LMFDB - Embedded newform 930.2.bg.d.391.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.2
Root			$0.0834312i$ of defining polynomial
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.d.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.978446 - 1.08667i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.978446 - 1.08667i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(1.01385 + 0.215501i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(-0.241819 - 2.30075i) q^{13} +(-1.43031 + 0.304022i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.15156 - 0.244772i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(0.720222 - 6.85246i) q^{19} +(0.978148 + 0.207912i) q^{20} +(1.33584 - 0.594756i) q^{21} +(-0.693554 - 0.770270i) q^{22} +(-1.62425 + 4.99892i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.15671 + 2.00349i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.33584 + 0.594756i) q^{28} +(2.58027 + 1.87468i) q^{29} -1.00000 q^{30} +(4.38497 - 3.43104i) q^{31} +1.00000 q^{32} +(0.838547 + 0.609240i) q^{33} +(-1.07551 - 0.478847i) q^{34} +(-0.451864 - 1.39070i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.71929 - 6.44200i) q^{37} +(-4.61045 + 5.12042i) q^{38} +(0.714888 - 2.20020i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(3.43349 - 1.52869i) q^{41} +(-1.43031 - 0.304022i) q^{42} +(-0.199669 + 1.89973i) q^{43} +(0.108344 + 1.03082i) q^{44} +(0.978148 - 0.207912i) q^{45} +(4.25234 - 3.08950i) q^{46} +(-0.374839 + 0.272336i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(0.508195 + 4.83515i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(1.15156 + 0.244772i) q^{51} +(2.11342 - 0.940955i) q^{52} +(-2.94892 - 3.27510i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.693554 - 0.770270i) q^{55} +(-0.731132 - 1.26636i) q^{56} +(3.44510 - 5.96709i) q^{57} +(-0.985576 - 3.03329i) q^{58} +(-6.65183 - 2.96159i) q^{59} +(0.809017 + 0.587785i) q^{60} +7.09221 q^{61} +(-5.56423 + 0.198351i) q^{62} +1.46226 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.11342 - 0.940955i) q^{65} +(-0.320296 - 0.985771i) q^{66} +(3.51170 - 6.08245i) q^{67} +(0.588645 + 1.01956i) q^{68} +(-3.51707 + 3.90610i) q^{69} +(-0.451864 + 1.39070i) q^{70} +(10.8407 + 12.0398i) q^{71} +(0.913545 - 0.406737i) q^{72} +(10.0440 + 2.13493i) q^{73} +(-0.777544 + 7.39784i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(6.73964 - 1.43255i) q^{76} +(1.22618 - 0.890870i) q^{77} +(-1.87160 + 1.35980i) q^{78} +(3.80512 - 0.808803i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-3.67630 - 0.781421i) q^{82} +(5.72445 - 2.54869i) q^{83} +(0.978446 + 1.08667i) q^{84} +(0.363803 - 1.11967i) q^{85} +(1.27817 - 1.41955i) q^{86} +(1.59470 + 2.76209i) q^{87} +(0.518250 - 0.897636i) q^{88} +(-2.27442 - 6.99995i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(-2.73678 - 1.98838i) q^{91} -5.25618 q^{92} +(5.40140 - 1.35089i) q^{93} +0.463327 q^{94} +(-5.57429 - 4.04996i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-4.37633 - 13.4690i) q^{97} +(2.43089 - 4.21043i) q^{98} +(0.518250 + 0.897636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.978446	−	1.08667i	0.369818	−	0.410724i	−0.529297	−	0.848436i	$-0.677544\pi$
$7$	0.978446	−	1.08667i	0.369818	−	0.410724i	0.899115	+	0.437712i	$0.144211\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.913545	+	0.406737i	−0.288888	+	0.128621i
$11$	1.01385	+	0.215501i	0.305688	+	0.0649759i	0.358202	−	0.933644i	$-0.383390\pi$
$11$	1.01385	+	0.215501i	0.305688	+	0.0649759i	−0.0525140	+	0.998620i	$0.516723\pi$
$12$	−0.104528	+	0.994522i	−0.0301748	+	0.287094i
$13$	−0.241819	−	2.30075i	−0.0670685	−	0.638114i	−0.975488	−	0.220054i	$-0.929377\pi$
$13$	−0.241819	−	2.30075i	−0.0670685	−	0.638114i	0.908419	−	0.418060i	$-0.137290\pi$
$14$	−1.43031	+	0.304022i	−0.382266	+	0.0812532i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.15156	−	0.244772i	0.279295	−	0.0593660i	−0.0661343	−	0.997811i	$-0.521067\pi$
$17$	1.15156	−	0.244772i	0.279295	−	0.0593660i	0.345429	+	0.938445i	$0.387733\pi$
$18$	−0.104528	−	0.994522i	−0.0246376	−	0.234411i
$19$	0.720222	−	6.85246i	0.165230	−	1.57206i	−0.526671	−	0.850069i	$-0.676560\pi$
$19$	0.720222	−	6.85246i	0.165230	−	1.57206i	0.691901	−	0.721992i	$-0.256773\pi$
$20$	0.978148	+	0.207912i	0.218720	+	0.0464905i
$21$	1.33584	−	0.594756i	0.291505	−	0.129786i
$22$	−0.693554	−	0.770270i	−0.147866	−	0.164222i
$23$	−1.62425	+	4.99892i	−0.338679	+	1.04235i	0.626202	+	0.779661i	$0.284609\pi$
$23$	−1.62425	+	4.99892i	−0.338679	+	1.04235i	−0.964881	+	0.262687i	$0.915391\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.15671	+	2.00349i	−0.226850	+	0.392916i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.33584	+	0.594756i	0.252451	+	0.112398i
$29$	2.58027	+	1.87468i	0.479145	+	0.348119i	0.800994	−	0.598672i	$-0.204305\pi$
$29$	2.58027	+	1.87468i	0.479145	+	0.348119i	−0.321850	+	0.946791i	$0.604305\pi$
$30$	−1.00000			−0.182574
$31$	4.38497	−	3.43104i	0.787564	−	0.616233i
$31$	4.38497	−	3.43104i	0.787564	−	0.616233i
$32$	1.00000			0.176777
$33$	0.838547	+	0.609240i	0.145972	+	0.106055i
$34$	−1.07551	−	0.478847i	−0.184448	−	0.0821216i
$35$	−0.451864	−	1.39070i	−0.0763790	−	0.235071i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.71929	−	6.44200i	−0.611448	−	1.05906i	−0.990997	−	0.133887i	$-0.957254\pi$
$37$	−3.71929	−	6.44200i	−0.611448	−	1.05906i	0.379549	−	0.925172i	$-0.376079\pi$
$38$	−4.61045	+	5.12042i	−0.747913	+	0.830642i
$39$	0.714888	−	2.20020i	0.114474	−	0.352314i
$40$	−0.669131	−	0.743145i	−0.105799	−	0.117502i
$41$	3.43349	−	1.52869i	0.536222	−	0.238741i	−0.120715	−	0.992687i	$-0.538519\pi$
$41$	3.43349	−	1.52869i	0.536222	−	0.238741i	0.656936	+	0.753946i	$0.271852\pi$
$42$	−1.43031	−	0.304022i	−0.220702	−	0.0469116i
$43$	−0.199669	+	1.89973i	−0.0304493	+	0.289705i	0.968692	+	0.248267i	$0.0798609\pi$
$43$	−0.199669	+	1.89973i	−0.0304493	+	0.289705i	−0.999141	+	0.0414390i	$0.986806\pi$
$44$	0.108344	+	1.03082i	0.0163334	+	0.155402i
$45$	0.978148	−	0.207912i	0.145814	−	0.0309936i
$46$	4.25234	−	3.08950i	0.626973	−	0.455523i
$47$	−0.374839	+	0.272336i	−0.0546759	+	0.0397244i	−0.614788	−	0.788693i	$-0.710758\pi$
$47$	−0.374839	+	0.272336i	−0.0546759	+	0.0397244i	0.560112	+	0.828417i	$0.310758\pi$
$48$	−0.978148	+	0.207912i	−0.141183	+	0.0300095i
$49$	0.508195	+	4.83515i	0.0725993	+	0.690736i
$50$	−0.104528	+	0.994522i	−0.0147826	+	0.140647i
$51$	1.15156	+	0.244772i	0.161251	+	0.0342750i
$52$	2.11342	−	0.940955i	0.293079	−	0.130487i
$53$	−2.94892	−	3.27510i	−0.405065	−	0.449870i	0.505753	−	0.862678i	$-0.331215\pi$
$53$	−2.94892	−	3.27510i	−0.405065	−	0.449870i	−0.910818	+	0.412808i	$0.864548\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.693554	−	0.770270i	0.0935189	−	0.103863i
$56$	−0.731132	−	1.26636i	−0.0977016	−	0.169224i
$57$	3.44510	−	5.96709i	0.456315	−	0.790361i
$58$	−0.985576	−	3.03329i	−0.129413	−	0.398291i
$59$	−6.65183	−	2.96159i	−0.865995	−	0.385566i	−0.0748500	−	0.997195i	$-0.523848\pi$
$59$	−6.65183	−	2.96159i	−0.865995	−	0.385566i	−0.791145	+	0.611629i	$0.790514\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	7.09221			0.908065			0.454032	−	0.890985i	$-0.349985\pi$
$61$	7.09221			0.908065			0.454032	+	0.890985i	$0.349985\pi$
$62$	−5.56423	+	0.198351i	−0.706658	+	0.0251906i
$63$	1.46226			0.184228
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.11342	−	0.940955i	−0.262138	−	0.116711i
$66$	−0.320296	−	0.985771i	−0.0394258	−	0.121340i
$67$	3.51170	−	6.08245i	0.429023	−	0.743089i	−0.567764	−	0.823191i	$-0.692191\pi$
$67$	3.51170	−	6.08245i	0.429023	−	0.743089i	0.996787	+	0.0801022i	$0.0255247\pi$
$68$	0.588645	+	1.01956i	0.0713837	+	0.123640i
$69$	−3.51707	+	3.90610i	−0.423405	+	0.470239i
$70$	−0.451864	+	1.39070i	−0.0540081	+	0.166220i
$71$	10.8407	+	12.0398i	1.28656	+	1.42887i	0.847849	+	0.530238i	$0.177897\pi$
$71$	10.8407	+	12.0398i	1.28656	+	1.42887i	0.438709	+	0.898629i	$0.355436\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	10.0440	+	2.13493i	1.17557	+	0.249874i	0.753969	−	0.656910i	$-0.228137\pi$
$73$	10.0440	+	2.13493i	1.17557	+	0.249874i	0.421596	+	0.906784i	$0.361470\pi$
$74$	−0.777544	+	7.39784i	−0.0903876	+	0.859981i
$75$	−0.104528	−	0.994522i	−0.0120699	−	0.114837i
$76$	6.73964	−	1.43255i	0.773089	−	0.164325i
$77$	1.22618	−	0.890870i	0.139736	−	0.101524i
$78$	−1.87160	+	1.35980i	−0.211917	+	0.153967i
$79$	3.80512	−	0.808803i	0.428110	−	0.0909975i	0.0111825	−	0.999937i	$-0.496440\pi$
$79$	3.80512	−	0.808803i	0.428110	−	0.0909975i	0.416927	+	0.908940i	$0.363107\pi$
$80$	0.104528	+	0.994522i	0.0116866	+	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−3.67630	−	0.781421i	−0.405979	−	0.0862935i
$83$	5.72445	−	2.54869i	0.628340	−	0.279755i	−0.0677578	−	0.997702i	$-0.521585\pi$
$83$	5.72445	−	2.54869i	0.628340	−	0.279755i	0.696098	+	0.717947i	$0.254918\pi$
$84$	0.978446	+	1.08667i	0.106757	+	0.118566i
$85$	0.363803	−	1.11967i	0.0394599	−	0.121445i
$86$	1.27817	−	1.41955i	0.137828	−	0.153074i
$87$	1.59470	+	2.76209i	0.170969	+	0.296128i
$88$	0.518250	−	0.897636i	0.0552457	−	0.0956883i
$89$	−2.27442	−	6.99995i	−0.241088	−	0.741993i	−0.996255	−	0.0864607i	$-0.972444\pi$
$89$	−2.27442	−	6.99995i	−0.241088	−	0.741993i	0.755167	−	0.655532i	$-0.227556\pi$
$90$	−0.913545	−	0.406737i	−0.0962961	−	0.0428738i
$91$	−2.73678	−	1.98838i	−0.286892	−	0.208439i
$92$	−5.25618			−0.547995
$93$	5.40140	−	1.35089i	0.560099	−	0.140080i
$94$	0.463327			0.0477885
$95$	−5.57429	−	4.04996i	−0.571910	−	0.415517i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−4.37633	−	13.4690i	−0.444349	−	1.36757i	−0.883196	−	0.469004i	$-0.844613\pi$
$97$	−4.37633	−	13.4690i	−0.444349	−	1.36757i	0.438847	−	0.898562i	$-0.355387\pi$
$98$	2.43089	−	4.21043i	0.245557	−	0.425317i
$99$	0.518250	+	0.897636i	0.0520861	+	0.0902158i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	−1.18945	+	3.66075i	−0.118355	+	0.364258i	−0.992632	−	0.121169i	$-0.961336\pi$
$101$	−1.18945	+	3.66075i	−0.118355	+	0.364258i	0.874277	+	0.485427i	$0.161336\pi$
$102$	−0.787761	−	0.874897i	−0.0779999	−	0.0866277i
$103$	−4.91037	+	2.18624i	−0.483833	+	0.215416i	−0.634133	−	0.773224i	$-0.718643\pi$
$103$	−4.91037	+	2.18624i	−0.483833	+	0.215416i	0.150300	+	0.988640i	$0.451976\pi$
$104$	−2.26287	−	0.480988i	−0.221893	−	0.0471648i
$105$	0.152848	−	1.45425i	0.0149165	−	0.141921i
$106$	0.460666	+	4.38294i	0.0447438	+	0.425709i
$107$	−11.9272	+	2.53522i	−1.15305	+	0.245088i	−0.744484	−	0.667640i	$-0.767305\pi$
$107$	−11.9272	+	2.53522i	−1.15305	+	0.245088i	−0.408566	+	0.912729i	$0.633971\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−2.26384	+	1.64478i	−0.216837	+	0.157541i	−0.690902	−	0.722949i	$-0.742786\pi$
$109$	−2.26384	+	1.64478i	−0.216837	+	0.157541i	0.474065	+	0.880490i	$0.342786\pi$
$110$	−1.01385	+	0.215501i	−0.0966669	+	0.0205472i
$111$	−0.777544	−	7.39784i	−0.0738012	−	0.702171i
$112$	−0.152848	+	1.45425i	−0.0144428	+	0.137414i
$113$	0.113254	+	0.0240729i	0.0106540	+	0.00226458i	0.213236	−	0.977001i	$-0.431600\pi$
$113$	0.113254	+	0.0240729i	0.0106540	+	0.00226458i	−0.202582	+	0.979265i	$0.564933\pi$
$114$	−6.29451	+	2.80250i	−0.589535	+	0.262478i
$115$	3.51707	+	3.90610i	0.327968	+	0.364246i
$116$	−0.985576	+	3.03329i	−0.0915085	+	0.281634i
$117$	1.54798	−	1.71921i	0.143111	−	0.158941i
$118$	3.64067	+	6.30582i	0.335151	+	0.580498i
$119$	0.860754	−	1.49087i	0.0789052	−	0.136668i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	−9.06755	−	4.03713i	−0.824322	−	0.367012i
$122$	−5.73772	−	4.16870i	−0.519469	−	0.377416i
$123$	3.75843			0.338886
$124$	4.61814	+	3.11010i	0.414722	+	0.279295i
$125$	−1.00000			−0.0894427
$126$	−1.18300	−	0.859497i	−0.105390	−	0.0765701i
$127$	−4.36548	−	1.94364i	−0.387374	−	0.172470i	0.203803	−	0.979012i	$-0.434670\pi$
$127$	−4.36548	−	1.94364i	−0.387374	−	0.172470i	−0.591177	+	0.806542i	$0.701337\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.955095	+	1.65427i	−0.0840914	+	0.145651i
$130$	1.15671	+	2.00349i	0.101450	+	0.175717i
$131$	−5.48301	+	6.08950i	−0.479053	+	0.532042i	−0.933426	−	0.358769i	$-0.883197\pi$
$131$	−5.48301	+	6.08950i	−0.479053	+	0.532042i	0.454373	+	0.890811i	$0.349863\pi$
$132$	−0.320296	+	0.985771i	−0.0278782	+	0.0858003i
$133$	−6.74169	−	7.48741i	−0.584579	−	0.649240i
$134$	−6.41620	+	2.85668i	−0.554275	+	0.246779i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	0.123060	−	1.17084i	0.0105523	−	0.100399i
$137$	0.000119774		0.00113958i	1.02330e−5		9.73605e-5i	0.994527	−	0.104480i	$-0.0333178\pi$
$137$	0.000119774		0.00113958i	1.02330e−5		9.73605e-5i	−0.994517	+	0.104577i	$0.966651\pi$
$138$	5.14132	−	1.09282i	0.437658	−	0.0930271i
$139$	10.6351	−	7.72689i	0.902061	−	0.655386i	−0.0369332	−	0.999318i	$-0.511759\pi$
$139$	10.6351	−	7.72689i	0.902061	−	0.655386i	0.938995	+	0.343932i	$0.111759\pi$
$140$	1.18300	−	0.859497i	0.0999815	−	0.0726408i
$141$	−0.453202	+	0.0963310i	−0.0381665	+	0.00811253i
$142$	−1.69349	−	16.1125i	−0.142114	−	1.35213i
$143$	0.250646	−	2.38473i	0.0209600	−	0.199421i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	2.91365	−	1.29724i	0.241966	−	0.107730i
$146$	−6.87092	−	7.63093i	−0.568641	−	0.631540i
$147$	−1.50237	+	4.62383i	−0.123914	+	0.381367i
$148$	4.97738	−	5.52795i	0.409138	−	0.454394i
$149$	6.91077	+	11.9698i	0.566153	+	0.980605i	0.996941	+	0.0781522i	$0.0249020\pi$
$149$	6.91077	+	11.9698i	0.566153	+	0.980605i	−0.430789	+	0.902453i	$0.641765\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	6.17926	+	19.0178i	0.502861	+	1.54765i	0.804337	+	0.594173i	$0.202520\pi$
$151$	6.17926	+	19.0178i	0.502861	+	1.54765i	−0.301477	+	0.953474i	$0.597480\pi$
$152$	−6.29451	−	2.80250i	−0.510553	−	0.227313i
$153$	0.952448	+	0.691994i	0.0770008	+	0.0559444i
$154$	−1.51564			−0.122134
$155$	−0.778885	−	5.51302i	−0.0625616	−	0.442816i
$156$	2.31343			0.185222
$157$	−9.03377	−	6.56342i	−0.720973	−	0.523818i	0.165722	−	0.986173i	$-0.447005\pi$
$157$	−9.03377	−	6.56342i	−0.720973	−	0.523818i	−0.886695	+	0.462355i	$0.847005\pi$
$158$	−3.55381	−	1.58226i	−0.282726	−	0.125878i
$159$	−1.36186	−	4.19139i	−0.108003	−	0.332399i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	3.84296	+	6.65620i	0.302868	+	0.524582i
$162$	0.669131	−	0.743145i	0.0525719	−	0.0583870i
$163$	−3.76598	+	11.5905i	−0.294974	+	0.907837i	0.688256	+	0.725468i	$0.258377\pi$
$163$	−3.76598	+	11.5905i	−0.294974	+	0.907837i	−0.983230	+	0.182369i	$0.941623\pi$
$164$	2.51488	+	2.79306i	0.196379	+	0.218101i
$165$	0.946891	−	0.421583i	0.0737153	−	0.0328202i
$166$	−6.12926	−	1.30281i	−0.475723	−	0.101118i
$167$	−0.0984623	+	0.936806i	−0.00761924	+	0.0724922i	−0.997671	−	0.0682129i	$-0.978270\pi$
$167$	−0.0984623	+	0.936806i	−0.00761924	+	0.0724922i	0.990052	+	0.140705i	$0.0449370\pi$
$168$	−0.152848	−	1.45425i	−0.0117925	−	0.112198i
$169$	7.48093	−	1.59012i	0.575456	−	0.122317i
$170$	−0.952448	+	0.691994i	−0.0730494	+	0.0530735i
$171$	5.57429	−	4.04996i	0.426277	−	0.309708i
$172$	−1.86845	+	0.397151i	−0.142468	+	0.0302825i
$173$	0.579226	+	5.51097i	0.0440378	+	0.418991i	0.994225	+	0.107313i	$0.0342246\pi$
$173$	0.579226	+	5.51097i	0.0440378	+	0.418991i	−0.950188	+	0.311679i	$0.899109\pi$
$174$	0.333382	−	3.17192i	0.0252736	−	0.240463i
$175$	−1.43031	−	0.304022i	−0.108121	−	0.0229819i
$176$	−0.946891	+	0.421583i	−0.0713746	+	0.0317780i
$177$	−4.87216	−	5.41109i	−0.366214	−	0.406722i
$178$	−2.27442	+	6.99995i	−0.170475	+	0.524668i
$179$	−7.35727	+	8.17108i	−0.549908	+	0.610735i	−0.952461	−	0.304662i	$-0.901457\pi$
$179$	−7.35727	+	8.17108i	−0.549908	+	0.610735i	0.402552	+	0.915397i	$0.368123\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−3.71130	+	6.42817i	−0.275859	+	0.477802i	−0.970351	−	0.241698i	$-0.922296\pi$
$181$	−3.71130	+	6.42817i	−0.275859	+	0.477802i	0.694492	+	0.719500i	$0.255629\pi$
$182$	1.04536	+	3.21727i	0.0774869	+	0.238480i
$183$	6.47906	+	2.88466i	0.478946	+	0.213240i
$184$	4.25234	+	3.08950i	0.313487	+	0.227761i
$185$	−7.43858			−0.546896
$186$	−5.16385	−	2.08197i	−0.378632	−	0.152658i
$187$	1.22026			0.0892344
$188$	−0.374839	−	0.272336i	−0.0273379	−	0.0198622i
$189$	1.33584	+	0.594756i	0.0971684	+	0.0432622i
$190$	2.12919	+	6.55297i	0.154468	+	0.475403i
$191$	−1.69842	+	2.94175i	−0.122893	+	0.212857i	−0.920907	−	0.389781i	$-0.872551\pi$
$191$	−1.69842	+	2.94175i	−0.122893	+	0.212857i	0.798014	+	0.602639i	$0.205884\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.2848	+	13.6437i	−0.884281	+	0.982093i	−0.999937	−	0.0111961i	$-0.996436\pi$
$193$	−12.2848	+	13.6437i	−0.884281	+	0.982093i	0.115657	+	0.993289i	$0.463103\pi$
$194$	−4.37633	+	13.4690i	−0.314202	+	0.967015i
$195$	−1.54798	−	1.71921i	−0.110853	−	0.123115i
$196$	−4.44146	+	1.97747i	−0.317247	+	0.141248i
$197$	−17.4221	−	3.70318i	−1.24127	−	0.263840i	−0.459936	−	0.887952i	$-0.652128\pi$
$197$	−17.4221	−	3.70318i	−1.24127	−	0.263840i	−0.781335	+	0.624111i	$0.785461\pi$
$198$	0.108344	−	1.03082i	0.00769966	−	0.0732574i
$199$	1.53343	+	14.5896i	0.108702	+	1.03423i	0.903861	+	0.427826i	$0.140721\pi$
$199$	1.53343	+	14.5896i	0.108702	+	1.03423i	−0.795159	+	0.606401i	$0.792613\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	5.68205	−	4.12825i	0.400781	−	0.291185i
$202$	3.11402	−	2.26247i	0.219102	−	0.159187i
$203$	4.56182	−	0.969645i	0.320177	−	0.0680557i
$204$	0.123060	+	1.17084i	0.00861595	+	0.0819752i
$205$	0.392863	−	3.73784i	0.0274387	−	0.261062i
$206$	5.25761	+	1.11754i	0.366315	+	0.0778627i
$207$	−4.80176	+	2.13788i	−0.333745	+	0.148593i
$208$	1.54798	+	1.71921i	0.107333	+	0.119206i
$209$	2.20691	−	6.79216i	0.152655	−	0.469824i
$210$	−0.978446	+	1.08667i	−0.0675192	+	0.0749876i
$211$	10.6591	+	18.4621i	0.733803	+	1.27098i	0.955247	+	0.295810i	$0.0955897\pi$
$211$	10.6591	+	18.4621i	0.733803	+	1.27098i	−0.221444	+	0.975173i	$0.571077\pi$
$212$	2.20354	−	3.81665i	0.151340	−	0.262128i
$213$	5.00645	+	15.4083i	0.343036	+	1.05576i
$214$	11.1395	+	4.95963i	0.761481	+	0.339033i
$215$	1.54538	+	1.12278i	0.105394	+	0.0765731i
$216$	1.00000			0.0680414
$217$	0.562030	−	8.12212i	0.0381531	−	0.551365i
$218$	2.79826			0.189522
$219$	8.30733	+	6.03563i	0.561357	+	0.407850i
$220$	0.946891	+	0.421583i	0.0638394	+	0.0284231i
$221$	−0.841631	−	2.59027i	−0.0566142	−	0.174241i
$222$	−3.71929	+	6.44200i	−0.249623	+	0.432359i
$223$	2.12146	+	3.67447i	0.142063	+	0.246061i	0.928273	−	0.371898i	$-0.121293\pi$
$223$	2.12146	+	3.67447i	0.142063	+	0.246061i	−0.786210	+	0.617959i	$0.787960\pi$
$224$	0.978446	−	1.08667i	0.0653752	−	0.0726065i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−0.0774747	−	0.0860443i	−0.00515354	−	0.00572358i
$227$	−4.25352	+	1.89379i	−0.282316	+	0.125695i	−0.543010	−	0.839726i	$-0.682715\pi$
$227$	−4.25352	+	1.89379i	−0.282316	+	0.125695i	0.260694	+	0.965422i	$0.416049\pi$
$228$	6.73964	+	1.43255i	0.446343	+	0.0948732i
$229$	1.28059	−	12.1840i	0.0846237	−	0.805141i	−0.867089	−	0.498152i	$-0.834012\pi$
$229$	1.28059	−	12.1840i	0.0846237	−	0.805141i	0.951713	−	0.306989i	$-0.0993214\pi$
$230$	−0.549420	−	5.22738i	−0.0362277	−	0.344684i
$231$	1.48252	−	0.315119i	0.0975425	−	0.0207333i
$232$	2.58027	−	1.87468i	0.169403	−	0.123079i
$233$	−14.7408	+	10.7098i	−0.965700	+	0.701622i	−0.954467	−	0.298315i	$-0.903575\pi$
$233$	−14.7408	+	10.7098i	−0.965700	+	0.701622i	−0.0112323	+	0.999937i	$0.503575\pi$
$234$	−2.26287	+	0.480988i	−0.147929	+	0.0314432i
$235$	0.0484308	+	0.460788i	0.00315928	+	0.0300585i
$236$	0.761107	−	7.24145i	0.0495438	−	0.471378i
$237$	3.80512	+	0.808803i	0.247169	+	0.0525374i
$238$	−1.57268	+	0.700201i	−0.101941	+	0.0453873i
$239$	19.0318	+	21.1370i	1.23107	+	1.36724i	0.906959	+	0.421219i	$0.138398\pi$
$239$	19.0318	+	21.1370i	1.23107	+	1.36724i	0.324109	+	0.946020i	$0.394936\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−9.41005	+	10.4509i	−0.606154	+	0.673203i	−0.965621	−	0.259956i	$-0.916292\pi$
$241$	−9.41005	+	10.4509i	−0.606154	+	0.673203i	0.359466	+	0.933158i	$0.382959\pi$
$242$	4.96283	+	8.59588i	0.319023	+	0.552564i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.19161	+	6.74509i	0.140304	+	0.431810i
$245$	4.44146	+	1.97747i	0.283754	+	0.126336i
$246$	−3.04063	−	2.20915i	−0.193864	−	0.140850i
$247$	−15.9400			−1.01424
$248$	−1.90808	−	5.23060i	−0.121164	−	0.332144i
$249$	6.26619			0.397104
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	3.77380	+	1.68020i	0.238200	+	0.106054i	0.522365	−	0.852722i	$-0.325050\pi$
$251$	3.77380	+	1.68020i	0.238200	+	0.106054i	−0.284165	+	0.958775i	$0.591716\pi$
$252$	0.451864	+	1.39070i	0.0284648	+	0.0876056i
$253$	−2.72402	+	4.71814i	−0.171257	+	0.296627i
$254$	2.38931	+	4.13840i	0.149919	+	0.259667i
$255$	0.787761	−	0.874897i	0.0493315	−	0.0547882i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.04596	+	8.93594i	0.501893	+	0.557409i	0.939850	−	0.341587i	$-0.110964\pi$
$257$	8.04596	+	8.93594i	0.501893	+	0.557409i	−0.437957	+	0.898996i	$0.644298\pi$
$258$	1.74505	−	0.776944i	0.108642	−	0.0483704i
$259$	−10.6395	−	2.26149i	−0.661105	−	0.140522i
$260$	0.241819	−	2.30075i	0.0149970	−	0.142687i
$261$	0.333382	+	3.17192i	0.0206358	+	0.196337i
$262$	8.01517	−	1.70368i	0.495179	−	0.105253i
$263$	−16.4211	+	11.9306i	−1.01257	+	0.735674i	−0.964746	−	0.263181i	$-0.915228\pi$
$263$	−16.4211	+	11.9306i	−1.01257	+	0.735674i	−0.0478226	+	0.998856i	$0.515228\pi$
$264$	0.838547	−	0.609240i	0.0516090	−	0.0374961i
$265$	−4.31078	+	0.916285i	−0.264809	+	0.0562869i
$266$	1.05316	+	10.0201i	0.0645731	+	0.614372i
$267$	0.769348	−	7.31986i	0.0470834	−	0.447968i
$268$	6.86993	+	1.46025i	0.419648	+	0.0891989i
$269$	−7.58179	+	3.37563i	−0.462270	+	0.205816i	−0.624638	−	0.780914i	$-0.714754\pi$
$269$	−7.58179	+	3.37563i	−0.462270	+	0.205816i	0.162368	+	0.986730i	$0.448087\pi$
$270$	−0.669131	−	0.743145i	−0.0407220	−	0.0452264i
$271$	−5.71392	+	17.5856i	−0.347096	+	1.06825i	0.613356	+	0.789807i	$0.289819\pi$
$271$	−5.71392	+	17.5856i	−0.347096	+	1.06825i	−0.960452	+	0.278445i	$0.910181\pi$
$272$	−0.787761	+	0.874897i	−0.0477650	+	0.0530484i
$273$	−1.69142	−	2.92963i	−0.102369	−	0.177309i
$274$	0.000572926	0	0.000992337i	3.46117e−5	0	5.99493e-5i
$275$	−0.320296	−	0.985771i	−0.0193146	−	0.0594442i
$276$	−4.80176	−	2.13788i	−0.289032	−	0.128685i
$277$	7.94071	+	5.76926i	0.477111	+	0.346641i	0.800206	−	0.599725i	$-0.204723\pi$
$277$	7.94071	+	5.76926i	0.477111	+	0.346641i	−0.323095	+	0.946366i	$0.604723\pi$
$278$	−13.1458			−0.788431
$279$	5.48388	+	0.962852i	0.328311	+	0.0576444i
$280$	−1.46226			−0.0873870
$281$	−13.9725	−	10.1516i	−0.833530	−	0.605595i	0.0870255	−	0.996206i	$-0.472264\pi$
$281$	−13.9725	−	10.1516i	−0.833530	−	0.605595i	−0.920556	+	0.390611i	$0.872264\pi$
$282$	0.423270	+	0.188452i	0.0252054	+	0.0112221i
$283$	−3.15294	−	9.70374i	−0.187423	−	0.576828i	0.812559	−	0.582879i	$-0.198074\pi$
$283$	−3.15294	−	9.70374i	−0.187423	−	0.576828i	−0.999982	+	0.00605132i	$0.998074\pi$
$284$	−8.10061	+	14.0307i	−0.480683	+	0.832567i
$285$	−3.44510	−	5.96709i	−0.204070	−	0.353460i
$286$	−1.60449	+	1.78196i	−0.0948753	+	0.105370i
$287$	1.69830	−	5.22683i	0.100247	−	0.308530i
$288$	0.669131	+	0.743145i	0.0394289	+	0.0437902i
$289$	−14.2641	+	6.35078i	−0.839064	+	0.373575i
$290$	−3.11970	−	0.663112i	−0.183195	−	0.0389393i
$291$	1.48034	−	14.0845i	0.0867792	−	0.825649i
$292$	1.07334	+	10.2122i	0.0628126	+	0.597622i
$293$	14.9610	−	3.18007i	0.874033	−	0.185782i	0.251010	−	0.967985i	$-0.419237\pi$
$293$	14.9610	−	3.18007i	0.874033	−	0.185782i	0.623024	+	0.782203i	$0.285904\pi$
$294$	3.93327	−	2.85768i	0.229393	−	0.166664i
$295$	−5.89072	+	4.27986i	−0.342971	+	0.249183i
$296$	−7.27603	+	1.54657i	−0.422911	+	0.0898925i
$297$	0.108344	+	1.03082i	0.00628675	+	0.0598144i
$298$	1.44474	−	13.7458i	0.0836918	−	0.796275i
$299$	11.8941	+	2.52816i	0.687851	+	0.146207i
$300$	0.913545	−	0.406737i	0.0527436	−	0.0234830i
$301$	1.86902	+	2.07575i	0.107728	+	0.119644i
$302$	6.17926	−	19.0178i	0.355576	−	1.09435i
$303$	−2.57558	+	2.86047i	−0.147963	+	0.164330i
$304$	3.44510	+	5.96709i	0.197590	+	0.342236i
$305$	3.54611	−	6.14203i	0.203049	−	0.351692i
$306$	−0.363803	−	1.11967i	−0.0207972	−	0.0640072i
$307$	−23.2496	−	10.3514i	−1.32692	−	0.590784i	−0.383858	−	0.923392i	$-0.625405\pi$
$307$	−23.2496	−	10.3514i	−1.32692	−	0.590784i	−0.943065	+	0.332608i	$0.892072\pi$
$308$	1.22618	+	0.890870i	0.0698679	+	0.0507620i
$309$	−5.37507			−0.305777
$310$	−2.61034	+	4.91794i	−0.148257	+	0.279320i
$311$	16.8818			0.957278			0.478639	−	0.878012i	$-0.341130\pi$
$311$	16.8818			0.957278			0.478639	+	0.878012i	$0.341130\pi$
$312$	−1.87160	−	1.35980i	−0.105959	−	0.0769834i
$313$	10.4031	+	4.63174i	0.588016	+	0.261801i	0.679105	−	0.734041i	$-0.262368\pi$
$313$	10.4031	+	4.63174i	0.588016	+	0.261801i	−0.0910892	+	0.995843i	$0.529035\pi$
$314$	3.45059	+	10.6198i	0.194728	+	0.599312i
$315$	0.731132	−	1.26636i	0.0411946	−	0.0713512i
$316$	1.94506	+	3.36895i	0.109418	+	0.189518i
$317$	−13.1651	+	14.6213i	−0.739426	+	0.821216i	−0.989120	−	0.147109i	$-0.953003\pi$
$317$	−13.1651	+	14.6213i	−0.739426	+	0.821216i	0.249694	+	0.968325i	$0.419670\pi$
$318$	−1.36186	+	4.19139i	−0.0763696	+	0.235041i
$319$	2.21202	+	2.45669i	0.123849	+	0.137548i
$320$	−0.913545	+	0.406737i	−0.0510687	+	0.0227373i
$321$	−11.9272	−	2.53522i	−0.665714	−	0.141502i
$322$	0.803398	−	7.64382i	0.0447716	−	0.425973i
$323$	−0.847911	−	8.06733i	−0.0471790	−	0.448878i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	−1.87160	+	1.35980i	−0.103818	+	0.0754280i
$326$	9.85946	−	7.16332i	0.546065	−	0.396740i
$327$	−2.73711	+	0.581791i	−0.151363	+	0.0321731i
$328$	−0.392863	−	3.73784i	−0.0216922	−	0.206388i
$329$	−0.0708186	+	0.673794i	−0.00390436	+	0.0371475i
$330$	−1.01385	−	0.215501i	−0.0558107	−	0.0118629i
$331$	−0.401605	+	0.178806i	−0.0220742	+	0.00982808i	−0.417744	−	0.908565i	$-0.637179\pi$
$331$	−0.401605	+	0.178806i	−0.0220742	+	0.00982808i	0.395670	+	0.918393i	$0.370512\pi$
$332$	4.19290	+	4.65669i	0.230115	+	0.255569i
$333$	2.29865	−	7.07451i	0.125965	−	0.387681i
$334$	0.630299	−	0.700017i	0.0344884	−	0.0383033i
$335$	−3.51170	−	6.08245i	−0.191865	−	0.332320i
$336$	−0.731132	+	1.26636i	−0.0398865	+	0.0690855i
$337$	−8.56716	−	26.3670i	−0.466683	−	1.43630i	−0.856854	−	0.515560i	$-0.827584\pi$
$337$	−8.56716	−	26.3670i	−0.466683	−	1.43630i	0.390171	−	0.920743i	$-0.372416\pi$
$338$	−6.98685	−	3.11074i	−0.380034	−	0.169202i
$339$	0.0936713	+	0.0680562i	0.00508753	+	0.00369630i
$340$	1.17729			0.0638475
$341$	5.18510	−	2.53360i	0.280789	−	0.137202i
$342$	−6.89020			−0.372580
$343$	14.0324	+	10.1952i	0.757681	+	0.550487i
$344$	1.74505	+	0.776944i	0.0940865	+	0.0418900i
$345$	1.62425	+	4.99892i	0.0874466	+	0.269133i
$346$	2.77066	−	4.79893i	0.148952	−	0.257992i
$347$	11.6978	+	20.2613i	0.627973	+	1.08768i	0.987958	+	0.154723i	$0.0494486\pi$
$347$	11.6978	+	20.2613i	0.627973	+	1.08768i	−0.359985	+	0.932958i	$0.617218\pi$
$348$	−2.13412	+	2.37018i	−0.114401	+	0.127055i
$349$	−3.19091	+	9.82062i	−0.170806	+	0.525686i	−0.999417	−	0.0341383i	$-0.989131\pi$
$349$	−3.19091	+	9.82062i	−0.170806	+	0.525686i	0.828611	+	0.559824i	$0.189131\pi$
$350$	0.978446	+	1.08667i	0.0523001	+	0.0580852i
$351$	2.11342	−	0.940955i	0.112806	−	0.0502245i
$352$	1.01385	+	0.215501i	0.0540384	+	0.0114862i
$353$	2.01965	−	19.2157i	0.107495	−	1.02275i	−0.799230	−	0.601025i	$-0.794759\pi$
$353$	2.01965	−	19.2157i	0.107495	−	1.02275i	0.906725	−	0.421722i	$-0.138574\pi$
$354$	0.761107	+	7.24145i	0.0404524	+	0.384879i
$355$	15.8472	−	3.36842i	0.841081	−	0.178777i
$356$	5.95451	−	4.32621i	0.315588	−	0.229288i
$357$	1.39273	−	1.01188i	0.0737111	−	0.0535542i
$358$	10.7550	−	2.28605i	0.568419	−	0.120821i
$359$	−1.83693	−	17.4772i	−0.0969494	−	0.922412i	−0.929589	−	0.368597i	$-0.879838\pi$
$359$	−1.83693	−	17.4772i	−0.0969494	−	0.922412i	0.832640	−	0.553815i	$-0.186828\pi$
$360$	0.104528	−	0.994522i	0.00550913	−	0.0524159i
$361$	−27.8527	−	5.92027i	−1.46593	−	0.311593i
$362$	6.78089	−	3.01905i	0.356396	−	0.158678i
$363$	−6.64157	−	7.37621i	−0.348592	−	0.387150i
$364$	1.04536	−	3.21727i	0.0547915	−	0.168631i
$365$	6.87092	−	7.63093i	0.359640	−	0.399421i
$366$	−3.54611	−	6.14203i	−0.185358	−	0.321049i
$367$	−8.08680	+	14.0067i	−0.422127	+	0.731146i	−0.996147	−	0.0876953i	$-0.972050\pi$
$367$	−8.08680	+	14.0067i	−0.422127	+	0.731146i	0.574020	+	0.818841i	$0.305383\pi$
$368$	−1.62425	−	4.99892i	−0.0846698	−	0.260587i
$369$	3.43349	+	1.52869i	0.178741	+	0.0795804i
$370$	6.01794	+	4.37229i	0.312858	+	0.227305i
$371$	−6.44432			−0.334573
$372$	2.95389	+	4.71959i	0.153152	+	0.244699i
$373$	15.0695			0.780270			0.390135	−	0.920758i	$-0.372428\pi$
$373$	15.0695			0.780270			0.390135	+	0.920758i	$0.372428\pi$
$374$	−0.987213	−	0.717252i	−0.0510476	−	0.0370882i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	0.143176	+	0.440650i	0.00738373	+	0.0227248i
$377$	3.68921	−	6.38990i	0.190004	−	0.329097i
$378$	−0.731132	−	1.26636i	−0.0376054	−	0.0651344i
$379$	−6.45485	+	7.16883i	−0.331563	+	0.368238i	−0.885757	−	0.464150i	$-0.846360\pi$
$379$	−6.45485	+	7.16883i	−0.331563	+	0.368238i	0.554194	+	0.832388i	$0.313027\pi$
$380$	2.12919	−	6.55297i	0.109225	−	0.336160i
$381$	−3.19752	−	3.55121i	−0.163814	−	0.181934i
$382$	3.10316	−	1.38162i	0.158772	−	0.0706897i
$383$	19.1440	+	4.06918i	0.978213	+	0.207926i	0.669159	−	0.743119i	$-0.266654\pi$
$383$	19.1440	+	4.06918i	0.978213	+	0.207926i	0.309054	+	0.951045i	$0.399988\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−0.158427	−	1.50734i	−0.00807420	−	0.0768209i
$386$	17.9582	−	3.81713i	0.914047	−	0.194287i
$387$	−1.54538	+	1.12278i	−0.0785559	+	0.0570742i
$388$	11.4574	−	8.32428i	0.581661	−	0.422601i
$389$	6.64056	−	1.41150i	0.336690	−	0.0715657i	−0.0364643	−	0.999335i	$-0.511610\pi$
$389$	6.64056	−	1.41150i	0.336690	−	0.0715657i	0.373154	+	0.927769i	$0.378276\pi$
$390$	0.241819	+	2.30075i	0.0122450	+	0.116503i
$391$	−0.646827	+	6.15415i	−0.0327114	+	0.311229i
$392$	4.75554	+	1.01082i	0.240191	+	0.0510542i
$393$	−7.48580	+	3.33289i	−0.377609	+	0.168122i
$394$	11.9181	+	13.2364i	0.600424	+	0.666839i
$395$	1.20212	−	3.69973i	0.0604850	−	0.186154i
$396$	−0.693554	+	0.770270i	−0.0348524	+	0.0387075i
$397$	−0.231824	−	0.401532i	−0.0116349	−	0.0201523i	0.860149	−	0.510042i	$-0.170370\pi$
$397$	−0.231824	−	0.401532i	−0.0116349	−	0.0201523i	−0.871784	+	0.489890i	$0.837037\pi$
$398$	7.33497	−	12.7045i	0.367669	−	0.636821i
$399$	−3.11344	−	9.58218i	−0.155867	−	0.479709i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	−25.6147	−	18.6102i	−1.27914	−	0.929349i	−0.279613	−	0.960113i	$-0.590206\pi$
$401$	−25.6147	−	18.6102i	−1.27914	−	0.929349i	−0.999527	+	0.0307636i	$0.990206\pi$
$402$	−7.02341			−0.350296
$403$	−8.95435	−	9.25904i	−0.446048	−	0.461226i
$404$	−3.84914			−0.191502
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−4.26053	−	1.89691i	−0.211447	−	0.0941421i
$407$	−2.38255	−	7.33274i	−0.118099	−	0.363470i
$408$	0.588645	−	1.01956i	0.0291423	−	0.0504759i
$409$	−17.5417	−	30.3831i	−0.867381	−	1.50235i	−0.864663	−	0.502352i	$-0.832468\pi$
$409$	−17.5417	−	30.3831i	−0.867381	−	1.50235i	−0.00271782	−	0.999996i	$-0.500865\pi$
$410$	−2.51488	+	2.79306i	−0.124201	+	0.137939i
$411$	−0.000354088		0.00108977i	−1.74659e−5		5.37544e-5i
$412$	−3.59662	−	3.99446i	−0.177193	−	0.196793i
$413$	−9.72673	+	4.33062i	−0.478621	+	0.213096i
$414$	5.14132	+	1.09282i	0.252682	+	0.0537092i
$415$	0.654996	−	6.23187i	0.0321525	−	0.305910i
$416$	−0.241819	−	2.30075i	−0.0118561	−	0.112804i
$417$	12.8585	−	2.73316i	0.629683	−	0.133843i
$418$	−5.77776	+	4.19779i	−0.282599	+	0.205320i
$419$	19.6819	−	14.2997i	0.961524	−	0.698588i	0.00801952	−	0.999968i	$-0.497447\pi$
$419$	19.6819	−	14.2997i	0.961524	−	0.698588i	0.953504	+	0.301380i	$0.0974473\pi$
$420$	1.43031	−	0.304022i	0.0697920	−	0.0148347i
$421$	−0.760126	−	7.23212i	−0.0370463	−	0.352472i	−0.997305	−	0.0733617i	$-0.976627\pi$
$421$	−0.760126	−	7.23212i	−0.0370463	−	0.352472i	0.960259	−	0.279110i	$-0.0900394\pi$
$422$	2.22836	−	21.2014i	0.108475	−	1.03207i
$423$	−0.453202	−	0.0963310i	−0.0220354	−	0.00468377i
$424$	−4.02607	+	1.79252i	−0.195523	+	0.0870526i
$425$	−0.787761	−	0.874897i	−0.0382120	−	0.0424387i
$426$	5.00645	−	15.4083i	0.242563	−	0.746533i
$427$	6.93934	−	7.70692i	0.335818	−	0.372964i
$428$	−6.09686	−	10.5601i	−0.294703	−	0.510440i
$429$	1.19893	−	2.07662i	0.0578851	−	0.100260i
$430$	−0.590281	−	1.81670i	−0.0284659	−	0.0876090i
$431$	−19.5641	−	8.71051i	−0.942370	−	0.419570i	−0.122724	−	0.992441i	$-0.539163\pi$
$431$	−19.5641	−	8.71051i	−0.942370	−	0.419570i	−0.819646	+	0.572870i	$0.805830\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−33.9025			−1.62925			−0.814626	−	0.579986i	$-0.803058\pi$
$433$	−33.9025			−1.62925			−0.814626	+	0.579986i	$0.803058\pi$
$434$	−5.22875	+	6.24058i	−0.250988	+	0.299557i
$435$	3.18939			0.152920
$436$	−2.26384	−	1.64478i	−0.108418	−	0.0787705i
$437$	33.0851	+	14.7304i	1.58267	+	0.704652i
$438$	−3.17312	−	9.76585i	−0.151617	−	0.466630i
$439$	−0.470443	+	0.814832i	−0.0224530	+	0.0388898i	−0.877034	−	0.480429i	$-0.840481\pi$
$439$	−0.470443	+	0.814832i	−0.0224530	+	0.0388898i	0.854581	+	0.519319i	$0.173814\pi$
$440$	−0.518250	−	0.897636i	−0.0247066	−	0.0427931i
$441$	−3.25317	+	3.61301i	−0.154913	+	0.172048i
$442$	−0.841631	+	2.59027i	−0.0400323	+	0.123207i
$443$	3.56250	+	3.95656i	0.169259	+	0.187982i	0.821807	−	0.569766i	$-0.192966\pi$
$443$	3.56250	+	3.95656i	0.169259	+	0.187982i	−0.652547	+	0.757748i	$0.726300\pi$
$444$	6.79549	−	3.02554i	0.322499	−	0.143586i
$445$	−7.19934	−	1.53027i	−0.341282	−	0.0725416i
$446$	0.443505	−	4.21967i	0.0210006	−	0.199807i
$447$	1.44474	+	13.7458i	0.0683341	+	0.650155i
$448$	−1.43031	+	0.304022i	−0.0675758	+	0.0143637i
$449$	19.7511	−	14.3500i	0.932112	−	0.677219i	−0.0143971	−	0.999896i	$-0.504583\pi$
$449$	19.7511	−	14.3500i	0.932112	−	0.677219i	0.946509	+	0.322677i	$0.104583\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	3.81048	−	0.809943i	0.179429	−	0.0381387i
$452$	0.0121027	+	0.115150i	0.000569265	+	0.00541619i
$453$	−2.09020	+	19.8870i	−0.0982063	+	0.934370i
$454$	4.55431	+	0.968048i	0.213744	+	0.0454328i
$455$	−3.09038	+	1.37593i	−0.144879	+	0.0645044i
$456$	−4.61045	−	5.12042i	−0.215904	−	0.239786i
$457$	6.21524	−	19.1286i	0.290737	−	0.894796i	−0.693883	−	0.720087i	$-0.744102\pi$
$457$	6.21524	−	19.1286i	0.290737	−	0.894796i	0.984620	−	0.174709i	$-0.0558983\pi$
$458$	−8.19759	+	9.10435i	−0.383048	+	0.425418i
$459$	0.588645	+	1.01956i	0.0274756	+	0.0475891i
$460$	−2.62809	+	4.55198i	−0.122535	+	0.212237i
$461$	−3.04689	−	9.37736i	−0.141908	−	0.436747i	0.854693	−	0.519134i	$-0.173746\pi$
$461$	−3.04689	−	9.37736i	−0.141908	−	0.436747i	−0.996600	+	0.0823873i	$0.973746\pi$
$462$	−1.38460	−	0.616466i	−0.0644176	−	0.0286806i
$463$	12.8645	+	9.34664i	0.597866	+	0.434375i	0.845121	−	0.534575i	$-0.179528\pi$
$463$	12.8645	+	9.34664i	0.597866	+	0.434375i	−0.247255	+	0.968951i	$0.579528\pi$
$464$	−3.18939			−0.148064
$465$	1.53080	−	5.35319i	0.0709891	−	0.248248i
$466$	18.2206			0.844053
$467$	2.96796	+	2.15635i	0.137341	+	0.0997839i	0.654334	−	0.756205i	$-0.272949\pi$
$467$	2.96796	+	2.15635i	0.137341	+	0.0997839i	−0.516994	+	0.855989i	$0.672949\pi$
$468$	2.11342	+	0.940955i	0.0976929	+	0.0434957i
$469$	−3.17363	−	9.76742i	−0.146545	−	0.451018i
$470$	0.231663	−	0.401253i	0.0106858	−	0.0185084i
$471$	−5.58318	−	9.67034i	−0.257259	−	0.445586i
$472$	−4.87216	+	5.41109i	−0.224260	+	0.249065i
$473$	−0.611827	+	1.88301i	−0.0281318	+	0.0865809i
$474$	−2.60300	−	2.89093i	−0.119560	−	0.132785i
$475$	−6.29451	+	2.80250i	−0.288812	+	0.128587i
$476$	1.68389	+	0.357922i	0.0771810	+	0.0164053i
$477$	0.460666	−	4.38294i	0.0210924	−	0.200681i
$478$	−2.97307	−	28.2868i	−0.135985	−	1.29381i
$479$	16.8905	−	3.59019i	0.771747	−	0.164040i	0.194824	−	0.980838i	$-0.437586\pi$
$479$	16.8905	−	3.59019i	0.771747	−	0.164040i	0.576923	+	0.816798i	$0.304253\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	−13.9221	+	10.1150i	−0.634792	+	0.461203i
$482$	13.7558	−	2.92388i	0.626559	−	0.133179i
$483$	0.803398	+	7.64382i	0.0365559	+	0.347806i
$484$	1.03751	−	9.87129i	0.0471598	−	0.448695i
$485$	−13.8526	−	2.94447i	−0.629015	−	0.133701i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−8.97286	−	9.96537i	−0.406599	−	0.451574i	0.504715	−	0.863286i	$-0.331598\pi$
$487$	−8.97286	−	9.96537i	−0.406599	−	0.451574i	−0.911314	+	0.411712i	$0.864931\pi$
$488$	2.19161	−	6.74509i	0.0992097	−	0.305336i
$489$	−8.15467	+	9.05668i	−0.368767	+	0.409557i
$490$	−2.43089	−	4.21043i	−0.109816	−	0.190208i
$491$	13.1442	−	22.7664i	0.593190	−	1.02743i	−0.400610	−	0.916249i	$-0.631202\pi$
$491$	13.1442	−	22.7664i	0.593190	−	1.02743i	0.993800	−	0.111186i	$-0.0354649\pi$
$492$	1.16142	+	3.57448i	0.0523608	+	0.161150i
$493$	3.43022	+	1.52723i	0.154489	+	0.0687830i
$494$	12.8957	+	9.36929i	0.580206	+	0.421544i
$495$	1.03650			0.0465872
$496$	−1.53080	+	5.35319i	−0.0687349	+	0.240365i
$497$	23.6905			1.06266
$498$	−5.06946	−	3.68318i	−0.227168	−	0.165047i
$499$	25.6927	+	11.4391i	1.15016	+	0.512085i	0.891114	−	0.453779i	$-0.149924\pi$
$499$	25.6927	+	11.4391i	1.15016	+	0.512085i	0.259048	+	0.965864i	$0.416591\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−0.470983	+	0.815767i	−0.0210420	+	0.0364458i
$502$	−2.06547	−	3.57750i	−0.0921864	−	0.159671i
$503$	−16.2259	+	18.0207i	−0.723477	+	0.803502i	−0.986927	−	0.161171i	$-0.948473\pi$
$503$	−16.2259	+	18.0207i	−0.723477	+	0.803502i	0.263450	+	0.964673i	$0.415140\pi$
$504$	0.451864	−	1.39070i	0.0201276	−	0.0619465i
$505$	2.57558	+	2.86047i	0.114612	+	0.127289i
$506$	4.97703	−	2.21591i	0.221256	−	0.0985094i
$507$	7.48093	+	1.59012i	0.332240	+	0.0706197i
$508$	0.499502	−	4.75244i	0.0221618	−	0.210855i
$509$	−3.31547	−	31.5446i	−0.146956	−	1.39819i	−0.780825	−	0.624750i	$-0.785201\pi$
$509$	−3.31547	−	31.5446i	−0.146956	−	1.39819i	0.633869	−	0.773440i	$-0.281466\pi$
$510$	−1.15156	+	0.244772i	−0.0509921	+	0.0108387i
$511$	12.1475	−	8.82568i	0.537374	−	0.390425i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	6.73964	−	1.43255i	0.297562	−	0.0632488i
$514$	−1.25690	−	11.9586i	−0.0554396	−	0.527472i
$515$	−0.561848	+	5.34562i	−0.0247580	+	0.235556i
$516$	−1.86845	−	0.397151i	−0.0822538	−	0.0174836i
$517$	−0.438720	+	0.195331i	−0.0192949	+	0.00859063i
$518$	7.27825	+	8.08332i	0.319788	+	0.355161i
$519$	−1.71236	+	5.27011i	−0.0751644	+	0.231332i
$520$	−1.54798	+	1.71921i	−0.0678836	+	0.0753924i
$521$	13.5763	+	23.5148i	0.594787	+	1.03020i	0.993577	+	0.113159i	$0.0360969\pi$
$521$	13.5763	+	23.5148i	0.594787	+	1.03020i	−0.398790	+	0.917042i	$0.630570\pi$
$522$	1.59470	−	2.76209i	0.0697979	−	0.120894i
$523$	3.56267	+	10.9648i	0.155785	+	0.479456i	0.998240	−	0.0593108i	$-0.0188903\pi$
$523$	3.56267	+	10.9648i	0.155785	+	0.479456i	−0.842455	+	0.538767i	$0.818890\pi$
$524$	−7.48580	−	3.33289i	−0.327019	−	0.145598i
$525$	−1.18300	−	0.859497i	−0.0516302	−	0.0375115i
$526$	20.2976			0.885018
$527$	4.20975	−	5.02438i	0.183379	−	0.218865i
$528$	−1.03650			−0.0451079
$529$	−3.74366	−	2.71993i	−0.162768	−	0.118258i
$530$	4.02607	+	1.79252i	0.174881	+	0.0778622i
$531$	−2.25006	−	6.92496i	−0.0976441	−	0.300518i
$532$	5.03765	−	8.72546i	0.218410	−	0.378297i
$533$	−4.34742	−	7.52996i	−0.188308	−	0.326159i
$534$	−4.92492	+	5.46968i	−0.213122	+	0.236696i
$535$	−3.76806	+	11.5969i	−0.162908	+	0.501378i
$536$	−4.69958	−	5.21941i	−0.202991	−	0.225444i
$537$	−10.0447	+	4.47218i	−0.433460	+	0.192989i
$538$	8.11795	+	1.72552i	0.349990	+	0.0743926i
$539$	−0.526744	+	5.01164i	−0.0226885	+	0.215867i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	−38.8419	+	8.25610i	−1.66994	+	0.354957i	−0.943270	−	0.332026i	$-0.892268\pi$
$541$	−38.8419	+	8.25610i	−1.66994	+	0.354957i	−0.726673	+	0.686984i	$0.758934\pi$
$542$	14.9592	−	10.8685i	0.642555	−	0.466843i
$543$	−6.00501	+	4.36290i	−0.257700	+	0.187230i
$544$	1.15156	−	0.244772i	0.0493729	−	0.0104945i
$545$	0.292498	+	2.78293i	0.0125292	+	0.119208i
$546$	−0.353603	+	3.36431i	−0.0151328	+	0.143979i
$547$	37.3794	+	7.94524i	1.59823	+	0.339714i	0.919013	−	0.394226i	$-0.128987\pi$
$547$	37.3794	+	7.94524i	1.59823	+	0.339714i	0.679214	+	0.733940i	$0.262321\pi$
$548$	−0.00104679		0.000466060i	−4.47166e−5		1.99091e-5i
$549$	4.74562	+	5.27054i	0.202538	+	0.224941i
$550$	−0.320296	+	0.985771i	−0.0136575	+	0.0420334i
$551$	14.7045	−	16.3310i	0.626434	−	0.695725i
$552$	2.62809	+	4.55198i	0.111859	+	0.193745i
$553$	2.84420	−	4.92630i	0.120948	−	0.209487i
$554$	−3.03308	−	9.33486i	−0.128863	−	0.396600i
$555$	−6.79549	−	3.02554i	−0.288452	−	0.128427i
$556$	10.6351	+	7.72689i	0.451031	+	0.327693i
$557$	−10.1450			−0.429857			−0.214929	−	0.976630i	$-0.568952\pi$
$557$	−10.1450			−0.429857			−0.214929	+	0.976630i	$0.568952\pi$
$558$	−3.87060	−	4.00231i	−0.163856	−	0.169431i
$559$	4.41909			0.186907
$560$	1.18300	+	0.859497i	0.0499907	+	0.0363204i
$561$	1.11476	+	0.496325i	0.0470654	+	0.0209549i
$562$	5.33703	+	16.4257i	0.225129	+	0.692875i
$563$	7.68366	−	13.3085i	0.323828	−	0.560886i	−0.657447	−	0.753501i	$-0.728364\pi$
$563$	7.68366	−	13.3085i	0.323828	−	0.560886i	0.981274	+	0.192615i	$0.0616969\pi$
$564$	−0.231663	−	0.401253i	−0.00975478	−	0.0168958i
$565$	0.0774747	−	0.0860443i	0.00325938	−	0.00361991i
$566$	−3.15294	+	9.70374i	−0.132528	+	0.407879i
$567$	0.978446	+	1.08667i	0.0410909	+	0.0456360i
$568$	14.8005	−	6.58963i	0.621017	−	0.276495i
$569$	9.13992	+	1.94275i	0.383165	+	0.0814443i	0.395467	−	0.918480i	$-0.370583\pi$
$569$	9.13992	+	1.94275i	0.383165	+	0.0814443i	−0.0123020	+	0.999924i	$0.503916\pi$
$570$	−0.720222	+	6.85246i	−0.0301668	+	0.287018i
$571$	−0.405409	−	3.85721i	−0.0169659	−	0.161419i	0.982759	−	0.184893i	$-0.0591940\pi$
$571$	−0.405409	−	3.85721i	−0.0169659	−	0.161419i	−0.999724	+	0.0234740i	$0.992527\pi$
$572$	2.34547	−	0.498545i	0.0980690	−	0.0208452i
$573$	−2.74810	+	1.99661i	−0.114803	+	0.0834096i
$574$	−4.44621	+	3.23036i	−0.185581	+	0.134833i
$575$	5.14132	−	1.09282i	0.214408	−	0.0455738i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	2.97511	−	28.3062i	0.123855	−	1.17840i	−0.739268	−	0.673411i	$-0.764828\pi$
$577$	2.97511	−	28.3062i	0.123855	−	1.17840i	0.863123	−	0.504993i	$-0.168505\pi$
$578$	15.2728	+	3.24633i	0.635264	+	0.135030i
$579$	−16.7721	+	7.46743i	−0.697026	+	0.310336i
$580$	2.13412	+	2.37018i	0.0886145	+	0.0984164i
$581$	2.83147	−	8.71437i	0.117469	−	0.361533i
$582$	−9.47630	+	10.5245i	−0.392805	+	0.436254i
$583$	−2.28397	−	3.95596i	−0.0945925	−	0.163839i
$584$	5.13421	−	8.89272i	0.212455	−	0.367983i
$585$	−0.714888	−	2.20020i	−0.0295570	−	0.0909671i
$586$	−13.9729	−	6.22115i	−0.577217	−	0.256993i
$587$	−25.3699	−	18.4323i	−1.04713	−	0.760782i	−0.0754627	−	0.997149i	$-0.524043\pi$
$587$	−25.3699	−	18.4323i	−1.04713	−	0.760782i	−0.971664	+	0.236367i	$0.924043\pi$
$588$	−4.86178			−0.200497
$589$	−20.3529	−	32.5189i	−0.838627	−	1.33992i
$590$	7.28134			0.299768
$591$	−14.4096	−	10.4692i	−0.592733	−	0.430646i
$592$	6.79549	+	3.02554i	0.279293	+	0.124349i
$593$	−3.99433	−	12.2933i	−0.164027	−	0.504824i	0.834936	−	0.550347i	$-0.185505\pi$
$593$	−3.99433	−	12.2933i	−0.164027	−	0.504824i	−0.998963	+	0.0455227i	$0.985505\pi$
$594$	0.518250	−	0.897636i	0.0212641	−	0.0368305i
$595$	−0.860754	−	1.49087i	−0.0352875	−	0.0611197i
$596$	−9.24842	+	10.2714i	−0.378830	+	0.420733i
$597$	−4.53326	+	13.9519i	−0.185534	+	0.571015i
$598$	−8.13648	−	9.03648i	−0.332726	−	0.369529i
$599$	−17.7348	+	7.89605i	−0.724625	+	0.322624i	−0.735693	−	0.677315i	$-0.763143\pi$
$599$	−17.7348	+	7.89605i	−0.724625	+	0.322624i	0.0110683	+	0.999939i	$0.496477\pi$
$600$	−0.978148	−	0.207912i	−0.0399327	−	0.00848796i
$601$	−2.41183	+	22.9471i	−0.0983807	+	0.936030i	0.828326	+	0.560246i	$0.189293\pi$
$601$	−2.41183	+	22.9471i	−0.0983807	+	0.936030i	−0.926707	+	0.375784i	$0.877373\pi$
$602$	−0.291969	−	2.77790i	−0.0118998	−	0.113219i
$603$	6.86993	−	1.46025i	0.279765	−	0.0594659i
$604$	−16.1775	+	11.7536i	−0.658253	+	0.478249i
$605$	−8.03003	+	5.83416i	−0.326467	+	0.237192i
$606$	3.76503	−	0.800281i	0.152944	−	0.0325092i
$607$	0.722961	+	6.87851i	0.0293441	+	0.279190i	0.999348	+	0.0361014i	$0.0114939\pi$
$607$	0.722961	+	6.87851i	0.0293441	+	0.279190i	−0.970004	+	0.243089i	$0.921839\pi$
$608$	0.720222	−	6.85246i	0.0292089	−	0.277904i
$609$	4.56182	+	0.969645i	0.184854	+	0.0392920i
$610$	−6.47906	+	2.88466i	−0.262329	+	0.116797i
$611$	0.717222	+	0.796556i	0.0290157	+	0.0322252i
$612$	−0.363803	+	1.11967i	−0.0147058	+	0.0452600i
$613$	3.57780	−	3.97355i	0.144506	−	0.160490i	−0.666547	−	0.745463i	$-0.732228\pi$
$613$	3.57780	−	3.97355i	0.144506	−	0.160490i	0.811053	+	0.584973i	$0.198895\pi$
$614$	12.7249	+	22.0402i	0.513536	+	0.889470i
$615$	1.87921	−	3.25489i	0.0757772	−	0.131250i
$616$	−0.468358	−	1.44146i	−0.0188707	−	0.0580780i
$617$	3.86872	+	1.72246i	0.155749	+	0.0693438i	0.483131	−	0.875548i	$-0.339500\pi$
$617$	3.86872	+	1.72246i	0.155749	+	0.0693438i	−0.327382	+	0.944892i	$0.606166\pi$
$618$	4.34852	+	3.15939i	0.174923	+	0.127089i
$619$	26.9761			1.08426			0.542130	−	0.840294i	$-0.317618\pi$
$619$	26.9761			1.08426			0.542130	+	0.840294i	$0.317618\pi$
$620$	5.00250	−	2.44438i	0.200905	−	0.0981686i
$621$	−5.25618			−0.210923
$622$	−13.6576	−	9.92286i	−0.547622	−	0.397870i
$623$	−9.83206	−	4.37752i	−0.393913	−	0.175381i
$624$	0.714888	+	2.20020i	0.0286184	+	0.0880785i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.69378	−	9.86192i	−0.227569	−	0.394162i
$627$	4.77873	−	5.30732i	0.190844	−	0.211954i
$628$	3.45059	−	10.6198i	0.137694	−	0.423777i
$629$	−5.85983	−	6.50800i	−0.233647	−	0.259491i
$630$	−1.33584	+	0.594756i	−0.0532213	+	0.0236957i
$631$	39.8913	+	8.47915i	1.58805	+	0.337550i	0.915441	−	0.402452i	$-0.131842\pi$
$631$	39.8913	+	8.47915i	1.58805	+	0.337550i	0.672605	+	0.740002i	$0.265175\pi$
$632$	0.406629	−	3.86882i	0.0161748	−	0.153893i
$633$	2.22836	+	21.2014i	0.0885693	+	0.842681i
$634$	19.2450	−	4.09065i	0.764317	−	0.162460i
$635$	−3.86598	+	2.80880i	−0.153417	+	0.111464i
$636$	3.56541	−	2.59042i	0.141378	−	0.102717i
$637$	11.0016	−	2.33846i	0.435899	−	0.0926532i
$638$	−0.345551	−	3.28770i	−0.0136805	−	0.130161i
$639$	−1.69349	+	16.1125i	−0.0669934	+	0.637399i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	13.8623	−	6.17189i	0.547528	−	0.243775i	−0.114280	−	0.993449i	$-0.536456\pi$
$641$	13.8623	−	6.17189i	0.547528	−	0.243775i	0.661808	+	0.749674i	$0.269789\pi$
$642$	8.15919	+	9.06169i	0.322017	+	0.357637i
$643$	−3.63218	+	11.1787i	−0.143239	+	0.440845i	−0.996780	−	0.0801803i	$-0.974450\pi$
$643$	−3.63218	+	11.1787i	−0.143239	+	0.440845i	0.853541	+	0.521026i	$0.174450\pi$
$644$	−5.14289	+	5.71175i	−0.202658	+	0.225075i
$645$	0.955095	+	1.65427i	0.0376068	+	0.0651369i
$646$	−4.05588	+	7.02500i	−0.159577	+	0.276395i
$647$	11.0777	+	34.0937i	0.435510	+	1.34036i	0.892563	+	0.450923i	$0.148905\pi$
$647$	11.0777	+	34.0937i	0.435510	+	1.34036i	−0.457053	+	0.889439i	$0.651095\pi$
$648$	0.913545	+	0.406737i	0.0358875	+	0.0159781i
$649$	−6.10574	−	4.43608i	−0.239671	−	0.174131i
$650$	2.31343			0.0907401
$651$	3.81700	−	7.19133i	0.149600	−	0.281850i
$652$	−12.1870			−0.477278
$653$	−27.5241	−	19.9974i	−1.07710	−	0.782559i	−0.0999252	−	0.994995i	$-0.531860\pi$
$653$	−27.5241	−	19.9974i	−1.07710	−	0.782559i	−0.977175	+	0.212436i	$0.931860\pi$
$654$	2.55634	+	1.13816i	0.0999608	+	0.0445054i
$655$	2.53216	+	7.79318i	0.0989395	+	0.304505i
$656$	−1.87921	+	3.25489i	−0.0733710	+	0.127082i
$657$	5.13421	+	8.89272i	0.200305	+	0.346938i
$658$	0.453340	−	0.503485i	0.0176730	−	0.0196279i
$659$	7.60365	−	23.4016i	0.296196	−	0.911597i	−0.686621	−	0.727015i	$-0.740907\pi$
$659$	7.60365	−	23.4016i	0.296196	−	0.911597i	0.982817	−	0.184582i	$-0.0590931\pi$
$660$	0.693554	+	0.770270i	0.0269966	+	0.0299827i
$661$	−7.51009	+	3.34371i	−0.292109	+	0.130055i	−0.547559	−	0.836767i	$-0.684443\pi$
$661$	−7.51009	+	3.34371i	−0.292109	+	0.130055i	0.255451	+	0.966822i	$0.417776\pi$
$662$	0.430005	+	0.0914004i	0.0167126	+	0.00355238i
$663$	0.284691	−	2.70865i	0.0110565	−	0.105195i
$664$	−0.654996	−	6.23187i	−0.0254188	−	0.241843i
$665$	−9.85513	+	2.09477i	−0.382166	+	0.0812318i
$666$	−6.01794	+	4.37229i	−0.233190	+	0.169423i
$667$	−13.5624	+	9.85364i	−0.525137	+	0.381534i
$668$	−0.921382	+	0.195846i	−0.0356493	+	0.00757750i
$669$	0.443505	+	4.21967i	0.0171469	+	0.163142i
$670$	−0.734146	+	6.98493i	−0.0283625	+	0.269851i
$671$	7.19044	+	1.52838i	0.277584	+	0.0590023i
$672$	1.33584	−	0.594756i	0.0515313	−	0.0229432i
$673$	27.4010	+	30.4319i	1.05623	+	1.17306i	0.984454	+	0.175642i	$0.0562003\pi$
$673$	27.4010	+	30.4319i	1.05623	+	1.17306i	0.0717768	+	0.997421i	$0.477133\pi$
$674$	−8.56716	+	26.3670i	−0.329995	+	1.01562i
$675$	0.669131	−	0.743145i	0.0257548	−	0.0286037i
$676$	3.82403	+	6.62341i	0.147078	+	0.254747i
$677$	−16.1745	+	28.0150i	−0.621636	+	1.07671i	0.367545	+	0.930006i	$0.380198\pi$
$677$	−16.1745	+	28.0150i	−0.621636	+	1.07671i	−0.989181	+	0.146700i	$0.953135\pi$
$678$	−0.0357792	−	0.110117i	−0.00137409	−	0.00422903i
$679$	−18.9184	−	8.42300i	−0.726021	−	0.323245i
$680$	−0.952448	−	0.691994i	−0.0365247	−	0.0265367i
$681$	−4.65606			−0.178420
$682$	−5.68404	−	0.997997i	−0.217653	−	0.0382153i
$683$	35.9916			1.37718			0.688591	−	0.725150i	$-0.258230\pi$
$683$	35.9916			1.37718			0.688591	+	0.725150i	$0.258230\pi$
$684$	5.57429	+	4.04996i	0.213138	+	0.154854i
$685$	0.00104679		0.000466060i	3.99957e−5		1.78072e-5i
$686$	−5.35992	−	16.4961i	−0.204643	−	0.629825i
$687$	6.12555	−	10.6098i	0.233704	−	0.404788i
$688$	−0.955095	−	1.65427i	−0.0364127	−	0.0630686i
$689$	−6.82210	+	7.57671i	−0.259901	+	0.288650i
$690$	1.62425	−	4.99892i	0.0618341	−	0.190306i
$691$	20.4985	+	22.7659i	0.779800	+	0.866055i	0.993846	−	0.110768i	$-0.0353311\pi$
$691$	20.4985	+	22.7659i	0.779800	+	0.866055i	−0.214047	+	0.976823i	$0.568664\pi$
$692$	−5.06225	+	2.25386i	−0.192438	+	0.0856789i
$693$	1.48252	+	0.315119i	0.0563162	+	0.0119704i
$694$	2.44552	−	23.2675i	0.0928305	−	0.883223i
$695$	−1.37411	−	13.0738i	−0.0521228	−	0.495916i
$696$	3.11970	−	0.663112i	0.118252	−	0.0251352i
$697$	3.57971	−	2.60081i	0.135591	−	0.0985126i
$698$	8.35392	−	6.06948i	0.316201	−	0.229733i
$699$	−17.8224	+	3.78827i	−0.674106	+	0.143286i
$700$	−0.152848	−	1.45425i	−0.00577712	−	0.0549656i
$701$	−2.05052	+	19.5094i	−0.0774472	+	0.736861i	0.885037	+	0.465522i	$0.154133\pi$
$701$	−2.05052	+	19.5094i	−0.0774472	+	0.736861i	−0.962484	+	0.271339i	$0.912533\pi$
$702$	−2.26287	−	0.480988i	−0.0854066	−	0.0181537i
$703$	−46.8223	+	20.8466i	−1.76594	+	0.786245i
$704$	−0.693554	−	0.770270i	−0.0261393	−	0.0290307i
$705$	−0.143176	+	0.440650i	−0.00539231	+	0.0165958i
$706$	−12.9286	+	14.3587i	−0.486575	+	0.540396i
$707$	2.81423	+	4.87439i	0.105840	+	0.183320i
$708$	3.64067	−	6.30582i	0.136825	−	0.236987i
$709$	5.26044	+	16.1900i	0.197560	+	0.608027i	0.999937	+	0.0112099i	$0.00356828\pi$
$709$	5.26044	+	16.1900i	0.197560	+	0.608027i	−0.802377	+	0.596817i	$0.796432\pi$
$710$	−14.8005	−	6.58963i	−0.555455	−	0.247304i
$711$	3.14718	+	2.28656i	0.118028	+	0.0857527i
$712$	−7.36018			−0.275834
$713$	10.0292	+	27.4930i	0.375598	+	1.02962i
$714$	−1.72151			−0.0644259
$715$	−1.93992	−	1.40943i	−0.0725488	−	0.0527098i
$716$	−10.0447	−	4.47218i	−0.375387	−	0.167133i
$717$	8.78926	+	27.0506i	0.328241	+	1.01022i
$718$	−8.78674	+	15.2191i	−0.327918	+	0.567971i
$719$	−16.0534	−	27.8052i	−0.598690	−	1.03696i	−0.993015	−	0.117990i	$-0.962355\pi$
$719$	−16.0534	−	27.8052i	−0.598690	−	1.03696i	0.394325	−	0.918971i	$-0.370978\pi$
$720$	−0.669131	+	0.743145i	−0.0249370	+	0.0276954i
$721$	−2.42880	+	7.47509i	−0.0904534	+	0.278387i
$722$	19.0534	+	21.1610i	0.709095	+	0.787530i
$723$	−12.8473	+	5.71997i	−0.477795	+	0.212728i
$724$	−7.26040	−	1.54325i	−0.269831	−	0.0573543i
$725$	0.333382	−	3.17192i	0.0123815	−	0.117802i
$726$	1.03751	+	9.87129i	0.0385058	+	0.366358i
$727$	19.7534	−	4.19871i	0.732613	−	0.155722i	0.173524	−	0.984830i	$-0.444484\pi$
$727$	19.7534	−	4.19871i	0.732613	−	0.155722i	0.559089	+	0.829108i	$0.311151\pi$
$728$	−2.73678	+	1.98838i	−0.101432	+	0.0736944i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−10.0440	+	2.13493i	−0.371746	+	0.0790171i
$731$	0.235069	+	2.23653i	0.00869433	+	0.0827210i
$732$	−0.741338	+	7.05336i	−0.0274006	+	0.260700i
$733$	−10.7791	−	2.29116i	−0.398134	−	0.0846261i	0.00449332	−	0.999990i	$-0.498570\pi$
$733$	−10.7791	−	2.29116i	−0.398134	−	0.0846261i	−0.402628	+	0.915364i	$0.631903\pi$
$734$	14.7753	−	6.57839i	0.545367	−	0.242813i
$735$	3.25317	+	3.61301i	0.119995	+	0.133268i
$736$	−1.62425	+	4.99892i	−0.0598706	+	0.184263i
$737$	4.87111	−	5.40992i	0.179430	−	0.199277i
$738$	−1.87921	−	3.25489i	−0.0691748	−	0.119814i
$739$	−6.16552	+	10.6790i	−0.226802	+	0.392833i	−0.956859	−	0.290554i	$-0.906160\pi$
$739$	−6.16552	+	10.6790i	−0.226802	+	0.392833i	0.730056	+	0.683387i	$0.239494\pi$
$740$	−2.29865	−	7.07451i	−0.0845000	−	0.260064i
$741$	−14.5619	−	6.48338i	−0.534945	−	0.238173i
$742$	5.21357	+	3.78788i	0.191396	+	0.139057i
$743$	5.65725			0.207544			0.103772	−	0.994601i	$-0.466909\pi$
$743$	5.65725			0.207544			0.103772	+	0.994601i	$0.466909\pi$
$744$	0.384356	−	5.55448i	0.0140912	−	0.203637i
$745$	13.8215			0.506382
$746$	−12.1915	−	8.85764i	−0.446362	−	0.324301i
$747$	5.72445	+	2.54869i	0.209447	+	0.0932517i
$748$	0.377082	+	1.16054i	0.0137875	+	0.0424335i
$749$	−8.91521	+	15.4416i	−0.325755	+	0.564224i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−30.3260	+	33.6805i	−1.10661	+	1.22902i	−0.135403	+	0.990791i	$0.543233\pi$
$751$	−30.3260	+	33.6805i	−1.10661	+	1.22902i	−0.971210	+	0.238227i	$0.923434\pi$
$752$	0.143176	−	0.440650i	0.00522108	−	0.0160688i
$753$	2.76414	+	3.06988i	0.100731	+	0.111873i
$754$	−6.74053	+	3.00108i	−0.245475	+	0.109293i
$755$	19.5595	+	4.15750i	0.711844	+	0.151307i
$756$	−0.152848	+	1.45425i	−0.00555904	+	0.0528907i
$757$	−3.32320	−	31.6182i	−0.120784	−	1.14918i	−0.872130	−	0.489274i	$-0.837262\pi$
$757$	−3.32320	−	31.6182i	−0.120784	−	1.14918i	0.751346	−	0.659908i	$-0.229405\pi$
$758$	9.43582	−	2.00564i	0.342724	−	0.0728483i
$759$	−4.40755	+	3.20227i	−0.159984	+	0.116235i
$760$	−5.57429	+	4.04996i	−0.202201	+	0.146908i
$761$	4.74455	−	1.00848i	0.171990	−	0.0365575i	−0.121112	−	0.992639i	$-0.538646\pi$
$761$	4.74455	−	1.00848i	0.171990	−	0.0365575i	0.293101	+	0.956081i	$0.405313\pi$
$762$	0.499502	+	4.75244i	0.0180950	+	0.172163i
$763$	−0.427709	+	4.06938i	−0.0154841	+	0.147322i
$764$	−3.32261	−	0.706242i	−0.120208	−	0.0255509i
$765$	1.07551	−	0.478847i	0.0388851	−	0.0173127i
$766$	−13.0960	−	14.5446i	−0.473178	−	0.525518i
$767$	−5.20534	+	16.0204i	−0.187954	+	0.578463i
$768$	0.669131	−	0.743145i	0.0241452	−	0.0268159i
$769$	−6.54204	−	11.3312i	−0.235912	−	0.408612i	0.723625	−	0.690193i	$-0.242474\pi$
$769$	−6.54204	−	11.3312i	−0.235912	−	0.408612i	−0.959537	+	0.281581i	$0.909141\pi$
$770$	−0.757819	+	1.31258i	−0.0273099	+	0.0473021i
$771$	3.71577	+	11.4360i	0.133820	+	0.411857i
$772$	−16.7721	−	7.46743i	−0.603642	−	0.268759i
$773$	−20.1755	−	14.6584i	−0.725663	−	0.527225i	0.162526	−	0.986704i	$-0.448036\pi$
$773$	−20.1755	−	14.6584i	−0.725663	−	0.527225i	−0.888188	+	0.459479i	$0.848036\pi$
$774$	1.91019			0.0686604
$775$	−5.16385	−	2.08197i	−0.185491	−	0.0747867i
$776$	−14.1621			−0.508390
$777$	−8.79982	−	6.39344i	−0.315692	−	0.229364i
$778$	−6.20199	−	2.76130i	−0.222352	−	0.0989975i
$779$	−8.00241	−	24.6289i	−0.286716	−	0.882421i
$780$	1.15671	−	2.00349i	0.0414170	−	0.0717363i
$781$	8.39629	+	14.5428i	0.300443	+	0.520382i
$782$	4.14061	−	4.59861i	0.148068	−	0.164446i
$783$	−0.985576	+	3.03329i	−0.0352216	+	0.108401i
$784$	−3.25317	−	3.61301i	−0.116185	−	0.129036i
$785$	−10.2010	+	4.54176i	−0.364088	+	0.162103i
$786$	8.01517	+	1.70368i	0.285892	+	0.0607681i
$787$	0.103088	−	0.980821i	0.00367471	−	0.0349625i	−0.992531	−	0.121994i	$-0.961071\pi$
$787$	0.103088	−	0.980821i	0.00367471	−	0.0349625i	0.996206	+	0.0870311i	$0.0277379\pi$
$788$	−1.86179	−	17.7137i	−0.0663234	−	0.631025i
$789$	−19.8541	+	4.22011i	−0.706823	+	0.150240i
$790$	−3.14718	+	2.28656i	−0.111972	+	0.0813522i
$791$	0.136972	−	0.0995161i	0.00487017	−	0.00353838i
$792$	1.01385	−	0.215501i	0.0360256	−	0.00765748i
$793$	−1.71503	−	16.3174i	−0.0609025	−	0.579449i
$794$	−0.0484645	+	0.461109i	−0.00171994	+	0.0163641i
$795$	−4.31078	−	0.916285i	−0.152888	−	0.0324973i
$796$	−13.4016	+	5.96680i	−0.475009	+	0.211488i
$797$	21.3832	+	23.7485i	0.757432	+	0.841214i	0.991378	−	0.131036i	$-0.0418303\pi$
$797$	21.3832	+	23.7485i	0.757432	+	0.841214i	−0.233945	+	0.972250i	$0.575164\pi$
$798$	−3.11344	+	9.58218i	−0.110215	+	0.339205i
$799$	−0.364990	+	0.405363i	−0.0129124	+	0.0143407i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	3.68009	−	6.37410i	0.130030	−	0.225218i
$802$	9.78396	+	30.1119i	0.345484	+	1.06329i
$803$	9.72307	+	4.32899i	0.343120	+	0.152767i
$804$	5.68205	+	4.12825i	0.200391	+	0.145592i
$805$	7.68592			0.270893
$806$	1.80189	+	12.7540i	0.0634690	+	0.449239i
$807$	−8.29931			−0.292149
$808$	3.11402	+	2.26247i	0.109551	+	0.0795933i
$809$	37.1773	+	16.5524i	1.30708	+	0.581951i	0.937739	−	0.347342i	$-0.112916\pi$
$809$	37.1773	+	16.5524i	1.30708	+	0.581951i	0.369344	+	0.929293i	$0.379582\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−0.595879	+	1.03209i	−0.0209242	+	0.0362417i	−0.876298	−	0.481770i	$-0.839994\pi$
$811$	−0.595879	+	1.03209i	−0.0209242	+	0.0362417i	0.855374	+	0.518011i	$0.173328\pi$
$812$	2.33187	+	4.03891i	0.0818325	+	0.141738i
$813$	−12.3727	+	13.7412i	−0.433928	+	0.481926i
$814$	−2.38255	+	7.33274i	−0.0835084	+	0.257012i
$815$	8.15467	+	9.05668i	0.285646	+	0.317242i
$816$	−1.07551	+	0.478847i	−0.0376503	+	0.0167630i
$817$	12.8740	+	2.73645i	0.450404	+	0.0957363i
$818$	−3.66721	+	34.8912i	−0.128221	+	1.21994i
$819$	−0.353603	−	3.36431i	−0.0123559	−	0.117558i
$820$	3.67630	−	0.781421i	0.128382	−	0.0272884i
$821$	10.4427	−	7.58706i	0.364452	−	0.264790i	−0.390454	−	0.920622i	$-0.627682\pi$
$821$	10.4427	−	7.58706i	0.364452	−	0.264790i	0.754907	+	0.655832i	$0.227682\pi$
$822$	0.000927014	0	0.000673515i	3.23333e−5	0	2.34915e-5i
$823$	32.5897	−	6.92715i	1.13601	−	0.241465i	0.398737	−	0.917065i	$-0.369449\pi$
$823$	32.5897	−	6.92715i	1.13601	−	0.241465i	0.737268	+	0.675600i	$0.236115\pi$
$824$	0.561848	+	5.34562i	0.0195729	+	0.186224i
$825$	0.108344	−	1.03082i	0.00377205	−	0.0358886i
$826$	10.4146	+	2.21368i	0.362369	+	0.0770239i
$827$	−42.6169	+	18.9743i	−1.48194	+	0.659800i	−0.978877	−	0.204452i	$-0.934459\pi$
$827$	−42.6169	+	18.9743i	−1.48194	+	0.659800i	−0.503059	+	0.864252i	$0.667792\pi$
$828$	−3.51707	−	3.90610i	−0.122227	−	0.135746i
$829$	16.2982	−	50.1609i	0.566062	−	1.74216i	−0.0987146	−	0.995116i	$-0.531473\pi$
$829$	16.2982	−	50.1609i	0.566062	−	1.74216i	0.664776	−	0.747043i	$-0.268527\pi$
$830$	−4.19290	+	4.65669i	−0.145538	+	0.161636i
$831$	4.90763	+	8.50026i	0.170244	+	0.294871i
$832$	−1.15671	+	2.00349i	−0.0401018	+	0.0694584i
$833$	1.76873	+	5.44359i	0.0612828	+	0.188609i
$834$	−12.0093	−	5.34686i	−0.415846	−	0.185147i
$835$	0.762067	+	0.553674i	0.0263724	+	0.0191607i
$836$	7.14170			0.247001
$837$	4.61814	+	3.11010i	0.159626	+	0.107501i
$838$	−24.3282			−0.840402
$839$	−27.5782	−	20.0367i	−0.952105	−	0.691744i	−0.000800913	−	1.00000i	$-0.500255\pi$
$839$	−27.5782	−	20.0367i	−0.952105	−	0.691744i	−0.951304	+	0.308255i	$0.900255\pi$
$840$	−1.33584	−	0.594756i	−0.0460910	−	0.0205210i
$841$	−5.81810	−	17.9063i	−0.200624	−	0.617458i
$842$	−3.63598	+	6.29770i	−0.125304	+	0.217033i
$843$	−8.63549	−	14.9571i	−0.297422	−	0.515150i
$844$	−14.2647	+	15.8425i	−0.491010	+	0.545322i
$845$	2.36338	−	7.27373i	0.0813027	−	0.250224i
$846$	0.310026	+	0.344319i	0.0106589	+	0.0118379i
$847$	−13.2591	+	5.90335i	−0.455590	+	0.202842i
$848$	4.31078	+	0.916285i	0.148033	+	0.0314653i
$849$	1.06652	−	10.1472i	0.0366027	−	0.348252i
$850$	0.123060	+	1.17084i	0.00422093	+	0.0401595i
$851$	38.2441	−	8.12904i	1.31099	−	0.278660i
$852$	−13.1071	+	9.52284i	−0.449040	+	0.326247i
$853$	14.1665	−	10.2926i	0.485051	−	0.352410i	−0.318227	−	0.948015i	$-0.603087\pi$
$853$	14.1665	−	10.2926i	0.485051	−	0.352410i	0.803278	+	0.595604i	$0.203087\pi$
$854$	−10.1441	+	2.15619i	−0.347123	+	0.0737832i
$855$	−0.720222	−	6.85246i	−0.0246311	−	0.234349i
$856$	−1.27459	+	12.1269i	−0.0435646	+	0.414489i
$857$	43.1036	+	9.16194i	1.47239	+	0.312966i	0.873090	−	0.487559i	$-0.162113\pi$
$857$	43.1036	+	9.16194i	1.47239	+	0.312966i	0.599299	+	0.800525i	$0.295446\pi$
$858$	−2.19056	+	0.975301i	−0.0747846	+	0.0332962i
$859$	−7.28304	−	8.08864i	−0.248494	−	0.275981i	0.605974	−	0.795484i	$-0.292784\pi$
$859$	−7.28304	−	8.08864i	−0.248494	−	0.275981i	−0.854468	+	0.519504i	$0.826117\pi$
$860$	−0.590281	+	1.81670i	−0.0201284	+	0.0619489i
$861$	3.67742	−	4.08419i	0.125326	−	0.139189i
$862$	10.7078	+	18.5464i	0.364709	+	0.631695i
$863$	−6.16267	+	10.6741i	−0.209780	+	0.363349i	−0.951645	−	0.307200i	$-0.900608\pi$
$863$	−6.16267	+	10.6741i	−0.209780	+	0.363349i	0.741865	+	0.670549i	$0.233941\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	5.06225	+	2.25386i	0.172122	+	0.0766336i
$866$	27.4277	+	19.9274i	0.932032	+	0.677161i
$867$	−15.6140			−0.530279
$868$	7.89827	−	1.97535i	0.268085	−	0.0670478i
$869$	4.03212			0.136780
$870$	−2.58027	−	1.87468i	−0.0874794	−	0.0635575i
$871$	−14.8434	−	6.60871i	−0.502950	−	0.223928i
$872$	0.864710	+	2.66130i	0.0292828	+	0.0901231i
$873$	7.08105	−	12.2647i	0.239657	−	0.415099i
$874$	−18.1081	−	31.3641i	−0.612515	−	1.06091i
$875$	−0.978446	+	1.08667i	−0.0330775	+	0.0367363i
$876$	−3.17312	+	9.76585i	−0.107210	+	0.329958i
$877$	5.90070	+	6.55340i	0.199253	+	0.221292i	0.834488	−	0.551026i	$-0.185764\pi$
$877$	5.90070	+	6.55340i	0.199253	+	0.221292i	−0.635235	+	0.772319i	$0.719097\pi$
$878$	0.859543	−	0.382693i	0.0290082	−	0.0129153i
$879$	14.9610	+	3.18007i	0.504623	+	0.107261i
$880$	−0.108344	+	1.03082i	−0.00365227	+	0.0347490i
$881$	−3.70908	−	35.2896i	−0.124962	−	1.18894i	−0.859778	−	0.510668i	$-0.829398\pi$
$881$	−3.70908	−	35.2896i	−0.124962	−	1.18894i	0.734816	−	0.678267i	$-0.237269\pi$
$882$	4.75554	−	1.01082i	0.160127	−	0.0340361i
$883$	−6.16580	+	4.47972i	−0.207496	+	0.150755i	−0.686680	−	0.726960i	$-0.740933\pi$
$883$	−6.16580	+	4.47972i	−0.207496	+	0.150755i	0.479184	+	0.877714i	$0.340933\pi$
$884$	2.20342	−	1.60088i	0.0741090	−	0.0538433i
$885$	−7.12222	+	1.51387i	−0.239411	+	0.0508883i
$886$	−0.556517	−	5.29491i	−0.0186966	−	0.177886i
$887$	−3.66576	+	34.8773i	−0.123084	+	1.17107i	0.742339	+	0.670024i	$0.233716\pi$
$887$	−3.66576	+	34.8773i	−0.123084	+	1.17107i	−0.865423	+	0.501042i	$0.832950\pi$
$888$	−7.27603	−	1.54657i	−0.244168	−	0.0518994i
$889$	−6.38349	+	2.84211i	−0.214095	+	0.0953214i
$890$	4.92492	+	5.46968i	0.165084	+	0.183344i
$891$	−0.320296	+	0.985771i	−0.0107303	+	0.0330246i
$892$	−2.83906	+	3.15310i	−0.0950589	+	0.105574i
$893$	1.59621	+	2.76471i	0.0534150	+	0.0925176i
$894$	6.91077	−	11.9698i	0.231131	−	0.400330i
$895$	3.39773	+	10.4571i	0.113573	+	0.349543i
$896$	1.33584	+	0.594756i	0.0446274	+	0.0198694i
$897$	9.83747	+	7.14734i	0.328464	+	0.238643i
$898$	−24.4137			−0.814696
$899$	17.7465	−	0.632620i	0.591879	−	0.0210990i
$900$	1.00000			0.0333333
$901$	−4.19752	−	3.04968i	−0.139840	−	0.101599i
$902$	−3.55882	−	1.58449i	−0.118496	−	0.0527577i
$903$	0.863147	+	2.65649i	0.0287237	+	0.0884026i
$904$	0.0578920	−	0.100272i	0.00192546	−	0.00333500i
$905$	3.71130	+	6.42817i	0.123368	+	0.213679i
$906$	13.3803	−	14.8603i	0.444530	−	0.493700i
$907$	−3.01075	+	9.26614i	−0.0999704	+	0.307677i	−0.988517	−	0.151109i	$-0.951716\pi$
$907$	−3.01075	+	9.26614i	−0.0999704	+	0.307677i	0.888547	+	0.458786i	$0.151716\pi$
$908$	−3.11551	−	3.46012i	−0.103392	−	0.114828i
$909$	−3.51636	+	1.56559i	−0.116630	+	0.0519272i
$910$	3.30892	+	0.703332i	0.109690	+	0.0233152i
$911$	0.824464	−	7.84425i	0.0273157	−	0.259891i	−0.972338	−	0.233578i	$-0.924957\pi$
$911$	0.824464	−	7.84425i	0.0273157	−	0.259891i	0.999654	−	0.0263134i	$-0.00837678\pi$
$912$	0.720222	+	6.85246i	0.0238489	+	0.226908i
$913$	6.35299	−	1.35037i	0.210253	−	0.0446907i
$914$	−16.2717	+	11.8221i	−0.538221	+	0.391040i
$915$	5.73772	−	4.16870i	0.189683	−	0.137813i
$916$	11.9834	−	2.54715i	0.395942	−	0.0841602i
$917$	1.25247	+	11.9165i	0.0413603	+	0.393517i
$918$	0.123060	−	1.17084i	0.00406160	−	0.0386435i
$919$	−56.0561	−	11.9151i	−1.84912	−	0.393042i	−0.856687	−	0.515836i	$-0.827481\pi$
$919$	−56.0561	−	11.9151i	−1.84912	−	0.393042i	−0.992432	+	0.122794i	$0.960815\pi$
$920$	4.80176	−	2.13788i	0.158309	−	0.0704838i
$921$	−17.0293	−	18.9129i	−0.561133	−	0.623202i
$922$	−3.04689	+	9.37736i	−0.100344	+	0.308827i
$923$	25.0792	−	27.8533i	0.825493	−	0.916803i
$924$	0.757819	+	1.31258i	0.0249304	+	0.0431807i
$925$	−3.71929	+	6.44200i	−0.122290	+	0.211812i
$926$	−4.91382	−	15.1232i	−0.161478	−	0.496978i
$927$	−4.91037	−	2.18624i	−0.161278	−	0.0718055i
$928$	2.58027	+	1.87468i	0.0847016	+	0.0615393i
$929$	4.71279			0.154622			0.0773108	−	0.997007i	$-0.475367\pi$
$929$	4.71279			0.154622			0.0773108	+	0.997007i	$0.475367\pi$
$930$	−4.38497	+	3.43104i	−0.143789	+	0.112508i
$931$	33.4987			1.09787
$932$	−14.7408	−	10.7098i	−0.482850	−	0.350811i
$933$	15.4223	+	6.86644i	0.504903	+	0.224797i
$934$	−1.13366	−	3.48904i	−0.0370945	−	0.114165i
$935$	0.610131	−	1.05678i	0.0199534	−	0.0345603i
$936$	−1.15671	−	2.00349i	−0.0378084	−	0.0654860i
$937$	8.66976	−	9.62874i	0.283229	−	0.314557i	−0.584697	−	0.811252i	$-0.698786\pi$
$937$	8.66976	−	9.62874i	0.283229	−	0.314557i	0.867925	+	0.496695i	$0.165453\pi$
$938$	−3.17363	+	9.76742i	−0.103623	+	0.318918i
$939$	7.61977	+	8.46261i	0.248662	+	0.276167i
$940$	−0.423270	+	0.188452i	−0.0138055	+	0.00614662i
$941$	9.85116	+	2.09393i	0.321139	+	0.0682601i	0.365661	−	0.930748i	$-0.380843\pi$
$941$	9.85116	+	2.09393i	0.321139	+	0.0682601i	−0.0445219	+	0.999008i	$0.514176\pi$
$942$	−1.16720	+	11.1052i	−0.0380295	+	0.361826i
$943$	2.06496	+	19.6467i	0.0672442	+	0.639786i
$944$	7.12222	−	1.51387i	0.231809	−	0.0492724i
$945$	1.18300	−	0.859497i	0.0384829	−	0.0279594i
$946$	1.60178	−	1.16376i	0.0520785	−	0.0378372i
$947$	−12.7970	+	2.72009i	−0.415847	+	0.0883909i	−0.411083	−	0.911598i	$-0.634850\pi$
$947$	−12.7970	+	2.72009i	−0.415847	+	0.0883909i	−0.00476319	+	0.999989i	$0.501516\pi$
$948$	0.406629	+	3.86882i	0.0132067	+	0.125653i
$949$	2.48310	−	23.6251i	0.0806048	−	0.766904i
$950$	6.73964	+	1.43255i	0.218663	+	0.0464782i
$951$	−17.9740	+	8.00252i	−0.582845	+	0.259499i
$952$	−1.15191	−	1.27933i	−0.0373338	−	0.0414633i
$953$	0.885611	−	2.72563i	0.0286878	−	0.0882918i	−0.935688	−	0.352830i	$-0.885219\pi$
$953$	0.885611	−	2.72563i	0.0286878	−	0.0882918i	0.964375	+	0.264538i	$0.0852195\pi$
$954$	−2.94892	+	3.27510i	−0.0954747	+	0.106035i
$955$	1.69842	+	2.94175i	0.0549595	+	0.0951927i
$956$	−14.2213	+	24.6320i	−0.459950	+	0.796657i
$957$	1.02155	+	3.14401i	0.0330220	+	0.101631i
$958$	−15.7750	−	7.02347i	−0.509666	−	0.226918i
$959$	0.00135554		0.000984857i	4.37726e−5		3.18027e-5i
$960$	−1.00000			−0.0322749
$961$	7.45590	−	30.0900i	0.240513	−	0.970646i
$962$	17.2086			0.554828
$963$	−9.86492	−	7.16728i	−0.317893	−	0.230962i
$964$	−12.8473	−	5.71997i	−0.413783	−	0.184228i
$965$	5.67336	+	17.4608i	0.182632	+	0.562083i
$966$	3.84296	−	6.65620i	0.123645	−	0.214160i
$967$	22.2996	+	38.6241i	0.717108	+	1.24207i	0.962141	+	0.272553i	$0.0878681\pi$
$967$	22.2996	+	38.6241i	0.717108	+	1.24207i	−0.245032	+	0.969515i	$0.578799\pi$
$968$	−6.64157	+	7.37621i	−0.213468	+	0.237080i
$969$	2.50667	−	7.71475i	0.0805260	−	0.247833i
$970$	9.47630	+	10.5245i	0.304266	+	0.337921i
$971$	−36.1329	+	16.0874i	−1.15956	+	0.516269i	−0.894106	−	0.447855i	$-0.852188\pi$
$971$	−36.1329	+	16.0874i	−1.15956	+	0.516269i	−0.265453	+	0.964124i	$0.585521\pi$
$972$	−0.978148	−	0.207912i	−0.0313741	−	0.00666877i
$973$	2.00931	−	19.1173i	0.0644154	−	0.612872i
$974$	1.40170	+	13.3363i	0.0449133	+	0.427322i
$975$	−2.26287	+	0.480988i	−0.0724699	+	0.0154040i
$976$	−5.73772	+	4.16870i	−0.183660	+	0.133437i
$977$	2.93787	−	2.13449i	0.0939908	−	0.0682883i	−0.539797	−	0.841795i	$-0.681499\pi$
$977$	2.93787	−	2.13449i	0.0939908	−	0.0682883i	0.633788	+	0.773507i	$0.281499\pi$
$978$	11.9207	−	2.53381i	0.381180	−	0.0810224i
$979$	−0.797430	−	7.58704i	−0.0254860	−	0.242483i
$980$	−0.508195	+	4.83515i	−0.0162337	+	0.154453i
$981$	−2.73711	−	0.581791i	−0.0873893	−	0.0185752i
$982$	−24.0157	+	10.6925i	−0.766370	+	0.341210i
$983$	2.39379	+	2.65857i	0.0763499	+	0.0847952i	0.780109	−	0.625643i	$-0.215163\pi$
$983$	2.39379	+	2.65857i	0.0763499	+	0.0847952i	−0.703759	+	0.710438i	$0.748497\pi$
$984$	1.16142	−	3.57448i	0.0370246	−	0.113950i
$985$	−11.9181	+	13.2364i	−0.379742	+	0.421746i
$986$	−1.87742	−	3.25179i	−0.0597892	−	0.103558i
$987$	−0.338753	+	0.586737i	−0.0107826	+	0.0186761i
$988$	−4.92573	−	15.1598i	−0.156708	−	0.482298i
$989$	−9.17227	−	4.08376i	−0.291661	−	0.129856i
$990$	−0.838547	−	0.609240i	−0.0266508	−	0.0193629i
$991$	25.0116			0.794519			0.397260	−	0.917706i	$-0.369961\pi$
$991$	25.0116			0.794519			0.397260	+	0.917706i	$0.369961\pi$
$992$	4.38497	−	3.43104i	0.139223	−	0.108936i
$993$	−0.439612			−0.0139507
$994$	−19.1660	−	13.9249i	−0.607908	−	0.441671i
$995$	13.4016	+	5.96680i	0.424861	+	0.189160i
$996$	1.93636	+	5.95950i	0.0613559	+	0.188834i
$997$	26.9384	−	46.6586i	0.853147	−	1.47769i	−0.0252062	−	0.999682i	$-0.508024\pi$
$997$	26.9384	−	46.6586i	0.853147	−	1.47769i	0.878353	−	0.478012i	$-0.158642\pi$
$998$	−14.0621	−	24.3562i	−0.445127	−	0.770983i
$999$	4.97738	−	5.52795i	0.157477	−	0.174896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.391.2	✓	16
31.18	even	15	inner	930.2.bg.d.421.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.391.2	✓	16	1.1	even	1	trivial
930.2.bg.d.421.2	yes	16	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.978446 - 1.08667i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.978446 - 1.08667i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(1.01385 + 0.215501i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(-0.241819 - 2.30075i) q^{13} +(-1.43031 + 0.304022i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.15156 - 0.244772i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(0.720222 - 6.85246i) q^{19} +(0.978148 + 0.207912i) q^{20} +(1.33584 - 0.594756i) q^{21} +(-0.693554 - 0.770270i) q^{22} +(-1.62425 + 4.99892i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.15671 + 2.00349i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.33584 + 0.594756i) q^{28} +(2.58027 + 1.87468i) q^{29} -1.00000 q^{30} +(4.38497 - 3.43104i) q^{31} +1.00000 q^{32} +(0.838547 + 0.609240i) q^{33} +(-1.07551 - 0.478847i) q^{34} +(-0.451864 - 1.39070i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.71929 - 6.44200i) q^{37} +(-4.61045 + 5.12042i) q^{38} +(0.714888 - 2.20020i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(3.43349 - 1.52869i) q^{41} +(-1.43031 - 0.304022i) q^{42} +(-0.199669 + 1.89973i) q^{43} +(0.108344 + 1.03082i) q^{44} +(0.978148 - 0.207912i) q^{45} +(4.25234 - 3.08950i) q^{46} +(-0.374839 + 0.272336i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(0.508195 + 4.83515i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(1.15156 + 0.244772i) q^{51} +(2.11342 - 0.940955i) q^{52} +(-2.94892 - 3.27510i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.693554 - 0.770270i) q^{55} +(-0.731132 - 1.26636i) q^{56} +(3.44510 - 5.96709i) q^{57} +(-0.985576 - 3.03329i) q^{58} +(-6.65183 - 2.96159i) q^{59} +(0.809017 + 0.587785i) q^{60} +7.09221 q^{61} +(-5.56423 + 0.198351i) q^{62} +1.46226 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.11342 - 0.940955i) q^{65} +(-0.320296 - 0.985771i) q^{66} +(3.51170 - 6.08245i) q^{67} +(0.588645 + 1.01956i) q^{68} +(-3.51707 + 3.90610i) q^{69} +(-0.451864 + 1.39070i) q^{70} +(10.8407 + 12.0398i) q^{71} +(0.913545 - 0.406737i) q^{72} +(10.0440 + 2.13493i) q^{73} +(-0.777544 + 7.39784i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(6.73964 - 1.43255i) q^{76} +(1.22618 - 0.890870i) q^{77} +(-1.87160 + 1.35980i) q^{78} +(3.80512 - 0.808803i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-3.67630 - 0.781421i) q^{82} +(5.72445 - 2.54869i) q^{83} +(0.978446 + 1.08667i) q^{84} +(0.363803 - 1.11967i) q^{85} +(1.27817 - 1.41955i) q^{86} +(1.59470 + 2.76209i) q^{87} +(0.518250 - 0.897636i) q^{88} +(-2.27442 - 6.99995i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(-2.73678 - 1.98838i) q^{91} -5.25618 q^{92} +(5.40140 - 1.35089i) q^{93} +0.463327 q^{94} +(-5.57429 - 4.04996i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-4.37633 - 13.4690i) q^{97} +(2.43089 - 4.21043i) q^{98} +(0.518250 + 0.897636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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Database

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