LMFDB - Embedded newform 215.2.q.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [215,2,Mod(31,215)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(215, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("215.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 215 = 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	215.q (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:	$1.71678364346$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	215.31
Dual form			215.2.q.b.111.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.574959 - 0.276886i) q^{2} +(-1.61221 + 1.09919i) q^{3} +(-0.993068 + 1.24527i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(-0.622606 + 1.07839i) q^{6} +(-2.11364 - 3.66093i) q^{7} +(-0.510182 + 2.23526i) q^{8} +(0.294993 - 0.751629i) q^{9} +O(q^{10})$	\(q+(0.574959 - 0.276886i) q^{2} +(-1.61221 + 1.09919i) q^{3} +(-0.993068 + 1.24527i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(-0.622606 + 1.07839i) q^{6} +(-2.11364 - 3.66093i) q^{7} +(-0.510182 + 2.23526i) q^{8} +(0.294993 - 0.751629i) q^{9} +(-0.609805 - 0.188100i) q^{10} +(-1.41440 - 1.77361i) q^{11} +(0.232253 - 3.09920i) q^{12} +(-3.19996 + 0.987056i) q^{13} +(-2.22891 - 1.51965i) q^{14} +(1.92947 + 0.290821i) q^{15} +(-0.383268 - 1.67920i) q^{16} +(-3.33167 + 3.09134i) q^{17} +(-0.0385066 - 0.513835i) q^{18} +(0.504698 + 1.28595i) q^{19} +(1.57497 - 0.237388i) q^{20} +(7.43168 + 3.57891i) q^{21} +(-1.30431 - 0.628123i) q^{22} +(1.53633 - 0.231565i) q^{23} +(-1.63444 - 4.16449i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-1.56654 + 1.45354i) q^{26} +(-0.952003 - 4.17100i) q^{27} +(6.65782 + 1.00351i) q^{28} +(3.34579 + 2.28112i) q^{29} +(1.18989 - 0.367033i) q^{30} +(-0.779997 + 10.4083i) q^{31} +(-3.54431 - 4.44442i) q^{32} +(4.22985 + 1.30474i) q^{33} +(-1.05963 + 2.69988i) q^{34} +(-0.940657 + 4.12129i) q^{35} +(0.643031 + 1.11376i) q^{36} +(-1.24501 + 2.15642i) q^{37} +(0.646241 + 0.599624i) q^{38} +(4.07405 - 5.10870i) q^{39} +(1.89435 - 1.29155i) q^{40} +(-0.962102 + 0.463324i) q^{41} +5.26386 q^{42} +(4.67763 - 4.59563i) q^{43} +3.61322 q^{44} +(-0.727482 + 0.350337i) q^{45} +(0.819210 - 0.558528i) q^{46} +(1.28061 - 1.60584i) q^{47} +(2.46367 + 2.28595i) q^{48} +(-5.43493 + 9.41358i) q^{49} +(0.319078 + 0.552659i) q^{50} +(1.97340 - 8.64602i) q^{51} +(1.94862 - 4.96502i) q^{52} +(-11.7629 - 3.62838i) q^{53} +(-1.70225 - 2.13456i) q^{54} +(-0.169527 + 2.26219i) q^{55} +(9.26145 - 2.85678i) q^{56} +(-2.22718 - 1.51847i) q^{57} +(2.55530 + 0.385150i) q^{58} +(-2.57109 - 11.2647i) q^{59} +(-2.27825 + 2.11391i) q^{60} +(0.544790 + 7.26971i) q^{61} +(2.43345 + 6.20033i) q^{62} +(-3.37517 + 0.508725i) q^{63} +(-0.164791 - 0.0793592i) q^{64} +(3.01710 + 1.45296i) q^{65} +(2.79325 - 0.421015i) q^{66} +(-2.30374 - 5.86982i) q^{67} +(-0.540969 - 7.21872i) q^{68} +(-2.22236 + 2.06205i) q^{69} +(0.600286 + 2.63003i) q^{70} +(-4.22399 - 0.636664i) q^{71} +(1.52958 + 1.04285i) q^{72} +(-12.3030 + 3.79498i) q^{73} +(-0.118747 + 1.58457i) q^{74} +(-1.21660 - 1.52556i) q^{75} +(-2.10255 - 0.648550i) q^{76} +(-3.50351 + 8.92680i) q^{77} +(0.927886 - 4.06534i) q^{78} +(-0.981858 - 1.70063i) q^{79} +(-0.861194 + 1.49163i) q^{80} +(7.89524 + 7.32571i) q^{81} +(-0.424881 + 0.532784i) q^{82} +(7.00429 - 4.77544i) q^{83} +(-11.8369 + 5.70033i) q^{84} +4.54493 q^{85} +(1.41698 - 3.93746i) q^{86} -7.90151 q^{87} +(4.68607 - 2.25669i) q^{88} +(12.3092 - 8.39227i) q^{89} +(-0.321269 + 0.402859i) q^{90} +(10.3771 + 9.62853i) q^{91} +(-1.23732 + 2.14310i) q^{92} +(-10.1832 - 17.6378i) q^{93} +(0.291667 - 1.27787i) q^{94} +(0.504698 - 1.28595i) q^{95} +(10.5994 + 3.26949i) q^{96} +(9.08877 + 11.3970i) q^{97} +(-0.518378 + 6.91727i) q^{98} +(-1.75033 + 0.539906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9}+O(q^{10}) $ 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9} + 14 q^{10} - 24 q^{11} + 15 q^{12} - 17 q^{14} - 4 q^{15} - 2 q^{16} + 13 q^{17} + 14 q^{18} + q^{19} - 8 q^{20} + 30 q^{21} - 37 q^{22} - 14 q^{23} - 15 q^{24} + 8 q^{25} - 56 q^{26} - 18 q^{27} + 111 q^{28} - 15 q^{29} + 2 q^{30} - 43 q^{31} - 9 q^{32} - 19 q^{33} + 33 q^{34} + 3 q^{35} - 61 q^{36} + 19 q^{37} - 24 q^{38} + 19 q^{39} + 3 q^{40} + 40 q^{41} + 140 q^{42} - 53 q^{43} + 104 q^{44} - 32 q^{45} - 34 q^{46} - 18 q^{47} - 54 q^{48} - 78 q^{49} - 7 q^{50} + 59 q^{51} - 25 q^{52} + 51 q^{53} - 24 q^{54} + 12 q^{55} - 20 q^{56} - 113 q^{57} - 112 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 87 q^{62} - 38 q^{63} + 50 q^{64} - 96 q^{66} - 28 q^{67} - 149 q^{68} + 112 q^{69} - q^{70} + 51 q^{71} - 208 q^{72} + 24 q^{73} - 19 q^{74} + 8 q^{75} + 248 q^{76} + 7 q^{77} + 242 q^{78} - 138 q^{79} - 55 q^{80} - 15 q^{81} - 98 q^{82} + 43 q^{83} + 132 q^{84} + 44 q^{85} - 30 q^{86} - 22 q^{87} - 66 q^{88} + 7 q^{89} + 98 q^{90} - 5 q^{91} - 102 q^{92} - 2 q^{93} + 16 q^{94} + q^{95} + 486 q^{96} - 67 q^{97} + 62 q^{98} + 11 q^{99}+O(q^{100}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9 + 14 * q^10 - 24 * q^11 + 15 * q^12 - 17 * q^14 - 4 * q^15 - 2 * q^16 + 13 * q^17 + 14 * q^18 + q^19 - 8 * q^20 + 30 * q^21 - 37 * q^22 - 14 * q^23 - 15 * q^24 + 8 * q^25 - 56 * q^26 - 18 * q^27 + 111 * q^28 - 15 * q^29 + 2 * q^30 - 43 * q^31 - 9 * q^32 - 19 * q^33 + 33 * q^34 + 3 * q^35 - 61 * q^36 + 19 * q^37 - 24 * q^38 + 19 * q^39 + 3 * q^40 + 40 * q^41 + 140 * q^42 - 53 * q^43 + 104 * q^44 - 32 * q^45 - 34 * q^46 - 18 * q^47 - 54 * q^48 - 78 * q^49 - 7 * q^50 + 59 * q^51 - 25 * q^52 + 51 * q^53 - 24 * q^54 + 12 * q^55 - 20 * q^56 - 113 * q^57 - 112 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 87 * q^62 - 38 * q^63 + 50 * q^64 - 96 * q^66 - 28 * q^67 - 149 * q^68 + 112 * q^69 - q^70 + 51 * q^71 - 208 * q^72 + 24 * q^73 - 19 * q^74 + 8 * q^75 + 248 * q^76 + 7 * q^77 + 242 * q^78 - 138 * q^79 - 55 * q^80 - 15 * q^81 - 98 * q^82 + 43 * q^83 + 132 * q^84 + 44 * q^85 - 30 * q^86 - 22 * q^87 - 66 * q^88 + 7 * q^89 + 98 * q^90 - 5 * q^91 - 102 * q^92 - 2 * q^93 + 16 * q^94 + q^95 + 486 * q^96 - 67 * q^97 + 62 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/215\mathbb{Z}\right)^\times$.

$n$	$46$	$87$
$\chi(n)$	$e\left(\frac{17}{21}\right)$	$1$

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 $

$2$	0.574959	−	0.276886i	0.406557	−	0.195788i	−0.219417	−	0.975631i	$-0.570416\pi$
$2$	0.574959	−	0.276886i	0.406557	−	0.195788i	0.625975	+	0.779843i	$0.284701\pi$
$3$	−1.61221	+	1.09919i	−0.930812	+	0.634617i	−0.930857	−	0.365383i	$-0.880938\pi$
$3$	−1.61221	+	1.09919i	−0.930812	+	0.634617i	4.55900e−5		1.00000i	$0.499985\pi$
$4$	−0.993068	+	1.24527i	−0.496534	+	0.622634i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$6$	−0.622606	+	1.07839i	−0.254178	+	0.440249i
$7$	−2.11364	−	3.66093i	−0.798880	−	1.38370i	−0.920346	−	0.391105i	$-0.872093\pi$
$7$	−2.11364	−	3.66093i	−0.798880	−	1.38370i	0.121466	−	0.992596i	$-0.461240\pi$
$8$	−0.510182	+	2.23526i	−0.180377	+	0.790282i
$9$	0.294993	−	0.751629i	0.0983309	−	0.250543i
$10$	−0.609805	−	0.188100i	−0.192837	−	0.0594824i
$11$	−1.41440	−	1.77361i	−0.426459	−	0.534763i	0.521459	−	0.853276i	$-0.325388\pi$
$11$	−1.41440	−	1.77361i	−0.426459	−	0.534763i	−0.947918	+	0.318513i	$0.896816\pi$
$12$	0.232253	−	3.09920i	0.0670457	−	0.894663i
$13$	−3.19996	+	0.987056i	−0.887508	+	0.273760i	−0.704799	−	0.709407i	$-0.748963\pi$
$13$	−3.19996	+	0.987056i	−0.887508	+	0.273760i	−0.182709	+	0.983167i	$0.558487\pi$
$14$	−2.22891	−	1.51965i	−0.595702	−	0.406143i
$15$	1.92947	+	0.290821i	0.498188	+	0.0750897i
$16$	−0.383268	−	1.67920i	−0.0958169	−	0.419801i
$17$	−3.33167	+	3.09134i	−0.808048	+	0.749759i	−0.971563	−	0.236782i	$-0.923907\pi$
$17$	−3.33167	+	3.09134i	−0.808048	+	0.749759i	0.163515	+	0.986541i	$0.447717\pi$
$18$	−0.0385066	−	0.513835i	−0.00907609	−	0.121112i
$19$	0.504698	+	1.28595i	0.115786	+	0.295017i	0.977005	−	0.213217i	$-0.0683940\pi$
$19$	0.504698	+	1.28595i	0.115786	+	0.295017i	−0.861219	+	0.508233i	$0.830299\pi$
$20$	1.57497	−	0.237388i	0.352173	−	0.0530816i
$21$	7.43168	+	3.57891i	1.62173	+	0.780982i
$22$	−1.30431	−	0.628123i	−0.278080	−	0.133916i
$23$	1.53633	−	0.231565i	0.320347	−	0.0482846i	0.0130996	−	0.999914i	$-0.495830\pi$
$23$	1.53633	−	0.231565i	0.320347	−	0.0482846i	0.307248	+	0.951630i	$0.400592\pi$
$24$	−1.63444	−	4.16449i	−0.333629	−	0.850074i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	−1.56654	+	1.45354i	−0.307224	+	0.285062i
$27$	−0.952003	−	4.17100i	−0.183213	−	0.802709i
$28$	6.65782	+	1.00351i	1.25821	+	0.189645i
$29$	3.34579	+	2.28112i	0.621298	+	0.423594i	0.832637	−	0.553819i	$-0.186830\pi$
$29$	3.34579	+	2.28112i	0.621298	+	0.423594i	−0.211339	+	0.977413i	$0.567782\pi$
$30$	1.18989	−	0.367033i	0.217244	−	0.0670107i
$31$	−0.779997	+	10.4083i	−0.140092	+	1.86939i	0.277458	+	0.960738i	$0.410508\pi$
$31$	−0.779997	+	10.4083i	−0.140092	+	1.86939i	−0.417549	+	0.908654i	$0.637111\pi$
$32$	−3.54431	−	4.44442i	−0.626551	−	0.785671i
$33$	4.22985	+	1.30474i	0.736322	+	0.227125i
$34$	−1.05963	+	2.69988i	−0.181724	+	0.463026i
$35$	−0.940657	+	4.12129i	−0.159000	+	0.696625i
$36$	0.643031	+	1.11376i	0.107172	+	0.185627i
$37$	−1.24501	+	2.15642i	−0.204678	+	0.354512i	−0.950030	−	0.312158i	$-0.898948\pi$
$37$	−1.24501	+	2.15642i	−0.204678	+	0.354512i	0.745352	+	0.666671i	$0.232281\pi$
$38$	0.646241	+	0.599624i	0.104834	+	0.0972718i
$39$	4.07405	−	5.10870i	0.652370	−	0.818046i
$40$	1.89435	−	1.29155i	0.299523	−	0.204211i
$41$	−0.962102	+	0.463324i	−0.150255	+	0.0723590i	−0.507500	−	0.861652i	$-0.669430\pi$
$41$	−0.962102	+	0.463324i	−0.150255	+	0.0723590i	0.357245	+	0.934011i	$0.383716\pi$
$42$	5.26386			0.812231
$43$	4.67763	−	4.59563i	0.713331	−	0.700827i
$43$	4.67763	−	4.59563i	0.713331	−	0.700827i
$44$	3.61322			0.544713
$45$	−0.727482	+	0.350337i	−0.108447	+	0.0522252i
$46$	0.819210	−	0.558528i	0.120786	−	0.0823504i
$47$	1.28061	−	1.60584i	0.186797	−	0.234236i	−0.679611	−	0.733572i	$-0.737852\pi$
$47$	1.28061	−	1.60584i	0.186797	−	0.234236i	0.866408	+	0.499337i	$0.166423\pi$
$48$	2.46367	+	2.28595i	0.355600	+	0.329949i
$49$	−5.43493	+	9.41358i	−0.776419	+	1.34480i
$50$	0.319078	+	0.552659i	0.0451244	+	0.0781578i
$51$	1.97340	−	8.64602i	0.276331	−	1.21069i
$52$	1.94862	−	4.96502i	0.270226	−	0.688524i
$53$	−11.7629	−	3.62838i	−1.61576	−	0.498396i	−0.650460	−	0.759541i	$-0.725424\pi$
$53$	−11.7629	−	3.62838i	−1.61576	−	0.498396i	−0.965300	+	0.261145i	$0.915900\pi$
$54$	−1.70225	−	2.13456i	−0.231647	−	0.290476i
$55$	−0.169527	+	2.26219i	−0.0228591	+	0.305033i
$56$	9.26145	−	2.85678i	1.23761	−	0.381753i
$57$	−2.22718	−	1.51847i	−0.294997	−	0.201126i
$58$	2.55530	+	0.385150i	0.335528	+	0.0505727i
$59$	−2.57109	−	11.2647i	−0.334727	−	1.46653i	−0.809861	−	0.586621i	$-0.800458\pi$
$59$	−2.57109	−	11.2647i	−0.334727	−	1.46653i	0.475135	−	0.879913i	$-0.342399\pi$
$60$	−2.27825	+	2.11391i	−0.294121	+	0.272904i
$61$	0.544790	+	7.26971i	0.0697532	+	0.930791i	0.916819	+	0.399303i	$0.130748\pi$
$61$	0.544790	+	7.26971i	0.0697532	+	0.930791i	−0.847066	+	0.531488i	$0.821633\pi$
$62$	2.43345	+	6.20033i	0.309049	+	0.787443i
$63$	−3.37517	+	0.508725i	−0.425231	+	0.0640933i
$64$	−0.164791	−	0.0793592i	−0.0205989	−	0.00991990i
$65$	3.01710	+	1.45296i	0.374226	+	0.180218i
$66$	2.79325	−	0.421015i	0.343825	−	0.0518233i
$67$	−2.30374	−	5.86982i	−0.281446	−	0.717113i	−0.999771	−	0.0214050i	$-0.993186\pi$
$67$	−2.30374	−	5.86982i	−0.281446	−	0.717113i	0.718325	−	0.695708i	$-0.244909\pi$
$68$	−0.540969	−	7.21872i	−0.0656021	−	0.875399i
$69$	−2.22236	+	2.06205i	−0.267541	+	0.248241i
$70$	0.600286	+	2.63003i	0.0717479	+	0.314348i
$71$	−4.22399	−	0.636664i	−0.501296	−	0.0755582i	−0.106473	−	0.994316i	$-0.533956\pi$
$71$	−4.22399	−	0.636664i	−0.501296	−	0.0755582i	−0.394823	+	0.918757i	$0.629194\pi$
$72$	1.52958	+	1.04285i	0.180263	+	0.122901i
$73$	−12.3030	+	3.79498i	−1.43996	+	0.444169i	−0.913782	−	0.406204i	$-0.866852\pi$
$73$	−12.3030	+	3.79498i	−1.43996	+	0.444169i	−0.526179	+	0.850374i	$0.676376\pi$
$74$	−0.118747	+	1.58457i	−0.0138041	+	0.184203i
$75$	−1.21660	−	1.52556i	−0.140480	−	0.176157i
$76$	−2.10255	−	0.648550i	−0.241179	−	0.0743938i
$77$	−3.50351	+	8.92680i	−0.399262	+	1.01730i
$78$	0.927886	−	4.06534i	0.105062	−	0.460309i
$79$	−0.981858	−	1.70063i	−0.110468	−	0.191336i	0.805491	−	0.592608i	$-0.201902\pi$
$79$	−0.981858	−	1.70063i	−0.110468	−	0.191336i	−0.915959	+	0.401272i	$0.868568\pi$
$80$	−0.861194	+	1.49163i	−0.0962844	+	0.166770i
$81$	7.89524	+	7.32571i	0.877249	+	0.813968i
$82$	−0.424881	+	0.532784i	−0.0469203	+	0.0588362i
$83$	7.00429	−	4.77544i	0.768821	−	0.524173i	−0.114228	−	0.993455i	$-0.536439\pi$
$83$	7.00429	−	4.77544i	0.768821	−	0.524173i	0.883049	+	0.469282i	$0.155487\pi$
$84$	−11.8369	+	5.70033i	−1.29151	+	0.621957i
$85$	4.54493			0.492967
$86$	1.41698	−	3.93746i	0.152797	−	0.424588i
$87$	−7.90151			−0.847131
$88$	4.68607	−	2.25669i	0.499537	−	0.240564i
$89$	12.3092	−	8.39227i	1.30477	−	0.889578i	0.306710	−	0.951803i	$-0.400772\pi$
$89$	12.3092	−	8.39227i	1.30477	−	0.889578i	0.998062	+	0.0622247i	$0.0198195\pi$
$90$	−0.321269	+	0.402859i	−0.0338647	+	0.0424650i
$91$	10.3771	+	9.62853i	1.08781	+	1.00934i
$92$	−1.23732	+	2.14310i	−0.129000	+	0.223434i
$93$	−10.1832	−	17.6378i	−1.05595	−	1.82896i
$94$	0.291667	−	1.27787i	0.0300831	−	0.131803i
$95$	0.504698	−	1.28595i	0.0517809	−	0.131936i
$96$	10.5994	+	3.26949i	1.08180	+	0.333691i
$97$	9.08877	+	11.3970i	0.922825	+	1.15719i	0.987236	+	0.159262i	$0.0509115\pi$
$97$	9.08877	+	11.3970i	0.922825	+	1.15719i	−0.0644115	+	0.997923i	$0.520517\pi$
$98$	−0.518378	+	6.91727i	−0.0523641	+	0.698750i
$99$	−1.75033	+	0.539906i	−0.175915	+	0.0542626i
$100$	−1.31600	−	0.897232i	−0.131600	−	0.0897232i
$101$	−15.1551	−	2.28427i	−1.50799	−	0.227293i	−0.657569	−	0.753395i	$-0.728415\pi$
$101$	−15.1551	−	2.28427i	−1.50799	−	0.227293i	−0.850422	+	0.526102i	$0.823653\pi$
$102$	−1.25934	−	5.51751i	−0.124693	−	0.546315i
$103$	−12.8092	+	11.8852i	−1.26213	+	1.17108i	−0.284977	+	0.958534i	$0.591986\pi$
$103$	−12.8092	+	11.8852i	−1.26213	+	1.17108i	−0.977150	+	0.212549i	$0.931823\pi$
$104$	−0.573760	−	7.65630i	−0.0562618	−	0.750762i
$105$	−3.01353	−	7.67835i	−0.294091	−	0.749331i
$106$	−7.76783	+	1.17081i	−0.754478	+	0.113719i
$107$	2.16639	+	1.04328i	0.209433	+	0.100857i	0.535660	−	0.844434i	$-0.320063\pi$
$107$	2.16639	+	1.04328i	0.209433	+	0.100857i	−0.326227	+	0.945292i	$0.605777\pi$
$108$	6.13941	+	2.95658i	0.590765	+	0.284497i
$109$	−1.47172	+	0.221826i	−0.140965	+	0.0212471i	−0.219146	−	0.975692i	$-0.570327\pi$
$109$	−1.47172	+	0.221826i	−0.140965	+	0.0212471i	0.0781805	+	0.996939i	$0.475089\pi$
$110$	0.528895	+	1.34760i	0.0504282	+	0.128489i
$111$	−0.363090	−	4.84510i	−0.0344630	−	0.459876i
$112$	−5.33736	+	4.95235i	−0.504333	+	0.467953i
$113$	2.33819	+	10.2443i	0.219958	+	0.963699i	0.957508	+	0.288407i	$0.0931255\pi$
$113$	2.33819	+	10.2443i	0.219958	+	0.963699i	−0.737550	+	0.675293i	$0.764017\pi$
$114$	−1.70098	−	0.256381i	−0.159311	−	0.0240123i
$115$	−1.28371	−	0.875222i	−0.119707	−	0.0816148i
$116$	−6.16321	+	1.90110i	−0.572239	+	0.176512i
$117$	−0.202064	+	2.69635i	−0.0186808	+	0.249278i
$118$	−4.59729	−	5.76482i	−0.423215	−	0.530695i
$119$	18.3591	+	5.66303i	1.68298	+	0.519129i
$120$	−1.63444	+	4.16449i	−0.149204	+	0.380165i
$121$	1.30259	−	5.70701i	0.118417	−	0.518819i
$122$	2.32611	+	4.02894i	0.210596	+	0.364763i
$123$	1.04183	−	1.80451i	0.0939389	−	0.162707i
$124$	−12.1866	−	11.3075i	−1.09439	−	1.01544i
$125$	0.623490	−	0.781831i	0.0557666	−	0.0699291i
$126$	−1.79972	+	1.22703i	−0.160332	+	0.109313i
$127$	−2.77776	+	1.33770i	−0.246486	+	0.118701i	−0.553048	−	0.833149i	$-0.686536\pi$
$127$	−2.77776	+	1.33770i	−0.246486	+	0.118701i	0.306562	+	0.951851i	$0.400821\pi$
$128$	11.2525			0.994594
$129$	−2.48987	+	12.5507i	−0.219221	+	1.10503i
$130$	2.13701			0.187428
$131$	−2.86982	+	1.38203i	−0.250738	+	0.120749i	−0.555032	−	0.831829i	$-0.687294\pi$
$131$	−2.86982	+	1.38203i	−0.250738	+	0.120749i	0.304294	+	0.952578i	$0.401580\pi$
$132$	−5.82527	+	3.97160i	−0.507025	+	0.345684i
$133$	3.64102	−	4.56569i	0.315716	−	0.395896i
$134$	−2.94982	−	2.73703i	−0.254826	−	0.236444i
$135$	−2.13913	+	3.70508i	−0.184107	+	0.318883i
$136$	−5.21017	−	9.02427i	−0.446768	−	0.773825i
$137$	3.18673	−	13.9620i	0.272260	−	1.19285i	−0.635078	−	0.772448i	$-0.719032\pi$
$137$	3.18673	−	13.9620i	0.272260	−	1.19285i	0.907338	−	0.420402i	$-0.138111\pi$
$138$	−0.706814	+	1.80093i	−0.0601680	+	0.153305i
$139$	−13.6884	−	4.22232i	−1.16104	−	0.358133i	−0.346391	−	0.938090i	$-0.612593\pi$
$139$	−13.6884	−	4.22232i	−1.16104	−	0.358133i	−0.814647	+	0.579958i	$0.803069\pi$
$140$	−4.19797	−	5.26409i	−0.354793	−	0.444897i
$141$	−0.299503	+	3.99659i	−0.0252227	+	0.336574i
$142$	−2.60490	+	0.803507i	−0.218599	+	0.0674288i
$143$	6.27668	+	4.27937i	0.524883	+	0.357859i
$144$	−1.37520	−	0.207278i	−0.114600	−	0.0172732i
$145$	−0.901082	−	3.94790i	−0.0748308	−	0.327855i
$146$	−6.02296	+	5.58849i	−0.498464	+	0.462507i
$147$	−1.58503	−	21.1507i	−0.130731	−	1.74448i
$148$	−1.44894	−	3.69183i	−0.119102	−	0.303467i
$149$	10.9210	−	1.64607i	0.894681	−	0.134852i	0.314422	−	0.949283i	$-0.398189\pi$
$149$	10.9210	−	1.64607i	0.894681	−	0.134852i	0.580259	+	0.814432i	$0.302951\pi$
$150$	−1.12190	−	0.540278i	−0.0916026	−	0.0441135i
$151$	−6.16646	−	2.96961i	−0.501819	−	0.241663i	0.165810	−	0.986158i	$-0.446976\pi$
$151$	−6.16646	−	2.96961i	−0.501819	−	0.241663i	−0.667629	+	0.744494i	$0.732691\pi$
$152$	−3.13191	+	0.472060i	−0.254032	+	0.0382891i
$153$	1.34072	+	3.41610i	0.108391	+	0.276175i
$154$	0.457327	+	6.10261i	0.0368525	+	0.491762i
$155$	7.65124	−	7.09932i	0.614563	−	0.570231i
$156$	2.31589	+	10.1466i	0.185419	+	0.812375i
$157$	−4.72257	−	0.711814i	−0.376903	−	0.0568089i	−0.0421407	−	0.999112i	$-0.513418\pi$
$157$	−4.72257	−	0.711814i	−0.376903	−	0.0568089i	−0.334762	+	0.942303i	$0.608656\pi$
$158$	−1.03541	−	0.705928i	−0.0823725	−	0.0561607i
$159$	22.9526	−	7.07993i	1.82026	−	0.561475i
$160$	−0.424813	+	5.66874i	−0.0335844	+	0.448153i
$161$	−4.09499	−	5.13495i	−0.322730	−	0.404691i
$162$	6.56782	+	2.02590i	0.516017	+	0.159170i
$163$	0.678873	−	1.72974i	0.0531735	−	0.135484i	−0.901819	−	0.432114i	$-0.857768\pi$
$163$	0.678873	−	1.72974i	0.0531735	−	0.135484i	0.954992	+	0.296630i	$0.0958630\pi$
$164$	0.378470	−	1.65819i	0.0295535	−	0.129483i
$165$	−2.21325	−	3.83347i	−0.172302	−	0.298435i
$166$	2.70493	−	4.68507i	0.209943	−	0.363632i
$167$	−5.72801	−	5.31482i	−0.443247	−	0.411273i	0.426720	−	0.904384i	$-0.359669\pi$
$167$	−5.72801	−	5.31482i	−0.443247	−	0.411273i	−0.869966	+	0.493111i	$0.835860\pi$
$168$	−11.7913	+	14.7858i	−0.909718	+	1.14075i
$169$	−1.47566	+	1.00609i	−0.113512	+	0.0773915i
$170$	2.61315	−	1.25842i	0.200419	−	0.0965168i
$171$	1.11544			0.0852997
$172$	1.07759	+	10.3887i	0.0821654	+	0.792128i
$173$	−2.42898			−0.184672			−0.0923360	−	0.995728i	$-0.529433\pi$
$173$	−2.42898			−0.184672			−0.0923360	+	0.995728i	$0.529433\pi$
$174$	−4.54304	+	2.18781i	−0.344407	+	0.165858i
$175$	3.49274	−	2.38131i	0.264026	−	0.180010i
$176$	−2.43615	+	3.05484i	−0.183632	+	0.230267i
$177$	16.5271	+	15.3349i	1.24225	+	1.15264i
$178$	4.75358	−	8.23344i	0.356296	−	0.617123i
$179$	2.56940	+	4.45033i	0.192046	+	0.332634i	0.945928	−	0.324376i	$-0.105154\pi$
$179$	2.56940	+	4.45033i	0.192046	+	0.332634i	−0.753882	+	0.657010i	$0.771821\pi$
$180$	0.286176	−	1.25382i	0.0213303	−	0.0934541i
$181$	−2.83958	+	7.23513i	−0.211064	+	0.537783i	−0.996724	−	0.0808757i	$-0.974228\pi$
$181$	−2.83958	+	7.23513i	−0.211064	+	0.537783i	0.785660	+	0.618659i	$0.212324\pi$
$182$	8.63240	+	2.66274i	0.639876	+	0.197376i
$183$	−8.86910	−	11.1215i	−0.655623	−	0.822125i
$184$	−0.266203	+	3.55223i	−0.0196247	+	0.261874i
$185$	2.37939	−	0.733944i	0.174936	−	0.0539607i
$186$	−10.7386	−	7.32143i	−0.787390	−	0.536834i
$187$	10.1951	+	1.53667i	0.745543	+	0.112372i
$188$	0.727963	+	3.18941i	0.0530922	+	0.232612i
$189$	−13.2575	+	12.3012i	−0.964344	+	0.894780i
$190$	−0.0658802	−	0.879111i	−0.00477946	−	0.0637774i
$191$	−2.75742	−	7.02580i	−0.199520	−	0.508369i	0.795738	−	0.605642i	$-0.207083\pi$
$191$	−2.75742	−	7.02580i	−0.199520	−	0.508369i	−0.995258	+	0.0972724i	$0.968988\pi$
$192$	0.352909	−	0.0531925i	0.0254690	−	0.00383884i
$193$	24.7329	+	11.9107i	1.78031	+	0.857352i	0.957176	+	0.289505i	$0.0934908\pi$
$193$	24.7329	+	11.9107i	1.78031	+	0.857352i	0.823134	+	0.567847i	$0.192223\pi$
$194$	8.38132	+	4.03623i	0.601744	+	0.289784i
$195$	−6.46129	+	0.973882i	−0.462702	+	0.0697412i
$196$	−6.32517	−	16.1163i	−0.451798	−	1.15116i
$197$	−0.747661	−	9.97684i	−0.0532687	−	0.710821i	−0.958353	−	0.285588i	$-0.907811\pi$
$197$	−0.747661	−	9.97684i	−0.0532687	−	0.710821i	0.905084	−	0.425233i	$-0.139808\pi$
$198$	−0.856877	+	0.795066i	−0.0608956	+	0.0565029i
$199$	4.61679	+	20.2275i	0.327275	+	1.43389i	0.824301	+	0.566151i	$0.191568\pi$
$199$	4.61679	+	20.2275i	0.327275	+	1.43389i	−0.497026	+	0.867736i	$0.665575\pi$
$200$	−2.26713	−	0.341715i	−0.160310	−	0.0241629i
$201$	10.1661	+	6.93116i	0.717065	+	0.488887i
$202$	−9.34605	+	2.88287i	−0.657586	+	0.202838i
$203$	1.27923	−	17.0702i	0.0897845	−	1.19809i
$204$	8.80689	+	11.0435i	0.616606	+	0.773199i
$205$	1.02041	+	0.314755i	0.0712686	+	0.0219834i
$206$	−4.07392	+	10.3802i	−0.283843	+	0.723221i
$207$	0.279156	−	1.22306i	0.0194027	−	0.0850086i
$208$	2.88391	+	4.99508i	0.199963	+	0.346346i
$209$	1.56692	−	2.71399i	0.108386	−	0.187730i
$210$	−3.85868	−	3.58033i	−0.266274	−	0.247066i
$211$	3.01243	−	3.77747i	0.207384	−	0.260052i	−0.667251	−	0.744833i	$-0.732529\pi$
$211$	3.01243	−	3.77747i	0.207384	−	0.260052i	0.874636	+	0.484781i	$0.161101\pi$
$212$	16.1997	−	11.0447i	1.11260	−	0.758556i
$213$	7.50979	−	3.61652i	0.514562	−	0.247800i
$214$	1.53445			0.104893
$215$	−6.55476	+	0.187241i	−0.447031	+	0.0127698i
$216$	9.80894			0.667414
$217$	39.7528	−	19.1439i	2.69860	−	1.29958i
$218$	−0.784759	+	0.535039i	−0.0531506	+	0.0362374i
$219$	15.6637	−	19.6417i	1.05846	−	1.32726i
$220$	−2.64867	−	2.45761i	−0.178574	−	0.165692i
$221$	7.60987	−	13.1807i	0.511895	−	0.886629i
$222$	−1.55030	−	2.68520i	−0.104049	−	0.180219i
$223$	−6.02082	+	26.3789i	−0.403184	+	1.76646i	0.211186	+	0.977446i	$0.432267\pi$
$223$	−6.02082	+	26.3789i	−0.403184	+	1.76646i	−0.614370	+	0.789018i	$0.710590\pi$
$224$	−8.77933	+	22.3694i	−0.586594	+	1.49462i
$225$	0.771572	+	0.237998i	0.0514381	+	0.0158666i
$226$	4.18085	+	5.24262i	0.278106	+	0.348734i
$227$	−1.47996	+	19.7487i	−0.0982283	+	1.31077i	0.702477	+	0.711707i	$0.252078\pi$
$227$	−1.47996	+	19.7487i	−0.0982283	+	1.31077i	−0.800705	+	0.599059i	$0.795541\pi$
$228$	4.10264	−	1.26550i	0.271704	−	0.0838095i
$229$	1.45088	+	0.989196i	0.0958771	+	0.0653679i	0.610310	−	0.792163i	$-0.291045\pi$
$229$	1.45088	+	0.989196i	0.0958771	+	0.0653679i	−0.514433	+	0.857531i	$0.671997\pi$
$230$	−0.980419	−	0.147774i	−0.0646469	−	0.00974395i
$231$	−4.16383	−	18.2429i	−0.273960	−	1.20030i
$232$	−6.80586	+	6.31491i	−0.446826	+	0.414594i
$233$	0.963447	+	12.8563i	0.0631175	+	0.842245i	0.935479	+	0.353383i	$0.114969\pi$
$233$	0.963447	+	12.8563i	0.0631175	+	0.842245i	−0.872361	+	0.488862i	$0.837412\pi$
$234$	0.630403	+	1.60624i	0.0412107	+	0.105003i
$235$	−2.03100	+	0.306125i	−0.132488	+	0.0199694i
$236$	16.5808	+	7.98488i	1.07932	+	0.519772i
$237$	3.45227	+	1.66253i	0.224249	+	0.107993i
$238$	12.1237	−	1.82736i	0.785865	−	0.118450i
$239$	−3.55227	−	9.05103i	−0.229777	−	0.585463i	0.768760	−	0.639538i	$-0.220874\pi$
$239$	−3.55227	−	9.05103i	−0.229777	−	0.585463i	−0.998537	+	0.0540750i	$0.982779\pi$
$240$	−0.251156	−	3.35144i	−0.0162120	−	0.216335i
$241$	11.6051	−	10.7679i	0.747549	−	0.693624i	−0.211338	−	0.977413i	$-0.567782\pi$
$241$	11.6051	−	10.7679i	0.747549	−	0.693624i	0.958887	+	0.283789i	$0.0915916\pi$
$242$	−0.831254	−	3.64196i	−0.0534350	−	0.234114i
$243$	−8.08970	−	1.21933i	−0.518955	−	0.0782198i
$244$	−9.59375	−	6.54091i	−0.614177	−	0.418739i
$245$	10.3869	−	3.20395i	0.663598	−	0.204693i
$246$	0.0993689	−	1.32599i	0.00633553	−	0.0845417i
$247$	−2.88431	−	3.61681i	−0.183524	−	0.230132i
$248$	−22.8673	−	7.05364i	−1.45208	−	0.447907i
$249$	−6.04329	+	15.3981i	−0.382978	+	0.975813i
$250$	0.142003	−	0.622156i	0.00898106	−	0.0393486i
$251$	−15.6738	−	27.1478i	−0.989320	−	1.71355i	−0.620890	−	0.783897i	$-0.713229\pi$
$251$	−15.6738	−	27.1478i	−0.989320	−	1.71355i	−0.368430	−	0.929656i	$-0.620104\pi$
$252$	2.71827	−	4.70818i	0.171235	−	0.296588i
$253$	−2.58370	−	2.39732i	−0.162436	−	0.150718i
$254$	−1.22671	+	1.53824i	−0.0769704	+	0.0965178i
$255$	−7.32739	+	4.99573i	−0.458859	+	0.312845i
$256$	6.79933	−	3.27438i	0.424958	−	0.204649i
$257$	−25.5190			−1.59183			−0.795916	−	0.605407i	$-0.793011\pi$
$257$	−25.5190			−1.59183			−0.795916	+	0.605407i	$0.793011\pi$
$258$	2.04354	+	7.90556i	0.127225	+	0.492178i
$259$	10.5260			0.654052
$260$	−4.80551	+	2.31421i	−0.298025	+	0.143521i
$261$	2.70154	−	1.84188i	0.167221	−	0.114010i
$262$	−1.26737	+	1.58923i	−0.0782981	+	0.0981827i
$263$	4.54539	+	4.21750i	0.280281	+	0.260062i	0.807768	−	0.589500i	$-0.200675\pi$
$263$	4.54539	+	4.21750i	0.280281	+	0.260062i	−0.527487	+	0.849563i	$0.676866\pi$
$264$	−5.07441	+	8.78914i	−0.312309	+	0.540934i
$265$	6.15490	+	10.6606i	0.378092	+	0.654875i
$266$	0.829261	−	3.63323i	0.0508452	−	0.222768i
$267$	−10.6204	+	27.0602i	−0.649956	+	1.65606i
$268$	9.59726	+	2.96036i	0.586246	+	0.180833i
$269$	10.8886	+	13.6538i	0.663887	+	0.832488i	0.993760	−	0.111537i	$-0.0355774\pi$
$269$	10.8886	+	13.6538i	0.663887	+	0.832488i	−0.329873	+	0.944025i	$0.607006\pi$
$270$	−0.204028	+	2.72256i	−0.0124167	+	0.165690i
$271$	0.475188	−	0.146576i	0.0288656	−	0.00890386i	−0.280289	−	0.959916i	$-0.590430\pi$
$271$	0.475188	−	0.146576i	0.0288656	−	0.00890386i	0.309154	+	0.951012i	$0.399954\pi$
$272$	6.46791	+	4.40974i	0.392174	+	0.267380i
$273$	−27.3136	−	4.11687i	−1.65310	−	0.249164i
$274$	−2.03363	−	8.90990i	−0.122856	−	0.538267i
$275$	1.66295	−	1.54299i	0.100280	−	0.0930459i
$276$	−0.360848	−	4.81519i	−0.0217205	−	0.289840i
$277$	6.15741	+	15.6888i	0.369963	+	0.942650i	0.987713	+	0.156276i	$0.0499490\pi$
$277$	6.15741	+	15.6888i	0.369963	+	0.942650i	−0.617750	+	0.786374i	$0.711956\pi$
$278$	−9.03938	+	1.36247i	−0.542146	+	0.0817154i
$279$	7.59311	+	3.65665i	0.454588	+	0.218918i
$280$	−8.73223	−	4.20522i	−0.521850	−	0.251310i
$281$	−26.3652	+	3.97392i	−1.57282	+	0.237064i	−0.876762	−	0.480924i	$-0.840301\pi$
$281$	−26.3652	+	3.97392i	−1.57282	+	0.237064i	−0.696056	+	0.717988i	$0.745063\pi$
$282$	0.934396	+	2.38080i	0.0556425	+	0.141775i
$283$	0.365409	+	4.87605i	0.0217213	+	0.289851i	0.997477	+	0.0709889i	$0.0226155\pi$
$283$	0.365409	+	4.87605i	0.0217213	+	0.289851i	−0.975756	+	0.218862i	$0.929765\pi$
$284$	4.98753	−	4.62775i	0.295955	−	0.274606i
$285$	0.599819	+	2.62798i	0.0355302	+	0.155668i
$286$	4.79373	+	0.722538i	0.283459	+	0.0427246i
$287$	3.72973	+	2.54289i	0.220159	+	0.150102i
$288$	−4.38610	+	1.35293i	−0.258454	+	0.0797224i
$289$	0.273241	−	3.64614i	0.0160730	−	0.214479i
$290$	−1.61120	−	2.02038i	−0.0946130	−	0.118641i
$291$	−27.1804	−	8.38405i	−1.59335	−	0.491482i
$292$	7.49198	−	19.0893i	0.438435	−	1.11711i
$293$	−2.70036	+	11.8311i	−0.157757	+	0.691177i	0.832743	+	0.553660i	$0.186769\pi$
$293$	−2.70036	+	11.8311i	−0.157757	+	0.691177i	−0.990499	+	0.137517i	$0.956088\pi$
$294$	−6.76765	−	11.7219i	−0.394697	−	0.683636i
$295$	−5.77718	+	10.0064i	−0.336360	+	0.582593i
$296$	−4.18496	−	3.88307i	−0.243246	−	0.225699i
$297$	−6.05119	+	7.58796i	−0.351126	+	0.440298i
$298$	5.82334	−	3.97028i	0.337337	−	0.229992i
$299$	−4.68763	+	2.25744i	−0.271092	+	0.130551i
$300$	3.10789			0.179434
$301$	−26.7111	−	7.41096i	−1.53960	−	0.427160i
$302$	−4.36770			−0.251333
$303$	26.9441	−	12.9756i	1.54790	−	0.745429i
$304$	1.96594	−	1.34035i	0.112754	−	0.0768745i
$305$	4.54530	−	5.69963i	0.260263	−	0.326360i
$306$	1.71673	+	1.59289i	0.0981388	+	0.0910595i
$307$	−9.19323	+	15.9231i	−0.524685	+	0.908782i	0.474901	+	0.880039i	$0.342484\pi$
$307$	−9.19323	+	15.9231i	−0.524685	+	0.908782i	−0.999587	+	0.0287429i	$0.990850\pi$
$308$	−7.63703	−	13.2277i	−0.435160	−	0.753719i
$309$	7.58708	−	33.2412i	0.431614	−	1.89102i
$310$	2.43345	−	6.20033i	0.138211	−	0.352155i
$311$	−18.1902	−	5.61093i	−1.03147	−	0.318167i	−0.267597	−	0.963531i	$-0.586229\pi$
$311$	−18.1902	−	5.61093i	−1.03147	−	0.318167i	−0.763875	+	0.645364i	$0.776706\pi$
$312$	9.34074	+	11.7129i	0.528815	+	0.663113i
$313$	2.24447	−	29.9503i	0.126865	−	1.69289i	−0.463771	−	0.885955i	$-0.653504\pi$
$313$	2.24447	−	29.9503i	0.126865	−	1.69289i	0.590635	−	0.806939i	$-0.298877\pi$
$314$	−2.91238	+	0.898349i	−0.164355	+	0.0506968i
$315$	2.82019	+	1.92278i	0.158900	+	0.108336i
$316$	3.09279	+	0.466163i	0.173983	+	0.0262237i
$317$	−0.0569013	−	0.249301i	−0.00319589	−	0.0140021i	0.973305	−	0.229516i	$-0.0737144\pi$
$317$	−0.0569013	−	0.249301i	−0.00319589	−	0.0140021i	−0.976501	+	0.215514i	$0.930857\pi$
$318$	11.2365	−	10.4259i	0.630109	−	0.584656i
$319$	−0.686489	−	9.16055i	−0.0384360	−	0.512893i
$320$	0.0668224	+	0.170261i	0.00373549	+	0.00951787i
$321$	−4.63944	+	0.699283i	−0.258948	+	0.0390302i
$322$	−3.77624	−	1.81854i	−0.210442	−	0.101343i
$323$	−5.65678	−	2.72416i	−0.314752	−	0.151577i
$324$	−16.9630	+	2.55676i	−0.942387	+	0.142042i
$325$	−1.22343	−	3.11725i	−0.0678636	−	0.172914i
$326$	−0.0886161	−	1.18250i	−0.00490799	−	0.0654926i
$327$	2.12890	−	1.97533i	0.117728	−	0.109236i
$328$	−0.544800	−	2.38692i	−0.0300815	−	0.131796i
$329$	−8.58562	−	1.29407i	−0.473340	−	0.0713446i
$330$	−2.33396	−	1.59127i	−0.128480	−	0.0875964i
$331$	−33.8022	+	10.4266i	−1.85794	+	0.573097i	−0.859899	+	0.510464i	$0.829474\pi$
$331$	−33.8022	+	10.4266i	−1.85794	+	0.573097i	−0.998037	+	0.0626334i	$0.980050\pi$
$332$	−1.00903	+	13.4646i	−0.0553776	+	0.738963i
$333$	1.25356	+	1.57191i	0.0686945	+	0.0861401i
$334$	−4.76496	−	1.46980i	−0.260727	−	0.0804237i
$335$	−2.30374	+	5.86982i	−0.125867	+	0.320703i
$336$	3.16140	−	13.8510i	0.172468	−	0.755634i
$337$	−0.709443	−	1.22879i	−0.0386458	−	0.0669365i	0.846056	−	0.533095i	$-0.178971\pi$
$337$	−0.709443	−	1.22879i	−0.0386458	−	0.0669365i	−0.884701	+	0.466158i	$0.845638\pi$
$338$	−0.569873	+	0.987049i	−0.0309970	+	0.0536884i
$339$	−15.0300	−	13.9458i	−0.816319	−	0.757433i
$340$	−4.51342	+	5.65965i	−0.244775	+	0.306938i
$341$	19.5635	−	13.3382i	1.05942	−	0.722303i
$342$	0.641331	−	0.308849i	0.0346792	−	0.0167006i
$343$	16.3590			0.883302
$344$	7.88596	+	12.8003i	0.425183	+	0.690146i
$345$	3.03165			0.163219
$346$	−1.39656	+	0.672549i	−0.0750797	+	0.0361565i
$347$	17.6856	−	12.0578i	0.949412	−	0.647298i	0.0136414	−	0.999907i	$-0.495658\pi$
$347$	17.6856	−	12.0578i	0.949412	−	0.647298i	0.935771	+	0.352609i	$0.114705\pi$
$348$	7.84674	−	9.83950i	0.420629	−	0.527452i
$349$	−22.4183	−	20.8011i	−1.20002	−	1.11346i	−0.990764	−	0.135597i	$-0.956705\pi$
$349$	−22.4183	−	20.8011i	−1.20002	−	1.11346i	−0.209257	−	0.977861i	$-0.567105\pi$
$350$	1.34883	−	2.33624i	0.0720980	−	0.124877i
$351$	7.16337	+	12.4073i	0.382353	+	0.662254i
$352$	−2.86957	+	12.5724i	−0.152949	+	0.670113i
$353$	−6.85668	+	17.4705i	−0.364944	+	0.929862i	0.623980	+	0.781440i	$0.285515\pi$
$353$	−6.85668	+	17.4705i	−0.364944	+	0.929862i	−0.988924	+	0.148422i	$0.952581\pi$
$354$	13.7484	+	4.24083i	0.730721	+	0.225398i
$355$	2.66336	+	3.33975i	0.141357	+	0.177256i
$356$	−1.77325	+	23.6623i	−0.0939819	+	1.25410i
$357$	−35.8235	+	11.0501i	−1.89598	+	0.584833i
$358$	2.70953	+	1.84733i	0.143203	+	0.0976343i
$359$	35.2161	+	5.30797i	1.85863	+	0.280144i	0.980243	−	0.197798i	$-0.0633791\pi$
$359$	35.2161	+	5.30797i	1.85863	+	0.280144i	0.878391	+	0.477942i	$0.158617\pi$
$360$	−0.411944	−	1.80485i	−0.0217114	−	0.0951237i
$361$	12.5290	−	11.6253i	0.659423	−	0.611855i
$362$	0.370662	+	4.94614i	0.0194815	+	0.259963i
$363$	4.17303	+	10.6327i	0.219027	+	0.558072i
$364$	−22.2953	+	3.36047i	−1.16859	+	0.176136i
$365$	11.6000	+	5.58627i	0.607172	+	0.292399i
$366$	−8.17875	−	3.93868i	−0.427510	−	0.205878i
$367$	−24.0686	+	3.62775i	−1.25637	+	0.189367i	−0.743287	−	0.668972i	$-0.766734\pi$
$367$	−24.0686	+	3.62775i	−1.25637	+	0.189367i	−0.513082	+	0.858340i	$0.671496\pi$
$368$	−0.977670	−	2.49106i	−0.0509646	−	0.129856i
$369$	0.0644346	+	0.859821i	0.00335433	+	0.0447605i
$370$	1.16483	−	1.08081i	0.0605567	−	0.0561884i
$371$	11.5793	+	50.7322i	0.601167	+	2.63389i
$372$	32.0764	+	4.83474i	1.66308	+	0.250670i
$373$	18.9510	+	12.9205i	0.981244	+	0.669000i	0.943876	−	0.330301i	$-0.107150\pi$
$373$	18.9510	+	12.9205i	0.981244	+	0.669000i	0.0373679	+	0.999302i	$0.488103\pi$
$374$	6.28727	−	1.93937i	0.325107	−	0.100282i
$375$	−0.145818	+	1.94581i	−0.00753003	+	0.100481i
$376$	2.93611	+	3.68177i	0.151419	+	0.189873i
$377$	−12.9580	−	3.99701i	−0.667370	−	0.205856i
$378$	−4.21651	+	10.7435i	−0.216874	+	0.552586i
$379$	0.463815	−	2.03211i	0.0238246	−	0.104382i	−0.961618	−	0.274393i	$-0.911523\pi$
$379$	0.463815	−	2.03211i	0.0238246	−	0.104382i	0.985442	+	0.170011i	$0.0543802\pi$
$380$	1.10015	+	1.90552i	0.0564366	+	0.0977510i
$381$	3.00795	−	5.20993i	0.154102	−	0.266913i
$382$	−3.53075	−	3.27605i	−0.180649	−	0.167618i
$383$	−10.4681	+	13.1266i	−0.534894	+	0.670736i	−0.973697	−	0.227847i	$-0.926831\pi$
$383$	−10.4681	+	13.1266i	−0.534894	+	0.670736i	0.438802	+	0.898584i	$0.355403\pi$
$384$	−18.1415	+	12.3687i	−0.925779	+	0.631185i
$385$	8.64002	−	4.16081i	0.440336	−	0.212055i
$386$	17.5183			0.891657
$387$	−2.07434	−	4.87152i	−0.105445	−	0.247633i
$388$	−23.2180			−1.17872
$389$	−16.5255	+	7.95825i	−0.837874	+	0.403499i	−0.803062	−	0.595895i	$-0.796798\pi$
$389$	−16.5255	+	7.95825i	−0.837874	+	0.403499i	−0.0348120	+	0.999394i	$0.511083\pi$
$390$	−3.44532	+	2.34898i	−0.174461	+	0.118945i
$391$	−4.40270	+	5.52081i	−0.222654	+	0.279199i
$392$	−18.2689	−	16.9511i	−0.922721	−	0.856160i
$393$	3.10765	−	5.38261i	0.156760	−	0.271517i
$394$	−3.19232	−	5.52926i	−0.160827	−	0.278560i
$395$	−0.436968	+	1.91448i	−0.0219862	+	0.0963280i
$396$	1.06587	−	2.71580i	0.0535621	−	0.136474i
$397$	15.2449	+	4.70243i	0.765120	+	0.236008i	0.652663	−	0.757648i	$-0.273652\pi$
$397$	15.2449	+	4.70243i	0.765120	+	0.236008i	0.112457	+	0.993657i	$0.464128\pi$
$398$	8.25515	+	10.3516i	0.413793	+	0.518881i
$399$	−0.851541	+	11.3630i	−0.0426304	+	0.568863i
$400$	1.64587	−	0.507683i	0.0822934	−	0.0253841i
$401$	−7.73156	−	5.27129i	−0.386096	−	0.263236i	0.354680	−	0.934988i	$-0.384590\pi$
$401$	−7.73156	−	5.27129i	−0.386096	−	0.263236i	−0.740776	+	0.671752i	$0.765542\pi$
$402$	7.76425	+	1.17027i	0.387246	+	0.0583679i
$403$	−7.77765	−	34.0761i	−0.387432	−	1.69745i
$404$	17.8946	−	16.6037i	0.890289	−	0.826067i
$405$	−0.804871	−	10.7403i	−0.0399943	−	0.533687i
$406$	−3.99098	−	10.1688i	−0.198069	−	0.504671i
$407$	5.58558	−	0.841890i	0.276867	−	0.0417310i
$408$	18.3193	+	8.82210i	0.906939	+	0.436759i
$409$	21.7308	+	10.4650i	1.07452	+	0.517460i	0.885560	−	0.464525i	$-0.153775\pi$
$409$	21.7308	+	10.4650i	1.07452	+	0.517460i	0.188957	+	0.981985i	$0.439489\pi$
$410$	0.673845	−	0.101566i	0.0332788	−	0.00501598i
$411$	10.2091	+	26.0125i	0.503580	+	1.28310i
$412$	−2.07985	−	27.7537i	−0.102467	−	1.36733i
$413$	−35.8048	+	33.2220i	−1.76184	+	1.63475i
$414$	−0.178145	−	0.780504i	−0.00875534	−	0.0383597i
$415$	−8.38263	−	1.26348i	−0.411487	−	0.0620217i
$416$	15.7285	+	10.7235i	0.771155	+	0.525764i
$417$	26.7098	−	8.23888i	1.30798	−	0.403460i
$418$	0.149451	−	1.99429i	0.00730990	−	0.0975438i
$419$	−13.1937	−	16.5444i	−0.644556	−	0.808248i	0.347008	−	0.937862i	$-0.387198\pi$
$419$	−13.1937	−	16.5444i	−0.644556	−	0.808248i	−0.991565	+	0.129614i	$0.958626\pi$
$420$	12.5542	+	3.87247i	0.612585	+	0.188957i
$421$	7.01224	−	17.8669i	0.341756	−	0.870780i	−0.651899	−	0.758306i	$-0.726027\pi$
$421$	7.01224	−	17.8669i	0.341756	−	0.870780i	0.993655	−	0.112474i	$-0.0358774\pi$
$422$	0.686096	−	3.00598i	0.0333987	−	0.146329i
$423$	−0.829224	−	1.43626i	−0.0403182	−	0.0698332i
$424$	14.1116	−	24.4420i	0.685319	−	1.18701i
$425$	−3.33167	−	3.09134i	−0.161610	−	0.149952i
$426$	3.31646	−	4.15870i	0.160683	−	0.201490i
$427$	25.4624	−	17.3600i	1.23221	−	0.840108i
$428$	−3.45053	+	1.66169i	−0.166788	+	0.0803207i
$429$	−14.8232			−0.715670
$430$	−3.71687	+	1.92258i	−0.179244	+	0.0927148i
$431$	23.3355			1.12403			0.562016	−	0.827127i	$-0.310026\pi$
$431$	23.3355			1.12403			0.562016	+	0.827127i	$0.310026\pi$
$432$	−6.63909	+	3.19722i	−0.319423	+	0.153826i
$433$	11.2112	−	7.64367i	0.538776	−	0.367331i	−0.263150	−	0.964755i	$-0.584761\pi$
$433$	11.2112	−	7.64367i	0.538776	−	0.367331i	0.801926	+	0.597424i	$0.203809\pi$
$434$	17.5555	−	22.0139i	0.842693	−	1.05670i
$435$	5.79222	+	5.37439i	0.277716	+	0.257682i
$436$	1.18529	−	2.05298i	0.0567649	−	0.0983197i
$437$	1.07316	+	1.85877i	0.0513363	+	0.0889172i
$438$	3.56749	−	15.6302i	0.170461	−	0.746840i
$439$	6.52831	−	16.6339i	0.311579	−	0.793891i	−0.686208	−	0.727405i	$-0.740726\pi$
$439$	6.52831	−	16.6339i	0.311579	−	0.793891i	0.997787	−	0.0664859i	$-0.0211787\pi$
$440$	−4.97007	−	1.53306i	−0.236939	−	0.0730860i
$441$	5.47225	+	6.86199i	0.260583	+	0.326761i
$442$	0.725821	−	9.68541i	0.0345238	−	0.460688i
$443$	−28.0929	+	8.66552i	−1.33473	+	0.411711i	−0.878327	−	0.478060i	$-0.841340\pi$
$443$	−28.0929	+	8.66552i	−1.33473	+	0.411711i	−0.456407	+	0.889771i	$0.650864\pi$
$444$	6.39402	+	4.35937i	0.303447	+	0.206886i
$445$	−14.7315	−	2.22041i	−0.698339	−	0.105258i
$446$	3.84222	+	16.8339i	0.181934	+	0.797107i
$447$	−15.7976	+	14.6580i	−0.747201	+	0.693301i
$448$	0.0577803	+	0.771025i	0.00272986	+	0.0364275i
$449$	4.99432	+	12.7253i	0.235697	+	0.600546i	0.998963	−	0.0455391i	$-0.0145006\pi$
$449$	4.99432	+	12.7253i	0.235697	+	0.600546i	−0.763266	+	0.646085i	$0.776405\pi$
$450$	0.509520	−	0.0767978i	0.0240190	−	0.00362029i
$451$	2.18256	+	1.05106i	0.102773	+	0.0494926i
$452$	−15.0788	−	7.26158i	−0.709248	−	0.341556i
$453$	13.2058	−	1.99045i	0.620462	−	0.0935197i
$454$	4.61721	+	11.7645i	0.216696	+	0.552133i
$455$	−1.05788	−	14.1164i	−0.0495942	−	0.661788i
$456$	4.53043	−	4.20362i	0.212157	−	0.196853i
$457$	−0.819699	−	3.59134i	−0.0383439	−	0.167996i	0.952131	−	0.305691i	$-0.0988876\pi$
$457$	−0.819699	−	3.59134i	−0.0383439	−	0.167996i	−0.990475	+	0.137696i	$0.956030\pi$
$458$	1.10809	+	0.167018i	0.0517778	+	0.00780424i
$459$	16.0657	+	10.9534i	0.749883	+	0.511262i
$460$	2.36470	−	0.729413i	0.110255	−	0.0340091i
$461$	1.30850	−	17.4607i	0.0609430	−	0.813227i	−0.880067	−	0.474849i	$-0.842503\pi$
$461$	1.30850	−	17.4607i	0.0609430	−	0.813227i	0.941010	−	0.338378i	$-0.109878\pi$
$462$	−7.44523	−	9.33602i	−0.346383	−	0.434351i
$463$	−1.89082	−	0.583240i	−0.0878738	−	0.0271055i	0.250507	−	0.968115i	$-0.419403\pi$
$463$	−1.89082	−	0.583240i	−0.0878738	−	0.0271055i	−0.338380	+	0.941009i	$0.609879\pi$
$464$	2.54814	−	6.49255i	0.118294	−	0.301409i
$465$	−4.53195	+	19.8558i	−0.210164	+	0.920789i
$466$	4.11367	+	7.12508i	0.190562	+	0.330063i
$467$	2.54596	−	4.40974i	0.117813	−	0.204058i	−0.801088	−	0.598547i	$-0.795745\pi$
$467$	2.54596	−	4.40974i	0.117813	−	0.204058i	0.918901	+	0.394489i	$0.129078\pi$
$468$	−3.15702	−	2.92929i	−0.145933	−	0.135406i
$469$	−16.6197	+	20.8405i	−0.767428	+	0.962324i
$470$	−1.08298	+	0.738365i	−0.0499542	+	0.0340582i
$471$	8.39621	−	4.04340i	0.386877	−	0.186310i
$472$	26.4911			1.21935
$473$	−14.7669	−	1.79619i	−0.678983	−	0.0825890i
$474$	2.44524			0.112314
$475$	−1.24464	+	0.599385i	−0.0571078	+	0.0275017i
$476$	−25.2838	+	17.2382i	−1.15888	+	0.790112i
$477$	−6.19716	+	7.77100i	−0.283749	+	0.355810i
$478$	−4.54851	−	4.22040i	−0.208044	−	0.193037i
$479$	−9.96590	+	17.2614i	−0.455354	+	0.788696i	−0.998708	−	0.0508076i	$-0.983820\pi$
$479$	−9.96590	+	17.2614i	−0.455354	+	0.788696i	0.543355	+	0.839503i	$0.317154\pi$
$480$	−5.54612	−	9.60616i	−0.253144	−	0.438459i
$481$	1.85547	−	8.12933i	0.0846020	−	0.370665i
$482$	3.69095	−	9.40440i	0.168118	−	0.428359i
$483$	12.2463	+	3.77748i	0.557225	+	0.171881i
$484$	5.81320	+	7.28952i	0.264236	+	0.331342i
$485$	1.08936	−	14.5365i	0.0494653	−	0.660068i
$486$	−4.98886	+	1.53886i	−0.226299	+	0.0698041i
$487$	12.4775	+	8.50699i	0.565408	+	0.385488i	0.812023	−	0.583625i	$-0.198366\pi$
$487$	12.4775	+	8.50699i	0.565408	+	0.385488i	−0.246616	+	0.969113i	$0.579319\pi$
$488$	−16.5276	−	2.49114i	−0.748170	−	0.112768i
$489$	0.806822	+	3.53492i	0.0364858	+	0.159855i
$490$	5.08494	−	4.71813i	0.229714	−	0.213143i
$491$	2.62743	+	35.0606i	0.118574	+	1.58226i	0.666351	+	0.745639i	$0.267855\pi$
$491$	2.62743	+	35.0606i	0.118574	+	1.58226i	−0.547776	+	0.836625i	$0.684526\pi$
$492$	1.21248	+	3.08936i	0.0546630	+	0.139279i
$493$	−18.1988	+	2.74303i	−0.819632	+	0.123540i
$494$	−2.65980	−	1.28089i	−0.119670	−	0.0576302i
$495$	1.65031	+	0.794750i	0.0741761	+	0.0357213i
$496$	17.7767	−	2.67940i	0.798196	−	0.120309i
$497$	6.59721	+	16.8094i	0.295925	+	0.754005i
$498$	0.788856	+	10.5265i	0.0353495	+	0.471706i
$499$	5.65827	−	5.25011i	0.253299	−	0.235027i	−0.543295	−	0.839542i	$-0.682823\pi$
$499$	5.65827	−	5.25011i	0.253299	−	0.235027i	0.796594	+	0.604515i	$0.206633\pi$
$500$	0.354422	+	1.55282i	0.0158502	+	0.0694444i
$501$	15.0768	+	2.27246i	0.673580	+	0.101526i
$502$	−16.5286	−	11.2690i	−0.737708	−	0.502961i
$503$	34.8749	−	10.7575i	1.55499	−	0.479652i	0.606137	−	0.795361i	$-0.292718\pi$
$503$	34.8749	−	10.7575i	1.55499	−	0.479652i	0.948856	+	0.315709i	$0.102242\pi$
$504$	0.584822	−	7.80390i	0.0260500	−	0.347614i
$505$	9.55579	+	11.9826i	0.425227	+	0.533218i
$506$	−2.14930	−	0.662972i	−0.0955482	−	0.0294727i
$507$	1.27320	−	3.24406i	0.0565448	−	0.144074i
$508$	1.09271	−	4.78747i	0.0484811	−	0.212410i
$509$	−11.8782	−	20.5737i	−0.526493	−	0.911913i	−0.999523	−	0.0308672i	$-0.990173\pi$
$509$	−11.8782	−	20.5737i	−0.526493	−	0.911913i	0.473030	−	0.881046i	$-0.343160\pi$
$510$	−2.82970	+	4.90119i	−0.125301	+	0.217028i
$511$	39.8973	+	37.0193i	1.76495	+	1.63764i
$512$	−11.0290	+	13.8299i	−0.487417	+	0.611201i
$513$	4.88321	−	3.32932i	0.215599	−	0.146993i
$514$	−14.6724	+	7.06585i	−0.647171	+	0.311661i
$515$	17.4738			0.769987
$516$	−13.1564	−	15.5643i	−0.579178	−	0.685179i
$517$	−4.65943			−0.204922
$518$	6.05200	−	2.91449i	0.265910	−	0.128055i
$519$	3.91603	−	2.66991i	0.171895	−	0.117196i
$520$	−4.78701	+	6.00272i	−0.209924	+	0.263237i
$521$	14.1626	+	13.1410i	0.620477	+	0.575718i	0.926495	−	0.376308i	$-0.122806\pi$
$521$	14.1626	+	13.1410i	0.620477	+	0.575718i	−0.306018	+	0.952026i	$0.598997\pi$
$522$	1.04329	−	1.80702i	0.0456634	−	0.0790912i
$523$	−18.5326	−	32.0994i	−0.810374	−	1.40361i	−0.912603	−	0.408848i	$-0.865931\pi$
$523$	−18.5326	−	32.0994i	−0.810374	−	1.40361i	0.102229	−	0.994761i	$-0.467403\pi$
$524$	1.12893	−	4.94615i	0.0493174	−	0.216074i
$525$	−3.01353	+	7.67835i	−0.131521	+	0.335111i
$526$	3.78118	+	1.16634i	0.164867	+	0.0508548i
$527$	−29.5770	−	37.0883i	−1.28839	−	1.61559i
$528$	0.569755	−	7.60285i	0.0247954	−	0.330871i
$529$	−19.6715	+	6.06785i	−0.855282	+	0.263820i
$530$	6.49058	+	4.42520i	0.281933	+	0.192218i
$531$	−9.22530	−	1.39049i	−0.400344	−	0.0603421i
$532$	2.06973	+	9.06808i	0.0897342	+	0.393151i
$533$	2.62136	−	2.43226i	0.113544	−	0.105353i
$534$	1.38632	+	18.4991i	0.0599919	+	0.800536i
$535$	−0.878466	−	2.23829i	−0.0379794	−	0.0967699i
$536$	14.2959	−	2.15476i	0.617488	−	0.0930713i
$537$	−9.03418	−	4.35063i	−0.389853	−	0.187744i
$538$	10.0410	+	4.83550i	0.432899	+	0.208473i
$539$	24.3832	−	3.67517i	1.05026	−	0.158301i
$540$	−2.48952	−	6.34319i	−0.107132	−	0.272967i
$541$	0.842344	+	11.2403i	0.0362152	+	0.483258i	0.985594	+	0.169126i	$0.0540945\pi$
$541$	0.842344	+	11.2403i	0.0362152	+	0.483258i	−0.949379	+	0.314132i	$0.898286\pi$
$542$	0.232629	−	0.215848i	0.00999226	−	0.00927146i
$543$	−3.37476	−	14.7858i	−0.144825	−	0.634519i
$544$	25.5477	+	3.85069i	1.09535	+	0.165097i
$545$	1.22973	+	0.838415i	0.0526758	+	0.0359137i
$546$	−16.8441	+	5.19572i	−0.720862	+	0.222356i
$547$	1.77716	−	23.7145i	0.0759857	−	1.01396i	−0.820720	−	0.571331i	$-0.806427\pi$
$547$	1.77716	−	23.7145i	0.0759857	−	1.01396i	0.896705	−	0.442628i	$-0.145954\pi$
$548$	14.2217	+	17.8335i	0.607522	+	0.761809i
$549$	5.62483	+	1.73503i	0.240062	+	0.0740494i
$550$	0.528895	−	1.34760i	0.0225522	−	0.0574620i
$551$	−1.24479	+	5.45379i	−0.0530300	+	0.232339i
$552$	−3.47540	−	6.01956i	−0.147923	−	0.256210i
$553$	−4.15058	+	7.18902i	−0.176501	+	0.305708i
$554$	7.88427	+	7.31553i	0.334970	+	0.310807i
$555$	−3.02934	+	3.79867i	−0.128588	+	0.161245i
$556$	18.8515	−	12.8527i	0.799480	−	0.545076i
$557$	−3.26458	+	1.57214i	−0.138325	+	0.0666137i	−0.501766	−	0.865003i	$-0.667316\pi$
$557$	−3.26458	+	1.57214i	−0.138325	+	0.0666137i	0.363441	+	0.931617i	$0.381602\pi$
$558$	5.37820			0.227677
$559$	−10.4321	+	19.3229i	−0.441229	+	0.817271i
$560$	7.28101			0.307679
$561$	−18.1258	+	8.72894i	−0.765273	+	0.368536i
$562$	−14.0586	+	9.58499i	−0.593026	+	0.404318i
$563$	2.98878	−	3.74781i	0.125962	−	0.157951i	−0.714851	−	0.699276i	$-0.753506\pi$
$563$	2.98878	−	3.74781i	0.125962	−	0.157951i	0.840813	+	0.541325i	$0.182077\pi$
$564$	−4.67940	−	4.34185i	−0.197038	−	0.182825i
$565$	5.25386	−	9.09995i	0.221031	−	0.382838i
$566$	1.56020	+	2.70235i	0.0655802	+	0.113588i
$567$	10.1312	−	44.3878i	0.425471	−	1.86411i
$568$	3.57811	−	9.11689i	0.150134	−	0.382536i
$569$	−6.89962	−	2.12825i	−0.289247	−	0.0892210i	0.146736	−	0.989176i	$-0.453123\pi$
$569$	−6.89962	−	2.12825i	−0.289247	−	0.0892210i	−0.435983	+	0.899955i	$0.643599\pi$
$570$	1.07252	+	1.34490i	0.0449230	+	0.0563316i
$571$	0.793411	−	10.5873i	0.0332032	−	0.443066i	−0.955684	−	0.294396i	$-0.904882\pi$
$571$	0.793411	−	10.5873i	0.0332032	−	0.443066i	0.988887	−	0.148670i	$-0.0474993\pi$
$572$	−11.5621	+	3.56645i	−0.483437	+	0.149121i
$573$	12.1682	+	8.29616i	0.508335	+	0.346577i
$574$	2.84853	+	0.429347i	0.118895	+	0.0179206i
$575$	0.345727	+	1.51473i	0.0144178	+	0.0631686i
$576$	−0.108261	+	0.100451i	−0.00451087	+	0.00418547i
$577$	1.33289	+	17.7862i	0.0554889	+	0.740448i	0.953676	+	0.300835i	$0.0972653\pi$
$577$	1.33289	+	17.7862i	0.0554889	+	0.740448i	−0.898187	+	0.439613i	$0.855116\pi$
$578$	−0.852462	−	2.17204i	−0.0354578	−	0.0903449i
$579$	−52.9668	+	7.98345i	−2.20122	+	0.331781i
$580$	5.81103	+	2.79844i	0.241290	+	0.116199i
$581$	−32.2871	−	15.5486i	−1.33949	−	0.645066i
$582$	−17.9490	+	2.70538i	−0.744012	+	0.112142i
$583$	10.2022	+	25.9948i	0.422532	+	1.07659i
$584$	−2.20597	−	29.4366i	−0.0912835	−	1.21809i
$585$	1.98211	−	1.83913i	0.0819502	−	0.0760386i
$586$	1.72325	+	7.55006i	0.0711868	+	0.311890i
$587$	13.5748	+	2.04607i	0.560290	+	0.0844502i	0.423081	−	0.906092i	$-0.360949\pi$
$587$	13.5748	+	2.04607i	0.560290	+	0.0844502i	0.137209	+	0.990542i	$0.456187\pi$
$588$	27.9123	+	19.0303i	1.15108	+	0.784796i
$589$	−13.7782	+	4.25003i	−0.567723	+	0.175119i
$590$	−0.551021	+	7.35286i	−0.0226852	+	0.302713i
$591$	12.1718	+	15.2630i	0.500682	+	0.627835i
$592$	4.09823	+	1.26414i	0.168436	+	0.0519557i
$593$	5.48977	−	13.9877i	0.225438	−	0.574406i	−0.772742	−	0.634721i	$-0.781115\pi$
$593$	5.48977	−	13.9877i	0.225438	−	0.574406i	0.998179	+	0.0603144i	$0.0192103\pi$
$594$	−1.37819	+	6.03825i	−0.0565479	+	0.247752i
$595$	−9.60633	−	16.6387i	−0.393821	−	0.682118i
$596$	−8.79547	+	15.2342i	−0.360276	+	0.624017i
$597$	−29.6770	−	27.5363i	−1.21460	−	1.12698i
$598$	−2.07014	+	2.59587i	−0.0846542	+	0.106153i
$599$	−11.4846	+	7.83006i	−0.469247	+	0.319928i	−0.774754	−	0.632262i	$-0.782126\pi$
$599$	−11.4846	+	7.83006i	−0.469247	+	0.319928i	0.305507	+	0.952190i	$0.401174\pi$
$600$	4.03071	−	1.94109i	0.164553	−	0.0792445i
$601$	31.9242			1.30221			0.651107	−	0.758986i	$-0.274305\pi$
$601$	31.9242			1.30221			0.651107	+	0.758986i	$0.274305\pi$
$602$	−17.4098	+	3.13492i	−0.709569	+	0.127770i
$603$	−5.09151			−0.207342
$604$	9.82167	−	4.72986i	0.399638	−	0.192455i
$605$	−4.83662	+	3.29755i	−0.196636	+	0.134064i
$606$	11.8990	−	14.9209i	0.483364	−	0.606119i
$607$	1.13719	+	1.05516i	0.0461571	+	0.0428275i	0.702914	−	0.711275i	$-0.251882\pi$
$607$	1.13719	+	1.05516i	0.0461571	+	0.0428275i	−0.656757	+	0.754102i	$0.728072\pi$
$608$	3.92650	−	6.80089i	0.159240	−	0.275813i
$609$	16.7009	+	28.9269i	0.676756	+	1.17218i
$610$	1.03522	−	4.53558i	0.0419147	−	0.183640i
$611$	−2.51286	+	6.40265i	−0.101659	+	0.259024i
$612$	−5.58538	−	1.72286i	−0.225776	−	0.0696426i
$613$	−6.11191	−	7.66409i	−0.246858	−	0.309550i	0.642930	−	0.765925i	$-0.277719\pi$
$613$	−6.11191	−	7.66409i	−0.246858	−	0.309550i	−0.889787	+	0.456376i	$0.849147\pi$
$614$	−0.876840	+	11.7006i	−0.0353864	+	0.472199i
$615$	−1.99109	+	0.614171i	−0.0802887	+	0.0247658i
$616$	−18.1662	−	12.3855i	−0.731939	−	0.499027i
$617$	−27.7294	−	4.17954i	−1.11635	−	0.168262i	−0.435146	−	0.900360i	$-0.643303\pi$
$617$	−27.7294	−	4.17954i	−1.11635	−	0.168262i	−0.681199	+	0.732098i	$0.738541\pi$
$618$	−4.84174	−	21.2131i	−0.194763	−	0.853314i
$619$	−36.1756	+	33.5660i	−1.45402	+	1.34913i	−0.639858	+	0.768493i	$0.721007\pi$
$619$	−36.1756	+	33.5660i	−1.45402	+	1.34913i	−0.814161	+	0.580639i	$0.802803\pi$
$620$	1.24235	+	16.5779i	0.0498938	+	0.665786i
$621$	−2.42845	−	6.18758i	−0.0974502	−	0.248299i
$622$	−12.0122	+	1.81055i	−0.481645	+	0.0725964i
$623$	−56.7407	−	27.3249i	−2.27327	−	1.09475i
$624$	−10.1400	−	4.88317i	−0.405925	−	0.195483i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−7.00234	−	17.8417i	−0.279870	−	0.713097i
$627$	0.456972	+	6.09787i	0.0182497	+	0.243525i
$628$	5.57624	−	5.17399i	0.222516	−	0.206465i
$629$	−2.51825	−	11.0332i	−0.100409	−	0.439922i
$630$	2.15388	+	0.324646i	0.0858128	+	0.0129342i
$631$	−6.48535	−	4.42164i	−0.258178	−	0.176023i	0.427313	−	0.904104i	$-0.359460\pi$
$631$	−6.48535	−	4.42164i	−0.258178	−	0.176023i	−0.685491	+	0.728081i	$0.740412\pi$
$632$	4.30226	−	1.32707i	0.171135	−	0.0527881i
$633$	−0.704530	+	9.40131i	−0.0280026	+	0.373668i
$634$	−0.101744	−	0.127583i	−0.00404076	−	0.00506695i
$635$	2.94610	+	0.908753i	0.116913	+	0.0360628i
$636$	−13.9771	+	35.6130i	−0.554226	+	1.41215i
$637$	8.09982	−	35.4876i	0.320926	−	1.40607i
$638$	−2.93113	−	5.07686i	−0.116044	−	0.200995i
$639$	−1.72458	+	2.98706i	−0.0682234	+	0.118166i
$640$	−8.24870	−	7.65367i	−0.326058	−	0.302538i
$641$	23.3650	−	29.2988i	0.922861	−	1.15723i	−0.0643684	−	0.997926i	$-0.520503\pi$
$641$	23.3650	−	29.2988i	0.922861	−	1.15723i	0.987229	−	0.159305i	$-0.0509253\pi$
$642$	−2.47386	+	1.68665i	−0.0976356	+	0.0665668i
$643$	35.4614	−	17.0773i	1.39846	−	0.673463i	0.425611	−	0.904906i	$-0.360059\pi$
$643$	35.4614	−	17.0773i	1.39846	−	0.673463i	0.972848	+	0.231444i	$0.0743449\pi$
$644$	10.4610			0.412221
$645$	10.3619	−	7.50679i	0.407998	−	0.295580i
$646$	−4.00670			−0.157641
$647$	21.6629	−	10.4323i	0.851656	−	0.410136i	0.0434637	−	0.999055i	$-0.486161\pi$
$647$	21.6629	−	10.4323i	0.851656	−	0.410136i	0.808192	+	0.588919i	$0.200446\pi$
$648$	−20.4028	+	13.9104i	−0.801499	+	0.546453i
$649$	−16.3425	+	20.4929i	−0.641501	+	0.804416i
$650$	−1.56654	−	1.45354i	−0.0614448	−	0.0570124i
$651$	−43.0472	+	74.5599i	−1.68715	+	2.92223i
$652$	1.47982	+	2.56313i	0.0579543	+	0.100380i
$653$	3.51134	−	15.3842i	0.137409	−	0.602030i	−0.858589	−	0.512664i	$-0.828659\pi$
$653$	3.51134	−	15.3842i	0.137409	−	0.602030i	0.995999	−	0.0893660i	$-0.0284841\pi$
$654$	0.677089	−	1.72519i	0.0264763	−	0.0674605i
$655$	3.04375	+	0.938873i	0.118929	+	0.0366848i
$656$	1.14676	+	1.43799i	0.0447734	+	0.0561440i
$657$	−0.776885	+	10.3668i	−0.0303092	+	0.404448i
$658$	−5.29468	+	1.63319i	−0.206408	+	0.0636685i
$659$	4.03406	+	2.75038i	0.157145	+	0.107139i	0.639339	−	0.768925i	$-0.279208\pi$
$659$	4.03406	+	2.75038i	0.157145	+	0.107139i	−0.482195	+	0.876064i	$0.660160\pi$
$660$	6.97160	+	1.05080i	0.271369	+	0.0409023i
$661$	1.49842	+	6.56502i	0.0582819	+	0.255350i	0.995673	−	0.0929297i	$-0.0296232\pi$
$661$	1.49842	+	6.56502i	0.0582819	+	0.255350i	−0.937391	+	0.348279i	$0.886766\pi$
$662$	−16.5479	+	15.3542i	−0.643152	+	0.596758i
$663$	2.21932	+	29.6147i	0.0861912	+	1.15014i
$664$	7.10087	+	18.0927i	0.275567	+	0.702134i
$665$	−5.77451	+	0.870368i	−0.223926	+	0.0337514i
$666$	1.15598	+	0.556692i	0.0447934	+	0.0215714i
$667$	5.66847	+	2.72979i	0.219484	+	0.105698i
$668$	12.3067	−	1.85493i	0.476159	−	0.0717695i
$669$	−19.2886	−	49.1465i	−0.745739	−	1.90011i
$670$	0.300716	+	4.01278i	0.0116177	+	0.155027i
$671$	12.1231	−	11.2486i	0.468006	−	0.434246i
$672$	−10.4340	−	45.7143i	−0.402500	−	1.76347i
$673$	−3.36412	−	0.507059i	−0.129677	−	0.0195457i	0.0838829	−	0.996476i	$-0.473268\pi$
$673$	−3.36412	−	0.507059i	−0.129677	−	0.0195457i	−0.213560	+	0.976930i	$0.568506\pi$
$674$	−0.748135	−	0.510070i	−0.0288171	−	0.0196472i
$675$	4.08819	−	1.26104i	0.157355	−	0.0485374i
$676$	0.212582	−	2.83671i	0.00817623	−	0.109104i
$677$	−13.1617	−	16.5043i	−0.505847	−	0.634311i	0.461690	−	0.887041i	$-0.347243\pi$
$677$	−13.1617	−	16.5043i	−0.505847	−	0.634311i	−0.967537	+	0.252730i	$0.918672\pi$
$678$	−12.5030	−	3.85668i	−0.480176	−	0.148115i
$679$	22.5131	−	57.3624i	0.863973	−	2.20137i
$680$	−2.31874	+	10.1591i	−0.0889197	+	0.389583i
$681$	−19.3215	−	33.4658i	−0.740402	−	1.28241i
$682$	7.55507	−	13.0858i	0.289299	−	0.501080i
$683$	−9.10987	−	8.45272i	−0.348579	−	0.323434i	0.486379	−	0.873748i	$-0.338318\pi$
$683$	−9.10987	−	8.45272i	−0.348579	−	0.323434i	−0.834958	+	0.550314i	$0.814508\pi$
$684$	−1.10771	+	1.38902i	−0.0423542	+	0.0531105i
$685$	−11.8326	+	8.06731i	−0.452099	+	0.308236i
$686$	9.40574	−	4.52956i	0.359113	−	0.172940i
$687$	−3.42645			−0.130727
$688$	−9.50979	−	6.09334i	−0.362557	−	0.232306i
$689$	41.2222			1.57044
$690$	1.74308	−	0.839421i	0.0663578	−	0.0319562i
$691$	−8.01479	+	5.46439i	−0.304897	+	0.207875i	−0.706097	−	0.708115i	$-0.749546\pi$
$691$	−8.01479	+	5.46439i	−0.304897	+	0.207875i	0.401200	+	0.915991i	$0.368593\pi$
$692$	2.41214	−	3.02473i	0.0916959	−	0.114983i
$693$	5.67613	+	5.26668i	0.215618	+	0.200065i
$694$	6.82985	−	11.8296i	0.259257	−	0.449047i
$695$	7.16242	+	12.4057i	0.271686	+	0.470574i
$696$	4.03121	−	17.6619i	0.152803	−	0.669473i
$697$	1.77311	−	4.51782i	0.0671615	−	0.171125i
$698$	−18.6491	−	5.75248i	−0.705879	−	0.217735i
$699$	−15.6848	−	19.6681i	−0.593253	−	0.743916i
$700$	−0.503159	+	6.71420i	−0.0190176	+	0.253773i
$701$	−6.86897	+	2.11880i	−0.259437	+	0.0800258i	−0.421745	−	0.906714i	$-0.638582\pi$
$701$	−6.86897	+	2.11880i	−0.259437	+	0.0800258i	0.162308	+	0.986740i	$0.448106\pi$
$702$	7.55405	+	5.15027i	0.285109	+	0.194384i
$703$	−3.40139	−	0.512677i	−0.128286	−	0.0193360i
$704$	0.0923292	+	0.404521i	0.00347979	+	0.0152459i
$705$	2.93792	−	2.72599i	0.110649	−	0.102667i
$706$	0.895030	+	11.9433i	0.0336849	+	0.449494i
$707$	23.6699	+	60.3099i	0.890198	+	2.26819i
$708$	−35.5086	+	5.35207i	−1.33450	+	0.201143i
$709$	−3.45137	−	1.66209i	−0.129619	−	0.0624212i	0.367950	−	0.929845i	$-0.380060\pi$
$709$	−3.45137	−	1.66209i	−0.129619	−	0.0624212i	−0.497569	+	0.867424i	$0.665774\pi$
$710$	2.45605	+	1.18277i	0.0921740	+	0.0443887i
$711$	−1.56788	+	0.236320i	−0.0588002	+	0.00886270i
$712$	12.4789	+	31.7958i	0.467667	+	1.19160i
$713$	1.21187	+	16.1713i	0.0453848	+	0.605619i
$714$	−17.5374	+	16.2724i	−0.656322	+	0.608978i
$715$	−1.69042	−	7.40623i	−0.0632182	−	0.276977i
$716$	−8.09345	−	1.21989i	−0.302466	−	0.0455895i
$717$	15.6758	+	10.6876i	0.585424	+	0.399135i
$718$	21.7175	−	6.69896i	0.810490	−	0.250003i
$719$	2.95232	−	39.3960i	0.110103	−	1.46922i	−0.619308	−	0.785148i	$-0.712587\pi$
$719$	2.95232	−	39.3960i	0.110103	−	1.46922i	0.729411	−	0.684076i	$-0.239794\pi$
$720$	0.867108	+	1.08732i	0.0323152	+	0.0405220i
$721$	70.5849	+	21.7725i	2.62872	+	0.810852i
$722$	3.98482	−	10.1531i	0.148300	−	0.377861i
$723$	−6.87387	+	30.1164i	−0.255642	+	1.12004i
$724$	−6.18978	−	10.7210i	−0.230041	−	0.398443i
$725$	−2.02471	+	3.50691i	−0.0751960	+	0.130243i
$726$	5.34336	+	4.95791i	0.198311	+	0.184005i
$727$	22.0917	−	27.7021i	0.819335	−	1.02741i	−0.179710	−	0.983720i	$-0.557516\pi$
$727$	22.0917	−	27.7021i	0.819335	−	1.02741i	0.999045	−	0.0436940i	$-0.0139127\pi$
$728$	−26.8164	+	18.2831i	−0.993883	+	0.677618i
$729$	−14.7287	+	7.09297i	−0.545507	+	0.262703i
$730$	8.21628			0.304098
$731$	−1.37766	+	29.7712i	−0.0509546	+	1.10113i
$732$	22.6569			0.837421
$733$	−15.3989	+	7.41572i	−0.568771	+	0.273906i	−0.696088	−	0.717956i	$-0.745078\pi$
$733$	−15.3989	+	7.41572i	−0.568771	+	0.273906i	0.127317	+	0.991862i	$0.459363\pi$
$734$	−12.8340	+	8.75005i	−0.473710	+	0.322970i
$735$	−13.2242	+	16.5827i	−0.487783	+	0.611660i
$736$	−6.47440	−	6.00737i	−0.238650	−	0.221435i
$737$	−7.15234	+	12.3882i	−0.263460	+	0.456326i
$738$	0.275119	+	0.476520i	0.0101273	+	0.0175410i
$739$	−0.622506	+	2.72738i	−0.0228993	+	0.100328i	−0.985086	−	0.172062i	$-0.944957\pi$
$739$	−0.622506	+	2.72738i	−0.0228993	+	0.100328i	0.962187	+	0.272390i	$0.0878142\pi$
$740$	−1.44894	+	3.69183i	−0.0532640	+	0.135714i
$741$	8.62569	+	2.66067i	0.316873	+	0.0977422i
$742$	20.7046	+	25.9628i	0.760091	+	0.953124i
$743$	0.525529	−	7.01269i	0.0192798	−	0.257271i	−0.979232	−	0.202741i	$-0.935015\pi$
$743$	0.525529	−	7.01269i	0.0192798	−	0.257271i	0.998512	−	0.0545297i	$-0.0173659\pi$
$744$	44.6203	−	13.7635i	1.63586	−	0.504596i
$745$	−9.12526	−	6.22150i	−0.334324	−	0.227938i
$746$	14.4735	+	2.18153i	0.529914	+	0.0798716i
$747$	−1.52315	−	6.67335i	−0.0557291	−	0.244165i
$748$	−12.0380	+	11.1697i	−0.440154	+	0.408403i
$749$	−0.759596	−	10.1361i	−0.0277550	−	0.370365i
$750$	0.454927	+	1.15914i	0.0166116	+	0.0423257i
$751$	−42.6756	+	6.43231i	−1.55725	+	0.234718i	−0.870499	−	0.492170i	$-0.836204\pi$
$751$	−42.6756	+	6.43231i	−1.55725	+	0.234718i	−0.686755	+	0.726889i	$0.740966\pi$
$752$	−3.18735	−	1.53495i	−0.116231	−	0.0559738i
$753$	55.1100	+	26.5396i	2.00832	+	0.967156i
$754$	−8.55702	+	1.28976i	−0.311628	+	0.0469704i
$755$	2.50049	+	6.37113i	0.0910020	+	0.231869i
$756$	−2.15265	−	28.7251i	−0.0782910	−	1.04472i
$757$	−0.645805	+	0.599219i	−0.0234722	+	0.0217790i	−0.691822	−	0.722068i	$-0.743192\pi$
$757$	−0.645805	+	0.599219i	−0.0234722	+	0.0217790i	0.668349	+	0.743847i	$0.267001\pi$
$758$	−0.295987	−	1.29680i	−0.0107507	−	0.0471020i
$759$	6.80058	+	1.02502i	0.246845	+	0.0372060i
$760$	2.61694	+	1.78420i	0.0949262	+	0.0647196i
$761$	30.5157	−	9.41285i	1.10619	−	0.341215i	0.312735	−	0.949840i	$-0.398755\pi$
$761$	30.5157	−	9.41285i	1.10619	−	0.341215i	0.793458	+	0.608625i	$0.208279\pi$
$762$	0.286895	−	3.82835i	0.0103931	−	0.138687i
$763$	3.92278	+	4.91901i	0.142014	+	0.178080i
$764$	11.4873	+	3.54337i	0.415596	+	0.128194i
$765$	1.34072	−	3.41610i	0.0484738	−	0.123509i
$766$	−2.38416	+	10.4457i	−0.0861433	+	0.377418i
$767$	19.3462	+	33.5086i	0.698551	+	1.20993i
$768$	−7.36280	+	12.7527i	−0.265682	+	0.460175i
$769$	19.5414	+	18.1318i	0.704681	+	0.653848i	0.948793	−	0.315899i	$-0.102306\pi$
$769$	19.5414	+	18.1318i	0.704681	+	0.653848i	−0.244112	+	0.969747i	$0.578497\pi$
$770$	3.81558	−	4.78459i	0.137504	−	0.172425i
$771$	41.1421	−	28.0502i	1.48170	−	1.01020i
$772$	−39.3934	+	18.9709i	−1.41780	+	0.682777i
$773$	13.0017			0.467640			0.233820	−	0.972280i	$-0.424877\pi$
$773$	13.0017			0.467640			0.233820	+	0.972280i	$0.424877\pi$
$774$	−2.54151	−	2.22656i	−0.0913528	−	0.0800322i
$775$	−10.4375			−0.374927
$776$	−30.1120	+	14.5012i	−1.08096	+	0.520563i
$777$	−16.9701	+	11.5700i	−0.608799	+	0.415072i
$778$	−7.29794	+	9.15132i	−0.261644	+	0.328091i
$779$	−1.08138	−	1.00337i	−0.0387445	−	0.0359496i
$780$	5.20375	−	9.01316i	0.186324	−	0.322723i
$781$	4.84524	+	8.39220i	0.173376	+	0.300297i
$782$	−1.00274	+	4.39328i	−0.0358578	+	0.157103i
$783$	6.32935	−	16.1269i	0.226193	−	0.576329i
$784$	17.8904	+	5.51844i	0.638941	+	0.197087i
$785$	2.97774	+	3.73396i	0.106280	+	0.133271i
$786$	0.296404	−	3.95524i	0.0105724	−	0.141079i
$787$	−15.6283	+	4.82069i	−0.557088	+	0.171839i	−0.560499	−	0.828155i	$-0.689391\pi$
$787$	−15.6283	+	4.82069i	−0.557088	+	0.171839i	0.00341071	+	0.999994i	$0.498914\pi$
$788$	13.1663	+	8.97664i	0.469031	+	0.319780i
$789$	−11.9640	−	1.80328i	−0.425928	−	0.0641984i
$790$	0.278854	+	1.22174i	0.00992117	+	0.0434675i
$791$	32.5614	−	30.2126i	1.15775	−	1.07424i
$792$	−0.313839	−	4.18789i	−0.0111518	−	0.148810i
$793$	−8.91891	−	22.7250i	−0.316720	−	0.806989i
$794$	10.0672	−	1.51739i	0.357273	−	0.0538502i
$795$	−21.6410	−	10.4218i	−0.767527	−	0.369622i
$796$	−29.7734	−	14.3381i	−1.05529	−	0.508201i
$797$	2.33288	−	0.351626i	0.0826350	−	0.0124552i	−0.107595	−	0.994195i	$-0.534315\pi$
$797$	2.33288	−	0.351626i	0.0826350	−	0.0124552i	0.190230	+	0.981740i	$0.439077\pi$
$798$	2.65666	+	6.76905i	0.0940446	+	0.239622i
$799$	0.697608	+	9.30893i	0.0246796	+	0.329326i
$800$	4.16713	−	3.86653i	0.147330	−	0.136703i
$801$	−2.67675	−	11.7276i	−0.0945783	−	0.414374i
$802$	−5.90487	−	0.890016i	−0.208508	−	0.0314276i
$803$	24.1323	+	16.4531i	0.851610	+	0.580618i
$804$	−18.7268	+	5.77646i	−0.660444	+	0.203720i
$805$	−0.490816	+	6.54949i	−0.0172990	+	0.230839i
$806$	−13.9070	−	17.4388i	−0.489854	−	0.614257i
$807$	−32.5628	−	10.0443i	−1.14626	−	0.353576i
$808$	12.8378	−	32.7102i	0.451632	−	1.15074i
$809$	5.49454	−	24.0732i	0.193178	−	0.846368i	−0.781705	−	0.623649i	$-0.785650\pi$
$809$	5.49454	−	24.0732i	0.193178	−	0.846368i	0.974883	−	0.222719i	$-0.0714932\pi$
$810$	−3.43659	−	5.95234i	−0.120749	−	0.209144i
$811$	22.1842	−	38.4242i	0.778993	−	1.34926i	−0.153530	−	0.988144i	$-0.549064\pi$
$811$	22.1842	−	38.4242i	0.778993	−	1.34926i	0.932523	−	0.361111i	$-0.117603\pi$
$812$	19.9866	+	18.5448i	0.701391	+	0.650796i
$813$	−0.604990	+	0.758633i	−0.0212179	+	0.0266064i
$814$	2.97837	−	2.03062i	0.104392	−	0.0711731i
$815$	−1.67417	+	0.806239i	−0.0586437	+	0.0282413i
$816$	−15.2748			−0.534724
$817$	8.27053	+	3.69578i	0.289349	+	0.129299i
$818$	15.3919			0.538165
$819$	10.2982	−	4.95938i	0.359850	−	0.173295i
$820$	−1.40529	+	0.958111i	−0.0490749	+	0.0334587i
$821$	−5.56561	+	6.97906i	−0.194241	+	0.243571i	−0.869409	−	0.494094i	$-0.835500\pi$
$821$	−5.56561	+	6.97906i	−0.194241	+	0.243571i	0.675167	+	0.737665i	$0.264071\pi$
$822$	13.0723	+	12.1293i	0.455949	+	0.423059i
$823$	−7.15092	+	12.3858i	−0.249265	+	0.431740i	−0.963322	−	0.268347i	$-0.913522\pi$
$823$	−7.15092	+	12.3858i	−0.249265	+	0.431740i	0.714057	+	0.700088i	$0.246856\pi$
$824$	−20.0314	−	34.6954i	−0.697828	−	1.20867i
$825$	−0.984990	+	4.31552i	−0.0342930	+	0.150247i
$826$	−11.3876	+	29.0151i	−0.396225	+	1.00956i
$827$	51.6230	+	15.9236i	1.79511	+	0.553717i	0.998697	−	0.0510384i	$-0.0162531\pi$
$827$	51.6230	+	15.9236i	1.79511	+	0.553717i	0.796411	+	0.604756i	$0.206729\pi$
$828$	1.24582	+	1.56221i	0.0432952	+	0.0542904i
$829$	4.06549	−	54.2502i	0.141200	−	1.88419i	−0.256315	−	0.966593i	$-0.582509\pi$
$829$	4.06549	−	54.2502i	0.141200	−	1.88419i	0.397516	−	0.917595i	$-0.369872\pi$
$830$	−5.16951	+	1.59458i	−0.179436	+	0.0553487i
$831$	−27.1720	−	18.5256i	−0.942587	−	0.642645i
$832$	0.605656	+	0.0912880i	0.0209973	+	0.00316484i
$833$	−10.9931	−	48.1641i	−0.380890	−	1.66879i
$834$	13.0758	−	12.1326i	0.452778	−	0.420116i
$835$	0.583935	+	7.79207i	0.0202079	+	0.269656i
$836$	1.82358	+	4.64641i	0.0630699	+	0.160699i
$837$	44.1557	−	6.65540i	1.52624	−	0.230044i
$838$	−12.1668	−	5.85921i	−0.420294	−	0.202403i
$839$	6.43974	+	3.10121i	0.222324	+	0.107066i	0.541731	−	0.840552i	$-0.317769\pi$
$839$	6.43974	+	3.10121i	0.222324	+	0.107066i	−0.319406	+	0.947618i	$0.603483\pi$
$840$	18.7005	−	2.81865i	0.645230	−	0.0972527i
$841$	−4.60408	−	11.7310i	−0.158761	−	0.404518i
$842$	−0.915337	−	12.2143i	−0.0315446	−	0.420933i
$843$	38.1383	−	35.3872i	1.31355	−	1.21880i
$844$	1.71241	+	7.50256i	0.0589436	+	0.258249i
$845$	1.76605	+	0.266189i	0.0607540	+	0.00915719i
$846$	−0.874448	−	0.596189i	−0.0300641	−	0.0204974i
$847$	−23.6462	+	7.29387i	−0.812492	+	0.250620i
$848$	−1.58445	+	21.1430i	−0.0544101	+	0.726053i
$849$	−5.94881	−	7.45958i	−0.204163	−	0.256012i
$850$	−2.77152	−	0.854900i	−0.0950623	−	0.0293228i
$851$	−1.41339	+	3.60127i	−0.0484505	+	0.123450i
$852$	−2.95419	+	12.9431i	−0.101209	+	0.443425i
$853$	4.96717	+	8.60340i	0.170073	+	0.294575i	0.938445	−	0.345428i	$-0.112266\pi$
$853$	4.96717	+	8.60340i	0.170073	+	0.294575i	−0.768372	+	0.640003i	$0.778933\pi$
$854$	9.83311	−	17.0314i	0.336482	−	0.582804i
$855$	−0.817674	−	0.758691i	−0.0279639	−	0.0259467i
$856$	−3.43725	+	4.31017i	−0.117483	+	0.147319i
$857$	−30.4616	+	20.7684i	−1.04055	+	0.709435i	−0.957888	−	0.287143i	$-0.907295\pi$
$857$	−30.4616	+	20.7684i	−1.04055	+	0.709435i	−0.0826619	+	0.996578i	$0.526342\pi$
$858$	−8.52272	+	4.10432i	−0.290961	+	0.140119i
$859$	24.6285			0.840314			0.420157	−	0.907451i	$-0.361975\pi$
$859$	24.6285			0.840314			0.420157	+	0.907451i	$0.361975\pi$
$860$	6.27616	−	8.34838i	0.214015	−	0.284677i
$861$	−8.80823			−0.300184
$862$	13.4169	−	6.46126i	0.456983	−	0.220071i
$863$	−11.3011	+	7.70494i	−0.384693	+	0.262279i	−0.740189	−	0.672398i	$-0.765264\pi$
$863$	−11.3011	+	7.70494i	−0.384693	+	0.262279i	0.355497	+	0.934678i	$0.384312\pi$
$864$	−15.1635	+	19.0144i	−0.515872	+	0.646883i
$865$	1.78057	+	1.65213i	0.0605411	+	0.0561740i
$866$	4.32956	−	7.49901i	0.147124	−	0.254827i
$867$	3.56728	+	6.17870i	0.121151	+	0.209840i
$868$	−15.6379	+	68.5141i	−0.530785	+	2.32552i
$869$	−1.62750	+	4.14681i	−0.0552092	+	0.140671i
$870$	4.81838	+	1.48627i	0.163358	+	0.0503894i
$871$	13.1657	+	16.5093i	0.446103	+	0.559395i
$872$	0.255008	−	3.40285i	0.00863566	−	0.115235i
$873$	11.2474	−	3.46936i	0.380667	−	0.117420i
$874$	1.13169	+	0.771574i	0.0382800	+	0.0260989i
$875$	−4.18006	−	0.630043i	−0.141312	−	0.0212993i
$876$	8.90401	+	39.0110i	0.300839	+	1.31806i
$877$	−17.9168	+	16.6243i	−0.605006	+	0.561363i	−0.922061	−	0.387044i	$-0.873496\pi$
$877$	−17.9168	+	16.6243i	−0.605006	+	0.561363i	0.317056	+	0.948407i	$0.397306\pi$
$878$	−0.852167	−	11.3714i	−0.0287593	−	0.383766i
$879$	−8.65099	−	22.0424i	−0.291791	−	0.743471i
$880$	3.86365	−	0.582351i	0.130244	−	0.0196311i
$881$	−13.2555	−	6.38353i	−0.446591	−	0.215067i	0.197052	−	0.980393i	$-0.436863\pi$
$881$	−13.2555	−	6.38353i	−0.446591	−	0.215067i	−0.643642	+	0.765326i	$0.722578\pi$
$882$	5.04630	+	2.43017i	0.169918	+	0.0818281i
$883$	−46.9633	+	7.07858i	−1.58044	+	0.238213i	−0.879815	−	0.475316i	$-0.842334\pi$
$883$	−46.9633	+	7.07858i	−1.58044	+	0.238213i	−0.700625	+	0.713529i	$0.747095\pi$
$884$	8.85636	+	22.5656i	0.297872	+	0.758964i
$885$	−1.68484	−	22.4826i	−0.0566352	−	0.755744i
$886$	−13.7529	+	12.7608i	−0.462038	+	0.428709i
$887$	0.255041	+	1.11741i	0.00856342	+	0.0375188i	0.979029	−	0.203720i	$-0.0653033\pi$
$887$	0.255041	+	1.11741i	0.00856342	+	0.0375188i	−0.970466	+	0.241239i	$0.922446\pi$
$888$	11.0153	+	1.66029i	0.369648	+	0.0557155i
$889$	10.7684	+	7.34176i	0.361160	+	0.246235i
$890$	−9.08478	+	2.80229i	−0.304523	+	0.0939328i
$891$	1.82587	−	24.3646i	0.0611690	−	0.816244i
$892$	−26.8698	−	33.6936i	−0.899666	−	1.12815i
$893$	2.71135	+	0.836341i	0.0907318	+	0.0279871i
$894$	−5.02437	+	12.8019i	−0.168040	+	0.428159i
$895$	1.14349	−	5.00996i	0.0382227	−	0.167465i
$896$	−23.7838	−	41.1947i	−0.794561	−	1.37622i
$897$	5.07610	−	8.79206i	0.169486	−	0.293558i
$898$	6.39499	+	5.93368i	0.213404	+	0.198010i
$899$	−26.3524	+	33.0449i	−0.878902	+	1.10211i
$900$	−1.06260	+	0.724465i	−0.0354198	+	0.0241488i
$901$	50.4066	−	24.2746i	1.67929	−	0.808703i
$902$	1.54590			0.0514730
$903$	51.2100	−	17.4125i	1.70416	−	0.579450i
$904$	−24.0914			−0.801270
$905$	7.00269	−	3.37232i	0.232777	−	0.112100i
$906$	7.04166	−	4.80092i	0.233943	−	0.159500i
$907$	9.05891	−	11.3595i	0.300796	−	0.377186i	−0.608346	−	0.793672i	$-0.708167\pi$
$907$	9.05891	−	11.3595i	0.300796	−	0.377186i	0.909142	+	0.416485i	$0.136738\pi$
$908$	−23.1227	−	21.4547i	−0.767353	−	0.712000i
$909$	−6.18757	+	10.7172i	−0.205229	+	0.355467i
$910$	−4.51687	−	7.82345i	−0.149733	−	0.259345i
$911$	2.34021	−	10.2531i	0.0775345	−	0.339701i	−0.921251	−	0.388968i	$-0.872832\pi$
$911$	2.34021	−	10.2531i	0.0775345	−	0.339701i	0.998786	+	0.0492675i	$0.0156887\pi$
$912$	−1.69621	+	4.32187i	−0.0561671	+	0.143111i
$913$	−18.3767	−	5.66845i	−0.608179	−	0.187598i
$914$	−1.46568	−	1.83791i	−0.0484805	−	0.0607926i
$915$	−1.06303	+	14.1852i	−0.0351427	+	0.468947i
$916$	−2.67264	+	0.824400i	−0.0883065	+	0.0272390i
$917$	11.1253	+	7.58510i	0.367390	+	0.250482i
$918$	12.2700	+	1.84940i	0.404969	+	0.0610393i
$919$	10.5499	+	46.2223i	0.348010	+	1.52473i	0.781692	+	0.623665i	$0.214357\pi$
$919$	10.5499	+	46.2223i	0.348010	+	1.52473i	−0.433681	+	0.901066i	$0.642786\pi$
$920$	2.61127	−	2.42291i	0.0860911	−	0.0798809i
$921$	−2.68108	−	35.7766i	−0.0883447	−	1.17888i
$922$	−4.08229	−	10.4015i	−0.134443	−	0.342555i
$923$	14.1450	−	2.13202i	0.465589	−	0.0701762i
$924$	26.8523	+	12.9314i	0.883375	+	0.425411i
$925$	−2.24343	−	1.08038i	−0.0737634	−	0.0355226i
$926$	−1.24863	+	0.188201i	−0.0410326	+	0.00618468i
$927$	5.15464	+	13.1338i	0.169301	+	0.431371i
$928$	−1.72025	−	22.9551i	−0.0564699	−	0.753539i
$929$	21.7621	−	20.1923i	0.713992	−	0.662487i	−0.237069	−	0.971493i	$-0.576187\pi$
$929$	21.7621	−	20.1923i	0.713992	−	0.662487i	0.951060	+	0.309006i	$0.0999962\pi$
$930$	2.89209	+	12.6711i	0.0948354	+	0.415501i
$931$	−14.8484	−	2.23803i	−0.486636	−	0.0733485i
$932$	−16.9663	−	11.5674i	−0.555750	−	0.378904i
$933$	35.4939	−	10.9484i	1.16202	−	0.358436i
$934$	0.242831	−	3.24036i	0.00794568	−	0.106028i
$935$	−6.42837	−	8.06092i	−0.210230	−	0.263620i
$936$	−5.92395	−	1.82730i	−0.193630	−	0.0597271i
$937$	−9.98993	+	25.4539i	−0.326357	+	0.831543i	0.669684	+	0.742646i	$0.266430\pi$
$937$	−9.98993	+	25.4539i	−0.326357	+	0.831543i	−0.996041	+	0.0888972i	$0.971666\pi$
$938$	−3.78523	+	16.5842i	−0.123592	+	0.541493i
$939$	29.3025	+	50.7534i	0.956251	+	1.65628i
$940$	1.63572	−	2.83315i	0.0533512	−	0.0924070i
$941$	15.6182	+	14.4915i	0.509138	+	0.472411i	0.892410	−	0.451224i	$-0.149013\pi$
$941$	15.6182	+	14.4915i	0.509138	+	0.472411i	−0.383273	+	0.923635i	$0.625203\pi$
$942$	3.70792	−	4.64958i	0.120810	−	0.151491i
$943$	−1.37082	+	0.934607i	−0.0446400	+	0.0304350i
$944$	−17.9303	+	8.63476i	−0.583580	+	0.281037i
$945$	18.0854			0.588318
$946$	−8.98770	+	3.05600i	−0.292215	+	0.0993593i
$947$	40.3744			1.31199			0.655996	−	0.754765i	$-0.272249\pi$
$947$	40.3744			1.31199			0.655996	+	0.754765i	$0.272249\pi$
$948$	−5.49863	+	2.64800i	−0.178587	+	0.0860031i
$949$	35.6233	−	24.2876i	1.15638	−	0.788408i
$950$	−0.549654	+	0.689244i	−0.0178331	+	0.0223620i
$951$	0.365766	+	0.339381i	0.0118608	+	0.0110052i
$952$	−22.0248	+	38.1481i	−0.713828	+	1.23639i
$953$	−0.290115	−	0.502493i	−0.00939774	−	0.0162774i	0.861288	−	0.508117i	$-0.169658\pi$
$953$	−0.290115	−	0.502493i	−0.00939774	−	0.0162774i	−0.870686	+	0.491839i	$0.836325\pi$
$954$	−1.41144	+	6.18391i	−0.0456969	+	0.200211i
$955$	−2.75742	+	7.02580i	−0.0892281	+	0.227350i
$956$	14.7986	+	4.56476i	0.478621	+	0.147635i
$957$	11.1759	+	14.0142i	0.361267	+	0.453014i
$958$	−0.950537	+	12.6840i	−0.0307104	+	0.409802i
$959$	−57.8493	+	17.8441i	−1.86805	+	0.576218i
$960$	−0.294881	−	0.201046i	−0.00951723	−	0.00648874i
$961$	−77.0713	−	11.6166i	−2.48617	−	0.374730i
$962$	−1.18408	−	5.18778i	−0.0381762	−	0.167261i
$963$	1.42323	−	1.32056i	0.0458628	−	0.0425545i
$964$	1.88434	+	25.1447i	0.0606904	+	0.809857i
$965$	−10.0291	−	25.5538i	−0.322849	−	0.822606i
$966$	8.08703	−	1.21892i	0.260196	−	0.0392182i
$967$	−26.7457	−	12.8801i	−0.860084	−	0.414195i	−0.0487735	−	0.998810i	$-0.515531\pi$
$967$	−26.7457	−	12.8801i	−0.860084	−	0.414195i	−0.811311	+	0.584615i	$0.801246\pi$
$968$	12.0921	+	5.82323i	0.388654	+	0.187166i
$969$	12.1143	−	1.82594i	0.389168	−	0.0586576i
$970$	−3.39861	−	8.65951i	−0.109123	−	0.278040i
$971$	1.51410	+	20.2043i	0.0485899	+	0.648387i	0.967329	+	0.253523i	$0.0815894\pi$
$971$	1.51410	+	20.2043i	0.0485899	+	0.648387i	−0.918739	+	0.394864i	$0.870792\pi$
$972$	9.55201	−	8.86297i	0.306381	−	0.284280i
$973$	13.4748	+	59.0368i	0.431981	+	1.89263i
$974$	9.52949	+	1.43634i	0.305344	+	0.0460233i
$975$	5.39887	+	3.68089i	0.172902	+	0.117883i
$976$	11.9985	−	3.70106i	0.384064	−	0.118468i
$977$	−1.30226	+	17.3775i	−0.0416631	+	0.555956i	0.936845	+	0.349746i	$0.113732\pi$
$977$	−1.30226	+	17.3775i	−0.0416631	+	0.555956i	−0.978508	+	0.206210i	$0.933887\pi$
$978$	1.44266	+	1.80904i	0.0461311	+	0.0578466i
$979$	−32.2948	−	9.96162i	−1.03215	−	0.318375i
$980$	−6.32517	+	16.1163i	−0.202050	+	0.514815i
$981$	−0.267416	+	1.17163i	−0.00853794	+	0.0374071i
$982$	11.2184	+	19.4309i	0.357995	+	0.620065i
$983$	−26.3347	+	45.6131i	−0.839947	+	1.45483i	0.0499902	+	0.998750i	$0.484081\pi$
$983$	−26.3347	+	45.6131i	−0.839947	+	1.45483i	−0.889938	+	0.456082i	$0.849252\pi$
$984$	3.50201	+	3.24939i	0.111640	+	0.103587i
$985$	−6.23790	+	7.82208i	−0.198756	+	0.249232i
$986$	−9.70405	+	6.61611i	−0.309040	+	0.210700i
$987$	15.2643	−	7.35089i	0.485867	−	0.233981i
$988$	7.36822			0.234414
$989$	6.12220	−	8.14358i	0.194675	−	0.258951i
$990$	1.16892			0.0371506
$991$	−50.6562	+	24.3947i	−1.60915	+	0.774924i	−0.999838	−	0.0180085i	$-0.994267\pi$
$991$	−50.6562	+	24.3947i	−1.60915	+	0.774924i	−0.609309	+	0.792933i	$0.708553\pi$
$992$	49.0236	−	33.4237i	1.55650	−	1.06120i
$993$	43.0355	−	53.9648i	1.36569	−	1.71252i
$994$	8.44740	+	7.83805i	0.267935	+	0.248608i
$995$	10.3738	−	17.9680i	0.328872	−	0.569624i
$996$	−13.1733	−	22.8168i	−0.417412	−	0.722979i
$997$	2.61495	−	11.4568i	0.0828161	−	0.362841i	−0.916491	−	0.400055i	$-0.868991\pi$
$997$	2.61495	−	11.4568i	0.0828161	−	0.362841i	0.999307	+	0.0372136i	$0.0118482\pi$
$998$	1.79959	−	4.58529i	0.0569651	−	0.145145i
$999$	10.1797	+	3.14001i	0.322070	+	0.0993454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	215.2.q.b.31.6	✓	96
43.5	odd	42		9245.2.a.ba.1.31		48
43.25	even	21	inner	215.2.q.b.111.6	yes	96
43.38	even	21		9245.2.a.bb.1.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.q.b.31.6	✓	96	1.1	even	1	trivial
215.2.q.b.111.6	yes	96	43.25	even	21	inner
9245.2.a.ba.1.31		48	43.5	odd	42
9245.2.a.bb.1.18		48	43.38	even	21

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:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.574959 - 0.276886i) q^{2} +(-1.61221 + 1.09919i) q^{3} +(-0.993068 + 1.24527i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(-0.622606 + 1.07839i) q^{6} +(-2.11364 - 3.66093i) q^{7} +(-0.510182 + 2.23526i) q^{8} +(0.294993 - 0.751629i) q^{9} +O(q^{10})\)	\(q+(0.574959 - 0.276886i) q^{2} +(-1.61221 + 1.09919i) q^{3} +(-0.993068 + 1.24527i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(-0.622606 + 1.07839i) q^{6} +(-2.11364 - 3.66093i) q^{7} +(-0.510182 + 2.23526i) q^{8} +(0.294993 - 0.751629i) q^{9} +(-0.609805 - 0.188100i) q^{10} +(-1.41440 - 1.77361i) q^{11} +(0.232253 - 3.09920i) q^{12} +(-3.19996 + 0.987056i) q^{13} +(-2.22891 - 1.51965i) q^{14} +(1.92947 + 0.290821i) q^{15} +(-0.383268 - 1.67920i) q^{16} +(-3.33167 + 3.09134i) q^{17} +(-0.0385066 - 0.513835i) q^{18} +(0.504698 + 1.28595i) q^{19} +(1.57497 - 0.237388i) q^{20} +(7.43168 + 3.57891i) q^{21} +(-1.30431 - 0.628123i) q^{22} +(1.53633 - 0.231565i) q^{23} +(-1.63444 - 4.16449i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-1.56654 + 1.45354i) q^{26} +(-0.952003 - 4.17100i) q^{27} +(6.65782 + 1.00351i) q^{28} +(3.34579 + 2.28112i) q^{29} +(1.18989 - 0.367033i) q^{30} +(-0.779997 + 10.4083i) q^{31} +(-3.54431 - 4.44442i) q^{32} +(4.22985 + 1.30474i) q^{33} +(-1.05963 + 2.69988i) q^{34} +(-0.940657 + 4.12129i) q^{35} +(0.643031 + 1.11376i) q^{36} +(-1.24501 + 2.15642i) q^{37} +(0.646241 + 0.599624i) q^{38} +(4.07405 - 5.10870i) q^{39} +(1.89435 - 1.29155i) q^{40} +(-0.962102 + 0.463324i) q^{41} +5.26386 q^{42} +(4.67763 - 4.59563i) q^{43} +3.61322 q^{44} +(-0.727482 + 0.350337i) q^{45} +(0.819210 - 0.558528i) q^{46} +(1.28061 - 1.60584i) q^{47} +(2.46367 + 2.28595i) q^{48} +(-5.43493 + 9.41358i) q^{49} +(0.319078 + 0.552659i) q^{50} +(1.97340 - 8.64602i) q^{51} +(1.94862 - 4.96502i) q^{52} +(-11.7629 - 3.62838i) q^{53} +(-1.70225 - 2.13456i) q^{54} +(-0.169527 + 2.26219i) q^{55} +(9.26145 - 2.85678i) q^{56} +(-2.22718 - 1.51847i) q^{57} +(2.55530 + 0.385150i) q^{58} +(-2.57109 - 11.2647i) q^{59} +(-2.27825 + 2.11391i) q^{60} +(0.544790 + 7.26971i) q^{61} +(2.43345 + 6.20033i) q^{62} +(-3.37517 + 0.508725i) q^{63} +(-0.164791 - 0.0793592i) q^{64} +(3.01710 + 1.45296i) q^{65} +(2.79325 - 0.421015i) q^{66} +(-2.30374 - 5.86982i) q^{67} +(-0.540969 - 7.21872i) q^{68} +(-2.22236 + 2.06205i) q^{69} +(0.600286 + 2.63003i) q^{70} +(-4.22399 - 0.636664i) q^{71} +(1.52958 + 1.04285i) q^{72} +(-12.3030 + 3.79498i) q^{73} +(-0.118747 + 1.58457i) q^{74} +(-1.21660 - 1.52556i) q^{75} +(-2.10255 - 0.648550i) q^{76} +(-3.50351 + 8.92680i) q^{77} +(0.927886 - 4.06534i) q^{78} +(-0.981858 - 1.70063i) q^{79} +(-0.861194 + 1.49163i) q^{80} +(7.89524 + 7.32571i) q^{81} +(-0.424881 + 0.532784i) q^{82} +(7.00429 - 4.77544i) q^{83} +(-11.8369 + 5.70033i) q^{84} +4.54493 q^{85} +(1.41698 - 3.93746i) q^{86} -7.90151 q^{87} +(4.68607 - 2.25669i) q^{88} +(12.3092 - 8.39227i) q^{89} +(-0.321269 + 0.402859i) q^{90} +(10.3771 + 9.62853i) q^{91} +(-1.23732 + 2.14310i) q^{92} +(-10.1832 - 17.6378i) q^{93} +(0.291667 - 1.27787i) q^{94} +(0.504698 - 1.28595i) q^{95} +(10.5994 + 3.26949i) q^{96} +(9.08877 + 11.3970i) q^{97} +(-0.518378 + 6.91727i) q^{98} +(-1.75033 + 0.539906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9}+O(q^{10}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9	\( 96 q + 3 q^{3} - 26 q^{4} + 8 q^{5} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 19 q^{9} + 14 q^{10} - 24 q^{11} + 15 q^{12} - 17 q^{14} - 4 q^{15} - 2 q^{16} + 13 q^{17} + 14 q^{18} + q^{19} - 8 q^{20} + 30 q^{21} - 37 q^{22} - 14 q^{23} - 15 q^{24} + 8 q^{25} - 56 q^{26} - 18 q^{27} + 111 q^{28} - 15 q^{29} + 2 q^{30} - 43 q^{31} - 9 q^{32} - 19 q^{33} + 33 q^{34} + 3 q^{35} - 61 q^{36} + 19 q^{37} - 24 q^{38} + 19 q^{39} + 3 q^{40} + 40 q^{41} + 140 q^{42} - 53 q^{43} + 104 q^{44} - 32 q^{45} - 34 q^{46} - 18 q^{47} - 54 q^{48} - 78 q^{49} - 7 q^{50} + 59 q^{51} - 25 q^{52} + 51 q^{53} - 24 q^{54} + 12 q^{55} - 20 q^{56} - 113 q^{57} - 112 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 87 q^{62} - 38 q^{63} + 50 q^{64} - 96 q^{66} - 28 q^{67} - 149 q^{68} + 112 q^{69} - q^{70} + 51 q^{71} - 208 q^{72} + 24 q^{73} - 19 q^{74} + 8 q^{75} + 248 q^{76} + 7 q^{77} + 242 q^{78} - 138 q^{79} - 55 q^{80} - 15 q^{81} - 98 q^{82} + 43 q^{83} + 132 q^{84} + 44 q^{85} - 30 q^{86} - 22 q^{87} - 66 q^{88} + 7 q^{89} + 98 q^{90} - 5 q^{91} - 102 q^{92} - 2 q^{93} + 16 q^{94} + q^{95} + 486 q^{96} - 67 q^{97} + 62 q^{98} + 11 q^{99}+O(q^{100}) \) 96 * q + 3 * q^3 - 26 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^7 - 20 * q^8 - 19 * q^9 + 14 * q^10 - 24 * q^11 + 15 * q^12 - 17 * q^14 - 4 * q^15 - 2 * q^16 + 13 * q^17 + 14 * q^18 + q^19 - 8 * q^20 + 30 * q^21 - 37 * q^22 - 14 * q^23 - 15 * q^24 + 8 * q^25 - 56 * q^26 - 18 * q^27 + 111 * q^28 - 15 * q^29 + 2 * q^30 - 43 * q^31 - 9 * q^32 - 19 * q^33 + 33 * q^34 + 3 * q^35 - 61 * q^36 + 19 * q^37 - 24 * q^38 + 19 * q^39 + 3 * q^40 + 40 * q^41 + 140 * q^42 - 53 * q^43 + 104 * q^44 - 32 * q^45 - 34 * q^46 - 18 * q^47 - 54 * q^48 - 78 * q^49 - 7 * q^50 + 59 * q^51 - 25 * q^52 + 51 * q^53 - 24 * q^54 + 12 * q^55 - 20 * q^56 - 113 * q^57 - 112 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 87 * q^62 - 38 * q^63 + 50 * q^64 - 96 * q^66 - 28 * q^67 - 149 * q^68 + 112 * q^69 - q^70 + 51 * q^71 - 208 * q^72 + 24 * q^73 - 19 * q^74 + 8 * q^75 + 248 * q^76 + 7 * q^77 + 242 * q^78 - 138 * q^79 - 55 * q^80 - 15 * q^81 - 98 * q^82 + 43 * q^83 + 132 * q^84 + 44 * q^85 - 30 * q^86 - 22 * q^87 - 66 * q^88 + 7 * q^89 + 98 * q^90 - 5 * q^91 - 102 * q^92 - 2 * q^93 + 16 * q^94 + q^95 + 486 * q^96 - 67 * q^97 + 62 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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