LMFDB - Embedded newform 37.2.f.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	37.9
Dual form			37.2.f.b.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 2.49362i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.93969 + 1.62760i) q^{5} +0.879385 q^{6} +(-2.34730 - 1.96962i) q^{7} +(3.05303 + 5.28801i) q^{8} +(2.70574 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.93969 + 1.62760i) q^{5} +0.879385 q^{6} +(-2.34730 - 1.96962i) q^{7} +(3.05303 + 5.28801i) q^{8} +(2.70574 + 0.984808i) q^{9} +(3.20574 - 5.55250i) q^{10} +(0.386659 + 0.669713i) q^{11} +(-0.266044 - 1.50881i) q^{12} +(-5.23783 + 1.90641i) q^{13} +(-3.87939 + 6.71929i) q^{14} +(-0.673648 + 0.565258i) q^{15} +(5.08512 - 4.26692i) q^{16} +(-1.55303 - 0.565258i) q^{17} +(1.26604 - 7.18009i) q^{18} +(-0.0393628 + 0.223238i) q^{19} +(-10.4966 - 3.82045i) q^{20} +(0.815207 - 0.684040i) q^{21} +(1.50000 - 1.25865i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-1.99273 + 0.725293i) q^{24} +(0.245100 + 1.39003i) q^{25} +(7.05690 + 12.2229i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(12.7023 + 4.62327i) q^{28} +(-0.798133 - 1.38241i) q^{29} +(1.70574 + 1.43128i) q^{30} -3.83750 q^{31} +(-3.52094 - 2.95442i) q^{32} +(-0.252374 + 0.0918566i) q^{33} +(-0.726682 + 4.12122i) q^{34} +(-1.34730 - 7.64090i) q^{35} -12.7023 q^{36} +(5.93629 - 1.32683i) q^{37} +0.573978 q^{38} +(-0.336152 - 1.90641i) q^{39} +(-2.68479 + 15.2262i) q^{40} +(6.85117 - 2.49362i) q^{41} +(-2.06418 - 1.73205i) q^{42} -1.46791 q^{43} +(-2.61334 - 2.19285i) q^{44} +(3.64543 + 6.31407i) q^{45} +(-14.2763 - 5.19615i) q^{46} +(-1.39053 + 2.40847i) q^{47} +(1.15270 + 1.99654i) q^{48} +(0.414878 + 2.35289i) q^{49} +(3.35844 - 1.22237i) q^{50} +(0.286989 - 0.497079i) q^{51} +(18.8366 - 15.8058i) q^{52} +(0.783119 - 0.657115i) q^{53} +(4.85844 + 1.76833i) q^{54} +(-0.340022 + 1.92836i) q^{55} +(3.24897 - 18.4258i) q^{56} +(-0.0739780 - 0.0269258i) q^{57} +(-3.09627 + 2.59808i) q^{58} +(-3.64543 + 3.05888i) q^{59} +(1.93969 - 3.35965i) q^{60} +(-2.26604 + 0.824773i) q^{61} +(1.68732 + 9.56926i) q^{62} +(-4.41147 - 7.64090i) q^{63} +(0.819078 - 1.41868i) q^{64} +(-13.2626 - 4.82721i) q^{65} +(0.340022 + 0.588936i) q^{66} +(8.69846 + 7.29888i) q^{67} +7.29086 q^{68} +(1.59627 + 1.33943i) q^{69} +(-18.4611 + 6.71929i) q^{70} +(-2.03074 + 11.5169i) q^{71} +(3.05303 + 17.3146i) q^{72} -2.92127 q^{73} +(-5.91875 - 14.2195i) q^{74} -0.490200 q^{75} +(-0.173648 - 0.984808i) q^{76} +(0.411474 - 2.33359i) q^{77} +(-4.60607 + 1.67647i) q^{78} +(-6.55690 - 5.50190i) q^{79} +16.8084 q^{80} +(6.07398 + 5.09667i) q^{81} +(-9.23055 - 15.9878i) q^{82} +(11.3576 + 4.13381i) q^{83} +(-2.34730 + 4.06564i) q^{84} +(-2.09240 - 3.62414i) q^{85} +(0.645430 + 3.66041i) q^{86} +(0.520945 - 0.189608i) q^{87} +(-2.36097 + 4.08931i) q^{88} +(-1.45677 + 1.22237i) q^{89} +(14.1420 - 11.8666i) q^{90} +(16.0496 + 5.84159i) q^{91} +(-4.59627 + 26.0667i) q^{92} +(0.231429 - 1.31250i) q^{93} +(6.61721 + 2.40847i) q^{94} +(-0.439693 + 0.368946i) q^{95} +(1.22281 - 1.02606i) q^{96} +(-7.49273 + 12.9778i) q^{97} +(5.68479 - 2.06910i) q^{98} +(0.386659 + 2.19285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	−0.594292	−	0.804249i	$-0.702568\pi$
$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	0.283383	−	0.959007i	$-0.408543\pi$
$3$	−0.0603074	+	0.342020i	−0.0348185	+	0.197465i	−0.997255	−	0.0740406i	$-0.976411\pi$
$3$	−0.0603074	+	0.342020i	−0.0348185	+	0.197465i	0.962437	+	0.271506i	$0.0875217\pi$
$4$	−4.14543	+	1.50881i	−2.07271	+	0.754407i
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	0.963561	−	0.267489i	$-0.0861937\pi$
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	−0.0961041	+	0.995371i	$0.530638\pi$
$6$	0.879385			0.359008
$7$	−2.34730	−	1.96962i	−0.887195	−	0.744445i	0.0804508	−	0.996759i	$-0.474364\pi$
$7$	−2.34730	−	1.96962i	−0.887195	−	0.744445i	−0.967645	+	0.252314i	$0.918808\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$	2.70574	+	0.984808i	0.901912	+	0.328269i
$10$	3.20574	−	5.55250i	1.01374	−	1.75585i
$11$	0.386659	+	0.669713i	0.116582	+	0.201926i	0.918411	−	0.395627i	$-0.129473\pi$
$11$	0.386659	+	0.669713i	0.116582	+	0.201926i	−0.801829	+	0.597554i	$0.796140\pi$
$12$	−0.266044	−	1.50881i	−0.0768004	−	0.435557i
$13$	−5.23783	+	1.90641i	−1.45271	+	0.528744i	−0.943347	−	0.331807i	$-0.892342\pi$
$13$	−5.23783	+	1.90641i	−1.45271	+	0.528744i	−0.509364	+	0.860551i	$0.670119\pi$
$14$	−3.87939	+	6.71929i	−1.03681	+	1.79581i
$15$	−0.673648	+	0.565258i	−0.173935	+	0.145949i
$16$	5.08512	−	4.26692i	1.27128	−	1.06673i
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	0.146748	−	0.989174i	$-0.453119\pi$
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	−0.523414	+	0.852079i	$0.675342\pi$
$18$	1.26604	−	7.18009i	0.298410	−	1.69236i
$19$	−0.0393628	+	0.223238i	−0.00903046	+	0.0512143i	−0.988990	−	0.147982i	$-0.952722\pi$
$19$	−0.0393628	+	0.223238i	−0.00903046	+	0.0512143i	0.979960	+	0.199197i	$0.0638332\pi$
$20$	−10.4966	−	3.82045i	−2.34711	−	0.854278i
$21$	0.815207	−	0.684040i	0.177893	−	0.149270i
$22$	1.50000	−	1.25865i	0.319801	−	0.268345i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−1.99273	+	0.725293i	−0.406763	+	0.148050i
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$	7.05690	+	12.2229i	1.38397	+	2.39711i
$27$	−1.02094	+	1.76833i	−0.196481	+	0.340315i
$28$	12.7023	+	4.62327i	2.40052	+	0.873716i
$29$	−0.798133	−	1.38241i	−0.148210	−	0.256707i	0.782356	−	0.622831i	$-0.214018\pi$
$29$	−0.798133	−	1.38241i	−0.148210	−	0.256707i	−0.930566	+	0.366125i	$0.880684\pi$
$30$	1.70574	+	1.43128i	0.311424	+	0.261315i
$31$	−3.83750			−0.689235			−0.344617	−	0.938743i	$-0.611991\pi$
$31$	−3.83750			−0.689235			−0.344617	+	0.938743i	$0.611991\pi$
$32$	−3.52094	−	2.95442i	−0.622421	−	0.522273i
$33$	−0.252374	+	0.0918566i	−0.0439327	+	0.0159902i
$34$	−0.726682	+	4.12122i	−0.124625	+	0.706783i
$35$	−1.34730	−	7.64090i	−0.227735	−	1.29155i
$36$	−12.7023			−2.11706
$37$	5.93629	−	1.32683i	0.975920	−	0.218129i
$37$	5.93629	−	1.32683i	0.975920	−	0.218129i
$38$	0.573978			0.0931115
$39$	−0.336152	−	1.90641i	−0.0538274	−	0.305270i
$40$	−2.68479	+	15.2262i	−0.424503	+	2.40748i
$41$	6.85117	−	2.49362i	1.06997	−	0.389438i	0.253806	−	0.967255i	$-0.418317\pi$
$41$	6.85117	−	2.49362i	1.06997	−	0.389438i	0.816166	+	0.577817i	$0.196095\pi$
$42$	−2.06418	−	1.73205i	−0.318510	−	0.267261i
$43$	−1.46791			−0.223854			−0.111927	−	0.993716i	$-0.535702\pi$
$43$	−1.46791			−0.223854			−0.111927	+	0.993716i	$0.535702\pi$
$44$	−2.61334	−	2.19285i	−0.393976	−	0.330585i
$45$	3.64543	+	6.31407i	0.543429	+	0.941246i
$46$	−14.2763	−	5.19615i	−2.10493	−	0.766131i
$47$	−1.39053	+	2.40847i	−0.202830	+	0.351311i	−0.949439	−	0.313951i	$-0.898347\pi$
$47$	−1.39053	+	2.40847i	−0.202830	+	0.351311i	0.746609	+	0.665263i	$0.231680\pi$
$48$	1.15270	+	1.99654i	0.166378	+	0.288176i
$49$	0.414878	+	2.35289i	0.0592682	+	0.336127i
$50$	3.35844	−	1.22237i	0.474955	−	0.172870i
$51$	0.286989	−	0.497079i	0.0401865	−	0.0696051i
$52$	18.8366	−	15.8058i	2.61217	−	2.19187i
$53$	0.783119	−	0.657115i	0.107570	−	0.0902616i	−0.587417	−	0.809285i	$-0.699855\pi$
$53$	0.783119	−	0.657115i	0.107570	−	0.0902616i	0.694986	+	0.719023i	$0.255410\pi$
$54$	4.85844	+	1.76833i	0.661150	+	0.240639i
$55$	−0.340022	+	1.92836i	−0.0458486	+	0.260020i
$56$	3.24897	−	18.4258i	0.434162	−	2.46225i
$57$	−0.0739780	−	0.0269258i	−0.00979862	−	0.00356641i
$58$	−3.09627	+	2.59808i	−0.406560	+	0.341144i
$59$	−3.64543	+	3.05888i	−0.474595	+	0.398232i	−0.848467	−	0.529248i	$-0.822474\pi$
$59$	−3.64543	+	3.05888i	−0.474595	+	0.398232i	0.373873	+	0.927480i	$0.378030\pi$
$60$	1.93969	−	3.35965i	0.250413	−	0.433728i
$61$	−2.26604	+	0.824773i	−0.290137	+	0.105601i	−0.482989	−	0.875627i	$-0.660449\pi$
$61$	−2.26604	+	0.824773i	−0.290137	+	0.105601i	0.192851	+	0.981228i	$0.438227\pi$
$62$	1.68732	+	9.56926i	0.214290	+	1.21530i
$63$	−4.41147	−	7.64090i	−0.555793	−	0.962663i
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	−13.2626	−	4.82721i	−1.64503	−	0.598741i
$66$	0.340022	+	0.588936i	0.0418539	+	0.0724930i
$67$	8.69846	+	7.29888i	1.06269	+	0.891700i	0.994370	−	0.105964i	$-0.0337928\pi$
$67$	8.69846	+	7.29888i	1.06269	+	0.891700i	0.0683164	+	0.997664i	$0.478237\pi$
$68$	7.29086			0.884147
$69$	1.59627	+	1.33943i	0.192168	+	0.161248i
$70$	−18.4611	+	6.71929i	−2.20652	+	0.803109i
$71$	−2.03074	+	11.5169i	−0.241005	+	1.36681i	0.588585	+	0.808435i	$0.299685\pi$
$71$	−2.03074	+	11.5169i	−0.241005	+	1.36681i	−0.829590	+	0.558372i	$0.811426\pi$
$72$	3.05303	+	17.3146i	0.359803	+	2.04055i
$73$	−2.92127			−0.341909			−0.170955	−	0.985279i	$-0.554685\pi$
$73$	−2.92127			−0.341909			−0.170955	+	0.985279i	$0.554685\pi$
$74$	−5.91875	−	14.2195i	−0.688040	−	1.65298i
$75$	−0.490200			−0.0566034
$76$	−0.173648	−	0.984808i	−0.0199188	−	0.112965i
$77$	0.411474	−	2.33359i	0.0468918	−	0.265937i
$78$	−4.60607	+	1.67647i	−0.521534	+	0.189823i
$79$	−6.55690	−	5.50190i	−0.737709	−	0.619012i	0.194512	−	0.980900i	$-0.437688\pi$
$79$	−6.55690	−	5.50190i	−0.737709	−	0.619012i	−0.932221	+	0.361889i	$0.882132\pi$
$80$	16.8084			1.87924
$81$	6.07398	+	5.09667i	0.674886	+	0.566297i
$82$	−9.23055	−	15.9878i	−1.01934	−	1.76556i
$83$	11.3576	+	4.13381i	1.24665	+	0.453745i	0.879270	−	0.476324i	$-0.158031\pi$
$83$	11.3576	+	4.13381i	1.24665	+	0.453745i	0.367385	+	0.930069i	$0.380253\pi$
$84$	−2.34730	+	4.06564i	−0.256111	+	0.443597i
$85$	−2.09240	−	3.62414i	−0.226952	−	0.393093i
$86$	0.645430	+	3.66041i	0.0695985	+	0.394713i
$87$	0.520945	−	0.189608i	0.0558511	−	0.0203281i
$88$	−2.36097	+	4.08931i	−0.251680	+	0.435922i
$89$	−1.45677	+	1.22237i	−0.154417	+	0.129571i	−0.716723	−	0.697358i	$-0.754359\pi$
$89$	−1.45677	+	1.22237i	−0.154417	+	0.129571i	0.562306	+	0.826929i	$0.309914\pi$
$90$	14.1420	−	11.8666i	1.49070	−	1.25085i
$91$	16.0496	+	5.84159i	1.68246	+	0.612365i
$92$	−4.59627	+	26.0667i	−0.479194	+	2.71764i
$93$	0.231429	−	1.31250i	0.0239981	−	0.136100i
$94$	6.61721	+	2.40847i	0.682513	+	0.248414i
$95$	−0.439693	+	0.368946i	−0.0451115	+	0.0378531i
$96$	1.22281	−	1.02606i	0.124803	−	0.104722i
$97$	−7.49273	+	12.9778i	−0.760771	+	1.31769i	0.181683	+	0.983357i	$0.441846\pi$
$97$	−7.49273	+	12.9778i	−0.760771	+	1.31769i	−0.942454	+	0.334337i	$0.891488\pi$
$98$	5.68479	−	2.06910i	0.574251	−	0.209010i
$99$	0.386659	+	2.19285i	0.0388607	+	0.220390i
$100$	−3.11334	−	5.39246i	−0.311334	−	0.539246i
$101$	3.90760	−	6.76817i	0.388821	−	0.673458i	−0.603470	−	0.797386i	$-0.706216\pi$
$101$	3.90760	−	6.76817i	0.388821	−	0.673458i	0.992291	+	0.123928i	$0.0395491\pi$
$102$	−1.36571	−	0.497079i	−0.135226	−	0.0492182i
$103$	−8.65910	−	14.9980i	−0.853207	−	1.47780i	−0.878299	−	0.478112i	$-0.841321\pi$
$103$	−8.65910	−	14.9980i	−0.853207	−	1.47780i	0.0250924	−	0.999685i	$-0.492012\pi$
$104$	−26.0724	−	21.8773i	−2.55661	−	2.14525i
$105$	2.69459			0.262965
$106$	−1.98293	−	1.66387i	−0.192599	−	0.161610i
$107$	3.25877	−	1.18610i	0.315037	−	0.114664i	−0.179662	−	0.983728i	$-0.557500\pi$
$107$	3.25877	−	1.18610i	0.315037	−	0.114664i	0.494699	+	0.869064i	$0.335278\pi$
$108$	1.56418	−	8.87089i	0.150513	−	0.853602i
$109$	0.652704	+	3.70167i	0.0625177	+	0.354555i	0.999979	+	0.00646615i	$0.00205825\pi$
$109$	0.652704	+	3.70167i	0.0625177	+	0.354555i	−0.937461	+	0.348089i	$0.886831\pi$
$110$	4.95811			0.472737
$111$	0.0957998	+	2.11035i	0.00909292	+	0.200305i
$112$	−20.3405			−1.92200
$113$	−2.37299	−	13.4579i	−0.223232	−	1.26601i	−0.866036	−	0.499981i	$-0.833340\pi$
$113$	−2.37299	−	13.4579i	−0.223232	−	1.26601i	0.642804	−	0.766030i	$-0.277771\pi$
$114$	−0.0346151	+	0.196312i	−0.00324200	+	0.0183863i
$115$	14.2763	−	5.19615i	1.33127	−	0.484544i
$116$	5.39440	+	4.52644i	0.500857	+	0.420269i
$117$	−16.0496			−1.48379
$118$	9.23055	+	7.74535i	0.849741	+	0.713018i
$119$	2.53209	+	4.38571i	0.232116	+	0.402037i
$120$	−5.04576	−	1.83651i	−0.460613	−	0.167649i
$121$	5.20099	−	9.00838i	0.472817	−	0.818943i
$122$	3.05303	+	5.28801i	0.276409	+	0.478754i
$123$	0.439693	+	2.49362i	0.0396457	+	0.224842i
$124$	15.9081	−	5.79006i	1.42859	−	0.519963i
$125$	4.54323	−	7.86911i	0.406359	−	0.703835i
$126$	−17.1138	+	14.3602i	−1.52462	+	1.27931i
$127$	−15.0608	+	12.6375i	−1.33643	+	1.12140i	−0.353899	+	0.935284i	$0.615144\pi$
$127$	−15.0608	+	12.6375i	−1.33643	+	1.12140i	−0.982528	+	0.186112i	$0.940411\pi$
$128$	−12.5360	−	4.56272i	−1.10803	−	0.403291i
$129$	0.0885259	−	0.502055i	0.00779427	−	0.0442035i
$130$	−6.20574	+	35.1945i	−0.544279	+	3.08676i
$131$	6.95084	+	2.52990i	0.607297	+	0.221038i	0.627320	−	0.778761i	$-0.284152\pi$
$131$	6.95084	+	2.52990i	0.607297	+	0.221038i	−0.0200229	+	0.999800i	$0.506374\pi$
$132$	0.907604	−	0.761570i	0.0789968	−	0.0662862i
$133$	0.532089	−	0.446476i	0.0461380	−	0.0387143i
$134$	14.3760	−	24.8999i	1.24190	−	2.15103i
$135$	−4.85844	+	1.76833i	−0.418148	+	0.152193i
$136$	−1.75237	−	9.93821i	−0.150265	−	0.852194i
$137$	−1.91147	−	3.31077i	−0.163308	−	0.282858i	0.772745	−	0.634717i	$-0.218883\pi$
$137$	−1.91147	−	3.31077i	−0.163308	−	0.282858i	−0.936053	+	0.351858i	$0.885550\pi$
$138$	2.63816	−	4.56942i	0.224575	−	0.388975i
$139$	17.0214	+	6.19529i	1.44374	+	0.525477i	0.940835	−	0.338866i	$-0.110043\pi$
$139$	17.0214	+	6.19529i	1.44374	+	0.525477i	0.502903	+	0.864343i	$0.332265\pi$
$140$	17.1138	+	29.6420i	1.44638	+	2.50520i
$141$	−0.739885	−	0.620838i	−0.0623096	−	0.0522840i
$142$	29.6117			2.48496
$143$	−3.30200	−	2.77071i	−0.276127	−	0.231698i
$144$	17.9611	−	6.53731i	1.49676	−	0.544776i
$145$	0.701867	−	3.98048i	0.0582869	−	0.330561i
$146$	1.28446	+	7.28455i	0.106303	+	0.602874i
$147$	−0.829755			−0.0684371
$148$	−22.6065	+	14.4570i	−1.85825	+	1.18836i
$149$	−15.6040			−1.27833			−0.639165	−	0.769070i	$-0.720720\pi$
$149$	−15.6040			−1.27833			−0.639165	+	0.769070i	$0.720720\pi$
$150$	0.215537	+	1.22237i	0.0175985	+	0.0998063i
$151$	2.67365	−	15.1630i	0.217578	−	1.23395i	−0.658797	−	0.752320i	$-0.728935\pi$
$151$	2.67365	−	15.1630i	0.217578	−	1.23395i	0.876376	−	0.481628i	$-0.159954\pi$
$152$	−1.30066	+	0.473401i	−0.105497	+	0.0383979i
$153$	−3.64543	−	3.05888i	−0.294716	−	0.247296i
$154$	−6.00000			−0.483494
$155$	−7.44356	−	6.24589i	−0.597881	−	0.501682i
$156$	4.26991	+	7.39571i	0.341867	+	0.592131i
$157$	0.992726	+	0.361323i	0.0792282	+	0.0288367i	0.381330	−	0.924439i	$-0.375466\pi$
$157$	0.992726	+	0.361323i	0.0792282	+	0.0288367i	−0.302102	+	0.953276i	$0.597688\pi$
$158$	−10.8366	+	18.7696i	−0.862115	+	1.49323i
$159$	0.177519	+	0.307471i	0.0140781	+	0.0243841i
$160$	−2.02094	−	11.4613i	−0.159770	−	0.906099i
$161$	−17.2763	+	6.28806i	−1.36156	+	0.495569i
$162$	10.0385	−	17.3872i	0.788698	−	1.36606i
$163$	−5.04710	+	4.23502i	−0.395320	+	0.331713i	−0.818681	−	0.574248i	$-0.805294\pi$
$163$	−5.04710	+	4.23502i	−0.395320	+	0.331713i	0.423362	+	0.905961i	$0.360850\pi$
$164$	−24.6386	+	20.6743i	−1.92395	+	1.61439i
$165$	−0.639033	−	0.232589i	−0.0497487	−	0.0181070i
$166$	5.31433	−	30.1391i	0.412472	−	2.33925i
$167$	−2.99660	+	16.9945i	−0.231884	+	1.31508i	0.617195	+	0.786810i	$0.288269\pi$
$167$	−2.99660	+	16.9945i	−0.231884	+	1.31508i	−0.849078	+	0.528267i	$0.822842\pi$
$168$	6.10607	+	2.22243i	0.471093	+	0.171464i
$169$	13.8418	−	11.6147i	1.06476	−	0.893437i
$170$	−8.11721	+	6.81115i	−0.622562	+	0.522391i
$171$	−0.326352	+	0.565258i	−0.0249567	+	0.0432264i
$172$	6.08512	−	2.21480i	0.463986	−	0.168877i
$173$	1.86706	+	10.5886i	0.141950	+	0.805038i	0.969766	+	0.244038i	$0.0784721\pi$
$173$	1.86706	+	10.5886i	0.141950	+	0.805038i	−0.827816	+	0.561000i	$0.810417\pi$
$174$	−0.701867	−	1.21567i	−0.0532084	−	0.0921596i
$175$	2.16250	−	3.74557i	0.163470	−	0.283138i
$176$	4.82383	+	1.75573i	0.363610	+	0.132343i
$177$	−0.826352	−	1.43128i	−0.0621124	−	0.107582i
$178$	3.68866	+	3.09516i	0.276477	+	0.231992i
$179$	−20.2003			−1.50984			−0.754920	−	0.655817i	$-0.772324\pi$
$179$	−20.2003			−1.50984			−0.754920	+	0.655817i	$0.772324\pi$
$180$	−24.6386	−	20.6743i	−1.83645	−	1.54097i
$181$	−9.85029	+	3.58521i	−0.732166	+	0.266487i	−0.681082	−	0.732208i	$-0.738490\pi$
$181$	−9.85029	+	3.58521i	−0.732166	+	0.266487i	−0.0510847	+	0.998694i	$0.516268\pi$
$182$	7.50980	−	42.5902i	0.556663	−	3.15700i
$183$	−0.145430	−	0.824773i	−0.0107505	−	0.0609690i
$184$	36.6364			2.70087
$185$	13.6741	+	7.08824i	1.00534	+	0.521138i
$186$	−3.37464			−0.247440
$187$	−0.221934	−	1.25865i	−0.0162294	−	0.0920416i
$188$	2.13041	−	12.0822i	0.155376	−	0.881184i
$189$	5.87939	−	2.13992i	0.427662	−	0.155656i
$190$	1.11334	+	0.934204i	0.0807702	+	0.0677743i
$191$	16.1848			1.17109			0.585545	−	0.810640i	$-0.300880\pi$
$191$	16.1848			1.17109			0.585545	+	0.810640i	$0.300880\pi$
$192$	0.435822	+	0.365698i	0.0314528	+	0.0263920i
$193$	4.32635	+	7.49346i	0.311418	+	0.539391i	0.978670	−	0.205441i	$-0.0658629\pi$
$193$	4.32635	+	7.49346i	0.311418	+	0.539391i	−0.667252	+	0.744832i	$0.732530\pi$
$194$	35.6562	+	12.9778i	2.55996	+	0.931750i
$195$	2.45084	−	4.24497i	0.175508	−	0.303989i
$196$	−5.26991	−	9.12776i	−0.376422	−	0.651983i
$197$	−2.80928	−	15.9322i	−0.200153	−	1.13512i	−0.904887	−	0.425651i	$-0.860045\pi$
$197$	−2.80928	−	15.9322i	−0.200153	−	1.13512i	0.704734	−	0.709471i	$-0.251066\pi$
$198$	5.29813	−	1.92836i	0.376522	−	0.137043i
$199$	−6.45084	+	11.1732i	−0.457288	+	0.792046i	−0.998817	−	0.0486366i	$-0.984512\pi$
$199$	−6.45084	+	11.1732i	−0.457288	+	0.792046i	0.541529	+	0.840682i	$0.317846\pi$
$200$	−6.60220	+	5.53990i	−0.466846	+	0.391730i
$201$	−3.02094	+	2.53487i	−0.213081	+	0.178796i
$202$	−18.5954	−	6.76817i	−1.30837	−	0.476207i
$203$	−0.849356	+	4.81694i	−0.0596131	+	0.338083i
$204$	−0.439693	+	2.49362i	−0.0307846	+	0.174588i
$205$	17.3478	+	6.31407i	1.21162	+	0.440994i
$206$	−33.5920	+	28.1870i	−2.34046	+	1.96388i
$207$	13.2344	−	11.1050i	0.919856	−	0.771851i
$208$	−18.5005	+	32.0437i	−1.28278	+	2.22183i
$209$	−0.164725	+	0.0599551i	−0.0113943	+	0.00414718i
$210$	−1.18479	−	6.71929i	−0.0817585	−	0.463675i
$211$	−0.837496	−	1.45059i	−0.0576556	−	0.0998625i	0.835757	−	0.549099i	$-0.185029\pi$
$211$	−0.837496	−	1.45059i	−0.0576556	−	0.0998625i	−0.893413	+	0.449237i	$0.851696\pi$
$212$	−2.25490	+	3.90560i	−0.154867	+	0.268238i
$213$	−3.81655	−	1.38911i	−0.261506	−	0.0951803i
$214$	−4.39053	−	7.60462i	−0.300130	−	0.519841i
$215$	−2.84730	−	2.38917i	−0.194184	−	0.162940i
$216$	−12.4679			−0.848334
$217$	9.00774	+	7.55839i	0.611485	+	0.513097i
$218$	8.94356	−	3.25519i	0.605735	−	0.220469i
$219$	0.176174	−	0.999135i	0.0119048	−	0.0675153i
$220$	−1.50000	−	8.50692i	−0.101130	−	0.573537i
$221$	9.21213			0.619675
$222$	5.22028	−	1.16679i	0.350363	−	0.0783100i
$223$	2.13610			0.143044			0.0715218	−	0.997439i	$-0.477214\pi$
$223$	2.13610			0.143044			0.0715218	+	0.997439i	$0.477214\pi$
$224$	2.44562	+	13.8698i	0.163405	+	0.926716i
$225$	−0.705737	+	4.00243i	−0.0470491	+	0.266829i
$226$	−32.5155	+	11.8347i	−2.16290	+	0.787230i
$227$	10.4304	+	8.75211i	0.692287	+	0.580898i	0.919568	−	0.392931i	$-0.128539\pi$
$227$	10.4304	+	8.75211i	0.692287	+	0.580898i	−0.227281	+	0.973829i	$0.572983\pi$
$228$	0.347296			0.0230003
$229$	−6.59492	−	5.53380i	−0.435805	−	0.365684i	0.398332	−	0.917241i	$-0.369589\pi$
$229$	−6.59492	−	5.53380i	−0.435805	−	0.365684i	−0.834137	+	0.551558i	$0.814034\pi$
$230$	−19.2344	−	33.3150i	−1.26828	−	2.19673i
$231$	0.773318	+	0.281465i	0.0508806	+	0.0185190i
$232$	4.87346	−	8.44107i	0.319958	−	0.554184i
$233$	3.79813	+	6.57856i	0.248824	+	0.430976i	0.963200	−	0.268786i	$-0.0866226\pi$
$233$	3.79813	+	6.57856i	0.248824	+	0.430976i	−0.714376	+	0.699762i	$0.753289\pi$
$234$	7.05690	+	40.0217i	0.461324	+	2.61630i
$235$	−6.61721	+	2.40847i	−0.431659	+	0.157111i
$236$	10.4966	−	18.1806i	0.683270	−	1.18346i
$237$	2.27719	−	1.91079i	0.147919	−	0.124119i
$238$	9.82295	−	8.24243i	0.636727	−	0.534278i
$239$	12.1557	+	4.42431i	0.786287	+	0.286185i	0.703792	−	0.710407i	$-0.251489\pi$
$239$	12.1557	+	4.42431i	0.786287	+	0.286185i	0.0824951	+	0.996591i	$0.473711\pi$
$240$	−1.01367	+	5.74881i	−0.0654322	+	0.371084i
$241$	−0.272136	+	1.54336i	−0.0175298	+	0.0994167i	−0.992317	−	0.123718i	$-0.960518\pi$
$241$	−0.272136	+	1.54336i	−0.0175298	+	0.0994167i	0.974788	+	0.223135i	$0.0716291\pi$
$242$	−24.7503	−	9.00838i	−1.59101	−	0.579080i
$243$	−6.80200	+	5.70756i	−0.436349	+	0.366140i
$244$	8.14930	−	6.83807i	0.521705	−	0.437763i
$245$	−3.02481	+	5.23913i	−0.193248	+	0.334716i
$246$	6.02481	−	2.19285i	0.384128	−	0.139811i
$247$	−0.219408	−	1.24432i	−0.0139606	−	0.0791743i
$248$	−11.7160	−	20.2927i	−0.743967	−	1.28859i
$249$	−2.09879	+	3.63522i	−0.133006	+	0.230372i
$250$	−21.6202	−	7.86911i	−1.36738	−	0.497686i
$251$	−1.17617	−	2.03719i	−0.0742395	−	0.128587i	0.826516	−	0.562913i	$-0.190320\pi$
$251$	−1.17617	−	2.03719i	−0.0742395	−	0.128587i	−0.900755	+	0.434327i	$0.856986\pi$
$252$	29.8161	+	25.0187i	1.87824	+	1.57603i
$253$	4.63991			0.291709
$254$	38.1352	+	31.9992i	2.39282	+	2.00781i
$255$	1.36571	−	0.497079i	0.0855244	−	0.0311283i
$256$	−5.29679	+	30.0396i	−0.331049	+	1.87747i
$257$	−1.90167	−	10.7849i	−0.118623	−	0.672745i	−0.984892	−	0.173168i	$-0.944600\pi$
$257$	−1.90167	−	10.7849i	−0.118623	−	0.672745i	0.866269	−	0.499578i	$-0.166511\pi$
$258$	−1.29086			−0.0803654
$259$	−16.5476	−	8.57775i	−1.02822	−	0.532995i
$260$	62.2627			3.86137
$261$	−0.798133	−	4.52644i	−0.0494032	−	0.280180i
$262$	3.25237	−	18.4451i	0.200932	−	1.13954i
$263$	16.6275	−	6.05191i	1.02529	−	0.373177i	0.226007	−	0.974126i	$-0.427433\pi$
$263$	16.6275	−	6.05191i	1.02529	−	0.373177i	0.799287	+	0.600949i	$0.205211\pi$
$264$	−1.25624	−	1.05411i	−0.0773165	−	0.0648762i
$265$	2.58853			0.159012
$266$	−1.34730	−	1.13052i	−0.0826080	−	0.0693164i
$267$	−0.330222	−	0.571962i	−0.0202093	−	0.0350035i
$268$	−47.0715	−	17.1326i	−2.87535	−	1.04654i
$269$	1.43717	−	2.48925i	0.0876256	−	0.151772i	−0.818881	−	0.573963i	$-0.805405\pi$
$269$	1.43717	−	2.48925i	0.0876256	−	0.151772i	0.906507	+	0.422191i	$0.138739\pi$
$270$	6.54576	+	11.3376i	0.398362	+	0.689984i
$271$	−3.38619	−	19.2041i	−0.205697	−	1.16656i	−0.896340	−	0.443368i	$-0.853784\pi$
$271$	−3.38619	−	19.2041i	−0.205697	−	1.16656i	0.690643	−	0.723196i	$-0.257327\pi$
$272$	−10.3093	+	3.75227i	−0.625092	+	0.227515i
$273$	−2.96585	+	5.13701i	−0.179502	+	0.310906i
$274$	−7.41534	+	6.22221i	−0.447977	+	0.375898i
$275$	−0.836152	+	0.701615i	−0.0504219	+	0.0423090i
$276$	−8.63816	−	3.14403i	−0.519956	−	0.189248i
$277$	−3.74123	+	21.2176i	−0.224789	+	1.27484i	0.638300	+	0.769788i	$0.279638\pi$
$277$	−3.74123	+	21.2176i	−0.224789	+	1.27484i	−0.863089	+	0.505052i	$0.831473\pi$
$278$	7.96451	−	45.1690i	0.477679	−	2.70905i
$279$	−10.3833	−	3.77920i	−0.621629	−	0.226255i
$280$	36.2918	−	30.4524i	2.16885	−	1.81988i
$281$	−4.86824	+	4.08494i	−0.290415	+	0.243687i	−0.776341	−	0.630313i	$-0.782927\pi$
$281$	−4.86824	+	4.08494i	−0.290415	+	0.243687i	0.485927	+	0.874000i	$0.338482\pi$
$282$	−1.22281	+	2.11797i	−0.0728173	+	0.126123i
$283$	−0.729208	+	0.265410i	−0.0433469	+	0.0157770i	−0.363603	−	0.931554i	$-0.618453\pi$
$283$	−0.729208	+	0.265410i	−0.0433469	+	0.0157770i	0.320256	+	0.947331i	$0.396231\pi$
$284$	−8.95858	−	50.8066i	−0.531594	−	3.01482i
$285$	−0.0996702	−	0.172634i	−0.00590395	−	0.0102259i
$286$	−5.45723	+	9.45221i	−0.322693	+	0.558921i
$287$	−20.9932	−	7.64090i	−1.23919	−	0.451028i
$288$	−6.61721	−	11.4613i	−0.389923	−	0.675366i
$289$	−10.9304	−	9.17166i	−0.642962	−	0.539509i
$290$	−10.2344			−0.600986
$291$	−3.98680	−	3.34532i	−0.233710	−	0.196106i
$292$	12.1099	−	4.40766i	0.708680	−	0.257939i
$293$	−5.73664	+	32.5341i	−0.335138	+	1.90066i	0.0907244	+	0.995876i	$0.471082\pi$
$293$	−5.73664	+	32.5341i	−0.335138	+	1.90066i	−0.425863	+	0.904788i	$0.640029\pi$
$294$	0.364837	+	2.06910i	0.0212777	+	0.120672i
$295$	−12.0496			−0.701557
$296$	25.1400	+	27.3403i	1.46123	+	1.58912i
$297$	−1.57903			−0.0916246
$298$	6.86097	+	38.9105i	0.397445	+	2.25402i
$299$	−5.80747	+	32.9358i	−0.335854	+	1.90473i
$300$	2.03209	−	0.739620i	0.117323	−	0.0427020i
$301$	3.44562	+	2.89122i	0.198602	+	0.166647i
$302$	−38.9864			−2.24341
$303$	2.07919	+	1.74465i	0.119446	+	0.100228i
$304$	0.752374	+	1.30315i	0.0431516	+	0.0747408i
$305$	−5.73783	−	2.08840i	−0.328547	−	0.119581i
$306$	−6.02481	+	10.4353i	−0.344416	+	0.596546i
$307$	−12.6814	−	21.9648i	−0.723765	−	1.25360i	−0.959480	−	0.281776i	$-0.909077\pi$
$307$	−12.6814	−	21.9648i	−0.723765	−	1.25360i	0.235715	−	0.971822i	$-0.424257\pi$
$308$	1.81521	+	10.2946i	0.103431	+	0.586587i
$309$	5.65183	−	2.05710i	0.321521	−	0.117024i
$310$	−12.3020	+	21.3077i	−0.698707	+	1.21020i
$311$	13.5929	−	11.4058i	0.770781	−	0.646762i	−0.170128	−	0.985422i	$-0.554418\pi$
$311$	13.5929	−	11.4058i	0.770781	−	0.646762i	0.940909	+	0.338660i	$0.109974\pi$
$312$	9.05484	−	7.59792i	0.512630	−	0.430147i
$313$	6.79561	+	2.47340i	0.384110	+	0.139805i	0.526856	−	0.849955i	$-0.323371\pi$
$313$	6.79561	+	2.47340i	0.384110	+	0.139805i	−0.142745	+	0.989759i	$0.545593\pi$
$314$	0.464508	−	2.63435i	0.0262137	−	0.148665i
$315$	3.87939	−	22.0011i	0.218579	−	1.23962i
$316$	35.4825	+	12.9146i	1.99605	+	0.726502i
$317$	20.6215	−	17.3035i	1.15822	−	0.971863i	0.158342	−	0.987384i	$-0.449385\pi$
$317$	20.6215	−	17.3035i	1.15822	−	0.971863i	0.999880	+	0.0155211i	$0.00494070\pi$
$318$	0.688663	−	0.577857i	0.0386183	−	0.0324046i
$319$	0.617211	−	1.06904i	0.0345572	−	0.0598548i
$320$	3.89780	−	1.41868i	0.217894	−	0.0793069i
$321$	0.209141	+	1.18610i	0.0116731	+	0.0662014i
$322$	23.2763	+	40.3158i	1.29714	+	2.24671i
$323$	0.187319	−	0.324446i	0.0104227	−	0.0180526i
$324$	−32.8692	−	11.9634i	−1.82607	−	0.664633i
$325$	−3.93376	−	6.81348i	−0.218206	−	0.377944i
$326$	12.7797	+	10.7235i	0.707803	+	0.593917i
$327$	−1.30541			−0.0721892
$328$	34.1031	+	28.6159i	1.88303	+	1.58005i
$329$	8.00774	−	2.91458i	0.441481	−	0.160686i
$330$	−0.299011	+	1.69577i	−0.0164600	+	0.0933493i
$331$	−5.87686	−	33.3293i	−0.323021	−	1.83195i	−0.523229	−	0.852192i	$-0.675273\pi$
$331$	−5.87686	−	33.3293i	−0.323021	−	1.83195i	0.200208	−	0.979753i	$-0.435838\pi$
$332$	−53.3191			−2.92627
$333$	17.3687	+	2.25606i	0.951799	+	0.123631i
$334$	43.6955			2.39091
$335$	4.99273	+	28.3152i	0.272782	+	1.54702i
$336$	1.22668	−	6.95686i	0.0669210	−	0.379528i
$337$	−12.1074	+	4.40674i	−0.659533	+	0.240050i	−0.650035	−	0.759905i	$-0.725246\pi$
$337$	−12.1074	+	4.40674i	−0.659533	+	0.240050i	−0.00949811	+	0.999955i	$0.503023\pi$
$338$	−35.0488	−	29.4094i	−1.90640	−	1.59966i
$339$	4.74598			0.257766
$340$	14.1420	+	11.8666i	0.766959	+	0.643555i
$341$	−1.48380	−	2.57002i	−0.0803524	−	0.139175i
$342$	1.55303	+	0.565258i	0.0839784	+	0.0305656i
$343$	−7.06418	+	12.2355i	−0.381430	+	0.660656i
$344$	−4.48158	−	7.76233i	−0.241631	−	0.418517i
$345$	0.916222	+	5.19615i	0.0493277	+	0.279751i
$346$	25.5831	−	9.31147i	1.37535	−	0.500588i
$347$	3.72668	−	6.45480i	0.200059	−	0.346512i	−0.748488	−	0.663148i	$-0.769220\pi$
$347$	3.72668	−	6.45480i	0.200059	−	0.346512i	0.948547	+	0.316636i	$0.102553\pi$
$348$	−1.87346	+	1.57202i	−0.100428	+	0.0842689i
$349$	14.4133	−	12.0942i	0.771525	−	0.647387i	−0.169574	−	0.985518i	$-0.554239\pi$
$349$	14.4133	−	12.0942i	0.771525	−	0.647387i	0.941099	+	0.338131i	$0.109795\pi$
$350$	−10.2909	−	3.74557i	−0.550070	−	0.200209i
$351$	1.97637	−	11.2085i	0.105491	−	0.598267i
$352$	0.617211	−	3.50038i	0.0328975	−	0.186571i
$353$	−21.3799	−	7.78163i	−1.13793	−	0.414174i	−0.296768	−	0.954950i	$-0.595909\pi$
$353$	−21.3799	−	7.78163i	−1.13793	−	0.414174i	−0.841167	+	0.540775i	$0.818131\pi$
$354$	−3.20574	+	2.68993i	−0.170383	+	0.142968i
$355$	−22.6839	+	19.0341i	−1.20394	+	1.01022i
$356$	4.19459	−	7.26525i	0.222313	−	0.385057i
$357$	−1.65270	+	0.601535i	−0.0874704	+	0.0318366i
$358$	8.88191	+	50.3718i	0.469424	+	2.66223i
$359$	5.47906	+	9.49000i	0.289173	+	0.500863i	0.973613	−	0.228207i	$-0.0732862\pi$
$359$	5.47906	+	9.49000i	0.289173	+	0.500863i	−0.684439	+	0.729070i	$0.739953\pi$
$360$	−22.2592	+	38.5541i	−1.17316	+	2.03198i
$361$	17.8059	+	6.48081i	0.937151	+	0.341095i
$362$	13.2713	+	22.9865i	0.697522	+	1.20814i
$363$	2.76739	+	2.32211i	0.145250	+	0.121879i
$364$	−75.3465			−3.94923
$365$	−5.66637	−	4.75465i	−0.296592	−	0.248870i
$366$	−1.99273	+	0.725293i	−0.104161	+	0.0379117i
$367$	3.46316	−	19.6406i	0.180776	−	1.02523i	−0.750488	−	0.660884i	$-0.770182\pi$
$367$	3.46316	−	19.6406i	0.180776	−	1.02523i	0.931264	−	0.364346i	$-0.118707\pi$
$368$	−6.91622	−	39.2238i	−0.360533	−	2.04468i
$369$	20.9932			1.09286
$370$	11.6630	−	37.2147i	0.606329	−	1.93470i
$371$	−3.13247			−0.162630
$372$	1.02094	+	5.79006i	0.0529335	+	0.300201i
$373$	−0.296951	+	1.68409i	−0.0153756	+	0.0871991i	−0.991530	−	0.129878i	$-0.958541\pi$
$373$	−0.296951	+	1.68409i	−0.0153756	+	0.0871991i	0.976154	+	0.217077i	$0.0696524\pi$
$374$	−3.04101	+	1.10684i	−0.157247	+	0.0572332i
$375$	2.41740	+	2.02844i	0.124834	+	0.104748i
$376$	−16.9813			−0.875745
$377$	6.81592	+	5.71924i	0.351038	+	0.294556i
$378$	−7.92127	−	13.7200i	−0.407426	−	0.705683i
$379$	−5.94609	−	2.16420i	−0.305430	−	0.111167i	0.184758	−	0.982784i	$-0.440850\pi$
$379$	−5.94609	−	2.16420i	−0.305430	−	0.111167i	−0.490188	+	0.871617i	$0.663072\pi$
$380$	1.26604	−	2.19285i	0.0649467	−	0.112491i
$381$	−3.41400	−	5.91322i	−0.174905	−	0.302944i
$382$	−7.11633	−	40.3587i	−0.364103	−	2.06493i
$383$	10.8302	−	3.94188i	0.553399	−	0.201421i	−0.0501573	−	0.998741i	$-0.515972\pi$
$383$	10.8302	−	3.94188i	0.553399	−	0.201421i	0.603556	+	0.797321i	$0.293750\pi$
$384$	2.31655	−	4.01239i	0.118216	−	0.204756i
$385$	4.59627	−	3.85673i	0.234247	−	0.196557i
$386$	16.7836	−	14.0831i	0.854262	−	0.716811i
$387$	−3.97178	−	1.44561i	−0.201897	−	0.0734845i
$388$	11.4795	−	65.1036i	0.582784	−	3.30513i
$389$	2.18046	−	12.3660i	0.110553	−	0.626980i	−0.878303	−	0.478105i	$-0.841324\pi$
$389$	2.18046	−	12.3660i	0.110553	−	0.626980i	0.988856	−	0.148875i	$-0.0475651\pi$
$390$	−11.6630	−	4.24497i	−0.590577	−	0.214953i
$391$	−7.59627	+	6.37402i	−0.384160	+	0.322348i
$392$	−11.1755	+	9.37732i	−0.564446	+	0.473626i
$393$	−1.28446	+	2.22475i	−0.0647926	+	0.112224i
$394$	−38.4937	+	14.0105i	−1.93928	+	0.705841i
$395$	−3.76352	−	21.3440i	−0.189363	−	1.07393i
$396$	−4.91147	−	8.50692i	−0.246811	−	0.427489i
$397$	−16.9757	+	29.4027i	−0.851984	+	1.47568i	0.0274319	+	0.999624i	$0.491267\pi$
$397$	−16.9757	+	29.4027i	−0.851984	+	1.47568i	−0.879415	+	0.476055i	$0.842066\pi$
$398$	30.6981	+	11.1732i	1.53875	+	0.560061i
$399$	0.120615	+	0.208911i	0.00603829	+	0.0104586i
$400$	7.17752	+	6.02265i	0.358876	+	0.301133i
$401$	13.5202			0.675168			0.337584	−	0.941295i	$-0.390390\pi$
$401$	13.5202			0.675168			0.337584	+	0.941295i	$0.390390\pi$
$402$	7.64930	+	6.41852i	0.381512	+	0.320127i
$403$	20.1001	−	7.31585i	1.00126	−	0.364429i
$404$	−5.98680	+	33.9528i	−0.297854	+	1.68922i
$405$	3.48633	+	19.7720i	0.173237	+	0.982476i
$406$	12.3851			0.614661
$407$	3.18392	+	3.46258i	0.157821	+	0.171634i
$408$	3.50475			0.173511
$409$	0.530029	+	3.00595i	0.0262083	+	0.148634i	0.995104	−	0.0988358i	$-0.0315119\pi$
$409$	0.530029	+	3.00595i	0.0262083	+	0.148634i	−0.968895	+	0.247470i	$0.920401\pi$
$410$	8.11721	−	46.0350i	0.400880	−	2.27351i
$411$	1.24763	−	0.454099i	0.0615409	−	0.0223990i
$412$	58.5249	+	49.1082i	2.88331	+	2.41939i
$413$	14.5817			0.717519
$414$	−33.5107	−	28.1188i	−1.64696	−	1.38197i
$415$	15.3020	+	26.5038i	0.751146	+	1.30102i
$416$	24.0744	+	8.76238i	1.18035	+	0.429611i
$417$	−3.14543	+	5.44804i	−0.154032	+	0.266792i
$418$	0.221934	+	0.384401i	0.0108551	+	0.0188017i
$419$	1.76217	+	9.99379i	0.0860878	+	0.488228i	0.997117	+	0.0758854i	$0.0241783\pi$
$419$	1.76217	+	9.99379i	0.0860878	+	0.488228i	−0.911029	+	0.412343i	$0.864711\pi$
$420$	−11.1702	+	4.06564i	−0.545052	+	0.198383i
$421$	−3.85251	+	6.67274i	−0.187760	+	0.325210i	−0.944503	−	0.328503i	$-0.893456\pi$
$421$	−3.85251	+	6.67274i	−0.187760	+	0.325210i	0.756743	+	0.653712i	$0.226789\pi$
$422$	−3.24897	+	2.72621i	−0.158157	+	0.132710i
$423$	−6.13429	+	5.14728i	−0.298259	+	0.250269i
$424$	5.86571	+	2.13495i	0.284864	+	0.103682i
$425$	0.405078	−	2.29731i	0.0196491	−	0.111436i
$426$	−1.78581	+	10.1278i	−0.0865226	+	0.490694i
$427$	6.94356	+	2.52725i	0.336023	+	0.122302i
$428$	−11.7194	+	9.83375i	−0.566479	+	0.475332i
$429$	1.14677	−	0.962258i	0.0553668	−	0.0464582i
$430$	−4.70574	+	8.15058i	−0.226931	+	0.393056i
$431$	−19.9491	+	7.26087i	−0.960913	+	0.349744i	−0.774391	−	0.632707i	$-0.781944\pi$
$431$	−19.9491	+	7.26087i	−0.960913	+	0.349744i	−0.186522	+	0.982451i	$0.559722\pi$
$432$	2.35369	+	13.3485i	0.113242	+	0.642228i
$433$	−8.22281	−	14.2423i	−0.395163	−	0.684443i	0.597959	−	0.801527i	$-0.295979\pi$
$433$	−8.22281	−	14.2423i	−0.395163	−	0.684443i	−0.993122	+	0.117084i	$0.962645\pi$
$434$	14.8871	−	25.7853i	0.714605	−	1.23773i
$435$	1.31908	+	0.480105i	0.0632449	+	0.0230193i
$436$	−8.29086	−	14.3602i	−0.397060	−	0.687728i
$437$	1.04189	+	0.874249i	0.0498403	+	0.0418210i
$438$	−2.56893			−0.122748
$439$	−16.7285	−	14.0369i	−0.798407	−	0.669943i	0.149404	−	0.988776i	$-0.452265\pi$
$439$	−16.7285	−	14.0369i	−0.798407	−	0.669943i	−0.947811	+	0.318833i	$0.896709\pi$
$440$	−11.2353	+	4.08931i	−0.535622	+	0.194950i
$441$	−1.19459	+	6.77487i	−0.0568854	+	0.322613i
$442$	−4.05051	−	22.9716i	−0.192663	−	1.09265i
$443$	−14.1830			−0.673856			−0.336928	−	0.941530i	$-0.609388\pi$
$443$	−14.1830			−0.673856			−0.336928	+	0.941530i	$0.609388\pi$
$444$	−3.58125	−	8.60375i	−0.169959	−	0.408316i
$445$	−4.81521			−0.228263
$446$	−0.939226	−	5.32661i	−0.0444736	−	0.252222i
$447$	0.941037	−	5.33688i	0.0445095	−	0.252426i
$448$	−4.71688	+	1.71680i	−0.222852	+	0.0811114i
$449$	−14.0688	−	11.8051i	−0.663946	−	0.557117i	0.247321	−	0.968934i	$-0.420450\pi$
$449$	−14.0688	−	11.8051i	−0.663946	−	0.557117i	−0.911267	+	0.411817i	$0.864894\pi$
$450$	10.2909			0.485116
$451$	4.31908	+	3.62414i	0.203377	+	0.170654i
$452$	30.1425	+	52.2083i	1.41778	+	2.45567i
$453$	5.02481	+	1.82888i	0.236086	+	0.0859284i
$454$	17.2383	−	29.8576i	0.809033	−	1.40129i
$455$	21.6236	+	37.4532i	1.01373	+	1.75583i
$456$	−0.0834734	−	0.473401i	−0.00390900	−	0.0221690i
$457$	−8.38413	+	3.05157i	−0.392193	+	0.142747i	−0.530587	−	0.847631i	$-0.678028\pi$
$457$	−8.38413	+	3.05157i	−0.392193	+	0.142747i	0.138394	+	0.990377i	$0.455806\pi$
$458$	−10.8995	+	18.8784i	−0.509298	+	0.882130i
$459$	2.58512	−	2.16918i	0.120663	−	0.101248i
$460$	−51.3414	+	43.0806i	−2.39381	+	2.00864i
$461$	−30.7751	−	11.2012i	−1.43334	−	0.521693i	−0.495454	−	0.868634i	$-0.664998\pi$
$461$	−30.7751	−	11.2012i	−1.43334	−	0.521693i	−0.937887	+	0.346941i	$0.887220\pi$
$462$	0.361844	−	2.05212i	0.0168345	−	0.0954733i
$463$	0.724155	−	4.10689i	0.0336544	−	0.190863i	−0.963346	−	0.268263i	$-0.913551\pi$
$463$	0.724155	−	4.10689i	0.0336544	−	0.190863i	0.997000	+	0.0773993i	$0.0246616\pi$
$464$	−9.95723	−	3.62414i	−0.462253	−	0.168246i
$465$	2.58512	−	2.16918i	0.119882	−	0.100593i
$466$	14.7344	−	12.3636i	0.682559	−	0.572735i
$467$	−12.2306	+	21.1839i	−0.565962	+	0.980276i	0.430997	+	0.902353i	$0.358162\pi$
$467$	−12.2306	+	21.1839i	−0.565962	+	0.980276i	−0.996959	+	0.0779223i	$0.975171\pi$
$468$	66.5326	−	24.2159i	3.07547	−	1.11938i
$469$	−6.04189	−	34.2653i	−0.278989	−	1.58222i
$470$	8.91534	+	15.4418i	0.411234	+	0.712278i
$471$	−0.183448	+	0.317742i	−0.00845285	+	0.0146408i
$472$	−27.3050	−	9.93821i	−1.25681	−	0.457443i
$473$	−0.567581	−	0.983080i	−0.0260974	−	0.0452021i
$474$	−5.76604	−	4.83829i	−0.264843	−	0.222230i
$475$	−0.319955			−0.0146806
$476$	−17.1138	−	14.3602i	−0.784410	−	0.658198i
$477$	2.76604	−	1.00676i	0.126648	−	0.0460963i
$478$	5.68779	−	32.2570i	0.260153	−	1.47540i
$479$	5.62314	+	31.8904i	0.256928	+	1.45711i	0.791075	+	0.611719i	$0.209522\pi$
$479$	5.62314	+	31.8904i	0.256928	+	1.45711i	−0.534147	+	0.845391i	$0.679367\pi$
$480$	4.04189			0.184486
$481$	−28.5638	+	18.2667i	−1.30240	+	0.832890i
$482$	3.96822			0.180747
$483$	−1.10876	−	6.28806i	−0.0504501	−	0.286117i
$484$	−7.96838	+	45.1909i	−0.362199	+	2.05413i
$485$	−35.6562	+	12.9778i	−1.61906	+	0.589291i
$486$	17.2233	+	14.4520i	0.781264	+	0.655558i
$487$	15.3013			0.693368			0.346684	−	0.937982i	$-0.387308\pi$
$487$	15.3013			0.693368			0.346684	+	0.937982i	$0.387308\pi$
$488$	−11.2797	−	9.46480i	−0.510609	−	0.428452i
$489$	−1.14409	−	1.98161i	−0.0517373	−	0.0896117i
$490$	14.3944	+	5.23913i	0.650273	+	0.236680i
$491$	4.65611	−	8.06461i	0.210127	−	0.363951i	−0.741627	−	0.670813i	$-0.765946\pi$
$491$	4.65611	−	8.06461i	0.210127	−	0.363951i	0.951754	+	0.306862i	$0.0992789\pi$
$492$	−5.58512	−	9.67372i	−0.251797	−	0.436125i
$493$	0.458111	+	2.59808i	0.0206323	+	0.117011i
$494$	−3.00640	+	1.09424i	−0.135264	+	0.0492321i
$495$	−2.81908	+	4.88279i	−0.126708	+	0.219465i
$496$	−19.5141	+	16.3743i	−0.876211	+	0.735228i
$497$	27.4507	−	23.0339i	1.23133	−	1.03321i
$498$	9.98767	+	3.63522i	0.447558	+	0.162898i
$499$	−1.03761	+	5.88457i	−0.0464497	+	0.263429i	−0.999185	−	0.0403733i	$-0.987145\pi$
$499$	−1.03761	+	5.88457i	−0.0464497	+	0.263429i	0.952735	+	0.303803i	$0.0982564\pi$
$500$	−6.96064	+	39.4757i	−0.311289	+	1.76541i
$501$	−5.63176	−	2.04979i	−0.251608	−	0.0915780i
$502$	−4.56283	+	3.82867i	−0.203649	+	0.170882i
$503$	32.9413	−	27.6411i	1.46878	−	1.23245i	0.551525	−	0.834159i	$-0.314046\pi$
$503$	32.9413	−	27.6411i	1.46878	−	1.23245i	0.917257	−	0.398296i	$-0.130398\pi$
$504$	26.9368	−	46.6558i	1.19986	−	2.07822i
$505$	18.5954	−	6.76817i	0.827484	−	0.301180i
$506$	−2.04013	−	11.5702i	−0.0906950	−	0.514357i
$507$	3.13769	+	5.43464i	0.139350	+	0.241361i
$508$	43.3658	−	75.1117i	1.92404	−	3.33254i
$509$	28.8701	+	10.5078i	1.27964	+	0.465752i	0.890314	−	0.455347i	$-0.150485\pi$
$509$	28.8701	+	10.5078i	1.27964	+	0.465752i	0.389329	+	0.921099i	$0.372707\pi$
$510$	−1.84002	−	3.18701i	−0.0814776	−	0.141123i
$511$	6.85710	+	5.75379i	0.303340	+	0.254533i
$512$	50.5553			2.23425
$513$	−0.354570	−	0.297520i	−0.0156547	−	0.0131358i
$514$	−26.0574	+	9.48411i	−1.14934	+	0.418326i
$515$	7.61468	−	43.1850i	0.335543	−	1.90296i
$516$	0.390530	+	2.21480i	0.0171921	+	0.0975013i
$517$	−2.15064			−0.0945852
$518$	−14.1138	+	45.0349i	−0.620125	+	1.97872i
$519$	−3.73412			−0.163910
$520$	−14.9650	−	84.8706i	−0.656258	−	3.72182i
$521$	1.18361	−	6.71259i	0.0518549	−	0.294084i	−0.947841	−	0.318744i	$-0.896739\pi$
$521$	1.18361	−	6.71259i	0.0518549	−	0.294084i	0.999696	+	0.0246597i	$0.00785023\pi$
$522$	−10.9363	+	3.98048i	−0.478668	+	0.174221i
$523$	16.7574	+	14.0612i	0.732751	+	0.614851i	0.930880	−	0.365325i	$-0.119042\pi$
$523$	16.7574	+	14.0612i	0.732751	+	0.614851i	−0.198129	+	0.980176i	$0.563487\pi$
$524$	−32.6313			−1.42551
$525$	1.15064	+	0.965505i	0.0502182	+	0.0421381i
$526$	−22.4021	−	38.8016i	−0.976780	−	1.69183i
$527$	5.95976	+	2.16918i	0.259611	+	0.0944908i
$528$	−0.891407	+	1.54396i	−0.0387935	+	0.0671923i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−1.13816	−	6.45480i	−0.0494383	−	0.280379i
$531$	−12.8760	+	4.68647i	−0.558770	+	0.203376i
$532$	−1.53209	+	2.65366i	−0.0664245	+	0.115051i
$533$	−31.1313	+	26.1223i	−1.34845	+	1.13148i
$534$	−1.28106	+	1.07494i	−0.0554369	+	0.0465170i
$535$	8.25150	+	3.00330i	0.356743	+	0.129844i
$536$	−12.0398	+	68.2813i	−0.520041	+	2.94930i
$537$	1.21823	−	6.90890i	0.0525703	−	0.298141i
$538$	−6.83915	−	2.48925i	−0.294856	−	0.107319i
$539$	−1.41534	+	1.18762i	−0.0609632	+	0.0511542i
$540$	17.4722	−	14.6610i	0.751886	−	0.630907i
$541$	11.5826	−	20.0616i	0.497975	−	0.862517i	−0.502023	−	0.864855i	$-0.667411\pi$
$541$	11.5826	−	20.0616i	0.497975	−	0.862517i	0.999997	+	0.00233704i	$0.000743903\pi$
$542$	−46.3987	+	16.8878i	−1.99300	+	0.725391i
$543$	−0.632170	−	3.58521i	−0.0271290	−	0.153856i
$544$	3.79813	+	6.57856i	0.162844	+	0.282053i
$545$	−4.75877	+	8.24243i	−0.203843	+	0.353067i
$546$	14.1138	+	5.13701i	0.604015	+	0.219844i
$547$	12.9047	+	22.3515i	0.551764	+	0.955683i	0.998147	+	0.0608412i	$0.0193783\pi$
$547$	12.9047	+	22.3515i	0.551764	+	0.955683i	−0.446384	+	0.894842i	$0.647288\pi$
$548$	12.9192	+	10.8405i	0.551882	+	0.463084i
$549$	−6.94356			−0.296344
$550$	2.11721	+	1.77655i	0.0902782	+	0.0757524i
$551$	0.340022	−	0.123758i	0.0144854	−	0.00527227i
$552$	−2.20945	+	12.5304i	−0.0940402	+	0.533329i
$553$	4.55438	+	25.8292i	0.193672	+	1.09837i
$554$	54.5536			2.31776
$555$	−3.24897	+	4.24935i	−0.137911	+	0.180375i
$556$	−79.9086			−3.38888
$557$	0.383256	+	2.17355i	0.0162391	+	0.0920963i	0.991850	−	0.127410i	$-0.0406664\pi$
$557$	0.383256	+	2.17355i	0.0162391	+	0.0920963i	−0.975611	+	0.219506i	$0.929555\pi$
$558$	−4.85844	+	27.5536i	−0.205674	+	1.16644i
$559$	7.68866	−	2.79844i	0.325196	−	0.118362i
$560$	−39.4543	−	33.1061i	−1.66725	−	1.39899i
$561$	0.443868			0.0187401
$562$	12.3268	+	10.3434i	0.519975	+	0.436311i
$563$	−7.37733	−	12.7779i	−0.310917	−	0.538524i	0.667644	−	0.744481i	$-0.267303\pi$
$563$	−7.37733	−	12.7779i	−0.310917	−	0.538524i	−0.978561	+	0.205956i	$0.933970\pi$
$564$	4.00387	+	1.45729i	0.168593	+	0.0613630i
$565$	17.3011	−	29.9664i	0.727864	−	1.26070i
$566$	0.982459	+	1.70167i	0.0412958	+	0.0715265i
$567$	−4.21894	−	23.9268i	−0.177179	−	1.00483i
$568$	−67.1015	+	24.4230i	−2.81552	+	1.02476i
$569$	13.7422	−	23.8021i	0.576101	−	0.997837i	−0.419820	−	0.907608i	$-0.637907\pi$
$569$	13.7422	−	23.8021i	0.576101	−	0.997837i	0.995921	−	0.0902294i	$-0.0287600\pi$
$570$	−0.386659	+	0.324446i	−0.0161954	+	0.0135895i
$571$	−2.36050	+	1.98069i	−0.0987839	+	0.0828895i	−0.690842	−	0.723006i	$-0.742760\pi$
$571$	−2.36050	+	1.98069i	−0.0987839	+	0.0828895i	0.592058	+	0.805895i	$0.298316\pi$
$572$	17.8687	+	6.50368i	0.747128	+	0.271932i
$573$	−0.976062	+	5.53553i	−0.0407756	+	0.231250i
$574$	−9.82295	+	55.7087i	−0.410002	+	2.32524i
$575$	7.95811	+	2.89652i	0.331876	+	0.120793i
$576$	3.61334	−	3.03195i	0.150556	−	0.126331i
$577$	4.47384	−	3.75400i	0.186248	−	0.156281i	−0.544896	−	0.838504i	$-0.683431\pi$
$577$	4.47384	−	3.75400i	0.186248	−	0.156281i	0.731145	+	0.682223i	$0.238986\pi$
$578$	−18.0646	+	31.2889i	−0.751390	+	1.30145i
$579$	−2.82383	+	1.02779i	−0.117354	+	0.0427134i
$580$	3.09627	+	17.5598i	0.128565	+	0.729131i
$581$	−18.5175	−	32.0733i	−0.768237	−	1.33063i
$582$	−6.58899	+	11.4125i	−0.273123	+	0.473062i
$583$	0.742878	+	0.270386i	0.0307669	+	0.0111982i
$584$	−8.91875	−	15.4477i	−0.369060	−	0.639231i
$585$	−31.1313	−	26.1223i	−1.28712	−	1.08002i
$586$	83.6501			3.45555
$587$	−35.3940	−	29.6991i	−1.46087	−	1.22581i	−0.924139	−	0.382057i	$-0.875216\pi$
$587$	−35.3940	−	29.6991i	−1.46087	−	1.22581i	−0.536727	−	0.843756i	$-0.680340\pi$
$588$	3.43969	−	1.25195i	0.141851	−	0.0516294i
$589$	0.151055	−	0.856674i	0.00622410	−	0.0352986i
$590$	5.29813	+	30.0472i	0.218121	+	1.23702i
$591$	5.61856			0.231116
$592$	24.5253	−	32.0768i	1.00798	−	1.31835i
$593$	5.31996			0.218464			0.109232	−	0.994016i	$-0.465161\pi$
$593$	5.31996			0.218464			0.109232	+	0.994016i	$0.465161\pi$
$594$	0.694288	+	3.93750i	0.0284870	+	0.161558i
$595$	−2.22668	+	12.6281i	−0.0912850	+	0.517703i
$596$	64.6853	−	23.5435i	2.64961	−	0.964381i
$597$	−3.43242	−	2.88014i	−0.140480	−	0.117876i
$598$	84.6828			3.46294
$599$	−0.841367	−	0.705990i	−0.0343773	−	0.0288460i	0.625437	−	0.780275i	$-0.284921\pi$
$599$	−0.841367	−	0.705990i	−0.0343773	−	0.0288460i	−0.659814	+	0.751429i	$0.729365\pi$
$600$	−1.49660	−	2.59218i	−0.0610983	−	0.105825i
$601$	−20.6275	−	7.50779i	−0.841412	−	0.306249i	−0.114878	−	0.993380i	$-0.536648\pi$
$601$	−20.6275	−	7.50779i	−0.841412	−	0.306249i	−0.726534	+	0.687131i	$0.758870\pi$
$602$	5.69459	−	9.86332i	0.232094	−	0.401999i
$603$	16.3478	+	28.3152i	0.665732	+	1.15308i
$604$	11.7947	+	66.8912i	0.479921	+	2.72177i
$605$	24.7503	−	9.00838i	1.00624	−	0.366243i
$606$	3.43629	−	5.95183i	0.139590	−	0.241776i
$607$	16.1570	−	13.5574i	0.655794	−	0.550277i	−0.253029	−	0.967459i	$-0.581427\pi$
$607$	16.1570	−	13.5574i	0.655794	−	0.550277i	0.908823	+	0.417182i	$0.136982\pi$
$608$	0.798133	−	0.669713i	0.0323686	−	0.0271605i
$609$	−1.59627	−	0.580994i	−0.0646840	−	0.0235430i
$610$	−2.68479	+	15.2262i	−0.108704	+	0.616491i
$611$	2.69182	−	15.2661i	0.108899	−	0.617599i
$612$	19.7271	+	7.18009i	0.797423	+	0.290238i
$613$	−28.7931	+	24.1603i	−1.16294	+	0.975826i	−0.999942	−	0.0107999i	$-0.996562\pi$
$613$	−28.7931	+	24.1603i	−1.16294	+	0.975826i	−0.163002	+	0.986626i	$0.552118\pi$
$614$	−49.1960	+	41.2803i	−1.98539	+	1.66594i
$615$	−3.20574	+	5.55250i	−0.129268	+	0.223898i
$616$	13.5963	−	4.94864i	0.547809	−	0.199386i
$617$	6.29561	+	35.7042i	0.253452	+	1.43740i	0.800016	+	0.599978i	$0.204824\pi$
$617$	6.29561	+	35.7042i	0.253452	+	1.43740i	−0.546565	+	0.837417i	$0.684065\pi$
$618$	−7.61468	−	13.1890i	−0.306308	−	0.530540i
$619$	−14.7824	+	25.6039i	−0.594155	+	1.02911i	0.399511	+	0.916729i	$0.369180\pi$
$619$	−14.7824	+	25.6039i	−0.594155	+	1.02911i	−0.993666	+	0.112378i	$0.964153\pi$
$620$	40.2806	+	14.6610i	1.61771	+	0.588798i
$621$	6.12567	+	10.6100i	0.245815	+	0.425763i
$622$	−34.4183	−	28.8804i	−1.38005	−	1.15800i
$623$	5.82707			0.233457
$624$	−9.84389	−	8.26001i	−0.394071	−	0.330665i
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$	3.17974	−	18.0332i	0.127088	−	0.720752i
$627$	−0.0105717	−	0.0599551i	−0.000422193	−	0.00239438i
$628$	−4.66044			−0.185972
$629$	−9.96926	−	1.29493i	−0.397500	−	0.0516321i
$630$	−56.5681			−2.25373
$631$	7.90033	+	44.8050i	0.314507	+	1.78366i	0.574970	+	0.818175i	$0.305014\pi$
$631$	7.90033	+	44.8050i	0.314507	+	1.78366i	−0.260462	+	0.965484i	$0.583875\pi$
$632$	9.07563	−	51.4704i	0.361009	−	2.04738i
$633$	0.546637	−	0.198960i	0.0217269	−	0.00790793i
$634$	−52.2156	−	43.8141i	−2.07375	−	1.74008i
$635$	−49.7820			−1.97554
$636$	−1.19981	−	1.00676i	−0.0475755	−	0.0399205i
$637$	−6.65863	−	11.5331i	−0.263825	−	0.456958i
$638$	−2.93717	−	1.06904i	−0.116284	−	0.0423237i
$639$	−16.8366	+	29.1619i	−0.666046	+	1.15363i
$640$	−16.8897	−	29.2537i	−0.667622	−	1.15636i
$641$	1.97549	+	11.2036i	0.0780272	+	0.442514i	0.998645	+	0.0520482i	$0.0165749\pi$
$641$	1.97549	+	11.2036i	0.0780272	+	0.442514i	−0.920617	+	0.390466i	$0.872314\pi$
$642$	2.86571	−	1.04303i	0.113101	−	0.0411653i
$643$	15.7324	−	27.2493i	0.620424	−	1.07461i	−0.368983	−	0.929436i	$-0.620294\pi$
$643$	15.7324	−	27.2493i	0.620424	−	1.07461i	0.989407	−	0.145169i	$-0.0463727\pi$
$644$	62.1302	−	52.1334i	2.44827	−	2.05435i
$645$	0.988856	−	0.829748i	0.0389362	−	0.0326713i
$646$	−0.891407	−	0.324446i	−0.0350719	−	0.0127651i
$647$	5.08559	−	28.8418i	0.199935	−	1.13389i	−0.705278	−	0.708931i	$-0.749178\pi$
$647$	5.08559	−	28.8418i	0.199935	−	1.13389i	0.905213	−	0.424958i	$-0.139711\pi$
$648$	−8.40719	+	47.6796i	−0.330266	+	1.87303i
$649$	−3.45811	−	1.25865i	−0.135743	−	0.0494063i
$650$	−15.2606	+	12.8051i	−0.598569	+	0.502259i
$651$	−3.12836	+	2.62500i	−0.122610	+	0.102882i
$652$	14.5326	−	25.1711i	0.569139	−	0.985777i
$653$	0.549163	−	0.199879i	0.0214904	−	0.00782187i	−0.331253	−	0.943542i	$-0.607471\pi$
$653$	0.549163	−	0.199879i	0.0214904	−	0.00782187i	0.352743	+	0.935720i	$0.385249\pi$
$654$	0.573978	+	3.25519i	0.0224443	+	0.127288i
$655$	9.36484	+	16.2204i	0.365914	+	0.633782i
$656$	24.1989	−	41.9138i	0.944809	−	1.63646i
$657$	−7.90420	−	2.87689i	−0.308372	−	0.112238i
$658$	−10.7888	−	18.6867i	−0.420591	−	0.728485i
$659$	−20.2233	−	16.9693i	−0.787787	−	0.661032i	0.157410	−	0.987533i	$-0.449686\pi$
$659$	−20.2233	−	16.9693i	−0.787787	−	0.661032i	−0.945197	+	0.326502i	$0.894130\pi$
$660$	3.00000			0.116775
$661$	26.7683	+	22.4613i	1.04117	+	0.873643i	0.992137	−	0.125154i	$-0.0399426\pi$
$661$	26.7683	+	22.4613i	1.04117	+	0.873643i	0.0490298	+	0.998797i	$0.484387\pi$
$662$	−80.5267	+	29.3093i	−3.12976	+	1.13914i
$663$	−0.555560	+	3.15074i	−0.0215761	+	0.122364i
$664$	12.8154	+	72.6796i	0.497333	+	2.82051i
$665$	1.75877			0.0682022
$666$	−2.01114	−	44.3029i	−0.0779303	−	1.71670i
$667$	−9.57760			−0.370846
$668$	−13.2194	−	74.9710i	−0.511474	−	2.90071i
$669$	−0.128822	+	0.730588i	−0.00498056	+	0.0282462i
$670$	68.4120	−	24.8999i	2.64299	−	0.961968i
$671$	−1.42855	−	1.19869i	−0.0551485	−	0.0462751i
$672$	−4.89124			−0.188684
$673$	−22.8327	−	19.1590i	−0.880138	−	0.738523i	0.0860696	−	0.996289i	$-0.472569\pi$
$673$	−22.8327	−	19.1590i	−0.880138	−	0.738523i	−0.966207	+	0.257766i	$0.917014\pi$
$674$	16.3123	+	28.2537i	0.628325	+	1.08829i
$675$	−2.70826	−	0.985727i	−0.104241	−	0.0379407i
$676$	−39.8560	+	69.0326i	−1.53292	+	2.65510i
$677$	−16.0829	−	27.8564i	−0.618116	−	1.07061i	−0.989829	−	0.142261i	$-0.954563\pi$
$677$	−16.0829	−	27.8564i	−0.618116	−	1.07061i	0.371713	−	0.928348i	$-0.378771\pi$
$678$	−2.08677	−	11.8347i	−0.0801420	−	0.454508i
$679$	43.1489	−	15.7049i	1.65590	−	0.602699i
$680$	12.7763	−	22.1292i	0.489949	−	0.848617i
$681$	−3.62243	+	3.03958i	−0.138812	+	0.116477i
$682$	−5.75624	+	4.83006i	−0.220418	+	0.184953i
$683$	−16.9427	−	6.16663i	−0.648294	−	0.235960i	−0.00311961	−	0.999995i	$-0.500993\pi$
$683$	−16.9427	−	6.16663i	−0.648294	−	0.235960i	−0.645174	+	0.764035i	$0.723215\pi$
$684$	0.500000	−	2.83564i	0.0191180	−	0.108423i
$685$	1.68092	−	9.53298i	0.0642247	−	0.364237i
$686$	33.6168	+	12.2355i	1.28350	+	0.467154i
$687$	2.29039	−	1.92187i	0.0873839	−	0.0733238i
$688$	−7.46451	+	6.26347i	−0.284582	+	0.238792i
$689$	−2.84911	+	4.93480i	−0.108542	+	0.188001i
$690$	12.5544	−	4.56942i	0.477937	−	0.173955i
$691$	1.87551	+	10.6366i	0.0713479	+	0.404634i	0.999476	+	0.0323729i	$0.0103064\pi$
$691$	1.87551	+	10.6366i	0.0713479	+	0.404634i	−0.928128	+	0.372261i	$0.878582\pi$
$692$	−23.7160	−	41.0773i	−0.901547	−	1.56153i
$693$	3.41147	−	5.90885i	0.129591	−	0.224459i
$694$	−17.7344	−	6.45480i	−0.673189	−	0.245021i
$695$	22.9329	+	39.7209i	0.869894	+	1.50670i
$696$	2.59311	+	2.17588i	0.0982916	+	0.0824765i
$697$	−12.0496			−0.456412
$698$	−36.4957	−	30.6235i	−1.38138	−	1.15912i
$699$	−2.47906	+	0.902302i	−0.0937665	+	0.0341282i
$700$	−3.31315	+	18.7898i	−0.125225	+	0.710188i
$701$	4.98814	+	28.2892i	0.188399	+	1.06847i	0.921509	+	0.388356i	$0.126957\pi$
$701$	4.98814	+	28.2892i	0.188399	+	1.06847i	−0.733110	+	0.680110i	$0.761932\pi$
$702$	−28.8188			−1.08770
$703$	0.0625289	+	1.37743i	0.00235832	+	0.0519508i
$704$	1.26682			0.0477449
$705$	−0.424678	−	2.40847i	−0.0159943	−	0.0907081i
$706$	−10.0039	+	56.7348i	−0.376501	+	2.13524i
$707$	−22.5030	+	8.19042i	−0.846312	+	0.308032i
$708$	5.58512	+	4.68647i	0.209902	+	0.176128i
$709$	42.2772			1.58776			0.793878	−	0.608078i	$-0.208059\pi$
$709$	42.2772			1.58776			0.793878	+	0.608078i	$0.208059\pi$
$710$	57.4377	+	48.1959i	2.15560	+	1.80876i
$711$	−12.3229	−	21.3440i	−0.462147	−	0.800462i
$712$	−10.9115	−	3.97145i	−0.408925	−	0.148836i
$713$	−11.5125	+	19.9402i	−0.431146	+	0.746767i
$714$	2.22668	+	3.85673i	0.0833315	+	0.144334i
$715$	−1.89528	−	10.7487i	−0.0708794	−	0.401977i
$716$	83.7388	−	30.4784i	3.12947	−	1.13903i
$717$	−2.24628	+	3.89067i	−0.0838889	+	0.145300i
$718$	21.2554	−	17.8354i	0.793243	−	0.665610i
$719$	−12.2790	+	10.3033i	−0.457929	+	0.384248i	−0.842368	−	0.538902i	$-0.818839\pi$
$719$	−12.2790	+	10.3033i	−0.457929	+	0.384248i	0.384439	+	0.923150i	$0.374395\pi$
$720$	45.4791	+	16.5530i	1.69491	+	0.616895i
$721$	−9.21482	+	52.2599i	−0.343178	+	1.94626i
$722$	8.33157	−	47.2507i	0.310069	−	1.75849i
$723$	−0.511449	−	0.186152i	−0.0190210	−	0.00692308i
$724$	35.4243	−	29.7245i	1.31653	−	1.10470i
$725$	1.72597	−	1.44826i	0.0641008	−	0.0537869i
$726$	4.57367	−	7.92183i	0.169745	−	0.294007i
$727$	40.6464	−	14.7941i	1.50749	−	0.548682i	0.549503	−	0.835492i	$-0.314817\pi$
$727$	40.6464	−	14.7941i	1.50749	−	0.548682i	0.957987	+	0.286810i	$0.0925950\pi$
$728$	18.1097	+	102.705i	0.671190	+	3.80651i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$	−9.36484	+	16.2204i	−0.346608	+	0.600343i
$731$	2.27972	+	0.829748i	0.0843183	+	0.0306894i
$732$	1.84730	+	3.19961i	0.0682780	+	0.118261i
$733$	1.18067	+	0.990703i	0.0436092	+	0.0365924i	0.664332	−	0.747438i	$-0.268716\pi$
$733$	1.18067	+	0.990703i	0.0436092	+	0.0365924i	−0.620723	+	0.784030i	$0.713161\pi$
$734$	−50.4989			−1.86395
$735$	−1.60947	−	1.35051i	−0.0593662	−	0.0498142i
$736$	−25.9145	+	9.43209i	−0.955220	+	0.347672i
$737$	−1.52481	+	8.64766i	−0.0561673	+	0.318540i
$738$	−9.23055	−	52.3491i	−0.339781	−	1.92700i
$739$	5.99825			0.220649			0.110325	−	0.993896i	$-0.464811\pi$
$739$	5.99825			0.220649			0.110325	+	0.993896i	$0.464811\pi$
$740$	−67.3799	−	8.75211i	−2.47693	−	0.321734i
$741$	0.438815			0.0161203
$742$	1.37733	+	7.81120i	0.0505632	+	0.286758i
$743$	2.48246	−	14.0787i	0.0910726	−	0.516498i	−0.904808	−	0.425820i	$-0.859986\pi$
$743$	2.48246	−	14.0787i	0.0910726	−	0.516498i	0.995880	−	0.0906779i	$-0.0289034\pi$
$744$	7.64708	−	2.78331i	0.280356	−	0.102041i
$745$	−30.2670	−	25.3970i	−1.10890	−	0.930474i
$746$	4.33006			0.158535
$747$	26.6596	+	22.3700i	0.975423	+	0.818477i
$748$	2.81908	+	4.88279i	0.103076	+	0.178532i
$749$	−9.98545	−	3.63441i	−0.364860	−	0.132798i
$750$	3.99525	−	6.91998i	0.145886	−	0.252682i
$751$	6.07873	+	10.5287i	0.221816	+	0.384196i	0.955359	−	0.295446i	$-0.0954683\pi$
$751$	6.07873	+	10.5287i	0.221816	+	0.384196i	−0.733544	+	0.679642i	$0.762135\pi$
$752$	3.20574	+	18.1806i	0.116901	+	0.662980i
$753$	0.767693	−	0.279418i	0.0279763	−	0.0101825i
$754$	11.2647	−	19.5110i	0.410236	−	0.710550i
$755$	29.8653	−	25.0600i	1.08691	−	0.912026i
$756$	−21.1438	+	17.7418i	−0.768994	+	0.645263i
$757$	29.4329	+	10.7127i	1.06976	+	0.389359i	0.816086	−	0.577931i	$-0.196140\pi$
$757$	29.4329	+	10.7127i	1.06976	+	0.389359i	0.253671	+	0.967291i	$0.418362\pi$
$758$	−2.78224	+	15.7789i	−0.101056	+	0.573115i
$759$	−0.279821	+	1.58694i	−0.0101569	+	0.0576024i
$760$	−3.29339	−	1.19869i	−0.119464	−	0.0434812i
$761$	20.4290	−	17.1420i	0.740551	−	0.621396i	−0.192434	−	0.981310i	$-0.561638\pi$
$761$	20.4290	−	17.1420i	0.740551	−	0.621396i	0.932986	+	0.359914i	$0.117194\pi$
$762$	−13.2442	+	11.1132i	−0.479788	+	0.402590i
$763$	5.75877	−	9.97448i	0.208481	−	0.361101i
$764$	−67.0929	+	24.4198i	−2.42734	+	0.883478i
$765$	−2.09240	−	11.8666i	−0.0756507	−	0.429037i
$766$	−14.5915	−	25.2733i	−0.527213	−	0.913160i
$767$	13.2626	−	22.9716i	0.478886	−	0.829455i
$768$	−9.95471	−	3.62322i	−0.359210	−	0.130742i
$769$	−1.78312	−	3.08845i	−0.0643009	−	0.111372i	0.832083	−	0.554651i	$-0.187148\pi$
$769$	−1.78312	−	3.08845i	−0.0643009	−	0.111372i	−0.896384	+	0.443279i	$0.853815\pi$
$770$	−11.6382	−	9.76557i	−0.419410	−	0.351927i
$771$	3.80335			0.136974
$772$	−29.2408	−	24.5360i	−1.05240	−	0.883069i
$773$	9.22833	−	3.35884i	0.331920	−	0.120809i	−0.170684	−	0.985326i	$-0.554598\pi$
$773$	9.22833	−	3.35884i	0.331920	−	0.120809i	0.502604	+	0.864517i	$0.332375\pi$
$774$	−1.85844	+	10.5397i	−0.0668003	+	0.378843i
$775$	−0.940570	−	5.33424i	−0.0337863	−	0.191611i
$776$	−91.5022			−3.28474
$777$	3.93170	−	5.14230i	0.141049	−	0.184479i
$778$	−31.7948			−1.13990
$779$	0.286989	+	1.62760i	0.0102824	+	0.0583147i
$780$	−3.75490	+	21.2951i	−0.134447	+	0.762487i
$781$	−8.49825	+	3.09311i	−0.304091	+	0.110680i
$782$	19.2344	+	16.1396i	0.687822	+	0.577151i
$783$	3.25940			0.116481
$784$	12.1493	+	10.1945i	0.433904	+	0.364088i
$785$	1.33750	+	2.31661i	0.0477373	+	0.0826834i
$786$	6.11246	+	2.22475i	0.218024	+	0.0793544i
$787$	−15.2015	+	26.3297i	−0.541873	+	0.938552i	0.456923	+	0.889506i	$0.348951\pi$
$787$	−15.2015	+	26.3297i	−0.541873	+	0.938552i	−0.998797	+	0.0490461i	$0.984382\pi$
$788$	35.6844	+	61.8072i	1.27120	+	2.20179i
$789$	1.06711	+	6.05191i	0.0379903	+	0.215454i
$790$	−51.5690	+	18.7696i	−1.83474	+	0.667791i
$791$	−20.9368	+	36.2635i	−0.744425	+	1.28938i
$792$	−10.4153	+	8.73951i	−0.370093	+	0.310545i
$793$	10.2968	−	8.64003i	0.365650	−	0.306817i
$794$	80.7832	+	29.4027i	2.86689	+	1.04346i
$795$	−0.156107	+	0.885328i	−0.00553655	+	0.0313993i
$796$	9.88326	−	56.0507i	0.350303	−	1.98667i
$797$	10.3071	+	3.75146i	0.365095	+	0.132884i	0.518052	−	0.855349i	$-0.326657\pi$
$797$	10.3071	+	3.75146i	0.365095	+	0.132884i	−0.152957	+	0.988233i	$0.548880\pi$
$798$	0.467911	−	0.392624i	0.0165639	−	0.0138987i
$799$	3.52094	−	2.95442i	0.124562	−	0.104520i
$800$	3.24376	−	5.61835i	0.114684	−	0.198639i
$801$	−5.14543	+	1.87278i	−0.181805	+	0.0661715i
$802$	−5.94475	−	33.7143i	−0.209916	−	1.19049i
$803$	−1.12954	−	1.95642i	−0.0398605	−	0.0690404i
$804$	8.69846	−	15.0662i	0.306771	−	0.531343i
$805$	−43.7452	−	15.9219i	−1.54181	−	0.561174i
$806$	−27.0808	−	46.9054i	−0.953882	−	1.65217i
$807$	0.764700	+	0.641660i	0.0269187	+	0.0225875i
$808$	47.7202			1.67879
$809$	19.2160	+	16.1241i	0.675599	+	0.566895i	0.914717	−	0.404096i	$-0.132414\pi$
$809$	19.2160	+	16.1241i	0.675599	+	0.566895i	−0.239118	+	0.970991i	$0.576858\pi$
$810$	47.7708	−	17.3872i	1.67850	−	0.610923i
$811$	2.78375	−	15.7874i	0.0977506	−	0.554371i	−0.896119	−	0.443814i	$-0.853625\pi$
$811$	2.78375	−	15.7874i	0.0977506	−	0.554371i	0.993870	−	0.110558i	$-0.0352637\pi$
$812$	−3.74691	−	21.2498i	−0.131491	−	0.745721i
$813$	6.77238			0.237518
$814$	7.23442	−	9.46195i	0.253566	−	0.331641i
$815$	−16.6827			−0.584371
$816$	−0.661626	−	3.75227i	−0.0231616	−	0.131356i
$817$	0.0577812	−	0.327693i	0.00202151	−	0.0114645i
$818$	7.26264	−	2.64339i	0.253932	−	0.0924238i
$819$	37.6732	+	31.6116i	1.31641	+	1.10460i
$820$	−81.4407			−2.84403
$821$	7.64930	+	6.41852i	0.266962	+	0.224008i	0.766435	−	0.642321i	$-0.222029\pi$
$821$	7.64930	+	6.41852i	0.266962	+	0.224008i	−0.499473	+	0.866329i	$0.666473\pi$
$822$	−1.68092	−	2.91144i	−0.0586289	−	0.101548i
$823$	−22.4209	−	8.16053i	−0.781542	−	0.284458i	−0.0797266	−	0.996817i	$-0.525405\pi$
$823$	−22.4209	−	8.16053i	−0.781542	−	0.284458i	−0.701816	+	0.712359i	$0.747627\pi$
$824$	52.8730	−	91.5788i	1.84192	−	3.19030i
$825$	−0.189540	−	0.328293i	−0.00659895	−	0.0114297i
$826$	−6.41147	−	36.3613i	−0.223084	−	1.26517i
$827$	14.8807	−	5.41614i	0.517454	−	0.188338i	−0.0700740	−	0.997542i	$-0.522324\pi$
$827$	14.8807	−	5.41614i	0.517454	−	0.188338i	0.587528	+	0.809204i	$0.300101\pi$
$828$	−38.1070	+	66.0033i	−1.32431	+	2.29377i
$829$	−22.0134	+	18.4715i	−0.764558	+	0.641540i	−0.939309	−	0.343072i	$-0.888532\pi$
$829$	−22.0134	+	18.4715i	−0.764558	+	0.641540i	0.174751	+	0.984613i	$0.444088\pi$
$830$	59.3624	−	49.8109i	2.06050	−	1.72896i
$831$	−7.03121	−	2.55915i	−0.243910	−	0.0887760i
$832$	−1.58559	+	8.99232i	−0.0549704	+	0.311753i
$833$	0.685670	−	3.88863i	0.0237571	−	0.134733i
$834$	14.9684	+	5.44804i	0.518313	+	0.188650i
$835$	−33.4727	+	28.0869i	−1.15837	+	0.971989i
$836$	0.592396	−	0.497079i	0.0204885	−	0.0171919i
$837$	3.91787	−	6.78595i	0.135421	−	0.234557i
$838$	24.1459	−	8.78839i	0.834106	−	0.303590i
$839$	−7.67711	−	43.5390i	−0.265043	−	1.50313i	−0.768912	−	0.639355i	$-0.779202\pi$
$839$	−7.67711	−	43.5390i	−0.265043	−	1.50313i	0.503869	−	0.863780i	$-0.331909\pi$
$840$	8.22668	+	14.2490i	0.283847	+	0.491638i
$841$	13.2260	−	22.9080i	0.456068	−	0.789933i
$842$	18.3332	+	6.67274i	0.631804	+	0.229958i
$843$	−1.10354	−	1.91139i	−0.0380080	−	0.0658317i
$844$	5.66044	+	4.74968i	0.194841	+	0.163491i
$845$	45.7529			1.57395
$846$	15.5326	+	13.0334i	0.534020	+	0.448096i
$847$	−29.9513	+	10.9014i	−1.02914	+	0.374576i
$848$	1.17840	−	6.68302i	0.0404663	−	0.229496i
$849$	−0.0467989	−	0.265410i	−0.00160614	−	0.00910885i
$850$	−5.90673			−0.202599
$851$	10.9145	−	34.8263i	0.374143	−	1.19383i
$852$	17.9172			0.613832
$853$	0.595638	+	3.37803i	0.0203942	+	0.115662i	0.993305	−	0.115518i	$-0.0368527\pi$
$853$	0.595638	+	3.37803i	0.0203942	+	0.115662i	−0.972911	+	0.231179i	$0.925742\pi$
$854$	3.24897	−	18.4258i	0.111177	−	0.630519i
$855$	−1.55303	+	0.565258i	−0.0531126	+	0.0193314i
$856$	16.2212	+	13.6112i	0.554430	+	0.465222i
$857$	49.0306			1.67485			0.837427	−	0.546549i	$-0.184059\pi$
$857$	49.0306			1.67485			0.837427	+	0.546549i	$0.184059\pi$
$858$	−2.90373	−	2.43652i	−0.0991318	−	0.0831815i
$859$	−18.6844	−	32.3623i	−0.637503	−	1.10419i	−0.985979	−	0.166870i	$-0.946634\pi$
$859$	−18.6844	−	32.3623i	−0.637503	−	1.10419i	0.348476	−	0.937318i	$-0.386699\pi$
$860$	15.4081	+	5.60808i	0.525411	+	0.191234i
$861$	3.87939	−	6.71929i	0.132209	−	0.228993i
$862$	26.8773	+	46.5529i	0.915445	+	1.58560i
$863$	0.605189	+	3.43220i	0.0206009	+	0.116833i	0.993374	−	0.114926i	$-0.0366630\pi$
$863$	0.605189	+	3.43220i	0.0206009	+	0.116833i	−0.972773	+	0.231759i	$0.925552\pi$
$864$	8.81908	−	3.20988i	0.300031	−	0.109202i
$865$	−13.6125	+	23.5775i	−0.462838	+	0.801658i
$866$	−31.8995	+	26.7668i	−1.08399	+	0.909574i
$867$	3.79607	−	3.18528i	0.128921	−	0.108178i
$868$	−48.7452	−	17.7418i	−1.65452	−	0.602195i
$869$	1.14941	−	6.51860i	0.0389909	−	0.221129i
$870$	0.617211	−	3.50038i	0.0209254	−	0.118674i
$871$	−59.4757	−	21.6474i	−2.01526	−	0.733494i
$872$	−17.5817	+	14.7528i	−0.595392	+	0.499593i
$873$	−33.0540	+	27.7356i	−1.11871	+	0.938707i
$874$	1.72193	−	2.98248i	0.0582453	−	0.100884i
$875$	−26.1634	+	9.52271i	−0.884486	+	0.321926i
$876$	0.777189	+	4.40766i	0.0262588	+	0.148921i
$877$	20.5638	+	35.6175i	0.694389	+	1.20272i	0.970386	+	0.241559i	$0.0776586\pi$
$877$	20.5638	+	35.6175i	0.694389	+	1.20272i	−0.275997	+	0.961158i	$0.589008\pi$
$878$	−27.6472	+	47.8864i	−0.933049	+	1.61609i
$879$	−10.7814	−	3.92410i	−0.363646	−	0.132356i
$880$	6.49912	+	11.2568i	0.219085	+	0.379467i
$881$	−0.294015	−	0.246707i	−0.00990560	−	0.00831179i	0.637821	−	0.770184i	$-0.279836\pi$
$881$	−0.294015	−	0.246707i	−0.00990560	−	0.00831179i	−0.647727	+	0.761873i	$0.724280\pi$
$882$	17.4192			0.586535
$883$	−19.8840	−	16.6846i	−0.669149	−	0.561483i	0.243664	−	0.969860i	$-0.421650\pi$
$883$	−19.8840	−	16.6846i	−0.669149	−	0.561483i	−0.912813	+	0.408377i	$0.866095\pi$
$884$	−38.1883	+	13.8994i	−1.28441	+	0.467487i
$885$	0.726682	−	4.12122i	0.0244271	−	0.138533i
$886$	6.23618	+	35.3671i	0.209508	+	1.18818i
$887$	−2.75784			−0.0925991			−0.0462995	−	0.998928i	$-0.514743\pi$
$887$	−2.75784			−0.0925991			−0.0462995	+	0.998928i	$0.514743\pi$
$888$	−10.8671	+	6.94955i	−0.364675	+	0.233212i
$889$	60.2431			2.02049
$890$	2.11721	+	12.0073i	0.0709691	+	0.402486i
$891$	−1.06475	+	6.03850i	−0.0356705	+	0.202297i
$892$	−8.85504	+	3.22297i	−0.296489	+	0.107913i
$893$	−0.482926	−	0.405223i	−0.0161605	−	0.0135603i
$894$	−13.7219			−0.458930
$895$	−39.1823	−	32.8779i	−1.30972	−	1.09899i
$896$	20.4388	+	35.4011i	0.682813	+	1.18267i
$897$	−10.9145	−	3.97254i	−0.364423	−	0.132639i
$898$	−23.2515	+	40.2728i	−0.775912	+	1.34392i
$899$	3.06283	+	5.30498i	0.102151	+	0.176931i
$900$	−3.11334	−	17.6566i	−0.103778	−	0.588554i
$901$	−1.58765	+	0.577857i	−0.0528922	+	0.0192512i
$902$	7.13816	−	12.3636i	0.237675	−	0.411664i
$903$	−1.19665	+	1.00411i	−0.0398221	+	0.0334147i
$904$	63.9206	−	53.6358i	2.12597	−	1.78390i
$905$	−24.9418	−	9.07808i	−0.829094	−	0.301765i
$906$	2.35117	−	13.3341i	0.0781123	−	0.442997i
$907$	−5.86366	+	33.2544i	−0.194699	+	1.10420i	0.718147	+	0.695892i	$0.244991\pi$
$907$	−5.86366	+	33.2544i	−0.194699	+	1.10420i	−0.912846	+	0.408304i	$0.866120\pi$
$908$	−56.4436	−	20.5438i	−1.87315	−	0.681770i
$909$	17.2383	−	14.4646i	0.571758	−	0.479762i
$910$	83.8863	−	70.3890i	2.78080	−	2.33337i
$911$	−19.0581	+	33.0096i	−0.631423	+	1.09366i	0.355839	+	0.934547i	$0.384195\pi$
$911$	−19.0581	+	33.0096i	−0.631423	+	1.09366i	−0.987261	+	0.159108i	$0.949138\pi$
$912$	−0.491077	+	0.178737i	−0.0162612	+	0.00591859i
$913$	1.62304	+	9.20469i	0.0537146	+	0.304631i
$914$	11.2959	+	19.5651i	0.373636	+	0.647156i
$915$	1.06031	−	1.83651i	0.0350527	−	0.0607130i
$916$	35.6883	+	12.9895i	1.17917	+	0.429184i
$917$	−11.3327	−	19.6289i	−0.374240	−	0.648203i
$918$	−6.54576	−	5.49254i	−0.216042	−	0.181281i
$919$	−25.2754			−0.833758			−0.416879	−	0.908962i	$-0.636876\pi$
$919$	−25.2754			−0.833758			−0.416879	+	0.908962i	$0.636876\pi$
$920$	71.0634	+	59.6292i	2.34289	+	1.96592i
$921$	8.27719	−	3.01265i	0.272743	−	0.0992702i
$922$	−14.4000	+	81.6666i	−0.474240	+	2.68955i
$923$	−11.3193	−	64.1951i	−0.372580	−	2.11301i
$924$	−3.63041			−0.119432
$925$	3.29932	+	7.92642i	0.108481	+	0.260619i
$926$	−10.5594			−0.347004
$927$	−8.65910	−	49.1082i	−0.284402	−	1.61292i
$928$	−1.27403	+	7.22540i	−0.0418222	+	0.237185i
$929$	−43.5492	+	15.8506i	−1.42880	+	0.520042i	−0.936588	−	0.350432i	$-0.886035\pi$
$929$	−43.5492	+	15.8506i	−1.42880	+	0.520042i	−0.492215	+	0.870474i	$0.663813\pi$
$930$	−6.54576	−	5.49254i	−0.214644	−	0.180108i
$931$	−0.541584			−0.0177497
$932$	−25.6707	−	21.5403i	−0.840872	−	0.705575i
$933$	3.08125	+	5.33688i	0.100876	+	0.174722i
$934$	58.2024	+	21.1839i	1.90444	+	0.693160i
$935$	1.61809	−	2.80261i	0.0529172	−	0.0916552i
$936$	−49.0001	−	84.8706i	−1.60162	−	2.77408i
$937$	3.46580	+	19.6555i	0.113223	+	0.642117i	0.987615	+	0.156898i	$0.0501493\pi$
$937$	3.46580	+	19.6555i	0.113223	+	0.642117i	−0.874392	+	0.485220i	$0.838740\pi$
$938$	−82.7880	+	30.1324i	−2.70312	+	0.983856i
$939$	−1.25578	+	2.17507i	−0.0409807	+	0.0709807i
$940$	23.7973	−	19.9683i	0.776181	−	0.651293i
$941$	−20.9800	+	17.6043i	−0.683928	+	0.573884i	−0.917151	−	0.398539i	$-0.869517\pi$
$941$	−20.9800	+	17.6043i	−0.683928	+	0.573884i	0.233223	+	0.972423i	$0.425073\pi$
$942$	0.872989	+	0.317742i	0.0284435	+	0.0103526i
$943$	7.59627	−	43.0806i	0.247368	−	1.40290i
$944$	−5.48545	+	31.1095i	−0.178536	+	1.01253i
$945$	14.8871	+	5.41847i	0.484278	+	0.176263i
$946$	−2.20187	+	1.84759i	−0.0715889	+	0.0600702i
$947$	15.7411	−	13.2083i	0.511516	−	0.429213i	−0.350146	−	0.936695i	$-0.613868\pi$
$947$	15.7411	−	13.2083i	0.511516	−	0.429213i	0.861662	+	0.507482i	$0.169424\pi$
$948$	−6.55690	+	11.3569i	−0.212958	+	0.368855i
$949$	15.3011	−	5.56915i	0.496696	−	0.180782i
$950$	0.140682	+	0.797847i	0.00456432	+	0.0258856i
$951$	4.67453	+	8.09652i	0.151582	+	0.262548i
$952$	−15.4611	+	26.7794i	−0.501097	+	0.867926i
$953$	35.7806	+	13.0231i	1.15905	+	0.421859i	0.848758	−	0.528782i	$-0.177351\pi$
$953$	35.7806	+	13.0231i	1.15905	+	0.421859i	0.310291	+	0.950642i	$0.399573\pi$
$954$	−3.72668	−	6.45480i	−0.120656	−	0.208982i
$955$	31.3935	+	26.3423i	1.01587	+	0.852417i
$956$	−57.0660			−1.84565
$957$	0.328411	+	0.275570i	0.0106160	+	0.00890790i
$958$	77.0502	−	28.0440i	2.48938	−	0.906059i
$959$	−2.03415	+	11.5362i	−0.0656861	+	0.372524i
$960$	0.250152	+	1.41868i	0.00807363	+	0.0457878i
$961$	−16.2736			−0.524956
$962$	58.1095	+	63.1955i	1.87353	+	2.03750i
$963$	9.98545			0.321777
$964$	−1.20052	−	6.80850i	−0.0386662	−	0.219287i
$965$	−3.80453	+	21.5766i	−0.122472	+	0.694574i
$966$	−15.1925	+	5.52963i	−0.488812	+	0.177913i
$967$	1.97637	+	1.65837i	0.0635557	+	0.0533295i	0.674012	−	0.738720i	$-0.264570\pi$
$967$	1.97637	+	1.65837i	0.0635557	+	0.0533295i	−0.610456	+	0.792050i	$0.709014\pi$
$968$	63.5152			2.04146
$969$	0.0996702	+	0.0836332i	0.00320187	+	0.00268669i
$970$	48.0394	+	83.2067i	1.54245	+	2.67161i
$971$	31.4996	+	11.4649i	1.01087	+	0.367927i	0.793767	−	0.608222i	$-0.208117\pi$
$971$	31.4996	+	11.4649i	1.01087	+	0.367927i	0.217103	+	0.976149i	$0.430339\pi$
$972$	19.5856	−	33.9232i	0.628208	−	1.08809i
$973$	−27.7520	−	48.0678i	−0.889687	−	1.54098i
$974$	−6.72786	−	38.1556i	−0.215575	−	1.22258i
$975$	2.56758	−	0.934523i	0.0822284	−	0.0299287i
$976$	−8.00387	+	13.8631i	−0.256198	+	0.443747i
$977$	−11.0273	+	9.25304i	−0.352796	+	0.296031i	−0.801912	−	0.597443i	$-0.796184\pi$
$977$	−11.0273	+	9.25304i	−0.352796	+	0.296031i	0.449116	+	0.893474i	$0.351739\pi$
$978$	−4.43835	+	3.72422i	−0.141923	+	0.119087i
$979$	−1.38191	−	0.502975i	−0.0441661	−	0.0160751i
$980$	4.63429	−	26.2823i	0.148037	−	0.839558i
$981$	−1.87939	+	10.6585i	−0.0600042	+	0.340300i
$982$	−22.1573	−	8.06461i	−0.707069	−	0.257352i
$983$	19.7520	−	16.5739i	0.629990	−	0.528624i	−0.270936	−	0.962597i	$-0.587333\pi$
$983$	19.7520	−	16.5739i	0.629990	−	0.528624i	0.900926	+	0.433973i	$0.142889\pi$
$984$	−11.8439	+	9.93821i	−0.377570	+	0.316818i
$985$	20.4820	−	35.4759i	0.652612	−	1.13036i
$986$	6.27719	−	2.28471i	0.199906	−	0.0727600i
$987$	0.513919	+	2.91458i	0.0163582	+	0.0927721i
$988$	2.78699	+	4.82721i	0.0886659	+	0.153574i
$989$	−4.40373	+	7.62749i	−0.140031	+	0.242540i
$990$	13.4153	+	4.88279i	0.426368	+	0.155185i
$991$	15.3525	+	26.5913i	0.487689	+	0.844701i	0.999900	−	0.0141581i	$-0.00450682\pi$
$991$	15.3525	+	26.5913i	0.487689	+	0.844701i	−0.512211	+	0.858860i	$0.671173\pi$
$992$	13.5116	+	11.3376i	0.428994	+	0.359969i
$993$	11.7537			0.372993
$994$	−69.5075	−	58.3238i	−2.20465	−	1.84992i
$995$	−30.6981	+	11.1732i	−0.973194	+	0.354214i
$996$	3.21554	−	18.2362i	0.101888	−	0.577837i
$997$	2.66921	+	15.1378i	0.0845346	+	0.479419i	0.997456	+	0.0712841i	$0.0227097\pi$
$997$	2.66921	+	15.1378i	0.0845346	+	0.479419i	−0.912921	+	0.408135i	$0.866179\pi$
$998$	15.1301			0.478935
$999$	−3.71436	+	11.8519i	−0.117517	+	0.374978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.b.9.1	✓	6
3.2	odd	2		333.2.x.a.46.1		6
4.3	odd	2		592.2.bc.c.305.1		6
5.2	odd	4		925.2.bc.b.749.2		12
5.3	odd	4		925.2.bc.b.749.1		12
5.4	even	2		925.2.p.a.601.1		6
37.2	odd	36		1369.2.b.e.1368.1		6
37.12	even	9		1369.2.a.i.1.1		3
37.25	even	18		1369.2.a.l.1.3		3
37.33	even	9	inner	37.2.f.b.33.1	yes	6
37.35	odd	36		1369.2.b.e.1368.6		6
111.107	odd	18		333.2.x.a.181.1		6
148.107	odd	18		592.2.bc.c.33.1		6
185.33	odd	36		925.2.bc.b.699.2		12
185.107	odd	36		925.2.bc.b.699.1		12
185.144	even	18		925.2.p.a.551.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.b.9.1	✓	6	1.1	even	1	trivial
37.2.f.b.33.1	yes	6	37.33	even	9	inner
333.2.x.a.46.1		6	3.2	odd	2
333.2.x.a.181.1		6	111.107	odd	18
592.2.bc.c.33.1		6	148.107	odd	18
592.2.bc.c.305.1		6	4.3	odd	2
925.2.p.a.551.1		6	185.144	even	18
925.2.p.a.601.1		6	5.4	even	2
925.2.bc.b.699.1		12	185.107	odd	36
925.2.bc.b.699.2		12	185.33	odd	36
925.2.bc.b.749.1		12	5.3	odd	4
925.2.bc.b.749.2		12	5.2	odd	4
1369.2.a.i.1.1		3	37.12	even	9
1369.2.a.l.1.3		3	37.25	even	18
1369.2.b.e.1368.1		6	37.2	odd	36
1369.2.b.e.1368.6		6	37.35	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.93969 + 1.62760i) q^{5} +0.879385 q^{6} +(-2.34730 - 1.96962i) q^{7} +(3.05303 + 5.28801i) q^{8} +(2.70574 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.439693 - 2.49362i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(-4.14543 + 1.50881i) q^{4} +(1.93969 + 1.62760i) q^{5} +0.879385 q^{6} +(-2.34730 - 1.96962i) q^{7} +(3.05303 + 5.28801i) q^{8} +(2.70574 + 0.984808i) q^{9} +(3.20574 - 5.55250i) q^{10} +(0.386659 + 0.669713i) q^{11} +(-0.266044 - 1.50881i) q^{12} +(-5.23783 + 1.90641i) q^{13} +(-3.87939 + 6.71929i) q^{14} +(-0.673648 + 0.565258i) q^{15} +(5.08512 - 4.26692i) q^{16} +(-1.55303 - 0.565258i) q^{17} +(1.26604 - 7.18009i) q^{18} +(-0.0393628 + 0.223238i) q^{19} +(-10.4966 - 3.82045i) q^{20} +(0.815207 - 0.684040i) q^{21} +(1.50000 - 1.25865i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-1.99273 + 0.725293i) q^{24} +(0.245100 + 1.39003i) q^{25} +(7.05690 + 12.2229i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(12.7023 + 4.62327i) q^{28} +(-0.798133 - 1.38241i) q^{29} +(1.70574 + 1.43128i) q^{30} -3.83750 q^{31} +(-3.52094 - 2.95442i) q^{32} +(-0.252374 + 0.0918566i) q^{33} +(-0.726682 + 4.12122i) q^{34} +(-1.34730 - 7.64090i) q^{35} -12.7023 q^{36} +(5.93629 - 1.32683i) q^{37} +0.573978 q^{38} +(-0.336152 - 1.90641i) q^{39} +(-2.68479 + 15.2262i) q^{40} +(6.85117 - 2.49362i) q^{41} +(-2.06418 - 1.73205i) q^{42} -1.46791 q^{43} +(-2.61334 - 2.19285i) q^{44} +(3.64543 + 6.31407i) q^{45} +(-14.2763 - 5.19615i) q^{46} +(-1.39053 + 2.40847i) q^{47} +(1.15270 + 1.99654i) q^{48} +(0.414878 + 2.35289i) q^{49} +(3.35844 - 1.22237i) q^{50} +(0.286989 - 0.497079i) q^{51} +(18.8366 - 15.8058i) q^{52} +(0.783119 - 0.657115i) q^{53} +(4.85844 + 1.76833i) q^{54} +(-0.340022 + 1.92836i) q^{55} +(3.24897 - 18.4258i) q^{56} +(-0.0739780 - 0.0269258i) q^{57} +(-3.09627 + 2.59808i) q^{58} +(-3.64543 + 3.05888i) q^{59} +(1.93969 - 3.35965i) q^{60} +(-2.26604 + 0.824773i) q^{61} +(1.68732 + 9.56926i) q^{62} +(-4.41147 - 7.64090i) q^{63} +(0.819078 - 1.41868i) q^{64} +(-13.2626 - 4.82721i) q^{65} +(0.340022 + 0.588936i) q^{66} +(8.69846 + 7.29888i) q^{67} +7.29086 q^{68} +(1.59627 + 1.33943i) q^{69} +(-18.4611 + 6.71929i) q^{70} +(-2.03074 + 11.5169i) q^{71} +(3.05303 + 17.3146i) q^{72} -2.92127 q^{73} +(-5.91875 - 14.2195i) q^{74} -0.490200 q^{75} +(-0.173648 - 0.984808i) q^{76} +(0.411474 - 2.33359i) q^{77} +(-4.60607 + 1.67647i) q^{78} +(-6.55690 - 5.50190i) q^{79} +16.8084 q^{80} +(6.07398 + 5.09667i) q^{81} +(-9.23055 - 15.9878i) q^{82} +(11.3576 + 4.13381i) q^{83} +(-2.34730 + 4.06564i) q^{84} +(-2.09240 - 3.62414i) q^{85} +(0.645430 + 3.66041i) q^{86} +(0.520945 - 0.189608i) q^{87} +(-2.36097 + 4.08931i) q^{88} +(-1.45677 + 1.22237i) q^{89} +(14.1420 - 11.8666i) q^{90} +(16.0496 + 5.84159i) q^{91} +(-4.59627 + 26.0667i) q^{92} +(0.231429 - 1.31250i) q^{93} +(6.61721 + 2.40847i) q^{94} +(-0.439693 + 0.368946i) q^{95} +(1.22281 - 1.02606i) q^{96} +(-7.49273 + 12.9778i) q^{97} +(5.68479 - 2.06910i) q^{98} +(0.386659 + 2.19285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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