LMFDB - Embedded newform 354.2.e.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			79.1
Character	$\chi$	$=$	354.79
Dual form			354.2.e.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907575 + 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(-0.314743 + 0.189375i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(0.132599 + 2.44564i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})$	\(q+(0.907575 + 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(-0.314743 + 0.189375i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(0.132599 + 2.44564i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-0.365169 + 0.0397146i) q^{10} +(0.669702 + 4.08500i) q^{11} +(-0.856857 - 0.515554i) q^{12} +(-2.31199 - 1.75753i) q^{13} +(-0.906555 + 2.27528i) q^{14} +(0.237800 - 0.279959i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.130198 + 2.40137i) q^{17} +(0.976621 - 0.214970i) q^{18} +(0.140693 + 0.133271i) q^{19} +(-0.348095 - 0.117287i) q^{20} +(-0.906555 - 2.27528i) q^{21} +(-1.10744 + 3.98865i) q^{22} +(7.76271 + 1.70870i) q^{23} +(-0.561187 - 0.827689i) q^{24} +(-2.27884 + 4.29835i) q^{25} +(-1.36034 - 2.56587i) q^{26} +(-0.561187 + 0.827689i) q^{27} +(-1.77813 + 1.68434i) q^{28} +(-5.73619 + 2.65384i) q^{29} +(0.333373 - 0.154235i) q^{30} +(6.02604 - 5.70817i) q^{31} +(-0.561187 + 0.827689i) q^{32} +(-1.93899 - 3.65733i) q^{33} +(-1.12647 + 2.12475i) q^{34} +(-0.504877 - 0.744638i) q^{35} +(0.976621 + 0.214970i) q^{36} +(2.75371 - 9.91797i) q^{37} +(0.0717302 + 0.180029i) q^{38} +(2.75215 + 0.927307i) q^{39} +(-0.266675 - 0.252608i) q^{40} +(-2.91503 + 0.641647i) q^{41} +(0.132599 - 2.44564i) q^{42} +(0.962890 - 5.87337i) q^{43} +(-2.67988 + 3.15500i) q^{44} +(-0.135960 + 0.341234i) q^{45} +(6.32778 + 4.81025i) q^{46} +(-5.91367 - 3.55814i) q^{47} +(-0.161782 - 0.986827i) q^{48} +(0.995387 - 0.108255i) q^{49} +(-3.87305 + 2.94422i) q^{50} +(-0.643378 - 2.31724i) q^{51} +(-0.157229 - 2.89991i) q^{52} +(7.25546 + 0.789079i) q^{53} +(-0.856857 + 0.515554i) q^{54} +(-0.984380 - 1.15890i) q^{55} +(-2.32102 + 0.782044i) q^{56} +(-0.175882 - 0.0813716i) q^{57} -6.32034 q^{58} +(3.31048 - 6.93114i) q^{59} +0.367323 q^{60} +(4.01886 + 1.85932i) q^{61} +(7.86588 - 2.65032i) q^{62} +(1.58560 + 1.86671i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(1.06052 + 0.115338i) q^{65} +(-0.224110 - 4.13346i) q^{66} +(-2.64748 - 9.53535i) q^{67} +(-1.91452 + 1.45538i) q^{68} +(-7.90195 + 0.859389i) q^{69} +(-0.145549 - 0.887807i) q^{70} +(11.7072 + 7.04400i) q^{71} +(0.796093 + 0.605174i) q^{72} +(-0.0878640 + 0.220522i) q^{73} +(6.66365 - 7.84505i) q^{74} +(0.787081 - 4.80098i) q^{75} +(-0.0104917 + 0.193509i) q^{76} +(-9.90165 + 2.17952i) q^{77} +(2.10842 + 1.99720i) q^{78} +(0.313136 + 0.105508i) q^{79} +(-0.135960 - 0.341234i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-2.91503 - 0.641647i) q^{82} +(-1.69518 - 2.50020i) q^{83} +(1.14724 - 2.16393i) q^{84} +(-0.413779 - 0.780471i) q^{85} +(3.34006 - 4.92622i) q^{86} +(4.58854 - 4.34650i) q^{87} +(-3.75694 + 1.73815i) q^{88} +(-0.341009 + 0.157768i) q^{89} +(-0.266675 + 0.252608i) q^{90} +(3.99172 - 5.88735i) q^{91} +(3.72317 + 7.02263i) q^{92} +(-3.88797 + 7.33349i) q^{93} +(-3.87308 - 5.71236i) q^{94} +(-0.0695203 - 0.0153026i) q^{95} +(0.267528 - 0.963550i) q^{96} +(-4.17050 - 10.4672i) q^{97} +(0.948844 + 0.319703i) q^{98} +(3.00528 + 2.84676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{4}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.907575	+	0.419889i	0.641753	+	0.296906i
$2$	0.907575	+	0.419889i	0.641753	+	0.296906i
$3$	−0.947653	+	0.319302i	−0.547128	+	0.184349i
$3$	−0.947653	+	0.319302i	−0.547128	+	0.184349i
$4$	0.647386	+	0.762162i	0.323693	+	0.381081i
$5$	−0.314743	+	0.189375i	−0.140757	+	0.0846909i	−0.584191	−	0.811617i	$-0.698588\pi$
$5$	−0.314743	+	0.189375i	−0.140757	+	0.0846909i	0.443433	+	0.896307i	$0.353760\pi$
$6$	−0.994138	−	0.108119i	−0.405855	−	0.0441394i
$7$	0.132599	+	2.44564i	0.0501176	+	0.924366i	0.910189	+	0.414192i	$0.135936\pi$
$7$	0.132599	+	2.44564i	0.0501176	+	0.924366i	−0.860072	+	0.510173i	$0.829581\pi$
$8$	0.267528	+	0.963550i	0.0945856	+	0.340666i
$9$	0.796093	−	0.605174i	0.265364	−	0.201725i
$10$	−0.365169	+	0.0397146i	−0.115477	+	0.0125589i
$11$	0.669702	+	4.08500i	0.201923	+	1.23167i	0.872046	+	0.489425i	$0.162793\pi$
$11$	0.669702	+	4.08500i	0.201923	+	1.23167i	−0.670123	+	0.742250i	$0.733759\pi$
$12$	−0.856857	−	0.515554i	−0.247353	−	0.148828i
$13$	−2.31199	−	1.75753i	−0.641231	−	0.487451i	0.233310	−	0.972402i	$-0.425044\pi$
$13$	−2.31199	−	1.75753i	−0.641231	−	0.487451i	−0.874541	+	0.484951i	$0.838837\pi$
$14$	−0.906555	+	2.27528i	−0.242287	+	0.608094i
$15$	0.237800	−	0.279959i	0.0613996	−	0.0722852i
$16$	−0.161782	+	0.986827i	−0.0404455	+	0.246707i
$17$	−0.130198	+	2.40137i	−0.0315778	+	0.582418i	0.939337	+	0.342994i	$0.111441\pi$
$17$	−0.130198	+	2.40137i	−0.0315778	+	0.582418i	−0.970915	+	0.239423i	$0.923042\pi$
$18$	0.976621	−	0.214970i	0.230192	−	0.0506690i
$19$	0.140693	+	0.133271i	0.0322772	+	0.0305745i	0.703668	−	0.710529i	$-0.251544\pi$
$19$	0.140693	+	0.133271i	0.0322772	+	0.0305745i	−0.671391	+	0.741103i	$0.734303\pi$
$20$	−0.348095	−	0.117287i	−0.0778363	−	0.0262261i
$21$	−0.906555	−	2.27528i	−0.197826	−	0.496507i
$22$	−1.10744	+	3.98865i	−0.236108	+	0.850383i
$23$	7.76271	+	1.70870i	1.61864	+	0.356289i	0.929638	−	0.368473i	$-0.120119\pi$
$23$	7.76271	+	1.70870i	1.61864	+	0.356289i	0.688999	+	0.724762i	$0.258050\pi$
$24$	−0.561187	−	0.827689i	−0.114552	−	0.168951i
$25$	−2.27884	+	4.29835i	−0.455768	+	0.859670i
$26$	−1.36034	−	2.56587i	−0.266784	−	0.503209i
$27$	−0.561187	+	0.827689i	−0.108001	+	0.159289i
$28$	−1.77813	+	1.68434i	−0.336035	+	0.318310i
$29$	−5.73619	+	2.65384i	−1.06518	+	0.492806i	−0.872580	−	0.488470i	$-0.837555\pi$
$29$	−5.73619	+	2.65384i	−1.06518	+	0.492806i	−0.192603	+	0.981277i	$0.561693\pi$
$30$	0.333373	−	0.154235i	0.0608653	−	0.0281593i
$31$	6.02604	−	5.70817i	1.08231	−	1.02522i	0.0827188	−	0.996573i	$-0.473640\pi$
$31$	6.02604	−	5.70817i	1.08231	−	1.02522i	0.999590	−	0.0286441i	$-0.00911895\pi$
$32$	−0.561187	+	0.827689i	−0.0992048	+	0.146316i
$33$	−1.93899	−	3.65733i	−0.337535	−	0.636659i
$34$	−1.12647	+	2.12475i	−0.193189	+	0.364392i
$35$	−0.504877	−	0.744638i	−0.0853398	−	0.125867i
$36$	0.976621	+	0.214970i	0.162770	+	0.0358284i
$37$	2.75371	−	9.91797i	0.452707	−	1.63050i	−0.287253	−	0.957855i	$-0.592742\pi$
$37$	2.75371	−	9.91797i	0.452707	−	1.63050i	0.739961	−	0.672650i	$-0.234844\pi$
$38$	0.0717302	+	0.180029i	0.0116362	+	0.0292046i
$39$	2.75215	+	0.927307i	0.440696	+	0.148488i
$40$	−0.266675	−	0.252608i	−0.0421650	−	0.0399408i
$41$	−2.91503	+	0.641647i	−0.455251	+	0.100208i	−0.436676	−	0.899619i	$-0.643844\pi$
$41$	−2.91503	+	0.641647i	−0.455251	+	0.100208i	−0.0185757	+	0.999827i	$0.505913\pi$
$42$	0.132599	−	2.44564i	0.0204604	−	0.377371i
$43$	0.962890	−	5.87337i	0.146839	−	0.895680i	−0.805936	−	0.592003i	$-0.798337\pi$
$43$	0.962890	−	5.87337i	0.146839	−	0.895680i	0.952775	−	0.303677i	$-0.0982144\pi$
$44$	−2.67988	+	3.15500i	−0.404007	+	0.475634i
$45$	−0.135960	+	0.341234i	−0.0202677	+	0.0508682i
$46$	6.32778	+	4.81025i	0.932980	+	0.709233i
$47$	−5.91367	−	3.55814i	−0.862598	−	0.519008i	0.0141825	−	0.999899i	$-0.495485\pi$
$47$	−5.91367	−	3.55814i	−0.862598	−	0.519008i	−0.876780	+	0.480892i	$0.840313\pi$
$48$	−0.161782	−	0.986827i	−0.0233512	−	0.142436i
$49$	0.995387	−	0.108255i	0.142198	−	0.0154650i
$50$	−3.87305	+	2.94422i	−0.547732	+	0.416375i
$51$	−0.643378	−	2.31724i	−0.0900909	−	0.324478i
$52$	−0.157229	−	2.89991i	−0.0218037	−	0.402146i
$53$	7.25546	+	0.789079i	0.996614	+	0.108388i	0.591863	−	0.806038i	$-0.298393\pi$
$53$	7.25546	+	0.789079i	0.996614	+	0.108388i	0.404751	+	0.914427i	$0.367358\pi$
$54$	−0.856857	+	0.515554i	−0.116603	+	0.0701580i
$55$	−0.984380	−	1.15890i	−0.132734	−	0.156266i
$56$	−2.32102	+	0.782044i	−0.310160	+	0.104505i
$57$	−0.175882	−	0.0813716i	−0.0232961	−	0.0107779i
$58$	−6.32034			−0.829902
$59$	3.31048	−	6.93114i	0.430987	−	0.902358i
$59$	3.31048	−	6.93114i	0.430987	−	0.902358i
$60$	0.367323			0.0474212
$61$	4.01886	+	1.85932i	0.514563	+	0.238062i	0.659946	−	0.751313i	$-0.270579\pi$
$61$	4.01886	+	1.85932i	0.514563	+	0.238062i	−0.145383	+	0.989375i	$0.546441\pi$
$62$	7.86588	−	2.65032i	0.998968	−	0.336591i
$63$	1.58560	+	1.86671i	0.199767	+	0.235184i
$64$	−0.856857	+	0.515554i	−0.107107	+	0.0644442i
$65$	1.06052	+	0.115338i	0.131541	+	0.0143059i
$66$	−0.224110	−	4.13346i	−0.0275860	−	0.508794i
$67$	−2.64748	−	9.53535i	−0.323441	−	1.16493i	−0.929290	−	0.369350i	$-0.879580\pi$
$67$	−2.64748	−	9.53535i	−0.323441	−	1.16493i	0.605850	−	0.795579i	$-0.292833\pi$
$68$	−1.91452	+	1.45538i	−0.232170	+	0.176491i
$69$	−7.90195	+	0.859389i	−0.951283	+	0.103458i
$70$	−0.145549	−	0.887807i	−0.0173964	−	0.106113i
$71$	11.7072	+	7.04400i	1.38939	+	0.835969i	0.996498	−	0.0836156i	$-0.0266468\pi$
$71$	11.7072	+	7.04400i	1.38939	+	0.835969i	0.392893	+	0.919584i	$0.371474\pi$
$72$	0.796093	+	0.605174i	0.0938205	+	0.0713205i
$73$	−0.0878640	+	0.220522i	−0.0102837	+	0.0258102i	−0.934029	−	0.357197i	$-0.883732\pi$
$73$	−0.0878640	+	0.220522i	−0.0102837	+	0.0258102i	0.923745	+	0.383008i	$0.125112\pi$
$74$	6.66365	−	7.84505i	0.774634	−	0.911969i
$75$	0.787081	−	4.80098i	0.0908843	−	0.554370i
$76$	−0.0104917	+	0.193509i	−0.00120349	+	0.0221970i
$77$	−9.90165	+	2.17952i	−1.12840	+	0.248379i
$78$	2.10842	+	1.99720i	0.238731	+	0.226138i
$79$	0.313136	+	0.105508i	0.0352305	+	0.0118705i	0.336862	−	0.941554i	$-0.390635\pi$
$79$	0.313136	+	0.105508i	0.0352305	+	0.0118705i	−0.301631	+	0.953425i	$0.597531\pi$
$80$	−0.135960	−	0.341234i	−0.0152008	−	0.0381511i
$81$	0.267528	−	0.963550i	0.0297254	−	0.107061i
$82$	−2.91503	−	0.641647i	−0.321911	−	0.0708580i
$83$	−1.69518	−	2.50020i	−0.186070	−	0.274433i	0.723201	−	0.690638i	$-0.242670\pi$
$83$	−1.69518	−	2.50020i	−0.186070	−	0.274433i	−0.909271	+	0.416205i	$0.863360\pi$
$84$	1.14724	−	2.16393i	0.125174	−	0.236104i
$85$	−0.413779	−	0.780471i	−0.0448807	−	0.0846539i
$86$	3.34006	−	4.92622i	0.360168	−	0.531208i
$87$	4.58854	−	4.34650i	0.491943	−	0.465993i
$88$	−3.75694	+	1.73815i	−0.400491	+	0.185287i
$89$	−0.341009	+	0.157768i	−0.0361469	+	0.0167233i	−0.437879	−	0.899034i	$-0.644270\pi$
$89$	−0.341009	+	0.157768i	−0.0361469	+	0.0167233i	0.401732	+	0.915757i	$0.368408\pi$
$90$	−0.266675	+	0.252608i	−0.0281100	+	0.0266272i
$91$	3.99172	−	5.88735i	0.418446	−	0.617162i
$92$	3.72317	+	7.02263i	0.388167	+	0.732160i
$93$	−3.88797	+	7.33349i	−0.403164	+	0.760447i
$94$	−3.87308	−	5.71236i	−0.399478	−	0.589185i
$95$	−0.0695203	−	0.0153026i	−0.00713264	−	0.00157001i
$96$	0.267528	−	0.963550i	0.0273045	−	0.0983419i
$97$	−4.17050	−	10.4672i	−0.423450	−	1.06278i	−0.973711	−	0.227786i	$-0.926851\pi$
$97$	−4.17050	−	10.4672i	−0.423450	−	1.06278i	0.550261	−	0.834993i	$-0.314528\pi$
$98$	0.948844	+	0.319703i	0.0958477	+	0.0322949i
$99$	3.00528	+	2.84676i	0.302042	+	0.286110i
$100$	−4.75133	+	1.04585i	−0.475133	+	0.104585i
$101$	−0.359069	+	6.62265i	−0.0357287	+	0.658978i	0.924742	+	0.380596i	$0.124281\pi$
$101$	−0.359069	+	6.62265i	−0.0357287	+	0.658978i	−0.960470	+	0.278382i	$0.910202\pi$
$102$	0.389069	−	2.37322i	0.0385236	−	0.234983i
$103$	2.50428	−	2.94827i	0.246754	−	0.290502i	−0.624816	−	0.780772i	$-0.714826\pi$
$103$	2.50428	−	2.94827i	0.246754	−	0.290502i	0.871570	+	0.490270i	$0.163102\pi$
$104$	1.07495	−	2.69791i	0.105407	−	0.264552i
$105$	0.716212	+	0.544450i	0.0698952	+	0.0531329i
$106$	6.25355	+	3.76264i	0.607399	+	0.365460i
$107$	2.91311	+	17.7692i	0.281621	+	1.71781i	0.626718	+	0.779246i	$0.284398\pi$
$107$	2.91311	+	17.7692i	0.281621	+	1.71781i	−0.345097	+	0.938567i	$0.612154\pi$
$108$	−0.994138	+	0.108119i	−0.0956610	+	0.0104038i
$109$	−2.15880	+	1.64107i	−0.206775	+	0.157186i	−0.703437	−	0.710758i	$-0.748352\pi$
$109$	−2.15880	+	1.64107i	−0.206775	+	0.157186i	0.496661	+	0.867944i	$0.334559\pi$
$110$	−0.406789	−	1.46512i	−0.0387858	−	0.139694i
$111$	0.557260	+	10.2781i	0.0528928	+	0.975551i
$112$	−2.43488	−	0.264809i	−0.230074	−	0.0250221i
$113$	−1.37448	+	0.826997i	−0.129300	+	0.0777974i	−0.578734	−	0.815516i	$-0.696453\pi$
$113$	−1.37448	+	0.826997i	−0.129300	+	0.0777974i	0.449434	+	0.893313i	$0.351626\pi$
$114$	−0.125459	−	0.147702i	−0.0117503	−	0.0138335i
$115$	−2.76684	+	0.932259i	−0.258010	+	0.0869336i
$116$	−5.73619	−	2.65384i	−0.532592	−	0.246403i
$117$	−2.90417			−0.268491
$118$	5.91482	−	4.90050i	0.544503	−	0.451128i
$119$	−5.89015			−0.539949
$120$	0.333373	+	0.154235i	0.0304327	+	0.0140796i
$121$	−5.81457	+	1.95916i	−0.528597	+	0.178105i
$122$	2.86671	+	3.37495i	0.259540	+	0.305554i
$123$	2.55756	−	1.53883i	0.230607	−	0.138752i
$124$	8.25172	+	0.897429i	0.741027	+	0.0805915i
$125$	−0.196181	−	3.61835i	−0.0175470	−	0.323635i
$126$	0.655239	+	2.35996i	0.0583734	+	0.210242i
$127$	−14.2591	+	10.8395i	−1.26529	+	0.961847i	−0.999997	−	0.00232176i	$-0.999261\pi$
$127$	−14.2591	+	10.8395i	−1.26529	+	0.961847i	−0.265290	+	0.964169i	$0.585468\pi$
$128$	−0.994138	+	0.108119i	−0.0878702	+	0.00955646i
$129$	0.962890	+	5.87337i	0.0847777	+	0.517121i
$130$	0.914068	+	0.549977i	0.0801691	+	0.0482361i
$131$	5.62030	+	4.27244i	0.491048	+	0.373285i	0.821198	−	0.570643i	$-0.193306\pi$
$131$	5.62030	+	4.27244i	0.491048	+	0.373285i	−0.330150	+	0.943929i	$0.607099\pi$
$132$	1.53220	−	3.84553i	0.133361	−	0.334711i
$133$	−0.307278	+	0.361756i	−0.0266444	+	0.0313682i
$134$	1.60101	−	9.76570i	0.138306	−	0.843628i
$135$	0.0198865	−	0.366784i	0.00171155	−	0.0315677i
$136$	−2.34867	+	0.516982i	−0.201397	+	0.0443308i
$137$	−8.24396	−	7.80910i	−0.704329	−	0.667176i	0.249208	−	0.968450i	$-0.419830\pi$
$137$	−8.24396	−	7.80910i	−0.704329	−	0.667176i	−0.953538	+	0.301274i	$0.902588\pi$
$138$	−7.53246	−	2.53798i	−0.641206	−	0.216047i
$139$	−1.32943	−	3.33662i	−0.112761	−	0.283009i	0.861756	−	0.507323i	$-0.169365\pi$
$139$	−1.32943	−	3.33662i	−0.112761	−	0.283009i	−0.974517	+	0.224315i	$0.927986\pi$
$140$	0.240684	−	0.866866i	0.0203415	−	0.0732636i
$141$	6.74023	+	1.48364i	0.567630	+	0.124945i
$142$	7.66748	+	11.3087i	0.643441	+	0.949004i
$143$	5.63117	−	10.6215i	0.470902	−	0.888216i
$144$	0.468408	+	0.883512i	0.0390340	+	0.0736260i
$145$	1.30286	−	1.92157i	0.108196	−	0.159577i
$146$	−0.172338	+	0.163247i	−0.0142628	+	0.0135104i
$147$	−0.908716	+	0.420417i	−0.0749496	+	0.0346754i
$148$	9.34182	−	4.32199i	0.767893	−	0.355265i
$149$	−6.86123	+	6.49930i	−0.562094	+	0.532444i	−0.915126	−	0.403168i	$-0.867909\pi$
$149$	−6.86123	+	6.49930i	−0.562094	+	0.532444i	0.353032	+	0.935611i	$0.385151\pi$
$150$	2.73022	−	4.02677i	0.222921	−	0.328784i
$151$	9.87239	+	18.6213i	0.803404	+	1.51538i	0.856124	+	0.516771i	$0.172866\pi$
$151$	9.87239	+	18.6213i	0.803404	+	1.51538i	−0.0527202	+	0.998609i	$0.516789\pi$
$152$	−0.0907743	+	0.171218i	−0.00736277	+	0.0138877i
$153$	1.34960	+	1.99051i	0.109108	+	0.160923i
$154$	−9.90165	−	2.17952i	−0.797898	−	0.175631i
$155$	−0.815672	+	2.93779i	−0.0655164	+	0.235969i
$156$	1.07495	+	2.69791i	0.0860645	+	0.216006i
$157$	8.58488	+	2.89258i	0.685148	+	0.230853i	0.640282	−	0.768140i	$-0.278817\pi$
$157$	8.58488	+	2.89258i	0.685148	+	0.230853i	0.0448658	+	0.998993i	$0.485714\pi$
$158$	0.239893	+	0.227238i	0.0190848	+	0.0180781i
$159$	−7.12762	+	1.56891i	−0.565257	+	0.124422i
$160$	0.0198865	−	0.366784i	0.00157216	−	0.0289968i
$161$	−3.14955	+	19.2114i	−0.248219	+	1.51407i
$162$	0.647386	−	0.762162i	0.0508635	−	0.0598811i
$163$	1.76458	−	4.42877i	0.138213	−	0.346888i	−0.843535	−	0.537074i	$-0.819530\pi$
$163$	1.76458	−	4.42877i	0.138213	−	0.346888i	0.981748	+	0.190186i	$0.0609090\pi$
$164$	−2.37619	−	1.80633i	−0.185549	−	0.141051i
$165$	1.30289	+	0.783923i	0.101430	+	0.0610283i
$166$	−0.488695	−	2.98091i	−0.0379301	−	0.231363i
$167$	18.0164	−	1.95941i	1.39415	−	0.151623i	0.619991	−	0.784609i	$-0.287136\pi$
$167$	18.0164	−	1.95941i	1.39415	−	0.151623i	0.774164	+	0.632986i	$0.218171\pi$
$168$	1.94982	−	1.48221i	0.150432	−	0.114355i
$169$	−1.22148	−	4.39936i	−0.0939597	−	0.338412i
$170$	−0.0478249	−	0.882078i	−0.00366800	−	0.0676523i
$171$	0.192657	+	0.0209527i	0.0147329	+	0.00160229i
$172$	5.09982	−	3.06846i	0.388858	−	0.233968i
$173$	−6.83970	−	8.05232i	−0.520013	−	0.612207i	0.437985	−	0.898982i	$-0.355692\pi$
$173$	−6.83970	−	8.05232i	−0.520013	−	0.612207i	−0.957998	+	0.286776i	$0.907417\pi$
$174$	5.98949	−	2.01810i	0.454062	−	0.152991i
$175$	−10.8144	−	5.00327i	−0.817492	−	0.378212i
$176$	−4.13954			−0.312029
$177$	−0.924060	+	7.62536i	−0.0694566	+	0.573157i
$178$	−0.375736			−0.0281626
$179$	−3.12097	−	1.44391i	−0.233272	−	0.107923i	0.299771	−	0.954011i	$-0.403090\pi$
$179$	−3.12097	−	1.44391i	−0.233272	−	0.107923i	−0.533043	+	0.846088i	$0.678952\pi$
$180$	−0.348095	+	0.117287i	−0.0259454	+	0.00874203i
$181$	−10.7481	−	12.6536i	−0.798897	−	0.940534i	0.200335	−	0.979727i	$-0.435797\pi$
$181$	−10.7481	−	12.6536i	−0.798897	−	0.940534i	−0.999232	+	0.0391936i	$0.987521\pi$
$182$	6.09482	−	3.66713i	0.451778	−	0.271826i
$183$	−4.40217	−	0.478765i	−0.325418	−	0.0353914i
$184$	0.430326	+	7.93689i	0.0317240	+	0.585115i
$185$	1.01150	+	3.64310i	0.0743670	+	0.267846i
$186$	−6.60787	+	5.02318i	−0.484513	+	0.368317i
$187$	−9.89680	+	1.07634i	−0.723725	+	0.0787099i
$188$	−1.11655	−	6.81066i	−0.0814329	−	0.496719i
$189$	−2.09864	−	1.26271i	−0.152654	−	0.0918488i
$190$	−0.0566696	−	0.0430791i	−0.00411124	−	0.00312528i
$191$	−1.19515	+	2.99961i	−0.0864783	+	0.217044i	−0.965855	−	0.259082i	$-0.916580\pi$
$191$	−1.19515	+	2.99961i	−0.0864783	+	0.217044i	0.879377	+	0.476126i	$0.157959\pi$
$192$	0.647386	−	0.762162i	0.0467211	−	0.0550043i
$193$	1.37044	−	8.35929i	0.0986461	−	0.601715i	−0.890523	−	0.454937i	$-0.849662\pi$
$193$	1.37044	−	8.35929i	0.0986461	−	0.601715i	0.989170	−	0.146777i	$-0.0468900\pi$
$194$	0.610005	−	11.2509i	0.0437958	−	0.807766i
$195$	−1.04183	+	0.229324i	−0.0746069	+	0.0164222i
$196$	0.726908	+	0.688564i	0.0519220	+	0.0491831i
$197$	−16.6380	−	5.60600i	−1.18541	−	0.399411i	−0.343564	−	0.939129i	$-0.611634\pi$
$197$	−16.6380	−	5.60600i	−1.18541	−	0.399411i	−0.841846	+	0.539718i	$0.818531\pi$
$198$	1.53220	+	3.84553i	0.108889	+	0.273290i
$199$	−5.37329	+	19.3528i	−0.380903	+	1.37189i	0.486239	+	0.873826i	$0.338368\pi$
$199$	−5.37329	+	19.3528i	−0.380903	+	1.37189i	−0.867142	+	0.498061i	$0.834045\pi$
$200$	−4.75133	−	1.04585i	−0.335970	−	0.0739526i
$201$	5.55354	+	8.19086i	0.391717	+	0.577739i
$202$	−3.10666	+	5.85978i	−0.218584	+	0.412293i
$203$	−7.25096	−	13.6768i	−0.508918	−	0.959921i
$204$	1.34960	−	1.99051i	0.0944907	−	0.139363i
$205$	0.795974	−	0.753987i	0.0555932	−	0.0526607i
$206$	3.51077	−	1.62426i	0.244607	−	0.113167i
$207$	7.21390	−	3.33751i	0.501401	−	0.231973i
$208$	2.10842	−	1.99720i	0.146192	−	0.138481i
$209$	−0.450192	+	0.663983i	−0.0311404	+	0.0459287i
$210$	0.421408	+	0.794860i	0.0290799	+	0.0548505i
$211$	−6.91905	+	13.0507i	−0.476327	+	0.898449i	0.522619	+	0.852566i	$0.324955\pi$
$211$	−6.91905	+	13.0507i	−0.476327	+	0.898449i	−0.998947	+	0.0458827i	$0.985390\pi$
$212$	4.09568	+	6.04068i	0.281293	+	0.414875i
$213$	−13.3435	−	2.93713i	−0.914284	−	0.201249i
$214$	−4.81722	+	17.3501i	−0.329299	+	1.18603i
$215$	0.809204	+	2.03095i	0.0551873	+	0.138510i
$216$	−0.947653	−	0.319302i	−0.0644796	−	0.0217257i
$217$	14.7592	+	13.9806i	1.00192	+	0.949067i
$218$	−2.64834	+	0.582944i	−0.179368	+	0.0394819i
$219$	0.0128516	−	0.237034i	0.000868430	−	0.0160172i
$220$	0.245997	−	1.50051i	0.0165851	−	0.101165i
$221$	4.52150	−	5.32312i	0.304149	−	0.358072i
$222$	−3.80989	+	9.56210i	−0.255703	+	0.641766i
$223$	18.7390	+	14.2450i	1.25486	+	0.953918i	0.999915	−	0.0130384i	$-0.00415038\pi$
$223$	18.7390	+	14.2450i	1.25486	+	0.953918i	0.254942	+	0.966956i	$0.417943\pi$
$224$	−2.09864	−	1.26271i	−0.140221	−	0.0843685i
$225$	0.787081	+	4.80098i	0.0524721	+	0.320066i
$226$	−1.59469	+	0.173433i	−0.106077	+	0.0115366i
$227$	12.2545	−	9.31563i	0.813360	−	0.618300i	−0.113572	−	0.993530i	$-0.536229\pi$
$227$	12.2545	−	9.31563i	0.813360	−	0.618300i	0.926932	+	0.375230i	$0.122436\pi$
$228$	−0.0518451	−	0.186729i	−0.00343353	−	0.0123664i
$229$	0.367045	+	6.76975i	0.0242550	+	0.447358i	0.985286	+	0.170916i	$0.0546726\pi$
$229$	0.367045	+	6.76975i	0.0242550	+	0.447358i	−0.961031	+	0.276442i	$0.910845\pi$
$230$	−2.90257	−	0.315673i	−0.191390	−	0.0208149i
$231$	8.68741	−	5.22704i	0.571589	−	0.343914i
$232$	−4.09170	−	4.81713i	−0.268634	−	0.316260i
$233$	12.0981	−	4.07632i	0.792572	−	0.267049i	0.106244	−	0.994340i	$-0.466118\pi$
$233$	12.0981	−	4.07632i	0.792572	−	0.267049i	0.686329	+	0.727291i	$0.259221\pi$
$234$	−2.63576	−	1.21943i	−0.172305	−	0.0797167i
$235$	2.53511			0.165372
$236$	7.42581	−	1.96401i	0.483379	−	0.127846i
$237$	−0.330433			−0.0214639
$238$	−5.34576	−	2.47321i	−0.346514	−	0.160314i
$239$	4.10813	−	1.38419i	0.265733	−	0.0895357i	−0.183281	−	0.983061i	$-0.558672\pi$
$239$	4.10813	−	1.38419i	0.265733	−	0.0895357i	0.449014	+	0.893525i	$0.351775\pi$
$240$	0.237800	+	0.279959i	0.0153499	+	0.0180713i
$241$	4.64903	−	2.79723i	0.299470	−	0.180185i	−0.357886	−	0.933765i	$-0.616502\pi$
$241$	4.64903	−	2.79723i	0.299470	−	0.180185i	0.657356	+	0.753580i	$0.271675\pi$
$242$	−6.09979	−	0.663392i	−0.392109	−	0.0426444i
$243$	0.0541389	+	0.998533i	0.00347301	+	0.0640559i
$244$	1.18465	+	4.26673i	0.0758395	+	0.273149i
$245$	−0.292790	+	0.222574i	−0.0187057	+	0.0142197i
$246$	2.96732	−	0.322715i	0.189189	−	0.0205756i
$247$	−0.0910523	−	0.555394i	−0.00579352	−	0.0353389i
$248$	7.11224	+	4.27929i	0.451628	+	0.271735i
$249$	2.40476	+	1.82805i	0.152395	+	0.115848i
$250$	1.34126	−	3.36630i	0.0848285	−	0.212904i
$251$	−6.28238	+	7.39620i	−0.396541	+	0.466844i	−0.923808	−	0.382856i	$-0.874941\pi$
$251$	−6.28238	+	7.39620i	−0.396541	+	0.466844i	0.527268	+	0.849699i	$0.323217\pi$
$252$	−0.396242	+	2.41697i	−0.0249609	+	0.152255i
$253$	−1.78135	+	32.8550i	−0.111992	+	2.06558i
$254$	−17.4926	+	3.85040i	−1.09758	+	0.241596i
$255$	0.641325	+	0.607495i	0.0401613	+	0.0380428i
$256$	−0.947653	−	0.319302i	−0.0592283	−	0.0199563i
$257$	2.45335	+	6.15745i	0.153036	+	0.384091i	0.985427	−	0.170097i	$-0.0544081\pi$
$257$	2.45335	+	6.15745i	0.153036	+	0.384091i	−0.832391	+	0.554188i	$0.813029\pi$
$258$	−1.59227	+	5.73483i	−0.0991303	+	0.357035i
$259$	24.6209	+	5.41948i	1.52987	+	0.336750i
$260$	0.598657	+	0.882953i	0.0371271	+	0.0547584i
$261$	−2.96050	+	5.58410i	−0.183250	+	0.345647i
$262$	3.30690	+	6.23747i	0.204301	+	0.385352i
$263$	0.471161	−	0.694911i	0.0290530	−	0.0428500i	−0.812885	−	0.582424i	$-0.802104\pi$
$263$	0.471161	−	0.694911i	0.0290530	−	0.0428500i	0.841938	+	0.539574i	$0.181415\pi$
$264$	3.00528	−	2.84676i	0.184962	−	0.175206i
$265$	−2.43304	+	1.12564i	−0.149460	+	0.0691477i
$266$	−0.430776	+	0.199298i	−0.0264125	+	0.0122197i
$267$	0.272783	−	0.258394i	0.0166940	−	0.0158134i
$268$	5.55354	−	8.19086i	0.339237	−	0.500337i
$269$	−9.13067	−	17.2223i	−0.556707	−	1.05006i	−0.988942	−	0.148300i	$-0.952620\pi$
$269$	−9.13067	−	17.2223i	−0.556707	−	1.05006i	0.432236	−	0.901761i	$-0.357725\pi$
$270$	0.172057	−	0.324534i	0.0104711	−	0.0197505i
$271$	6.34193	+	9.35364i	0.385245	+	0.568193i	0.970027	−	0.242997i	$-0.0781305\pi$
$271$	6.34193	+	9.35364i	0.385245	+	0.568193i	−0.584782	+	0.811190i	$0.698820\pi$
$272$	−2.34867	−	0.516982i	−0.142409	−	0.0313466i
$273$	−1.90293	+	6.85373i	−0.115170	+	0.414806i
$274$	−4.20306	−	10.5489i	−0.253916	−	0.637282i
$275$	−19.0849	−	6.43046i	−1.15086	−	0.387771i
$276$	−5.77061	−	5.46621i	−0.347350	−	0.329027i
$277$	14.9656	−	3.29417i	0.899194	−	0.197927i	0.258761	−	0.965941i	$-0.416686\pi$
$277$	14.9656	−	3.29417i	0.899194	−	0.197927i	0.640433	+	0.768014i	$0.278755\pi$
$278$	0.194452	−	3.58645i	0.0116624	−	0.215101i
$279$	1.34285	−	8.19104i	0.0803944	−	0.490384i
$280$	0.582427	−	0.685686i	0.0348067	−	0.0409776i
$281$	2.68192	−	6.73110i	0.159990	−	0.401544i	−0.827027	−	0.562162i	$-0.809970\pi$
$281$	2.68192	−	6.73110i	0.159990	−	0.401544i	0.987017	+	0.160618i	$0.0513489\pi$
$282$	5.49430	+	4.17666i	0.327181	+	0.248716i
$283$	−25.8713	−	15.5663i	−1.53789	−	0.925319i	−0.996415	−	0.0846035i	$-0.973038\pi$
$283$	−25.8713	−	15.5663i	−1.53789	−	0.925319i	−0.541477	−	0.840715i	$-0.682135\pi$
$284$	2.21042	+	13.4830i	0.131164	+	0.800068i
$285$	0.0707673	−	0.00769641i	0.00419189	−	0.000455896i
$286$	9.57057	−	7.27536i	0.565920	−	0.430201i
$287$	−1.95577	−	7.04404i	−0.115445	−	0.415796i
$288$	0.0541389	+	0.998533i	0.00319017	+	0.0588391i
$289$	11.1507	+	1.21271i	0.655925	+	0.0713361i
$290$	1.98928	−	1.19691i	0.116815	−	0.0702851i
$291$	7.29436	+	8.58759i	0.427603	+	0.503413i
$292$	−0.224955	+	0.0757963i	−0.0131645	+	0.00443564i
$293$	−13.4668	−	6.23041i	−0.786739	−	0.363984i	−0.0149708	−	0.999888i	$-0.504766\pi$
$293$	−13.4668	−	6.23041i	−0.786739	−	0.363984i	−0.771769	+	0.635904i	$0.780628\pi$
$294$	−1.00126			−0.0583945
$295$	0.270633	+	2.80845i	0.0157569	+	0.163514i
$296$	10.2932			0.598278
$297$	−3.75694	−	1.73815i	−0.218000	−	0.100857i
$298$	−8.95607	+	3.01765i	−0.518811	+	0.174808i
$299$	−14.9442	−	17.5937i	−0.864247	−	1.01747i
$300$	4.16867	−	2.50821i	0.240678	−	0.144811i
$301$	14.4918	+	1.57608i	0.835295	+	0.0908438i
$302$	1.14106	+	21.0455i	0.0656604	+	1.21103i
$303$	−1.77435	−	6.39062i	−0.101934	−	0.367132i
$304$	−0.154277	+	0.117279i	−0.00884841	+	0.00672639i
$305$	−1.61702	+	0.175861i	−0.0925902	+	0.0100698i
$306$	0.389069	+	2.37322i	0.0222416	+	0.135668i
$307$	−22.6863	−	13.6499i	−1.29478	−	0.779040i	−0.309645	−	0.950852i	$-0.600210\pi$
$307$	−22.6863	−	13.6499i	−1.29478	−	0.779040i	−0.985130	+	0.171812i	$0.945038\pi$
$308$	−8.07134	−	6.13567i	−0.459907	−	0.349612i
$309$	−1.43180	+	3.59356i	−0.0814525	+	0.204430i
$310$	−1.97383	+	2.32377i	−0.112106	+	0.131981i
$311$	4.27135	−	26.0541i	0.242206	−	1.47739i	−0.533234	−	0.845968i	$-0.679023\pi$
$311$	4.27135	−	26.0541i	0.242206	−	1.47739i	0.775440	−	0.631422i	$-0.217528\pi$
$312$	−0.157229	+	2.89991i	−0.00890132	+	0.164175i
$313$	−11.5555	+	2.54356i	−0.653157	+	0.143771i	−0.529174	−	0.848514i	$-0.677498\pi$
$313$	−11.5555	+	2.54356i	−0.653157	+	0.143771i	−0.123983	+	0.992284i	$0.539567\pi$
$314$	6.57686	+	6.22993i	0.371154	+	0.351576i
$315$	−0.852565	−	0.287262i	−0.0480366	−	0.0161854i
$316$	0.122306	+	0.306964i	0.00688024	+	0.0172681i
$317$	3.40937	−	12.2794i	0.191489	−	0.689682i	−0.803985	−	0.594650i	$-0.797291\pi$
$317$	3.40937	−	12.2794i	0.191489	−	0.689682i	0.995474	−	0.0950324i	$-0.0302955\pi$
$318$	−7.12762	−	1.56891i	−0.399697	−	0.0879799i
$319$	−14.6825	−	21.6551i	−0.822062	−	1.21245i
$320$	0.172057	−	0.324534i	0.00961828	−	0.0181420i
$321$	−8.43435	−	15.9089i	−0.470760	−	0.887947i
$322$	−10.9251	+	16.1133i	−0.608832	+	0.897960i
$323$	−0.338352	+	0.320504i	−0.0188264	+	0.0178333i
$324$	0.907575	−	0.419889i	0.0504209	−	0.0233272i
$325$	12.8231	−	5.93262i	0.711300	−	0.329083i
$326$	3.46108	−	3.27851i	0.191692	−	0.181580i
$327$	1.52179	−	2.24448i	0.0841553	−	0.124120i
$328$	−1.39811	−	2.63712i	−0.0771978	−	0.145611i
$329$	7.91778	−	14.9345i	0.436521	−	0.823367i
$330$	0.853310	+	1.25854i	0.0469732	+	0.0692803i
$331$	27.8554	+	6.13143i	1.53107	+	0.337014i	0.899018	−	0.437913i	$-0.144282\pi$
$331$	27.8554	+	6.13143i	1.53107	+	0.337014i	0.632051	+	0.774926i	$0.282213\pi$
$332$	0.808123	−	2.91060i	0.0443515	−	0.159740i
$333$	−3.80989	−	9.56210i	−0.208781	−	0.524000i
$334$	17.1740	+	5.78660i	0.939720	+	0.316629i
$335$	2.63903	+	2.49982i	0.144186	+	0.136580i
$336$	2.39197	−	0.526513i	0.130493	−	0.0287236i
$337$	0.125730	−	2.31895i	0.00684894	−	0.126321i	−0.993109	−	0.117191i	$-0.962611\pi$
$337$	0.125730	−	2.31895i	0.00684894	−	0.126321i	0.999958	−	0.00913011i	$-0.00290624\pi$
$338$	0.738661	−	4.50563i	0.0401779	−	0.245074i
$339$	1.03847	−	1.22258i	0.0564019	−	0.0664014i
$340$	0.326970	−	0.820633i	0.0177324	−	0.0445051i
$341$	27.3535	+	20.7936i	1.48128	+	1.12604i
$342$	0.166053	+	0.0999107i	0.00897912	+	0.00540255i
$343$	3.17043	+	19.3388i	0.171187	+	1.04420i
$344$	5.91688	−	0.643500i	0.319017	−	0.0346952i
$345$	2.32434	−	1.76692i	0.125138	−	0.0951275i
$346$	−2.82646	−	10.1800i	−0.151952	−	0.547280i
$347$	−0.888701	−	16.3911i	−0.0477079	−	0.879921i	−0.920238	−	0.391360i	$-0.872005\pi$
$347$	−0.888701	−	16.3911i	−0.0477079	−	0.879921i	0.872530	−	0.488561i	$-0.162478\pi$
$348$	6.28329	+	0.683349i	0.336820	+	0.0366314i
$349$	30.2621	−	18.2081i	1.61989	−	0.974656i	0.641699	−	0.766957i	$-0.278230\pi$
$349$	30.2621	−	18.2081i	1.61989	−	0.974656i	0.978193	−	0.207700i	$-0.0665977\pi$
$350$	−7.71406	−	9.08170i	−0.412334	−	0.485437i
$351$	2.75215	−	0.927307i	0.146899	−	0.0494960i
$352$	−3.75694	−	1.73815i	−0.200246	−	0.0926435i
$353$	−24.5155			−1.30483			−0.652413	−	0.757863i	$-0.726243\pi$
$353$	−24.5155			−1.30483			−0.652413	+	0.757863i	$0.726243\pi$
$354$	−4.04046	+	6.53259i	−0.214748	+	0.347203i
$355$	−5.01872			−0.266366
$356$	−0.341009	−	0.157768i	−0.0180734	−	0.00836167i
$357$	5.58182	−	1.88073i	0.295421	−	0.0995390i
$358$	−2.22623	−	2.62092i	−0.117660	−	0.138520i
$359$	−3.49704	+	2.10410i	−0.184567	+	0.111050i	−0.604838	−	0.796348i	$-0.706762\pi$
$359$	−3.49704	+	2.10410i	−0.184567	+	0.111050i	0.420272	+	0.907398i	$0.361935\pi$
$360$	−0.365169	−	0.0397146i	−0.0192461	−	0.00209314i
$361$	−1.02661	−	18.9346i	−0.0540319	−	0.996560i
$362$	−4.44157	−	15.9971i	−0.233444	−	0.840788i
$363$	4.88463	−	3.71320i	0.256377	−	0.194893i
$364$	7.07130	−	0.769050i	0.370637	−	0.0403092i
$365$	−0.0141067	−	0.0860470i	−0.000738378	−	0.00450391i
$366$	−3.79428	−	2.28294i	−0.198330	−	0.119331i
$367$	−7.75831	−	5.89771i	−0.404980	−	0.307858i	0.382780	−	0.923839i	$-0.374967\pi$
$367$	−7.75831	−	5.89771i	−0.404980	−	0.307858i	−0.787761	+	0.615981i	$0.788760\pi$
$368$	−2.94206	+	7.38401i	−0.153365	+	0.384918i
$369$	−1.93233	+	2.27491i	−0.100593	+	0.118427i
$370$	−0.611683	+	3.73110i	−0.0317999	+	0.193971i
$371$	−0.967739	+	17.8489i	−0.0502425	+	0.926668i
$372$	−8.10632	+	1.78434i	−0.420293	+	0.0925135i
$373$	−25.8407	−	24.4776i	−1.33798	−	1.26740i	−0.936110	−	0.351708i	$-0.885601\pi$
$373$	−25.8407	−	24.4776i	−1.33798	−	1.26740i	−0.401873	−	0.915696i	$-0.631641\pi$
$374$	−9.43403	−	3.17870i	−0.487822	−	0.164366i
$375$	1.34126	+	3.36630i	0.0692622	+	0.173835i
$376$	1.84637	−	6.65002i	0.0952192	−	0.342949i
$377$	17.9262	+	3.94586i	0.923248	+	0.203222i
$378$	−1.37448	−	2.02720i	−0.0706955	−	0.104268i
$379$	4.21849	−	7.95691i	0.216689	−	0.408719i	−0.751208	−	0.660065i	$-0.770529\pi$
$379$	4.21849	−	7.95691i	0.216689	−	0.408719i	0.967897	+	0.251346i	$0.0808733\pi$
$380$	−0.0333435	−	0.0628924i	−0.00171048	−	0.00322631i
$381$	10.0516	−	14.8250i	0.514959	−	0.759507i
$382$	−2.34420	+	2.22054i	−0.119940	+	0.113613i
$383$	7.52902	−	3.48330i	0.384715	−	0.177988i	−0.217992	−	0.975951i	$-0.569951\pi$
$383$	7.52902	−	3.48330i	0.384715	−	0.177988i	0.602707	+	0.797962i	$0.294089\pi$
$384$	0.907575	−	0.419889i	0.0463145	−	0.0214274i
$385$	2.70373	−	2.56111i	0.137795	−	0.130526i
$386$	4.75375	−	7.01125i	0.241959	−	0.356863i
$387$	−2.78786	−	5.25846i	−0.141715	−	0.267303i
$388$	5.27775	−	9.95489i	0.267937	−	0.505383i
$389$	−17.6330	−	26.0067i	−0.894028	−	1.31859i	−0.947411	−	0.320019i	$-0.896311\pi$
$389$	−17.6330	−	26.0067i	−0.894028	−	1.31859i	0.0533832	−	0.998574i	$-0.483000\pi$
$390$	−1.04183	−	0.229324i	−0.0527550	−	0.0116123i
$391$	−5.11392	+	18.4187i	−0.258622	+	0.931472i
$392$	0.370603	+	0.930144i	0.0187183	+	0.0469794i
$393$	−6.69030	−	2.25422i	−0.337481	−	0.113711i
$394$	−12.7464	−	12.0740i	−0.642152	−	0.608279i
$395$	−0.118538	+	0.0260921i	−0.00596428	+	0.00131284i
$396$	−0.224110	+	4.13346i	−0.0112619	+	0.207714i
$397$	0.0934388	−	0.569951i	0.00468956	−	0.0286050i	−0.984378	−	0.176068i	$-0.943662\pi$
$397$	0.0934388	−	0.569951i	0.00468956	−	0.0286050i	0.989068	+	0.147462i	$0.0471106\pi$
$398$	−13.0027	+	15.3080i	−0.651767	+	0.767320i
$399$	0.175684	−	0.440934i	0.00879520	−	0.0220743i
$400$	−3.87305	−	2.94422i	−0.193653	−	0.147211i
$401$	18.6402	+	11.2155i	0.930849	+	0.560073i	0.898293	−	0.439397i	$-0.144808\pi$
$401$	18.6402	+	11.2155i	0.930849	+	0.560073i	0.0325559	+	0.999470i	$0.489635\pi$
$402$	1.60101	+	9.76570i	0.0798509	+	0.487069i
$403$	−23.9644	+	2.60629i	−1.19375	+	0.129828i
$404$	−5.27999	+	4.01374i	−0.262689	+	0.199691i
$405$	0.0982692	+	0.353934i	0.00488304	+	0.0175871i
$406$	−0.838070	−	15.4573i	−0.0415927	−	0.767133i
$407$	42.3591	+	4.60683i	2.09966	+	0.228352i
$408$	2.06065	−	1.23985i	0.102018	−	0.0613819i
$409$	−22.4027	−	26.3745i	−1.10774	−	1.30414i	−0.948458	−	0.316903i	$-0.897357\pi$
$409$	−22.4027	−	26.3745i	−1.10774	−	1.30414i	−0.159285	−	0.987233i	$-0.550919\pi$
$410$	1.03900	−	0.350079i	0.0513124	−	0.0172892i
$411$	10.3059	+	4.76801i	0.508351	+	0.235188i
$412$	3.86830			0.190577
$413$	17.3901	+	7.17718i	0.855709	+	0.353166i
$414$	7.94854			0.390650
$415$	1.00702	+	0.465897i	0.0494327	+	0.0228700i
$416$	2.75215	−	0.927307i	0.134935	−	0.0454650i
$417$	2.32523	+	2.73747i	0.113867	+	0.134055i
$418$	−0.687382	+	0.413584i	−0.0336210	+	0.0202291i
$419$	−29.6842	−	3.22835i	−1.45017	−	0.157715i	−0.651117	−	0.758978i	$-0.725699\pi$
$419$	−29.6842	−	3.22835i	−1.45017	−	0.157715i	−0.799052	+	0.601262i	$0.794665\pi$
$420$	0.0487066	+	0.898340i	0.00237664	+	0.0438345i
$421$	10.0263	+	36.1115i	0.488652	+	1.75997i	0.636828	+	0.771006i	$0.280246\pi$
$421$	10.0263	+	36.1115i	0.488652	+	1.75997i	−0.148176	+	0.988961i	$0.547340\pi$
$422$	−11.7594	+	8.93928i	−0.572440	+	0.435157i
$423$	−6.86113	+	0.746192i	−0.333599	+	0.0362811i
$424$	1.18072	+	7.20210i	0.0573411	+	0.349765i
$425$	−10.0252	−	6.03198i	−0.486295	−	0.292594i
$426$	−10.8770	−	8.26848i	−0.526992	−	0.400609i
$427$	−4.01434	+	10.0752i	−0.194268	+	0.487575i
$428$	−11.6571	+	13.7238i	−0.563467	+	0.663365i
$429$	−1.94493	+	11.8636i	−0.0939022	+	0.572778i
$430$	−0.118360	+	2.18302i	−0.00570781	+	0.105274i
$431$	22.9866	−	5.05972i	1.10722	−	0.243718i	0.376517	−	0.926410i	$-0.377122\pi$
$431$	22.9866	−	5.05972i	1.10722	−	0.243718i	0.730707	+	0.682692i	$0.239191\pi$
$432$	−0.725995	−	0.687699i	−0.0349295	−	0.0330870i
$433$	3.58845	+	1.20909i	0.172450	+	0.0581052i	0.404202	−	0.914670i	$-0.367549\pi$
$433$	3.58845	+	1.20909i	0.172450	+	0.0581052i	−0.231752	+	0.972775i	$0.574446\pi$
$434$	7.52475	+	18.8857i	0.361199	+	0.906542i
$435$	−0.621095	+	2.23698i	−0.0297792	+	0.107255i
$436$	−2.64834	−	0.582944i	−0.126833	−	0.0279179i
$437$	0.864437	+	1.27495i	0.0413516	+	0.0609891i
$438$	0.111192	−	0.209730i	0.00531294	−	0.0100213i
$439$	1.41841	+	2.67541i	0.0676971	+	0.127690i	0.915051	−	0.403339i	$-0.132150\pi$
$439$	1.41841	+	2.67541i	0.0676971	+	0.127690i	−0.847354	+	0.531029i	$0.821806\pi$
$440$	0.853310	−	1.25854i	0.0406800	−	0.0599985i
$441$	0.726908	−	0.688564i	0.0346147	−	0.0327887i
$442$	6.33872	−	2.93260i	0.301502	−	0.139490i
$443$	−11.8329	+	5.47450i	−0.562200	+	0.260101i	−0.680341	−	0.732895i	$-0.738168\pi$
$443$	−11.8329	+	5.47450i	−0.562200	+	0.260101i	0.118142	+	0.992997i	$0.462306\pi$
$444$	−7.47279	+	7.07860i	−0.354643	+	0.335935i
$445$	0.0774531	−	0.114235i	0.00367163	−	0.00541525i
$446$	11.0257	+	20.7967i	0.522084	+	0.984755i
$447$	4.42683	−	8.34989i	0.209382	−	0.394936i
$448$	−1.37448	−	2.02720i	−0.0649380	−	0.0957764i
$449$	3.68001	+	0.810031i	0.173670	+	0.0382277i	0.300954	−	0.953639i	$-0.402695\pi$
$449$	3.68001	+	0.810031i	0.173670	+	0.0382277i	−0.127284	+	0.991866i	$0.540626\pi$
$450$	−1.30155	+	4.68774i	−0.0613554	+	0.220982i
$451$	−4.57333	−	11.4782i	−0.215350	−	0.540487i
$452$	−1.52013	−	0.512190i	−0.0715007	−	0.0240914i
$453$	−15.3014	−	14.4943i	−0.718923	−	0.681000i
$454$	15.0334	−	3.30910i	0.705553	−	0.155304i
$455$	−0.141452	+	2.60893i	−0.00663138	+	0.122309i
$456$	0.0313522	−	0.191240i	0.00146820	−	0.00895564i
$457$	−21.9711	+	25.8663i	−1.02776	+	1.20998i	−0.0503302	+	0.998733i	$0.516027\pi$
$457$	−21.9711	+	25.8663i	−1.02776	+	1.20998i	−0.977433	+	0.211244i	$0.932249\pi$
$458$	−2.50942	+	6.29818i	−0.117258	+	0.294294i
$459$	−1.91452	−	1.45538i	−0.0893622	−	0.0679314i
$460$	−2.50175	−	1.50525i	−0.116645	−	0.0701828i
$461$	5.02308	+	30.6394i	0.233948	+	1.42702i	0.798685	+	0.601749i	$0.205529\pi$
$461$	5.02308	+	30.6394i	0.233948	+	1.42702i	−0.564737	+	0.825271i	$0.691022\pi$
$462$	10.0793	−	1.09619i	0.468929	−	0.0509991i
$463$	−1.10076	+	0.836777i	−0.0511567	+	0.0388883i	−0.630440	−	0.776238i	$-0.717126\pi$
$463$	−1.10076	+	0.836777i	−0.0511567	+	0.0388883i	0.579283	+	0.815126i	$0.303332\pi$
$464$	−1.69087	−	6.08997i	−0.0784967	−	0.282720i
$465$	−0.165065	−	3.04445i	−0.00765471	−	0.141183i
$466$	12.6915	+	1.38029i	0.587924	+	0.0639406i
$467$	28.1027	−	16.9088i	1.30044	−	0.782447i	0.314451	−	0.949274i	$-0.398180\pi$
$467$	28.1027	−	16.9088i	1.30044	−	0.782447i	0.985986	+	0.166827i	$0.0533521\pi$
$468$	−1.88012	−	2.21345i	−0.0869087	−	0.102317i
$469$	22.9690	−	7.73916i	1.06061	−	0.357361i
$470$	2.30080	+	1.06446i	0.106128	+	0.0491001i
$471$	−9.05909			−0.417421
$472$	7.56415	+	1.33553i	0.348168	+	0.0614729i
$473$	24.6376			1.13284
$474$	−0.299893	−	0.138745i	−0.0137745	−	0.00637278i
$475$	−0.893464	+	0.301043i	−0.0409949	+	0.0138128i
$476$	−3.81320	−	4.48925i	−0.174778	−	0.205764i
$477$	6.25355	−	3.76264i	0.286331	−	0.172279i
$478$	4.30964	+	0.468702i	0.197118	+	0.0214379i
$479$	1.60762	+	29.6508i	0.0734541	+	1.35478i	0.770356	+	0.637615i	$0.220079\pi$
$479$	1.60762	+	29.6508i	0.0734541	+	1.35478i	−0.696901	+	0.717167i	$0.745438\pi$
$480$	0.0982692	+	0.353934i	0.00448536	+	0.0161548i
$481$	−23.7977	+	18.0905i	−1.08508	+	0.824858i
$482$	5.39387	−	0.586619i	0.245684	−	0.0267198i
$483$	−3.14955	−	19.2114i	−0.143309	−	0.874148i
$484$	−5.25747	−	3.16331i	−0.238976	−	0.143787i
$485$	3.29485	+	2.50468i	0.149611	+	0.113732i
$486$	−0.370138	+	0.928977i	−0.0167898	+	0.0421392i
$487$	9.10960	−	10.7246i	0.412795	−	0.485980i	−0.515992	−	0.856593i	$-0.672577\pi$
$487$	9.10960	−	10.7246i	0.412795	−	0.485980i	0.928787	+	0.370613i	$0.120852\pi$
$488$	−0.716392	+	4.36980i	−0.0324295	+	0.197811i
$489$	−0.258100	+	4.76037i	−0.0116717	+	0.215271i
$490$	−0.359186	+	0.0790627i	−0.0162264	+	0.00357169i
$491$	−19.8637	−	18.8159i	−0.896438	−	0.849151i	0.0927672	−	0.995688i	$-0.470429\pi$
$491$	−19.8637	−	18.8159i	−0.896438	−	0.849151i	−0.989205	+	0.146537i	$0.953187\pi$
$492$	2.82857	+	0.953055i	0.127522	+	0.0429671i
$493$	−5.62602	−	14.1202i	−0.253383	−	0.635943i
$494$	0.150567	−	0.542294i	0.00677434	−	0.0243990i
$495$	−1.48500	−	0.326872i	−0.0667456	−	0.0146918i
$496$	4.65807	+	6.87013i	0.209153	+	0.308478i
$497$	−15.6747	+	29.5657i	−0.703108	+	1.32620i
$498$	1.41492	+	2.66883i	0.0634042	+	0.119593i
$499$	−24.5362	+	36.1882i	−1.09839	+	1.62001i	−0.379009	+	0.925393i	$0.623735\pi$
$499$	−24.5362	+	36.1882i	−1.09839	+	1.62001i	−0.719383	+	0.694614i	$0.755575\pi$
$500$	2.63077	−	2.49199i	0.117651	−	0.111445i
$501$	−16.4477	+	7.60952i	−0.734829	+	0.339968i
$502$	−8.80732	+	4.07470i	−0.393090	+	0.181863i
$503$	−9.70271	+	9.19089i	−0.432622	+	0.409802i	−0.872776	−	0.488121i	$-0.837683\pi$
$503$	−9.70271	+	9.19089i	−0.432622	+	0.409802i	0.440154	+	0.897922i	$0.354924\pi$
$504$	−1.37448	+	2.02720i	−0.0612241	+	0.0902988i
$505$	−1.14115	−	2.15243i	−0.0507804	−	0.0957819i
$506$	−15.4122	+	29.0704i	−0.685155	+	1.29234i
$507$	2.56226	+	3.77905i	0.113794	+	0.167833i
$508$	−17.4926	−	3.85040i	−0.776107	−	0.170834i
$509$	−8.99133	+	32.3838i	−0.398534	+	1.43539i	0.443651	+	0.896200i	$0.353683\pi$
$509$	−8.99133	+	32.3838i	−0.398534	+	1.43539i	−0.842185	+	0.539189i	$0.818731\pi$
$510$	0.326970	+	0.820633i	0.0144785	+	0.0363382i
$511$	−0.550968	−	0.185643i	−0.0243734	−	0.00821236i
$512$	−0.725995	−	0.687699i	−0.0320848	−	0.0303923i
$513$	−0.189262	+	0.0416598i	−0.00835613	+	0.00183932i
$514$	−0.358844	+	6.61848i	−0.0158279	+	0.291929i
$515$	−0.229878	+	1.40220i	−0.0101296	+	0.0617881i
$516$	−3.85310	+	4.53622i	−0.169623	+	0.199696i
$517$	10.5746	−	26.5403i	0.465071	−	1.16724i
$518$	20.0698	+	15.2567i	0.881816	+	0.670339i
$519$	9.05278	+	5.44688i	0.397373	+	0.239091i
$520$	0.172584	+	1.05272i	0.00756831	+	0.0461646i
$521$	−9.27431	+	1.00864i	−0.406315	+	0.0441894i	−0.308995	−	0.951064i	$-0.599993\pi$
$521$	−9.27431	+	1.00864i	−0.406315	+	0.0441894i	−0.0973201	+	0.995253i	$0.531027\pi$
$522$	−5.03158	+	3.82491i	−0.220226	+	0.167412i
$523$	−4.00359	−	14.4196i	−0.175065	−	0.630526i	−0.998047	−	0.0624596i	$-0.980106\pi$
$523$	−4.00359	−	14.4196i	−0.175065	−	0.630526i	0.822983	−	0.568066i	$-0.192308\pi$
$524$	0.382213	+	7.04950i	0.0166971	+	0.307959i
$525$	11.8459	+	1.28831i	0.516995	+	0.0562266i
$526$	0.719400	−	0.432848i	0.0313673	−	0.0188731i
$527$	12.9228	+	15.2139i	0.562928	+	0.662730i
$528$	3.92284	−	1.32176i	0.170720	−	0.0575222i
$529$	36.4658	+	16.8709i	1.58547	+	0.733516i
$530$	−2.68081			−0.116447
$531$	−1.55910	−	7.52125i	−0.0676592	−	0.326394i
$532$	−0.474644			−0.0205784
$533$	7.86724	+	3.63977i	0.340768	+	0.157656i
$534$	0.356068	−	0.119973i	0.0154086	−	0.00519175i
$535$	−4.28192	−	5.04106i	−0.185123	−	0.217944i
$536$	8.47951	−	5.10195i	0.366259	−	0.220371i
$537$	3.41864	+	0.371799i	0.147525	+	0.0160443i
$538$	−1.05533	−	19.4644i	−0.0454984	−	0.839169i
$539$	1.10883	+	3.99366i	0.0477609	+	0.172019i
$540$	0.292423	−	0.222294i	0.0125839	−	0.00956602i
$541$	−5.98677	+	0.651100i	−0.257391	+	0.0279930i	−0.235905	−	0.971776i	$-0.575805\pi$
$541$	−5.98677	+	0.651100i	−0.257391	+	0.0279930i	−0.0214864	+	0.999769i	$0.506840\pi$
$542$	1.82828	+	11.1520i	0.0785316	+	0.479021i
$543$	14.2257	+	8.55934i	0.610485	+	0.367317i
$544$	−1.91452	−	1.45538i	−0.0820844	−	0.0623990i
$545$	0.368689	−	0.925338i	0.0157929	−	0.0396371i
$546$	−4.60486	+	5.42126i	−0.197070	+	0.232008i
$547$	−2.66041	+	16.2278i	−0.113751	+	0.693851i	0.866958	+	0.498380i	$0.166072\pi$
$547$	−2.66041	+	16.2278i	−0.113751	+	0.693851i	−0.980710	+	0.195471i	$0.937377\pi$
$548$	0.614769	−	11.3387i	0.0262616	−	0.484367i
$549$	4.32461	−	0.951918i	0.184570	−	0.0406269i
$550$	−14.6209	−	13.8497i	−0.623439	−	0.590552i
$551$	−1.16072	−	0.391093i	−0.0494484	−	0.0166611i
$552$	−2.94206	−	7.38401i	−0.125222	−	0.314284i
$553$	−0.216513	+	0.779808i	−0.00920705	+	0.0331608i
$554$	14.9656	+	3.29417i	0.635826	+	0.139956i
$555$	−2.12180	−	3.12942i	−0.0900653	−	0.132836i
$556$	1.68239	−	3.17333i	0.0713493	−	0.134579i
$557$	−0.242884	−	0.458128i	−0.0102913	−	0.0194115i	0.878313	−	0.478086i	$-0.158669\pi$
$557$	−0.242884	−	0.458128i	−0.0102913	−	0.0194115i	−0.888604	+	0.458674i	$0.848324\pi$
$558$	4.65807	−	6.87013i	0.197192	−	0.290836i
$559$	−12.5488	+	11.8869i	−0.530758	+	0.502761i
$560$	0.816508	−	0.377757i	0.0345038	−	0.0159631i
$561$	9.03505	−	4.18006i	0.381460	−	0.176482i
$562$	5.26036	−	4.98288i	0.221895	−	0.210190i
$563$	0.0812917	−	0.119896i	0.00342604	−	0.00505302i	−0.825972	−	0.563711i	$-0.809373\pi$
$563$	0.0812917	−	0.119896i	0.00342604	−	0.00505302i	0.829398	+	0.558658i	$0.188684\pi$
$564$	3.23276	+	6.09763i	0.136124	+	0.256757i
$565$	0.275996	−	0.520583i	0.0116112	−	0.0219011i
$566$	−16.9441	−	24.9907i	−0.712213	−	1.05044i
$567$	2.39197	+	0.526513i	0.100453	+	0.0221115i
$568$	−3.65523	+	13.1650i	−0.153370	+	0.552389i
$569$	1.62064	+	4.06751i	0.0679409	+	0.170519i	0.959026	−	0.283317i	$-0.0914347\pi$
$569$	1.62064	+	4.06751i	0.0679409	+	0.170519i	−0.891086	+	0.453835i	$0.850055\pi$
$570$	0.0674583	+	0.0227293i	0.00282552	+	0.000952028i
$571$	−6.72442	−	6.36971i	−0.281408	−	0.266564i	0.533956	−	0.845512i	$-0.320705\pi$
$571$	−6.72442	−	6.36971i	−0.281408	−	0.266564i	−0.815364	+	0.578948i	$0.803463\pi$
$572$	11.7409	−	2.58436i	0.490910	−	0.108057i
$573$	0.174811	−	3.22421i	0.00730285	−	0.134693i
$574$	1.18271	−	7.21420i	0.0493653	−	0.301115i
$575$	−25.0346	+	29.4730i	−1.04401	+	1.22911i
$576$	−0.370138	+	0.928977i	−0.0154224	+	0.0387074i
$577$	12.9406	+	9.83715i	0.538722	+	0.409526i	0.838842	−	0.544376i	$-0.183233\pi$
$577$	12.9406	+	9.83715i	0.538722	+	0.409526i	−0.300119	+	0.953902i	$0.597026\pi$
$578$	9.61092	+	5.78270i	0.399761	+	0.240528i
$579$	1.37044	+	8.35929i	0.0569533	+	0.347400i
$580$	2.30800	−	0.251010i	0.0958343	−	0.0104226i
$581$	5.88982	−	4.47732i	0.244351	−	0.185751i
$582$	3.01435	+	10.8567i	0.124949	+	0.450025i
$583$	1.63561	+	30.1670i	0.0677400	+	1.24939i
$584$	−0.235990	−	0.0256655i	−0.00976534	−	0.00106204i
$585$	0.914068	−	0.549977i	0.0377921	−	0.0227387i
$586$	−9.60606	−	11.3091i	−0.396823	−	0.467176i
$587$	40.6131	−	13.6842i	1.67628	−	0.564806i	0.689138	−	0.724630i	$-0.257989\pi$
$587$	40.6131	−	13.6842i	1.67628	−	0.564806i	0.987146	+	0.159824i	$0.0510927\pi$
$588$	−0.908716	−	0.420417i	−0.0374748	−	0.0173377i
$589$	1.60856			0.0662794
$590$	−0.933618	+	2.66252i	−0.0384364	+	0.109614i
$591$	17.5571			0.722202
$592$	9.34182	+	4.32199i	0.383946	+	0.177632i
$593$	−41.3738	+	13.9405i	−1.69902	+	0.572467i	−0.991016	−	0.133742i	$-0.957301\pi$
$593$	−41.3738	+	13.9405i	−1.69902	+	0.572467i	−0.708004	+	0.706208i	$0.750404\pi$
$594$	−2.67988	−	3.15500i	−0.109957	−	0.129451i
$595$	1.85388	−	1.11545i	0.0760019	−	0.0457288i
$596$	−9.39539	−	1.02181i	−0.384850	−	0.0418550i
$597$	−1.08738	−	20.0555i	−0.0445034	−	0.820816i
$598$	−6.17561	−	22.2425i	−0.252539	−	0.909565i
$599$	−30.1356	+	22.9085i	−1.23131	+	0.936017i	−0.999326	−	0.0367029i	$-0.988314\pi$
$599$	−30.1356	+	22.9085i	−1.23131	+	0.936017i	−0.231983	+	0.972720i	$0.574521\pi$
$600$	4.83655	−	0.526007i	0.197452	−	0.0214741i
$601$	−5.30841	−	32.3799i	−0.216535	−	1.32080i	−0.841545	−	0.540187i	$-0.818354\pi$
$601$	−5.30841	−	32.3799i	−0.216535	−	1.32080i	0.625010	−	0.780616i	$-0.285095\pi$
$602$	12.4906	+	7.51537i	0.509081	+	0.306304i
$603$	−7.87819	−	5.98884i	−0.320825	−	0.243885i
$604$	−7.80120	+	19.5795i	−0.317426	+	0.796680i
$605$	1.45908	−	1.71776i	0.0593201	−	0.0698370i
$606$	1.07300	−	6.54500i	0.0435876	−	0.265873i
$607$	−0.0705954	+	1.30206i	−0.00286538	+	0.0528488i	−0.999616	−	0.0276955i	$-0.991183\pi$
$607$	−0.0705954	+	1.30206i	−0.00286538	+	0.0528488i	0.996751	+	0.0805444i	$0.0256659\pi$
$608$	−0.189262	+	0.0416598i	−0.00767560	+	0.00168953i
$609$	11.2384	+	10.6456i	0.455403	+	0.431381i
$610$	−1.54141	−	0.519361i	−0.0624098	−	0.0210283i
$611$	7.41882	+	18.6198i	0.300133	+	0.753278i
$612$	−0.643378	+	2.31724i	−0.0260070	+	0.0936688i
$613$	25.8429	+	5.68845i	1.04378	+	0.229754i	0.703594	−	0.710603i	$-0.251578\pi$
$613$	25.8429	+	5.68845i	1.04378	+	0.229754i	0.340190	+	0.940357i	$0.389509\pi$
$614$	−14.8581	−	21.9140i	−0.599623	−	0.884378i
$615$	−0.513558	+	0.968674i	−0.0207087	+	0.0390607i
$616$	−4.74905	−	8.95765i	−0.191345	−	0.360914i
$617$	−15.0179	+	22.1497i	−0.604597	+	0.891713i	−0.999637	−	0.0269506i	$-0.991420\pi$
$617$	−15.0179	+	22.1497i	−0.604597	+	0.891713i	0.395040	+	0.918664i	$0.370731\pi$
$618$	−2.80837	+	2.66023i	−0.112969	+	0.107010i
$619$	17.0783	−	7.90127i	0.686436	−	0.317579i	−0.0454886	−	0.998965i	$-0.514484\pi$
$619$	17.0783	−	7.90127i	0.686436	−	0.317579i	0.731924	+	0.681386i	$0.238622\pi$
$620$	−2.76712	+	1.28021i	−0.111130	+	0.0514144i
$621$	−5.77061	+	5.46621i	−0.231566	+	0.219351i
$622$	14.8164	−	21.8525i	0.594083	−	0.876206i
$623$	−0.431060	−	0.813066i	−0.0172701	−	0.0325748i
$624$	−1.36034	+	2.56587i	−0.0544571	+	0.102717i
$625$	−12.9041	−	19.0321i	−0.516164	−	0.761286i
$626$	−11.5555	−	2.54356i	−0.461852	−	0.101661i
$627$	0.214615	−	0.772973i	0.00857089	−	0.0308695i
$628$	3.35312	+	8.41569i	0.133804	+	0.335822i
$629$	23.4582	+	7.90398i	0.935339	+	0.315152i
$630$	−0.653148	−	0.618695i	−0.0260221	−	0.0246494i
$631$	−18.1068	+	3.98560i	−0.720819	+	0.158664i	−0.560206	−	0.828353i	$-0.689278\pi$
$631$	−18.1068	+	3.98560i	−0.720819	+	0.158664i	−0.160613	+	0.987017i	$0.551347\pi$
$632$	−0.0178893	+	0.329948i	−0.000711597	+	0.0131246i
$633$	2.38975	−	14.5768i	0.0949840	−	0.579377i
$634$	8.25026	−	9.71296i	0.327660	−	0.385751i
$635$	2.43522	−	6.11195i	0.0966389	−	0.242545i
$636$	−5.81008	−	4.41671i	−0.230385	−	0.175134i
$637$	−2.49159	−	1.49914i	−0.0987203	−	0.0593980i
$638$	−4.23275	−	25.8186i	−0.167576	−	1.02217i
$639$	13.5829	−	1.47723i	0.537330	−	0.0584382i
$640$	0.292423	−	0.222294i	0.0115590	−	0.00878695i
$641$	−11.6311	−	41.8915i	−0.459401	−	1.65461i	−0.723656	−	0.690161i	$-0.757540\pi$
$641$	−11.6311	−	41.8915i	−0.459401	−	1.65461i	0.264254	−	0.964453i	$-0.414874\pi$
$642$	−0.974847	−	17.9800i	−0.0384741	−	0.709614i
$643$	−50.1768	−	5.45706i	−1.97878	−	0.215205i	−0.999944	−	0.0105593i	$-0.996639\pi$
$643$	−50.1768	−	5.45706i	−1.97878	−	0.215205i	−0.978836	−	0.204646i	$-0.934396\pi$
$644$	−16.6812	+	10.0367i	−0.657330	+	0.395502i
$645$	−1.41533	−	1.66626i	−0.0557286	−	0.0656087i
$646$	−0.441656	+	0.148811i	−0.0173767	+	0.00585490i
$647$	−28.7467	−	13.2996i	−1.13015	−	0.522862i	−0.236500	−	0.971631i	$-0.576000\pi$
$647$	−28.7467	−	13.2996i	−1.13015	−	0.522862i	−0.893647	+	0.448770i	$0.851862\pi$
$648$	1.00000			0.0392837
$649$	30.5308	+	8.88151i	1.19844	+	0.348630i
$650$	14.1290			0.554186
$651$	−18.4506	−	8.53616i	−0.723137	−	0.334559i
$652$	4.51781	−	1.52223i	0.176931	−	0.0596150i
$653$	−10.9891	−	12.9374i	−0.430039	−	0.506280i	0.503876	−	0.863776i	$-0.331907\pi$
$653$	−10.9891	−	12.9374i	−0.430039	−	0.506280i	−0.933915	+	0.357495i	$0.883631\pi$
$654$	2.32357	−	1.39805i	0.0908589	−	0.0546680i
$655$	−2.57804	−	0.280379i	−0.100733	−	0.0109553i
$656$	−0.161595	−	2.98044i	−0.00630921	−	0.116366i
$657$	0.0635063	+	0.228729i	0.00247762	+	0.00892357i
$658$	13.4568	−	10.2296i	0.524602	−	0.398792i
$659$	−5.94295	+	0.646334i	−0.231504	+	0.0251776i	−0.223136	−	0.974787i	$-0.571629\pi$
$659$	−5.94295	+	0.646334i	−0.231504	+	0.0251776i	−0.00836851	+	0.999965i	$0.502664\pi$
$660$	0.245997	+	1.50051i	0.00957542	+	0.0584075i
$661$	41.9390	+	25.2339i	1.63124	+	0.981483i	0.973633	+	0.228120i	$0.0732580\pi$
$661$	41.9390	+	25.2339i	1.63124	+	0.981483i	0.657605	+	0.753363i	$0.271570\pi$
$662$	22.7063	+	17.2609i	0.882506	+	0.670864i
$663$	−2.58513	+	6.48819i	−0.100398	+	0.251980i
$664$	1.95556	−	2.30226i	0.0758905	−	0.0893452i
$665$	0.0282063	−	0.172051i	0.00109379	−	0.00667185i
$666$	0.557260	−	10.2781i	0.0215934	−	0.398267i
$667$	−49.0630	+	10.7996i	−1.89973	+	0.418162i
$668$	13.1570	+	12.4630i	0.509059	+	0.482206i
$669$	−22.3065	−	7.51595i	−0.862421	−	0.290583i
$670$	1.34547	+	3.37688i	0.0519801	+	0.130460i
$671$	−4.90391	+	17.6623i	−0.189313	+	0.681844i
$672$	2.39197	+	0.526513i	0.0922723	+	0.0203107i
$673$	9.58487	+	14.1366i	0.369470	+	0.544927i	0.966293	−	0.257446i	$-0.0828809\pi$
$673$	9.58487	+	14.1366i	0.369470	+	0.544927i	−0.596823	+	0.802373i	$0.703571\pi$
$674$	1.08781	−	2.05183i	0.0419009	−	0.0790335i
$675$	−2.27884	−	4.29835i	−0.0877127	−	0.165444i
$676$	2.56226	−	3.77905i	0.0985483	−	0.145348i
$677$	17.7537	−	16.8172i	0.682330	−	0.646337i	−0.265871	−	0.964009i	$-0.585660\pi$
$677$	17.7537	−	16.8172i	0.682330	−	0.646337i	0.948201	+	0.317672i	$0.102901\pi$
$678$	1.45584	−	0.673542i	0.0559111	−	0.0258672i
$679$	25.0459	−	11.5875i	0.961174	−	0.444686i
$680$	0.641325	−	0.607495i	0.0245937	−	0.0232964i
$681$	−8.63852	+	12.7409i	−0.331029	+	0.488231i
$682$	16.0944	+	30.3572i	0.616286	+	1.16244i
$683$	2.04006	−	3.84796i	0.0780607	−	0.147238i	−0.841409	−	0.540399i	$-0.818273\pi$
$683$	2.04006	−	3.84796i	0.0780607	−	0.147238i	0.919470	+	0.393160i	$0.128618\pi$
$684$	0.108754	+	0.160400i	0.00415832	+	0.00613306i
$685$	4.07358	+	0.896662i	0.155643	+	0.0342597i
$686$	−5.24274	+	18.8826i	−0.200169	+	0.720942i
$687$	−2.50942	−	6.29818i	−0.0957404	−	0.240290i
$688$	5.64022	+	1.90041i	0.215031	+	0.0724525i
$689$	−15.3877	−	14.5760i	−0.586226	−	0.555303i
$690$	2.85142	−	0.627645i	0.108552	−	0.0238940i
$691$	−0.324753	+	5.98972i	−0.0123542	+	0.227860i	0.985835	+	0.167715i	$0.0536389\pi$
$691$	−0.324753	+	5.98972i	−0.0123542	+	0.227860i	−0.998190	+	0.0601444i	$0.980844\pi$
$692$	1.70924	−	10.4259i	0.0649757	−	0.396334i
$693$	−6.56365	+	7.72732i	−0.249332	+	0.293537i
$694$	6.07589	−	15.2493i	0.230638	−	0.578857i
$695$	1.05030	+	0.798418i	0.0398402	+	0.0302857i
$696$	5.41563	+	3.25848i	0.205279	+	0.123512i
$697$	−1.16130	−	7.08361i	−0.0439873	−	0.268311i
$698$	35.1105	−	3.81850i	1.32895	−	0.144532i
$699$	−10.1632	+	7.72588i	−0.384408	+	0.292220i
$700$	−3.18779	−	11.4814i	−0.120487	−	0.433955i
$701$	1.96840	+	36.3049i	0.0743453	+	1.37122i	0.763126	+	0.646249i	$0.223663\pi$
$701$	1.96840	+	36.3049i	0.0743453	+	1.37122i	−0.688781	+	0.724969i	$0.741854\pi$
$702$	2.88715	+	0.313996i	0.108968	+	0.0118510i
$703$	1.70921	−	1.02840i	0.0644641	−	0.0387867i
$704$	−2.67988	−	3.15500i	−0.101002	−	0.118908i
$705$	−2.40240	+	0.809464i	−0.0904797	+	0.0304862i
$706$	−22.2496	−	10.2938i	−0.837376	−	0.387412i
$707$	−16.2442			−0.610927
$708$	−6.40998	+	4.23227i	−0.240902	+	0.159058i
$709$	−8.09076			−0.303855			−0.151928	−	0.988392i	$-0.548548\pi$
$709$	−8.09076			−0.303855			−0.151928	+	0.988392i	$0.548548\pi$
$710$	−4.55487	−	2.10731i	−0.170941	−	0.0790858i
$711$	0.313136	−	0.105508i	0.0117435	−	0.00395685i
$712$	−0.243247	−	0.286372i	−0.00911605	−	0.0107322i
$713$	56.5320	−	34.0141i	2.11714	−	1.27384i
$714$	5.85562	+	0.636837i	0.219141	+	0.0238330i
$715$	0.239073	+	4.40945i	0.00894084	+	0.164904i
$716$	−0.919976	−	3.31345i	−0.0343811	−	0.123830i
$717$	−3.45111	+	2.62346i	−0.128884	+	0.0979750i
$718$	−4.05731	+	0.441260i	−0.151418	+	0.0164677i
$719$	3.19987	+	19.5183i	0.119335	+	0.727911i	0.976926	+	0.213579i	$0.0685120\pi$
$719$	3.19987	+	19.5183i	0.119335	+	0.727911i	−0.857591	+	0.514332i	$0.828040\pi$
$720$	−0.314743	−	0.189375i	−0.0117298	−	0.00705758i
$721$	7.54248	+	5.73364i	0.280896	+	0.213532i
$722$	7.01872	−	17.6157i	0.261210	−	0.655587i
$723$	−3.51251	+	4.13524i	−0.130632	+	0.153791i
$724$	2.68594	−	16.3835i	0.0998222	−	0.608889i
$725$	1.66471	−	30.7038i	0.0618259	−	1.14031i
$726$	5.99231	−	1.31901i	0.222395	−	0.0489529i
$727$	−27.9299	−	26.4566i	−1.03586	−	0.981221i	−0.0360268	−	0.999351i	$-0.511470\pi$
$727$	−27.9299	−	26.4566i	−1.03586	−	0.981221i	−0.999836	+	0.0181298i	$0.994229\pi$
$728$	6.74065	+	2.27119i	0.249825	+	0.0841759i
$729$	−0.370138	−	0.928977i	−0.0137088	−	0.0344065i
$730$	0.0233273	−	0.0840174i	0.000863383	−	0.00310962i
$731$	13.9788	+	3.07696i	0.517023	+	0.113805i
$732$	−2.48501	−	3.66512i	−0.0918486	−	0.135467i
$733$	6.91276	−	13.0388i	0.255329	−	0.481601i	−0.722400	−	0.691476i	$-0.756961\pi$
$733$	6.91276	−	13.0388i	0.255329	−	0.481601i	0.977728	+	0.209875i	$0.0673057\pi$
$734$	−4.56487	−	8.61025i	−0.168492	−	0.317810i
$735$	0.206396	−	0.304411i	0.00761302	−	0.0112284i
$736$	−5.77061	+	5.46621i	−0.212707	+	0.201487i
$737$	37.1789	−	17.2008i	1.36950	−	0.633600i
$738$	−2.70894	+	1.25329i	−0.0997176	+	0.0461343i
$739$	1.60166	−	1.51717i	0.0589179	−	0.0558100i	−0.657674	−	0.753303i	$-0.728460\pi$
$739$	1.60166	−	1.51717i	0.0589179	−	0.0558100i	0.716592	+	0.697493i	$0.245701\pi$
$740$	−2.12180	+	3.12942i	−0.0779989	+	0.115040i
$741$	0.263624	+	0.497248i	0.00968448	+	0.0182669i
$742$	−8.37285	+	15.7929i	−0.307377	+	0.579774i
$743$	22.8084	+	33.6398i	0.836758	+	1.23413i	0.970015	+	0.243045i	$0.0781462\pi$
$743$	22.8084	+	33.6398i	0.836758	+	1.23413i	−0.133257	+	0.991082i	$0.542544\pi$
$744$	−8.10632	−	1.78434i	−0.297192	−	0.0654169i
$745$	0.928722	−	3.34495i	0.0340257	−	0.122550i
$746$	−13.1745	−	33.0655i	−0.482353	−	1.21062i
$747$	−2.86258	−	0.964515i	−0.104736	−	0.0352897i
$748$	−7.22740	−	6.84615i	−0.264260	−	0.250320i
$749$	−43.0708	+	9.48060i	−1.57377	+	0.346414i
$750$	−0.196181	+	3.61835i	−0.00716353	+	0.132124i
$751$	6.66056	−	40.6276i	0.243047	−	1.48252i	−0.529903	−	0.848058i	$-0.677772\pi$
$751$	6.66056	−	40.6276i	0.243047	−	1.48252i	0.772951	−	0.634466i	$-0.218780\pi$
$752$	4.46799	−	5.26012i	0.162931	−	0.191817i
$753$	3.59191	−	9.01500i	0.130896	−	0.328525i
$754$	14.6126	+	11.1082i	0.532159	+	0.404537i
$755$	−6.63367	−	3.99135i	−0.241424	−	0.145260i
$756$	−0.396242	−	2.41697i	−0.0144112	−	0.0879043i
$757$	−5.56975	+	0.605747i	−0.202436	+	0.0220162i	−0.208775	−	0.977964i	$-0.566948\pi$
$757$	−5.56975	+	0.605747i	−0.202436	+	0.0220162i	0.00633917	+	0.999980i	$0.497982\pi$
$758$	7.16962	−	5.45020i	0.260412	−	0.197960i
$759$	−8.80256	−	31.7040i	−0.319513	−	1.15078i
$760$	−0.00385386	−	0.0710802i	−0.000139794	−	0.00257835i
$761$	−11.1858	−	1.21653i	−0.405486	−	0.0440993i	−0.0968962	−	0.995294i	$-0.530891\pi$
$761$	−11.1858	−	1.21653i	−0.405486	−	0.0440993i	−0.308590	+	0.951195i	$0.599857\pi$
$762$	15.3474	−	9.23424i	0.555979	−	0.334521i
$763$	−4.29973	−	5.06204i	−0.155661	−	0.183258i
$764$	−3.05992	+	1.03101i	−0.110704	+	0.0373005i
$765$	−0.801728	−	0.370919i	−0.0289865	−	0.0134106i
$766$	8.29576			0.299738
$767$	−19.8355	+	10.2065i	−0.716218	+	0.368535i
$768$	1.00000			0.0360844
$769$	2.20904	+	1.02201i	0.0796599	+	0.0368546i	0.459314	−	0.888274i	$-0.348095\pi$
$769$	2.20904	+	1.02201i	0.0796599	+	0.0368546i	−0.379655	+	0.925128i	$0.623957\pi$
$770$	3.52922	−	1.18913i	0.127184	−	0.0428534i
$771$	−4.29101	−	5.05177i	−0.154537	−	0.181935i
$772$	7.25833	−	4.36719i	0.261233	−	0.157179i
$773$	−22.9687	−	2.49800i	−0.826126	−	0.0898466i	−0.314719	−	0.949185i	$-0.601910\pi$
$773$	−22.9687	−	2.49800i	−0.826126	−	0.0898466i	−0.511408	+	0.859338i	$0.670876\pi$
$774$	−0.322223	−	5.94305i	−0.0115821	−	0.213618i
$775$	10.8033	+	38.9100i	0.388067	+	1.39769i
$776$	8.96990	−	6.81874i	0.322001	−	0.244779i
$777$	−25.0626	+	2.72572i	−0.899114	+	0.0977846i
$778$	−5.08333	−	31.0070i	−0.182246	−	1.11165i
$779$	−0.495637	−	0.298215i	−0.0177580	−	0.0106847i
$780$	−0.849247	−	0.645581i	−0.0304079	−	0.0231155i
$781$	−20.9344	+	52.5414i	−0.749092	+	1.88008i
$782$	−12.3751	+	14.5691i	−0.442531	+	0.520988i
$783$	1.02252	−	6.23708i	0.0365418	−	0.222895i
$784$	−0.0542069	+	0.999788i	−0.00193596	+	0.0357067i
$785$	−3.24981	+	0.715338i	−0.115991	+	0.0255315i
$786$	−5.12543	−	4.85506i	−0.182818	−	0.173174i
$787$	−28.7045	−	9.67168i	−1.02321	−	0.344758i	−0.242830	−	0.970069i	$-0.578076\pi$
$787$	−28.7045	−	9.67168i	−1.02321	−	0.344758i	−0.780376	+	0.625311i	$0.784972\pi$
$788$	−6.49854	−	16.3101i	−0.231501	−	0.581024i
$789$	−0.224611	+	0.808977i	−0.00799637	+	0.0288003i
$790$	−0.118538	−	0.0260921i	−0.00421739	−	0.000928317i
$791$	−2.20479	−	3.25183i	−0.0783934	−	0.115622i
$792$	−1.93899	+	3.65733i	−0.0688991	+	0.129958i
$793$	−6.02376	−	11.3620i	−0.213910	−	0.403477i
$794$	0.324119	−	0.478040i	0.0115026	−	0.0169650i
$795$	1.94626	−	1.84359i	0.0690266	−	0.0653855i
$796$	−18.2286	+	8.43345i	−0.646096	+	0.298916i
$797$	−14.6367	+	6.77165i	−0.518458	+	0.239864i	−0.661626	−	0.749834i	$-0.730133\pi$
$797$	−14.6367	+	6.77165i	−0.518458	+	0.239864i	0.143168	+	0.989698i	$0.454271\pi$
$798$	0.344590	−	0.326413i	0.0121983	−	0.0115549i
$799$	9.31435	−	13.7376i	0.329518	−	0.486003i
$800$	−2.27884	−	4.29835i	−0.0805692	−	0.151970i
$801$	−0.175998	+	0.331968i	−0.00621859	+	0.0117295i
$802$	12.2082	+	18.0057i	0.431086	+	0.635804i
$803$	−0.959676	−	0.211241i	−0.0338662	−	0.00745452i
$804$	−2.64748	+	9.53535i	−0.0933693	+	0.336286i
$805$	−2.64685	−	6.64309i	−0.0932892	−	0.234138i
$806$	−22.8439	−	7.69700i	−0.804641	−	0.271115i
$807$	14.1518	+	13.4053i	0.498167	+	0.471889i
$808$	−6.47731	+	1.42576i	−0.227871	+	0.0501582i
$809$	1.50315	−	27.7240i	0.0528479	−	0.974723i	−0.845096	−	0.534614i	$-0.820457\pi$
$809$	1.50315	−	27.7240i	0.0528479	−	0.974723i	0.897944	−	0.440109i	$-0.145060\pi$
$810$	−0.0594262	+	0.362484i	−0.00208802	+	0.0127364i
$811$	22.4817	−	26.4675i	0.789440	−	0.929401i	−0.209386	−	0.977833i	$-0.567147\pi$
$811$	22.4817	−	26.4675i	0.789440	−	0.929401i	0.998826	+	0.0484322i	$0.0154225\pi$
$812$	5.72974	−	14.3806i	0.201074	−	0.504659i
$813$	−8.99658	−	6.83902i	−0.315524	−	0.239855i
$814$	36.5097	+	21.9672i	1.27967	+	0.769949i
$815$	0.283306	+	1.72809i	0.00992378	+	0.0605324i
$816$	2.39080	−	0.260015i	0.0836947	−	0.00910235i
$817$	0.918224	−	0.698015i	0.0321246	−	0.0244205i
$818$	−9.25778	−	33.3435i	−0.323691	−	1.16583i
$819$	−0.385090	−	7.10256i	−0.0134561	−	0.248184i
$820$	1.08996	+	0.118541i	0.0380631	+	0.00413962i
$821$	39.7460	−	23.9144i	1.38715	−	0.834618i	0.390837	−	0.920460i	$-0.372186\pi$
$821$	39.7460	−	23.9144i	1.38715	−	0.834618i	0.996309	+	0.0858418i	$0.0273580\pi$
$822$	7.35133	+	8.65465i	0.256407	+	0.301866i
$823$	28.1806	−	9.49516i	0.982315	−	0.330981i	0.218089	−	0.975929i	$-0.430018\pi$
$823$	28.1806	−	9.49516i	0.982315	−	0.330981i	0.764226	+	0.644948i	$0.223121\pi$
$824$	3.51077	+	1.62426i	0.122304	+	0.0565836i
$825$	20.1391			0.701155
$826$	12.7692	+	13.8157i	0.444296	+	0.480711i
$827$	−3.87067			−0.134596			−0.0672981	−	0.997733i	$-0.521438\pi$
$827$	−3.87067			−0.134596			−0.0672981	+	0.997733i	$0.521438\pi$
$828$	7.21390	+	3.33751i	0.250700	+	0.115986i
$829$	6.82000	−	2.29793i	0.236869	−	0.0798103i	−0.198364	−	0.980128i	$-0.563563\pi$
$829$	6.82000	−	2.29793i	0.236869	−	0.0798103i	0.435232	+	0.900318i	$0.356666\pi$
$830$	0.718322	+	0.845674i	0.0249333	+	0.0293538i
$831$	−13.1303	+	7.90026i	−0.455486	+	0.274057i
$832$	2.88715	+	0.313996i	0.100094	+	0.0108859i
$833$	0.130362	+	2.40439i	0.00451678	+	0.0833071i
$834$	0.960886	+	3.46080i	0.0332728	+	0.119838i
$835$	−5.29949	+	4.02857i	−0.183396	+	0.139414i
$836$	−0.797511	+	0.0867345i	−0.0275825	+	0.00299978i
$837$	1.34285	+	8.19104i	0.0464158	+	0.283124i
$838$	−25.5851	−	15.3941i	−0.883823	−	0.531779i
$839$	−1.46532	−	1.11391i	−0.0505885	−	0.0384564i	0.579574	−	0.814919i	$-0.303219\pi$
$839$	−1.46532	−	1.11391i	−0.0505885	−	0.0384564i	−0.630163	+	0.776463i	$0.717012\pi$
$840$	−0.332998	+	0.835762i	−0.0114895	+	0.0288365i
$841$	7.08677	−	8.34319i	0.244371	−	0.287696i
$842$	−6.06319	+	36.9838i	−0.208951	+	1.27455i
$843$	−0.392275	+	7.23509i	−0.0135107	+	0.249190i
$844$	−14.4261	+	3.17542i	−0.496566	+	0.109302i
$845$	1.21758	+	1.15335i	0.0418859	+	0.0396765i
$846$	−6.54031	−	2.20369i	−0.224860	−	0.0757643i
$847$	−5.56240	−	13.9606i	−0.191126	−	0.479691i
$848$	−1.95249	+	7.03222i	−0.0670487	+	0.241488i
$849$	29.4874	+	6.49067i	1.01200	+	0.222759i
$850$	−6.56589	−	9.68396i	−0.225208	−	0.332157i
$851$	38.3231	−	72.2851i	1.31370	−	2.47790i
$852$	−6.39985	−	12.0714i	−0.219255	−	0.413559i
$853$	−8.93757	+	13.1819i	−0.306017	+	0.451341i	−0.949339	−	0.314255i	$-0.898245\pi$
$853$	−8.93757	+	13.1819i	−0.306017	+	0.451341i	0.643322	+	0.765596i	$0.277556\pi$
$854$	−7.87381	+	7.45847i	−0.269436	+	0.255223i
$855$	−0.0646054	+	0.0298896i	−0.00220946	+	0.00102220i
$856$	−16.3422	+	7.56069i	−0.558564	+	0.258419i
$857$	26.5378	−	25.1380i	0.906515	−	0.858697i	−0.0839484	−	0.996470i	$-0.526753\pi$
$857$	26.5378	−	25.1380i	0.906515	−	0.858697i	0.990464	+	0.137773i	$0.0439945\pi$
$858$	−6.74655	+	9.95042i	−0.230323	+	0.339702i
$859$	21.4295	+	40.4203i	0.731165	+	1.37912i	0.917939	+	0.396721i	$0.129852\pi$
$859$	21.4295	+	40.4203i	0.731165	+	1.37912i	−0.186774	+	0.982403i	$0.559803\pi$
$860$	−1.02404	+	1.93155i	−0.0349196	+	0.0658654i
$861$	4.10256	+	6.05082i	0.139815	+	0.206212i
$862$	22.9866	+	5.05972i	0.782925	+	0.172335i
$863$	11.3421	−	40.8507i	0.386091	−	1.39057i	−0.474042	−	0.880502i	$-0.657205\pi$
$863$	11.3421	−	40.8507i	0.386091	−	1.39057i	0.860132	−	0.510071i	$-0.170381\pi$
$864$	−0.370138	−	0.928977i	−0.0125924	−	0.0316044i
$865$	3.67765	+	1.23915i	0.125044	+	0.0421322i
$866$	2.74911	+	2.60409i	0.0934185	+	0.0884907i
$867$	−10.9542	+	2.41121i	−0.372025	+	0.0818890i
$868$	−1.10062	+	20.2998i	−0.0373575	+	0.689018i
$869$	−0.221292	+	1.34982i	−0.00750680	+	0.0457895i
$870$	−1.50298	+	1.76944i	−0.0509556	+	0.0599896i
$871$	−10.6377	+	26.6987i	−0.360446	+	0.904650i
$872$	−2.15880	−	1.64107i	−0.0731061	−	0.0555738i
$873$	−9.65456	−	5.80895i	−0.326757	−	0.196603i
$874$	0.249205	+	1.52008i	0.00842947	+	0.0514175i
$875$	8.82318	−	0.959578i	0.298278	−	0.0324397i
$876$	0.188978	−	0.143657i	0.00638497	−	0.00485373i
$877$	8.39214	+	30.2258i	0.283382	+	1.02065i	0.959002	+	0.283401i	$0.0914626\pi$
$877$	8.39214	+	30.2258i	0.283382	+	1.02065i	−0.675619	+	0.737251i	$0.736124\pi$
$878$	0.163941	+	3.02371i	0.00553274	+	0.102045i
$879$	14.7512	+	1.60429i	0.497547	+	0.0541115i
$880$	1.30289	−	0.783923i	0.0439204	−	0.0264260i
$881$	36.3430	+	42.7863i	1.22443	+	1.44151i	0.860016	+	0.510267i	$0.170454\pi$
$881$	36.3430	+	42.7863i	1.22443	+	1.44151i	0.364410	+	0.931238i	$0.381271\pi$
$882$	0.948844	−	0.319703i	0.0319492	−	0.0107650i
$883$	−6.39467	−	2.95849i	−0.215198	−	0.0995610i	0.309329	−	0.950955i	$-0.399896\pi$
$883$	−6.39467	−	2.95849i	−0.215198	−	0.0995610i	−0.524527	+	0.851394i	$0.675758\pi$
$884$	6.98423			0.234905
$885$	−1.15321	−	2.57502i	−0.0387647	−	0.0865584i
$886$	−13.0380			−0.438019
$887$	−52.5401	−	24.3076i	−1.76412	−	0.816171i	−0.980921	−	0.194405i	$-0.937722\pi$
$887$	−52.5401	−	24.3076i	−1.76412	−	0.816171i	−0.783203	−	0.621766i	$-0.786416\pi$
$888$	−9.75434	+	3.28662i	−0.327334	+	0.110292i
$889$	−28.4002	−	33.4353i	−0.952511	−	1.12138i
$890$	0.118260	−	0.0711549i	0.00396410	−	0.00238512i
$891$	4.11527	+	0.447563i	0.137867	+	0.0149939i
$892$	1.27436	+	23.5042i	0.0426688	+	0.786979i
$893$	−0.357813	−	1.28873i	−0.0119738	−	0.0431256i
$894$	7.52371	−	5.71937i	0.251630	−	0.191284i
$895$	1.25574	−	0.136570i	0.0419749	−	0.00456504i
$896$	−0.396242	−	2.41697i	−0.0132375	−	0.0807452i
$897$	19.7796	+	11.9010i	0.660423	+	0.397363i
$898$	2.99976	+	2.28036i	0.100103	+	0.0760966i
$899$	−19.4179	+	48.7353i	−0.647624	+	1.62541i
$900$	−3.14958	+	3.70797i	−0.104986	+	0.123599i
$901$	−2.83952	+	17.3203i	−0.0945981	+	0.577023i
$902$	0.668926	−	12.3376i	0.0222728	−	0.410798i
$903$	−14.2365	+	3.13368i	−0.473760	+	0.104283i
$904$	−1.16457	−	1.10314i	−0.0387329	−	0.0366897i
$905$	5.77915	+	1.94722i	0.192105	+	0.0647278i
$906$	−7.80120	−	19.5795i	−0.259178	−	0.650486i
$907$	−4.78935	+	17.2497i	−0.159028	+	0.572766i	0.840493	+	0.541822i	$0.182265\pi$
$907$	−4.78935	+	17.2497i	−0.159028	+	0.572766i	−0.999521	+	0.0309444i	$0.990149\pi$
$908$	15.0334	+	3.30910i	0.498901	+	0.109816i
$909$	3.72200	+	5.48954i	0.123451	+	0.182077i
$910$	−1.22384	+	2.30841i	−0.0405699	+	0.0765230i
$911$	3.49703	+	6.59609i	0.115862	+	0.218538i	0.934660	−	0.355543i	$-0.115704\pi$
$911$	3.49703	+	6.59609i	0.115862	+	0.218538i	−0.818798	+	0.574081i	$0.805359\pi$
$912$	0.108754	−	0.160400i	0.00360121	−	0.00531139i
$913$	9.07807	−	8.59920i	0.300440	−	0.284592i
$914$	−30.8014	+	14.2502i	−1.01882	+	0.471356i
$915$	1.47622	−	0.682972i	0.0488023	−	0.0225784i
$916$	−4.92203	+	4.66239i	−0.162628	+	0.154050i
$917$	−9.70362	+	14.3118i	−0.320442	+	0.472616i
$918$	−1.12647	−	2.12475i	−0.0371792	−	0.0701274i
$919$	25.0319	−	47.2152i	0.825727	−	1.55749i	−0.00445166	−	0.999990i	$-0.501417\pi$
$919$	25.0319	−	47.2152i	0.825727	−	1.55749i	0.830179	−	0.557497i	$-0.188238\pi$
$920$	−1.63849	−	2.41659i	−0.0540193	−	0.0796725i
$921$	25.8572	+	5.69159i	0.852023	+	0.187544i
$922$	−8.30634	+	29.9167i	−0.273555	+	0.985255i
$923$	−14.6869	−	36.8615i	−0.483427	−	1.21331i
$924$	9.60796	+	3.23730i	0.316079	+	0.106499i
$925$	36.3557	+	34.4379i	1.19537	+	1.13231i
$926$	−1.35038	+	0.297241i	−0.0443762	+	0.00976793i
$927$	0.209425	−	3.86262i	0.00687843	−	0.126865i
$928$	1.02252	−	6.23708i	0.0335658	−	0.204742i
$929$	−2.72319	+	3.20598i	−0.0893449	+	0.105185i	−0.805018	−	0.593251i	$-0.797844\pi$
$929$	−2.72319	+	3.20598i	−0.0893449	+	0.105185i	0.715673	+	0.698436i	$0.246120\pi$
$930$	1.12852	−	2.83237i	0.0370057	−	0.0928772i
$931$	0.154471	+	0.117426i	0.00506259	+	0.00384848i
$932$	10.9390	+	6.58175i	0.358317	+	0.215592i
$933$	4.27135	+	26.0541i	0.139838	+	0.852971i
$934$	32.6051	−	3.54602i	1.06687	−	0.116029i
$935$	2.91112	−	2.21297i	0.0952037	−	0.0723720i
$936$	−0.776949	−	2.79832i	−0.0253954	−	0.0914658i
$937$	−0.513485	−	9.47067i	−0.0167748	−	0.309393i	−0.994865	−	0.101211i	$-0.967728\pi$
$937$	−0.513485	−	9.47067i	−0.0167748	−	0.309393i	0.978090	−	0.208182i	$-0.0667546\pi$
$938$	24.0957	+	2.62056i	0.786752	+	0.0855645i
$939$	10.1385	−	6.10011i	0.330856	−	0.199070i
$940$	1.64119	+	1.93216i	0.0535299	+	0.0630202i
$941$	−25.0589	+	8.44334i	−0.816898	+	0.275245i	−0.696570	−	0.717489i	$-0.745291\pi$
$941$	−25.0589	+	8.44334i	−0.816898	+	0.275245i	−0.120328	+	0.992734i	$0.538395\pi$
$942$	−8.22181	−	3.80381i	−0.267881	−	0.123935i
$943$	−23.7249			−0.772590
$944$	6.30426	+	4.38820i	0.205186	+	0.142824i
$945$	0.899659			0.0292659
$946$	22.3605	+	10.3451i	0.727001	+	0.336347i
$947$	−11.8410	+	3.98970i	−0.384781	+	0.129648i	−0.505043	−	0.863094i	$-0.668523\pi$
$947$	−11.8410	+	3.98970i	−0.384781	+	0.129648i	0.120261	+	0.992742i	$0.461627\pi$
$948$	−0.213918	−	0.251843i	−0.00694772	−	0.00817949i
$949$	0.590715	−	0.355421i	0.0191754	−	0.0115375i
$950$	−0.937291	−	0.101936i	−0.0304097	−	0.00330726i
$951$	0.689944	+	12.7253i	0.0223730	+	0.412645i
$952$	−1.57578	−	5.67546i	−0.0510714	−	0.183943i
$953$	−25.5269	+	19.4050i	−0.826896	+	0.628590i	−0.930608	−	0.366017i	$-0.880721\pi$
$953$	−25.5269	+	19.4050i	−0.826896	+	0.628590i	0.103712	+	0.994607i	$0.466928\pi$
$954$	7.25546	−	0.789079i	0.234904	−	0.0255474i
$955$	−0.191884	−	1.17044i	−0.00620921	−	0.0378745i
$956$	3.71452	+	2.23495i	0.120136	+	0.0722835i
$957$	20.8284	+	15.8333i	0.673287	+	0.511819i
$958$	−10.9910	+	27.5854i	−0.355104	+	0.891244i
$959$	18.0051	−	21.1973i	0.581415	−	0.684495i
$960$	−0.0594262	+	0.362484i	−0.00191797	+	0.0116991i
$961$	2.05166	−	37.8407i	0.0661827	−	1.22067i
$962$	−29.1942	+	6.42614i	−0.941260	+	0.207187i
$963$	13.0726	+	12.3830i	0.421258	+	0.399036i
$964$	5.14166	+	1.73243i	0.165602	+	0.0557977i
$965$	1.15170	+	2.89055i	0.0370746	+	0.0930502i
$966$	5.20820	−	18.7582i	0.167571	−	0.603536i
$967$	17.6054	+	3.87524i	0.566152	+	0.124619i	0.488818	−	0.872386i	$-0.337428\pi$
$967$	17.6054	+	3.87524i	0.566152	+	0.124619i	0.0773338	+	0.997005i	$0.475359\pi$
$968$	−3.44331	−	5.07850i	−0.110672	−	0.163229i
$969$	0.218303	−	0.411763i	0.00701290	−	0.0132277i
$970$	1.93864	+	3.65666i	0.0622459	+	0.117408i
$971$	−21.8624	+	32.2446i	−0.701598	+	1.03478i	0.295248	+	0.955421i	$0.404598\pi$
$971$	−21.8624	+	32.2446i	−0.701598	+	1.03478i	−0.996846	+	0.0793587i	$0.974713\pi$
$972$	−0.725995	+	0.687699i	−0.0232863	+	0.0220580i
$973$	7.98390	−	3.69374i	0.255952	−	0.118416i
$974$	12.7708	−	5.90840i	0.409203	−	0.189317i
$975$	−10.2576	+	9.71652i	−0.328506	+	0.311178i
$976$	−2.48501	+	3.66512i	−0.0795433	+	0.117318i
$977$	−3.11673	−	5.87877i	−0.0997129	−	0.188079i	0.828637	−	0.559787i	$-0.189117\pi$
$977$	−3.11673	−	5.87877i	−0.0997129	−	0.188079i	−0.928350	+	0.371708i	$0.878772\pi$
$978$	−2.23307	+	4.21202i	−0.0714058	+	0.134686i
$979$	−0.872856	−	1.28737i	−0.0278966	−	0.0411444i
$980$	−0.359186	−	0.0790627i	−0.0114738	−	0.00252557i
$981$	−0.725467	+	2.61290i	−0.0231624	+	0.0834234i
$982$	−10.1272	−	25.4174i	−0.323173	−	0.811103i
$983$	−15.7991	−	5.32335i	−0.503914	−	0.169788i	0.0558521	−	0.998439i	$-0.482212\pi$
$983$	−15.7991	−	5.32335i	−0.503914	−	0.169788i	−0.559766	+	0.828651i	$0.689109\pi$
$984$	2.16696	+	2.05265i	0.0690802	+	0.0654362i
$985$	6.29834	−	1.38637i	0.200682	−	0.0441734i
$986$	0.822899	−	15.1775i	0.0262064	−	0.483349i
$987$	−2.73470	+	16.6809i	−0.0870463	+	0.530959i
$988$	0.364354	−	0.428951i	0.0115917	−	0.0136468i
$989$	17.5105	−	43.9480i	0.556801	−	1.39746i
$990$	−1.21050	−	0.920195i	−0.0384721	−	0.0292457i
$991$	23.6303	+	14.2179i	0.750641	+	0.451645i	0.838785	−	0.544462i	$-0.183266\pi$
$991$	23.6303	+	14.2179i	0.750641	+	0.451645i	−0.0881448	+	0.996108i	$0.528094\pi$
$992$	1.34285	+	8.19104i	0.0426356	+	0.260066i
$993$	−28.3550	+	3.08379i	−0.899819	+	0.0978612i
$994$	−26.6403	+	20.2514i	−0.844979	+	0.642336i
$995$	−1.97373	−	7.10874i	−0.0625715	−	0.225362i
$996$	0.163537	+	3.01627i	0.00518188	+	0.0955742i
$997$	44.8928	+	4.88238i	1.42177	+	0.154627i	0.786465	−	0.617635i	$-0.211909\pi$
$997$	44.8928	+	4.88238i	1.42177	+	0.154627i	0.635304	+	0.772262i	$0.280875\pi$
$998$	−37.4635	+	22.5410i	−1.18589	+	0.713524i
$999$	6.66365	+	7.84505i	0.210829	+	0.248207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.79.1	✓	56
59.3	even	29	inner	354.2.e.a.121.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.79.1	✓	56	1.1	even	1	trivial
354.2.e.a.121.1	yes	56	59.3	even	29	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.907575 + 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(-0.314743 + 0.189375i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(0.132599 + 2.44564i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})\)	\(q+(0.907575 + 0.419889i) q^{2} +(-0.947653 + 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(-0.314743 + 0.189375i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(0.132599 + 2.44564i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-0.365169 + 0.0397146i) q^{10} +(0.669702 + 4.08500i) q^{11} +(-0.856857 - 0.515554i) q^{12} +(-2.31199 - 1.75753i) q^{13} +(-0.906555 + 2.27528i) q^{14} +(0.237800 - 0.279959i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.130198 + 2.40137i) q^{17} +(0.976621 - 0.214970i) q^{18} +(0.140693 + 0.133271i) q^{19} +(-0.348095 - 0.117287i) q^{20} +(-0.906555 - 2.27528i) q^{21} +(-1.10744 + 3.98865i) q^{22} +(7.76271 + 1.70870i) q^{23} +(-0.561187 - 0.827689i) q^{24} +(-2.27884 + 4.29835i) q^{25} +(-1.36034 - 2.56587i) q^{26} +(-0.561187 + 0.827689i) q^{27} +(-1.77813 + 1.68434i) q^{28} +(-5.73619 + 2.65384i) q^{29} +(0.333373 - 0.154235i) q^{30} +(6.02604 - 5.70817i) q^{31} +(-0.561187 + 0.827689i) q^{32} +(-1.93899 - 3.65733i) q^{33} +(-1.12647 + 2.12475i) q^{34} +(-0.504877 - 0.744638i) q^{35} +(0.976621 + 0.214970i) q^{36} +(2.75371 - 9.91797i) q^{37} +(0.0717302 + 0.180029i) q^{38} +(2.75215 + 0.927307i) q^{39} +(-0.266675 - 0.252608i) q^{40} +(-2.91503 + 0.641647i) q^{41} +(0.132599 - 2.44564i) q^{42} +(0.962890 - 5.87337i) q^{43} +(-2.67988 + 3.15500i) q^{44} +(-0.135960 + 0.341234i) q^{45} +(6.32778 + 4.81025i) q^{46} +(-5.91367 - 3.55814i) q^{47} +(-0.161782 - 0.986827i) q^{48} +(0.995387 - 0.108255i) q^{49} +(-3.87305 + 2.94422i) q^{50} +(-0.643378 - 2.31724i) q^{51} +(-0.157229 - 2.89991i) q^{52} +(7.25546 + 0.789079i) q^{53} +(-0.856857 + 0.515554i) q^{54} +(-0.984380 - 1.15890i) q^{55} +(-2.32102 + 0.782044i) q^{56} +(-0.175882 - 0.0813716i) q^{57} -6.32034 q^{58} +(3.31048 - 6.93114i) q^{59} +0.367323 q^{60} +(4.01886 + 1.85932i) q^{61} +(7.86588 - 2.65032i) q^{62} +(1.58560 + 1.86671i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(1.06052 + 0.115338i) q^{65} +(-0.224110 - 4.13346i) q^{66} +(-2.64748 - 9.53535i) q^{67} +(-1.91452 + 1.45538i) q^{68} +(-7.90195 + 0.859389i) q^{69} +(-0.145549 - 0.887807i) q^{70} +(11.7072 + 7.04400i) q^{71} +(0.796093 + 0.605174i) q^{72} +(-0.0878640 + 0.220522i) q^{73} +(6.66365 - 7.84505i) q^{74} +(0.787081 - 4.80098i) q^{75} +(-0.0104917 + 0.193509i) q^{76} +(-9.90165 + 2.17952i) q^{77} +(2.10842 + 1.99720i) q^{78} +(0.313136 + 0.105508i) q^{79} +(-0.135960 - 0.341234i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-2.91503 - 0.641647i) q^{82} +(-1.69518 - 2.50020i) q^{83} +(1.14724 - 2.16393i) q^{84} +(-0.413779 - 0.780471i) q^{85} +(3.34006 - 4.92622i) q^{86} +(4.58854 - 4.34650i) q^{87} +(-3.75694 + 1.73815i) q^{88} +(-0.341009 + 0.157768i) q^{89} +(-0.266675 + 0.252608i) q^{90} +(3.99172 - 5.88735i) q^{91} +(3.72317 + 7.02263i) q^{92} +(-3.88797 + 7.33349i) q^{93} +(-3.87308 - 5.71236i) q^{94} +(-0.0695203 - 0.0153026i) q^{95} +(0.267528 - 0.963550i) q^{96} +(-4.17050 - 10.4672i) q^{97} +(0.948844 + 0.319703i) q^{98} +(3.00528 + 2.84676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

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