LMFDB - Embedded newform 378.2.w.b.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.10671 - 1.33237i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.28151 - 0.830401i) q^{5} +(0.584268 - 1.63053i) q^{6} +(-2.63284 - 0.261069i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.550401 - 2.94908i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.10671 - 1.33237i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.28151 - 0.830401i) q^{5} +(0.584268 - 1.63053i) q^{6} +(-2.63284 - 0.261069i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.550401 - 2.94908i) q^{9} -2.42793 q^{10} +(0.465805 - 0.169539i) q^{11} +(-0.00864229 - 1.73203i) q^{12} +(-0.788435 - 4.47144i) q^{13} +(-2.56335 + 0.655160i) q^{14} +(-3.63136 + 2.12079i) q^{15} +(0.173648 - 0.984808i) q^{16} +6.29535 q^{17} +(-1.52585 - 2.58298i) q^{18} +5.58294 q^{19} +(-2.28151 + 0.830401i) q^{20} +(-3.26162 + 3.21898i) q^{21} +(0.379728 - 0.318629i) q^{22} +(1.20957 + 6.85980i) q^{23} +(-0.600510 - 1.62462i) q^{24} +(0.685485 + 0.575191i) q^{25} +(-2.27021 - 3.93211i) q^{26} +(-4.53838 - 2.53043i) q^{27} +(-2.18468 + 1.49237i) q^{28} +(-1.02033 + 5.78655i) q^{29} +(-2.68700 + 3.23489i) q^{30} +(3.86184 - 3.24047i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.289621 - 0.808253i) q^{33} +(5.91569 - 2.15314i) q^{34} +(5.79005 + 2.78194i) q^{35} +(-2.31726 - 1.90533i) q^{36} +(-1.47008 + 2.54625i) q^{37} +(5.24625 - 1.90948i) q^{38} +(-6.83016 - 3.89808i) q^{39} +(-1.85990 + 1.56064i) q^{40} +(1.60186 + 9.08461i) q^{41} +(-1.96396 + 4.14039i) q^{42} +(4.29683 + 3.60547i) q^{43} +(0.247850 - 0.429288i) q^{44} +(-1.19317 + 7.18539i) q^{45} +(3.48281 + 6.03241i) q^{46} +(-5.52147 - 4.63307i) q^{47} +(-1.11995 - 1.32126i) q^{48} +(6.86369 + 1.37471i) q^{49} +(0.840872 + 0.306053i) q^{50} +(6.96711 - 8.38771i) q^{51} +(-3.47816 - 2.91852i) q^{52} +(2.07398 - 3.59225i) q^{53} +(-5.13014 - 0.825605i) q^{54} -1.20352 q^{55} +(-1.54251 + 2.14957i) q^{56} +(6.17868 - 7.43853i) q^{57} +(1.02033 + 5.78655i) q^{58} +(-1.15079 - 6.52646i) q^{59} +(-1.41856 + 3.95881i) q^{60} +(-9.76866 - 8.19688i) q^{61} +(2.52064 - 4.36588i) q^{62} +(0.679205 + 7.90814i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.91426 + 10.8563i) q^{65} +(-0.00428398 - 0.858566i) q^{66} +(-6.63243 - 2.41401i) q^{67} +(4.82252 - 4.04657i) q^{68} +(10.4784 + 5.98020i) q^{69} +(6.39235 + 0.633857i) q^{70} +(3.13190 + 5.42461i) q^{71} +(-2.82918 - 0.997877i) q^{72} +(-1.56466 - 2.71007i) q^{73} +(-0.510554 + 2.89549i) q^{74} +(1.52500 - 0.276751i) q^{75} +(4.27678 - 3.58865i) q^{76} +(-1.27065 + 0.324762i) q^{77} +(-7.75147 - 1.32695i) q^{78} +(12.5910 - 4.58276i) q^{79} +(-1.21396 + 2.10265i) q^{80} +(-8.39412 + 3.24635i) q^{81} +(4.61238 + 7.98887i) q^{82} +(1.50763 - 8.55021i) q^{83} +(-0.429425 + 4.56241i) q^{84} +(-14.3629 - 5.22766i) q^{85} +(5.27084 + 1.91843i) q^{86} +(6.58061 + 7.76347i) q^{87} +(0.0860773 - 0.488169i) q^{88} +0.576882 q^{89} +(1.33633 + 7.16015i) q^{90} +(0.908469 + 11.9784i) q^{91} +(5.33598 + 4.47742i) q^{92} +(-0.0435682 - 8.73164i) q^{93} +(-6.77309 - 2.46520i) q^{94} +(-12.7375 - 4.63608i) q^{95} +(-1.50430 - 0.858530i) q^{96} +(-0.578333 - 0.485279i) q^{97} +(6.91993 - 1.05572i) q^{98} +(-0.756364 - 1.28038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.10671	−	1.33237i	0.638957	−	0.769242i
$3$	1.10671	−	1.33237i	0.638957	−	0.769242i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−2.28151	−	0.830401i	−1.02032	−	0.371366i	−0.222933	−	0.974834i	$-0.571563\pi$
$5$	−2.28151	−	0.830401i	−1.02032	−	0.371366i	−0.797388	+	0.603467i	$0.793785\pi$
$6$	0.584268	−	1.63053i	0.238526	−	0.665661i
$7$	−2.63284	−	0.261069i	−0.995120	−	0.0986748i
$7$	−2.63284	−	0.261069i	−0.995120	−	0.0986748i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.550401	−	2.94908i	−0.183467	−	0.983026i
$10$	−2.42793			−0.767778
$11$	0.465805	−	0.169539i	0.140446	−	0.0511180i	−0.270841	−	0.962624i	$-0.587302\pi$
$11$	0.465805	−	0.169539i	0.140446	−	0.0511180i	0.411287	+	0.911506i	$0.365080\pi$
$12$	−0.00864229	−	1.73203i	−0.00249481	−	0.499994i
$13$	−0.788435	−	4.47144i	−0.218672	−	1.24015i	−0.874419	−	0.485172i	$-0.838757\pi$
$13$	−0.788435	−	4.47144i	−0.218672	−	1.24015i	0.655746	−	0.754981i	$-0.272354\pi$
$14$	−2.56335	+	0.655160i	−0.685084	+	0.175099i
$15$	−3.63136	+	2.12079i	−0.937612	+	0.547587i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	6.29535			1.52685			0.763423	−	0.645898i	$-0.223517\pi$
$17$	6.29535			1.52685			0.763423	+	0.645898i	$0.223517\pi$
$18$	−1.52585	−	2.58298i	−0.359647	−	0.608814i
$19$	5.58294			1.28081			0.640407	−	0.768035i	$-0.278766\pi$
$19$	5.58294			1.28081			0.640407	+	0.768035i	$0.278766\pi$
$20$	−2.28151	+	0.830401i	−0.510160	+	0.185683i
$21$	−3.26162	+	3.21898i	−0.711744	+	0.702439i
$22$	0.379728	−	0.318629i	0.0809582	−	0.0679320i
$23$	1.20957	+	6.85980i	0.252212	+	1.43037i	0.803128	+	0.595806i	$0.203167\pi$
$23$	1.20957	+	6.85980i	0.252212	+	1.43037i	−0.550916	+	0.834561i	$0.685722\pi$
$24$	−0.600510	−	1.62462i	−0.122579	−	0.331624i
$25$	0.685485	+	0.575191i	0.137097	+	0.115038i
$26$	−2.27021	−	3.93211i	−0.445224	−	0.771151i
$27$	−4.53838	−	2.53043i	−0.873413	−	0.486981i
$28$	−2.18468	+	1.49237i	−0.412866	+	0.282031i
$29$	−1.02033	+	5.78655i	−0.189470	+	1.07454i	0.730607	+	0.682798i	$0.239237\pi$
$29$	−1.02033	+	5.78655i	−0.189470	+	1.07454i	−0.920077	+	0.391738i	$0.871874\pi$
$30$	−2.68700	+	3.23489i	−0.490578	+	0.590608i
$31$	3.86184	−	3.24047i	0.693608	−	0.582006i	−0.226339	−	0.974048i	$-0.572676\pi$
$31$	3.86184	−	3.24047i	0.693608	−	0.582006i	0.919947	+	0.392043i	$0.128231\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.289621	−	0.808253i	0.0504166	−	0.140699i
$34$	5.91569	−	2.15314i	1.01453	−	0.369260i
$35$	5.79005	+	2.78194i	0.978697	+	0.470234i
$36$	−2.31726	−	1.90533i	−0.386210	−	0.317556i
$37$	−1.47008	+	2.54625i	−0.241680	+	0.418602i	−0.961193	−	0.275877i	$-0.911032\pi$
$37$	−1.47008	+	2.54625i	−0.241680	+	0.418602i	0.719513	+	0.694479i	$0.244365\pi$
$38$	5.24625	−	1.90948i	0.851054	−	0.309758i
$39$	−6.83016	−	3.89808i	−1.09370	−	0.624193i
$40$	−1.85990	+	1.56064i	−0.294076	+	0.246759i
$41$	1.60186	+	9.08461i	0.250169	+	1.41878i	0.808176	+	0.588941i	$0.200455\pi$
$41$	1.60186	+	9.08461i	0.250169	+	1.41878i	−0.558007	+	0.829836i	$0.688434\pi$
$42$	−1.96396	+	4.14039i	−0.303046	+	0.638876i
$43$	4.29683	+	3.60547i	0.655261	+	0.549829i	0.908662	−	0.417532i	$-0.137105\pi$
$43$	4.29683	+	3.60547i	0.655261	+	0.549829i	−0.253401	+	0.967361i	$0.581549\pi$
$44$	0.247850	−	0.429288i	0.0373648	−	0.0647177i
$45$	−1.19317	+	7.18539i	−0.177868	+	1.07114i
$46$	3.48281	+	6.03241i	0.513512	+	0.889430i
$47$	−5.52147	−	4.63307i	−0.805390	−	0.675802i	0.144113	−	0.989561i	$-0.453967\pi$
$47$	−5.52147	−	4.63307i	−0.805390	−	0.675802i	−0.949503	+	0.313759i	$0.898412\pi$
$48$	−1.11995	−	1.32126i	−0.161650	−	0.190707i
$49$	6.86369	+	1.37471i	0.980527	+	0.196386i
$50$	0.840872	+	0.306053i	0.118917	+	0.0432824i
$51$	6.96711	−	8.38771i	0.975590	−	1.17451i
$52$	−3.47816	−	2.91852i	−0.482334	−	0.404726i
$53$	2.07398	−	3.59225i	0.284884	−	0.493433i	−0.687697	−	0.725998i	$-0.741378\pi$
$53$	2.07398	−	3.59225i	0.284884	−	0.493433i	0.972581	+	0.232565i	$0.0747117\pi$
$54$	−5.13014	−	0.825605i	−0.698124	−	0.112351i
$55$	−1.20352			−0.162283
$56$	−1.54251	+	2.14957i	−0.206127	+	0.287249i
$57$	6.17868	−	7.43853i	0.818386	−	0.985257i
$58$	1.02033	+	5.78655i	0.133975	+	0.759812i
$59$	−1.15079	−	6.52646i	−0.149820	−	0.849673i	−0.963370	−	0.268177i	$-0.913579\pi$
$59$	−1.15079	−	6.52646i	−0.149820	−	0.849673i	0.813549	−	0.581496i	$-0.197532\pi$
$60$	−1.41856	+	3.95881i	−0.183135	+	0.511081i
$61$	−9.76866	−	8.19688i	−1.25075	−	1.04950i	−0.996605	−	0.0823370i	$-0.973762\pi$
$61$	−9.76866	−	8.19688i	−1.25075	−	1.04950i	−0.254145	−	0.967166i	$-0.581794\pi$
$62$	2.52064	−	4.36588i	0.320122	−	0.554467i
$63$	0.679205	+	7.90814i	0.0855718	+	0.996332i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.91426	+	10.8563i	−0.237435	+	1.34656i
$66$	−0.00428398	−	0.858566i	−0.000527321	−	0.105682i
$67$	−6.63243	−	2.41401i	−0.810280	−	0.294918i	−0.0965407	−	0.995329i	$-0.530778\pi$
$67$	−6.63243	−	2.41401i	−0.810280	−	0.294918i	−0.713740	+	0.700411i	$0.753000\pi$
$68$	4.82252	−	4.04657i	0.584816	−	0.490719i
$69$	10.4784	+	5.98020i	1.26145	+	0.719931i
$70$	6.39235	+	0.633857i	0.764032	+	0.0757604i
$71$	3.13190	+	5.42461i	0.371688	+	0.643783i	0.989825	−	0.142287i	$-0.0454457\pi$
$71$	3.13190	+	5.42461i	0.371688	+	0.643783i	−0.618137	+	0.786070i	$0.712112\pi$
$72$	−2.82918	−	0.997877i	−0.333422	−	0.117601i
$73$	−1.56466	−	2.71007i	−0.183130	−	0.317190i	0.759815	−	0.650139i	$-0.225290\pi$
$73$	−1.56466	−	2.71007i	−0.183130	−	0.317190i	−0.942945	+	0.332949i	$0.891956\pi$
$74$	−0.510554	+	2.89549i	−0.0593506	+	0.336594i
$75$	1.52500	−	0.276751i	0.176091	−	0.0319564i
$76$	4.27678	−	3.58865i	0.490581	−	0.411646i
$77$	−1.27065	+	0.324762i	−0.144804	+	0.0370101i
$78$	−7.75147	−	1.32695i	−0.877681	−	0.150247i
$79$	12.5910	−	4.58276i	1.41660	−	0.515601i	0.483542	−	0.875321i	$-0.339350\pi$
$79$	12.5910	−	4.58276i	1.41660	−	0.515601i	0.933060	+	0.359720i	$0.117128\pi$
$80$	−1.21396	+	2.10265i	−0.135725	+	0.235083i
$81$	−8.39412	+	3.24635i	−0.932680	+	0.360706i
$82$	4.61238	+	7.98887i	0.509352	+	0.882223i
$83$	1.50763	−	8.55021i	0.165484	−	0.938507i	−0.783080	−	0.621921i	$-0.786352\pi$
$83$	1.50763	−	8.55021i	0.165484	−	0.938507i	0.948564	−	0.316586i	$-0.102537\pi$
$84$	−0.429425	+	4.56241i	−0.0468541	+	0.497800i
$85$	−14.3629	−	5.22766i	−1.55787	−	0.567020i
$86$	5.27084	+	1.91843i	0.568370	+	0.206870i
$87$	6.58061	+	7.76347i	0.705515	+	0.832331i
$88$	0.0860773	−	0.488169i	0.00917587	−	0.0520390i
$89$	0.576882			0.0611493			0.0305747	−	0.999532i	$-0.490266\pi$
$89$	0.576882			0.0611493			0.0305747	+	0.999532i	$0.490266\pi$
$90$	1.33633	+	7.16015i	0.140862	+	0.754746i
$91$	0.908469	+	11.9784i	0.0952334	+	1.25568i
$92$	5.33598	+	4.47742i	0.556314	+	0.466803i
$93$	−0.0435682	−	8.73164i	−0.00451781	−	0.905429i
$94$	−6.77309	−	2.46520i	−0.698591	−	0.254266i
$95$	−12.7375	−	4.63608i	−1.30684	−	0.475652i
$96$	−1.50430	−	0.858530i	−0.153532	−	0.0876234i
$97$	−0.578333	−	0.485279i	−0.0587208	−	0.0492726i	0.612955	−	0.790118i	$-0.289981\pi$
$97$	−0.578333	−	0.485279i	−0.0587208	−	0.0492726i	−0.671676	+	0.740845i	$0.734425\pi$
$98$	6.91993	−	1.05572i	0.699019	−	0.106644i
$99$	−0.756364	−	1.28038i	−0.0760174	−	0.128683i
$100$	0.894838			0.0894838
$101$	−2.94551	+	16.7048i	−0.293089	+	1.66219i	0.381780	+	0.924253i	$0.375311\pi$
$101$	−2.94551	+	16.7048i	−0.293089	+	1.66219i	−0.674869	+	0.737937i	$0.735800\pi$
$102$	3.67817	−	10.2648i	0.364193	−	1.01636i
$103$	13.1378	+	4.78177i	1.29451	+	0.471162i	0.895204	−	0.445657i	$-0.147030\pi$
$103$	13.1378	+	4.78177i	1.29451	+	0.471162i	0.399303	+	0.916819i	$0.369252\pi$
$104$	−4.26659	−	1.55291i	−0.418374	−	0.152276i
$105$	10.1145	−	4.63567i	0.987069	−	0.452395i
$106$	0.720287	−	4.08495i	0.0699605	−	0.396766i
$107$	5.82281	+	10.0854i	0.562913	+	0.974993i	0.997241	+	0.0742385i	$0.0236526\pi$
$107$	5.82281	+	10.0854i	0.562913	+	0.974993i	−0.434328	+	0.900755i	$0.643014\pi$
$108$	−5.10313	+	0.978798i	−0.491049	+	0.0941849i
$109$	5.22277	−	9.04611i	0.500251	−	0.866460i	−0.499749	−	0.866170i	$-0.666574\pi$
$109$	5.22277	−	9.04611i	0.500251	−	0.866460i	1.00000		0.000289674i	$-9.22061e-5\pi$
$110$	−1.13094	+	0.411629i	−0.107831	+	0.0392473i
$111$	1.76560	+	4.77664i	0.167583	+	0.453379i
$112$	−0.714290	+	2.54751i	−0.0674941	+	0.240717i
$113$	−6.62139	+	5.55601i	−0.622888	+	0.522665i	−0.898710	−	0.438544i	$-0.855494\pi$
$113$	−6.62139	+	5.55601i	−0.622888	+	0.522665i	0.275822	+	0.961209i	$0.411050\pi$
$114$	3.26193	−	9.10316i	0.305508	−	0.852589i
$115$	2.93674	−	16.6551i	0.273853	−	1.55310i
$116$	2.93791	+	5.08861i	0.272778	+	0.472466i
$117$	−12.7527	+	4.78624i	−1.17898	+	0.442488i
$118$	−3.31357	−	5.73927i	−0.305039	−	0.528343i
$119$	−16.5746	−	1.64352i	−1.51940	−	0.150661i
$120$	0.0209829	+	4.20524i	0.00191546	+	0.383884i
$121$	−8.23826	+	6.91272i	−0.748933	+	0.628429i
$122$	−11.9830	−	4.36147i	−1.08489	−	0.394869i
$123$	13.8768	+	7.91973i	1.25123	+	0.714098i
$124$	0.875409	−	4.96469i	0.0786140	−	0.445842i
$125$	4.98352	+	8.63171i	0.445740	+	0.772044i
$126$	3.34299	+	7.19892i	0.297817	+	0.641331i
$127$	−3.80173	+	6.58480i	−0.337349	+	0.584306i	−0.983933	−	0.178537i	$-0.942864\pi$
$127$	−3.80173	+	6.58480i	−0.337349	+	0.584306i	0.646584	+	0.762843i	$0.276197\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	9.55914	−	1.73476i	0.841635	−	0.152737i
$130$	1.91426	+	10.8563i	0.167892	+	0.952163i
$131$	0.940361	+	5.33306i	0.0821598	+	0.465951i	0.997933	+	0.0642565i	$0.0204676\pi$
$131$	0.940361	+	5.33306i	0.0821598	+	0.465951i	−0.915774	+	0.401695i	$0.868421\pi$
$132$	−0.297672	−	0.805323i	−0.0259091	−	0.0700944i
$133$	−14.6990	−	1.45753i	−1.27456	−	0.126384i
$134$	−7.05809			−0.609726
$135$	8.25309	+	9.54186i	0.710313	+	0.821233i
$136$	3.14768	−	5.45193i	0.269911	−	0.467499i
$137$	−6.40167	−	5.37164i	−0.546931	−	0.458930i	0.326969	−	0.945035i	$-0.393973\pi$
$137$	−6.40167	−	5.37164i	−0.546931	−	0.458930i	−0.873900	+	0.486105i	$0.838417\pi$
$138$	11.8918	+	2.03572i	1.01230	+	0.173292i
$139$	3.04837	+	1.10952i	0.258560	+	0.0941080i	0.468048	−	0.883703i	$-0.344958\pi$
$139$	3.04837	+	1.10952i	0.258560	+	0.0941080i	−0.209488	+	0.977811i	$0.567180\pi$
$140$	6.22363	−	1.59068i	0.525993	−	0.134437i
$141$	−12.2836	+	2.22918i	−1.03447	+	0.187731i
$142$	4.79835	+	4.02629i	0.402669	+	0.337879i
$143$	−1.12534	−	1.94915i	−0.0941057	−	0.162996i
$144$	−2.99985	+	0.0299374i	−0.249988	+	0.00249478i
$145$	7.13304	−	12.3548i	0.592367	−	1.02601i
$146$	−2.39720	−	2.01149i	−0.198394	−	0.166472i
$147$	9.42770	−	7.62355i	0.777583	−	0.628780i
$148$	0.510554	+	2.89549i	0.0419672	+	0.238008i
$149$	−1.82735	+	1.53333i	−0.149703	+	0.125615i	−0.714563	−	0.699571i	$-0.753374\pi$
$149$	−1.82735	+	1.53333i	−0.149703	+	0.125615i	0.564860	+	0.825186i	$0.308930\pi$
$150$	1.33837	−	0.781640i	0.109278	−	0.0638206i
$151$	4.76253	−	1.73342i	0.387569	−	0.141064i	−0.140884	−	0.990026i	$-0.544994\pi$
$151$	4.76253	−	1.73342i	0.387569	−	0.141064i	0.528453	+	0.848962i	$0.322772\pi$
$152$	2.79147	−	4.83497i	0.226418	−	0.392168i
$153$	−3.46497	−	18.5655i	−0.280126	−	1.50093i
$154$	−1.08295	+	0.739765i	−0.0872663	+	0.0596120i
$155$	−11.5017	+	4.18628i	−0.923840	+	0.336250i
$156$	−7.73784	+	1.40424i	−0.619523	+	0.112429i
$157$	−3.31649	−	18.8088i	−0.264685	−	1.50110i	−0.769931	−	0.638127i	$-0.779709\pi$
$157$	−3.31649	−	18.8088i	−0.264685	−	1.50110i	0.505246	−	0.862975i	$-0.331402\pi$
$158$	10.2643	−	8.61278i	0.816585	−	0.685196i
$159$	−2.49090	−	6.73887i	−0.197541	−	0.534427i
$160$	−0.421605	+	2.39104i	−0.0333308	+	0.189029i
$161$	−1.39372	−	18.3765i	−0.109840	−	1.44827i
$162$	−6.77757	+	5.92153i	−0.532496	+	0.465239i
$163$	1.67121	+	2.89462i	0.130899	+	0.226725i	0.924024	−	0.382336i	$-0.124880\pi$
$163$	1.67121	+	2.89462i	0.130899	+	0.226725i	−0.793124	+	0.609060i	$0.791547\pi$
$164$	7.06657	+	5.92956i	0.551806	+	0.463020i
$165$	−1.33195	+	1.60353i	−0.103692	+	0.124835i
$166$	−1.50763	−	8.55021i	−0.117015	−	0.663625i
$167$	1.61877	−	1.35831i	0.125265	−	0.105109i	−0.578003	−	0.816034i	$-0.696168\pi$
$167$	1.61877	−	1.35831i	0.125265	−	0.105109i	0.703268	+	0.710925i	$0.251723\pi$
$168$	1.15691	+	4.43414i	0.0892574	+	0.342101i
$169$	−7.15611	+	2.60461i	−0.550470	+	0.200355i
$170$	−15.2847			−1.17228
$171$	−3.07286	−	16.4645i	−0.234987	−	1.25907i
$172$	5.60912			0.427691
$173$	−0.213252	+	1.20941i	−0.0162133	+	0.0919499i	−0.991841	−	0.127484i	$-0.959310\pi$
$173$	−0.213252	+	1.20941i	−0.0162133	+	0.0919499i	0.975627	+	0.219434i	$0.0704210\pi$
$174$	8.83901	+	5.04457i	0.670084	+	0.382428i
$175$	−1.65461	−	1.69334i	−0.125077	−	0.128005i
$176$	−0.0860773	−	0.488169i	−0.00648832	−	0.0367971i
$177$	−9.96923	−	5.68960i	−0.749333	−	0.427657i
$178$	0.542091	−	0.197305i	0.0406315	−	0.0147886i
$179$	−1.98153			−0.148106			−0.0740532	−	0.997254i	$-0.523593\pi$
$179$	−1.98153			−0.148106			−0.0740532	+	0.997254i	$0.523593\pi$
$180$	3.70466	+	6.27129i	0.276129	+	0.467434i
$181$	−10.9770	+	19.0127i	−0.815913	+	1.41320i	0.0927571	+	0.995689i	$0.470432\pi$
$181$	−10.9770	+	19.0127i	−0.815913	+	1.41320i	−0.908670	+	0.417514i	$0.862901\pi$
$182$	4.95054	+	10.9453i	0.366958	+	0.811320i
$183$	−21.7323	+	3.94390i	−1.60650	+	0.291541i
$184$	6.54554	+	2.38238i	0.482544	+	0.175632i
$185$	5.46841	−	4.58854i	0.402045	−	0.337356i
$186$	−3.02734	−	8.19016i	−0.221975	−	0.600532i
$187$	2.93241	−	1.06731i	0.214439	−	0.0780493i
$188$	−7.20777			−0.525681
$189$	11.2882	+	7.84704i	0.821097	+	0.570788i
$190$	−13.5550			−0.983382
$191$	14.2988	−	5.20435i	1.03463	−	0.376573i	0.231786	−	0.972767i	$-0.425543\pi$
$191$	14.2988	−	5.20435i	1.03463	−	0.376573i	0.802841	+	0.596194i	$0.203321\pi$
$192$	−1.70722	−	0.292253i	−0.123208	−	0.0210915i
$193$	−12.1108	+	10.1622i	−0.871758	+	0.731492i	−0.964468	−	0.264201i	$-0.914892\pi$
$193$	−12.1108	+	10.1622i	−0.871758	+	0.731492i	0.0927095	+	0.995693i	$0.470447\pi$
$194$	−0.709430	−	0.258211i	−0.0509341	−	0.0185385i
$195$	12.3461	+	14.5653i	0.884121	+	1.04304i
$196$	6.14153	−	3.35881i	0.438681	−	0.239915i
$197$	8.29357	−	14.3649i	0.590893	−	1.02346i	−0.403220	−	0.915103i	$-0.632109\pi$
$197$	8.29357	−	14.3649i	0.590893	−	1.02346i	0.994112	−	0.108353i	$-0.0345577\pi$
$198$	−1.14867	−	0.944473i	−0.0816321	−	0.0671208i
$199$	0.102869			0.00729216			0.00364608	−	0.999993i	$-0.498839\pi$
$199$	0.102869			0.00729216			0.00364608	+	0.999993i	$0.498839\pi$
$200$	0.840872	−	0.306053i	0.0594587	−	0.0216412i
$201$	−10.5565	+	6.16523i	−0.744598	+	0.434862i
$202$	2.94551	+	16.7048i	0.207245	+	1.17535i
$203$	4.19704	−	14.9687i	0.294575	−	1.05060i
$204$	−0.0544062	−	10.9037i	−0.00380920	−	0.763414i
$205$	3.88920	−	22.0568i	0.271634	−	1.54051i
$206$	13.9810			0.974099
$207$	19.5643	−	7.34275i	1.35981	−	0.510356i
$208$	−4.54041			−0.314821
$209$	2.60056	−	0.946528i	0.179885	−	0.0654727i
$210$	7.91898	−	7.81545i	0.546462	−	0.539318i
$211$	0.815288	−	0.684108i	0.0561267	−	0.0470959i	−0.614293	−	0.789078i	$-0.710559\pi$
$211$	0.815288	−	0.684108i	0.0561267	−	0.0470959i	0.670420	+	0.741982i	$0.266114\pi$
$212$	−0.720287	−	4.08495i	−0.0494695	−	0.280556i
$213$	10.6937	+	1.83061i	0.732718	+	0.125432i
$214$	8.92107	+	7.48566i	0.609832	+	0.511710i
$215$	−6.80927	−	11.7940i	−0.464388	−	0.804344i
$216$	−4.46061	+	2.66514i	−0.303506	+	0.181340i
$217$	−11.0136	+	7.52343i	−0.747652	+	0.510724i
$218$	1.81385	−	10.2869i	0.122849	−	0.696714i
$219$	−5.34243	−	0.914554i	−0.361008	−	0.0617998i
$220$	−0.921952	+	0.773610i	−0.0621580	+	0.0521568i
$221$	−4.96347	−	28.1493i	−0.333879	−	1.89352i
$222$	3.29283	+	3.88471i	0.221000	+	0.260724i
$223$	−9.85068	+	3.58536i	−0.659651	+	0.240093i	−0.650085	−	0.759861i	$-0.725267\pi$
$223$	−9.85068	+	3.58536i	−0.659651	+	0.240093i	−0.00956510	+	0.999954i	$0.503045\pi$
$224$	0.200085	+	2.63817i	0.0133687	+	0.176270i
$225$	1.31899	−	2.33814i	0.0879326	−	0.155876i
$226$	−4.32181	+	7.48559i	−0.287482	+	0.497934i
$227$	15.4892	−	5.63762i	1.02806	−	0.374182i	0.227716	−	0.973728i	$-0.426874\pi$
$227$	15.4892	−	5.63762i	1.02806	−	0.374182i	0.800340	+	0.599546i	$0.204652\pi$
$228$	−0.0482494	−	9.66982i	−0.00319540	−	0.640399i
$229$	−11.0372	+	9.26131i	−0.729358	+	0.612004i	−0.929957	−	0.367669i	$-0.880156\pi$
$229$	−11.0372	+	9.26131i	−0.729358	+	0.612004i	0.200598	+	0.979674i	$0.435711\pi$
$230$	−2.93674	−	16.6551i	−0.193643	−	1.09820i
$231$	−0.973536	+	2.05239i	−0.0640540	+	0.135037i
$232$	4.50114	+	3.77691i	0.295514	+	0.247966i
$233$	−5.49441	+	9.51660i	−0.359951	+	0.623453i	−0.987952	−	0.154759i	$-0.950540\pi$
$233$	−5.49441	+	9.51660i	−0.359951	+	0.623453i	0.628001	+	0.778212i	$0.283873\pi$
$234$	−10.3466	+	8.85926i	−0.676378	+	0.579148i
$235$	8.74998	+	15.1554i	0.570786	+	0.988630i
$236$	−5.07669	−	4.25985i	−0.330464	−	0.277292i
$237$	7.82867	−	21.8477i	0.508527	−	1.41916i
$238$	−16.1372	+	4.12446i	−1.04602	+	0.267349i
$239$	1.51848	+	0.552682i	0.0982223	+	0.0357500i	0.390664	−	0.920533i	$-0.372245\pi$
$239$	1.51848	+	0.552682i	0.0982223	+	0.0357500i	−0.292442	+	0.956283i	$0.594468\pi$
$240$	1.45800	+	3.94446i	0.0941132	+	0.254614i
$241$	6.59097	+	5.53048i	0.424561	+	0.356249i	0.829895	−	0.557919i	$-0.188400\pi$
$241$	6.59097	+	5.53048i	0.424561	+	0.356249i	−0.405334	+	0.914169i	$0.632845\pi$
$242$	−5.37714	+	9.31348i	−0.345656	+	0.598693i
$243$	−4.96449	+	14.7768i	−0.318472	+	0.947932i
$244$	−12.7521			−0.816369
$245$	−14.5180	−	8.83601i	−0.927520	−	0.564512i
$246$	15.7486	+	2.69596i	1.00410	+	0.171888i
$247$	−4.40179	−	24.9638i	−0.280079	−	1.58841i
$248$	−0.875409	−	4.96469i	−0.0555885	−	0.315258i
$249$	−9.72350	−	11.4713i	−0.616202	−	0.726963i
$250$	7.63520	+	6.40669i	0.482892	+	0.405195i
$251$	5.06248	−	8.76847i	0.319541	−	0.553461i	−0.660851	−	0.750517i	$-0.729805\pi$
$251$	5.06248	−	8.76847i	0.319541	−	0.553461i	0.980392	+	0.197056i	$0.0631380\pi$
$252$	5.60356	+	5.62140i	0.352991	+	0.354115i
$253$	1.72643	+	2.99026i	0.108540	+	0.187996i
$254$	−1.32033	+	7.48795i	−0.0828448	+	0.469836i
$255$	−22.8607	+	13.3511i	−1.43159	+	0.836081i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−12.0947	+	10.1486i	−0.754446	+	0.633055i	−0.936675	−	0.350201i	$-0.886113\pi$
$257$	−12.0947	+	10.1486i	−0.754446	+	0.633055i	0.182229	+	0.983256i	$0.441669\pi$
$258$	8.38933	−	4.89956i	0.522297	−	0.305033i
$259$	4.53523	−	6.32009i	0.281806	−	0.392711i
$260$	5.51190	+	9.54689i	0.341834	+	0.592073i
$261$	17.6266	−	0.175907i	1.09106	−	0.0108884i
$262$	2.70766	+	4.68981i	0.167280	+	0.289737i
$263$	−5.02580	+	28.5027i	−0.309904	+	1.75755i	0.289568	+	0.957158i	$0.406488\pi$
$263$	−5.02580	+	28.5027i	−0.309904	+	1.75755i	−0.599472	+	0.800396i	$0.704623\pi$
$264$	−0.555157	−	0.654946i	−0.0341676	−	0.0403091i
$265$	−7.71481	+	6.47350i	−0.473917	+	0.397664i
$266$	−14.3110	+	3.65772i	−0.877466	+	0.224269i
$267$	0.638439	−	0.768618i	0.0390718	−	0.0470386i
$268$	−6.63243	+	2.41401i	−0.405140	+	0.147459i
$269$	4.59009	−	7.95027i	0.279863	−	0.484736i	−0.691488	−	0.722388i	$-0.743044\pi$
$269$	4.59009	−	7.95027i	0.279863	−	0.484736i	0.971350	+	0.237652i	$0.0763777\pi$
$270$	11.0189	+	6.14370i	0.670587	+	0.373894i
$271$	12.9536	+	22.4363i	0.786875	+	1.36291i	0.927872	+	0.372898i	$0.121636\pi$
$271$	12.9536	+	22.4363i	0.786875	+	1.36291i	−0.140997	+	0.990010i	$0.545031\pi$
$272$	1.09318	−	6.19971i	0.0662835	−	0.375913i
$273$	16.9650	+	12.0462i	1.02677	+	0.729067i
$274$	−7.85281	−	2.85819i	−0.474405	−	0.172669i
$275$	0.416820	+	0.151710i	0.0251352	+	0.00914846i
$276$	11.8709	−	2.15429i	0.714545	−	0.129673i
$277$	0.285128	−	1.61704i	0.0171317	−	0.0971586i	−0.975043	−	0.222016i	$-0.928736\pi$
$277$	0.285128	−	1.61704i	0.0171317	−	0.0971586i	0.992175	+	0.124857i	$0.0398474\pi$
$278$	3.24401			0.194563
$279$	−11.6820	−	9.60532i	−0.699381	−	0.575055i
$280$	5.30426	−	3.62336i	0.316990	−	0.216537i
$281$	−8.92874	−	7.49210i	−0.532644	−	0.446941i	0.336369	−	0.941730i	$-0.390801\pi$
$281$	−8.92874	−	7.49210i	−0.532644	−	0.446941i	−0.869013	+	0.494789i	$0.835245\pi$
$282$	−10.7804	+	6.29598i	−0.641962	+	0.374920i
$283$	−29.3828	−	10.6945i	−1.74663	−	0.635720i	−0.747048	−	0.664770i	$-0.768530\pi$
$283$	−29.3828	−	10.6945i	−1.74663	−	0.635720i	−0.999578	+	0.0290496i	$0.990752\pi$
$284$	5.88605	+	2.14235i	0.349273	+	0.127125i
$285$	−20.2737	+	11.8403i	−1.20091	+	0.701357i
$286$	−1.72412	−	1.44671i	−0.101949	−	0.0855458i
$287$	−1.84573	−	24.3365i	−0.108950	−	1.43654i
$288$	−2.80870	+	1.05414i	−0.165504	+	0.0621159i
$289$	22.6314			1.33126
$290$	2.47728	−	14.0493i	0.145471	−	0.825006i
$291$	−1.28661	+	0.233490i	−0.0754226	+	0.0136874i
$292$	−2.94060	−	1.07029i	−0.172086	−	0.0626341i
$293$	−24.3483	−	8.86207i	−1.42244	−	0.517728i	−0.487689	−	0.873018i	$-0.662160\pi$
$293$	−24.3483	−	8.86207i	−1.42244	−	0.517728i	−0.934756	+	0.355290i	$0.884382\pi$
$294$	6.25173	−	10.3883i	0.364608	−	0.605855i
$295$	−2.79404	+	15.8458i	−0.162675	+	0.922577i
$296$	1.47008	+	2.54625i	0.0854467	+	0.147998i
$297$	−2.54301	−	0.409252i	−0.147560	−	0.0237472i
$298$	−1.19272	+	2.06585i	−0.0690924	+	0.119672i
$299$	29.7195	−	10.8170i	1.71872	−	0.625564i
$300$	0.990323	−	1.19225i	0.0571763	−	0.0688347i
$301$	−10.3716	−	10.6144i	−0.597809	−	0.611803i
$302$	3.88245	−	3.25776i	0.223410	−	0.187463i
$303$	18.9971	+	22.4118i	1.09136	+	1.28753i
$304$	0.969468	−	5.49813i	0.0556028	−	0.315339i
$305$	15.4806	+	26.8131i	0.886415	+	1.53532i
$306$	−9.60577	−	16.2608i	−0.549125	−	0.929565i
$307$	−1.69924	−	2.94317i	−0.0969806	−	0.167975i	0.813453	−	0.581631i	$-0.197585\pi$
$307$	−1.69924	−	2.94317i	−0.0969806	−	0.167975i	−0.910433	+	0.413655i	$0.864252\pi$
$308$	−0.764622	+	1.06554i	−0.0435684	+	0.0607149i
$309$	20.9108	−	12.2124i	1.18957	−	0.694737i
$310$	−9.37628	+	7.86763i	−0.532537	+	0.446852i
$311$	13.8224	+	5.03094i	0.783796	+	0.285278i	0.702755	−	0.711432i	$-0.251953\pi$
$311$	13.8224	+	5.03094i	0.783796	+	0.285278i	0.0810413	+	0.996711i	$0.474175\pi$
$312$	−6.79092	+	3.96605i	−0.384460	+	0.224533i
$313$	−5.07028	+	28.7550i	−0.286589	+	1.62533i	0.412963	+	0.910748i	$0.364494\pi$
$313$	−5.07028	+	28.7550i	−0.286589	+	1.62533i	−0.699553	+	0.714581i	$0.746617\pi$
$314$	−9.54946	−	16.5401i	−0.538907	−	0.933415i
$315$	5.01731	−	18.6065i	0.282694	−	1.04836i
$316$	6.69955	−	11.6040i	0.376879	−	0.652774i
$317$	−12.1098	−	10.1613i	−0.680152	−	0.570715i	0.235899	−	0.971778i	$-0.424197\pi$
$317$	−12.1098	−	10.1613i	−0.680152	−	0.570715i	−0.916051	+	0.401063i	$0.868641\pi$
$318$	−4.64551	−	5.48053i	−0.260507	−	0.307333i
$319$	0.505775	+	2.86839i	0.0283180	+	0.160599i
$320$	0.421605	+	2.39104i	0.0235685	+	0.133663i
$321$	19.8816	+	3.40347i	1.10968	+	0.189963i
$322$	−7.59481	−	16.7916i	−0.423242	−	0.935760i
$323$	35.1466			1.95561
$324$	−4.34355	+	7.88248i	−0.241308	+	0.437916i
$325$	2.03147	−	3.51860i	0.112686	−	0.195177i
$326$	2.56045	+	2.14847i	0.141810	+	0.118993i
$327$	−6.27265	−	16.9700i	−0.346879	−	0.938445i
$328$	8.66843	+	3.15505i	0.478634	+	0.174209i
$329$	13.3276	+	13.6396i	0.734774	+	0.751976i
$330$	−0.703180	+	1.96238i	−0.0387088	+	0.108026i
$331$	16.9535	+	14.2257i	0.931849	+	0.781914i	0.976148	−	0.217104i	$-0.0696611\pi$
$331$	16.9535	+	14.2257i	0.931849	+	0.781914i	−0.0442993	+	0.999018i	$0.514106\pi$
$332$	−4.34105	−	7.51893i	−0.238246	−	0.412655i
$333$	8.31823	+	2.93392i	0.455836	+	0.160778i
$334$	1.05658	−	1.83005i	0.0578135	−	0.100136i
$335$	13.1273	+	11.0151i	0.717223	+	0.601822i
$336$	2.60370	+	3.77104i	0.142044	+	0.205727i
$337$	−4.11372	−	23.3301i	−0.224089	−	1.27087i	−0.864420	−	0.502771i	$-0.832314\pi$
$337$	−4.11372	−	23.3301i	−0.224089	−	1.27087i	0.640331	−	0.768099i	$-0.278797\pi$
$338$	−5.83371	+	4.89506i	−0.317312	+	0.266256i
$339$	0.0747006	+	14.9710i	0.00405718	+	0.813112i
$340$	−14.3629	+	5.22766i	−0.778937	+	0.283510i
$341$	1.24948	−	2.16416i	0.0676631	−	0.117196i
$342$	−8.51874	−	14.4206i	−0.460641	−	0.779778i
$343$	−17.7121	−	5.41127i	−0.956363	−	0.292181i
$344$	5.27084	−	1.91843i	0.284185	−	0.103435i
$345$	−18.9406	−	22.3451i	−1.01973	−	1.20302i
$346$	0.213252	+	1.20941i	0.0114645	+	0.0650184i
$347$	−4.44843	+	3.73268i	−0.238804	+	0.200381i	−0.754333	−	0.656491i	$-0.772040\pi$
$347$	−4.44843	+	3.73268i	−0.238804	+	0.200381i	0.515529	+	0.856872i	$0.327595\pi$
$348$	10.0313	+	1.71722i	0.537734	+	0.0920529i
$349$	−5.65533	+	32.0730i	−0.302723	+	1.71683i	0.331310	+	0.943522i	$0.392509\pi$
$349$	−5.65533	+	32.0730i	−0.302723	+	1.71683i	−0.634033	+	0.773306i	$0.718602\pi$
$350$	−2.13398	−	1.02531i	−0.114066	−	0.0548053i
$351$	−7.73642	+	22.2882i	−0.412940	+	1.18965i
$352$	−0.247850	−	0.429288i	−0.0132104	−	0.0228811i
$353$	7.07932	+	5.94026i	0.376794	+	0.316168i	0.811442	−	0.584432i	$-0.198683\pi$
$353$	7.07932	+	5.94026i	0.376794	+	0.316168i	−0.434648	+	0.900600i	$0.643127\pi$
$354$	−11.3140	−	1.93680i	−0.601331	−	0.102940i
$355$	−2.64085	−	14.9770i	−0.140162	−	0.794898i
$356$	0.441917	−	0.370812i	0.0234215	−	0.0196530i
$357$	−20.5330	+	20.2646i	−1.08672	+	1.07252i
$358$	−1.86203	+	0.677723i	−0.0984112	+	0.0358188i
$359$	−27.4526			−1.44889			−0.724446	−	0.689332i	$-0.757904\pi$
$359$	−27.4526			−1.44889			−0.724446	+	0.689332i	$0.757904\pi$
$360$	5.62615	+	4.62601i	0.296524	+	0.243812i
$361$	12.1693			0.640487
$362$	−3.81227	+	21.6204i	−0.200368	+	1.13635i
$363$	0.0929416	+	18.6267i	0.00487817	+	0.977650i
$364$	8.39550	+	8.59204i	0.440044	+	0.450345i
$365$	1.31934	+	7.48235i	0.0690574	+	0.391644i
$366$	−19.0728	+	11.1389i	−0.996950	+	0.582241i
$367$	−14.9992	+	5.45926i	−0.782952	+	0.284971i	−0.702403	−	0.711779i	$-0.747890\pi$
$367$	−14.9992	+	5.45926i	−0.782952	+	0.284971i	−0.0805491	+	0.996751i	$0.525667\pi$
$368$	6.96562			0.363108
$369$	25.9095	−	9.72419i	1.34880	−	0.506221i
$370$	3.56925	−	6.18212i	0.185556	−	0.321393i
$371$	−6.39829	+	8.91636i	−0.332183	+	0.462914i
$372$	−5.64597	−	6.66082i	−0.292730	−	0.345348i
$373$	29.1469	+	10.6086i	1.50917	+	0.549292i	0.958416	−	0.285376i	$-0.0921186\pi$
$373$	29.1469	+	10.6086i	1.50917	+	0.549292i	0.550753	+	0.834669i	$0.314341\pi$
$374$	2.39052	−	2.00588i	0.123611	−	0.103722i
$375$	17.0159	+	2.91290i	0.878697	+	0.150421i
$376$	−6.77309	+	2.46520i	−0.349295	+	0.127133i
$377$	26.6787			1.37402
$378$	13.2913	+	3.51301i	0.683631	+	0.180690i
$379$	17.9032			0.919625			0.459812	−	0.888016i	$-0.347917\pi$
$379$	17.9032			0.919625			0.459812	+	0.888016i	$0.347917\pi$
$380$	−12.7375	+	4.63608i	−0.653421	+	0.237826i
$381$	4.56596	+	12.3527i	0.233921	+	0.632850i
$382$	11.6565	−	9.78097i	0.596399	−	0.500438i
$383$	−14.5201	−	5.28488i	−0.741943	−	0.270045i	−0.0567314	−	0.998389i	$-0.518068\pi$
$383$	−14.5201	−	5.28488i	−0.741943	−	0.270045i	−0.685211	+	0.728344i	$0.740290\pi$
$384$	−1.70422	+	0.309275i	−0.0869679	+	0.0157826i
$385$	3.16868	+	0.314202i	0.161491	+	0.0160132i
$386$	−7.90480	+	13.6915i	−0.402343	+	0.696879i
$387$	8.26783	−	14.6561i	0.420277	−	0.745014i
$388$	−0.754959			−0.0383273
$389$	−0.129211	+	0.0470291i	−0.00655128	+	0.00238447i	−0.345294	−	0.938495i	$-0.612221\pi$
$389$	−0.129211	+	0.0470291i	−0.00655128	+	0.00238447i	0.338742	+	0.940879i	$0.389998\pi$
$390$	16.5831	+	9.46427i	0.839720	+	0.479242i
$391$	7.61465	+	43.1848i	0.385089	+	2.18395i
$392$	4.62237	−	5.25677i	0.233465	−	0.265507i
$393$	8.14629	+	4.64922i	0.410926	+	0.234522i
$394$	2.88033	−	16.3352i	0.145109	−	0.822953i
$395$	−32.5321			−1.63687
$396$	−1.40242	−	0.494647i	−0.0704743	−	0.0248570i
$397$	14.5512			0.730304			0.365152	−	0.930948i	$-0.381017\pi$
$397$	14.5512			0.730304			0.365152	+	0.930948i	$0.381017\pi$
$398$	0.0966648	−	0.0351831i	0.00484537	−	0.00176357i
$399$	−18.2094	+	17.9714i	−0.911612	+	0.899694i
$400$	0.685485	−	0.575191i	0.0342743	−	0.0287595i
$401$	4.03829	+	22.9023i	0.201663	+	1.14369i	0.902605	+	0.430469i	$0.141652\pi$
$401$	4.03829	+	22.9023i	0.201663	+	1.14369i	−0.700943	+	0.713218i	$0.747237\pi$
$402$	−7.81123	+	9.40396i	−0.389589	+	0.469027i
$403$	−17.5344	−	14.7131i	−0.873449	−	0.732911i
$404$	8.48125	+	14.6900i	0.421958	+	0.730853i
$405$	21.8470	−	0.436093i	1.08559	−	0.0216697i
$406$	−1.17566	−	15.5014i	−0.0583472	−	0.769324i
$407$	−0.253081	+	1.43529i	−0.0125448	+	0.0711449i
$408$	−3.78042	−	10.2275i	−0.187159	−	0.506339i
$409$	9.03189	−	7.57865i	0.446598	−	0.374740i	−0.391574	−	0.920147i	$-0.628069\pi$
$409$	9.03189	−	7.57865i	0.446598	−	0.374740i	0.838172	+	0.545407i	$0.183625\pi$
$410$	−3.88920	−	22.0568i	−0.192074	−	1.08931i
$411$	−14.2418	+	2.58454i	−0.702494	+	0.127486i
$412$	13.1378	−	4.78177i	0.647253	−	0.235581i
$413$	1.32599	+	17.4836i	0.0652478	+	0.860310i
$414$	15.8731	−	13.5913i	0.780120	−	0.667977i
$415$	−10.5398	+	18.2554i	−0.517377	+	0.896123i
$416$	−4.26659	+	1.55291i	−0.209187	+	0.0761378i
$417$	4.85194	−	2.83364i	0.237600	−	0.138764i
$418$	2.12000	−	1.77889i	0.103693	−	0.0870084i
$419$	1.32264	+	7.50109i	0.0646154	+	0.366452i	0.999920	+	0.0126098i	$0.00401393\pi$
$419$	1.32264	+	7.50109i	0.0646154	+	0.366452i	−0.935305	+	0.353842i	$0.884875\pi$
$420$	4.76837	−	10.0526i	0.232672	−	0.490515i
$421$	7.54967	+	6.33493i	0.367948	+	0.308745i	0.807949	−	0.589252i	$-0.200577\pi$
$421$	7.54967	+	6.33493i	0.367948	+	0.308745i	−0.440001	+	0.897997i	$0.645022\pi$
$422$	0.532142	−	0.921696i	0.0259042	−	0.0448675i
$423$	−10.6242	+	18.8333i	−0.516568	+	0.915706i
$424$	−2.07398	−	3.59225i	−0.100722	−	0.174455i
$425$	4.31537	+	3.62103i	0.209326	+	0.175646i
$426$	10.6749	−	1.93724i	0.517199	−	0.0938594i
$427$	23.5794	+	24.1314i	1.14109	+	1.16780i
$428$	10.9433	+	3.98304i	0.528965	+	0.192527i
$429$	−3.84240	−	0.657768i	−0.185513	−	0.0317573i
$430$	−10.4324	−	8.75382i	−0.503095	−	0.422147i
$431$	−0.630736	+	1.09247i	−0.0303815	+	0.0526223i	−0.880816	−	0.473458i	$-0.843006\pi$
$431$	−0.630736	+	1.09247i	−0.0303815	+	0.0526223i	0.850435	+	0.526080i	$0.176339\pi$
$432$	−3.28007	+	4.03003i	−0.157812	+	0.193895i
$433$	−28.7517			−1.38172			−0.690859	−	0.722990i	$-0.742767\pi$
$433$	−28.7517			−1.38172			−0.690859	+	0.722990i	$0.742767\pi$
$434$	−7.77623	+	10.8366i	−0.373271	+	0.520173i
$435$	−8.56692	−	23.1769i	−0.410752	−	1.11125i
$436$	−1.81385	−	10.2869i	−0.0868676	−	0.492651i
$437$	6.75295	+	38.2979i	0.323037	+	1.83204i
$438$	−5.33304	+	0.967821i	−0.254823	+	0.0462443i
$439$	−9.21423	−	7.73166i	−0.439771	−	0.369012i	0.395852	−	0.918314i	$-0.370449\pi$
$439$	−9.21423	−	7.73166i	−0.439771	−	0.369012i	−0.835624	+	0.549302i	$0.814894\pi$
$440$	−0.601762	+	1.04228i	−0.0286879	+	0.0496888i
$441$	0.276331	−	20.9982i	0.0131586	−	0.999913i
$442$	−14.2918	−	24.7540i	−0.679789	−	1.17743i
$443$	4.80177	−	27.2322i	0.228139	−	1.29384i	−0.628454	−	0.777847i	$-0.716312\pi$
$443$	4.80177	−	27.2322i	0.228139	−	1.29384i	0.856593	−	0.515993i	$-0.172577\pi$
$444$	4.42289	+	2.52422i	0.209901	+	0.119794i
$445$	−1.31616	−	0.479043i	−0.0623919	−	0.0227088i
$446$	−8.03035	+	6.73826i	−0.380248	+	0.319066i
$447$	0.0206157	+	4.13165i	0.000975087	+	0.195420i
$448$	1.09033	+	2.41064i	0.0515131	+	0.113892i
$449$	−2.26810	−	3.92846i	−0.107038	−	0.185396i	0.807531	−	0.589825i	$-0.200803\pi$
$449$	−2.26810	−	3.92846i	−0.107038	−	0.185396i	−0.914569	+	0.404430i	$0.867470\pi$
$450$	0.439755	−	2.64825i	0.0207303	−	0.124840i
$451$	2.28635	+	3.96008i	0.107660	+	0.186473i
$452$	−1.50095	+	8.51229i	−0.0705986	+	0.400385i
$453$	2.96117	−	8.26382i	0.139128	−	0.388268i
$454$	12.6269	−	10.5953i	0.592611	−	0.497260i
$455$	7.87420	−	28.0832i	0.369148	−	1.31656i
$456$	−3.35261	−	9.07016i	−0.157000	−	0.424749i
$457$	17.8791	−	6.50748i	0.836351	−	0.304407i	0.111888	−	0.993721i	$-0.464310\pi$
$457$	17.8791	−	6.50748i	0.836351	−	0.304407i	0.724463	+	0.689314i	$0.242088\pi$
$458$	−7.20402	+	12.4777i	−0.336622	+	0.583046i
$459$	−28.5707	−	15.9299i	−1.33357	−	0.743545i
$460$	−8.45602	−	14.6462i	−0.394264	−	0.682885i
$461$	2.08142	−	11.8043i	0.0969416	−	0.549783i	−0.897193	−	0.441638i	$-0.854398\pi$
$461$	2.08142	−	11.8043i	0.0969416	−	0.549783i	0.994135	−	0.108145i	$-0.0344912\pi$
$462$	−0.212866	+	2.26158i	−0.00990342	+	0.105218i
$463$	12.7063	+	4.62470i	0.590510	+	0.214928i	0.619954	−	0.784638i	$-0.287151\pi$
$463$	12.7063	+	4.62470i	0.590510	+	0.214928i	−0.0294437	+	0.999566i	$0.509374\pi$
$464$	5.52147	+	2.00965i	0.256328	+	0.0932956i
$465$	−7.15136	+	19.9575i	−0.331636	+	0.925506i
$466$	−1.90819	+	10.8219i	−0.0883951	+	0.501314i
$467$	1.11978			0.0518174			0.0259087	−	0.999664i	$-0.491752\pi$
$467$	1.11978			0.0518174			0.0259087	+	0.999664i	$0.491752\pi$
$468$	−6.69257	+	11.8637i	−0.309364	+	0.548401i
$469$	16.8319	+	8.08722i	0.777225	+	0.373433i
$470$	13.4057	+	11.2488i	0.618361	+	0.518866i
$471$	−28.7306	−	16.3970i	−1.32383	−	0.755534i
$472$	−6.22748	−	2.26662i	−0.286643	−	0.104329i
$473$	2.61275	+	0.950965i	0.120135	+	0.0437254i
$474$	−0.115799	−	23.2076i	−0.00531882	−	1.06596i
$475$	3.82703	+	3.21126i	0.175596	+	0.147343i
$476$	−13.7534	+	9.39497i	−0.630384	+	0.430618i
$477$	−11.7353	−	4.13916i	−0.537324	−	0.189519i
$478$	1.61593			0.0739110
$479$	5.84342	−	33.1397i	0.266993	−	1.51419i	−0.496308	−	0.868147i	$-0.665311\pi$
$479$	5.84342	−	33.1397i	0.266993	−	1.51419i	0.763300	−	0.646044i	$-0.223578\pi$
$480$	2.71915	+	3.20792i	0.124112	+	0.146421i
$481$	12.5445	+	4.56582i	0.571979	+	0.208183i
$482$	8.08502	+	2.94271i	0.368262	+	0.134037i
$483$	−26.0267	−	18.4805i	−1.18426	−	0.840891i
$484$	−1.86746	+	10.5909i	−0.0848846	+	0.481405i
$485$	0.916494	+	1.58741i	0.0416158	+	0.0720808i
$486$	0.388864	+	15.5836i	0.0176392	+	0.706887i
$487$	13.1567	−	22.7880i	0.596186	−	1.03262i	−0.397192	−	0.917735i	$-0.630015\pi$
$487$	13.1567	−	22.7880i	0.596186	−	1.03262i	0.993378	−	0.114889i	$-0.0366512\pi$
$488$	−11.9830	+	4.36147i	−0.542447	+	0.197434i
$489$	5.70624	+	0.976833i	0.258045	+	0.0441739i
$490$	−16.6645	−	3.33769i	−0.752827	−	0.150781i
$491$	−17.8478	+	14.9761i	−0.805458	+	0.675860i	−0.949519	−	0.313709i	$-0.898428\pi$
$491$	−17.8478	+	14.9761i	−0.805458	+	0.675860i	0.144061	+	0.989569i	$0.453984\pi$
$492$	15.7210	−	2.85298i	0.708756	−	0.128622i
$493$	−6.42331	+	36.4284i	−0.289291	+	1.64065i
$494$	−12.6744	−	21.9528i	−0.570250	−	0.987702i
$495$	0.662420	+	3.54928i	0.0297736	+	0.159528i
$496$	−2.52064	−	4.36588i	−0.113180	−	0.196034i
$497$	−6.82959	−	15.0998i	−0.306349	−	0.677317i
$498$	−13.0605	−	7.45385i	−0.585256	−	0.334015i
$499$	0.821815	−	0.689585i	0.0367895	−	0.0308701i	−0.624208	−	0.781259i	$-0.714578\pi$
$499$	0.821815	−	0.689585i	0.0367895	−	0.0308701i	0.660997	+	0.750389i	$0.270134\pi$
$500$	9.36596	+	3.40893i	0.418858	+	0.152452i
$501$	−0.0182625	−	3.66006i	−0.000815910	−	0.163519i
$502$	1.75818	−	9.97114i	0.0784714	−	0.445034i
$503$	−15.6567	−	27.1181i	−0.698096	−	1.20914i	−0.969126	−	0.246567i	$-0.920698\pi$
$503$	−15.6567	−	27.1181i	−0.698096	−	1.20914i	0.271030	−	0.962571i	$-0.412636\pi$
$504$	7.18825	+	3.36586i	0.320190	+	0.149927i
$505$	20.5919	−	35.6662i	0.916327	−	1.58712i
$506$	2.64504	+	2.21945i	0.117586	+	0.0986667i
$507$	−4.44941	+	12.4171i	−0.197605	+	0.551462i
$508$	1.32033	+	7.48795i	0.0585801	+	0.332224i
$509$	−3.71236	−	21.0538i	−0.164548	−	0.933195i	−0.949530	−	0.313677i	$-0.898439\pi$
$509$	−3.71236	−	21.0538i	−0.164548	−	0.933195i	0.784982	−	0.619518i	$-0.212672\pi$
$510$	−16.9156	+	20.3648i	−0.749037	+	0.901767i
$511$	3.41199	+	7.54368i	0.150937	+	0.333713i
$512$	−1.00000			−0.0441942
$513$	−25.3375	−	14.1272i	−1.11868	−	0.623733i
$514$	−7.89425	+	13.6732i	−0.348200	+	0.603101i
$515$	−26.0032	−	21.8193i	−1.14584	−	0.961472i
$516$	6.20764	−	7.47340i	0.273276	−	0.328998i
$517$	−3.35742	−	1.22200i	−0.147659	−	0.0537435i
$518$	2.10013	−	7.49008i	0.0922744	−	0.329095i
$519$	1.37537	+	1.62259i	0.0603722	+	0.0712240i
$520$	8.44472	+	7.08596i	0.370326	+	0.310740i
$521$	11.1469	+	19.3070i	0.488354	+	0.845854i	0.999910	−	0.0133956i	$-0.00426408\pi$
$521$	11.1469	+	19.3070i	0.488354	+	0.845854i	−0.511556	+	0.859250i	$0.670931\pi$
$522$	16.5034	−	6.19395i	0.722335	−	0.271102i
$523$	9.00531	−	15.5977i	0.393775	−	0.682038i	−0.599169	−	0.800622i	$-0.704502\pi$
$523$	9.00531	−	15.5977i	0.393775	−	0.682038i	0.992944	+	0.118585i	$0.0378357\pi$
$524$	4.14838	+	3.48090i	0.181223	+	0.152064i
$525$	−4.08732	+	0.330511i	−0.178385	+	0.0144247i
$526$	5.02580	+	28.5027i	0.219135	+	1.24278i
$527$	24.3117	−	20.3999i	1.05903	−	0.888634i
$528$	−0.745682	−	0.425573i	−0.0324516	−	0.0185207i
$529$	−23.9808	+	8.72831i	−1.04265	+	0.379492i
$530$	−5.03549	+	8.72172i	−0.218728	+	0.378847i
$531$	−18.6136	+	6.98595i	−0.807763	+	0.303164i
$532$	−12.1970	+	8.33179i	−0.528805	+	0.361229i
$533$	39.3583	−	14.3252i	1.70480	−	0.620495i
$534$	0.337053	−	0.940623i	0.0145857	−	0.0407047i
$535$	−4.90986	−	27.8452i	−0.212272	−	1.20385i
$536$	−5.40681	+	4.53685i	−0.233539	+	0.195962i
$537$	−2.19297	+	2.64012i	−0.0946337	+	0.113930i
$538$	1.59412	−	9.04071i	0.0687274	−	0.389773i
$539$	3.43021	−	0.523319i	0.147749	−	0.0225410i
$540$	12.4556	+	2.00451i	0.536005	+	0.0862604i
$541$	−11.7482	−	20.3485i	−0.505096	−	0.874851i	−0.999983	−	0.00589386i	$-0.998124\pi$
$541$	−11.7482	−	20.3485i	−0.505096	−	0.874851i	0.494887	−	0.868957i	$-0.335209\pi$
$542$	19.8461	+	16.6528i	0.852462	+	0.715300i
$543$	13.1836	+	35.6669i	0.565762	+	1.53061i
$544$	−1.09318	−	6.19971i	−0.0468695	−	0.265810i
$545$	−19.4277	+	16.3018i	−0.832190	+	0.698291i
$546$	20.0620	+	5.51731i	0.858572	+	0.236119i
$547$	35.3508	−	12.8666i	1.51149	−	0.550137i	0.552484	−	0.833524i	$-0.313680\pi$
$547$	35.3508	−	12.8666i	1.51149	−	0.550137i	0.959006	+	0.283386i	$0.0914579\pi$
$548$	−8.35678			−0.356984
$549$	−18.7966	+	33.3201i	−0.802217	+	1.42207i
$550$	0.443571			0.0189139
$551$	−5.69642	+	32.3060i	−0.242676	+	1.37628i
$552$	10.4182	−	6.08446i	0.443428	−	0.258972i
$553$	−34.3466	+	8.77855i	−1.46057	+	0.373302i
$554$	−0.285128	−	1.61704i	−0.0121139	−	0.0687015i
$555$	−0.0616930	−	12.3641i	−0.00261872	−	0.524826i
$556$	3.04837	−	1.10952i	0.129280	−	0.0470540i
$557$	−2.85496			−0.120969			−0.0604843	−	0.998169i	$-0.519265\pi$
$557$	−2.85496			−0.120969			−0.0604843	+	0.998169i	$0.519265\pi$
$558$	−14.2627	−	5.03058i	−0.603787	−	0.212961i
$559$	12.7339	−	22.0557i	0.538585	−	0.932856i
$560$	3.74511	−	5.21901i	0.158260	−	0.220543i
$561$	1.82327	−	5.08824i	0.0769784	−	0.214826i
$562$	−10.9527	−	3.98646i	−0.462013	−	0.168159i
$563$	28.5887	−	23.9888i	1.20487	−	1.01101i	0.205393	−	0.978680i	$-0.434153\pi$
$563$	28.5887	−	23.9888i	1.20487	−	1.01101i	0.999477	−	0.0323267i	$-0.0102917\pi$
$564$	−7.97689	+	9.60339i	−0.335888	+	0.404376i
$565$	19.7205	−	7.17766i	0.829646	−	0.301966i
$566$	−31.2685			−1.31431
$567$	22.9479	−	6.35568i	0.963721	−	0.266913i
$568$	6.26380			0.262823
$569$	−25.0665	+	9.12345i	−1.05084	+	0.382475i	−0.808980	−	0.587836i	$-0.799980\pi$
$569$	−25.0665	+	9.12345i	−1.05084	+	0.382475i	−0.241861	+	0.970311i	$0.577758\pi$
$570$	−15.0014	+	18.0602i	−0.628339	+	0.756459i
$571$	17.2151	−	14.4452i	0.720431	−	0.604514i	−0.207073	−	0.978325i	$-0.566394\pi$
$571$	17.2151	−	14.4452i	0.720431	−	0.604514i	0.927505	+	0.373812i	$0.121949\pi$
$572$	−2.11495	−	0.769778i	−0.0884304	−	0.0321861i
$573$	8.89051	−	24.8110i	0.371406	−	1.03649i
$574$	−10.0580	−	22.2376i	−0.419813	−	0.928178i
$575$	−3.11655	+	5.39802i	−0.129969	+	0.225113i
$576$	−2.27878	+	1.95120i	−0.0949490	+	0.0813000i
$577$	−13.0903			−0.544956			−0.272478	−	0.962162i	$-0.587843\pi$
$577$	−13.0903			−0.544956			−0.272478	+	0.962162i	$0.587843\pi$
$578$	21.2666	−	7.74041i	0.884574	−	0.321959i
$579$	0.136631	+	27.3827i	0.00567819	+	1.13799i
$580$	−2.47728	−	14.0493i	−0.102863	−	0.583367i
$581$	−6.20155	+	22.1177i	−0.257283	+	0.917598i
$582$	−1.12916	+	0.659456i	−0.0468053	+	0.0273353i
$583$	0.357046	−	2.02491i	0.0147873	−	0.0838632i
$584$	−3.12932			−0.129492
$585$	33.0698	−	0.330024i	1.36727	−	0.0136448i
$586$	−25.9110			−1.07037
$587$	−15.5107	+	5.64543i	−0.640195	+	0.233012i	−0.641663	−	0.766987i	$-0.721755\pi$
$587$	−15.5107	+	5.64543i	−0.640195	+	0.233012i	0.00146756	+	0.999999i	$0.499533\pi$
$588$	2.32171	−	11.9000i	0.0957458	−	0.490747i
$589$	21.5605	−	18.0914i	0.888383	−	0.745442i
$590$	2.79404	+	15.8458i	0.115029	+	0.652361i
$591$	−9.96075	−	26.9478i	−0.409730	−	1.10848i
$592$	2.25229	+	1.88990i	0.0925687	+	0.0776744i
$593$	−6.11871	−	10.5979i	−0.251265	−	0.435205i	0.712609	−	0.701561i	$-0.247513\pi$
$593$	−6.11871	−	10.5979i	−0.251265	−	0.435205i	−0.963875	+	0.266357i	$0.914180\pi$
$594$	−2.52962	+	0.485190i	−0.103792	+	0.0199076i
$595$	36.4504	+	17.5133i	1.49432	+	0.717975i
$596$	−0.414227	+	2.34920i	−0.0169674	+	0.0962270i
$597$	0.113845	−	0.137059i	0.00465938	−	0.00560943i
$598$	24.2275	−	20.3293i	0.990738	−	0.831328i
$599$	3.46199	+	19.6339i	0.141453	+	0.802219i	0.970147	+	0.242517i	$0.0779732\pi$
$599$	3.46199	+	19.6339i	0.141453	+	0.802219i	−0.828694	+	0.559702i	$0.810916\pi$
$600$	0.522825	−	1.45906i	0.0213442	−	0.0595659i
$601$	−39.4215	+	14.3482i	−1.60804	+	0.585277i	−0.981050	−	0.193754i	$-0.937934\pi$
$601$	−39.4215	+	14.3482i	−1.60804	+	0.585277i	−0.626986	+	0.779031i	$0.715712\pi$
$602$	−13.3764	−	6.42697i	−0.545183	−	0.261944i
$603$	−3.46860	+	20.8882i	−0.141252	+	0.850634i
$604$	2.53409	−	4.38917i	0.103111	−	0.178593i
$605$	24.5360	−	8.93036i	0.997529	−	0.363071i
$606$	25.5167	+	14.5628i	1.03655	+	0.591574i
$607$	−0.705073	+	0.591626i	−0.0286180	+	0.0240134i	−0.656984	−	0.753904i	$-0.728168\pi$
$607$	−0.705073	+	0.591626i	−0.0286180	+	0.0240134i	0.628366	+	0.777917i	$0.283724\pi$
$608$	−0.969468	−	5.49813i	−0.0393171	−	0.222978i
$609$	−15.2989	−	22.1580i	−0.619942	−	0.897885i
$610$	23.7176	+	19.9014i	0.960298	+	0.805786i
$611$	−16.3631	+	28.3418i	−0.661982	+	1.14659i
$612$	−14.5880	−	11.9947i	−0.589684	−	0.484859i
$613$	−24.3324	−	42.1450i	−0.982778	−	1.70222i	−0.651424	−	0.758714i	$-0.725828\pi$
$613$	−24.3324	−	42.1450i	−0.982778	−	1.70222i	−0.331354	−	0.943507i	$-0.607505\pi$
$614$	−2.60338	−	2.18450i	−0.105064	−	0.0881591i
$615$	−25.0835	−	29.5922i	−1.01146	−	1.19327i
$616$	−0.354073	+	1.26280i	−0.0142660	+	0.0508796i
$617$	−3.99753	−	1.45498i	−0.160935	−	0.0585754i	0.260297	−	0.965529i	$-0.416180\pi$
$617$	−3.99753	−	1.45498i	−0.160935	−	0.0585754i	−0.421231	+	0.906953i	$0.638402\pi$
$618$	15.4728	−	18.6278i	0.622408	−	0.749318i
$619$	−17.0410	−	14.2991i	−0.684935	−	0.574729i	0.232508	−	0.972594i	$-0.425307\pi$
$619$	−17.0410	−	14.2991i	−0.684935	−	0.574729i	−0.917444	+	0.397865i	$0.869751\pi$
$620$	−6.11993	+	10.6000i	−0.245782	+	0.425708i
$621$	11.8687	−	34.1931i	0.476276	−	1.37212i
$622$	14.7095			0.589796
$623$	−1.51884	−	0.150606i	−0.0608509	−	0.00603390i
$624$	−5.02491	+	6.04950i	−0.201157	+	0.242174i
$625$	−4.97909	−	28.2378i	−0.199164	−	1.12951i
$626$	5.07028	+	28.7550i	0.202649	+	1.14928i
$627$	1.61694	−	4.51243i	0.0645743	−	0.180209i
$628$	−14.6306	−	12.2765i	−0.583825	−	0.489888i
$629$	−9.25467	+	16.0296i	−0.369008	+	0.639140i
$630$	−1.64906	−	19.2004i	−0.0657002	−	0.764962i
$631$	−8.26259	−	14.3112i	−0.328929	−	0.569721i	0.653371	−	0.757038i	$-0.273354\pi$
$631$	−8.26259	−	14.3112i	−0.328929	−	0.569721i	−0.982300	+	0.187317i	$0.940021\pi$
$632$	2.32673	−	13.1955i	0.0925524	−	0.524891i
$633$	−0.00919784	−	1.84337i	−0.000365581	−	0.0732674i
$634$	−14.8548	−	5.40671i	−0.589960	−	0.214728i
$635$	14.1417	−	11.8663i	0.561196	−	0.470900i
$636$	−6.23980	−	3.56116i	−0.247424	−	0.141209i
$637$	0.735337	−	31.7744i	0.0291351	−	1.25895i
$638$	1.45632	+	2.52242i	0.0576563	+	0.0998636i
$639$	14.2738	−	12.2219i	0.564663	−	0.483492i
$640$	1.21396	+	2.10265i	0.0479862	+	0.0831145i
$641$	−1.85385	+	10.5137i	−0.0732227	+	0.415267i	0.926059	+	0.377378i	$0.123174\pi$
$641$	−1.85385	+	10.5137i	−0.0732227	+	0.415267i	−0.999282	+	0.0378885i	$0.987937\pi$
$642$	19.8467	−	3.60170i	0.783285	−	0.142148i
$643$	25.5742	−	21.4593i	1.00855	−	0.846272i	0.0204021	−	0.999792i	$-0.493505\pi$
$643$	25.5742	−	21.4593i	1.00855	−	0.846272i	0.988146	+	0.153520i	$0.0490609\pi$
$644$	−12.8799	−	13.1814i	−0.507537	−	0.519419i
$645$	−23.2498	−	3.98005i	−0.915459	−	0.156714i
$646$	33.0270	−	12.0208i	1.29943	−	0.472954i
$647$	−9.81000	+	16.9914i	−0.385671	+	0.668001i	−0.991862	−	0.127318i	$-0.959363\pi$
$647$	−9.81000	+	16.9914i	−0.385671	+	0.668001i	0.606191	+	0.795319i	$0.292697\pi$
$648$	−1.38564	+	8.89269i	−0.0544329	+	0.349338i
$649$	−1.64254	−	2.84496i	−0.0644752	−	0.111674i
$650$	0.705521	−	4.00121i	0.0276728	−	0.156940i
$651$	−2.16485	+	23.0004i	−0.0848473	+	0.901456i
$652$	3.14085	+	1.14318i	0.123005	+	0.0447703i
$653$	16.2204	+	5.90374i	0.634753	+	0.231031i	0.639299	−	0.768958i	$-0.279225\pi$
$653$	16.2204	+	5.90374i	0.634753	+	0.231031i	−0.00454562	+	0.999990i	$0.501447\pi$
$654$	−11.6985	−	13.8012i	−0.457446	−	0.539671i
$655$	2.28313	−	12.9483i	0.0892093	−	0.505931i
$656$	9.22475			0.360166
$657$	−7.13103	+	6.10594i	−0.278208	+	0.238215i
$658$	17.1889	+	8.25873i	0.670092	+	0.321959i
$659$	−15.2604	−	12.8050i	−0.594462	−	0.498813i	0.295198	−	0.955436i	$-0.404614\pi$
$659$	−15.2604	−	12.8050i	−0.594462	−	0.498813i	−0.889660	+	0.456623i	$0.849059\pi$
$660$	0.0104012	+	2.08454i	0.000404866	+	0.0811405i
$661$	26.4208	+	9.61638i	1.02765	+	0.374034i	0.800185	−	0.599753i	$-0.204734\pi$
$661$	26.4208	+	9.61638i	1.02765	+	0.374034i	0.227464	+	0.973787i	$0.426957\pi$
$662$	20.7966	+	7.56933i	0.808281	+	0.294190i
$663$	−42.9982	−	24.5398i	−1.66991	−	0.953047i
$664$	−6.65088	−	5.58075i	−0.258104	−	0.216575i
$665$	32.3255	+	15.5314i	1.25353	+	0.602283i
$666$	8.82004	−	0.0880208i	0.341770	−	0.00341074i
$667$	−40.9287			−1.58477
$668$	0.366946	−	2.08106i	0.0141976	−	0.0805185i
$669$	−6.12481	+	17.0927i	−0.236799	+	0.660840i
$670$	16.1031	+	5.86104i	0.622116	+	0.226432i
$671$	−5.93999	−	2.16198i	−0.229311	−	0.0834622i
$672$	3.73645	+	2.65310i	0.144137	+	0.102346i
$673$	3.33296	−	18.9021i	0.128476	−	0.728624i	−0.850706	−	0.525641i	$-0.823825\pi$
$673$	3.33296	−	18.9021i	0.128476	−	0.728624i	0.979182	−	0.202983i	$-0.0650635\pi$
$674$	−11.8450	−	20.5161i	−0.456252	−	0.790251i
$675$	−1.65552	−	4.34501i	−0.0637209	−	0.167239i
$676$	−3.80768	+	6.59510i	−0.146449	+	0.253658i
$677$	22.9507	−	8.35336i	0.882066	−	0.321046i	0.139022	−	0.990289i	$-0.455604\pi$
$677$	22.9507	−	8.35336i	0.882066	−	0.321046i	0.743043	+	0.669244i	$0.233382\pi$
$678$	5.19057	+	14.0426i	0.199343	+	0.539302i
$679$	1.39597	+	1.42865i	0.0535722	+	0.0548264i
$680$	−11.7087	+	9.82479i	−0.449009	+	0.376764i
$681$	9.63066	−	26.8765i	0.369048	−	1.02991i
$682$	0.433940	−	2.46099i	0.0166164	−	0.0942364i
$683$	−10.4258	−	18.0581i	−0.398934	−	0.690973i	0.594661	−	0.803977i	$-0.297286\pi$
$683$	−10.4258	−	18.0581i	−0.398934	−	0.690973i	−0.993595	+	0.113003i	$0.963953\pi$
$684$	−12.9371	−	10.6374i	−0.494664	−	0.406730i
$685$	10.1448	+	17.5714i	0.387614	+	0.671367i
$686$	−18.4947	+	0.972958i	−0.706130	+	0.0371477i
$687$	0.124518	+	24.9551i	0.00475067	+	0.952098i
$688$	4.29683	−	3.60547i	0.163815	−	0.137457i
$689$	−17.6977	−	6.44144i	−0.674229	−	0.245399i
$690$	−25.4408	−	14.5195i	−0.968515	−	0.552748i
$691$	−6.91666	+	39.2263i	−0.263122	+	1.49224i	0.511207	+	0.859457i	$0.329198\pi$
$691$	−6.91666	+	39.2263i	−0.263122	+	1.49224i	−0.774330	+	0.632783i	$0.781913\pi$
$692$	0.614035	+	1.06354i	0.0233421	+	0.0404297i
$693$	1.65712	+	3.56850i	0.0629487	+	0.135556i
$694$	−2.90351	+	5.02902i	−0.110216	+	0.190899i
$695$	−6.03354	−	5.06274i	−0.228865	−	0.192041i
$696$	10.0137	−	1.81724i	0.379567	−	0.0688824i
$697$	10.0843	+	57.1908i	0.381969	+	2.16626i
$698$	5.65533	+	32.0730i	0.214058	+	1.21398i
$699$	6.59890	+	17.8526i	0.249593	+	0.675249i
$700$	−2.35596	−	0.233614i	−0.0890471	−	0.00882979i
$701$	13.9999			0.528769			0.264385	−	0.964417i	$-0.414831\pi$
$701$	13.9999			0.528769			0.264385	+	0.964417i	$0.414831\pi$
$702$	0.353145	+	23.5900i	0.0133286	+	0.890349i
$703$	−8.20737	+	14.2156i	−0.309547	+	0.536151i
$704$	−0.379728	−	0.318629i	−0.0143115	−	0.0120088i
$705$	29.8762	+	5.11441i	1.12520	+	0.192620i
$706$	8.68407	+	3.16074i	0.326829	+	0.118956i
$707$	12.1162	−	43.2121i	0.455675	−	1.62516i
$708$	−11.2941	+	2.04961i	−0.424457	+	0.0770290i
$709$	11.8248	+	9.92221i	0.444091	+	0.372637i	0.837238	−	0.546839i	$-0.184169\pi$
$709$	11.8248	+	9.92221i	0.444091	+	0.372637i	−0.393147	+	0.919476i	$0.628614\pi$
$710$	−7.60403	−	13.1706i	−0.285374	−	0.494283i
$711$	−20.4451	−	34.6096i	−0.766749	−	1.29796i
$712$	0.288441	−	0.499594i	0.0108098	−	0.0187231i
$713$	26.9001	+	22.5719i	1.00742	+	0.845324i
$714$	−12.3638	+	26.0652i	−0.462705	+	0.975466i
$715$	0.948899	+	5.38148i	0.0354868	+	0.201256i
$716$	−1.51794	+	1.27370i	−0.0567281	+	0.0476005i
$717$	2.41689	−	1.41152i	0.0902603	−	0.0527140i
$718$	−25.7970	+	9.38933i	−0.962735	+	0.350407i
$719$	−13.5133	+	23.4058i	−0.503962	+	0.872888i	0.496028	+	0.868307i	$0.334792\pi$
$719$	−13.5133	+	23.4058i	−0.503962	+	0.872888i	−0.999990	+	0.00458095i	$0.998542\pi$
$720$	6.86904	+	2.42278i	0.255994	+	0.0902915i
$721$	−33.3414	−	16.0195i	−1.24170	−	0.596597i
$722$	11.4354	−	4.16213i	0.425580	−	0.154898i
$723$	14.6629	−	2.66097i	0.545319	−	0.0989624i
$724$	3.81227	+	21.6204i	0.141682	+	0.803518i
$725$	−4.02779	+	3.37972i	−0.149588	+	0.125520i
$726$	6.45805	+	17.4716i	0.239681	+	0.648432i
$727$	2.23232	−	12.6601i	0.0827923	−	0.469538i	−0.915019	−	0.403411i	$-0.867825\pi$
$727$	2.23232	−	12.6601i	0.0827923	−	0.469538i	0.997811	−	0.0661274i	$-0.0210644\pi$
$728$	10.8278	+	5.20245i	0.401306	+	0.192816i
$729$	14.1939	+	22.9681i	0.525699	+	0.850671i
$730$	3.79889	+	6.57987i	0.140603	+	0.243532i
$731$	27.0501	+	22.6977i	1.00048	+	0.839505i
$732$	−14.1128	+	16.9905i	−0.521625	+	0.627985i
$733$	2.56884	+	14.5686i	0.0948824	+	0.538105i	0.994783	+	0.102010i	$0.0325275\pi$
$733$	2.56884	+	14.5686i	0.0948824	+	0.538105i	−0.899901	+	0.436094i	$0.856361\pi$
$734$	−12.2275	+	10.2601i	−0.451324	+	0.378706i
$735$	−27.8400	+	9.56442i	−1.02689	+	0.352789i
$736$	6.54554	−	2.38238i	0.241272	−	0.0878158i
$737$	−3.49869			−0.128876
$738$	21.0211	−	17.9993i	0.773799	−	0.662565i
$739$	−6.21566			−0.228647			−0.114323	−	0.993444i	$-0.536470\pi$
$739$	−6.21566			−0.228647			−0.114323	+	0.993444i	$0.536470\pi$
$740$	1.23959	−	7.03005i	0.0455681	−	0.258430i
$741$	−38.1324	−	21.7628i	−1.40083	−	0.799476i
$742$	−2.96285	+	10.5670i	−0.108770	+	0.387926i
$743$	6.26606	+	35.5366i	0.229879	+	1.30371i	0.853134	+	0.521692i	$0.174699\pi$
$743$	6.26606	+	35.5366i	0.229879	+	1.30371i	−0.623254	+	0.782019i	$0.714190\pi$
$744$	−7.58361	−	4.32809i	−0.278029	−	0.158675i
$745$	5.44240	−	1.98087i	0.199394	−	0.0725735i
$746$	31.0175			1.13563
$747$	−26.0450	+	0.259920i	−0.952938	+	0.00950996i
$748$	1.56030	−	2.70252i	0.0570503	−	0.0988139i
$749$	−12.6975	−	28.0734i	−0.463958	−	1.02578i
$750$	16.9860	−	3.08255i	0.620240	−	0.112559i
$751$	−12.3433	−	4.49258i	−0.450412	−	0.163937i	0.106847	−	0.994276i	$-0.465925\pi$
$751$	−12.3433	−	4.49258i	−0.450412	−	0.163937i	−0.557259	+	0.830339i	$0.688147\pi$
$752$	−5.52147	+	4.63307i	−0.201347	+	0.168951i
$753$	−6.08014	−	16.4492i	−0.221573	−	0.599442i
$754$	25.0697	−	9.12464i	0.912986	−	0.332300i
$755$	−12.3052			−0.447831
$756$	13.6913	−	1.24475i	0.497946	−	0.0452710i
$757$	38.4896			1.39893			0.699463	−	0.714669i	$-0.253422\pi$
$757$	38.4896			1.39893			0.699463	+	0.714669i	$0.253422\pi$
$758$	16.8235	−	6.12325i	0.611057	−	0.222406i
$759$	5.89477	+	1.00911i	0.213967	+	0.0366282i
$760$	−10.3837	+	8.71298i	−0.376657	+	0.316053i
$761$	10.1143	+	3.68129i	0.366641	+	0.133447i	0.518769	−	0.854914i	$-0.326390\pi$
$761$	10.1143	+	3.68129i	0.366641	+	0.133447i	−0.152128	+	0.988361i	$0.548613\pi$
$762$	8.51548	+	10.0461i	0.308483	+	0.363933i
$763$	−16.1124	+	22.4534i	−0.583307	+	0.812869i
$764$	7.60825	−	13.1779i	0.275257	−	0.476759i
$765$	−7.51143	+	45.2346i	−0.271576	+	1.63546i
$766$	−15.4520			−0.558302
$767$	−28.2753	+	10.2914i	−1.02096	+	0.371600i
$768$	−1.49566	+	0.873499i	−0.0539700	+	0.0315197i
$769$	−4.60792	−	26.1328i	−0.166166	−	0.942373i	−0.947854	−	0.318704i	$-0.896753\pi$
$769$	−4.60792	−	26.1328i	−0.166166	−	0.942373i	0.781689	−	0.623669i	$-0.214359\pi$
$770$	3.08505	−	0.788500i	0.111178	−	0.0284156i
$771$	0.136449	+	27.3461i	0.00491408	+	0.984847i
$772$	−2.74531	+	15.5694i	−0.0988057	+	0.560355i
$773$	−16.1984			−0.582614			−0.291307	−	0.956630i	$-0.594090\pi$
$773$	−16.1984			−0.582614			−0.291307	+	0.956630i	$0.594090\pi$
$774$	2.75652	−	16.6000i	0.0990811	−	0.596676i
$775$	4.51113			0.162044
$776$	−0.709430	+	0.258211i	−0.0254670	+	0.00926925i
$777$	−3.40150	−	13.0371i	−0.122028	−	0.467702i
$778$	−0.105334	+	0.0883858i	−0.00377641	+	0.00316878i
$779$	8.94310	+	50.7188i	0.320420	+	1.81719i
$780$	18.8200	+	3.22174i	0.673865	+	0.115357i
$781$	2.37854	+	1.99583i	0.0851109	+	0.0714165i
$782$	21.9255	+	37.9761i	0.784055	+	1.35802i
$783$	19.2731	−	23.6798i	0.688764	−	0.846245i
$784$	2.54569	−	6.52070i	0.0909174	−	0.232882i
$785$	−8.05221	+	45.6663i	−0.287396	+	1.62990i
$786$	9.24513	+	1.58264i	0.329763	+	0.0564510i
$787$	17.4845	−	14.6713i	0.623257	−	0.522975i	−0.275569	−	0.961281i	$-0.588866\pi$
$787$	17.4845	−	14.6713i	0.623257	−	0.522975i	0.898825	+	0.438307i	$0.144422\pi$
$788$	−2.88033	−	16.3352i	−0.102607	−	0.581916i
$789$	32.4140	+	38.2404i	1.15397	+	1.36139i
$790$	−30.5702	+	11.1266i	−1.08764	+	0.395868i
$791$	18.8836	−	12.8994i	0.671422	−	0.458651i
$792$	−1.48702	+	0.0148400i	−0.0528391	+	0.000527315i
$793$	−28.9499	+	50.1427i	−1.02804	+	1.78062i
$794$	13.6737	−	4.97681i	0.485260	−	0.176620i
$795$	0.0870363	+	17.4432i	0.00308686	+	0.618647i
$796$	0.0788019	−	0.0661226i	0.00279306	−	0.00234365i
$797$	3.14602	+	17.8420i	0.111438	+	0.631995i	0.988452	+	0.151531i	$0.0484204\pi$
$797$	3.14602	+	17.8420i	0.111438	+	0.631995i	−0.877015	+	0.480464i	$0.840468\pi$
$798$	−10.9647	+	23.1156i	−0.388146	+	0.818282i
$799$	−34.7596	−	29.1668i	−1.22971	−	1.03185i
$800$	0.447419	−	0.774952i	0.0158186	−	0.0273987i
$801$	−0.317516	−	1.70127i	−0.0112189	−	0.0601114i
$802$	11.6278	+	20.1400i	0.410592	+	0.711166i
$803$	−1.18829	−	0.997095i	−0.0419339	−	0.0351867i
$804$	−4.12381	+	11.5084i	−0.145436	+	0.405871i
$805$	−12.0801	+	43.0835i	−0.425768	+	1.51849i
$806$	−21.5091	−	7.82867i	−0.757626	−	0.275753i
$807$	−5.51279	−	14.9143i	−0.194059	−	0.525008i
$808$	12.9940	+	10.9033i	0.457129	+	0.383576i
$809$	−9.16498	+	15.8742i	−0.322223	+	0.558107i	−0.980946	−	0.194278i	$-0.937764\pi$
$809$	−9.16498	+	15.8742i	−0.322223	+	0.558107i	0.658723	+	0.752385i	$0.271097\pi$
$810$	20.3803	−	7.88191i	0.716091	−	0.276942i
$811$	−36.6387			−1.28656			−0.643279	−	0.765632i	$-0.722426\pi$
$811$	−36.6387			−1.28656			−0.643279	+	0.765632i	$0.722426\pi$
$812$	−6.40657	−	14.1645i	−0.224826	−	0.497076i
$813$	44.2292	+	7.57145i	1.55119	+	0.265542i
$814$	0.253081	+	1.43529i	0.00887049	+	0.0503070i
$815$	−1.40918	−	7.99188i	−0.0493616	−	0.279943i
$816$	−7.05046	−	8.31777i	−0.246816	−	0.291180i
$817$	23.9890	+	20.1291i	0.839268	+	0.704229i
$818$	5.89515	−	10.2107i	0.206119	−	0.357008i
$819$	34.8252	−	9.27208i	1.21689	−	0.323993i
$820$	−11.1985	−	19.3964i	−0.391069	−	0.677352i
$821$	−2.25758	+	12.8034i	−0.0787900	+	0.446840i	0.919735	+	0.392541i	$0.128404\pi$
$821$	−2.25758	+	12.8034i	−0.0787900	+	0.446840i	−0.998525	+	0.0542998i	$0.982707\pi$
$822$	−12.4989	+	7.29964i	−0.435949	+	0.254604i
$823$	51.0460	+	18.5792i	1.77935	+	0.647631i	0.999773	+	0.0213262i	$0.00678886\pi$
$823$	51.0460	+	18.5792i	1.77935	+	0.647631i	0.779578	+	0.626305i	$0.215433\pi$
$824$	10.7100	−	8.98679i	0.373102	−	0.313070i
$825$	0.663431	−	0.387458i	0.0230977	−	0.0134896i
$826$	7.22576	+	15.9757i	0.251416	+	0.555864i
$827$	−15.3927	−	26.6610i	−0.535258	−	0.927094i	−0.999151	−	0.0412030i	$-0.986881\pi$
$827$	−15.3927	−	26.6610i	−0.535258	−	0.927094i	0.463893	−	0.885891i	$-0.346452\pi$
$828$	10.2673	−	18.2006i	0.356814	−	0.632514i
$829$	−7.79650	−	13.5039i	−0.270784	−	0.469011i	0.698279	−	0.715826i	$-0.253949\pi$
$829$	−7.79650	−	13.5039i	−0.270784	−	0.469011i	−0.969063	+	0.246815i	$0.920616\pi$
$830$	−3.66042	+	20.7593i	−0.127055	+	0.720566i
$831$	−1.83894	−	2.16949i	−0.0637921	−	0.0752586i
$832$	−3.47816	+	2.91852i	−0.120583	+	0.101182i
$833$	43.2093	+	8.65425i	1.49711	+	0.299852i
$834$	3.59017	−	4.32221i	0.124317	−	0.149666i
$835$	−4.82119	+	1.75477i	−0.166844	+	0.0607263i
$836$	1.38373	−	2.39669i	0.0478573	−	0.0828913i
$837$	−25.7263	+	4.93439i	−0.889231	+	0.170558i
$838$	3.80840	+	6.59634i	0.131559	+	0.227867i
$839$	−2.66307	+	15.1030i	−0.0919392	+	0.521413i	0.903703	+	0.428160i	$0.140838\pi$
$839$	−2.66307	+	15.1030i	−0.0919392	+	0.521413i	−0.995642	+	0.0932537i	$0.970273\pi$
$840$	1.04261	−	11.0772i	0.0359736	−	0.382200i
$841$	−5.19206	−	1.88976i	−0.179037	−	0.0651640i
$842$	9.26104	+	3.37074i	0.319157	+	0.116164i
$843$	−19.8637	+	3.60479i	−0.684143	+	0.124156i
$844$	0.184811	−	1.04811i	0.00636145	−	0.0360776i
$845$	18.4896			0.636061
$846$	−3.54216	+	21.3312i	−0.121782	+	0.733382i
$847$	23.4947	−	16.0493i	0.807288	−	0.551461i
$848$	−3.17753	−	2.66626i	−0.109117	−	0.0915599i
$849$	−46.7671	+	27.3130i	−1.60504	+	0.937381i
$850$	5.29359	+	1.92671i	0.181569	+	0.0660855i
$851$	−19.2449	−	7.00459i	−0.659708	−	0.240114i
$852$	9.36852	−	5.47143i	0.320960	−	0.187448i
$853$	−8.30479	−	6.96855i	−0.284351	−	0.238599i	0.489445	−	0.872034i	$-0.337200\pi$
$853$	−8.30479	−	6.96855i	−0.284351	−	0.238599i	−0.773795	+	0.633436i	$0.781644\pi$
$854$	30.4108	+	14.6114i	1.04064	+	0.499993i
$855$	−6.66141	+	40.1156i	−0.227815	+	1.37193i
$856$	11.6456			0.398039
$857$	8.25962	−	46.8426i	0.282143	−	1.60011i	−0.433171	−	0.901312i	$-0.642605\pi$
$857$	8.25962	−	46.8426i	0.282143	−	1.60011i	0.715315	−	0.698803i	$-0.246283\pi$
$858$	−3.83565	+	0.696079i	−0.130947	+	0.0237637i
$859$	11.7152	+	4.26400i	0.399719	+	0.145486i	0.534054	−	0.845450i	$-0.320668\pi$
$859$	11.7152	+	4.26400i	0.399719	+	0.145486i	−0.134335	+	0.990936i	$0.542890\pi$
$860$	−12.7972	−	4.65781i	−0.436382	−	0.158830i
$861$	−34.4678	−	24.4742i	−1.17466	−	0.834078i
$862$	−0.219052	+	1.24231i	−0.00746096	+	0.0423132i
$863$	−22.6720	−	39.2691i	−0.771765	−	1.33674i	−0.936595	−	0.350414i	$-0.886041\pi$
$863$	−22.6720	−	39.2691i	−0.771765	−	1.33674i	0.164830	−	0.986322i	$-0.447292\pi$
$864$	−1.70390	+	4.90884i	−0.0579679	+	0.167002i
$865$	1.49083	−	2.58220i	0.0506898	−	0.0877974i
$866$	−27.0177	+	9.83366i	−0.918100	+	0.334161i
$867$	25.0464	−	30.1534i	0.850619	−	1.02406i
$868$	−3.60094	+	12.8427i	−0.122224	+	0.435909i
$869$	5.08801	−	4.26935i	0.172599	−	0.144828i
$870$	−15.9773	−	18.8491i	−0.541680	−	0.639046i
$871$	−5.56484	+	31.5598i	−0.188557	+	1.06936i
$872$	−5.22277	−	9.04611i	−0.176865	−	0.306340i
$873$	−1.11281	+	1.97265i	−0.0376629	+	0.0667639i
$874$	19.4443	+	33.6786i	0.657714	+	1.13919i
$875$	−10.8673	−	24.0270i	−0.367383	−	0.812259i
$876$	−4.68041	+	2.73346i	−0.158136	+	0.0923551i
$877$	−3.64944	+	3.06225i	−0.123233	+	0.103405i	−0.702321	−	0.711860i	$-0.747853\pi$
$877$	−3.64944	+	3.06225i	−0.123233	+	0.103405i	0.579088	+	0.815265i	$0.303409\pi$
$878$	−11.3029	−	4.11393i	−0.381455	−	0.138838i
$879$	−38.7540	+	22.6332i	−1.30714	+	0.763399i
$880$	−0.208990	+	1.18524i	−0.00704504	+	0.0399544i
$881$	−26.5414	−	45.9711i	−0.894203	−	1.54881i	−0.834788	−	0.550572i	$-0.814410\pi$
$881$	−26.5414	−	45.9711i	−0.894203	−	1.54881i	−0.0594154	−	0.998233i	$-0.518924\pi$
$882$	−6.92213	−	19.8263i	−0.233080	−	0.667588i
$883$	−19.8854	+	34.4426i	−0.669198	+	1.15908i	0.308931	+	0.951085i	$0.400029\pi$
$883$	−19.8854	+	34.4426i	−0.669198	+	1.15908i	−0.978129	+	0.208000i	$0.933304\pi$
$884$	−21.8962	−	18.3731i	−0.736450	−	0.617955i
$885$	18.0202	+	21.2593i	0.605743	+	0.714624i
$886$	−4.80177	−	27.2322i	−0.161318	−	0.914883i
$887$	−2.96716	−	16.8276i	−0.0996274	−	0.565015i	−0.993231	−	0.116158i	$-0.962942\pi$
$887$	−2.96716	−	16.8276i	−0.0996274	−	0.565015i	0.893603	−	0.448857i	$-0.148169\pi$
$888$	5.01949	+	0.859270i	0.168443	+	0.0288352i
$889$	11.7284	−	16.3442i	0.393359	−	0.548167i
$890$	−1.40063			−0.0469491
$891$	−3.35964	+	2.93530i	−0.112552	+	0.0983362i
$892$	−5.24144	+	9.07844i	−0.175496	+	0.303969i
$893$	−30.8261	−	25.8661i	−1.03155	−	0.865577i
$894$	1.43248	+	3.87543i	0.0479093	+	0.129614i
$895$	4.52087	+	1.64546i	0.151116	+	0.0550018i
$896$	1.84906	+	1.89235i	0.0617728	+	0.0632189i
$897$	18.4785	−	51.5685i	0.616980	−	1.72182i
$898$	−3.47493	−	2.91581i	−0.115960	−	0.0973019i
$899$	14.8108	+	25.6531i	0.493969	+	0.855579i
$900$	−0.492520	−	2.63895i	−0.0164173	−	0.0879649i
$901$	13.0565	−	22.6145i	0.434974	−	0.753397i
$902$	3.50289	+	2.93928i	0.116634	+	0.0978672i
$903$	−25.6206	+	2.07174i	−0.852599	+	0.0689433i
$904$	1.50095	+	8.51229i	0.0499208	+	0.283115i
$905$	40.8322	−	34.2623i	1.35731	−	1.13892i
$906$	−0.0438007	−	8.77824i	−0.00145518	−	0.291637i
$907$	33.0896	−	12.0436i	1.09872	−	0.399902i	0.271876	−	0.962332i	$-0.412356\pi$
$907$	33.0896	−	12.0436i	1.09872	−	0.399902i	0.826845	+	0.562431i	$0.190134\pi$
$908$	8.24165	−	14.2749i	0.273509	−	0.473731i
$909$	50.8850	−	0.507813i	1.68775	−	0.0168431i
$910$	−2.20570	−	29.0827i	−0.0731182	−	0.964083i
$911$	11.9610	−	4.35344i	0.396285	−	0.144236i	−0.136188	−	0.990683i	$-0.543485\pi$
$911$	11.9610	−	4.35344i	0.396285	−	0.144236i	0.532473	+	0.846447i	$0.321263\pi$
$912$	−6.25260	−	7.37650i	−0.207044	−	0.244260i
$913$	−0.747332	−	4.23833i	−0.0247331	−	0.140268i
$914$	14.5752	−	12.2301i	0.482105	−	0.404534i
$915$	52.8574	+	9.04848i	1.74741	+	0.299134i
$916$	−2.50193	+	14.1891i	−0.0826661	+	0.468823i
$917$	−1.08353	−	14.2866i	−0.0357812	−	0.471784i
$918$	−32.2961	−	5.19747i	−1.06593	−	0.171542i
$919$	25.4994	+	44.1662i	0.841147	+	1.45691i	0.888925	+	0.458052i	$0.151453\pi$
$919$	25.4994	+	44.1662i	0.841147	+	1.45691i	−0.0477779	+	0.998858i	$0.515214\pi$
$920$	−12.9554	−	10.8708i	−0.427126	−	0.358401i
$921$	−5.80193	−	0.993213i	−0.191180	−	0.0327275i
$922$	−2.08142	−	11.8043i	−0.0685481	−	0.388755i
$923$	21.7865	−	18.2810i	0.717111	−	0.601728i
$924$	0.573479	+	2.19800i	0.0188661	+	0.0723089i
$925$	−2.47230	+	0.899844i	−0.0812887	+	0.0295867i
$926$	13.5217			0.444351
$927$	6.87075	−	41.3763i	0.225665	−	1.35898i
$928$	5.87582			0.192883
$929$	6.17609	−	35.0263i	0.202631	−	1.14918i	−0.698494	−	0.715616i	$-0.746146\pi$
$929$	6.17609	−	35.0263i	0.202631	−	1.14918i	0.901125	−	0.433560i	$-0.142743\pi$
$930$	0.105780	+	21.1998i	0.00346868	+	0.695169i
$931$	38.3196	+	7.67490i	1.25587	+	0.251535i
$932$	1.90819	+	10.8219i	0.0625048	+	0.354482i
$933$	22.0004	−	12.8487i	0.720260	−	0.420648i
$934$	1.05225	−	0.382988i	0.0344307	−	0.0125318i
$935$	−7.57660			−0.247781
$936$	−2.23132	+	13.4372i	−0.0729331	+	0.439210i
$937$	16.1691	−	28.0056i	0.528220	−	0.914905i	−0.471238	−	0.882006i	$-0.656193\pi$
$937$	16.1691	−	28.0056i	0.528220	−	0.914905i	0.999459	−	0.0328986i	$-0.0104738\pi$
$938$	18.5828	+	1.84265i	0.606750	+	0.0601646i
$939$	32.7009	+	38.5788i	1.06715	+	1.25897i
$940$	16.4446	+	5.98534i	0.536363	+	0.195220i
$941$	−21.9612	+	18.4277i	−0.715916	+	0.600725i	−0.926252	−	0.376904i	$-0.876989\pi$
$941$	−21.9612	+	18.4277i	−0.715916	+	0.600725i	0.210336	+	0.977629i	$0.432544\pi$
$942$	−32.6060	−	5.58171i	−1.06236	−	0.181862i
$943$	−60.3810	+	21.9769i	−1.96628	+	0.715666i
$944$	−6.62714			−0.215695
$945$	−19.2380	−	27.2768i	−0.625811	−	0.887315i
$946$	2.78044			0.0903998
$947$	−13.7720	+	5.01258i	−0.447529	+	0.162887i	−0.555946	−	0.831218i	$-0.687644\pi$
$947$	−13.7720	+	5.01258i	−0.447529	+	0.162887i	0.108417	+	0.994105i	$0.465422\pi$
$948$	−8.04630	−	21.7684i	−0.261332	−	0.707006i
$949$	−10.8843	+	9.13300i	−0.353319	+	0.296470i
$950$	4.69454	+	1.70867i	0.152311	+	0.0554367i
$951$	−26.9405	+	4.88907i	−0.873606	+	0.158539i
$952$	−9.71065	+	13.5323i	−0.314724	+	0.438585i
$953$	8.87335	−	15.3691i	0.287436	−	0.497854i	−0.685761	−	0.727827i	$-0.740530\pi$
$953$	8.87335	−	15.3691i	0.287436	−	0.497854i	0.973197	+	0.229973i	$0.0738638\pi$
$954$	−12.4433	+	0.124179i	−0.402866	+	0.00402046i
$955$	−36.9446			−1.19550
$956$	1.51848	−	0.552682i	0.0491112	−	0.0178750i
$957$	4.38149	+	2.50059i	0.141634	+	0.0808326i
$958$	−5.84342	−	33.1397i	−0.188792	−	1.07069i
$959$	15.4522	+	15.8139i	0.498977	+	0.510658i
$960$	3.65234	+	2.08445i	0.117879	+	0.0672753i
$961$	−0.969913	+	5.50065i	−0.0312875	+	0.177440i
$962$	13.3496			0.430407
$963$	26.5378	−	22.7230i	0.855168	−	0.732237i
$964$	8.60389			0.277113
$965$	36.0697	−	13.1283i	1.16112	−	0.422615i
$966$	−30.7778	−	8.46431i	−0.990259	−	0.272335i
$967$	−22.5131	+	18.8907i	−0.723971	+	0.607484i	−0.928481	−	0.371381i	$-0.878884\pi$
$967$	−22.5131	+	18.8907i	−0.723971	+	0.607484i	0.204510	+	0.978865i	$0.434440\pi$
$968$	1.86746	+	10.5909i	0.0600225	+	0.340404i
$969$	38.8970	−	46.8281i	1.24955	−	1.50434i
$970$	1.40415	+	1.17822i	0.0450845	+	0.0378304i
$971$	5.86809	+	10.1638i	0.188316	+	0.326173i	0.944689	−	0.327968i	$-0.106364\pi$
$971$	5.86809	+	10.1638i	0.188316	+	0.326173i	−0.756373	+	0.654141i	$0.773030\pi$
$972$	5.69532	+	14.5108i	0.182677	+	0.465434i
$973$	−7.73621	−	3.71701i	−0.248012	−	0.119162i
$974$	4.56927	−	25.9136i	0.146409	−	0.830325i
$975$	−2.43983	−	6.60072i	−0.0781372	−	0.211392i
$976$	−9.76866	+	8.19688i	−0.312687	+	0.262376i
$977$	9.42483	+	53.4508i	0.301527	+	1.71004i	0.639418	+	0.768859i	$0.279175\pi$
$977$	9.42483	+	53.4508i	0.301527	+	1.71004i	−0.337892	+	0.941185i	$0.609714\pi$
$978$	5.69621	−	1.03373i	0.182145	−	0.0330550i
$979$	0.268714	−	0.0978040i	0.00858815	−	0.00312583i
$980$	−16.8011	+	2.56321i	−0.536691	+	0.0818787i
$981$	−29.5523	−	10.4234i	−0.943532	−	0.332793i
$982$	−11.6493	+	20.1772i	−0.371744	+	0.643880i
$983$	−0.0436833	+	0.0158994i	−0.00139328	+	0.000507113i	−0.342717	−	0.939439i	$-0.611347\pi$
$983$	−0.0436833	+	0.0158994i	−0.00139328	+	0.000507113i	0.341323	+	0.939946i	$0.389125\pi$
$984$	13.7971	−	8.05781i	0.439835	−	0.256874i
$985$	−30.8505	+	25.8866i	−0.982977	+	0.824816i
$986$	6.42331	+	36.4284i	0.204560	+	1.16012i
$987$	32.9227	−	2.66221i	1.04794	−	0.0847391i
$988$	−19.4184	−	16.2939i	−0.617781	−	0.518379i
$989$	−19.5355	+	33.8365i	−0.621192	+	1.07594i
$990$	1.83640	+	3.10867i	0.0583646	+	0.0988001i
$991$	28.7600	+	49.8137i	0.913591	+	1.58239i	0.808952	+	0.587875i	$0.200035\pi$
$991$	28.7600	+	49.8137i	0.913591	+	1.58239i	0.104639	+	0.994510i	$0.466631\pi$
$992$	−3.86184	−	3.24047i	−0.122614	−	0.102885i
$993$	37.7164	−	6.84463i	1.19689	−	0.217208i
$994$	−11.5821	−	11.8533i	−0.367363	−	0.375963i
$995$	−0.234695	−	0.0854221i	−0.00744034	−	0.00270806i
$996$	−14.8222	−	2.53737i	−0.469661	−	0.0803996i
$997$	10.3830	+	8.71237i	0.328833	+	0.275924i	0.792224	−	0.610230i	$-0.208923\pi$
$997$	10.3830	+	8.71237i	0.328833	+	0.275924i	−0.463391	+	0.886154i	$0.653367\pi$
$998$	0.536402	−	0.929075i	0.0169795	−	0.0294094i
$999$	13.1149	−	7.83595i	0.414937	−	0.247918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.9	yes	72
7.2	even	3		378.2.v.a.79.9	yes	72
27.13	even	9		378.2.v.a.67.9	✓	72
189.121	even	9	inner	378.2.w.b.121.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.9	✓	72	27.13	even	9
378.2.v.a.79.9	yes	72	7.2	even	3
378.2.w.b.25.9	yes	72	1.1	even	1	trivial
378.2.w.b.121.9	yes	72	189.121	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.10671 - 1.33237i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.28151 - 0.830401i) q^{5} +(0.584268 - 1.63053i) q^{6} +(-2.63284 - 0.261069i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.550401 - 2.94908i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.10671 - 1.33237i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.28151 - 0.830401i) q^{5} +(0.584268 - 1.63053i) q^{6} +(-2.63284 - 0.261069i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.550401 - 2.94908i) q^{9} -2.42793 q^{10} +(0.465805 - 0.169539i) q^{11} +(-0.00864229 - 1.73203i) q^{12} +(-0.788435 - 4.47144i) q^{13} +(-2.56335 + 0.655160i) q^{14} +(-3.63136 + 2.12079i) q^{15} +(0.173648 - 0.984808i) q^{16} +6.29535 q^{17} +(-1.52585 - 2.58298i) q^{18} +5.58294 q^{19} +(-2.28151 + 0.830401i) q^{20} +(-3.26162 + 3.21898i) q^{21} +(0.379728 - 0.318629i) q^{22} +(1.20957 + 6.85980i) q^{23} +(-0.600510 - 1.62462i) q^{24} +(0.685485 + 0.575191i) q^{25} +(-2.27021 - 3.93211i) q^{26} +(-4.53838 - 2.53043i) q^{27} +(-2.18468 + 1.49237i) q^{28} +(-1.02033 + 5.78655i) q^{29} +(-2.68700 + 3.23489i) q^{30} +(3.86184 - 3.24047i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.289621 - 0.808253i) q^{33} +(5.91569 - 2.15314i) q^{34} +(5.79005 + 2.78194i) q^{35} +(-2.31726 - 1.90533i) q^{36} +(-1.47008 + 2.54625i) q^{37} +(5.24625 - 1.90948i) q^{38} +(-6.83016 - 3.89808i) q^{39} +(-1.85990 + 1.56064i) q^{40} +(1.60186 + 9.08461i) q^{41} +(-1.96396 + 4.14039i) q^{42} +(4.29683 + 3.60547i) q^{43} +(0.247850 - 0.429288i) q^{44} +(-1.19317 + 7.18539i) q^{45} +(3.48281 + 6.03241i) q^{46} +(-5.52147 - 4.63307i) q^{47} +(-1.11995 - 1.32126i) q^{48} +(6.86369 + 1.37471i) q^{49} +(0.840872 + 0.306053i) q^{50} +(6.96711 - 8.38771i) q^{51} +(-3.47816 - 2.91852i) q^{52} +(2.07398 - 3.59225i) q^{53} +(-5.13014 - 0.825605i) q^{54} -1.20352 q^{55} +(-1.54251 + 2.14957i) q^{56} +(6.17868 - 7.43853i) q^{57} +(1.02033 + 5.78655i) q^{58} +(-1.15079 - 6.52646i) q^{59} +(-1.41856 + 3.95881i) q^{60} +(-9.76866 - 8.19688i) q^{61} +(2.52064 - 4.36588i) q^{62} +(0.679205 + 7.90814i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.91426 + 10.8563i) q^{65} +(-0.00428398 - 0.858566i) q^{66} +(-6.63243 - 2.41401i) q^{67} +(4.82252 - 4.04657i) q^{68} +(10.4784 + 5.98020i) q^{69} +(6.39235 + 0.633857i) q^{70} +(3.13190 + 5.42461i) q^{71} +(-2.82918 - 0.997877i) q^{72} +(-1.56466 - 2.71007i) q^{73} +(-0.510554 + 2.89549i) q^{74} +(1.52500 - 0.276751i) q^{75} +(4.27678 - 3.58865i) q^{76} +(-1.27065 + 0.324762i) q^{77} +(-7.75147 - 1.32695i) q^{78} +(12.5910 - 4.58276i) q^{79} +(-1.21396 + 2.10265i) q^{80} +(-8.39412 + 3.24635i) q^{81} +(4.61238 + 7.98887i) q^{82} +(1.50763 - 8.55021i) q^{83} +(-0.429425 + 4.56241i) q^{84} +(-14.3629 - 5.22766i) q^{85} +(5.27084 + 1.91843i) q^{86} +(6.58061 + 7.76347i) q^{87} +(0.0860773 - 0.488169i) q^{88} +0.576882 q^{89} +(1.33633 + 7.16015i) q^{90} +(0.908469 + 11.9784i) q^{91} +(5.33598 + 4.47742i) q^{92} +(-0.0435682 - 8.73164i) q^{93} +(-6.77309 - 2.46520i) q^{94} +(-12.7375 - 4.63608i) q^{95} +(-1.50430 - 0.858530i) q^{96} +(-0.578333 - 0.485279i) q^{97} +(6.91993 - 1.05572i) q^{98} +(-0.756364 - 1.28038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more