LMFDB - Embedded newform 847.2.u.a.221.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(23,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("847.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.u (of order $33$, degree $20$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$1720$
Relative dimension:	$86$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			221.20
Character	$\chi$	$=$	847.221
Dual form			847.2.u.a.23.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02678 + 1.44191i) q^{2} +(0.607575 - 1.05235i) q^{3} +(-0.370686 - 1.07103i) q^{4} +(2.00114 + 1.90808i) q^{5} +(0.893547 + 1.95660i) q^{6} +(0.986575 - 2.45493i) q^{7} +(-1.47193 - 0.432196i) q^{8} +(0.761704 + 1.31931i) q^{9} +O(q^{10})$	\(q+(-1.02678 + 1.44191i) q^{2} +(0.607575 - 1.05235i) q^{3} +(-0.370686 - 1.07103i) q^{4} +(2.00114 + 1.90808i) q^{5} +(0.893547 + 1.95660i) q^{6} +(0.986575 - 2.45493i) q^{7} +(-1.47193 - 0.432196i) q^{8} +(0.761704 + 1.31931i) q^{9} +(-4.80599 + 0.926279i) q^{10} +(-1.30719 - 3.04816i) q^{11} +(-1.35231 - 0.260637i) q^{12} +(-2.60065 + 3.00130i) q^{13} +(2.52678 + 3.94321i) q^{14} +(3.22381 - 0.946597i) q^{15} +(3.91629 - 3.07980i) q^{16} +(0.275441 + 5.78221i) q^{17} +(-2.68442 - 0.256331i) q^{18} +(-0.334006 + 7.01166i) q^{19} +(1.30181 - 2.85057i) q^{20} +(-1.98403 - 2.52978i) q^{21} +(5.73734 + 1.24493i) q^{22} +(-1.65865 + 1.30437i) q^{23} +(-1.34913 + 1.28639i) q^{24} +(0.125870 + 2.64233i) q^{25} +(-1.65732 - 6.83155i) q^{26} +5.49662 q^{27} +(-2.99500 - 0.146640i) q^{28} +(4.52146 + 2.90577i) q^{29} +(-1.94523 + 5.62038i) q^{30} +(4.49884 - 0.867080i) q^{31} +(0.273645 + 5.74452i) q^{32} +(-4.00195 - 0.476360i) q^{33} +(-8.62022 - 5.53988i) q^{34} +(6.65847 - 3.03018i) q^{35} +(1.13066 - 1.30485i) q^{36} +(2.61397 - 7.55257i) q^{37} +(-9.76720 - 7.68101i) q^{38} +(1.57834 + 4.56031i) q^{39} +(-2.12086 - 3.67344i) q^{40} +(2.14293 + 4.69236i) q^{41} +(5.68485 - 0.263266i) q^{42} +(7.86525 + 2.30945i) q^{43} +(-2.78010 + 2.52994i) q^{44} +(-0.993076 + 4.09352i) q^{45} +(-0.177725 - 3.73091i) q^{46} +(-0.682923 + 0.0652112i) q^{47} +(-0.861594 - 5.99252i) q^{48} +(-5.05334 - 4.84394i) q^{49} +(-3.93923 - 2.53159i) q^{50} +(6.25227 + 3.22327i) q^{51} +(4.17850 + 1.67282i) q^{52} +(-1.32071 - 1.03862i) q^{53} +(-5.64380 + 7.92561i) q^{54} +(3.20026 - 8.59401i) q^{55} +(-2.51318 + 3.18708i) q^{56} +(7.17580 + 4.61160i) q^{57} +(-8.83237 + 3.53595i) q^{58} +(4.36073 + 6.12379i) q^{59} +(-2.20885 - 3.10190i) q^{60} +(-7.69186 + 0.734483i) q^{61} +(-3.36905 + 7.37720i) q^{62} +(3.99029 - 0.568331i) q^{63} +(-0.181414 - 0.116588i) q^{64} +(-10.9310 + 1.04378i) q^{65} +(4.79597 - 5.28131i) q^{66} +(-7.19463 - 0.687004i) q^{67} +(6.09080 - 2.43839i) q^{68} +(0.364907 + 2.53798i) q^{69} +(-2.46752 + 12.7122i) q^{70} +(8.56067 + 5.50161i) q^{71} +(-0.550971 - 2.27113i) q^{72} +(2.62154 + 1.04951i) q^{73} +(8.20613 + 11.5239i) q^{74} +(2.85714 + 1.47296i) q^{75} +(7.63348 - 2.24139i) q^{76} +(-8.77264 + 0.201827i) q^{77} +(-8.19614 - 2.40660i) q^{78} +(-5.52833 - 5.27125i) q^{79} +(13.7135 + 1.30948i) q^{80} +(1.05450 - 1.82645i) q^{81} +(-8.96624 - 1.72810i) q^{82} +(-1.43289 + 9.96596i) q^{83} +(-1.97401 + 3.06270i) q^{84} +(-10.4817 + 12.0966i) q^{85} +(-11.4059 + 8.96967i) q^{86} +(5.80502 - 2.99269i) q^{87} +(0.606686 + 5.05162i) q^{88} +(12.3077 + 6.34505i) q^{89} +(-4.88279 - 5.63504i) q^{90} +(4.80226 + 9.34541i) q^{91} +(2.01185 + 1.29294i) q^{92} +(1.82091 - 5.26118i) q^{93} +(0.607180 - 1.05167i) q^{94} +(-14.0472 + 13.3940i) q^{95} +(6.21152 + 3.20226i) q^{96} +(-8.90359 - 2.61433i) q^{97} +(12.1731 - 2.31280i) q^{98} +(3.02577 - 4.04638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9}+O(q^{10}) $ 1720 * q - 11 * q^2 - 20 * q^3 + 73 * q^4 - 7 * q^5 + 8 * q^6 - 24 * q^7 - 32 * q^8 - 844 * q^9	\( 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9} - 39 q^{10} - 22 q^{11} + 49 q^{12} - 28 q^{13} - 8 q^{14} - 26 q^{15} + 61 q^{16} - 17 q^{17} - 2 q^{18} - 13 q^{19} - 76 q^{20} + 13 q^{21} - 132 q^{22} + 23 q^{23} - 36 q^{24} + 75 q^{25} + 7 q^{26} + 28 q^{27} - 38 q^{28} - 20 q^{29} + 51 q^{30} - 5 q^{31} - 23 q^{32} + 59 q^{33} + 4 q^{34} - 16 q^{35} - 18 q^{36} - 52 q^{37} - 13 q^{38} - 46 q^{39} + 110 q^{40} - 52 q^{41} + 33 q^{42} - 48 q^{43} - 4 q^{44} + 60 q^{45} - 45 q^{46} - 19 q^{47} - 2 q^{48} - 92 q^{49} - 68 q^{50} + 127 q^{51} - 75 q^{52} - 97 q^{53} - 213 q^{54} - 60 q^{55} - 18 q^{56} - 18 q^{57} + 54 q^{58} - 7 q^{59} - 20 q^{60} - 23 q^{61} - 64 q^{62} + 125 q^{63} - 412 q^{64} + 19 q^{65} - 46 q^{66} + 7 q^{67} - 27 q^{68} - 6 q^{69} - 40 q^{70} - 24 q^{71} - 11 q^{72} - 25 q^{73} + 29 q^{74} + 81 q^{75} + 184 q^{76} - 284 q^{77} + 2 q^{78} - 55 q^{79} + 7 q^{80} - 772 q^{81} + 27 q^{82} + 8 q^{83} - q^{84} - 232 q^{85} - 37 q^{86} - 38 q^{87} + 23 q^{88} - 126 q^{89} + 448 q^{90} + 17 q^{91} + 416 q^{92} + 2 q^{93} + 144 q^{94} + 69 q^{95} - 47 q^{96} - 62 q^{97} + 96 q^{98} + 330 q^{99}+O(q^{100}) \) 1720 * q - 11 * q^2 - 20 * q^3 + 73 * q^4 - 7 * q^5 + 8 * q^6 - 24 * q^7 - 32 * q^8 - 844 * q^9 - 39 * q^10 - 22 * q^11 + 49 * q^12 - 28 * q^13 - 8 * q^14 - 26 * q^15 + 61 * q^16 - 17 * q^17 - 2 * q^18 - 13 * q^19 - 76 * q^20 + 13 * q^21 - 132 * q^22 + 23 * q^23 - 36 * q^24 + 75 * q^25 + 7 * q^26 + 28 * q^27 - 38 * q^28 - 20 * q^29 + 51 * q^30 - 5 * q^31 - 23 * q^32 + 59 * q^33 + 4 * q^34 - 16 * q^35 - 18 * q^36 - 52 * q^37 - 13 * q^38 - 46 * q^39 + 110 * q^40 - 52 * q^41 + 33 * q^42 - 48 * q^43 - 4 * q^44 + 60 * q^45 - 45 * q^46 - 19 * q^47 - 2 * q^48 - 92 * q^49 - 68 * q^50 + 127 * q^51 - 75 * q^52 - 97 * q^53 - 213 * q^54 - 60 * q^55 - 18 * q^56 - 18 * q^57 + 54 * q^58 - 7 * q^59 - 20 * q^60 - 23 * q^61 - 64 * q^62 + 125 * q^63 - 412 * q^64 + 19 * q^65 - 46 * q^66 + 7 * q^67 - 27 * q^68 - 6 * q^69 - 40 * q^70 - 24 * q^71 - 11 * q^72 - 25 * q^73 + 29 * q^74 + 81 * q^75 + 184 * q^76 - 284 * q^77 + 2 * q^78 - 55 * q^79 + 7 * q^80 - 772 * q^81 + 27 * q^82 + 8 * q^83 - q^84 - 232 * q^85 - 37 * q^86 - 38 * q^87 + 23 * q^88 - 126 * q^89 + 448 * q^90 + 17 * q^91 + 416 * q^92 + 2 * q^93 + 144 * q^94 + 69 * q^95 - 47 * q^96 - 62 * q^97 + 96 * q^98 + 330 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−1.02678	+	1.44191i	−0.726040	+	1.01958i	0.272313	+	0.962209i	$0.412212\pi$
$2$	−1.02678	+	1.44191i	−0.726040	+	1.01958i	−0.998353	+	0.0573721i	$0.981728\pi$
$3$	0.607575	−	1.05235i	0.350784	−	0.607575i	−0.635603	−	0.772016i	$-0.719249\pi$
$3$	0.607575	−	1.05235i	0.350784	−	0.607575i	0.986387	+	0.164441i	$0.0525819\pi$
$4$	−0.370686	−	1.07103i	−0.185343	−	0.535513i
$5$	2.00114	+	1.90808i	0.894936	+	0.853320i	0.989843	−	0.142166i	$-0.0454068\pi$
$5$	2.00114	+	1.90808i	0.894936	+	0.853320i	−0.0949067	+	0.995486i	$0.530255\pi$
$6$	0.893547	+	1.95660i	0.364789	+	0.798777i
$7$	0.986575	−	2.45493i	0.372890	−	0.927875i
$7$	0.986575	−	2.45493i	0.372890	−	0.927875i
$8$	−1.47193	−	0.432196i	−0.520404	−	0.152805i
$9$	0.761704	+	1.31931i	0.253901	+	0.439770i
$10$	−4.80599	+	0.926279i	−1.51979	+	0.292915i
$11$	−1.30719	−	3.04816i	−0.394133	−	0.919053i
$11$	−1.30719	−	3.04816i	−0.394133	−	0.919053i
$12$	−1.35231	−	0.260637i	−0.390380	−	0.0752395i
$13$	−2.60065	+	3.00130i	−0.721289	+	0.832412i	−0.991461	−	0.130400i	$-0.958374\pi$
$13$	−2.60065	+	3.00130i	−0.721289	+	0.832412i	0.270172	+	0.962812i	$0.412919\pi$
$14$	2.52678	+	3.94321i	0.675311	+	1.05387i
$15$	3.22381	−	0.946597i	0.832385	−	0.244410i
$16$	3.91629	−	3.07980i	0.979071	−	0.769950i
$17$	0.275441	+	5.78221i	0.0668042	+	1.40239i	0.744781	+	0.667309i	$0.232554\pi$
$17$	0.275441	+	5.78221i	0.0668042	+	1.40239i	−0.677977	+	0.735084i	$0.737143\pi$
$18$	−2.68442	−	0.256331i	−0.632724	−	0.0604178i
$19$	−0.334006	+	7.01166i	−0.0766263	+	1.60858i	0.554013	+	0.832508i	$0.313096\pi$
$19$	−0.334006	+	7.01166i	−0.0766263	+	1.60858i	−0.630639	+	0.776076i	$0.717207\pi$
$20$	1.30181	−	2.85057i	0.291094	−	0.637406i
$21$	−1.98403	−	2.52978i	−0.432951	−	0.552043i
$22$	5.73734	+	1.24493i	1.22321	+	0.265419i
$23$	−1.65865	+	1.30437i	−0.345852	+	0.271981i	−0.775941	−	0.630806i	$-0.782725\pi$
$23$	−1.65865	+	1.30437i	−0.345852	+	0.271981i	0.430089	+	0.902786i	$0.358482\pi$
$24$	−1.34913	+	1.28639i	−0.275390	+	0.262584i
$25$	0.125870	+	2.64233i	0.0251739	+	0.528466i
$26$	−1.65732	−	6.83155i	−0.325027	−	1.33978i
$27$	5.49662			1.05783
$28$	−2.99500	−	0.146640i	−0.566002	−	0.0277124i
$29$	4.52146	+	2.90577i	0.839614	+	0.539587i	0.888319	−	0.459226i	$-0.151873\pi$
$29$	4.52146	+	2.90577i	0.839614	+	0.539587i	−0.0487054	+	0.998813i	$0.515510\pi$
$30$	−1.94523	+	5.62038i	−0.355149	+	1.02614i
$31$	4.49884	−	0.867080i	0.808016	−	0.155732i	0.231518	−	0.972831i	$-0.425631\pi$
$31$	4.49884	−	0.867080i	0.808016	−	0.155732i	0.576498	+	0.817098i	$0.304419\pi$
$32$	0.273645	+	5.74452i	0.0483741	+	1.01550i
$33$	−4.00195	−	0.476360i	−0.696650	−	0.0829236i
$34$	−8.62022	−	5.53988i	−1.47836	−	0.950081i
$35$	6.65847	−	3.03018i	1.12549	−	0.512195i
$36$	1.13066	−	1.30485i	0.188444	−	0.217476i
$37$	2.61397	−	7.55257i	0.429734	−	1.24163i	−0.497602	−	0.867405i	$-0.665786\pi$
$37$	2.61397	−	7.55257i	0.429734	−	1.24163i	0.927336	−	0.374229i	$-0.122093\pi$
$38$	−9.76720	−	7.68101i	−1.58445	−	1.24602i
$39$	1.57834	+	4.56031i	0.252737	+	0.730234i
$40$	−2.12086	−	3.67344i	−0.335338	−	0.580822i
$41$	2.14293	+	4.69236i	0.334669	+	0.732823i	0.999905	−	0.0138103i	$-0.00439609\pi$
$41$	2.14293	+	4.69236i	0.334669	+	0.732823i	−0.665235	+	0.746634i	$0.731669\pi$
$42$	5.68485	−	0.263266i	0.877192	−	0.0406229i
$43$	7.86525	+	2.30945i	1.19944	+	0.352187i	0.819639	−	0.572881i	$-0.194174\pi$
$43$	7.86525	+	2.30945i	1.19944	+	0.352187i	0.379801	+	0.925068i	$0.375992\pi$
$44$	−2.78010	+	2.52994i	−0.419115	+	0.381403i
$45$	−0.993076	+	4.09352i	−0.148039	+	0.610225i
$46$	−0.177725	−	3.73091i	−0.0262041	−	0.550093i
$47$	−0.682923	+	0.0652112i	−0.0996145	+	0.00951203i	−0.144744	−	0.989469i	$-0.546236\pi$
$47$	−0.682923	+	0.0652112i	−0.0996145	+	0.00951203i	0.0451297	+	0.998981i	$0.485630\pi$
$48$	−0.861594	−	5.99252i	−0.124360	−	0.864946i
$49$	−5.05334	−	4.84394i	−0.721906	−	0.691991i
$50$	−3.93923	−	2.53159i	−0.557091	−	0.358021i
$51$	6.25227	+	3.22327i	0.875493	+	0.451348i
$52$	4.17850	+	1.67282i	0.579453	+	0.231978i
$53$	−1.32071	−	1.03862i	−0.181413	−	0.142665i	0.523323	−	0.852135i	$-0.324692\pi$
$53$	−1.32071	−	1.03862i	−0.181413	−	0.142665i	−0.704736	+	0.709469i	$0.748935\pi$
$54$	−5.64380	+	7.92561i	−0.768024	+	1.07854i
$55$	3.20026	−	8.59401i	0.431523	−	1.15882i
$56$	−2.51318	+	3.18708i	−0.335837	+	0.425891i
$57$	7.17580	+	4.61160i	0.950457	+	0.610822i
$58$	−8.83237	+	3.53595i	−1.15975	+	0.464292i
$59$	4.36073	+	6.12379i	0.567719	+	0.797249i	0.994234	−	0.107231i	$-0.0341985\pi$
$59$	4.36073	+	6.12379i	0.567719	+	0.797249i	−0.426516	+	0.904480i	$0.640259\pi$
$60$	−2.20885	−	3.10190i	−0.285161	−	0.400453i
$61$	−7.69186	+	0.734483i	−0.984841	+	0.0940409i	−0.575033	−	0.818131i	$-0.695011\pi$
$61$	−7.69186	+	0.734483i	−0.984841	+	0.0940409i	−0.409809	+	0.912171i	$0.634405\pi$
$62$	−3.36905	+	7.37720i	−0.427870	+	0.936905i
$63$	3.99029	−	0.568331i	0.502729	−	0.0716029i
$64$	−0.181414	−	0.116588i	−0.0226768	−	0.0145735i
$65$	−10.9310	+	1.04378i	−1.35582	+	0.129465i
$66$	4.79597	−	5.28131i	0.590343	−	0.650085i
$67$	−7.19463	−	0.687004i	−0.878964	−	0.0839309i	−0.354191	−	0.935173i	$-0.615244\pi$
$67$	−7.19463	−	0.687004i	−0.878964	−	0.0839309i	−0.524773	+	0.851242i	$0.675850\pi$
$68$	6.09080	−	2.43839i	0.738618	−	0.295698i
$69$	0.364907	+	2.53798i	0.0439296	+	0.305537i
$70$	−2.46752	+	12.7122i	−0.294925	+	1.51940i
$71$	8.56067	+	5.50161i	1.01596	+	0.652921i	0.938930	−	0.344108i	$-0.111819\pi$
$71$	8.56067	+	5.50161i	1.01596	+	0.652921i	0.0770344	+	0.997028i	$0.475455\pi$
$72$	−0.550971	−	2.27113i	−0.0649325	−	0.267656i
$73$	2.62154	+	1.04951i	0.306829	+	0.122836i	0.519967	−	0.854186i	$-0.325944\pi$
$73$	2.62154	+	1.04951i	0.306829	+	0.122836i	−0.213138	+	0.977022i	$0.568369\pi$
$74$	8.20613	+	11.5239i	0.953943	+	1.33963i
$75$	2.85714	+	1.47296i	0.329914	+	0.170082i
$76$	7.63348	−	2.24139i	0.875620	−	0.257105i
$77$	−8.77264	+	0.201827i	−0.999735	+	0.0230003i
$78$	−8.19614	−	2.40660i	−0.928030	−	0.272494i
$79$	−5.52833	−	5.27125i	−0.621985	−	0.593062i	0.312127	−	0.950040i	$-0.398958\pi$
$79$	−5.52833	−	5.27125i	−0.621985	−	0.593062i	−0.934113	+	0.356978i	$0.883807\pi$
$80$	13.7135	+	1.30948i	1.53322	+	0.146405i
$81$	1.05450	−	1.82645i	0.117167	−	0.202939i
$82$	−8.96624	−	1.72810i	−0.990156	−	0.190837i
$83$	−1.43289	+	9.96596i	−0.157280	+	1.09391i	0.746338	+	0.665567i	$0.231810\pi$
$83$	−1.43289	+	9.96596i	−0.157280	+	1.09391i	−0.903618	+	0.428339i	$0.859099\pi$
$84$	−1.97401	+	3.06270i	−0.215382	+	0.334168i
$85$	−10.4817	+	12.0966i	−1.13690	+	1.31206i
$86$	−11.4059	+	8.96967i	−1.22993	+	0.967224i
$87$	5.80502	−	2.99269i	0.622363	−	0.320850i
$88$	0.606686	+	5.05162i	0.0646730	+	0.538505i
$89$	12.3077	+	6.34505i	1.30461	+	0.672574i	0.963565	−	0.267473i	$-0.0861885\pi$
$89$	12.3077	+	6.34505i	1.30461	+	0.672574i	0.341046	+	0.940047i	$0.389219\pi$
$90$	−4.88279	−	5.63504i	−0.514692	−	0.593986i
$91$	4.80226	+	9.34541i	0.503413	+	0.979665i
$92$	2.01185	+	1.29294i	0.209750	+	0.134798i
$93$	1.82091	−	5.26118i	0.188820	−	0.545559i
$94$	0.607180	−	1.05167i	0.0626259	−	0.108471i
$95$	−14.0472	+	13.3940i	−1.44121	+	1.37419i
$96$	6.21152	+	3.20226i	0.633960	+	0.326829i
$97$	−8.90359	−	2.61433i	−0.904023	−	0.265445i	−0.203500	−	0.979075i	$-0.565232\pi$
$97$	−8.90359	−	2.61433i	−0.904023	−	0.265445i	−0.700523	+	0.713630i	$0.747050\pi$
$98$	12.1731	−	2.31280i	1.22967	−	0.233628i
$99$	3.02577	−	4.04638i	0.304101	−	0.406677i
$100$	2.78335	−	1.11428i	0.278335	−	0.111428i
$101$	−5.87684	−	8.25287i	−0.584768	−	0.821191i	0.411140	−	0.911572i	$-0.365131\pi$
$101$	−5.87684	−	8.25287i	−0.584768	−	0.821191i	−0.995907	+	0.0903812i	$0.971191\pi$
$102$	−11.0673	+	5.70561i	−1.09583	+	0.564939i
$103$	7.52512	−	10.5676i	0.741472	−	1.04125i	−0.255748	−	0.966743i	$-0.582322\pi$
$103$	7.52512	−	10.5676i	0.741472	−	1.04125i	0.997220	−	0.0745083i	$-0.0237387\pi$
$104$	5.12511	−	3.29371i	0.502558	−	0.322975i
$105$	0.856705	−	8.84812i	0.0836059	−	0.863488i
$106$	2.85366	−	0.837910i	0.277172	−	0.0813850i
$107$	−1.40978	−	1.34422i	−0.136289	−	0.129951i	0.618869	−	0.785494i	$-0.287591\pi$
$107$	−1.40978	−	1.34422i	−0.136289	−	0.129951i	−0.755158	+	0.655543i	$0.772440\pi$
$108$	−2.03752	−	5.88702i	−0.196060	−	0.566479i
$109$	−4.72735	−	13.6588i	−0.452798	−	1.30828i	−0.908404	−	0.418093i	$-0.862698\pi$
$109$	−4.72735	−	13.6588i	−0.452798	−	1.30828i	0.455606	−	0.890182i	$-0.349423\pi$
$110$	9.10579	+	13.4386i	0.868203	+	1.28132i
$111$	−6.35977	−	7.33957i	−0.603643	−	0.696641i
$112$	−3.69698	−	12.6527i	−0.349332	−	1.19556i
$113$	−12.3477	−	3.62561i	−1.16157	−	0.341068i	−0.356529	−	0.934284i	$-0.616040\pi$
$113$	−12.3477	−	3.62561i	−1.16157	−	0.341068i	−0.805043	+	0.593216i	$0.797858\pi$
$114$	−14.0174	+	5.61173i	−1.31285	+	0.525587i
$115$	−5.80803	−	0.554600i	−0.541602	−	0.0517167i
$116$	1.43611	−	5.91973i	0.133339	−	0.549633i
$117$	−5.94057	−	1.14495i	−0.549206	−	0.105851i
$118$	−13.3074			−1.22505
$119$	14.4667	+	5.02840i	1.32616	+	0.460952i
$120$	−5.15433			−0.470524
$121$	−7.58250	+	7.96904i	−0.689319	+	0.724458i
$122$	6.83876	−	11.8451i	0.619152	−	1.07240i
$123$	6.24000	+	0.595848i	0.562642	+	0.0537258i
$124$	−2.59632	−	4.49696i	−0.233156	−	0.403839i
$125$	4.26361	−	4.92047i	0.381349	−	0.440100i
$126$	−3.27765	+	6.33717i	−0.291997	+	0.564560i
$127$	−3.01593	−	6.60396i	−0.267620	−	0.586007i	0.727340	−	0.686277i	$-0.240756\pi$
$127$	−3.01593	−	6.60396i	−0.267620	−	0.586007i	−0.994960	+	0.100271i	$0.968029\pi$
$128$	−10.3238	+	4.13301i	−0.912501	+	0.365310i
$129$	7.20908	−	6.87385i	0.634725	−	0.605209i
$130$	9.71864	−	16.8332i	0.852381	−	1.47637i
$131$	6.26060	−	18.0888i	0.546992	−	1.58043i	−0.244759	−	0.969584i	$-0.578709\pi$
$131$	6.26060	−	18.0888i	0.546992	−	1.58043i	0.791751	−	0.610844i	$-0.209170\pi$
$132$	0.973271	+	4.46277i	0.0847123	+	0.388434i
$133$	16.8836	+	7.73749i	1.46399	+	0.670925i
$134$	8.37787	−	9.66857i	0.723737	−	0.835237i
$135$	10.9995	+	10.4880i	0.946686	+	0.902664i
$136$	2.09362	−	8.63003i	0.179527	−	0.740019i
$137$	−16.4834	−	6.59895i	−1.40827	−	0.563786i	−0.461918	−	0.886923i	$-0.652838\pi$
$137$	−16.4834	−	6.59895i	−1.40827	−	0.563786i	−0.946352	+	0.323137i	$0.895263\pi$
$138$	−4.03421	−	2.07978i	−0.343415	−	0.177043i
$139$	−8.25445	−	18.0747i	−0.700133	−	1.53308i	−0.839810	−	0.542880i	$-0.817334\pi$
$139$	−8.25445	−	18.0747i	−0.700133	−	1.53308i	0.139677	−	0.990197i	$-0.455394\pi$
$140$	−5.71361	−	6.00815i	−0.482888	−	0.507781i
$141$	−0.346302	+	0.758295i	−0.0291639	+	0.0638600i
$142$	−16.7227	+	6.69475i	−1.40334	+	0.561811i
$143$	12.5480	+	4.00389i	1.04932	+	0.334822i
$144$	7.04626	+	2.82090i	0.587189	+	0.235075i
$145$	3.50363	+	14.4422i	0.290960	+	1.19936i
$146$	−4.20503	+	2.70241i	−0.348011	+	0.223653i
$147$	−8.16781	+	2.37483i	−0.673670	+	0.195873i
$148$	−9.05796			−0.744559
$149$	−3.57214	+	10.3210i	−0.292641	+	0.845532i	0.698839	+	0.715279i	$0.253700\pi$
$149$	−3.57214	+	10.3210i	−0.292641	+	0.845532i	−0.991481	+	0.130253i	$0.958421\pi$
$150$	−5.05750	+	2.60732i	−0.412943	+	0.212887i
$151$	11.2212	−	2.16271i	0.913167	−	0.175998i	0.289036	−	0.957318i	$-0.406665\pi$
$151$	11.2212	−	2.16271i	0.913167	−	0.175998i	0.624131	+	0.781320i	$0.285453\pi$
$152$	3.52205	−	10.1763i	0.285676	−	0.825406i
$153$	−7.41873	+	4.76773i	−0.599769	+	0.385448i
$154$	8.71652	−	12.8565i	0.702398	−	1.03601i
$155$	10.6573	+	6.84901i	0.856012	+	0.550125i
$156$	4.29914	−	3.38088i	0.344207	−	0.270687i
$157$	2.66601	+	7.70292i	0.212770	+	0.614760i	0.999998	−	0.00190258i	$-0.000605609\pi$
$157$	2.66601	+	7.70292i	0.212770	+	0.614760i	−0.787228	+	0.616662i	$0.788484\pi$
$158$	13.2770	−	2.55893i	1.05626	−	0.203578i
$159$	−1.89542	+	0.758812i	−0.150317	+	0.0601777i
$160$	−10.4134	+	12.0177i	−0.823252	+	0.950084i
$161$	1.56577	+	5.35872i	0.123400	+	0.422326i
$162$	1.55083	+	3.39584i	0.121845	+	0.266803i
$163$	2.48503	+	2.36947i	0.194643	+	0.185591i	0.781133	−	0.624365i	$-0.214642\pi$
$163$	2.48503	+	2.36947i	0.194643	+	0.185591i	−0.586490	+	0.809956i	$0.699491\pi$
$164$	4.23128	−	4.03452i	0.330408	−	0.315043i
$165$	−7.09952	−	8.58930i	−0.552697	−	0.668676i
$166$	−12.8987	−	12.2989i	−1.00113	−	0.954580i
$167$	−10.9661	+	7.04747i	−0.848581	+	0.545350i	−0.891132	−	0.453745i	$-0.850088\pi$
$167$	−10.9661	+	7.04747i	−0.848581	+	0.545350i	0.0425512	+	0.999094i	$0.486451\pi$
$168$	1.82698	+	4.58113i	0.140955	+	0.353442i
$169$	−0.394381	−	2.74298i	−0.0303370	−	0.210999i
$170$	−6.67971	−	27.5341i	−0.512310	−	2.11177i
$171$	−9.50497	+	4.90015i	−0.726863	+	0.374724i
$172$	−0.442059	−	9.27997i	−0.0337067	−	0.707591i
$173$	4.96560	−	3.90499i	0.377528	−	0.296891i	−0.411307	−	0.911497i	$-0.634927\pi$
$173$	4.96560	−	3.90499i	0.377528	−	0.296891i	0.788834	+	0.614606i	$0.210685\pi$
$174$	−1.64527	+	11.4431i	−0.124728	+	0.867500i
$175$	6.61091	+	2.29785i	0.499738	+	0.173702i
$176$	−14.5070	−	7.91156i	−1.09351	−	0.596356i
$177$	9.09385	−	0.868357i	0.683535	−	0.0652697i
$178$	−21.7862	+	11.2316i	−1.63294	+	0.841841i
$179$	3.82695	+	3.00955i	0.286040	+	0.224944i	0.750861	−	0.660460i	$-0.229639\pi$
$179$	3.82695	+	3.00955i	0.286040	+	0.224944i	−0.464821	+	0.885405i	$0.653881\pi$
$180$	4.75238	−	0.453797i	0.354221	−	0.0338240i
$181$	−2.67504	+	5.85752i	−0.198834	+	0.435386i	−0.982616	−	0.185651i	$-0.940561\pi$
$181$	−2.67504	+	5.85752i	−0.198834	+	0.435386i	0.783782	+	0.621036i	$0.213288\pi$
$182$	−18.4060	−	2.67124i	−1.36435	−	0.198006i
$183$	−3.90045	+	8.54079i	−0.288329	+	0.631353i
$184$	3.00515	−	1.20308i	0.221543	−	0.0886923i
$185$	19.6418	−	10.1261i	1.44410	−	0.744483i
$186$	5.71645	+	8.02763i	0.419151	+	0.588615i
$187$	17.2650	−	8.39804i	1.26254	−	0.614126i
$188$	0.322992	+	0.707255i	0.0235566	+	0.0515819i
$189$	5.42283	−	13.4938i	0.394453	−	0.981531i
$190$	−4.88952	−	34.0074i	−0.354723	−	2.46715i
$191$	−1.05908	−	0.545995i	−0.0766325	−	0.0395068i	0.419484	−	0.907763i	$-0.362211\pi$
$191$	−1.05908	−	0.545995i	−0.0766325	−	0.0395068i	−0.496117	+	0.868256i	$0.665241\pi$
$192$	−0.232914	+	0.120076i	−0.0168091	+	0.00866571i
$193$	8.67210	−	8.26883i	0.624231	−	0.595203i	−0.310494	−	0.950575i	$-0.600494\pi$
$193$	8.67210	−	8.26883i	0.624231	−	0.595203i	0.934725	+	0.355372i	$0.115646\pi$
$194$	12.9116	−	10.1538i	0.927000	−	0.729001i
$195$	−5.54297	+	12.1374i	−0.396940	+	0.869178i
$196$	−3.31478	+	7.20784i	−0.236770	+	0.514845i
$197$	18.6972	−	5.49001i	1.33212	−	0.391147i	0.463271	−	0.886217i	$-0.346676\pi$
$197$	18.6972	−	5.49001i	1.33212	−	0.391147i	0.868853	+	0.495070i	$0.164858\pi$
$198$	2.72771	+	8.51760i	0.193850	+	0.605320i
$199$	−5.28287	+	5.03721i	−0.374493	+	0.357078i	−0.853829	−	0.520553i	$-0.825726\pi$
$199$	−5.28287	+	5.03721i	−0.374493	+	0.357078i	0.479337	+	0.877631i	$0.340877\pi$
$200$	0.956735	−	3.94371i	0.0676514	−	0.278863i
$201$	−5.09425	+	7.15387i	−0.359321	+	0.504595i
$202$	17.9341			1.26184
$203$	11.5942	−	8.23310i	0.813754	−	0.577851i
$204$	1.13458	−	7.89116i	0.0794363	−	0.552492i
$205$	−4.66511	+	13.4789i	−0.325825	+	0.941410i
$206$	7.51079	+	21.7010i	0.523302	+	1.51198i
$207$	−2.98427	−	1.19472i	−0.207421	−	0.0830389i
$208$	−0.941449	+	19.7634i	−0.0652777	+	1.37035i
$209$	21.8092	−	8.14747i	1.50858	−	0.563572i
$210$	11.8785	+	10.3203i	0.819695	+	0.712170i
$211$	2.25610	+	2.60368i	0.155316	+	0.179244i	0.828075	−	0.560618i	$-0.189436\pi$
$211$	2.25610	+	2.60368i	0.155316	+	0.179244i	−0.672759	+	0.739862i	$0.734891\pi$
$212$	−0.622818	+	1.79951i	−0.0427753	+	0.123591i
$213$	10.9909	−	5.66619i	0.753083	−	0.388241i
$214$	3.38577	−	0.652554i	0.231447	−	0.0446077i
$215$	11.3328	+	19.6291i	0.772894	+	1.33869i
$216$	−8.09062	−	2.37562i	−0.550497	−	0.161641i
$217$	2.30982	−	11.8998i	0.156801	−	0.807809i
$218$	24.5486	+	7.20813i	1.66264	+	0.488196i
$219$	2.69724	−	2.12113i	0.182262	−	0.143333i
$220$	−10.3907	−	0.241885i	−0.700540	−	0.0163079i
$221$	−18.0705	−	14.2108i	−1.21555	−	0.955922i
$222$	17.1130	−	1.63410i	1.14855	−	0.109673i
$223$	−18.2053	−	11.6998i	−1.21912	−	0.783478i	−0.236955	−	0.971521i	$-0.576149\pi$
$223$	−18.2053	−	11.6998i	−1.21912	−	0.783478i	−0.982161	+	0.188043i	$0.939786\pi$
$224$	14.3724	+	4.99562i	0.960293	+	0.333784i
$225$	−3.39018	+	2.17874i	−0.226012	+	0.145249i
$226$	17.9061	−	14.0815i	1.19109	−	0.936687i
$227$	2.65808	−	10.9568i	0.176423	−	0.727226i	−0.813012	−	0.582247i	$-0.802174\pi$
$227$	2.65808	−	10.9568i	0.176423	−	0.727226i	0.989435	−	0.144978i	$-0.0463113\pi$
$228$	2.27918	−	9.39491i	0.150942	−	0.622193i
$229$	−8.63077	−	1.66344i	−0.570337	−	0.109924i	−0.104074	−	0.994570i	$-0.533188\pi$
$229$	−8.63077	−	1.66344i	−0.570337	−	0.109924i	−0.466263	+	0.884646i	$0.654400\pi$
$230$	6.76323	−	7.80518i	0.445954	−	0.514658i
$231$	−5.11765	+	9.35453i	−0.336717	+	0.615483i
$232$	−5.39939	−	6.23123i	−0.354487	−	0.409100i
$233$	−8.28674	−	14.3531i	−0.542883	−	0.940300i	−0.998737	−	0.0502457i	$-0.984000\pi$
$233$	−8.28674	−	14.3531i	−0.542883	−	0.940300i	0.455854	−	0.890054i	$-0.349334\pi$
$234$	7.75055	−	7.39014i	0.506669	−	0.483108i
$235$	−1.49105	−	1.17258i	−0.0972654	−	0.0764904i
$236$	4.94227	−	6.94045i	0.321715	−	0.451785i
$237$	−8.90608	+	2.61506i	−0.578512	+	0.169867i
$238$	−22.1045	+	15.6965i	−1.43282	+	1.01745i
$239$	3.77691			0.244308			0.122154	−	0.992511i	$-0.461020\pi$
$239$	3.77691			0.244308			0.122154	+	0.992511i	$0.461020\pi$
$240$	9.71005	−	13.6359i	0.626781	−	0.880191i
$241$	7.17648	−	12.4300i	0.462278	−	0.800688i	−0.536796	−	0.843712i	$-0.680366\pi$
$241$	7.17648	−	12.4300i	0.462278	−	0.800688i	0.999074	+	0.0430235i	$0.0136990\pi$
$242$	−3.70507	−	19.1157i	−0.238171	−	1.22880i
$243$	6.96356	+	12.0612i	0.446712	+	0.773729i
$244$	3.63791	+	7.96591i	0.232893	+	0.509965i
$245$	−0.869804	−	19.3356i	−0.0555697	−	1.23530i
$246$	−7.26624	+	8.38569i	−0.463279	+	0.534652i
$247$	−20.1755	−	19.2373i	−1.28374	−	1.22404i
$248$	−6.99671	−	0.668105i	−0.444291	−	0.0424247i
$249$	9.61711	+	7.56298i	0.609459	+	0.479284i
$250$	2.71708	+	11.1999i	0.171843	+	0.708347i
$251$	17.6954			1.11692			0.558461	−	0.829531i	$-0.311392\pi$
$251$	17.6954			1.11692			0.558461	+	0.829531i	$0.311392\pi$
$252$	−2.08784	−	4.06303i	−0.131522	−	0.255947i
$253$	6.14410	+	3.35075i	0.386276	+	0.210660i
$254$	12.6190	+	2.43211i	0.791785	+	0.152604i
$255$	6.36140	+	18.3801i	0.398366	+	1.15100i
$256$	4.74247	−	19.5487i	0.296404	−	1.22179i
$257$	−5.58503	−	5.32532i	−0.348385	−	0.332184i	0.495601	−	0.868551i	$-0.334948\pi$
$257$	−5.58503	−	5.32532i	−0.348385	−	0.332184i	−0.843985	+	0.536367i	$0.819796\pi$
$258$	2.50932	+	17.4527i	0.156224	+	1.08656i
$259$	−15.9621	−	13.8683i	−0.991839	−	0.861733i
$260$	5.16988	+	11.3204i	0.320622	+	0.702064i
$261$	−0.389592	+	8.17854i	−0.0241151	+	0.506239i
$262$	19.6541	+	27.6004i	1.21424	+	1.70516i
$263$	−2.77356	−	2.18115i	−0.171025	−	0.134496i	0.528978	−	0.848636i	$-0.322575\pi$
$263$	−2.77356	−	2.18115i	−0.171025	−	0.134496i	−0.700003	+	0.714140i	$0.746818\pi$
$264$	5.68469	+	2.43079i	0.349868	+	0.149605i
$265$	−0.661155	−	4.59844i	−0.0406145	−	0.282480i
$266$	−28.4924	+	16.3999i	−1.74698	+	1.00554i
$267$	14.1551	−	9.09691i	0.866276	−	0.556722i
$268$	1.93115	+	7.96029i	0.117964	+	0.486252i
$269$	6.61320	−	11.4544i	0.403214	−	0.698387i	−0.590898	−	0.806746i	$-0.701226\pi$
$269$	6.61320	−	11.4544i	0.403214	−	0.698387i	0.994112	+	0.108359i	$0.0345598\pi$
$270$	−26.4167	+	5.09141i	−1.60767	+	0.309853i
$271$	0.301158	−	6.32208i	0.0182940	−	0.384039i	−0.971090	−	0.238714i	$-0.923274\pi$
$271$	0.301158	−	6.32208i	0.0182940	−	0.384039i	0.989384	−	0.145325i	$-0.0464228\pi$
$272$	18.8868	+	21.7965i	1.14518	+	1.32161i
$273$	12.7524	+	0.624379i	0.771810	+	0.0377891i
$274$	26.4398	−	16.9918i	1.59729	−	1.02651i
$275$	7.88970	−	3.83770i	0.475767	−	0.231422i
$276$	2.58298	−	1.33162i	0.155477	−	0.0801540i
$277$	17.3047	+	6.92778i	1.03974	+	0.416250i	0.827794	−	0.561031i	$-0.189595\pi$
$277$	17.3047	+	6.92778i	1.03974	+	0.416250i	0.211947	+	0.977281i	$0.432020\pi$
$278$	34.5375	+	6.65656i	2.07142	+	0.399234i
$279$	4.57073	+	5.27491i	0.273643	+	0.315800i
$280$	−11.1104	+	1.58244i	−0.663974	+	0.0945688i
$281$	−6.22002	+	7.17829i	−0.371055	+	0.428221i	−0.910313	−	0.413920i	$-0.864159\pi$
$281$	−6.22002	+	7.17829i	−0.371055	+	0.428221i	0.539258	+	0.842141i	$0.318705\pi$
$282$	−0.737816	−	1.27793i	−0.0439363	−	0.0760999i
$283$	1.58983	+	0.151811i	0.0945058	+	0.00902421i	0.142202	−	0.989838i	$-0.454582\pi$
$283$	1.58983	+	0.151811i	0.0945058	+	0.00902421i	−0.0476960	+	0.998862i	$0.515188\pi$
$284$	2.71905	−	11.2081i	0.161346	−	0.665076i
$285$	5.56044	+	22.9205i	0.329372	+	1.35769i
$286$	−18.6572	+	13.9819i	−1.10322	+	0.826767i
$287$	13.6336	−	0.631373i	0.804764	−	0.0372687i
$288$	−7.37037	+	4.73665i	−0.434303	+	0.279110i
$289$	−16.4351	+	1.56936i	−0.966771	+	0.0923154i
$290$	−24.4217	−	9.77696i	−1.43409	−	0.574123i
$291$	−8.16080	+	7.78131i	−0.478395	+	0.456148i
$292$	0.152281	−	3.19678i	0.00891159	−	0.187077i
$293$	−5.30497	+	3.40930i	−0.309920	+	0.199173i	−0.686349	−	0.727272i	$-0.740788\pi$
$293$	−5.30497	+	3.40930i	−0.309920	+	0.199173i	0.376430	+	0.926445i	$0.377152\pi$
$294$	4.96223	−	14.2156i	0.289403	−	0.829073i
$295$	−2.95826	+	20.5752i	−0.172237	+	1.19793i
$296$	−7.11176	+	9.98707i	−0.413363	+	0.580487i
$297$	−7.18514	−	16.7546i	−0.416924	−	0.972198i
$298$	−11.2142	−	15.7481i	−0.649618	−	0.912262i
$299$	0.398727	−	8.37032i	0.0230590	−	0.484068i
$300$	0.518474	−	3.60607i	0.0299341	−	0.208196i
$301$	13.4292	−	17.0302i	0.774045	−	0.981604i
$302$	−8.40322	+	18.4005i	−0.483551	+	1.05883i
$303$	−12.2555	+	1.17026i	−0.704063	+	0.0672298i
$304$	20.2864	+	28.4883i	1.16351	+	1.63392i
$305$	−16.7939	−	13.2069i	−0.961617	−	0.756224i
$306$	0.742762	−	15.5925i	0.0424609	−	0.891363i
$307$	6.78131	−	14.8490i	0.387030	−	0.847478i	−0.611392	−	0.791328i	$-0.709390\pi$
$307$	6.78131	−	14.8490i	0.387030	−	0.847478i	0.998422	−	0.0561499i	$-0.0178825\pi$
$308$	3.46805	+	9.32091i	0.197611	+	0.531108i
$309$	−6.54870	−	14.3397i	−0.372543	−	0.815754i
$310$	−20.8182	+	8.33436i	−1.18240	+	0.473360i
$311$	26.1095	+	10.4527i	1.48054	+	0.592717i	0.964555	−	0.263883i	$-0.0850033\pi$
$311$	26.1095	+	10.4527i	1.48054	+	0.592717i	0.515981	+	0.856600i	$0.327428\pi$
$312$	−0.352248	−	7.39459i	−0.0199421	−	0.418636i
$313$	−1.47987	+	31.0662i	−0.0836471	+	1.75597i	0.434496	+	0.900674i	$0.356927\pi$
$313$	−1.47987	+	31.0662i	−0.0836471	+	1.75597i	−0.518143	+	0.855294i	$0.673376\pi$
$314$	−13.8443	−	4.06504i	−0.781277	−	0.229404i
$315$	9.06954	+	6.47649i	0.511011	+	0.364909i
$316$	−3.59637	+	7.87496i	−0.202312	+	0.443001i
$317$	13.8853	+	7.15838i	0.779878	+	0.402055i	0.801715	−	0.597707i	$-0.203921\pi$
$317$	13.8853	+	7.15838i	0.779878	+	0.402055i	−0.0218373	+	0.999762i	$0.506952\pi$
$318$	0.852038	−	3.51215i	0.0477799	−	0.196951i
$319$	2.94681	−	17.5805i	0.164990	−	0.984319i
$320$	−0.140576	−	0.579461i	−0.00785843	−	0.0323929i
$321$	−2.27114	+	0.666868i	−0.126763	+	0.0372209i
$322$	−9.33445	−	3.24452i	−0.520189	−	0.180810i
$323$	−40.6349			−2.26099
$324$	−2.34706	−	0.452359i	−0.130392	−	0.0251311i
$325$	−8.25778	−	6.49399i	−0.458059	−	0.360222i
$326$	−5.96813	+	1.15026i	−0.330544	+	0.0637071i
$327$	−17.2461	−	3.32391i	−0.953710	−	0.183813i
$328$	−1.12621	−	7.83297i	−0.0621846	−	0.432503i
$329$	−0.513665	+	1.74086i	−0.0283193	+	0.0959768i
$330$	19.6746	−	1.41754i	1.08305	−	0.0780329i
$331$	7.93360	+	4.09006i	0.436070	+	0.224810i	0.662261	−	0.749273i	$-0.269597\pi$
$331$	7.93360	+	4.09006i	0.436070	+	0.224810i	−0.226191	+	0.974083i	$0.572627\pi$
$332$	11.2050	−	2.15958i	0.614952	−	0.118522i
$333$	11.9553	−	2.30419i	0.655144	−	0.126269i
$334$	1.09792	−	23.0482i	0.0600756	−	1.26114i
$335$	−13.0866	−	15.1027i	−0.714997	−	0.825150i
$336$	−15.5612	−	3.79692i	−0.848935	−	0.207139i
$337$	−11.1791	−	3.28247i	−0.608963	−	0.178808i	−0.0373109	−	0.999304i	$-0.511879\pi$
$337$	−11.1791	−	3.28247i	−0.608963	−	0.178808i	−0.571652	+	0.820496i	$0.693697\pi$
$338$	4.36006	+	2.24777i	0.237156	+	0.122262i
$339$	−11.3176	+	10.7913i	−0.614685	+	0.586101i
$340$	16.8412	+	6.74218i	0.913340	+	0.365646i
$341$	−8.52384	−	12.5797i	−0.461592	−	0.681230i
$342$	2.69392	−	18.7366i	0.145670	−	1.01316i
$343$	−16.8770	+	7.62668i	−0.911273	+	0.411802i
$344$	−10.5789	−	6.79867i	−0.570378	−	0.366560i
$345$	−4.11245	+	5.77513i	−0.221407	+	0.310922i
$346$	0.532068	+	11.1695i	0.0286041	+	0.600475i
$347$	−20.4439	−	8.18450i	−1.09749	−	0.439367i	−0.248956	−	0.968515i	$-0.580088\pi$
$347$	−20.4439	−	8.18450i	−1.09749	−	0.439367i	−0.848530	+	0.529147i	$0.822512\pi$
$348$	−5.35709	−	5.10797i	−0.287170	−	0.273816i
$349$	13.4782	−	3.95757i	0.721474	−	0.211844i	0.0996742	−	0.995020i	$-0.468220\pi$
$349$	13.4782	−	3.95757i	0.721474	−	0.211844i	0.621800	+	0.783176i	$0.286402\pi$
$350$	−10.1012	+	7.17292i	−0.539933	+	0.383409i
$351$	−14.2948	+	16.4970i	−0.762998	+	0.880547i
$352$	17.1525	−	8.34330i	0.914231	−	0.444699i
$353$	2.41058	−	0.464602i	0.128302	−	0.0247283i	−0.124696	−	0.992195i	$-0.539795\pi$
$353$	2.41058	−	0.464602i	0.128302	−	0.0247283i	0.252998	+	0.967467i	$0.418583\pi$
$354$	−8.08526	+	14.0041i	−0.429727	+	0.744308i
$355$	6.63357	+	27.3439i	0.352073	+	1.45127i
$356$	2.23343	−	15.5339i	0.118372	−	0.823293i
$357$	14.0812	−	12.1689i	0.745258	−	0.644045i
$358$	−8.26891	+	2.42797i	−0.437026	+	0.128322i
$359$	2.17306	+	0.418823i	0.114690	+	0.0221046i	0.246273	−	0.969200i	$-0.420794\pi$
$359$	2.17306	+	0.418823i	0.114690	+	0.0221046i	−0.131583	+	0.991305i	$0.542006\pi$
$360$	3.23094	−	5.59615i	0.170285	−	0.294943i
$361$	−30.1378	−	2.87781i	−1.58620	−	0.151464i
$362$	−5.69932	−	9.87151i	−0.299550	−	0.518835i
$363$	3.77929	+	12.8213i	0.198361	+	0.672941i
$364$	8.22904	−	8.60755i	0.431319	−	0.451158i
$365$	3.24353	+	7.10233i	0.169774	+	0.371753i
$366$	−8.31012	−	14.3936i	−0.434377	−	0.752363i
$367$	−7.42036	−	21.4397i	−0.387340	−	1.11914i	−0.955185	−	0.296010i	$-0.904344\pi$
$367$	−7.42036	−	21.4397i	−0.387340	−	1.11914i	0.567845	−	0.823135i	$-0.307777\pi$
$368$	−2.47852	+	10.2166i	−0.129202	+	0.532577i
$369$	−4.55840	+	6.40138i	−0.237301	+	0.333242i
$370$	−5.56693	+	38.7189i	−0.289411	+	2.01290i
$371$	−3.85271	+	2.21757i	−0.200023	+	0.115131i
$372$	−6.30984			−0.327150
$373$	8.27871	−	23.9197i	0.428655	−	1.23852i	−0.499497	−	0.866316i	$-0.666482\pi$
$373$	8.27871	−	23.9197i	0.428655	−	1.23852i	0.928152	−	0.372202i	$-0.121397\pi$
$374$	−5.61814	+	33.5174i	−0.290507	+	1.73315i
$375$	−2.58760	−	7.47638i	−0.133623	−	0.386078i
$376$	1.03340	+	0.199171i	0.0532933	+	0.0102714i
$377$	−20.4798	+	6.01341i	−1.05476	+	0.309707i
$378$	13.8888	+	21.6743i	0.714361	+	1.11481i
$379$	−3.29447	−	22.9136i	−0.169226	−	1.17699i	−0.880490	−	0.474066i	$-0.842786\pi$
$379$	−3.29447	−	22.9136i	−0.169226	−	1.17699i	0.711264	−	0.702925i	$-0.248123\pi$
$380$	19.5524	+	10.0800i	1.00302	+	0.517091i
$381$	−8.78209	−	0.838588i	−0.449920	−	0.0429622i
$382$	1.87471	−	0.966482i	0.0959186	−	0.0494495i
$383$	−13.4250	+	1.28194i	−0.685988	+	0.0655039i	−0.432229	−	0.901764i	$-0.642273\pi$
$383$	−13.4250	+	1.28194i	−0.685988	+	0.0655039i	−0.253758	+	0.967268i	$0.581667\pi$
$384$	−1.92309	+	13.3754i	−0.0981371	+	0.682558i
$385$	−17.9404	−	16.3350i	−0.914326	−	0.832510i
$386$	3.01856	+	20.9946i	0.153641	+	1.06860i
$387$	2.94412	+	12.1358i	0.149658	+	0.616899i
$388$	0.500418	+	10.5051i	0.0254049	+	0.533314i
$389$	2.20236	−	2.09995i	0.111664	−	0.106472i	−0.632190	−	0.774813i	$-0.717844\pi$
$389$	2.20236	−	2.09995i	0.111664	−	0.106472i	0.743855	+	0.668341i	$0.232995\pi$
$390$	−11.8096	−	20.4548i	−0.598003	−	1.03577i
$391$	−7.99903	−	9.23137i	−0.404528	−	0.466850i
$392$	5.34461	+	9.31395i	0.269944	+	0.470426i
$393$	−15.2320	−	17.5787i	−0.768354	−	0.886727i
$394$	−11.2818	+	32.5967i	−0.568370	+	1.64220i
$395$	−1.00497	−	21.0970i	−0.0505657	−	1.06150i
$396$	−5.45539	−	1.74074i	−0.274144	−	0.0874755i
$397$	−0.805717	+	16.9141i	−0.0404378	+	0.848893i	0.883983	+	0.467519i	$0.154852\pi$
$397$	−0.805717	+	16.9141i	−0.0404378	+	0.848893i	−0.924421	+	0.381374i	$0.875451\pi$
$398$	−1.83885	−	12.7895i	−0.0921732	−	0.641079i
$399$	18.4006	−	13.0664i	0.921183	−	0.654137i
$400$	8.63079	+	9.96047i	0.431540	+	0.498023i
$401$	34.4875	−	13.8067i	1.72222	−	0.689474i	0.722225	−	0.691658i	$-0.243119\pi$
$401$	34.4875	−	13.8067i	1.72222	−	0.689474i	0.999998	+	0.00218386i	$0.000695144\pi$
$402$	−5.08455	−	14.6908i	−0.253594	−	0.732713i
$403$	−9.09752	+	15.7574i	−0.453180	+	0.784930i
$404$	−6.66057	+	9.35347i	−0.331376	+	0.465352i
$405$	5.59522	−	1.64290i	0.278029	−	0.0816365i
$406$	−0.0332961	+	25.1713i	−0.00165246	+	1.24923i
$407$	−26.4384	+	1.90486i	−1.31050	+	0.0944206i
$408$	−7.80980	−	7.44662i	−0.386642	−	0.368663i
$409$	0.902172	+	18.9389i	0.0446095	+	0.936470i	0.904627	+	0.426205i	$0.140150\pi$
$409$	0.902172	+	18.9389i	0.0446095	+	0.936470i	−0.860017	+	0.510265i	$0.829547\pi$
$410$	−14.6453	−	20.5665i	−0.723281	−	1.01571i
$411$	−16.9593	+	13.3369i	−0.836541	+	0.657863i
$412$	−14.1076	−	4.14236i	−0.695030	−	0.204079i
$413$	19.3356	−	4.66370i	0.951445	−	0.229486i
$414$	4.78685	−	3.07632i	0.235261	−	0.151193i
$415$	−21.8833	+	17.2092i	−1.07421	+	0.844766i
$416$	−17.9527	−	14.1182i	−0.880204	−	0.692200i
$417$	−24.0362	−	2.29517i	−1.17706	−	0.112395i
$418$	−10.6453	+	39.8125i	−0.520679	+	1.94729i
$419$	−13.0652	+	28.6088i	−0.638277	+	1.39763i	0.263173	+	0.964749i	$0.415231\pi$
$419$	−13.0652	+	28.6088i	−0.638277	+	1.39763i	−0.901450	+	0.432884i	$0.857496\pi$
$420$	−9.79413	+	2.36232i	−0.477905	+	0.115269i
$421$	−2.78482	+	19.3689i	−0.135724	+	0.943981i	0.802179	+	0.597083i	$0.203674\pi$
$421$	−2.78482	+	19.3689i	−0.135724	+	0.943981i	−0.937903	+	0.346897i	$0.887235\pi$
$422$	−6.07076	+	0.579688i	−0.295520	+	0.0282187i
$423$	−0.606219	−	0.851315i	−0.0294754	−	0.0413924i
$424$	1.49510	+	2.09957i	0.0726085	+	0.101964i
$425$	−15.2438	+	1.45561i	−0.739435	+	0.0706075i
$426$	−3.11506	+	21.6657i	−0.150925	+	1.04971i
$427$	−5.78549	+	19.6076i	−0.279979	+	0.948877i
$428$	−0.917112	+	2.00820i	−0.0443303	+	0.0970698i
$429$	11.8374	−	10.7722i	0.571513	−	0.520088i
$430$	−39.9395	−	3.81376i	−1.92606	−	0.183916i
$431$	−2.07720	−	1.63353i	−0.100055	−	0.0786844i	0.566878	−	0.823802i	$-0.308151\pi$
$431$	−2.07720	−	1.63353i	−0.100055	−	0.0786844i	−0.666933	+	0.745117i	$0.732393\pi$
$432$	21.5263	−	16.9285i	1.03569	−	0.814473i
$433$	−1.67140	+	1.07414i	−0.0803224	+	0.0516201i	−0.580186	−	0.814484i	$-0.697020\pi$
$433$	−1.67140	+	1.07414i	−0.0803224	+	0.0516201i	0.499863	+	0.866104i	$0.333384\pi$
$434$	14.7867	+	15.5489i	0.709783	+	0.746373i
$435$	17.3269	+	5.08765i	0.830763	+	0.243934i
$436$	−12.8766	+	10.1262i	−0.616675	+	0.484959i
$437$	−8.59182	−	12.0655i	−0.411003	−	0.577172i
$438$	0.289011	+	6.06709i	0.0138095	+	0.289897i
$439$	8.78182	+	8.37345i	0.419133	+	0.399643i	0.870082	−	0.492907i	$-0.164066\pi$
$439$	8.78182	+	8.37345i	0.419133	+	0.399643i	−0.450949	+	0.892550i	$0.648914\pi$
$440$	−8.42484	+	11.2666i	−0.401639	+	0.537114i
$441$	2.54151	−	10.3566i	0.121024	−	0.493170i
$442$	39.0450	−	11.4646i	1.85718	−	0.545318i
$443$	20.9976	−	29.4870i	0.997624	−	1.40097i	0.0830519	−	0.996545i	$-0.473533\pi$
$443$	20.9976	−	29.4870i	0.997624	−	1.40097i	0.914572	−	0.404422i	$-0.132527\pi$
$444$	−5.50339	+	9.53215i	−0.261179	+	0.452376i
$445$	12.5225	+	36.1814i	0.593623	+	1.71516i
$446$	35.5628	−	14.2372i	1.68395	−	0.674150i
$447$	8.69100	+	10.0300i	0.411070	+	0.474401i
$448$	−0.465193	+	0.330336i	−0.0219783	+	0.0156069i
$449$	4.92424	+	34.2489i	0.232389	+	1.61630i	0.687717	+	0.725979i	$0.258613\pi$
$449$	4.92424	+	34.2489i	0.232389	+	1.61630i	−0.455327	+	0.890324i	$0.650478\pi$
$450$	0.339424	−	7.12539i	0.0160006	−	0.335894i
$451$	11.5018	−	12.6658i	0.541600	−	0.596409i
$452$	0.693990	+	14.5686i	0.0326425	+	0.685251i
$453$	4.54179	−	13.1226i	0.213392	−	0.616555i
$454$	13.0694	+	15.0828i	0.613375	+	0.707873i
$455$	−8.22182	+	27.8645i	−0.385445	+	1.30631i
$456$	−8.56912	−	9.88929i	−0.401286	−	0.463109i
$457$	−5.72519	−	9.91633i	−0.267813	−	0.463866i	0.700484	−	0.713669i	$-0.252968\pi$
$457$	−5.72519	−	9.91633i	−0.267813	−	0.463866i	−0.968297	+	0.249802i	$0.919634\pi$
$458$	11.2604	−	10.7368i	0.526164	−	0.501696i
$459$	1.51399	+	31.7827i	0.0706672	+	1.48349i
$460$	1.55896	+	6.42613i	0.0726870	+	0.299620i
$461$	3.35651	+	23.3451i	0.156328	+	1.08729i	0.905327	+	0.424716i	$0.139626\pi$
$461$	3.35651	+	23.3451i	0.156328	+	1.08729i	−0.748998	+	0.662572i	$0.769465\pi$
$462$	−8.23366	−	16.9842i	−0.383065	−	0.790175i
$463$	2.42626	−	16.8750i	0.112758	−	0.784248i	−0.852458	−	0.522795i	$-0.824889\pi$
$463$	2.42626	−	16.8750i	0.112758	−	0.784248i	0.965216	−	0.261453i	$-0.0842016\pi$
$464$	26.6565	−	2.54539i	1.23750	−	0.118167i
$465$	13.6827	−	7.05390i	0.634518	−	0.327117i
$466$	29.2044	+	2.78868i	1.35287	+	0.129183i
$467$	−7.76556	−	4.00342i	−0.359347	−	0.185256i	0.269093	−	0.963114i	$-0.413276\pi$
$467$	−7.76556	−	4.00342i	−0.359347	−	0.185256i	−0.628440	+	0.777858i	$0.716306\pi$
$468$	0.975812	+	6.78692i	0.0451069	+	0.313726i
$469$	−8.78458	+	16.9845i	−0.405634	+	0.784272i
$470$	3.22172	−	0.945981i	0.148607	−	0.0436349i
$471$	9.72598	+	1.87453i	0.448149	+	0.0863737i
$472$	−3.77199	−	10.8985i	−0.173620	−	0.501642i
$473$	−3.24184	−	26.9934i	−0.149060	−	1.24116i
$474$	5.37388	−	15.5268i	0.246831	−	0.713170i
$475$	−18.5692			−0.852011
$476$	0.0229610	−	17.3581i	0.00105241	−	0.795608i
$477$	0.364269	−	2.53354i	0.0166787	−	0.116003i
$478$	−3.87804	+	5.44595i	−0.177377	+	0.249092i
$479$	−3.97166	+	16.3714i	−0.181470	+	0.748029i	0.806222	+	0.591614i	$0.201509\pi$
$479$	−3.97166	+	16.3714i	−0.181470	+	0.748029i	−0.987691	+	0.156415i	$0.950006\pi$
$480$	6.31993	+	18.2602i	0.288464	+	0.833462i
$481$	15.8696	+	27.4869i	0.723589	+	1.25329i
$482$	10.5543	+	23.1107i	0.480734	+	1.05266i
$483$	6.59058	+	1.60809i	0.299882	+	0.0731706i
$484$	11.3458	+	5.16705i	0.515717	+	0.234866i
$485$	−12.8290	−	22.2204i	−0.582533	−	1.00898i
$486$	−24.5412	−	2.34340i	−1.11321	−	0.106299i
$487$	6.49729	−	11.2536i	0.294421	−	0.509951i	−0.680429	−	0.732814i	$-0.738207\pi$
$487$	6.49729	−	11.2536i	0.294421	−	0.509951i	0.974850	+	0.222862i	$0.0715400\pi$
$488$	11.6393	+	2.24329i	0.526886	+	0.101549i
$489$	4.00336	−	1.17549i	0.181038	−	0.0531577i
$490$	28.7732	+	18.5991i	1.29984	+	0.840223i
$491$	4.97887	−	34.6288i	0.224693	−	1.56277i	−0.495256	−	0.868747i	$-0.664926\pi$
$491$	4.97887	−	34.6288i	0.224693	−	1.56277i	0.719949	−	0.694027i	$-0.244165\pi$
$492$	−1.67491	−	6.90407i	−0.0755108	−	0.311260i
$493$	−15.5564	+	26.9444i	−0.700623	+	1.21352i
$494$	48.4541	−	9.33875i	2.18005	−	0.420170i
$495$	13.7758	−	2.32396i	0.619177	−	0.104454i
$496$	14.9483	−	17.2513i	0.671199	−	0.774605i
$497$	21.9518	−	15.5881i	0.984672	−	0.699221i
$498$	−20.7797	+	6.10147i	−0.931161	+	0.273414i
$499$	5.76662	+	5.49846i	0.258150	+	0.246145i	0.808090	−	0.589059i	$-0.200501\pi$
$499$	5.76662	+	5.49846i	0.258150	+	0.246145i	−0.549941	+	0.835204i	$0.685350\pi$
$500$	−6.85041	−	2.74249i	−0.306360	−	0.122648i
$501$	0.753697	+	15.8220i	0.0336727	+	0.706876i
$502$	−18.1692	+	25.5150i	−0.810930	+	1.13879i
$503$	10.0923	+	6.48591i	0.449992	+	0.289192i	0.745942	−	0.666011i	$-0.232000\pi$
$503$	10.0923	+	6.48591i	0.449992	+	0.289192i	−0.295950	+	0.955204i	$0.595636\pi$
$504$	−6.11904	−	0.888048i	−0.272564	−	0.0395568i
$505$	3.98677	−	27.7286i	0.177409	−	1.23391i
$506$	−11.1401	+	5.41875i	−0.495237	+	0.240893i
$507$	−3.12620	−	1.25154i	−0.138839	−	0.0555829i
$508$	−5.95505	+	5.67813i	−0.264213	+	0.251926i
$509$	−19.1448	−	9.86982i	−0.848577	−	0.437472i	−0.0216399	−	0.999766i	$-0.506889\pi$
$509$	−19.1448	−	9.86982i	−0.848577	−	0.437472i	−0.826938	+	0.562294i	$0.809919\pi$
$510$	−33.0340	−	9.69966i	−1.46277	−	0.429508i
$511$	5.16282	−	5.40028i	0.228390	−	0.238894i
$512$	8.75339	+	10.1020i	0.386849	+	0.446447i
$513$	−1.83591	+	38.5404i	−0.0810573	+	1.70160i
$514$	13.4132	−	2.58518i	0.591630	−	0.114027i
$515$	35.2225	−	6.78859i	1.55209	−	0.299141i
$516$	−10.0344	−	5.17308i	−0.441739	−	0.227732i
$517$	1.09148	+	1.99641i	0.0480034	+	0.0878020i
$518$	36.3863	−	8.77627i	1.59872	−	0.385607i
$519$	−1.09245	−	7.59813i	−0.0479531	−	0.333521i
$520$	16.5407	+	3.18796i	0.725358	+	0.139801i
$521$	−19.1947	+	3.69948i	−0.840935	+	0.162077i	−0.591490	−	0.806312i	$-0.701460\pi$
$521$	−19.1947	+	3.69948i	−0.840935	+	0.162077i	−0.249445	+	0.968389i	$0.580248\pi$
$522$	−11.3927	−	8.95929i	−0.498643	−	0.392137i
$523$	−12.7434	−	2.45609i	−0.557231	−	0.107398i	−0.0971425	−	0.995270i	$-0.530970\pi$
$523$	−12.7434	−	2.45609i	−0.557231	−	0.107398i	−0.460089	+	0.887873i	$0.652182\pi$
$524$	−21.6943			−0.947720
$525$	6.43478	−	5.56088i	0.280837	−	0.242697i
$526$	5.99284	−	1.75966i	0.261300	−	0.0767246i
$527$	6.25281	+	25.7744i	0.272377	+	1.12275i
$528$	−17.1399	+	10.4596i	−0.745917	+	0.455198i
$529$	−4.37274	+	18.0247i	−0.190119	+	0.783682i
$530$	7.30937	+	3.76824i	0.317499	+	0.163682i
$531$	−4.75759	+	10.4177i	−0.206462	+	0.452088i
$532$	2.02854	−	20.9509i	0.0879484	−	0.908338i
$533$	−19.6562	−	5.77158i	−0.851404	−	0.249995i
$534$	−1.41720	+	29.7508i	−0.0613284	+	1.28744i
$535$	−0.256279	−	5.37995i	−0.0110799	−	0.232596i
$536$	10.2930	+	4.12071i	0.444592	+	0.177988i
$537$	5.49227	−	2.19877i	0.237009	−	0.0948840i
$538$	9.72588	+	21.2967i	0.419312	+	0.918166i
$539$	−8.15940	+	21.7353i	−0.351450	+	0.936207i
$540$	7.15556	−	15.6685i	0.307926	−	0.674265i
$541$	1.04776	−	21.9951i	0.0450466	−	0.945645i	−0.857349	−	0.514736i	$-0.827890\pi$
$541$	1.04776	−	21.9951i	0.0450466	−	0.945645i	0.902395	−	0.430909i	$-0.141807\pi$
$542$	8.80661	+	6.92560i	0.378276	+	0.297480i
$543$	4.53888	+	6.37396i	0.194782	+	0.273533i
$544$	−33.1407	+	3.16455i	−1.42089	+	0.135679i
$545$	16.6020	−	36.3533i	0.711152	−	1.55720i
$546$	−13.9941	+	17.7466i	−0.598894	+	0.759486i
$547$	1.57699	−	10.9682i	0.0674272	−	0.468967i	−0.927933	−	0.372747i	$-0.878416\pi$
$547$	1.57699	−	10.9682i	0.0674272	−	0.468967i	0.995360	−	0.0962195i	$-0.0306751\pi$
$548$	−0.957493	+	20.1003i	−0.0409021	+	0.858640i
$549$	−6.82793	−	9.58849i	−0.291409	−	0.409227i
$550$	−2.56735	+	15.3167i	−0.109472	+	0.653104i
$551$	−21.8844	+	30.7324i	−0.932308	+	1.30924i
$552$	0.559792	−	3.89344i	0.0238263	−	0.165716i
$553$	−18.3946	+	8.37116i	−0.782220	+	0.355978i
$554$	−27.7573	+	17.8385i	−1.17929	+	0.757886i
$555$	1.27771	−	26.8225i	0.0542358	−	1.13855i
$556$	−16.2987	+	15.5408i	−0.691218	+	0.659075i
$557$	40.4096	+	16.1776i	1.71221	+	0.685465i	0.999866	−	0.0163673i	$-0.00521012\pi$
$557$	40.4096	+	16.1776i	1.71221	+	0.685465i	0.712342	+	0.701832i	$0.247634\pi$
$558$	−12.2990	+	1.17442i	−0.520660	+	0.0497170i
$559$	−27.3861	+	17.6000i	−1.15831	+	0.744399i
$560$	16.7441	−	32.3738i	0.707568	−	1.36804i
$561$	1.65212	−	23.2713i	0.0697524	−	0.982516i
$562$	−3.96384	−	16.3392i	−0.167205	−	0.689227i
$563$	7.00318	−	28.8675i	0.295149	−	1.21662i	−0.610302	−	0.792169i	$-0.708952\pi$
$563$	7.00318	−	28.8675i	0.295149	−	1.21662i	0.905451	−	0.424451i	$-0.139533\pi$
$564$	0.940523	+	0.0898090i	0.0396032	+	0.00378164i
$565$	−17.7915	−	30.8157i	−0.748492	−	1.29643i
$566$	−1.85130	+	2.13651i	−0.0778159	+	0.0898043i
$567$	−3.44346	−	4.39065i	−0.144612	−	0.184390i
$568$	−10.2229	−	11.7979i	−0.428943	−	0.495027i
$569$	−34.3004	−	6.61087i	−1.43795	−	0.277142i	−0.590079	−	0.807346i	$-0.700903\pi$
$569$	−34.3004	−	6.61087i	−1.43795	−	0.277142i	−0.847870	+	0.530204i	$0.822115\pi$
$570$	−38.7584	−	15.5165i	−1.62341	−	0.649916i
$571$	−38.8600	+	20.0337i	−1.62624	+	0.838385i	−0.628055	+	0.778169i	$0.716149\pi$
$571$	−38.8600	+	20.0337i	−1.62624	+	0.838385i	−0.998185	+	0.0602166i	$0.980821\pi$
$572$	−0.363084	−	14.9234i	−0.0151813	−	0.623979i
$573$	−1.21805	+	0.782794i	−0.0508848	+	0.0327017i
$574$	−13.0882	+	20.3066i	−0.546292	+	0.847580i
$575$	−3.65536	−	4.21851i	−0.152439	−	0.175924i
$576$	0.0156316	−	0.328147i	0.000651316	−	0.0136728i
$577$	−19.2554	+	3.71118i	−0.801615	+	0.154499i	−0.573575	−	0.819153i	$-0.694444\pi$
$577$	−19.2554	+	3.71118i	−0.801615	+	0.154499i	−0.228040	+	0.973652i	$0.573232\pi$
$578$	14.6123	−	25.3092i	0.607791	−	1.05273i
$579$	−3.43276	−	14.1500i	−0.142661	−	0.588055i
$580$	14.1692	−	9.10597i	0.588343	−	0.378105i
$581$	23.0521	+	13.3498i	0.956361	+	0.553843i
$582$	−2.84059	−	19.7568i	−0.117746	−	0.818944i
$583$	−1.43945	+	5.38340i	−0.0596158	+	0.222958i
$584$	−3.40513	−	2.67782i	−0.140905	−	0.110809i
$585$	−9.70325	−	13.6263i	−0.401180	−	0.563378i
$586$	0.531133	−	11.1498i	0.0219409	−	0.460596i
$587$	−15.1663	−	33.2095i	−0.625978	−	1.37070i	−0.911090	−	0.412207i	$-0.864758\pi$
$587$	−15.1663	−	33.2095i	−0.625978	−	1.37070i	0.285112	−	0.958494i	$-0.407969\pi$
$588$	5.57120	+	7.86762i	0.229752	+	0.324455i
$589$	4.57703	+	31.8339i	0.188593	+	1.31169i
$590$	−26.6300	−	25.3916i	−1.09634	−	1.04536i
$591$	5.58257	−	23.0117i	0.229636	−	0.946574i
$592$	−13.0234	−	37.6285i	−0.535257	−	1.54652i
$593$	34.4985	+	6.64904i	1.41668	+	0.273044i	0.839406	−	0.543504i	$-0.182903\pi$
$593$	34.4985	+	6.64904i	1.41668	+	0.273044i	0.577278	+	0.816548i	$0.304115\pi$
$594$	31.5360	+	6.84290i	1.29394	+	0.280768i
$595$	19.3552	+	37.6661i	0.793485	+	1.54416i
$596$	12.3782			0.507032
$597$	2.09117	+	8.61992i	0.0855859	+	0.352790i
$598$	11.6598	+	9.16937i	0.476805	+	0.374963i
$599$	26.6048	+	2.54045i	1.08704	+	0.103800i	0.623159	−	0.782095i	$-0.285849\pi$
$599$	26.6048	+	2.54045i	1.08704	+	0.103800i	0.463885	+	0.885895i	$0.346455\pi$
$600$	−3.56889	−	3.40293i	−0.145699	−	0.138924i
$601$	24.8483	−	28.6765i	1.01358	−	1.16974i	0.0281626	−	0.999603i	$-0.491034\pi$
$601$	24.8483	−	28.6765i	1.01358	−	1.16974i	0.985421	−	0.170134i	$-0.0544201\pi$
$602$	10.7672	+	36.8498i	0.438836	+	1.50189i
$603$	−4.57381	−	10.0152i	−0.186260	−	0.407852i
$604$	−6.47584	−	11.2165i	−0.263498	−	0.456392i
$605$	−30.3792	+	1.47912i	−1.23509	+	0.0601348i
$606$	10.8963	−	18.8729i	0.442632	−	0.766660i
$607$	25.4101	−	35.6835i	1.03136	−	1.44835i	0.142714	−	0.989764i	$-0.454417\pi$
$607$	25.4101	−	35.6835i	1.03136	−	1.44835i	0.888651	−	0.458585i	$-0.151644\pi$
$608$	−40.3700			−1.63722
$609$	−1.61977	−	17.2034i	−0.0656362	−	0.697117i
$610$	36.2867	−	10.6547i	1.46920	−	0.431397i
$611$	1.58032	−	2.21925i	0.0639329	−	0.0897813i
$612$	7.85637	+	6.17832i	0.317575	+	0.249744i
$613$	−15.2532	+	14.5439i	−0.616071	+	0.587422i	−0.932489	−	0.361197i	$-0.882368\pi$
$613$	−15.2532	+	14.5439i	−0.616071	+	0.587422i	0.316419	+	0.948620i	$0.397520\pi$
$614$	14.4480	+	25.0246i	0.583073	+	1.00991i
$615$	11.3502	+	13.0988i	0.457683	+	0.528195i
$616$	12.9999	+	3.49443i	0.523781	+	0.140795i
$617$	−7.23438	+	8.34892i	−0.291245	+	0.336115i	−0.882450	−	0.470407i	$-0.844107\pi$
$617$	−7.23438	+	8.34892i	−0.291245	+	0.336115i	0.591204	+	0.806522i	$0.298653\pi$
$618$	27.4005	+	5.28101i	1.10221	+	0.212433i
$619$	−0.663742	+	2.73598i	−0.0266780	+	0.109968i	−0.983594	−	0.180397i	$-0.942262\pi$
$619$	−0.663742	+	2.73598i	−0.0266780	+	0.109968i	0.956916	+	0.290365i	$0.0937769\pi$
$620$	3.38497	−	13.9530i	0.135944	−	0.560367i
$621$	−9.11695	+	7.16965i	−0.365851	+	0.287708i
$622$	−41.8804	+	26.9149i	−1.67925	+	1.07919i
$623$	27.7191	−	23.9546i	1.11054	−	0.959721i
$624$	20.2261	+	12.9985i	0.809691	+	0.520357i
$625$	31.0875	−	2.96849i	1.24350	−	0.118740i
$626$	−43.2751	−	34.0319i	−1.72962	−	1.36019i
$627$	4.67675	−	27.9012i	0.186771	−	1.11427i
$628$	7.26177	−	5.71072i	0.289776	−	0.227883i
$629$	44.3906	+	13.0342i	1.76997	+	0.519709i
$630$	−18.6509	+	6.42751i	−0.743068	+	0.256078i
$631$	3.29935	+	0.968776i	0.131345	+	0.0385664i	0.346744	−	0.937960i	$-0.387287\pi$
$631$	3.29935	+	0.968776i	0.131345	+	0.0385664i	−0.215399	+	0.976526i	$0.569105\pi$
$632$	5.85907	+	10.1482i	0.233061	+	0.403674i
$633$	4.11073	−	0.792279i	0.163387	−	0.0314903i
$634$	−24.5788	+	12.6713i	−0.976150	+	0.503240i
$635$	6.56561	−	18.9701i	0.260548	−	0.752804i
$636$	1.51531	+	1.74876i	0.0600860	+	0.0693430i
$637$	27.6801	−	2.56925i	1.09672	−	0.101797i
$638$	22.3237	+	22.3003i	0.883804	+	0.882876i
$639$	−0.737631	+	15.4848i	−0.0291802	+	0.612568i
$640$	−28.5454	−	11.4279i	−1.12836	−	0.451726i
$641$	−5.67561	−	16.3986i	−0.224173	−	0.647706i	−0.999862	−	0.0165908i	$-0.994719\pi$
$641$	−5.67561	−	16.3986i	−0.224173	−	0.647706i	0.775689	−	0.631115i	$-0.217402\pi$
$642$	1.37040	−	3.95950i	0.0540852	−	0.156269i
$643$	2.22682	−	15.4879i	0.0878172	−	0.610782i	−0.897623	−	0.440763i	$-0.854708\pi$
$643$	2.22682	−	15.4879i	0.0878172	−	0.610782i	0.985441	−	0.170019i	$-0.0543830\pi$
$644$	5.15892	−	3.66337i	0.203290	−	0.144357i
$645$	27.5422			1.08447
$646$	41.7229	−	58.5917i	1.64157	−	2.30526i
$647$	−2.77956	+	11.4575i	−0.109276	+	0.450442i	−0.999992	−	0.00411949i	$-0.998689\pi$
$647$	−2.77956	+	11.4575i	−0.109276	+	0.450442i	0.890716	+	0.454561i	$0.150204\pi$
$648$	−2.34153	+	2.23265i	−0.0919841	+	0.0877066i
$649$	12.9659	−	21.2971i	0.508958	−	0.835986i
$650$	17.8426	−	5.23906i	0.699845	−	0.205493i
$651$	−11.1193	−	9.66075i	−0.435802	−	0.378635i
$652$	1.61660	−	3.53986i	0.0633110	−	0.138632i
$653$	−29.7048	+	23.3601i	−1.16244	+	0.914152i	−0.997395	−	0.0721345i	$-0.977019\pi$
$653$	−29.7048	+	23.3601i	−1.16244	+	0.914152i	−0.165044	+	0.986286i	$0.552776\pi$
$654$	22.5006	−	21.4543i	0.879844	−	0.838929i
$655$	47.0433	−	24.2525i	1.83813	−	0.947623i
$656$	22.8439	+	11.7768i	0.891903	+	0.459808i
$657$	0.612214	+	4.25804i	0.0238848	+	0.166122i
$658$	−1.98274	−	2.52813i	−0.0772952	−	0.0985568i
$659$	13.3321	+	29.1932i	0.519344	+	1.13720i	0.969687	+	0.244349i	$0.0785743\pi$
$659$	13.3321	+	29.1932i	0.519344	+	1.13720i	−0.450343	+	0.892855i	$0.648698\pi$
$660$	−6.56768	+	10.7877i	−0.255646	+	0.419910i
$661$	7.24962	+	10.1807i	0.281977	+	0.395982i	0.931137	−	0.364671i	$-0.118818\pi$
$661$	7.24962	+	10.1807i	0.281977	+	0.395982i	−0.649159	+	0.760653i	$0.724879\pi$
$662$	−14.0435	+	7.23993i	−0.545816	+	0.281388i
$663$	−25.9340	+	10.3824i	−1.00719	+	0.403219i
$664$	6.41636	−	14.0499i	0.249003	−	0.545241i
$665$	19.0226	+	47.6990i	0.737667	+	1.84969i
$666$	−8.95295	+	19.6042i	−0.346920	+	0.759648i
$667$	−11.2897	+	1.07804i	−0.437139	+	0.0417417i
$668$	11.6130	+	9.13255i	0.449320	+	0.353349i
$669$	−23.3734	+	12.0498i	−0.903668	+	0.465873i
$670$	35.2137	−	3.36250i	1.36042	−	0.129905i
$671$	12.2935	+	22.4859i	0.474587	+	0.868057i
$672$	13.9894	−	12.0896i	0.539654	−	0.466365i
$673$	6.52616	−	45.3904i	0.251565	−	1.74967i	−0.337261	−	0.941411i	$-0.609500\pi$
$673$	6.52616	−	45.3904i	0.251565	−	1.74967i	0.588825	−	0.808260i	$-0.299591\pi$
$674$	16.2114	−	12.7488i	0.624441	−	0.491066i
$675$	0.691858	+	14.5239i	0.0266296	+	0.559025i
$676$	−2.79161	+	1.43918i	−0.107370	+	0.0553529i
$677$	−0.348966	−	1.43846i	−0.0134118	−	0.0552844i	0.964712	−	0.263306i	$-0.0848128\pi$
$677$	−0.348966	−	1.43846i	−0.0134118	−	0.0552844i	−0.978124	+	0.208021i	$0.933298\pi$
$678$	−3.93939	−	27.3991i	−0.151291	−	1.05225i
$679$	−15.2021	+	19.2784i	−0.583401	+	0.739839i
$680$	20.6564	−	13.2751i	0.792138	−	0.509076i
$681$	−9.91538	−	9.45429i	−0.379958	−	0.362289i
$682$	26.8908	+	0.625992i	1.02970	+	0.0239705i
$683$	−28.2187	+	26.9065i	−1.07976	+	1.02955i	−0.0802961	+	0.996771i	$0.525587\pi$
$683$	−28.2187	+	26.9065i	−1.07976	+	1.02955i	−0.999463	+	0.0327768i	$0.989565\pi$
$684$	8.77154	+	8.36365i	0.335388	+	0.319792i
$685$	−20.3942	−	44.6570i	−0.779222	−	1.70626i
$686$	6.33197	−	32.1660i	0.241756	−	1.22810i
$687$	−6.99437	+	8.07194i	−0.266852	+	0.307964i
$688$	37.9152	−	15.1790i	1.44550	−	0.578693i
$689$	6.55190	−	1.26278i	0.249608	−	0.0481079i
$690$	−4.10462	−	11.8595i	−0.156260	−	0.451484i
$691$	27.4814	−	21.6116i	1.04544	−	0.822144i	0.0610496	−	0.998135i	$-0.480555\pi$
$691$	27.4814	−	21.6116i	1.04544	−	0.822144i	0.984392	+	0.175991i	$0.0563128\pi$
$692$	−6.02302	−	3.87076i	−0.228961	−	0.147144i
$693$	−6.94843	−	11.4201i	−0.263949	−	0.433814i
$694$	32.7926	−	21.0745i	1.24479	−	0.799978i
$695$	17.9697	−	51.9201i	0.681631	−	1.96944i
$696$	−9.83798	+	1.89612i	−0.372908	+	0.0718721i
$697$	−26.5420	+	13.6833i	−1.00535	+	0.518293i
$698$	−8.13270	+	23.4979i	−0.307827	+	0.889408i
$699$	−20.1393			−0.761738
$700$	0.0104926	−	7.93224i	0.000396583	−	0.299810i
$701$	−36.0044	+	23.1386i	−1.35987	+	0.873934i	−0.998293	−	0.0584090i	$-0.981397\pi$
$701$	−36.0044	+	23.1386i	−1.35987	+	0.873934i	−0.361575	+	0.932343i	$0.617761\pi$
$702$	−9.10965	−	37.5505i	−0.343821	−	1.41725i
$703$	52.0830	+	20.8509i	1.96435	+	0.786405i
$704$	−0.118235	+	0.705381i	−0.00445614	+	0.0265851i
$705$	−2.13989	+	0.856681i	−0.0805928	+	0.0322645i
$706$	−1.80522	+	3.95287i	−0.0679403	+	0.148768i
$707$	−26.0581	+	6.28515i	−0.980017	+	0.236377i
$708$	−4.30099	−	9.41786i	−0.161641	−	0.353945i
$709$	19.4820	+	10.0437i	0.731662	+	0.377198i	0.783445	−	0.621461i	$-0.213460\pi$
$709$	19.4820	+	10.0437i	0.731662	+	0.377198i	−0.0517839	+	0.998658i	$0.516491\pi$
$710$	−46.2385	−	18.5111i	−1.73530	−	0.694710i
$711$	2.74346	−	11.3087i	0.102888	−	0.424110i
$712$	−15.3737	−	14.6588i	−0.576153	−	0.549361i
$713$	−6.33099	+	7.30635i	−0.237097	+	0.273625i
$714$	3.08810	+	32.7985i	0.115569	+	1.22745i
$715$	17.4705	+	31.9549i	0.653359	+	1.19505i
$716$	1.80471	−	5.21436i	0.0674451	−	0.194870i
$717$	2.29476	−	3.97464i	0.0856993	−	0.148436i
$718$	−2.83515	+	2.70331i	−0.105807	+	0.100887i
$719$	31.2609	−	12.5150i	1.16584	−	0.466731i	0.293654	−	0.955912i	$-0.405129\pi$
$719$	31.2609	−	12.5150i	1.16584	−	0.466731i	0.872182	+	0.489181i	$0.162704\pi$
$720$	8.71804	+	19.0899i	0.324902	+	0.711437i
$721$	−18.5185	−	28.8993i	−0.689664	−	1.07627i
$722$	35.0943	−	40.5010i	1.30608	−	1.50729i
$723$	−8.72050	−	15.1044i	−0.324319	−	0.561737i
$724$	7.26515	+	0.693738i	0.270007	+	0.0257826i
$725$	−7.10888	+	12.3129i	−0.264017	+	0.457291i
$726$	−22.3675	−	7.71518i	−0.830136	−	0.286337i
$727$	−10.9707			−0.406881			−0.203441	−	0.979087i	$-0.565212\pi$
$727$	−10.9707			−0.406881			−0.203441	+	0.979087i	$0.565212\pi$
$728$	−3.02951	−	15.8313i	−0.112281	−	0.586746i
$729$	23.2506			0.861132
$730$	−13.5713	−	2.61565i	−0.502295	−	0.0968094i
$731$	−11.1873	+	46.1147i	−0.413777	+	1.70561i
$732$	10.5932	+	1.01153i	0.391538	+	0.0373873i
$733$	−9.09122	+	3.63957i	−0.335792	+	0.134431i	−0.533430	−	0.845844i	$-0.679097\pi$
$733$	−9.09122	+	3.63957i	−0.335792	+	0.134431i	0.197638	+	0.980275i	$0.436673\pi$
$734$	38.5331	+	11.3143i	1.42228	+	0.417620i
$735$	−20.8763	−	10.8325i	−0.770034	−	0.399562i
$736$	−7.94688	−	9.17119i	−0.292926	−	0.338055i
$737$	7.31066	+	22.8284i	0.269292	+	0.840895i
$738$	−4.54972	−	13.1456i	−0.167478	−	0.483895i
$739$	14.2507	+	41.1746i	0.524219	+	1.51463i	0.827353	+	0.561683i	$0.189846\pi$
$739$	14.2507	+	41.1746i	0.524219	+	1.51463i	−0.303134	+	0.952948i	$0.598033\pi$
$740$	−18.1262	−	17.2833i	−0.666333	−	0.635347i
$741$	−32.5025	+	9.54360i	−1.19401	+	0.350593i
$742$	0.758340	−	7.83219i	0.0278395	−	0.287529i
$743$	−37.9190	+	24.3691i	−1.39111	+	0.894014i	−0.999657	−	0.0261828i	$-0.991665\pi$
$743$	−37.9190	+	24.3691i	−1.39111	+	0.894014i	−0.391456	+	0.920197i	$0.628028\pi$
$744$	−4.95411	+	6.95707i	−0.181626	+	0.255059i
$745$	−26.8417	+	13.8379i	−0.983404	+	0.506980i
$746$	25.9896	+	36.4973i	0.951548	+	1.33626i
$747$	−14.2396	+	5.70069i	−0.521001	+	0.208577i
$748$	−15.3944	−	15.3783i	−0.562876	−	0.562285i
$749$	−4.69083	+	2.13473i	−0.171399	+	0.0780015i
$750$	13.4371	+	3.94549i	0.490654	+	0.144069i
$751$	45.0744	+	23.2375i	1.64479	+	0.847947i	0.996227	+	0.0867835i	$0.0276589\pi$
$751$	45.0744	+	23.2375i	1.64479	+	0.847947i	0.648560	+	0.761163i	$0.275371\pi$
$752$	−2.47368	+	2.35865i	−0.0902059	+	0.0860112i
$753$	10.7513	−	18.6218i	0.391798	−	0.678614i
$754$	12.3574	−	35.7044i	0.450030	−	1.30028i
$755$	26.5817	+	17.0830i	0.967409	+	0.621716i
$756$	−16.4624	−	0.806027i	−0.598731	−	0.0293149i
$757$	−29.5672	−	34.1223i	−1.07464	−	1.24020i	−0.969331	−	0.245758i	$-0.920963\pi$
$757$	−29.5672	−	34.1223i	−1.07464	−	1.24020i	−0.105306	−	0.994440i	$-0.533582\pi$
$758$	36.4219	+	18.7768i	1.32290	+	0.682003i
$759$	7.25917	−	4.42992i	0.263491	−	0.160796i
$760$	26.4653	−	13.6438i	0.959997	−	0.494913i
$761$	−24.7715	+	19.4806i	−0.897968	+	0.706170i	−0.956381	−	0.292123i	$-0.905638\pi$
$761$	−24.7715	+	19.4806i	−0.897968	+	0.706170i	0.0584131	+	0.998292i	$0.481396\pi$
$762$	10.2264	−	11.8019i	0.370464	−	0.427538i
$763$	−38.1952	−	1.87011i	−1.38276	−	0.0677024i
$764$	−0.192188	+	1.33670i	−0.00695311	+	0.0483600i
$765$	−23.9431	−	4.61466i	−0.865665	−	0.166843i
$766$	11.9361	−	20.6739i	0.431268	−	0.746978i
$767$	−29.7201	−	2.83792i	−1.07313	−	0.102471i
$768$	−17.6907	−	16.8681i	−0.638359	−	0.608674i
$769$	−9.19210	−	2.69905i	−0.331476	−	0.0973301i	0.111760	−	0.993735i	$-0.464351\pi$
$769$	−9.19210	−	2.69905i	−0.331476	−	0.0973301i	−0.443236	+	0.896405i	$0.646169\pi$
$770$	41.9743	−	9.09589i	1.51265	−	0.327793i
$771$	−8.99743	+	2.64188i	−0.324035	+	0.0951451i
$772$	−12.0707	−	6.22290i	−0.434436	−	0.223967i
$773$	1.28727	+	1.80772i	0.0463000	+	0.0650193i	0.837077	−	0.547085i	$-0.184263\pi$
$773$	1.28727	+	1.80772i	0.0463000	+	0.0650193i	−0.790777	+	0.612104i	$0.790323\pi$
$774$	−20.5217	−	8.21563i	−0.737636	−	0.295305i
$775$	2.85738	+	11.7783i	0.102640	+	0.423088i
$776$	11.9755	+	7.69620i	0.429896	+	0.276278i
$777$	−24.2925	+	8.37175i	−0.871489	+	0.300335i
$778$	0.766593	+	5.33177i	0.0274837	+	0.191153i
$779$	−33.6170	+	13.4582i	−1.20445	+	0.482190i
$780$	15.0542	+	1.43750i	0.539026	+	0.0514708i
$781$	5.57933	−	33.2859i	0.199644	−	1.19106i
$782$	21.5240	−	2.05529i	0.769695	−	0.0734970i
$783$	24.8528	+	15.9719i	0.888165	+	0.570789i
$784$	−34.7087	−	3.40696i	−1.23960	−	0.121677i
$785$	−9.36275	+	20.5016i	−0.334171	+	0.731732i
$786$	40.9867	−	3.91375i	1.46195	−	0.139599i
$787$	−9.23982	−	12.9755i	−0.329364	−	0.462527i	0.616376	−	0.787452i	$-0.288600\pi$
$787$	−9.23982	−	12.9755i	−0.329364	−	0.462527i	−0.945740	+	0.324925i	$0.894661\pi$
$788$	−12.8107	−	17.9902i	−0.456364	−	0.640873i
$789$	−3.98048	+	1.59355i	−0.141709	+	0.0567317i
$790$	31.4517	+	20.2128i	1.11900	+	0.719140i
$791$	−21.0825	+	26.7357i	−0.749608	+	0.950613i
$792$	−6.20254	+	4.64825i	−0.220398	+	0.165168i
$793$	17.7994	−	24.9957i	0.632075	−	0.887625i
$794$	−23.5612	−	18.5287i	−0.836156	−	0.657560i
$795$	−5.24087	−	2.09813i	−0.185875	−	0.0744130i
$796$	7.35326	+	3.79087i	0.260629	+	0.134364i
$797$	24.1555	+	15.5238i	0.855630	+	0.549880i	0.893326	−	0.449409i	$-0.148365\pi$
$797$	24.1555	+	15.5238i	0.855630	+	0.549880i	−0.0376958	+	0.999289i	$0.512002\pi$
$798$	−0.0528426	+	39.9482i	−0.00187061	+	1.41415i
$799$	−0.565170	−	3.93084i	−0.0199943	−	0.139063i
$800$	−15.1445	+	1.44612i	−0.535438	+	0.0511281i
$801$	1.00372	+	21.0707i	0.0354647	+	0.744497i
$802$	−15.5030	+	63.9041i	−0.547429	+	2.25653i
$803$	−0.227795	−	9.36278i	−0.00803872	−	0.330405i
$804$	9.55034	+	2.80423i	0.336815	+	0.0988977i
$805$	−7.09156	+	13.7111i	−0.249945	+	0.483254i
$806$	−13.3795	−	29.2970i	−0.471273	−	1.03194i
$807$	−8.03603	−	13.9188i	−0.282882	−	0.489966i
$808$	5.08341	+	14.6876i	0.178834	+	0.516707i
$809$	14.0702	+	11.0649i	0.494681	+	0.389022i	0.834100	−	0.551614i	$-0.185988\pi$
$809$	14.0702	+	11.0649i	0.494681	+	0.389022i	−0.339418	+	0.940636i	$0.610230\pi$
$810$	−3.37612	+	9.75466i	−0.118625	+	0.342744i
$811$	−16.8215	+	19.4131i	−0.590684	+	0.681686i	−0.969867	−	0.243636i	$-0.921660\pi$
$811$	−16.8215	+	19.4131i	−0.590684	+	0.681686i	0.379183	+	0.925322i	$0.376205\pi$
$812$	−13.1157	−	9.36580i	−0.460270	−	0.328675i
$813$	−6.47007	−	4.15806i	−0.226915	−	0.145830i
$814$	24.3996	−	40.0775i	0.855207	−	1.40472i
$815$	0.451745	+	9.48329i	0.0158239	+	0.332185i
$816$	34.4127	−	6.63251i	1.20469	−	0.232184i
$817$	−18.8201	+	54.3771i	−0.658432	+	1.90241i
$818$	−28.2345	−	18.1452i	−0.987195	−	0.634432i
$819$	−8.67159	+	13.4541i	−0.303010	+	0.470124i
$820$	16.1656			0.564526
$821$	−10.4700	−	43.1578i	−0.365405	−	1.50622i	−0.796904	−	0.604106i	$-0.793530\pi$
$821$	−10.4700	−	43.1578i	−0.365405	−	1.50622i	0.431499	−	0.902113i	$-0.357985\pi$
$822$	−1.81720	−	38.1478i	−0.0633822	−	1.33056i
$823$	21.3621	−	20.3687i	0.744636	−	0.710009i	−0.219442	−	0.975625i	$-0.570424\pi$
$823$	21.3621	−	20.3687i	0.744636	−	0.710009i	0.964079	+	0.265616i	$0.0855753\pi$
$824$	−15.6437	+	12.3023i	−0.544973	+	0.428572i
$825$	0.754976	−	10.6344i	0.0262849	−	0.370243i
$826$	−13.1288	+	32.6687i	−0.456808	+	1.13669i
$827$	2.68437	−	5.87795i	0.0933447	−	0.204396i	−0.857200	−	0.514983i	$-0.827798\pi$
$827$	2.68437	−	5.87795i	0.0933447	−	0.204396i	0.950545	+	0.310587i	$0.100525\pi$
$828$	−0.173352	+	3.63910i	−0.00602438	+	0.126467i
$829$	37.5759	+	3.58806i	1.30506	+	0.124618i	0.724317	−	0.689467i	$-0.242155\pi$
$829$	37.5759	+	3.58806i	1.30506	+	0.124618i	0.580746	+	0.814085i	$0.302761\pi$
$830$	−2.34481	−	49.2236i	−0.0813895	−	1.70858i
$831$	17.8044	−	14.0015i	0.617628	−	0.485708i
$832$	0.821710	−	0.241276i	0.0284877	−	0.00836473i
$833$	26.6168	−	30.5537i	0.922217	−	1.05862i
$834$	27.9892	−	32.3012i	0.969186	−	1.11850i
$835$	−35.3918	−	6.82121i	−1.22478	−	0.236058i
$836$	−16.8105	−	20.3381i	−0.581404	−	0.703408i
$837$	24.7284	−	4.76602i	0.854740	−	0.164738i
$838$	−27.8362	−	48.2136i	−0.961584	−	1.66551i
$839$	34.4140	+	10.1049i	1.18810	+	0.348859i	0.815293	−	0.579049i	$-0.196576\pi$
$839$	34.4140	+	10.1049i	1.18810	+	0.348859i	0.372811	+	0.927907i	$0.378394\pi$
$840$	−5.08513	+	12.6535i	−0.175454	+	0.436588i
$841$	−0.0469087	−	0.102716i	−0.00161754	−	0.00354192i
$842$	−25.0687	−	23.9029i	−0.863924	−	0.823750i
$843$	3.77495	+	10.9070i	0.130016	+	0.375657i
$844$	1.95230	−	3.38148i	0.0672010	−	0.116395i
$845$	4.44462	−	6.24159i	0.152900	−	0.214717i
$846$	1.84997			0.0636032
$847$	12.0827	+	26.4766i	0.415167	+	0.909745i
$848$	−8.37101			−0.287462
$849$	1.12570	−	1.58083i	0.0386340	−	0.0542538i
$850$	13.5532	−	23.4748i	0.464870	−	0.805178i
$851$	5.51572	+	15.9366i	0.189077	+	0.546301i
$852$	−10.1428	−	9.67114i	−0.347486	−	0.331328i
$853$	5.42935	+	11.8886i	0.185897	+	0.407058i	0.979519	−	0.201354i	$-0.0645341\pi$
$853$	5.42935	+	11.8886i	0.185897	+	0.407058i	−0.793621	+	0.608412i	$0.791807\pi$
$854$	−22.3319	−	28.4747i	−0.764181	−	0.974385i
$855$	−28.3706	−	8.33037i	−0.970255	−	0.284893i
$856$	1.49412	+	2.58790i	0.0510681	+	0.0884526i
$857$	10.5850	−	2.04010i	0.361578	−	0.0696885i	−0.00522681	−	0.999986i	$-0.501664\pi$
$857$	10.5850	−	2.04010i	0.361578	−	0.0696885i	0.366805	+	0.930298i	$0.380452\pi$
$858$	3.37822	+	28.1290i	0.115330	+	0.960308i
$859$	27.6146	+	5.32227i	0.942197	+	0.181594i	0.637147	−	0.770743i	$-0.280115\pi$
$859$	27.6146	+	5.32227i	0.942197	+	0.181594i	0.305050	+	0.952336i	$0.401327\pi$
$860$	16.8223	−	19.4140i	0.573636	−	0.662011i
$861$	7.61899	−	14.7309i	0.259655	−	0.502028i
$862$	4.48822	−	1.31786i	0.152869	−	0.0448865i
$863$	−15.5764	+	12.2494i	−0.530227	+	0.416975i	−0.847053	−	0.531509i	$-0.821625\pi$
$863$	−15.5764	+	12.2494i	−0.530227	+	0.416975i	0.316826	+	0.948484i	$0.397383\pi$
$864$	1.50412	+	31.5755i	0.0511714	+	1.07422i
$865$	17.3879	+	1.66034i	0.591206	+	0.0564533i
$866$	0.167340	−	3.51291i	0.00568646	−	0.119373i
$867$	−8.33404	+	18.2490i	−0.283039	+	0.619769i
$868$	−13.6012	+	1.93719i	−0.461654	+	0.0657526i
$869$	−8.84101	+	23.7417i	−0.299911	+	0.805383i
$870$	−25.1268	+	19.7599i	−0.851878	+	0.669924i
$871$	20.7726	−	19.8066i	0.703852	−	0.671122i
$872$	1.05503	+	22.1479i	0.0357279	+	0.750022i
$873$	−3.33279	−	13.7379i	−0.112798	−	0.464959i
$874$	26.2192			0.886879
$875$	−7.87303	−	15.3213i	−0.266157	−	0.517953i
$876$	−3.27161	−	2.10254i	−0.110538	−	0.0710382i
$877$	−7.42107	+	21.4418i	−0.250592	+	0.724037i	0.747612	+	0.664135i	$0.231200\pi$
$877$	−7.42107	+	21.4418i	−0.250592	+	0.724037i	−0.998204	+	0.0599022i	$0.980921\pi$
$878$	−21.0907	+	4.06489i	−0.711776	+	0.137184i
$879$	0.364610	+	7.65410i	0.0122980	+	0.258166i
$880$	−13.9347	−	43.5127i	−0.469739	−	1.46681i
$881$	−33.8062	−	21.7259i	−1.13896	−	0.731966i	−0.171549	−	0.985176i	$-0.554877\pi$
$881$	−33.8062	−	21.7259i	−1.13896	−	0.731966i	−0.967411	+	0.253210i	$0.918514\pi$
$882$	12.3236	+	14.2985i	0.414958	+	0.481455i
$883$	1.38363	−	1.59680i	0.0465629	−	0.0537365i	−0.731990	−	0.681315i	$-0.761408\pi$
$883$	1.38363	−	1.59680i	0.0465629	−	0.0537365i	0.778553	+	0.627579i	$0.215954\pi$
$884$	−8.52166	+	24.6217i	−0.286614	+	0.828118i
$885$	19.8549	+	15.6141i	0.667416	+	0.524862i
$886$	20.9576	+	60.5530i	0.704084	+	2.03432i
$887$	−9.33247	−	16.1643i	−0.313354	−	0.542745i	0.665732	−	0.746191i	$-0.268119\pi$
$887$	−9.33247	−	16.1643i	−0.313354	−	0.542745i	−0.979086	+	0.203446i	$0.934786\pi$
$888$	6.18898	+	13.5520i	0.207689	+	0.454775i
$889$	−19.1877	+	0.888585i	−0.643534	+	0.0298022i
$890$	−65.0279	−	19.0939i	−2.17974	−	0.640030i
$891$	−6.94574	−	0.826765i	−0.232691	−	0.0276977i
$892$	−5.78237	+	23.8353i	−0.193608	+	0.798064i
$893$	−0.229138	−	4.81020i	−0.00766781	−	0.160967i
$894$	−23.3860	+	2.23309i	−0.782143	+	0.0746856i
$895$	1.91580	+	13.3247i	0.0640380	+	0.445394i
$896$	−0.0389184	+	29.4216i	−0.00130017	+	0.982908i
$897$	−8.56626	−	5.50520i	−0.286019	−	0.183813i
$898$	−54.4397	−	28.0656i	−1.81668	−	0.936562i
$899$	22.8609	+	9.15211i	0.762452	+	0.305240i
$900$	3.59017	+	2.82334i	0.119672	+	0.0941114i
$901$	5.64173	−	7.92270i	0.187953	−	0.263943i
$902$	6.45307	+	29.5895i	0.214864	+	0.985222i
$903$	−9.76250	−	24.4793i	−0.324876	−	0.814622i
$904$	16.6079	+	10.6732i	0.552370	+	0.354987i
$905$	−16.5297	+	6.61751i	−0.549467	+	0.219973i
$906$	14.2582	+	20.0228i	0.473697	+	0.665214i
$907$	5.96625	+	8.37843i	0.198106	+	0.278201i	0.901664	−	0.432436i	$-0.142346\pi$
$907$	5.96625	+	8.37843i	0.198106	+	0.278201i	−0.703558	+	0.710638i	$0.748407\pi$
$908$	−12.7203	+	1.21464i	−0.422137	+	0.0403092i
$909$	6.41168	−	14.0396i	0.212662	−	0.465665i
$910$	−31.7361	−	40.4657i	−1.05204	−	1.34143i
$911$	−38.8022	−	24.9367i	−1.28557	−	0.826188i	−0.294010	−	0.955802i	$-0.594990\pi$
$911$	−38.8022	−	24.9367i	−1.28557	−	0.826188i	−0.991564	+	0.129614i	$0.958626\pi$
$912$	42.3053	−	4.03967i	1.40087	−	0.133767i
$913$	32.2509	−	8.65975i	1.06735	−	0.286596i
$914$	20.1769	+	1.92666i	0.667392	+	0.0637282i
$915$	−24.1019	+	9.64893i	−0.796783	+	0.318984i
$916$	1.41771	+	9.86039i	0.0468425	+	0.325796i
$917$	−38.2302	−	33.2153i	−1.26247	−	1.09687i
$918$	−47.3821	−	30.4506i	−1.56384	−	1.00502i
$919$	8.31670	+	34.2819i	0.274343	+	1.13086i	0.927557	+	0.373683i	$0.121905\pi$
$919$	8.31670	+	34.2819i	0.274343	+	1.13086i	−0.653214	+	0.757173i	$0.726580\pi$
$920$	8.30929	+	3.32654i	0.273949	+	0.109673i
$921$	−11.5062	−	16.1582i	−0.379143	−	0.532431i
$922$	−37.1077	−	19.1304i	−1.22208	−	0.630025i
$923$	−38.7753	+	11.3854i	−1.27630	+	0.374757i
$924$	11.9160	+	2.01355i	0.392007	+	0.0662408i
$925$	20.2854	+	5.95633i	0.666980	+	0.195843i
$926$	21.8409	+	20.8253i	0.717738	+	0.684361i
$927$	19.6738	+	1.87862i	0.646172	+	0.0617020i
$928$	−15.4550	+	26.7688i	−0.507334	+	0.878728i
$929$	−46.9707	−	9.05287i	−1.54106	−	0.297015i	−0.653220	−	0.757168i	$-0.726582\pi$
$929$	−46.9707	−	9.05287i	−1.54106	−	0.297015i	−0.887840	+	0.460153i	$0.847795\pi$
$930$	−3.87797	+	26.9719i	−0.127164	+	0.884442i
$931$	35.6519	−	33.8144i	1.16844	−	1.10822i
$932$	−12.3007	+	14.1958i	−0.402923	+	0.464998i
$933$	26.8634	−	21.1256i	0.879468	−	0.691621i
$934$	13.7460	−	7.08658i	0.449784	−	0.231880i
$935$	50.5739	+	16.1374i	1.65394	+	0.527751i
$936$	8.24924	+	4.25278i	0.269635	+	0.139006i
$937$	−26.5127	−	30.5973i	−0.866134	−	0.999571i	−0.999963	−	0.00856708i	$-0.997273\pi$
$937$	−26.5127	−	30.5973i	−0.866134	−	0.999571i	0.133830	−	0.991004i	$-0.457272\pi$
$938$	−15.4703	−	30.1058i	−0.505122	−	0.982990i
$939$	31.7935	+	20.4324i	1.03754	+	0.666787i
$940$	−0.703147	+	2.03161i	−0.0229341	+	0.0662638i
$941$	5.00698	−	8.67234i	0.163223	−	0.282710i	−0.772800	−	0.634650i	$-0.781144\pi$
$941$	5.00698	−	8.67234i	0.163223	−	0.282710i	0.936023	+	0.351940i	$0.114478\pi$
$942$	−12.6893	+	12.0992i	−0.413439	+	0.394214i
$943$	−9.67495	−	4.98778i	−0.315060	−	0.162425i
$944$	35.9379	+	10.5523i	1.16968	+	0.343449i
$945$	36.5991	−	16.6558i	1.19057	−	0.541813i
$946$	42.2506	+	23.0418i	1.37368	+	0.749152i
$947$	−51.9762	+	20.8082i	−1.68900	+	0.676174i	−0.998871	−	0.0475110i	$-0.984871\pi$
$947$	−51.9762	+	20.8082i	−1.68900	+	0.676174i	−0.690130	+	0.723685i	$0.742447\pi$
$948$	6.10215	+	8.56928i	0.198189	+	0.278317i
$949$	−9.96760	+	5.13866i	−0.323562	+	0.166808i
$950$	19.0664	−	26.7750i	0.618595	−	0.868695i
$951$	15.9695	−	10.2630i	0.517847	−	0.332800i
$952$	−19.1206	−	13.6539i	−0.619702	−	0.442524i
$953$	31.4875	−	9.24557i	1.01998	−	0.299493i	0.271350	−	0.962481i	$-0.412530\pi$
$953$	31.4875	−	9.24557i	1.01998	−	0.299493i	0.748631	+	0.662987i	$0.230712\pi$
$954$	3.27911	+	3.12662i	0.106165	+	0.101228i
$955$	−1.07757	−	3.11343i	−0.0348692	−	0.100748i
$956$	−1.40005	−	4.04517i	−0.0452807	−	0.130830i
$957$	−16.7105	−	13.7826i	−0.540172	−	0.445527i
$958$	−19.5280	−	22.5365i	−0.630922	−	0.728122i
$959$	−32.4620	+	33.9551i	−1.04825	+	1.09647i
$960$	−0.695207	−	0.204131i	−0.0224377	−	0.00658831i
$961$	−9.29167	+	3.71982i	−0.299731	+	0.119994i
$962$	−55.9279	−	5.34047i	−1.80319	−	0.172184i
$963$	0.699612	−	2.88384i	0.0225447	−	0.0929304i
$964$	−15.9731	−	3.07856i	−0.514459	−	0.0991538i
$965$	33.1317			1.06655
$966$	−9.08576	+	7.85184i	−0.292329	+	0.252629i
$967$	−36.1065			−1.16111			−0.580554	−	0.814222i	$-0.697164\pi$
$967$	−36.1065			−1.16111			−0.580554	+	0.814222i	$0.697164\pi$
$968$	14.6051	−	8.45271i	0.469425	−	0.271680i
$969$	−24.6888	+	42.7622i	−0.793118	+	1.37372i
$970$	45.2122	+	4.31724i	1.45168	+	0.138618i
$971$	−12.5800	−	21.7893i	−0.403713	−	0.699251i	0.590458	−	0.807069i	$-0.298947\pi$
$971$	−12.5800	−	21.7893i	−0.403713	−	0.699251i	−0.994171	+	0.107817i	$0.965614\pi$
$972$	10.3366	−	11.9291i	0.331547	−	0.382625i
$973$	−52.5157	+	2.43201i	−1.68358	+	0.0779668i
$974$	9.55542	+	20.9235i	0.306175	+	0.670431i
$975$	−11.8512	+	4.74450i	−0.379542	+	0.151946i
$976$	−27.8614	+	26.5658i	−0.891823	+	0.850352i
$977$	20.6165	−	35.7088i	0.659580	−	1.14243i	−0.321144	−	0.947030i	$-0.604067\pi$
$977$	20.6165	−	35.7088i	0.659580	−	1.14243i	0.980724	−	0.195396i	$-0.0625992\pi$
$978$	−2.41561	+	6.97944i	−0.0772426	+	0.223178i
$979$	3.25221	−	45.8099i	0.103941	−	1.46409i
$980$	−20.3865	+	8.09900i	−0.651222	+	0.258713i
$981$	14.4193	−	16.6408i	0.460374	−	0.531300i
$982$	44.8192	+	42.7350i	1.43024	+	1.36373i
$983$	1.86946	−	7.70602i	0.0596265	−	0.245784i	−0.934197	−	0.356758i	$-0.883882\pi$
$983$	1.86946	−	7.70602i	0.0596265	−	0.245784i	0.993823	+	0.110974i	$0.0353972\pi$
$984$	−8.92730	−	3.57395i	−0.284592	−	0.113933i
$985$	47.8911	+	24.6896i	1.52594	+	0.786676i
$986$	−22.8784	−	50.0967i	−0.728596	−	1.59540i
$987$	1.51991	+	1.59826i	0.0483792	+	0.0508732i
$988$	−13.1249	+	28.7395i	−0.417558	+	0.914324i
$989$	−16.0581	+	6.42867i	−0.510616	+	0.204420i
$990$	−10.7937	+	22.2496i	−0.343048	+	0.707139i
$991$	19.5742	+	7.83631i	0.621793	+	0.248929i	0.661099	−	0.750299i	$-0.270090\pi$
$991$	19.5742	+	7.83631i	0.621793	+	0.248929i	−0.0393055	+	0.999227i	$0.512515\pi$
$992$	6.21205	+	25.6064i	0.197233	+	0.813004i
$993$	9.12444	−	5.86392i	0.289555	−	0.186086i
$994$	−0.0630409	+	47.6579i	−0.00199954	+	1.51162i
$995$	−20.1831			−0.639849
$996$	4.53522	−	13.1037i	0.143704	−	0.415205i
$997$	15.5157	−	7.99892i	0.491388	−	0.253328i	−0.194678	−	0.980867i	$-0.562366\pi$
$997$	15.5157	−	7.99892i	0.491388	−	0.253328i	0.686066	+	0.727539i	$0.259336\pi$
$998$	−13.8493	+	2.66923i	−0.438392	+	0.0844931i
$999$	14.3680	−	41.5136i	0.454584	−	1.31343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.u.a.221.20	yes	1720
7.2	even	3	inner	847.2.u.a.100.67	yes	1720
121.23	even	11	inner	847.2.u.a.144.67	yes	1720
847.23	even	33	inner	847.2.u.a.23.20	✓	1720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.u.a.23.20	✓	1720	847.23	even	33	inner
847.2.u.a.100.67	yes	1720	7.2	even	3	inner
847.2.u.a.144.67	yes	1720	121.23	even	11	inner
847.2.u.a.221.20	yes	1720	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.u (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02678 + 1.44191i) q^{2} +(0.607575 - 1.05235i) q^{3} +(-0.370686 - 1.07103i) q^{4} +(2.00114 + 1.90808i) q^{5} +(0.893547 + 1.95660i) q^{6} +(0.986575 - 2.45493i) q^{7} +(-1.47193 - 0.432196i) q^{8} +(0.761704 + 1.31931i) q^{9} +O(q^{10})\)	\(q+(-1.02678 + 1.44191i) q^{2} +(0.607575 - 1.05235i) q^{3} +(-0.370686 - 1.07103i) q^{4} +(2.00114 + 1.90808i) q^{5} +(0.893547 + 1.95660i) q^{6} +(0.986575 - 2.45493i) q^{7} +(-1.47193 - 0.432196i) q^{8} +(0.761704 + 1.31931i) q^{9} +(-4.80599 + 0.926279i) q^{10} +(-1.30719 - 3.04816i) q^{11} +(-1.35231 - 0.260637i) q^{12} +(-2.60065 + 3.00130i) q^{13} +(2.52678 + 3.94321i) q^{14} +(3.22381 - 0.946597i) q^{15} +(3.91629 - 3.07980i) q^{16} +(0.275441 + 5.78221i) q^{17} +(-2.68442 - 0.256331i) q^{18} +(-0.334006 + 7.01166i) q^{19} +(1.30181 - 2.85057i) q^{20} +(-1.98403 - 2.52978i) q^{21} +(5.73734 + 1.24493i) q^{22} +(-1.65865 + 1.30437i) q^{23} +(-1.34913 + 1.28639i) q^{24} +(0.125870 + 2.64233i) q^{25} +(-1.65732 - 6.83155i) q^{26} +5.49662 q^{27} +(-2.99500 - 0.146640i) q^{28} +(4.52146 + 2.90577i) q^{29} +(-1.94523 + 5.62038i) q^{30} +(4.49884 - 0.867080i) q^{31} +(0.273645 + 5.74452i) q^{32} +(-4.00195 - 0.476360i) q^{33} +(-8.62022 - 5.53988i) q^{34} +(6.65847 - 3.03018i) q^{35} +(1.13066 - 1.30485i) q^{36} +(2.61397 - 7.55257i) q^{37} +(-9.76720 - 7.68101i) q^{38} +(1.57834 + 4.56031i) q^{39} +(-2.12086 - 3.67344i) q^{40} +(2.14293 + 4.69236i) q^{41} +(5.68485 - 0.263266i) q^{42} +(7.86525 + 2.30945i) q^{43} +(-2.78010 + 2.52994i) q^{44} +(-0.993076 + 4.09352i) q^{45} +(-0.177725 - 3.73091i) q^{46} +(-0.682923 + 0.0652112i) q^{47} +(-0.861594 - 5.99252i) q^{48} +(-5.05334 - 4.84394i) q^{49} +(-3.93923 - 2.53159i) q^{50} +(6.25227 + 3.22327i) q^{51} +(4.17850 + 1.67282i) q^{52} +(-1.32071 - 1.03862i) q^{53} +(-5.64380 + 7.92561i) q^{54} +(3.20026 - 8.59401i) q^{55} +(-2.51318 + 3.18708i) q^{56} +(7.17580 + 4.61160i) q^{57} +(-8.83237 + 3.53595i) q^{58} +(4.36073 + 6.12379i) q^{59} +(-2.20885 - 3.10190i) q^{60} +(-7.69186 + 0.734483i) q^{61} +(-3.36905 + 7.37720i) q^{62} +(3.99029 - 0.568331i) q^{63} +(-0.181414 - 0.116588i) q^{64} +(-10.9310 + 1.04378i) q^{65} +(4.79597 - 5.28131i) q^{66} +(-7.19463 - 0.687004i) q^{67} +(6.09080 - 2.43839i) q^{68} +(0.364907 + 2.53798i) q^{69} +(-2.46752 + 12.7122i) q^{70} +(8.56067 + 5.50161i) q^{71} +(-0.550971 - 2.27113i) q^{72} +(2.62154 + 1.04951i) q^{73} +(8.20613 + 11.5239i) q^{74} +(2.85714 + 1.47296i) q^{75} +(7.63348 - 2.24139i) q^{76} +(-8.77264 + 0.201827i) q^{77} +(-8.19614 - 2.40660i) q^{78} +(-5.52833 - 5.27125i) q^{79} +(13.7135 + 1.30948i) q^{80} +(1.05450 - 1.82645i) q^{81} +(-8.96624 - 1.72810i) q^{82} +(-1.43289 + 9.96596i) q^{83} +(-1.97401 + 3.06270i) q^{84} +(-10.4817 + 12.0966i) q^{85} +(-11.4059 + 8.96967i) q^{86} +(5.80502 - 2.99269i) q^{87} +(0.606686 + 5.05162i) q^{88} +(12.3077 + 6.34505i) q^{89} +(-4.88279 - 5.63504i) q^{90} +(4.80226 + 9.34541i) q^{91} +(2.01185 + 1.29294i) q^{92} +(1.82091 - 5.26118i) q^{93} +(0.607180 - 1.05167i) q^{94} +(-14.0472 + 13.3940i) q^{95} +(6.21152 + 3.20226i) q^{96} +(-8.90359 - 2.61433i) q^{97} +(12.1731 - 2.31280i) q^{98} +(3.02577 - 4.04638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9}+O(q^{10}) \) 1720 * q - 11 * q^2 - 20 * q^3 + 73 * q^4 - 7 * q^5 + 8 * q^6 - 24 * q^7 - 32 * q^8 - 844 * q^9	\( 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9} - 39 q^{10} - 22 q^{11} + 49 q^{12} - 28 q^{13} - 8 q^{14} - 26 q^{15} + 61 q^{16} - 17 q^{17} - 2 q^{18} - 13 q^{19} - 76 q^{20} + 13 q^{21} - 132 q^{22} + 23 q^{23} - 36 q^{24} + 75 q^{25} + 7 q^{26} + 28 q^{27} - 38 q^{28} - 20 q^{29} + 51 q^{30} - 5 q^{31} - 23 q^{32} + 59 q^{33} + 4 q^{34} - 16 q^{35} - 18 q^{36} - 52 q^{37} - 13 q^{38} - 46 q^{39} + 110 q^{40} - 52 q^{41} + 33 q^{42} - 48 q^{43} - 4 q^{44} + 60 q^{45} - 45 q^{46} - 19 q^{47} - 2 q^{48} - 92 q^{49} - 68 q^{50} + 127 q^{51} - 75 q^{52} - 97 q^{53} - 213 q^{54} - 60 q^{55} - 18 q^{56} - 18 q^{57} + 54 q^{58} - 7 q^{59} - 20 q^{60} - 23 q^{61} - 64 q^{62} + 125 q^{63} - 412 q^{64} + 19 q^{65} - 46 q^{66} + 7 q^{67} - 27 q^{68} - 6 q^{69} - 40 q^{70} - 24 q^{71} - 11 q^{72} - 25 q^{73} + 29 q^{74} + 81 q^{75} + 184 q^{76} - 284 q^{77} + 2 q^{78} - 55 q^{79} + 7 q^{80} - 772 q^{81} + 27 q^{82} + 8 q^{83} - q^{84} - 232 q^{85} - 37 q^{86} - 38 q^{87} + 23 q^{88} - 126 q^{89} + 448 q^{90} + 17 q^{91} + 416 q^{92} + 2 q^{93} + 144 q^{94} + 69 q^{95} - 47 q^{96} - 62 q^{97} + 96 q^{98} + 330 q^{99}+O(q^{100}) \) 1720 * q - 11 * q^2 - 20 * q^3 + 73 * q^4 - 7 * q^5 + 8 * q^6 - 24 * q^7 - 32 * q^8 - 844 * q^9 - 39 * q^10 - 22 * q^11 + 49 * q^12 - 28 * q^13 - 8 * q^14 - 26 * q^15 + 61 * q^16 - 17 * q^17 - 2 * q^18 - 13 * q^19 - 76 * q^20 + 13 * q^21 - 132 * q^22 + 23 * q^23 - 36 * q^24 + 75 * q^25 + 7 * q^26 + 28 * q^27 - 38 * q^28 - 20 * q^29 + 51 * q^30 - 5 * q^31 - 23 * q^32 + 59 * q^33 + 4 * q^34 - 16 * q^35 - 18 * q^36 - 52 * q^37 - 13 * q^38 - 46 * q^39 + 110 * q^40 - 52 * q^41 + 33 * q^42 - 48 * q^43 - 4 * q^44 + 60 * q^45 - 45 * q^46 - 19 * q^47 - 2 * q^48 - 92 * q^49 - 68 * q^50 + 127 * q^51 - 75 * q^52 - 97 * q^53 - 213 * q^54 - 60 * q^55 - 18 * q^56 - 18 * q^57 + 54 * q^58 - 7 * q^59 - 20 * q^60 - 23 * q^61 - 64 * q^62 + 125 * q^63 - 412 * q^64 + 19 * q^65 - 46 * q^66 + 7 * q^67 - 27 * q^68 - 6 * q^69 - 40 * q^70 - 24 * q^71 - 11 * q^72 - 25 * q^73 + 29 * q^74 + 81 * q^75 + 184 * q^76 - 284 * q^77 + 2 * q^78 - 55 * q^79 + 7 * q^80 - 772 * q^81 + 27 * q^82 + 8 * q^83 - q^84 - 232 * q^85 - 37 * q^86 - 38 * q^87 + 23 * q^88 - 126 * q^89 + 448 * q^90 + 17 * q^91 + 416 * q^92 + 2 * q^93 + 144 * q^94 + 69 * q^95 - 47 * q^96 - 62 * q^97 + 96 * q^98 + 330 * q^99

Introduction

L-functions

Modular forms

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Database

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