LMFDB - Embedded newform 215.2.q.b.111.6

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			111.6
Character	$\chi$	$=$	215.111
Dual form			215.2.q.b.31.6

$q$-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 $\left(\mathbb{Z}/215\mathbb{Z}\right)^\times$.

$n$	$46$	$87$
$\chi(n)$	$e\left(\frac{4}{21}\right)$	$1$

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	0.625975	−	0.779843i	$-0.284701\pi$
$2$	0.574959	+	0.276886i	0.406557	+	0.195788i	−0.219417	+	0.975631i	$0.570416\pi$
$3$	−1.61221	−	1.09919i	−0.930812	−	0.634617i	4.55900e−5	−	1.00000i	$-0.499985\pi$
$3$	−1.61221	−	1.09919i	−0.930812	−	0.634617i	−0.930857	+	0.365383i	$0.880938\pi$
$4$	−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	0.121466	+	0.992596i	$0.461240\pi$
$7$	−2.11364	+	3.66093i	−0.798880	+	1.38370i	−0.920346	+	0.391105i	$0.872093\pi$
$8$	−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	−0.947918	−	0.318513i	$-0.896816\pi$
$11$	−1.41440	+	1.77361i	−0.426459	+	0.534763i	0.521459	+	0.853276i	$0.325388\pi$
$12$	0.232253	+	3.09920i	0.0670457	+	0.894663i
$13$	−3.19996	−	0.987056i	−0.887508	−	0.273760i	−0.182709	−	0.983167i	$-0.558487\pi$
$13$	−3.19996	−	0.987056i	−0.887508	−	0.273760i	−0.704799	+	0.709407i	$0.748963\pi$
$14$	−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	0.163515	−	0.986541i	$-0.447717\pi$
$17$	−3.33167	−	3.09134i	−0.808048	−	0.749759i	−0.971563	+	0.236782i	$0.923907\pi$
$18$	−0.0385066	+	0.513835i	−0.00907609	+	0.121112i
$19$	0.504698	−	1.28595i	0.115786	−	0.295017i	−0.861219	−	0.508233i	$-0.830299\pi$
$19$	0.504698	−	1.28595i	0.115786	−	0.295017i	0.977005	+	0.213217i	$0.0683940\pi$
$20$	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	0.307248	−	0.951630i	$-0.400592\pi$
$23$	1.53633	+	0.231565i	0.320347	+	0.0482846i	0.0130996	+	0.999914i	$0.495830\pi$
$24$	−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	−0.211339	−	0.977413i	$-0.567782\pi$
$29$	3.34579	−	2.28112i	0.621298	−	0.423594i	0.832637	+	0.553819i	$0.186830\pi$
$30$	1.18989	+	0.367033i	0.217244	+	0.0670107i
$31$	−0.779997	−	10.4083i	−0.140092	−	1.86939i	−0.417549	−	0.908654i	$-0.637111\pi$
$31$	−0.779997	−	10.4083i	−0.140092	−	1.86939i	0.277458	−	0.960738i	$-0.410508\pi$
$32$	−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	0.745352	−	0.666671i	$-0.232281\pi$
$37$	−1.24501	−	2.15642i	−0.204678	−	0.354512i	−0.950030	+	0.312158i	$0.898948\pi$
$38$	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	0.357245	−	0.934011i	$-0.383716\pi$
$41$	−0.962102	−	0.463324i	−0.150255	−	0.0723590i	−0.507500	+	0.861652i	$0.669430\pi$
$42$	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	0.866408	−	0.499337i	$-0.166423\pi$
$47$	1.28061	+	1.60584i	0.186797	+	0.234236i	−0.679611	+	0.733572i	$0.737852\pi$
$48$	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	−0.965300	−	0.261145i	$-0.915900\pi$
$53$	−11.7629	+	3.62838i	−1.61576	+	0.498396i	−0.650460	+	0.759541i	$0.725424\pi$
$54$	−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	0.475135	+	0.879913i	$0.342399\pi$
$59$	−2.57109	+	11.2647i	−0.334727	+	1.46653i	−0.809861	+	0.586621i	$0.800458\pi$
$60$	−2.27825	−	2.11391i	−0.294121	−	0.272904i
$61$	0.544790	−	7.26971i	0.0697532	−	0.930791i	−0.847066	−	0.531488i	$-0.821633\pi$
$61$	0.544790	−	7.26971i	0.0697532	−	0.930791i	0.916819	−	0.399303i	$-0.130748\pi$
$62$	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	0.718325	+	0.695708i	$0.244909\pi$
$67$	−2.30374	+	5.86982i	−0.281446	+	0.717113i	−0.999771	+	0.0214050i	$0.993186\pi$
$68$	−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	−0.394823	−	0.918757i	$-0.629194\pi$
$71$	−4.22399	+	0.636664i	−0.501296	+	0.0755582i	−0.106473	+	0.994316i	$0.533956\pi$
$72$	1.52958	−	1.04285i	0.180263	−	0.122901i
$73$	−12.3030	−	3.79498i	−1.43996	−	0.444169i	−0.526179	−	0.850374i	$-0.676376\pi$
$73$	−12.3030	−	3.79498i	−1.43996	−	0.444169i	−0.913782	+	0.406204i	$0.866852\pi$
$74$	−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	−0.915959	−	0.401272i	$-0.868568\pi$
$79$	−0.981858	+	1.70063i	−0.110468	+	0.191336i	0.805491	+	0.592608i	$0.201902\pi$
$80$	−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	0.883049	−	0.469282i	$-0.155487\pi$
$83$	7.00429	+	4.77544i	0.768821	+	0.524173i	−0.114228	+	0.993455i	$0.536439\pi$
$84$	−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	0.998062	−	0.0622247i	$-0.0198195\pi$
$89$	12.3092	+	8.39227i	1.30477	+	0.889578i	0.306710	+	0.951803i	$0.400772\pi$
$90$	−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	−0.0644115	−	0.997923i	$-0.520517\pi$
$97$	9.08877	−	11.3970i	0.922825	−	1.15719i	0.987236	−	0.159262i	$-0.0509115\pi$
$98$	−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	−0.850422	−	0.526102i	$-0.823653\pi$
$101$	−15.1551	+	2.28427i	−1.50799	+	0.227293i	−0.657569	+	0.753395i	$0.728415\pi$
$102$	−1.25934	+	5.51751i	−0.124693	+	0.546315i
$103$	−12.8092	−	11.8852i	−1.26213	−	1.17108i	−0.977150	−	0.212549i	$-0.931823\pi$
$103$	−12.8092	−	11.8852i	−1.26213	−	1.17108i	−0.284977	−	0.958534i	$-0.591986\pi$
$104$	−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	−0.326227	−	0.945292i	$-0.605777\pi$
$107$	2.16639	−	1.04328i	0.209433	−	0.100857i	0.535660	+	0.844434i	$0.320063\pi$
$108$	6.13941	−	2.95658i	0.590765	−	0.284497i
$109$	−1.47172	−	0.221826i	−0.140965	−	0.0212471i	0.0781805	−	0.996939i	$-0.475089\pi$
$109$	−1.47172	−	0.221826i	−0.140965	−	0.0212471i	−0.219146	+	0.975692i	$0.570327\pi$
$110$	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	−0.737550	−	0.675293i	$-0.764017\pi$
$113$	2.33819	−	10.2443i	0.219958	−	0.963699i	0.957508	−	0.288407i	$-0.0931255\pi$
$114$	−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	0.306562	−	0.951851i	$-0.400821\pi$
$127$	−2.77776	−	1.33770i	−0.246486	−	0.118701i	−0.553048	+	0.833149i	$0.686536\pi$
$128$	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	0.304294	−	0.952578i	$-0.401580\pi$
$131$	−2.86982	−	1.38203i	−0.250738	−	0.120749i	−0.555032	+	0.831829i	$0.687294\pi$
$132$	−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	0.907338	+	0.420402i	$0.138111\pi$
$137$	3.18673	+	13.9620i	0.272260	+	1.19285i	−0.635078	+	0.772448i	$0.719032\pi$
$138$	−0.706814	−	1.80093i	−0.0601680	−	0.153305i
$139$	−13.6884	+	4.22232i	−1.16104	+	0.358133i	−0.814647	−	0.579958i	$-0.803069\pi$
$139$	−13.6884	+	4.22232i	−1.16104	+	0.358133i	−0.346391	+	0.938090i	$0.612593\pi$
$140$	−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	0.580259	−	0.814432i	$-0.302951\pi$
$149$	10.9210	+	1.64607i	0.894681	+	0.134852i	0.314422	+	0.949283i	$0.398189\pi$
$150$	−1.12190	+	0.540278i	−0.0916026	+	0.0441135i
$151$	−6.16646	+	2.96961i	−0.501819	+	0.241663i	−0.667629	−	0.744494i	$-0.732691\pi$
$151$	−6.16646	+	2.96961i	−0.501819	+	0.241663i	0.165810	+	0.986158i	$0.446976\pi$
$152$	−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	−0.334762	−	0.942303i	$-0.608656\pi$
$157$	−4.72257	+	0.711814i	−0.376903	+	0.0568089i	−0.0421407	+	0.999112i	$0.513418\pi$
$158$	−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	0.954992	−	0.296630i	$-0.0958630\pi$
$163$	0.678873	+	1.72974i	0.0531735	+	0.135484i	−0.901819	+	0.432114i	$0.857768\pi$
$164$	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	−0.869966	−	0.493111i	$-0.835860\pi$
$167$	−5.72801	+	5.31482i	−0.443247	+	0.411273i	0.426720	+	0.904384i	$0.359669\pi$
$168$	−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	−0.753882	−	0.657010i	$-0.771821\pi$
$179$	2.56940	−	4.45033i	0.192046	−	0.332634i	0.945928	+	0.324376i	$0.105154\pi$
$180$	0.286176	+	1.25382i	0.0213303	+	0.0934541i
$181$	−2.83958	−	7.23513i	−0.211064	−	0.537783i	0.785660	−	0.618659i	$-0.212324\pi$
$181$	−2.83958	−	7.23513i	−0.211064	−	0.537783i	−0.996724	+	0.0808757i	$0.974228\pi$
$182$	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	−0.995258	−	0.0972724i	$-0.968988\pi$
$191$	−2.75742	+	7.02580i	−0.199520	+	0.508369i	0.795738	+	0.605642i	$0.207083\pi$
$192$	0.352909	+	0.0531925i	0.0254690	+	0.00383884i
$193$	24.7329	−	11.9107i	1.78031	−	0.857352i	0.823134	−	0.567847i	$-0.192223\pi$
$193$	24.7329	−	11.9107i	1.78031	−	0.857352i	0.957176	−	0.289505i	$-0.0934908\pi$
$194$	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	0.905084	+	0.425233i	$0.139808\pi$
$197$	−0.747661	+	9.97684i	−0.0532687	+	0.710821i	−0.958353	+	0.285588i	$0.907811\pi$
$198$	−0.856877	−	0.795066i	−0.0608956	−	0.0565029i
$199$	4.61679	−	20.2275i	0.327275	−	1.43389i	−0.497026	−	0.867736i	$-0.665575\pi$
$199$	4.61679	−	20.2275i	0.327275	−	1.43389i	0.824301	−	0.566151i	$-0.191568\pi$
$200$	−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	0.874636	−	0.484781i	$-0.161101\pi$
$211$	3.01243	+	3.77747i	0.207384	+	0.260052i	−0.667251	+	0.744833i	$0.732529\pi$
$212$	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	−0.614370	−	0.789018i	$-0.710590\pi$
$223$	−6.02082	−	26.3789i	−0.403184	−	1.76646i	0.211186	−	0.977446i	$-0.432267\pi$
$224$	−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	−0.800705	−	0.599059i	$-0.795541\pi$
$227$	−1.47996	−	19.7487i	−0.0982283	−	1.31077i	0.702477	−	0.711707i	$-0.252078\pi$
$228$	4.10264	+	1.26550i	0.271704	+	0.0838095i
$229$	1.45088	−	0.989196i	0.0958771	−	0.0653679i	−0.514433	−	0.857531i	$-0.671997\pi$
$229$	1.45088	−	0.989196i	0.0958771	−	0.0653679i	0.610310	+	0.792163i	$0.291045\pi$
$230$	−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	−0.872361	−	0.488862i	$-0.837412\pi$
$233$	0.963447	−	12.8563i	0.0631175	−	0.842245i	0.935479	−	0.353383i	$-0.114969\pi$
$234$	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	−0.998537	−	0.0540750i	$-0.982779\pi$
$239$	−3.55227	+	9.05103i	−0.229777	+	0.585463i	0.768760	+	0.639538i	$0.220874\pi$
$240$	−0.251156	+	3.35144i	−0.0162120	+	0.216335i
$241$	11.6051	+	10.7679i	0.747549	+	0.693624i	0.958887	−	0.283789i	$-0.0915916\pi$
$241$	11.6051	+	10.7679i	0.747549	+	0.693624i	−0.211338	+	0.977413i	$0.567782\pi$
$242$	−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	−0.368430	+	0.929656i	$0.620104\pi$
$251$	−15.6738	+	27.1478i	−0.989320	+	1.71355i	−0.620890	+	0.783897i	$0.713229\pi$
$252$	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	−0.527487	−	0.849563i	$-0.676866\pi$
$263$	4.54539	−	4.21750i	0.280281	−	0.260062i	0.807768	+	0.589500i	$0.200675\pi$
$264$	−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	−0.329873	−	0.944025i	$-0.607006\pi$
$269$	10.8886	−	13.6538i	0.663887	−	0.832488i	0.993760	+	0.111537i	$0.0355774\pi$
$270$	−0.204028	−	2.72256i	−0.0124167	−	0.165690i
$271$	0.475188	+	0.146576i	0.0288656	+	0.00890386i	0.309154	−	0.951012i	$-0.399954\pi$
$271$	0.475188	+	0.146576i	0.0288656	+	0.00890386i	−0.280289	+	0.959916i	$0.590430\pi$
$272$	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	−0.617750	−	0.786374i	$-0.711956\pi$
$277$	6.15741	−	15.6888i	0.369963	−	0.942650i	0.987713	−	0.156276i	$-0.0499490\pi$
$278$	−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	−0.696056	−	0.717988i	$-0.745063\pi$
$281$	−26.3652	−	3.97392i	−1.57282	−	0.237064i	−0.876762	+	0.480924i	$0.840301\pi$
$282$	0.934396	−	2.38080i	0.0556425	−	0.141775i
$283$	0.365409	−	4.87605i	0.0217213	−	0.289851i	−0.975756	−	0.218862i	$-0.929765\pi$
$283$	0.365409	−	4.87605i	0.0217213	−	0.289851i	0.997477	−	0.0709889i	$-0.0226155\pi$
$284$	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	−0.990499	−	0.137517i	$-0.956088\pi$
$293$	−2.70036	−	11.8311i	−0.157757	−	0.691177i	0.832743	−	0.553660i	$-0.186769\pi$
$294$	−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	−0.999587	−	0.0287429i	$-0.990850\pi$
$307$	−9.19323	−	15.9231i	−0.524685	−	0.908782i	0.474901	−	0.880039i	$-0.342484\pi$
$308$	−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	−0.763875	−	0.645364i	$-0.776706\pi$
$311$	−18.1902	+	5.61093i	−1.03147	+	0.318167i	−0.267597	+	0.963531i	$0.586229\pi$
$312$	9.34074	−	11.7129i	0.528815	−	0.663113i
$313$	2.24447	+	29.9503i	0.126865	+	1.69289i	0.590635	+	0.806939i	$0.298877\pi$
$313$	2.24447	+	29.9503i	0.126865	+	1.69289i	−0.463771	+	0.885955i	$0.653504\pi$
$314$	−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	−0.976501	−	0.215514i	$-0.930857\pi$
$317$	−0.0569013	+	0.249301i	−0.00319589	+	0.0140021i	0.973305	+	0.229516i	$0.0737144\pi$
$318$	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	−0.998037	−	0.0626334i	$-0.980050\pi$
$331$	−33.8022	−	10.4266i	−1.85794	−	0.573097i	−0.859899	−	0.510464i	$-0.829474\pi$
$332$	−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	−0.884701	−	0.466158i	$-0.845638\pi$
$337$	−0.709443	+	1.22879i	−0.0386458	+	0.0669365i	0.846056	+	0.533095i	$0.178971\pi$
$338$	−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	0.935771	−	0.352609i	$-0.114705\pi$
$347$	17.6856	+	12.0578i	0.949412	+	0.647298i	0.0136414	+	0.999907i	$0.495658\pi$
$348$	7.84674	+	9.83950i	0.420629	+	0.527452i
$349$	−22.4183	+	20.8011i	−1.20002	+	1.11346i	−0.209257	+	0.977861i	$0.567105\pi$
$349$	−22.4183	+	20.8011i	−1.20002	+	1.11346i	−0.990764	+	0.135597i	$0.956705\pi$
$350$	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	−0.988924	−	0.148422i	$-0.952581\pi$
$353$	−6.85668	−	17.4705i	−0.364944	−	0.929862i	0.623980	−	0.781440i	$-0.285515\pi$
$354$	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	0.878391	−	0.477942i	$-0.158617\pi$
$359$	35.2161	−	5.30797i	1.85863	−	0.280144i	0.980243	+	0.197798i	$0.0633791\pi$
$360$	−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	−0.513082	−	0.858340i	$-0.671496\pi$
$367$	−24.0686	−	3.62775i	−1.25637	−	0.189367i	−0.743287	+	0.668972i	$0.766734\pi$
$368$	−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	0.0373679	−	0.999302i	$-0.488103\pi$
$373$	18.9510	−	12.9205i	0.981244	−	0.669000i	0.943876	+	0.330301i	$0.107150\pi$
$374$	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	0.985442	−	0.170011i	$-0.0543802\pi$
$379$	0.463815	+	2.03211i	0.0238246	+	0.104382i	−0.961618	+	0.274393i	$0.911523\pi$
$380$	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	0.438802	−	0.898584i	$-0.355403\pi$
$383$	−10.4681	−	13.1266i	−0.534894	−	0.670736i	−0.973697	+	0.227847i	$0.926831\pi$
$384$	−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	−0.0348120	−	0.999394i	$-0.511083\pi$
$389$	−16.5255	−	7.95825i	−0.837874	−	0.403499i	−0.803062	+	0.595895i	$0.796798\pi$
$390$	−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	0.112457	−	0.993657i	$-0.464128\pi$
$397$	15.2449	−	4.70243i	0.765120	−	0.236008i	0.652663	+	0.757648i	$0.273652\pi$
$398$	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	−0.740776	−	0.671752i	$-0.765542\pi$
$401$	−7.73156	+	5.27129i	−0.386096	+	0.263236i	0.354680	+	0.934988i	$0.384590\pi$
$402$	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	0.188957	−	0.981985i	$-0.439489\pi$
$409$	21.7308	−	10.4650i	1.07452	−	0.517460i	0.885560	+	0.464525i	$0.153775\pi$
$410$	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	−0.991565	−	0.129614i	$-0.958626\pi$
$419$	−13.1937	+	16.5444i	−0.644556	+	0.808248i	0.347008	+	0.937862i	$0.387198\pi$
$420$	12.5542	−	3.87247i	0.612585	−	0.188957i
$421$	7.01224	+	17.8669i	0.341756	+	0.870780i	0.993655	+	0.112474i	$0.0358774\pi$
$421$	7.01224	+	17.8669i	0.341756	+	0.870780i	−0.651899	+	0.758306i	$0.726027\pi$
$422$	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	0.801926	−	0.597424i	$-0.203809\pi$
$433$	11.2112	+	7.64367i	0.538776	+	0.367331i	−0.263150	+	0.964755i	$0.584761\pi$
$434$	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	0.997787	+	0.0664859i	$0.0211787\pi$
$439$	6.52831	+	16.6339i	0.311579	+	0.793891i	−0.686208	+	0.727405i	$0.740726\pi$
$440$	−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	−0.456407	−	0.889771i	$-0.650864\pi$
$443$	−28.0929	−	8.66552i	−1.33473	−	0.411711i	−0.878327	+	0.478060i	$0.841340\pi$
$444$	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	−0.763266	−	0.646085i	$-0.776405\pi$
$449$	4.99432	−	12.7253i	0.235697	−	0.600546i	0.998963	+	0.0455391i	$0.0145006\pi$
$450$	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	−0.990475	−	0.137696i	$-0.956030\pi$
$457$	−0.819699	+	3.59134i	−0.0383439	+	0.167996i	0.952131	+	0.305691i	$0.0988876\pi$
$458$	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	0.941010	+	0.338378i	$0.109878\pi$
$461$	1.30850	+	17.4607i	0.0609430	+	0.813227i	−0.880067	+	0.474849i	$0.842503\pi$
$462$	−7.44523	+	9.33602i	−0.346383	+	0.434351i
$463$	−1.89082	+	0.583240i	−0.0878738	+	0.0271055i	−0.338380	−	0.941009i	$-0.609879\pi$
$463$	−1.89082	+	0.583240i	−0.0878738	+	0.0271055i	0.250507	+	0.968115i	$0.419403\pi$
$464$	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	0.918901	−	0.394489i	$-0.129078\pi$
$467$	2.54596	+	4.40974i	0.117813	+	0.204058i	−0.801088	+	0.598547i	$0.795745\pi$
$468$	−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	0.543355	−	0.839503i	$-0.317154\pi$
$479$	−9.96590	−	17.2614i	−0.455354	−	0.788696i	−0.998708	+	0.0508076i	$0.983820\pi$
$480$	−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	−0.246616	−	0.969113i	$-0.579319\pi$
$487$	12.4775	−	8.50699i	0.565408	−	0.385488i	0.812023	+	0.583625i	$0.198366\pi$
$488$	−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	−0.547776	−	0.836625i	$-0.684526\pi$
$491$	2.62743	−	35.0606i	0.118574	−	1.58226i	0.666351	−	0.745639i	$-0.267855\pi$
$492$	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	0.796594	−	0.604515i	$-0.206633\pi$
$499$	5.65827	+	5.25011i	0.253299	+	0.235027i	−0.543295	+	0.839542i	$0.682823\pi$
$500$	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	0.948856	−	0.315709i	$-0.102242\pi$
$503$	34.8749	+	10.7575i	1.55499	+	0.479652i	0.606137	+	0.795361i	$0.292718\pi$
$504$	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	0.473030	+	0.881046i	$0.343160\pi$
$509$	−11.8782	+	20.5737i	−0.526493	+	0.911913i	−0.999523	+	0.0308672i	$0.990173\pi$
$510$	−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	−0.306018	−	0.952026i	$-0.598997\pi$
$521$	14.1626	−	13.1410i	0.620477	−	0.575718i	0.926495	+	0.376308i	$0.122806\pi$
$522$	1.04329	+	1.80702i	0.0456634	+	0.0790912i
$523$	−18.5326	+	32.0994i	−0.810374	+	1.40361i	0.102229	+	0.994761i	$0.467403\pi$
$523$	−18.5326	+	32.0994i	−0.810374	+	1.40361i	−0.912603	+	0.408848i	$0.865931\pi$
$524$	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	−0.949379	−	0.314132i	$-0.898286\pi$
$541$	0.842344	−	11.2403i	0.0362152	−	0.483258i	0.985594	−	0.169126i	$-0.0540945\pi$
$542$	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	0.896705	+	0.442628i	$0.145954\pi$
$547$	1.77716	+	23.7145i	0.0759857	+	1.01396i	−0.820720	+	0.571331i	$0.806427\pi$
$548$	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	0.363441	−	0.931617i	$-0.381602\pi$
$557$	−3.26458	−	1.57214i	−0.138325	−	0.0666137i	−0.501766	+	0.865003i	$0.667316\pi$
$558$	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	0.840813	−	0.541325i	$-0.182077\pi$
$563$	2.98878	+	3.74781i	0.125962	+	0.157951i	−0.714851	+	0.699276i	$0.753506\pi$
$564$	−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	−0.435983	−	0.899955i	$-0.643599\pi$
$569$	−6.89962	+	2.12825i	−0.289247	+	0.0892210i	0.146736	+	0.989176i	$0.453123\pi$
$570$	1.07252	−	1.34490i	0.0449230	−	0.0563316i
$571$	0.793411	+	10.5873i	0.0332032	+	0.443066i	0.988887	+	0.148670i	$0.0474993\pi$
$571$	0.793411	+	10.5873i	0.0332032	+	0.443066i	−0.955684	+	0.294396i	$0.904882\pi$
$572$	−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	−0.898187	−	0.439613i	$-0.855116\pi$
$577$	1.33289	−	17.7862i	0.0554889	−	0.740448i	0.953676	−	0.300835i	$-0.0972653\pi$
$578$	−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	0.137209	−	0.990542i	$-0.456187\pi$
$587$	13.5748	−	2.04607i	0.560290	−	0.0844502i	0.423081	+	0.906092i	$0.360949\pi$
$588$	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	0.998179	−	0.0603144i	$-0.0192103\pi$
$593$	5.48977	+	13.9877i	0.225438	+	0.574406i	−0.772742	+	0.634721i	$0.781115\pi$
$594$	−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	0.305507	−	0.952190i	$-0.401174\pi$
$599$	−11.4846	−	7.83006i	−0.469247	−	0.319928i	−0.774754	+	0.632262i	$0.782126\pi$
$600$	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	−0.656757	−	0.754102i	$-0.728072\pi$
$607$	1.13719	−	1.05516i	0.0461571	−	0.0428275i	0.702914	+	0.711275i	$0.251882\pi$
$608$	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	−0.889787	−	0.456376i	$-0.849147\pi$
$613$	−6.11191	+	7.66409i	−0.246858	+	0.309550i	0.642930	+	0.765925i	$0.277719\pi$
$614$	−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	−0.681199	−	0.732098i	$-0.738541\pi$
$617$	−27.7294	+	4.17954i	−1.11635	+	0.168262i	−0.435146	+	0.900360i	$0.643303\pi$
$618$	−4.84174	+	21.2131i	−0.194763	+	0.853314i
$619$	−36.1756	−	33.5660i	−1.45402	−	1.34913i	−0.814161	−	0.580639i	$-0.802803\pi$
$619$	−36.1756	−	33.5660i	−1.45402	−	1.34913i	−0.639858	−	0.768493i	$-0.721007\pi$
$620$	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	−0.685491	−	0.728081i	$-0.740412\pi$
$631$	−6.48535	+	4.42164i	−0.258178	+	0.176023i	0.427313	+	0.904104i	$0.359460\pi$
$632$	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	0.987229	+	0.159305i	$0.0509253\pi$
$641$	23.3650	+	29.2988i	0.922861	+	1.15723i	−0.0643684	+	0.997926i	$0.520503\pi$
$642$	−2.47386	−	1.68665i	−0.0976356	−	0.0665668i
$643$	35.4614	+	17.0773i	1.39846	+	0.673463i	0.972848	−	0.231444i	$-0.0743449\pi$
$643$	35.4614	+	17.0773i	1.39846	+	0.673463i	0.425611	+	0.904906i	$0.360059\pi$
$644$	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	0.808192	−	0.588919i	$-0.200446\pi$
$647$	21.6629	+	10.4323i	0.851656	+	0.410136i	0.0434637	+	0.999055i	$0.486161\pi$
$648$	−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	0.995999	+	0.0893660i	$0.0284841\pi$
$653$	3.51134	+	15.3842i	0.137409	+	0.602030i	−0.858589	+	0.512664i	$0.828659\pi$
$654$	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	−0.482195	−	0.876064i	$-0.660160\pi$
$659$	4.03406	−	2.75038i	0.157145	−	0.107139i	0.639339	+	0.768925i	$0.279208\pi$
$660$	6.97160	−	1.05080i	0.271369	−	0.0409023i
$661$	1.49842	−	6.56502i	0.0582819	−	0.255350i	−0.937391	−	0.348279i	$-0.886766\pi$
$661$	1.49842	−	6.56502i	0.0582819	−	0.255350i	0.995673	+	0.0929297i	$0.0296232\pi$
$662$	−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	−0.213560	−	0.976930i	$-0.568506\pi$
$673$	−3.36412	+	0.507059i	−0.129677	+	0.0195457i	0.0838829	+	0.996476i	$0.473268\pi$
$674$	−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	−0.967537	−	0.252730i	$-0.918672\pi$
$677$	−13.1617	+	16.5043i	−0.505847	+	0.634311i	0.461690	+	0.887041i	$0.347243\pi$
$678$	−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	−0.834958	−	0.550314i	$-0.814508\pi$
$683$	−9.10987	+	8.45272i	−0.348579	+	0.323434i	0.486379	+	0.873748i	$0.338318\pi$
$684$	−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	0.401200	−	0.915991i	$-0.368593\pi$
$691$	−8.01479	−	5.46439i	−0.304897	−	0.207875i	−0.706097	+	0.708115i	$0.749546\pi$
$692$	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	0.162308	−	0.986740i	$-0.448106\pi$
$701$	−6.86897	−	2.11880i	−0.259437	−	0.0800258i	−0.421745	+	0.906714i	$0.638582\pi$
$702$	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	−0.497569	−	0.867424i	$-0.665774\pi$
$709$	−3.45137	+	1.66209i	−0.129619	+	0.0624212i	0.367950	+	0.929845i	$0.380060\pi$
$710$	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	0.729411	+	0.684076i	$0.239794\pi$
$719$	2.95232	+	39.3960i	0.110103	+	1.46922i	−0.619308	+	0.785148i	$0.712587\pi$
$720$	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	0.999045	+	0.0436940i	$0.0139127\pi$
$727$	22.0917	+	27.7021i	0.819335	+	1.02741i	−0.179710	+	0.983720i	$0.557516\pi$
$728$	−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	0.127317	−	0.991862i	$-0.459363\pi$
$733$	−15.3989	−	7.41572i	−0.568771	−	0.273906i	−0.696088	+	0.717956i	$0.745078\pi$
$734$	−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	0.962187	−	0.272390i	$-0.0878142\pi$
$739$	−0.622506	−	2.72738i	−0.0228993	−	0.100328i	−0.985086	+	0.172062i	$0.944957\pi$
$740$	−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	0.998512	+	0.0545297i	$0.0173659\pi$
$743$	0.525529	+	7.01269i	0.0192798	+	0.257271i	−0.979232	+	0.202741i	$0.935015\pi$
$744$	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	−0.686755	−	0.726889i	$-0.740966\pi$
$751$	−42.6756	−	6.43231i	−1.55725	−	0.234718i	−0.870499	+	0.492170i	$0.836204\pi$
$752$	−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	0.668349	−	0.743847i	$-0.267001\pi$
$757$	−0.645805	−	0.599219i	−0.0234722	−	0.0217790i	−0.691822	+	0.722068i	$0.743192\pi$
$758$	−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	0.793458	−	0.608625i	$-0.208279\pi$
$761$	30.5157	+	9.41285i	1.10619	+	0.341215i	0.312735	+	0.949840i	$0.398755\pi$
$762$	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	−0.244112	−	0.969747i	$-0.578497\pi$
$769$	19.5414	−	18.1318i	0.704681	−	0.653848i	0.948793	+	0.315899i	$0.102306\pi$
$770$	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	0.00341071	−	0.999994i	$-0.498914\pi$
$787$	−15.6283	−	4.82069i	−0.557088	−	0.171839i	−0.560499	+	0.828155i	$0.689391\pi$
$788$	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	0.190230	−	0.981740i	$-0.439077\pi$
$797$	2.33288	+	0.351626i	0.0826350	+	0.0124552i	−0.107595	+	0.994195i	$0.534315\pi$
$798$	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	0.974883	+	0.222719i	$0.0714932\pi$
$809$	5.49454	+	24.0732i	0.193178	+	0.846368i	−0.781705	+	0.623649i	$0.785650\pi$
$810$	−3.43659	+	5.95234i	−0.120749	+	0.209144i
$811$	22.1842	+	38.4242i	0.778993	+	1.34926i	0.932523	+	0.361111i	$0.117603\pi$
$811$	22.1842	+	38.4242i	0.778993	+	1.34926i	−0.153530	+	0.988144i	$0.549064\pi$
$812$	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	0.675167	−	0.737665i	$-0.264071\pi$
$821$	−5.56561	−	6.97906i	−0.194241	−	0.243571i	−0.869409	+	0.494094i	$0.835500\pi$
$822$	13.0723	−	12.1293i	0.455949	−	0.423059i
$823$	−7.15092	−	12.3858i	−0.249265	−	0.431740i	0.714057	−	0.700088i	$-0.246856\pi$
$823$	−7.15092	−	12.3858i	−0.249265	−	0.431740i	−0.963322	+	0.268347i	$0.913522\pi$
$824$	−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	0.796411	−	0.604756i	$-0.206729\pi$
$827$	51.6230	−	15.9236i	1.79511	−	0.553717i	0.998697	+	0.0510384i	$0.0162531\pi$
$828$	1.24582	−	1.56221i	0.0432952	−	0.0542904i
$829$	4.06549	+	54.2502i	0.141200	+	1.88419i	0.397516	+	0.917595i	$0.369872\pi$
$829$	4.06549	+	54.2502i	0.141200	+	1.88419i	−0.256315	+	0.966593i	$0.582509\pi$
$830$	−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	−0.319406	−	0.947618i	$-0.603483\pi$
$839$	6.43974	−	3.10121i	0.222324	−	0.107066i	0.541731	+	0.840552i	$0.317769\pi$
$840$	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	−0.768372	−	0.640003i	$-0.778933\pi$
$853$	4.96717	−	8.60340i	0.170073	−	0.294575i	0.938445	+	0.345428i	$0.112266\pi$
$854$	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	−0.0826619	−	0.996578i	$-0.526342\pi$
$857$	−30.4616	−	20.7684i	−1.04055	−	0.709435i	−0.957888	+	0.287143i	$0.907295\pi$
$858$	−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	0.355497	−	0.934678i	$-0.384312\pi$
$863$	−11.3011	−	7.70494i	−0.384693	−	0.262279i	−0.740189	+	0.672398i	$0.765264\pi$
$864$	−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	0.317056	−	0.948407i	$-0.397306\pi$
$877$	−17.9168	−	16.6243i	−0.605006	−	0.561363i	−0.922061	+	0.387044i	$0.873496\pi$
$878$	−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	−0.643642	−	0.765326i	$-0.722578\pi$
$881$	−13.2555	+	6.38353i	−0.446591	+	0.215067i	0.197052	+	0.980393i	$0.436863\pi$
$882$	5.04630	−	2.43017i	0.169918	−	0.0818281i
$883$	−46.9633	−	7.07858i	−1.58044	−	0.238213i	−0.700625	−	0.713529i	$-0.747095\pi$
$883$	−46.9633	−	7.07858i	−1.58044	−	0.238213i	−0.879815	+	0.475316i	$0.842334\pi$
$884$	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	−0.970466	−	0.241239i	$-0.922446\pi$
$887$	0.255041	−	1.11741i	0.00856342	−	0.0375188i	0.979029	+	0.203720i	$0.0653033\pi$
$888$	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	0.909142	−	0.416485i	$-0.136738\pi$
$907$	9.05891	+	11.3595i	0.300796	+	0.377186i	−0.608346	+	0.793672i	$0.708167\pi$
$908$	−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	0.998786	−	0.0492675i	$-0.0156887\pi$
$911$	2.34021	+	10.2531i	0.0775345	+	0.339701i	−0.921251	+	0.388968i	$0.872832\pi$
$912$	−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	−0.433681	−	0.901066i	$-0.642786\pi$
$919$	10.5499	−	46.2223i	0.348010	−	1.52473i	0.781692	−	0.623665i	$-0.214357\pi$
$920$	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	0.951060	−	0.309006i	$-0.0999962\pi$
$929$	21.7621	+	20.1923i	0.713992	+	0.662487i	−0.237069	+	0.971493i	$0.576187\pi$
$930$	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	−0.996041	−	0.0888972i	$-0.971666\pi$
$937$	−9.98993	−	25.4539i	−0.326357	−	0.831543i	0.669684	−	0.742646i	$-0.266430\pi$
$938$	−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	−0.383273	−	0.923635i	$-0.625203\pi$
$941$	15.6182	−	14.4915i	0.509138	−	0.472411i	0.892410	+	0.451224i	$0.149013\pi$
$942$	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	−0.870686	−	0.491839i	$-0.836325\pi$
$953$	−0.290115	+	0.502493i	−0.00939774	+	0.0162774i	0.861288	+	0.508117i	$0.169658\pi$
$954$	−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	−0.811311	−	0.584615i	$-0.801246\pi$
$967$	−26.7457	+	12.8801i	−0.860084	+	0.414195i	−0.0487735	+	0.998810i	$0.515531\pi$
$968$	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	−0.918739	−	0.394864i	$-0.870792\pi$
$971$	1.51410	−	20.2043i	0.0485899	−	0.648387i	0.967329	−	0.253523i	$-0.0815894\pi$
$972$	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	−0.978508	−	0.206210i	$-0.933887\pi$
$977$	−1.30226	−	17.3775i	−0.0416631	−	0.555956i	0.936845	−	0.349746i	$-0.113732\pi$
$978$	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	−0.889938	−	0.456082i	$-0.849252\pi$
$983$	−26.3347	−	45.6131i	−0.839947	−	1.45483i	0.0499902	−	0.998750i	$-0.484081\pi$
$984$	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	−0.609309	−	0.792933i	$-0.708553\pi$
$991$	−50.6562	−	24.3947i	−1.60915	−	0.774924i	−0.999838	+	0.0180085i	$0.994267\pi$
$992$	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	0.999307	−	0.0372136i	$-0.0118482\pi$
$997$	2.61495	+	11.4568i	0.0828161	+	0.362841i	−0.916491	+	0.400055i	$0.868991\pi$
$998$	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.111.6	yes	96
43.17	even	21		9245.2.a.bb.1.18		48
43.26	odd	42		9245.2.a.ba.1.31		48
43.31	even	21	inner	215.2.q.b.31.6	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.q.b.31.6	✓	96	43.31	even	21	inner
215.2.q.b.111.6	yes	96	1.1	even	1	trivial
9245.2.a.ba.1.31		48	43.26	odd	42
9245.2.a.bb.1.18		48	43.17	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

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Representations

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Database

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