LMFDB - Embedded newform 43.2.e.a.21.1

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			21.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	43.21
Dual form			43.2.e.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62349 - 0.781831i) q^{2} +(1.12349 - 0.541044i) q^{3} +(0.777479 + 0.974928i) q^{4} +(-0.500000 - 2.19064i) q^{5} -2.24698 q^{6} +1.69202 q^{7} +(0.301938 + 1.32288i) q^{8} +(-0.900969 + 1.12978i) q^{9} +O(q^{10})$	\(q+(-1.62349 - 0.781831i) q^{2} +(1.12349 - 0.541044i) q^{3} +(0.777479 + 0.974928i) q^{4} +(-0.500000 - 2.19064i) q^{5} -2.24698 q^{6} +1.69202 q^{7} +(0.301938 + 1.32288i) q^{8} +(-0.900969 + 1.12978i) q^{9} +(-0.900969 + 3.94740i) q^{10} +(-0.708947 + 0.888992i) q^{11} +(1.40097 + 0.674671i) q^{12} +(1.45593 + 6.37883i) q^{13} +(-2.74698 - 1.32288i) q^{14} +(-1.74698 - 2.19064i) q^{15} +(1.09903 - 4.81517i) q^{16} +(0.801938 - 3.51352i) q^{17} +(2.34601 - 1.12978i) q^{18} +(-2.77144 - 3.47527i) q^{19} +(1.74698 - 2.19064i) q^{20} +(1.90097 - 0.915458i) q^{21} +(1.84601 - 0.888992i) q^{22} +(-2.31551 + 2.90356i) q^{23} +(1.05496 + 1.32288i) q^{24} +(-0.0440730 + 0.0212244i) q^{25} +(2.62349 - 11.4943i) q^{26} +(-1.23341 + 5.40391i) q^{27} +(1.31551 + 1.64960i) q^{28} +(5.40581 + 2.60330i) q^{29} +(1.12349 + 4.92233i) q^{30} +(-9.30074 - 4.47900i) q^{31} +(-3.85690 + 4.83639i) q^{32} +(-0.315511 + 1.38235i) q^{33} +(-4.04892 + 5.07718i) q^{34} +(-0.846011 - 3.70662i) q^{35} -1.80194 q^{36} +3.65279 q^{37} +(1.78232 + 7.80887i) q^{38} +(5.08695 + 6.37883i) q^{39} +(2.74698 - 1.32288i) q^{40} +(-3.96077 - 1.90741i) q^{41} -3.80194 q^{42} +(1.67241 - 6.34059i) q^{43} -1.41789 q^{44} +(2.92543 + 1.40881i) q^{45} +(6.02930 - 2.90356i) q^{46} +(-1.96346 - 2.46210i) q^{47} +(-1.37047 - 6.00442i) q^{48} -4.13706 q^{49} +0.0881460 q^{50} +(-1.00000 - 4.38129i) q^{51} +(-5.08695 + 6.37883i) q^{52} +(-2.48039 + 10.8673i) q^{53} +(6.22737 - 7.80887i) q^{54} +(2.30194 + 1.10855i) q^{55} +(0.510885 + 2.23833i) q^{56} +(-4.99396 - 2.40496i) q^{57} +(-6.74094 - 8.45287i) q^{58} +(-0.0353438 + 0.154851i) q^{59} +(0.777479 - 3.40636i) q^{60} +(0.643104 - 0.309703i) q^{61} +(11.5978 + 14.5432i) q^{62} +(-1.52446 + 1.91161i) q^{63} +(1.14310 - 0.550490i) q^{64} +(13.2458 - 6.37883i) q^{65} +(1.59299 - 1.99755i) q^{66} +(-1.30798 - 1.64015i) q^{67} +(4.04892 - 1.94986i) q^{68} +(-1.03050 + 4.51491i) q^{69} +(-1.52446 + 6.67909i) q^{70} +(-2.32304 - 2.91301i) q^{71} +(-1.76659 - 0.850747i) q^{72} +(-0.318864 - 1.39703i) q^{73} +(-5.93027 - 2.85587i) q^{74} +(-0.0380322 + 0.0476909i) q^{75} +(1.23341 - 5.40391i) q^{76} +(-1.19955 + 1.50419i) q^{77} +(-3.27144 - 14.3331i) q^{78} -0.0609989 q^{79} -11.0978 q^{80} +(0.573376 + 2.51212i) q^{81} +(4.93900 + 6.19331i) q^{82} +(11.0673 - 5.32975i) q^{83} +(2.37047 + 1.14156i) q^{84} -8.09783 q^{85} +(-7.67241 + 8.98634i) q^{86} +7.48188 q^{87} +(-1.39008 - 0.669429i) q^{88} +(9.56734 - 4.60739i) q^{89} +(-3.64795 - 4.57438i) q^{90} +(2.46346 + 10.7931i) q^{91} -4.63102 q^{92} -12.8726 q^{93} +(1.26271 + 5.53229i) q^{94} +(-6.22737 + 7.80887i) q^{95} +(-1.71648 + 7.52039i) q^{96} +(2.18449 - 2.73926i) q^{97} +(6.71648 + 3.23449i) q^{98} +(-0.365625 - 1.60191i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−1.62349	−	0.781831i	−1.14798	−	0.552838i	−0.239554	−	0.970883i	$-0.577001\pi$
$2$	−1.62349	−	0.781831i	−1.14798	−	0.552838i	−0.908426	+	0.418045i	$0.862716\pi$
$3$	1.12349	−	0.541044i	0.648647	−	0.312372i	−0.0804740	−	0.996757i	$-0.525643\pi$
$3$	1.12349	−	0.541044i	0.648647	−	0.312372i	0.729121	+	0.684385i	$0.239929\pi$
$4$	0.777479	+	0.974928i	0.388740	+	0.487464i
$5$	−0.500000	−	2.19064i	−0.223607	−	0.979685i	−0.954738	−	0.297448i	$-0.903864\pi$
$5$	−0.500000	−	2.19064i	−0.223607	−	0.979685i	0.731131	−	0.682237i	$-0.238993\pi$
$6$	−2.24698			−0.917326
$7$	1.69202			0.639524			0.319762	−	0.947498i	$-0.396397\pi$
$7$	1.69202			0.639524			0.319762	+	0.947498i	$0.396397\pi$
$8$	0.301938	+	1.32288i	0.106751	+	0.467707i
$9$	−0.900969	+	1.12978i	−0.300323	+	0.376593i
$10$	−0.900969	+	3.94740i	−0.284911	+	1.24828i
$11$	−0.708947	+	0.888992i	−0.213756	+	0.268041i	−0.877137	−	0.480240i	$-0.840549\pi$
$11$	−0.708947	+	0.888992i	−0.213756	+	0.268041i	0.663381	+	0.748282i	$0.269121\pi$
$12$	1.40097	+	0.674671i	0.404425	+	0.194761i
$13$	1.45593	+	6.37883i	0.403801	+	1.76917i	0.611771	+	0.791035i	$0.290457\pi$
$13$	1.45593	+	6.37883i	0.403801	+	1.76917i	−0.207970	+	0.978135i	$0.566686\pi$
$14$	−2.74698	−	1.32288i	−0.734161	−	0.353553i
$15$	−1.74698	−	2.19064i	−0.451068	−	0.565622i
$16$	1.09903	−	4.81517i	0.274758	−	1.20379i
$17$	0.801938	−	3.51352i	0.194498	−	0.852153i	−0.779645	−	0.626222i	$-0.784600\pi$
$17$	0.801938	−	3.51352i	0.194498	−	0.852153i	0.974143	−	0.225931i	$-0.0725425\pi$
$18$	2.34601	−	1.12978i	0.552960	−	0.266292i
$19$	−2.77144	−	3.47527i	−0.635812	−	0.797282i	0.354661	−	0.934995i	$-0.384596\pi$
$19$	−2.77144	−	3.47527i	−0.635812	−	0.797282i	−0.990472	+	0.137713i	$0.956025\pi$
$20$	1.74698	−	2.19064i	0.390637	−	0.489843i
$21$	1.90097	−	0.915458i	0.414825	−	0.199769i
$22$	1.84601	−	0.888992i	0.393571	−	0.189534i
$23$	−2.31551	+	2.90356i	−0.482817	+	0.605434i	−0.962257	−	0.272141i	$-0.912268\pi$
$23$	−2.31551	+	2.90356i	−0.482817	+	0.605434i	0.479440	+	0.877575i	$0.340840\pi$
$24$	1.05496	+	1.32288i	0.215342	+	0.270031i
$25$	−0.0440730	+	0.0212244i	−0.00881460	+	0.00424489i
$26$	2.62349	−	11.4943i	0.514509	−	2.25421i
$27$	−1.23341	+	5.40391i	−0.237369	+	1.03998i
$28$	1.31551	+	1.64960i	0.248608	+	0.311745i
$29$	5.40581	+	2.60330i	1.00383	+	0.483421i	0.862238	−	0.506503i	$-0.169062\pi$
$29$	5.40581	+	2.60330i	1.00383	+	0.483421i	0.141596	+	0.989924i	$0.454777\pi$
$30$	1.12349	+	4.92233i	0.205120	+	0.898690i
$31$	−9.30074	−	4.47900i	−1.67046	−	0.804452i	−0.997925	−	0.0643894i	$-0.979490\pi$
$31$	−9.30074	−	4.47900i	−1.67046	−	0.804452i	−0.672538	−	0.740063i	$-0.734796\pi$
$32$	−3.85690	+	4.83639i	−0.681809	+	0.854962i
$33$	−0.315511	+	1.38235i	−0.0549235	+	0.240635i
$34$	−4.04892	+	5.07718i	−0.694384	+	0.870729i
$35$	−0.846011	−	3.70662i	−0.143002	−	0.626532i
$36$	−1.80194			−0.300323
$37$	3.65279			0.600515			0.300258	−	0.953858i	$-0.402927\pi$
$37$	3.65279			0.600515			0.300258	+	0.953858i	$0.402927\pi$
$38$	1.78232	+	7.80887i	0.289131	+	1.26677i
$39$	5.08695	+	6.37883i	0.814564	+	1.02143i
$40$	2.74698	−	1.32288i	0.434336	−	0.209165i
$41$	−3.96077	−	1.90741i	−0.618569	−	0.297887i	0.0982338	−	0.995163i	$-0.468681\pi$
$41$	−3.96077	−	1.90741i	−0.618569	−	0.297887i	−0.716802	+	0.697276i	$0.754395\pi$
$42$	−3.80194			−0.586652
$43$	1.67241	−	6.34059i	0.255040	−	0.966931i
$43$	1.67241	−	6.34059i	0.255040	−	0.966931i
$44$	−1.41789			−0.213756
$45$	2.92543	+	1.40881i	0.436097	+	0.210013i
$46$	6.02930	−	2.90356i	0.888972	−	0.428106i
$47$	−1.96346	−	2.46210i	−0.286400	−	0.359134i	0.617731	−	0.786389i	$-0.288052\pi$
$47$	−1.96346	−	2.46210i	−0.286400	−	0.359134i	−0.904131	+	0.427255i	$0.859481\pi$
$48$	−1.37047	−	6.00442i	−0.197810	−	0.866663i
$49$	−4.13706			−0.591009
$50$	0.0881460			0.0124657
$51$	−1.00000	−	4.38129i	−0.140028	−	0.613503i
$52$	−5.08695	+	6.37883i	−0.705433	+	0.884585i
$53$	−2.48039	+	10.8673i	−0.340707	+	1.49274i	0.456878	+	0.889529i	$0.348968\pi$
$53$	−2.48039	+	10.8673i	−0.340707	+	1.49274i	−0.797585	+	0.603206i	$0.793890\pi$
$54$	6.22737	−	7.80887i	0.847437	−	1.06265i
$55$	2.30194	+	1.10855i	0.310393	+	0.149477i
$56$	0.510885	+	2.23833i	0.0682699	+	0.299110i
$57$	−4.99396	−	2.40496i	−0.661466	−	0.318545i
$58$	−6.74094	−	8.45287i	−0.885129	−	1.10992i
$59$	−0.0353438	+	0.154851i	−0.00460137	+	0.0201599i	−0.977176	−	0.212429i	$-0.931863\pi$
$59$	−0.0353438	+	0.154851i	−0.00460137	+	0.0201599i	0.972575	+	0.232589i	$0.0747197\pi$
$60$	0.777479	−	3.40636i	0.100372	−	0.439759i
$61$	0.643104	−	0.309703i	0.0823410	−	0.0396534i	−0.392260	−	0.919854i	$-0.628307\pi$
$61$	0.643104	−	0.309703i	0.0823410	−	0.0396534i	0.474601	+	0.880201i	$0.342592\pi$
$62$	11.5978	+	14.5432i	1.47293	+	1.84699i
$63$	−1.52446	+	1.91161i	−0.192064	+	0.240840i
$64$	1.14310	−	0.550490i	0.142888	−	0.0688112i
$65$	13.2458	−	6.37883i	1.64294	−	0.791197i
$66$	1.59299	−	1.99755i	0.196084	−	0.245881i
$67$	−1.30798	−	1.64015i	−0.159795	−	0.200377i	0.695488	−	0.718538i	$-0.255188\pi$
$67$	−1.30798	−	1.64015i	−0.159795	−	0.200377i	−0.855283	+	0.518161i	$0.826617\pi$
$68$	4.04892	−	1.94986i	0.491003	−	0.236455i
$69$	−1.03050	+	4.51491i	−0.124058	+	0.543532i
$70$	−1.52446	+	6.67909i	−0.182208	+	0.798304i
$71$	−2.32304	−	2.91301i	−0.275695	−	0.345710i	0.624637	−	0.780916i	$-0.285247\pi$
$71$	−2.32304	−	2.91301i	−0.275695	−	0.345710i	−0.900331	+	0.435206i	$0.856676\pi$
$72$	−1.76659	−	0.850747i	−0.208195	−	0.100261i
$73$	−0.318864	−	1.39703i	−0.0373202	−	0.163510i	0.952834	−	0.303492i	$-0.0981527\pi$
$73$	−0.318864	−	1.39703i	−0.0373202	−	0.163510i	−0.990154	+	0.139982i	$0.955296\pi$
$74$	−5.93027	−	2.85587i	−0.689380	−	0.331988i
$75$	−0.0380322	+	0.0476909i	−0.00439158	+	0.00550687i
$76$	1.23341	−	5.40391i	0.141481	−	0.619870i
$77$	−1.19955	+	1.50419i	−0.136702	+	0.171419i
$78$	−3.27144	−	14.3331i	−0.370417	−	1.62290i
$79$	−0.0609989			−0.00686292			−0.00343146	−	0.999994i	$-0.501092\pi$
$79$	−0.0609989			−0.00686292			−0.00343146	+	0.999994i	$0.501092\pi$
$80$	−11.0978			−1.24078
$81$	0.573376	+	2.51212i	0.0637084	+	0.279125i
$82$	4.93900	+	6.19331i	0.545421	+	0.683937i
$83$	11.0673	−	5.32975i	1.21480	−	0.585016i	0.286940	−	0.957949i	$-0.407362\pi$
$83$	11.0673	−	5.32975i	1.21480	−	0.585016i	0.927858	+	0.372933i	$0.121648\pi$
$84$	2.37047	+	1.14156i	0.258639	+	0.124554i
$85$	−8.09783			−0.878333
$86$	−7.67241	+	8.98634i	−0.827337	+	0.969022i
$87$	7.48188			0.802141
$88$	−1.39008	−	0.669429i	−0.148183	−	0.0713614i
$89$	9.56734	−	4.60739i	1.01414	−	0.488382i	0.148423	−	0.988924i	$-0.452580\pi$
$89$	9.56734	−	4.60739i	1.01414	−	0.488382i	0.865712	+	0.500542i	$0.166866\pi$
$90$	−3.64795	−	4.57438i	−0.384528	−	0.482182i
$91$	2.46346	+	10.7931i	0.258241	+	1.13143i
$92$	−4.63102			−0.482817
$93$	−12.8726			−1.33483
$94$	1.26271	+	5.53229i	0.130238	+	0.570612i
$95$	−6.22737	+	7.80887i	−0.638914	+	0.801173i
$96$	−1.71648	+	7.52039i	−0.175188	+	0.767547i
$97$	2.18449	−	2.73926i	0.221801	−	0.278130i	−0.658464	−	0.752613i	$-0.728793\pi$
$97$	2.18449	−	2.73926i	0.221801	−	0.278130i	0.880265	+	0.474483i	$0.157365\pi$
$98$	6.71648	+	3.23449i	0.678467	+	0.326732i
$99$	−0.365625	−	1.60191i	−0.0367467	−	0.160998i
$100$	−0.0549581	−	0.0264664i	−0.00549581	−	0.00264664i
$101$	8.02595	+	10.0642i	0.798612	+	1.00143i	0.999761	+	0.0218670i	$0.00696105\pi$
$101$	8.02595	+	10.0642i	0.798612	+	1.00143i	−0.201149	+	0.979561i	$0.564468\pi$
$102$	−1.80194	+	7.89481i	−0.178418	+	0.781702i
$103$	−0.826396	+	3.62068i	−0.0814273	+	0.356756i	−0.999184	−	0.0403866i	$-0.987141\pi$
$103$	−0.826396	+	3.62068i	−0.0814273	+	0.356756i	0.917757	+	0.397143i	$0.129998\pi$
$104$	−7.99880	+	3.85202i	−0.784347	+	0.377722i
$105$	−2.95593	−	3.70662i	−0.288469	−	0.361729i
$106$	12.5233	−	15.7037i	1.21637	−	1.52528i
$107$	−4.54892	+	2.19064i	−0.439760	+	0.211777i	−0.640645	−	0.767838i	$-0.721333\pi$
$107$	−4.54892	+	2.19064i	−0.439760	+	0.211777i	0.200884	+	0.979615i	$0.435619\pi$
$108$	−6.22737	+	2.99894i	−0.599229	+	0.288573i
$109$	1.35690	−	1.70149i	0.129967	−	0.162974i	−0.712590	−	0.701581i	$-0.752478\pi$
$109$	1.35690	−	1.70149i	0.129967	−	0.162974i	0.842557	+	0.538607i	$0.181049\pi$
$110$	−2.87047	−	3.59945i	−0.273689	−	0.343195i
$111$	4.10388	−	1.97632i	0.389523	−	0.187584i
$112$	1.85958	−	8.14737i	0.175714	−	0.769854i
$113$	2.61380	−	11.4518i	0.245886	−	1.07730i	−0.689672	−	0.724122i	$-0.742245\pi$
$113$	2.61380	−	11.4518i	0.245886	−	1.07730i	0.935558	−	0.353174i	$-0.114898\pi$
$114$	6.22737	+	7.80887i	0.583246	+	0.731368i
$115$	7.51842	+	3.62068i	0.701096	+	0.337630i
$116$	1.66487	+	7.29429i	0.154580	+	0.677258i
$117$	−8.51842	−	4.10225i	−0.787528	−	0.379254i
$118$	0.178448	−	0.223767i	0.0164275	−	0.0205994i
$119$	1.35690	−	5.94495i	0.124386	−	0.544973i
$120$	2.37047	−	2.97247i	0.216393	−	0.271349i
$121$	2.16003	+	9.46371i	0.196366	+	0.860337i
$122$	−1.28621			−0.116448
$123$	−5.48188			−0.494284
$124$	−2.86443	−	12.5499i	−0.257233	−	1.12701i
$125$	−6.93631	−	8.69786i	−0.620403	−	0.777960i
$126$	3.96950	−	1.91161i	0.353631	−	0.170300i
$127$	18.2201	+	8.77435i	1.61677	+	0.778598i	0.999964	−	0.00851340i	$-0.00270993\pi$
$127$	18.2201	+	8.77435i	1.61677	+	0.778598i	0.616811	+	0.787111i	$0.288424\pi$
$128$	10.0858			0.891463
$129$	−1.55161	−	8.02843i	−0.136611	−	0.706864i
$130$	−26.4916			−2.32346
$131$	−1.85474	−	0.893196i	−0.162049	−	0.0780389i	0.351101	−	0.936338i	$-0.385807\pi$
$131$	−1.85474	−	0.893196i	−0.162049	−	0.0780389i	−0.513150	+	0.858299i	$0.671522\pi$
$132$	−1.59299	+	0.767144i	−0.138652	+	0.0667713i
$133$	−4.68933	−	5.88024i	−0.406617	−	0.509881i
$134$	0.841166	+	3.68539i	0.0726657	+	0.318369i
$135$	12.4547			1.07193
$136$	4.89008			0.419321
$137$	−3.47166	−	15.2103i	−0.296604	−	1.29951i	−0.875148	−	0.483855i	$-0.839236\pi$
$137$	−3.47166	−	15.2103i	−0.296604	−	1.29951i	0.578545	−	0.815651i	$-0.303621\pi$
$138$	5.20291	−	6.52424i	0.442901	−	0.555380i
$139$	1.57457	−	6.89865i	0.133553	−	0.585136i	−0.863217	−	0.504833i	$-0.831554\pi$
$139$	1.57457	−	6.89865i	0.133553	−	0.585136i	0.996770	−	0.0803030i	$-0.0255888\pi$
$140$	2.95593	−	3.70662i	0.249821	−	0.313266i
$141$	−3.53803	−	1.70383i	−0.297956	−	0.143488i
$142$	1.49396	+	6.54546i	0.125370	+	0.549283i
$143$	−6.70291	−	3.22795i	−0.560525	−	0.269935i
$144$	4.44989	+	5.57998i	0.370824	+	0.464998i
$145$	3.00000	−	13.1439i	0.249136	−	1.09154i
$146$	−0.574572	+	2.51737i	−0.0475520	+	0.208339i
$147$	−4.64795	+	2.23833i	−0.383356	+	0.184615i
$148$	2.83997	+	3.56121i	0.233444	+	0.292730i
$149$	−3.61745	+	4.53614i	−0.296353	+	0.371615i	−0.907608	−	0.419819i	$-0.862094\pi$
$149$	−3.61745	+	4.53614i	−0.296353	+	0.371615i	0.611255	+	0.791434i	$0.290665\pi$
$150$	0.0990311	−	0.0476909i	0.00808586	−	0.00389394i
$151$	−6.71164	+	3.23215i	−0.546185	+	0.263029i	−0.686565	−	0.727069i	$-0.740882\pi$
$151$	−6.71164	+	3.23215i	−0.546185	+	0.263029i	0.140379	+	0.990098i	$0.455168\pi$
$152$	3.76055	−	4.71558i	0.305021	−	0.382484i
$153$	3.24698	+	4.07158i	0.262503	+	0.329168i
$154$	3.12349	−	1.50419i	0.251698	−	0.121211i
$155$	−5.16152	+	22.6141i	−0.414583	+	1.81641i
$156$	−2.26391	+	9.91882i	−0.181258	+	0.794141i
$157$	8.23825	+	10.3304i	0.657484	+	0.824459i	0.993067	−	0.117552i	$-0.0375047\pi$
$157$	8.23825	+	10.3304i	0.657484	+	0.824459i	−0.335583	+	0.942011i	$0.608933\pi$
$158$	0.0990311	+	0.0476909i	0.00787849	+	0.00379408i
$159$	3.09299	+	13.5513i	0.245290	+	1.07469i
$160$	12.5233	+	6.03089i	0.990051	+	0.476783i
$161$	−3.91789	+	4.91288i	−0.308773	+	0.387190i
$162$	1.03319	−	4.52669i	0.0811749	−	0.355650i
$163$	−8.84481	+	11.0910i	−0.692779	+	0.868718i	−0.996461	−	0.0840557i	$-0.973213\pi$
$163$	−8.84481	+	11.0910i	−0.692779	+	0.868718i	0.303682	+	0.952774i	$0.401784\pi$
$164$	−1.21983	−	5.34444i	−0.0952529	−	0.417330i
$165$	3.18598			0.248028
$166$	−22.1347			−1.71798
$167$	−2.10776	−	9.23470i	−0.163103	−	0.714603i	−0.988646	−	0.150263i	$-0.951988\pi$
$167$	−2.10776	−	9.23470i	−0.163103	−	0.714603i	0.825543	−	0.564340i	$-0.190869\pi$
$168$	1.78501	+	2.23833i	0.137717	+	0.172691i
$169$	−26.8572	+	12.9337i	−2.06594	+	0.994903i
$170$	13.1468	+	6.33114i	1.00831	+	0.485576i
$171$	6.42327			0.491200
$172$	7.48188	−	3.29920i	0.570488	−	0.251561i
$173$	4.76271			0.362102			0.181051	−	0.983474i	$-0.442050\pi$
$173$	4.76271			0.362102			0.181051	+	0.983474i	$0.442050\pi$
$174$	−12.1468	−	5.84957i	−0.920843	−	0.443455i
$175$	−0.0745725	+	0.0359122i	−0.00563715	+	0.00271471i
$176$	3.50149	+	4.39073i	0.263935	+	0.330964i
$177$	0.0440730	+	0.193096i	0.00331273	+	0.0145140i
$178$	−19.1347			−1.43420
$179$	1.64742			0.123134			0.0615668	−	0.998103i	$-0.480390\pi$
$179$	1.64742			0.123134			0.0615668	+	0.998103i	$0.480390\pi$
$180$	0.900969	+	3.94740i	0.0671543	+	0.294222i
$181$	1.41939	−	1.77985i	0.105502	−	0.132296i	−0.726277	−	0.687402i	$-0.758751\pi$
$181$	1.41939	−	1.77985i	0.105502	−	0.132296i	0.831779	+	0.555106i	$0.187322\pi$
$182$	4.43900	−	19.4485i	0.329041	−	1.44162i
$183$	0.554958	−	0.695895i	0.0410237	−	0.0514421i
$184$	−4.54019	−	2.18644i	−0.334707	−	0.161186i
$185$	−1.82640	−	8.00197i	−0.134279	−	0.588316i
$186$	20.8986	+	10.0642i	1.53236	+	0.737945i
$187$	2.55496	+	3.20382i	0.186837	+	0.234286i
$188$	0.873822	−	3.82846i	0.0637300	−	0.279219i
$189$	−2.08695	+	9.14352i	−0.151803	+	0.665093i
$190$	16.2153	−	7.80887i	1.17638	−	0.566515i
$191$	−9.37196	−	11.7521i	−0.678131	−	0.850350i	0.317049	−	0.948409i	$-0.397308\pi$
$191$	−9.37196	−	11.7521i	−0.678131	−	0.850350i	−0.995181	+	0.0980593i	$0.968737\pi$
$192$	0.986426	−	1.23694i	0.0711892	−	0.0892684i
$193$	−8.87531	+	4.27413i	−0.638859	+	0.307658i	−0.725129	−	0.688614i	$-0.758220\pi$
$193$	−8.87531	+	4.27413i	−0.638859	+	0.307658i	0.0862695	+	0.996272i	$0.472505\pi$
$194$	−5.68814	+	2.73926i	−0.408384	+	0.196668i
$195$	11.4303	−	14.3331i	0.818539	−	1.02642i
$196$	−3.21648	−	4.03334i	−0.229749	−	0.288096i
$197$	−9.87531	+	4.75570i	−0.703587	+	0.338830i	−0.751235	−	0.660035i	$-0.770542\pi$
$197$	−9.87531	+	4.75570i	−0.703587	+	0.338830i	0.0476483	+	0.998864i	$0.484827\pi$
$198$	−0.658834	+	2.88654i	−0.0468213	+	0.205137i
$199$	5.41939	−	23.7439i	0.384170	−	1.68316i	−0.300082	−	0.953914i	$-0.597014\pi$
$199$	5.41939	−	23.7439i	0.384170	−	1.68316i	0.684252	−	0.729246i	$-0.260129\pi$
$200$	−0.0413846	−	0.0518946i	−0.00292633	−	0.00366951i
$201$	−2.35690	−	1.13502i	−0.166243	−	0.0800582i
$202$	−5.16152	−	22.6141i	−0.363163	−	1.59112i
$203$	9.14675	+	4.40484i	0.641976	+	0.309159i
$204$	3.49396	−	4.38129i	0.244626	−	0.306751i
$205$	−2.19806	+	9.63034i	−0.153519	+	0.672612i
$206$	4.17241	−	5.23203i	0.290705	−	0.364533i
$207$	−1.19418	−	5.23203i	−0.0830011	−	0.363651i
$208$	32.3153			2.24066
$209$	5.05429			0.349613
$210$	1.90097	+	8.32869i	0.131179	+	0.574734i
$211$	6.42878	+	8.06144i	0.442575	+	0.554972i	0.952220	−	0.305413i	$-0.0987945\pi$
$211$	6.42878	+	8.06144i	0.442575	+	0.554972i	−0.509645	+	0.860385i	$0.670223\pi$
$212$	−12.5233	+	6.03089i	−0.860101	+	0.414203i
$213$	−4.18598	−	2.01586i	−0.286819	−	0.138125i
$214$	9.09783			0.621915
$215$	−14.7262	−	0.493353i	−1.00432	−	0.0336464i
$216$	−7.52111			−0.511746
$217$	−15.7371	−	7.57857i	−1.06830	−	0.514467i
$218$	−3.53319	+	1.70149i	−0.239298	+	0.115240i
$219$	−1.11410	−	1.39703i	−0.0752837	−	0.0944027i
$220$	0.708947	+	3.10610i	0.0477972	+	0.209413i
$221$	23.5797			1.58614
$222$	−8.20775			−0.550868
$223$	−0.630490	−	2.76236i	−0.0422207	−	0.184981i	0.949420	−	0.314008i	$-0.101672\pi$
$223$	−0.630490	−	2.76236i	−0.0422207	−	0.184981i	−0.991641	+	0.129027i	$0.958815\pi$
$224$	−6.52595	+	8.18328i	−0.436033	+	0.546769i
$225$	0.0157295	−	0.0689153i	0.00104863	−	0.00459435i
$226$	−13.1969	+	16.5483i	−0.877842	+	1.10078i
$227$	11.7702	+	5.66825i	0.781218	+	0.376215i	0.781596	−	0.623785i	$-0.214406\pi$
$227$	11.7702	+	5.66825i	0.781218	+	0.376215i	−0.000377606		1.00000i	$0.500120\pi$
$228$	−1.53803	−	6.73856i	−0.101859	−	0.446272i
$229$	16.1419	+	7.77353i	1.06669	+	0.513690i	0.883038	−	0.469302i	$-0.155495\pi$
$229$	16.1419	+	7.77353i	1.06669	+	0.513690i	0.183650	+	0.982992i	$0.441209\pi$
$230$	−9.37531	−	11.7563i	−0.618190	−	0.775186i
$231$	−0.533852	+	2.33896i	−0.0351249	+	0.153892i
$232$	−1.81163	+	7.93725i	−0.118939	+	0.521106i
$233$	8.41550	−	4.05269i	0.551318	−	0.265501i	−0.137418	−	0.990513i	$-0.543880\pi$
$233$	8.41550	−	4.05269i	0.551318	−	0.265501i	0.688736	+	0.725012i	$0.258166\pi$
$234$	10.6223	+	13.3199i	0.694401	+	0.870751i
$235$	−4.41185	+	5.53229i	−0.287798	+	0.360887i
$236$	−0.178448	+	0.0859360i	−0.0116160	+	0.00559396i
$237$	−0.0685317	+	0.0330031i	−0.00445161	+	0.00214378i
$238$	−6.85086	+	8.59070i	−0.444075	+	0.556852i
$239$	4.51507	+	5.66171i	0.292055	+	0.366226i	0.906113	−	0.423035i	$-0.139035\pi$
$239$	4.51507	+	5.66171i	0.292055	+	0.366226i	−0.614058	+	0.789261i	$0.710464\pi$
$240$	−12.4683	+	6.00442i	−0.804826	+	0.387584i
$241$	0.0244587	−	0.107160i	0.00157552	−	0.00690281i	−0.974134	−	0.225971i	$-0.927445\pi$
$241$	0.0244587	−	0.107160i	0.00157552	−	0.00690281i	0.975710	+	0.219068i	$0.0703017\pi$
$242$	3.89224	−	17.0530i	0.250203	−	1.09621i
$243$	−8.36443	−	10.4887i	−0.536578	−	0.672848i
$244$	0.801938	+	0.386193i	0.0513388	+	0.0247235i
$245$	2.06853	+	9.06283i	0.132154	+	0.579003i
$246$	8.89977	+	4.28590i	0.567429	+	0.273259i
$247$	18.1332	−	22.7383i	1.15379	−	1.44680i
$248$	3.11692	−	13.6561i	0.197924	−	0.867163i
$249$	9.55041	−	11.9758i	0.605233	−	0.758938i
$250$	4.46077	+	19.5439i	0.282124	+	1.23607i
$251$	−27.8974			−1.76087			−0.880433	−	0.474170i	$-0.842748\pi$
$251$	−27.8974			−1.76087			−0.880433	+	0.474170i	$0.842748\pi$
$252$	−3.04892			−0.192064
$253$	−0.939665	−	4.11694i	−0.0590762	−	0.258830i
$254$	−22.7201	−	28.4901i	−1.42559	−	1.78763i
$255$	−9.09783	+	4.38129i	−0.569729	+	0.274367i
$256$	−18.6603	−	8.98634i	−1.16627	−	0.561646i
$257$	−2.66487			−0.166230			−0.0831151	−	0.996540i	$-0.526487\pi$
$257$	−2.66487			−0.166230			−0.0831151	+	0.996540i	$0.526487\pi$
$258$	−3.75786	+	14.2472i	−0.233954	+	0.886990i
$259$	6.18060			0.384044
$260$	16.5172	+	7.95427i	1.02435	+	0.493303i
$261$	−7.81163	+	3.76188i	−0.483528	+	0.232855i
$262$	2.31282	+	2.90019i	0.142887	+	0.179174i
$263$	5.37047	+	23.5296i	0.331157	+	1.45090i	0.816893	+	0.576789i	$0.195695\pi$
$263$	5.37047	+	23.5296i	0.331157	+	1.45090i	−0.485736	+	0.874106i	$0.661448\pi$
$264$	−1.92394			−0.118410
$265$	25.0465			1.53860
$266$	3.01573	+	13.2128i	0.184906	+	0.810127i
$267$	8.25600	−	10.3527i	0.505259	−	0.633575i
$268$	0.582105	−	2.55037i	0.0355577	−	0.155789i
$269$	18.7989	−	23.5731i	1.14619	−	1.43727i	0.265164	−	0.964203i	$-0.414574\pi$
$269$	18.7989	−	23.5731i	1.14619	−	1.43727i	0.881024	−	0.473071i	$-0.156855\pi$
$270$	−20.2201	−	9.73750i	−1.23056	−	0.592605i
$271$	3.04676	+	13.3487i	0.185078	+	0.810878i	0.979164	+	0.203073i	$0.0650927\pi$
$271$	3.04676	+	13.3487i	0.185078	+	0.810878i	−0.794086	+	0.607805i	$0.792050\pi$
$272$	−16.0368	−	7.72293i	−0.972376	−	0.468272i
$273$	8.60723	+	10.7931i	0.520933	+	0.653229i
$274$	−6.25571	+	27.4081i	−0.377921	+	1.65578i
$275$	0.0123771	−	0.0542276i	0.000746366	−	0.00327004i
$276$	−5.20291	+	2.50559i	−0.313178	+	0.150819i
$277$	−11.5809	−	14.5220i	−0.695829	−	0.872542i	0.300875	−	0.953664i	$-0.402721\pi$
$277$	−11.5809	−	14.5220i	−0.695829	−	0.872542i	−0.996704	+	0.0811212i	$0.974150\pi$
$278$	−7.94989	+	9.96884i	−0.476802	+	0.597891i
$279$	13.4400	−	6.47234i	0.804629	−	0.387489i
$280$	4.64795	−	2.23833i	0.277768	−	0.133766i
$281$	−1.69351	+	2.12360i	−0.101027	+	0.126683i	−0.829775	−	0.558099i	$-0.811531\pi$
$281$	−1.69351	+	2.12360i	−0.101027	+	0.126683i	0.728748	+	0.684782i	$0.240103\pi$
$282$	4.41185	+	5.53229i	0.262722	+	0.329443i
$283$	−15.3274	+	7.38127i	−0.911117	+	0.438771i	−0.829891	−	0.557925i	$-0.811598\pi$
$283$	−15.3274	+	7.38127i	−0.911117	+	0.438771i	−0.0812254	+	0.996696i	$0.525883\pi$
$284$	1.03385	−	4.52960i	0.0613478	−	0.268782i
$285$	−2.77144	+	12.1425i	−0.164166	+	0.719258i
$286$	8.35839	+	10.4811i	0.494242	+	0.619760i
$287$	−6.70171	−	3.22737i	−0.395589	−	0.190506i
$288$	−1.98911	−	8.71488i	−0.117210	−	0.513529i
$289$	3.61476	+	1.74078i	0.212633	+	0.102399i
$290$	−15.1468	+	18.9934i	−0.889448	+	1.11533i
$291$	0.972189	−	4.25944i	0.0569907	−	0.249693i
$292$	1.11410	−	1.39703i	0.0651976	−	0.0817552i
$293$	2.45473	+	10.7549i	0.143407	+	0.628307i	0.994629	+	0.103502i	$0.0330047\pi$
$293$	2.45473	+	10.7549i	0.143407	+	0.628307i	−0.851222	+	0.524805i	$0.824138\pi$
$294$	9.29590			0.542148
$295$	0.356896			0.0207793
$296$	1.10292	+	4.83219i	0.0641057	+	0.280865i
$297$	−3.92961	−	4.92757i	−0.228019	−	0.285927i
$298$	9.41939	−	4.53614i	0.545650	−	0.262771i
$299$	−21.8925	−	10.5429i	−1.26608	−	0.609711i
$300$	−0.0760644			−0.00439158
$301$	2.82975	−	10.7284i	0.163104	−	0.618375i
$302$	13.4233			0.772422
$303$	14.4623	+	6.96466i	0.830835	+	0.400109i
$304$	−19.7799	+	9.52551i	−1.13446	+	0.546326i
$305$	−1.00000	−	1.25396i	−0.0572598	−	0.0718016i
$306$	−2.08815	−	9.14877i	−0.119371	−	0.523000i
$307$	15.7952			0.901482			0.450741	−	0.892655i	$-0.351160\pi$
$307$	15.7952			0.901482			0.450741	+	0.892655i	$0.351160\pi$
$308$	−2.39911			−0.136702
$309$	1.03050	+	4.51491i	0.0586231	+	0.256844i
$310$	26.0601	−	32.6783i	1.48011	−	1.85600i
$311$	2.75182	−	12.0565i	0.156042	−	0.683663i	−0.835016	−	0.550226i	$-0.814542\pi$
$311$	2.75182	−	12.0565i	0.156042	−	0.683663i	0.991057	−	0.133437i	$-0.0426013\pi$
$312$	−6.90246	+	8.65541i	−0.390775	+	0.490016i
$313$	5.25667	+	2.53148i	0.297124	+	0.143088i	0.576507	−	0.817092i	$-0.304415\pi$
$313$	5.25667	+	2.53148i	0.297124	+	0.143088i	−0.279382	+	0.960180i	$0.590130\pi$
$314$	−5.29805	−	23.2123i	−0.298986	−	1.30995i
$315$	4.94989	+	2.38374i	0.278894	+	0.134309i
$316$	−0.0474254	−	0.0594696i	−0.00266789	−	0.00334542i
$317$	−5.82304	+	25.5124i	−0.327055	+	1.43292i	0.497660	+	0.867372i	$0.334193\pi$
$317$	−5.82304	+	25.5124i	−0.327055	+	1.43292i	−0.824715	+	0.565548i	$0.808665\pi$
$318$	5.57338	−	24.4186i	0.312539	−	1.36932i
$319$	−6.14675	+	2.96012i	−0.344152	+	0.165735i
$320$	−1.77748	−	2.22889i	−0.0993641	−	0.124599i
$321$	−3.92543	+	4.92233i	−0.219096	+	0.274738i
$322$	10.2017	−	4.91288i	0.568519	−	0.273784i
$323$	−14.4330	+	6.95055i	−0.803071	+	0.386739i
$324$	−2.00335	+	2.51212i	−0.111297	+	0.139562i
$325$	−0.199554	−	0.250233i	−0.0110693	−	0.0138804i
$326$	23.0308	−	11.0910i	1.27556	−	0.614276i
$327$	0.603875	−	2.64575i	0.0333944	−	0.146310i
$328$	1.32736	−	5.81553i	0.0732910	−	0.321109i
$329$	−3.32222	−	4.16593i	−0.183160	−	0.229675i
$330$	−5.17241	−	2.49090i	−0.284732	−	0.137120i
$331$	−4.06465	−	17.8084i	−0.223413	−	0.978837i	−0.954887	−	0.296968i	$-0.904025\pi$
$331$	−4.06465	−	17.8084i	−0.223413	−	0.978837i	0.731474	−	0.681869i	$-0.238833\pi$
$332$	13.8007	+	6.64609i	0.757414	+	0.364751i
$333$	−3.29105	+	4.12685i	−0.180349	+	0.226150i
$334$	−3.79805	+	16.6404i	−0.207820	+	0.910520i
$335$	−2.93900	+	3.68539i	−0.160575	+	0.201354i
$336$	−2.31886	−	10.1596i	−0.126504	−	0.554252i
$337$	−7.09113			−0.386278			−0.193139	−	0.981171i	$-0.561867\pi$
$337$	−7.09113			−0.386278			−0.193139	+	0.981171i	$0.561867\pi$
$338$	53.7144			2.92168
$339$	−3.25936	−	14.2802i	−0.177024	−	0.775593i
$340$	−6.29590	−	7.89481i	−0.341443	−	0.428156i
$341$	10.5755	−	5.09291i	0.572697	−	0.275796i
$342$	−10.4281	−	5.02192i	−0.563888	−	0.271554i
$343$	−18.8442			−1.01749
$344$	8.89277	+	0.297924i	0.479466	+	0.0160630i
$345$	10.4058			0.560230
$346$	−7.73221	−	3.72364i	−0.415686	−	0.200184i
$347$	2.89612	−	1.39470i	0.155472	−	0.0748714i	−0.354530	−	0.935045i	$-0.615359\pi$
$347$	2.89612	−	1.39470i	0.155472	−	0.0748714i	0.510002	+	0.860173i	$0.329645\pi$
$348$	5.81700	+	7.29429i	0.311824	+	0.391015i
$349$	−6.08599	−	26.6645i	−0.325776	−	1.42732i	−0.827099	−	0.562056i	$-0.810010\pi$
$349$	−6.08599	−	26.6645i	−0.325776	−	1.42732i	0.501324	−	0.865260i	$-0.332847\pi$
$350$	0.149145			0.00797213
$351$	−36.2664			−1.93575
$352$	−1.56518	−	6.85750i	−0.0834243	−	0.365506i
$353$	−14.4013	+	18.0586i	−0.766502	+	0.961163i	−0.999937	−	0.0112093i	$-0.996432\pi$
$353$	−14.4013	+	18.0586i	−0.766502	+	0.961163i	0.233435	+	0.972372i	$0.425003\pi$
$354$	0.0794168	−	0.347948i	0.00422096	−	0.0184932i
$355$	−5.21983	+	6.54546i	−0.277040	+	0.347397i
$356$	11.9303	+	5.74532i	0.632303	+	0.304501i
$357$	−1.69202	−	7.41323i	−0.0895513	−	0.392350i
$358$	−2.67456	−	1.28800i	−0.141355	−	0.0680730i
$359$	−0.158834	−	0.199171i	−0.00838292	−	0.0105118i	0.777622	−	0.628732i	$-0.216426\pi$
$359$	−0.158834	−	0.199171i	−0.00838292	−	0.0105118i	−0.786005	+	0.618220i	$0.787854\pi$
$360$	−0.980386	+	4.29535i	−0.0516709	+	0.226385i
$361$	−0.168759	+	0.739383i	−0.00888207	+	0.0389149i
$362$	−3.69591	+	1.77985i	−0.194253	+	0.0935471i
$363$	7.54706	+	9.46371i	0.396118	+	0.496716i
$364$	−8.60723	+	10.7931i	−0.451141	+	0.565713i
$365$	−2.90097	+	1.39703i	−0.151844	+	0.0731240i
$366$	−1.44504	+	0.695895i	−0.0755335	+	0.0363750i
$367$	−9.23341	+	11.5783i	−0.481980	+	0.604384i	−0.962059	−	0.272842i	$-0.912037\pi$
$367$	−9.23341	+	11.5783i	−0.481980	+	0.604384i	0.480079	+	0.877225i	$0.340608\pi$
$368$	11.4363	+	14.3407i	0.596159	+	0.747560i
$369$	5.72348	−	2.75628i	0.297952	−	0.143486i
$370$	−3.29105	+	14.4190i	−0.171094	+	0.749610i
$371$	−4.19687	+	18.3877i	−0.217890	+	0.954640i
$372$	−10.0082	−	12.5499i	−0.518901	−	0.650681i
$373$	−20.2467	−	9.75032i	−1.04834	−	0.504852i	−0.171272	−	0.985224i	$-0.554788\pi$
$373$	−20.2467	−	9.75032i	−1.04834	−	0.504852i	−0.877065	+	0.480372i	$0.840502\pi$
$374$	−1.64310	−	7.19891i	−0.0849629	−	0.372247i
$375$	−12.4988	−	6.01911i	−0.645435	−	0.310825i
$376$	2.66421	−	3.34081i	0.137396	−	0.172289i
$377$	−8.73556	+	38.2730i	−0.449904	+	1.97116i
$378$	10.5368	−	13.2128i	0.541956	−	0.679592i
$379$	5.79686	+	25.3977i	0.297765	+	1.30459i	0.873447	+	0.486919i	$0.161879\pi$
$379$	5.79686	+	25.3977i	0.297765	+	1.30459i	−0.575683	+	0.817673i	$0.695264\pi$
$380$	−12.4547			−0.638914
$381$	25.2174			1.29193
$382$	6.02715	+	26.4067i	0.308376	+	1.35108i
$383$	7.69418	+	9.64819i	0.393154	+	0.493000i	0.938533	−	0.345190i	$-0.112186\pi$
$383$	7.69418	+	9.64819i	0.393154	+	0.493000i	−0.545379	+	0.838190i	$0.683614\pi$
$384$	11.3312	−	5.45684i	0.578245	−	0.278468i
$385$	3.89493	+	1.87570i	0.198504	+	0.0955944i
$386$	17.7506			0.903483
$387$	5.65668	+	7.60212i	0.287545	+	0.386438i
$388$	4.36898			0.221801
$389$	17.9417	+	8.64026i	0.909680	+	0.438079i	0.829375	−	0.558692i	$-0.188696\pi$
$389$	17.9417	+	8.64026i	0.909680	+	0.438079i	0.0803044	+	0.996770i	$0.474411\pi$
$390$	−29.7630	+	14.3331i	−1.50711	+	0.725785i
$391$	8.34481	+	10.4641i	0.422015	+	0.529191i
$392$	−1.24914	−	5.47282i	−0.0630909	−	0.276419i
$393$	−2.56704			−0.129490
$394$	19.7506			0.995022
$395$	0.0304995	+	0.133627i	0.00153459	+	0.00672350i
$396$	1.27748	−	1.60191i	0.0641957	−	0.0804989i
$397$	−2.03050	+	8.89620i	−0.101908	+	0.446487i	0.898070	+	0.439852i	$0.144969\pi$
$397$	−2.03050	+	8.89620i	−0.101908	+	0.446487i	−0.999978	+	0.00663518i	$0.997888\pi$
$398$	−27.3620	+	34.3109i	−1.37153	+	1.71985i
$399$	−8.44989	−	4.06925i	−0.423023	−	0.203717i
$400$	0.0537617	+	0.235545i	0.00268808	+	0.0117773i
$401$	−0.0392287	−	0.0188915i	−0.00195899	−	0.000943398i	0.432904	−	0.901440i	$-0.357489\pi$
$401$	−0.0392287	−	0.0188915i	−0.00195899	−	0.000943398i	−0.434863	+	0.900497i	$0.643203\pi$
$402$	2.93900	+	3.68539i	0.146584	+	0.183811i
$403$	15.0296	−	65.8490i	0.748678	−	3.28017i
$404$	−3.57188	+	15.6494i	−0.177708	+	0.778589i
$405$	5.21648	−	2.51212i	0.259209	−	0.124828i
$406$	−11.4058	−	14.3024i	−0.566061	−	0.709818i
$407$	−2.58964	+	3.24730i	−0.128364	+	0.160963i
$408$	5.49396	−	2.64575i	0.271992	−	0.130984i
$409$	9.62833	−	4.63676i	0.476090	−	0.229273i	−0.180420	−	0.983590i	$-0.557746\pi$
$409$	9.62833	−	4.63676i	0.476090	−	0.229273i	0.656511	+	0.754316i	$0.272032\pi$
$410$	11.0978	−	13.9162i	0.548083	−	0.687274i
$411$	−12.1298	−	15.2103i	−0.598320	−	0.750270i
$412$	−4.17241	+	2.00933i	−0.205560	+	0.0989924i
$413$	−0.0598025	+	0.262012i	−0.00294269	+	0.0128928i
$414$	−2.15183	+	9.42780i	−0.105757	+	0.463351i
$415$	−17.2092	−	21.5797i	−0.844769	−	1.05931i
$416$	−36.4659	−	17.5611i	−1.78789	−	0.861002i
$417$	−1.96346	−	8.60248i	−0.0961510	−	0.421265i
$418$	−8.20560	−	3.95161i	−0.401349	−	0.193279i
$419$	−4.60202	+	5.77074i	−0.224823	+	0.281919i	−0.881431	−	0.472313i	$-0.843419\pi$
$419$	−4.60202	+	5.77074i	−0.224823	+	0.281919i	0.656608	+	0.754232i	$0.271991\pi$
$420$	1.31551	−	5.76363i	0.0641904	−	0.281236i
$421$	6.10537	−	7.65589i	0.297557	−	0.373125i	−0.610468	−	0.792041i	$-0.709018\pi$
$421$	6.10537	−	7.65589i	0.297557	−	0.373125i	0.908025	+	0.418916i	$0.137590\pi$
$422$	−4.13437	−	18.1139i	−0.201258	−	0.881770i
$423$	4.55065			0.221260
$424$	−15.1250			−0.734534
$425$	0.0392287	+	0.171872i	0.00190287	+	0.00833702i
$426$	5.21983	+	6.54546i	0.252902	+	0.317129i
$427$	1.08815	−	0.524023i	0.0526591	−	0.0253593i
$428$	−5.67241	−	2.73169i	−0.274186	−	0.132041i
$429$	−9.27711			−0.447903
$430$	23.5221	+	12.3143i	1.13433	+	0.593850i
$431$	27.3297			1.31643			0.658214	−	0.752831i	$-0.271312\pi$
$431$	27.3297			1.31643			0.658214	+	0.752831i	$0.271312\pi$
$432$	24.6652	+	11.8781i	1.18670	+	0.571486i
$433$	2.50269	−	1.20523i	0.120272	−	0.0579197i	−0.372780	−	0.927920i	$-0.621596\pi$
$433$	2.50269	−	1.20523i	0.120272	−	0.0579197i	0.493052	+	0.870000i	$0.335881\pi$
$434$	19.6238	+	24.6074i	0.941972	+	1.18120i
$435$	−3.74094	−	16.3901i	−0.179364	−	0.785846i
$436$	2.71379			0.129967
$437$	16.5080			0.789683
$438$	0.716480	+	3.13910i	0.0342347	+	0.149992i
$439$	5.97434	−	7.49159i	0.285140	−	0.357554i	−0.618547	−	0.785748i	$-0.712278\pi$
$439$	5.97434	−	7.49159i	0.285140	−	0.357554i	0.903687	+	0.428194i	$0.140850\pi$
$440$	−0.771438	+	3.37989i	−0.0367769	+	0.161130i
$441$	3.72737	−	4.67397i	0.177494	−	0.222570i
$442$	−38.2814	−	18.4354i	−1.82086	−	0.876881i
$443$	−5.29052	−	23.1793i	−0.251360	−	1.10128i	−0.930217	−	0.367010i	$-0.880381\pi$
$443$	−5.29052	−	23.1793i	−0.251360	−	1.10128i	0.678857	−	0.734271i	$-0.262476\pi$
$444$	5.11745	+	2.46443i	0.242863	+	0.116957i
$445$	−14.8768	−	18.6549i	−0.705228	−	0.884328i
$446$	−1.13610	+	4.97760i	−0.0537961	+	0.235696i
$447$	−1.60992	+	7.05350i	−0.0761464	+	0.333619i
$448$	1.93416	−	0.931441i	0.0913803	−	0.0440064i
$449$	−11.4412	−	14.3468i	−0.539942	−	0.677065i	0.434768	−	0.900543i	$-0.356831\pi$
$449$	−11.4412	−	14.3468i	−0.539942	−	0.677065i	−0.974709	+	0.223477i	$0.928259\pi$
$450$	−0.0794168	+	0.0995855i	−0.00374374	+	0.00469451i
$451$	4.50365	−	2.16884i	0.212068	−	0.102127i
$452$	13.1969	−	6.35528i	0.620728	−	0.298927i
$453$	−5.79172	+	7.26258i	−0.272119	+	0.341226i
$454$	−14.6773	−	18.4047i	−0.688838	−	0.863775i
$455$	22.4121	−	10.7931i	1.05070	−	0.505989i
$456$	1.67360	−	7.33254i	0.0783737	−	0.343377i
$457$	−8.85892	+	38.8135i	−0.414403	+	1.81562i	0.148281	+	0.988945i	$0.452626\pi$
$457$	−8.85892	+	38.8135i	−0.414403	+	1.81562i	−0.562684	+	0.826672i	$0.690231\pi$
$458$	−20.1286	−	25.2405i	−0.940549	−	1.17941i
$459$	17.9976	+	8.66719i	0.840056	+	0.404550i
$460$	2.31551	+	10.1449i	0.107961	+	0.473009i
$461$	17.3257	+	8.34363i	0.806940	+	0.388602i	0.791416	−	0.611278i	$-0.209344\pi$
$461$	17.3257	+	8.34363i	0.806940	+	0.388602i	0.0155237	+	0.999880i	$0.495058\pi$
$462$	2.69537	−	3.37989i	0.125400	−	0.157247i
$463$	−3.32855	+	14.5833i	−0.154691	+	0.677745i	0.836793	+	0.547519i	$0.184428\pi$
$463$	−3.32855	+	14.5833i	−0.154691	+	0.677745i	−0.991484	+	0.130226i	$0.958430\pi$
$464$	18.4765	−	23.1688i	0.857750	−	1.07558i
$465$	6.43631	+	28.1993i	0.298477	+	1.30771i
$466$	−16.8310			−0.779681
$467$	25.7904			1.19344			0.596720	−	0.802450i	$-0.296470\pi$
$467$	25.7904			1.19344			0.596720	+	0.802450i	$0.296470\pi$
$468$	−2.62349	−	11.4943i	−0.121271	−	0.531322i
$469$	−2.21313	−	2.77517i	−0.102193	−	0.128146i
$470$	11.4879	−	5.53229i	0.529898	−	0.255186i
$471$	14.8448	+	7.14889i	0.684013	+	0.329403i
$472$	−0.215521			−0.00992014
$473$	4.45108	+	5.98190i	0.204661	+	0.275048i
$474$	0.137063			0.00629553
$475$	0.195906	+	0.0943435i	0.00898880	+	0.00432878i
$476$	6.85086	−	3.29920i	0.314008	−	0.151218i
$477$	−10.0429	−	12.5934i	−0.459832	−	0.576611i
$478$	−2.90366	−	12.7218i	−0.132810	−	0.581879i
$479$	−29.7157			−1.35775			−0.678873	−	0.734256i	$-0.737531\pi$
$479$	−29.7157			−1.35775			−0.678873	+	0.734256i	$0.737531\pi$
$480$	17.3327			0.791127
$481$	5.31820	+	23.3006i	0.242489	+	1.06241i
$482$	−0.123490	+	0.154851i	−0.00562481	+	0.00705328i
$483$	−1.74363	+	7.63933i	−0.0793378	+	0.347602i
$484$	−7.54706	+	9.46371i	−0.343048	+	0.430169i
$485$	−7.09299	−	3.41580i	−0.322076	−	0.155104i
$486$	5.37920	+	23.5678i	0.244005	+	1.06906i
$487$	−1.37047	−	0.659983i	−0.0621019	−	0.0299067i	0.402575	−	0.915387i	$-0.368115\pi$
$487$	−1.37047	−	0.659983i	−0.0621019	−	0.0299067i	−0.464677	+	0.885480i	$0.653830\pi$
$488$	0.603875	+	0.757236i	0.0273362	+	0.0342785i
$489$	−3.93631	+	17.2461i	−0.178006	+	0.779896i
$490$	3.72737	−	16.3307i	0.168385	−	0.737744i
$491$	−25.8245	+	12.4364i	−1.16544	+	0.561249i	−0.913638	−	0.406529i	$-0.866739\pi$
$491$	−25.8245	+	12.4364i	−1.16544	+	0.561249i	−0.251807	+	0.967777i	$0.581025\pi$
$492$	−4.26205	−	5.34444i	−0.192148	−	0.240946i
$493$	13.4819	−	16.9057i	0.607193	−	0.761396i
$494$	−47.2165	+	22.7383i	−2.12437	+	1.02304i
$495$	−3.32640	+	1.60191i	−0.149510	+	0.0720004i
$496$	−31.7890	+	39.8621i	−1.42737	+	1.78986i
$497$	−3.93064	−	4.92887i	−0.176313	−	0.221090i
$498$	−24.8681	+	11.9758i	−1.11437	+	0.536650i
$499$	4.63198	−	20.2940i	0.207356	−	0.908486i	−0.758962	−	0.651135i	$-0.774293\pi$
$499$	4.63198	−	20.2940i	0.207356	−	0.908486i	0.966318	−	0.257351i	$-0.0828497\pi$
$500$	3.08695	−	13.5248i	0.138053	−	0.604848i
$501$	−7.36443	−	9.23470i	−0.329018	−	0.412576i
$502$	45.2911	+	21.8110i	2.02144	+	0.973475i
$503$	−0.812396	−	3.55934i	−0.0362229	−	0.158703i	0.953582	−	0.301134i	$-0.0973652\pi$
$503$	−0.812396	−	3.55934i	−0.0362229	−	0.158703i	−0.989805	+	0.142431i	$0.954508\pi$
$504$	−2.98911	−	1.43948i	−0.133146	−	0.0641196i
$505$	18.0341	−	22.6141i	0.802509	−	1.00631i
$506$	−1.69322	+	7.41847i	−0.0752727	+	0.329791i
$507$	−23.1761	+	29.0619i	−1.02928	+	1.29068i
$508$	5.61141	+	24.5852i	0.248966	+	1.09079i
$509$	−6.27114			−0.277964			−0.138982	−	0.990295i	$-0.544383\pi$
$509$	−6.27114			−0.277964			−0.138982	+	0.990295i	$0.544383\pi$
$510$	18.1957			0.805718
$511$	−0.539524	−	2.36381i	−0.0238671	−	0.104569i
$512$	10.6923	+	13.4077i	0.472538	+	0.592544i
$513$	22.1984	−	10.6902i	0.980081	−	0.471982i
$514$	4.32640	+	2.08348i	0.190829	+	0.0918985i
$515$	8.34481			0.367716
$516$	6.62080	−	7.75464i	0.291465	−	0.341379i
$517$	3.58078			0.157482
$518$	−10.0341	−	4.83219i	−0.440875	−	0.212314i
$519$	5.35086	−	2.57684i	0.234876	−	0.113111i
$520$	12.4378	+	15.5965i	0.545434	+	0.683952i
$521$	0.0286390	+	0.125476i	0.00125470	+	0.00549719i	0.975551	−	0.219771i	$-0.0705312\pi$
$521$	0.0286390	+	0.125476i	0.00125470	+	0.00549719i	−0.974297	+	0.225269i	$0.927674\pi$
$522$	15.6233			0.683811
$523$	−21.6209			−0.945414			−0.472707	−	0.881220i	$-0.656723\pi$
$523$	−21.6209			−0.945414			−0.472707	+	0.881220i	$0.656723\pi$
$524$	−0.571220	−	2.50268i	−0.0249539	−	0.109330i
$525$	−0.0643513	+	0.0806940i	−0.00280852	+	0.00352177i
$526$	9.67725	−	42.3988i	0.421948	−	1.84868i
$527$	−23.1957	+	29.0864i	−1.01042	+	1.26703i
$528$	6.30947	+	3.03848i	0.274584	+	0.132233i
$529$	2.04892	+	8.97689i	0.0890834	+	0.390300i
$530$	−40.6628	−	19.5822i	−1.76628	−	0.850595i
$531$	−0.143104	−	0.179447i	−0.00621019	−	0.00778733i
$532$	2.08695	−	9.14352i	0.0904807	−	0.396422i
$533$	6.40044	−	28.0421i	0.277234	−	1.21464i
$534$	−21.4976	+	10.3527i	−0.930292	+	0.448005i
$535$	7.07338	+	8.86973i	0.305809	+	0.383472i
$536$	1.77479	−	2.22552i	0.0766593	−	0.0961277i
$537$	1.85086	−	0.891325i	0.0798703	−	0.0384635i
$538$	−48.9499	+	23.5731i	−2.11038	+	1.01631i
$539$	2.93296	−	3.67782i	0.126332	−	0.158415i
$540$	9.68329	+	12.1425i	0.416703	+	0.522528i
$541$	−12.6603	+	6.09689i	−0.544310	+	0.262126i	−0.685770	−	0.727818i	$-0.740535\pi$
$541$	−12.6603	+	6.09689i	−0.544310	+	0.262126i	0.141460	+	0.989944i	$0.454820\pi$
$542$	5.49007	−	24.0536i	0.235819	−	1.03319i
$543$	0.631687	−	2.76760i	0.0271083	−	0.118769i
$544$	13.8998	+	17.4298i	0.595948	+	0.747295i
$545$	−4.40581	−	2.12173i	−0.188724	−	0.0908848i
$546$	−5.53534	−	24.2519i	−0.236891	−	1.03789i
$547$	30.3913	+	14.6357i	1.29944	+	0.625777i	0.950312	−	0.311298i	$-0.100764\pi$
$547$	30.3913	+	14.6357i	1.29944	+	0.625777i	0.349127	+	0.937075i	$0.386478\pi$
$548$	12.1298	−	15.2103i	0.518160	−	0.649753i
$549$	−0.229521	+	1.00560i	−0.00979573	+	0.0429179i
$550$	−0.0624909	+	0.0783611i	−0.00266462	+	0.00334133i
$551$	−5.93469	−	26.0016i	−0.252826	−	1.10770i
$552$	−6.28382			−0.267457
$553$	−0.103211			−0.00438900
$554$	7.44773	+	32.6306i	0.316424	+	1.38634i
$555$	−6.38135	−	8.00197i	−0.270873	−	0.339665i
$556$	7.94989	−	3.82846i	0.337150	−	0.162363i
$557$	−22.9376	−	11.0462i	−0.971896	−	0.468040i	−0.120586	−	0.992703i	$-0.538477\pi$
$557$	−22.9376	−	11.0462i	−0.971896	−	0.468040i	−0.851310	+	0.524663i	$0.824192\pi$
$558$	−26.8799			−1.13792
$559$	42.8805	+	1.43657i	1.81365	+	0.0607606i
$560$	−18.7778			−0.793506
$561$	4.60388	+	2.21711i	0.194376	+	0.0936064i
$562$	4.40970	−	2.12360i	0.186012	−	0.0895786i
$563$	−4.00484	−	5.02192i	−0.168784	−	0.211649i	0.690244	−	0.723576i	$-0.257503\pi$
$563$	−4.00484	−	5.02192i	−0.168784	−	0.211649i	−0.859029	+	0.511928i	$0.828932\pi$
$564$	−1.08964	−	4.77402i	−0.0458820	−	0.201022i
$565$	−26.3937			−1.11039
$566$	30.6547			1.28851
$567$	0.970165	+	4.25057i	0.0407431	+	0.178507i
$568$	3.15213	−	3.95264i	0.132260	−	0.165849i
$569$	0.272398	−	1.19345i	0.0114195	−	0.0500321i	−0.968897	−	0.247464i	$-0.920403\pi$
$569$	0.272398	−	1.19345i	0.0114195	−	0.0500321i	0.980317	+	0.197432i	$0.0632600\pi$
$570$	13.9928	−	17.5464i	0.586092	−	0.734937i
$571$	33.2657	+	16.0199i	1.39213	+	0.670413i	0.971548	−	0.236844i	$-0.0761130\pi$
$571$	33.2657	+	16.0199i	1.39213	+	0.670413i	0.420578	+	0.907256i	$0.361827\pi$
$572$	−2.06435	−	9.04451i	−0.0863149	−	0.378170i
$573$	−16.8877	−	8.13268i	−0.705493	−	0.339748i
$574$	8.35690	+	10.4792i	0.348810	+	0.437394i
$575$	0.0404251	−	0.177114i	0.00168584	−	0.00738616i
$576$	−0.407969	+	1.78743i	−0.0169987	+	0.0744762i
$577$	23.2364	−	11.1901i	0.967344	−	0.465848i	0.117610	−	0.993060i	$-0.462477\pi$
$577$	23.2364	−	11.1901i	0.967344	−	0.465848i	0.849734	+	0.527212i	$0.176763\pi$
$578$	−4.50753	−	5.65227i	−0.187489	−	0.235103i
$579$	−7.65883	+	9.60387i	−0.318290	+	0.399123i
$580$	15.1468	−	7.29429i	0.628935	−	0.302879i
$581$	18.7262	−	9.01805i	0.776892	−	0.374132i
$582$	−4.90850	+	6.15507i	−0.203464	+	0.255136i
$583$	−7.90246	−	9.90937i	−0.327286	−	0.410404i
$584$	1.75182	−	0.843634i	0.0724910	−	0.0349098i
$585$	−4.72737	+	20.7119i	−0.195452	+	0.856333i
$586$	4.42327	−	19.3796i	0.182724	−	0.800565i
$587$	5.87651	+	7.36891i	0.242550	+	0.304147i	0.888174	−	0.459508i	$-0.151974\pi$
$587$	5.87651	+	7.36891i	0.242550	+	0.304147i	−0.645624	+	0.763655i	$0.723403\pi$
$588$	−5.79590	−	2.79116i	−0.239019	−	0.115105i
$589$	10.2107	+	44.7359i	0.420724	+	1.84331i
$590$	−0.579417	−	0.279032i	−0.0238542	−	0.0114876i
$591$	−8.52177	+	10.6860i	−0.350539	+	0.439562i
$592$	4.01453	−	17.5888i	0.164996	−	0.722896i
$593$	−5.43565	+	6.81609i	−0.223215	+	0.279903i	−0.880811	−	0.473468i	$-0.843002\pi$
$593$	−5.43565	+	6.81609i	−0.223215	+	0.279903i	0.657596	+	0.753371i	$0.271573\pi$
$594$	2.52715	+	11.0722i	0.103690	+	0.454296i
$595$	−13.7017			−0.561715
$596$	−7.23490			−0.296353
$597$	−6.75786	−	29.6081i	−0.276581	−	1.21178i
$598$	27.2995	+	34.2325i	1.11636	+	1.39987i
$599$	−16.9194	+	8.14795i	−0.691307	+	0.332916i	−0.746337	−	0.665569i	$-0.768189\pi$
$599$	−16.9194	+	8.14795i	−0.691307	+	0.332916i	0.0550292	+	0.998485i	$0.482475\pi$
$600$	−0.0745725	−	0.0359122i	−0.00304441	−	0.00146611i
$601$	−13.5646			−0.553313			−0.276657	−	0.960969i	$-0.589226\pi$
$601$	−13.5646			−0.553313			−0.276657	+	0.960969i	$0.589226\pi$
$602$	−12.9819	+	15.2051i	−0.529102	+	0.619713i
$603$	3.03146			0.123451
$604$	−8.36927	−	4.03043i	−0.340541	−	0.163996i
$605$	19.6516	−	9.46371i	0.798951	−	0.384755i
$606$	−18.0341	−	22.6141i	−0.732587	−	0.918635i
$607$	6.71714	+	29.4297i	0.272640	+	1.19452i	0.906883	+	0.421382i	$0.138455\pi$
$607$	6.71714	+	29.4297i	0.272640	+	1.19452i	−0.634243	+	0.773134i	$0.718688\pi$
$608$	27.4969			1.11515
$609$	12.6595			0.512989
$610$	0.643104	+	2.81762i	0.0260385	+	0.114082i
$611$	12.8467	−	16.1092i	0.519721	−	0.651709i
$612$	−1.44504	+	6.33114i	−0.0584124	+	0.255921i
$613$	2.80380	−	3.51585i	0.113244	−	0.142004i	−0.721979	−	0.691915i	$-0.756767\pi$
$613$	2.80380	−	3.51585i	0.113244	−	0.142004i	0.835223	+	0.549911i	$0.185339\pi$
$614$	−25.6434	−	12.3492i	−1.03488	−	0.498374i
$615$	2.74094	+	12.0088i	0.110525	+	0.484243i
$616$	−2.35205	−	1.13269i	−0.0947669	−	0.0456373i
$617$	−17.8056	−	22.3275i	−0.716826	−	0.898871i	0.281328	−	0.959612i	$-0.409225\pi$
$617$	−17.8056	−	22.3275i	−0.716826	−	0.898871i	−0.998154	+	0.0607405i	$0.980654\pi$
$618$	1.85690	−	8.13559i	0.0746953	−	0.327262i
$619$	0.646457	−	2.83231i	0.0259833	−	0.113840i	−0.960273	−	0.279061i	$-0.909977\pi$
$619$	0.646457	−	2.83231i	0.0259833	−	0.113840i	0.986257	+	0.165221i	$0.0528338\pi$
$620$	−26.0601	+	12.5499i	−1.04660	+	0.504015i
$621$	−12.8346	−	16.0941i	−0.515034	−	0.645833i
$622$	−13.8937	+	17.4222i	−0.557088	+	0.698566i
$623$	16.1881	−	7.79580i	0.648564	−	0.312332i
$624$	36.3059	−	17.4840i	1.45340	−	0.699920i
$625$	−15.7383	+	19.7351i	−0.629530	+	0.789406i
$626$	−6.55496	−	8.21966i	−0.261989	−	0.328524i
$627$	5.67845	−	2.73460i	0.226775	−	0.109209i
$628$	−3.66637	+	16.0634i	−0.146304	+	0.640999i
$629$	2.92931	−	12.8342i	0.116799	−	0.511731i
$630$	−6.17241	−	7.73995i	−0.245915	−	0.308367i
$631$	−13.6223	−	6.56015i	−0.542295	−	0.261155i	0.142621	−	0.989777i	$-0.454447\pi$
$631$	−13.6223	−	6.56015i	−0.542295	−	0.261155i	−0.684916	+	0.728622i	$0.740161\pi$
$632$	−0.0184179	−	0.0806940i	−0.000732624	−	0.00320983i
$633$	11.5843	+	5.57869i	0.460433	+	0.221733i
$634$	29.4001	−	36.8665i	1.16763	−	1.46416i
$635$	10.1114	−	44.3010i	0.401259	−	1.75803i
$636$	−10.8068	+	13.5513i	−0.428517	+	0.537343i
$637$	−6.02326	−	26.3896i	−0.238650	−	1.04560i
$638$	12.2935			0.486704
$639$	5.38404			0.212989
$640$	−5.04288	−	22.0943i	−0.199337	−	0.873353i
$641$	2.12432	+	2.66381i	0.0839055	+	0.105214i	0.822012	−	0.569470i	$-0.192851\pi$
$641$	2.12432	+	2.66381i	0.0839055	+	0.105214i	−0.738107	+	0.674684i	$0.764280\pi$
$642$	10.2213	−	4.92233i	0.403403	−	0.194269i
$643$	−0.880395	−	0.423976i	−0.0347194	−	0.0167200i	0.416443	−	0.909162i	$-0.363276\pi$
$643$	−0.880395	−	0.423976i	−0.0347194	−	0.0167200i	−0.451163	+	0.892442i	$0.648991\pi$
$644$	−7.83579			−0.308773
$645$	−16.8116	+	7.41323i	−0.661957	+	0.291896i
$646$	28.8659			1.13571
$647$	14.8262	+	7.13990i	0.582876	+	0.280699i	0.701995	−	0.712181i	$-0.252293\pi$
$647$	14.8262	+	7.13990i	0.582876	+	0.280699i	−0.119119	+	0.992880i	$0.538007\pi$
$648$	−3.15010	+	1.51701i	−0.123748	+	0.0595938i
$649$	−0.112605	−	0.141202i	−0.00442012	−	0.00554266i
$650$	0.128334	+	0.562269i	0.00503368	+	0.0220540i
$651$	−21.7808			−0.853655
$652$	−17.6896			−0.692779
$653$	−7.50066	−	32.8626i	−0.293524	−	1.28601i	−0.879584	−	0.475744i	$-0.842179\pi$
$653$	−7.50066	−	32.8626i	−0.293524	−	1.28601i	0.586060	−	0.810267i	$-0.300678\pi$
$654$	−3.04892	+	3.82322i	−0.119222	+	0.149500i
$655$	−1.02930	+	4.50967i	−0.0402182	+	0.176207i
$656$	−13.5375	+	16.9755i	−0.528551	+	0.662781i
$657$	1.86563	+	0.898438i	0.0727850	+	0.0350514i
$658$	2.13653	+	9.36075i	0.0832906	+	0.364920i
$659$	31.6247	+	15.2297i	1.23193	+	0.593264i	0.932608	−	0.360890i	$-0.117527\pi$
$659$	31.6247	+	15.2297i	1.23193	+	0.593264i	0.299317	+	0.954154i	$0.403241\pi$
$660$	2.47703	+	3.10610i	0.0964184	+	0.120905i
$661$	−0.468837	+	2.05411i	−0.0182356	+	0.0798955i	−0.983227	−	0.182386i	$-0.941618\pi$
$661$	−0.468837	+	2.05411i	−0.0182356	+	0.0798955i	0.964991	+	0.262282i	$0.0844750\pi$
$662$	−7.32424	+	32.0896i	−0.284665	+	1.24720i
$663$	26.4916	−	12.7577i	1.02885	−	0.495467i
$664$	10.3922	+	13.0315i	0.403297	+	0.505719i
$665$	−10.5368	+	13.2128i	−0.408601	+	0.512369i
$666$	8.56949	−	4.12685i	0.332061	−	0.159912i
$667$	−20.0761	+	9.66812i	−0.777348	+	0.374351i
$668$	7.36443	−	9.23470i	0.284938	−	0.357301i
$669$	−2.20291	−	2.76236i	−0.0851693	−	0.106799i
$670$	7.65279	−	3.68539i	0.295653	−	0.142379i
$671$	−0.180604	+	0.791277i	−0.00697213	+	0.0305469i
$672$	−2.90432	+	12.7247i	−0.112037	+	0.490865i
$673$	10.9088	+	13.6792i	0.420503	+	0.527294i	0.946289	−	0.323323i	$-0.104800\pi$
$673$	10.9088	+	13.6792i	0.420503	+	0.527294i	−0.525785	+	0.850617i	$0.676229\pi$
$674$	11.5124	+	5.54407i	0.443440	+	0.213550i
$675$	−0.0603349	−	0.264345i	−0.00232229	−	0.0101746i
$676$	−33.4904	−	16.1281i	−1.28809	−	0.620312i
$677$	−18.3463	+	23.0055i	−0.705106	+	0.884175i	−0.997393	−	0.0721557i	$-0.977012\pi$
$677$	−18.3463	+	23.0055i	−0.705106	+	0.884175i	0.292288	+	0.956330i	$0.405584\pi$
$678$	−5.87316	+	25.7320i	−0.225557	+	0.988231i
$679$	3.69620	−	4.63489i	0.141847	−	0.177871i
$680$	−2.44504	−	10.7124i	−0.0937631	−	0.410803i
$681$	16.2905			0.624254
$682$	−21.1511			−0.809916
$683$	11.5378	+	50.5504i	0.441481	+	1.93426i	0.343815	+	0.939038i	$0.388281\pi$
$683$	11.5378	+	50.5504i	0.441481	+	1.93426i	0.0976667	+	0.995219i	$0.468862\pi$
$684$	4.99396	+	6.26223i	0.190949	+	0.239442i
$685$	−31.5846	+	15.2103i	−1.20678	+	0.581156i
$686$	30.5933	+	14.7329i	1.16806	+	0.562507i
$687$	22.3411			0.852366
$688$	−28.6930	−	15.0214i	−1.09391	−	0.572687i
$689$	−72.9318			−2.77848
$690$	−16.8937	−	8.13559i	−0.643133	−	0.309717i
$691$	−1.13826	+	0.548157i	−0.0433014	+	0.0208529i	−0.455409	−	0.890282i	$-0.650507\pi$
$691$	−1.13826	+	0.548157i	−0.0433014	+	0.0208529i	0.412108	+	0.911135i	$0.364793\pi$
$692$	3.70291	+	4.64330i	0.140763	+	0.176512i
$693$	−0.618645	−	2.71046i	−0.0235004	−	0.102962i
$694$	−5.79225			−0.219871
$695$	−15.8998			−0.603113
$696$	2.25906	+	9.89759i	0.0856295	+	0.375167i
$697$	−9.87800	+	12.3866i	−0.374156	+	0.469177i
$698$	−10.9666	+	48.0477i	−0.415091	+	1.81863i
$699$	7.26205	−	9.10632i	0.274676	−	0.344433i
$700$	−0.0929903	−	0.0447818i	−0.00351470	−	0.00169259i
$701$	−7.56398	−	33.1400i	−0.285688	−	1.25168i	−0.890379	−	0.455220i	$-0.849561\pi$
$701$	−7.56398	−	33.1400i	−0.285688	−	1.25168i	0.604691	−	0.796460i	$-0.293296\pi$
$702$	58.8781	+	28.3542i	2.22221	+	1.07016i
$703$	−10.1235	−	12.6945i	−0.381815	−	0.478780i
$704$	−0.321020	+	1.40648i	−0.0120989	+	0.0530087i
$705$	−1.96346	+	8.60248i	−0.0739482	+	0.323988i
$706$	37.4991	−	18.0586i	1.41130	−	0.679645i
$707$	13.5801	+	17.0289i	0.510732	+	0.640437i
$708$	−0.153989	+	0.193096i	−0.00578727	+	0.00725701i
$709$	−31.6797	+	15.2561i	−1.18976	+	0.572956i	−0.920739	−	0.390179i	$-0.872413\pi$
$709$	−31.6797	+	15.2561i	−1.18976	+	0.572956i	−0.269017	+	0.963135i	$0.586699\pi$
$710$	13.5918	−	6.54546i	0.510091	−	0.245647i
$711$	0.0549581	−	0.0689153i	0.00206109	−	0.00258453i
$712$	8.98374	+	11.2653i	0.336680	+	0.422183i
$713$	34.5410	−	16.6341i	1.29357	−	0.622951i
$714$	−3.04892	+	13.3582i	−0.114103	+	0.499917i
$715$	−3.71983	+	16.2977i	−0.139114	+	0.609498i
$716$	1.28083	+	1.60611i	0.0478669	+	0.0600232i
$717$	8.13587	+	3.91803i	0.303840	+	0.146321i
$718$	0.102147	+	0.447533i	0.00381208	+	0.0167018i
$719$	−22.0722	−	10.6294i	−0.823153	−	0.396410i	−0.0256105	−	0.999672i	$-0.508153\pi$
$719$	−22.0722	−	10.6294i	−0.823153	−	0.396410i	−0.797543	+	0.603262i	$0.793867\pi$
$720$	9.99880	−	12.5381i	0.372633	−	0.467268i
$721$	−1.39828	+	6.12627i	−0.0520747	+	0.228154i
$722$	0.852052	−	1.06844i	0.0317101	−	0.0397632i
$723$	−0.0304995	−	0.133627i	−0.00113429	−	0.00496964i
$724$	2.83877			0.105502
$725$	−0.293504			−0.0109005
$726$	−4.85354	−	21.2648i	−0.180132	−	0.789209i
$727$	−24.3071	−	30.4801i	−0.901500	−	1.13044i	−0.990920	−	0.134451i	$-0.957073\pi$
$727$	−24.3071	−	30.4801i	−0.901500	−	1.13044i	0.0894207	−	0.995994i	$-0.471498\pi$
$728$	−13.5341	+	6.51770i	−0.501609	+	0.241562i
$729$	−22.0368	−	10.6124i	−0.816179	−	0.393051i
$730$	5.80194			0.214739
$731$	−20.9366	−	10.9608i	−0.774368	−	0.405399i
$732$	1.10992			0.0410237
$733$	5.28232	+	2.54383i	0.195107	+	0.0939586i	0.528886	−	0.848693i	$-0.322610\pi$
$733$	5.28232	+	2.54383i	0.195107	+	0.0939586i	−0.333779	+	0.942651i	$0.608324\pi$
$734$	24.0426	−	11.5783i	0.887430	−	0.427364i
$735$	7.22737	+	9.06283i	0.266585	+	0.334287i
$736$	−5.11207	−	22.3975i	−0.188433	−	0.825581i
$737$	2.38537			0.0878663
$738$	−11.4470			−0.421368
$739$	5.02542	+	22.0178i	0.184863	+	0.809938i	0.979271	+	0.202553i	$0.0649240\pi$
$739$	5.02542	+	22.0178i	0.184863	+	0.809938i	−0.794408	+	0.607384i	$0.792219\pi$
$740$	6.38135	−	8.00197i	0.234583	−	0.294158i
$741$	8.07002	−	35.3571i	0.296460	−	1.29887i
$742$	21.1896	−	26.5710i	0.777896	−	0.975450i
$743$	40.4424	+	19.4760i	1.48369	+	0.714507i	0.988066	−	0.154032i	$-0.0492258\pi$
$743$	40.4424	+	19.4760i	1.48369	+	0.714507i	0.495622	+	0.868538i	$0.334940\pi$
$744$	−3.88673	−	17.0289i	−0.142494	−	0.624309i
$745$	11.7458	+	5.65647i	0.430332	+	0.207237i
$746$	25.2473	+	31.6591i	0.924368	+	1.15912i
$747$	−3.94989	+	17.3056i	−0.144519	+	0.633178i
$748$	−1.13706	+	4.98180i	−0.0415752	+	0.182153i
$749$	−7.69687	+	3.70662i	−0.281237	+	0.135437i
$750$	15.5858	+	19.5439i	0.569111	+	0.713643i
$751$	−0.297093	+	0.372543i	−0.0108411	+	0.0135943i	−0.787222	−	0.616669i	$-0.788482\pi$
$751$	−0.297093	+	0.372543i	−0.0108411	+	0.0135943i	0.776381	+	0.630263i	$0.217053\pi$
$752$	−14.0133	+	6.74847i	−0.511014	+	0.246091i
$753$	−31.3424	+	15.0937i	−1.14218	+	0.550046i
$754$	44.1051	−	55.3061i	1.60621	−	2.01413i
$755$	10.4363	+	13.0867i	0.379816	+	0.476275i
$756$	−10.5368	+	5.07427i	−0.383221	+	0.184550i
$757$	2.40001	−	10.5151i	0.0872298	−	0.382179i	−0.912402	−	0.409294i	$-0.865775\pi$
$757$	2.40001	−	10.5151i	0.0872298	−	0.382179i	0.999632	+	0.0271153i	$0.00863213\pi$
$758$	10.4456	−	45.7651i	0.379400	−	1.66226i
$759$	−3.28315	−	4.11694i	−0.119171	−	0.149436i
$760$	−12.2104	−	5.88024i	−0.442919	−	0.213299i
$761$	−1.97381	−	8.64784i	−0.0715506	−	0.313484i	0.926470	−	0.376368i	$-0.122827\pi$
$761$	−1.97381	−	8.64784i	−0.0715506	−	0.313484i	−0.998021	+	0.0628843i	$0.979970\pi$
$762$	−40.9403	−	19.7158i	−1.48311	−	0.714228i
$763$	2.29590	−	2.87896i	0.0831171	−	0.104225i
$764$	4.17092	−	18.2740i	0.150898	−	0.661129i
$765$	7.29590	−	9.14877i	0.263784	−	0.330774i
$766$	−4.94816	−	21.6793i	−0.178784	−	0.783305i
$767$	−1.03923			−0.0375244
$768$	−25.8267			−0.931940
$769$	−8.63222	−	37.8202i	−0.311286	−	1.36383i	−0.852403	−	0.522885i	$-0.824856\pi$
$769$	−8.63222	−	37.8202i	−0.311286	−	1.36383i	0.541117	−	0.840947i	$-0.318001\pi$
$770$	−4.85690	−	6.09035i	−0.175030	−	0.219481i
$771$	−2.99396	+	1.44181i	−0.107825	+	0.0519257i
$772$	−11.0673	−	5.32975i	−0.398322	−	0.191822i
$773$	44.4730			1.59958			0.799792	−	0.600277i	$-0.204943\pi$
$773$	44.4730			1.59958			0.799792	+	0.600277i	$0.204943\pi$
$774$	−3.23998	−	16.7645i	−0.116459	−	0.602589i
$775$	0.504976			0.0181393
$776$	4.28328	+	2.06272i	0.153761	+	0.0740473i
$777$	6.94385	−	3.34398i	0.249109	−	0.119965i
$778$	−22.3729	−	28.0548i	−0.802108	−	1.00581i
$779$	4.34827	+	19.0510i	0.155793	+	0.682574i
$780$	22.8605			0.818539
$781$	4.23655			0.151596
$782$	−5.36658	−	23.5125i	−0.191909	−	0.840807i
$783$	−20.7356	+	26.0016i	−0.741029	+	0.929220i
$784$	−4.54676	+	19.9207i	−0.162384	+	0.711452i
$785$	18.5112	−	23.2123i	0.660692	−	0.828482i
$786$	4.16756	+	2.00699i	0.148652	+	0.0715871i
$787$	2.36413	+	10.3579i	0.0842722	+	0.369221i	0.999426	−	0.0338847i	$-0.0107879\pi$
$787$	2.36413	+	10.3579i	0.0842722	+	0.369221i	−0.915154	+	0.403106i	$0.867931\pi$
$788$	−12.3143	−	5.93026i	−0.438679	−	0.211257i
$789$	18.7642	+	23.5296i	0.668023	+	0.837675i
$790$	0.0549581	−	0.240787i	0.00195532	−	0.00856683i
$791$	4.42261	−	19.3767i	0.157250	−	0.688956i
$792$	2.00873	−	0.967353i	0.0713771	−	0.0343734i
$793$	2.91185	+	3.65135i	0.103403	+	0.129663i
$794$	10.2518	−	12.8554i	0.363824	−	0.456220i
$795$	28.1395	−	13.5513i	0.998006	−	0.480614i
$796$	27.3620	−	13.1769i	0.969822	−	0.467041i
$797$	0.329453	−	0.413121i	0.0116698	−	0.0146335i	−0.775962	−	0.630779i	$-0.782735\pi$
$797$	0.329453	−	0.413121i	0.0116698	−	0.0146335i	0.787632	+	0.616146i	$0.211307\pi$
$798$	10.5368	+	13.2128i	0.373000	+	0.467727i
$799$	−10.2252	+	4.92420i	−0.361742	+	0.174206i
$800$	0.0673352	−	0.295015i	0.00238066	−	0.0104304i
$801$	−3.41454	+	14.9601i	−0.120647	+	0.528589i
$802$	0.0489173	+	0.0613404i	0.00172733	+	0.00216600i
$803$	1.46801	+	0.706956i	0.0518049	+	0.0249479i
$804$	−0.725873	−	3.18026i	−0.0255996	−	0.112159i
$805$	12.7213	+	6.12627i	0.448368	+	0.215923i
$806$	−75.8832	+	95.1545i	−2.67287	+	3.35168i
$807$	8.36629	−	36.6551i	0.294507	−	1.29032i
$808$	−10.8904	+	13.6561i	−0.383122	+	0.480420i
$809$	−2.38381	−	10.4441i	−0.0838102	−	0.367196i	0.915579	−	0.402138i	$-0.131733\pi$
$809$	−2.38381	−	10.4441i	−0.0838102	−	0.367196i	−0.999389	+	0.0349414i	$0.988876\pi$
$810$	−10.4330			−0.366577
$811$	−52.4782			−1.84276			−0.921379	−	0.388666i	$-0.872936\pi$
$811$	−52.4782			−1.84276			−0.921379	+	0.388666i	$0.872936\pi$
$812$	2.81700	+	12.3421i	0.0988574	+	0.433123i
$813$	10.6453	+	13.3487i	0.373346	+	0.468161i
$814$	6.74309	−	3.24730i	0.236345	−	0.113818i
$815$	28.7189	+	13.8303i	1.00598	+	0.484455i
$816$	−22.1957			−0.777004
$817$	−26.6703	+	11.7605i	−0.933074	+	0.411447i
$818$	−19.2567			−0.673294
$819$	−14.4133	−	6.94110i	−0.503643	−	0.242542i
$820$	−11.0978	+	5.34444i	−0.387553	+	0.186636i
$821$	8.79321	+	11.0263i	0.306885	+	0.384822i	0.911228	−	0.411903i	$-0.135136\pi$
$821$	8.79321	+	11.0263i	0.306885	+	0.384822i	−0.604343	+	0.796724i	$0.706564\pi$
$822$	7.80074	+	34.1773i	0.272082	+	1.19207i
$823$	45.8146			1.59700			0.798498	−	0.601997i	$-0.205628\pi$
$823$	45.8146			1.59700			0.798498	+	0.601997i	$0.205628\pi$
$824$	−5.03923			−0.175550
$825$	−0.0154340	−	0.0676206i	−0.000537342	−	0.00235425i
$826$	0.301938	−	0.378618i	0.0105058	−	0.0131738i
$827$	8.55938	−	37.5011i	0.297639	−	1.30404i	−0.575994	−	0.817454i	$-0.695385\pi$
$827$	8.55938	−	37.5011i	0.297639	−	1.30404i	0.873633	−	0.486586i	$-0.161758\pi$
$828$	4.17241	−	5.23203i	0.145001	−	0.181826i
$829$	−17.3751	−	8.36740i	−0.603461	−	0.290612i	0.107099	−	0.994248i	$-0.465844\pi$
$829$	−17.3751	−	8.36740i	−0.603461	−	0.290612i	−0.710560	+	0.703637i	$0.751558\pi$
$830$	11.0673	+	48.4892i	0.384153	+	1.68308i
$831$	−20.8681	−	10.0495i	−0.723906	−	0.348615i
$832$	5.17576	+	6.49020i	0.179437	+	0.225007i
$833$	−3.31767	+	14.5356i	−0.114950	+	0.503630i
$834$	−3.53803	+	15.5011i	−0.122512	+	0.536760i
$835$	−19.1761	+	9.23470i	−0.663615	+	0.319580i
$836$	3.92961	+	4.92757i	0.135908	+	0.170424i
$837$	35.6757	−	44.7359i	1.23313	−	1.54630i
$838$	11.9831	−	5.77074i	0.413948	−	0.199347i
$839$	5.32424	−	2.56402i	0.183813	−	0.0885198i	−0.339714	−	0.940529i	$-0.610330\pi$
$839$	5.32424	−	2.56402i	0.183813	−	0.0885198i	0.523527	+	0.852009i	$0.324616\pi$
$840$	4.01089	−	5.02949i	0.138389	−	0.173534i
$841$	4.36443	+	5.47282i	0.150498	+	0.188718i
$842$	−15.8976	+	7.65589i	−0.547868	+	0.263839i
$843$	−0.753684	+	3.30211i	−0.0259583	+	0.113731i
$844$	−2.86108	+	12.5352i	−0.0984823	+	0.431479i
$845$	41.7618	+	52.3677i	1.43665	+	1.80150i
$846$	−7.38793	−	3.55784i	−0.254002	−	0.122321i
$847$	3.65482	+	16.0128i	0.125581	+	0.550206i
$848$	49.6018	+	23.8870i	1.70333	+	0.820281i
$849$	−13.2265	+	16.5856i	−0.453934	+	0.569215i
$850$	0.0706876	−	0.309703i	0.00242456	−	0.0106227i
$851$	−8.45808	+	10.6061i	−0.289939	+	0.363572i
$852$	−1.28919	−	5.64832i	−0.0441670	−	0.193508i
$853$	27.6021			0.945077			0.472538	−	0.881310i	$-0.343338\pi$
$853$	27.6021			0.945077			0.472538	+	0.881310i	$0.343338\pi$
$854$	−2.17629			−0.0744712
$855$	−3.21164	−	14.0711i	−0.109836	−	0.481221i
$856$	−4.27144	−	5.35621i	−0.145995	−	0.183072i
$857$	−15.3780	+	7.40566i	−0.525303	+	0.252972i	−0.677689	−	0.735349i	$-0.737018\pi$
$857$	−15.3780	+	7.40566i	−0.525303	+	0.252972i	0.152386	+	0.988321i	$0.451304\pi$
$858$	15.0613	+	7.25314i	0.514184	+	0.247618i
$859$	4.80838			0.164060			0.0820299	−	0.996630i	$-0.473860\pi$
$859$	4.80838			0.164060			0.0820299	+	0.996630i	$0.473860\pi$
$860$	−10.9683	−	14.7405i	−0.374016	−	0.502648i
$861$	−9.27545			−0.316107
$862$	−44.3696	−	21.3673i	−1.51123	−	0.727772i
$863$	−49.0045	+	23.5993i	−1.66813	+	0.803330i	−0.669992	+	0.742369i	$0.733702\pi$
$863$	−49.0045	+	23.5993i	−1.66813	+	0.803330i	−0.998140	+	0.0609613i	$0.980583\pi$
$864$	−21.3783	−	26.8075i	−0.727304	−	0.912011i
$865$	−2.38135	−	10.4334i	−0.0809685	−	0.354746i
$866$	−5.00538			−0.170090
$867$	5.00298			0.169910
$868$	−4.84667	−	21.2347i	−0.164507	−	0.720752i
$869$	0.0432450	−	0.0542276i	0.00146699	−	0.00183954i
$870$	−6.74094	+	29.5340i	−0.228539	+	1.00130i
$871$	8.55794	−	10.7313i	0.289975	−	0.363617i
$872$	2.66056	+	1.28126i	0.0900980	+	0.0433889i
$873$	1.12661	+	4.93598i	0.0381298	+	0.167058i
$874$	−26.8005	−	12.9064i	−0.906541	−	0.436567i
$875$	−11.7364	−	14.7170i	−0.396762	−	0.497524i
$876$	0.495820	−	2.17233i	0.0167522	−	0.0733962i
$877$	3.00269	−	13.1556i	0.101394	−	0.444234i	−0.898592	−	0.438786i	$-0.855409\pi$
$877$	3.00269	−	13.1556i	0.101394	−	0.444234i	0.999985	−	0.00544828i	$-0.00173425\pi$
$878$	−15.5565	+	7.49159i	−0.525005	+	0.252829i
$879$	8.57673	+	10.7549i	0.289286	+	0.362753i
$880$	7.86778	−	9.86589i	0.265223	−	0.332579i
$881$	31.8550	−	15.3406i	1.07322	−	0.516837i	0.188079	−	0.982154i	$-0.439774\pi$
$881$	31.8550	−	15.3406i	1.07322	−	0.516837i	0.885144	+	0.465317i	$0.154060\pi$
$882$	−9.70560	+	4.67397i	−0.326804	+	0.157381i
$883$	33.4753	−	41.9767i	1.12653	−	1.41263i	0.228035	−	0.973653i	$-0.426770\pi$
$883$	33.4753	−	41.9767i	1.12653	−	1.41263i	0.898499	−	0.438976i	$-0.144659\pi$
$884$	18.3327	+	22.9885i	0.616597	+	0.773188i
$885$	0.400969	−	0.193096i	0.0134784	−	0.00649087i
$886$	−9.53319	+	41.7676i	−0.320274	+	1.40321i
$887$	2.16325	−	9.47782i	0.0726349	−	0.318234i	−0.925538	−	0.378654i	$-0.876387\pi$
$887$	2.16325	−	9.47782i	0.0726349	−	0.318234i	0.998173	+	0.0604202i	$0.0192441\pi$
$888$	3.85354	+	4.83219i	0.129316	+	0.162158i
$889$	30.8288	+	14.8464i	1.03397	+	0.497932i
$890$	9.56734	+	41.9172i	0.320698	+	1.40507i
$891$	−2.63975	−	1.27124i	−0.0884350	−	0.0425881i
$892$	2.20291	−	2.76236i	0.0737588	−	0.0924906i
$893$	−3.11487	+	13.6471i	−0.104235	+	0.456683i
$894$	8.12833	−	10.1926i	0.271852	−	0.340892i
$895$	−0.823708	−	3.60890i	−0.0275335	−	0.120632i
$896$	17.0653			0.570112
$897$	−30.3002			−1.01169
$898$	7.35786	+	32.2369i	0.245535	+	1.07576i
$899$	−38.6179	−	48.4253i	−1.28798	−	1.61507i
$900$	0.0794168	−	0.0382451i	0.00264723	−	0.00127484i
$901$	36.1933	+	17.4298i	1.20577	+	0.580670i
$902$	−9.00730			−0.299910
$903$	−2.62535	−	13.5843i	−0.0873662	−	0.452057i
$904$	15.9385			0.530108
$905$	−4.60872	−	2.21944i	−0.153199	−	0.0737768i
$906$	15.0809	−	7.26258i	0.501030	−	0.241283i
$907$	−17.9849	−	22.5523i	−0.597178	−	0.748837i	0.387758	−	0.921761i	$-0.373250\pi$
$907$	−17.9849	−	22.5523i	−0.597178	−	0.748837i	−0.984935	+	0.172924i	$0.944678\pi$
$908$	3.62498	+	15.8821i	0.120299	+	0.527065i
$909$	−18.6015			−0.616972
$910$	−44.8243			−1.48591
$911$	−3.18814	−	13.9681i	−0.105628	−	0.462785i	−0.999884	−	0.0152300i	$-0.995152\pi$
$911$	−3.18814	−	13.9681i	−0.105628	−	0.462785i	0.894256	−	0.447555i	$-0.147705\pi$
$912$	−17.0688	+	21.4036i	−0.565205	+	0.708745i
$913$	−3.10806	+	13.6173i	−0.102862	+	0.450666i
$914$	44.7280	−	56.0871i	1.47947	−	1.85520i
$915$	−1.80194	−	0.867767i	−0.0595702	−	0.0286875i
$916$	4.97136	+	21.7810i	0.164258	+	0.719663i
$917$	−3.13826	−	1.51131i	−0.103634	−	0.0499077i
$918$	−22.4426	−	28.1422i	−0.740718	−	0.928831i
$919$	−9.54785	+	41.8319i	−0.314955	+	1.37991i	0.531325	+	0.847168i	$0.321694\pi$
$919$	−9.54785	+	41.8319i	−0.314955	+	1.37991i	−0.846280	+	0.532738i	$0.821163\pi$
$920$	−2.51961	+	11.0392i	−0.0830692	+	0.363950i
$921$	17.7458	−	8.54592i	0.584743	−	0.281598i
$922$	−21.6048	−	27.0916i	−0.711517	−	0.892215i
$923$	15.1994	−	19.0594i	0.500294	−	0.627349i
$924$	−2.69537	+	1.29802i	−0.0886713	+	0.0427018i
$925$	−0.160990	+	0.0775285i	−0.00529330	+	0.00254912i
$926$	16.8056	−	21.0735i	0.552266	−	0.692519i
$927$	−3.34601	−	4.19576i	−0.109897	−	0.137807i
$928$	−33.4403	+	16.1040i	−1.09773	+	0.528639i
$929$	4.27061	−	18.7108i	0.140114	−	0.613880i	−0.855293	−	0.518145i	$-0.826623\pi$
$929$	4.27061	−	18.7108i	0.140114	−	0.613880i	0.995407	−	0.0957351i	$-0.0305202\pi$
$930$	11.5978	−	50.8134i	0.380308	−	1.66624i
$931$	11.4656	+	14.3774i	0.375770	+	0.471201i
$932$	10.4940	+	5.05362i	0.343741	+	0.165537i
$933$	−3.43147	−	15.0342i	−0.112341	−	0.492199i
$934$	−41.8705	−	20.1638i	−1.37005	−	0.659779i
$935$	5.74094	−	7.19891i	0.187749	−	0.235430i
$936$	2.85474	−	12.5074i	0.0933101	−	0.408818i
$937$	21.8699	−	27.4240i	0.714460	−	0.895904i	−0.283550	−	0.958957i	$-0.591512\pi$
$937$	21.8699	−	27.4240i	0.714460	−	0.895904i	0.998010	+	0.0630532i	$0.0200838\pi$
$938$	1.42327	+	6.23576i	0.0464715	+	0.203605i
$939$	7.27545			0.237425
$940$	−8.82371			−0.287798
$941$	1.98499	+	8.69682i	0.0647089	+	0.283508i	0.996922	−	0.0784020i	$-0.0249818\pi$
$941$	1.98499	+	8.69682i	0.0647089	+	0.283508i	−0.932213	+	0.361910i	$0.882125\pi$
$942$	−18.5112	−	23.2123i	−0.603127	−	0.756297i
$943$	14.7095	−	7.08371i	0.479007	−	0.230677i
$944$	0.706791	+	0.340373i	0.0230041	+	0.0110782i
$945$	21.0737			0.685527
$946$	−2.54945	−	13.1915i	−0.0828898	−	0.428894i
$947$	27.3672			0.889314			0.444657	−	0.895701i	$-0.353326\pi$
$947$	27.3672			0.889314			0.444657	+	0.895701i	$0.353326\pi$
$948$	−0.0854576	−	0.0411542i	−0.00277553	−	0.00133663i
$949$	8.44720	−	4.06796i	0.274208	−	0.132051i
$950$	−0.244291	−	0.306331i	−0.00792585	−	0.00993871i
$951$	7.26122	+	31.8135i	0.235461	+	1.03162i
$952$	8.27413			0.268166
$953$	−52.1221			−1.68840			−0.844200	−	0.536028i	$-0.819924\pi$
$953$	−52.1221			−1.68840			−0.844200	+	0.536028i	$0.819924\pi$
$954$	6.45862	+	28.2970i	0.209105	+	0.916151i
$955$	−21.0586	+	26.4067i	−0.681440	+	0.854499i
$956$	−2.00939	+	8.80373i	−0.0649884	+	0.284733i
$957$	−5.30426	+	6.65133i	−0.171462	+	0.215007i
$958$	48.2432	+	23.2327i	1.55867	+	0.750614i
$959$	−5.87412	−	25.7362i	−0.189685	−	0.831065i
$960$	−3.20291	−	1.54244i	−0.103373	−	0.0497820i
$961$	47.1142	+	59.0793i	1.51981	+	1.90578i
$962$	9.58306	−	41.9861i	0.308970	−	1.35369i
$963$	1.62349	−	7.11297i	0.0523162	−	0.229212i
$964$	0.123490	−	0.0594696i	0.00397734	−	0.00191539i
$965$	13.8007	+	17.3056i	0.444262	+	0.557086i
$966$	8.80343	−	11.0392i	0.283246	−	0.355179i
$967$	−9.15548	+	4.40905i	−0.294420	+	0.141785i	−0.575263	−	0.817968i	$-0.695100\pi$
$967$	−9.15548	+	4.40905i	−0.294420	+	0.141785i	0.280843	+	0.959754i	$0.409386\pi$
$968$	−11.8671	+	5.71490i	−0.381424	+	0.183684i
$969$	−12.4547	+	15.6177i	−0.400104	+	0.501714i
$970$	8.84481	+	11.0910i	0.283990	+	0.356112i
$971$	−6.72348	+	3.23786i	−0.215767	+	0.103908i	−0.538645	−	0.842533i	$-0.681064\pi$
$971$	−6.72348	+	3.23786i	−0.215767	+	0.103908i	0.322879	+	0.946440i	$0.395349\pi$
$972$	3.72252	−	16.3094i	0.119400	−	0.523125i
$973$	2.66421	−	11.6727i	0.0854107	−	0.374209i
$974$	1.70895	+	2.14295i	0.0547582	+	0.0686646i
$975$	−0.359584	−	0.173167i	−0.0115159	−	0.00554577i
$976$	−0.784479	−	3.43703i	−0.0251106	−	0.110017i
$977$	2.00388	+	0.965020i	0.0641100	+	0.0308737i	0.465664	−	0.884962i	$-0.345816\pi$
$977$	2.00388	+	0.965020i	0.0641100	+	0.0308737i	−0.401554	+	0.915835i	$0.631530\pi$
$978$	19.8741	−	24.9214i	0.635504	−	0.796897i
$979$	−2.68681	+	11.7717i	−0.0858708	+	0.376224i
$980$	−7.22737	+	9.06283i	−0.230870	+	0.289501i
$981$	0.699791	+	3.06599i	0.0223426	+	0.0978894i
$982$	51.6491			1.64819
$983$	−21.5050			−0.685902			−0.342951	−	0.939353i	$-0.611427\pi$
$983$	−21.5050			−0.685902			−0.342951	+	0.939353i	$0.611427\pi$
$984$	−1.65519	−	7.25184i	−0.0527654	−	0.231180i
$985$	15.3557	+	19.2554i	0.489273	+	0.613529i
$986$	−35.1051	+	16.9057i	−1.11798	+	0.538388i
$987$	−5.98643	−	2.88291i	−0.190550	−	0.0917641i
$988$	36.2664			1.15379
$989$	14.5378	+	19.5376i	0.462275	+	0.621261i
$990$	6.65279			0.211440
$991$	−45.7602	−	22.0369i	−1.45362	−	0.700027i	−0.470401	−	0.882453i	$-0.655891\pi$
$991$	−45.7602	−	22.0369i	−1.45362	−	0.700027i	−0.983220	+	0.182426i	$0.941605\pi$
$992$	57.5342	−	27.7070i	1.82671	−	0.879699i
$993$	−14.2017	−	17.8084i	−0.450678	−	0.565132i
$994$	2.52781	+	11.0751i	0.0801773	+	0.351280i
$995$	−54.7241			−1.73487
$996$	19.1008			0.605233
$997$	0.222652	+	0.975504i	0.00705147	+	0.0308945i	0.978331	−	0.207046i	$-0.0663849\pi$
$997$	0.222652	+	0.975504i	0.00705147	+	0.0308945i	−0.971280	+	0.237940i	$0.923528\pi$
$998$	−23.3865	+	29.3257i	−0.740287	+	0.928290i
$999$	−4.50538	+	19.7393i	−0.142544	+	0.624525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.e.a.21.1	✓	6
3.2	odd	2		387.2.u.c.64.1		6
4.3	odd	2		688.2.u.b.193.1		6
43.16	even	7		1849.2.a.k.1.3		3
43.27	odd	14		1849.2.a.j.1.1		3
43.41	even	7	inner	43.2.e.a.41.1	yes	6
129.41	odd	14		387.2.u.c.127.1		6
172.127	odd	14		688.2.u.b.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.a.21.1	✓	6	1.1	even	1	trivial
43.2.e.a.41.1	yes	6	43.41	even	7	inner
387.2.u.c.64.1		6	3.2	odd	2
387.2.u.c.127.1		6	129.41	odd	14
688.2.u.b.193.1		6	4.3	odd	2
688.2.u.b.385.1		6	172.127	odd	14
1849.2.a.j.1.1		3	43.27	odd	14
1849.2.a.k.1.3		3	43.16	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)

\(f(q)\)	\(=\)	\(q+(-1.62349 - 0.781831i) q^{2} +(1.12349 - 0.541044i) q^{3} +(0.777479 + 0.974928i) q^{4} +(-0.500000 - 2.19064i) q^{5} -2.24698 q^{6} +1.69202 q^{7} +(0.301938 + 1.32288i) q^{8} +(-0.900969 + 1.12978i) q^{9} +O(q^{10})\)	\(q+(-1.62349 - 0.781831i) q^{2} +(1.12349 - 0.541044i) q^{3} +(0.777479 + 0.974928i) q^{4} +(-0.500000 - 2.19064i) q^{5} -2.24698 q^{6} +1.69202 q^{7} +(0.301938 + 1.32288i) q^{8} +(-0.900969 + 1.12978i) q^{9} +(-0.900969 + 3.94740i) q^{10} +(-0.708947 + 0.888992i) q^{11} +(1.40097 + 0.674671i) q^{12} +(1.45593 + 6.37883i) q^{13} +(-2.74698 - 1.32288i) q^{14} +(-1.74698 - 2.19064i) q^{15} +(1.09903 - 4.81517i) q^{16} +(0.801938 - 3.51352i) q^{17} +(2.34601 - 1.12978i) q^{18} +(-2.77144 - 3.47527i) q^{19} +(1.74698 - 2.19064i) q^{20} +(1.90097 - 0.915458i) q^{21} +(1.84601 - 0.888992i) q^{22} +(-2.31551 + 2.90356i) q^{23} +(1.05496 + 1.32288i) q^{24} +(-0.0440730 + 0.0212244i) q^{25} +(2.62349 - 11.4943i) q^{26} +(-1.23341 + 5.40391i) q^{27} +(1.31551 + 1.64960i) q^{28} +(5.40581 + 2.60330i) q^{29} +(1.12349 + 4.92233i) q^{30} +(-9.30074 - 4.47900i) q^{31} +(-3.85690 + 4.83639i) q^{32} +(-0.315511 + 1.38235i) q^{33} +(-4.04892 + 5.07718i) q^{34} +(-0.846011 - 3.70662i) q^{35} -1.80194 q^{36} +3.65279 q^{37} +(1.78232 + 7.80887i) q^{38} +(5.08695 + 6.37883i) q^{39} +(2.74698 - 1.32288i) q^{40} +(-3.96077 - 1.90741i) q^{41} -3.80194 q^{42} +(1.67241 - 6.34059i) q^{43} -1.41789 q^{44} +(2.92543 + 1.40881i) q^{45} +(6.02930 - 2.90356i) q^{46} +(-1.96346 - 2.46210i) q^{47} +(-1.37047 - 6.00442i) q^{48} -4.13706 q^{49} +0.0881460 q^{50} +(-1.00000 - 4.38129i) q^{51} +(-5.08695 + 6.37883i) q^{52} +(-2.48039 + 10.8673i) q^{53} +(6.22737 - 7.80887i) q^{54} +(2.30194 + 1.10855i) q^{55} +(0.510885 + 2.23833i) q^{56} +(-4.99396 - 2.40496i) q^{57} +(-6.74094 - 8.45287i) q^{58} +(-0.0353438 + 0.154851i) q^{59} +(0.777479 - 3.40636i) q^{60} +(0.643104 - 0.309703i) q^{61} +(11.5978 + 14.5432i) q^{62} +(-1.52446 + 1.91161i) q^{63} +(1.14310 - 0.550490i) q^{64} +(13.2458 - 6.37883i) q^{65} +(1.59299 - 1.99755i) q^{66} +(-1.30798 - 1.64015i) q^{67} +(4.04892 - 1.94986i) q^{68} +(-1.03050 + 4.51491i) q^{69} +(-1.52446 + 6.67909i) q^{70} +(-2.32304 - 2.91301i) q^{71} +(-1.76659 - 0.850747i) q^{72} +(-0.318864 - 1.39703i) q^{73} +(-5.93027 - 2.85587i) q^{74} +(-0.0380322 + 0.0476909i) q^{75} +(1.23341 - 5.40391i) q^{76} +(-1.19955 + 1.50419i) q^{77} +(-3.27144 - 14.3331i) q^{78} -0.0609989 q^{79} -11.0978 q^{80} +(0.573376 + 2.51212i) q^{81} +(4.93900 + 6.19331i) q^{82} +(11.0673 - 5.32975i) q^{83} +(2.37047 + 1.14156i) q^{84} -8.09783 q^{85} +(-7.67241 + 8.98634i) q^{86} +7.48188 q^{87} +(-1.39008 - 0.669429i) q^{88} +(9.56734 - 4.60739i) q^{89} +(-3.64795 - 4.57438i) q^{90} +(2.46346 + 10.7931i) q^{91} -4.63102 q^{92} -12.8726 q^{93} +(1.26271 + 5.53229i) q^{94} +(-6.22737 + 7.80887i) q^{95} +(-1.71648 + 7.52039i) q^{96} +(2.18449 - 2.73926i) q^{97} +(6.71648 + 3.23449i) q^{98} +(-0.365625 - 1.60191i) 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

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