LMFDB - Embedded newform 43.2.e.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			4.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	43.4
Dual form			43.2.e.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777479 + 0.974928i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-0.500000 - 0.240787i) q^{5} -0.554958 q^{6} +1.35690 q^{7} +(-2.74698 - 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +O(q^{10})$	\(q+(-0.777479 + 0.974928i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-0.500000 - 0.240787i) q^{5} -0.554958 q^{6} +1.35690 q^{7} +(-2.74698 - 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +(0.623490 - 0.300257i) q^{10} +(0.480386 - 2.10471i) q^{11} +(-0.123490 + 0.154851i) q^{12} +(-1.42543 - 0.686450i) q^{13} +(-1.05496 + 1.32288i) q^{14} +(-0.0549581 - 0.240787i) q^{15} +(2.62349 - 1.26341i) q^{16} +(-2.24698 + 1.08209i) q^{17} +(2.17845 + 2.73169i) q^{18} +(1.29105 + 5.65647i) q^{19} +(0.0549581 - 0.240787i) q^{20} +(0.376510 + 0.472129i) q^{21} +(1.67845 + 2.10471i) q^{22} +(-1.13437 + 4.97002i) q^{23} +(-0.301938 - 1.32288i) q^{24} +(-2.92543 - 3.66837i) q^{25} +(1.77748 - 0.855989i) q^{26} +(2.32640 - 1.12033i) q^{27} +(0.134375 + 0.588735i) q^{28} +(-3.74094 + 4.69099i) q^{29} +(0.277479 + 0.133627i) q^{30} +(4.75451 - 5.96197i) q^{31} +(0.548917 - 2.40496i) q^{32} +(0.865625 - 0.416863i) q^{33} +(0.692021 - 3.03194i) q^{34} +(-0.678448 - 0.326723i) q^{35} +1.24698 q^{36} -7.18598 q^{37} +(-6.51842 - 3.13910i) q^{38} +(-0.156678 - 0.686450i) q^{39} +(1.05496 + 1.32288i) q^{40} +(6.54288 - 8.20451i) q^{41} -0.753020 q^{42} +(-3.91454 + 5.26083i) q^{43} +0.960771 q^{44} +(-0.969501 + 1.21572i) q^{45} +(-3.96346 - 4.97002i) q^{46} +(2.43416 + 10.6647i) q^{47} +(1.16756 + 0.562269i) q^{48} -5.15883 q^{49} +5.85086 q^{50} +(-1.00000 - 0.481575i) q^{51} +(0.156678 - 0.686450i) q^{52} +(2.77144 - 1.33465i) q^{53} +(-0.716480 + 3.13910i) q^{54} +(-0.746980 + 0.936683i) q^{55} +(-3.72737 - 1.79500i) q^{56} +(-1.60992 + 2.01877i) q^{57} +(-1.66487 - 7.29429i) q^{58} +(6.57338 - 3.16557i) q^{59} +(0.0990311 - 0.0476909i) q^{60} +(5.04892 + 6.33114i) q^{61} +(2.11596 + 9.27061i) q^{62} +(0.846011 - 3.70662i) q^{63} +(5.54892 + 6.95812i) q^{64} +(0.547425 + 0.686450i) q^{65} +(-0.266594 + 1.16802i) q^{66} +(-1.64310 - 7.19891i) q^{67} +(-0.692021 - 0.867767i) q^{68} +(-2.04407 + 0.984374i) q^{69} +(0.846011 - 0.407417i) q^{70} +(0.374354 + 1.64015i) q^{71} +(-5.32640 + 6.67909i) q^{72} +(3.58426 + 1.72609i) q^{73} +(5.58695 - 7.00581i) q^{74} +(0.464656 - 2.03579i) q^{75} +(-2.32640 + 1.12033i) q^{76} +(0.651833 - 2.85587i) q^{77} +(0.791053 + 0.380951i) q^{78} -2.08815 q^{79} -1.61596 q^{80} +(-6.53803 - 3.14855i) q^{81} +(2.91185 + 12.7577i) q^{82} +(0.571884 + 0.717120i) q^{83} +(-0.167563 + 0.210117i) q^{84} +1.38404 q^{85} +(-2.08546 - 7.90658i) q^{86} -2.67025 q^{87} +(-4.10388 + 5.14610i) q^{88} +(-0.928116 - 1.16382i) q^{89} +(-0.431468 - 1.89039i) q^{90} +(-1.93416 - 0.931441i) q^{91} -2.26875 q^{92} +3.39373 q^{93} +(-12.2899 - 5.91848i) q^{94} +(0.716480 - 3.13910i) q^{95} +(0.989115 - 0.476333i) q^{96} +(3.36563 - 14.7458i) q^{97} +(4.01089 - 5.02949i) q^{98} +(-5.44989 - 2.62453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9} - q^{10} - 10 q^{11} + 4 q^{12} + 5 q^{13} - 7 q^{14} - q^{15} + 11 q^{16} - 4 q^{17} + 9 q^{18} + 2 q^{19} + q^{20} + 7 q^{21} + 6 q^{22} + q^{23} + 7 q^{24} - 4 q^{25} + 11 q^{26} - 4 q^{27} - 7 q^{28} + 6 q^{29} + 2 q^{30} - 6 q^{31} - 15 q^{32} + 13 q^{33} - 6 q^{34} - 2 q^{36} - 14 q^{37} - 11 q^{38} - 3 q^{39} + 7 q^{40} + 2 q^{41} - 14 q^{42} - 13 q^{43} - 20 q^{44} + 4 q^{45} + 5 q^{46} + 17 q^{47} + 6 q^{48} - 14 q^{49} + 8 q^{50} - 6 q^{51} + 3 q^{52} - 2 q^{53} + 15 q^{54} + 5 q^{55} - 11 q^{57} - 12 q^{58} + 12 q^{59} + 5 q^{60} + 12 q^{61} + 33 q^{62} + 15 q^{64} + 29 q^{65} - 5 q^{66} - 18 q^{67} + 6 q^{68} - 16 q^{69} + 26 q^{71} - 14 q^{72} - 9 q^{73} + 15 q^{75} + 4 q^{76} + 28 q^{77} - q^{78} - 20 q^{79} - 30 q^{80} - 24 q^{81} + 10 q^{82} + 20 q^{83} - 12 q^{85} - 23 q^{86} - 12 q^{87} - 7 q^{88} + 11 q^{89} - 8 q^{90} - 14 q^{91} + 2 q^{92} - 44 q^{93} - 27 q^{94} - 15 q^{95} + 9 q^{96} + 28 q^{97} + 21 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9 - q^10 - 10 * q^11 + 4 * q^12 + 5 * q^13 - 7 * q^14 - q^15 + 11 * q^16 - 4 * q^17 + 9 * q^18 + 2 * q^19 + q^20 + 7 * q^21 + 6 * q^22 + q^23 + 7 * q^24 - 4 * q^25 + 11 * q^26 - 4 * q^27 - 7 * q^28 + 6 * q^29 + 2 * q^30 - 6 * q^31 - 15 * q^32 + 13 * q^33 - 6 * q^34 - 2 * q^36 - 14 * q^37 - 11 * q^38 - 3 * q^39 + 7 * q^40 + 2 * q^41 - 14 * q^42 - 13 * q^43 - 20 * q^44 + 4 * q^45 + 5 * q^46 + 17 * q^47 + 6 * q^48 - 14 * q^49 + 8 * q^50 - 6 * q^51 + 3 * q^52 - 2 * q^53 + 15 * q^54 + 5 * q^55 - 11 * q^57 - 12 * q^58 + 12 * q^59 + 5 * q^60 + 12 * q^61 + 33 * q^62 + 15 * q^64 + 29 * q^65 - 5 * q^66 - 18 * q^67 + 6 * q^68 - 16 * q^69 + 26 * q^71 - 14 * q^72 - 9 * q^73 + 15 * q^75 + 4 * q^76 + 28 * q^77 - q^78 - 20 * q^79 - 30 * q^80 - 24 * q^81 + 10 * q^82 + 20 * q^83 - 12 * q^85 - 23 * q^86 - 12 * q^87 - 7 * q^88 + 11 * q^89 - 8 * q^90 - 14 * q^91 + 2 * q^92 - 44 * q^93 - 27 * q^94 - 15 * q^95 + 9 * q^96 + 28 * q^97 + 21 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

Coefficient data

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

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

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

$2$	−0.777479	+	0.974928i	−0.549761	+	0.689378i	−0.976628	−	0.214936i	$-0.931046\pi$
$2$	−0.777479	+	0.974928i	−0.549761	+	0.689378i	0.426867	+	0.904314i	$0.359617\pi$
$3$	0.277479	+	0.347948i	0.160203	+	0.200888i	0.855454	−	0.517879i	$-0.173278\pi$
$3$	0.277479	+	0.347948i	0.160203	+	0.200888i	−0.695251	+	0.718767i	$0.744707\pi$
$4$	0.0990311	+	0.433884i	0.0495156	+	0.216942i
$5$	−0.500000	−	0.240787i	−0.223607	−	0.107683i	0.318727	−	0.947847i	$-0.396745\pi$
$5$	−0.500000	−	0.240787i	−0.223607	−	0.107683i	−0.542334	+	0.840163i	$0.682459\pi$
$6$	−0.554958			−0.226561
$7$	1.35690			0.512858			0.256429	−	0.966563i	$-0.417454\pi$
$7$	1.35690			0.512858			0.256429	+	0.966563i	$0.417454\pi$
$8$	−2.74698	−	1.32288i	−0.971204	−	0.467707i
$9$	0.623490	−	2.73169i	0.207830	−	0.910562i
$10$	0.623490	−	0.300257i	0.197165	−	0.0949496i
$11$	0.480386	−	2.10471i	0.144842	−	0.634593i	−0.849429	−	0.527703i	$-0.823053\pi$
$11$	0.480386	−	2.10471i	0.144842	−	0.634593i	0.994271	−	0.106890i	$-0.0340894\pi$
$12$	−0.123490	+	0.154851i	−0.0356484	+	0.0447017i
$13$	−1.42543	−	0.686450i	−0.395342	−	0.190387i	0.225641	−	0.974211i	$-0.427552\pi$
$13$	−1.42543	−	0.686450i	−0.395342	−	0.190387i	−0.620984	+	0.783824i	$0.713267\pi$
$14$	−1.05496	+	1.32288i	−0.281949	+	0.353553i
$15$	−0.0549581	−	0.240787i	−0.0141901	−	0.0621710i
$16$	2.62349	−	1.26341i	0.655872	−	0.315852i
$17$	−2.24698	+	1.08209i	−0.544973	+	0.262445i	−0.686051	−	0.727553i	$-0.740657\pi$
$17$	−2.24698	+	1.08209i	−0.544973	+	0.262445i	0.141078	+	0.989998i	$0.454943\pi$
$18$	2.17845	+	2.73169i	0.513465	+	0.643865i
$19$	1.29105	+	5.65647i	0.296188	+	1.29768i	0.875754	+	0.482758i	$0.160365\pi$
$19$	1.29105	+	5.65647i	0.296188	+	1.29768i	−0.579566	+	0.814925i	$0.696778\pi$
$20$	0.0549581	−	0.240787i	0.0122890	−	0.0538417i
$21$	0.376510	+	0.472129i	0.0821613	+	0.103027i
$22$	1.67845	+	2.10471i	0.357846	+	0.448725i
$23$	−1.13437	+	4.97002i	−0.236534	+	1.03632i	0.707563	+	0.706651i	$0.249795\pi$
$23$	−1.13437	+	4.97002i	−0.236534	+	1.03632i	−0.944096	+	0.329670i	$0.893062\pi$
$24$	−0.301938	−	1.32288i	−0.0616328	−	0.270031i
$25$	−2.92543	−	3.66837i	−0.585086	−	0.733674i
$26$	1.77748	−	0.855989i	0.348592	−	0.167873i
$27$	2.32640	−	1.12033i	0.447715	−	0.215608i
$28$	0.134375	+	0.588735i	0.0253945	+	0.111260i
$29$	−3.74094	+	4.69099i	−0.694675	+	0.871095i	−0.996613	−	0.0822327i	$-0.973795\pi$
$29$	−3.74094	+	4.69099i	−0.694675	+	0.871095i	0.301938	+	0.953327i	$0.402366\pi$
$30$	0.277479	+	0.133627i	0.0506605	+	0.0243968i
$31$	4.75451	−	5.96197i	0.853936	−	1.07080i	−0.142775	−	0.989755i	$-0.545602\pi$
$31$	4.75451	−	5.96197i	0.853936	−	1.07080i	0.996710	−	0.0810462i	$-0.0258261\pi$
$32$	0.548917	−	2.40496i	0.0970358	−	0.425142i
$33$	0.865625	−	0.416863i	0.150686	−	0.0725665i
$34$	0.692021	−	3.03194i	0.118681	−	0.519974i
$35$	−0.678448	−	0.326723i	−0.114679	−	0.0552263i
$36$	1.24698			0.207830
$37$	−7.18598			−1.18137			−0.590684	−	0.806903i	$-0.701142\pi$
$37$	−7.18598			−1.18137			−0.590684	+	0.806903i	$0.701142\pi$
$38$	−6.51842	−	3.13910i	−1.05743	−	0.509230i
$39$	−0.156678	−	0.686450i	−0.0250885	−	0.109920i
$40$	1.05496	+	1.32288i	0.166804	+	0.209165i
$41$	6.54288	−	8.20451i	1.02183	−	1.28133i	0.0627950	−	0.998026i	$-0.479999\pi$
$41$	6.54288	−	8.20451i	1.02183	−	1.28133i	0.959031	−	0.283302i	$-0.0914300\pi$
$42$	−0.753020			−0.116194
$43$	−3.91454	+	5.26083i	−0.596962	+	0.802269i
$43$	−3.91454	+	5.26083i	−0.596962	+	0.802269i
$44$	0.960771			0.144842
$45$	−0.969501	+	1.21572i	−0.144525	+	0.181228i
$46$	−3.96346	−	4.97002i	−0.584380	−	0.732790i
$47$	2.43416	+	10.6647i	0.355058	+	1.55561i	0.765324	+	0.643646i	$0.222579\pi$
$47$	2.43416	+	10.6647i	0.355058	+	1.55561i	−0.410265	+	0.911966i	$0.634564\pi$
$48$	1.16756	+	0.562269i	0.168523	+	0.0811565i
$49$	−5.15883			−0.736976
$50$	5.85086			0.827436
$51$	−1.00000	−	0.481575i	−0.140028	−	0.0674339i
$52$	0.156678	−	0.686450i	0.0217273	−	0.0951934i
$53$	2.77144	−	1.33465i	0.380686	−	0.183329i	−0.233747	−	0.972297i	$-0.575099\pi$
$53$	2.77144	−	1.33465i	0.380686	−	0.183329i	0.614434	+	0.788969i	$0.289385\pi$
$54$	−0.716480	+	3.13910i	−0.0975006	+	0.427178i
$55$	−0.746980	+	0.936683i	−0.100723	+	0.126302i
$56$	−3.72737	−	1.79500i	−0.498090	−	0.239868i
$57$	−1.60992	+	2.01877i	−0.213239	+	0.267393i
$58$	−1.66487	−	7.29429i	−0.218609	−	0.957787i
$59$	6.57338	−	3.16557i	0.855781	−	0.412122i	0.0460606	−	0.998939i	$-0.485333\pi$
$59$	6.57338	−	3.16557i	0.855781	−	0.412122i	0.809720	+	0.586816i	$0.199619\pi$
$60$	0.0990311	−	0.0476909i	0.0127849	−	0.00615687i
$61$	5.04892	+	6.33114i	0.646448	+	0.810620i	0.991793	−	0.127856i	$-0.0408096\pi$
$61$	5.04892	+	6.33114i	0.646448	+	0.810620i	−0.345345	+	0.938476i	$0.612238\pi$
$62$	2.11596	+	9.27061i	0.268727	+	1.17737i
$63$	0.846011	−	3.70662i	0.106587	−	0.466990i
$64$	5.54892	+	6.95812i	0.693615	+	0.869765i
$65$	0.547425	+	0.686450i	0.0678998	+	0.0851436i
$66$	−0.266594	+	1.16802i	−0.0328154	+	0.143774i
$67$	−1.64310	−	7.19891i	−0.200737	−	0.879487i	−0.970489	−	0.241144i	$-0.922477\pi$
$67$	−1.64310	−	7.19891i	−0.200737	−	0.879487i	0.769752	−	0.638343i	$-0.220380\pi$
$68$	−0.692021	−	0.867767i	−0.0839199	−	0.105232i
$69$	−2.04407	+	0.984374i	−0.246077	+	0.118505i
$70$	0.846011	−	0.407417i	0.101118	−	0.0486957i
$71$	0.374354	+	1.64015i	0.0444277	+	0.194650i	0.992272	−	0.124084i	$-0.0395993\pi$
$71$	0.374354	+	1.64015i	0.0444277	+	0.194650i	−0.947844	+	0.318735i	$0.896742\pi$
$72$	−5.32640	+	6.67909i	−0.627722	+	0.787138i
$73$	3.58426	+	1.72609i	0.419506	+	0.202023i	0.631715	−	0.775201i	$-0.282351\pi$
$73$	3.58426	+	1.72609i	0.419506	+	0.202023i	−0.212209	+	0.977224i	$0.568066\pi$
$74$	5.58695	−	7.00581i	0.649470	−	0.814409i
$75$	0.464656	−	2.03579i	0.0536539	−	0.235073i
$76$	−2.32640	+	1.12033i	−0.266856	+	0.128511i
$77$	0.651833	−	2.85587i	0.0742833	−	0.325456i
$78$	0.791053	+	0.380951i	0.0895691	+	0.0431342i
$79$	−2.08815			−0.234935			−0.117467	−	0.993077i	$-0.537478\pi$
$79$	−2.08815			−0.234935			−0.117467	+	0.993077i	$0.537478\pi$
$80$	−1.61596			−0.180669
$81$	−6.53803	−	3.14855i	−0.726448	−	0.349839i
$82$	2.91185	+	12.7577i	0.321560	+	1.40885i
$83$	0.571884	+	0.717120i	0.0627724	+	0.0787141i	0.812226	−	0.583342i	$-0.198255\pi$
$83$	0.571884	+	0.717120i	0.0627724	+	0.0787141i	−0.749454	+	0.662056i	$0.769684\pi$
$84$	−0.167563	+	0.210117i	−0.0182826	+	0.0229257i
$85$	1.38404			0.150121
$86$	−2.08546	−	7.90658i	−0.224881	−	0.852589i
$87$	−2.67025			−0.286281
$88$	−4.10388	+	5.14610i	−0.437475	+	0.548576i
$89$	−0.928116	−	1.16382i	−0.0983801	−	0.123365i	0.730204	−	0.683229i	$-0.239425\pi$
$89$	−0.928116	−	1.16382i	−0.0983801	−	0.123365i	−0.828585	+	0.559864i	$0.810853\pi$
$90$	−0.431468	−	1.89039i	−0.0454808	−	0.199264i
$91$	−1.93416	−	0.931441i	−0.202755	−	0.0976415i
$92$	−2.26875			−0.236534
$93$	3.39373			0.351914
$94$	−12.2899	−	5.91848i	−1.26760	−	0.610445i
$95$	0.716480	−	3.13910i	0.0735093	−	0.322065i
$96$	0.989115	−	0.476333i	0.100951	−	0.0486155i
$97$	3.36563	−	14.7458i	0.341727	−	1.49721i	−0.453699	−	0.891155i	$-0.649896\pi$
$97$	3.36563	−	14.7458i	0.341727	−	1.49721i	0.795426	−	0.606051i	$-0.207247\pi$
$98$	4.01089	−	5.02949i	0.405161	−	0.508055i
$99$	−5.44989	−	2.62453i	−0.547734	−	0.263775i
$100$	1.30194	−	1.63258i	0.130194	−	0.163258i
$101$	0.755176	+	3.30864i	0.0751429	+	0.329222i	0.998502	−	0.0547150i	$-0.0174250\pi$
$101$	0.755176	+	3.30864i	0.0751429	+	0.329222i	−0.923359	+	0.383937i	$0.874568\pi$
$102$	1.24698	−	0.600514i	0.123469	−	0.0594597i
$103$	4.59299	−	2.21187i	0.452561	−	0.217942i	−0.193696	−	0.981062i	$-0.562048\pi$
$103$	4.59299	−	2.21187i	0.452561	−	0.217942i	0.646257	+	0.763120i	$0.276333\pi$
$104$	3.00753	+	3.77133i	0.294913	+	0.369809i
$105$	−0.0745725	−	0.326723i	−0.00727753	−	0.0318849i
$106$	−0.853543	+	3.73962i	−0.0829035	+	0.363224i
$107$	0.192021	+	0.240787i	0.0185634	+	0.0232778i	0.791027	−	0.611782i	$-0.209547\pi$
$107$	0.192021	+	0.240787i	0.0185634	+	0.0232778i	−0.772463	+	0.635060i	$0.780976\pi$
$108$	0.716480	+	0.898438i	0.0689433	+	0.0864522i
$109$	−3.04892	+	13.3582i	−0.292033	+	1.27948i	0.589657	+	0.807654i	$0.299263\pi$
$109$	−3.04892	+	13.3582i	−0.292033	+	1.27948i	−0.881691	+	0.471828i	$0.843594\pi$
$110$	−0.332437	−	1.45650i	−0.0316966	−	0.138872i
$111$	−1.99396	−	2.50035i	−0.189258	−	0.237322i
$112$	3.55980	−	1.71431i	0.336370	−	0.161987i
$113$	17.0124	−	8.19273i	1.60039	−	0.770707i	0.600801	−	0.799398i	$-0.294848\pi$
$113$	17.0124	−	8.19273i	1.60039	−	0.770707i	0.999588	+	0.0286911i	$0.00913393\pi$
$114$	−0.716480	−	3.13910i	−0.0671045	−	0.294004i
$115$	1.76391	−	2.21187i	0.164485	−	0.206258i
$116$	−2.40581	−	1.15858i	−0.223374	−	0.107571i
$117$	−2.76391	+	3.46583i	−0.255523	+	0.320416i
$118$	−2.02446	+	8.86973i	−0.186367	+	0.816525i
$119$	−3.04892	+	1.46828i	−0.279494	+	0.134597i
$120$	−0.167563	+	0.734141i	−0.0152963	+	0.0670176i
$121$	5.71164	+	2.75058i	0.519240	+	0.250053i
$122$	−10.0978			−0.914215
$123$	4.67025			0.421102
$124$	3.05765	+	1.47248i	0.274585	+	0.132233i
$125$	1.19687	+	5.24381i	0.107051	+	0.469021i
$126$	2.95593	+	3.70662i	0.263335	+	0.330212i
$127$	−3.11410	+	3.90495i	−0.276331	+	0.346509i	−0.900559	−	0.434734i	$-0.856842\pi$
$127$	−3.11410	+	3.90495i	−0.276331	+	0.346509i	0.624228	+	0.781243i	$0.285414\pi$
$128$	−6.16421			−0.544844
$129$	−2.91670	+	0.0977147i	−0.256801	+	0.00860330i
$130$	−1.09485			−0.0960248
$131$	−11.1773	+	14.0158i	−0.976561	+	1.22457i	−0.00210326	+	0.999998i	$0.500669\pi$
$131$	−11.1773	+	14.0158i	−0.976561	+	1.22457i	−0.974458	+	0.224571i	$0.927902\pi$
$132$	0.266594	+	0.334298i	0.0232040	+	0.0290969i
$133$	1.75182	+	7.67524i	0.151902	+	0.665528i
$134$	8.29590	+	3.99509i	0.716656	+	0.345124i
$135$	−1.43296			−0.123330
$136$	7.60388			0.652027
$137$	11.2702	+	5.42746i	0.962882	+	0.463699i	0.848184	−	0.529701i	$-0.177696\pi$
$137$	11.2702	+	5.42746i	0.962882	+	0.463699i	0.114697	+	0.993400i	$0.463410\pi$
$138$	0.629531	−	2.75815i	0.0535892	−	0.234790i
$139$	5.46950	−	2.63397i	0.463917	−	0.223411i	−0.187299	−	0.982303i	$-0.559973\pi$
$139$	5.46950	−	2.63397i	0.463917	−	0.223411i	0.651216	+	0.758892i	$0.274259\pi$
$140$	0.0745725	−	0.326723i	0.00630252	−	0.0276132i
$141$	−3.03534	+	3.80620i	−0.255622	+	0.320540i
$142$	−1.89008	−	0.910216i	−0.158612	−	0.0763837i
$143$	−2.12953	+	2.67035i	−0.178080	+	0.223306i
$144$	−1.81551	−	7.95427i	−0.151293	−	0.662856i
$145$	3.00000	−	1.44472i	0.249136	−	0.119978i
$146$	−4.46950	+	2.15240i	−0.369898	+	0.178134i
$147$	−1.43147	−	1.79500i	−0.118066	−	0.148049i
$148$	−0.711636	−	3.11788i	−0.0584961	−	0.256288i
$149$	0.612605	−	2.68400i	0.0501865	−	0.219882i	−0.943616	−	0.331042i	$-0.892600\pi$
$149$	0.612605	−	2.68400i	0.0501865	−	0.219882i	0.993802	+	0.111161i	$0.0354569\pi$
$150$	1.62349	+	2.03579i	0.132557	+	0.166222i
$151$	−11.6283	−	14.5815i	−0.946300	−	1.18662i	−0.982308	−	0.187272i	$-0.940036\pi$
$151$	−11.6283	−	14.5815i	−0.946300	−	1.18662i	0.0360077	−	0.999352i	$-0.488536\pi$
$152$	3.93631	−	17.2461i	0.319277	−	1.39884i
$153$	1.55496	+	6.81272i	0.125711	+	0.550776i
$154$	2.27748	+	2.85587i	0.183524	+	0.230132i
$155$	−3.81282	+	1.83616i	−0.306253	+	0.147484i
$156$	0.282323	−	0.135960i	0.0226040	−	0.0108855i
$157$	−2.94385	−	12.8978i	−0.234944	−	1.02936i	−0.945476	−	0.325693i	$-0.894402\pi$
$157$	−2.94385	−	12.8978i	−0.234944	−	1.02936i	0.710531	−	0.703666i	$-0.248455\pi$
$158$	1.62349	−	2.03579i	0.129158	−	0.161959i
$159$	1.23341	+	0.593977i	0.0978155	+	0.0471054i
$160$	−0.853543	+	1.07031i	−0.0674785	+	0.0846154i
$161$	−1.53923	+	6.74380i	−0.121308	+	0.531486i
$162$	8.15279	−	3.92618i	0.640544	−	0.308470i
$163$	2.32908	−	10.2044i	0.182428	−	0.799269i	−0.798042	−	0.602602i	$-0.794131\pi$
$163$	2.32908	−	10.2044i	0.182428	−	0.799269i	0.980470	−	0.196668i	$-0.0630120\pi$
$164$	4.20775	+	2.02635i	0.328570	+	0.158231i
$165$	−0.533188			−0.0415086
$166$	−1.14377			−0.0887736
$167$	−13.1223	−	6.31936i	−1.01543	−	0.489007i	−0.149285	−	0.988794i	$-0.547697\pi$
$167$	−13.1223	−	6.31936i	−1.01543	−	0.489007i	−0.866148	+	0.499787i	$0.833412\pi$
$168$	−0.409698	−	1.79500i	−0.0316089	−	0.138488i
$169$	−6.54474	−	8.20684i	−0.503441	−	0.631295i
$170$	−1.07606	+	1.34934i	−0.0825304	+	0.103490i
$171$	16.2567			1.24318
$172$	−2.67025	−	1.17747i	−0.203605	−	0.0897813i
$173$	−8.78986			−0.668280			−0.334140	−	0.942523i	$-0.608446\pi$
$173$	−8.78986			−0.668280			−0.334140	+	0.942523i	$0.608446\pi$
$174$	2.07606	−	2.60330i	0.157386	−	0.197356i
$175$	−3.96950	−	4.97760i	−0.300066	−	0.376271i
$176$	−1.39881	−	6.12860i	−0.105439	−	0.461961i
$177$	2.92543	+	1.40881i	0.219889	+	0.105893i
$178$	1.85623			0.139130
$179$	−21.4034			−1.59977			−0.799883	−	0.600155i	$-0.795105\pi$
$179$	−21.4034			−1.59977			−0.799883	+	0.600155i	$0.795105\pi$
$180$	−0.623490	−	0.300257i	−0.0464722	−	0.0223798i
$181$	−5.85958	+	25.6725i	−0.435539	+	1.90822i	−0.0173811	+	0.999849i	$0.505533\pi$
$181$	−5.85958	+	25.6725i	−0.435539	+	1.90822i	−0.418158	+	0.908374i	$0.637324\pi$
$182$	2.41185	−	1.16149i	0.178779	−	0.0860952i
$183$	−0.801938	+	3.51352i	−0.0592809	+	0.259727i
$184$	9.69083	−	12.1519i	0.714417	−	0.895851i
$185$	3.59299	+	1.73029i	0.264162	+	0.127214i
$186$	−2.63856	+	3.30864i	−0.193468	+	0.242602i
$187$	1.19806	+	5.24905i	0.0876110	+	0.383849i
$188$	−4.38620	+	2.11228i	−0.319896	+	0.154054i
$189$	3.15668	−	1.52018i	0.229615	−	0.110577i
$190$	2.50335	+	3.13910i	0.181612	+	0.227735i
$191$	−1.93362	−	8.47176i	−0.139912	−	0.612995i	−0.995453	−	0.0952590i	$-0.969632\pi$
$191$	−1.93362	−	8.47176i	−0.139912	−	0.612995i	0.855540	−	0.517736i	$-0.173225\pi$
$192$	−0.881355	+	3.86147i	−0.0636063	+	0.278677i
$193$	1.28501	+	1.61135i	0.0924972	+	0.115988i	0.825926	−	0.563778i	$-0.190653\pi$
$193$	1.28501	+	1.61135i	0.0924972	+	0.115988i	−0.733429	+	0.679766i	$0.762081\pi$
$194$	11.7594	+	14.7458i	0.844273	+	1.05868i
$195$	−0.0869495	+	0.380951i	−0.00622659	+	0.0272805i
$196$	−0.510885	−	2.23833i	−0.0364918	−	0.159881i
$197$	0.285012	+	0.357394i	0.0203063	+	0.0254632i	0.791881	−	0.610676i	$-0.209102\pi$
$197$	0.285012	+	0.357394i	0.0203063	+	0.0254632i	−0.771575	+	0.636139i	$0.780531\pi$
$198$	6.79590	−	3.27273i	0.482963	−	0.232583i
$199$	−1.85958	+	0.895529i	−0.131822	+	0.0634823i	−0.498632	−	0.866814i	$-0.666164\pi$
$199$	−1.85958	+	0.895529i	−0.131822	+	0.0634823i	0.366810	+	0.930296i	$0.380450\pi$
$200$	3.18329	+	13.9469i	0.225093	+	0.986196i
$201$	2.04892	−	2.56926i	0.144519	−	0.181222i
$202$	−3.81282	−	1.83616i	−0.268269	−	0.129192i
$203$	−5.07606	+	6.36518i	−0.356270	+	0.446748i
$204$	0.109916	−	0.481575i	0.00769568	−	0.0337170i
$205$	−5.24698	+	2.52681i	−0.366465	+	0.176480i
$206$	−1.41454	+	6.19752i	−0.0985558	+	0.431801i
$207$	12.8693	+	6.19752i	0.894476	+	0.430757i
$208$	−4.60686			−0.319428
$209$	12.5254			0.866401
$210$	0.376510	+	0.181318i	0.0259817	+	0.0125121i
$211$	−0.188137	−	0.824280i	−0.0129519	−	0.0567458i	0.968039	−	0.250800i	$-0.0806935\pi$
$211$	−0.188137	−	0.824280i	−0.0129519	−	0.0567458i	−0.980991	+	0.194054i	$0.937836\pi$
$212$	0.853543	+	1.07031i	0.0586216	+	0.0735092i
$213$	−0.466812	+	0.585364i	−0.0319854	+	0.0401085i
$214$	−0.384043			−0.0262526
$215$	3.22401	−	1.68784i	0.219876	−	0.115110i
$216$	−7.87263			−0.535664
$217$	6.45138	−	8.08977i	0.437948	−	0.549170i
$218$	−10.6528	−	13.3582i	−0.721498	−	0.904730i
$219$	0.393969	+	1.72609i	0.0266219	+	0.116638i
$220$	−0.480386	−	0.231342i	−0.0323876	−	0.0155970i
$221$	3.94571			0.265417
$222$	3.98792			0.267652
$223$	21.5661	+	10.3857i	1.44418	+	0.695478i	0.981573	−	0.191088i	$-0.0612014\pi$
$223$	21.5661	+	10.3857i	1.44418	+	0.695478i	0.462602	+	0.886566i	$0.346916\pi$
$224$	0.744824	−	3.26329i	0.0497656	−	0.218037i
$225$	−11.8448	+	5.70416i	−0.789654	+	0.380277i
$226$	−5.23945	+	22.9555i	−0.348523	+	1.52698i
$227$	−3.29859	+	4.13630i	−0.218935	+	0.274536i	−0.879154	−	0.476537i	$-0.841892\pi$
$227$	−3.29859	+	4.13630i	−0.218935	+	0.274536i	0.660220	+	0.751073i	$0.270463\pi$
$228$	−1.03534	−	0.498595i	−0.0685673	−	0.0330203i
$229$	9.54138	−	11.9645i	0.630512	−	0.790638i	−0.359268	−	0.933234i	$-0.616974\pi$
$229$	9.54138	−	11.9645i	0.630512	−	0.790638i	0.989781	+	0.142597i	$0.0455452\pi$
$230$	0.785012	+	3.43936i	0.0517621	+	0.226785i
$231$	1.17456	−	0.565640i	0.0772806	−	0.0372164i
$232$	16.4819	−	7.93725i	1.08209	−	0.521106i
$233$	−15.9758	−	20.0331i	−1.04661	−	1.31241i	−0.948342	−	0.317250i	$-0.897241\pi$
$233$	−15.9758	−	20.0331i	−1.04661	−	1.31241i	−0.0982699	−	0.995160i	$-0.531331\pi$
$234$	−1.23005	−	5.38922i	−0.0804111	−	0.352304i
$235$	1.35086	−	5.91848i	0.0881201	−	0.386079i
$236$	2.02446	+	2.53859i	0.131781	+	0.165248i
$237$	−0.579417	−	0.726566i	−0.0376372	−	0.0471955i
$238$	0.939001	−	4.11403i	0.0608664	−	0.266673i
$239$	1.48254	+	6.49544i	0.0958976	+	0.420155i	0.999974	−	0.00721601i	$-0.00229695\pi$
$239$	1.48254	+	6.49544i	0.0958976	+	0.420155i	−0.904076	+	0.427371i	$0.859440\pi$
$240$	−0.448394	−	0.562269i	−0.0289437	−	0.0362943i
$241$	−2.34601	+	1.12978i	−0.151120	+	0.0727755i	−0.507915	−	0.861407i	$-0.669584\pi$
$241$	−2.34601	+	1.12978i	−0.151120	+	0.0727755i	0.356795	+	0.934183i	$0.383869\pi$
$242$	−7.12229	+	3.42992i	−0.457838	+	0.220483i
$243$	−2.44235	−	10.7006i	−0.156677	−	0.686447i
$244$	−2.24698	+	2.81762i	−0.143848	+	0.180380i
$245$	2.57942	+	1.24218i	0.164793	+	0.0793601i
$246$	−3.63102	+	4.55316i	−0.231506	+	0.290299i
$247$	2.04258	−	8.94913i	0.129966	−	0.569420i
$248$	−20.9475	+	10.0878i	−1.33017	+	0.640575i
$249$	−0.0908344	+	0.397972i	−0.00575640	+	0.0252204i
$250$	−6.04288	−	2.91010i	−0.382185	−	0.184051i
$251$	6.64609			0.419497			0.209749	−	0.977755i	$-0.432735\pi$
$251$	6.64609			0.419497			0.209749	+	0.977755i	$0.432735\pi$
$252$	1.69202			0.106587
$253$	9.91550	+	4.77505i	0.623382	+	0.300205i
$254$	−1.38590	−	6.07204i	−0.0869593	−	0.380994i
$255$	0.384043	+	0.481575i	0.0240497	+	0.0301574i
$256$	−6.30529	+	7.90658i	−0.394081	+	0.494161i
$257$	1.40581			0.0876922			0.0438461	−	0.999038i	$-0.486039\pi$
$257$	1.40581			0.0876922			0.0438461	+	0.999038i	$0.486039\pi$
$258$	2.17241	−	2.91954i	0.135248	−	0.181763i
$259$	−9.75063			−0.605875
$260$	−0.243627	+	0.305499i	−0.0151091	+	0.0189462i
$261$	10.4819	+	13.1439i	0.648812	+	0.813584i
$262$	−4.97434	−	21.7940i	−0.307316	−	1.34644i
$263$	2.83244	+	1.36403i	0.174656	+	0.0841097i	0.519169	−	0.854672i	$-0.326242\pi$
$263$	2.83244	+	1.36403i	0.174656	+	0.0841097i	−0.344513	+	0.938782i	$0.611956\pi$
$264$	−2.92931			−0.180287
$265$	−1.70709			−0.104866
$266$	−8.84481	−	4.25944i	−0.542310	−	0.261163i
$267$	0.147416	−	0.645872i	0.00902171	−	0.0395267i
$268$	2.96077	−	1.42583i	0.180858	−	0.0870966i
$269$	2.56531	−	11.2394i	0.156410	−	0.685276i	−0.834529	−	0.550964i	$-0.814260\pi$
$269$	2.56531	−	11.2394i	0.156410	−	0.685276i	0.990939	−	0.134312i	$-0.0428825\pi$
$270$	1.11410	−	1.39703i	0.0678018	−	0.0850207i
$271$	12.0341	+	5.79534i	0.731022	+	0.352042i	0.762086	−	0.647476i	$-0.224175\pi$
$271$	12.0341	+	5.79534i	0.731022	+	0.352042i	−0.0310638	+	0.999517i	$0.509890\pi$
$272$	−4.52781	+	5.67770i	−0.274539	+	0.344261i
$273$	−0.212595	−	0.931441i	−0.0128669	−	0.0563734i
$274$	−14.0538	+	6.76793i	−0.849019	+	0.408866i
$275$	−9.12618	+	4.39494i	−0.550329	+	0.265025i
$276$	−0.629531	−	0.789406i	−0.0378933	−	0.0475167i
$277$	−2.95324	−	12.9390i	−0.177443	−	0.777428i	−0.982805	−	0.184645i	$-0.940886\pi$
$277$	−2.95324	−	12.9390i	−0.177443	−	0.777428i	0.805362	−	0.592783i	$-0.201971\pi$
$278$	−1.68449	+	7.38023i	−0.101029	+	0.442637i
$279$	−13.3218	−	16.7051i	−0.797558	−	1.00011i
$280$	1.43147	+	1.79500i	0.0855466	+	0.107272i
$281$	3.54192	−	15.5182i	0.211293	−	0.925735i	−0.752397	−	0.658710i	$-0.771102\pi$
$281$	3.54192	−	15.5182i	0.211293	−	0.925735i	0.963690	−	0.267025i	$-0.0860406\pi$
$282$	−1.35086	−	5.91848i	−0.0804422	−	0.352441i
$283$	14.8267	+	18.5921i	0.881355	+	1.10518i	0.993762	+	0.111522i	$0.0355727\pi$
$283$	14.8267	+	18.5921i	0.881355	+	1.10518i	−0.112407	+	0.993662i	$0.535856\pi$
$284$	−0.674563	+	0.324852i	−0.0400280	+	0.0192764i
$285$	1.29105	−	0.621738i	0.0764754	−	0.0368286i
$286$	−0.947730	−	4.15228i	−0.0560405	−	0.245529i
$287$	8.87800	−	11.1327i	0.524052	−	0.657140i
$288$	−6.22737	−	2.99894i	−0.366951	−	0.176714i
$289$	−6.72132	+	8.42827i	−0.395372	+	0.495781i
$290$	−0.923936	+	4.04803i	−0.0542554	+	0.237708i
$291$	6.06465	−	2.92058i	0.355516	−	0.171207i
$292$	−0.393969	+	1.72609i	−0.0230553	+	0.101012i
$293$	−11.4330	−	5.50582i	−0.667921	−	0.321654i	0.0690159	−	0.997616i	$-0.478014\pi$
$293$	−11.4330	−	5.50582i	−0.667921	−	0.321654i	−0.736937	+	0.675962i	$0.763728\pi$
$294$	2.86294			0.166970
$295$	−4.04892			−0.235737
$296$	19.7397	+	9.50616i	1.14735	+	0.552534i
$297$	−1.24041	−	5.43458i	−0.0719757	−	0.315346i
$298$	2.14042	+	2.68400i	0.123991	+	0.155480i
$299$	5.02864	−	6.30571i	0.290814	−	0.364669i
$300$	0.929312			0.0536539
$301$	−5.31163	+	7.13840i	−0.306157	+	0.411451i
$302$	23.2567			1.33827
$303$	−0.941689	+	1.18084i	−0.0540986	+	0.0678376i
$304$	10.5335	+	13.2086i	0.604137	+	0.757563i
$305$	−1.00000	−	4.38129i	−0.0572598	−	0.250872i
$306$	−7.85086	−	3.78077i	−0.448804	−	0.216132i
$307$	18.1903			1.03817			0.519087	−	0.854721i	$-0.326272\pi$
$307$	18.1903			1.03817			0.519087	+	0.854721i	$0.326272\pi$
$308$	1.30367			0.0742833
$309$	2.04407	+	0.984374i	0.116283	+	0.0559991i
$310$	1.17427	−	5.14480i	0.0666939	−	0.292205i
$311$	−6.56249	+	3.16033i	−0.372125	+	0.179206i	−0.610593	−	0.791944i	$-0.709069\pi$
$311$	−6.56249	+	3.16033i	−0.372125	+	0.179206i	0.238468	+	0.971150i	$0.423355\pi$
$312$	−0.477697	+	2.09293i	−0.0270443	+	0.118489i
$313$	−11.6799	+	14.6462i	−0.660189	+	0.827851i	−0.993364	−	0.115014i	$-0.963309\pi$
$313$	−11.6799	+	14.6462i	−0.660189	+	0.827851i	0.333175	+	0.942865i	$0.391880\pi$
$314$	14.8632	+	7.15776i	0.838781	+	0.403936i
$315$	−1.31551	+	1.64960i	−0.0741207	+	0.0929444i
$316$	−0.206791	−	0.906013i	−0.0116329	−	0.0509672i
$317$	−3.12565	+	1.50523i	−0.175554	+	0.0845422i	−0.519597	−	0.854412i	$-0.673918\pi$
$317$	−3.12565	+	1.50523i	−0.175554	+	0.0845422i	0.344043	+	0.938954i	$0.388203\pi$
$318$	−1.53803	+	0.740677i	−0.0862486	+	0.0415351i
$319$	8.07606	+	10.1271i	0.452173	+	0.567007i
$320$	−1.09903	−	4.81517i	−0.0614377	−	0.269176i
$321$	−0.0304995	+	0.133627i	−0.00170231	+	0.00745832i
$322$	−5.37800	−	6.74380i	−0.299704	−	0.375817i
$323$	−9.02177	−	11.3129i	−0.501985	−	0.629469i
$324$	0.718636	−	3.14855i	0.0399242	−	0.174919i
$325$	1.65183	+	7.23715i	0.0916272	+	0.401445i
$326$	8.13773	+	10.2044i	0.450707	+	0.565169i
$327$	−5.49396	+	2.64575i	−0.303817	+	0.146310i
$328$	−28.8267	+	13.8822i	−1.59169	+	0.766516i
$329$	3.30290	+	14.4709i	0.182095	+	0.797809i
$330$	0.414542	−	0.519820i	0.0228198	−	0.0286151i
$331$	12.5368	+	6.03742i	0.689087	+	0.331847i	0.745448	−	0.666564i	$-0.232236\pi$
$331$	12.5368	+	6.03742i	0.689087	+	0.331847i	−0.0563612	+	0.998410i	$0.517950\pi$
$332$	−0.254512	+	0.319148i	−0.0139682	+	0.0175155i
$333$	−4.48039	+	19.6299i	−0.245524	+	1.07571i
$334$	16.3632	−	7.88012i	0.895356	−	0.431181i
$335$	−0.911854	+	3.99509i	−0.0498199	+	0.218275i
$336$	1.58426	+	0.762940i	0.0864285	+	0.0416218i
$337$	−3.05323			−0.166320			−0.0831600	−	0.996536i	$-0.526501\pi$
$337$	−3.05323			−0.166320			−0.0831600	+	0.996536i	$0.526501\pi$
$338$	13.0895			0.711974
$339$	7.57122	+	3.64611i	0.411212	+	0.198029i
$340$	0.137063	+	0.600514i	0.00743330	+	0.0325674i
$341$	−10.2642	−	12.8709i	−0.555838	−	0.696998i
$342$	−12.6392	+	15.8491i	−0.683451	+	0.857020i
$343$	−16.4983			−0.890823
$344$	17.7126	−	9.27295i	0.954999	−	0.499964i
$345$	1.25906			0.0677856
$346$	6.83393	−	8.56948i	0.367394	−	0.460698i
$347$	8.99396	+	11.2781i	0.482821	+	0.605438i	0.962258	−	0.272138i	$-0.0877306\pi$
$347$	8.99396	+	11.2781i	0.482821	+	0.605438i	−0.479437	+	0.877576i	$0.659159\pi$
$348$	−0.264438	−	1.15858i	−0.0141754	−	0.0621063i
$349$	−25.5770	−	12.3172i	−1.36911	−	0.659327i	−0.402459	−	0.915438i	$-0.631845\pi$
$349$	−25.5770	−	12.3172i	−1.36911	−	0.659327i	−0.966647	+	0.256111i	$0.917559\pi$
$350$	7.93900			0.424357
$351$	−4.08516			−0.218050
$352$	−4.79805	−	2.31062i	−0.255737	−	0.123156i
$353$	3.02984	−	13.2746i	0.161262	−	0.706534i	−0.828042	−	0.560666i	$-0.810545\pi$
$353$	3.02984	−	13.2746i	0.161262	−	0.706534i	0.989304	−	0.145869i	$-0.0465976\pi$
$354$	−3.64795	+	1.75676i	−0.193886	+	0.0933707i
$355$	0.207751	−	0.910216i	0.0110263	−	0.0483093i
$356$	0.413050	−	0.517949i	0.0218916	−	0.0274512i
$357$	−1.35690	−	0.653447i	−0.0718145	−	0.0345841i
$358$	16.6407	−	20.8668i	0.879489	−	1.10284i
$359$	7.29590	+	31.9654i	0.385063	+	1.68707i	0.681339	+	0.731968i	$0.261398\pi$
$359$	7.29590	+	31.9654i	0.385063	+	1.68707i	−0.296277	+	0.955102i	$0.595745\pi$
$360$	4.27144	−	2.05702i	0.225125	−	0.108414i
$361$	−13.2104	+	6.36181i	−0.695286	+	0.334832i
$362$	−20.4731	−	25.6725i	−1.07604	−	1.34932i
$363$	0.627802	+	2.75058i	0.0329510	+	0.144368i
$364$	0.212595	−	0.931441i	0.0111430	−	0.0488208i
$365$	−1.37651	−	1.72609i	−0.0720498	−	0.0903476i
$366$	−2.80194	−	3.51352i	−0.146460	−	0.183655i
$367$	−5.67360	+	24.8577i	−0.296160	+	1.29756i	0.579635	+	0.814876i	$0.303195\pi$
$367$	−5.67360	+	24.8577i	−0.296160	+	1.29756i	−0.875795	+	0.482684i	$0.839662\pi$
$368$	3.30313	+	14.4720i	0.172188	+	0.754404i
$369$	−18.3327	−	22.9885i	−0.954364	−	1.19673i
$370$	−4.48039	+	2.15764i	−0.232924	+	0.112170i
$371$	3.76055	−	1.81099i	0.195238	−	0.0940218i
$372$	0.336085	+	1.47248i	0.0174252	+	0.0763448i
$373$	17.1863	−	21.5509i	0.889872	−	1.11586i	−0.102762	−	0.994706i	$-0.532768\pi$
$373$	17.1863	−	21.5509i	0.889872	−	1.11586i	0.992633	−	0.121158i	$-0.0386607\pi$
$374$	−6.04892	−	2.91301i	−0.312782	−	0.150628i
$375$	−1.49247	+	1.87149i	−0.0770707	+	0.0966436i
$376$	7.42154	−	32.5159i	0.382737	−	1.67688i
$377$	8.55257	−	4.11870i	0.440480	−	0.212124i
$378$	−0.972189	+	4.25944i	−0.0500040	+	0.219082i
$379$	−25.3708	−	12.2179i	−1.30321	−	0.627592i	−0.351959	−	0.936015i	$-0.614484\pi$
$379$	−25.3708	−	12.2179i	−1.30321	−	0.627592i	−0.951249	+	0.308423i	$0.900199\pi$
$380$	1.43296			0.0735093
$381$	−2.22282			−0.113878
$382$	9.76271	+	4.70147i	0.499504	+	0.240548i
$383$	−6.36927	−	27.9056i	−0.325455	−	1.42591i	−0.827693	−	0.561181i	$-0.810347\pi$
$383$	−6.36927	−	27.9056i	−0.325455	−	1.42591i	0.502239	−	0.864729i	$-0.332510\pi$
$384$	−1.71044	−	2.14482i	−0.0872855	−	0.109453i
$385$	−1.01357	+	1.27098i	−0.0516565	+	0.0647752i
$386$	−2.57002			−0.130811
$387$	11.9303	+	13.9734i	0.606450	+	0.710307i
$388$	6.73125			0.341727
$389$	22.0206	−	27.6129i	1.11649	−	1.40003i	0.210050	−	0.977691i	$-0.432637\pi$
$389$	22.0206	−	27.6129i	1.11649	−	1.40003i	0.906437	−	0.422340i	$-0.138791\pi$
$390$	−0.303798	−	0.380951i	−0.0153834	−	0.0192902i
$391$	−2.82908	−	12.3950i	−0.143073	−	0.626844i
$392$	14.1712	+	6.82450i	0.715754	+	0.344689i
$393$	−7.97823			−0.402448
$394$	−0.570024			−0.0287174
$395$	1.04407	+	0.502799i	0.0525330	+	0.0252986i
$396$	0.599031	−	2.62453i	0.0301024	−	0.131887i
$397$	−3.04407	+	1.46595i	−0.152778	+	0.0735738i	−0.508710	−	0.860938i	$-0.669878\pi$
$397$	−3.04407	+	1.46595i	−0.152778	+	0.0735738i	0.355933	+	0.934512i	$0.384163\pi$
$398$	0.572712	−	2.50922i	0.0287075	−	0.125776i
$399$	−2.18449	+	2.73926i	−0.109361	+	0.137135i
$400$	−12.3095	−	5.92793i	−0.615474	−	0.296396i
$401$	−10.5429	+	13.2203i	−0.526486	+	0.660193i	−0.971972	−	0.235096i	$-0.924459\pi$
$401$	−10.5429	+	13.2203i	−0.526486	+	0.660193i	0.445486	+	0.895289i	$0.353031\pi$
$402$	0.911854	+	3.99509i	0.0454791	+	0.199257i
$403$	−10.8698	+	5.23462i	−0.541464	+	0.260755i
$404$	−1.36078	+	0.655317i	−0.0677014	+	0.0326033i
$405$	2.51089	+	3.14855i	0.124767	+	0.156453i
$406$	−2.25906	−	9.89759i	−0.112115	−	0.491209i
$407$	−3.45204	+	15.1244i	−0.171111	+	0.749688i
$408$	2.10992	+	2.64575i	0.104456	+	0.130984i
$409$	1.16003	+	1.45463i	0.0573598	+	0.0719269i	0.809684	−	0.586866i	$-0.199639\pi$
$409$	1.16003	+	1.45463i	0.0573598	+	0.0719269i	−0.752324	+	0.658793i	$0.771067\pi$
$410$	1.61596	−	7.07997i	0.0798064	−	0.349655i
$411$	1.23878	+	5.42746i	0.0611047	+	0.267717i
$412$	1.41454	+	1.77378i	0.0696895	+	0.0873879i
$413$	8.91939	−	4.29535i	0.438894	−	0.211360i
$414$	−16.0477	+	7.72818i	−0.788702	+	0.379819i
$415$	−0.113269	−	0.496262i	−0.00556014	−	0.0243606i
$416$	−2.43333	+	3.05130i	−0.119304	+	0.149602i
$417$	2.43416	+	1.17223i	0.119201	+	0.0574043i
$418$	−9.73825	+	12.2114i	−0.476313	+	0.597278i
$419$	3.67414	−	16.0974i	0.179493	−	0.786411i	−0.802371	−	0.596826i	$-0.796428\pi$
$419$	3.67414	−	16.0974i	0.179493	−	0.786411i	0.981864	−	0.189586i	$-0.0607145\pi$
$420$	0.134375	−	0.0647116i	0.00655683	−	0.00315760i
$421$	−4.89277	+	21.4366i	−0.238459	+	1.04476i	0.703938	+	0.710261i	$0.251423\pi$
$421$	−4.89277	+	21.4366i	−0.238459	+	1.04476i	−0.942397	+	0.334496i	$0.891434\pi$
$422$	0.949886	+	0.457441i	0.0462397	+	0.0222679i
$423$	30.6504			1.49027
$424$	−9.37867			−0.455468
$425$	10.5429	+	5.07718i	0.511405	+	0.246279i
$426$	−0.207751	−	0.910216i	−0.0100656	−	0.0441001i
$427$	6.85086	+	8.59070i	0.331536	+	0.415733i
$428$	−0.0854576	+	0.107160i	−0.00413075	+	0.00517980i
$429$	−1.52004			−0.0733883
$430$	−0.861076	+	4.45544i	−0.0415248	+	0.214861i
$431$	19.1884			0.924271			0.462136	−	0.886809i	$-0.347083\pi$
$431$	19.1884			0.924271			0.462136	+	0.886809i	$0.347083\pi$
$432$	4.68784	−	5.87837i	0.225544	−	0.282823i
$433$	8.60872	+	10.7950i	0.413709	+	0.518774i	0.944404	−	0.328789i	$-0.106640\pi$
$433$	8.60872	+	10.7950i	0.413709	+	0.518774i	−0.530695	+	0.847563i	$0.678069\pi$
$434$	2.87113	+	12.5793i	0.137819	+	0.603824i
$435$	1.33513	+	0.642963i	0.0640144	+	0.0308277i
$436$	−6.09783			−0.292033
$437$	−29.5773			−1.41488
$438$	−1.98911	−	0.957907i	−0.0950436	−	0.0457706i
$439$	−2.66152	+	11.6609i	−0.127028	+	0.556544i	0.870857	+	0.491536i	$0.163564\pi$
$439$	−2.66152	+	11.6609i	−0.127028	+	0.556544i	−0.997885	+	0.0650079i	$0.979293\pi$
$440$	3.29105	−	1.58489i	0.156895	−	0.0755565i
$441$	−3.21648	+	14.0923i	−0.153166	+	0.671063i
$442$	−3.06770	+	3.84678i	−0.145916	+	0.182973i
$443$	13.3545	+	6.43119i	0.634492	+	0.305555i	0.723342	−	0.690490i	$-0.242605\pi$
$443$	13.3545	+	6.43119i	0.634492	+	0.305555i	−0.0888504	+	0.996045i	$0.528319\pi$
$444$	0.887395	−	1.11276i	0.0421139	−	0.0528092i
$445$	0.183825	+	0.805389i	0.00871413	+	0.0381791i
$446$	−26.8925	+	12.9508i	−1.27340	+	0.613236i
$447$	1.10388	−	0.531598i	0.0522115	−	0.0251437i
$448$	7.52930	+	9.44145i	0.355726	+	0.446066i
$449$	4.31431	+	18.9022i	0.203605	+	0.892052i	0.968720	+	0.248158i	$0.0798252\pi$
$449$	4.31431	+	18.9022i	0.203605	+	0.892052i	−0.765114	+	0.643894i	$0.777318\pi$
$450$	3.64795	−	15.9827i	0.171966	−	0.753432i
$451$	−14.1250	−	17.7122i	−0.665119	−	0.834033i
$452$	5.23945	+	6.57006i	0.246443	+	0.309030i
$453$	1.84697	−	8.09211i	0.0867782	−	0.380200i
$454$	−1.46801	−	6.43177i	−0.0688971	−	0.301858i
$455$	0.742799	+	0.931441i	0.0348230	+	0.0436666i
$456$	7.09299	−	3.41580i	0.332160	−	0.159960i
$457$	−19.3872	+	9.33636i	−0.906893	+	0.436737i	−0.828374	−	0.560176i	$-0.810734\pi$
$457$	−19.3872	+	9.33636i	−0.906893	+	0.436737i	−0.0785194	+	0.996913i	$0.525019\pi$
$458$	4.24632	+	18.6043i	0.198417	+	0.869323i
$459$	−4.01507	+	5.03473i	−0.187407	+	0.235001i
$460$	1.13437	+	0.546286i	0.0528905	+	0.0254707i
$461$	20.7344	−	26.0001i	0.965696	−	1.21094i	−0.0117875	−	0.999931i	$-0.503752\pi$
$461$	20.7344	−	26.0001i	0.965696	−	1.21094i	0.977483	−	0.211014i	$-0.0676764\pi$
$462$	−0.361740	+	1.58489i	−0.0168297	+	0.0737356i
$463$	15.8192	−	7.61811i	0.735179	−	0.354043i	−0.0285400	−	0.999593i	$-0.509086\pi$
$463$	15.8192	−	7.61811i	0.735179	−	0.354043i	0.763719	+	0.645549i	$0.223371\pi$
$464$	−3.88769	+	17.0331i	−0.180482	+	0.790741i
$465$	−1.69687	−	0.817168i	−0.0786903	−	0.0378952i
$466$	31.9517			1.48013
$467$	−15.8398			−0.732980			−0.366490	−	0.930422i	$-0.619441\pi$
$467$	−15.8398			−0.732980			−0.366490	+	0.930422i	$0.619441\pi$
$468$	−1.77748	−	0.855989i	−0.0821640	−	0.0395681i
$469$	−2.22952	−	9.76817i	−0.102950	−	0.451052i
$470$	4.71983	+	5.91848i	0.217710	+	0.272999i
$471$	3.67092	−	4.60318i	0.169147	−	0.212103i
$472$	−22.2446			−1.02389
$473$	9.19202	+	10.7662i	0.422650	+	0.495030i
$474$	1.15883			0.0532270
$475$	16.9731	−	21.2837i	0.778781	−	0.976561i
$476$	−0.939001	−	1.17747i	−0.0430390	−	0.0539693i
$477$	−1.91789	−	8.40285i	−0.0878144	−	0.384740i
$478$	−7.48523	−	3.60470i	−0.342366	−	0.164875i
$479$	28.5652			1.30518			0.652590	−	0.757712i	$-0.273683\pi$
$479$	28.5652			1.30518			0.652590	+	0.757712i	$0.273683\pi$
$480$	−0.609252			−0.0278084
$481$	10.2431	+	4.93281i	0.467045	+	0.224917i
$482$	0.722521	−	3.16557i	0.0329099	−	0.144188i
$483$	−2.77359	+	1.33569i	−0.126203	+	0.0607761i
$484$	−0.627802	+	2.75058i	−0.0285364	+	0.125026i
$485$	−5.23341	+	6.56248i	−0.237637	+	0.297987i
$486$	12.3312	+	5.93841i	0.559356	+	0.269372i
$487$	1.16756	−	1.46408i	0.0529073	−	0.0663437i	−0.754674	−	0.656100i	$-0.772205\pi$
$487$	1.16756	−	1.46408i	0.0529073	−	0.0663437i	0.807581	+	0.589757i	$0.200776\pi$
$488$	−5.49396	−	24.0706i	−0.248700	−	1.08963i
$489$	4.19687	−	2.02110i	0.189789	−	0.0913975i
$490$	−3.21648	+	1.54898i	−0.145306	+	0.0699756i
$491$	−18.2268	−	22.8557i	−0.822565	−	1.03146i	−0.998889	−	0.0471321i	$-0.984992\pi$
$491$	−18.2268	−	22.8557i	−0.822565	−	1.03146i	0.176323	−	0.984332i	$-0.443580\pi$
$492$	0.462500	+	2.02635i	0.0208511	+	0.0913547i
$493$	3.32975	−	14.5886i	0.149964	−	0.657037i
$494$	7.13669	+	8.94913i	0.321095	+	0.402640i
$495$	2.09299	+	2.62453i	0.0940729	+	0.117964i
$496$	4.94103	−	21.6480i	0.221859	−	0.972026i
$497$	0.507960	+	2.22552i	0.0227851	+	0.0998281i
$498$	−0.317372	−	0.397972i	−0.0142218	−	0.0178335i
$499$	−22.4650	+	10.8186i	−1.00567	+	0.484305i	−0.862859	−	0.505445i	$-0.831328\pi$
$499$	−22.4650	+	10.8186i	−1.00567	+	0.484305i	−0.142811	+	0.989750i	$0.545614\pi$
$500$	−2.15668	+	1.03860i	−0.0964496	+	0.0464477i
$501$	−1.44235	−	6.31936i	−0.0644396	−	0.282328i
$502$	−5.16719	+	6.47946i	−0.230623	+	0.289192i
$503$	−38.0942	−	18.3452i	−1.69854	−	0.817973i	−0.994132	−	0.108176i	$-0.965499\pi$
$503$	−38.0942	−	18.3452i	−1.69854	−	0.817973i	−0.704407	−	0.709797i	$-0.748787\pi$
$504$	−7.22737	+	9.06283i	−0.321932	+	0.403691i
$505$	0.419091	−	1.83616i	0.0186493	−	0.0817080i
$506$	−12.3644	+	5.95439i	−0.549666	+	0.264705i
$507$	1.03952	−	4.55445i	0.0461669	−	0.202270i
$508$	−2.00269	−	0.964444i	−0.0888549	−	0.0427903i
$509$	−18.1153			−0.802946			−0.401473	−	0.915871i	$-0.631502\pi$
$509$	−18.1153			−0.802946			−0.401473	+	0.915871i	$0.631502\pi$
$510$	−0.768086			−0.0340114
$511$	4.86347	+	2.34212i	0.215147	+	0.103609i
$512$	−5.54945	−	24.3137i	−0.245253	−	1.07453i
$513$	9.34063	+	11.7128i	0.412399	+	0.517132i
$514$	−1.09299	+	1.37057i	−0.0482097	+	0.0604531i
$515$	−2.82908			−0.124664
$516$	−0.331241	−	1.25583i	−0.0145821	−	0.0552849i
$517$	23.6155			1.03861
$518$	7.58091	−	9.50616i	0.333086	−	0.417677i
$519$	−2.43900	−	3.05841i	−0.107060	−	0.134249i
$520$	−0.595679	−	2.60984i	−0.0261222	−	0.114449i
$521$	−1.13610	−	0.547119i	−0.0497736	−	0.0239697i	0.408831	−	0.912610i	$-0.365936\pi$
$521$	−1.13610	−	0.547119i	−0.0497736	−	0.0239697i	−0.458605	+	0.888640i	$0.651651\pi$
$522$	−20.9638			−0.917559
$523$	36.9788			1.61697			0.808485	−	0.588516i	$-0.200288\pi$
$523$	36.9788			1.61697			0.808485	+	0.588516i	$0.200288\pi$
$524$	−7.18814	−	3.46162i	−0.314015	−	0.151222i
$525$	0.630490	−	2.76236i	0.0275168	−	0.120559i
$526$	−3.53199	+	1.70092i	−0.154002	+	0.0741635i
$527$	−4.23191	+	18.5412i	−0.184345	+	0.807669i
$528$	1.74429	−	2.18727i	0.0759105	−	0.0951888i
$529$	−2.69202	−	1.29641i	−0.117044	−	0.0563656i
$530$	1.32722	−	1.66429i	0.0576509	−	0.0722920i
$531$	−4.54892	−	19.9301i	−0.197406	−	0.864893i
$532$	−3.15668	+	1.52018i	−0.136859	+	0.0659080i
$533$	−14.9584	+	7.20358i	−0.647919	+	0.312021i
$534$	0.515065	+	0.645872i	0.0222891	+	0.0279496i
$535$	−0.0380322	−	0.166630i	−0.00164428	−	0.00720404i
$536$	−5.00969	+	21.9489i	−0.216386	+	0.948047i
$537$	−5.93900	−	7.44727i	−0.256287	−	0.321373i
$538$	8.96309	+	11.2394i	0.386426	+	0.484563i
$539$	−2.47823	+	10.8578i	−0.106745	+	0.467680i
$540$	−0.141908	−	0.621738i	−0.00610673	−	0.0267554i
$541$	−0.305290	−	0.382822i	−0.0131254	−	0.0164588i	0.775225	−	0.631685i	$-0.217636\pi$
$541$	−0.305290	−	0.382822i	−0.0131254	−	0.0164588i	−0.788351	+	0.615226i	$0.789065\pi$
$542$	−15.0063	+	7.22667i	−0.644577	+	0.310412i
$543$	−10.5586	+	5.08476i	−0.453113	+	0.218208i
$544$	1.36898	+	5.99788i	0.0586944	+	0.257157i
$545$	4.74094	−	5.94495i	0.203080	−	0.254654i
$546$	1.07338	+	0.516911i	0.0459363	+	0.0221217i
$547$	−7.53617	+	9.45006i	−0.322223	+	0.404055i	−0.916390	−	0.400287i	$-0.868911\pi$
$547$	−7.53617	+	9.45006i	−0.322223	+	0.404055i	0.594167	+	0.804342i	$0.297482\pi$
$548$	−1.23878	+	5.42746i	−0.0529182	+	0.231850i
$549$	20.4426	−	9.84466i	0.872471	−	0.420160i
$550$	2.81067	−	12.3143i	0.119847	−	0.525085i
$551$	−31.3642	−	15.1042i	−1.33616	−	0.643460i
$552$	6.91723			0.294417
$553$	−2.83340			−0.120488
$554$	14.9107	+	7.18059i	0.633493	+	0.305074i
$555$	0.394928	+	1.73029i	0.0167638	+	0.0734468i
$556$	1.68449	+	2.11228i	0.0714382	+	0.0895807i
$557$	25.8369	−	32.3985i	1.09475	−	1.37277i	0.173022	−	0.984918i	$-0.444647\pi$
$557$	25.8369	−	32.3985i	1.09475	−	1.37277i	0.921723	−	0.387849i	$-0.126782\pi$
$558$	26.6437			1.12792
$559$	9.19119	−	4.81180i	0.388746	−	0.203517i
$560$	−2.19269			−0.0926579
$561$	−1.49396	+	1.87337i	−0.0630750	+	0.0790936i
$562$	12.3753	+	15.5182i	0.522021	+	0.654594i
$563$	3.61745	+	15.8491i	0.152457	+	0.667959i	0.992166	+	0.124923i	$0.0398683\pi$
$563$	3.61745	+	15.8491i	0.152457	+	0.667959i	−0.839709	+	0.543036i	$0.817275\pi$
$564$	−1.95204	−	0.940054i	−0.0821958	−	0.0395834i
$565$	−10.4789			−0.440850
$566$	−29.6534			−1.24642
$567$	−8.87143	−	4.27225i	−0.372565	−	0.179418i
$568$	1.14138	−	5.00069i	0.0478910	−	0.209824i
$569$	−28.5248	+	13.7368i	−1.19582	+	0.575877i	−0.922481	−	0.386041i	$-0.873842\pi$
$569$	−28.5248	+	13.7368i	−1.19582	+	0.575877i	−0.273338	+	0.961918i	$0.588128\pi$
$570$	−0.397616	+	1.74207i	−0.0166543	+	0.0729674i
$571$	9.91252	−	12.4299i	0.414826	−	0.520175i	−0.529889	−	0.848067i	$-0.677767\pi$
$571$	9.91252	−	12.4299i	0.414826	−	0.520175i	0.944715	+	0.327891i	$0.106338\pi$
$572$	−1.36951	−	0.659521i	−0.0572621	−	0.0275760i
$573$	2.41119	−	3.02354i	0.100729	−	0.126310i
$574$	3.95108	+	17.3108i	0.164915	+	0.722540i
$575$	21.5504	−	10.3781i	0.898714	−	0.432798i
$576$	22.4671	−	10.8196i	0.936129	−	0.450816i
$577$	9.87598	+	12.3841i	0.411142	+	0.515556i	0.943684	−	0.330847i	$-0.107335\pi$
$577$	9.87598	+	12.3841i	0.411142	+	0.515556i	−0.532542	+	0.846404i	$0.678763\pi$
$578$	−2.99127	−	13.1056i	−0.124420	−	0.545122i
$579$	−0.204103	+	0.894234i	−0.00848223	+	0.0371631i
$580$	0.923936	+	1.15858i	0.0383643	+	0.0481074i
$581$	0.775987	+	0.973057i	0.0321934	+	0.0403692i
$582$	−1.86778	+	8.18328i	−0.0774220	+	0.339208i
$583$	−1.47770	−	6.47421i	−0.0612000	−	0.268135i
$584$	−7.56249	−	9.48306i	−0.312938	−	0.392412i
$585$	2.21648	−	1.06740i	0.0916402	−	0.0441316i
$586$	14.2567	−	6.86565i	0.588938	−	0.283617i
$587$	6.72252	+	29.4533i	0.277468	+	1.21567i	0.900982	+	0.433855i	$0.142847\pi$
$587$	6.72252	+	29.4533i	0.277468	+	1.21567i	−0.623514	+	0.781812i	$0.714296\pi$
$588$	0.637063	−	0.798852i	0.0262720	−	0.0329441i
$589$	39.8620	+	19.1965i	1.64249	+	0.790980i
$590$	3.14795	−	3.94740i	0.129599	−	0.162512i
$591$	−0.0452695	+	0.198338i	−0.00186214	+	0.00815855i
$592$	−18.8523	+	9.07881i	−0.774827	+	0.373137i
$593$	−6.13049	+	26.8594i	−0.251749	+	1.10298i	0.678079	+	0.734989i	$0.262813\pi$
$593$	−6.13049	+	26.8594i	−0.251749	+	1.10298i	−0.929828	+	0.367995i	$0.880044\pi$
$594$	6.26271	+	3.01596i	0.256962	+	0.123746i
$595$	1.87800			0.0769906
$596$	1.22521			0.0501865
$597$	−0.827593	−	0.398548i	−0.0338711	−	0.0163115i
$598$	2.23795	+	9.80512i	0.0915168	+	0.400961i
$599$	−9.64042	−	12.0887i	−0.393897	−	0.493931i	0.544853	−	0.838532i	$-0.316586\pi$
$599$	−9.64042	−	12.0887i	−0.393897	−	0.493931i	−0.938749	+	0.344601i	$0.888014\pi$
$600$	−3.96950	+	4.97760i	−0.162054	+	0.203210i
$601$	3.03684			0.123875			0.0619376	−	0.998080i	$-0.480272\pi$
$601$	3.03684			0.123875			0.0619376	+	0.998080i	$0.480272\pi$
$602$	−2.82975	−	10.7284i	−0.115332	−	0.437257i
$603$	−20.6896			−0.842547
$604$	5.17510	−	6.48936i	0.210572	−	0.264048i
$605$	−2.19351	−	2.75058i	−0.0891790	−	0.111827i
$606$	−0.419091	−	1.83616i	−0.0170244	−	0.0745888i
$607$	−4.81647	−	2.31949i	−0.195495	−	0.0941452i	0.333575	−	0.942723i	$-0.391745\pi$
$607$	−4.81647	−	2.31949i	−0.195495	−	0.0941452i	−0.529070	+	0.848578i	$0.677459\pi$
$608$	14.3123			0.580440
$609$	−3.62325			−0.146822
$610$	5.04892	+	2.43143i	0.204425	+	0.0984457i
$611$	3.85109	−	16.8727i	0.155799	−	0.682598i
$612$	−2.80194	+	1.34934i	−0.113262	+	0.0545439i
$613$	1.93320	−	8.46989i	0.0780811	−	0.342096i	−0.920765	−	0.390117i	$-0.872434\pi$
$613$	1.93320	−	8.46989i	0.0780811	−	0.342096i	0.998846	+	0.0480216i	$0.0152916\pi$
$614$	−14.1426	+	17.7342i	−0.570748	+	0.715695i
$615$	−2.33513	−	1.12454i	−0.0941614	−	0.0453457i
$616$	−5.56853	+	6.98272i	−0.224363	+	0.281342i
$617$	3.87196	+	16.9642i	0.155879	+	0.682952i	0.991109	+	0.133051i	$0.0424774\pi$
$617$	3.87196	+	16.9642i	0.155879	+	0.682952i	−0.835230	+	0.549901i	$0.814665\pi$
$618$	−2.54892	+	1.22749i	−0.102532	+	0.0493770i
$619$	2.33028	−	1.12220i	0.0936619	−	0.0451052i	−0.386466	−	0.922304i	$-0.626304\pi$
$619$	2.33028	−	1.12220i	0.0936619	−	0.0451052i	0.480128	+	0.877198i	$0.340590\pi$
$620$	−1.17427	−	1.47248i	−0.0471597	−	0.0591364i
$621$	2.92908	+	12.8331i	0.117540	+	0.514975i
$622$	2.02111	−	8.85505i	0.0810390	−	0.355055i
$623$	−1.25936	−	1.57918i	−0.0504551	−	0.0632686i
$624$	−1.27831	−	1.60295i	−0.0511732	−	0.0641692i
$625$	−4.55615	+	19.9618i	−0.182246	+	0.798473i
$626$	−5.19806	−	22.7742i	−0.207756	−	0.910240i
$627$	3.47554	+	4.35819i	0.138800	+	0.174049i
$628$	5.30463	−	2.55457i	0.211678	−	0.101939i
$629$	16.1468	−	7.77587i	0.643813	−	0.310044i
$630$	−0.585458	−	2.56506i	−0.0233252	−	0.102194i
$631$	−1.76995	+	2.21944i	−0.0704605	+	0.0883546i	−0.815813	−	0.578316i	$-0.803710\pi$
$631$	−1.76995	+	2.21944i	−0.0704605	+	0.0883546i	0.745352	+	0.666671i	$0.232281\pi$
$632$	5.73609	+	2.76236i	0.228170	+	0.109881i
$633$	0.234603	−	0.294182i	0.00932461	−	0.0116927i
$634$	0.962632	−	4.21757i	0.0382310	−	0.167501i
$635$	2.49731	−	1.20264i	0.0991028	−	0.0477254i
$636$	−0.135571	+	0.593977i	−0.00537576	+	0.0235527i
$637$	7.35354	+	3.54128i	0.291358	+	0.140311i
$638$	−16.1521			−0.639469
$639$	4.71379			0.186475
$640$	3.08211	+	1.48426i	0.121831	+	0.0586707i
$641$	5.20602	+	22.8091i	0.205626	+	0.900904i	0.967438	+	0.253107i	$0.0814525\pi$
$641$	5.20602	+	22.8091i	0.205626	+	0.900904i	−0.761813	+	0.647797i	$0.775690\pi$
$642$	−0.106564	−	0.133627i	−0.00420574	−	0.00527383i
$643$	−18.8388	+	23.6231i	−0.742929	+	0.931603i	−0.999389	−	0.0349516i	$-0.988872\pi$
$643$	−18.8388	+	23.6231i	−0.742929	+	0.931603i	0.256460	+	0.966555i	$0.417444\pi$
$644$	−3.07846			−0.121308
$645$	1.48188	+	0.653447i	0.0583489	+	0.0257294i
$646$	18.0435			0.709914
$647$	−26.3342	+	33.0221i	−1.03531	+	1.29823i	−0.0818670	+	0.996643i	$0.526088\pi$
$647$	−26.3342	+	33.0221i	−1.03531	+	1.29823i	−0.953438	+	0.301588i	$0.902483\pi$
$648$	13.7947	+	17.2980i	0.541907	+	0.679530i
$649$	−3.50484	−	15.3557i	−0.137577	−	0.602765i
$650$	−8.33997	−	4.01632i	−0.327121	−	0.157533i
$651$	4.60494			0.180482
$652$	4.65817			0.182428
$653$	1.32736	+	0.639221i	0.0519434	+	0.0250146i	0.459675	−	0.888087i	$-0.347966\pi$
$653$	1.32736	+	0.639221i	0.0519434	+	0.0250146i	−0.407732	+	0.913102i	$0.633680\pi$
$654$	1.69202	−	7.41323i	0.0661633	−	0.289880i
$655$	8.96346	−	4.31657i	0.350231	−	0.168663i
$656$	6.79954	−	29.7908i	0.265478	−	1.16313i
$657$	6.94989	−	8.71488i	0.271141	−	0.340000i
$658$	−16.6761	−	8.03076i	−0.650100	−	0.313072i
$659$	−9.86257	+	12.3673i	−0.384191	+	0.481760i	−0.935895	−	0.352280i	$-0.885407\pi$
$659$	−9.86257	+	12.3673i	−0.384191	+	0.481760i	0.551704	+	0.834040i	$0.313978\pi$
$660$	−0.0528022	−	0.231342i	−0.00205532	−	0.00900496i
$661$	−8.28328	+	3.98902i	−0.322182	+	0.155155i	−0.587983	−	0.808873i	$-0.700078\pi$
$661$	−8.28328	+	3.98902i	−0.322182	+	0.155155i	0.265801	+	0.964028i	$0.414364\pi$
$662$	−15.6332	+	7.52854i	−0.607601	+	0.292605i
$663$	1.09485	+	1.37290i	0.0425205	+	0.0533190i
$664$	−0.622293	−	2.72645i	−0.0241497	−	0.105807i
$665$	0.972189	−	4.25944i	0.0376999	−	0.165174i
$666$	−15.6543	−	19.6299i	−0.606591	−	0.760641i
$667$	−19.0707	−	23.9139i	−0.738420	−	0.925949i
$668$	1.44235	−	6.31936i	0.0558063	−	0.244504i
$669$	2.37047	+	10.3857i	0.0916476	+	0.401535i
$670$	−3.18598	−	3.99509i	−0.123085	−	0.154344i
$671$	15.7506	−	7.58510i	0.608046	−	0.292820i
$672$	1.34213	−	0.646334i	0.0517736	−	0.0249329i
$673$	−8.03856	−	35.2193i	−0.309864	−	1.35760i	−0.854727	−	0.519078i	$-0.826276\pi$
$673$	−8.03856	−	35.2193i	−0.309864	−	1.35760i	0.544863	−	0.838525i	$-0.316582\pi$
$674$	2.37382	−	2.97668i	0.0914362	−	0.114657i
$675$	−10.9155	−	5.25663i	−0.420138	−	0.202328i
$676$	2.91268	−	3.65239i	0.112026	−	0.140476i
$677$	−2.27210	+	9.95473i	−0.0873240	+	0.382591i	−0.999638	−	0.0268996i	$-0.991437\pi$
$677$	−2.27210	+	9.95473i	−0.0873240	+	0.382591i	0.912314	+	0.409491i	$0.134294\pi$
$678$	−9.44116	+	4.54662i	−0.362585	+	0.174612i
$679$	4.56680	−	20.0085i	0.175258	−	0.767855i
$680$	−3.80194	−	1.83092i	−0.145798	−	0.0702125i
$681$	−2.35450			−0.0902247
$682$	20.5284			0.786073
$683$	−24.7059	−	11.8977i	−0.945345	−	0.455254i	−0.103293	−	0.994651i	$-0.532938\pi$
$683$	−24.7059	−	11.8977i	−0.945345	−	0.455254i	−0.842052	+	0.539397i	$0.818652\pi$
$684$	1.60992	+	7.05350i	0.0615567	+	0.269697i
$685$	−4.32826	−	5.42746i	−0.165374	−	0.207373i
$686$	12.8271	−	16.0846i	0.489739	−	0.614114i
$687$	6.81056			0.259839
$688$	−3.62319	+	18.7474i	−0.138133	+	0.714738i
$689$	−4.86666			−0.185405
$690$	−0.978894	+	1.22749i	−0.0372658	+	0.0467299i
$691$	−13.1664	−	16.5101i	−0.500872	−	0.628074i	0.465554	−	0.885020i	$-0.345855\pi$
$691$	−13.1664	−	16.5101i	−0.500872	−	0.628074i	−0.966426	+	0.256946i	$0.917284\pi$
$692$	−0.870469	−	3.81378i	−0.0330903	−	0.144978i
$693$	−7.39493	−	3.56121i	−0.280910	−	0.135279i
$694$	−17.9879			−0.682812
$695$	−3.36898			−0.127793
$696$	7.33513	+	3.53241i	0.278037	+	0.133896i
$697$	−5.82371	+	25.5153i	−0.220589	+	0.966462i
$698$	31.8940	−	15.3594i	1.20721	−	0.581360i
$699$	2.53750	−	11.1175i	0.0959771	−	0.420503i
$700$	1.76659	−	2.21524i	0.0667710	−	0.0837282i
$701$	0.209480	+	0.100880i	0.00791195	+	0.00381019i	0.437836	−	0.899055i	$-0.355745\pi$
$701$	0.209480	+	0.100880i	0.00791195	+	0.00381019i	−0.429924	+	0.902865i	$0.641460\pi$
$702$	3.17613	−	3.98274i	0.119875	−	0.150319i
$703$	−9.27748	−	40.6473i	−0.349907	−	1.53304i
$704$	17.3104	−	8.33626i	0.652411	−	0.314185i
$705$	2.43416	−	1.17223i	0.0916756	−	0.0441487i
$706$	10.5861	+	13.2746i	0.398414	+	0.499595i
$707$	1.02470	+	4.48948i	0.0385376	+	0.168844i
$708$	−0.321552	+	1.40881i	−0.0120847	+	0.0529464i
$709$	11.1645	+	13.9998i	0.419292	+	0.525775i	0.945955	−	0.324299i	$-0.105128\pi$
$709$	11.1645	+	13.9998i	0.419292	+	0.525775i	−0.526663	+	0.850074i	$0.676557\pi$
$710$	0.725873	+	0.910216i	0.0272415	+	0.0341598i
$711$	−1.30194	+	5.70416i	−0.0488265	+	0.213923i
$712$	1.00993	+	4.42477i	0.0378486	+	0.165825i
$713$	24.2377	+	30.3931i	0.907710	+	1.13823i
$714$	1.69202	−	0.814835i	0.0633223	−	0.0304944i
$715$	1.70775	−	0.822410i	0.0638663	−	0.0307564i
$716$	−2.11960	−	9.28660i	−0.0792134	−	0.347056i
$717$	−1.84870	+	2.31820i	−0.0690409	+	0.0865746i
$718$	−36.8364	−	17.7395i	−1.37472	−	0.662031i
$719$	−3.95444	+	4.95870i	−0.147476	+	0.184928i	−0.850082	−	0.526650i	$-0.823448\pi$
$719$	−3.95444	+	4.95870i	−0.147476	+	0.184928i	0.702607	+	0.711578i	$0.252019\pi$
$720$	−1.00753	+	4.41429i	−0.0375485	+	0.164511i
$721$	6.23221	−	3.00127i	0.232100	−	0.111773i
$722$	4.06853	−	17.8254i	0.151415	−	0.663393i
$723$	−1.04407	−	0.502799i	−0.0388295	−	0.0186993i
$724$	−11.7192			−0.435539
$725$	28.1521			1.04554
$726$	−3.16972	−	1.52646i	−0.117639	−	0.0566521i
$727$	2.27077	+	9.94891i	0.0842184	+	0.368985i	0.999422	−	0.0340079i	$-0.0108272\pi$
$727$	2.27077	+	9.94891i	0.0842184	+	0.368985i	−0.915203	+	0.402993i	$0.867970\pi$
$728$	4.08091	+	5.11730i	0.151249	+	0.189660i
$729$	−10.5278	+	13.2015i	−0.389919	+	0.488943i
$730$	2.75302			0.101894
$731$	3.10321	−	16.0569i	0.114776	−	0.593885i
$732$	−1.60388			−0.0592809
$733$	−3.01842	+	3.78498i	−0.111488	+	0.139801i	−0.834444	−	0.551092i	$-0.814211\pi$
$733$	−3.01842	+	3.78498i	−0.111488	+	0.139801i	0.722957	+	0.690894i	$0.242783\pi$
$734$	−19.8233	−	24.8577i	−0.731693	−	0.917514i
$735$	0.283520	+	1.24218i	0.0104578	+	0.0458186i
$736$	11.3300	+	5.45626i	0.417631	+	0.201120i
$737$	−15.9409			−0.587191
$738$	36.6655			1.34967
$739$	−22.0797	−	10.6330i	−0.812215	−	0.391142i	−0.0188003	−	0.999823i	$-0.505985\pi$
$739$	−22.0797	−	10.6330i	−0.812215	−	0.391142i	−0.793415	+	0.608681i	$0.791699\pi$
$740$	−0.394928	+	1.73029i	−0.0145178	+	0.0636068i
$741$	3.68060	−	1.77249i	0.135210	−	0.0651139i
$742$	−1.15817	+	5.07427i	−0.0425177	+	0.186282i
$743$	−15.9544	+	20.0061i	−0.585309	+	0.733954i	−0.983008	−	0.183562i	$-0.941237\pi$
$743$	−15.9544	+	20.0061i	−0.585309	+	0.733954i	0.397699	+	0.917516i	$0.369809\pi$
$744$	−9.32251	−	4.48948i	−0.341780	−	0.164593i
$745$	−0.952575	+	1.19449i	−0.0348996	+	0.0437628i
$746$	7.64861	+	33.5108i	0.280036	+	1.22692i
$747$	2.31551	−	1.11509i	0.0847201	−	0.0407991i
$748$	−2.15883	+	1.03964i	−0.0789348	+	0.0380130i
$749$	0.260553	+	0.326723i	0.00952040	+	0.0119382i
$750$	−0.664210	−	2.91010i	−0.0242535	−	0.106262i
$751$	−4.87047	+	21.3389i	−0.177726	+	0.778668i	0.804951	+	0.593341i	$0.202192\pi$
$751$	−4.87047	+	21.3389i	−0.177726	+	0.778668i	−0.982677	+	0.185327i	$0.940666\pi$
$752$	19.8599	+	24.9035i	0.724215	+	0.908137i
$753$	1.84415	+	2.31249i	0.0672046	+	0.0842719i
$754$	−2.63401	+	11.5403i	−0.0959249	+	0.420274i
$755$	2.30313	+	10.0907i	0.0838196	+	0.367238i
$756$	0.972189	+	1.21909i	0.0353582	+	0.0443377i
$757$	25.6102	−	12.3332i	0.930819	−	0.448259i	0.0938976	−	0.995582i	$-0.470067\pi$
$757$	25.6102	−	12.3332i	0.930819	−	0.448259i	0.836921	+	0.547323i	$0.184353\pi$
$758$	31.6368	−	15.2355i	1.14910	−	0.553378i
$759$	1.08987	+	4.77505i	0.0395600	+	0.173323i
$760$	−6.12080	+	7.67524i	−0.222025	+	0.278410i
$761$	26.4964	+	12.7600i	0.960494	+	0.462550i	0.847353	−	0.531029i	$-0.178195\pi$
$761$	26.4964	+	12.7600i	0.960494	+	0.462550i	0.113141	+	0.993579i	$0.463909\pi$
$762$	1.72819	−	2.16709i	0.0626058	−	0.0785052i
$763$	−4.13706	+	18.1257i	−0.149772	+	0.656193i
$764$	3.48427	−	1.67794i	0.126056	−	0.0607056i
$765$	0.862937	−	3.78077i	0.0311995	−	0.136694i
$766$	32.1579	+	15.4864i	1.16191	+	0.559548i
$767$	−11.5429			−0.416789
$768$	−4.50066			−0.162404
$769$	−17.2763	−	8.31982i	−0.622999	−	0.300020i	0.0956272	−	0.995417i	$-0.469514\pi$
$769$	−17.2763	−	8.31982i	−0.622999	−	0.300020i	−0.718626	+	0.695397i	$0.755229\pi$
$770$	−0.451083	−	1.97632i	−0.0162559	−	0.0712217i
$771$	0.390084	+	0.489150i	0.0140485	+	0.0176163i
$772$	−0.571884	+	0.717120i	−0.0205826	+	0.0258097i
$773$	−39.5725			−1.42333			−0.711663	−	0.702521i	$-0.752057\pi$
$773$	−39.5725			−1.42333			−0.711663	+	0.702521i	$0.752057\pi$
$774$	−22.8986	+	0.767144i	−0.823072	+	0.0275744i
$775$	−35.7797			−1.28524
$776$	−28.7521	+	36.0540i	−1.03214	+	1.29426i
$777$	−2.70560	−	3.39271i	−0.0970627	−	0.121713i
$778$	9.80008	+	42.9369i	0.351350	+	1.53936i
$779$	54.8558	+	26.4171i	1.96541	+	0.946492i
$780$	−0.173899			−0.00622659
$781$	3.63188			0.129959
$782$	14.2838	+	6.87872i	0.510788	+	0.245983i
$783$	−3.44743	+	15.1042i	−0.123201	+	0.539780i
$784$	−13.5341	+	6.51770i	−0.483362	+	0.232775i
$785$	−1.63371	+	7.15776i	−0.0583096	+	0.255471i
$786$	6.20291	−	7.77820i	0.221250	−	0.277439i
$787$	12.3487	+	5.94682i	0.440184	+	0.211981i	0.640831	−	0.767682i	$-0.278590\pi$
$787$	12.3487	+	5.94682i	0.440184	+	0.211981i	−0.200647	+	0.979664i	$0.564304\pi$
$788$	−0.126842	+	0.159055i	−0.00451857	+	0.00566610i
$789$	0.311331	+	1.36403i	0.0110837	+	0.0485607i
$790$	−1.30194	+	0.626980i	−0.0463209	+	0.0223070i
$791$	23.0840	−	11.1167i	0.820773	−	0.395264i
$792$	11.4988	+	14.4190i	0.408592	+	0.512358i
$793$	−2.85086	−	12.4904i	−0.101237	−	0.443548i
$794$	0.937509	−	4.10750i	0.0332710	−	0.145770i
$795$	−0.473681	−	0.593977i	−0.0167997	−	0.0210662i
$796$	−0.572712	−	0.718158i	−0.0202992	−	0.0254544i
$797$	8.09472	−	35.4653i	0.286730	−	1.25624i	−0.602254	−	0.798305i	$-0.705730\pi$
$797$	8.09472	−	35.4653i	0.286730	−	1.25624i	0.888983	−	0.457940i	$-0.151412\pi$
$798$	−0.972189	−	4.25944i	−0.0344151	−	0.150782i
$799$	−17.0097	−	21.3295i	−0.601760	−	0.754583i
$800$	−10.4281	+	5.02192i	−0.368690	+	0.177552i
$801$	−3.75786	+	1.80969i	−0.132778	+	0.0639423i
$802$	−4.69202	−	20.5571i	−0.165681	−	0.725896i
$803$	5.35474	−	6.71463i	0.188965	−	0.236954i
$804$	1.31767	+	0.634555i	0.0464705	+	0.0223790i
$805$	2.39344	−	3.00127i	0.0843575	−	0.105781i
$806$	3.34767	−	14.6671i	0.117917	−	0.516626i
$807$	4.62253	−	2.22609i	0.162721	−	0.0783622i
$808$	2.30247	−	10.0878i	0.0810006	−	0.354887i
$809$	34.0274	+	16.3868i	1.19634	+	0.576128i	0.922631	−	0.385685i	$-0.126035\pi$
$809$	34.0274	+	16.3868i	1.19634	+	0.576128i	0.273710	+	0.961812i	$0.411749\pi$
$810$	−5.02177			−0.176447
$811$	−37.9694			−1.33329			−0.666643	−	0.745377i	$-0.732269\pi$
$811$	−37.9694			−1.33329			−0.666643	+	0.745377i	$0.732269\pi$
$812$	−3.26444	−	1.57207i	−0.114559	−	0.0551689i
$813$	1.32275	+	5.79534i	0.0463908	+	0.203251i
$814$	−12.0613	−	15.1244i	−0.422748	−	0.530109i
$815$	−3.62163	+	4.54138i	−0.126860	+	0.159078i
$816$	−3.23191			−0.113140
$817$	−34.8116	−	15.3505i	−1.21790	−	0.537045i
$818$	−2.32006			−0.0811190
$819$	−3.75033	+	4.70277i	−0.131047	+	0.164328i
$820$	−1.61596	−	2.02635i	−0.0564317	−	0.0707631i
$821$	−3.74578	−	16.4113i	−0.130729	−	0.572760i	−0.997282	−	0.0736758i	$-0.976527\pi$
$821$	−3.74578	−	16.4113i	−0.130729	−	0.572760i	0.866554	−	0.499084i	$-0.166330\pi$
$822$	−6.25451	−	3.01201i	−0.218151	−	0.105056i
$823$	17.7205			0.617698			0.308849	−	0.951111i	$-0.400056\pi$
$823$	17.7205			0.617698			0.308849	+	0.951111i	$0.400056\pi$
$824$	−15.5429			−0.541462
$825$	−4.06153	−	1.95593i	−0.141404	−	0.0680968i
$826$	−2.74698	+	12.0353i	−0.0955796	+	0.418762i
$827$	44.1492	−	21.2611i	1.53522	−	0.739322i	0.540440	−	0.841383i	$-0.318258\pi$
$827$	44.1492	−	21.2611i	1.53522	−	0.739322i	0.994778	+	0.102060i	$0.0325435\pi$
$828$	−1.41454	+	6.19752i	−0.0491587	+	0.215379i
$829$	28.5262	−	35.7708i	0.990757	−	1.24237i	0.0206269	−	0.999787i	$-0.493434\pi$
$829$	28.5262	−	35.7708i	0.990757	−	1.24237i	0.970131	−	0.242583i	$-0.0779948\pi$
$830$	0.571884	+	0.275405i	0.0198504	+	0.00955944i
$831$	3.68263	−	4.61787i	0.127749	−	0.160192i
$832$	−3.13318	−	13.7274i	−0.108623	−	0.475910i
$833$	11.5918	−	5.58231i	0.401632	−	0.193416i
$834$	−3.03534	+	1.46174i	−0.105105	+	0.0506161i
$835$	5.03952	+	6.31936i	0.174400	+	0.218691i
$836$	1.24041	+	5.43458i	0.0429004	+	0.187959i
$837$	4.38149	−	19.1965i	0.151446	−	0.663530i
$838$	12.8373	+	16.0974i	0.443457	+	0.556077i
$839$	13.6332	+	17.0955i	0.470670	+	0.590201i	0.959335	−	0.282270i	$-0.0910875\pi$
$839$	13.6332	+	17.0955i	0.470670	+	0.590201i	−0.488665	+	0.872471i	$0.662516\pi$
$840$	−0.227365	+	0.996152i	−0.00784485	+	0.0343705i
$841$	−1.55765	−	6.82450i	−0.0537119	−	0.235327i
$842$	−17.0951	−	21.4366i	−0.589138	−	0.738755i
$843$	6.38231	−	3.07356i	0.219819	−	0.105859i
$844$	0.339010	−	0.163259i	0.0116692	−	0.00561960i
$845$	1.29627	+	5.67931i	0.0445929	+	0.195374i
$846$	−23.8300	+	29.8819i	−0.819294	+	1.02736i
$847$	7.75010	+	3.73225i	0.266296	+	0.128242i
$848$	5.58463	−	7.00290i	0.191777	−	0.240481i
$849$	−2.35498	+	10.3178i	−0.0808226	+	0.354107i
$850$	−13.1468	+	6.33114i	−0.450930	+	0.217156i
$851$	8.15160	−	35.7145i	0.279433	−	1.22428i
$852$	−0.300209	−	0.144573i	−0.0102850	−	0.00495299i
$853$	−32.3217			−1.10667			−0.553337	−	0.832957i	$-0.686646\pi$
$853$	−32.3217			−1.10667			−0.553337	+	0.832957i	$0.686646\pi$
$854$	−13.7017			−0.468863
$855$	−8.12833	−	3.91440i	−0.277983	−	0.133870i
$856$	−0.208947	−	0.915458i	−0.00714167	−	0.0312897i
$857$	−11.3237	−	14.1995i	−0.386810	−	0.485045i	0.549860	−	0.835257i	$-0.314681\pi$
$857$	−11.3237	−	14.1995i	−0.386810	−	0.485045i	−0.936671	+	0.350212i	$0.886110\pi$
$858$	1.18180	−	1.48193i	0.0403460	−	0.0505923i
$859$	53.6402			1.83018			0.915091	−	0.403248i	$-0.132119\pi$
$859$	53.6402			1.83018			0.915091	+	0.403248i	$0.132119\pi$
$860$	1.05161	+	1.23170i	0.0358595	+	0.0420005i
$861$	6.33704			0.215966
$862$	−14.9186	+	18.7073i	−0.508128	+	0.637173i
$863$	−34.3036	−	43.0153i	−1.16771	−	1.46426i	−0.858166	−	0.513372i	$-0.828396\pi$
$863$	−34.3036	−	43.0153i	−1.16771	−	1.46426i	−0.309540	−	0.950886i	$-0.600175\pi$
$864$	−1.41736	−	6.20987i	−0.0482196	−	0.211264i
$865$	4.39493	+	2.11649i	0.149432	+	0.0719627i
$866$	−17.2174			−0.585072
$867$	−4.79763			−0.162936
$868$	4.14891	+	1.99801i	0.140823	+	0.0678168i
$869$	−1.00312	+	4.39494i	−0.0340284	+	0.149088i
$870$	−1.66487	+	0.801761i	−0.0564445	+	0.0271823i
$871$	−2.59956	+	11.3894i	−0.0880829	+	0.385916i
$872$	26.0465	−	32.6613i	0.882047	−	1.10605i
$873$	−38.1824	−	18.3877i	−1.29228	−	0.622328i
$874$	22.9957	−	28.8358i	0.777843	−	0.975384i
$875$	1.62402	+	7.11531i	0.0549020	+	0.240541i
$876$	−0.709907	+	0.341873i	−0.0239855	+	0.0115508i
$877$	9.10872	−	4.38653i	0.307580	−	0.148123i	−0.273726	−	0.961808i	$-0.588256\pi$
$877$	9.10872	−	4.38653i	0.307580	−	0.148123i	0.581306	+	0.813685i	$0.302542\pi$
$878$	−9.29925	−	11.6609i	−0.313834	−	0.393536i
$879$	−1.25667	−	5.50582i	−0.0423864	−	0.185707i
$880$	−0.776283	+	3.40112i	−0.0261685	+	0.114652i
$881$	25.2709	+	31.6887i	0.851398	+	1.06762i	0.996932	+	0.0782666i	$0.0249385\pi$
$881$	25.2709	+	31.6887i	0.851398	+	1.06762i	−0.145534	+	0.989353i	$0.546490\pi$
$882$	−11.2383	−	14.0923i	−0.378412	−	0.474513i
$883$	0.104776	−	0.459056i	0.00352601	−	0.0154484i	−0.973134	−	0.230238i	$-0.926049\pi$
$883$	0.104776	−	0.459056i	0.00352601	−	0.0154484i	0.976660	+	0.214790i	$0.0689066\pi$
$884$	0.390748	+	1.71198i	0.0131423	+	0.0575800i
$885$	−1.12349	−	1.40881i	−0.0377657	−	0.0473567i
$886$	−16.6528	+	8.01956i	−0.559462	+	0.269422i
$887$	31.6552	−	15.2444i	1.06288	−	0.511856i	0.181074	−	0.983469i	$-0.442043\pi$
$887$	31.6552	−	15.2444i	1.06288	−	0.511856i	0.881805	+	0.471614i	$0.156328\pi$
$888$	2.16972	+	9.50616i	0.0728110	+	0.319006i
$889$	−4.22550	+	5.29862i	−0.141719	+	0.177710i
$890$	−0.928116	−	0.446957i	−0.0311105	−	0.0149820i
$891$	−9.76755	+	12.2481i	−0.327225	+	0.410328i
$892$	−2.37047	+	10.3857i	−0.0793692	+	0.347739i
$893$	−57.1822	+	27.5375i	−1.91353	+	0.921506i
$894$	−0.339970	+	1.48951i	−0.0113703	+	0.0498165i
$895$	10.7017	+	5.15367i	0.357719	+	0.172268i
$896$	−8.36419			−0.279428
$897$	3.58940			0.119847
$898$	−21.7826	−	10.4900i	−0.726895	−	0.350054i
$899$	10.1812	+	44.6067i	0.339562	+	1.48772i
$900$	−3.64795	−	4.57438i	−0.121598	−	0.152479i
$901$	−4.78315	+	5.99788i	−0.159350	+	0.199818i
$902$	28.2500			0.940621
$903$	−3.95766	+	0.132589i	−0.131703	+	0.00441227i
$904$	−57.5706			−1.91477
$905$	9.11141	−	11.4253i	0.302873	−	0.379791i
$906$	6.45324	+	8.09211i	0.214394	+	0.268842i
$907$	1.96788	+	8.62183i	0.0653423	+	0.286283i	0.997034	−	0.0769678i	$-0.0245239\pi$
$907$	1.96788	+	8.62183i	0.0653423	+	0.286283i	−0.931691	+	0.363251i	$0.881667\pi$
$908$	−2.12133	−	1.02158i	−0.0703989	−	0.0339023i
$909$	9.50902			0.315394
$910$	−1.48560			−0.0492471
$911$	14.2594	+	6.86694i	0.472434	+	0.227512i	0.654923	−	0.755696i	$-0.272701\pi$
$911$	14.2594	+	6.86694i	0.472434	+	0.227512i	−0.182489	+	0.983208i	$0.558415\pi$
$912$	−1.67307	+	7.33020i	−0.0554009	+	0.242727i
$913$	1.78405	−	0.859154i	0.0590435	−	0.0284339i
$914$	5.97083	−	26.1599i	0.197497	−	0.865293i
$915$	1.24698	−	1.56366i	0.0412239	−	0.0516931i
$916$	6.13610	+	2.95499i	0.202743	+	0.0976357i
$917$	−15.1664	+	19.0180i	−0.500838	+	0.628030i
$918$	−1.78687	−	7.82880i	−0.0589756	−	0.258389i
$919$	34.8618	−	16.7886i	1.14998	−	0.553803i	0.240956	−	0.970536i	$-0.422539\pi$
$919$	34.8618	−	16.7886i	1.14998	−	0.553803i	0.909029	+	0.416733i	$0.136825\pi$
$920$	−7.77144	+	3.74253i	−0.256217	+	0.123387i
$921$	5.04743	+	6.32927i	0.166318	+	0.208557i
$922$	9.22766	+	40.4290i	0.303897	+	1.33146i
$923$	0.592268	−	2.59489i	0.0194947	−	0.0854120i
$924$	0.361740	+	0.453608i	0.0119004	+	0.0149226i
$925$	21.0221	+	26.3608i	0.691201	+	0.866739i
$926$	−4.87196	+	21.3455i	−0.160103	+	0.701455i
$927$	−3.17845	−	13.9257i	−0.104394	−	0.457380i
$928$	9.22819	+	11.5718i	0.302930	+	0.379863i
$929$	−3.71960	+	1.79126i	−0.122036	+	0.0587694i	−0.493906	−	0.869516i	$-0.664431\pi$
$929$	−3.71960	+	1.79126i	−0.122036	+	0.0587694i	0.371870	+	0.928285i	$0.378717\pi$
$930$	2.11596	−	1.01899i	0.0693850	−	0.0334140i
$931$	−6.66033	−	29.1808i	−0.218283	−	0.956362i
$932$	7.10992	−	8.91555i	0.232893	−	0.292039i
$933$	−2.92058	−	1.40648i	−0.0956156	−	0.0460460i
$934$	12.3151	−	15.4427i	0.402964	−	0.505301i
$935$	0.664874	−	2.91301i	0.0217437	−	0.0952655i
$936$	12.1773	−	5.86426i	0.398026	−	0.191679i
$937$	−0.502451	+	2.20138i	−0.0164144	+	0.0719161i	−0.982472	−	0.186411i	$-0.940314\pi$
$937$	−0.502451	+	2.20138i	−0.0164144	+	0.0719161i	0.966057	+	0.258328i	$0.0831714\pi$
$938$	11.2567	+	5.42093i	0.367543	+	0.176999i
$939$	−8.33704			−0.272069
$940$	2.70171			0.0881201
$941$	−46.6301	−	22.4559i	−1.52010	−	0.732041i	−0.527060	−	0.849828i	$-0.676706\pi$
$941$	−46.6301	−	22.4559i	−1.52010	−	0.732041i	−0.993039	+	0.117787i	$0.962420\pi$
$942$	1.63371	+	7.15776i	0.0532292	+	0.233212i
$943$	33.3545	+	41.8252i	1.08617	+	1.36202i
$944$	13.2458	−	16.6097i	0.431114	−	0.540599i
$945$	−1.94438			−0.0632506
$946$	−17.6429	+	0.591068i	−0.573619	+	0.0192173i
$947$	−24.0965			−0.783031			−0.391516	−	0.920171i	$-0.628049\pi$
$947$	−24.0965			−0.783031			−0.391516	+	0.920171i	$0.628049\pi$
$948$	0.257865	−	0.323352i	0.00837506	−	0.0105020i
$949$	−3.92423	−	4.92083i	−0.127386	−	0.159737i
$950$	7.55376	+	33.0952i	0.245076	+	1.07375i
$951$	−1.39104	−	0.669891i	−0.0451077	−	0.0217227i
$952$	10.3177			0.334398
$953$	47.1189			1.52633			0.763165	−	0.646204i	$-0.223644\pi$
$953$	47.1189			1.52633			0.763165	+	0.646204i	$0.223644\pi$
$954$	9.68329	+	4.66323i	0.313508	+	0.150978i
$955$	−1.07308	+	4.70147i	−0.0347241	+	0.152136i
$956$	−2.67145	+	1.28650i	−0.0864008	+	0.0416084i
$957$	−1.28275	+	5.62010i	−0.0414654	+	0.181672i
$958$	−22.2089	+	27.8490i	−0.717536	+	0.899762i
$959$	15.2925	+	7.36450i	0.493822	+	0.237812i
$960$	1.37047	−	1.71851i	0.0442317	−	0.0554648i
$961$	−6.04155	−	26.4698i	−0.194889	−	0.853863i
$962$	−12.7729	+	6.15112i	−0.411816	+	0.198320i
$963$	0.777479	−	0.374414i	0.0250539	−	0.0120653i
$964$	−0.722521	−	0.906013i	−0.0232708	−	0.0291807i
$965$	−0.254512	−	1.11509i	−0.00819304	−	0.0358961i
$966$	0.854207	−	3.74253i	0.0274837	−	0.120414i
$967$	−4.42274	−	5.54594i	−0.142226	−	0.178345i	0.705617	−	0.708594i	$-0.250670\pi$
$967$	−4.42274	−	5.54594i	−0.142226	−	0.178345i	−0.847842	+	0.530248i	$0.822099\pi$
$968$	−12.0511	−	15.1116i	−0.387336	−	0.485704i
$969$	1.43296	−	6.27821i	0.0460333	−	0.201685i
$970$	−2.32908	−	10.2044i	−0.0747824	−	0.327643i
$971$	17.3327	+	21.7346i	0.556234	+	0.697495i	0.977857	−	0.209276i	$-0.0671108\pi$
$971$	17.3327	+	21.7346i	0.556234	+	0.697495i	−0.421623	+	0.906771i	$0.638539\pi$
$972$	4.40097	−	2.11939i	0.141161	−	0.0679796i
$973$	7.42154	−	3.57403i	0.237924	−	0.114578i
$974$	0.519614	+	2.27658i	0.0166495	+	0.0729463i
$975$	−2.05980	+	2.58291i	−0.0659665	+	0.0827193i
$976$	21.2446	+	10.2309i	0.680023	+	0.327482i
$977$	19.1163	−	23.9710i	0.611583	−	0.766901i	−0.375550	−	0.926802i	$-0.622546\pi$
$977$	19.1163	−	23.9710i	0.611583	−	0.766901i	0.987133	+	0.159901i	$0.0511176\pi$
$978$	−1.29254	+	5.66301i	−0.0413310	+	0.181083i
$979$	−2.89536	+	1.39433i	−0.0925359	+	0.0445630i
$980$	−0.283520	+	1.24218i	−0.00905671	+	0.0396800i
$981$	34.5894	+	16.6574i	1.10435	+	0.531829i
$982$	36.4537			1.16328
$983$	14.7797			0.471399			0.235700	−	0.971826i	$-0.424262\pi$
$983$	14.7797			0.471399			0.235700	+	0.971826i	$0.424262\pi$
$984$	−12.8291	−	6.17816i	−0.408976	−	0.196953i
$985$	−0.0564501	−	0.247324i	−0.00179865	−	0.00788040i
$986$	11.6340	+	14.5886i	0.370502	+	0.464595i
$987$	−4.11865	+	5.16462i	−0.131098	+	0.164392i
$988$	4.08516			0.129966
$989$	−21.7059	−	25.4231i	−0.690207	−	0.808408i
$990$	−4.18598			−0.133039
$991$	−38.8573	+	48.7255i	−1.23434	+	1.54782i	−0.506152	+	0.862444i	$0.668932\pi$
$991$	−38.8573	+	48.7255i	−1.23434	+	1.54782i	−0.728192	+	0.685373i	$0.759639\pi$
$992$	−11.7285	−	14.7071i	−0.372380	−	0.466950i
$993$	1.37800	+	6.03742i	0.0437296	+	0.191592i
$994$	−2.56465	−	1.23507i	−0.0813457	−	0.0391740i
$995$	1.14542			0.0363124
$996$	−0.181669			−0.00575640
$997$	−27.7613	−	13.3691i	−0.879208	−	0.423404i	−0.0608731	−	0.998146i	$-0.519388\pi$
$997$	−27.7613	−	13.3691i	−0.879208	−	0.423404i	−0.818335	+	0.574741i	$0.805103\pi$
$998$	6.91872	−	30.3129i	0.219008	−	0.959538i
$999$	−16.7174	+	8.05069i	−0.528916	+	0.254713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.e.a.4.1	✓	6
3.2	odd	2		387.2.u.c.262.1		6
4.3	odd	2		688.2.u.b.305.1		6
43.11	even	7	inner	43.2.e.a.11.1	yes	6
43.21	even	7		1849.2.a.k.1.1		3
43.22	odd	14		1849.2.a.j.1.3		3
129.11	odd	14		387.2.u.c.226.1		6
172.11	odd	14		688.2.u.b.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.a.4.1	✓	6	1.1	even	1	trivial
43.2.e.a.11.1	yes	6	43.11	even	7	inner
387.2.u.c.226.1		6	129.11	odd	14
387.2.u.c.262.1		6	3.2	odd	2
688.2.u.b.97.1		6	172.11	odd	14
688.2.u.b.305.1		6	4.3	odd	2
1849.2.a.j.1.3		3	43.22	odd	14
1849.2.a.k.1.1		3	43.21	even	7

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777479 + 0.974928i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-0.500000 - 0.240787i) q^{5} -0.554958 q^{6} +1.35690 q^{7} +(-2.74698 - 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +O(q^{10})\)	\(q+(-0.777479 + 0.974928i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-0.500000 - 0.240787i) q^{5} -0.554958 q^{6} +1.35690 q^{7} +(-2.74698 - 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +(0.623490 - 0.300257i) q^{10} +(0.480386 - 2.10471i) q^{11} +(-0.123490 + 0.154851i) q^{12} +(-1.42543 - 0.686450i) q^{13} +(-1.05496 + 1.32288i) q^{14} +(-0.0549581 - 0.240787i) q^{15} +(2.62349 - 1.26341i) q^{16} +(-2.24698 + 1.08209i) q^{17} +(2.17845 + 2.73169i) q^{18} +(1.29105 + 5.65647i) q^{19} +(0.0549581 - 0.240787i) q^{20} +(0.376510 + 0.472129i) q^{21} +(1.67845 + 2.10471i) q^{22} +(-1.13437 + 4.97002i) q^{23} +(-0.301938 - 1.32288i) q^{24} +(-2.92543 - 3.66837i) q^{25} +(1.77748 - 0.855989i) q^{26} +(2.32640 - 1.12033i) q^{27} +(0.134375 + 0.588735i) q^{28} +(-3.74094 + 4.69099i) q^{29} +(0.277479 + 0.133627i) q^{30} +(4.75451 - 5.96197i) q^{31} +(0.548917 - 2.40496i) q^{32} +(0.865625 - 0.416863i) q^{33} +(0.692021 - 3.03194i) q^{34} +(-0.678448 - 0.326723i) q^{35} +1.24698 q^{36} -7.18598 q^{37} +(-6.51842 - 3.13910i) q^{38} +(-0.156678 - 0.686450i) q^{39} +(1.05496 + 1.32288i) q^{40} +(6.54288 - 8.20451i) q^{41} -0.753020 q^{42} +(-3.91454 + 5.26083i) q^{43} +0.960771 q^{44} +(-0.969501 + 1.21572i) q^{45} +(-3.96346 - 4.97002i) q^{46} +(2.43416 + 10.6647i) q^{47} +(1.16756 + 0.562269i) q^{48} -5.15883 q^{49} +5.85086 q^{50} +(-1.00000 - 0.481575i) q^{51} +(0.156678 - 0.686450i) q^{52} +(2.77144 - 1.33465i) q^{53} +(-0.716480 + 3.13910i) q^{54} +(-0.746980 + 0.936683i) q^{55} +(-3.72737 - 1.79500i) q^{56} +(-1.60992 + 2.01877i) q^{57} +(-1.66487 - 7.29429i) q^{58} +(6.57338 - 3.16557i) q^{59} +(0.0990311 - 0.0476909i) q^{60} +(5.04892 + 6.33114i) q^{61} +(2.11596 + 9.27061i) q^{62} +(0.846011 - 3.70662i) q^{63} +(5.54892 + 6.95812i) q^{64} +(0.547425 + 0.686450i) q^{65} +(-0.266594 + 1.16802i) q^{66} +(-1.64310 - 7.19891i) q^{67} +(-0.692021 - 0.867767i) q^{68} +(-2.04407 + 0.984374i) q^{69} +(0.846011 - 0.407417i) q^{70} +(0.374354 + 1.64015i) q^{71} +(-5.32640 + 6.67909i) q^{72} +(3.58426 + 1.72609i) q^{73} +(5.58695 - 7.00581i) q^{74} +(0.464656 - 2.03579i) q^{75} +(-2.32640 + 1.12033i) q^{76} +(0.651833 - 2.85587i) q^{77} +(0.791053 + 0.380951i) q^{78} -2.08815 q^{79} -1.61596 q^{80} +(-6.53803 - 3.14855i) q^{81} +(2.91185 + 12.7577i) q^{82} +(0.571884 + 0.717120i) q^{83} +(-0.167563 + 0.210117i) q^{84} +1.38404 q^{85} +(-2.08546 - 7.90658i) q^{86} -2.67025 q^{87} +(-4.10388 + 5.14610i) q^{88} +(-0.928116 - 1.16382i) q^{89} +(-0.431468 - 1.89039i) q^{90} +(-1.93416 - 0.931441i) q^{91} -2.26875 q^{92} +3.39373 q^{93} +(-12.2899 - 5.91848i) q^{94} +(0.716480 - 3.13910i) q^{95} +(0.989115 - 0.476333i) q^{96} +(3.36563 - 14.7458i) q^{97} +(4.01089 - 5.02949i) q^{98} +(-5.44989 - 2.62453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9	\( 6 q - 5 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} - 7 q^{8} - q^{9} - q^{10} - 10 q^{11} + 4 q^{12} + 5 q^{13} - 7 q^{14} - q^{15} + 11 q^{16} - 4 q^{17} + 9 q^{18} + 2 q^{19} + q^{20} + 7 q^{21} + 6 q^{22} + q^{23} + 7 q^{24} - 4 q^{25} + 11 q^{26} - 4 q^{27} - 7 q^{28} + 6 q^{29} + 2 q^{30} - 6 q^{31} - 15 q^{32} + 13 q^{33} - 6 q^{34} - 2 q^{36} - 14 q^{37} - 11 q^{38} - 3 q^{39} + 7 q^{40} + 2 q^{41} - 14 q^{42} - 13 q^{43} - 20 q^{44} + 4 q^{45} + 5 q^{46} + 17 q^{47} + 6 q^{48} - 14 q^{49} + 8 q^{50} - 6 q^{51} + 3 q^{52} - 2 q^{53} + 15 q^{54} + 5 q^{55} - 11 q^{57} - 12 q^{58} + 12 q^{59} + 5 q^{60} + 12 q^{61} + 33 q^{62} + 15 q^{64} + 29 q^{65} - 5 q^{66} - 18 q^{67} + 6 q^{68} - 16 q^{69} + 26 q^{71} - 14 q^{72} - 9 q^{73} + 15 q^{75} + 4 q^{76} + 28 q^{77} - q^{78} - 20 q^{79} - 30 q^{80} - 24 q^{81} + 10 q^{82} + 20 q^{83} - 12 q^{85} - 23 q^{86} - 12 q^{87} - 7 q^{88} + 11 q^{89} - 8 q^{90} - 14 q^{91} + 2 q^{92} - 44 q^{93} - 27 q^{94} - 15 q^{95} + 9 q^{96} + 28 q^{97} + 21 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 - 4 * q^6 - 7 * q^8 - q^9 - q^10 - 10 * q^11 + 4 * q^12 + 5 * q^13 - 7 * q^14 - q^15 + 11 * q^16 - 4 * q^17 + 9 * q^18 + 2 * q^19 + q^20 + 7 * q^21 + 6 * q^22 + q^23 + 7 * q^24 - 4 * q^25 + 11 * q^26 - 4 * q^27 - 7 * q^28 + 6 * q^29 + 2 * q^30 - 6 * q^31 - 15 * q^32 + 13 * q^33 - 6 * q^34 - 2 * q^36 - 14 * q^37 - 11 * q^38 - 3 * q^39 + 7 * q^40 + 2 * q^41 - 14 * q^42 - 13 * q^43 - 20 * q^44 + 4 * q^45 + 5 * q^46 + 17 * q^47 + 6 * q^48 - 14 * q^49 + 8 * q^50 - 6 * q^51 + 3 * q^52 - 2 * q^53 + 15 * q^54 + 5 * q^55 - 11 * q^57 - 12 * q^58 + 12 * q^59 + 5 * q^60 + 12 * q^61 + 33 * q^62 + 15 * q^64 + 29 * q^65 - 5 * q^66 - 18 * q^67 + 6 * q^68 - 16 * q^69 + 26 * q^71 - 14 * q^72 - 9 * q^73 + 15 * q^75 + 4 * q^76 + 28 * q^77 - q^78 - 20 * q^79 - 30 * q^80 - 24 * q^81 + 10 * q^82 + 20 * q^83 - 12 * q^85 - 23 * q^86 - 12 * q^87 - 7 * q^88 + 11 * q^89 - 8 * q^90 - 14 * q^91 + 2 * q^92 - 44 * q^93 - 27 * q^94 - 15 * q^95 + 9 * q^96 + 28 * q^97 + 21 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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