LMFDB - Embedded newform 570.2.u.j.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 + 2.42499i$ of defining polynomial
Character	$\chi$	$=$	570.541
Dual form			570.2.u.j.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.284816 + 0.493316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.284816 + 0.493316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.173648 - 0.984808i) q^{10} +(-0.953304 - 1.65117i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.59946 - 3.02030i) q^{13} +(-0.535279 - 0.194826i) q^{14} +(0.939693 - 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.808506 - 4.58527i) q^{17} +1.00000 q^{18} +(-1.57962 + 4.06261i) q^{19} +1.00000 q^{20} +(-0.0989156 - 0.560978i) q^{21} +(1.46055 - 1.22554i) q^{22} +(1.76686 - 0.643084i) q^{23} +(0.939693 + 0.342020i) q^{24} +(0.766044 + 0.642788i) q^{25} +(2.34938 - 4.06924i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.0989156 - 0.560978i) q^{28} +(0.782583 - 4.43825i) q^{29} +(0.500000 + 0.866025i) q^{30} +(3.44569 - 5.96811i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.79163 + 0.652099i) q^{33} +(4.37521 - 1.59245i) q^{34} +(0.436364 - 0.366153i) q^{35} +(0.173648 + 0.984808i) q^{36} -6.61134 q^{37} +(-4.27519 - 0.850158i) q^{38} +4.69876 q^{39} +(0.173648 + 0.984808i) q^{40} +(2.55140 - 2.14088i) q^{41} +(0.535279 - 0.194826i) q^{42} +(-6.29766 - 2.29216i) q^{43} +(1.46055 + 1.22554i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.940125 + 1.62835i) q^{46} +(1.88720 - 10.7028i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(3.33776 + 5.78117i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.56671 + 2.99282i) q^{51} +(4.41539 + 1.60707i) q^{52} +(-7.96555 + 2.89922i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(0.331079 + 1.87764i) q^{55} +0.569632 q^{56} +(-1.40134 - 4.12750i) q^{57} +4.50672 q^{58} +(0.205101 + 1.16319i) q^{59} +(-0.766044 + 0.642788i) q^{60} +(-0.352216 + 0.128196i) q^{61} +(6.47578 + 2.35699i) q^{62} +(0.436364 + 0.366153i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.34938 + 4.06924i) q^{65} +(-0.331079 + 1.87764i) q^{66} +(0.00191067 - 0.0108359i) q^{67} +(2.32800 + 4.03222i) q^{68} +(-0.940125 + 1.62835i) q^{69} +(0.436364 + 0.366153i) q^{70} +(4.16738 + 1.51680i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(-10.4802 + 8.79396i) q^{73} +(-1.14805 - 6.51090i) q^{74} -1.00000 q^{75} +(0.0948636 - 4.35787i) q^{76} +1.08607 q^{77} +(0.815931 + 4.62737i) q^{78} +(-11.8218 + 9.91966i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(2.55140 + 2.14088i) q^{82} +(3.95026 - 6.84206i) q^{83} +(0.284816 + 0.493316i) q^{84} +(-0.808506 + 4.58527i) q^{85} +(1.16376 - 6.60002i) q^{86} +(2.25336 + 3.90293i) q^{87} +(-0.953304 + 1.65117i) q^{88} +(-12.0772 - 10.1340i) q^{89} +(-0.939693 - 0.342020i) q^{90} +(2.51515 - 0.915439i) q^{91} +(-1.44036 + 1.20860i) q^{92} +(1.19668 + 6.78668i) q^{93} +10.8680 q^{94} +(2.87385 - 3.27734i) q^{95} -1.00000 q^{96} +(-0.389975 - 2.21166i) q^{97} +(-5.11374 + 4.29094i) q^{98} +(-1.79163 + 0.652099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^7 - 6 * q^8	$ 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	−0.284816	+	0.493316i	−0.107650	+	0.186456i	−0.914818	−	0.403866i	$-0.867666\pi$
$7$	−0.284816	+	0.493316i	−0.107650	+	0.186456i	0.807168	+	0.590322i	$0.200999\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.173648	−	0.984808i	0.0549124	−	0.311424i
$11$	−0.953304	−	1.65117i	−0.287432	−	0.497847i	0.685764	−	0.727824i	$-0.259468\pi$
$11$	−0.953304	−	1.65117i	−0.287432	−	0.497847i	−0.973196	+	0.229977i	$0.926135\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.59946	−	3.02030i	−0.998310	−	0.837681i	−0.0115604	−	0.999933i	$-0.503680\pi$
$13$	−3.59946	−	3.02030i	−0.998310	−	0.837681i	−0.986749	+	0.162252i	$0.948124\pi$
$14$	−0.535279	−	0.194826i	−0.143059	−	0.0520694i
$15$	0.939693	−	0.342020i	0.242628	−	0.0883092i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.808506	−	4.58527i	−0.196092	−	1.11209i	−0.910856	−	0.412725i	$-0.864577\pi$
$17$	−0.808506	−	4.58527i	−0.196092	−	1.11209i	0.714764	−	0.699366i	$-0.246534\pi$
$18$	1.00000			0.235702
$19$	−1.57962	+	4.06261i	−0.362390	+	0.932027i
$19$	−1.57962	+	4.06261i	−0.362390	+	0.932027i
$20$	1.00000			0.223607
$21$	−0.0989156	−	0.560978i	−0.0215852	−	0.122416i
$22$	1.46055	−	1.22554i	0.311390	−	0.261287i
$23$	1.76686	−	0.643084i	0.368415	−	0.134092i	−0.151177	−	0.988507i	$-0.548306\pi$
$23$	1.76686	−	0.643084i	0.368415	−	0.134092i	0.519592	+	0.854415i	$0.326084\pi$
$24$	0.939693	+	0.342020i	0.191814	+	0.0698146i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	2.34938	−	4.06924i	0.460751	−	0.798044i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	0.0989156	−	0.560978i	0.0186933	−	0.106015i
$29$	0.782583	−	4.43825i	0.145322	−	0.824163i	−0.821786	−	0.569796i	$-0.807022\pi$
$29$	0.782583	−	4.43825i	0.145322	−	0.824163i	0.967108	−	0.254366i	$-0.0818668\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	3.44569	−	5.96811i	0.618864	−	1.07190i	−0.370829	−	0.928701i	$-0.620927\pi$
$31$	3.44569	−	5.96811i	0.618864	−	1.07190i	0.989693	−	0.143203i	$-0.0457401\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	1.79163	+	0.652099i	0.311882	+	0.113516i
$34$	4.37521	−	1.59245i	0.750343	−	0.273102i
$35$	0.436364	−	0.366153i	0.0737589	−	0.0618911i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−6.61134			−1.08690			−0.543449	−	0.839442i	$-0.682882\pi$
$37$	−6.61134			−1.08690			−0.543449	+	0.839442i	$0.682882\pi$
$38$	−4.27519	−	0.850158i	−0.693527	−	0.137914i
$39$	4.69876			0.752403
$40$	0.173648	+	0.984808i	0.0274562	+	0.155712i
$41$	2.55140	−	2.14088i	0.398462	−	0.334349i	−0.421437	−	0.906858i	$-0.638474\pi$
$41$	2.55140	−	2.14088i	0.398462	−	0.334349i	0.819899	+	0.572508i	$0.194030\pi$
$42$	0.535279	−	0.194826i	0.0825954	−	0.0300623i
$43$	−6.29766	−	2.29216i	−0.960384	−	0.349551i	−0.186200	−	0.982512i	$-0.559617\pi$
$43$	−6.29766	−	2.29216i	−0.960384	−	0.349551i	−0.774184	+	0.632961i	$0.781840\pi$
$44$	1.46055	+	1.22554i	0.220186	+	0.184758i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	0.940125	+	1.62835i	0.138614	+	0.240086i
$47$	1.88720	−	10.7028i	0.275277	−	1.56117i	−0.462806	−	0.886460i	$-0.653157\pi$
$47$	1.88720	−	10.7028i	0.275277	−	1.56117i	0.738082	−	0.674711i	$-0.235732\pi$
$48$	−0.173648	+	0.984808i	−0.0250640	+	0.142145i
$49$	3.33776	+	5.78117i	0.476823	+	0.825881i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	3.56671	+	2.99282i	0.499439	+	0.419079i
$52$	4.41539	+	1.60707i	0.612304	+	0.222860i
$53$	−7.96555	+	2.89922i	−1.09415	+	0.398239i	−0.825157	−	0.564903i	$-0.808914\pi$
$53$	−7.96555	+	2.89922i	−1.09415	+	0.398239i	−0.268995	+	0.963142i	$0.586691\pi$
$54$	−0.766044	+	0.642788i	−0.104245	+	0.0874723i
$55$	0.331079	+	1.87764i	0.0446427	+	0.253181i
$56$	0.569632			0.0761203
$57$	−1.40134	−	4.12750i	−0.185611	−	0.546701i
$58$	4.50672			0.591761
$59$	0.205101	+	1.16319i	0.0267019	+	0.151434i	0.995244	−	0.0974172i	$-0.0310581\pi$
$59$	0.205101	+	1.16319i	0.0267019	+	0.151434i	−0.968542	+	0.248851i	$0.919947\pi$
$60$	−0.766044	+	0.642788i	−0.0988959	+	0.0829835i
$61$	−0.352216	+	0.128196i	−0.0450966	+	0.0164138i	−0.364470	−	0.931215i	$-0.618750\pi$
$61$	−0.352216	+	0.128196i	−0.0450966	+	0.0164138i	0.319373	+	0.947629i	$0.396528\pi$
$62$	6.47578	+	2.35699i	0.822424	+	0.299338i
$63$	0.436364	+	0.366153i	0.0549767	+	0.0461309i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.34938	+	4.06924i	0.291405	+	0.504728i
$66$	−0.331079	+	1.87764i	−0.0407530	+	0.231122i
$67$	0.00191067	−	0.0108359i	0.000233425	−	0.00132382i	−0.984691	−	0.174310i	$-0.944231\pi$
$67$	0.00191067	−	0.0108359i	0.000233425	−	0.00132382i	0.984924	+	0.172986i	$0.0553416\pi$
$68$	2.32800	+	4.03222i	0.282312	+	0.488978i
$69$	−0.940125	+	1.62835i	−0.113178	+	0.196030i
$70$	0.436364	+	0.366153i	0.0521554	+	0.0437636i
$71$	4.16738	+	1.51680i	0.494577	+	0.180011i	0.577253	−	0.816565i	$-0.304125\pi$
$71$	4.16738	+	1.51680i	0.494577	+	0.180011i	−0.0826763	+	0.996576i	$0.526347\pi$
$72$	−0.939693	+	0.342020i	−0.110744	+	0.0403075i
$73$	−10.4802	+	8.79396i	−1.22662	+	1.02926i	−0.228167	+	0.973622i	$0.573273\pi$
$73$	−10.4802	+	8.79396i	−1.22662	+	1.02926i	−0.998451	+	0.0556331i	$0.982282\pi$
$74$	−1.14805	−	6.51090i	−0.133458	−	0.756877i
$75$	−1.00000			−0.115470
$76$	0.0948636	−	4.35787i	0.0108816	−	0.499882i
$77$	1.08607			0.123769
$78$	0.815931	+	4.62737i	0.0923860	+	0.523947i
$79$	−11.8218	+	9.91966i	−1.33006	+	1.11605i	−0.345991	+	0.938238i	$0.612457\pi$
$79$	−11.8218	+	9.91966i	−1.33006	+	1.11605i	−0.984065	+	0.177811i	$0.943098\pi$
$80$	−0.939693	+	0.342020i	−0.105061	+	0.0382390i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	2.55140	+	2.14088i	0.281755	+	0.236421i
$83$	3.95026	−	6.84206i	0.433598	−	0.751013i	−0.563582	−	0.826060i	$-0.690577\pi$
$83$	3.95026	−	6.84206i	0.433598	−	0.751013i	0.997180	+	0.0750465i	$0.0239105\pi$
$84$	0.284816	+	0.493316i	0.0310760	+	0.0538252i
$85$	−0.808506	+	4.58527i	−0.0876948	+	0.497342i
$86$	1.16376	−	6.60002i	0.125492	−	0.711698i
$87$	2.25336	+	3.90293i	0.241585	+	0.418438i
$88$	−0.953304	+	1.65117i	−0.101623	+	0.176015i
$89$	−12.0772	−	10.1340i	−1.28018	−	1.07420i	−0.993219	−	0.116255i	$-0.962911\pi$
$89$	−12.0772	−	10.1340i	−1.28018	−	1.07420i	−0.286960	−	0.957943i	$-0.592645\pi$
$90$	−0.939693	−	0.342020i	−0.0990523	−	0.0360521i
$91$	2.51515	−	0.915439i	0.263659	−	0.0959641i
$92$	−1.44036	+	1.20860i	−0.150167	+	0.126005i
$93$	1.19668	+	6.78668i	0.124089	+	0.703746i
$94$	10.8680			1.12094
$95$	2.87385	−	3.27734i	0.294851	−	0.336248i
$96$	−1.00000			−0.102062
$97$	−0.389975	−	2.21166i	−0.0395960	−	0.224560i	0.958588	−	0.284796i	$-0.0919258\pi$
$97$	−0.389975	−	2.21166i	−0.0395960	−	0.224560i	−0.998184	+	0.0602359i	$0.980815\pi$
$98$	−5.11374	+	4.29094i	−0.516566	+	0.433450i
$99$	−1.79163	+	0.652099i	−0.180065	+	0.0655384i
$100$	−0.939693	−	0.342020i	−0.0939693	−	0.0342020i
$101$	−1.71477	−	1.43886i	−0.170626	−	0.143172i	0.553476	−	0.832865i	$-0.313301\pi$
$101$	−1.71477	−	1.43886i	−0.170626	−	0.143172i	−0.724102	+	0.689693i	$0.757745\pi$
$102$	−2.32800	+	4.03222i	−0.230506	+	0.399249i
$103$	6.13637	+	10.6285i	0.604634	+	1.04726i	0.992109	+	0.125377i	$0.0400141\pi$
$103$	6.13637	+	10.6285i	0.604634	+	1.04726i	−0.387475	+	0.921880i	$0.626653\pi$
$104$	−0.815931	+	4.62737i	−0.0800086	+	0.453751i
$105$	−0.0989156	+	0.560978i	−0.00965318	+	0.0547459i
$106$	−4.23838	−	7.34109i	−0.411668	−	0.713030i
$107$	−2.76692	+	4.79244i	−0.267488	+	0.463303i	−0.968212	−	0.250129i	$-0.919527\pi$
$107$	−2.76692	+	4.79244i	−0.267488	+	0.463303i	0.700724	+	0.713432i	$0.252860\pi$
$108$	−0.766044	−	0.642788i	−0.0737127	−	0.0618523i
$109$	1.26215	+	0.459386i	0.120892	+	0.0440012i	0.401758	−	0.915746i	$-0.368399\pi$
$109$	1.26215	+	0.459386i	0.120892	+	0.0440012i	−0.280866	+	0.959747i	$0.590622\pi$
$110$	−1.79163	+	0.652099i	−0.170825	+	0.0621752i
$111$	5.06458	−	4.24969i	0.480709	−	0.403363i
$112$	0.0989156	+	0.560978i	0.00934665	+	0.0530075i
$113$	−20.2828			−1.90804			−0.954022	−	0.299736i	$-0.903101\pi$
$113$	−20.2828			−1.90804			−0.954022	+	0.299736i	$0.903101\pi$
$114$	3.82145	−	2.09678i	0.357912	−	0.196381i
$115$	−1.88025			−0.175334
$116$	0.782583	+	4.43825i	0.0726610	+	0.412081i
$117$	−3.59946	+	3.02030i	−0.332770	+	0.279227i
$118$	−1.10990	+	0.403970i	−0.102174	+	0.0371885i
$119$	2.49226	+	0.907109i	0.228465	+	0.0831546i
$120$	−0.766044	−	0.642788i	−0.0699300	−	0.0586782i
$121$	3.68242	−	6.37814i	0.334766	−	0.579831i
$122$	−0.187410	−	0.324604i	−0.0169673	−	0.0293883i
$123$	−0.578356	+	3.28002i	−0.0521486	+	0.295749i
$124$	−1.19668	+	6.78668i	−0.107465	+	0.609462i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.284816	+	0.493316i	−0.0253734	+	0.0439481i
$127$	−7.49567	−	6.28961i	−0.665133	−	0.558113i	0.246487	−	0.969146i	$-0.420724\pi$
$127$	−7.49567	−	6.28961i	−0.665133	−	0.558113i	−0.911620	+	0.411033i	$0.865168\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	6.29766	−	2.29216i	0.554478	−	0.201814i
$130$	−3.59946	+	3.02030i	−0.315693	+	0.264898i
$131$	−0.429855	−	2.43783i	−0.0375566	−	0.212994i	0.960254	−	0.279127i	$-0.0900450\pi$
$131$	−0.429855	−	2.43783i	−0.0375566	−	0.212994i	−0.997811	+	0.0661327i	$0.978934\pi$
$132$	−1.90661			−0.165949
$133$	−1.55425	−	1.93635i	−0.134771	−	0.167903i
$134$	0.0110031			0.000950524
$135$	−0.173648	−	0.984808i	−0.0149453	−	0.0847588i
$136$	−3.56671	+	2.99282i	−0.305842	+	0.256632i
$137$	−1.74155	+	0.633871i	−0.148790	+	0.0541553i	−0.415342	−	0.909665i	$-0.636338\pi$
$137$	−1.74155	+	0.633871i	−0.148790	+	0.0541553i	0.266551	+	0.963821i	$0.414116\pi$
$138$	−1.76686	−	0.643084i	−0.150405	−	0.0547429i
$139$	15.0867	+	12.6593i	1.27964	+	1.07374i	0.993294	+	0.115618i	$0.0368847\pi$
$139$	15.0867	+	12.6593i	1.27964	+	1.07374i	0.286345	+	0.958127i	$0.407560\pi$
$140$	−0.284816	+	0.493316i	−0.0240714	+	0.0416928i
$141$	5.43398	+	9.41193i	0.457624	+	0.792627i
$142$	−0.770101	+	4.36746i	−0.0646254	+	0.366509i
$143$	−1.55566	+	8.82259i	−0.130091	+	0.737782i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.25336	+	3.90293i	−0.187131	+	0.324121i
$146$	−10.4802	−	8.79396i	−0.867350	−	0.727793i
$147$	−6.27294	−	2.28316i	−0.517383	−	0.188312i
$148$	6.21263	−	2.26121i	0.510675	−	0.185870i
$149$	−0.692265	+	0.580880i	−0.0567126	+	0.0475875i	−0.670703	−	0.741726i	$-0.734008\pi$
$149$	−0.692265	+	0.580880i	−0.0567126	+	0.0475875i	0.613991	+	0.789313i	$0.289563\pi$
$150$	−0.173648	−	0.984808i	−0.0141783	−	0.0804092i
$151$	3.05941			0.248972			0.124486	−	0.992221i	$-0.460272\pi$
$151$	3.05941			0.248972			0.124486	+	0.992221i	$0.460272\pi$
$152$	4.30813	−	0.663313i	0.349436	−	0.0538018i
$153$	−4.65600			−0.376416
$154$	0.188593	+	1.06957i	0.0151973	+	0.0861881i
$155$	−5.27910	+	4.42969i	−0.424028	+	0.355801i
$156$	−4.41539	+	1.60707i	−0.353514	+	0.128669i
$157$	−5.96739	−	2.17195i	−0.476249	−	0.173341i	0.0927318	−	0.995691i	$-0.470440\pi$
$157$	−5.96739	−	2.17195i	−0.476249	−	0.173341i	−0.568981	+	0.822351i	$0.692662\pi$
$158$	−11.8218	−	9.91966i	−0.940491	−	0.789166i
$159$	4.23838	−	7.34109i	0.336125	−	0.582186i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−0.185986	+	1.05478i	−0.0146578	+	0.0831283i
$162$	0.173648	−	0.984808i	0.0136431	−	0.0773738i
$163$	2.68689	+	4.65383i	0.210453	+	0.364516i	0.951857	−	0.306544i	$-0.0991726\pi$
$163$	2.68689	+	4.65383i	0.210453	+	0.364516i	−0.741403	+	0.671060i	$0.765839\pi$
$164$	−1.66531	+	2.88440i	−0.130039	+	0.225234i
$165$	−1.46055	−	1.22554i	−0.113703	−	0.0954085i
$166$	7.42407	+	2.70214i	0.576219	+	0.209727i
$167$	22.3726	−	8.14297i	1.73125	−	0.630122i	0.732528	−	0.680737i	$-0.238340\pi$
$167$	22.3726	−	8.14297i	1.73125	−	0.630122i	0.998718	+	0.0506144i	$0.0161180\pi$
$168$	−0.436364	+	0.366153i	−0.0336662	+	0.0282493i
$169$	1.57643	+	8.94040i	0.121264	+	0.687723i
$170$	−4.65600			−0.357099
$171$	3.72659	+	2.26109i	0.284980	+	0.172910i
$172$	6.70183			0.511010
$173$	2.20814	+	12.5230i	0.167882	+	0.952104i	0.946043	+	0.324040i	$0.105041\pi$
$173$	2.20814	+	12.5230i	0.167882	+	0.952104i	−0.778162	+	0.628064i	$0.783848\pi$
$174$	−3.45235	+	2.89686i	−0.261722	+	0.219611i
$175$	−0.535279	+	0.194826i	−0.0404633	+	0.0147274i
$176$	−1.79163	−	0.652099i	−0.135049	−	0.0491538i
$177$	−0.904798	−	0.759216i	−0.0680088	−	0.0570661i
$178$	7.88282	−	13.6534i	0.590843	−	1.02337i
$179$	−6.48826	−	11.2380i	−0.484955	−	0.839968i	0.514895	−	0.857253i	$-0.327831\pi$
$179$	−6.48826	−	11.2380i	−0.484955	−	0.839968i	−0.999851	+	0.0172857i	$0.994498\pi$
$180$	0.173648	−	0.984808i	0.0129430	−	0.0734032i
$181$	4.04578	−	22.9447i	0.300720	−	1.70547i	−0.342276	−	0.939600i	$-0.611198\pi$
$181$	4.04578	−	22.9447i	0.300720	−	1.70547i	0.642996	−	0.765870i	$-0.277691\pi$
$182$	1.33828	+	2.31797i	0.0992001	+	0.171820i
$183$	0.187410	−	0.324604i	0.0138538	−	0.0239954i
$184$	−1.44036	−	1.20860i	−0.106184	−	0.0890993i
$185$	6.21263	+	2.26121i	0.456762	+	0.166248i
$186$	−6.47578	+	2.35699i	−0.474827	+	0.172823i
$187$	−6.80031	+	5.70614i	−0.497288	+	0.417274i
$188$	1.88720	+	10.7028i	0.137638	+	0.780585i
$189$	−0.569632			−0.0414347
$190$	3.72659	+	2.26109i	0.270355	+	0.164037i
$191$	10.7637			0.778833			0.389416	−	0.921062i	$-0.372677\pi$
$191$	10.7637			0.778833			0.389416	+	0.921062i	$0.372677\pi$
$192$	−0.173648	−	0.984808i	−0.0125320	−	0.0710724i
$193$	−1.44151	+	1.20957i	−0.103762	+	0.0870668i	−0.693193	−	0.720752i	$-0.743797\pi$
$193$	−1.44151	+	1.20957i	−0.103762	+	0.0870668i	0.589431	+	0.807819i	$0.299352\pi$
$194$	2.11034	−	0.768101i	0.151514	−	0.0551464i
$195$	−4.41539	−	1.60707i	−0.316192	−	0.115085i
$196$	−5.11374	−	4.29094i	−0.365267	−	0.306496i
$197$	−2.09286	+	3.62494i	−0.149110	+	0.258266i	−0.930899	−	0.365277i	$-0.880974\pi$
$197$	−2.09286	+	3.62494i	−0.149110	+	0.258266i	0.781789	+	0.623543i	$0.214308\pi$
$198$	−0.953304	−	1.65117i	−0.0677484	−	0.117344i
$199$	2.41847	−	13.7158i	0.171440	−	0.972287i	−0.770732	−	0.637159i	$-0.780109\pi$
$199$	2.41847	−	13.7158i	0.171440	−	0.972287i	0.942173	−	0.335128i	$-0.108780\pi$
$200$	0.173648	−	0.984808i	0.0122788	−	0.0696364i
$201$	0.00550155	+	0.00952897i	0.000388050	+	0.000672122i
$202$	1.11923	−	1.93857i	0.0787491	−	0.136397i
$203$	1.96657	+	1.65015i	0.138026	+	0.115818i
$204$	−4.37521	−	1.59245i	−0.306326	−	0.111494i
$205$	−3.12976	+	1.13914i	−0.218592	+	0.0795609i
$206$	−9.40146	+	7.88876i	−0.655031	+	0.549636i
$207$	−0.326502	−	1.85169i	−0.0226935	−	0.128701i
$208$	−4.69876			−0.325800
$209$	8.21392	−	1.26468i	0.568169	−	0.0874796i
$210$	−0.569632			−0.0393084
$211$	3.48235	+	19.7494i	0.239735	+	1.35961i	0.832409	+	0.554162i	$0.186961\pi$
$211$	3.48235	+	19.7494i	0.239735	+	1.35961i	−0.592673	+	0.805443i	$0.701928\pi$
$212$	6.49357	−	5.44876i	0.445981	−	0.374222i
$213$	−4.16738	+	1.51680i	−0.285544	+	0.103930i
$214$	−5.20010	−	1.89268i	−0.355472	−	0.129381i
$215$	5.13390	+	4.30785i	0.350129	+	0.293793i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	1.96278	+	3.39963i	0.133242	+	0.230782i
$218$	−0.233237	+	1.32275i	−0.0157968	+	0.0895879i
$219$	2.37568	−	13.4731i	0.160533	−	0.910430i
$220$	−0.953304	−	1.65117i	−0.0642718	−	0.111322i
$221$	−10.9387	+	18.9464i	−0.735818	+	1.27447i
$222$	5.06458	+	4.24969i	0.339912	+	0.285220i
$223$	1.56178	+	0.568442i	0.104585	+	0.0380657i	0.393782	−	0.919204i	$-0.371166\pi$
$223$	1.56178	+	0.568442i	0.104585	+	0.0380657i	−0.289198	+	0.957269i	$0.593389\pi$
$224$	−0.535279	+	0.194826i	−0.0357649	+	0.0130173i
$225$	0.766044	−	0.642788i	0.0510696	−	0.0428525i
$226$	−3.52207	−	19.9746i	−0.234285	−	1.32869i
$227$	−7.90839			−0.524898			−0.262449	−	0.964946i	$-0.584530\pi$
$227$	−7.90839			−0.524898			−0.262449	+	0.964946i	$0.584530\pi$
$228$	2.72851	+	3.39930i	0.180700	+	0.225124i
$229$	4.92852			0.325685			0.162843	−	0.986652i	$-0.447934\pi$
$229$	4.92852			0.325685			0.162843	+	0.986652i	$0.447934\pi$
$230$	−0.326502	−	1.85169i	−0.0215289	−	0.122097i
$231$	−0.831975	+	0.698110i	−0.0547399	+	0.0459323i
$232$	−4.23493	+	1.54139i	−0.278037	+	0.101197i
$233$	14.3979	+	5.24041i	0.943239	+	0.343311i	0.767444	−	0.641116i	$-0.221528\pi$
$233$	14.3979	+	5.24041i	0.943239	+	0.343311i	0.175795	+	0.984427i	$0.443750\pi$
$234$	−3.59946	−	3.02030i	−0.235304	−	0.197443i
$235$	−5.43398	+	9.41193i	−0.354474	+	0.613966i
$236$	−0.590565	−	1.02289i	−0.0384425	−	0.0665844i
$237$	2.67978	−	15.1978i	0.174071	−	0.987203i
$238$	−0.460552	+	2.61192i	−0.0298531	+	0.169305i
$239$	−4.15623	−	7.19881i	−0.268844	−	0.465652i	0.699719	−	0.714418i	$-0.253308\pi$
$239$	−4.15623	−	7.19881i	−0.268844	−	0.465652i	−0.968564	+	0.248766i	$0.919975\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−3.30336	−	2.77185i	−0.212788	−	0.178550i	0.530164	−	0.847895i	$-0.322130\pi$
$241$	−3.30336	−	2.77185i	−0.212788	−	0.178550i	−0.742952	+	0.669345i	$0.766575\pi$
$242$	6.92069	+	2.51892i	0.444879	+	0.161923i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	0.287129	−	0.240930i	0.0183816	−	0.0154240i
$245$	−1.15919	−	6.57410i	−0.0740580	−	0.420004i
$246$	−3.33062			−0.212353
$247$	17.9561	−	9.85226i	1.14252	−	0.626884i
$248$	−6.89138			−0.437603
$249$	1.37191	+	7.78050i	0.0869414	+	0.493069i
$250$	0.766044	−	0.642788i	0.0484489	−	0.0406535i
$251$	11.7205	−	4.26593i	0.739794	−	0.269263i	0.0554893	−	0.998459i	$-0.482328\pi$
$251$	11.7205	−	4.26593i	0.739794	−	0.269263i	0.684305	+	0.729196i	$0.260106\pi$
$252$	−0.535279	−	0.194826i	−0.0337194	−	0.0122729i
$253$	−2.74619	−	2.30433i	−0.172652	−	0.144872i
$254$	4.89245	−	8.47397i	0.306980	−	0.531704i
$255$	−2.32800	−	4.03222i	−0.145785	−	0.252507i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.717462	+	4.06893i	−0.0447540	+	0.253813i	−0.998974	−	0.0452940i	$-0.985578\pi$
$257$	−0.717462	+	4.06893i	−0.0447540	+	0.253813i	0.954220	+	0.299107i	$0.0966886\pi$
$258$	3.35092	+	5.80396i	0.208619	+	0.361339i
$259$	1.88302	−	3.26148i	0.117005	−	0.202659i
$260$	−3.59946	−	3.02030i	−0.223229	−	0.187311i
$261$	−4.23493	−	1.54139i	−0.262136	−	0.0954096i
$262$	2.32615	−	0.846650i	0.143710	−	0.0523062i
$263$	11.2197	−	9.41447i	0.691838	−	0.580521i	−0.227600	−	0.973755i	$-0.573088\pi$
$263$	11.2197	−	9.41447i	0.691838	−	0.580521i	0.919439	+	0.393233i	$0.128644\pi$
$264$	−0.331079	−	1.87764i	−0.0203765	−	0.115561i
$265$	8.47676			0.520723
$266$	1.63704	−	1.86688i	0.100373	−	0.114466i
$267$	15.7656			0.964842
$268$	0.00191067	+	0.0108359i	0.000116713	+	0.000661911i
$269$	−1.43482	+	1.20396i	−0.0874827	+	0.0734067i	−0.685480	−	0.728091i	$-0.740408\pi$
$269$	−1.43482	+	1.20396i	−0.0874827	+	0.0734067i	0.597998	+	0.801498i	$0.295963\pi$
$270$	0.939693	−	0.342020i	0.0571879	−	0.0208147i
$271$	26.4699	+	9.63425i	1.60793	+	0.585239i	0.981029	−	0.193860i	$-0.0621007\pi$
$271$	26.4699	+	9.63425i	1.60793	+	0.585239i	0.626901	+	0.779099i	$0.284323\pi$
$272$	−3.56671	−	2.99282i	−0.216263	−	0.181466i
$273$	−1.33828	+	2.31797i	−0.0809965	+	0.140290i
$274$	−0.926658	−	1.60502i	−0.0559815	−	0.0969627i
$275$	0.331079	−	1.87764i	0.0199648	−	0.113226i
$276$	0.326502	−	1.85169i	0.0196531	−	0.111458i
$277$	−3.03662	−	5.25958i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$277$	−3.03662	−	5.25958i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$278$	−9.84715	+	17.0558i	−0.590593	+	1.02294i
$279$	−5.27910	−	4.42969i	−0.316052	−	0.265199i
$280$	−0.535279	−	0.194826i	−0.0319891	−	0.0116431i
$281$	1.82516	−	0.664303i	0.108880	−	0.0396290i	−0.287006	−	0.957929i	$-0.592660\pi$
$281$	1.82516	−	0.664303i	0.108880	−	0.0396290i	0.395886	+	0.918300i	$0.370438\pi$
$282$	−8.32534	+	6.98579i	−0.495767	+	0.415998i
$283$	−5.55461	−	31.5017i	−0.330187	−	1.87258i	−0.470387	−	0.882460i	$-0.655886\pi$
$283$	−5.55461	−	31.5017i	−0.330187	−	1.87258i	0.140200	−	0.990123i	$-0.455226\pi$
$284$	−4.43483			−0.263159
$285$	−0.0948636	+	4.35787i	−0.00561923	+	0.258138i
$286$	−8.95869			−0.529739
$287$	0.329450	+	1.86841i	0.0194468	+	0.110288i
$288$	0.766044	−	0.642788i	0.0451396	−	0.0378766i
$289$	−4.39622	+	1.60009i	−0.258601	+	0.0941232i
$290$	−4.23493	−	1.54139i	−0.248684	−	0.0905134i
$291$	1.72036	+	1.44356i	0.100850	+	0.0846228i
$292$	6.84049	−	11.8481i	0.400309	−	0.693356i
$293$	15.1364	+	26.2170i	0.884279	+	1.53162i	0.846538	+	0.532328i	$0.178683\pi$
$293$	15.1364	+	26.2170i	0.884279	+	1.53162i	0.0377408	+	0.999288i	$0.487984\pi$
$294$	1.15919	−	6.57410i	0.0676054	−	0.383409i
$295$	0.205101	−	1.16319i	0.0119414	−	0.0677233i
$296$	3.30567	+	5.72559i	0.192138	+	0.332793i
$297$	0.953304	−	1.65117i	0.0553163	−	0.0958107i
$298$	−0.692265	−	0.580880i	−0.0401019	−	0.0336495i
$299$	−8.30204	−	3.02169i	−0.480119	−	0.174749i
$300$	0.939693	−	0.342020i	0.0542532	−	0.0197465i
$301$	2.92444	−	2.45389i	0.168562	−	0.141440i
$302$	0.531262	+	3.01294i	0.0305707	+	0.173375i
$303$	2.23847			0.128597
$304$	1.40134	+	4.12750i	0.0803721	+	0.236728i
$305$	0.374820			0.0214622
$306$	−0.808506	−	4.58527i	−0.0462192	−	0.262122i
$307$	−5.30689	+	4.45301i	−0.302880	+	0.254147i	−0.781542	−	0.623853i	$-0.785567\pi$
$307$	−5.30689	+	4.45301i	−0.302880	+	0.254147i	0.478662	+	0.877999i	$0.341122\pi$
$308$	−1.02057	+	0.371457i	−0.0581523	+	0.0211657i
$309$	−11.5326	−	4.19752i	−0.656067	−	0.238789i
$310$	−5.27910	−	4.42969i	−0.299833	−	0.251590i
$311$	8.15638	−	14.1273i	0.462506	−	0.801084i	−0.536579	−	0.843850i	$-0.680284\pi$
$311$	8.15638	−	14.1273i	0.462506	−	0.801084i	0.999085	+	0.0427660i	$0.0136170\pi$
$312$	−2.34938	−	4.06924i	−0.133007	−	0.230376i
$313$	3.66102	−	20.7627i	0.206933	−	1.17358i	−0.687435	−	0.726246i	$-0.741263\pi$
$313$	3.66102	−	20.7627i	0.206933	−	1.17358i	0.894368	−	0.447331i	$-0.147626\pi$
$314$	1.10273	−	6.25388i	0.0622306	−	0.352927i
$315$	−0.284816	−	0.493316i	−0.0160476	−	0.0277952i
$316$	7.71613	−	13.3647i	0.434066	−	0.751824i
$317$	−4.97606	−	4.17541i	−0.279483	−	0.234514i	0.492261	−	0.870448i	$-0.336171\pi$
$317$	−4.97606	−	4.17541i	−0.279483	−	0.234514i	−0.771744	+	0.635934i	$0.780615\pi$
$318$	7.96555	+	2.89922i	0.446686	+	0.162580i
$319$	−8.07435	+	2.93882i	−0.452077	+	0.164543i
$320$	0.766044	−	0.642788i	0.0428232	−	0.0359329i
$321$	−0.960941	−	5.44976i	−0.0536345	−	0.304176i
$322$	−1.07105			−0.0596874
$323$	19.9053	+	3.95834i	1.10756	+	0.220248i
$324$	1.00000			0.0555556
$325$	−0.815931	−	4.62737i	−0.0452597	−	0.256680i
$326$	−4.11655	+	3.45420i	−0.227995	+	0.191310i
$327$	−1.26215	+	0.459386i	−0.0697972	+	0.0254041i
$328$	−3.12976	−	1.13914i	−0.172812	−	0.0628984i
$329$	4.74238	+	3.97933i	0.261456	+	0.219388i
$330$	0.953304	−	1.65117i	0.0524777	−	0.0908940i
$331$	11.0710	+	19.1755i	0.608516	+	1.05398i	0.991485	+	0.130219i	$0.0415681\pi$
$331$	11.0710	+	19.1755i	0.608516	+	1.05398i	−0.382969	+	0.923761i	$0.625099\pi$
$332$	−1.37191	+	7.78050i	−0.0752935	+	0.427010i
$333$	−1.14805	+	6.51090i	−0.0629126	+	0.356795i
$334$	11.9042	+	20.6187i	0.651371	+	1.12821i
$335$	−0.00550155	+	0.00952897i	−0.000300582	+	0.000520623i
$336$	−0.436364	−	0.366153i	−0.0238056	−	0.0199753i
$337$	11.3230	+	4.12124i	0.616804	+	0.224498i	0.631478	−	0.775394i	$-0.282449\pi$
$337$	11.3230	+	4.12124i	0.616804	+	0.224498i	−0.0146739	+	0.999892i	$0.504671\pi$
$338$	−8.53083	+	3.10497i	−0.464016	+	0.168888i
$339$	15.5375	−	13.0375i	0.843882	−	0.708101i
$340$	−0.808506	−	4.58527i	−0.0438474	−	0.248671i
$341$	−13.1392			−0.711525
$342$	−1.57962	+	4.06261i	−0.0854161	+	0.219681i
$343$	−7.79002			−0.420622
$344$	1.16376	+	6.60002i	0.0627458	+	0.355849i
$345$	1.44036	−	1.20860i	0.0775461	−	0.0650689i
$346$	−11.9493	+	4.34918i	−0.642397	+	0.233813i
$347$	18.4364	+	6.71030i	0.989717	+	0.360228i	0.785611	−	0.618721i	$-0.212349\pi$
$347$	18.4364	+	6.71030i	0.989717	+	0.360228i	0.204107	+	0.978949i	$0.434571\pi$
$348$	−3.45235	−	2.89686i	−0.185065	−	0.155288i
$349$	−5.34275	+	9.25392i	−0.285991	+	0.495351i	−0.972849	−	0.231441i	$-0.925656\pi$
$349$	−5.34275	+	9.25392i	−0.285991	+	0.495351i	0.686858	+	0.726792i	$0.258989\pi$
$350$	−0.284816	−	0.493316i	−0.0152241	−	0.0263689i
$351$	0.815931	−	4.62737i	0.0435512	−	0.246991i
$352$	0.331079	−	1.87764i	0.0176466	−	0.100079i
$353$	−5.82862	−	10.0955i	−0.310226	−	0.537328i	0.668185	−	0.743995i	$-0.267071\pi$
$353$	−5.82862	−	10.0955i	−0.310226	−	0.537328i	−0.978411	+	0.206668i	$0.933738\pi$
$354$	0.590565	−	1.02289i	0.0313882	−	0.0543659i
$355$	−3.39728	−	2.85066i	−0.180309	−	0.151297i
$356$	14.8149	+	5.39217i	0.785186	+	0.285784i
$357$	−2.49226	+	0.907109i	−0.131905	+	0.0480093i
$358$	9.94059	−	8.34115i	0.525377	−	0.440843i
$359$	0.494680	+	2.80547i	0.0261082	+	0.148067i	0.995075	−	0.0991233i	$-0.0316038\pi$
$359$	0.494680	+	2.80547i	0.0261082	+	0.148067i	−0.968967	+	0.247190i	$0.920493\pi$
$360$	1.00000			0.0527046
$361$	−14.0096	−	12.8348i	−0.737347	−	0.675514i
$362$	23.2987			1.22455
$363$	1.27889	+	7.25296i	0.0671244	+	0.380681i
$364$	−2.05037	+	1.72046i	−0.107468	+	0.0901768i
$365$	12.8559	−	4.67917i	0.672909	−	0.244919i
$366$	0.352216	+	0.128196i	0.0184106	+	0.00670092i
$367$	−15.7655	−	13.2289i	−0.822954	−	0.690541i	0.130707	−	0.991421i	$-0.458275\pi$
$367$	−15.7655	−	13.2289i	−0.822954	−	0.690541i	−0.953662	+	0.300880i	$0.902720\pi$
$368$	0.940125	−	1.62835i	0.0490074	−	0.0848834i
$369$	−1.66531	−	2.88440i	−0.0866926	−	0.150156i
$370$	−1.14805	+	6.51090i	−0.0596841	+	0.338486i
$371$	0.838484	−	4.75528i	0.0435319	−	0.246882i
$372$	−3.44569	−	5.96811i	−0.178651	−	0.309432i
$373$	18.8711	−	32.6858i	0.977110	−	1.69240i	0.304323	−	0.952569i	$-0.401570\pi$
$373$	18.8711	−	32.6858i	0.977110	−	1.69240i	0.672788	−	0.739836i	$-0.265097\pi$
$374$	−6.80031	−	5.70614i	−0.351636	−	0.295057i
$375$	0.939693	+	0.342020i	0.0485255	+	0.0176618i
$376$	−10.2125	+	3.71706i	−0.526671	+	0.191693i
$377$	−16.2217	+	13.6117i	−0.835462	+	0.701036i
$378$	−0.0989156	−	0.560978i	−0.00508767	−	0.0288536i
$379$	−30.6063			−1.57214			−0.786071	−	0.618136i	$-0.787888\pi$
$379$	−30.6063			−1.57214			−0.786071	+	0.618136i	$0.787888\pi$
$380$	−1.57962	+	4.06261i	−0.0810328	+	0.208407i
$381$	9.78490			0.501296
$382$	1.86909	+	10.6002i	0.0956311	+	0.542351i
$383$	−1.12457	+	0.943628i	−0.0574629	+	0.0482171i	−0.671067	−	0.741397i	$-0.734164\pi$
$383$	−1.12457	+	0.943628i	−0.0574629	+	0.0482171i	0.613604	+	0.789614i	$0.289719\pi$
$384$	0.939693	−	0.342020i	0.0479535	−	0.0174536i
$385$	−1.02057	−	0.371457i	−0.0520130	−	0.0189312i
$386$	−1.44151	−	1.20957i	−0.0733709	−	0.0615655i
$387$	−3.35092	+	5.80396i	−0.170337	+	0.295032i
$388$	1.12289	+	1.94490i	0.0570060	+	0.0987373i
$389$	5.48171	−	31.0883i	0.277934	−	1.57624i	−0.451552	−	0.892245i	$-0.649129\pi$
$389$	5.48171	−	31.0883i	0.277934	−	1.57624i	0.729486	−	0.683996i	$-0.239759\pi$
$390$	0.815931	−	4.62737i	0.0413163	−	0.234316i
$391$	−4.37723	−	7.58158i	−0.221366	−	0.383417i
$392$	3.33776	−	5.78117i	0.168582	−	0.291993i
$393$	1.89630	+	1.59118i	0.0956555	+	0.0802645i
$394$	−3.93329	−	1.43160i	−0.198156	−	0.0721230i
$395$	14.5016	−	5.27814i	0.729653	−	0.265572i
$396$	1.46055	−	1.22554i	0.0733952	−	0.0615859i
$397$	−4.86385	−	27.5843i	−0.244110	−	1.38442i	−0.822551	−	0.568691i	$-0.807450\pi$
$397$	−4.86385	−	27.5843i	−0.244110	−	1.38442i	0.578441	−	0.815724i	$-0.303661\pi$
$398$	13.9274			0.698117
$399$	2.43529	+	0.484278i	0.121917	+	0.0242442i
$400$	1.00000			0.0500000
$401$	5.37096	+	30.4602i	0.268213	+	1.52111i	0.759728	+	0.650241i	$0.225332\pi$
$401$	5.37096	+	30.4602i	0.268213	+	1.52111i	−0.491515	+	0.870869i	$0.663557\pi$
$402$	−0.00842887	+	0.00707266i	−0.000420394	+	0.000352752i
$403$	−30.4281	+	11.0749i	−1.51573	+	0.551681i
$404$	2.10347	+	0.765602i	0.104652	+	0.0380901i
$405$	0.766044	+	0.642788i	0.0380651	+	0.0319404i
$406$	−1.28359	+	2.22324i	−0.0637033	+	0.110337i
$407$	6.30262	+	10.9165i	0.312409	+	0.541109i
$408$	0.808506	−	4.58527i	0.0400270	−	0.227005i
$409$	1.18287	−	6.70841i	0.0584893	−	0.331710i	−0.941497	−	0.337023i	$-0.890580\pi$
$409$	1.18287	−	6.70841i	0.0584893	−	0.331710i	0.999986	+	0.00531310i	$0.00169122\pi$
$410$	−1.66531	−	2.88440i	−0.0822438	−	0.142450i
$411$	0.926658	−	1.60502i	0.0457087	−	0.0791697i
$412$	−9.40146	−	7.88876i	−0.463177	−	0.388651i
$413$	−0.632235	−	0.230115i	−0.0311102	−	0.0113232i
$414$	1.76686	−	0.643084i	0.0868363	−	0.0316058i
$415$	−6.05216	+	5.07836i	−0.297089	+	0.249287i
$416$	−0.815931	−	4.62737i	−0.0400043	−	0.226876i
$417$	−19.6943			−0.964434
$418$	2.67180	+	7.86953i	0.130682	+	0.384911i
$419$	−37.5839			−1.83610			−0.918048	−	0.396469i	$-0.870235\pi$
$419$	−37.5839			−1.83610			−0.918048	+	0.396469i	$0.870235\pi$
$420$	−0.0989156	−	0.560978i	−0.00482659	−	0.0273729i
$421$	−19.2387	+	16.1432i	−0.937639	+	0.786772i	−0.977173	−	0.212446i	$-0.931857\pi$
$421$	−19.2387	+	16.1432i	−0.937639	+	0.786772i	0.0395342	+	0.999218i	$0.487413\pi$
$422$	−18.8447	+	6.85890i	−0.917344	+	0.333886i
$423$	−10.2125	−	3.71706i	−0.496551	−	0.180730i
$424$	6.49357	+	5.44876i	0.315356	+	0.264615i
$425$	2.32800	−	4.03222i	0.112925	−	0.195591i
$426$	−2.21742	−	3.84068i	−0.107434	−	0.186081i
$427$	0.0370756	−	0.210266i	0.00179421	−	0.0101755i
$428$	0.960941	−	5.44976i	0.0464488	−	0.263424i
$429$	−4.47935	−	7.75845i	−0.216265	−	0.374582i
$430$	−3.35092	+	5.80396i	−0.161595	+	0.279892i
$431$	15.5506	+	13.0485i	0.749044	+	0.628522i	0.935250	−	0.353988i	$-0.115175\pi$
$431$	15.5506	+	13.0485i	0.749044	+	0.628522i	−0.186206	+	0.982511i	$0.559619\pi$
$432$	0.939693	+	0.342020i	0.0452110	+	0.0164555i
$433$	7.65383	−	2.78577i	0.367820	−	0.133875i	−0.151496	−	0.988458i	$-0.548409\pi$
$433$	7.65383	−	2.78577i	0.367820	−	0.133875i	0.519316	+	0.854582i	$0.326187\pi$
$434$	−3.00715	+	2.52330i	−0.144348	+	0.121122i
$435$	−0.782583	−	4.43825i	−0.0375220	−	0.212798i
$436$	−1.34316			−0.0643255
$437$	−0.178367	+	8.19388i	−0.00853247	+	0.391967i
$438$	13.6810			0.653702
$439$	1.99301	+	11.3029i	0.0951211	+	0.539459i	0.994710	+	0.102721i	$0.0327550\pi$
$439$	1.99301	+	11.3029i	0.0951211	+	0.539459i	−0.899589	+	0.436737i	$0.856134\pi$
$440$	1.46055	−	1.22554i	0.0696288	−	0.0584255i
$441$	6.27294	−	2.28316i	0.298711	−	0.108722i
$442$	−20.5581	−	7.48252i	−0.977847	−	0.355907i
$443$	11.2849	+	9.46912i	0.536160	+	0.449891i	0.870222	−	0.492660i	$-0.163975\pi$
$443$	11.2849	+	9.46912i	0.536160	+	0.449891i	−0.334063	+	0.942551i	$0.608420\pi$
$444$	−3.30567	+	5.72559i	−0.156880	+	0.271724i
$445$	7.88282	+	13.6534i	0.373682	+	0.647236i
$446$	−0.288606	+	1.63676i	−0.0136659	+	0.0775030i
$447$	0.156924	−	0.889959i	0.00742224	−	0.0420936i
$448$	−0.284816	−	0.493316i	−0.0134563	−	0.0233070i
$449$	−6.51113	+	11.2776i	−0.307279	+	0.532223i	−0.977766	−	0.209698i	$-0.932752\pi$
$449$	−6.51113	+	11.2776i	−0.307279	+	0.532223i	0.670487	+	0.741921i	$0.266085\pi$
$450$	0.766044	+	0.642788i	0.0361117	+	0.0303013i
$451$	−5.96722	−	2.17189i	−0.280986	−	0.102270i
$452$	19.0596	−	6.93712i	0.896488	−	0.326295i
$453$	−2.34365	+	1.96655i	−0.110114	+	0.0923968i
$454$	−1.37328	−	7.78824i	−0.0644511	−	0.365520i
$455$	−2.67657			−0.125479
$456$	−2.87385	+	3.27734i	−0.134580	+	0.153476i
$457$	29.2379			1.36769			0.683845	−	0.729628i	$-0.260307\pi$
$457$	29.2379			1.36769			0.683845	+	0.729628i	$0.260307\pi$
$458$	0.855828	+	4.85364i	0.0399902	+	0.226796i
$459$	3.56671	−	2.99282i	0.166480	−	0.139693i
$460$	1.76686	−	0.643084i	0.0823802	−	0.0299839i
$461$	−8.72931	−	3.17721i	−0.406565	−	0.147977i	0.130639	−	0.991430i	$-0.458297\pi$
$461$	−8.72931	−	3.17721i	−0.406565	−	0.147977i	−0.537204	+	0.843453i	$0.680519\pi$
$462$	−0.831975	−	0.698110i	−0.0387070	−	0.0324790i
$463$	11.2797	−	19.5369i	0.524210	−	0.907958i	−0.475393	−	0.879774i	$-0.657694\pi$
$463$	11.2797	−	19.5369i	0.524210	−	0.907958i	0.999603	−	0.0281845i	$-0.00897261\pi$
$464$	−2.25336	−	3.90293i	−0.104610	−	0.181189i
$465$	1.19668	−	6.78668i	0.0554945	−	0.314725i
$466$	−2.66063	+	15.0892i	−0.123251	+	0.698992i
$467$	2.61234	+	4.52470i	0.120885	+	0.209378i	0.920117	−	0.391644i	$-0.128094\pi$
$467$	2.61234	+	4.52470i	0.120885	+	0.209378i	−0.799232	+	0.601022i	$0.794760\pi$
$468$	2.34938	−	4.06924i	0.108600	−	0.188101i
$469$	0.00480136	+	0.00402882i	0.000221706	+	0.000186034i
$470$	−10.2125	−	3.71706i	−0.471069	−	0.171455i
$471$	5.96739	−	2.17195i	0.274963	−	0.100078i
$472$	0.904798	−	0.759216i	0.0416467	−	0.0349457i
$473$	2.21884	+	12.5836i	0.102022	+	0.578597i
$474$	15.4323			0.708827
$475$	−3.82145	+	2.09678i	−0.175340	+	0.0962068i
$476$	−2.65221			−0.121564
$477$	1.47197	+	8.34798i	0.0673970	+	0.382228i
$478$	6.36772	−	5.34315i	0.291253	−	0.244390i
$479$	−22.6914	+	8.25900i	−1.03680	+	0.377363i	−0.803665	−	0.595082i	$-0.797120\pi$
$479$	−22.6914	+	8.25900i	−1.03680	+	0.377363i	−0.233132	+	0.972445i	$0.574897\pi$
$480$	0.939693	+	0.342020i	0.0428909	+	0.0156110i
$481$	23.7972	+	19.9683i	1.08506	+	0.910474i
$482$	2.15611	−	3.73450i	0.0982083	−	0.170102i
$483$	−0.535526	−	0.927558i	−0.0243673	−	0.0422054i
$484$	−1.27889	+	7.25296i	−0.0581314	+	0.329680i
$485$	−0.389975	+	2.21166i	−0.0177079	+	0.100426i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−5.50254	+	9.53068i	−0.249344	+	0.431876i	−0.963344	−	0.268269i	$-0.913548\pi$
$487$	−5.50254	+	9.53068i	−0.249344	+	0.431876i	0.714000	+	0.700146i	$0.246882\pi$
$488$	0.287129	+	0.240930i	0.0129977	+	0.0109064i
$489$	−5.04970	−	1.83794i	−0.228355	−	0.0831146i
$490$	6.27294	−	2.28316i	0.283382	−	0.103143i
$491$	−23.0133	+	19.3104i	−1.03857	+	0.871467i	−0.991846	−	0.127440i	$-0.959324\pi$
$491$	−23.0133	+	19.3104i	−1.03857	+	0.871467i	−0.0467280	+	0.998908i	$0.514879\pi$
$492$	−0.578356	−	3.28002i	−0.0260743	−	0.147875i
$493$	−20.9833			−0.945040
$494$	12.8206	+	15.9725i	0.576827	+	0.718635i
$495$	1.90661			0.0856957
$496$	−1.19668	−	6.78668i	−0.0537323	−	0.304731i
$497$	−1.93520	+	1.62383i	−0.0868056	+	0.0728386i
$498$	−7.42407	+	2.70214i	−0.332680	+	0.121086i
$499$	5.84390	+	2.12700i	0.261609	+	0.0952178i	0.469495	−	0.882935i	$-0.344436\pi$
$499$	5.84390	+	2.12700i	0.261609	+	0.0952178i	−0.207886	+	0.978153i	$0.566658\pi$
$500$	0.766044	+	0.642788i	0.0342585	+	0.0287463i
$501$	−11.9042	+	20.6187i	−0.531842	+	0.921177i
$502$	6.23637	+	10.8017i	0.278343	+	0.482104i
$503$	1.93726	−	10.9867i	0.0863780	−	0.489874i	−0.910673	−	0.413129i	$-0.864436\pi$
$503$	1.93726	−	10.9867i	0.0863780	−	0.489874i	0.997051	−	0.0767455i	$-0.0244529\pi$
$504$	0.0989156	−	0.560978i	0.00440605	−	0.0249880i
$505$	1.11923	+	1.93857i	0.0498053	+	0.0862653i
$506$	1.79245	−	3.10462i	0.0796842	−	0.138017i
$507$	−6.95440	−	5.83543i	−0.308856	−	0.259161i
$508$	9.19480	+	3.34663i	0.407953	+	0.148483i
$509$	15.6478	−	5.69532i	0.693575	−	0.252441i	0.0289100	−	0.999582i	$-0.490796\pi$
$509$	15.6478	−	5.69532i	0.693575	−	0.252441i	0.664665	+	0.747141i	$0.268574\pi$
$510$	3.56671	−	2.99282i	0.157936	−	0.132524i
$511$	−1.35326	−	7.67473i	−0.0598648	−	0.339510i
$512$	1.00000			0.0441942
$513$	−4.30813	+	0.663313i	−0.190209	+	0.0292860i
$514$	−4.13170			−0.182241
$515$	−2.13114	−	12.0863i	−0.0939092	−	0.532585i
$516$	−5.13390	+	4.30785i	−0.226007	+	0.189643i
$517$	−19.4713	+	7.08698i	−0.856347	+	0.311685i
$518$	3.53891	+	1.28806i	0.155491	+	0.0565941i
$519$	−9.74114	−	8.17379i	−0.427589	−	0.358789i
$520$	2.34938	−	4.06924i	0.103027	−	0.178448i
$521$	0.870091	+	1.50704i	0.0381194	+	0.0660247i	0.884456	−	0.466624i	$-0.154530\pi$
$521$	0.870091	+	1.50704i	0.0381194	+	0.0660247i	−0.846336	+	0.532649i	$0.821197\pi$
$522$	0.782583	−	4.43825i	0.0342527	−	0.194257i
$523$	−1.38403	+	7.84922i	−0.0605194	+	0.343223i	0.939480	+	0.342603i	$0.111308\pi$
$523$	−1.38403	+	7.84922i	−0.0605194	+	0.343223i	−1.00000		0.000619935i	$0.999803\pi$
$524$	1.23772	+	2.14379i	0.0540700	+	0.0936520i
$525$	0.284816	−	0.493316i	0.0124304	−	0.0215301i
$526$	11.2197	+	9.41447i	0.489204	+	0.410491i
$527$	−30.1512	−	10.9742i	−1.31341	−	0.478042i
$528$	1.79163	−	0.652099i	0.0779705	−	0.0283789i
$529$	−14.9108	+	12.5116i	−0.648295	+	0.543984i
$530$	1.47197	+	8.34798i	0.0639385	+	0.362613i
$531$	1.18113			0.0512567
$532$	2.12279	+	1.28799i	0.0920345	+	0.0558414i
$533$	−15.6498			−0.677867
$534$	2.73768	+	15.5261i	0.118471	+	0.671881i
$535$	4.23916	−	3.55708i	0.183275	−	0.153786i
$536$	−0.0103395	+	0.00376328i	−0.000446600	+	0.000162549i
$537$	12.1939	+	4.43823i	0.526208	+	0.191524i
$538$	−1.43482	−	1.20396i	−0.0618596	−	0.0519064i
$539$	6.36380	−	11.0224i	0.274108	−	0.474770i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	3.30740	−	18.7572i	0.142196	−	0.806436i	−0.827379	−	0.561644i	$-0.810169\pi$
$541$	3.30740	−	18.7572i	0.142196	−	0.806436i	0.969576	−	0.244792i	$-0.0787198\pi$
$542$	−4.89144	+	27.7407i	−0.210105	+	1.19157i
$543$	11.6494	+	20.1773i	0.499921	+	0.865889i
$544$	2.32800	−	4.03222i	0.0998122	−	0.172880i
$545$	−1.02892	−	0.863364i	−0.0440740	−	0.0369824i
$546$	−2.51515	−	0.915439i	−0.107638	−	0.0391772i
$547$	−37.3758	+	13.6037i	−1.59807	+	0.581651i	−0.979032	−	0.203706i	$-0.934701\pi$
$547$	−37.3758	+	13.6037i	−1.59807	+	0.581651i	−0.619042	+	0.785358i	$0.712479\pi$
$548$	1.41972	−	1.19129i	0.0606475	−	0.0508893i
$549$	0.0650869	+	0.369126i	0.00277784	+	0.0157539i
$550$	1.90661			0.0812981
$551$	16.7947	+	10.1901i	0.715478	+	0.434112i
$552$	1.88025			0.0800288
$553$	−1.52649	−	8.65716i	−0.0649130	−	0.368140i
$554$	4.65237	−	3.90380i	0.197660	−	0.165857i
$555$	−6.21263	+	2.26121i	−0.263711	+	0.0959831i
$556$	−18.5066	−	6.73585i	−0.784854	−	0.285664i
$557$	−23.8999	−	20.0544i	−1.01267	−	0.849731i	−0.0239810	−	0.999712i	$-0.507634\pi$
$557$	−23.8999	−	20.0544i	−1.01267	−	0.849731i	−0.988689	+	0.149982i	$0.952079\pi$
$558$	3.44569	−	5.96811i	0.145868	−	0.252650i
$559$	15.7451	+	27.2714i	0.665948	+	1.15346i
$560$	0.0989156	−	0.560978i	0.00417995	−	0.0237057i
$561$	1.54151	−	8.74231i	0.0650824	−	0.369101i
$562$	0.971146	+	1.68207i	0.0409653	+	0.0709540i
$563$	−2.73643	+	4.73964i	−0.115327	+	0.199752i	−0.917910	−	0.396788i	$-0.870125\pi$
$563$	−2.73643	+	4.73964i	−0.115327	+	0.199752i	0.802583	+	0.596540i	$0.203458\pi$
$564$	−8.32534	−	6.98579i	−0.350560	−	0.294155i
$565$	19.0596	+	6.93712i	0.801843	+	0.291847i
$566$	30.0586	−	10.9404i	1.26346	−	0.459861i
$567$	0.436364	−	0.366153i	0.0183256	−	0.0153770i
$568$	−0.770101	−	4.36746i	−0.0323127	−	0.183254i
$569$	24.5025			1.02720			0.513600	−	0.858030i	$-0.328312\pi$
$569$	24.5025			1.02720			0.513600	+	0.858030i	$0.328312\pi$
$570$	−4.30813	+	0.663313i	−0.180448	+	0.0277831i
$571$	−33.1124			−1.38571			−0.692854	−	0.721077i	$-0.743647\pi$
$571$	−33.1124			−1.38571			−0.692854	+	0.721077i	$0.743647\pi$
$572$	−1.55566	−	8.82259i	−0.0650454	−	0.368891i
$573$	−8.24546	+	6.91876i	−0.344459	+	0.289035i
$574$	−1.78281	+	0.648890i	−0.0744131	+	0.0270842i
$575$	1.76686	+	0.643084i	0.0736831	+	0.0268184i
$576$	0.766044	+	0.642788i	0.0319185	+	0.0267828i
$577$	−22.1409	+	38.3492i	−0.921739	+	1.59650i	−0.125014	+	0.992155i	$0.539898\pi$
$577$	−22.1409	+	38.3492i	−0.921739	+	1.59650i	−0.796724	+	0.604343i	$0.793436\pi$
$578$	−2.33918	−	4.05158i	−0.0972971	−	0.168524i
$579$	0.326764	−	1.85317i	0.0135798	−	0.0770151i
$580$	0.782583	−	4.43825i	0.0324950	−	0.184288i
$581$	2.25020	+	3.89746i	0.0933540	+	0.161694i
$582$	−1.12289	+	1.94490i	−0.0465452	+	0.0806187i
$583$	12.3807	+	10.3886i	0.512756	+	0.430254i
$584$	12.8559	+	4.67917i	0.531981	+	0.193625i
$585$	4.41539	−	1.60707i	0.182554	−	0.0664442i
$586$	−23.1903	+	19.4590i	−0.957984	+	0.803844i
$587$	3.00117	+	17.0205i	0.123872	+	0.702510i	0.981972	+	0.189028i	$0.0605337\pi$
$587$	3.00117	+	17.0205i	0.123872	+	0.702510i	−0.858100	+	0.513482i	$0.828355\pi$
$588$	6.67552			0.275294
$589$	18.8032	+	23.4258i	0.774773	+	0.965245i
$590$	1.18113			0.0486263
$591$	−0.726843	−	4.12213i	−0.0298983	−	0.169562i
$592$	−5.06458	+	4.24969i	−0.208153	+	0.174661i
$593$	23.5442	−	8.56938i	0.966843	−	0.351902i	0.190132	−	0.981759i	$-0.439109\pi$
$593$	23.5442	−	8.56938i	0.966843	−	0.351902i	0.776712	+	0.629856i	$0.216886\pi$
$594$	1.79163	+	0.652099i	0.0735113	+	0.0267559i
$595$	−2.03171	−	1.70481i	−0.0832920	−	0.0698903i
$596$	0.451844	−	0.782617i	0.0185083	−	0.0320572i
$597$	6.96369	+	12.0615i	0.285005	+	0.493643i
$598$	1.53415	−	8.70062i	0.0627362	−	0.355795i
$599$	−4.27906	+	24.2677i	−0.174838	+	0.991553i	0.763494	+	0.645815i	$0.223482\pi$
$599$	−4.27906	+	24.2677i	−0.174838	+	0.991553i	−0.938331	+	0.345738i	$0.887629\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	3.16194	−	5.47663i	0.128978	−	0.223397i	−0.794303	−	0.607522i	$-0.792164\pi$
$601$	3.16194	−	5.47663i	0.128978	−	0.223397i	0.923281	+	0.384125i	$0.125497\pi$
$602$	2.92444	+	2.45389i	0.119191	+	0.100013i
$603$	−0.0103395	−	0.00376328i	−0.000421059	−	0.000153253i
$604$	−2.87491	+	1.04638i	−0.116978	+	0.0425767i
$605$	−5.64180	+	4.73403i	−0.229372	+	0.192466i
$606$	0.388706	+	2.20446i	0.0157901	+	0.0895502i
$607$	27.6975			1.12421			0.562104	−	0.827067i	$-0.309992\pi$
$607$	27.6975			1.12421			0.562104	+	0.827067i	$0.309992\pi$
$608$	−3.82145	+	2.09678i	−0.154980	+	0.0850356i
$609$	−2.56717			−0.104027
$610$	0.0650869	+	0.369126i	0.00263529	+	0.0149455i
$611$	−39.1187	+	32.8245i	−1.58257	+	1.32794i
$612$	4.37521	−	1.59245i	0.176857	−	0.0643708i
$613$	1.96075	+	0.713655i	0.0791940	+	0.0288243i	0.381313	−	0.924446i	$-0.375472\pi$
$613$	1.96075	+	0.713655i	0.0791940	+	0.0288243i	−0.302119	+	0.953270i	$0.597694\pi$
$614$	−5.30689	−	4.45301i	−0.214169	−	0.179709i
$615$	1.66531	−	2.88440i	0.0671518	−	0.116310i
$616$	−0.543033	−	0.940561i	−0.0218794	−	0.0378963i
$617$	−1.78757	+	10.1378i	−0.0719648	+	0.408133i	0.927451	+	0.373946i	$0.121995\pi$
$617$	−1.78757	+	10.1378i	−0.0719648	+	0.408133i	−0.999415	+	0.0341870i	$0.989116\pi$
$618$	2.13114	−	12.0863i	0.0857269	−	0.486182i
$619$	−6.92292	−	11.9909i	−0.278256	−	0.481953i	0.692696	−	0.721230i	$-0.256423\pi$
$619$	−6.92292	−	11.9909i	−0.278256	−	0.481953i	−0.970951	+	0.239277i	$0.923090\pi$
$620$	3.44569	−	5.96811i	0.138382	−	0.239685i
$621$	1.44036	+	1.20860i	0.0577995	+	0.0484995i
$622$	15.3290	+	5.57929i	0.614636	+	0.223709i
$623$	8.43903	−	3.07155i	0.338102	−	0.123059i
$624$	3.59946	−	3.02030i	0.144094	−	0.120909i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	21.0830			0.842646
$627$	−5.47931	+	6.24861i	−0.218823	+	0.249545i
$628$	6.35036			0.253407
$629$	5.34531	+	30.3148i	0.213132	+	1.20873i
$630$	0.436364	−	0.366153i	0.0173851	−	0.0145879i
$631$	−5.48847	+	1.99764i	−0.218492	+	0.0795247i	−0.448947	−	0.893558i	$-0.648201\pi$
$631$	−5.48847	+	1.99764i	−0.218492	+	0.0795247i	0.230455	+	0.973083i	$0.425979\pi$
$632$	14.5016	+	5.27814i	0.576842	+	0.209953i
$633$	−15.3623	−	12.8905i	−0.610597	−	0.512352i
$634$	3.24789	−	5.62551i	0.128990	−	0.223418i
$635$	4.89245	+	8.47397i	0.194151	+	0.336279i
$636$	−1.47197	+	8.34798i	−0.0583676	+	0.331019i
$637$	5.44676	−	30.8901i	0.215809	−	1.22391i
$638$	−4.29627	−	7.44136i	−0.170091	−	0.294606i
$639$	2.21742	−	3.84068i	0.0877196	−	0.151935i
$640$	0.766044	+	0.642788i	0.0302806	+	0.0254084i
$641$	−32.0892	−	11.6795i	−1.26745	−	0.461313i	−0.381185	−	0.924499i	$-0.624484\pi$
$641$	−32.0892	−	11.6795i	−1.26745	−	0.461313i	−0.886261	+	0.463186i	$0.846706\pi$
$642$	5.20010	−	1.89268i	0.205232	−	0.0746983i
$643$	32.7931	−	27.5167i	1.29323	−	1.08515i	0.301961	−	0.953320i	$-0.402359\pi$
$643$	32.7931	−	27.5167i	1.29323	−	1.08515i	0.991272	−	0.131831i	$-0.0420855\pi$
$644$	−0.185986	−	1.05478i	−0.00732888	−	0.0415642i
$645$	−6.70183			−0.263884
$646$	−0.441685	+	20.2902i	−0.0173779	+	0.798309i
$647$	−13.7631			−0.541082			−0.270541	−	0.962708i	$-0.587203\pi$
$647$	−13.7631			−0.541082			−0.270541	+	0.962708i	$0.587203\pi$
$648$	0.173648	+	0.984808i	0.00682154	+	0.0386869i
$649$	1.72510	−	1.44753i	0.0677159	−	0.0568204i
$650$	4.41539	−	1.60707i	0.173186	−	0.0630345i
$651$	−3.68881	−	1.34262i	−0.144576	−	0.0526214i
$652$	−4.11655	−	3.45420i	−0.161217	−	0.135277i
$653$	20.6026	−	35.6848i	0.806244	−	1.39646i	−0.109204	−	0.994019i	$-0.534830\pi$
$653$	20.6026	−	35.6848i	0.806244	−	1.39646i	0.915448	−	0.402436i	$-0.131836\pi$
$654$	−0.671578	−	1.16321i	−0.0262608	−	0.0454850i
$655$	−0.429855	+	2.43783i	−0.0167958	+	0.0952539i
$656$	0.578356	−	3.28002i	0.0225810	−	0.128063i
$657$	6.84049	+	11.8481i	0.266873	+	0.462237i
$658$	−3.09537	+	5.36134i	−0.120670	+	0.209007i
$659$	−19.3097	−	16.2028i	−0.752199	−	0.631170i	0.183884	−	0.982948i	$-0.441133\pi$
$659$	−19.3097	−	16.2028i	−0.752199	−	0.631170i	−0.936083	+	0.351778i	$0.885577\pi$
$660$	1.79163	+	0.652099i	0.0697389	+	0.0253829i
$661$	13.5635	−	4.93669i	0.527557	−	0.192015i	−0.0644901	−	0.997918i	$-0.520542\pi$
$661$	13.5635	−	4.93669i	0.527557	−	0.192015i	0.592047	+	0.805903i	$0.298320\pi$
$662$	−16.9617	+	14.2326i	−0.659236	+	0.553165i
$663$	−3.79898	−	21.5451i	−0.147540	−	0.836741i
$664$	−7.90053			−0.306600
$665$	0.798246	+	2.35116i	0.0309547	+	0.0911740i
$666$	−6.61134			−0.256184
$667$	−1.47145	−	8.34503i	−0.0569749	−	0.323121i
$668$	−18.2383	+	15.3038i	−0.705663	+	0.592121i
$669$	−1.56178	+	0.568442i	−0.0603820	+	0.0219772i
$670$	−0.0103395	−	0.00376328i	−0.000399451	−	0.000145388i
$671$	0.547443	+	0.459359i	0.0211338	+	0.0177334i
$672$	0.284816	−	0.493316i	0.0109870	−	0.0190301i
$673$	−9.96944	−	17.2676i	−0.384294	−	0.665616i	0.607377	−	0.794414i	$-0.292222\pi$
$673$	−9.96944	−	17.2676i	−0.384294	−	0.665616i	−0.991671	+	0.128797i	$0.958888\pi$
$674$	−2.09241	+	11.8666i	−0.0805965	+	0.457086i
$675$	−0.173648	+	0.984808i	−0.00668372	+	0.0379053i
$676$	−4.53916	−	7.86206i	−0.174583	−	0.302387i
$677$	−24.4845	+	42.4083i	−0.941014	+	1.62988i	−0.177472	+	0.984126i	$0.556792\pi$
$677$	−24.4845	+	42.4083i	−0.941014	+	1.62988i	−0.763542	+	0.645758i	$0.776541\pi$
$678$	15.5375	+	13.0375i	0.596715	+	0.500703i
$679$	1.20212	+	0.437535i	0.0461331	+	0.0167911i
$680$	4.37521	−	1.59245i	0.167782	−	0.0610675i
$681$	6.05818	−	5.08341i	0.232150	−	0.194797i
$682$	−2.28159	−	12.9395i	−0.0873666	−	0.495481i
$683$	−3.53652			−0.135321			−0.0676606	−	0.997708i	$-0.521553\pi$
$683$	−3.53652			−0.135321			−0.0676606	+	0.997708i	$0.521553\pi$
$684$	−4.27519	−	0.850158i	−0.163466	−	0.0325066i
$685$	1.85332			0.0708116
$686$	−1.35272	−	7.67167i	−0.0516472	−	0.292906i
$687$	−3.77546	+	3.16799i	−0.144043	+	0.120866i
$688$	−6.29766	+	2.29216i	−0.240096	+	0.0873878i
$689$	37.4282	+	13.6227i	1.42590	+	0.518985i
$690$	1.44036	+	1.20860i	0.0548334	+	0.0460107i
$691$	7.55414	−	13.0841i	0.287373	−	0.497744i	−0.685809	−	0.727782i	$-0.740551\pi$
$691$	7.55414	−	13.0841i	0.287373	−	0.497744i	0.973182	+	0.230037i	$0.0738848\pi$
$692$	−6.35808	−	11.0125i	−0.241698	−	0.418633i
$693$	0.188593	−	1.06957i	0.00716407	−	0.0406295i
$694$	−3.40691	+	19.3215i	−0.129324	+	0.733435i
$695$	−9.84715	−	17.0558i	−0.373524	−	0.646962i
$696$	2.25336	−	3.90293i	0.0854134	−	0.147940i
$697$	−11.8793	−	9.96795i	−0.449962	−	0.377563i
$698$	−10.0411	−	3.65466i	−0.380061	−	0.138331i
$699$	−14.3979	+	5.24041i	−0.544579	+	0.198211i
$700$	0.436364	−	0.366153i	0.0164930	−	0.0138393i
$701$	−2.87500	−	16.3049i	−0.108587	−	0.615829i	−0.989727	−	0.142972i	$-0.954334\pi$
$701$	−2.87500	−	16.3049i	−0.108587	−	0.615829i	0.881139	−	0.472856i	$-0.156777\pi$
$702$	4.69876			0.177343
$703$	10.4434	−	26.8593i	0.393881	−	1.01302i
$704$	1.90661			0.0718580
$705$	−1.88720	−	10.7028i	−0.0710761	−	0.403093i
$706$	8.92997	−	7.49313i	0.336084	−	0.282008i
$707$	1.19821	−	0.436112i	0.0450632	−	0.0164017i
$708$	1.10990	+	0.403970i	0.0417126	+	0.0151821i
$709$	27.0565	+	22.7031i	1.01613	+	0.852632i	0.989136	−	0.147003i	$-0.0469628\pi$
$709$	27.0565	+	22.7031i	1.01613	+	0.852632i	0.0269918	+	0.999636i	$0.491407\pi$
$710$	2.21742	−	3.84068i	0.0832182	−	0.144138i
$711$	7.71613	+	13.3647i	0.289377	+	0.501216i
$712$	−2.73768	+	15.5261i	−0.102599	+	0.581866i
$713$	2.25005	−	12.7607i	0.0842650	−	0.477891i
$714$	−1.32611	−	2.29688i	−0.0496282	−	0.0859586i
$715$	4.47935	−	7.75845i	0.167518	−	0.290150i
$716$	9.94059	+	8.34115i	0.371497	+	0.311723i
$717$	7.81116	+	2.84303i	0.291713	+	0.106175i
$718$	−2.67695	+	0.974329i	−0.0999028	+	0.0363616i
$719$	25.4566	−	21.3607i	0.949373	−	0.796618i	−0.0298191	−	0.999555i	$-0.509493\pi$
$719$	25.4566	−	21.3607i	0.949373	−	0.796618i	0.979192	+	0.202937i	$0.0650487\pi$
$720$	0.173648	+	0.984808i	0.00647149	+	0.0367016i
$721$	−6.99095			−0.260357
$722$	10.2070	−	16.0255i	0.379867	−	0.596407i
$723$	4.31223			0.160373
$724$	4.04578	+	22.9447i	0.150360	+	0.852735i
$725$	3.45235	−	2.89686i	0.128217	−	0.107587i
$726$	−6.92069	+	2.51892i	−0.256851	+	0.0934861i
$727$	24.3987	+	8.88039i	0.904897	+	0.329355i	0.752213	−	0.658920i	$-0.228986\pi$
$727$	24.3987	+	8.88039i	0.904897	+	0.329355i	0.152683	+	0.988275i	$0.451209\pi$
$728$	−2.05037	−	1.72046i	−0.0759917	−	0.0637646i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	6.84049	+	11.8481i	0.253178	+	0.438517i
$731$	−5.41847	+	30.7297i	−0.200409	+	1.13658i
$732$	−0.0650869	+	0.369126i	−0.00240568	+	0.0136433i
$733$	4.31650	+	7.47640i	0.159434	+	0.276147i	0.934665	−	0.355531i	$-0.115700\pi$
$733$	4.31650	+	7.47640i	0.159434	+	0.276147i	−0.775231	+	0.631678i	$0.782367\pi$
$734$	10.2902	−	17.8232i	0.379819	−	0.657866i
$735$	5.11374	+	4.29094i	0.188623	+	0.158274i
$736$	1.76686	+	0.643084i	0.0651272	+	0.0237044i
$737$	−0.0197135	+	0.00717511i	−0.000726155	+	0.000264299i
$738$	2.55140	−	2.14088i	0.0939184	−	0.0788069i
$739$	3.73234	+	21.1671i	0.137296	+	0.778645i	0.973233	+	0.229820i	$0.0738137\pi$
$739$	3.73234	+	21.1671i	0.137296	+	0.778645i	−0.835937	+	0.548825i	$0.815075\pi$
$740$	−6.61134			−0.243038
$741$	−7.42226	+	19.0892i	−0.272663	+	0.701260i
$742$	4.82864			0.177265
$743$	−5.21959	−	29.6018i	−0.191488	−	1.08598i	−0.917332	−	0.398124i	$-0.869661\pi$
$743$	−5.21959	−	29.6018i	−0.191488	−	1.08598i	0.725843	−	0.687860i	$-0.241450\pi$
$744$	5.27910	−	4.42969i	0.193541	−	0.162400i
$745$	0.849189	−	0.309080i	0.0311119	−	0.0113238i
$746$	35.4661	+	12.9086i	1.29851	+	0.472618i
$747$	−6.05216	−	5.07836i	−0.221437	−	0.185808i
$748$	4.43859	−	7.68786i	0.162291	−	0.281096i
$749$	−1.57613	−	2.72993i	−0.0575904	−	0.0997495i
$750$	−0.173648	+	0.984808i	−0.00634073	+	0.0359601i
$751$	1.58443	−	8.98572i	0.0578165	−	0.327894i	−0.942157	−	0.335172i	$-0.891206\pi$
$751$	1.58443	−	8.98572i	0.0578165	−	0.327894i	0.999974	+	0.00727815i	$0.00231673\pi$
$752$	−5.43398	−	9.41193i	−0.198157	−	0.343218i
$753$	−6.23637	+	10.8017i	−0.227266	+	0.393636i
$754$	−16.2217	−	13.6117i	−0.590761	−	0.495707i
$755$	−2.87491	−	1.04638i	−0.104629	−	0.0380817i
$756$	0.535279	−	0.194826i	0.0194679	−	0.00708575i
$757$	29.9104	−	25.0978i	1.08711	−	0.912194i	0.0906186	−	0.995886i	$-0.471116\pi$
$757$	29.9104	−	25.0978i	1.08711	−	0.912194i	0.996492	+	0.0836918i	$0.0266711\pi$
$758$	−5.31473	−	30.1414i	−0.193040	−	1.09478i
$759$	3.58490			0.130124
$760$	−4.27519	−	0.850158i	−0.155077	−	0.0308385i
$761$	−50.6368			−1.83558			−0.917791	−	0.397063i	$-0.870029\pi$
$761$	−50.6368			−1.83558			−0.917791	+	0.397063i	$0.870029\pi$
$762$	1.69913	+	9.63625i	0.0615530	+	0.349084i
$763$	−0.586104	+	0.491800i	−0.0212184	+	0.0178044i
$764$	−10.1146	+	3.68140i	−0.365932	+	0.133188i
$765$	4.37521	+	1.59245i	0.158186	+	0.0575750i
$766$	−1.12457	−	0.943628i	−0.0406324	−	0.0340947i
$767$	2.77492	−	4.80631i	0.100197	−	0.173546i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	7.65295	−	43.4021i	0.275973	−	1.56512i	−0.459883	−	0.887980i	$-0.652109\pi$
$769$	7.65295	−	43.4021i	0.275973	−	1.56512i	0.735855	−	0.677139i	$-0.236780\pi$
$770$	0.188593	−	1.06957i	0.00679643	−	0.0385445i
$771$	−2.06585	−	3.57815i	−0.0743997	−	0.128864i
$772$	0.940879	−	1.62965i	0.0338630	−	0.0586524i
$773$	−36.2688	−	30.4332i	−1.30450	−	1.09460i	−0.989349	−	0.145563i	$-0.953501\pi$
$773$	−36.2688	−	30.4332i	−1.30450	−	1.09460i	−0.315150	−	0.949042i	$-0.602055\pi$
$774$	−6.29766	−	2.29216i	−0.226365	−	0.0823900i
$775$	6.47578	−	2.35699i	0.232617	−	0.0846656i
$776$	−1.72036	+	1.44356i	−0.0617575	+	0.0518207i
$777$	0.653965	+	3.70882i	0.0234609	+	0.133053i
$778$	31.5679			1.13176
$779$	4.66731	+	13.7471i	0.167224	+	0.492542i
$780$	4.69876			0.168243
$781$	−1.46828	−	8.32703i	−0.0525392	−	0.297965i
$782$	6.70630	−	5.62725i	0.239817	−	0.201230i
$783$	4.23493	−	1.54139i	0.151344	−	0.0550847i
$784$	6.27294	+	2.28316i	0.224033	+	0.0815415i
$785$	4.86466	+	4.08193i	0.173627	+	0.145690i
$786$	−1.23772	+	2.14379i	−0.0441480	+	0.0764665i
$787$	20.7694	+	35.9736i	0.740349	+	1.28232i	0.952337	+	0.305049i	$0.0986729\pi$
$787$	20.7694	+	35.9736i	0.740349	+	1.28232i	−0.211988	+	0.977272i	$0.567994\pi$
$788$	0.726843	−	4.12213i	0.0258927	−	0.146845i
$789$	−2.54331	+	14.4238i	−0.0905441	+	0.513501i
$790$	7.71613	+	13.3647i	0.274527	+	0.475496i
$791$	5.77687	−	10.0058i	0.205402	−	0.355766i
$792$	1.46055	+	1.22554i	0.0518983	+	0.0435478i
$793$	1.65498	+	0.602362i	0.0587700	+	0.0213905i
$794$	26.3206	−	9.57992i	0.934084	−	0.339979i
$795$	−6.49357	+	5.44876i	−0.230303	+	0.193247i
$796$	2.41847	+	13.7158i	0.0857202	+	0.486144i
$797$	−39.8335			−1.41097			−0.705487	−	0.708722i	$-0.749272\pi$
$797$	−39.8335			−1.41097			−0.705487	+	0.708722i	$0.749272\pi$
$798$	−0.0540374	+	2.48238i	−0.00191290	+	0.0878754i
$799$	−50.6012			−1.79014
$800$	0.173648	+	0.984808i	0.00613939	+	0.0348182i
$801$	−12.0772	+	10.1340i	−0.426726	+	0.358066i
$802$	−29.0648	+	10.5787i	−1.02631	+	0.373547i
$803$	24.5112	+	8.92134i	0.864981	+	0.314827i
$804$	−0.00842887	−	0.00707266i	−0.000297263	−	0.000249434i
$805$	0.535526	−	0.927558i	0.0188748	−	0.0326921i
$806$	−16.1905	−	28.0427i	−0.570285	−	0.987762i
$807$	0.325248	−	1.84457i	0.0114493	−	0.0649320i
$808$	−0.388706	+	2.20446i	−0.0136746	+	0.0775527i
$809$	−20.1288	−	34.8641i	−0.707690	−	1.22575i	−0.965712	−	0.259616i	$-0.916404\pi$
$809$	−20.1288	−	34.8641i	−0.707690	−	1.22575i	0.258022	−	0.966139i	$-0.416929\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	11.0461	+	9.26878i	0.387881	+	0.325471i	0.815787	−	0.578352i	$-0.196304\pi$
$811$	11.0461	+	9.26878i	0.387881	+	0.325471i	−0.427906	+	0.903823i	$0.640749\pi$
$812$	−2.41235	−	0.878025i	−0.0846570	−	0.0308126i
$813$	−26.4699	+	9.63425i	−0.928339	+	0.337888i
$814$	−9.65617	+	8.10249i	−0.338449	+	0.283992i
$815$	−0.933147	−	5.29214i	−0.0326867	−	0.185376i
$816$	4.65600			0.162993
$817$	19.2601	−	21.9642i	0.673825	−	0.768430i
$818$	6.81190			0.238172
$819$	−0.464781	−	2.63590i	−0.0162407	−	0.0921059i
$820$	2.55140	−	2.14088i	0.0890988	−	0.0747628i
$821$	−41.6527	+	15.1603i	−1.45369	+	0.529099i	−0.943619	−	0.331034i	$-0.892603\pi$
$821$	−41.6527	+	15.1603i	−1.45369	+	0.529099i	−0.510070	+	0.860133i	$0.670380\pi$
$822$	1.74155	+	0.633871i	0.0607434	+	0.0221088i
$823$	12.2560	+	10.2840i	0.427216	+	0.358477i	0.830900	−	0.556421i	$-0.187826\pi$
$823$	12.2560	+	10.2840i	0.427216	+	0.358477i	−0.403684	+	0.914899i	$0.632270\pi$
$824$	6.13637	−	10.6285i	0.213771	−	0.370261i
$825$	0.953304	+	1.65117i	0.0331898	+	0.0574864i
$826$	0.116832	−	0.662588i	0.00406511	−	0.0230544i
$827$	5.17438	−	29.3454i	0.179931	−	1.02044i	−0.752366	−	0.658745i	$-0.771087\pi$
$827$	5.17438	−	29.3454i	0.179931	−	1.02044i	0.932297	−	0.361694i	$-0.117801\pi$
$828$	0.940125	+	1.62835i	0.0326716	+	0.0565889i
$829$	17.6436	−	30.5596i	0.612787	−	1.06138i	−0.377981	−	0.925813i	$-0.623382\pi$
$829$	17.6436	−	30.5596i	0.612787	−	1.06138i	0.990768	−	0.135565i	$-0.0432851\pi$
$830$	−6.05216	−	5.07836i	−0.210073	−	0.176273i
$831$	5.70697	+	2.07717i	0.197973	+	0.0720562i
$832$	4.41539	−	1.60707i	0.153076	−	0.0557151i
$833$	23.8096	−	19.9786i	0.824954	−	0.692219i
$834$	−3.41988	−	19.3951i	−0.118421	−	0.671598i
$835$	−23.8085			−0.823926
$836$	−7.28602	+	3.99774i	−0.251992	+	0.138265i
$837$	6.89138			0.238201
$838$	−6.52638	−	37.0130i	−0.225450	−	1.27859i
$839$	29.9098	−	25.0973i	1.03260	−	0.866456i	0.0414438	−	0.999141i	$-0.486804\pi$
$839$	29.9098	−	25.0973i	1.03260	−	0.866456i	0.991158	+	0.132685i	$0.0423598\pi$
$840$	0.535279	−	0.194826i	0.0184689	−	0.00672213i
$841$	8.16545	+	2.97198i	0.281567	+	0.102482i
$842$	−19.2387	−	16.1432i	−0.663011	−	0.556332i
$843$	−0.971146	+	1.68207i	−0.0334480	+	0.0579337i
$844$	−10.0270	−	17.3673i	−0.345145	−	0.597808i
$845$	1.57643	−	8.94040i	0.0542310	−	0.307559i
$846$	1.88720	−	10.7028i	0.0648833	−	0.367971i
$847$	2.09763	+	3.63320i	0.0720753	+	0.124838i
$848$	−4.23838	+	7.34109i	−0.145547	+	0.252094i
$849$	24.5040	+	20.5613i	0.840975	+	0.705662i
$850$	4.37521	+	1.59245i	0.150069	+	0.0546205i
$851$	−11.6813	+	4.25165i	−0.400430	+	0.145745i
$852$	3.39728	−	2.85066i	0.116389	−	0.0976619i
$853$	−7.00668	−	39.7368i	−0.239904	−	1.36056i	−0.832036	−	0.554722i	$-0.812825\pi$
$853$	−7.00668	−	39.7368i	−0.239904	−	1.36056i	0.592132	−	0.805841i	$-0.298287\pi$
$854$	0.213510			0.00730616
$855$	−2.72851	−	3.39930i	−0.0933132	−	0.116253i
$856$	5.53384			0.189143
$857$	−10.0743	−	57.1341i	−0.344131	−	1.95166i	−0.304723	−	0.952441i	$-0.598564\pi$
$857$	−10.0743	−	57.1341i	−0.344131	−	1.95166i	−0.0394077	−	0.999223i	$-0.512547\pi$
$858$	6.86276	−	5.75854i	0.234291	−	0.196593i
$859$	−21.4748	+	7.81618i	−0.732710	+	0.266684i	−0.681311	−	0.731994i	$-0.738590\pi$
$859$	−21.4748	+	7.81618i	−0.732710	+	0.266684i	−0.0513982	+	0.998678i	$0.516368\pi$
$860$	−6.29766	−	2.29216i	−0.214748	−	0.0781620i
$861$	−1.45336	−	1.21952i	−0.0495304	−	0.0415610i
$862$	−10.1499	+	17.5802i	−0.345707	+	0.598782i
$863$	−2.05196	−	3.55410i	−0.0698495	−	0.120983i	0.828985	−	0.559270i	$-0.188919\pi$
$863$	−2.05196	−	3.55410i	−0.0698495	−	0.120983i	−0.898835	+	0.438287i	$0.855585\pi$
$864$	−0.173648	+	0.984808i	−0.00590763	+	0.0335038i
$865$	2.20814	−	12.5230i	0.0750789	−	0.425794i
$866$	4.07252	+	7.05381i	0.138390	+	0.239698i
$867$	2.33918	−	4.05158i	0.0794428	−	0.137599i
$868$	−3.00715	−	2.52330i	−0.102069	−	0.0856463i
$869$	27.6488	+	10.0634i	0.937922	+	0.341376i
$870$	4.23493	−	1.54139i	0.143578	−	0.0522580i
$871$	−0.0396052	+	0.0332327i	−0.00134197	+	0.00112605i
$872$	−0.233237	−	1.32275i	−0.00789838	−	0.0447940i
$873$	−2.24578			−0.0760080
$874$	−8.10037	+	1.24720i	−0.273999	+	0.0421870i
$875$	0.569632			0.0192571
$876$	2.37568	+	13.4731i	0.0802666	+	0.455215i
$877$	33.9981	−	28.5278i	1.14803	−	0.963315i	0.148362	−	0.988933i	$-0.452600\pi$
$877$	33.9981	−	28.5278i	1.14803	−	0.963315i	0.999672	+	0.0256181i	$0.00815540\pi$
$878$	−10.7851	+	3.92546i	−0.363980	+	0.132478i
$879$	−28.4472	−	10.3539i	−0.959499	−	0.349229i
$880$	1.46055	+	1.22554i	0.0492350	+	0.0413131i
$881$	18.8166	−	32.5914i	0.633948	−	1.09803i	−0.352788	−	0.935703i	$-0.614766\pi$
$881$	18.8166	−	32.5914i	0.633948	−	1.09803i	0.986737	−	0.162328i	$-0.0519002\pi$
$882$	3.33776	+	5.78117i	0.112388	+	0.194662i
$883$	−4.31496	+	24.4714i	−0.145210	+	0.823527i	0.821988	+	0.569504i	$0.192865\pi$
$883$	−4.31496	+	24.4714i	−0.145210	+	0.823527i	−0.967198	+	0.254022i	$0.918246\pi$
$884$	3.79898	−	21.5451i	0.127773	−	0.724639i
$885$	0.590565	+	1.02289i	0.0198516	+	0.0343840i
$886$	−7.36566	+	12.7577i	−0.247454	+	0.428604i
$887$	−9.09084	−	7.62812i	−0.305241	−	0.256127i	0.477281	−	0.878751i	$-0.341622\pi$
$887$	−9.09084	−	7.62812i	−0.305241	−	0.256127i	−0.782522	+	0.622623i	$0.786067\pi$
$888$	−6.21263	−	2.26121i	−0.208482	−	0.0758813i
$889$	5.23766	−	1.90635i	0.175665	−	0.0639370i
$890$	−12.0772	+	10.1340i	−0.404828	+	0.339691i
$891$	0.331079	+	1.87764i	0.0110916	+	0.0629034i
$892$	−1.66201			−0.0556483
$893$	40.5004	+	24.5734i	1.35530	+	0.822317i
$894$	0.903688			0.0302239
$895$	2.25335	+	12.7794i	0.0753212	+	0.427168i
$896$	0.436364	−	0.366153i	0.0145779	−	0.0122323i
$897$	8.30204	−	3.02169i	0.277197	−	0.100891i
$898$	−12.2369	−	4.45387i	−0.408351	−	0.148628i
$899$	−23.7914	−	19.9634i	−0.793488	−	0.665816i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	19.7339	+	34.1801i	0.657432	+	1.13871i
$902$	1.10270	−	6.25371i	0.0367158	−	0.208226i
$903$	−0.662916	+	3.75958i	−0.0220605	+	0.125111i
$904$	10.1414	+	17.5654i	0.337298	+	0.584217i
$905$	−11.6494	+	20.1773i	−0.387238	+	0.670715i
$906$	−2.34365	−	1.96655i	−0.0778625	−	0.0653344i
$907$	−31.4711	−	11.4546i	−1.04498	−	0.380342i	−0.238215	−	0.971212i	$-0.576562\pi$
$907$	−31.4711	−	11.4546i	−1.04498	−	0.380342i	−0.806767	+	0.590870i	$0.798785\pi$
$908$	7.43145	−	2.70483i	0.246621	−	0.0897628i
$909$	−1.71477	+	1.43886i	−0.0568752	+	0.0477240i
$910$	−0.464781	−	2.63590i	−0.0154073	−	0.0873793i
$911$	−49.8592			−1.65191			−0.825955	−	0.563736i	$-0.809364\pi$
$911$	−49.8592			−1.65191			−0.825955	+	0.563736i	$0.809364\pi$
$912$	−3.72659	−	2.26109i	−0.123400	−	0.0748721i
$913$	−15.0632			−0.498520
$914$	5.07710	+	28.7937i	0.167936	+	0.952410i
$915$	−0.287129	+	0.240930i	−0.00949219	+	0.00796490i
$916$	−4.63129	+	1.68565i	−0.153022	+	0.0556955i
$917$	1.32505	+	0.482279i	0.0437570	+	0.0159263i
$918$	3.56671	+	2.99282i	0.117719	+	0.0987778i
$919$	4.26840	−	7.39308i	0.140801	−	0.243875i	−0.786997	−	0.616957i	$-0.788365\pi$
$919$	4.26840	−	7.39308i	0.140801	−	0.243875i	0.927799	+	0.373081i	$0.121699\pi$
$920$	0.940125	+	1.62835i	0.0309950	+	0.0536849i
$921$	1.20297	−	6.82241i	0.0396394	−	0.224806i
$922$	1.61311	−	9.14841i	0.0531250	−	0.301287i
$923$	−10.4191	−	18.0464i	−0.342949	−	0.594005i
$924$	0.543033	−	0.940561i	0.0178645	−	0.0309422i
$925$	−5.06458	−	4.24969i	−0.166522	−	0.139729i
$926$	21.1988	+	7.71574i	0.696636	+	0.253555i
$927$	11.5326	−	4.19752i	0.378780	−	0.137865i
$928$	3.45235	−	2.89686i	0.113329	−	0.0950942i
$929$	3.34689	+	18.9812i	0.109808	+	0.622751i	0.989191	+	0.146636i	$0.0468445\pi$
$929$	3.34689	+	18.9812i	0.109808	+	0.622751i	−0.879383	+	0.476116i	$0.842044\pi$
$930$	6.89138			0.225977
$931$	−28.7590	+	4.42796i	−0.942539	+	0.145121i
$932$	−15.3219			−0.501887
$933$	2.83268	+	16.0649i	0.0927379	+	0.525943i
$934$	−4.00233	+	3.35836i	−0.130960	+	0.109889i
$935$	8.34182	−	3.03617i	0.272807	−	0.0992935i
$936$	4.41539	+	1.60707i	0.144321	+	0.0525287i
$937$	35.6913	+	29.9485i	1.16598	+	0.978376i	0.999970	−	0.00774733i	$-0.00246608\pi$
$937$	35.6913	+	29.9485i	1.16598	+	0.978376i	0.166013	+	0.986124i	$0.446911\pi$
$938$	−0.00313386	+	0.00542801i	−0.000102324	+	0.000177231i
$939$	10.5415	+	18.2584i	0.344009	+	0.595841i
$940$	1.88720	−	10.7028i	0.0615537	−	0.349088i
$941$	9.54065	−	54.1077i	0.311016	−	1.76386i	−0.282720	−	0.959202i	$-0.591237\pi$
$941$	9.54065	−	54.1077i	0.311016	−	1.76386i	0.593737	−	0.804660i	$-0.297652\pi$
$942$	3.17518	+	5.49957i	0.103453	+	0.179186i
$943$	3.13120	−	5.42340i	0.101966	−	0.176610i
$944$	0.904798	+	0.759216i	0.0294487	+	0.0247104i
$945$	0.535279	+	0.194826i	0.0174126	+	0.00633768i
$946$	−12.0072	+	4.37025i	−0.390387	+	0.142089i
$947$	20.4019	−	17.1192i	0.662973	−	0.556301i	−0.248003	−	0.968759i	$-0.579774\pi$
$947$	20.4019	−	17.1192i	0.662973	−	0.556301i	0.910976	+	0.412458i	$0.135330\pi$
$948$	2.67978	+	15.1978i	0.0870353	+	0.493602i
$949$	64.2836			2.08673
$950$	−2.72851	−	3.39930i	−0.0885246	−	0.110288i
$951$	6.49578			0.210640
$952$	−0.460552	−	2.61192i	−0.0149266	−	0.0846527i
$953$	−6.55331	+	5.49888i	−0.212283	+	0.178126i	−0.742729	−	0.669592i	$-0.766469\pi$
$953$	−6.55331	+	5.49888i	−0.212283	+	0.178126i	0.530446	+	0.847719i	$0.322024\pi$
$954$	−7.96555	+	2.89922i	−0.257894	+	0.0938658i
$955$	−10.1146	−	3.68140i	−0.327299	−	0.119127i
$956$	6.36772	+	5.34315i	0.205947	+	0.172810i
$957$	4.29627	−	7.44136i	0.138879	−	0.240545i
$958$	−12.0738	−	20.9125i	−0.390088	−	0.675653i
$959$	0.183322	−	1.03967i	0.00591977	−	0.0335727i
$960$	−0.173648	+	0.984808i	−0.00560447	+	0.0317845i
$961$	−8.24554	−	14.2817i	−0.265985	−	0.460700i
$962$	−15.5325	+	26.9032i	−0.500789	+	0.867393i
$963$	4.23916	+	3.55708i	0.136605	+	0.114625i
$964$	4.05217	+	1.47487i	0.130512	+	0.0475023i
$965$	1.76827	−	0.643599i	0.0569227	−	0.0207182i
$966$	0.820473	−	0.688459i	0.0263983	−	0.0221508i
$967$	5.11318	+	28.9983i	0.164429	+	0.932521i	0.949652	+	0.313308i	$0.101437\pi$
$967$	5.11318	+	28.9983i	0.164429	+	0.932521i	−0.785223	+	0.619213i	$0.787452\pi$
$968$	−7.36484			−0.236715
$969$	−17.7927	+	9.76261i	−0.571584	+	0.313620i
$970$	−2.24578			−0.0721075
$971$	−7.36742	−	41.7827i	−0.236432	−	1.34087i	−0.839577	−	0.543240i	$-0.817197\pi$
$971$	−7.36742	−	41.7827i	−0.236432	−	1.34087i	0.603146	−	0.797631i	$-0.293914\pi$
$972$	−0.766044	+	0.642788i	−0.0245709	+	0.0206174i
$973$	−10.5420	+	3.83696i	−0.337960	+	0.123007i
$974$	−10.3414	−	3.76396i	−0.331360	−	0.120605i
$975$	3.59946	+	3.02030i	0.115275	+	0.0967271i
$976$	−0.187410	+	0.324604i	−0.00599885	+	0.0103903i
$977$	0.790147	+	1.36857i	0.0252790	+	0.0437846i	0.878388	−	0.477948i	$-0.158619\pi$
$977$	0.790147	+	1.36857i	0.0252790	+	0.0437846i	−0.853109	+	0.521732i	$0.825286\pi$
$978$	0.933147	−	5.29214i	0.0298388	−	0.169224i
$979$	−5.21968	+	29.6023i	−0.166822	+	0.946092i
$980$	3.33776	+	5.78117i	0.106621	+	0.184673i
$981$	0.671578	−	1.16321i	0.0214418	−	0.0371383i
$982$	−23.0133	−	19.3104i	−0.734383	−	0.616220i
$983$	25.2590	+	9.19354i	0.805638	+	0.293228i	0.711821	−	0.702361i	$-0.247871\pi$
$983$	25.2590	+	9.19354i	0.805638	+	0.293228i	0.0938175	+	0.995589i	$0.470093\pi$
$984$	3.12976	−	1.13914i	0.0997730	−	0.0363144i
$985$	3.20645	−	2.69053i	0.102166	−	0.0857274i
$986$	−3.64371	−	20.6645i	−0.116039	−	0.658092i
$987$	−6.19074			−0.197053
$988$	−13.5035	+	15.3994i	−0.429605	+	0.489921i
$989$	−12.6011			−0.400692
$990$	0.331079	+	1.87764i	0.0105224	+	0.0596754i
$991$	16.8506	−	14.1393i	0.535276	−	0.449150i	−0.334643	−	0.942345i	$-0.608616\pi$
$991$	16.8506	−	14.1393i	0.535276	−	0.449150i	0.869919	+	0.493195i	$0.164171\pi$
$992$	6.47578	−	2.35699i	0.205606	−	0.0748345i
$993$	−20.8066	−	7.57299i	−0.660278	−	0.240322i
$994$	−1.93520	−	1.62383i	−0.0613808	−	0.0515046i
$995$	−6.96369	+	12.0615i	−0.220764	+	0.382374i
$996$	−3.95026	−	6.84206i	−0.125169	−	0.216799i
$997$	−2.88487	+	16.3609i	−0.0913646	+	0.518154i	0.904436	+	0.426609i	$0.140292\pi$
$997$	−2.88487	+	16.3609i	−0.0913646	+	0.518154i	−0.995801	+	0.0915457i	$0.970819\pi$
$998$	−1.07991	+	6.12447i	−0.0341839	+	0.193867i
$999$	−3.30567	−	5.72559i	−0.104587	−	0.181150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.j.541.1	yes	12
19.17	even	9	inner	570.2.u.j.511.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.j.511.1	✓	12	19.17	even	9	inner
570.2.u.j.541.1	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.284816 + 0.493316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.284816 + 0.493316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.173648 - 0.984808i) q^{10} +(-0.953304 - 1.65117i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.59946 - 3.02030i) q^{13} +(-0.535279 - 0.194826i) q^{14} +(0.939693 - 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.808506 - 4.58527i) q^{17} +1.00000 q^{18} +(-1.57962 + 4.06261i) q^{19} +1.00000 q^{20} +(-0.0989156 - 0.560978i) q^{21} +(1.46055 - 1.22554i) q^{22} +(1.76686 - 0.643084i) q^{23} +(0.939693 + 0.342020i) q^{24} +(0.766044 + 0.642788i) q^{25} +(2.34938 - 4.06924i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.0989156 - 0.560978i) q^{28} +(0.782583 - 4.43825i) q^{29} +(0.500000 + 0.866025i) q^{30} +(3.44569 - 5.96811i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.79163 + 0.652099i) q^{33} +(4.37521 - 1.59245i) q^{34} +(0.436364 - 0.366153i) q^{35} +(0.173648 + 0.984808i) q^{36} -6.61134 q^{37} +(-4.27519 - 0.850158i) q^{38} +4.69876 q^{39} +(0.173648 + 0.984808i) q^{40} +(2.55140 - 2.14088i) q^{41} +(0.535279 - 0.194826i) q^{42} +(-6.29766 - 2.29216i) q^{43} +(1.46055 + 1.22554i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.940125 + 1.62835i) q^{46} +(1.88720 - 10.7028i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(3.33776 + 5.78117i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.56671 + 2.99282i) q^{51} +(4.41539 + 1.60707i) q^{52} +(-7.96555 + 2.89922i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(0.331079 + 1.87764i) q^{55} +0.569632 q^{56} +(-1.40134 - 4.12750i) q^{57} +4.50672 q^{58} +(0.205101 + 1.16319i) q^{59} +(-0.766044 + 0.642788i) q^{60} +(-0.352216 + 0.128196i) q^{61} +(6.47578 + 2.35699i) q^{62} +(0.436364 + 0.366153i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.34938 + 4.06924i) q^{65} +(-0.331079 + 1.87764i) q^{66} +(0.00191067 - 0.0108359i) q^{67} +(2.32800 + 4.03222i) q^{68} +(-0.940125 + 1.62835i) q^{69} +(0.436364 + 0.366153i) q^{70} +(4.16738 + 1.51680i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(-10.4802 + 8.79396i) q^{73} +(-1.14805 - 6.51090i) q^{74} -1.00000 q^{75} +(0.0948636 - 4.35787i) q^{76} +1.08607 q^{77} +(0.815931 + 4.62737i) q^{78} +(-11.8218 + 9.91966i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(2.55140 + 2.14088i) q^{82} +(3.95026 - 6.84206i) q^{83} +(0.284816 + 0.493316i) q^{84} +(-0.808506 + 4.58527i) q^{85} +(1.16376 - 6.60002i) q^{86} +(2.25336 + 3.90293i) q^{87} +(-0.953304 + 1.65117i) q^{88} +(-12.0772 - 10.1340i) q^{89} +(-0.939693 - 0.342020i) q^{90} +(2.51515 - 0.915439i) q^{91} +(-1.44036 + 1.20860i) q^{92} +(1.19668 + 6.78668i) q^{93} +10.8680 q^{94} +(2.87385 - 3.27734i) q^{95} -1.00000 q^{96} +(-0.389975 - 2.21166i) q^{97} +(-5.11374 + 4.29094i) q^{98} +(-1.79163 + 0.652099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^7 - 6 * q^8	\( 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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