0.0580936	−	0.775205i	−0.947839	−	0.318749i	$-0.896737\pi$
$479$	−1.27144	−	16.9662i	−0.0580936	−	0.775205i	0.889746	−	0.456457i	$-0.150882\pi$
$480$	−10.9406	+	3.37473i	−0.499368	+	0.154035i
$481$	−0.557641	+	7.44120i	−0.0254262	+	0.339289i
$482$	6.99187	+	30.6334i	0.318471	+	1.39531i
$483$	−24.4730	+	16.4274i	−1.11356	+	0.747472i
$484$	7.22067	−	31.6358i	0.328212	−	1.43799i
$485$	−1.51659	−	0.467808i	−0.0688650	−	0.0212420i
$486$	−7.04442	+	17.9489i	−0.319541	+	0.814178i
$487$	19.9443	−	18.5056i	0.903764	−	0.838570i	−0.0836881	−	0.996492i	$-0.526670\pi$
$487$	19.9443	−	18.5056i	0.903764	−	0.838570i	0.987452	+	0.157922i	$0.0504795\pi$
$488$	−35.9789	+	24.5300i	−1.62869	+	1.11042i
$489$	−20.2178			−0.914282
$490$	21.1769	+	6.86925i	0.956676	+	0.310321i
$491$	−20.1029			−0.907232			−0.453616	−	0.891197i	$-0.649866\pi$
$491$	−20.1029			−0.907232			−0.453616	+	0.891197i	$0.649866\pi$
$492$	−49.7180	+	33.8972i	−2.24146	+	1.52820i
$493$	19.9398	−	18.5014i	0.898041	−	0.833260i
$494$	1.27510	−	3.24890i	0.0573695	−	0.146175i
$495$	−1.73540	−	0.535299i	−0.0780002	−	0.0240599i
$496$	1.23223	−	5.39874i	0.0553286	−	0.242410i
$497$	6.77191	+	17.6284i	0.303762	+	0.790743i
$498$	11.6121	+	50.8759i	0.520350	+	2.27980i
$499$	1.25560	−	16.7549i	0.0562086	−	0.750052i	−0.895893	−	0.444270i	$-0.853463\pi$
$499$	1.25560	−	16.7549i	0.0562086	−	0.750052i	0.952102	−	0.305782i	$-0.0989178\pi$
$500$	−45.5246	+	14.0425i	−2.03592	+	0.627999i
$501$	−2.29588	−	30.6363i	−0.102572	−	1.36873i
$502$	−19.9183	−	50.7511i	−0.888999	−	2.26513i
$503$	−36.0451	−	17.3584i	−1.60717	−	0.773972i	−0.607379	−	0.794413i	$-0.707779\pi$
$503$	−36.0451	−	17.3584i	−1.60717	−	0.773972i	−0.999791	+	0.0204405i	$0.993493\pi$
$504$	−12.5827	−	1.98973i	−0.560479	−	0.0886294i
$505$	−8.65594	+	4.16848i	−0.385184	+	0.185495i
$506$	27.2158	+	25.2526i	1.20989	+	1.12261i
$507$	1.48489	+	0.223811i	0.0659464	+	0.00993981i
$508$	25.9921	+	45.0197i	1.15322	+	1.99743i
$509$	−18.2004	+	31.5240i	−0.806718	+	1.39728i	0.108407	+	0.994107i	$0.465425\pi$
$509$	−18.2004	+	31.5240i	−0.806718	+	1.39728i	−0.915125	+	0.403170i	$0.867908\pi$
$510$	−8.56864	+	10.7447i	−0.379426	+	0.475785i
$511$	12.2262	+	15.5607i	0.540854	+	0.688365i
$512$	−31.6120	−	39.6401i	−1.39706	−	1.75186i
$513$	7.59558	−	1.14485i	0.335353	−	0.0505463i
$514$	25.4091	+	17.3236i	1.12075	+	0.764111i
$515$	−12.6656	−	8.63527i	−0.558114	−	0.380515i
$516$	8.07440	−	1.21702i	0.355455	−	0.0535763i
$517$	−0.488738	−	0.612858i	−0.0214947	−	0.0269535i
$518$	−31.1675	−	39.6680i	−1.36942	−	1.74291i
$519$	−11.0690	+	13.8801i	−0.485875	+	0.609267i
$520$	4.02213	−	6.96654i	0.176382	−	0.305503i
$521$	20.1452	+	34.8925i	0.882576	+	1.52867i	0.848467	+	0.529249i	$0.177526\pi$
$521$	20.1452	+	34.8925i	0.882576	+	1.52867i	0.0341092	+	0.999418i	$0.489141\pi$
$522$	−17.7942	−	2.68204i	−0.778830	−	0.117390i
$523$	14.5616	+	13.5112i	0.636736	+	0.590804i	0.931044	−	0.364906i	$-0.118899\pi$
$523$	14.5616	+	13.5112i	0.636736	+	0.590804i	−0.294309	+	0.955710i	$0.595089\pi$
$524$	40.8390	−	19.6670i	1.78406	−	0.859157i
$525$	13.5418	+	2.14138i	0.591012	+	0.0934576i
$526$	61.3345	+	29.5371i	2.67431	+	1.28788i
$527$	−0.780805	−	1.98946i	−0.0340124	−	0.0866622i
$528$	−1.63864	−	21.8661i	−0.0713126	−	0.951601i
$529$	30.6155	−	9.44363i	1.33111	−	0.410592i
$530$	0.935645	−	12.4853i	0.0406418	−	0.542327i
$531$	−0.891989	−	3.90806i	−0.0387090	−	0.169595i
$532$	5.86949	+	15.2793i	0.254475	+	0.662440i
$533$	1.96869	−	8.62539i	0.0852734	−	0.373607i
$534$	−43.8667	−	13.5311i	−1.89830	−	0.585548i
$535$	−2.71484	+	6.91729i	−0.117373	+	0.299060i
$536$	69.5554	−	64.5380i	3.00434	−	2.78762i
$537$	6.85217	−	4.67173i	0.295693	−	0.201600i
$538$	26.2118			1.13007
$539$	−7.02571	+	11.7723i	−0.302619	+	0.507067i
$540$	31.7038			1.36431
$541$	−1.01934	+	0.694973i	−0.0438248	+	0.0298792i	−0.585034	−	0.811009i	$-0.698919\pi$
$541$	−1.01934	+	0.694973i	−0.0438248	+	0.0298792i	0.541210	+	0.840888i	$0.317967\pi$
$542$	12.3310	−	11.4415i	0.529664	−	0.491456i
$543$	5.55558	−	14.1554i	0.238413	−	0.607466i
$544$	16.8435	+	5.19554i	0.722160	+	0.222757i
$545$	3.30040	−	14.4600i	0.141374	−	0.619398i
$546$	−8.42918	+	5.65804i	−0.360736	+	0.242142i
$547$	6.83501	+	29.9461i	0.292244	+	1.28040i	0.881394	+	0.472381i	$0.156605\pi$
$547$	6.83501	+	29.9461i	0.292244	+	1.28040i	−0.589151	+	0.808023i	$0.700537\pi$
$548$	7.23459	−	96.5388i	0.309046	−	4.12393i
$549$	4.79662	−	1.47956i	0.204715	−	0.0631462i
$550$	−1.29052	−	17.2208i	−0.0550280	−	0.734297i
$551$	4.71711	+	12.0190i	0.200956	+	0.512027i
$552$	−64.8705	−	31.2400i	−2.76107	−	1.32966i
$553$	−5.72784	+	5.23807i	−0.243572	+	0.222745i
$554$	−20.4447	+	9.84564i	−0.868611	+	0.418301i
$555$	10.2240	+	9.48653i	0.433987	+	0.402681i
$556$	64.2445	+	9.68329i	2.72457	+	0.410663i
$557$	−20.6202	−	35.7153i	−0.873708	−	1.51331i	−0.858133	−	0.513428i	$-0.828375\pi$
$557$	−20.6202	−	35.7153i	−0.873708	−	1.51331i	−0.0155749	−	0.999879i	$-0.504958\pi$
$558$	−0.706945	+	1.22446i	−0.0299274	+	0.0518357i
$559$	−0.748540	+	0.938640i	−0.0316599	+	0.0397002i
$560$	5.29023	+	23.9761i	0.223553	+	1.01318i
$561$	−5.27645	−	6.61646i	−0.222772	−	0.279347i
$562$	2.83478	−	0.427274i	0.119578	−	0.0180235i
$563$	36.9347	+	25.1816i	1.55661	+	1.06128i	0.967384	+	0.253313i	$0.0815201\pi$
$563$	36.9347	+	25.1816i	1.55661	+	1.06128i	0.589227	+	0.807967i	$0.299432\pi$
$564$	2.24924	+	1.53350i	0.0947099	+	0.0645721i
$565$	−2.50295	+	0.377259i	−0.105300	+	0.0158714i
$566$	−5.36642	−	6.72927i	−0.225567	−	0.282853i
$567$	−14.7510	−	7.23559i	−0.619482	−	0.303866i
$568$	−28.7616	+	36.0659i	−1.20681	+	1.51329i
$569$	3.36921	−	5.83564i	0.141245	−	0.244643i	−0.786721	−	0.617309i	$-0.788223\pi$
$569$	3.36921	−	5.83564i	0.141245	−	0.244643i	0.927966	+	0.372666i	$0.121556\pi$
$570$	−3.26171	−	5.64945i	−0.136618	−	0.236629i
$571$	28.5870	+	4.30879i	1.19633	+	0.180317i	0.716844	−	0.697234i	$-0.245586\pi$
$571$	28.5870	+	4.30879i	1.19633	+	0.180317i	0.479483	+	0.877551i	$0.340824\pi$
$572$	6.50254	+	6.03348i	0.271885	+	0.252272i
$573$	4.78453	−	2.30411i	0.199876	−	0.0962554i
$574$	29.5305	+	52.0136i	1.23258	+	2.17101i
$575$	−23.0655	−	11.1077i	−0.961896	−	0.463225i
$576$	−0.201621	−	0.513722i	−0.00840087	−	0.0214051i
$577$	2.93798	+	39.2047i	0.122310	+	1.63211i	0.634276	+	0.773106i	$0.281298\pi$
$577$	2.93798	+	39.2047i	0.122310	+	1.63211i	−0.511966	+	0.859005i	$0.671083\pi$
$578$	−21.2913	+	6.56750i	−0.885602	+	0.273172i
$579$	−0.460899	+	6.15027i	−0.0191543	+	0.255597i
$580$	11.8583	+	51.9544i	0.492388	+	2.15729i
$581$	35.6178	−	5.10531i	1.47767	−	0.211804i
$582$	−1.08874	+	4.77010i	−0.0451299	+	0.197727i
$583$	7.36732	+	2.27252i	0.305123	+	0.0941180i
$584$	−17.6607	+	44.9988i	−0.730807	+	1.86207i
$585$	−0.679752	+	0.630717i	−0.0281043	+	0.0260769i
$586$	−43.8471	+	29.8945i	−1.81131	+	1.23493i
$587$	−8.99176			−0.371130			−0.185565	−	0.982632i	$-0.559411\pi$
$587$	−8.99176			−0.371130			−0.185565	+	0.982632i	$0.559411\pi$
$588$	11.2646	−	46.2584i	0.464545	−	1.90767i
$589$	1.01447			0.0418003
$590$	−14.1392	+	9.63993i	−0.582101	+	0.396870i
$591$	−18.3703	+	17.0452i	−0.755654	+	0.701144i
$592$	20.3261	−	51.7899i	0.835396	−	2.12855i
$593$	−0.923707	−	0.284926i	−0.0379321	−	0.0117005i	0.275731	−	0.961235i	$-0.411080\pi$
$593$	−0.923707	−	0.284926i	−0.0379321	−	0.0117005i	−0.313663	+	0.949534i	$0.601556\pi$
$594$	−6.26250	+	27.4378i	−0.256954	+	1.12579i
$595$	6.89961	+	6.49541i	0.282857	+	0.266286i
$596$	6.06406	+	26.5684i	0.248394	+	1.08828i
$597$	0.372169	−	4.96625i	0.0152319	−	0.203255i
$598$	18.1147	−	5.58765i	0.740765	−	0.228496i
$599$	−1.25956	−	16.8077i	−0.0514642	−	0.686742i	−0.961954	−	0.273211i	$-0.911914\pi$
$599$	−1.25956	−	16.8077i	−0.0514642	−	0.686742i	0.910490	−	0.413531i	$-0.135705\pi$
$600$	12.2354	+	31.1753i	0.499508	+	1.27273i
$601$	10.6285	+	5.11843i	0.433547	+	0.208785i	0.637911	−	0.770110i	$-0.279799\pi$
$601$	10.6285	+	5.11843i	0.433547	+	0.208785i	−0.204365	+	0.978895i	$0.565513\pi$
$602$	−0.547986	−	8.09796i	−0.0223342	−	0.330048i
$603$	−9.85451	+	4.74568i	−0.401307	+	0.193259i
$604$	−2.61158	−	2.42319i	−0.106264	−	0.0985983i
$605$	8.81770	+	1.32906i	0.358491	+	0.0540338i
$606$	14.8089	+	25.6498i	0.601572	+	1.04195i
$607$	11.2167	−	19.4280i	0.455273	−	0.788557i	−0.543430	−	0.839454i	$-0.682875\pi$
$607$	11.2167	−	19.4280i	0.455273	−	0.788557i	0.998704	+	0.0508975i	$0.0162082\pi$
$608$	−5.21665	+	6.54147i	−0.211563	+	0.265292i
$609$	8.62175	−	36.5536i	0.349371	−	1.48123i
$610$	−13.3608	−	16.7539i	−0.540962	−	0.678344i
$611$	−0.395776	+	0.0596536i	−0.0160114	+	0.00241333i
$612$	−8.02259	−	5.46971i	−0.324294	−	0.221100i
$613$	33.7141	+	22.9859i	1.36170	+	0.928391i	0.999992	−	0.00390100i	$-0.00124173\pi$
$613$	33.7141	+	22.9859i	1.36170	+	0.928391i	0.361707	+	0.932292i	$0.382194\pi$
$614$	11.4074	−	1.71938i	0.460363	−	0.0693886i
$615$	−10.3101	−	12.9285i	−0.415745	−	0.521328i
$616$	−33.4878	−	0.242228i	−1.34926	−	0.00975964i
$617$	−2.10079	+	2.63431i	−0.0845748	+	0.106053i	−0.822319	−	0.569027i	$-0.807320\pi$
$617$	−2.10079	+	2.63431i	−0.0845748	+	0.106053i	0.737744	+	0.675081i	$0.235891\pi$
$618$	−23.6287	+	40.9261i	−0.950485	+	1.64629i
$619$	14.0160	+	24.2763i	0.563349	+	0.975748i	0.997201	+	0.0747646i	$0.0238205\pi$
$619$	14.0160	+	24.2763i	0.563349	+	0.975748i	−0.433853	+	0.900984i	$0.642846\pi$
$620$	4.14030	+	0.624049i	0.166278	+	0.0250624i
$621$	30.5840	+	28.3778i	1.22729	+	1.13876i
$622$	−61.8908	+	29.8050i	−2.48160	+	1.19507i
$623$	−11.7770	+	29.3805i	−0.471834	+	1.17711i
$624$	−10.0874	−	4.85783i	−0.403818	−	0.194469i
$625$	1.52047	+	3.87410i	0.0608189	+	0.154964i
$626$	−3.81668	−	50.9301i	−0.152545	−	2.03558i
$627$	3.83857	−	1.18404i	0.153298	−	0.0472861i
$628$	2.38801	−	31.8658i	0.0952920	−	1.27158i
$629$	−4.77805	−	20.9340i	−0.190513	−	0.834693i
$630$	0.513687	−	6.24790i	0.0204658	−	0.248922i
$631$	4.33141	−	18.9771i	0.172431	−	0.755468i	−0.812562	−	0.582874i	$-0.801928\pi$
$631$	4.33141	−	18.9771i	0.172431	−	0.755468i	0.984993	−	0.172594i	$-0.0552148\pi$
$632$	−18.1179	−	5.58862i	−0.720690	−	0.222303i
$633$	−6.80278	+	17.3332i	−0.270386	+	0.688933i
$634$	−61.3796	+	56.9519i	−2.43769	+	2.26185i
$635$	−11.8033	+	8.04738i	−0.468401	+	0.319351i
$636$	−26.7749			−1.06170
$637$	3.41194	+	6.11217i	0.135186	+	0.242173i
$638$	−47.3060			−1.87286
$639$	4.39358	−	2.99549i	0.173807	−	0.118500i
$640$	9.45111	−	8.76935i	0.373588	−	0.346639i
$641$	−3.48703	+	8.88481i	−0.137729	+	0.350929i	−0.983052	−	0.183328i	$-0.941313\pi$
$641$	−3.48703	+	8.88481i	−0.137729	+	0.350929i	0.845322	+	0.534256i	$0.179408\pi$
$642$	21.8906	+	6.75236i	0.863954	+	0.266494i
$643$	0.629054	−	2.75606i	0.0248075	−	0.108689i	−0.961008	−	0.276519i	$-0.910819\pi$
$643$	0.629054	−	2.75606i	0.0248075	−	0.108689i	0.985816	+	0.167831i	$0.0536762\pi$
$644$	−45.0069	+	76.6681i	−1.77352	+	3.02115i
$645$	0.499328	+	2.18770i	0.0196610	+	0.0861406i
$646$	−0.750520	+	10.0150i	−0.0295288	+	0.394035i
$647$	−1.18873	+	0.366674i	−0.0467337	+	0.0144154i	−0.318034	−	0.948079i	$-0.603023\pi$
$647$	−1.18873	+	0.366674i	−0.0467337	+	0.0144154i	0.271300	+	0.962495i	$0.412546\pi$
$648$	−2.99926	−	40.0223i	−0.117822	−	1.57222i
$649$	−3.84988	−	9.80934i	−0.151121	−	0.385050i
$650$	−7.94438	−	3.82581i	−0.311604	−	0.150061i
$651$	−2.42601	−	1.67986i	−0.0950829	−	0.0658388i
$652$	−54.9415	+	26.4585i	−2.15168	+	1.03619i
$653$	18.9439	+	17.5774i	0.741331	+	0.687855i	0.957478	−	0.288506i	$-0.0931585\pi$
$653$	18.9439	+	17.5774i	0.741331	+	0.687855i	−0.216147	+	0.976361i	$0.569349\pi$
$654$	−45.2133	−	6.81482i	−1.76798	−	0.266480i
$655$	6.22819	+	10.7875i	0.243356	+	0.421504i
$656$	−32.9816	+	57.1259i	−1.28772	+	2.23039i
$657$	3.47431	−	4.35665i	0.135546	−	0.169969i
$658$	1.70235	−	2.10329i	0.0663645	−	0.0819947i
$659$	22.5621	+	28.2920i	0.878896	+	1.10210i	0.994069	+	0.108755i	$0.0346865\pi$
$659$	22.5621	+	28.2920i	0.878896	+	1.10210i	−0.115172	+	0.993346i	$0.536742\pi$
$660$	16.3946	−	2.47108i	0.638157	−	0.0961868i
$661$	−18.7959	−	12.8148i	−0.731076	−	0.498439i	0.139654	−	0.990200i	$-0.455401\pi$
$661$	−18.7959	−	12.8148i	−0.731076	−	0.498439i	−0.870730	+	0.491761i	$0.836353\pi$
$662$	−15.5938	−	10.6317i	−0.606071	−	0.413212i
$663$	−4.27283	+	0.644025i	−0.165943	+	0.0250119i
$664$	54.8016	+	68.7190i	2.12671	+	2.66681i
$665$	−4.06656	+	1.92224i	−0.157695	+	0.0745414i
$666$	−8.85686	+	11.1062i	−0.343196	+	0.430355i
$667$	−35.0646	+	60.7337i	−1.35771	+	2.35162i
$668$	−46.3318	−	80.2491i	−1.79263	−	3.10493i
$669$	−39.5007	−	5.95377i	−1.52718	−	0.230186i
$670$	34.2287	+	31.7596i	1.32237	+	1.22698i
$671$	11.8889	−	5.72540i	0.458966	−	0.221026i
$672$	23.3072	−	7.00511i	0.899096	−	0.270228i
$673$	16.7049	+	8.04466i	0.643927	+	0.310099i	0.727198	−	0.686428i	$-0.240822\pi$
$673$	16.7049	+	8.04466i	0.643927	+	0.310099i	−0.0832706	+	0.996527i	$0.526537\pi$
$674$	−7.54504	−	19.2244i	−0.290624	−	0.740498i
$675$	−1.45023	−	19.3520i	−0.0558195	−	0.744860i
$676$	4.32806	−	1.33503i	0.166464	−	0.0513473i
$677$	−1.15745	+	15.4450i	−0.0444843	+	0.593601i	0.929769	+	0.368144i	$0.120007\pi$
$677$	−1.15745	+	15.4450i	−0.0444843	+	0.593601i	−0.974253	+	0.225457i	$0.927612\pi$
$678$	1.73640	+	7.60767i	0.0666861	+	0.292171i
$679$	3.21648	+	1.01769i	0.123437	+	0.0390553i
$680$	−5.15084	+	22.5673i	−0.197526	+	0.865416i
$681$	4.25876	+	1.31365i	0.163196	+	0.0503393i
$682$	−1.35792	+	3.45992i	−0.0519974	+	0.132487i
$683$	−19.4296	+	18.0280i	−0.743453	+	0.689824i	−0.957961	−	0.286899i	$-0.907376\pi$
$683$	−19.4296	+	18.0280i	−0.743453	+	0.689824i	0.214508	+	0.976722i	$0.431185\pi$
$684$	3.80809	−	2.59631i	0.145606	−	0.0992725i
$685$	26.6039			1.01648
$686$	−44.9080	−	14.9269i	−1.71460	−	0.569910i
$687$	26.4573			1.00941
$688$	7.39584	−	5.04240i	0.281964	−	0.192240i
$689$	2.88577	−	2.67760i	0.109939	−	0.102008i
$690$	12.9448	−	32.9828i	0.492800	−	1.25563i
$691$	24.0645	+	7.42292i	0.915458	+	0.282381i	0.716468	−	0.697620i	$-0.245758\pi$
$691$	24.0645	+	7.42292i	0.915458	+	0.282381i	0.198990	+	0.980002i	$0.436234\pi$
$692$	−11.9153	+	52.2045i	−0.452953	+	1.98452i
$693$	3.68052	+	1.16451i	0.139812	+	0.0442361i
$694$	14.9594	+	65.5413i	0.567850	+	2.48791i
$695$	−1.33425	+	17.8043i	−0.0506109	+	0.675355i
$696$	87.6659	−	27.0414i	3.32297	−	1.02500i
$697$	1.90249	+	25.3870i	0.0720619	+	0.961600i
$698$	−31.8081	−	81.0458i	−1.20396	−	3.06763i
$699$	−14.0818	−	6.78141i	−0.532621	−	0.256497i
$700$	39.6019	−	11.9026i	1.49681	−	0.449874i
$701$	−29.3953	+	14.1560i	−1.11024	+	0.534665i	−0.896865	−	0.442305i	$-0.854161\pi$
$701$	−29.3953	+	14.1560i	−1.11024	+	0.534665i	−0.213378	+	0.976970i	$0.568447\pi$
$702$	10.5340	+	9.77411i	0.397580	+	0.368900i
$703$	10.0785	+	1.51908i	0.380116	+	0.0572933i
$704$	−0.725383	−	1.25640i	−0.0273389	−	0.0473524i
$705$	−0.374047	+	0.647869i	−0.0140874	+	0.0244002i
$706$	25.0675	−	31.4336i	0.943426	−	1.18302i
$707$	18.4631	−	8.72743i	0.694378	−	0.328229i
$708$	22.8171	+	28.6118i	0.857521	+	1.07530i
$709$	0.735830	−	0.110909i	0.0276347	−	0.00416526i	−0.135210	−	0.990817i	$-0.543171\pi$
$709$	0.735830	−	0.110909i	0.0276347	−	0.00416526i	0.162845	+	0.986652i	$0.447933\pi$
$710$	−18.7564	−	12.7879i	−0.703914	−	0.479920i
$711$	1.80583	+	1.23120i	0.0677241	+	0.0461735i
$712$	−76.4571	+	11.5240i	−2.86535	+	0.431882i
$713$	3.43548	+	4.30796i	0.128660	+	0.161334i
$714$	18.3787	−	22.7072i	0.687805	−	0.849797i
$715$	−1.51987	+	1.90585i	−0.0568397	+	0.0712748i
$716$	12.5069	−	21.6626i	0.467404	−	0.809568i
$717$	9.63073	+	16.6809i	0.359666	+	0.622960i
$718$	74.2667	+	11.1939i	2.77161	+	0.417753i
$719$	33.4728	+	31.0582i	1.24833	+	1.15828i	0.980861	+	0.194710i	$0.0623765\pi$
$719$	33.4728	+	31.0582i	1.24833	+	1.15828i	0.267465	+	0.963568i	$0.413814\pi$
$720$	6.22904	−	2.99975i	0.232143	−	0.111794i
$721$	26.7892	+	18.5498i	0.997683	+	0.690832i
$722$	39.4467	+	18.9965i	1.46805	+	0.706977i
$723$	6.74623	+	17.1891i	0.250895	+	0.639270i
$724$	−3.42755	−	45.7374i	−0.127384	−	1.69982i
$725$	31.1706	−	9.61487i	1.15765	−	0.357087i
$726$	2.05437	−	27.4136i	0.0762447	−	1.01742i
$727$	−5.61102	−	24.5835i	−0.208101	−	0.911750i	−0.965829	−	0.259180i	$-0.916548\pi$
$727$	−5.61102	−	24.5835i	−0.208101	−	0.911750i	0.757728	−	0.652571i	$-0.226309\pi$
$728$	−8.65655	+	14.7462i	−0.320833	+	0.546531i
$729$	−6.66703	+	29.2102i	−0.246927	+	1.08186i
$730$	−22.7318	−	7.01183i	−0.841341	−	0.259519i
$731$	1.26213	−	3.21586i	0.0466817	−	0.118943i
$732$	−33.5931	+	31.1698i	−1.24164	+	1.15207i
$733$	14.1945	−	9.67767i	0.524287	−	0.357453i	−0.272072	−	0.962277i	$-0.587709\pi$
$733$	14.1945	−	9.67767i	0.524287	−	0.357453i	0.796359	+	0.604824i	$0.206757\pi$
$734$	59.8191			2.20796
$735$	12.9079	+	2.13696i	0.476115	+	0.0788229i
$736$	−45.4447			−1.67511
$737$	−23.7570	+	16.1972i	−0.875099	+	0.596633i
$738$	12.3462	−	11.4556i	0.454469	−	0.421686i
$739$	−0.621870	+	1.58450i	−0.0228759	+	0.0582867i	−0.941855	−	0.336019i	$-0.890920\pi$
$739$	−0.621870	+	1.58450i	−0.0228759	+	0.0582867i	0.918980	+	0.394305i	$0.129015\pi$
$740$	40.1984	+	12.3996i	1.47772	+	0.455817i
$741$	0.456412	−	1.99967i	0.0167667	−	0.0734598i
$742$	−2.18077	+	26.5244i	−0.0800585	+	0.973741i
$743$	−9.21096	−	40.3559i	−0.337917	−	1.48051i	−0.803391	−	0.595451i	$-0.796973\pi$
$743$	−9.21096	−	40.3559i	−0.337917	−	1.48051i	0.465474	−	0.885062i	$-0.345884\pi$
$744$	0.538669	−	7.18804i	0.0197486	−	0.263526i
$745$	−7.15622	+	2.20740i	−0.262184	+	0.0808729i
$746$	−5.42244	−	72.3574i	−0.198529	−	2.64919i
$747$	−3.70161	−	9.43156i	−0.135435	−	0.345083i
$748$	−22.9974	−	11.0750i	−0.840869	−	0.404941i
$749$	5.87700	−	14.6616i	0.214741	−	0.535725i
$750$	−36.3637	+	17.5119i	−1.32782	+	0.639443i
$751$	22.1004	+	20.5061i	0.806453	+	0.748279i	0.971254	−	0.238048i	$-0.0765074\pi$
$751$	22.1004	+	20.5061i	0.806453	+	0.748279i	−0.164800	+	0.986327i	$0.552698\pi$
$752$	2.95084	+	0.444767i	0.107606	+	0.0162190i
$753$	−16.0201	−	27.7476i	−0.583805	−	1.01118i
$754$	−12.0772	+	20.9184i	−0.439827	+	0.761802i
$755$	0.610415	−	0.765436i	0.0222153	−	0.0278571i
$756$	−67.3895	−	0.487450i	−2.45093	−	0.0177284i
$757$	−18.7847	−	23.5553i	−0.682743	−	0.856133i	0.312860	−	0.949799i	$-0.398713\pi$
$757$	−18.7847	−	23.5553i	−0.682743	−	0.856133i	−0.995604	+	0.0936661i	$0.970141\pi$
$758$	−2.28637	+	0.344616i	−0.0830449	+	0.0125170i
$759$	18.0274	+	12.2909i	0.654352	+	0.446130i
$760$	−9.07832	−	6.18949i	−0.329305	−	0.224516i
$761$	40.5065	−	6.10537i	1.46836	−	0.221320i	0.634340	−	0.773054i	$-0.281272\pi$
$761$	40.5065	−	6.10537i	1.46836	−	0.221320i	0.834020	+	0.551735i	$0.186034\pi$
$762$	27.4586	+	34.4319i	0.994719	+	1.24734i
$763$	−7.23765	+	30.6854i	−0.262020	+	1.11089i
$764$	9.98654	−	12.5227i	0.361300	−	0.453056i
$765$	1.33415	−	2.31082i	0.0482365	−	0.0835480i
$766$	0.838717	+	1.45270i	0.0303041	+	0.0524882i
$767$	−5.32049	−	0.801935i	−0.192112	−	0.0289562i
$768$	−30.7670	−	28.5476i	−1.11021	−	1.03012i
$769$	11.9113	−	5.73618i	0.429533	−	0.206852i	−0.206610	−	0.978423i	$-0.566243\pi$
$769$	11.9113	−	5.73618i	0.429533	−	0.206852i	0.636143	+	0.771571i	$0.280529\pi$
$770$	−1.11265	−	16.4424i	−0.0400972	−	0.592543i
$771$	16.2829	+	7.84145i	0.586416	+	0.282403i
$772$	6.79619	+	17.3164i	0.244600	+	0.623231i
$773$	−0.548389	−	7.31774i	−0.0197242	−	0.263201i	−0.998344	−	0.0575239i	$-0.981679\pi$
$773$	−0.548389	−	7.31774i	−0.0197242	−	0.263201i	0.978620	−	0.205677i	$-0.0659396\pi$
$774$	−2.18394	+	0.673657i	−0.0785002	+	0.0242141i
$775$	0.191530	−	2.55579i	0.00687996	−	0.0918066i
$776$	1.83379	+	8.03437i	0.0658293	+	0.288417i
$777$	−21.5864	−	20.3217i	−0.774406	−	0.729039i
$778$	−3.48631	+	15.2745i	−0.124990	+	0.547618i
$779$	−11.5474	−	3.56190i	−0.413728	−	0.127618i
$780$	3.09284	−	7.88042i	0.110741	−	0.282164i
$781$	10.2473	−	9.50807i	0.366676	−	0.340225i
$782$	−45.0706	+	30.7286i	−1.61172	+	1.09885i
$783$	−53.1606			−1.89980
$784$	−10.8763	−	51.0449i	−0.388438	−	1.82303i
$785$	8.78149			0.313425
$786$	31.7283	−	21.6320i	1.13171	−	0.771587i
$787$	5.34873	−	4.96289i	0.190662	−	0.176908i	−0.579066	−	0.815281i	$-0.696583\pi$
$787$	5.34873	−	4.96289i	0.190662	−	0.176908i	0.769727	+	0.638373i	$0.220392\pi$
$788$	−27.6145	+	70.3605i	−0.983725	+	2.50649i
$789$	38.2295	+	11.7922i	1.36101	+	0.419815i
$790$	2.07622	−	9.09652i	0.0738686	−	0.323639i
$791$	5.32606	−	0.763418i	0.189373	−	0.0271440i
$792$	2.09836	+	9.19349i	0.0745618	+	0.326677i
$793$	0.503510	−	6.71888i	0.0178802	−	0.238594i
$794$	−35.5133	+	10.9544i	−1.26032	+	0.388757i
$795$	−0.549859	−	7.33736i	−0.0195015	−	0.260229i
$796$	−5.48782	−	13.9827i	−0.194511	−	0.495605i
$797$	42.3773	+	20.4079i	1.50108	+	0.722883i	0.990573	−	0.136989i	$-0.0437424\pi$
$797$	42.3773	+	20.4079i	1.50108	+	0.722883i	0.510510	+	0.859872i	$0.329457\pi$
$798$	6.84623	+	12.0586i	0.242354	+	0.426870i
$799$	1.03767	−	0.499714i	0.0367100	−	0.0176786i
$800$	15.4953	+	14.3776i	0.547843	+	0.508324i
$801$	8.81347	+	1.32842i	0.311409	+	0.0469373i
$802$	7.96142	+	13.7896i	0.281128	+	0.486927i
$803$	7.32436	−	12.6862i	0.258471	−	0.447685i
$804$	62.2584	−	78.0695i	2.19568	−	2.75330i
$805$	−21.9343	−	10.7591i	−0.773082	−	0.379209i
$806$	1.18328	+	1.48378i	0.0416791	+	0.0522639i
$807$	15.2320	−	2.29586i	0.536193	−	0.0808181i
$808$	41.2177	+	28.1017i	1.45003	+	0.988616i
$809$	−12.3063	−	8.39031i	−0.432667	−	0.294988i	0.327334	−	0.944909i	$-0.393850\pi$
$809$	−12.3063	−	8.39031i	−0.432667	−	0.294988i	−0.760002	+	0.649921i	$0.774802\pi$
$810$	19.5299	−	2.94366i	0.686210	−	0.103430i
$811$	−24.7396	−	31.0225i	−0.868724	−	1.08935i	−0.995247	−	0.0973819i	$-0.968953\pi$
$811$	−24.7396	−	31.0225i	−0.868724	−	1.08935i	0.126523	−	0.991964i	$-0.459618\pi$
$812$	−24.4071	−	110.617i	−0.856521	−	3.88188i
$813$	6.16361	−	7.72892i	0.216167	−	0.271065i
$814$	−18.6716	+	32.3401i	−0.654438	+	1.13352i
$815$	−8.37892	−	14.5127i	−0.293501	−	0.508358i
$816$	31.8575	+	4.80174i	1.11523	+	0.168095i
$817$	1.20208	+	1.11537i	0.0420555	+	0.0390218i
$818$	0.561605	−	0.270455i	0.0196360	−	0.00945622i
$819$	1.45458	−	1.33020i	0.0508270	−	0.0464810i
$820$	−44.9368	−	21.6404i	−1.56926	−	0.755716i
$821$	−15.5015	−	39.4972i	−0.541006	−	1.37846i	−0.896193	−	0.443665i	$-0.853678\pi$
$821$	−15.5015	−	39.4972i	−0.541006	−	1.37846i	0.355187	−	0.934795i	$-0.384417\pi$
$822$	−6.12900	−	81.7859i	−0.213774	−	2.85261i
$823$	−10.8353	+	3.34224i	−0.377694	+	0.116503i	−0.477789	−	0.878475i	$-0.658562\pi$
$823$	−10.8353	+	3.34224i	−0.377694	+	0.116503i	0.100095	+	0.994978i	$0.468085\pi$
$824$	−5.94825	+	79.3739i	−0.207217	+	2.76512i
$825$	−2.25829	−	9.89423i	−0.0786237	−	0.344473i
$826$	30.2024	−	20.2732i	1.05088	−	0.705396i
$827$	−8.22592	+	36.0401i	−0.286043	+	1.25324i	0.603861	+	0.797090i	$0.293628\pi$
$827$	−8.22592	+	36.0401i	−0.286043	+	1.25324i	−0.889904	+	0.456148i	$0.849229\pi$
$828$	23.9214	+	7.37878i	0.831327	+	0.256430i
$829$	13.1424	−	33.4864i	0.456456	−	1.16303i	−0.498660	−	0.866797i	$-0.666174\pi$
$829$	13.1424	−	33.4864i	0.456456	−	1.16303i	0.955116	−	0.296232i	$-0.0957303\pi$
$830$	−31.7072	+	29.4200i	−1.10057	+	1.02118i
$831$	−11.0183	+	7.51218i	−0.382222	+	0.260595i
$832$	−0.740761			−0.0256813
$833$	−14.5659	−	13.9127i	−0.504680	−	0.482047i
$834$	55.0415			1.90593
$835$	21.0398	−	14.3447i	0.728113	−	0.496419i
$836$	8.88171	−	8.24103i	0.307180	−	0.285022i
$837$	−1.52597	+	3.88812i	−0.0527454	+	0.134393i
$838$	84.8668	+	26.1779i	2.93167	+	0.904302i
$839$	−5.77872	+	25.3182i	−0.199503	+	0.874082i	0.771730	+	0.635951i	$0.219392\pi$
$839$	−5.77872	+	25.3182i	−0.199503	+	0.874082i	−0.971233	+	0.238131i	$0.923465\pi$
$840$	11.4608	+	29.8345i	0.395437	+	1.02939i
$841$	−13.4307	−	58.8438i	−0.463128	−	2.02910i
$842$	5.06927	−	67.6447i	0.174699	−	2.33119i
$843$	1.60991	−	0.496591i	0.0554482	−	0.0171035i
$844$	4.19701	+	56.0052i	0.144467	+	1.92778i
$845$	0.454731	+	1.15864i	0.0156432	+	0.0398583i
$846$	−0.686482	−	0.330592i	−0.0236017	−	0.0113660i
$847$	−18.7225	−	2.96061i	−0.643311	−	0.101728i
$848$	−26.4443	+	12.7349i	−0.908101	+	0.437318i
$849$	−3.70792	−	3.44044i	−0.127255	−	0.118076i
$850$	25.0895	+	3.78164i	0.860564	+	0.129709i
$851$	27.6798	+	47.9429i	0.948853	+	1.64346i
$852$	−24.2731	+	42.0423i	−0.831584	+	1.44035i
$853$	−27.8836	+	34.9650i	−0.954718	+	1.19718i	0.0255840	+	0.999673i	$0.491855\pi$
$853$	−27.8836	+	34.9650i	−0.954718	+	1.19718i	−0.980302	+	0.197506i	$0.936716\pi$
$854$	28.1420	+	35.8174i	0.963001	+	1.22565i
$855$	0.789693	+	0.990244i	0.0270069	+	0.0338656i
$856$	38.1540	−	5.75080i	1.30408	−	0.196558i
$857$	−9.83162	−	6.70308i	−0.335842	−	0.228973i	0.383643	−	0.923482i	$-0.374669\pi$
$857$	−9.83162	−	6.70308i	−0.335842	−	0.228973i	−0.719484	+	0.694509i	$0.755622\pi$
$858$	6.20912	+	4.23331i	0.211976	+	0.144523i
$859$	20.5960	−	3.10435i	0.702728	−	0.105919i	0.212048	−	0.977259i	$-0.431987\pi$
$859$	20.5960	−	3.10435i	0.702728	−	0.105919i	0.490680	+	0.871340i	$0.336749\pi$
$860$	4.21989	+	5.29157i	0.143897	+	0.180441i
$861$	21.7165	+	27.6393i	0.740095	+	0.941947i
$862$	51.7286	−	64.8656i	1.76188	−	2.20933i
$863$	19.2365	−	33.3186i	0.654819	−	1.13418i	−0.327121	−	0.944983i	$-0.606078\pi$
$863$	19.2365	−	33.3186i	0.654819	−	1.13418i	0.981939	−	0.189197i	$-0.0605883\pi$
$864$	−17.2244	−	29.8335i	−0.585986	−	1.01496i
$865$	−14.5507	−	2.19317i	−0.494739	−	0.0745699i
$866$	−61.1557	−	56.7442i	−2.07816	−	1.92825i
$867$	−11.7975	+	5.68136i	−0.400663	+	0.192949i
$868$	−8.79101	−	1.39014i	−0.298386	−	0.0471843i
$869$	5.17657	+	2.49291i	0.175603	+	0.0845661i
$870$	16.4940	+	42.0259i	0.559197	+	1.42481i
$871$	1.09714	+	14.6403i	0.0371751	+	0.496068i
$872$	−73.5924	+	22.7002i	−2.49215	+	0.768727i
$873$	0.0709911	−	0.947310i	0.00240268	−	0.0320616i
$874$	−5.76172	−	25.2437i	−0.194893	−	0.853882i
$875$	9.97954	+	25.9784i	0.337370	+	0.878231i
$876$	−11.3202	+	49.5970i	−0.382474	+	1.67573i
$877$	−37.2609	−	11.4935i	−1.25821	−	0.388107i	−0.407242	−	0.913320i	$-0.633509\pi$
$877$	−37.2609	−	11.4935i	−1.25821	−	0.388107i	−0.850971	+	0.525213i	$0.823985\pi$
$878$	36.3414	−	92.5964i	1.22646	−	3.12498i
$879$	−22.8618	+	21.2126i	−0.771109	+	0.715485i
$880$	15.0168	−	10.2383i	0.506216	−	0.345132i
$881$	3.87059			0.130404			0.0652018	−	0.997872i	$-0.479231\pi$
$881$	3.87059			0.130404			0.0652018	+	0.997872i	$0.479231\pi$
$882$	−1.18795	+	13.2726i	−0.0400005	+	0.446913i
$883$	−24.4117			−0.821519			−0.410760	−	0.911744i	$-0.634736\pi$
$883$	−24.4117			−0.821519			−0.410760	+	0.911744i	$0.634736\pi$
$884$	−10.7685	+	7.34184i	−0.362184	+	0.246933i
$885$	−7.37214	+	6.84035i	−0.247812	+	0.229936i
$886$	14.0965	−	35.9174i	0.473582	−	1.20667i
$887$	12.1942	+	3.76140i	0.409440	+	0.126295i	0.492631	−	0.870238i	$-0.336035\pi$
$887$	12.1942	+	3.76140i	0.409440	+	0.126295i	−0.0831916	+	0.996534i	$0.526511\pi$
$888$	16.1151	−	70.6048i	0.540787	−	2.36934i
$889$	25.2129	−	16.9240i	0.845613	−	0.567613i
$890$	−8.46693	−	37.0960i	−0.283812	−	1.24346i
$891$	−0.908873	+	12.1281i	−0.0304484	+	0.406305i
$892$	−115.134	+	35.5141i	−3.85496	+	1.18910i
$893$	0.0408542	+	0.545161i	0.00136713	+	0.0182431i
$894$	8.43466	+	21.4912i	0.282097	+	0.718772i
$895$	6.19321	+	2.98249i	0.207016	+	0.0996938i
$896$	−20.2241	+	18.4948i	−0.675640	+	0.617868i
$897$	10.0373	−	4.83371i	0.335136	−	0.161393i
$898$	−30.3266	−	28.1389i	−1.01201	−	0.939008i
$899$	−6.94241	−	1.04640i	−0.231542	−	0.0348994i
$900$	−5.82205	−	10.0841i	−0.194068	−	0.336136i
$901$	−5.66392	+	9.81020i	−0.188693	+	0.326825i
$902$	27.6050	−	34.6156i	0.919145	−	1.15257i
$903$	−1.02773	−	4.65785i	−0.0342009	−	0.155003i
$904$	8.19469	+	10.2758i	0.272551	+	0.341769i
$905$	12.4634	−	1.87856i	0.414298	−	0.0624453i
$906$	−2.49373	−	1.70020i	−0.0828488	−	0.0564853i
$907$	1.72514	+	1.17618i	0.0572823	+	0.0390544i	0.591623	−	0.806215i	$-0.298488\pi$
$907$	1.72514	+	1.17618i	0.0572823	+	0.0390544i	−0.534340	+	0.845269i	$0.679440\pi$
$908$	13.2922	−	2.00348i	0.441118	−	0.0664879i
$909$	−3.58539	−	4.49594i	−0.118920	−	0.149121i
$910$	−7.55477	−	3.70574i	−0.250438	−	0.122844i
$911$	0.0998111	−	0.125159i	0.00330689	−	0.00414671i	−0.780175	−	0.625561i	$-0.784870\pi$
$911$	0.0998111	−	0.125159i	0.00330689	−	0.00414671i	0.783482	+	0.621414i	$0.213442\pi$
$912$	−7.64632	+	13.2438i	−0.253195	+	0.438546i
$913$	−13.3175	−	23.0666i	−0.440745	−	0.763393i
$914$	−12.4327	−	1.87392i	−0.411236	−	0.0619839i
$915$	−9.23160	−	8.56567i	−0.305187	−	0.283172i
$916$	71.8971	−	34.6238i	2.37555	−	1.14400i
$917$	−13.0728	−	23.0257i	−0.431701	−	0.760377i
$918$	−37.2553	−	17.9412i	−1.22961	−	0.592148i
$919$	6.57683	+	16.7575i	0.216950	+	0.552779i	0.997370	−	0.0724763i	$-0.0230902\pi$
$919$	6.57683	+	16.7575i	0.216950	+	0.552779i	−0.780420	+	0.625255i	$0.784995\pi$
$920$	−4.45981	−	59.5121i	−0.147036	−	1.96205i
$921$	6.47839	−	1.99832i	0.213470	−	0.0658468i
$922$	1.37340	−	18.3267i	0.0452305	−	0.603559i
$923$	−1.58827	−	6.95867i	−0.0522786	−	0.229048i
$924$	−34.8862	+	5.00046i	−1.14767	+	0.164503i
$925$	5.72990	−	25.1043i	0.188398	−	0.825425i
$926$	1.17582	+	0.362693i	0.0386399	+	0.0119188i
$927$	3.35214	−	8.54110i	0.110099	−	0.280527i
$928$	42.4471	−	39.3851i	1.39339	−	1.29288i
$929$	−17.9954	+	12.2690i	−0.590409	+	0.402534i	−0.821342	−	0.570436i	$-0.806774\pi$
$929$	−17.9954	+	12.2690i	−0.590409	+	0.402534i	0.230934	+	0.972970i	$0.425822\pi$
$930$	3.54720			0.116317
$931$	8.67344	−	4.02339i	0.284260	−	0.131861i
$932$	−47.1415			−1.54417
$933$	−33.3551	+	22.7411i	−1.09200	+	0.744511i
$934$	−12.1563	+	11.2794i	−0.397766	+	0.369073i
$935$	2.56268	−	6.52961i	0.0838087	−	0.213541i
$936$	4.60100	+	1.41922i	0.150389	+	0.0463887i
$937$	−11.3210	+	49.6007i	−0.369842	+	1.62039i	0.357363	+	0.933966i	$0.383676\pi$
$937$	−11.3210	+	49.6007i	−0.369842	+	1.62039i	−0.727205	+	0.686420i	$0.759181\pi$
$938$	−72.2681	−	68.0344i	−2.35964	−	2.22140i
$939$	−6.67885	−	29.2620i	−0.217956	−	0.954928i
$940$	−0.168620	+	2.25008i	−0.00549977	+	0.0733894i
$941$	−1.60606	+	0.495405i	−0.0523562	+	0.0161497i	−0.320823	−	0.947139i	$-0.603959\pi$
$941$	−1.60606	+	0.495405i	−0.0523562	+	0.0161497i	0.268466	+	0.963289i	$0.413483\pi$
$942$	−2.02308	−	26.9961i	−0.0659154	−	0.879581i
$943$	−23.9795	−	61.0987i	−0.780879	−	1.98965i
$944$	36.1439	+	17.4060i	1.17638	+	0.566517i
$945$	−1.25035	−	18.4773i	−0.0406740	−	0.601067i
$946$	−5.41312	+	2.60682i	−0.175996	+	0.0847551i
$947$	35.6540	+	33.0821i	1.15860	+	1.07502i	0.996092	+	0.0883164i	$0.0281487\pi$
$947$	35.6540	+	33.0821i	1.15860	+	1.07502i	0.162508	+	0.986707i	$0.448042\pi$
$948$	−19.7305	−	2.97389i	−0.640816	−	0.0965875i
$949$	−3.73982	−	6.47756i	−0.121400	−	0.210270i
$950$	−6.02190	+	10.4302i	−0.195376	+	0.338402i
$951$	−30.6802	+	38.4718i	−0.994875	+	1.24753i
$952$	11.2956	−	47.8898i	0.366092	−	1.55212i
$953$	13.4043	+	16.8085i	0.434209	+	0.544481i	0.950007	−	0.312230i	$-0.101076\pi$
$953$	13.4043	+	16.8085i	0.434209	+	0.544481i	−0.515798	+	0.856710i	$0.672504\pi$
$954$	7.41037	−	1.11693i	0.239920	−	0.0361621i
$955$	3.63679	+	2.47952i	0.117684	+	0.0802355i
$956$	48.0011	+	32.7266i	1.55247	+	1.05845i
$957$	−27.4902	+	4.14349i	−0.888633	+	0.133940i
$958$	−27.1058	−	33.9896i	−0.875749	−	1.09816i
$959$	−56.5492	−	0.409038i	−1.82607	−	0.0132085i
$960$	−0.863250	+	1.08248i	−0.0278613	+	0.0349370i
$961$	15.2242	−	26.3691i	0.491103	−	0.850615i
$962$	9.53370	+	16.5129i	0.307379	+	0.532396i
$963$	−4.39815	−	0.662914i	−0.141728	−	0.0213621i
$964$	40.8276	+	37.8825i	1.31497	+	1.22011i
$965$	−4.60579	+	2.21803i	−0.148266	+	0.0714009i
$966$	−28.0226	+	69.9092i	−0.901611	+	2.24929i
$967$	−21.7636	−	10.4808i	−0.699872	−	0.337040i	0.0498841	−	0.998755i	$-0.484115\pi$
$967$	−21.7636	−	10.4808i	−0.699872	−	0.337040i	−0.749756	+	0.661715i	$0.769829\pi$
$968$	−16.9163	−	43.1020i	−0.543710	−	1.38535i
$969$	0.441065	+	5.88560i	0.0141690	+	0.189073i
$970$	−3.87527	+	1.19536i	−0.124427	+	0.0383808i
$971$	−3.08004	+	41.1002i	−0.0988431	+	1.31897i	0.698573	+	0.715539i	$0.253819\pi$
$971$	−3.08004	+	41.1002i	−0.0988431	+	1.31897i	−0.797416	+	0.603430i	$0.793800\pi$
$972$	7.60526	+	33.3208i	0.243939	+	1.06877i
$973$	3.10982	−	37.8243i	0.0996962	−	1.21259i
$974$	15.4699	−	67.7782i	0.495688	−	2.17175i
$975$	−4.95170	−	1.52740i	−0.158581	−	0.0489158i
$976$	−18.3530	+	46.7627i	−0.587465	+	1.49684i
$977$	19.9470	−	18.5081i	0.638161	−	0.592127i	−0.293277	−	0.956028i	$-0.594746\pi$
$977$	19.9470	−	18.5081i	0.638161	−	0.592127i	0.931438	+	0.363901i	$0.118555\pi$
$978$	−42.6848	+	29.1020i	−1.36491	+	0.930579i
$979$	23.4307			0.748848
$980$	37.8735	−	11.0850i	1.20983	−	0.354099i
$981$	8.87765			0.283442
$982$	−42.4422	+	28.9366i	−1.35438	+	0.923403i
$983$	−26.7112	+	24.7844i	−0.851956	+	0.790500i	−0.979523	−	0.201330i	$-0.935474\pi$
$983$	−26.7112	+	24.7844i	−0.851956	+	0.790500i	0.127567	+	0.991830i	$0.459283\pi$
$984$	−31.3695	+	79.9281i	−1.00002	+	2.54802i
$985$	−19.8486	−	6.12247i	−0.632428	−	0.195078i
$986$	15.4664	−	67.7626i	0.492550	−	2.15800i
$987$	0.805036	−	1.37136i	0.0256246	−	0.0436508i
$988$	−1.37662	−	6.03136i	−0.0437961	−	0.191883i
$989$	−0.665604	+	8.88187i	−0.0211650	+	0.282427i
$990$	−4.43436	+	1.36782i	−0.140933	+	0.0434722i
$991$	1.84775	+	24.6565i	0.0586957	+	0.783240i	0.946435	+	0.322894i	$0.104656\pi$
$991$	1.84775	+	24.6565i	0.0586957	+	0.783240i	−0.887740	+	0.460346i	$0.847725\pi$
$992$	−1.66215	−	4.23510i	−0.0527734	−	0.134464i
$993$	−9.99302	−	4.81239i	−0.317119	−	0.152716i
$994$	39.6719	+	27.4703i	1.25832	+	0.871304i
$995$	3.71910	−	1.79103i	0.117904	−	0.0567794i
$996$	67.8064	+	62.9151i	2.14853	+	1.99354i
$997$	−32.1156	−	4.84065i	−1.01711	−	0.153305i	−0.380735	−	0.924684i	$-0.624329\pi$
$997$	−32.1156	−	4.84065i	−1.01711	−	0.153305i	−0.636376	+	0.771379i	$0.719567\pi$
$998$	−21.4664	−	37.1810i	−0.679509	−	1.17694i
$999$	−20.9823	+	36.3425i	−0.663852	+	1.14983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.625.26	yes	324
49.4	even	21	inner	637.2.bl.a.53.26	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.26	✓	324	49.4	even	21	inner
637.2.bl.a.625.26	yes	324	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11124 - 1.43942i) q^{2} +(1.10080 - 1.02139i) q^{3} +(1.65473 - 4.21619i) q^{4} +(1.18938 + 0.366875i) q^{5} +(0.853840 - 3.74092i) q^{6} +(-2.52250 - 0.798115i) q^{7} +(-1.43814 - 6.30090i) q^{8} +(-0.0556743 + 0.742922i) q^{9} +O(q^{10})\)	\(q+(2.11124 - 1.43942i) q^{2} +(1.10080 - 1.02139i) q^{3} +(1.65473 - 4.21619i) q^{4} +(1.18938 + 0.366875i) q^{5} +(0.853840 - 3.74092i) q^{6} +(-2.52250 - 0.798115i) q^{7} +(-1.43814 - 6.30090i) q^{8} +(-0.0556743 + 0.742922i) q^{9} +(3.03916 - 0.937455i) q^{10} +(0.146357 + 1.95300i) q^{11} +(-2.48485 - 6.33130i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-6.47444 + 1.94593i) q^{14} +(1.68399 - 0.810966i) q^{15} +(-5.46551 - 5.07125i) q^{16} +(-2.84540 - 0.428874i) q^{17} +(0.951835 + 1.64863i) q^{18} +(0.682942 - 1.18289i) q^{19} +(3.51492 - 4.40757i) q^{20} +(-3.59195 + 1.69790i) q^{21} +(3.12019 + 3.91260i) q^{22} +(7.33596 - 1.10572i) q^{23} +(-8.01878 - 5.46711i) q^{24} +(-2.85117 - 1.94389i) q^{25} +(2.52671 - 0.380840i) q^{26} +(3.50634 + 4.39682i) q^{27} +(-7.53907 + 9.31467i) q^{28} +(-5.89378 + 7.39056i) q^{29} +(2.38799 - 4.13611i) q^{30} +(0.371359 + 0.643212i) q^{31} +(-6.05718 - 0.912973i) q^{32} +(2.15589 + 2.00037i) q^{33} +(-6.62465 + 3.19026i) q^{34} +(-2.70740 - 1.87470i) q^{35} +(3.04017 + 1.46407i) q^{36} +(2.72620 + 6.94624i) q^{37} +(-0.260821 - 3.48041i) q^{38} +(1.43495 - 0.442623i) q^{39} +(0.601149 - 8.02177i) q^{40} +(-1.96869 - 8.62539i) q^{41} +(-5.13949 + 8.75500i) q^{42} +(-0.267151 + 1.17046i) q^{43} +(8.47642 + 2.61463i) q^{44} +(-0.338777 + 0.863190i) q^{45} +(13.8964 - 12.8940i) q^{46} +(-0.330699 + 0.225467i) q^{47} -11.1961 q^{48} +(5.72602 + 4.02649i) q^{49} -8.81759 q^{50} +(-3.57025 + 2.43416i) q^{51} +(3.32020 - 3.08069i) q^{52} +(1.43822 - 3.66452i) q^{53} +(13.7316 + 4.23564i) q^{54} +(-0.542434 + 2.37656i) q^{55} +(-1.40114 + 17.0418i) q^{56} +(-0.456412 - 1.99967i) q^{57} +(-1.80506 + 24.0869i) q^{58} +(-5.14154 + 1.58596i) q^{59} +(-0.632636 - 8.44194i) q^{60} +(-2.46157 - 6.27197i) q^{61} +(1.70988 + 0.823436i) q^{62} +(0.733375 - 1.82959i) q^{63} +(-0.667403 + 0.321404i) q^{64} +(0.912412 + 0.846595i) q^{65} +(7.43099 + 1.12004i) q^{66} +(7.34068 + 12.7144i) q^{67} +(-6.51658 + 11.2871i) q^{68} +(6.94604 - 8.71005i) q^{69} +(-8.41447 - 0.0608646i) q^{70} +(-4.45024 - 5.58042i) q^{71} +(4.76114 - 0.717626i) q^{72} +(-6.17997 - 4.21343i) q^{73} +(15.7542 + 10.7410i) q^{74} +(-5.12404 + 0.772324i) q^{75} +(-3.85720 - 4.83678i) q^{76} +(1.18954 - 5.04326i) q^{77} +(2.39241 - 2.99998i) q^{78} +(1.46684 - 2.54065i) q^{79} +(-4.64005 - 8.03680i) q^{80} +(6.14059 + 0.925546i) q^{81} +(-16.5719 - 15.3765i) q^{82} +(-12.2530 + 5.90075i) q^{83} +(1.21493 + 17.9539i) q^{84} +(-3.22691 - 1.55400i) q^{85} +(1.12077 + 2.85568i) q^{86} +(1.06080 + 14.1554i) q^{87} +(12.0952 - 3.73087i) q^{88} +(0.894049 - 11.9303i) q^{89} +(0.527253 + 2.31005i) q^{90} +(-1.92641 - 1.81355i) q^{91} +(7.47713 - 32.7595i) q^{92} +(1.06576 + 0.328744i) q^{93} +(-0.373644 + 0.952031i) q^{94} +(1.24625 - 1.15635i) q^{95} +(-7.60024 + 5.18175i) q^{96} -1.27511 q^{97} +(17.8848 + 0.258747i) q^{98} -1.45908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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