LMFDB - Embedded newform 690.2.e.a.551.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(551,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("690.551");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.e (of order $2$, degree $1$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$16$
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} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 3x^14 - 12x^13 + 15x^12 - 4x^11 + 45x^10 - 66x^9 - 32x^8 - 198x^7 + 405x^6 - 108x^5 + 1215x^4 - 2916x^3 + 2187x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.5
Root			$1.73162 + 0.0386882i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.a.551.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +1.00000i q^{10} +4.50428 q^{11} +(0.0386882 - 1.73162i) q^{12} -5.89898 q^{13} -2.83902 q^{14} +(0.0386882 - 1.73162i) q^{15} +1.00000 q^{16} -5.40124 q^{17} +(-0.133986 + 2.99701i) q^{18} -2.26797i q^{19} +1.00000 q^{20} +(4.91611 + 0.109837i) q^{21} -4.50428i q^{22} +(3.64088 - 3.12154i) q^{23} +(-1.73162 - 0.0386882i) q^{24} +1.00000 q^{25} +5.89898i q^{26} +(0.347962 - 5.18449i) q^{27} +2.83902i q^{28} -4.81253i q^{29} +(-1.73162 - 0.0386882i) q^{30} -9.92135 q^{31} -1.00000i q^{32} +(-0.174262 + 7.79970i) q^{33} +5.40124i q^{34} +2.83902i q^{35} +(2.99701 + 0.133986i) q^{36} -3.92624i q^{37} -2.26797 q^{38} +(0.228221 - 10.2148i) q^{39} -1.00000i q^{40} -2.24625i q^{41} +(0.109837 - 4.91611i) q^{42} -11.5505i q^{43} -4.50428 q^{44} +(2.99701 + 0.133986i) q^{45} +(-3.12154 - 3.64088i) q^{46} +1.55237i q^{47} +(-0.0386882 + 1.73162i) q^{48} -1.06006 q^{49} -1.00000i q^{50} +(0.208964 - 9.35288i) q^{51} +5.89898 q^{52} -6.08832 q^{53} +(-5.18449 - 0.347962i) q^{54} -4.50428 q^{55} +2.83902 q^{56} +(3.92726 + 0.0877437i) q^{57} -4.81253 q^{58} +10.8538i q^{59} +(-0.0386882 + 1.73162i) q^{60} -11.6821i q^{61} +9.92135i q^{62} +(-0.380390 + 8.50857i) q^{63} -1.00000 q^{64} +5.89898 q^{65} +(7.79970 + 0.174262i) q^{66} +3.47626i q^{67} +5.40124 q^{68} +(5.26445 + 6.42538i) q^{69} +2.83902 q^{70} +9.84805i q^{71} +(0.133986 - 2.99701i) q^{72} +0.323623 q^{73} -3.92624 q^{74} +(-0.0386882 + 1.73162i) q^{75} +2.26797i q^{76} -12.7878i q^{77} +(-10.2148 - 0.228221i) q^{78} -5.69882i q^{79} -1.00000 q^{80} +(8.96410 + 0.803115i) q^{81} -2.24625 q^{82} -4.31060 q^{83} +(-4.91611 - 0.109837i) q^{84} +5.40124 q^{85} -11.5505 q^{86} +(8.33347 + 0.186188i) q^{87} +4.50428i q^{88} +11.6518 q^{89} +(0.133986 - 2.99701i) q^{90} +16.7474i q^{91} +(-3.64088 + 3.12154i) q^{92} +(0.383839 - 17.1800i) q^{93} +1.55237 q^{94} +2.26797i q^{95} +(1.73162 + 0.0386882i) q^{96} +8.21290i q^{97} +1.06006i q^{98} +(-13.4994 - 0.603512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9	$ 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9} - 12 q^{11} - 12 q^{14} + 16 q^{16} + 8 q^{18} + 16 q^{20} - 4 q^{21} + 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} - 2 q^{30} + 4 q^{31} - 28 q^{33} - 2 q^{36} - 16 q^{38} - 8 q^{39} + 12 q^{44} - 2 q^{45} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 8 q^{53} - 26 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 8 q^{58} - 16 q^{64} + 10 q^{66} + 30 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} - 24 q^{74} - 12 q^{78} - 16 q^{80} + 22 q^{81} - 16 q^{82} - 40 q^{83} + 4 q^{84} - 40 q^{86} + 20 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9 - 12 * q^11 - 12 * q^14 + 16 * q^16 + 8 * q^18 + 16 * q^20 - 4 * q^21 + 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 - 2 * q^30 + 4 * q^31 - 28 * q^33 - 2 * q^36 - 16 * q^38 - 8 * q^39 + 12 * q^44 - 2 * q^45 - 4 * q^46 - 4 * q^49 - 2 * q^51 - 8 * q^53 - 26 * q^54 + 12 * q^55 + 12 * q^56 + 28 * q^57 - 8 * q^58 - 16 * q^64 + 10 * q^66 + 30 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 - 24 * q^74 - 12 * q^78 - 16 * q^80 + 22 * q^81 - 16 * q^82 - 40 * q^83 + 4 * q^84 - 40 * q^86 + 20 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.0386882	+	1.73162i	−0.0223366	+	0.999751i
$3$	−0.0386882	+	1.73162i	−0.0223366	+	0.999751i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.73162	+	0.0386882i	0.706930	+	0.0157944i
$7$		−	2.83902i		−	1.07305i	−0.843884	−	0.536525i	$-0.819737\pi$
$7$		−	2.83902i		−	1.07305i	0.843884	−	0.536525i	$-0.180263\pi$
$8$			1.00000i			0.353553i
$9$	−2.99701	−	0.133986i	−0.999002	−	0.0446621i
$10$			1.00000i			0.316228i
$11$	4.50428			1.35809			0.679046	−	0.734096i	$-0.262394\pi$
$11$	4.50428			1.35809			0.679046	+	0.734096i	$0.262394\pi$
$12$	0.0386882	−	1.73162i	0.0111683	−	0.499875i
$13$	−5.89898			−1.63608			−0.818042	−	0.575159i	$-0.804940\pi$
$13$	−5.89898			−1.63608			−0.818042	+	0.575159i	$0.804940\pi$
$14$	−2.83902			−0.758761
$15$	0.0386882	−	1.73162i	0.00998924	−	0.447102i
$16$	1.00000			0.250000
$17$	−5.40124			−1.30999			−0.654996	−	0.755632i	$-0.727330\pi$
$17$	−5.40124			−1.30999			−0.654996	+	0.755632i	$0.727330\pi$
$18$	−0.133986	+	2.99701i	−0.0315809	+	0.706401i
$19$		−	2.26797i		−	0.520309i	−0.965567	−	0.260154i	$-0.916227\pi$
$19$		−	2.26797i		−	0.520309i	0.965567	−	0.260154i	$-0.0837734\pi$
$20$	1.00000			0.223607
$21$	4.91611	+	0.109837i	1.07278	+	0.0239683i
$22$		−	4.50428i		−	0.960316i
$23$	3.64088	−	3.12154i	0.759176	−	0.650885i
$23$	3.64088	−	3.12154i	0.759176	−	0.650885i
$24$	−1.73162	−	0.0386882i	−0.353465	−	0.00789719i
$25$	1.00000			0.200000
$26$			5.89898i			1.15689i
$27$	0.347962	−	5.18449i	0.0669653	−	0.997755i
$28$			2.83902i			0.536525i
$29$		−	4.81253i		−	0.893665i	−0.894618	−	0.446832i	$-0.852552\pi$
$29$		−	4.81253i		−	0.893665i	0.894618	−	0.446832i	$-0.147448\pi$
$30$	−1.73162	−	0.0386882i	−0.316149	−	0.00706346i
$31$	−9.92135			−1.78193			−0.890964	−	0.454075i	$-0.849970\pi$
$31$	−9.92135			−1.78193			−0.890964	+	0.454075i	$0.849970\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.174262	+	7.79970i	−0.0303352	+	1.35775i
$34$			5.40124i			0.926304i
$35$			2.83902i			0.479883i
$36$	2.99701	+	0.133986i	0.499501	+	0.0223310i
$37$		−	3.92624i		−	0.645470i	−0.946489	−	0.322735i	$-0.895398\pi$
$37$		−	3.92624i		−	0.645470i	0.946489	−	0.322735i	$-0.104602\pi$
$38$	−2.26797			−0.367914
$39$	0.228221	−	10.2148i	0.0365446	−	1.63568i
$40$		−	1.00000i		−	0.158114i
$41$		−	2.24625i		−	0.350805i	−0.984497	−	0.175402i	$-0.943877\pi$
$41$		−	2.24625i		−	0.350805i	0.984497	−	0.175402i	$-0.0561226\pi$
$42$	0.109837	−	4.91611i	0.0169482	−	0.758572i
$43$		−	11.5505i		−	1.76143i	−0.473648	−	0.880714i	$-0.657063\pi$
$43$		−	11.5505i		−	1.76143i	0.473648	−	0.880714i	$-0.342937\pi$
$44$	−4.50428			−0.679046
$45$	2.99701	+	0.133986i	0.446767	+	0.0199735i
$46$	−3.12154	−	3.64088i	−0.460245	−	0.536819i
$47$			1.55237i			0.226437i	0.993570	+	0.113218i	$0.0361160\pi$
$47$			1.55237i			0.226437i	−0.993570	+	0.113218i	$0.963884\pi$
$48$	−0.0386882	+	1.73162i	−0.00558415	+	0.249938i
$49$	−1.06006			−0.151437
$50$		−	1.00000i		−	0.141421i
$51$	0.208964	−	9.35288i	0.0292608	−	1.30967i
$52$	5.89898			0.818042
$53$	−6.08832			−0.836295			−0.418147	−	0.908379i	$-0.637320\pi$
$53$	−6.08832			−0.836295			−0.418147	+	0.908379i	$0.637320\pi$
$54$	−5.18449	−	0.347962i	−0.705520	−	0.0473516i
$55$	−4.50428			−0.607357
$56$	2.83902			0.379381
$57$	3.92726	+	0.0877437i	0.520179	+	0.0116219i
$58$	−4.81253			−0.631916
$59$			10.8538i			1.41305i	0.707690	+	0.706523i	$0.249737\pi$
$59$			10.8538i			1.41305i	−0.707690	+	0.706523i	$0.750263\pi$
$60$	−0.0386882	+	1.73162i	−0.00499462	+	0.223551i
$61$		−	11.6821i		−	1.49574i	−0.663843	−	0.747872i	$-0.731076\pi$
$61$		−	11.6821i		−	1.49574i	0.663843	−	0.747872i	$-0.268924\pi$
$62$			9.92135i			1.26001i
$63$	−0.380390	+	8.50857i	−0.0479247	+	1.07198i
$64$	−1.00000			−0.125000
$65$	5.89898			0.731679
$66$	7.79970	+	0.174262i	0.960077	+	0.0214502i
$67$			3.47626i			0.424693i	0.977194	+	0.212346i	$0.0681105\pi$
$67$			3.47626i			0.424693i	−0.977194	+	0.212346i	$0.931890\pi$
$68$	5.40124			0.654996
$69$	5.26445	+	6.42538i	0.633765	+	0.773525i
$70$	2.83902			0.339328
$71$			9.84805i			1.16875i	0.811484	+	0.584374i	$0.198660\pi$
$71$			9.84805i			1.16875i	−0.811484	+	0.584374i	$0.801340\pi$
$72$	0.133986	−	2.99701i	0.0157904	−	0.353201i
$73$	0.323623			0.0378772			0.0189386	−	0.999821i	$-0.493971\pi$
$73$	0.323623			0.0378772			0.0189386	+	0.999821i	$0.493971\pi$
$74$	−3.92624			−0.456416
$75$	−0.0386882	+	1.73162i	−0.00446732	+	0.199950i
$76$			2.26797i			0.260154i
$77$		−	12.7878i		−	1.45730i
$78$	−10.2148	−	0.228221i	−1.15660	−	0.0258409i
$79$		−	5.69882i		−	0.641168i	−0.947220	−	0.320584i	$-0.896121\pi$
$79$		−	5.69882i		−	0.641168i	0.947220	−	0.320584i	$-0.103879\pi$
$80$	−1.00000			−0.111803
$81$	8.96410	+	0.803115i	0.996011	+	0.0892350i
$82$	−2.24625			−0.248056
$83$	−4.31060			−0.473150			−0.236575	−	0.971613i	$-0.576025\pi$
$83$	−4.31060			−0.473150			−0.236575	+	0.971613i	$0.576025\pi$
$84$	−4.91611	−	0.109837i	−0.536391	−	0.0119842i
$85$	5.40124			0.585846
$86$	−11.5505			−1.24552
$87$	8.33347	+	0.186188i	0.893442	+	0.0199614i
$88$			4.50428i			0.480158i
$89$	11.6518			1.23509			0.617543	−	0.786537i	$-0.288128\pi$
$89$	11.6518			1.23509			0.617543	+	0.786537i	$0.288128\pi$
$90$	0.133986	−	2.99701i	0.0141234	−	0.315912i
$91$			16.7474i			1.75560i
$92$	−3.64088	+	3.12154i	−0.379588	+	0.325443i
$93$	0.383839	−	17.1800i	0.0398022	−	1.78148i
$94$	1.55237			0.160115
$95$			2.26797i			0.232689i
$96$	1.73162	+	0.0386882i	0.176733	+	0.00394859i
$97$			8.21290i			0.833893i	0.908931	+	0.416947i	$0.136900\pi$
$97$			8.21290i			0.833893i	−0.908931	+	0.416947i	$0.863100\pi$
$98$			1.06006i			0.107082i
$99$	−13.4994	−	0.603512i	−1.35674	−	0.0606552i
$100$	−1.00000			−0.100000
$101$			8.57100i			0.852846i	0.904524	+	0.426423i	$0.140227\pi$
$101$			8.57100i			0.852846i	−0.904524	+	0.426423i	$0.859773\pi$
$102$	−9.35288	−	0.208964i	−0.926073	−	0.0206905i
$103$			7.45638i			0.734699i	0.930083	+	0.367350i	$0.119735\pi$
$103$			7.45638i			0.734699i	−0.930083	+	0.367350i	$0.880265\pi$
$104$		−	5.89898i		−	0.578443i
$105$	−4.91611	−	0.109837i	−0.479763	−	0.0107190i
$106$			6.08832i			0.591350i
$107$	−15.4707			−1.49561			−0.747807	−	0.663916i	$-0.768893\pi$
$107$	−15.4707			−1.49561			−0.747807	+	0.663916i	$0.768893\pi$
$108$	−0.347962	+	5.18449i	−0.0334826	+	0.498878i
$109$			11.6976i			1.12043i	0.828347	+	0.560215i	$0.189282\pi$
$109$			11.6976i			1.12043i	−0.828347	+	0.560215i	$0.810718\pi$
$110$			4.50428i			0.429466i
$111$	6.79875	+	0.151899i	0.645309	+	0.0144176i
$112$		−	2.83902i		−	0.268263i
$113$	8.40341			0.790527			0.395263	−	0.918568i	$-0.370653\pi$
$113$	8.40341			0.790527			0.395263	+	0.918568i	$0.370653\pi$
$114$	0.0877437	−	3.92726i	0.00821795	−	0.367822i
$115$	−3.64088	+	3.12154i	−0.339514	+	0.291085i
$116$			4.81253i			0.446832i
$117$	17.6793	+	0.790383i	1.63445	+	0.0730709i
$118$	10.8538			0.999174
$119$			15.3342i			1.40569i
$120$	1.73162	+	0.0386882i	0.158074	+	0.00353173i
$121$	9.28856			0.844414
$122$	−11.6821			−1.05765
$123$	3.88964	+	0.0869031i	0.350717	+	0.00783579i
$124$	9.92135			0.890964
$125$	−1.00000			−0.0894427
$126$	8.50857	+	0.380390i	0.758004	+	0.0338879i
$127$	−13.8803			−1.23168			−0.615839	−	0.787872i	$-0.711183\pi$
$127$	−13.8803			−1.23168			−0.615839	+	0.787872i	$0.711183\pi$
$128$			1.00000i			0.0883883i
$129$	20.0010	+	0.446866i	1.76099	+	0.0393444i
$130$		−	5.89898i		−	0.517375i
$131$			7.37577i			0.644424i	0.946667	+	0.322212i	$0.104426\pi$
$131$			7.37577i			0.644424i	−0.946667	+	0.322212i	$0.895574\pi$
$132$	0.174262	−	7.79970i	0.0151676	−	0.678877i
$133$	−6.43883			−0.558317
$134$	3.47626			0.300303
$135$	−0.347962	+	5.18449i	−0.0299478	+	0.446210i
$136$		−	5.40124i		−	0.463152i
$137$	−1.02064			−0.0871996			−0.0435998	−	0.999049i	$-0.513883\pi$
$137$	−1.02064			−0.0871996			−0.0435998	+	0.999049i	$0.513883\pi$
$138$	6.42538	−	5.26445i	0.546965	−	0.448140i
$139$	−0.625898			−0.0530880			−0.0265440	−	0.999648i	$-0.508450\pi$
$139$	−0.625898			−0.0530880			−0.0265440	+	0.999648i	$0.508450\pi$
$140$		−	2.83902i		−	0.239941i
$141$	−2.68812	−	0.0600584i	−0.226380	−	0.00505783i
$142$	9.84805			0.826430
$143$	−26.5707			−2.22195
$144$	−2.99701	−	0.133986i	−0.249751	−	0.0111655i
$145$			4.81253i			0.399659i
$146$		−	0.323623i		−	0.0267832i
$147$	0.0410117	−	1.83562i	0.00338259	−	0.151399i
$148$			3.92624i			0.322735i
$149$	−8.47908			−0.694633			−0.347317	−	0.937748i	$-0.612907\pi$
$149$	−8.47908			−0.694633			−0.347317	+	0.937748i	$0.612907\pi$
$150$	1.73162	+	0.0386882i	0.141386	+	0.00315887i
$151$	23.4124			1.90527			0.952637	−	0.304110i	$-0.0983592\pi$
$151$	23.4124			1.90527			0.952637	+	0.304110i	$0.0983592\pi$
$152$	2.26797			0.183957
$153$	16.1875	+	0.723691i	1.30868	+	0.0585070i
$154$	−12.7878			−1.03047
$155$	9.92135			0.796902
$156$	−0.228221	+	10.2148i	−0.0182723	+	0.817838i
$157$		−	0.880316i		−	0.0702569i	−0.999383	−	0.0351284i	$-0.988816\pi$
$157$		−	0.880316i		−	0.0702569i	0.999383	−	0.0351284i	$-0.0111840\pi$
$158$	−5.69882			−0.453374
$159$	0.235546	−	10.5426i	0.0186800	−	0.836086i
$160$			1.00000i			0.0790569i
$161$	−8.86211	−	10.3366i	−0.698432	−	0.814634i
$162$	0.803115	−	8.96410i	0.0630987	−	0.704286i
$163$	12.2560			0.959964			0.479982	−	0.877278i	$-0.340643\pi$
$163$	12.2560			0.959964			0.479982	+	0.877278i	$0.340643\pi$
$164$			2.24625i			0.175402i
$165$	0.174262	−	7.79970i	0.0135663	−	0.607206i
$166$			4.31060i			0.334568i
$167$		−	21.5502i		−	1.66761i	−0.552062	−	0.833803i	$-0.686159\pi$
$167$		−	21.5502i		−	1.66761i	0.552062	−	0.833803i	$-0.313841\pi$
$168$	−0.109837	+	4.91611i	−0.00847408	+	0.379286i
$169$	21.7980			1.67677
$170$		−	5.40124i		−	0.414256i
$171$	−0.303877	+	6.79713i	−0.0232381	+	0.519789i
$172$			11.5505i			0.880714i
$173$			2.77254i			0.210792i	0.994430	+	0.105396i	$0.0336111\pi$
$173$			2.77254i			0.210792i	−0.994430	+	0.105396i	$0.966389\pi$
$174$	0.186188	−	8.33347i	0.0141149	−	0.631759i
$175$		−	2.83902i		−	0.214610i
$176$	4.50428			0.339523
$177$	−18.7947	−	0.419914i	−1.41269	−	0.0315627i
$178$		−	11.6518i		−	0.873338i
$179$		−	5.79371i		−	0.433042i	−0.976278	−	0.216521i	$-0.930529\pi$
$179$		−	5.79371i		−	0.433042i	0.976278	−	0.216521i	$-0.0694710\pi$
$180$	−2.99701	−	0.133986i	−0.223384	−	0.00998675i
$181$		−	19.0813i		−	1.41830i	−0.705058	−	0.709150i	$-0.749079\pi$
$181$		−	19.0813i		−	1.41830i	0.705058	−	0.709150i	$-0.250921\pi$
$182$	16.7474			1.24140
$183$	20.2290	+	0.451960i	1.49537	+	0.0334099i
$184$	3.12154	+	3.64088i	0.230123	+	0.268409i
$185$			3.92624i			0.288663i
$186$	−17.1800	−	0.383839i	−1.25970	−	0.0281444i
$187$	−24.3287			−1.77909
$188$		−	1.55237i		−	0.113218i
$189$	−14.7189	−	0.987872i	−1.07064	−	0.0718571i
$190$	2.26797			0.164536
$191$	12.9022			0.933573			0.466787	−	0.884370i	$-0.345412\pi$
$191$	12.9022			0.933573			0.466787	+	0.884370i	$0.345412\pi$
$192$	0.0386882	−	1.73162i	0.00279208	−	0.124969i
$193$	2.08785			0.150286			0.0751432	−	0.997173i	$-0.476059\pi$
$193$	2.08785			0.150286			0.0751432	+	0.997173i	$0.476059\pi$
$194$	8.21290			0.589652
$195$	−0.228221	+	10.2148i	−0.0163432	+	0.731496i
$196$	1.06006			0.0757185
$197$		−	1.94161i		−	0.138334i	−0.997605	−	0.0691671i	$-0.977966\pi$
$197$		−	1.94161i		−	0.138334i	0.997605	−	0.0691671i	$-0.0220342\pi$
$198$	−0.603512	+	13.4994i	−0.0428897	+	0.959358i
$199$		−	20.2897i		−	1.43830i	−0.694855	−	0.719149i	$-0.744532\pi$
$199$		−	20.2897i		−	1.43830i	0.694855	−	0.719149i	$-0.255468\pi$
$200$			1.00000i			0.0707107i
$201$	−6.01955	−	0.134490i	−0.424587	−	0.00948620i
$202$	8.57100			0.603053
$203$	−13.6629			−0.958947
$204$	−0.208964	+	9.35288i	−0.0146304	+	0.654833i
$205$			2.24625i			0.156885i
$206$	7.45638			0.519511
$207$	−11.3300	+	8.86743i	−0.787489	+	0.616329i
$208$	−5.89898			−0.409021
$209$		−	10.2156i		−	0.706627i
$210$	−0.109837	+	4.91611i	−0.00757945	+	0.339244i
$211$	−8.99923			−0.619532			−0.309766	−	0.950813i	$-0.600251\pi$
$211$	−8.99923			−0.619532			−0.309766	+	0.950813i	$0.600251\pi$
$212$	6.08832			0.418147
$213$	−17.0531	−	0.381003i	−1.16846	−	0.0261059i
$214$			15.4707i			1.05756i
$215$			11.5505i			0.787735i
$216$	5.18449	+	0.347962i	0.352760	+	0.0236758i
$217$			28.1670i			1.91210i
$218$	11.6976			0.792264
$219$	−0.0125204	+	0.560391i	−0.000846048	+	0.0378677i
$220$	4.50428			0.303679
$221$	31.8618			2.14326
$222$	0.151899	−	6.79875i	0.0101948	−	0.456302i
$223$	13.9192			0.932099			0.466049	−	0.884759i	$-0.345677\pi$
$223$	13.9192			0.932099			0.466049	+	0.884759i	$0.345677\pi$
$224$	−2.83902			−0.189690
$225$	−2.99701	−	0.133986i	−0.199800	−	0.00893242i
$226$		−	8.40341i		−	0.558987i
$227$	−11.5024			−0.763442			−0.381721	−	0.924278i	$-0.624668\pi$
$227$	−11.5024			−0.763442			−0.381721	+	0.924278i	$0.624668\pi$
$228$	−3.92726	−	0.0877437i	−0.260089	−	0.00581097i
$229$		−	14.9027i		−	0.984797i	−0.870370	−	0.492398i	$-0.836120\pi$
$229$		−	14.9027i		−	0.984797i	0.870370	−	0.492398i	$-0.163880\pi$
$230$	3.12154	+	3.64088i	0.205828	+	0.240073i
$231$	22.1435	+	0.494735i	1.45694	+	0.0325512i
$232$	4.81253			0.315958
$233$		−	3.74448i		−	0.245309i	−0.992449	−	0.122655i	$-0.960859\pi$
$233$		−	3.74448i		−	0.245309i	0.992449	−	0.122655i	$-0.0391407\pi$
$234$	0.790383	−	17.6793i	0.0516689	−	1.15573i
$235$		−	1.55237i		−	0.101266i
$236$		−	10.8538i		−	0.706523i
$237$	9.86819	+	0.220477i	0.641008	+	0.0143215i
$238$	15.3342			0.993971
$239$		−	23.2940i		−	1.50676i	−0.657585	−	0.753381i	$-0.728422\pi$
$239$		−	23.2940i		−	1.50676i	0.657585	−	0.753381i	$-0.271578\pi$
$240$	0.0386882	−	1.73162i	0.00249731	−	0.111776i
$241$			29.3778i			1.89239i	0.323598	+	0.946195i	$0.395107\pi$
$241$			29.3778i			1.89239i	−0.323598	+	0.946195i	$0.604893\pi$
$242$		−	9.28856i		−	0.597091i
$243$	−1.73749	+	15.4913i	−0.111460	+	0.993769i
$244$			11.6821i			0.747872i
$245$	1.06006			0.0677246
$246$	0.0869031	−	3.88964i	0.00554074	−	0.247995i
$247$			13.3787i			0.851268i
$248$		−	9.92135i		−	0.630006i
$249$	0.166769	−	7.46432i	0.0105686	−	0.473032i
$250$			1.00000i			0.0632456i
$251$	28.0442			1.77014			0.885068	−	0.465462i	$-0.154112\pi$
$251$	28.0442			1.77014			0.885068	+	0.465462i	$0.154112\pi$
$252$	0.380390	−	8.50857i	0.0239623	−	0.535990i
$253$	16.3996	−	14.0603i	1.03103	−	0.883962i
$254$			13.8803i			0.870928i
$255$	−0.208964	+	9.35288i	−0.0130858	+	0.585700i
$256$	1.00000			0.0625000
$257$			10.1173i			0.631102i	0.948909	+	0.315551i	$0.102189\pi$
$257$			10.1173i			0.631102i	−0.948909	+	0.315551i	$0.897811\pi$
$258$	0.446866	−	20.0010i	0.0278207	−	1.24521i
$259$	−11.1467			−0.692621
$260$	−5.89898			−0.365839
$261$	−0.644813	+	14.4232i	−0.0399129	+	0.892773i
$262$	7.37577			0.455677
$263$	−27.9974			−1.72639			−0.863197	−	0.504867i	$-0.831541\pi$
$263$	−27.9974			−1.72639			−0.863197	+	0.504867i	$0.831541\pi$
$264$	−7.79970	−	0.174262i	−0.480038	−	0.0107251i
$265$	6.08832			0.374002
$266$			6.43883i			0.394790i
$267$	−0.450786	+	20.1765i	−0.0275877	+	1.23478i
$268$		−	3.47626i		−	0.212346i
$269$			11.8305i			0.721318i	0.932698	+	0.360659i	$0.117448\pi$
$269$			11.8305i			0.721318i	−0.932698	+	0.360659i	$0.882552\pi$
$270$	5.18449	+	0.347962i	0.315518	+	0.0211763i
$271$	−27.3595			−1.66197			−0.830987	−	0.556292i	$-0.812224\pi$
$271$	−27.3595			−1.66197			−0.830987	+	0.556292i	$0.812224\pi$
$272$	−5.40124			−0.327498
$273$	−29.0000	−	0.647924i	−1.75516	−	0.0392142i
$274$			1.02064i			0.0616594i
$275$	4.50428			0.271618
$276$	−5.26445	−	6.42538i	−0.316883	−	0.386763i
$277$	−17.9484			−1.07842			−0.539208	−	0.842173i	$-0.681276\pi$
$277$	−17.9484			−1.07842			−0.539208	+	0.842173i	$0.681276\pi$
$278$			0.625898i			0.0375389i
$279$	29.7344	+	1.32932i	1.78015	+	0.0795846i
$280$	−2.83902			−0.169664
$281$	0.662441			0.0395179			0.0197590	−	0.999805i	$-0.493710\pi$
$281$	0.662441			0.0395179			0.0197590	+	0.999805i	$0.493710\pi$
$282$	−0.0600584	+	2.68812i	−0.00357643	+	0.160075i
$283$		−	25.7017i		−	1.52781i	−0.645331	−	0.763903i	$-0.723280\pi$
$283$		−	25.7017i		−	1.52781i	0.645331	−	0.763903i	$-0.276720\pi$
$284$		−	9.84805i		−	0.584374i
$285$	−3.92726	−	0.0877437i	−0.232631	−	0.00519749i
$286$			26.5707i			1.57116i
$287$	−6.37715			−0.376431
$288$	−0.133986	+	2.99701i	−0.00789522	+	0.176600i
$289$	12.1733			0.716079
$290$	4.81253			0.282602
$291$	−14.2216	−	0.317742i	−0.833685	−	0.0186264i
$292$	−0.323623			−0.0189386
$293$	19.4320			1.13523			0.567614	−	0.823295i	$-0.307867\pi$
$293$	19.4320			1.13523			0.567614	+	0.823295i	$0.307867\pi$
$294$	−1.83562	−	0.0410117i	−0.107055	−	0.00239185i
$295$		−	10.8538i		−	0.631933i
$296$	3.92624			0.228208
$297$	1.56732	−	23.3524i	0.0909450	−	1.35504i
$298$			8.47908i			0.491180i
$299$	−21.4775	+	18.4139i	−1.24208	+	1.06490i
$300$	0.0386882	−	1.73162i	0.00223366	−	0.0999751i
$301$	−32.7920			−1.89010
$302$		−	23.4124i		−	1.34723i
$303$	−14.8417	−	0.331596i	−0.852633	−	0.0190497i
$304$		−	2.26797i		−	0.130077i
$305$			11.6821i			0.668917i
$306$	0.723691	−	16.1875i	0.0413707	−	0.925380i
$307$	1.65943			0.0947088			0.0473544	−	0.998878i	$-0.484921\pi$
$307$	1.65943			0.0947088			0.0473544	+	0.998878i	$0.484921\pi$
$308$			12.7878i			0.728651i
$309$	−12.9116	−	0.288474i	−0.734516	−	0.0164107i
$310$		−	9.92135i		−	0.563495i
$311$			12.5570i			0.712043i	0.934478	+	0.356022i	$0.115867\pi$
$311$			12.5570i			0.712043i	−0.934478	+	0.356022i	$0.884133\pi$
$312$	10.2148	+	0.228221i	0.578299	+	0.0129205i
$313$		−	13.5424i		−	0.765459i	−0.923860	−	0.382730i	$-0.874984\pi$
$313$		−	13.5424i		−	0.765459i	0.923860	−	0.382730i	$-0.125016\pi$
$314$	−0.880316			−0.0496791
$315$	0.380390	−	8.50857i	0.0214326	−	0.479404i
$316$			5.69882i			0.320584i
$317$		−	11.1266i		−	0.624935i	−0.949929	−	0.312467i	$-0.898845\pi$
$317$		−	11.1266i		−	0.624935i	0.949929	−	0.312467i	$-0.101155\pi$
$318$	−10.5426	−	0.235546i	−0.591202	−	0.0132088i
$319$		−	21.6770i		−	1.21368i
$320$	1.00000			0.0559017
$321$	0.598535	−	26.7894i	0.0334070	−	1.49524i
$322$	−10.3366	+	8.86211i	−0.576033	+	0.493866i
$323$			12.2499i			0.681600i
$324$	−8.96410	−	0.803115i	−0.498005	−	0.0446175i
$325$	−5.89898			−0.327217
$326$		−	12.2560i		−	0.678797i
$327$	−20.2558	−	0.452560i	−1.12015	−	0.0250266i
$328$	2.24625			0.124028
$329$	4.40722			0.242978
$330$	−7.79970	−	0.174262i	−0.429359	−	0.00959283i
$331$	−5.37160			−0.295250			−0.147625	−	0.989043i	$-0.547163\pi$
$331$	−5.37160			−0.295250			−0.147625	+	0.989043i	$0.547163\pi$
$332$	4.31060			0.236575
$333$	−0.526062	+	11.7670i	−0.0288280	+	0.644826i
$334$	−21.5502			−1.17918
$335$		−	3.47626i		−	0.189928i
$336$	4.91611	+	0.109837i	0.268196	+	0.00599208i
$337$		−	17.9318i		−	0.976809i	−0.872617	−	0.488404i	$-0.837579\pi$
$337$		−	17.9318i		−	0.976809i	0.872617	−	0.488404i	$-0.162421\pi$
$338$		−	21.7980i		−	1.18566i
$339$	−0.325113	+	14.5515i	−0.0176577	+	0.790330i
$340$	−5.40124			−0.292923
$341$	−44.6886			−2.42002
$342$	6.79713	+	0.303877i	0.367547	+	0.0164318i
$343$		−	16.8636i		−	0.910551i
$344$	11.5505			0.622759
$345$	−5.26445	−	6.42538i	−0.283428	−	0.345931i
$346$	2.77254			0.149053
$347$			9.99097i			0.536343i	0.963371	+	0.268172i	$0.0864195\pi$
$347$			9.99097i			0.536343i	−0.963371	+	0.268172i	$0.913581\pi$
$348$	−8.33347	−	0.186188i	−0.446721	−	0.00998072i
$349$	−15.3124			−0.819657			−0.409828	−	0.912163i	$-0.634411\pi$
$349$	−15.3124			−0.819657			−0.409828	+	0.912163i	$0.634411\pi$
$350$	−2.83902			−0.151752
$351$	−2.05262	+	30.5832i	−0.109561	+	1.63241i
$352$		−	4.50428i		−	0.240079i
$353$		−	8.49859i		−	0.452334i	−0.974089	−	0.226167i	$-0.927380\pi$
$353$		−	8.49859i		−	0.452334i	0.974089	−	0.226167i	$-0.0726195\pi$
$354$	−0.419914	+	18.7947i	−0.0223182	+	0.998925i
$355$		−	9.84805i		−	0.522680i
$356$	−11.6518			−0.617543
$357$	−26.5531	−	0.593253i	−1.40534	−	0.0313983i
$358$	−5.79371			−0.306207
$359$	23.5828			1.24465			0.622327	−	0.782758i	$-0.286188\pi$
$359$	23.5828			1.24465			0.622327	+	0.782758i	$0.286188\pi$
$360$	−0.133986	+	2.99701i	−0.00706170	+	0.157956i
$361$	13.8563			0.729279
$362$	−19.0813			−1.00289
$363$	−0.359357	+	16.0842i	−0.0188614	+	0.844204i
$364$		−	16.7474i		−	0.877800i
$365$	−0.323623			−0.0169392
$366$	0.451960	−	20.2290i	0.0236243	−	1.05739i
$367$			34.0961i			1.77980i	0.456155	+	0.889900i	$0.349226\pi$
$367$			34.0961i			1.77980i	−0.456155	+	0.889900i	$0.650774\pi$
$368$	3.64088	−	3.12154i	0.189794	−	0.162721i
$369$	−0.300966	+	6.73201i	−0.0156677	+	0.350455i
$370$	3.92624			0.204115
$371$			17.2849i			0.897386i
$372$	−0.383839	+	17.1800i	−0.0199011	+	0.890741i
$373$		−	3.12850i		−	0.161988i	−0.996715	−	0.0809938i	$-0.974191\pi$
$373$		−	3.12850i		−	0.161988i	0.996715	−	0.0809938i	$-0.0258094\pi$
$374$			24.3287i			1.25801i
$375$	0.0386882	−	1.73162i	0.00199785	−	0.0894204i
$376$	−1.55237			−0.0800575
$377$			28.3890i			1.46211i
$378$	−0.987872	+	14.7189i	−0.0508106	+	0.757058i
$379$			0.796283i			0.0409023i	0.999791	+	0.0204511i	$0.00651026\pi$
$379$			0.796283i			0.0409023i	−0.999791	+	0.0204511i	$0.993490\pi$
$380$		−	2.26797i		−	0.116345i
$381$	0.537004	−	24.0354i	0.0275115	−	1.23137i
$382$		−	12.9022i		−	0.660136i
$383$	11.8370			0.604842			0.302421	−	0.953174i	$-0.402205\pi$
$383$	11.8370			0.604842			0.302421	+	0.953174i	$0.402205\pi$
$384$	−1.73162	−	0.0386882i	−0.0883663	−	0.00197430i
$385$			12.7878i			0.651725i
$386$		−	2.08785i		−	0.106269i
$387$	−1.54760	+	34.6168i	−0.0786691	+	1.75967i
$388$		−	8.21290i		−	0.416947i
$389$	0.884618			0.0448519			0.0224260	−	0.999749i	$-0.492861\pi$
$389$	0.884618			0.0448519			0.0224260	+	0.999749i	$0.492861\pi$
$390$	10.2148	+	0.228221i	0.517246	+	0.0115564i
$391$	−19.6653	+	16.8601i	−0.994515	+	0.852654i
$392$		−	1.06006i		−	0.0535410i
$393$	−12.7720	−	0.285355i	−0.644264	−	0.0143943i
$394$	−1.94161			−0.0978170
$395$			5.69882i			0.286739i
$396$	13.4994	+	0.603512i	0.678369	+	0.0303276i
$397$	5.97733			0.299993			0.149997	−	0.988686i	$-0.452074\pi$
$397$	5.97733			0.299993			0.149997	+	0.988686i	$0.452074\pi$
$398$	−20.2897			−1.01703
$399$	0.249106	−	11.1496i	0.0124709	−	0.558178i
$400$	1.00000			0.0500000
$401$	13.0800			0.653184			0.326592	−	0.945165i	$-0.394100\pi$
$401$	13.0800			0.653184			0.326592	+	0.945165i	$0.394100\pi$
$402$	−0.134490	+	6.01955i	−0.00670775	+	0.300228i
$403$	58.5259			2.91538
$404$		−	8.57100i		−	0.426423i
$405$	−8.96410	−	0.803115i	−0.445429	−	0.0399071i
$406$			13.6629i			0.678078i
$407$		−	17.6849i		−	0.876607i
$408$	9.35288	+	0.208964i	0.463037	+	0.0103453i
$409$	−0.595984			−0.0294695			−0.0147348	−	0.999891i	$-0.504690\pi$
$409$	−0.595984			−0.0294695			−0.0147348	+	0.999891i	$0.504690\pi$
$410$	2.24625			0.110934
$411$	0.0394869	−	1.76737i	0.00194774	−	0.0871778i
$412$		−	7.45638i		−	0.367350i
$413$	30.8142			1.51627
$414$	8.86743	+	11.3300i	0.435811	+	0.556839i
$415$	4.31060			0.211599
$416$			5.89898i			0.289221i
$417$	0.0242148	−	1.08382i	0.00118581	−	0.0530747i
$418$	−10.2156			−0.499661
$419$	1.73544			0.0847816			0.0423908	−	0.999101i	$-0.486503\pi$
$419$	1.73544			0.0847816			0.0423908	+	0.999101i	$0.486503\pi$
$420$	4.91611	+	0.109837i	0.239881	+	0.00535948i
$421$			5.82242i			0.283767i	0.989883	+	0.141884i	$0.0453159\pi$
$421$			5.82242i			0.283767i	−0.989883	+	0.141884i	$0.954684\pi$
$422$			8.99923i			0.438076i
$423$	0.207997	−	4.65247i	0.0101131	−	0.226211i
$424$		−	6.08832i		−	0.295675i
$425$	−5.40124			−0.261998
$426$	−0.381003	+	17.0531i	−0.0184596	+	0.826224i
$427$	−33.1659			−1.60501
$428$	15.4707			0.747807
$429$	1.02797	−	46.0103i	0.0496309	−	2.22140i
$430$	11.5505			0.557013
$431$	−6.19650			−0.298475			−0.149237	−	0.988801i	$-0.547682\pi$
$431$	−6.19650			−0.298475			−0.149237	+	0.988801i	$0.547682\pi$
$432$	0.347962	−	5.18449i	0.0167413	−	0.249439i
$433$		−	10.6171i		−	0.510226i	−0.966911	−	0.255113i	$-0.917887\pi$
$433$		−	10.6171i		−	0.510226i	0.966911	−	0.255113i	$-0.0821127\pi$
$434$	28.1670			1.35206
$435$	−8.33347	−	0.186188i	−0.399559	−	0.00892703i
$436$		−	11.6976i		−	0.560215i
$437$	−7.07956	−	8.25742i	−0.338661	−	0.395006i
$438$	0.560391	+	0.0125204i	0.0267765	+	0.000598246i
$439$	−24.8996			−1.18839			−0.594197	−	0.804319i	$-0.702530\pi$
$439$	−24.8996			−1.18839			−0.594197	+	0.804319i	$0.702530\pi$
$440$		−	4.50428i		−	0.214733i
$441$	3.17700	+	0.142033i	0.151286	+	0.00676349i
$442$		−	31.8618i		−	1.51551i
$443$		−	8.79242i		−	0.417741i	−0.977943	−	0.208870i	$-0.933021\pi$
$443$		−	8.79242i		−	0.417741i	0.977943	−	0.208870i	$-0.0669786\pi$
$444$	−6.79875	−	0.151899i	−0.322654	−	0.00720880i
$445$	−11.6518			−0.552348
$446$		−	13.9192i		−	0.659093i
$447$	0.328040	−	14.6825i	0.0155158	−	0.694460i
$448$			2.83902i			0.134131i
$449$		−	21.0781i		−	0.994739i	−0.867539	−	0.497370i	$-0.834299\pi$
$449$		−	21.0781i		−	0.994739i	0.867539	−	0.497370i	$-0.165701\pi$
$450$	−0.133986	+	2.99701i	−0.00631617	+	0.141280i
$451$		−	10.1177i		−	0.476425i
$452$	−8.40341			−0.395263
$453$	−0.905782	+	40.5413i	−0.0425574	+	1.90480i
$454$			11.5024i			0.539835i
$455$		−	16.7474i		−	0.785128i
$456$	−0.0877437	+	3.92726i	−0.00410897	+	0.183911i
$457$		−	7.66411i		−	0.358512i	−0.983802	−	0.179256i	$-0.942631\pi$
$457$		−	7.66411i		−	0.358512i	0.983802	−	0.179256i	$-0.0573690\pi$
$458$	−14.9027			−0.696357
$459$	−1.87942	+	28.0026i	−0.0877240	+	1.30705i
$460$	3.64088	−	3.12154i	0.169757	−	0.145542i
$461$		−	36.6333i		−	1.70618i	−0.521761	−	0.853092i	$-0.674725\pi$
$461$		−	36.6333i		−	1.70618i	0.521761	−	0.853092i	$-0.325275\pi$
$462$	0.494735	−	22.1435i	0.0230172	−	1.03021i
$463$	7.73369			0.359415			0.179708	−	0.983720i	$-0.442485\pi$
$463$	7.73369			0.359415			0.179708	+	0.983720i	$0.442485\pi$
$464$		−	4.81253i		−	0.223416i
$465$	−0.383839	+	17.1800i	−0.0178001	+	0.796703i
$466$	−3.74448			−0.173460
$467$	−20.9022			−0.967237			−0.483618	−	0.875279i	$-0.660678\pi$
$467$	−20.9022			−0.967237			−0.483618	+	0.875279i	$0.660678\pi$
$468$	−17.6793	−	0.790383i	−0.817226	−	0.0365355i
$469$	9.86918			0.455717
$470$	−1.55237			−0.0716056
$471$	1.52437	+	0.0340578i	0.0702394	+	0.00156930i
$472$	−10.8538			−0.499587
$473$		−	52.0265i		−	2.39218i
$474$	0.220477	−	9.86819i	0.0101268	−	0.453261i
$475$		−	2.26797i		−	0.104062i
$476$		−	15.3342i		−	0.702844i
$477$	18.2467	+	0.815751i	0.835460	+	0.0373507i
$478$	−23.2940			−1.06544
$479$	−33.1326			−1.51387			−0.756933	−	0.653492i	$-0.773303\pi$
$479$	−33.1326			−1.51387			−0.756933	+	0.653492i	$0.773303\pi$
$480$	−1.73162	−	0.0386882i	−0.0790372	−	0.00176586i
$481$			23.1608i			1.05604i
$482$	29.3778			1.33812
$483$	18.2418	−	14.9459i	0.830032	−	0.680062i
$484$	−9.28856			−0.422207
$485$		−	8.21290i		−	0.372928i
$486$	15.4913	+	1.73749i	0.702701	+	0.0788143i
$487$	10.1567			0.460244			0.230122	−	0.973162i	$-0.426087\pi$
$487$	10.1567			0.460244			0.230122	+	0.973162i	$0.426087\pi$
$488$	11.6821			0.528825
$489$	−0.474162	+	21.2227i	−0.0214423	+	0.959724i
$490$		−	1.06006i		−	0.0478886i
$491$			28.9321i			1.30569i	0.757492	+	0.652844i	$0.226424\pi$
$491$			28.9321i			1.30569i	−0.757492	+	0.652844i	$0.773576\pi$
$492$	−3.88964	−	0.0869031i	−0.175359	−	0.00391790i
$493$			25.9936i			1.17069i
$494$	13.3787			0.601938
$495$	13.4994	+	0.603512i	0.606751	+	0.0271258i
$496$	−9.92135			−0.445482
$497$	27.9588			1.25413
$498$	−7.46432	−	0.166769i	−0.334484	−	0.00747311i
$499$	5.77406			0.258482			0.129241	−	0.991613i	$-0.458746\pi$
$499$	5.77406			0.258482			0.129241	+	0.991613i	$0.458746\pi$
$500$	1.00000			0.0447214
$501$	37.3168	+	0.833738i	1.66719	+	0.0372487i
$502$		−	28.0442i		−	1.25168i
$503$	40.2622			1.79520			0.897601	−	0.440809i	$-0.145308\pi$
$503$	40.2622			1.79520			0.897601	+	0.440809i	$0.145308\pi$
$504$	−8.50857	−	0.380390i	−0.379002	−	0.0169439i
$505$		−	8.57100i		−	0.381404i
$506$	−14.0603	−	16.3996i	−0.625056	−	0.729049i
$507$	−0.843325	+	37.7458i	−0.0374534	+	1.67635i
$508$	13.8803			0.615839
$509$		−	38.6823i		−	1.71456i	−0.514846	−	0.857282i	$-0.672151\pi$
$509$		−	38.6823i		−	1.71456i	0.514846	−	0.857282i	$-0.327849\pi$
$510$	9.35288	+	0.208964i	0.414152	+	0.00925307i
$511$		−	0.918773i		−	0.0406441i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.7583	−	0.789168i	−0.519141	−	0.0348426i
$514$	10.1173			0.446256
$515$		−	7.45638i		−	0.328567i
$516$	−20.0010	−	0.446866i	−0.880495	−	0.0196722i
$517$			6.99233i			0.307522i
$518$			11.1467i			0.489757i
$519$	−4.80098	−	0.107264i	−0.210740	−	0.00470839i
$520$			5.89898i			0.258688i
$521$	−18.5534			−0.812838			−0.406419	−	0.913687i	$-0.633223\pi$
$521$	−18.5534			−0.812838			−0.406419	+	0.913687i	$0.633223\pi$
$522$	14.4232	+	0.644813i	0.631286	+	0.0282227i
$523$		−	30.0881i		−	1.31566i	−0.753166	−	0.657830i	$-0.771474\pi$
$523$		−	30.0881i		−	1.31566i	0.753166	−	0.657830i	$-0.228526\pi$
$524$		−	7.37577i		−	0.322212i
$525$	4.91611	+	0.109837i	0.214557	+	0.00479366i
$526$			27.9974i			1.22074i
$527$	53.5875			2.33431
$528$	−0.174262	+	7.79970i	−0.00758380	+	0.339438i
$529$	3.51204	−	22.7303i	0.152697	−	0.988273i
$530$		−	6.08832i		−	0.264460i
$531$	1.45426	−	32.5289i	0.0631096	−	1.41164i
$532$	6.43883			0.279159
$533$			13.2506i			0.573946i
$534$	20.1765	+	0.450786i	0.873120	+	0.0195074i
$535$	15.4707			0.668859
$536$	−3.47626			−0.150152
$537$	10.0325	+	0.224148i	0.432934	+	0.00967270i
$538$	11.8305			0.510049
$539$	−4.77480			−0.205665
$540$	0.347962	−	5.18449i	0.0149739	−	0.223105i
$541$	−34.7417			−1.49366			−0.746831	−	0.665014i	$-0.768425\pi$
$541$	−34.7417			−1.49366			−0.746831	+	0.665014i	$0.768425\pi$
$542$			27.3595i			1.17519i
$543$	33.0415	+	0.738219i	1.41795	+	0.0316800i
$544$			5.40124i			0.231576i
$545$		−	11.6976i		−	0.501072i
$546$	−0.647924	+	29.0000i	−0.0277286	+	1.24109i
$547$	17.2491			0.737518			0.368759	−	0.929525i	$-0.379783\pi$
$547$	17.2491			0.737518			0.368759	+	0.929525i	$0.379783\pi$
$548$	1.02064			0.0435998
$549$	−1.56525	+	35.0114i	−0.0668031	+	1.49425i
$550$		−	4.50428i		−	0.192063i
$551$	−10.9147			−0.464981
$552$	−6.42538	+	5.26445i	−0.273483	+	0.224070i
$553$	−16.1791			−0.688005
$554$			17.9484i			0.762555i
$555$	−6.79875	−	0.151899i	−0.288591	−	0.00644775i
$556$	0.625898			0.0265440
$557$	31.7721			1.34623			0.673114	−	0.739539i	$-0.264957\pi$
$557$	31.7721			1.34623			0.673114	+	0.739539i	$0.264957\pi$
$558$	1.32932	−	29.7344i	0.0562748	−	1.25876i
$559$			68.1360i			2.88184i
$560$			2.83902i			0.119971i
$561$	0.941232	−	42.1280i	0.0397388	−	1.77865i
$562$		−	0.662441i		−	0.0279434i
$563$	−1.96043			−0.0826222			−0.0413111	−	0.999146i	$-0.513153\pi$
$563$	−1.96043			−0.0826222			−0.0413111	+	0.999146i	$0.513153\pi$
$564$	2.68812	+	0.0600584i	0.113190	+	0.00252892i
$565$	−8.40341			−0.353534
$566$	−25.7017			−1.08032
$567$	2.28006	−	25.4493i	0.0957537	−	1.06877i
$568$	−9.84805			−0.413215
$569$	6.75996			0.283392			0.141696	−	0.989910i	$-0.454744\pi$
$569$	6.75996			0.283392			0.141696	+	0.989910i	$0.454744\pi$
$570$	−0.0877437	+	3.92726i	−0.00367518	+	0.164495i
$571$			28.8048i			1.20544i	0.797951	+	0.602722i	$0.205917\pi$
$571$			28.8048i			1.20544i	−0.797951	+	0.602722i	$0.794083\pi$
$572$	26.5707			1.11098
$573$	−0.499164	+	22.3418i	−0.0208529	+	0.933341i
$574$			6.37715i			0.266177i
$575$	3.64088	−	3.12154i	0.151835	−	0.130177i
$576$	2.99701	+	0.133986i	0.124875	+	0.00558276i
$577$	44.8855			1.86861			0.934303	−	0.356479i	$-0.116023\pi$
$577$	44.8855			1.86861			0.934303	+	0.356479i	$0.116023\pi$
$578$		−	12.1733i		−	0.506344i
$579$	−0.0807749	+	3.61535i	−0.00335689	+	0.150249i
$580$		−	4.81253i		−	0.199829i
$581$			12.2379i			0.507714i
$582$	−0.317742	+	14.2216i	−0.0131708	+	0.589505i
$583$	−27.4235			−1.13577
$584$			0.323623i			0.0133916i
$585$	−17.6793	−	0.790383i	−0.730949	−	0.0326783i
$586$		−	19.4320i		−	0.802727i
$587$			2.23860i			0.0923968i	0.998932	+	0.0461984i	$0.0147106\pi$
$587$			2.23860i			0.0923968i	−0.998932	+	0.0461984i	$0.985289\pi$
$588$	−0.0410117	+	1.83562i	−0.00169129	+	0.0756996i
$589$			22.5013i			0.927152i
$590$	−10.8538			−0.446844
$591$	3.36213	+	0.0751174i	0.138300	+	0.00308992i
$592$		−	3.92624i		−	0.161367i
$593$			22.0150i			0.904048i	0.892006	+	0.452024i	$0.149298\pi$
$593$			22.0150i			0.904048i	−0.892006	+	0.452024i	$0.850702\pi$
$594$	−23.3524	−	1.56732i	−0.958161	−	0.0643078i
$595$		−	15.3342i		−	0.628642i
$596$	8.47908			0.347317
$597$	35.1340	+	0.784971i	1.43794	+	0.0321267i
$598$	18.4139	+	21.4775i	0.753000	+	0.878280i
$599$		−	5.53313i		−	0.226078i	−0.993591	−	0.113039i	$-0.963942\pi$
$599$		−	5.53313i		−	0.226078i	0.993591	−	0.113039i	$-0.0360584\pi$
$600$	−1.73162	−	0.0386882i	−0.0706930	−	0.00157944i
$601$	10.0314			0.409190			0.204595	−	0.978847i	$-0.434412\pi$
$601$	10.0314			0.409190			0.204595	+	0.978847i	$0.434412\pi$
$602$			32.7920i			1.33650i
$603$	0.465771	−	10.4184i	0.0189677	−	0.424269i
$604$	−23.4124			−0.952637
$605$	−9.28856			−0.377634
$606$	−0.331596	+	14.8417i	−0.0134702	+	0.602903i
$607$	13.3385			0.541392			0.270696	−	0.962665i	$-0.412746\pi$
$607$	13.3385			0.541392			0.270696	+	0.962665i	$0.412746\pi$
$608$	−2.26797			−0.0919784
$609$	0.528592	−	23.6589i	0.0214196	−	0.958708i
$610$	11.6821			0.472996
$611$		−	9.15742i		−	0.370470i
$612$	−16.1875	−	0.723691i	−0.654342	−	0.0292535i
$613$		−	4.93121i		−	0.199170i	−0.995029	−	0.0995849i	$-0.968249\pi$
$613$		−	4.93121i		−	0.199170i	0.995029	−	0.0995849i	$-0.0317515\pi$
$614$		−	1.65943i		−	0.0669692i
$615$	−3.88964	−	0.0869031i	−0.156846	−	0.00350427i
$616$	12.7878			0.515234
$617$	−40.0242			−1.61131			−0.805657	−	0.592383i	$-0.798187\pi$
$617$	−40.0242			−1.61131			−0.805657	+	0.592383i	$0.798187\pi$
$618$	−0.288474	+	12.9116i	−0.0116041	+	0.519381i
$619$		−	10.5263i		−	0.423088i	−0.977368	−	0.211544i	$-0.932151\pi$
$619$		−	10.5263i		−	0.423088i	0.977368	−	0.211544i	$-0.0678492\pi$
$620$	−9.92135			−0.398451
$621$	−14.9167	−	19.9623i	−0.598586	−	0.801059i
$622$	12.5570			0.503491
$623$		−	33.0797i		−	1.32531i
$624$	0.228221	−	10.2148i	0.00913614	−	0.408919i
$625$	1.00000			0.0400000
$626$	−13.5424			−0.541261
$627$	17.6895	+	0.395222i	0.706451	+	0.0157837i
$628$			0.880316i			0.0351284i
$629$			21.2065i			0.845560i
$630$	−8.50857	−	0.380390i	−0.338990	−	0.0151551i
$631$		−	14.8373i		−	0.590665i	−0.955395	−	0.295333i	$-0.904570\pi$
$631$		−	14.8373i		−	0.590665i	0.955395	−	0.295333i	$-0.0954304\pi$
$632$	5.69882			0.226687
$633$	0.348164	−	15.5832i	0.0138383	−	0.619378i
$634$	−11.1266			−0.441896
$635$	13.8803			0.550823
$636$	−0.235546	+	10.5426i	−0.00934000	+	0.418043i
$637$	6.25327			0.247763
$638$	−21.6770			−0.858201
$639$	1.31950	−	29.5147i	0.0521987	−	1.16758i
$640$		−	1.00000i		−	0.0395285i
$641$	27.3936			1.08198			0.540992	−	0.841028i	$-0.318049\pi$
$641$	27.3936			1.08198			0.540992	+	0.841028i	$0.318049\pi$
$642$	−26.7894	−	0.598535i	−1.05729	−	0.0236223i
$643$		−	9.23957i		−	0.364373i	−0.983264	−	0.182187i	$-0.941683\pi$
$643$		−	9.23957i		−	0.364373i	0.983264	−	0.182187i	$-0.0583175\pi$
$644$	8.86211	+	10.3366i	0.349216	+	0.407317i
$645$	−20.0010	−	0.446866i	−0.787538	−	0.0175953i
$646$	12.2499			0.481964
$647$			26.5662i			1.04443i	0.852815	+	0.522213i	$0.174893\pi$
$647$			26.5662i			1.04443i	−0.852815	+	0.522213i	$0.825107\pi$
$648$	−0.803115	+	8.96410i	−0.0315494	+	0.352143i
$649$			48.8886i			1.91905i
$650$			5.89898i			0.231377i
$651$	−48.7744	−	1.08973i	−1.91162	−	0.0427098i
$652$	−12.2560			−0.479982
$653$			40.1114i			1.56968i	0.619699	+	0.784840i	$0.287255\pi$
$653$			40.1114i			1.56968i	−0.619699	+	0.784840i	$0.712745\pi$
$654$	−0.452560	+	20.2558i	−0.0176965	+	0.792066i
$655$		−	7.37577i		−	0.288195i
$656$		−	2.24625i		−	0.0877012i
$657$	−0.969899	−	0.0433610i	−0.0378394	−	0.00169167i
$658$		−	4.40722i		−	0.171811i
$659$	−18.0278			−0.702263			−0.351132	−	0.936326i	$-0.614203\pi$
$659$	−18.0278			−0.702263			−0.351132	+	0.936326i	$0.614203\pi$
$660$	−0.174262	+	7.79970i	−0.00678315	+	0.303603i
$661$		−	44.4660i		−	1.72953i	−0.502179	−	0.864764i	$-0.667468\pi$
$661$		−	44.4660i		−	1.72953i	0.502179	−	0.864764i	$-0.332532\pi$
$662$			5.37160i			0.208773i
$663$	−1.23267	+	55.1725i	−0.0478731	+	2.14272i
$664$		−	4.31060i		−	0.167284i
$665$	6.43883			0.249687
$666$	11.7670	+	0.526062i	0.455961	+	0.0203845i
$667$	−15.0225	−	17.5219i	−0.581673	−	0.678449i
$668$			21.5502i			0.833803i
$669$	−0.538508	+	24.1028i	−0.0208199	+	0.931866i
$670$	−3.47626			−0.134300
$671$		−	52.6196i		−	2.03136i
$672$	0.109837	−	4.91611i	0.00423704	−	0.189643i
$673$	−5.30845			−0.204626			−0.102313	−	0.994752i	$-0.532624\pi$
$673$	−5.30845			−0.204626			−0.102313	+	0.994752i	$0.532624\pi$
$674$	−17.9318			−0.690708
$675$	0.347962	−	5.18449i	0.0133931	−	0.199551i
$676$	−21.7980			−0.838385
$677$	−16.8563			−0.647842			−0.323921	−	0.946084i	$-0.605001\pi$
$677$	−16.8563			−0.647842			−0.323921	+	0.946084i	$0.605001\pi$
$678$	14.5515	+	0.325113i	0.558847	+	0.0124859i
$679$	23.3166			0.894810
$680$			5.40124i			0.207128i
$681$	0.445007	−	19.9178i	0.0170527	−	0.763252i
$682$			44.6886i			1.71121i
$683$		−	10.9720i		−	0.419833i	−0.977719	−	0.209916i	$-0.932681\pi$
$683$		−	10.9720i		−	0.419833i	0.977719	−	0.209916i	$-0.0673192\pi$
$684$	0.303877	−	6.79713i	0.0116190	−	0.259895i
$685$	1.02064			0.0389968
$686$	−16.8636			−0.643857
$687$	25.8058	+	0.576557i	0.984551	+	0.0219970i
$688$		−	11.5505i		−	0.440357i
$689$	35.9149			1.36825
$690$	−6.42538	+	5.26445i	−0.244610	+	0.200414i
$691$	10.3095			0.392190			0.196095	−	0.980585i	$-0.437174\pi$
$691$	10.3095			0.392190			0.196095	+	0.980585i	$0.437174\pi$
$692$		−	2.77254i		−	0.105396i
$693$	−1.71339	+	38.3250i	−0.0650861	+	1.45585i
$694$	9.99097			0.379252
$695$	0.625898			0.0237417
$696$	−0.186188	+	8.33347i	−0.00705744	+	0.315879i
$697$			12.1325i			0.459551i
$698$			15.3124i			0.579585i
$699$	6.48402	+	0.144867i	0.245248	+	0.00547938i
$700$			2.83902i			0.107305i
$701$	10.9168			0.412323			0.206162	−	0.978518i	$-0.433903\pi$
$701$	10.9168			0.412323			0.206162	+	0.978518i	$0.433903\pi$
$702$	30.5832	+	2.05262i	1.15429	+	0.0774712i
$703$	−8.90460			−0.335843
$704$	−4.50428			−0.169762
$705$	2.68812	+	0.0600584i	0.101240	+	0.00226193i
$706$	−8.49859			−0.319849
$707$	24.3333			0.915147
$708$	18.7947	+	0.419914i	0.706347	+	0.0157813i
$709$		−	17.8897i		−	0.671863i	−0.941886	−	0.335932i	$-0.890949\pi$
$709$		−	17.8897i		−	0.671863i	0.941886	−	0.335932i	$-0.109051\pi$
$710$	−9.84805			−0.369591
$711$	−0.763564	+	17.0794i	−0.0286359	+	0.640528i
$712$			11.6518i			0.436669i
$713$	−36.1225	+	30.9698i	−1.35280	+	1.15983i
$714$	−0.593253	+	26.5531i	−0.0222019	+	0.993723i
$715$	26.5707			0.993687
$716$			5.79371i			0.216521i
$717$	40.3363	+	0.901201i	1.50639	+	0.0336560i
$718$		−	23.5828i		−	0.880103i
$719$		−	11.7246i		−	0.437252i	−0.975809	−	0.218626i	$-0.929843\pi$
$719$		−	11.7246i		−	0.437252i	0.975809	−	0.218626i	$-0.0701575\pi$
$720$	2.99701	+	0.133986i	0.111692	+	0.00499337i
$721$	21.1689			0.788369
$722$		−	13.8563i		−	0.515678i
$723$	−50.8711	−	1.13657i	−1.89192	−	0.0422696i
$724$			19.0813i			0.709150i
$725$		−	4.81253i		−	0.178733i
$726$	16.0842	+	0.359357i	0.596942	+	0.0133370i
$727$		−	17.9754i		−	0.666670i	−0.942809	−	0.333335i	$-0.891826\pi$
$727$		−	17.9754i		−	0.666670i	0.942809	−	0.333335i	$-0.108174\pi$
$728$	−16.7474			−0.620698
$729$	−26.7578	−	3.60801i	−0.991031	−	0.133630i
$730$			0.323623i			0.0119778i
$731$			62.3867i			2.30746i
$732$	−20.2290	−	0.451960i	−0.747686	−	0.0167049i
$733$			2.11900i			0.0782669i	0.999234	+	0.0391335i	$0.0124597\pi$
$733$			2.11900i			0.0782669i	−0.999234	+	0.0391335i	$0.987540\pi$
$734$	34.0961			1.25851
$735$	−0.0410117	+	1.83562i	−0.00151274	+	0.0677078i
$736$	−3.12154	−	3.64088i	−0.115061	−	0.134205i
$737$			15.6581i			0.576772i
$738$	6.73201	+	0.300966i	0.247809	+	0.0110787i
$739$	−9.43652			−0.347128			−0.173564	−	0.984823i	$-0.555528\pi$
$739$	−9.43652			−0.347128			−0.173564	+	0.984823i	$0.555528\pi$
$740$		−	3.92624i		−	0.144331i
$741$	−23.1669	−	0.517599i	−0.851056	−	0.0190145i
$742$	17.2849			0.634548
$743$	23.0507			0.845649			0.422825	−	0.906212i	$-0.361039\pi$
$743$	23.0507			0.845649			0.422825	+	0.906212i	$0.361039\pi$
$744$	17.1800	+	0.383839i	0.629849	+	0.0140722i
$745$	8.47908			0.310649
$746$	−3.12850			−0.114543
$747$	12.9189	+	0.577562i	0.472678	+	0.0211319i
$748$	24.3287			0.889545
$749$			43.9218i			1.60487i
$750$	−1.73162	−	0.0386882i	−0.0632298	−	0.00141269i
$751$			7.57725i			0.276498i	0.990398	+	0.138249i	$0.0441474\pi$
$751$			7.57725i			0.276498i	−0.990398	+	0.138249i	$0.955853\pi$
$752$			1.55237i			0.0566092i
$753$	−1.08498	+	48.5619i	−0.0395389	+	1.76969i
$754$	28.3890			1.03387
$755$	−23.4124			−0.852064
$756$	14.7189	+	0.987872i	0.535321	+	0.0359286i
$757$			20.5957i			0.748562i	0.927315	+	0.374281i	$0.122110\pi$
$757$			20.5957i			0.748562i	−0.927315	+	0.374281i	$0.877890\pi$
$758$	0.796283			0.0289223
$759$	23.7126	+	28.9417i	0.860712	+	1.05052i
$760$	−2.26797			−0.0822680
$761$		−	34.2533i		−	1.24168i	−0.783937	−	0.620840i	$-0.786792\pi$
$761$		−	34.2533i		−	1.24168i	0.783937	−	0.620840i	$-0.213208\pi$
$762$	−24.0354	−	0.537004i	−0.870711	−	0.0194536i
$763$	33.2099			1.20228
$764$	−12.9022			−0.466787
$765$	−16.1875	−	0.723691i	−0.585262	−	0.0261651i
$766$		−	11.8370i		−	0.427688i
$767$		−	64.0265i		−	2.31186i
$768$	−0.0386882	+	1.73162i	−0.00139604	+	0.0624844i
$769$		−	29.2604i		−	1.05516i	−0.849506	−	0.527579i	$-0.823100\pi$
$769$		−	29.2604i		−	1.05516i	0.849506	−	0.527579i	$-0.176900\pi$
$770$	12.7878			0.460839
$771$	−17.5194	−	0.391421i	−0.630944	−	0.0140967i
$772$	−2.08785			−0.0751432
$773$	−9.29477			−0.334310			−0.167155	−	0.985931i	$-0.553458\pi$
$773$	−9.29477			−0.334310			−0.167155	+	0.985931i	$0.553458\pi$
$774$	34.6168	+	1.54760i	1.24428	+	0.0556274i
$775$	−9.92135			−0.356385
$776$	−8.21290			−0.294826
$777$	0.431245	−	19.3018i	0.0154708	−	0.692449i
$778$		−	0.884618i		−	0.0317151i
$779$	−5.09443			−0.182527
$780$	0.228221	−	10.2148i	0.00817162	−	0.365748i
$781$			44.3584i			1.58727i
$782$	16.8601	+	19.6653i	0.602918	+	0.703228i
$783$	−24.9505	−	1.67458i	−0.891659	−	0.0598445i
$784$	−1.06006			−0.0378592
$785$			0.880316i			0.0314198i
$786$	−0.285355	+	12.7720i	−0.0101783	+	0.455563i
$787$			0.973427i			0.0346989i	0.999849	+	0.0173495i	$0.00552278\pi$
$787$			0.973427i			0.0346989i	−0.999849	+	0.0173495i	$0.994477\pi$
$788$			1.94161i			0.0691671i
$789$	1.08317	−	48.4808i	0.0385618	−	1.72596i
$790$	5.69882			0.202755
$791$		−	23.8575i		−	0.848275i
$792$	0.603512	−	13.4994i	0.0214449	−	0.479679i
$793$			68.9127i			2.44716i
$794$		−	5.97733i		−	0.212127i
$795$	−0.235546	+	10.5426i	−0.00835395	+	0.373909i
$796$			20.2897i			0.719149i
$797$	5.60386			0.198499			0.0992494	−	0.995063i	$-0.468356\pi$
$797$	5.60386			0.198499			0.0992494	+	0.995063i	$0.468356\pi$
$798$	−11.1496	−	0.249106i	−0.394691	−	0.00881827i
$799$		−	8.38473i		−	0.296630i
$800$		−	1.00000i		−	0.0353553i
$801$	−34.9205	−	1.56118i	−1.23385	−	0.0551616i
$802$		−	13.0800i		−	0.461871i
$803$	1.45769			0.0514407
$804$	6.01955	+	0.134490i	0.212293	+	0.00474310i
$805$	8.86211	+	10.3366i	0.312348	+	0.364316i
$806$		−	58.5259i		−	2.06149i
$807$	−20.4859	−	0.457700i	−0.721138	−	0.0161118i
$808$	−8.57100			−0.301527
$809$			15.8931i			0.558771i	0.960179	+	0.279386i	$0.0901308\pi$
$809$			15.8931i			0.558771i	−0.960179	+	0.279386i	$0.909869\pi$
$810$	−0.803115	+	8.96410i	−0.0282186	+	0.314966i
$811$	11.5179			0.404448			0.202224	−	0.979339i	$-0.435183\pi$
$811$	11.5179			0.404448			0.202224	+	0.979339i	$0.435183\pi$
$812$	13.6629			0.479474
$813$	1.05849	−	47.3763i	0.0371229	−	1.66156i
$814$	−17.6849			−0.619855
$815$	−12.2560			−0.429309
$816$	0.208964	−	9.35288i	0.00731520	−	0.327416i
$817$	−26.1961			−0.916486
$818$			0.595984i			0.0208381i
$819$	2.24392	−	50.1919i	0.0784088	−	1.75385i
$820$		−	2.24625i		−	0.0784423i
$821$		−	31.1611i		−	1.08753i	−0.839238	−	0.543765i	$-0.816998\pi$
$821$		−	31.1611i		−	1.08753i	0.839238	−	0.543765i	$-0.183002\pi$
$822$	−1.76737	−	0.0394869i	−0.0616440	−	0.00137726i
$823$	−19.3618			−0.674910			−0.337455	−	0.941342i	$-0.609566\pi$
$823$	−19.3618			−0.674910			−0.337455	+	0.941342i	$0.609566\pi$
$824$	−7.45638			−0.259755
$825$	−0.174262	+	7.79970i	−0.00606704	+	0.271551i
$826$		−	30.8142i		−	1.07216i
$827$	−44.5168			−1.54800			−0.774000	−	0.633185i	$-0.781747\pi$
$827$	−44.5168			−1.54800			−0.774000	+	0.633185i	$0.781747\pi$
$828$	11.3300	−	8.86743i	0.393744	−	0.308165i
$829$	41.1500			1.42920			0.714599	−	0.699534i	$-0.246609\pi$
$829$	41.1500			1.42920			0.714599	+	0.699534i	$0.246609\pi$
$830$		−	4.31060i		−	0.149623i
$831$	0.694391	−	31.0798i	0.0240882	−	1.07815i
$832$	5.89898			0.204510
$833$	5.72562			0.198381
$834$	−1.08382	−	0.0242148i	−0.0375295	−	0.000838491i
$835$			21.5502i			0.745776i
$836$			10.2156i			0.353314i
$837$	−3.45225	+	51.4371i	−0.119327	+	1.77793i
$838$		−	1.73544i		−	0.0599496i
$839$	49.6415			1.71381			0.856907	−	0.515471i	$-0.172383\pi$
$839$	49.6415			1.71381			0.856907	+	0.515471i	$0.172383\pi$
$840$	0.109837	−	4.91611i	0.00378972	−	0.169622i
$841$	5.83955			0.201364
$842$	5.82242			0.200654
$843$	−0.0256286	+	1.14710i	−0.000882697	+	0.0395081i
$844$	8.99923			0.309766
$845$	−21.7980			−0.749874
$846$	−4.65247	−	0.207997i	−0.159955	−	0.00715107i
$847$		−	26.3704i		−	0.906099i
$848$	−6.08832			−0.209074
$849$	44.5055	+	0.994351i	1.52743	+	0.0341260i
$850$			5.40124i			0.185261i
$851$	−12.2559	−	14.2950i	−0.420127	−	0.490025i
$852$	17.0531	+	0.381003i	0.584228	+	0.0130529i
$853$	24.2372			0.829866			0.414933	−	0.909852i	$-0.363805\pi$
$853$	24.2372			0.829866			0.414933	+	0.909852i	$0.363805\pi$
$854$			33.1659i			1.13491i
$855$	0.303877	−	6.79713i	0.0103924	−	0.232457i
$856$		−	15.4707i		−	0.528779i
$857$		−	3.50082i		−	0.119586i	−0.998211	−	0.0597928i	$-0.980956\pi$
$857$		−	3.50082i		−	0.119586i	0.998211	−	0.0597928i	$-0.0190440\pi$
$858$	−46.0103	−	1.02797i	−1.57077	−	0.0350944i
$859$	−40.7312			−1.38973			−0.694865	−	0.719140i	$-0.744536\pi$
$859$	−40.7312			−1.38973			−0.694865	+	0.719140i	$0.744536\pi$
$860$		−	11.5505i		−	0.393867i
$861$	0.246720	−	11.0428i	0.00840820	−	0.376337i
$862$			6.19650i			0.211054i
$863$			25.6426i			0.872885i	0.899732	+	0.436443i	$0.143762\pi$
$863$			25.6426i			0.872885i	−0.899732	+	0.436443i	$0.856238\pi$
$864$	−5.18449	−	0.347962i	−0.176380	−	0.0118379i
$865$		−	2.77254i		−	0.0942692i
$866$	−10.6171			−0.360784
$867$	−0.470964	+	21.0796i	−0.0159948	+	0.715900i
$868$		−	28.1670i		−	0.956049i
$869$		−	25.6691i		−	0.870765i
$870$	−0.186188	+	8.33347i	−0.00631236	+	0.282531i
$871$		−	20.5064i		−	0.694833i
$872$	−11.6976			−0.396132
$873$	1.10042	−	24.6141i	0.0372434	−	0.833061i
$874$	−8.25742	+	7.07956i	−0.279311	+	0.239470i
$875$			2.83902i			0.0959765i
$876$	0.0125204	−	0.560391i	0.000423024	−	0.0189339i
$877$	−7.61737			−0.257220			−0.128610	−	0.991695i	$-0.541052\pi$
$877$	−7.61737			−0.257220			−0.128610	+	0.991695i	$0.541052\pi$
$878$			24.8996i			0.840322i
$879$	−0.751787	+	33.6488i	−0.0253571	+	1.13494i
$880$	−4.50428			−0.151839
$881$	−29.4034			−0.990625			−0.495313	−	0.868715i	$-0.664947\pi$
$881$	−29.4034			−0.990625			−0.495313	+	0.868715i	$0.664947\pi$
$882$	0.142033	−	3.17700i	0.00478251	−	0.106975i
$883$	−40.6782			−1.36893			−0.684466	−	0.729045i	$-0.739965\pi$
$883$	−40.6782			−1.36893			−0.684466	+	0.729045i	$0.739965\pi$
$884$	−31.8618			−1.07163
$885$	18.7947	+	0.419914i	0.631776	+	0.0141153i
$886$	−8.79242			−0.295387
$887$		−	10.4780i		−	0.351818i	−0.984406	−	0.175909i	$-0.943713\pi$
$887$		−	10.4780i		−	0.351818i	0.984406	−	0.175909i	$-0.0562865\pi$
$888$	−0.151899	+	6.79875i	−0.00509739	+	0.228151i
$889$			39.4065i			1.32165i
$890$			11.6518i			0.390569i
$891$	40.3768	+	3.61746i	1.35267	+	0.121189i
$892$	−13.9192			−0.466049
$893$	3.52074			0.117817
$894$	−14.6825	−	0.328040i	−0.491057	−	0.0109713i
$895$			5.79371i			0.193662i
$896$	2.83902			0.0948451
$897$	−31.0549	−	37.9032i	−1.03689	−	1.26555i
$898$	−21.0781			−0.703387
$899$			47.7468i			1.59245i
$900$	2.99701	+	0.133986i	0.0999002	+	0.00446621i
$901$	32.8844			1.09554
$902$	−10.1177			−0.336883
$903$	1.26866	−	56.7833i	0.0422185	−	1.88963i
$904$			8.40341i			0.279493i
$905$			19.0813i			0.634283i
$906$	40.5413	+	0.905782i	1.34690	+	0.0300926i
$907$		−	9.40371i		−	0.312245i	−0.987738	−	0.156122i	$-0.950101\pi$
$907$		−	9.40371i		−	0.312245i	0.987738	−	0.156122i	$-0.0498995\pi$
$908$	11.5024			0.381721
$909$	1.14840	−	25.6873i	0.0380899	−	0.851995i
$910$	−16.7474			−0.555170
$911$	9.82692			0.325580			0.162790	−	0.986661i	$-0.447951\pi$
$911$	9.82692			0.325580			0.162790	+	0.986661i	$0.447951\pi$
$912$	3.92726	+	0.0877437i	0.130045	+	0.00290548i
$913$	−19.4162			−0.642582
$914$	−7.66411			−0.253506
$915$	−20.2290	−	0.451960i	−0.668750	−	0.0149413i
$916$			14.9027i			0.492398i
$917$	20.9400			0.691500
$918$	28.0026	+	1.87942i	0.924225	+	0.0620302i
$919$			4.10377i			0.135371i	0.997707	+	0.0676854i	$0.0215614\pi$
$919$			4.10377i			0.135371i	−0.997707	+	0.0676854i	$0.978439\pi$
$920$	−3.12154	−	3.64088i	−0.102914	−	0.120036i
$921$	−0.0642004	+	2.87350i	−0.00211547	+	0.0946851i
$922$	−36.6333			−1.20645
$923$		−	58.0935i		−	1.91217i
$924$	−22.1435	−	0.494735i	−0.728469	−	0.0162756i
$925$		−	3.92624i		−	0.129094i
$926$		−	7.73369i		−	0.254145i
$927$	0.999053	−	22.3468i	0.0328132	−	0.733966i
$928$	−4.81253			−0.157979
$929$		−	19.7111i		−	0.646700i	−0.946279	−	0.323350i	$-0.895191\pi$
$929$		−	19.7111i		−	0.646700i	0.946279	−	0.323350i	$-0.104809\pi$
$930$	17.1800	+	0.383839i	0.563354	+	0.0125866i
$931$			2.40418i			0.0787939i
$932$			3.74448i			0.122655i
$933$	−21.7440	−	0.485808i	−0.711866	−	0.0159046i
$934$			20.9022i			0.683940i
$935$	24.3287			0.795633
$936$	−0.790383	+	17.6793i	−0.0258345	+	0.577866i
$937$			19.7228i			0.644317i	0.946686	+	0.322158i	$0.104408\pi$
$937$			19.7228i			0.644317i	−0.946686	+	0.322158i	$0.895592\pi$
$938$		−	9.86918i		−	0.322240i
$939$	23.4502	+	0.523929i	0.765268	+	0.0170978i
$940$			1.55237i			0.0506328i
$941$	−7.92304			−0.258284			−0.129142	−	0.991626i	$-0.541222\pi$
$941$	−7.92304			−0.258284			−0.129142	+	0.991626i	$0.541222\pi$
$942$	0.0340578	−	1.52437i	0.00110966	−	0.0496667i
$943$	−7.01174	−	8.17832i	−0.228334	−	0.266323i
$944$			10.8538i			0.353261i
$945$	14.7189	+	0.987872i	0.478805	+	0.0321355i
$946$	−52.0265			−1.69153
$947$		−	25.4088i		−	0.825676i	−0.910804	−	0.412838i	$-0.864538\pi$
$947$		−	25.4088i		−	0.825676i	0.910804	−	0.412838i	$-0.135462\pi$
$948$	−9.86819	−	0.220477i	−0.320504	−	0.00716076i
$949$	−1.90905			−0.0619702
$950$	−2.26797			−0.0735827
$951$	19.2671	+	0.430469i	0.624779	+	0.0139589i
$952$	−15.3342			−0.496985
$953$	16.9287			0.548375			0.274187	−	0.961676i	$-0.411591\pi$
$953$	16.9287			0.548375			0.274187	+	0.961676i	$0.411591\pi$
$954$	0.815751	−	18.2467i	0.0264109	−	0.590760i
$955$	−12.9022			−0.417507
$956$			23.2940i			0.753381i
$957$	37.5363	+	0.838643i	1.21338	+	0.0271095i
$958$			33.1326i			1.07047i
$959$			2.89764i			0.0935695i
$960$	−0.0386882	+	1.73162i	−0.00124865	+	0.0558878i
$961$	67.4332			2.17526
$962$	23.1608			0.746735
$963$	46.3659	+	2.07287i	1.49412	+	0.0667972i
$964$		−	29.3778i		−	0.946195i
$965$	−2.08785			−0.0672101
$966$	−14.9459	−	18.2418i	−0.480876	−	0.586921i
$967$	−4.75852			−0.153024			−0.0765118	−	0.997069i	$-0.524378\pi$
$967$	−4.75852			−0.153024			−0.0765118	+	0.997069i	$0.524378\pi$
$968$			9.28856i			0.298546i
$969$	−21.2121	−	0.473924i	−0.681430	−	0.0152246i
$970$	−8.21290			−0.263700
$971$	−40.7463			−1.30761			−0.653806	−	0.756662i	$-0.726829\pi$
$971$	−40.7463			−1.30761			−0.653806	+	0.756662i	$0.726829\pi$
$972$	1.73749	−	15.4913i	0.0557301	−	0.496884i
$973$			1.77694i			0.0569661i
$974$		−	10.1567i		−	0.325442i
$975$	0.228221	−	10.2148i	0.00730892	−	0.327135i
$976$		−	11.6821i		−	0.373936i
$977$	12.7653			0.408397			0.204198	−	0.978930i	$-0.434541\pi$
$977$	12.7653			0.408397			0.204198	+	0.978930i	$0.434541\pi$
$978$	21.2227	+	0.474162i	0.678628	+	0.0151620i
$979$	52.4829			1.67736
$980$	−1.06006			−0.0338623
$981$	1.56732	−	35.0579i	0.0500407	−	1.11931i
$982$	28.9321			0.923261
$983$	9.29880			0.296586			0.148293	−	0.988944i	$-0.452622\pi$
$983$	9.29880			0.296586			0.148293	+	0.988944i	$0.452622\pi$
$984$	−0.0869031	+	3.88964i	−0.00277037	+	0.123997i
$985$			1.94161i			0.0618649i
$986$	25.9936			0.827805
$987$	−0.170507	+	7.63163i	−0.00542731	+	0.242917i
$988$		−	13.3787i		−	0.425634i
$989$	−36.0552	−	42.0539i	−1.14649	−	1.33723i
$990$	0.603512	−	13.4994i	0.0191809	−	0.429038i
$991$	−49.5107			−1.57276			−0.786379	−	0.617744i	$-0.788047\pi$
$991$	−49.5107			−1.57276			−0.786379	+	0.617744i	$0.788047\pi$
$992$			9.92135i			0.315003i
$993$	0.207817	−	9.30157i	0.00659489	−	0.295176i
$994$		−	27.9588i		−	0.886801i
$995$			20.2897i			0.643227i
$996$	−0.166769	+	7.46432i	−0.00528429	+	0.236516i
$997$	−4.07381			−0.129019			−0.0645095	−	0.997917i	$-0.520548\pi$
$997$	−4.07381			−0.129019			−0.0645095	+	0.997917i	$0.520548\pi$
$998$		−	5.77406i		−	0.182775i
$999$	−20.3555	−	1.36618i	−0.644021	−	0.0432241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.a.551.5	✓	16
3.2	odd	2		690.2.e.b.551.13	yes	16
23.22	odd	2		690.2.e.b.551.5	yes	16
69.68	even	2	inner	690.2.e.a.551.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.5	✓	16	1.1	even	1	trivial
690.2.e.a.551.13	yes	16	69.68	even	2	inner
690.2.e.b.551.5	yes	16	23.22	odd	2
690.2.e.b.551.13	yes	16	3.2	odd	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +1.00000i q^{10} +4.50428 q^{11} +(0.0386882 - 1.73162i) q^{12} -5.89898 q^{13} -2.83902 q^{14} +(0.0386882 - 1.73162i) q^{15} +1.00000 q^{16} -5.40124 q^{17} +(-0.133986 + 2.99701i) q^{18} -2.26797i q^{19} +1.00000 q^{20} +(4.91611 + 0.109837i) q^{21} -4.50428i q^{22} +(3.64088 - 3.12154i) q^{23} +(-1.73162 - 0.0386882i) q^{24} +1.00000 q^{25} +5.89898i q^{26} +(0.347962 - 5.18449i) q^{27} +2.83902i q^{28} -4.81253i q^{29} +(-1.73162 - 0.0386882i) q^{30} -9.92135 q^{31} -1.00000i q^{32} +(-0.174262 + 7.79970i) q^{33} +5.40124i q^{34} +2.83902i q^{35} +(2.99701 + 0.133986i) q^{36} -3.92624i q^{37} -2.26797 q^{38} +(0.228221 - 10.2148i) q^{39} -1.00000i q^{40} -2.24625i q^{41} +(0.109837 - 4.91611i) q^{42} -11.5505i q^{43} -4.50428 q^{44} +(2.99701 + 0.133986i) q^{45} +(-3.12154 - 3.64088i) q^{46} +1.55237i q^{47} +(-0.0386882 + 1.73162i) q^{48} -1.06006 q^{49} -1.00000i q^{50} +(0.208964 - 9.35288i) q^{51} +5.89898 q^{52} -6.08832 q^{53} +(-5.18449 - 0.347962i) q^{54} -4.50428 q^{55} +2.83902 q^{56} +(3.92726 + 0.0877437i) q^{57} -4.81253 q^{58} +10.8538i q^{59} +(-0.0386882 + 1.73162i) q^{60} -11.6821i q^{61} +9.92135i q^{62} +(-0.380390 + 8.50857i) q^{63} -1.00000 q^{64} +5.89898 q^{65} +(7.79970 + 0.174262i) q^{66} +3.47626i q^{67} +5.40124 q^{68} +(5.26445 + 6.42538i) q^{69} +2.83902 q^{70} +9.84805i q^{71} +(0.133986 - 2.99701i) q^{72} +0.323623 q^{73} -3.92624 q^{74} +(-0.0386882 + 1.73162i) q^{75} +2.26797i q^{76} -12.7878i q^{77} +(-10.2148 - 0.228221i) q^{78} -5.69882i q^{79} -1.00000 q^{80} +(8.96410 + 0.803115i) q^{81} -2.24625 q^{82} -4.31060 q^{83} +(-4.91611 - 0.109837i) q^{84} +5.40124 q^{85} -11.5505 q^{86} +(8.33347 + 0.186188i) q^{87} +4.50428i q^{88} +11.6518 q^{89} +(0.133986 - 2.99701i) q^{90} +16.7474i q^{91} +(-3.64088 + 3.12154i) q^{92} +(0.383839 - 17.1800i) q^{93} +1.55237 q^{94} +2.26797i q^{95} +(1.73162 + 0.0386882i) q^{96} +8.21290i q^{97} +1.06006i q^{98} +(-13.4994 - 0.603512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9	\( 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9} - 12 q^{11} - 12 q^{14} + 16 q^{16} + 8 q^{18} + 16 q^{20} - 4 q^{21} + 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} - 2 q^{30} + 4 q^{31} - 28 q^{33} - 2 q^{36} - 16 q^{38} - 8 q^{39} + 12 q^{44} - 2 q^{45} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 8 q^{53} - 26 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 8 q^{58} - 16 q^{64} + 10 q^{66} + 30 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} - 24 q^{74} - 12 q^{78} - 16 q^{80} + 22 q^{81} - 16 q^{82} - 40 q^{83} + 4 q^{84} - 40 q^{86} + 20 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9 - 12 * q^11 - 12 * q^14 + 16 * q^16 + 8 * q^18 + 16 * q^20 - 4 * q^21 + 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 - 2 * q^30 + 4 * q^31 - 28 * q^33 - 2 * q^36 - 16 * q^38 - 8 * q^39 + 12 * q^44 - 2 * q^45 - 4 * q^46 - 4 * q^49 - 2 * q^51 - 8 * q^53 - 26 * q^54 + 12 * q^55 + 12 * q^56 + 28 * q^57 - 8 * q^58 - 16 * q^64 + 10 * q^66 + 30 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 - 24 * q^74 - 12 * q^78 - 16 * q^80 + 22 * q^81 - 16 * q^82 - 40 * q^83 + 4 * q^84 - 40 * q^86 + 20 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 - 8 * q^99

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