LMFDB - Embedded newform 189.2.h.b.46.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(37,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, degree $2$, not 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.5
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	189.46
Dual form			189.2.h.b.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38687 q^{2} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-0.138560 - 2.64212i) q^{7} +4.05086 q^{8} +O(q^{10})$	\(q+2.38687 q^{2} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-0.138560 - 2.64212i) q^{7} +4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +(-0.676857 - 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(-0.330725 - 6.30640i) q^{14} +2.27458 q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(1.31415 - 2.27617i) q^{23} +(-1.76573 - 3.05833i) q^{25} +(-1.74958 - 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} +(-0.521720 + 0.903646i) q^{29} +3.27458 q^{31} -2.67259 q^{32} +(-3.95060 + 6.84263i) q^{34} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(-2.63342 - 4.56121i) q^{38} +(-5.91601 + 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +(-2.50244 - 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} -3.97914 q^{47} +(-6.96160 + 0.732185i) q^{49} +(-4.21456 - 7.29984i) q^{50} +(-2.71001 - 4.69388i) q^{52} +(3.22743 - 5.59008i) q^{53} +3.95402 q^{55} +(-0.561287 - 10.7029i) q^{56} +(-1.24528 + 2.15688i) q^{58} +12.2140 q^{59} +0.559734 q^{61} +7.81600 q^{62} -10.9283 q^{64} +4.28200 q^{65} +12.8118 q^{67} +(-6.11928 + 10.5989i) q^{68} +(16.4353 + 8.37348i) q^{70} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(12.9791 + 22.4805i) q^{74} +(-4.07903 - 7.06509i) q^{76} +(-3.00371 + 1.95078i) q^{77} +0.767677 q^{79} +(-3.32187 + 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(-5.18258 + 8.97649i) q^{86} +(-2.74185 - 4.74903i) q^{88} +(-3.20356 - 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +(4.85859 - 8.41533i) q^{92} -9.49769 q^{94} +6.44514 q^{95} +(-4.14143 + 7.17316i) q^{97} +(-16.6164 + 1.74763i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.38687			1.68777			0.843886	−	0.536523i	$-0.180263\pi$
$2$	2.38687			1.68777			0.843886	+	0.536523i	$0.180263\pi$
$3$		0			0
$3$		0			0
$4$	3.69714			1.84857
$5$	−1.46043	+	2.52954i	−0.653125	+	1.13125i	0.329235	+	0.944248i	$0.393209\pi$
$5$	−1.46043	+	2.52954i	−0.653125	+	1.13125i	−0.982360	+	0.186998i	$0.940124\pi$
$6$		0			0
$7$	−0.138560	−	2.64212i	−0.0523708	−	0.998628i
$7$	−0.138560	−	2.64212i	−0.0523708	−	0.998628i
$8$	4.05086			1.43219
$9$		0			0
$10$	−3.48586	+	6.03769i	−1.10233	+	1.90929i
$11$	−0.676857	−	1.17235i	−0.204080	−	0.353477i	0.745759	−	0.666216i	$-0.232087\pi$
$11$	−0.676857	−	1.17235i	−0.204080	−	0.353477i	−0.949839	+	0.312738i	$0.898754\pi$
$12$		0			0
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	0.746291	−	0.665620i	$-0.231833\pi$
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	−0.949589	+	0.313497i	$0.898499\pi$
$14$	−0.330725	−	6.30640i	−0.0883899	−	1.68546i
$15$		0			0
$16$	2.27458			0.568645
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	−0.993899	−	0.110297i	$-0.964820\pi$
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	0.592469	+	0.805593i	$0.298153\pi$
$18$		0			0
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	0.711268	−	0.702921i	$-0.248121\pi$
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	−0.964381	+	0.264516i	$0.914788\pi$
$20$	−5.39943	+	9.35209i	−1.20735	+	2.09119i
$21$		0			0
$22$	−1.61557	−	2.79825i	−0.344441	−	0.596589i
$23$	1.31415	−	2.27617i	0.274019	−	0.474614i	−0.695868	−	0.718169i	$-0.744980\pi$
$23$	1.31415	−	2.27617i	0.274019	−	0.474614i	0.969887	+	0.243555i	$0.0783136\pi$
$24$		0			0
$25$	−1.76573	−	3.05833i	−0.353146	−	0.611666i
$26$	−1.74958	−	3.03036i	−0.343121	−	0.594302i
$27$		0			0
$28$	−0.512277	−	9.76830i	−0.0968112	−	1.84603i
$29$	−0.521720	+	0.903646i	−0.0968810	+	0.167803i	−0.910392	−	0.413747i	$-0.864220\pi$
$29$	−0.521720	+	0.903646i	−0.0968810	+	0.167803i	0.813511	+	0.581549i	$0.197553\pi$
$30$		0			0
$31$	3.27458			0.588132			0.294066	−	0.955785i	$-0.404991\pi$
$31$	3.27458			0.588132			0.294066	+	0.955785i	$0.404991\pi$
$32$	−2.67259			−0.472452
$33$		0			0
$34$	−3.95060	+	6.84263i	−0.677521	+	1.17350i
$35$	6.88572	+	3.50815i	1.16390	+	0.592985i
$36$		0			0
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$	−2.63342	−	4.56121i	−0.427197	−	0.739926i
$39$		0			0
$40$	−5.91601	+	10.2468i	−0.935403	+	1.62017i
$41$	0.904289	+	1.56627i	0.141226	+	0.244611i	0.927959	−	0.372683i	$-0.121562\pi$
$41$	0.904289	+	1.56627i	0.141226	+	0.244611i	−0.786732	+	0.617294i	$0.788229\pi$
$42$		0			0
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	−0.982731	−	0.185038i	$-0.940759\pi$
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	0.651613	+	0.758551i	$0.274093\pi$
$44$	−2.50244	−	4.33435i	−0.377257	−	0.653428i
$45$		0			0
$46$	3.13670	−	5.43292i	0.462481	−	0.801041i
$47$	−3.97914			−0.580417			−0.290209	−	0.956963i	$-0.593725\pi$
$47$	−3.97914			−0.580417			−0.290209	+	0.956963i	$0.593725\pi$
$48$		0			0
$49$	−6.96160	+	0.732185i	−0.994515	+	0.104598i
$50$	−4.21456	−	7.29984i	−0.596029	−	1.03235i
$51$		0			0
$52$	−2.71001	−	4.69388i	−0.375811	−	0.650924i
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	−0.554612	−	0.832109i	$-0.687133\pi$
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	0.997934	+	0.0642533i	$0.0204666\pi$
$54$		0			0
$55$	3.95402			0.533160
$56$	−0.561287	−	10.7029i	−0.0750052	−	1.43023i
$57$		0			0
$58$	−1.24528	+	2.15688i	−0.163513	+	0.283213i
$59$	12.2140			1.59013			0.795064	−	0.606526i	$-0.207437\pi$
$59$	12.2140			1.59013			0.795064	+	0.606526i	$0.207437\pi$
$60$		0			0
$61$	0.559734			0.0716666			0.0358333	−	0.999358i	$-0.488591\pi$
$61$	0.559734			0.0716666			0.0358333	+	0.999358i	$0.488591\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	4.28200			0.531117
$66$		0			0
$67$	12.8118			1.56521			0.782603	−	0.622521i	$-0.213891\pi$
$67$	12.8118			1.56521			0.782603	+	0.622521i	$0.213891\pi$
$68$	−6.11928	+	10.5989i	−0.742072	+	1.28531i
$69$		0			0
$70$	16.4353	+	8.37348i	1.96439	+	1.00082i
$71$	−12.9177			−1.53305			−0.766525	−	0.642214i	$-0.778016\pi$
$71$	−12.9177			−1.53305			−0.766525	+	0.642214i	$0.778016\pi$
$72$		0			0
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$	12.9791	+	22.4805i	1.50879	+	2.61331i
$75$		0			0
$76$	−4.07903	−	7.06509i	−0.467897	−	0.810422i
$77$	−3.00371	+	1.95078i	−0.342304	+	0.222312i
$78$		0			0
$79$	0.767677			0.0863704			0.0431852	−	0.999067i	$-0.486249\pi$
$79$	0.767677			0.0863704			0.0431852	+	0.999067i	$0.486249\pi$
$80$	−3.32187	+	5.75365i	−0.371397	+	0.643278i
$81$		0			0
$82$	2.15842	+	3.73849i	0.238358	+	0.412847i
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	−0.806974	−	0.590587i	$-0.798896\pi$
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	0.914950	+	0.403567i	$0.132230\pi$
$84$		0			0
$85$	−4.83443	−	8.37348i	−0.524368	−	0.908232i
$86$	−5.18258	+	8.97649i	−0.558852	+	0.967960i
$87$		0			0
$88$	−2.74185	−	4.74903i	−0.292283	−	0.506248i
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	0.644777	−	0.764371i	$-0.276950\pi$
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	−0.984353	+	0.176208i	$0.943617\pi$
$90$		0			0
$91$	−3.25286	+	2.11259i	−0.340992	+	0.221460i
$92$	4.85859	−	8.41533i	0.506543	−	0.877359i
$93$		0			0
$94$	−9.49769			−0.979612
$95$	6.44514			0.661258
$96$		0			0
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	−0.995988	−	0.0894847i	$-0.971478\pi$
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	0.575490	+	0.817809i	$0.304811\pi$
$98$	−16.6164	+	1.74763i	−1.67851	+	0.176537i
$99$		0			0
$100$	−6.52815	−	11.3071i	−0.652815	−	1.13071i
$101$	−8.11331	−	14.0527i	−0.807305	−	1.39829i	−0.914724	−	0.404079i	$-0.867592\pi$
$101$	−8.11331	−	14.0527i	−0.807305	−	1.39829i	0.107419	−	0.994214i	$-0.465741\pi$
$102$		0			0
$103$	1.11342	−	1.92849i	0.109708	−	0.190020i	−0.805944	−	0.591992i	$-0.798342\pi$
$103$	1.11342	−	1.92849i	0.109708	−	0.190020i	0.915652	+	0.401972i	$0.131675\pi$
$104$	−2.96929	−	5.14295i	−0.291162	−	0.504308i
$105$		0			0
$106$	7.70346	−	13.3428i	0.748226	−	1.29597i
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	0.884501	+	0.466537i	$0.154499\pi$
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	−0.0382175	+	0.999269i	$0.512168\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$	9.43773			0.899852
$111$		0			0
$112$	−0.315166	−	6.00972i	−0.0297804	−	0.567865i
$113$	0.844555	+	1.46281i	0.0794491	+	0.137610i	0.903012	−	0.429615i	$-0.141351\pi$
$113$	0.844555	+	1.46281i	0.0794491	+	0.137610i	−0.823563	+	0.567224i	$0.808017\pi$
$114$		0			0
$115$	3.83845	+	6.64839i	0.357937	+	0.619966i
$116$	−1.92887	+	3.34091i	−0.179092	+	0.310196i
$117$		0			0
$118$	29.1532			2.68377
$119$	7.80372	+	3.97585i	0.715366	+	0.364466i
$120$		0			0
$121$	4.58373	−	7.93925i	0.416703	−	0.721750i
$122$	1.33601			0.120957
$123$		0			0
$124$	12.1066			1.08720
$125$	−4.28942			−0.383657
$126$		0			0
$127$	−3.96918			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$127$	−3.96918			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$128$	−20.7392			−1.83310
$129$		0			0
$130$	10.2206			0.896403
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	−0.725844	−	0.687860i	$-0.758550\pi$
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	0.958626	+	0.284669i	$0.0918837\pi$
$132$		0			0
$133$	−4.89611	+	3.17982i	−0.424547	+	0.275725i
$134$	30.5800			2.64171
$135$		0			0
$136$	−6.70473	+	11.6129i	−0.574925	+	0.995800i
$137$	−3.74772	−	6.49124i	−0.320189	−	0.554584i	0.660338	−	0.750969i	$-0.270413\pi$
$137$	−3.74772	−	6.49124i	−0.320189	−	0.554584i	−0.980527	+	0.196385i	$0.937080\pi$
$138$		0			0
$139$	7.03285	+	12.1812i	0.596518	+	1.03320i	0.993331	+	0.115300i	$0.0367830\pi$
$139$	7.03285	+	12.1812i	0.596518	+	1.03320i	−0.396812	+	0.917900i	$0.629884\pi$
$140$	25.4575	+	12.9701i	2.15155	+	1.09618i
$141$		0			0
$142$	−30.8329			−2.58744
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$		0			0
$145$	−1.52388	−	2.63943i	−0.126551	−	0.219193i
$146$	12.4779	−	21.6123i	1.03268	−	1.78865i
$147$		0			0
$148$	20.1041	+	34.8212i	1.65254	+	2.86229i
$149$	1.08986	−	1.88769i	0.0892846	−	0.154645i	−0.817924	−	0.575326i	$-0.804875\pi$
$149$	1.08986	−	1.88769i	0.0892846	−	0.154645i	0.907209	+	0.420680i	$0.138209\pi$
$150$		0			0
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	−0.996486	−	0.0837595i	$-0.973307\pi$
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	0.425705	−	0.904862i	$-0.360026\pi$
$152$	−4.46929	−	7.74103i	−0.362507	−	0.627880i
$153$		0			0
$154$	−7.16946	+	4.65626i	−0.577731	+	0.375212i
$155$	−4.78231	+	8.28320i	−0.384124	+	0.665322i
$156$		0			0
$157$	2.96623			0.236731			0.118365	−	0.992970i	$-0.462235\pi$
$157$	2.96623			0.236731			0.118365	+	0.992970i	$0.462235\pi$
$158$	1.83234			0.145773
$159$		0			0
$160$	3.90314	−	6.76043i	0.308570	−	0.534459i
$161$	−6.19601	−	3.15675i	−0.488314	−	0.248787i
$162$		0			0
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	0.858317	−	0.513120i	$-0.171511\pi$
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	−0.873534	+	0.486764i	$0.838177\pi$
$164$	3.34329	+	5.79074i	0.261067	+	0.452181i
$165$		0			0
$166$	2.34798	−	4.06682i	0.182239	−	0.315646i
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	0.689606	−	0.724185i	$-0.257784\pi$
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	−0.971965	+	0.235124i	$0.924450\pi$
$168$		0			0
$169$	5.42542	−	9.39710i	0.417340	−	0.722854i
$170$	−11.5392	−	19.9864i	−0.885013	−	1.53289i
$171$		0			0
$172$	−8.02756	+	13.9041i	−0.612096	+	1.06018i
$173$	4.05508			0.308302			0.154151	−	0.988047i	$-0.450736\pi$
$173$	4.05508			0.308302			0.154151	+	0.988047i	$0.450736\pi$
$174$		0			0
$175$	−7.83582	+	5.08903i	−0.592332	+	0.384695i
$176$	−1.53957	−	2.66661i	−0.116049	−	0.201003i
$177$		0			0
$178$	−7.64647	−	13.2441i	−0.573127	−	0.992685i
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$	−7.76415	+	5.04248i	−0.575517	+	0.373774i
$183$		0			0
$184$	5.32343	−	9.22045i	0.392448	−	0.679740i
$185$	−31.7657			−2.33546
$186$		0			0
$187$	4.48117			0.327695
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	−8.28714			−0.599637			−0.299818	−	0.953996i	$-0.596926\pi$
$191$	−8.28714			−0.599637			−0.299818	+	0.953996i	$0.596926\pi$
$192$		0			0
$193$	−18.7848			−1.35216			−0.676082	−	0.736827i	$-0.736323\pi$
$193$	−18.7848			−1.35216			−0.676082	+	0.736827i	$0.736323\pi$
$194$	−9.88504	+	17.1214i	−0.709705	+	1.22924i
$195$		0			0
$196$	−25.7380	+	2.70699i	−1.83843	+	0.193357i
$197$	−5.99634			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$197$	−5.99634			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$198$		0			0
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	−0.489221	−	0.872160i	$-0.662719\pi$
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	0.999923	−	0.0124022i	$-0.00394785\pi$
$200$	−7.15272	−	12.3889i	−0.505773	−	0.876025i
$201$		0			0
$202$	−19.3654	−	33.5419i	−1.36255	−	2.36000i
$203$	2.45983	+	1.25324i	0.172646	+	0.0879601i
$204$		0			0
$205$	−5.28261			−0.368954
$206$	2.65758	−	4.60306i	0.185162	−	0.320710i
$207$		0			0
$208$	−1.66727	−	2.88780i	−0.115604	−	0.200233i
$209$	−1.49354	+	2.58690i	−0.103311	+	0.178939i
$210$		0			0
$211$	−6.92418	−	11.9930i	−0.476680	−	0.825634i	0.522963	−	0.852356i	$-0.324827\pi$
$211$	−6.92418	−	11.9930i	−0.476680	−	0.825634i	−0.999643	+	0.0267212i	$0.991493\pi$
$212$	11.9323	−	20.6673i	0.819512	−	1.41944i
$213$		0			0
$214$	20.8947	+	36.1907i	1.42833	+	2.47395i
$215$	−6.34204	−	10.9847i	−0.432523	−	0.749153i
$216$		0			0
$217$	−0.453726	−	8.65184i	−0.0308010	−	0.587325i
$218$	−18.6156	+	32.2431i	−1.26081	+	2.18378i
$219$		0			0
$220$	14.6186			0.985584
$221$	4.85287			0.326439
$222$		0			0
$223$	2.33756	−	4.04878i	0.156535	−	0.271126i	−0.777082	−	0.629399i	$-0.783301\pi$
$223$	2.33756	−	4.04878i	0.156535	−	0.271126i	0.933617	+	0.358273i	$0.116634\pi$
$224$	0.370314	+	7.06130i	0.0247427	+	0.471803i
$225$		0			0
$226$	2.01584	+	3.49154i	0.134092	+	0.232254i
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	0.982097	+	0.188376i	$0.0603222\pi$
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	−0.327910	+	0.944709i	$0.606344\pi$
$228$		0			0
$229$	−14.0364	+	24.3118i	−0.927552	+	1.60657i	−0.140148	+	0.990131i	$0.544758\pi$
$229$	−14.0364	+	24.3118i	−0.927552	+	1.60657i	−0.787404	+	0.616437i	$0.788575\pi$
$230$	9.16188	+	15.8688i	0.604116	+	1.04636i
$231$		0			0
$232$	−2.11342	+	3.66054i	−0.138753	+	0.240326i
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	0.998517	−	0.0544448i	$-0.0173389\pi$
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	−0.546409	+	0.837518i	$0.684006\pi$
$234$		0			0
$235$	5.81127	−	10.0654i	0.379085	−	0.656595i
$236$	45.1569			2.93947
$237$		0			0
$238$	18.6265	+	9.48983i	1.20737	+	0.615135i
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	0.629834	−	0.776730i	$-0.283123\pi$
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	−0.987585	+	0.157087i	$0.949790\pi$
$240$		0			0
$241$	11.5849	+	20.0656i	0.746247	+	1.29254i	0.949610	+	0.313435i	$0.101480\pi$
$241$	11.5849	+	20.0656i	0.746247	+	1.29254i	−0.203362	+	0.979104i	$0.565187\pi$
$242$	10.9408	−	18.9499i	0.703299	−	1.21815i
$243$		0			0
$244$	2.06942			0.132481
$245$	8.31486	−	18.6790i	0.531217	−	1.19336i
$246$		0			0
$247$	−1.61743	+	2.80147i	−0.102915	+	0.178253i
$248$	13.2649			0.842320
$249$		0			0
$250$	−10.2383			−0.647525
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$	−9.47392			−0.594447
$255$		0			0
$256$	−27.6452			−1.72782
$257$	5.18798	−	8.98585i	0.323618	−	0.560522i	−0.657614	−	0.753355i	$-0.728434\pi$
$257$	5.18798	−	8.98585i	0.323618	−	0.560522i	0.981232	+	0.192833i	$0.0617676\pi$
$258$		0			0
$259$	24.1311	−	15.6721i	1.49944	−	0.973820i
$260$	15.8312			0.981807
$261$		0			0
$262$	6.35937	−	11.0148i	0.392883	−	0.680494i
$263$	−9.56654	−	16.5697i	−0.589898	−	1.02173i	−0.994245	−	0.107128i	$-0.965835\pi$
$263$	−9.56654	−	16.5697i	−0.589898	−	1.02173i	0.404347	−	0.914605i	$-0.367499\pi$
$264$		0			0
$265$	9.42689	+	16.3279i	0.579090	+	1.00301i
$266$	−11.6864	+	7.58981i	−0.716538	+	0.465361i
$267$		0			0
$268$	47.3669			2.89340
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	−0.699311	−	0.714818i	$-0.746510\pi$
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	0.968706	+	0.248212i	$0.0798430\pi$
$270$		0			0
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	−0.997744	−	0.0671321i	$-0.978615\pi$
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	0.440734	−	0.897638i	$-0.354718\pi$
$272$	−3.76474	+	6.52073i	−0.228271	+	0.395377i
$273$		0			0
$274$	−8.94531	−	15.4937i	−0.540406	−	0.936010i
$275$	−2.39029	+	4.14011i	−0.144140	+	0.249658i
$276$		0			0
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	0.779101	−	0.626899i	$-0.215676\pi$
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	−0.932460	+	0.361272i	$0.882343\pi$
$278$	16.7865	+	29.0750i	1.00679	+	1.74381i
$279$		0			0
$280$	27.8931	+	14.2110i	1.66693	+	0.849270i
$281$	0.853180	−	1.47775i	0.0508964	−	0.0881552i	−0.839455	−	0.543430i	$-0.817125\pi$
$281$	0.853180	−	1.47775i	0.0508964	−	0.0881552i	0.890351	+	0.455274i	$0.150459\pi$
$282$		0			0
$283$	−12.4883			−0.742352			−0.371176	−	0.928562i	$-0.621045\pi$
$283$	−12.4883			−0.742352			−0.371176	+	0.928562i	$0.621045\pi$
$284$	−47.7586			−2.83395
$285$		0			0
$286$	−2.36843	+	4.10224i	−0.140048	+	0.242571i
$287$	4.01299	−	2.60626i	0.236879	−	0.153843i
$288$		0			0
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$	−3.63729	−	6.29997i	−0.213589	−	0.369947i
$291$		0			0
$292$	19.3276	−	33.4764i	1.13106	−	1.95906i
$293$	2.60202	+	4.50684i	0.152012	+	0.263292i	0.931967	−	0.362543i	$-0.118091\pi$
$293$	2.60202	+	4.50684i	0.152012	+	0.263292i	−0.779955	+	0.625835i	$0.784758\pi$
$294$		0			0
$295$	−17.8377	+	30.8959i	−1.03855	+	1.79883i
$296$	22.0275	+	38.1527i	1.28032	+	2.21758i
$297$		0			0
$298$	2.60135	−	4.50566i	0.150692	−	0.261006i
$299$	−3.85309			−0.222830
$300$		0			0
$301$	10.2373	+	5.21571i	0.590067	+	0.300628i
$302$	−16.7412	−	28.9966i	−0.963347	−	1.66857i
$303$		0			0
$304$	−2.50953	−	4.34663i	−0.143931	−	0.249297i
$305$	−0.817453	+	1.41587i	−0.0468072	+	0.0810725i
$306$		0			0
$307$	5.00136			0.285442			0.142721	−	0.989763i	$-0.454415\pi$
$307$	5.00136			0.285442			0.142721	+	0.989763i	$0.454415\pi$
$308$	−11.1051	+	7.21231i	−0.632774	+	0.410960i
$309$		0			0
$310$	−11.4147	+	19.7709i	−0.648313	+	1.12291i
$311$	32.3968			1.83706			0.918528	−	0.395355i	$-0.129379\pi$
$311$	32.3968			1.83706			0.918528	+	0.395355i	$0.129379\pi$
$312$		0			0
$313$	1.51907			0.0858629			0.0429315	−	0.999078i	$-0.486330\pi$
$313$	1.51907			0.0858629			0.0429315	+	0.999078i	$0.486330\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	21.5089			1.20806			0.604029	−	0.796962i	$-0.293561\pi$
$317$	21.5089			1.20806			0.604029	+	0.796962i	$0.293561\pi$
$318$		0			0
$319$	1.41252			0.0790860
$320$	15.9600	−	27.6436i	0.892193	−	1.54532i
$321$		0			0
$322$	−14.7891	−	7.53475i	−0.824162	−	0.419895i
$323$	7.30441			0.406428
$324$		0			0
$325$	−2.58856	+	4.48352i	−0.143588	+	0.248701i
$326$	−0.463715	−	0.803178i	−0.0256828	−	0.0444839i
$327$		0			0
$328$	3.66315	+	6.34476i	0.202263	+	0.350330i
$329$	0.551350	+	10.5134i	0.0303969	+	0.579621i
$330$		0			0
$331$	19.4780			1.07061			0.535305	−	0.844659i	$-0.320197\pi$
$331$	19.4780			1.07061			0.535305	+	0.844659i	$0.320197\pi$
$332$	3.63691	−	6.29931i	0.199601	−	0.345719i
$333$		0			0
$334$	−8.70942	−	15.0852i	−0.476558	−	0.825423i
$335$	−18.7107	+	32.4079i	−1.02228	+	1.77063i
$336$		0			0
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	0.967316	−	0.253575i	$-0.0816063\pi$
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	−0.703260	+	0.710933i	$0.748273\pi$
$338$	12.9498	−	22.4296i	0.704374	−	1.22001i
$339$		0			0
$340$	−17.8736	−	30.9580i	−0.969332	−	1.67893i
$341$	−2.21642	−	3.83896i	−0.120026	−	0.207891i
$342$		0			0
$343$	2.89912	+	18.2919i	0.156538	+	0.987672i
$344$	−8.79558	+	15.2344i	−0.474226	+	0.821383i
$345$		0			0
$346$	9.67895			0.520344
$347$	−2.02604			−0.108763			−0.0543817	−	0.998520i	$-0.517319\pi$
$347$	−2.02604			−0.108763			−0.0543817	+	0.998520i	$0.517319\pi$
$348$		0			0
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	−0.561346	−	0.827581i	$-0.689716\pi$
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	0.997379	+	0.0723497i	$0.0230498\pi$
$350$	−18.7031	+	12.1469i	−0.999722	+	0.649276i
$351$		0			0
$352$	1.80896	+	3.13321i	0.0964180	+	0.167001i
$353$	8.53072	+	14.7756i	0.454045	+	0.786428i	0.998633	−	0.0522753i	$-0.0166473\pi$
$353$	8.53072	+	14.7756i	0.454045	+	0.786428i	−0.544588	+	0.838704i	$0.683314\pi$
$354$		0			0
$355$	18.8655	−	32.6759i	1.00127	−	1.73426i
$356$	−11.8440	−	20.5144i	−0.627731	−	1.08726i
$357$		0			0
$358$	−12.6323	+	21.8798i	−0.667639	+	1.15639i
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	0.824215	−	0.566277i	$-0.191617\pi$
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	−0.902518	+	0.430652i	$0.858283\pi$
$360$		0			0
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$	−46.8570			−2.46275
$363$		0			0
$364$	−12.0263	+	7.81056i	−0.630349	+	0.409385i
$365$	15.2695	+	26.4475i	0.799240	+	1.38432i
$366$		0			0
$367$	5.07874	+	8.79664i	0.265108	+	0.459181i	0.967592	−	0.252519i	$-0.0812590\pi$
$367$	5.07874	+	8.79664i	0.265108	+	0.459181i	−0.702484	+	0.711700i	$0.747926\pi$
$368$	2.98914	−	5.17733i	0.155819	−	0.269887i
$369$		0			0
$370$	−75.8207			−3.94173
$371$	−15.2168	−	7.75270i	−0.790019	−	0.402500i
$372$		0			0
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	−0.320904	−	0.947112i	$-0.603987\pi$
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	0.980675	−	0.195645i	$-0.0626799\pi$
$374$	10.6960			0.553075
$375$		0			0
$376$	−16.1189			−0.831271
$377$	1.52969			0.0787829
$378$		0			0
$379$	9.85497			0.506216			0.253108	−	0.967438i	$-0.418547\pi$
$379$	9.85497			0.506216			0.253108	+	0.967438i	$0.418547\pi$
$380$	23.8286			1.22238
$381$		0			0
$382$	−19.7803			−1.01205
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	0.271419	+	0.962461i	$0.412507\pi$
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	−0.969225	+	0.246175i	$0.920826\pi$
$384$		0			0
$385$	−0.547870	−	10.4470i	−0.0279220	−	0.532428i
$386$	−44.8370			−2.28214
$387$		0			0
$388$	−15.3114	+	26.5202i	−0.777321	+	1.34636i
$389$	2.09223	+	3.62385i	0.106080	+	0.183736i	0.914179	−	0.405311i	$-0.132837\pi$
$389$	2.09223	+	3.62385i	0.106080	+	0.183736i	−0.808099	+	0.589047i	$0.799503\pi$
$390$		0			0
$391$	4.35019	+	7.53475i	0.219999	+	0.381049i
$392$	−28.2005	+	2.96598i	−1.42434	+	0.149805i
$393$		0			0
$394$	−14.3125			−0.721053
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$		0			0
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$	17.1958	−	29.7840i	0.861948	−	1.49294i
$399$		0			0
$400$	−4.01629	−	6.95642i	−0.200815	−	0.347821i
$401$	−3.42402	+	5.93057i	−0.170987	+	0.296158i	−0.938765	−	0.344557i	$-0.888029\pi$
$401$	−3.42402	+	5.93057i	−0.170987	+	0.296158i	0.767778	+	0.640716i	$0.221362\pi$
$402$		0			0
$403$	−2.40027	−	4.15739i	−0.119566	−	0.207095i
$404$	−29.9961	−	51.9547i	−1.49236	−	2.58485i
$405$		0			0
$406$	5.87130	+	2.99132i	0.291388	+	0.148457i
$407$	7.36113	−	12.7499i	0.364878	−	0.631987i
$408$		0			0
$409$	−18.2698			−0.903384			−0.451692	−	0.892174i	$-0.649179\pi$
$409$	−18.2698			−0.903384			−0.451692	+	0.892174i	$0.649179\pi$
$410$	−12.6089			−0.622709
$411$		0			0
$412$	4.11646	−	7.12991i	0.202803	−	0.351265i
$413$	−1.69237	−	32.2709i	−0.0832763	−	1.58795i
$414$		0			0
$415$	2.87328	+	4.97666i	0.141044	+	0.244295i
$416$	1.95901	+	3.39311i	0.0960485	+	0.166361i
$417$		0			0
$418$	−3.56490	+	6.17458i	−0.174365	+	0.302009i
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	−0.998366	−	0.0571410i	$-0.981802\pi$
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	0.449698	−	0.893181i	$-0.351532\pi$
$420$		0			0
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	−0.492232	−	0.870464i	$-0.663819\pi$
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	0.999960	−	0.00894684i	$-0.00284791\pi$
$422$	−16.5271	−	28.6258i	−0.804527	−	1.39348i
$423$		0			0
$424$	13.0739	−	22.6446i	0.634923	−	1.09972i
$425$	11.6901			0.567053
$426$		0			0
$427$	−0.0775568	−	1.47888i	−0.00375324	−	0.0715682i
$428$	32.3649	+	56.0577i	1.56442	+	2.70965i
$429$		0			0
$430$	−15.1376	−	26.2191i	−0.730001	−	1.26440i
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	−0.512370	−	0.858765i	$-0.671232\pi$
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	0.999897	+	0.0143427i	$0.00456557\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$	−1.08299	−	20.6508i	−0.0519850	−	0.991270i
$435$		0			0
$436$	−28.8346	+	49.9431i	−1.38093	+	2.39184i
$437$	−5.79956			−0.277431
$438$		0			0
$439$	−35.4781			−1.69328			−0.846639	−	0.532168i	$-0.821377\pi$
$439$	−35.4781			−1.69328			−0.846639	+	0.532168i	$0.821377\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	19.2063			0.912517			0.456258	−	0.889847i	$-0.349189\pi$
$443$	19.2063			0.912517			0.456258	+	0.889847i	$0.349189\pi$
$444$		0			0
$445$	18.7143			0.887144
$446$	5.57946	−	9.66391i	0.264195	−	0.457599i
$447$		0			0
$448$	1.51422	+	28.8738i	0.0715404	+	1.36416i
$449$	29.6082			1.39730			0.698648	−	0.715465i	$-0.253785\pi$
$449$	29.6082			1.39730			0.698648	+	0.715465i	$0.253785\pi$
$450$		0			0
$451$	1.22415	−	2.12029i	0.0576429	−	0.0998405i
$452$	3.12244	+	5.40823i	0.146867	+	0.254382i
$453$		0			0
$454$	23.5257	+	40.7478i	1.10412	+	1.91239i
$455$	−0.593314	−	11.3136i	−0.0278150	−	0.530388i
$456$		0			0
$457$	−9.56196			−0.447290			−0.223645	−	0.974671i	$-0.571796\pi$
$457$	−9.56196			−0.447290			−0.223645	+	0.974671i	$0.571796\pi$
$458$	−33.5031	+	58.0290i	−1.56550	+	2.71152i
$459$		0			0
$460$	14.1913	+	24.5800i	0.661673	+	1.14605i
$461$	−10.9187	+	18.9118i	−0.508536	+	0.880809i	0.491416	+	0.870925i	$0.336480\pi$
$461$	−10.9187	+	18.9118i	−0.508536	+	0.880809i	−0.999951	+	0.00988416i	$0.996854\pi$
$462$		0			0
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	0.991631	+	0.129102i	$0.0412094\pi$
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	−0.384010	+	0.923329i	$0.625457\pi$
$464$	−1.18670	+	2.05542i	−0.0550909	+	0.0954203i
$465$		0			0
$466$	16.4721	+	28.5305i	0.763054	+	1.32165i
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	0.913758	+	0.406258i	$0.133167\pi$
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	−0.105049	+	0.994467i	$0.533500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$	13.8707	−	24.0248i	0.639809	−	1.10818i
$471$		0			0
$472$	49.4772			2.27737
$473$	5.87861			0.270299
$474$		0			0
$475$	−3.89623	+	6.74848i	−0.178771	+	0.309641i
$476$	28.8515	+	14.6993i	1.32240	+	0.673741i
$477$		0			0
$478$	−13.2010	−	22.8649i	−0.603801	−	1.04581i
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	−0.974662	−	0.223684i	$-0.928192\pi$
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	0.293615	−	0.955924i	$-0.405142\pi$
$480$		0			0
$481$	7.97172	−	13.8074i	0.363479	−	0.629565i
$482$	27.6516	+	47.8939i	1.25949	+	2.18151i
$483$		0			0
$484$	16.9467	−	29.3525i	0.770304	−	1.33421i
$485$	−12.0965	−	20.9518i	−0.549276	−	0.951374i
$486$		0			0
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	0.491283	+	0.871000i	$0.336528\pi$
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	−0.999950	+	0.0100365i	$0.996805\pi$
$488$	2.26740			0.102640
$489$		0			0
$490$	19.8465	−	44.5843i	0.896572	−	2.01411i
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	−0.925493	−	0.378765i	$-0.876349\pi$
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	0.134726	−	0.990883i	$-0.456984\pi$
$492$		0			0
$493$	−1.72704	−	2.99132i	−0.0777819	−	0.134722i
$494$	−3.86060	+	6.68675i	−0.173696	+	0.300851i
$495$		0			0
$496$	7.44830			0.334438
$497$	1.78988	+	34.1302i	0.0802871	+	1.53095i
$498$		0			0
$499$	4.46760	−	7.73811i	0.199997	−	0.346405i	−0.748530	−	0.663101i	$-0.769240\pi$
$499$	4.46760	−	7.73811i	0.199997	−	0.346405i	0.948527	+	0.316696i	$0.102573\pi$
$500$	−15.8586			−0.709217
$501$		0			0
$502$	18.5794			0.829241
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$	−8.49239			−0.377533
$507$		0			0
$508$	−14.6746			−0.651082
$509$	−14.0555	+	24.3449i	−0.623000	+	1.07907i	0.365924	+	0.930645i	$0.380753\pi$
$509$	−14.0555	+	24.3449i	−0.623000	+	1.07907i	−0.988924	+	0.148423i	$0.952580\pi$
$510$		0			0
$511$	−24.6479	−	12.5576i	−1.09036	−	0.555517i
$512$	−24.5070			−1.08307
$513$		0			0
$514$	12.3830	−	21.4480i	0.546192	−	0.946033i
$515$	3.25214	+	5.63287i	0.143306	+	0.248214i
$516$		0			0
$517$	2.69331	+	4.66495i	0.118452	+	0.205164i
$518$	57.5979	−	37.4074i	2.53071	−	1.64359i
$519$		0			0
$520$	17.3458			0.760662
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	−0.943797	−	0.330524i	$-0.892774\pi$
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	0.758141	+	0.652090i	$0.226108\pi$
$522$		0			0
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	0.956339	+	0.292259i	$0.0944069\pi$
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	−0.225066	+	0.974344i	$0.572260\pi$
$524$	9.85035	−	17.0613i	0.430315	−	0.745327i
$525$		0			0
$526$	−22.8341	−	39.5498i	−0.995613	−	1.72445i
$527$	−5.41988	+	9.38751i	−0.236094	+	0.408926i
$528$		0			0
$529$	8.04603	+	13.9361i	0.349827	+	0.605919i
$530$	22.5008	+	38.9725i	0.977371	+	1.69286i
$531$		0			0
$532$	−18.1016	+	11.7562i	−0.784806	+	0.509698i
$533$	1.32569	−	2.29616i	0.0574220	−	0.0994579i
$534$		0			0
$535$	−51.1387			−2.21092
$536$	51.8987			2.24168
$537$		0			0
$538$	10.5461	−	18.2665i	0.454677	−	0.787523i
$539$	5.57039	+	7.66586i	0.239934	+	0.330192i
$540$		0			0
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$	−21.8865	−	37.9085i	−0.940106	−	1.62831i
$543$		0			0
$544$	4.42350	−	7.66173i	0.189656	−	0.328494i
$545$	−22.7803	−	39.4567i	−0.975802	−	1.69014i
$546$		0			0
$547$	−2.88599	+	4.99869i	−0.123396	+	0.213728i	−0.921105	−	0.389315i	$-0.872712\pi$
$547$	−2.88599	+	4.99869i	−0.123396	+	0.213728i	0.797709	+	0.603043i	$0.206045\pi$
$548$	−13.8558	−	23.9990i	−0.591892	−	1.02519i
$549$		0			0
$550$	−5.70532	+	9.88190i	−0.243276	+	0.421366i
$551$	2.30244			0.0980874
$552$		0			0
$553$	−0.106369	−	2.02829i	−0.00452329	−	0.0862518i
$554$	−6.09227	−	10.5521i	−0.258836	−	0.448317i
$555$		0			0
$556$	26.0014	+	45.0358i	1.10271	+	1.90994i
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	0.258661	+	0.965968i	$0.416719\pi$
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	−0.965883	+	0.258977i	$0.916614\pi$
$558$		0			0
$559$	6.36623			0.269263
$560$	15.6621	+	7.97956i	0.661845	+	0.337198i
$561$		0			0
$562$	2.03643	−	3.52720i	0.0859015	−	0.148786i
$563$	−2.19131			−0.0923528			−0.0461764	−	0.998933i	$-0.514704\pi$
$563$	−2.19131			−0.0923528			−0.0461764	+	0.998933i	$0.514704\pi$
$564$		0			0
$565$	−4.93367			−0.207561
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	−18.9860			−0.795936			−0.397968	−	0.917399i	$-0.630284\pi$
$569$	−18.9860			−0.795936			−0.397968	+	0.917399i	$0.630284\pi$
$570$		0			0
$571$	−21.7380			−0.909709			−0.454854	−	0.890566i	$-0.650309\pi$
$571$	−21.7380			−0.909709			−0.454854	+	0.890566i	$0.650309\pi$
$572$	−3.66858	+	6.35417i	−0.153391	+	0.265681i
$573$		0			0
$574$	9.57847	−	6.22081i	0.399798	−	0.259652i
$575$	−9.28172			−0.387074
$576$		0			0
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$	7.21083	+	12.4895i	0.299931	+	0.519496i
$579$		0			0
$580$	−5.63398	−	9.75835i	−0.233938	−	0.405193i
$581$	−4.63803	−	2.36299i	−0.192418	−	0.0980333i
$582$		0			0
$583$	−8.73804			−0.361893
$584$	21.1767	−	36.6792i	0.876299	−	1.51780i
$585$		0			0
$586$	6.21069	+	10.7572i	0.256561	+	0.444377i
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	−0.611886	−	0.790946i	$-0.709589\pi$
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	0.990922	+	0.134436i	$0.0429222\pi$
$588$		0			0
$589$	−3.61282	−	6.25759i	−0.148864	−	0.257840i
$590$	−42.5763	+	73.7444i	−1.75284	+	3.03601i
$591$		0			0
$592$	12.3685	+	21.4230i	0.508344	+	0.880478i
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	−0.996577	−	0.0826662i	$-0.973656\pi$
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$594$		0			0
$595$	−21.4539	+	13.9334i	−0.879524	+	0.571213i
$596$	4.02936	−	6.97905i	0.165049	−	0.285873i
$597$		0			0
$598$	−9.19682			−0.376086
$599$	−0.402823			−0.0164589			−0.00822945	−	0.999966i	$-0.502620\pi$
$599$	−0.402823			−0.0164589			−0.00822945	+	0.999966i	$0.502620\pi$
$600$		0			0
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	−0.495268	−	0.868740i	$-0.664930\pi$
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	0.999985	−	0.00545577i	$-0.00173663\pi$
$602$	24.4351	+	12.4492i	0.995899	+	0.507392i
$603$		0			0
$604$	−25.9313	−	44.9143i	−1.05513	−	1.82754i
$605$	13.3885	+	23.1895i	0.544318	+	0.942787i
$606$		0			0
$607$	−12.0348	+	20.8449i	−0.488479	+	0.846070i	−0.999912	−	0.0132531i	$-0.995781\pi$
$607$	−12.0348	+	20.8449i	−0.488479	+	0.846070i	0.511434	+	0.859323i	$0.329115\pi$
$608$	2.94865	+	5.10721i	0.119584	+	0.207125i
$609$		0			0
$610$	−1.95115	+	3.37950i	−0.0789999	+	0.136832i
$611$	2.91672	+	5.05190i	0.117998	+	0.204378i
$612$		0			0
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$	11.9376			0.481762
$615$		0			0
$616$	−12.1676	+	7.90233i	−0.490246	+	0.318394i
$617$	20.9315	+	36.2544i	0.842669	+	1.45955i	0.887630	+	0.460558i	$0.152350\pi$
$617$	20.9315	+	36.2544i	0.842669	+	1.45955i	−0.0449604	+	0.998989i	$0.514316\pi$
$618$		0			0
$619$	−7.41095	−	12.8361i	−0.297871	−	0.515928i	0.677777	−	0.735267i	$-0.262943\pi$
$619$	−7.41095	−	12.8361i	−0.297871	−	0.515928i	−0.975649	+	0.219339i	$0.929610\pi$
$620$	−17.6809	+	30.6242i	−0.710081	+	1.22990i
$621$		0			0
$622$	77.3270			3.10053
$623$	−14.2165	+	9.23301i	−0.569572	+	0.369913i
$624$		0			0
$625$	15.0930	−	26.1419i	0.603722	−	1.04568i
$626$	3.62582			0.144917
$627$		0			0
$628$	10.9666			0.437614
$629$	−36.0007			−1.43544
$630$		0			0
$631$	−21.0294			−0.837169			−0.418585	−	0.908178i	$-0.637474\pi$
$631$	−21.0294			−0.837169			−0.418585	+	0.908178i	$0.637474\pi$
$632$	3.10975			0.123699
$633$		0			0
$634$	51.3388			2.03893
$635$	5.79673	−	10.0402i	0.230036	−	0.398434i
$636$		0			0
$637$	6.03244	+	8.30173i	0.239014	+	0.328926i
$638$	3.37150			0.133479
$639$		0			0
$640$	30.2882	−	52.4607i	1.19725	−	2.07369i
$641$	5.96592	+	10.3333i	0.235640	+	0.408140i	0.959458	−	0.281850i	$-0.0909481\pi$
$641$	5.96592	+	10.3333i	0.235640	+	0.408140i	−0.723819	+	0.689990i	$0.757615\pi$
$642$		0			0
$643$	−19.9678	−	34.5852i	−0.787452	−	1.36391i	−0.927524	−	0.373765i	$-0.878067\pi$
$643$	−19.9678	−	34.5852i	−0.787452	−	1.36391i	0.140072	−	0.990141i	$-0.455267\pi$
$644$	−22.9075	−	11.6710i	−0.902683	−	0.459900i
$645$		0			0
$646$	17.4347			0.685958
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	−0.875582	−	0.483070i	$-0.839522\pi$
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	0.856142	+	0.516741i	$0.172855\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$	−6.17856	+	10.7016i	−0.242343	+	0.419751i
$651$		0			0
$652$	−0.718272	−	1.24408i	−0.0281297	−	0.0487221i
$653$	11.3573	−	19.6715i	0.444447	−	0.769804i	−0.553567	−	0.832805i	$-0.686734\pi$
$653$	11.3573	−	19.6715i	0.444447	−	0.769804i	0.998014	+	0.0630004i	$0.0200669\pi$
$654$		0			0
$655$	7.78211	+	13.4790i	0.304072	+	0.526668i
$656$	2.05688	+	3.56262i	0.0803076	+	0.139097i
$657$		0			0
$658$	1.31600	+	25.0940i	0.0513031	+	0.978267i
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	−0.201220	−	0.979546i	$-0.564491\pi$
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	0.948922	−	0.315512i	$-0.102176\pi$
$660$		0			0
$661$	33.9258			1.31956			0.659780	−	0.751459i	$-0.270649\pi$
$661$	33.9258			1.31956			0.659780	+	0.751459i	$0.270649\pi$
$662$	46.4915			1.80694
$663$		0			0
$664$	3.98486	−	6.90198i	0.154642	−	0.267849i
$665$	−0.893040	−	17.0288i	−0.0346306	−	0.660350i
$666$		0			0
$667$	1.37124	+	2.37505i	0.0530944	+	0.0919623i
$668$	−13.4905	−	23.3662i	−0.521962	−	0.904064i
$669$		0			0
$670$	−44.6601	+	77.3535i	−1.72537	+	2.98843i
$671$	−0.378860	−	0.656205i	−0.0146257	−	0.0253325i
$672$		0			0
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	0.368626	+	0.929578i	$0.379828\pi$
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	−0.989351	+	0.145549i	$0.953505\pi$
$674$	11.5702	+	20.0401i	0.445666	+	0.771916i
$675$		0			0
$676$	20.0585	−	34.7424i	0.771483	−	1.33625i
$677$	37.9684			1.45924			0.729622	−	0.683850i	$-0.239696\pi$
$677$	37.9684			1.45924			0.729622	+	0.683850i	$0.239696\pi$
$678$		0			0
$679$	19.5262	+	9.94823i	0.749346	+	0.381778i
$680$	−19.5836	−	33.9198i	−0.750997	−	1.30076i
$681$		0			0
$682$	−5.29031	−	9.16309i	−0.202577	−	0.350873i
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$	6.91982	+	43.6605i	0.264200	+	1.66696i
$687$		0			0
$688$	−4.93877	+	8.55420i	−0.188289	+	0.326126i
$689$	−9.46285			−0.360506
$690$		0			0
$691$	2.69148			0.102389			0.0511943	−	0.998689i	$-0.483697\pi$
$691$	2.69148			0.102389			0.0511943	+	0.998689i	$0.483697\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	−41.0840			−1.55841
$696$		0			0
$697$	−5.98689			−0.226770
$698$	19.4429	−	33.6761i	0.735924	−	1.27466i
$699$		0			0
$700$	−28.9702	+	18.8149i	−1.09497	+	0.711135i
$701$	11.8515			0.447625			0.223813	−	0.974632i	$-0.428150\pi$
$701$	11.8515			0.447625			0.223813	+	0.974632i	$0.428150\pi$
$702$		0			0
$703$	11.9988	−	20.7826i	0.452544	−	0.783829i
$704$	7.39689	+	12.8118i	0.278781	+	0.482862i
$705$		0			0
$706$	20.3617	+	35.2675i	0.766323	+	1.32731i
$707$	−36.0047	+	23.3835i	−1.35410	+	0.879427i
$708$		0			0
$709$	−41.0333			−1.54104			−0.770520	−	0.637416i	$-0.780003\pi$
$709$	−41.0333			−1.54104			−0.770520	+	0.637416i	$0.780003\pi$
$710$	45.0294	−	77.9931i	1.68992	−	2.92703i
$711$		0			0
$712$	−12.9772	−	22.4771i	−0.486339	−	0.842364i
$713$	4.30328	−	7.45351i	0.161159	−	0.279136i
$714$		0			0
$715$	−2.89830	−	5.02001i	−0.108390	−	0.187738i
$716$	−19.5669	+	33.8908i	−0.731248	+	1.26656i
$717$		0			0
$718$	−3.54123	−	6.13359i	−0.132158	−	0.228904i
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	0.602516	−	0.798107i	$-0.294165\pi$
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	−0.992439	+	0.122741i	$0.960832\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$	16.8644	−	29.2100i	0.627628	−	1.08708i
$723$		0			0
$724$	−72.5792			−2.69738
$725$	3.68487			0.136853
$726$		0			0
$727$	1.32165	−	2.28917i	0.0490173	−	0.0849005i	−0.840476	−	0.541849i	$-0.817724\pi$
$727$	1.32165	−	2.28917i	0.0490173	−	0.0849005i	0.889493	+	0.456949i	$0.151058\pi$
$728$	−13.1769	+	8.55782i	−0.488368	+	0.317174i
$729$		0			0
$730$	36.4462	+	63.1267i	1.34893	+	2.33642i
$731$	−7.18756	−	12.4492i	−0.265841	−	0.460451i
$732$		0			0
$733$	−7.07446	+	12.2533i	−0.261301	+	0.452587i	−0.966588	−	0.256335i	$-0.917485\pi$
$733$	−7.07446	+	12.2533i	−0.261301	+	0.452587i	0.705287	+	0.708922i	$0.250818\pi$
$734$	12.1223	+	20.9964i	0.447442	+	0.774992i
$735$		0			0
$736$	−3.51218	+	6.08327i	−0.129461	+	0.224232i
$737$	−8.67174	−	15.0199i	−0.319428	−	0.553265i
$738$		0			0
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	−0.973595	−	0.228282i	$-0.926689\pi$
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	0.684495	+	0.729017i	$0.260023\pi$
$740$	−117.442			−4.31727
$741$		0			0
$742$	−36.3206	−	18.5047i	−1.33337	−	0.679328i
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	0.605022	−	0.796208i	$-0.293164\pi$
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	−0.992048	+	0.125861i	$0.959831\pi$
$744$		0			0
$745$	3.18333	+	5.51368i	0.116628	+	0.202006i
$746$	30.4142	−	52.6789i	1.11354	−	1.92871i
$747$		0			0
$748$	16.5675			0.605768
$749$	38.8480	−	25.2301i	1.41947	−	0.921888i
$750$		0			0
$751$	−6.51848	+	11.2903i	−0.237863	+	0.411990i	−0.960101	−	0.279654i	$-0.909780\pi$
$751$	−6.51848	+	11.2903i	−0.237863	+	0.411990i	0.722238	+	0.691644i	$0.243113\pi$
$752$	−9.05088			−0.330052
$753$		0			0
$754$	3.65116			0.132968
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$	23.5225			0.854377
$759$		0			0
$760$	26.1084			0.947050
$761$	−3.02038	+	5.23146i	−0.109489	+	0.189640i	−0.915563	−	0.402174i	$-0.868255\pi$
$761$	−3.02038	+	5.23146i	−0.109489	+	0.189640i	0.806074	+	0.591814i	$0.201588\pi$
$762$		0			0
$763$	36.7719	+	18.7346i	1.33123	+	0.678238i
$764$	−30.6388			−1.10847
$765$		0			0
$766$	−32.5959	+	56.4577i	−1.17774	+	2.03990i
$767$	−8.95288	−	15.5068i	−0.323270	−	0.559920i
$768$		0			0
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	0.867968	−	0.496619i	$-0.165425\pi$
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	−0.864069	+	0.503373i	$0.832092\pi$
$770$	−1.30769	−	24.9356i	−0.0471260	−	0.898617i
$771$		0			0
$772$	−69.4503			−2.49957
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	0.299316	+	0.954154i	$0.403241\pi$
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	−0.975980	+	0.217861i	$0.930092\pi$
$774$		0			0
$775$	−5.78202	−	10.0148i	−0.207696	−	0.359741i
$776$	−16.7763	+	29.0575i	−0.602235	+	1.04310i
$777$		0			0
$778$	4.99388	+	8.64965i	0.179039	+	0.310105i
$779$	1.99539	−	3.45612i	0.0714923	−	0.123828i
$780$		0			0
$781$	8.74345	+	15.1441i	0.312865	+	0.541898i
$782$	10.3833	+	17.9845i	0.371307	+	0.643123i
$783$		0			0
$784$	−15.8347	+	1.66541i	−0.565526	+	0.0594791i
$785$	−4.33198	+	7.50321i	−0.154615	+	0.267801i
$786$		0			0
$787$	30.8135			1.09838			0.549191	−	0.835697i	$-0.314936\pi$
$787$	30.8135			1.09838			0.549191	+	0.835697i	$0.314936\pi$
$788$	−22.1693			−0.789750
$789$		0			0
$790$	−2.67601	+	4.63499i	−0.0952083	+	0.164906i
$791$	3.74791	−	2.43410i	0.133260	−	0.0865468i
$792$		0			0
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$	36.6037	+	63.3994i	1.29902	+	2.24996i
$795$		0			0
$796$	26.6355	−	46.1340i	0.944070	−	1.63518i
$797$	17.9792	+	31.1408i	0.636855	+	1.10306i	0.986119	+	0.166040i	$0.0530981\pi$
$797$	17.9792	+	31.1408i	0.636855	+	1.10306i	−0.349264	+	0.937024i	$0.613569\pi$
$798$		0			0
$799$	6.58602	−	11.4073i	0.232997	−	0.403562i
$800$	4.71907	+	8.17367i	0.166844	+	0.288983i
$801$		0			0
$802$	−8.17268	+	14.1555i	−0.288587	+	0.499848i
$803$	−14.1537			−0.499472
$804$		0			0
$805$	17.0340	−	11.0628i	0.600369	−	0.389914i
$806$	−5.72914	−	9.92315i	−0.201800	−	0.349528i
$807$		0			0
$808$	−32.8659	−	56.9254i	−1.15622	−	2.00263i
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	−0.288511	−	0.957477i	$-0.593160\pi$
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	0.973455	−	0.228880i	$-0.0735065\pi$
$810$		0			0
$811$	−28.2811			−0.993082			−0.496541	−	0.868013i	$-0.665397\pi$
$811$	−28.2811			−0.993082			−0.496541	+	0.868013i	$0.665397\pi$
$812$	9.09435	+	4.63340i	0.319149	+	0.162601i
$813$		0			0
$814$	17.5701	−	30.4322i	0.615830	−	1.06665i
$815$	1.13492			0.0397544
$816$		0			0
$817$	9.58227			0.335241
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	−41.5834			−1.45127			−0.725635	−	0.688080i	$-0.758454\pi$
$821$	−41.5834			−1.45127			−0.725635	+	0.688080i	$0.758454\pi$
$822$		0			0
$823$	8.45998			0.294896			0.147448	−	0.989070i	$-0.452894\pi$
$823$	8.45998			0.294896			0.147448	+	0.989070i	$0.452894\pi$
$824$	4.51029	−	7.81205i	0.157123	−	0.272146i
$825$		0			0
$826$	−4.03947	−	77.0263i	−0.140551	−	2.68009i
$827$	−44.2823			−1.53985			−0.769923	−	0.638137i	$-0.779706\pi$
$827$	−44.2823			−1.53985			−0.769923	+	0.638137i	$0.779706\pi$
$828$		0			0
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$	6.85813	+	11.8786i	0.238049	+	0.412314i
$831$		0			0
$832$	8.01045	+	13.8745i	0.277712	+	0.481012i
$833$	9.42339	−	21.1693i	0.326501	−	0.733471i
$834$		0			0
$835$	21.3158			0.737665
$836$	−5.52185	+	9.56412i	−0.190977	+	0.330782i
$837$		0			0
$838$	−26.8068	−	46.4308i	−0.926027	−	1.60393i
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	0.488945	+	0.872314i	$0.337382\pi$
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	−0.999919	+	0.0127182i	$0.995952\pi$
$840$		0			0
$841$	13.9556	+	24.1718i	0.481228	+	0.833512i
$842$	24.8657	−	43.0687i	0.856929	−	1.48424i
$843$		0			0
$844$	−25.5997	−	44.3400i	−0.881178	−	1.52624i
$845$	15.8469	+	27.4477i	0.545151	+	0.944228i
$846$		0			0
$847$	−21.6116	−	11.0107i	−0.742583	−	0.378332i
$848$	7.34105	−	12.7151i	0.252093	−	0.436638i
$849$		0			0
$850$	27.9027			0.957055
$851$	28.5839			0.979844
$852$		0			0
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	0.484124	+	0.875000i	$0.339139\pi$
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	−0.999834	+	0.0182366i	$0.994195\pi$
$854$	−0.185118	−	3.52990i	−0.00633460	−	0.120791i
$855$		0			0
$856$	35.4613	+	61.4208i	1.21204	+	2.09932i
$857$	18.5447	+	32.1204i	0.633475	+	1.09721i	0.986836	+	0.161724i	$0.0517053\pi$
$857$	18.5447	+	32.1204i	0.633475	+	1.09721i	−0.353361	+	0.935487i	$0.614961\pi$
$858$		0			0
$859$	1.89166	−	3.27646i	0.0645427	−	0.111791i	−0.831948	−	0.554853i	$-0.812774\pi$
$859$	1.89166	−	3.27646i	0.0645427	−	0.111791i	0.896491	+	0.443062i	$0.146108\pi$
$860$	−23.4474	−	40.6121i	−0.799551	−	1.38486i
$861$		0			0
$862$	24.1583	−	41.8434i	0.822835	−	1.42519i
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	0.862368	−	0.506282i	$-0.168981\pi$
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	−0.869637	+	0.493691i	$0.835647\pi$
$864$		0			0
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$	−51.7388			−1.75815
$867$		0			0
$868$	−1.67749	−	31.9871i	−0.0569378	−	1.08571i
$869$	−0.519608	−	0.899987i	−0.0176265	−	0.0305300i
$870$		0			0
$871$	−9.39105	−	16.2658i	−0.318203	−	0.551145i
$872$	−31.5933	+	54.7212i	−1.06988	+	1.85309i
$873$		0			0
$874$	−13.8428			−0.468240
$875$	0.594342	+	11.3332i	0.0200924	+	0.383130i
$876$		0			0
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	−0.945291	−	0.326228i	$-0.894222\pi$
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	0.755167	+	0.655532i	$0.227556\pi$
$878$	−84.6816			−2.85786
$879$		0			0
$880$	8.99374			0.303179
$881$	35.4810			1.19538			0.597692	−	0.801726i	$-0.296084\pi$
$881$	35.4810			1.19538			0.597692	+	0.801726i	$0.296084\pi$
$882$		0			0
$883$	−5.30092			−0.178390			−0.0891952	−	0.996014i	$-0.528429\pi$
$883$	−5.30092			−0.178390			−0.0891952	+	0.996014i	$0.528429\pi$
$884$	17.9418			0.603447
$885$		0			0
$886$	45.8428			1.54012
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.260767	−	0.965402i	$-0.416025\pi$
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.705679	−	0.708532i	$-0.250642\pi$
$888$		0			0
$889$	0.549971	+	10.4871i	0.0184454	+	0.351725i
$890$	44.6686			1.49730
$891$		0			0
$892$	8.64231	−	14.9689i	0.289366	−	0.501197i
$893$	4.39016	+	7.60398i	0.146911	+	0.254458i
$894$		0			0
$895$	−15.4585	−	26.7749i	−0.516720	−	0.894985i
$896$	2.87363	+	54.7955i	0.0960011	+	1.83059i
$897$		0			0
$898$	70.6708			2.35832
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$		0			0
$901$	10.6837	+	18.5047i	0.355925	+	0.616480i
$902$	2.92188	−	5.06085i	0.0972881	−	0.168508i
$903$		0			0
$904$	3.42117	+	5.92565i	0.113787	+	0.197084i
$905$	28.6700	−	49.6579i	0.953023	−	1.65068i
$906$		0			0
$907$	−10.4486	−	18.0975i	−0.346939	−	0.600917i	0.638765	−	0.769402i	$-0.279446\pi$
$907$	−10.4486	−	18.0975i	−0.346939	−	0.600917i	−0.985704	+	0.168485i	$0.946112\pi$
$908$	36.4402	+	63.1163i	1.20931	+	2.09459i
$909$		0			0
$910$	−1.41616	−	27.0040i	−0.0469454	−	0.895173i
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	−0.990639	−	0.136508i	$-0.956412\pi$
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	0.613539	+	0.789665i	$0.289746\pi$
$912$		0			0
$913$	−2.66332			−0.0881430
$914$	−22.8231			−0.754923
$915$		0			0
$916$	−51.8946	+	89.8841i	−1.71465	+	2.96986i
$917$	−12.5618	−	6.40002i	−0.414828	−	0.211347i
$918$		0			0
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	0.990339	+	0.138664i	$0.0442809\pi$
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	−0.375083	+	0.926991i	$0.622386\pi$
$920$	15.5490	+	26.9317i	0.512636	+	0.887911i
$921$		0			0
$922$	−26.0616	+	45.1399i	−0.858292	+	1.48660i
$923$	9.46870	+	16.4003i	0.311666	+	0.539822i
$924$		0			0
$925$	19.2031	−	33.2607i	0.631394	−	1.09361i
$926$	31.2070	+	54.0521i	1.02553	+	1.77626i
$927$		0			0
$928$	1.39434	−	2.41508i	0.0457716	−	0.0792787i
$929$	−5.66725			−0.185937			−0.0929683	−	0.995669i	$-0.529636\pi$
$929$	−5.66725			−0.185937			−0.0929683	+	0.995669i	$0.529636\pi$
$930$		0			0
$931$	9.07987	+	12.4955i	0.297581	+	0.409524i
$932$	25.5145	+	44.1923i	0.835754	+	1.44757i
$933$		0			0
$934$	41.7138	+	72.2503i	1.36492	+	2.36410i
$935$	−6.54444	+	11.3353i	−0.214026	+	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$	−4.23717	−	80.7961i	−0.138349	−	2.63809i
$939$		0			0
$940$	21.4851	−	37.2133i	0.700766	−	1.21376i
$941$	−20.4552			−0.666819			−0.333410	−	0.942782i	$-0.608199\pi$
$941$	−20.4552			−0.666819			−0.333410	+	0.942782i	$0.608199\pi$
$942$		0			0
$943$	4.75348			0.154795
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	4.76687			0.154902			0.0774512	−	0.996996i	$-0.475322\pi$
$947$	4.76687			0.154902			0.0774512	+	0.996996i	$0.475322\pi$
$948$		0			0
$949$	−15.3277			−0.497558
$950$	−9.29980	+	16.1077i	−0.301725	+	0.522604i
$951$		0			0
$952$	31.6118	+	16.1056i	1.02454	+	0.521986i
$953$	48.9412			1.58536			0.792680	−	0.609638i	$-0.208685\pi$
$953$	48.9412			1.58536			0.792680	+	0.609638i	$0.208685\pi$
$954$		0			0
$955$	12.1028	−	20.9627i	0.391638	−	0.678337i
$956$	−20.4478	−	35.4166i	−0.661328	−	1.14545i
$957$		0			0
$958$	−35.5773	−	61.6217i	−1.14945	−	1.99091i
$959$	−16.6313	+	10.8013i	−0.537054	+	0.348794i
$960$		0			0
$961$	−20.2771			−0.654101
$962$	19.0275	−	32.9565i	0.613470	−	1.06256i
$963$		0			0
$964$	42.8309	+	74.1854i	1.37949	+	2.38935i
$965$	27.4340	−	47.5171i	0.883132	−	1.52963i
$966$		0			0
$967$	−2.95856	−	5.12438i	−0.0951409	−	0.164789i	0.814526	−	0.580126i	$-0.196997\pi$
$967$	−2.95856	−	5.12438i	−0.0951409	−	0.164789i	−0.909667	+	0.415337i	$0.863664\pi$
$968$	18.5680	−	32.1608i	0.596799	−	1.03369i
$969$		0			0
$970$	−28.8729	−	50.0093i	−0.927052	−	1.60570i
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	−0.999200	+	0.0399914i	$0.987267\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$	−26.7933	+	46.4074i	−0.858513	+	1.48699i
$975$		0			0
$976$	1.27316			0.0407528
$977$	−22.8455			−0.730893			−0.365447	−	0.930832i	$-0.619084\pi$
$977$	−22.8455			−0.730893			−0.365447	+	0.930832i	$0.619084\pi$
$978$		0			0
$979$	−4.33670	+	7.51139i	−0.138602	+	0.240065i
$980$	30.7412	−	69.0589i	0.981992	−	2.20601i
$981$		0			0
$982$	−41.8232	−	72.4400i	−1.33463	−	2.31165i
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	0.501315	−	0.865265i	$-0.332850\pi$
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	−0.999999	+	0.00151933i	$0.999516\pi$
$984$		0			0
$985$	8.75726	−	15.1680i	0.279029	−	0.483293i
$986$	−4.12221	−	7.13988i	−0.131278	−	0.227380i
$987$		0			0
$988$	−5.97988	+	10.3574i	−0.190245	+	0.329514i
$989$	5.70679	+	9.88444i	0.181465	+	0.314307i
$990$		0			0
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	−0.804927	−	0.593374i	$-0.797796\pi$
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	0.916340	+	0.400400i	$0.131129\pi$
$992$	−8.75161			−0.277864
$993$		0			0
$994$	4.27221	+	81.4642i	0.135506	+	2.58389i
$995$	21.0429	+	36.4474i	0.667105	+	1.15546i
$996$		0			0
$997$	10.6439	+	18.4358i	0.337095	+	0.583866i	0.983885	−	0.178802i	$-0.0572222\pi$
$997$	10.6439	+	18.4358i	0.337095	+	0.583866i	−0.646790	+	0.762668i	$0.723889\pi$
$998$	10.6636	−	18.4698i	0.337549	−	0.584653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.h.b.46.5		10
3.2	odd	2		63.2.h.b.25.1	yes	10
4.3	odd	2		3024.2.q.i.2881.2		10
7.2	even	3		189.2.g.b.100.1		10
7.3	odd	6		1323.2.f.f.883.1		10
7.4	even	3		1323.2.f.e.883.1		10
7.5	odd	6		1323.2.g.f.667.1		10
7.6	odd	2		1323.2.h.f.802.5		10
9.2	odd	6		567.2.e.f.487.5		10
9.4	even	3		189.2.g.b.172.1		10
9.5	odd	6		63.2.g.b.4.5	✓	10
9.7	even	3		567.2.e.e.487.1		10
12.11	even	2		1008.2.q.i.529.4		10
21.2	odd	6		63.2.g.b.16.5	yes	10
21.5	even	6		441.2.g.f.79.5		10
21.11	odd	6		441.2.f.e.295.5		10
21.17	even	6		441.2.f.f.295.5		10
21.20	even	2		441.2.h.f.214.1		10
28.23	odd	6		3024.2.t.i.289.4		10
36.23	even	6		1008.2.t.i.193.3		10
36.31	odd	6		3024.2.t.i.1873.4		10
63.2	odd	6		567.2.e.f.163.5		10
63.4	even	3		1323.2.f.e.442.1		10
63.5	even	6		441.2.h.f.373.1		10
63.11	odd	6		3969.2.a.z.1.1		5
63.13	odd	6		1323.2.g.f.361.1		10
63.16	even	3		567.2.e.e.163.1		10
63.23	odd	6		63.2.h.b.58.1	yes	10
63.25	even	3		3969.2.a.bc.1.5		5
63.31	odd	6		1323.2.f.f.442.1		10
63.32	odd	6		441.2.f.e.148.5		10
63.38	even	6		3969.2.a.ba.1.1		5
63.40	odd	6		1323.2.h.f.226.5		10
63.41	even	6		441.2.g.f.67.5		10
63.52	odd	6		3969.2.a.bb.1.5		5
63.58	even	3	inner	189.2.h.b.37.5		10
63.59	even	6		441.2.f.f.148.5		10
84.23	even	6		1008.2.t.i.961.3		10
252.23	even	6		1008.2.q.i.625.4		10
252.247	odd	6		3024.2.q.i.2305.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	9.5	odd	6
63.2.g.b.16.5	yes	10	21.2	odd	6
63.2.h.b.25.1	yes	10	3.2	odd	2
63.2.h.b.58.1	yes	10	63.23	odd	6
189.2.g.b.100.1		10	7.2	even	3
189.2.g.b.172.1		10	9.4	even	3
189.2.h.b.37.5		10	63.58	even	3	inner
189.2.h.b.46.5		10	1.1	even	1	trivial
441.2.f.e.148.5		10	63.32	odd	6
441.2.f.e.295.5		10	21.11	odd	6
441.2.f.f.148.5		10	63.59	even	6
441.2.f.f.295.5		10	21.17	even	6
441.2.g.f.67.5		10	63.41	even	6
441.2.g.f.79.5		10	21.5	even	6
441.2.h.f.214.1		10	21.20	even	2
441.2.h.f.373.1		10	63.5	even	6
567.2.e.e.163.1		10	63.16	even	3
567.2.e.e.487.1		10	9.7	even	3
567.2.e.f.163.5		10	63.2	odd	6
567.2.e.f.487.5		10	9.2	odd	6
1008.2.q.i.529.4		10	12.11	even	2
1008.2.q.i.625.4		10	252.23	even	6
1008.2.t.i.193.3		10	36.23	even	6
1008.2.t.i.961.3		10	84.23	even	6
1323.2.f.e.442.1		10	63.4	even	3
1323.2.f.e.883.1		10	7.4	even	3
1323.2.f.f.442.1		10	63.31	odd	6
1323.2.f.f.883.1		10	7.3	odd	6
1323.2.g.f.361.1		10	63.13	odd	6
1323.2.g.f.667.1		10	7.5	odd	6
1323.2.h.f.226.5		10	63.40	odd	6
1323.2.h.f.802.5		10	7.6	odd	2
3024.2.q.i.2305.2		10	252.247	odd	6
3024.2.q.i.2881.2		10	4.3	odd	2
3024.2.t.i.289.4		10	28.23	odd	6
3024.2.t.i.1873.4		10	36.31	odd	6
3969.2.a.z.1.1		5	63.11	odd	6
3969.2.a.ba.1.1		5	63.38	even	6
3969.2.a.bb.1.5		5	63.52	odd	6
3969.2.a.bc.1.5		5	63.25	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.38687 q^{2} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-0.138560 - 2.64212i) q^{7} +4.05086 q^{8} +O(q^{10})\)	\(q+2.38687 q^{2} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-0.138560 - 2.64212i) q^{7} +4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +(-0.676857 - 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(-0.330725 - 6.30640i) q^{14} +2.27458 q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(1.31415 - 2.27617i) q^{23} +(-1.76573 - 3.05833i) q^{25} +(-1.74958 - 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} +(-0.521720 + 0.903646i) q^{29} +3.27458 q^{31} -2.67259 q^{32} +(-3.95060 + 6.84263i) q^{34} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(-2.63342 - 4.56121i) q^{38} +(-5.91601 + 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +(-2.50244 - 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} -3.97914 q^{47} +(-6.96160 + 0.732185i) q^{49} +(-4.21456 - 7.29984i) q^{50} +(-2.71001 - 4.69388i) q^{52} +(3.22743 - 5.59008i) q^{53} +3.95402 q^{55} +(-0.561287 - 10.7029i) q^{56} +(-1.24528 + 2.15688i) q^{58} +12.2140 q^{59} +0.559734 q^{61} +7.81600 q^{62} -10.9283 q^{64} +4.28200 q^{65} +12.8118 q^{67} +(-6.11928 + 10.5989i) q^{68} +(16.4353 + 8.37348i) q^{70} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(12.9791 + 22.4805i) q^{74} +(-4.07903 - 7.06509i) q^{76} +(-3.00371 + 1.95078i) q^{77} +0.767677 q^{79} +(-3.32187 + 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(-5.18258 + 8.97649i) q^{86} +(-2.74185 - 4.74903i) q^{88} +(-3.20356 - 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +(4.85859 - 8.41533i) q^{92} -9.49769 q^{94} +6.44514 q^{95} +(-4.14143 + 7.17316i) q^{97} +(-16.6164 + 1.74763i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more