LMFDB - Embedded newform 798.2.bp.b.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 30x^{10} + 393x^{8} - 2717x^{6} + 10056x^{4} - 18960x^{2} + 18496 $ x^12 - 30x^10 + 393x^8 - 2717x^6 + 10056x^4 - 18960*x^2 + 18496
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.1
Root			$1.35206 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.367804 + 2.08592i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.367804 + 2.08592i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.62256 - 1.36149i) q^{10} +(-0.0542909 - 0.0940346i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.542564 + 3.07703i) q^{13} +(-1.28699 + 2.31164i) q^{14} +(-1.62256 + 1.36149i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.853313 + 4.83938i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.85484 - 2.03476i) q^{19} -2.11810 q^{20} +(1.28699 - 2.31164i) q^{21} +(-0.0188550 + 0.106932i) q^{22} +(6.26594 + 2.28062i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.482676 + 0.175680i) q^{25} +(1.56225 - 2.70590i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.47178 - 0.943555i) q^{28} +(-3.83121 - 1.39444i) q^{29} +2.11810 q^{30} -9.16300 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0188550 - 0.106932i) q^{33} +(3.76437 - 3.15868i) q^{34} +(5.60328 - 0.0873773i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.62088 + 8.00360i) q^{37} +(-4.26089 - 0.919128i) q^{38} +(-1.56225 + 2.70590i) q^{39} +(1.62256 + 1.36149i) q^{40} +(-2.19499 + 12.4484i) q^{41} +(-2.47178 + 0.943555i) q^{42} +(-6.01862 - 5.05023i) q^{43} +(0.0831785 - 0.0697951i) q^{44} -2.11810 q^{45} +(-3.33404 - 5.77472i) q^{46} +(1.68578 + 9.56051i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-0.256827 - 0.444837i) q^{50} +(-3.76437 + 3.15868i) q^{51} +(-2.93607 + 1.06864i) q^{52} +(0.0551795 + 0.312938i) q^{53} +(0.939693 - 0.342020i) q^{54} +(0.216117 - 0.0786602i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(4.26089 + 0.919128i) q^{57} +(2.03854 + 3.53086i) q^{58} +(-0.593722 + 3.36716i) q^{59} +(-1.62256 - 1.36149i) q^{60} +(3.99884 + 1.45546i) q^{61} +(7.01927 + 5.88986i) q^{62} +(2.47178 - 0.943555i) q^{63} +(-0.500000 - 0.866025i) q^{64} -6.61801 q^{65} +(-0.0831785 + 0.0697951i) q^{66} +(5.85605 - 4.91381i) q^{67} -4.91403 q^{68} +(3.33404 + 5.77472i) q^{69} +(-4.34853 - 3.53479i) q^{70} +(4.84925 + 4.06900i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-10.7381 - 9.01037i) q^{73} +(1.60482 - 9.10136i) q^{74} +(0.256827 + 0.444837i) q^{75} +(2.67323 + 3.44294i) q^{76} +(-0.217164 + 0.188069i) q^{77} +(2.93607 - 1.06864i) q^{78} +(11.3036 - 4.11418i) q^{79} +(-0.367804 - 2.08592i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(9.68316 - 8.12514i) q^{82} +(-4.97094 - 8.60993i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-9.78071 - 3.55989i) q^{85} +(1.36431 + 7.73739i) q^{86} +(-2.03854 - 3.53086i) q^{87} -0.108582 q^{88} +(4.59178 - 3.85296i) q^{89} +(1.62256 + 1.36149i) q^{90} +(7.72309 - 2.94814i) q^{91} +(-1.15790 + 6.56677i) q^{92} +(-7.01927 - 5.88986i) q^{93} +(4.85400 - 8.40737i) q^{94} +(2.82651 + 8.78928i) q^{95} +(0.500000 + 0.866025i) q^{96} +(14.1557 - 5.15224i) q^{97} +(6.64930 + 2.18788i) q^{98} +(0.0831785 - 0.0697951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{12} + 12 q^{13} - 6 q^{15} - 18 q^{17} + 6 q^{18} - 3 q^{19} - 21 q^{22} - 3 q^{23} + 21 q^{25} - 6 q^{26} - 6 q^{27} - 12 q^{29} - 6 q^{31} + 21 q^{33} - 9 q^{34} + 12 q^{35} - 3 q^{37} + 3 q^{38} + 6 q^{39} + 6 q^{40} - 24 q^{41} - 21 q^{43} - 6 q^{44} - 6 q^{46} + 18 q^{47} - 78 q^{49} + 6 q^{50} + 9 q^{51} - 15 q^{52} + 36 q^{53} + 30 q^{55} - 30 q^{56} - 3 q^{57} + 15 q^{58} - 33 q^{59} - 6 q^{60} + 33 q^{62} - 6 q^{64} + 24 q^{65} + 6 q^{66} + 51 q^{67} - 6 q^{68} + 6 q^{69} - 3 q^{70} + 6 q^{71} - 3 q^{73} - 6 q^{75} + 9 q^{76} + 15 q^{78} + 30 q^{79} + 3 q^{80} - 3 q^{82} - 27 q^{83} + 30 q^{84} - 36 q^{85} + 3 q^{86} - 15 q^{87} + 12 q^{89} + 6 q^{90} + 21 q^{91} - 3 q^{92} - 33 q^{93} + 6 q^{94} + 21 q^{95} + 6 q^{96} + 30 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8 + 6 * q^10 - 6 * q^12 + 12 * q^13 - 6 * q^15 - 18 * q^17 + 6 * q^18 - 3 * q^19 - 21 * q^22 - 3 * q^23 + 21 * q^25 - 6 * q^26 - 6 * q^27 - 12 * q^29 - 6 * q^31 + 21 * q^33 - 9 * q^34 + 12 * q^35 - 3 * q^37 + 3 * q^38 + 6 * q^39 + 6 * q^40 - 24 * q^41 - 21 * q^43 - 6 * q^44 - 6 * q^46 + 18 * q^47 - 78 * q^49 + 6 * q^50 + 9 * q^51 - 15 * q^52 + 36 * q^53 + 30 * q^55 - 30 * q^56 - 3 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 + 33 * q^62 - 6 * q^64 + 24 * q^65 + 6 * q^66 + 51 * q^67 - 6 * q^68 + 6 * q^69 - 3 * q^70 + 6 * q^71 - 3 * q^73 - 6 * q^75 + 9 * q^76 + 15 * q^78 + 30 * q^79 + 3 * q^80 - 3 * q^82 - 27 * q^83 + 30 * q^84 - 36 * q^85 + 3 * q^86 - 15 * q^87 + 12 * q^89 + 6 * q^90 + 21 * q^91 - 3 * q^92 - 33 * q^93 + 6 * q^94 + 21 * q^95 + 6 * q^96 + 30 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.367804	+	2.08592i	−0.164487	+	0.932852i	0.785105	+	0.619363i	$0.212609\pi$
$5$	−0.367804	+	2.08592i	−0.164487	+	0.932852i	−0.949592	+	0.313489i	$0.898502\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	1.62256	−	1.36149i	0.513098	−	0.430540i
$11$	−0.0542909	−	0.0940346i	−0.0163693	−	0.0283525i	0.857725	−	0.514109i	$-0.171877\pi$
$11$	−0.0542909	−	0.0940346i	−0.0163693	−	0.0283525i	−0.874094	+	0.485757i	$0.838544\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.542564	+	3.07703i	0.150480	+	0.853416i	0.962802	+	0.270207i	$0.0870920\pi$
$13$	0.542564	+	3.07703i	0.150480	+	0.853416i	−0.812322	+	0.583209i	$0.801797\pi$
$14$	−1.28699	+	2.31164i	−0.343962	+	0.617811i
$15$	−1.62256	+	1.36149i	−0.418943	+	0.351535i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.853313	+	4.83938i	−0.206959	+	1.17372i	0.687369	+	0.726309i	$0.258766\pi$
$17$	−0.853313	+	4.83938i	−0.206959	+	1.17372i	−0.894328	+	0.447413i	$0.852345\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	3.85484	−	2.03476i	0.884360	−	0.466805i
$19$	3.85484	−	2.03476i	0.884360	−	0.466805i
$20$	−2.11810			−0.473622
$21$	1.28699	−	2.31164i	0.280844	−	0.504440i
$22$	−0.0188550	+	0.106932i	−0.00401991	+	0.0227980i
$23$	6.26594	+	2.28062i	1.30654	+	0.475541i	0.899121	−	0.437700i	$-0.144207\pi$
$23$	6.26594	+	2.28062i	1.30654	+	0.475541i	0.407418	+	0.913242i	$0.366429\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	0.482676	+	0.175680i	0.0965353	+	0.0351360i
$26$	1.56225	−	2.70590i	0.306383	−	0.530670i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	2.47178	−	0.943555i	0.467123	−	0.178315i
$29$	−3.83121	−	1.39444i	−0.711437	−	0.258942i	−0.0391509	−	0.999233i	$-0.512465\pi$
$29$	−3.83121	−	1.39444i	−0.711437	−	0.258942i	−0.672286	+	0.740291i	$0.734688\pi$
$30$	2.11810			0.386710
$31$	−9.16300			−1.64572			−0.822862	−	0.568241i	$-0.807624\pi$
$31$	−9.16300			−1.64572			−0.822862	+	0.568241i	$0.807624\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.0188550	−	0.106932i	0.00328224	−	0.0186145i
$34$	3.76437	−	3.15868i	0.645584	−	0.541709i
$35$	5.60328	−	0.0873773i	0.947128	−	0.0147695i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	4.62088	+	8.00360i	0.759668	+	1.31578i	0.943020	+	0.332737i	$0.107972\pi$
$37$	4.62088	+	8.00360i	0.759668	+	1.31578i	−0.183352	+	0.983047i	$0.558695\pi$
$38$	−4.26089	−	0.919128i	−0.691208	−	0.149102i
$39$	−1.56225	+	2.70590i	−0.250160	+	0.433291i
$40$	1.62256	+	1.36149i	0.256549	+	0.215270i
$41$	−2.19499	+	12.4484i	−0.342800	+	1.94412i	−0.0134522	+	0.999910i	$0.504282\pi$
$41$	−2.19499	+	12.4484i	−0.342800	+	1.94412i	−0.329348	+	0.944209i	$0.606829\pi$
$42$	−2.47178	+	0.943555i	−0.381404	+	0.145594i
$43$	−6.01862	−	5.05023i	−0.917832	−	0.770152i	0.0557611	−	0.998444i	$-0.482241\pi$
$43$	−6.01862	−	5.05023i	−0.917832	−	0.770152i	−0.973593	+	0.228292i	$0.926686\pi$
$44$	0.0831785	−	0.0697951i	0.0125396	−	0.0105220i
$45$	−2.11810			−0.315748
$46$	−3.33404	−	5.77472i	−0.491577	−	0.851437i
$47$	1.68578	+	9.56051i	0.245896	+	1.39454i	0.818403	+	0.574644i	$0.194860\pi$
$47$	1.68578	+	9.56051i	0.245896	+	1.39454i	−0.572507	+	0.819900i	$0.694029\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−0.256827	−	0.444837i	−0.0363208	−	0.0629094i
$51$	−3.76437	+	3.15868i	−0.527117	+	0.442304i
$52$	−2.93607	+	1.06864i	−0.407160	+	0.148194i
$53$	0.0551795	+	0.312938i	0.00757949	+	0.0429854i	0.988363	−	0.152114i	$-0.0486081\pi$
$53$	0.0551795	+	0.312938i	0.00757949	+	0.0429854i	−0.980783	+	0.195100i	$0.937497\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	0.216117	−	0.0786602i	0.0291412	−	0.0106065i
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	4.26089	+	0.919128i	0.564369	+	0.121742i
$58$	2.03854	+	3.53086i	0.267674	+	0.463624i
$59$	−0.593722	+	3.36716i	−0.0772960	+	0.438367i	0.921459	+	0.388476i	$0.126998\pi$
$59$	−0.593722	+	3.36716i	−0.0772960	+	0.438367i	−0.998755	+	0.0498909i	$0.984113\pi$
$60$	−1.62256	−	1.36149i	−0.209471	−	0.175767i
$61$	3.99884	+	1.45546i	0.511999	+	0.186352i	0.585083	−	0.810973i	$-0.301062\pi$
$61$	3.99884	+	1.45546i	0.511999	+	0.186352i	−0.0730842	+	0.997326i	$0.523284\pi$
$62$	7.01927	+	5.88986i	0.891448	+	0.748014i
$63$	2.47178	−	0.943555i	0.311415	−	0.118877i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−6.61801			−0.820863
$66$	−0.0831785	+	0.0697951i	−0.0102386	+	0.00859118i
$67$	5.85605	−	4.91381i	0.715430	−	0.600317i	−0.210687	−	0.977554i	$-0.567570\pi$
$67$	5.85605	−	4.91381i	0.715430	−	0.600317i	0.926117	+	0.377237i	$0.123126\pi$
$68$	−4.91403			−0.595914
$69$	3.33404	+	5.77472i	0.401371	+	0.695195i
$70$	−4.34853	−	3.53479i	−0.519749	−	0.422488i
$71$	4.84925	+	4.06900i	0.575500	+	0.482902i	0.883466	−	0.468496i	$-0.155204\pi$
$71$	4.84925	+	4.06900i	0.575500	+	0.482902i	−0.307966	+	0.951397i	$0.599648\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	−10.7381	−	9.01037i	−1.25680	−	1.05458i	−0.996015	−	0.0891886i	$-0.971573\pi$
$73$	−10.7381	−	9.01037i	−1.25680	−	1.05458i	−0.260790	−	0.965396i	$-0.583983\pi$
$74$	1.60482	−	9.10136i	0.186556	−	1.05801i
$75$	0.256827	+	0.444837i	0.0296558	+	0.0513653i
$76$	2.67323	+	3.44294i	0.306640	+	0.394933i
$77$	−0.217164	+	0.188069i	−0.0247481	+	0.0214325i
$78$	2.93607	−	1.06864i	0.332445	−	0.121000i
$79$	11.3036	−	4.11418i	1.27176	−	0.462882i	0.384060	−	0.923308i	$-0.374526\pi$
$79$	11.3036	−	4.11418i	1.27176	−	0.462882i	0.887698	+	0.460426i	$0.152303\pi$
$80$	−0.367804	−	2.08592i	−0.0411218	−	0.233213i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	9.68316	−	8.12514i	1.06933	−	0.897271i
$83$	−4.97094	−	8.60993i	−0.545632	−	0.945062i	−0.998567	−	0.0535187i	$-0.982956\pi$
$83$	−4.97094	−	8.60993i	−0.545632	−	0.945062i	0.452935	−	0.891544i	$-0.350377\pi$
$84$	2.50000	+	0.866025i	0.272772	+	0.0944911i
$85$	−9.78071	−	3.55989i	−1.06087	−	0.386124i
$86$	1.36431	+	7.73739i	0.147117	+	0.834345i
$87$	−2.03854	−	3.53086i	−0.218555	−	0.378548i
$88$	−0.108582			−0.0115749
$89$	4.59178	−	3.85296i	0.486728	−	0.408413i	−0.366124	−	0.930566i	$-0.619315\pi$
$89$	4.59178	−	3.85296i	0.486728	−	0.408413i	0.852852	+	0.522153i	$0.174871\pi$
$90$	1.62256	+	1.36149i	0.171033	+	0.143513i
$91$	7.72309	−	2.94814i	0.809600	−	0.309049i
$92$	−1.15790	+	6.56677i	−0.120719	+	0.684633i
$93$	−7.01927	−	5.88986i	−0.727864	−	0.610751i
$94$	4.85400	−	8.40737i	0.500652	−	0.867154i
$95$	2.82651	+	8.78928i	0.289994	+	0.901761i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	14.1557	−	5.15224i	1.43729	−	0.523130i	0.498278	−	0.867018i	$-0.333966\pi$
$97$	14.1557	−	5.15224i	1.43729	−	0.523130i	0.939011	+	0.343887i	$0.111744\pi$
$98$	6.64930	+	2.18788i	0.671681	+	0.221009i
$99$	0.0831785	−	0.0697951i	0.00835975	−	0.00701467i
$100$	−0.0891950	+	0.505850i	−0.00891950	+	0.0505850i
$101$	16.0439	+	5.83951i	1.59643	+	0.581053i	0.978692	−	0.205332i	$-0.0658273\pi$
$101$	16.0439	+	5.83951i	1.59643	+	0.581053i	0.617737	+	0.786385i	$0.288050\pi$
$102$	4.91403			0.486562
$103$	−0.220827			−0.0217587			−0.0108793	−	0.999941i	$-0.503463\pi$
$103$	−0.220827			−0.0217587			−0.0108793	+	0.999941i	$0.503463\pi$
$104$	2.93607	+	1.06864i	0.287906	+	0.104789i
$105$	4.34853	+	3.53479i	0.424373	+	0.344960i
$106$	0.158883	−	0.275193i	0.0154321	−	0.0267292i
$107$	−0.400012	+	0.692842i	−0.0386707	+	0.0669795i	−0.884713	−	0.466136i	$-0.845646\pi$
$107$	−0.400012	+	0.692842i	−0.0386707	+	0.0669795i	0.846042	+	0.533116i	$0.178979\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	−16.0333	+	5.83563i	−1.53571	+	0.558952i	−0.965011	−	0.262209i	$-0.915549\pi$
$109$	−16.0333	+	5.83563i	−1.53571	+	0.558952i	−0.570697	+	0.821161i	$0.693327\pi$
$110$	−0.216117	−	0.0786602i	−0.0206060	−	0.00749996i
$111$	−1.60482	+	9.10136i	−0.152322	+	0.863863i
$112$	1.35844	+	2.27038i	0.128361	+	0.214531i
$113$	5.03710			0.473850			0.236925	−	0.971528i	$-0.423860\pi$
$113$	5.03710			0.473850			0.236925	+	0.971528i	$0.423860\pi$
$114$	−2.67323	−	3.44294i	−0.250371	−	0.322461i
$115$	−7.06183	+	12.2314i	−0.658519	+	1.14059i
$116$	0.707978	−	4.01514i	0.0657341	−	0.372797i
$117$	−2.93607	+	1.06864i	−0.271440	+	0.0987961i
$118$	2.61919	−	2.19776i	0.241116	−	0.202320i
$119$	12.9997	−	0.202717i	1.19168	−	0.0185830i
$120$	0.367804	+	2.08592i	0.0335758	+	0.190418i
$121$	5.49410	−	9.51607i	0.499464	−	0.865097i
$122$	−2.12774	−	3.68535i	−0.192636	−	0.333656i
$123$	−9.68316	+	8.12514i	−0.873101	+	0.732619i
$124$	−1.59114	−	9.02380i	−0.142888	−	0.810361i
$125$	−5.83923	+	10.1138i	−0.522277	+	0.904610i
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	−1.70479	−	9.66837i	−0.151276	−	0.857929i	−0.962112	−	0.272655i	$-0.912098\pi$
$127$	−1.70479	−	9.66837i	−0.151276	−	0.857929i	0.810836	−	0.585274i	$-0.199013\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−1.36431	−	7.73739i	−0.120121	−	0.681240i
$130$	5.06969	+	4.25397i	0.444641	+	0.373098i
$131$	−10.8476	−	9.10219i	−0.947756	−	0.795262i	0.0311622	−	0.999514i	$-0.490079\pi$
$131$	−10.8476	−	9.10219i	−0.947756	−	0.795262i	−0.978918	+	0.204253i	$0.934524\pi$
$132$	0.108582			0.00945083
$133$	−7.21387	−	8.99778i	−0.625522	−	0.780207i
$134$	−7.64452			−0.660386
$135$	−1.62256	−	1.36149i	−0.139648	−	0.117178i
$136$	3.76437	+	3.15868i	0.322792	+	0.270855i
$137$	−1.60117	−	9.08068i	−0.136797	−	0.775814i	−0.973591	−	0.228297i	$-0.926684\pi$
$137$	−1.60117	−	9.08068i	−0.136797	−	0.775814i	0.836794	−	0.547517i	$-0.184427\pi$
$138$	1.15790	−	6.56677i	0.0985669	−	0.559001i
$139$	3.07587	+	17.4441i	0.260892	+	1.47959i	0.780483	+	0.625177i	$0.214973\pi$
$139$	3.07587	+	17.4441i	0.260892	+	1.47959i	−0.519591	+	0.854415i	$0.673916\pi$
$140$	1.05905	+	5.50298i	0.0895061	+	0.465087i
$141$	−4.85400	+	8.40737i	−0.408780	+	0.708029i
$142$	−1.09924	−	6.23407i	−0.0922458	−	0.523152i
$143$	0.259891	−	0.218075i	0.0217332	−	0.0182363i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.31784	−	7.47871i	0.358577	−	0.621073i
$146$	2.43414	+	13.8047i	0.201451	+	1.14248i
$147$	−6.64930	−	2.18788i	−0.548425	−	0.180453i
$148$	−7.07960	+	5.94049i	−0.581940	+	0.488305i
$149$	14.7063	−	5.35265i	1.20478	−	0.438506i	0.339893	−	0.940464i	$-0.389609\pi$
$149$	14.7063	−	5.35265i	1.20478	−	0.438506i	0.864892	+	0.501958i	$0.167387\pi$
$150$	0.0891950	−	0.505850i	0.00728274	−	0.0413025i
$151$	0.282256	−	0.488882i	0.0229697	−	0.0397847i	−0.854312	−	0.519760i	$-0.826021\pi$
$151$	0.282256	−	0.488882i	0.0229697	−	0.0397847i	0.877282	+	0.479976i	$0.159355\pi$
$152$	0.165268	−	4.35576i	0.0134050	−	0.353299i
$153$	−4.91403			−0.397276
$154$	0.287246	−	0.00447929i	0.0231469	−	0.000360952i
$155$	3.37019	−	19.1133i	0.270700	−	1.53522i
$156$	−2.93607	−	1.06864i	−0.235074	−	0.0855599i
$157$	9.74217	−	3.54586i	0.777509	−	0.282990i	0.0773757	−	0.997002i	$-0.475346\pi$
$157$	9.74217	−	3.54586i	0.777509	−	0.282990i	0.700134	+	0.714012i	$0.253124\pi$
$158$	−11.3036	−	4.11418i	−0.899268	−	0.327307i
$159$	−0.158883	+	0.275193i	−0.0126002	+	0.0218243i
$160$	−1.05905	+	1.83433i	−0.0837252	+	0.145016i
$161$	2.79224	−	17.4197i	0.220060	−	1.37286i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	−1.94357			−0.152233			−0.0761163	−	0.997099i	$-0.524252\pi$
$163$	−1.94357			−0.152233			−0.0761163	+	0.997099i	$0.524252\pi$
$164$	−12.6405			−0.987055
$165$	0.216117	+	0.0786602i	0.0168247	+	0.00612369i
$166$	−1.72639	+	9.79085i	−0.133994	+	0.759917i
$167$	−10.1936	+	8.55346i	−0.788805	+	0.661886i	−0.945449	−	0.325769i	$-0.894377\pi$
$167$	−10.1936	+	8.55346i	−0.788805	+	0.661886i	0.156644	+	0.987655i	$0.449932\pi$
$168$	−1.35844	−	2.27038i	−0.104806	−	0.175164i
$169$	3.04224	−	1.10729i	0.234019	−	0.0851758i
$170$	5.20421	+	9.01395i	0.399144	+	0.691338i
$171$	2.67323	+	3.44294i	0.204427	+	0.263288i
$172$	3.92838	−	6.80415i	0.299536	−	0.518812i
$173$	−19.0851	−	16.0143i	−1.45102	−	1.21755i	−0.931835	−	0.362883i	$-0.881792\pi$
$173$	−19.0851	−	16.0143i	−1.45102	−	1.21755i	−0.519182	−	0.854664i	$-0.673763\pi$
$174$	−0.707978	+	4.01514i	−0.0536717	+	0.304387i
$175$	0.215091	−	1.34187i	0.0162594	−	0.101436i
$176$	0.0831785	+	0.0697951i	0.00626982	+	0.00526100i
$177$	−2.61919	+	2.19776i	−0.196870	+	0.165194i
$178$	−5.99414			−0.449280
$179$	4.37167	+	7.57196i	0.326754	+	0.565955i	0.981866	−	0.189577i	$-0.0607117\pi$
$179$	4.37167	+	7.57196i	0.326754	+	0.565955i	−0.655112	+	0.755532i	$0.727378\pi$
$180$	−0.367804	−	2.08592i	−0.0274145	−	0.155475i
$181$	5.00758	+	1.82261i	0.372211	+	0.135474i	0.521351	−	0.853342i	$-0.325428\pi$
$181$	5.00758	+	1.82261i	0.372211	+	0.135474i	−0.149140	+	0.988816i	$0.547651\pi$
$182$	−7.81126	−	2.70590i	−0.579009	−	0.200575i
$183$	2.12774	+	3.68535i	0.157287	+	0.272429i
$184$	5.10804	−	4.28616i	0.376570	−	0.315980i
$185$	−18.3945	+	6.69504i	−1.35239	+	0.492229i
$186$	1.59114	+	9.02380i	0.116668	+	0.661657i
$187$	0.501396	−	0.182493i	0.0366657	−	0.0133452i
$188$	−9.12253	+	3.32033i	−0.665329	+	0.242160i
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$	3.48440	−	8.54983i	0.252785	−	0.620270i
$191$	−2.56028	−	4.43454i	−0.185256	−	0.320872i	0.758407	−	0.651781i	$-0.225978\pi$
$191$	−2.56028	−	4.43454i	−0.185256	−	0.320872i	−0.943663	+	0.330909i	$0.892645\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	−5.70663	−	4.78843i	−0.410772	−	0.344679i	0.413867	−	0.910337i	$-0.364178\pi$
$193$	−5.70663	−	4.78843i	−0.410772	−	0.344679i	−0.824640	+	0.565658i	$0.808622\pi$
$194$	−14.1557	−	5.15224i	−1.01632	−	0.369909i
$195$	−5.06969	−	4.25397i	−0.363048	−	0.304633i
$196$	−3.68732	−	5.95010i	−0.263380	−	0.425007i
$197$	−11.7292	−	20.3156i	−0.835671	−	1.44742i	−0.893483	−	0.449097i	$-0.851746\pi$
$197$	−11.7292	−	20.3156i	−0.835671	−	1.44742i	0.0578123	−	0.998327i	$-0.481587\pi$
$198$	−0.108582			−0.00771657
$199$	13.2506	−	11.1186i	0.939312	−	0.788177i	−0.0381532	−	0.999272i	$-0.512147\pi$
$199$	13.2506	−	11.1186i	0.939312	−	0.788177i	0.977465	+	0.211095i	$0.0677030\pi$
$200$	0.393481	−	0.330170i	0.0278233	−	0.0233465i
$201$	7.64452			0.539203
$202$	−8.53679	−	14.7862i	−0.600647	−	1.04035i
$203$	−1.70727	+	10.6510i	−0.119827	+	0.747553i
$204$	−3.76437	−	3.15868i	−0.263558	−	0.221152i
$205$	−25.1591	−	9.15717i	−1.75719	−	0.639564i
$206$	0.169163	+	0.141945i	0.0117861	+	0.00988975i
$207$	−1.15790	+	6.56677i	−0.0804796	+	0.456422i
$208$	−1.56225	−	2.70590i	−0.108323	−	0.187620i
$209$	−0.400620	−	0.252019i	−0.0277115	−	0.0174325i
$210$	−1.05905	−	5.50298i	−0.0730814	−	0.379742i
$211$	1.23052	−	0.447871i	0.0847122	−	0.0308327i	−0.299316	−	0.954154i	$-0.596759\pi$
$211$	1.23052	−	0.447871i	0.0847122	−	0.0308327i	0.384029	+	0.923321i	$0.374536\pi$
$212$	−0.298602	+	0.108682i	−0.0205081	+	0.00746434i
$213$	1.09924	+	6.23407i	0.0753184	+	0.427152i
$214$	0.751777	−	0.273625i	0.0513904	−	0.0187046i
$215$	12.7480	−	10.6969i	0.869410	−	0.729521i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	4.58150	+	23.8062i	0.311013	+	1.61607i
$218$	16.0333	+	5.83563i	1.08591	+	0.395239i
$219$	−2.43414	−	13.8047i	−0.164484	−	0.932834i
$220$	0.114994	+	0.199175i	0.00775287	+	0.0134284i
$221$	−15.3539			−1.03282
$222$	7.07960	−	5.94049i	0.475152	−	0.398700i
$223$	4.42394	+	3.71213i	0.296249	+	0.248583i	0.778781	−	0.627296i	$-0.215838\pi$
$223$	4.42394	+	3.71213i	0.296249	+	0.248583i	−0.482532	+	0.875878i	$0.660283\pi$
$224$	0.418748	−	2.61240i	0.0279788	−	0.174549i
$225$	−0.0891950	+	0.505850i	−0.00594633	+	0.0337233i
$226$	−3.85864	−	3.23778i	−0.256673	−	0.215374i
$227$	−1.34684	+	2.33279i	−0.0893927	+	0.154833i	−0.907255	−	0.420582i	$-0.861826\pi$
$227$	−1.34684	+	2.33279i	−0.0893927	+	0.154833i	0.817862	+	0.575415i	$0.195159\pi$
$228$	−0.165268	+	4.35576i	−0.0109452	+	0.288468i
$229$	12.3044	+	21.3119i	0.813098	+	1.40833i	0.910686	+	0.413100i	$0.135554\pi$
$229$	12.3044	+	21.3119i	0.813098	+	1.40833i	−0.0975874	+	0.995227i	$0.531113\pi$
$230$	13.2719	−	4.83057i	0.875123	−	0.318519i
$231$	−0.287246	+	0.00447929i	−0.0188994	+	0.000294716i
$232$	−3.12323	+	2.62070i	−0.205050	+	0.172057i
$233$	0.801858	−	4.54756i	0.0525315	−	0.297921i	−0.947211	−	0.320611i	$-0.896112\pi$
$233$	0.801858	−	4.54756i	0.0525315	−	0.297921i	0.999743	+	0.0226899i	$0.00722302\pi$
$234$	2.93607	+	1.06864i	0.191937	+	0.0698594i
$235$	−20.5625			−1.34135
$236$	−3.41911			−0.222565
$237$	11.3036	+	4.11418i	0.734250	+	0.267245i
$238$	−10.0887	−	8.20077i	−0.653952	−	0.531577i
$239$	4.85486	−	8.40887i	0.314035	−	0.543925i	−0.665197	−	0.746668i	$-0.731652\pi$
$239$	4.85486	−	8.40887i	0.314035	−	0.543925i	0.979232	+	0.202743i	$0.0649857\pi$
$240$	1.05905	−	1.83433i	0.0683614	−	0.118405i
$241$	−1.23938	−	0.451096i	−0.0798352	−	0.0290576i	0.301794	−	0.953373i	$-0.402415\pi$
$241$	−1.23938	−	0.451096i	−0.0798352	−	0.0290576i	−0.381629	+	0.924316i	$0.624637\pi$
$242$	−10.3255	+	3.75819i	−0.663751	+	0.241586i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	−0.738955	+	4.19082i	−0.0473068	+	0.268290i
$245$	−3.02865	−	14.5141i	−0.193494	−	0.927270i
$246$	12.6405			0.805927
$247$	8.35251	+	10.7575i	0.531457	+	0.684482i
$248$	−4.58150	+	7.93539i	−0.290926	+	0.503898i
$249$	1.72639	−	9.79085i	0.109406	−	0.620470i
$250$	10.9742	−	3.99427i	0.694067	−	0.252620i
$251$	6.29264	−	5.28015i	0.397188	−	0.333280i	−0.422218	−	0.906495i	$-0.638748\pi$
$251$	6.29264	−	5.28015i	0.397188	−	0.333280i	0.819406	+	0.573214i	$0.194304\pi$
$252$	1.35844	+	2.27038i	0.0855737	+	0.143021i
$253$	−0.125727	−	0.713032i	−0.00790438	−	0.0448280i
$254$	−4.90876	+	8.50222i	−0.308003	+	0.533477i
$255$	−5.20421	−	9.01395i	−0.325900	−	0.564475i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−1.98798	−	11.2744i	−0.124007	−	0.703279i	−0.981893	−	0.189438i	$-0.939333\pi$
$257$	−1.98798	−	11.2744i	−0.124007	−	0.703279i	0.857886	−	0.513841i	$-0.171778\pi$
$258$	−3.92838	+	6.80415i	−0.244570	+	0.423608i
$259$	18.4835	−	16.0072i	1.14851	−	0.994639i
$260$	−1.14920	−	6.51747i	−0.0712707	−	0.404196i
$261$	0.707978	−	4.01514i	0.0438228	−	0.248531i
$262$	2.45894	+	13.9454i	0.151914	+	0.861547i
$263$	−2.37921	−	1.99640i	−0.146708	−	0.123103i	0.566480	−	0.824076i	$-0.308305\pi$
$263$	−2.37921	−	1.99640i	−0.146708	−	0.123103i	−0.713188	+	0.700973i	$0.752749\pi$
$264$	−0.0831785	−	0.0697951i	−0.00511928	−	0.00429559i
$265$	−0.673060			−0.0413458
$266$	−0.257519	+	11.5297i	−0.0157895	+	0.706930i
$267$	5.99414			0.366836
$268$	5.85605	+	4.91381i	0.357715	+	0.300158i
$269$	−19.7971	−	16.6118i	−1.20705	−	1.01284i	−0.999400	−	0.0346355i	$-0.988973\pi$
$269$	−19.7971	−	16.6118i	−1.20705	−	1.01284i	−0.207653	−	0.978202i	$-0.566583\pi$
$270$	0.367804	+	2.08592i	0.0223838	+	0.126945i
$271$	−0.674444	+	3.82496i	−0.0409695	+	0.232350i	−0.998416	−	0.0562608i	$-0.982082\pi$
$271$	−0.674444	+	3.82496i	−0.0409695	+	0.232350i	0.957447	+	0.288611i	$0.0931933\pi$
$272$	−0.853313	−	4.83938i	−0.0517397	−	0.293430i
$273$	7.81126	+	2.70590i	0.472759	+	0.163768i
$274$	−4.61038	+	7.98541i	−0.278523	+	0.482416i
$275$	−0.00968495	−	0.0549261i	−0.000584025	−	0.00331217i
$276$	−5.10804	+	4.28616i	−0.307468	+	0.257996i
$277$	−2.53227	−	4.38601i	−0.152149	−	0.263530i	0.779868	−	0.625944i	$-0.215286\pi$
$277$	−2.53227	−	4.38601i	−0.152149	−	0.263530i	−0.932017	+	0.362414i	$0.881953\pi$
$278$	8.85662	−	15.3401i	0.531185	−	0.920039i
$279$	−1.59114	−	9.02380i	−0.0952590	−	0.540241i
$280$	2.72597	−	4.89627i	0.162908	−	0.292608i
$281$	1.49003	−	1.25029i	0.0888880	−	0.0745859i	−0.597261	−	0.802047i	$-0.703744\pi$
$281$	1.49003	−	1.25029i	0.0888880	−	0.0745859i	0.686149	+	0.727461i	$0.259300\pi$
$282$	9.12253	−	3.32033i	0.543239	−	0.197723i
$283$	4.26393	−	24.1820i	0.253464	−	1.43747i	−0.546520	−	0.837446i	$-0.684048\pi$
$283$	4.26393	−	24.1820i	0.253464	−	1.43747i	0.799984	−	0.600022i	$-0.204841\pi$
$284$	−3.16512	+	5.48215i	−0.187815	+	0.325306i
$285$	−3.48440	+	8.54983i	−0.206398	+	0.506448i
$286$	−0.339264			−0.0200611
$287$	33.4395	−	0.521453i	1.97387	−	0.0307804i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	−6.71666	−	2.44466i	−0.395097	−	0.143804i
$290$	−8.11488	+	2.95357i	−0.476522	+	0.173440i
$291$	14.1557	+	5.15224i	0.829819	+	0.302029i
$292$	7.00882	−	12.1396i	0.410160	−	0.710419i
$293$	4.19964	−	7.27399i	0.245346	−	0.424951i	−0.716883	−	0.697193i	$-0.754432\pi$
$293$	4.19964	−	7.27399i	0.245346	−	0.424951i	0.962229	+	0.272242i	$0.0877652\pi$
$294$	3.68732	+	5.95010i	0.215049	+	0.347017i
$295$	−6.80526	−	2.47691i	−0.396218	−	0.144211i
$296$	9.24176			0.537167
$297$	0.108582			0.00630056
$298$	−14.7063	−	5.35265i	−0.851911	−	0.310070i
$299$	−3.61786	+	20.5179i	−0.209226	+	1.18658i
$300$	−0.393481	+	0.330170i	−0.0227177	+	0.0190624i
$301$	−10.1116	+	18.1620i	−0.582821	+	1.04684i
$302$	−0.530468	+	0.193075i	−0.0305250	+	0.0111102i
$303$	8.53679	+	14.7862i	0.490426	+	0.849442i
$304$	−2.92643	+	3.23048i	−0.167843	+	0.185281i
$305$	−4.50676	+	7.80594i	−0.258056	+	0.446967i
$306$	3.76437	+	3.15868i	0.215195	+	0.180570i
$307$	−1.23861	+	7.02453i	−0.0706914	+	0.400911i	0.928845	+	0.370468i	$0.120803\pi$
$307$	−1.23861	+	7.02453i	−0.0706914	+	0.400911i	−0.999537	+	0.0304426i	$0.990308\pi$
$308$	−0.222922	−	0.181207i	−0.0127022	−	0.0103252i
$309$	−0.169163	−	0.141945i	−0.00962335	−	0.00807495i
$310$	−14.8675	+	12.4753i	−0.844418	+	0.708551i
$311$	28.5063			1.61645			0.808223	−	0.588877i	$-0.200430\pi$
$311$	28.5063			1.61645			0.808223	+	0.588877i	$0.200430\pi$
$312$	1.56225	+	2.70590i	0.0884451	+	0.153191i
$313$	−3.31814	−	18.8181i	−0.187552	−	1.06366i	−0.922632	−	0.385681i	$-0.873966\pi$
$313$	−3.31814	−	18.8181i	−0.187552	−	1.06366i	0.735080	−	0.677981i	$-0.237145\pi$
$314$	−9.74217	−	3.54586i	−0.549782	−	0.200104i
$315$	1.05905	+	5.50298i	0.0596707	+	0.310058i
$316$	6.01453	+	10.4175i	0.338344	+	0.586029i
$317$	−25.6248	+	21.5018i	−1.43923	+	1.20766i	−0.499242	+	0.866463i	$0.666388\pi$
$317$	−25.6248	+	21.5018i	−1.43923	+	1.20766i	−0.939992	+	0.341198i	$0.889167\pi$
$318$	0.298602	−	0.108682i	0.0167448	−	0.00609461i
$319$	0.0768736	+	0.435972i	0.00430409	+	0.0244097i
$320$	1.99036	−	0.724433i	0.111265	−	0.0404970i
$321$	−0.751777	+	0.273625i	−0.0419601	+	0.0152722i
$322$	−13.3362	+	11.5494i	−0.743195	+	0.643626i
$323$	6.55757	+	20.3913i	0.364873	+	1.13460i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.278690	+	1.58053i	−0.0154589	+	0.0876720i
$326$	1.48886	+	1.24931i	0.0824606	+	0.0691927i
$327$	−16.0333	−	5.83563i	−0.886642	−	0.322711i
$328$	9.68316	+	8.12514i	0.534663	+	0.448636i
$329$	23.9961	−	9.16003i	1.32295	−	0.505009i
$330$	−0.114994	−	0.199175i	−0.00633019	−	0.0109642i
$331$	−10.2690			−0.564433			−0.282217	−	0.959351i	$-0.591070\pi$
$331$	−10.2690			−0.564433			−0.282217	+	0.959351i	$0.591070\pi$
$332$	7.61593	−	6.39052i	0.417978	−	0.350725i
$333$	−7.07960	+	5.94049i	−0.387960	+	0.325537i
$334$	13.3068			0.728116
$335$	8.09593	+	14.0226i	0.442328	+	0.766135i
$336$	−0.418748	+	2.61240i	−0.0228446	+	0.142518i
$337$	−18.9679	−	15.9160i	−1.03325	−	0.867000i	−0.0420159	−	0.999117i	$-0.513378\pi$
$337$	−18.9679	−	15.9160i	−1.03325	−	0.867000i	−0.991234	+	0.132117i	$0.957822\pi$
$338$	−3.04224	−	1.10729i	−0.165476	−	0.0602284i
$339$	3.85864	+	3.23778i	0.209573	+	0.175852i
$340$	1.80740	−	10.2503i	0.0980201	−	0.555900i
$341$	0.497468	+	0.861640i	0.0269394	+	0.0466604i
$342$	0.165268	−	4.35576i	0.00893669	−	0.235533i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−7.38294	+	2.68717i	−0.398061	+	0.144882i
$345$	−13.2719	+	4.83057i	−0.714535	+	0.260069i
$346$	4.32625	+	24.5354i	0.232581	+	1.31903i
$347$	0.668290	−	0.243238i	0.0358757	−	0.0130577i	−0.324020	−	0.946050i	$-0.605035\pi$
$347$	0.668290	−	0.243238i	0.0358757	−	0.0130577i	0.359896	+	0.932993i	$0.382812\pi$
$348$	3.12323	−	2.62070i	0.167423	−	0.140484i
$349$	4.63291	+	8.02443i	0.247994	+	0.429538i	0.962969	−	0.269612i	$-0.0868954\pi$
$349$	4.63291	+	8.02443i	0.247994	+	0.429538i	−0.714975	+	0.699150i	$0.753562\pi$
$350$	−1.02731	+	0.889674i	−0.0549119	+	0.0475551i
$351$	−2.93607	−	1.06864i	−0.156716	−	0.0570399i
$352$	−0.0188550	−	0.106932i	−0.00100498	−	0.00569951i
$353$	−5.31931	−	9.21331i	−0.283118	−	0.490375i	0.689033	−	0.724730i	$-0.258035\pi$
$353$	−5.31931	−	9.21331i	−0.283118	−	0.490375i	−0.972151	+	0.234355i	$0.924702\pi$
$354$	3.41911			0.181723
$355$	−10.2712	+	8.61855i	−0.545138	+	0.457425i
$356$	4.59178	+	3.85296i	0.243364	+	0.204207i
$357$	10.0887	+	8.20077i	0.533949	+	0.434031i
$358$	1.51827	−	8.61052i	0.0802429	−	0.455080i
$359$	1.60500	+	1.34675i	0.0847084	+	0.0710788i	0.684159	−	0.729333i	$-0.260170\pi$
$359$	1.60500	+	1.34675i	0.0847084	+	0.0710788i	−0.599450	+	0.800412i	$0.704614\pi$
$360$	−1.05905	+	1.83433i	−0.0558168	+	0.0966776i
$361$	10.7195	−	15.6873i	0.564186	−	0.825648i
$362$	−2.66448	−	4.61501i	−0.140042	−	0.242560i
$363$	10.3255	−	3.75819i	0.541950	−	0.197254i
$364$	4.24445	+	7.09382i	0.222470	+	0.371817i
$365$	22.7445	−	19.0849i	1.19050	−	0.998948i
$366$	0.738955	−	4.19082i	0.0386258	−	0.219058i
$367$	9.87257	+	3.59332i	0.515344	+	0.187570i	0.586583	−	0.809889i	$-0.300473\pi$
$367$	9.87257	+	3.59332i	0.515344	+	0.187570i	−0.0712385	+	0.997459i	$0.522695\pi$
$368$	−6.66808			−0.347598
$369$	−12.6405			−0.658036
$370$	18.3945	+	6.69504i	0.956282	+	0.348058i
$371$	0.785448	−	0.299830i	0.0407784	−	0.0155664i
$372$	4.58150	−	7.93539i	0.237540	−	0.411431i
$373$	−16.9845	+	29.4181i	−0.879426	+	1.52321i	−0.0274541	+	0.999623i	$0.508740\pi$
$373$	−16.9845	+	29.4181i	−0.879426	+	1.52321i	−0.851972	+	0.523587i	$0.824593\pi$
$374$	−0.501396	−	0.182493i	−0.0259266	−	0.00943650i
$375$	−10.9742	+	3.99427i	−0.566704	+	0.206263i
$376$	9.12253	+	3.32033i	0.470459	+	0.171233i
$377$	2.21208	−	12.5453i	0.113928	−	0.646117i
$378$	−1.35844	−	2.27038i	−0.0698707	−	0.116776i
$379$	−6.12036			−0.314382			−0.157191	−	0.987568i	$-0.550244\pi$
$379$	−6.12036			−0.314382			−0.157191	+	0.987568i	$0.550244\pi$
$380$	−8.16493	+	4.30982i	−0.418852	+	0.221089i
$381$	4.90876	−	8.50222i	0.251483	−	0.435582i
$382$	−0.889177	+	5.04277i	−0.0454943	+	0.258011i
$383$	1.33423	−	0.485619i	0.0681758	−	0.0248140i	−0.307707	−	0.951481i	$-0.599562\pi$
$383$	1.33423	−	0.485619i	0.0681758	−	0.0248140i	0.375883	+	0.926667i	$0.377339\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	−0.312424	−	0.522159i	−0.0159226	−	0.0266117i
$386$	1.29359	+	7.33630i	0.0658419	+	0.373408i
$387$	3.92838	−	6.80415i	0.199691	−	0.345874i
$388$	7.53206	+	13.0459i	0.382383	+	0.662306i
$389$	−8.18730	+	6.86996i	−0.415113	+	0.348321i	−0.826300	−	0.563230i	$-0.809559\pi$
$389$	−8.18730	+	6.86996i	−0.415113	+	0.348321i	0.411188	+	0.911551i	$0.365114\pi$
$390$	1.14920	+	6.51747i	0.0581923	+	0.330025i
$391$	−16.3836	+	28.3772i	−0.828553	+	1.43510i
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$	−2.45894	−	13.9454i	−0.124037	−	0.703450i
$394$	−4.07351	+	23.1020i	−0.205220	+	1.16386i
$395$	4.42434	+	25.0917i	0.222613	+	1.26250i
$396$	0.0831785	+	0.0697951i	0.00417988	+	0.00350733i
$397$	12.0702	+	10.1281i	0.605787	+	0.508316i	0.893300	−	0.449461i	$-0.148384\pi$
$397$	12.0702	+	10.1281i	0.605787	+	0.508316i	−0.287513	+	0.957777i	$0.592828\pi$
$398$	−17.2975			−0.867044
$399$	0.257519	−	11.5297i	0.0128921	−	0.577206i
$400$	−0.513653			−0.0256827
$401$	12.2262	+	10.2590i	0.610549	+	0.512312i	0.894817	−	0.446433i	$-0.147306\pi$
$401$	12.2262	+	10.2590i	0.610549	+	0.512312i	−0.284268	+	0.958745i	$0.591750\pi$
$402$	−5.85605	−	4.91381i	−0.292073	−	0.245078i
$403$	−4.97152	−	28.1949i	−0.247649	−	1.40449i
$404$	−2.96480	+	16.8142i	−0.147504	+	0.836538i
$405$	−0.367804	−	2.08592i	−0.0182763	−	0.103650i
$406$	8.15417	−	7.06172i	0.404685	−	0.350467i
$407$	0.501744	−	0.869046i	0.0248705	−	0.0430770i
$408$	0.853313	+	4.83938i	0.0422453	+	0.239585i
$409$	−4.67857	+	3.92579i	−0.231340	+	0.194118i	−0.751088	−	0.660202i	$-0.770471\pi$
$409$	−4.67857	+	3.92579i	−0.231340	+	0.194118i	0.519747	+	0.854320i	$0.326026\pi$
$410$	13.3869	+	23.1868i	0.661131	+	1.14511i
$411$	4.61038	−	7.98541i	0.227413	−	0.393891i
$412$	−0.0383461	−	0.217472i	−0.00188918	−	0.0107141i
$413$	9.04501	−	0.141047i	0.445076	−	0.00694048i
$414$	5.10804	−	4.28616i	0.251047	−	0.210653i
$415$	19.7880	−	7.20223i	0.971353	−	0.353544i
$416$	−0.542564	+	3.07703i	−0.0266014	+	0.150864i
$417$	−8.85662	+	15.3401i	−0.433710	+	0.751209i
$418$	0.144898	+	0.450572i	0.00708719	+	0.0220382i
$419$	−9.12717			−0.445892			−0.222946	−	0.974831i	$-0.571567\pi$
$419$	−9.12717			−0.445892			−0.222946	+	0.974831i	$0.571567\pi$
$420$	−2.72597	+	4.89627i	−0.133014	+	0.238914i
$421$	−6.56464	+	37.2299i	−0.319941	+	1.81448i	0.223130	+	0.974789i	$0.428373\pi$
$421$	−6.56464	+	37.2299i	−0.319941	+	1.81448i	−0.543071	+	0.839687i	$0.682739\pi$
$422$	−1.23052	−	0.447871i	−0.0599006	−	0.0218020i
$423$	−9.12253	+	3.32033i	−0.443553	+	0.161440i
$424$	0.298602	+	0.108682i	0.0145014	+	0.00527808i
$425$	−1.26205	+	2.18594i	−0.0612186	+	0.106034i
$426$	3.16512	−	5.48215i	0.153351	−	0.265611i
$427$	1.78197	−	11.1170i	0.0862357	−	0.537990i
$428$	−0.751777	−	0.273625i	−0.0363385	−	0.0132261i
$429$	0.339264			0.0163798
$430$	−16.6414			−0.802519
$431$	−13.4313	−	4.88861i	−0.646965	−	0.235476i	−0.00236651	−	0.999997i	$-0.500753\pi$
$431$	−13.4313	−	4.88861i	−0.646965	−	0.235476i	−0.644599	+	0.764521i	$0.722976\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	29.1913	−	24.4944i	1.40285	−	1.17713i	0.443026	−	0.896509i	$-0.353905\pi$
$433$	29.1913	−	24.4944i	1.40285	−	1.17713i	0.959819	−	0.280618i	$-0.0905396\pi$
$434$	11.7927	−	21.1815i	0.566067	−	1.01675i
$435$	8.11488	−	2.95357i	0.389079	−	0.141613i
$436$	−8.53112	−	14.7763i	−0.408567	−	0.707658i
$437$	28.7947	−	3.95826i	1.37744	−	0.189349i
$438$	−7.00882	+	12.1396i	−0.334895	+	0.580054i
$439$	28.8997	+	24.2497i	1.37931	+	1.15738i	0.969468	+	0.245219i	$0.0788598\pi$
$439$	28.8997	+	24.2497i	1.37931	+	1.15738i	0.409840	+	0.912158i	$0.365585\pi$
$440$	0.0399368	−	0.226493i	0.00190391	−	0.0107976i
$441$	−3.68732	−	5.95010i	−0.175587	−	0.283338i
$442$	11.7618	+	9.86930i	0.559451	+	0.469435i
$443$	10.0509	−	8.43367i	0.477531	−	0.400696i	−0.372002	−	0.928232i	$-0.621328\pi$
$443$	10.0509	−	8.43367i	0.477531	−	0.400696i	0.849533	+	0.527536i	$0.176884\pi$
$444$	−9.24176			−0.438595
$445$	6.34810	+	10.9952i	0.300929	+	0.521224i
$446$	−1.00283	−	5.68731i	−0.0474852	−	0.269302i
$447$	14.7063	+	5.35265i	0.695583	+	0.253171i
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	−4.03989	−	6.99730i	−0.190654	−	0.330223i	0.754813	−	0.655940i	$-0.227728\pi$
$449$	−4.03989	−	6.99730i	−0.190654	−	0.330223i	−0.945467	+	0.325717i	$0.894394\pi$
$450$	0.393481	−	0.330170i	0.0185489	−	0.0155644i
$451$	1.28975	−	0.469431i	0.0607320	−	0.0221047i
$452$	0.874683	+	4.96057i	0.0411416	+	0.233326i
$453$	0.530468	−	0.193075i	0.0249236	−	0.00907144i
$454$	2.53122	−	0.921290i	0.118796	−	0.0432383i
$455$	3.30900	+	17.1941i	0.155128	+	0.806071i
$456$	2.92643	−	3.23048i	0.137043	−	0.151281i
$457$	19.5294	+	33.8259i	0.913546	+	1.58231i	0.809017	+	0.587786i	$0.200000\pi$
$457$	19.5294	+	33.8259i	0.913546	+	1.58231i	0.104529	+	0.994522i	$0.466666\pi$
$458$	4.27328	−	24.2350i	0.199677	−	1.13242i
$459$	−3.76437	−	3.15868i	−0.175706	−	0.147435i
$460$	−13.2719	−	4.83057i	−0.618805	−	0.225227i
$461$	13.2994	+	11.1596i	0.619417	+	0.519752i	0.897620	−	0.440770i	$-0.145295\pi$
$461$	13.2994	+	11.1596i	0.619417	+	0.519752i	−0.278204	+	0.960522i	$0.589739\pi$
$462$	0.222922	+	0.181207i	0.0103713	+	0.00843049i
$463$	−9.24601	−	16.0146i	−0.429698	−	0.744260i	0.567148	−	0.823616i	$-0.308047\pi$
$463$	−9.24601	−	16.0146i	−0.429698	−	0.744260i	−0.996846	+	0.0793564i	$0.974713\pi$
$464$	4.07708			0.189274
$465$	14.8675	−	12.4753i	0.689464	−	0.578529i
$466$	−3.53738	+	2.96821i	−0.163866	+	0.137500i
$467$	36.9347			1.70914			0.854568	−	0.519340i	$-0.173822\pi$
$467$	36.9347			1.70914			0.854568	+	0.519340i	$0.173822\pi$
$468$	−1.56225	−	2.70590i	−0.0722151	−	0.125080i
$469$	−15.6945	−	12.7575i	−0.724703	−	0.589089i
$470$	15.7518	+	13.2173i	0.726576	+	0.609670i
$471$	9.74217	+	3.54586i	0.448895	+	0.163385i
$472$	2.61919	+	2.19776i	0.120558	+	0.101160i
$473$	−0.148139	+	0.840140i	−0.00681146	+	0.0386297i
$474$	−6.01453	−	10.4175i	−0.276257	−	0.478491i
$475$	2.21810	−	0.304911i	0.101774	−	0.0139903i
$476$	2.45702	+	12.7670i	0.112617	+	0.585176i
$477$	−0.298602	+	0.108682i	−0.0136721	+	0.00497622i
$478$	−9.12416	+	3.32092i	−0.417329	+	0.151895i
$479$	−4.42171	−	25.0768i	−0.202033	−	1.14579i	−0.902040	−	0.431652i	$-0.857931\pi$
$479$	−4.42171	−	25.0768i	−0.202033	−	1.14579i	0.700007	−	0.714136i	$-0.253180\pi$
$480$	−1.99036	+	0.724433i	−0.0908472	+	0.0330657i
$481$	−22.1202	+	18.5611i	−1.00860	+	0.846312i
$482$	0.659458	+	1.14221i	0.0300375	+	0.0520265i
$483$	13.3362	−	11.5494i	0.606816	−	0.525518i
$484$	10.3255	+	3.75819i	0.469343	+	0.170827i
$485$	5.54065	+	31.4226i	0.251588	+	1.42683i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−12.3362			−0.559007			−0.279503	−	0.960145i	$-0.590170\pi$
$487$	−12.3362			−0.559007			−0.279503	+	0.960145i	$0.590170\pi$
$488$	3.25988	−	2.73537i	0.147568	−	0.123824i
$489$	−1.48886	−	1.24931i	−0.0673288	−	0.0564956i
$490$	−7.00938	+	13.0652i	−0.316652	+	0.590226i
$491$	2.64606	−	15.0065i	0.119415	−	0.677236i	−0.865054	−	0.501678i	$-0.832716\pi$
$491$	2.64606	−	15.0065i	0.119415	−	0.677236i	0.984469	−	0.175557i	$-0.0561727\pi$
$492$	−9.68316	−	8.12514i	−0.436551	−	0.366309i
$493$	10.0175	−	17.3508i	0.451164	−	0.781439i
$494$	0.516381	−	13.6096i	0.0232331	−	0.612325i
$495$	0.114994	+	0.199175i	0.00516858	+	0.00895224i
$496$	8.61041	−	3.13393i	0.386619	−	0.140718i
$497$	8.14696	−	14.6332i	0.365441	−	0.656390i
$498$	−7.61593	+	6.39052i	−0.341278	+	0.286366i
$499$	5.59721	−	31.7433i	0.250565	−	1.42103i	−0.556639	−	0.830755i	$-0.687909\pi$
$499$	5.59721	−	31.7433i	0.250565	−	1.42103i	0.807204	−	0.590272i	$-0.200980\pi$
$500$	−10.9742	−	3.99427i	−0.490780	−	0.178629i
$501$	−13.3068			−0.594505
$502$	−8.21446			−0.366629
$503$	25.4658	+	9.26879i	1.13546	+	0.413275i	0.840273	−	0.542163i	$-0.182395\pi$
$503$	25.4658	+	9.26879i	1.13546	+	0.413275i	0.295191	+	0.955438i	$0.404617\pi$
$504$	0.418748	−	2.61240i	0.0186525	−	0.116366i
$505$	−18.0818	+	31.3186i	−0.804628	+	1.39366i
$506$	−0.362016	+	0.627030i	−0.0160936	+	0.0278749i
$507$	3.04224	+	1.10729i	0.135111	+	0.0491763i
$508$	9.22545	−	3.35779i	0.409313	−	0.148978i
$509$	−17.2293	−	6.27096i	−0.763676	−	0.277955i	−0.0693273	−	0.997594i	$-0.522085\pi$
$509$	−17.2293	−	6.27096i	−0.763676	−	0.277955i	−0.694349	+	0.719639i	$0.744307\pi$
$510$	−1.80740	+	10.2503i	−0.0800331	+	0.453890i
$511$	−18.0406	+	32.4037i	−0.798067	+	1.43346i
$512$	−1.00000			−0.0441942
$513$	−0.165268	+	4.35576i	−0.00729678	+	0.192312i
$514$	−5.72417	+	9.91456i	−0.252482	+	0.437312i
$515$	0.0812210	−	0.460627i	0.00357902	−	0.0202976i
$516$	7.38294	−	2.68717i	0.325016	−	0.118296i
$517$	0.807497	−	0.677570i	0.0355137	−	0.0297995i
$518$	−24.4484	+	0.381247i	−1.07420	+	0.0167511i
$519$	−4.32625	−	24.5354i	−0.189901	−	1.07698i
$520$	−3.30900	+	5.73136i	−0.145109	+	0.251337i
$521$	15.0557	+	26.0772i	0.659601	+	1.14246i	0.980719	+	0.195423i	$0.0626080\pi$
$521$	15.0557	+	26.0772i	0.659601	+	1.14246i	−0.321118	+	0.947039i	$0.604059\pi$
$522$	−3.12323	+	2.62070i	−0.136700	+	0.114705i
$523$	0.210925	+	1.19621i	0.00922309	+	0.0523068i	0.989072	−	0.147434i	$-0.0471013\pi$
$523$	0.210925	+	1.19621i	0.00922309	+	0.0523068i	−0.979849	+	0.199740i	$0.935990\pi$
$524$	7.08024	−	12.2633i	0.309302	−	0.535727i
$525$	1.02731	−	0.889674i	0.0448353	−	0.0388285i
$526$	0.539323	+	3.05866i	0.0235156	+	0.133364i
$527$	7.81891	−	44.3432i	0.340597	−	1.93162i
$528$	0.0188550	+	0.106932i	0.000820560	+	0.00465363i
$529$	16.4418	+	13.7963i	0.714861	+	0.599839i
$530$	0.515594	+	0.432635i	0.0223960	+	0.0187925i
$531$	−3.41911			−0.148377
$532$	7.60841	−	8.66672i	0.329866	−	0.375750i
$533$	−39.4952			−1.71073
$534$	−4.59178	−	3.85296i	−0.198706	−	0.166734i
$535$	−1.29809	−	1.08922i	−0.0561212	−	0.0470913i
$536$	−1.32746	−	7.52839i	−0.0573374	−	0.325177i
$537$	−1.51827	+	8.61052i	−0.0655180	+	0.371571i
$538$	4.48765	+	25.4507i	0.193476	+	1.09726i
$539$	0.597200	+	0.470173i	0.0257232	+	0.0202518i
$540$	1.05905	−	1.83433i	0.0455743	−	0.0789369i
$541$	−1.21567	−	6.89440i	−0.0522657	−	0.296413i	0.947459	−	0.319877i	$-0.103642\pi$
$541$	−1.21567	−	6.89440i	−0.0522657	−	0.296413i	−0.999725	+	0.0234638i	$0.992531\pi$
$542$	2.97529	−	2.49657i	0.127800	−	0.107237i
$543$	2.66448	+	4.61501i	0.114344	+	0.198049i
$544$	−2.45702	+	4.25568i	−0.105344	+	0.182461i
$545$	−6.27556	−	35.5905i	−0.268816	−	1.52453i
$546$	−4.24445	−	7.09382i	−0.181646	−	0.303587i
$547$	−5.04794	+	4.23573i	−0.215834	+	0.181107i	−0.744294	−	0.667852i	$-0.767214\pi$
$547$	−5.04794	+	4.23573i	−0.215834	+	0.181107i	0.528460	+	0.848958i	$0.322770\pi$
$548$	8.66468	−	3.15369i	0.370137	−	0.134719i
$549$	−0.738955	+	4.19082i	−0.0315378	+	0.178860i
$550$	−0.0278867	+	0.0483012i	−0.00118909	+	0.00205957i
$551$	−17.6060	+	2.42021i	−0.750042	+	0.103104i
$552$	6.66808			0.283812
$553$	−16.3408	−	27.3106i	−0.694881	−	1.16136i
$554$	−0.879447	+	4.98759i	−0.0373641	+	0.211902i
$555$	−18.3945	−	6.69504i	−0.780801	−	0.284188i
$556$	−16.6450	+	6.05828i	−0.705905	+	0.256928i
$557$	−11.7605	−	4.28049i	−0.498310	−	0.181370i	0.0806236	−	0.996745i	$-0.474309\pi$
$557$	−11.7605	−	4.28049i	−0.498310	−	0.181370i	−0.578934	+	0.815375i	$0.696531\pi$
$558$	−4.58150	+	7.93539i	−0.193950	+	0.335932i
$559$	12.2742	−	21.2596i	0.519145	−	0.899185i
$560$	−5.23548	+	1.99854i	−0.221239	+	0.0844539i
$561$	0.501396	+	0.182493i	0.0211690	+	0.00770487i
$562$	−1.94510			−0.0820492
$563$	−10.5241			−0.443539			−0.221770	−	0.975099i	$-0.571183\pi$
$563$	−10.5241			−0.443539			−0.221770	+	0.975099i	$0.571183\pi$
$564$	−9.12253	−	3.32033i	−0.384128	−	0.139811i
$565$	−1.85267	+	10.5070i	−0.0779422	+	0.442032i
$566$	−18.8102	+	15.7836i	−0.790653	+	0.663436i
$567$	1.35844	+	2.27038i	0.0570491	+	0.0953471i
$568$	5.94848	−	2.16507i	0.249593	−	0.0908444i
$569$	−8.11524	−	14.0560i	−0.340208	−	0.589258i	0.644263	−	0.764804i	$-0.277164\pi$
$569$	−8.11524	−	14.0560i	−0.340208	−	0.589258i	−0.984471	+	0.175546i	$0.943831\pi$
$570$	8.16493	−	4.30982i	0.341991	−	0.180518i
$571$	−5.74342	+	9.94790i	−0.240355	+	0.416307i	−0.960815	−	0.277189i	$-0.910597\pi$
$571$	−5.74342	+	9.94790i	−0.240355	+	0.416307i	0.720461	+	0.693496i	$0.243930\pi$
$572$	0.259891	+	0.218075i	0.0108666	+	0.00911817i
$573$	0.889177	−	5.04277i	0.0371459	−	0.210665i
$574$	−25.9513	−	21.0950i	−1.08319	−	0.880489i
$575$	2.62376	+	2.20160i	0.109419	+	0.0918130i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−28.7616			−1.19736			−0.598681	−	0.800988i	$-0.704308\pi$
$577$	−28.7616			−1.19736			−0.598681	+	0.800988i	$0.704308\pi$
$578$	3.57386	+	6.19010i	0.148653	+	0.257474i
$579$	−1.29359	−	7.33630i	−0.0537597	−	0.304886i
$580$	8.11488	+	2.95357i	0.336952	+	0.122640i
$581$	−19.8838	+	17.2199i	−0.824918	+	0.714400i
$582$	−7.53206	−	13.0459i	−0.312214	−	0.540771i
$583$	0.0264313	−	0.0221785i	0.00109467	−	0.000918539i
$584$	−13.1723	+	4.79432i	−0.545073	+	0.198390i
$585$	−1.14920	−	6.51747i	−0.0475138	−	0.269464i
$586$	−7.89275	+	2.87272i	−0.326046	+	0.118671i
$587$	−19.3814	+	7.05426i	−0.799956	+	0.291160i	−0.709468	−	0.704737i	$-0.751065\pi$
$587$	−19.3814	+	7.05426i	−0.799956	+	0.291160i	−0.0904879	+	0.995898i	$0.528843\pi$
$588$	1.00000	−	6.92820i	0.0412393	−	0.285714i
$589$	−35.3219	+	18.6445i	−1.45541	+	0.768232i
$590$	3.62100	+	6.27176i	0.149074	+	0.258204i
$591$	4.07351	−	23.1020i	0.167562	−	0.950290i
$592$	−7.07960	−	5.94049i	−0.290970	−	0.244153i
$593$	18.1670	+	6.61224i	0.746029	+	0.271532i	0.686934	−	0.726720i	$-0.258956\pi$
$593$	18.1670	+	6.61224i	0.746029	+	0.271532i	0.0590950	+	0.998252i	$0.481179\pi$
$594$	−0.0831785	−	0.0697951i	−0.00341286	−	0.00286373i
$595$	−4.35850	+	27.1910i	−0.178681	+	1.11472i
$596$	7.82504	+	13.5534i	0.320526	+	0.555168i
$597$	17.2975			0.707938
$598$	15.9601	−	13.3921i	0.652657	−	0.547644i
$599$	16.6202	−	13.9460i	0.679083	−	0.569818i	−0.236655	−	0.971594i	$-0.576051\pi$
$599$	16.6202	−	13.9460i	0.679083	−	0.569818i	0.915738	+	0.401776i	$0.131607\pi$
$600$	0.513653			0.0209698
$601$	11.1582	+	19.3266i	0.455152	+	0.788346i	0.998697	−	0.0510336i	$-0.0162516\pi$
$601$	11.1582	+	19.3266i	0.455152	+	0.788346i	−0.543545	+	0.839380i	$0.682918\pi$
$602$	19.4202	−	7.41328i	0.791508	−	0.302143i
$603$	5.85605	+	4.91381i	0.238477	+	0.200106i
$604$	0.530468	+	0.193075i	0.0215845	+	0.00785610i
$605$	17.8290	+	14.9603i	0.724853	+	0.608223i
$606$	2.96480	−	16.8142i	0.120437	−	0.683030i
$607$	9.13386	+	15.8203i	0.370732	+	0.642126i	0.989678	−	0.143307i	$-0.0457736\pi$
$607$	9.13386	+	15.8203i	0.370732	+	0.642126i	−0.618947	+	0.785433i	$0.712440\pi$
$608$	4.31829	−	0.593613i	0.175130	−	0.0240742i
$609$	−8.15417	+	7.06172i	−0.330424	+	0.286155i
$610$	8.46994	−	3.08280i	0.342938	−	0.124819i
$611$	−28.5034	+	10.3744i	−1.15312	+	0.419703i
$612$	−0.853313	−	4.83938i	−0.0344931	−	0.195620i
$613$	35.4019	−	12.8852i	1.42987	−	0.520430i	0.492976	−	0.870043i	$-0.335909\pi$
$613$	35.4019	−	12.8852i	1.42987	−	0.520430i	0.936894	+	0.349613i	$0.113687\pi$
$614$	5.46411	−	4.58493i	0.220514	−	0.185033i
$615$	−13.3869	−	23.1868i	−0.539811	−	0.934981i
$616$	0.0542909	+	0.282104i	0.00218744	+	0.0113663i
$617$	−29.1444	−	10.6077i	−1.17331	−	0.427049i	−0.319475	−	0.947595i	$-0.603506\pi$
$617$	−29.1444	−	10.6077i	−1.17331	−	0.427049i	−0.853834	+	0.520546i	$0.825729\pi$
$618$	0.0383461	+	0.217472i	0.00154251	+	0.00874800i
$619$	8.66613	+	15.0102i	0.348321	+	0.603310i	0.985951	−	0.167033i	$-0.0534186\pi$
$619$	8.66613	+	15.0102i	0.348321	+	0.603310i	−0.637630	+	0.770343i	$0.720085\pi$
$620$	19.4082			0.779450
$621$	−5.10804	+	4.28616i	−0.204979	+	0.171998i
$622$	−21.8371	−	18.3235i	−0.875589	−	0.734706i
$623$	−12.3062	−	10.0033i	−0.493037	−	0.400774i
$624$	0.542564	−	3.07703i	0.0217199	−	0.123180i
$625$	−16.9816	−	14.2492i	−0.679264	−	0.569970i
$626$	−9.55420	+	16.5484i	−0.381863	+	0.661405i
$627$	−0.144898	−	0.450572i	−0.00578666	−	0.0179941i
$628$	5.18370	+	8.97843i	0.206852	+	0.358278i
$629$	−42.6755	+	15.5326i	−1.70158	+	0.619326i
$630$	2.72597	−	4.89627i	0.108605	−	0.195072i
$631$	5.54885	−	4.65604i	0.220896	−	0.185354i	−0.525623	−	0.850717i	$-0.676168\pi$
$631$	5.54885	−	4.65604i	0.220896	−	0.185354i	0.746520	+	0.665363i	$0.231723\pi$
$632$	2.08883	−	11.8463i	0.0830890	−	0.471221i
$633$	1.23052	+	0.447871i	0.0489086	+	0.0178013i
$634$	33.4508			1.32850
$635$	20.7945			0.825204
$636$	−0.298602	−	0.108682i	−0.0118404	−	0.00430954i
$637$	−11.5210	−	18.5911i	−0.456480	−	0.736606i
$638$	0.221349	−	0.383387i	0.00876328	−	0.0151784i
$639$	−3.16512	+	5.48215i	−0.125210	+	0.216871i
$640$	−1.99036	−	0.724433i	−0.0786760	−	0.0286357i
$641$	−8.84259	+	3.21844i	−0.349261	+	0.127121i	−0.510693	−	0.859763i	$-0.670611\pi$
$641$	−8.84259	+	3.21844i	−0.349261	+	0.127121i	0.161432	+	0.986884i	$0.448389\pi$
$642$	0.751777	+	0.273625i	0.0296703	+	0.0107991i
$643$	2.26833	−	12.8643i	0.0894541	−	0.507319i	−0.906852	−	0.421449i	$-0.861522\pi$
$643$	2.26833	−	12.8643i	0.0894541	−	0.507319i	0.996306	−	0.0858706i	$-0.0273672\pi$
$644$	17.6399	−	0.275076i	0.695111	−	0.0108395i
$645$	16.6414			0.655254
$646$	8.08388	−	19.8358i	0.318056	−	0.780428i
$647$	−18.1323	+	31.4060i	−0.712854	+	1.23470i	0.250928	+	0.968006i	$0.419264\pi$
$647$	−18.1323	+	31.4060i	−0.712854	+	1.23470i	−0.963782	+	0.266693i	$0.914069\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	0.348864	−	0.126976i	0.0136941	−	0.00498424i
$650$	1.22943	−	1.03162i	0.0482223	−	0.0404633i
$651$	−11.7927	+	21.1815i	−0.462192	+	0.830169i
$652$	−0.337498	−	1.91405i	−0.0132175	−	0.0749599i
$653$	−5.88498	+	10.1931i	−0.230297	+	0.398886i	−0.957896	−	0.287117i	$-0.907303\pi$
$653$	−5.88498	+	10.1931i	−0.230297	+	0.398886i	0.727598	+	0.686003i	$0.240636\pi$
$654$	8.53112	+	14.7763i	0.333593	+	0.577801i
$655$	22.9762	−	19.2793i	0.897755	−	0.753306i
$656$	−2.19499	−	12.4484i	−0.0857001	−	0.486030i
$657$	7.00882	−	12.1396i	0.273440	−	0.473612i
$658$	−24.2700	−	8.40737i	−0.946143	−	0.327754i
$659$	1.93589	+	10.9790i	0.0754117	+	0.427681i	0.999017	+	0.0443355i	$0.0141171\pi$
$659$	1.93589	+	10.9790i	0.0754117	+	0.427681i	−0.923605	+	0.383346i	$0.874772\pi$
$660$	−0.0399368	+	0.226493i	−0.00155454	+	0.00881623i
$661$	0.369296	+	2.09438i	0.0143639	+	0.0814619i	0.991147	−	0.132769i	$-0.0423867\pi$
$661$	0.369296	+	2.09438i	0.0143639	+	0.0814619i	−0.976783	+	0.214231i	$0.931276\pi$
$662$	7.86648	+	6.60076i	0.305739	+	0.256546i
$663$	−11.7618	−	9.86930i	−0.456789	−	0.383292i
$664$	−9.94189			−0.385820
$665$	21.4220	−	11.7381i	0.830708	−	0.455186i
$666$	9.24176			0.358111
$667$	−20.8259	−	17.4750i	−0.806383	−	0.676636i
$668$	−10.1936	−	8.55346i	−0.394403	−	0.330943i
$669$	1.00283	+	5.68731i	0.0387715	+	0.219884i
$670$	2.81169	−	15.9459i	0.108625	−	0.616043i
$671$	−0.0802371	−	0.455047i	−0.00309752	−	0.0175669i
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	11.7705	−	20.3870i	0.453718	−	0.785862i	−0.544896	−	0.838504i	$-0.683431\pi$
$673$	11.7705	−	20.3870i	0.453718	−	0.785862i	0.998613	+	0.0526417i	$0.0167641\pi$
$674$	4.29968	+	24.3847i	0.165618	+	0.939264i
$675$	−0.393481	+	0.330170i	−0.0151451	+	0.0127082i
$676$	1.61874	+	2.80374i	0.0622593	+	0.107836i
$677$	3.49461	−	6.05284i	0.134309	−	0.232629i	−0.791024	−	0.611784i	$-0.790452\pi$
$677$	3.49461	−	6.05284i	0.134309	−	0.232629i	0.925333	+	0.379155i	$0.123785\pi$
$678$	−0.874683	−	4.96057i	−0.0335920	−	0.190510i
$679$	−20.4637	−	34.2013i	−0.785326	−	1.31253i
$680$	−7.97331	+	6.69040i	−0.305762	+	0.256565i
$681$	−2.53122	+	0.921290i	−0.0969967	+	0.0353039i
$682$	0.172769	−	0.979820i	0.00661566	−	0.0375193i
$683$	−0.653363	+	1.13166i	−0.0250002	+	0.0433017i	−0.878255	−	0.478193i	$-0.841292\pi$
$683$	−0.653363	+	1.13166i	−0.0250002	+	0.0433017i	0.853255	+	0.521495i	$0.174625\pi$
$684$	−2.92643	+	3.23048i	−0.111895	+	0.123520i
$685$	19.5305			0.746222
$686$	2.35962	−	18.3693i	0.0900908	−	0.701344i
$687$	−4.27328	+	24.2350i	−0.163036	+	0.924621i
$688$	7.38294	+	2.68717i	0.281472	+	0.102447i
$689$	−0.932984	+	0.339578i	−0.0355439	+	0.0129369i
$690$	13.2719	+	4.83057i	0.505252	+	0.183897i
$691$	−2.48244	+	4.29971i	−0.0944364	+	0.163569i	−0.909373	−	0.415981i	$-0.863438\pi$
$691$	−2.48244	+	4.29971i	−0.0944364	+	0.163569i	0.814937	+	0.579550i	$0.196772\pi$
$692$	12.4569	−	21.5761i	0.473542	−	0.820199i
$693$	−0.222922	−	0.181207i	−0.00846811	−	0.00688347i
$694$	−0.668290	−	0.243238i	−0.0253679	−	0.00923317i
$695$	−37.5184			−1.42315
$696$	−4.07708			−0.154541
$697$	−58.3696	−	21.2448i	−2.21091	−	0.804705i
$698$	1.60899	−	9.12505i	0.0609012	−	0.345388i
$699$	3.53738	−	2.96821i	0.133796	−	0.112268i
$700$	1.35883	−	0.0211896i	0.0513591	−	0.000800891i
$701$	41.8972	−	15.2493i	1.58244	−	0.575960i	0.606704	−	0.794928i	$-0.292491\pi$
$701$	41.8972	−	15.2493i	1.58244	−	0.575960i	0.975732	+	0.218968i	$0.0702690\pi$
$702$	1.56225	+	2.70590i	0.0589634	+	0.102128i
$703$	34.0981	+	21.4502i	1.28603	+	0.809010i
$704$	−0.0542909	+	0.0940346i	−0.00204617	+	0.00354406i
$705$	−15.7518	−	13.2173i	−0.593247	−	0.497793i
$706$	−1.84738	+	10.4770i	−0.0695269	+	0.394307i
$707$	7.14953	−	44.6031i	0.268886	−	1.67747i
$708$	−2.61919	−	2.19776i	−0.0984351	−	0.0825968i
$709$	2.55435	−	2.14336i	0.0959307	−	0.0804954i	−0.593561	−	0.804789i	$-0.702278\pi$
$709$	2.55435	−	2.14336i	0.0959307	−	0.0804954i	0.689492	+	0.724294i	$0.257834\pi$
$710$	13.4081			0.503197
$711$	6.01453	+	10.4175i	0.225563	+	0.390686i
$712$	−1.04087	−	5.90308i	−0.0390083	−	0.221227i
$713$	−57.4148	−	20.8973i	−2.15020	−	0.782610i
$714$	−2.45702	−	12.7670i	−0.0919515	−	0.477794i
$715$	0.359298	+	0.622322i	0.0134370	+	0.0232735i
$716$	−6.69779	+	5.62012i	−0.250308	+	0.210034i
$717$	9.12416	−	3.32092i	0.340748	−	0.124022i
$718$	−0.363823	−	2.06334i	−0.0135777	−	0.0770032i
$719$	−16.0440	+	5.83954i	−0.598340	+	0.217778i	−0.623394	−	0.781908i	$-0.714247\pi$
$719$	−16.0440	+	5.83954i	−0.598340	+	0.217778i	0.0250537	+	0.999686i	$0.492024\pi$
$720$	1.99036	−	0.724433i	0.0741764	−	0.0269980i
$721$	0.110413	+	0.573724i	0.00411201	+	0.0213666i
$722$	−18.2952	+	5.12679i	−0.680879	+	0.190799i
$723$	−0.659458	−	1.14221i	−0.0245255	−	0.0424794i
$724$	−0.925364	+	5.24800i	−0.0343909	+	0.195040i
$725$	−1.60426	−	1.34613i	−0.0595806	−	0.0499940i
$726$	−10.3255	−	3.75819i	−0.383217	−	0.139479i
$727$	−19.2320	−	16.1375i	−0.713274	−	0.598508i	0.212242	−	0.977217i	$-0.431924\pi$
$727$	−19.2320	−	16.1375i	−0.713274	−	0.598508i	−0.925516	+	0.378709i	$0.876368\pi$
$728$	1.30838	−	8.16246i	0.0484918	−	0.302521i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−29.6908			−1.09891
$731$	29.5757	−	24.8170i	1.09390	−	0.917889i
$732$	−3.25988	+	2.73537i	−0.120489	+	0.101102i
$733$	33.6649			1.24344			0.621721	−	0.783239i	$-0.286434\pi$
$733$	33.6649			1.24344			0.621721	+	0.783239i	$0.286434\pi$
$734$	−5.25309	−	9.09861i	−0.193895	−	0.335836i
$735$	7.00938	−	13.0652i	0.258545	−	0.481917i
$736$	5.10804	+	4.28616i	0.188285	+	0.157990i
$737$	−0.779998	−	0.283896i	−0.0287316	−	0.0104574i
$738$	9.68316	+	8.12514i	0.356442	+	0.299090i
$739$	3.25079	−	18.4362i	0.119582	−	0.678185i	−0.864797	−	0.502122i	$-0.832553\pi$
$739$	3.25079	−	18.4362i	0.119582	−	0.678185i	0.984379	−	0.176063i	$-0.0563362\pi$
$740$	−9.78749	−	16.9524i	−0.359795	−	0.623184i
$741$	−0.516381	+	13.6096i	−0.0189697	+	0.499961i
$742$	−0.794415	−	0.275193i	−0.0291639	−	0.0101027i
$743$	−27.0879	+	9.85918i	−0.993758	+	0.361698i	−0.787174	−	0.616731i	$-0.788457\pi$
$743$	−27.0879	+	9.85918i	−0.993758	+	0.361698i	−0.206584	+	0.978429i	$0.566235\pi$
$744$	−8.61041	+	3.13393i	−0.315673	+	0.114896i
$745$	5.75617	+	32.6448i	0.210890	+	1.19601i
$746$	31.9205	−	11.6181i	1.16869	−	0.425369i
$747$	7.61593	−	6.39052i	0.278652	−	0.233817i
$748$	0.266787	+	0.462089i	0.00975471	+	0.0168957i
$749$	2.00006	+	0.692842i	0.0730807	+	0.0253159i
$750$	10.9742	+	3.99427i	0.400720	+	0.145850i
$751$	7.35000	+	41.6839i	0.268205	+	1.52107i	0.759750	+	0.650215i	$0.225321\pi$
$751$	7.35000	+	41.6839i	0.268205	+	1.52107i	−0.491545	+	0.870852i	$0.663568\pi$
$752$	−4.85400	−	8.40737i	−0.177007	−	0.306585i
$753$	8.21446			0.299352
$754$	−9.75853	+	8.18838i	−0.355385	+	0.298203i
$755$	0.915955	+	0.768577i	0.0333350	+	0.0279714i
$756$	−0.418748	+	2.61240i	−0.0152297	+	0.0950122i
$757$	−7.38706	+	41.8941i	−0.268487	+	1.52267i	0.490430	+	0.871481i	$0.336840\pi$
$757$	−7.38706	+	41.8941i	−0.268487	+	1.52267i	−0.758917	+	0.651187i	$0.774271\pi$
$758$	4.68847	+	3.93409i	0.170293	+	0.142893i
$759$	0.362016	−	0.627030i	0.0131403	−	0.0227597i
$760$	9.02500	+	1.94681i	0.327371	+	0.0706180i
$761$	2.41361	+	4.18050i	0.0874933	+	0.151543i	0.906451	−	0.422311i	$-0.138781\pi$
$761$	2.41361	+	4.18050i	0.0874933	+	0.151543i	−0.818958	+	0.573854i	$0.805448\pi$
$762$	−9.22545	+	3.35779i	−0.334203	+	0.121640i
$763$	23.1780	+	38.7378i	0.839102	+	1.40240i
$764$	3.92258	−	3.29144i	0.141914	−	0.119080i
$765$	1.80740	−	10.2503i	0.0653467	−	0.370600i
$766$	−1.33423	−	0.485619i	−0.0482076	−	0.0175461i
$767$	−10.6830			−0.385741
$768$	1.00000			0.0360844
$769$	18.3169	+	6.66682i	0.660526	+	0.240412i	0.650463	−	0.759538i	$-0.274575\pi$
$769$	18.3169	+	6.66682i	0.660526	+	0.240412i	0.0100626	+	0.999949i	$0.496797\pi$
$770$	−0.0963067	+	0.600819i	−0.00347065	+	0.0216520i
$771$	5.72417	−	9.91456i	0.206151	−	0.357064i
$772$	3.72474	−	6.45144i	0.134056	−	0.232192i
$773$	−25.1552	−	9.15575i	−0.904770	−	0.329309i	−0.152607	−	0.988287i	$-0.548767\pi$
$773$	−25.1552	−	9.15575i	−0.904770	−	0.329309i	−0.752163	+	0.658978i	$0.770989\pi$
$774$	−7.38294	+	2.68717i	−0.265374	+	0.0965883i
$775$	−4.42276	−	1.60975i	−0.158870	−	0.0578241i
$776$	2.61586	−	14.8353i	0.0939039	−	0.532555i
$777$	24.4484	−	0.381247i	0.877083	−	0.0136772i
$778$	10.6878			0.383175
$779$	16.8682	+	52.4529i	0.604365	+	1.87932i
$780$	3.30900	−	5.73136i	0.118481	−	0.205216i
$781$	0.119357	−	0.676907i	0.00427093	−	0.0242216i
$782$	30.7910	−	11.2070i	1.10109	−	0.400762i
$783$	3.12323	−	2.62070i	0.111615	−	0.0936561i
$784$	5.21941	−	4.66452i	0.186407	−	0.166590i
$785$	3.81317	+	21.6256i	0.136098	+	0.771850i
$786$	−7.08024	+	12.2633i	−0.252544	+	0.437419i
$787$	−10.1801	−	17.6324i	−0.362881	−	0.628529i	0.625553	−	0.780182i	$-0.284874\pi$
$787$	−10.1801	−	17.6324i	−0.362881	−	0.628529i	−0.988434	+	0.151653i	$0.951540\pi$
$788$	17.9702	−	15.0788i	0.640161	−	0.537159i
$789$	−0.539323	−	3.05866i	−0.0192004	−	0.108891i
$790$	12.7394	−	22.0653i	0.453247	−	0.785047i
$791$	−2.51855	−	13.0868i	−0.0895493	−	0.465312i
$792$	−0.0188550	−	0.106932i	−0.000669985	−	0.00379967i
$793$	−2.30887	+	13.0942i	−0.0819903	+	0.464990i
$794$	−2.73610	−	15.5172i	−0.0971004	−	0.550684i
$795$	−0.515594	−	0.432635i	−0.0182862	−	0.0153440i
$796$	13.2506	+	11.1186i	0.469656	+	0.394088i
$797$	3.02636			0.107199			0.0535996	−	0.998563i	$-0.482931\pi$
$797$	3.02636			0.107199			0.0535996	+	0.998563i	$0.482931\pi$
$798$	−7.60841	+	8.66672i	−0.269335	+	0.306799i
$799$	−47.7054			−1.68770
$800$	0.393481	+	0.330170i	0.0139117	+	0.0116733i
$801$	4.59178	+	3.85296i	0.162243	+	0.136138i
$802$	−2.77146	−	15.7177i	−0.0978638	−	0.555013i
$803$	−0.264303	+	1.49894i	−0.00932706	+	0.0528964i
$804$	1.32746	+	7.52839i	0.0468158	+	0.265506i
$805$	35.3091	+	12.2314i	1.24448	+	0.431102i
$806$	−14.3149	+	24.7942i	−0.504221	+	0.873337i
$807$	−4.48765	−	25.4507i	−0.157973	−	0.895908i
$808$	13.0791	−	10.9747i	0.460122	−	0.386088i
$809$	15.5344	+	26.9064i	0.546161	+	0.945978i	0.998533	+	0.0541490i	$0.0172446\pi$
$809$	15.5344	+	26.9064i	0.546161	+	0.945978i	−0.452372	+	0.891829i	$0.649422\pi$
$810$	−1.05905	+	1.83433i	−0.0372112	+	0.0644517i
$811$	−4.67603	−	26.5191i	−0.164198	−	0.931211i	−0.949888	−	0.312591i	$-0.898803\pi$
$811$	−4.67603	−	26.5191i	−0.164198	−	0.931211i	0.785690	−	0.618620i	$-0.212308\pi$
$812$	−10.7856	+	0.168191i	−0.378502	+	0.00590233i
$813$	−2.97529	+	2.49657i	−0.104348	+	0.0875584i
$814$	−0.942970	+	0.343213i	−0.0330511	+	0.0120296i
$815$	0.714855	−	4.05414i	0.0250403	−	0.142010i
$816$	2.45702	−	4.25568i	0.0860128	−	0.148978i
$817$	−33.4768	−	7.22137i	−1.17120	−	0.252644i
$818$	6.10744			0.213542
$819$	4.24445	+	7.09382i	0.148313	+	0.247878i
$820$	4.64922	−	26.3670i	0.162358	−	0.920776i
$821$	−17.8563	−	6.49915i	−0.623188	−	0.226822i	0.0110757	−	0.999939i	$-0.496474\pi$
$821$	−17.8563	−	6.49915i	−0.623188	−	0.226822i	−0.634264	+	0.773117i	$0.718697\pi$
$822$	−8.66468	+	3.15369i	−0.302215	+	0.109997i
$823$	−25.5966	−	9.31641i	−0.892243	−	0.324750i	−0.145103	−	0.989417i	$-0.546351\pi$
$823$	−25.5966	−	9.31641i	−0.892243	−	0.324750i	−0.747140	+	0.664667i	$0.768574\pi$
$824$	−0.110413	+	0.191241i	−0.00384643	+	0.00666221i
$825$	0.0278867	−	0.0483012i	0.000970891	−	0.00168163i
$826$	−7.01954	−	5.70597i	−0.244241	−	0.198536i
$827$	16.2821	+	5.92621i	0.566185	+	0.206074i	0.609223	−	0.792999i	$-0.291481\pi$
$827$	16.2821	+	5.92621i	0.566185	+	0.206074i	−0.0430382	+	0.999073i	$0.513704\pi$
$828$	−6.66808			−0.231732
$829$	0.734249			0.0255015			0.0127508	−	0.999919i	$-0.495941\pi$
$829$	0.734249			0.0255015			0.0127508	+	0.999919i	$0.495941\pi$
$830$	−19.7880	−	7.20223i	−0.686850	−	0.249993i
$831$	0.879447	−	4.98759i	0.0305077	−	0.173018i
$832$	2.39351	−	2.00839i	0.0829799	−	0.0696284i
$833$	−7.02654	−	33.6729i	−0.243455	−	1.16670i
$834$	16.6450	−	6.05828i	0.576369	−	0.209781i
$835$	−14.0926	−	24.4091i	−0.487694	−	0.844711i
$836$	0.178624	−	0.438297i	0.00617783	−	0.0151588i
$837$	4.58150	−	7.93539i	0.158360	−	0.274287i
$838$	6.99182	+	5.86683i	0.241528	+	0.202666i
$839$	−6.87956	+	39.0159i	−0.237509	+	1.34698i	0.599757	+	0.800182i	$0.295264\pi$
$839$	−6.87956	+	39.0159i	−0.237509	+	1.34698i	−0.837266	+	0.546796i	$0.815847\pi$
$840$	5.23548	−	1.99854i	0.180641	−	0.0689563i
$841$	−9.48163	−	7.95603i	−0.326953	−	0.274346i
$842$	28.9597	−	24.3001i	0.998019	−	0.837437i
$843$	1.94510			0.0669929
$844$	0.654744	+	1.13405i	0.0225372	+	0.0390356i
$845$	1.19076	+	6.75314i	0.0409634	+	0.232315i
$846$	9.12253	+	3.32033i	0.313639	+	0.114155i
$847$	−27.4705	−	9.51607i	−0.943898	−	0.326976i
$848$	−0.158883	−	0.275193i	−0.00545607	−	0.00945018i
$849$	18.8102	−	15.7836i	0.645565	−	0.541693i
$850$	2.37189	−	0.863296i	0.0813551	−	0.0296108i
$851$	10.7010	+	60.6886i	0.366827	+	2.08038i
$852$	−5.94848	+	2.16507i	−0.203792	+	0.0741741i
$853$	11.7829	−	4.28861i	0.403437	−	0.146839i	−0.132328	−	0.991206i	$-0.542245\pi$
$853$	11.7829	−	4.28861i	0.403437	−	0.146839i	0.535766	+	0.844367i	$0.320023\pi$
$854$	−8.51095	+	7.37070i	−0.291239	+	0.252220i
$855$	−8.16493	+	4.30982i	−0.279235	+	0.147393i
$856$	0.400012	+	0.692842i	0.0136721	+	0.0236808i
$857$	4.78409	−	27.1319i	0.163421	−	0.926808i	−0.787256	−	0.616626i	$-0.788499\pi$
$857$	4.78409	−	27.1319i	0.163421	−	0.926808i	0.950677	−	0.310182i	$-0.100390\pi$
$858$	−0.259891	−	0.218075i	−0.00887255	−	0.00744495i
$859$	1.19072	+	0.433386i	0.0406268	+	0.0147869i	0.362254	−	0.932080i	$-0.382007\pi$
$859$	1.19072	+	0.433386i	0.0406268	+	0.0147869i	−0.321627	+	0.946867i	$0.604230\pi$
$860$	12.7480	+	10.6969i	0.434705	+	0.364761i
$861$	25.9513	+	21.0950i	0.884418	+	0.718916i
$862$	7.14667	+	12.3784i	0.243417	+	0.421610i
$863$	37.3536			1.27153			0.635766	−	0.771882i	$-0.280684\pi$
$863$	37.3536			1.27153			0.635766	+	0.771882i	$0.280684\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	40.4242	−	33.9200i	1.37447	−	1.15331i
$866$	−38.1066			−1.29491
$867$	−3.57386	−	6.19010i	−0.121375	−	0.210227i
$868$	−22.6489	+	8.64580i	−0.768755	+	0.293458i
$869$	−1.00056	−	0.839570i	−0.0339417	−	0.0284804i
$870$	−8.11488	−	2.95357i	−0.275120	−	0.100136i
$871$	18.2972	+	15.3532i	0.619978	+	0.520223i
$872$	−2.96283	+	16.8030i	−0.100334	+	0.569022i
$873$	7.53206	+	13.0459i	0.254922	+	0.441537i
$874$	−24.6023	−	15.4767i	−0.832186	−	0.523506i
$875$	29.1962	+	10.1138i	0.987011	+	0.341911i
$876$	13.1723	−	4.79432i	0.445050	−	0.161985i
$877$	45.7515	−	16.6522i	1.54492	−	0.562304i	0.577700	−	0.816249i	$-0.303950\pi$
$877$	45.7515	−	16.6522i	1.54492	−	0.562304i	0.967219	+	0.253945i	$0.0817282\pi$
$878$	−6.55103	−	37.1527i	−0.221087	−	1.25384i
$879$	7.89275	−	2.87272i	0.266216	−	0.0968946i
$880$	−0.176180	+	0.147833i	−0.00593904	+	0.00498345i
$881$	−13.9143	−	24.1003i	−0.468785	−	0.811960i	0.530578	−	0.847636i	$-0.321975\pi$
$881$	−13.9143	−	24.1003i	−0.468785	−	0.811960i	−0.999363	+	0.0356759i	$0.988642\pi$
$882$	−1.00000	+	6.92820i	−0.0336718	+	0.233285i
$883$	−2.61357	−	0.951263i	−0.0879538	−	0.0320126i	0.297668	−	0.954669i	$-0.403791\pi$
$883$	−2.61357	−	0.951263i	−0.0879538	−	0.0320126i	−0.385622	+	0.922657i	$0.626013\pi$
$884$	−2.66618	−	15.1206i	−0.0896733	−	0.508562i
$885$	−3.62100	−	6.27176i	−0.121719	−	0.210823i
$886$	−13.1205			−0.440791
$887$	−5.63583	+	4.72902i	−0.189232	+	0.158785i	−0.732482	−	0.680786i	$-0.761638\pi$
$887$	−5.63583	+	4.72902i	−0.189232	+	0.158785i	0.543250	+	0.839571i	$0.317194\pi$
$888$	7.07960	+	5.94049i	0.237576	+	0.199350i
$889$	−24.2668	+	9.26337i	−0.813881	+	0.310683i
$890$	2.20467	−	12.5033i	0.0739007	−	0.419112i
$891$	0.0831785	+	0.0697951i	0.00278658	+	0.00233822i
$892$	−2.88752	+	5.00134i	−0.0966814	+	0.167457i
$893$	25.9517	+	33.4241i	0.868441	+	1.11849i
$894$	−7.82504	−	13.5534i	−0.261709	−	0.453293i
$895$	−17.4024	+	6.33397i	−0.581699	+	0.211721i
$896$	2.64543	−	0.0412527i	0.0883776	−	0.00137816i
$897$	−15.9601	+	13.3921i	−0.532892	+	0.447149i
$898$	−1.40304	+	7.95704i	−0.0468201	+	0.265530i
$899$	35.1054	+	12.7773i	1.17083	+	0.426147i
$900$	−0.513653			−0.0171218
$901$	−1.56151			−0.0520215
$902$	−1.28975	−	0.469431i	−0.0429440	−	0.0156303i
$903$	−19.4202	+	7.41328i	−0.646263	+	0.246699i
$904$	2.51855	−	4.36225i	0.0837657	−	0.145086i
$905$	−5.64363	+	9.77506i	−0.187601	+	0.324934i
$906$	−0.530468	−	0.193075i	−0.0176236	−	0.00641448i
$907$	−7.77896	+	2.83131i	−0.258296	+	0.0940121i	−0.467923	−	0.883769i	$-0.654997\pi$
$907$	−7.77896	+	2.83131i	−0.258296	+	0.0940121i	0.209627	+	0.977782i	$0.432775\pi$
$908$	−2.53122	−	0.921290i	−0.0840016	−	0.0305741i
$909$	−2.96480	+	16.8142i	−0.0983361	+	0.557692i
$910$	8.51730	−	15.2984i	0.282346	−	0.507138i
$911$	36.6980			1.21586			0.607929	−	0.793991i	$-0.292001\pi$
$911$	36.6980			1.21586			0.607929	+	0.793991i	$0.292001\pi$
$912$	−4.31829	+	0.593613i	−0.142993	+	0.0196565i
$913$	−0.539754	+	0.934882i	−0.0178633	+	0.0309401i
$914$	6.78248	−	38.4654i	0.224345	−	1.27232i
$915$	−8.46994	+	3.08280i	−0.280007	+	0.101914i
$916$	−18.8514	+	15.8182i	−0.622869	+	0.522649i
$917$	−18.2244	+	32.7339i	−0.601822	+	1.08097i
$918$	0.853313	+	4.83938i	0.0281635	+	0.159723i
$919$	16.0195	−	27.7465i	0.528434	−	0.915274i	−0.471017	−	0.882124i	$-0.656113\pi$
$919$	16.0195	−	27.7465i	0.528434	−	0.915274i	0.999450	−	0.0331496i	$-0.0105538\pi$
$920$	7.06183	+	12.2314i	0.232821	+	0.403259i
$921$	−5.46411	+	4.58493i	−0.180049	+	0.151079i
$922$	−3.01474	−	17.0974i	−0.0992851	−	0.563074i
$923$	−9.88943	+	17.1290i	−0.325515	+	0.563808i
$924$	−0.0542909	−	0.282104i	−0.00178604	−	0.00928054i
$925$	0.824319	+	4.67494i	0.0271034	+	0.153711i
$926$	−3.21111	+	18.2111i	−0.105523	+	0.598453i
$927$	−0.0383461	−	0.217472i	−0.00125945	−	0.00714271i
$928$	−3.12323	−	2.62070i	−0.102525	−	0.0860287i
$929$	9.65925	+	8.10507i	0.316910	+	0.265919i	0.787341	−	0.616518i	$-0.211457\pi$
$929$	9.65925	+	8.10507i	0.316910	+	0.265919i	−0.470431	+	0.882437i	$0.655902\pi$
$930$	−19.4082			−0.636418
$931$	−19.7700	+	23.2411i	−0.647935	+	0.761695i
$932$	4.61772			0.151258
$933$	21.8371	+	18.3235i	0.714915	+	0.599885i
$934$	−28.2936	−	23.7412i	−0.925796	−	0.776835i
$935$	0.196251	+	1.11299i	0.00641809	+	0.0363988i
$936$	−0.542564	+	3.07703i	−0.0177343	+	0.100576i
$937$	−1.17943	−	6.68886i	−0.0385302	−	0.218515i	0.959463	−	0.281834i	$-0.0909427\pi$
$937$	−1.17943	−	6.68886i	−0.0385302	−	0.218515i	−0.997993	+	0.0633185i	$0.979832\pi$
$938$	3.82226	+	19.8611i	0.124801	+	0.648486i
$939$	9.55420	−	16.5484i	0.311790	−	0.540035i
$940$	−3.57064	−	20.2501i	−0.116462	−	0.660486i
$941$	15.3376	−	12.8698i	0.499991	−	0.419542i	−0.357600	−	0.933875i	$-0.616405\pi$
$941$	15.3376	−	12.8698i	0.499991	−	0.419542i	0.857591	+	0.514333i	$0.171960\pi$
$942$	−5.18370	−	8.97843i	−0.168894	−	0.292533i
$943$	−42.1438	+	72.9952i	−1.37239	+	2.37705i
$944$	−0.593722	−	3.36716i	−0.0193240	−	0.109592i
$945$	−2.72597	+	4.89627i	−0.0886758	+	0.159276i
$946$	0.653513	−	0.548363i	0.0212475	−	0.0178288i
$947$	−37.8396	+	13.7725i	−1.22962	+	0.447545i	−0.873467	−	0.486883i	$-0.838134\pi$
$947$	−37.8396	+	13.7725i	−1.22962	+	0.447545i	−0.356153	+	0.934428i	$0.615912\pi$
$948$	−2.08883	+	11.8463i	−0.0678419	+	0.384751i
$949$	21.8991	−	37.9303i	0.710875	−	1.23127i
$950$	−1.89516	−	1.19219i	−0.0614871	−	0.0386799i
$951$	−33.4508			−1.08472
$952$	6.32431	−	11.3595i	0.204972	−	0.368162i
$953$	1.22290	−	6.93542i	0.0396137	−	0.224660i	−0.958574	−	0.284845i	$-0.908058\pi$
$953$	1.22290	−	6.93542i	0.0396137	−	0.224660i	0.998187	+	0.0601847i	$0.0191690\pi$
$954$	0.298602	+	0.108682i	0.00966761	+	0.00351872i
$955$	10.1918	−	3.70951i	0.329798	−	0.120037i
$956$	9.12416	+	3.32092i	0.295096	+	0.107406i
$957$	−0.221349	+	0.383387i	−0.00715518	+	0.0123931i
$958$	−12.7318	+	22.0522i	−0.411346	+	0.712473i
$959$	−22.7917	+	8.70029i	−0.735982	+	0.280947i
$960$	1.99036	+	0.724433i	0.0642387	+	0.0233810i
$961$	52.9606			1.70841
$962$	28.8759			0.930997
$963$	−0.751777	−	0.273625i	−0.0242257	−	0.00881743i
$964$	0.229027	−	1.29888i	0.00737647	−	0.0418341i
$965$	12.0872	−	10.1424i	0.389101	−	0.326495i
$966$	−17.6399	+	0.275076i	−0.567555	+	0.00885043i
$967$	28.7721	−	10.4722i	0.925248	−	0.336763i	0.164924	−	0.986306i	$-0.447262\pi$
$967$	28.7721	−	10.4722i	0.925248	−	0.336763i	0.760324	+	0.649543i	$0.225040\pi$
$968$	−5.49410	−	9.51607i	−0.176587	−	0.305858i
$969$	−8.08388	+	19.8358i	−0.259692	+	0.637216i
$970$	15.9537	−	27.6326i	0.512241	−	0.887228i
$971$	−23.8890	−	20.0453i	−0.766635	−	0.643283i	0.173210	−	0.984885i	$-0.444586\pi$
$971$	−23.8890	−	20.0453i	−0.766635	−	0.643283i	−0.939845	+	0.341602i	$0.889030\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	43.7832	−	16.7134i	1.40363	−	0.535807i
$974$	9.45008	+	7.92956i	0.302800	+	0.254080i
$975$	−1.22943	+	1.03162i	−0.0393734	+	0.0330382i
$976$	−4.25547			−0.136214
$977$	−0.522433	−	0.904880i	−0.0167141	−	0.0289497i	0.857547	−	0.514405i	$-0.171987\pi$
$977$	−0.522433	−	0.904880i	−0.0167141	−	0.0289497i	−0.874261	+	0.485455i	$0.838654\pi$
$978$	0.337498	+	1.91405i	0.0107920	+	0.0612045i
$979$	−0.611604	−	0.222606i	−0.0195469	−	0.00711450i
$980$	13.7676	−	5.50298i	0.439791	−	0.175786i
$981$	−8.53112	−	14.7763i	−0.272378	−	0.471772i
$982$	−11.6730	+	9.79482i	−0.372501	+	0.312565i
$983$	−17.1464	+	6.24077i	−0.546885	+	0.199050i	−0.600662	−	0.799503i	$-0.705096\pi$
$983$	−17.1464	+	6.24077i	−0.546885	+	0.199050i	0.0537772	+	0.998553i	$0.482874\pi$
$984$	2.19499	+	12.4484i	0.0699739	+	0.396841i
$985$	46.6907	−	16.9940i	1.48769	−	0.541475i
$986$	−18.8267	+	6.85235i	−0.599563	+	0.218223i
$987$	24.2700	+	8.40737i	0.772522	+	0.267610i
$988$	−9.14365	+	10.0936i	−0.290898	+	0.321121i
$989$	−26.1947	−	45.3706i	−0.832944	−	1.44270i
$990$	0.0399368	−	0.226493i	0.00126928	−	0.00719842i
$991$	20.1454	+	16.9040i	0.639940	+	0.536973i	0.904000	−	0.427533i	$-0.140617\pi$
$991$	20.1454	+	16.9040i	0.639940	+	0.536973i	−0.264060	+	0.964506i	$0.585062\pi$
$992$	−8.61041	−	3.13393i	−0.273381	−	0.0995024i
$993$	−7.86648	−	6.60076i	−0.249635	−	0.209469i
$994$	−15.6470	+	5.97294i	−0.496292	+	0.189450i
$995$	18.3189	+	31.7292i	0.580748	+	1.00588i
$996$	9.94189			0.315021
$997$	−16.9587	+	14.2300i	−0.537087	+	0.450670i	−0.870540	−	0.492097i	$-0.836231\pi$
$997$	−16.9587	+	14.2300i	−0.537087	+	0.450670i	0.333453	+	0.942767i	$0.391786\pi$
$998$	−24.6919	+	20.7190i	−0.781609	+	0.655848i
$999$	−9.24176			−0.292396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.b.613.1	yes	12
7.2	even	3		798.2.bq.b.499.2	yes	12
19.4	even	9		798.2.bq.b.403.2	yes	12
133.23	even	9	inner	798.2.bp.b.289.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.b.289.1	✓	12	133.23	even	9	inner
798.2.bp.b.613.1	yes	12	1.1	even	1	trivial
798.2.bq.b.403.2	yes	12	19.4	even	9
798.2.bq.b.499.2	yes	12	7.2	even	3

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.367804 + 2.08592i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.367804 + 2.08592i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.62256 - 1.36149i) q^{10} +(-0.0542909 - 0.0940346i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.542564 + 3.07703i) q^{13} +(-1.28699 + 2.31164i) q^{14} +(-1.62256 + 1.36149i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.853313 + 4.83938i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.85484 - 2.03476i) q^{19} -2.11810 q^{20} +(1.28699 - 2.31164i) q^{21} +(-0.0188550 + 0.106932i) q^{22} +(6.26594 + 2.28062i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.482676 + 0.175680i) q^{25} +(1.56225 - 2.70590i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.47178 - 0.943555i) q^{28} +(-3.83121 - 1.39444i) q^{29} +2.11810 q^{30} -9.16300 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0188550 - 0.106932i) q^{33} +(3.76437 - 3.15868i) q^{34} +(5.60328 - 0.0873773i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.62088 + 8.00360i) q^{37} +(-4.26089 - 0.919128i) q^{38} +(-1.56225 + 2.70590i) q^{39} +(1.62256 + 1.36149i) q^{40} +(-2.19499 + 12.4484i) q^{41} +(-2.47178 + 0.943555i) q^{42} +(-6.01862 - 5.05023i) q^{43} +(0.0831785 - 0.0697951i) q^{44} -2.11810 q^{45} +(-3.33404 - 5.77472i) q^{46} +(1.68578 + 9.56051i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-0.256827 - 0.444837i) q^{50} +(-3.76437 + 3.15868i) q^{51} +(-2.93607 + 1.06864i) q^{52} +(0.0551795 + 0.312938i) q^{53} +(0.939693 - 0.342020i) q^{54} +(0.216117 - 0.0786602i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(4.26089 + 0.919128i) q^{57} +(2.03854 + 3.53086i) q^{58} +(-0.593722 + 3.36716i) q^{59} +(-1.62256 - 1.36149i) q^{60} +(3.99884 + 1.45546i) q^{61} +(7.01927 + 5.88986i) q^{62} +(2.47178 - 0.943555i) q^{63} +(-0.500000 - 0.866025i) q^{64} -6.61801 q^{65} +(-0.0831785 + 0.0697951i) q^{66} +(5.85605 - 4.91381i) q^{67} -4.91403 q^{68} +(3.33404 + 5.77472i) q^{69} +(-4.34853 - 3.53479i) q^{70} +(4.84925 + 4.06900i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-10.7381 - 9.01037i) q^{73} +(1.60482 - 9.10136i) q^{74} +(0.256827 + 0.444837i) q^{75} +(2.67323 + 3.44294i) q^{76} +(-0.217164 + 0.188069i) q^{77} +(2.93607 - 1.06864i) q^{78} +(11.3036 - 4.11418i) q^{79} +(-0.367804 - 2.08592i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(9.68316 - 8.12514i) q^{82} +(-4.97094 - 8.60993i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-9.78071 - 3.55989i) q^{85} +(1.36431 + 7.73739i) q^{86} +(-2.03854 - 3.53086i) q^{87} -0.108582 q^{88} +(4.59178 - 3.85296i) q^{89} +(1.62256 + 1.36149i) q^{90} +(7.72309 - 2.94814i) q^{91} +(-1.15790 + 6.56677i) q^{92} +(-7.01927 - 5.88986i) q^{93} +(4.85400 - 8.40737i) q^{94} +(2.82651 + 8.78928i) q^{95} +(0.500000 + 0.866025i) q^{96} +(14.1557 - 5.15224i) q^{97} +(6.64930 + 2.18788i) q^{98} +(0.0831785 - 0.0697951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{12} + 12 q^{13} - 6 q^{15} - 18 q^{17} + 6 q^{18} - 3 q^{19} - 21 q^{22} - 3 q^{23} + 21 q^{25} - 6 q^{26} - 6 q^{27} - 12 q^{29} - 6 q^{31} + 21 q^{33} - 9 q^{34} + 12 q^{35} - 3 q^{37} + 3 q^{38} + 6 q^{39} + 6 q^{40} - 24 q^{41} - 21 q^{43} - 6 q^{44} - 6 q^{46} + 18 q^{47} - 78 q^{49} + 6 q^{50} + 9 q^{51} - 15 q^{52} + 36 q^{53} + 30 q^{55} - 30 q^{56} - 3 q^{57} + 15 q^{58} - 33 q^{59} - 6 q^{60} + 33 q^{62} - 6 q^{64} + 24 q^{65} + 6 q^{66} + 51 q^{67} - 6 q^{68} + 6 q^{69} - 3 q^{70} + 6 q^{71} - 3 q^{73} - 6 q^{75} + 9 q^{76} + 15 q^{78} + 30 q^{79} + 3 q^{80} - 3 q^{82} - 27 q^{83} + 30 q^{84} - 36 q^{85} + 3 q^{86} - 15 q^{87} + 12 q^{89} + 6 q^{90} + 21 q^{91} - 3 q^{92} - 33 q^{93} + 6 q^{94} + 21 q^{95} + 6 q^{96} + 30 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8 + 6 * q^10 - 6 * q^12 + 12 * q^13 - 6 * q^15 - 18 * q^17 + 6 * q^18 - 3 * q^19 - 21 * q^22 - 3 * q^23 + 21 * q^25 - 6 * q^26 - 6 * q^27 - 12 * q^29 - 6 * q^31 + 21 * q^33 - 9 * q^34 + 12 * q^35 - 3 * q^37 + 3 * q^38 + 6 * q^39 + 6 * q^40 - 24 * q^41 - 21 * q^43 - 6 * q^44 - 6 * q^46 + 18 * q^47 - 78 * q^49 + 6 * q^50 + 9 * q^51 - 15 * q^52 + 36 * q^53 + 30 * q^55 - 30 * q^56 - 3 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 + 33 * q^62 - 6 * q^64 + 24 * q^65 + 6 * q^66 + 51 * q^67 - 6 * q^68 + 6 * q^69 - 3 * q^70 + 6 * q^71 - 3 * q^73 - 6 * q^75 + 9 * q^76 + 15 * q^78 + 30 * q^79 + 3 * q^80 - 3 * q^82 - 27 * q^83 + 30 * q^84 - 36 * q^85 + 3 * q^86 - 15 * q^87 + 12 * q^89 + 6 * q^90 + 21 * q^91 - 3 * q^92 - 33 * q^93 + 6 * q^94 + 21 * q^95 + 6 * q^96 + 30 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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