LMFDB - Embedded newform 525.2.bo.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	525.4
Dual form			525.2.bo.a.394.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550698 - 2.59083i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-4.58205 + 2.04006i) q^{4} +(0.479670 + 2.18401i) q^{5} +(2.14285 - 1.55687i) q^{6} +(0.0455325 - 2.64536i) q^{7} +(4.69504 + 6.46216i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.550698 - 2.59083i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-4.58205 + 2.04006i) q^{4} +(0.479670 + 2.18401i) q^{5} +(2.14285 - 1.55687i) q^{6} +(0.0455325 - 2.64536i) q^{7} +(4.69504 + 6.46216i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(5.39426 - 2.44548i) q^{10} +(-2.21656 - 2.46174i) q^{11} +(-3.72738 - 3.35615i) q^{12} +(-5.90497 + 1.91864i) q^{13} +(-6.87876 + 1.33883i) q^{14} +(-1.80010 + 1.32652i) q^{15} +(7.44454 - 8.26800i) q^{16} +(-6.61091 + 0.694835i) q^{17} +(2.29385 + 1.32436i) q^{18} +(1.24247 + 0.553181i) q^{19} +(-6.65339 - 9.02871i) q^{20} +(2.43518 - 1.03437i) q^{21} +(-5.15729 + 7.09841i) q^{22} +(-1.74873 - 8.22715i) q^{23} +(-3.99384 + 6.91753i) q^{24} +(-4.53983 + 2.09521i) q^{25} +(8.22274 + 14.2422i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(5.18806 + 12.2141i) q^{28} +(-2.27611 - 1.65369i) q^{29} +(4.42810 + 3.93324i) q^{30} +(0.481844 + 4.58444i) q^{31} +(-11.6856 - 6.74671i) q^{32} +(1.34735 - 3.02621i) q^{33} +(5.44082 + 16.7451i) q^{34} +(5.79934 - 1.16946i) q^{35} +(1.54993 - 4.77020i) q^{36} +(2.76796 + 2.49228i) q^{37} +(0.748976 - 3.52366i) q^{38} +(-4.15454 - 4.61408i) q^{39} +(-11.8614 + 13.3537i) q^{40} +(1.46924 + 4.52186i) q^{41} +(-4.02092 - 5.73951i) q^{42} +1.43994i q^{43} +(15.1785 + 6.75790i) q^{44} +(-1.94400 - 1.10493i) q^{45} +(-20.3521 + 9.06136i) q^{46} +(-1.21087 - 0.127268i) q^{47} +(10.5812 + 3.43803i) q^{48} +(-6.99585 - 0.240900i) q^{49} +(7.92842 + 10.6081i) q^{50} +(-3.32366 - 5.75675i) q^{51} +(23.1427 - 20.8378i) q^{52} +(-3.48036 - 7.81701i) q^{53} +(-0.276866 + 2.63420i) q^{54} +(4.31325 - 6.02182i) q^{55} +(17.3085 - 12.1258i) q^{56} +1.36005i q^{57} +(-3.03098 + 6.80770i) q^{58} +(2.19520 + 0.466605i) q^{59} +(5.54196 - 9.75049i) q^{60} +(8.18483 - 1.73974i) q^{61} +(11.6122 - 3.77302i) q^{62} +(1.93542 + 1.80393i) q^{63} +(-4.16827 + 12.8286i) q^{64} +(-7.02278 - 11.9762i) q^{65} +(-8.58238 - 1.82424i) q^{66} +(2.75720 - 0.289793i) q^{67} +(28.8740 - 16.6704i) q^{68} +(6.80460 - 4.94383i) q^{69} +(-6.22355 - 14.3811i) q^{70} +(-6.06221 - 4.40445i) q^{71} +(-7.94392 - 0.834939i) q^{72} +(-9.18298 + 8.26839i) q^{73} +(4.93277 - 8.54381i) q^{74} +(-3.76059 - 3.29515i) q^{75} -6.82157 q^{76} +(-6.61311 + 5.75151i) q^{77} +(-9.66641 + 13.3047i) q^{78} +(-1.14184 + 10.8638i) q^{79} +(21.6283 + 12.2931i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(10.9063 - 6.29674i) q^{82} +(-1.78152 - 2.45205i) q^{83} +(-9.04793 + 9.70744i) q^{84} +(-4.68858 - 14.1050i) q^{85} +(3.73065 - 0.792975i) q^{86} +(0.584944 - 2.75195i) q^{87} +(5.50133 - 25.8817i) q^{88} +(-1.75412 + 0.372850i) q^{89} +(-1.79212 + 5.64506i) q^{90} +(4.80663 + 15.7081i) q^{91} +(24.7967 + 34.1297i) q^{92} +(-3.99211 + 2.30484i) q^{93} +(0.337095 + 3.20725i) q^{94} +(-0.612183 + 2.97891i) q^{95} +(1.41045 - 13.4195i) q^{96} +(2.81329 - 3.87215i) q^{97} +(3.22847 + 18.2577i) q^{98} +3.31260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.550698	−	2.59083i	−0.389403	−	1.83200i	−0.537807	−	0.843068i	$-0.680747\pi$
$2$	−0.550698	−	2.59083i	−0.389403	−	1.83200i	0.148404	−	0.988927i	$-0.452586\pi$
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$4$	−4.58205	+	2.04006i	−2.29103	+	1.02003i
$5$	0.479670	+	2.18401i	0.214515	+	0.976721i
$5$	0.479670	+	2.18401i	0.214515	+	0.976721i
$6$	2.14285	−	1.55687i	0.874816	−	0.635591i
$7$	0.0455325	−	2.64536i	0.0172097	−	0.999852i
$7$	0.0455325	−	2.64536i	0.0172097	−	0.999852i
$8$	4.69504	+	6.46216i	1.65995	+	2.28472i
$9$	−0.669131	+	0.743145i	−0.223044	+	0.247715i
$10$	5.39426	−	2.44548i	1.70581	−	0.773328i
$11$	−2.21656	−	2.46174i	−0.668318	−	0.742242i	0.309684	−	0.950840i	$-0.399777\pi$
$11$	−2.21656	−	2.46174i	−0.668318	−	0.742242i	−0.978002	+	0.208598i	$0.933110\pi$
$12$	−3.72738	−	3.35615i	−1.07600	−	0.968836i
$13$	−5.90497	+	1.91864i	−1.63774	+	0.532136i	−0.976033	−	0.217623i	$-0.930170\pi$
$13$	−5.90497	+	1.91864i	−1.63774	+	0.532136i	−0.661712	+	0.749758i	$0.730170\pi$
$14$	−6.87876	+	1.33883i	−1.83843	+	0.357817i
$15$	−1.80010	+	1.32652i	−0.464783	+	0.342506i
$16$	7.44454	−	8.26800i	1.86114	−	2.06700i
$17$	−6.61091	+	0.694835i	−1.60338	+	0.168522i	−0.863547	−	0.504268i	$-0.831762\pi$
$17$	−6.61091	+	0.694835i	−1.60338	+	0.168522i	−0.739834	+	0.672790i	$0.765096\pi$
$18$	2.29385	+	1.32436i	0.540666	+	0.312154i
$19$	1.24247	+	0.553181i	0.285041	+	0.126909i	0.544277	−	0.838906i	$-0.316804\pi$
$19$	1.24247	+	0.553181i	0.285041	+	0.126909i	−0.259236	+	0.965814i	$0.583471\pi$
$20$	−6.65339	−	9.02871i	−1.48774	−	2.01888i
$21$	2.43518	−	1.03437i	0.531399	−	0.225718i
$22$	−5.15729	+	7.09841i	−1.09954	+	1.51339i
$23$	−1.74873	−	8.22715i	−0.364636	−	1.71548i	−0.652483	−	0.757803i	$-0.726273\pi$
$23$	−1.74873	−	8.22715i	−0.364636	−	1.71548i	0.287847	−	0.957676i	$-0.407061\pi$
$24$	−3.99384	+	6.91753i	−0.815238	+	1.41203i
$25$	−4.53983	+	2.09521i	−0.907967	+	0.419042i
$26$	8.22274	+	14.2422i	1.61261	+	2.79313i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	5.18806	+	12.2141i	0.980452	+	2.30824i
$29$	−2.27611	−	1.65369i	−0.422663	−	0.307083i	0.356045	−	0.934469i	$-0.384125\pi$
$29$	−2.27611	−	1.65369i	−0.422663	−	0.307083i	−0.778708	+	0.627386i	$0.784125\pi$
$30$	4.42810	+	3.93324i	0.808456	+	0.718108i
$31$	0.481844	+	4.58444i	0.0865417	+	0.823389i	0.948578	+	0.316543i	$0.102522\pi$
$31$	0.481844	+	4.58444i	0.0865417	+	0.823389i	−0.862036	+	0.506846i	$0.830811\pi$
$32$	−11.6856	−	6.74671i	−2.06575	−	1.19266i
$33$	1.34735	−	3.02621i	0.234544	−	0.526795i
$34$	5.44082	+	16.7451i	0.933092	+	2.87176i
$35$	5.79934	−	1.16946i	0.980268	−	0.197674i
$36$	1.54993	−	4.77020i	0.258322	−	0.795033i
$37$	2.76796	+	2.49228i	0.455050	+	0.409729i	0.864523	−	0.502594i	$-0.167621\pi$
$37$	2.76796	+	2.49228i	0.455050	+	0.409729i	−0.409473	+	0.912322i	$0.634287\pi$
$38$	0.748976	−	3.52366i	0.121500	−	0.571613i
$39$	−4.15454	−	4.61408i	−0.665258	−	0.738844i
$40$	−11.8614	+	13.3537i	−1.87545	+	2.11141i
$41$	1.46924	+	4.52186i	0.229457	+	0.706196i	0.997809	+	0.0661678i	$0.0210773\pi$
$41$	1.46924	+	4.52186i	0.229457	+	0.706196i	−0.768352	+	0.640028i	$0.778923\pi$
$42$	−4.02092	−	5.73951i	−0.620442	−	0.885625i
$43$			1.43994i			0.219589i	0.993954	+	0.109795i	$0.0350193\pi$
$43$			1.43994i			0.219589i	−0.993954	+	0.109795i	$0.964981\pi$
$44$	15.1785	+	6.75790i	2.28824	+	1.01879i
$45$	−1.94400	−	1.10493i	−0.289794	−	0.164713i
$46$	−20.3521	+	9.06136i	−3.00076	+	1.33602i
$47$	−1.21087	−	0.127268i	−0.176624	−	0.0185639i	0.0158037	−	0.999875i	$-0.494969\pi$
$47$	−1.21087	−	0.127268i	−0.176624	−	0.0185639i	−0.192427	+	0.981311i	$0.561636\pi$
$48$	10.5812	+	3.43803i	1.52726	+	0.496237i
$49$	−6.99585	−	0.240900i	−0.999408	−	0.0344143i
$50$	7.92842	+	10.6081i	1.12125	+	1.50021i
$51$	−3.32366	−	5.75675i	−0.465406	−	0.806106i
$52$	23.1427	−	20.8378i	3.20932	−	2.88969i
$53$	−3.48036	−	7.81701i	−0.478064	−	1.07375i	−0.978174	−	0.207787i	$-0.933374\pi$
$53$	−3.48036	−	7.81701i	−0.478064	−	1.07375i	0.500110	−	0.865962i	$-0.333293\pi$
$54$	−0.276866	+	2.63420i	−0.0376767	+	0.358470i
$55$	4.31325	−	6.02182i	0.581599	−	0.811982i
$56$	17.3085	−	12.1258i	2.31295	−	1.62038i
$57$			1.36005i			0.180143i
$58$	−3.03098	+	6.80770i	−0.397988	+	0.893895i
$59$	2.19520	+	0.466605i	0.285791	+	0.0607468i	0.348577	−	0.937280i	$-0.386665\pi$
$59$	2.19520	+	0.466605i	0.285791	+	0.0607468i	−0.0627855	+	0.998027i	$0.519998\pi$
$60$	5.54196	−	9.75049i	0.715464	−	1.25878i
$61$	8.18483	−	1.73974i	1.04796	−	0.222751i	0.348416	−	0.937340i	$-0.386720\pi$
$61$	8.18483	−	1.73974i	1.04796	−	0.222751i	0.699544	+	0.714589i	$0.253386\pi$
$62$	11.6122	−	3.77302i	1.47475	−	0.479174i
$63$	1.93542	+	1.80393i	0.243840	+	0.227274i
$64$	−4.16827	+	12.8286i	−0.521034	+	1.60358i
$65$	−7.02278	−	11.9762i	−0.871068	−	1.48547i
$66$	−8.58238	−	1.82424i	−1.05642	−	0.224549i
$67$	2.75720	−	0.289793i	0.336845	−	0.0354039i	0.0654039	−	0.997859i	$-0.479166\pi$
$67$	2.75720	−	0.289793i	0.336845	−	0.0354039i	0.271441	+	0.962455i	$0.412500\pi$
$68$	28.8740	−	16.6704i	3.50149	−	2.02159i
$69$	6.80460	−	4.94383i	0.819178	−	0.595168i
$70$	−6.22355	−	14.3811i	−0.743857	−	1.71887i
$71$	−6.06221	−	4.40445i	−0.719452	−	0.522712i	0.166757	−	0.985998i	$-0.446670\pi$
$71$	−6.06221	−	4.40445i	−0.719452	−	0.522712i	−0.886209	+	0.463286i	$0.846670\pi$
$72$	−7.94392	−	0.834939i	−0.936199	−	0.0983985i
$73$	−9.18298	+	8.26839i	−1.07479	+	0.967742i	−0.999567	−	0.0294248i	$-0.990632\pi$
$73$	−9.18298	+	8.26839i	−1.07479	+	0.967742i	−0.0752196	+	0.997167i	$0.523966\pi$
$74$	4.93277	−	8.54381i	0.573423	−	0.993198i
$75$	−3.76059	−	3.29515i	−0.434235	−	0.380491i
$76$	−6.82157			−0.782487
$77$	−6.61311	+	5.75151i	−0.753634	+	0.655445i
$78$	−9.66641	+	13.3047i	−1.09451	+	1.50646i
$79$	−1.14184	+	10.8638i	−0.128467	+	1.22228i	0.720358	+	0.693603i	$0.243978\pi$
$79$	−1.14184	+	10.8638i	−0.128467	+	1.22228i	−0.848824	+	0.528675i	$0.822689\pi$
$80$	21.6283	+	12.2931i	2.41812	+	1.37441i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	10.9063	−	6.29674i	1.20440	−	0.695358i
$83$	−1.78152	−	2.45205i	−0.195547	−	0.269148i	0.699972	−	0.714170i	$-0.253196\pi$
$83$	−1.78152	−	2.45205i	−0.195547	−	0.269148i	−0.895519	+	0.445023i	$0.853196\pi$
$84$	−9.04793	+	9.70744i	−0.987210	+	1.05917i
$85$	−4.68858	−	14.1050i	−0.508548	−	1.52991i
$86$	3.73065	−	0.792975i	0.402287	−	0.0855087i
$87$	0.584944	−	2.75195i	0.0627126	−	0.295040i
$88$	5.50133	−	25.8817i	0.586443	−	2.75900i
$89$	−1.75412	+	0.372850i	−0.185937	+	0.0395221i	−0.299939	−	0.953958i	$-0.596966\pi$
$89$	−1.75412	+	0.372850i	−0.185937	+	0.0395221i	0.114002	+	0.993481i	$0.463633\pi$
$90$	−1.79212	+	5.64506i	−0.188906	+	0.595042i
$91$	4.80663	+	15.7081i	0.503872	+	1.64666i
$92$	24.7967	+	34.1297i	2.58523	+	3.55827i
$93$	−3.99211	+	2.30484i	−0.413962	+	0.239001i
$94$	0.337095	+	3.20725i	0.0347687	+	0.330802i
$95$	−0.612183	+	2.97891i	−0.0628086	+	0.305629i
$96$	1.41045	−	13.4195i	0.143953	−	1.36962i
$97$	2.81329	−	3.87215i	0.285646	−	0.393158i	−0.641948	−	0.766748i	$-0.721873\pi$
$97$	2.81329	−	3.87215i	0.285646	−	0.393158i	0.927594	+	0.373590i	$0.121873\pi$
$98$	3.22847	+	18.2577i	0.326125	+	1.84431i
$99$	3.31260			0.332928
$100$	16.5274	−	18.8619i	1.65274	−	1.88619i
$101$	−6.40749	+	11.0981i	−0.637569	+	1.10430i	0.348396	+	0.937347i	$0.386726\pi$
$101$	−6.40749	+	11.0981i	−0.637569	+	1.10430i	−0.985965	+	0.166954i	$0.946607\pi$
$102$	−13.0844	+	11.7813i	−1.29555	+	1.16652i
$103$	9.84230	+	1.03447i	0.969790	+	0.101929i	0.576158	−	0.817339i	$-0.304551\pi$
$103$	9.84230	+	1.03447i	0.969790	+	0.101929i	0.393633	+	0.919268i	$0.371218\pi$
$104$	−40.1226	−	29.1508i	−3.93435	−	2.85847i
$105$	3.42716	+	4.82230i	0.334456	+	0.470609i
$106$	−18.3359	+	13.3218i	−1.78094	+	1.29393i
$107$	2.97797	−	1.71933i	0.287892	−	0.166214i	−0.349099	−	0.937086i	$-0.613512\pi$
$107$	2.97797	−	1.71933i	0.287892	−	0.166214i	0.636991	+	0.770872i	$0.280179\pi$
$108$	4.98820	−	0.524281i	0.479990	−	0.0504490i
$109$	6.32277	+	1.34395i	0.605612	+	0.128727i	0.500504	−	0.865734i	$-0.333148\pi$
$109$	6.32277	+	1.34395i	0.605612	+	0.128727i	0.105108	+	0.994461i	$0.466481\pi$
$110$	−17.9768	−	7.85871i	−1.71402	−	0.749299i
$111$	−1.15098	+	3.54236i	−0.109246	+	0.336226i
$112$	−21.5329	−	20.0699i	−2.03466	−	1.89643i
$113$	12.2645	−	3.98499i	1.15375	−	0.374877i	0.331196	−	0.943562i	$-0.392548\pi$
$113$	12.2645	−	3.98499i	1.15375	−	0.374877i	0.822555	+	0.568685i	$0.192548\pi$
$114$	3.52366	−	0.748976i	0.330021	−	0.0701481i
$115$	17.1294	−	7.76558i	1.59732	−	0.724144i
$116$	13.8029	+	2.93389i	1.28157	+	0.272405i
$117$	2.52537	−	5.67207i	0.233470	−	0.524383i
$118$		−	5.94436i		−	0.547223i
$119$	1.53708	+	17.5199i	0.140904	+	1.60604i
$120$	−17.0237	−	5.40447i	−1.55404	−	0.493358i
$121$	0.00279238	−	0.0265678i	0.000253853	−	0.00241525i
$122$	−9.01474	−	20.2474i	−0.816157	−	1.83312i
$123$	−3.53333	+	3.18142i	−0.318590	+	0.286859i
$124$	−11.5604	−	20.0231i	−1.03815	−	1.79813i
$125$	−6.75359	−	8.91005i	−0.604060	−	0.796939i
$126$	3.60784	−	6.00776i	0.321412	−	0.535214i
$127$	−3.85232	−	1.25170i	−0.341838	−	0.111070i	0.133067	−	0.991107i	$-0.457518\pi$
$127$	−3.85232	−	1.25170i	−0.341838	−	0.111070i	−0.474905	+	0.880037i	$0.657518\pi$
$128$	8.69326	+	0.913699i	0.768383	+	0.0807603i
$129$	−1.31545	+	0.585678i	−0.115819	+	0.0515661i
$130$	−27.1610	+	24.7901i	−2.38217	+	2.17424i
$131$	−13.2400	−	5.89483i	−1.15678	−	0.515033i	−0.263559	−	0.964643i	$-0.584896\pi$
$131$	−13.2400	−	5.89483i	−1.15678	−	0.515033i	−0.893225	+	0.449610i	$0.851563\pi$
$132$			16.6149i			1.44614i
$133$	1.51994	−	3.26158i	0.131795	−	0.282815i
$134$	−2.26919	−	6.98385i	−0.196028	−	0.603312i
$135$	0.218704	−	2.22535i	0.0188231	−	0.191527i
$136$	−35.5286	−	39.4585i	−3.04655	−	3.38354i
$137$	0.0191265	−	0.0899832i	0.00163409	−	0.00768778i	−0.977323	−	0.211754i	$-0.932082\pi$
$137$	0.0191265	−	0.0899832i	0.00163409	−	0.00768778i	0.978957	+	0.204066i	$0.0654158\pi$
$138$	−16.5559	−	14.9070i	−1.40933	−	1.26897i
$139$	−1.06302	+	3.27165i	−0.0901645	+	0.277498i	−0.985963	−	0.166962i	$-0.946604\pi$
$139$	−1.06302	+	3.27165i	−0.0901645	+	0.277498i	0.895799	+	0.444460i	$0.146604\pi$
$140$	−24.1871	+	17.1895i	−2.04419	+	1.45278i
$141$	−0.376241	−	1.15795i	−0.0316852	−	0.0975170i
$142$	−8.07275	+	18.1317i	−0.677450	+	1.52158i
$143$	17.8119	+	10.2837i	1.48951	+	0.859967i
$144$	1.16295	+	11.0647i	0.0969126	+	0.922062i
$145$	2.51990	−	5.76428i	0.209266	−	0.478697i
$146$	26.4791	+	19.2382i	2.19142	+	1.59216i
$147$	−2.62540	−	6.48901i	−0.216539	−	0.535205i
$148$	−17.7673	−	5.77296i	−1.46047	−	0.474534i
$149$	−0.0773927	−	0.134048i	−0.00634026	−	0.0109816i	0.862838	−	0.505481i	$-0.168685\pi$
$149$	−0.0773927	−	0.134048i	−0.00634026	−	0.0109816i	−0.869178	+	0.494499i	$0.835352\pi$
$150$	−6.46622	+	11.5577i	−0.527965	+	0.943681i
$151$	−4.34414	+	7.52427i	−0.353521	+	0.612317i	−0.986864	−	0.161555i	$-0.948349\pi$
$151$	−4.34414	+	7.52427i	−0.353521	+	0.612317i	0.633343	+	0.773872i	$0.281682\pi$
$152$	2.25867	+	10.6262i	0.183203	+	0.861900i
$153$	3.90720	−	5.37780i	0.315878	−	0.434769i
$154$	18.5430	+	13.9661i	1.49424	+	1.12542i
$155$	−9.78135	+	3.25137i	−0.785657	+	0.261156i
$156$	28.4493	+	12.6664i	2.27777	+	1.01413i
$157$	−8.01657	−	4.62837i	−0.639792	−	0.369384i	0.144742	−	0.989469i	$-0.453765\pi$
$157$	−8.01657	−	4.62837i	−0.639792	−	0.369384i	−0.784534	+	0.620085i	$0.787098\pi$
$158$	28.7752	−	3.02440i	2.28923	−	0.240608i
$159$	5.72560	−	6.35893i	0.454070	−	0.504296i
$160$	9.12966	−	28.7578i	0.721763	−	2.27350i
$161$	−21.8434	+	4.25143i	−1.72150	+	0.335060i
$162$	−2.51908	+	0.818497i	−0.197917	+	0.0643072i
$163$	−13.3753	−	12.0431i	−1.04763	−	0.943292i	−0.0491727	−	0.998790i	$-0.515658\pi$
$163$	−13.3753	−	12.0431i	−1.04763	−	0.943292i	−0.998459	+	0.0554986i	$0.982325\pi$
$164$	−15.9570	−	17.7221i	−1.24603	−	1.38386i
$165$	7.25556	+	1.49106i	0.564845	+	0.116079i
$166$	−5.37177	+	5.96596i	−0.416930	+	0.463048i
$167$	−4.73069	−	6.51124i	−0.366072	−	0.503855i	0.585756	−	0.810487i	$-0.300798\pi$
$167$	−4.73069	−	6.51124i	−0.366072	−	0.503855i	−0.951828	+	0.306633i	$0.900798\pi$
$168$	18.1175	+	10.8801i	1.39780	+	0.839418i
$169$	20.6703	−	15.0178i	1.59002	−	1.15522i
$170$	−33.9618	+	19.9149i	−2.60475	+	1.52741i
$171$	−1.24247	+	0.553181i	−0.0950137	+	0.0423028i
$172$	−2.93757	−	6.59790i	−0.223988	−	0.503085i
$173$	−0.632064	−	2.97363i	−0.0480549	−	0.226081i	0.947566	−	0.319559i	$-0.103535\pi$
$173$	−0.632064	−	2.97363i	−0.0480549	−	0.226081i	−0.995621	+	0.0934783i	$0.970201\pi$
$174$	−7.45196			−0.564931
$175$	5.33588	+	12.1049i	0.403354	+	0.915044i
$176$	−36.8549			−2.77804
$177$	0.466605	+	2.19520i	0.0350722	+	0.165002i
$178$	1.93199	+	4.33931i	0.144808	+	0.325245i
$179$	8.03268	−	3.57638i	0.600391	−	0.267311i	−0.0839543	−	0.996470i	$-0.526755\pi$
$179$	8.03268	−	3.57638i	0.600391	−	0.267311i	0.684345	+	0.729159i	$0.260088\pi$
$180$	11.1616	+	1.09695i	0.831939	+	0.0817619i
$181$	14.4659	−	10.5101i	1.07524	−	0.781209i	0.0983945	−	0.995147i	$-0.468629\pi$
$181$	14.4659	−	10.5101i	1.07524	−	0.781209i	0.976847	+	0.213939i	$0.0686293\pi$
$182$	38.0501	−	21.1036i	2.82046	−	1.56430i
$183$	4.91840	+	6.76960i	0.363579	+	0.500423i
$184$	44.9548	−	49.9274i	3.31411	−	3.68070i
$185$	−4.11547	+	7.24073i	−0.302576	+	0.532349i
$186$	8.16991	+	9.07361i	0.599047	+	0.665309i
$187$	16.3640	+	14.7342i	1.19665	+	1.07747i
$188$	5.80791	−	1.88710i	0.423585	−	0.137631i
$189$	−0.860765	+	2.50182i	−0.0626114	+	0.181980i
$190$	8.05498	−	0.0544170i	0.584369	−	0.00394782i
$191$	−7.22212	+	8.02098i	−0.522574	+	0.580377i	−0.945432	−	0.325818i	$-0.894360\pi$
$191$	−7.22212	+	8.02098i	−0.522574	+	0.580377i	0.422858	+	0.906196i	$0.361027\pi$
$192$	−13.4149	+	1.40996i	−0.968138	+	0.101755i
$193$	−2.23617	−	1.29105i	−0.160963	−	0.0929319i	0.417355	−	0.908744i	$-0.362957\pi$
$193$	−2.23617	−	1.29105i	−0.160963	−	0.0929319i	−0.578318	+	0.815812i	$0.696291\pi$
$194$	−11.5814	−	5.15636i	−0.831494	−	0.370205i
$195$	8.08441	−	11.2868i	0.578936	−	0.808264i
$196$	32.5468	−	13.1682i	2.32477	−	0.940582i
$197$	10.9454	−	15.0650i	0.779826	−	1.07334i	−0.215475	−	0.976509i	$-0.569130\pi$
$197$	10.9454	−	15.0650i	0.779826	−	1.07334i	0.995301	−	0.0968294i	$-0.0308701\pi$
$198$	−1.82424	−	8.58238i	−0.129643	−	0.609923i
$199$	3.48442	−	6.03519i	0.247004	−	0.427823i	−0.715689	−	0.698419i	$-0.753887\pi$
$199$	3.48442	−	6.03519i	0.247004	−	0.427823i	0.962693	+	0.270596i	$0.0872206\pi$
$200$	−34.8543	−	19.5001i	−2.46457	−	1.37886i
$201$	1.38619	+	2.40095i	0.0977744	+	0.169350i
$202$	32.2819	+	10.4890i	2.27135	+	0.738005i
$203$	−4.47824	+	5.94583i	−0.314311	+	0.417315i
$204$	26.9733	+	19.5973i	1.88851	+	1.37208i
$205$	−9.17105	+	5.37784i	−0.640534	+	0.375605i
$206$	−2.74001	−	26.0694i	−0.190905	−	1.81634i
$207$	7.28410	+	4.20548i	0.506280	+	0.292301i
$208$	−28.0965	+	63.1057i	−1.94814	+	4.37559i
$209$	−1.39221	−	4.28478i	−0.0963012	−	0.296385i
$210$	10.6064	−	11.5348i	0.731914	−	0.795978i
$211$	−2.52532	+	7.77213i	−0.173850	+	0.535055i	−0.999579	−	0.0290116i	$-0.990764\pi$
$211$	−2.52532	+	7.77213i	−0.173850	+	0.535055i	0.825729	+	0.564067i	$0.190764\pi$
$212$	31.8944	+	28.7178i	2.19051	+	1.97235i
$213$	1.55795	−	7.32956i	0.106749	−	0.502213i
$214$	−6.09447	−	6.76860i	−0.416609	−	0.462692i
$215$	−3.14486	+	0.690698i	−0.214478	+	0.0471052i
$216$	−2.46833	−	7.59673i	−0.167948	−	0.516892i
$217$	12.1494	−	1.06591i	0.824757	−	0.0723586i
$218$		−	17.1214i		−	1.15960i
$219$	−11.2886	−	5.02601i	−0.762813	−	0.339626i
$220$	−7.47868	+	36.3916i	−0.504212	+	2.45352i
$221$	37.7041	−	16.7869i	2.53625	−	1.12921i
$222$	9.81150	+	1.03123i	0.658505	+	0.0692117i
$223$	0.813475	+	0.264314i	0.0544743	+	0.0176998i	0.336127	−	0.941817i	$-0.390883\pi$
$223$	0.813475	+	0.264314i	0.0544743	+	0.0176998i	−0.281653	+	0.959516i	$0.590883\pi$
$224$	−18.3795	+	30.6055i	−1.22804	+	2.04492i
$225$	1.48070	−	4.77572i	0.0987131	−	0.318382i
$226$	−17.0785	−	29.5809i	−1.13605	−	1.96769i
$227$	9.91837	−	8.93054i	0.658305	−	0.592741i	−0.270764	−	0.962646i	$-0.587276\pi$
$227$	9.91837	−	8.93054i	0.658305	−	0.592741i	0.929070	+	0.369905i	$0.120610\pi$
$228$	−2.77458	−	6.23181i	−0.183751	−	0.412712i
$229$	−3.01572	+	28.6927i	−0.199284	+	1.89606i	0.200873	+	0.979617i	$0.435622\pi$
$229$	−3.01572	+	28.6927i	−0.199284	+	1.89606i	−0.400157	+	0.916446i	$0.631045\pi$
$230$	−29.5524	−	40.1029i	−1.94863	−	2.64431i
$231$	−7.94405	−	3.70203i	−0.522680	−	0.243575i
$232$		−	22.4727i		−	1.47541i
$233$	−7.34104	+	16.4882i	−0.480927	+	1.08018i	0.496332	+	0.868133i	$0.334680\pi$
$233$	−7.34104	+	16.4882i	−0.480927	+	1.08018i	−0.977259	+	0.212048i	$0.931987\pi$
$234$	−16.0861	−	3.41921i	−1.05158	−	0.223521i
$235$	−0.302864	−	2.70561i	−0.0197567	−	0.176494i
$236$	−11.0104	+	2.34034i	−0.716719	+	0.152343i
$237$	−10.3890	+	3.37560i	−0.674841	+	0.219269i
$238$	44.5446	−	13.6305i	2.88740	−	0.883532i
$239$	−8.39412	+	25.8344i	−0.542970	+	1.67109i	0.182797	+	0.983151i	$0.441485\pi$
$239$	−8.39412	+	25.8344i	−0.542970	+	1.67109i	−0.725767	+	0.687940i	$0.758515\pi$
$240$	−2.43324	+	24.7585i	−0.157065	+	1.59816i
$241$	−1.46948	−	0.312347i	−0.0946574	−	0.0201201i	0.160339	−	0.987062i	$-0.448741\pi$
$241$	−1.46948	−	0.312347i	−0.0946574	−	0.0201201i	−0.254997	+	0.966942i	$0.582074\pi$
$242$	−0.0703703	+	0.00739622i	−0.00452358	+	0.000475447i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−33.9541	+	24.6691i	−2.17369	+	1.57928i
$245$	−2.82957	−	15.3946i	−0.180775	−	0.983525i
$246$	10.1883	+	7.40226i	0.649585	+	0.471951i
$247$	−8.39808	−	0.882674i	−0.534357	−	0.0561632i
$248$	−27.3631	+	24.6379i	−1.73756	+	1.56451i
$249$	1.51545	−	2.62484i	0.0960378	−	0.166342i
$250$	−19.3653	+	22.4042i	−1.22477	+	1.41696i
$251$	−3.61785			−0.228357			−0.114178	−	0.993460i	$-0.536424\pi$
$251$	−3.61785			−0.228357			−0.114178	+	0.993460i	$0.536424\pi$
$252$	−12.5483	−	4.31732i	−0.790469	−	0.271966i
$253$	−16.3769	+	22.5409i	−1.02961	+	1.41713i
$254$	−1.12147	+	10.6700i	−0.0703670	+	0.669497i
$255$	10.9786	−	10.0203i	0.687504	−	0.627493i
$256$	0.399803	+	3.80387i	0.0249877	+	0.237742i
$257$	0.581175	−	0.335542i	0.0362527	−	0.0209305i	−0.481764	−	0.876301i	$-0.660004\pi$
$257$	0.581175	−	0.335542i	0.0362527	−	0.0209305i	0.518017	+	0.855370i	$0.326670\pi$
$258$	2.24181	+	3.08559i	0.139569	+	0.192100i
$259$	6.71901	−	7.20877i	0.417499	−	0.447931i
$260$	56.6110	+	40.5488i	3.51086	+	2.51473i
$261$	2.75195	−	0.584944i	0.170341	−	0.0362071i
$262$	−7.98126	+	37.5489i	−0.493084	+	2.31978i
$263$	−0.880139	+	4.14073i	−0.0542717	+	0.255328i	−0.996917	−	0.0784692i	$-0.974997\pi$
$263$	−0.880139	+	4.14073i	−0.0542717	+	0.255328i	0.942645	+	0.333797i	$0.108330\pi$
$264$	25.8817	−	5.50133i	1.59291	−	0.338583i
$265$	15.4030	−	11.3507i	0.946201	−	0.697270i
$266$	−9.28724	−	2.14175i	−0.569437	−	0.131319i
$267$	−1.05408	−	1.45082i	−0.0645088	−	0.0887887i
$268$	−12.0424	+	6.95270i	−0.735608	+	0.424704i
$269$	−2.29047	−	21.7924i	−0.139653	−	1.32871i	−0.809900	−	0.586568i	$-0.800479\pi$
$269$	−2.29047	−	21.7924i	−0.139653	−	1.32871i	0.670248	−	0.742138i	$-0.266188\pi$
$270$	−5.88594	+	0.658869i	−0.358207	+	0.0400975i
$271$	0.869690	−	8.27455i	0.0528299	−	0.502643i	−0.935828	−	0.352457i	$-0.885346\pi$
$271$	0.869690	−	8.27455i	0.0528299	−	0.502643i	0.988658	−	0.150186i	$-0.0479871\pi$
$272$	−43.4703	+	59.8317i	−2.63577	+	3.62783i
$273$	−12.3951	+	10.7801i	−0.750183	+	0.652444i
$274$	−0.243664			−0.0147203
$275$	15.2207	+	6.53172i	0.917841	+	0.393878i
$276$	−21.0933	+	36.5347i	−1.26967	+	2.19913i
$277$	−1.16130	+	1.04564i	−0.0697759	+	0.0628265i	−0.703281	−	0.710912i	$-0.748282\pi$
$277$	−1.16130	+	1.04564i	−0.0697759	+	0.0628265i	0.633505	+	0.773739i	$0.281616\pi$
$278$	9.06170	+	0.952423i	0.543485	+	0.0571225i
$279$	−3.72932	−	2.70951i	−0.223268	−	0.162214i
$280$	34.7853	+	31.9857i	2.07882	+	1.91151i
$281$	1.92681	−	1.39991i	0.114944	−	0.0835115i	−0.528828	−	0.848729i	$-0.677368\pi$
$281$	1.92681	−	1.39991i	0.114944	−	0.0835115i	0.643772	+	0.765217i	$0.277368\pi$
$282$	−2.79286	+	1.61246i	−0.166312	+	0.0960205i
$283$	−28.2314	+	2.96724i	−1.67818	+	0.176384i	−0.895201	−	0.445663i	$-0.852968\pi$
$283$	−28.2314	+	2.96724i	−1.67818	+	0.176384i	−0.782980	+	0.622047i	$0.786301\pi$
$284$	36.7627	+	7.81416i	2.18147	+	0.463685i
$285$	−2.97036	+	0.652374i	−0.175949	+	0.0386433i
$286$	16.8344	−	51.8109i	0.995438	−	3.06364i
$287$	12.0288	−	3.68078i	0.710040	−	0.217270i
$288$	12.8330	−	4.16970i	0.756192	−	0.245702i
$289$	26.5928	−	5.65248i	1.56428	−	0.332499i
$290$	−16.3220	−	3.35426i	−0.958460	−	0.196969i
$291$	4.68166	+	0.995117i	0.274444	+	0.0583348i
$292$	25.2089	−	56.6201i	1.47524	−	3.31344i
$293$		−	9.62645i		−	0.562383i	−0.959652	−	0.281192i	$-0.909270\pi$
$293$		−	9.62645i		−	0.562383i	0.959652	−	0.281192i	$-0.0907296\pi$
$294$	−15.3661	+	10.3755i	−0.896172	+	0.605109i
$295$	0.0339012	+	5.01817i	0.00197381	+	0.292169i
$296$	−3.10986	+	29.5884i	−0.180757	+	1.71979i
$297$	1.34735	+	3.02621i	0.0781814	+	0.175598i
$298$	−0.304676	+	0.274332i	−0.0176494	+	0.0158916i
$299$	26.1112	+	45.2259i	1.51005	+	2.61548i
$300$	23.9535	+	7.42670i	1.38296	+	0.428781i
$301$	3.80917	+	0.0655643i	0.219557	+	0.00377906i
$302$	21.8864	+	7.11133i	1.25942	+	0.409211i
$303$	−12.7448	−	1.33953i	−0.732168	−	0.0769539i
$304$	13.8233	−	6.15453i	0.792820	−	0.352986i
$305$	7.72563	+	17.0413i	0.442368	+	0.975781i
$306$	−16.0847	−	7.16135i	−0.919499	−	0.409387i
$307$		−	16.0439i		−	0.915673i	−0.889037	−	0.457836i	$-0.848625\pi$
$307$		−	16.0439i		−	0.915673i	0.889037	−	0.457836i	$-0.151375\pi$
$308$	18.5682	−	39.8448i	1.05802	−	2.27037i
$309$	3.05819	+	9.41214i	0.173974	+	0.535438i
$310$	13.8103	+	23.5513i	0.784374	+	1.33762i
$311$	−0.0371585	−	0.0412687i	−0.00210706	−	0.00234013i	0.742090	−	0.670300i	$-0.233835\pi$
$311$	−0.0371585	−	0.0412687i	−0.00210706	−	0.00234013i	−0.744197	+	0.667960i	$0.767168\pi$
$312$	10.3112	−	48.5105i	0.583759	−	2.74637i
$313$	−15.9091	−	14.3246i	−0.899234	−	0.809674i	0.0831520	−	0.996537i	$-0.473501\pi$
$313$	−15.9091	−	14.3246i	−0.899234	−	0.809674i	−0.982386	+	0.186863i	$0.940168\pi$
$314$	−7.57662	+	23.3184i	−0.427573	+	1.31593i
$315$	−3.01144	+	5.09227i	−0.169676	+	0.286917i
$316$	−16.9309	−	52.1081i	−0.952440	−	2.93131i
$317$	−0.299167	+	0.671939i	−0.0168029	+	0.0377399i	−0.921752	−	0.387780i	$-0.873242\pi$
$317$	−0.299167	+	0.671939i	−0.0168029	+	0.0377399i	0.904949	+	0.425520i	$0.139909\pi$
$318$	−19.6280	−	11.3322i	−1.10068	−	0.635480i
$319$	0.974178	+	9.26869i	0.0545435	+	0.518947i
$320$	−30.0173	−	2.95006i	−1.67802	−	0.164913i
$321$	2.78194	+	2.02120i	0.155273	+	0.112812i
$322$	23.0439	+	54.2513i	1.28418	+	3.02331i
$323$	−8.59820	−	2.79372i	−0.478417	−	0.155447i
$324$	2.50784	+	4.34371i	0.139324	+	0.241317i
$325$	22.7876	−	21.0825i	1.26403	−	1.16945i
$326$	−23.8360	+	41.2852i	−1.32016	+	2.28658i
$327$	1.34395	+	6.32277i	0.0743204	+	0.349650i
$328$	−22.3229	+	30.7248i	−1.23257	+	1.69649i
$329$	−0.391803	+	3.19739i	−0.0216008	+	0.176278i
$330$	−0.132540	−	19.6191i	−0.00729611	−	1.07999i
$331$	−17.6831	−	7.87302i	−0.971951	−	0.432740i	−0.141565	−	0.989929i	$-0.545213\pi$
$331$	−17.6831	−	7.87302i	−0.971951	−	0.432740i	−0.830386	+	0.557189i	$0.811880\pi$
$332$	13.1653	+	7.60102i	0.722542	+	0.417160i
$333$	−3.70425	+	0.389333i	−0.202992	+	0.0213353i
$334$	−14.2643	+	15.8422i	−0.780510	+	0.866844i
$335$	1.95546	+	5.88275i	0.106838	+	0.321409i
$336$	9.57661	−	27.8344i	0.522447	−	1.51849i
$337$	−18.7216	+	6.08301i	−1.01983	+	0.331362i	−0.770762	−	0.637124i	$-0.780124\pi$
$337$	−18.7216	+	6.08301i	−1.01983	+	0.331362i	−0.249067	+	0.968486i	$0.580124\pi$
$338$	−50.2918	−	45.2830i	−2.73551	−	2.46307i
$339$	8.62891	+	9.58338i	0.468658	+	0.520498i
$340$	50.2584	+	55.0650i	2.72565	+	2.98632i
$341$	10.2176	−	11.3478i	0.553317	−	0.614520i
$342$	2.11742	+	2.91438i	0.114497	+	0.157592i
$343$	−0.955806	+	18.4956i	−0.0516087	+	0.998667i
$344$	−9.30515	+	6.76059i	−0.501700	+	0.364507i
$345$	14.0614	+	12.4899i	0.757038	+	0.672436i
$346$	−7.35609	+	3.27514i	−0.395466	+	0.176073i
$347$	−4.81721	−	10.8196i	−0.258601	−	0.580828i	0.736855	−	0.676051i	$-0.236310\pi$
$347$	−4.81721	−	10.8196i	−0.258601	−	0.580828i	−0.995456	+	0.0952231i	$0.969644\pi$
$348$	2.93389	+	13.8029i	0.157273	+	0.739912i
$349$	−12.6114			−0.675070			−0.337535	−	0.941313i	$-0.609593\pi$
$349$	−12.6114			−0.675070			−0.337535	+	0.941313i	$0.609593\pi$
$350$	28.4233	−	20.4905i	1.51929	−	1.09526i
$351$	6.20886			0.331404
$352$	9.29328	+	43.7215i	0.495334	+	2.33036i
$353$	5.63835	+	12.6639i	0.300099	+	0.674033i	0.999158	−	0.0410307i	$-0.0130641\pi$
$353$	5.63835	+	12.6639i	0.300099	+	0.674033i	−0.699059	+	0.715064i	$0.746397\pi$
$354$	5.43045	−	2.41779i	0.288625	−	0.128504i
$355$	6.71153	−	15.3526i	0.356211	−	0.814833i
$356$	7.27685	−	5.28694i	0.385672	−	0.280207i
$357$	−15.3800	+	8.53016i	−0.813997	+	0.451464i
$358$	−13.6894	−	18.8418i	−0.723506	−	0.995821i
$359$	9.74960	−	10.8280i	0.514564	−	0.571481i	−0.428733	−	0.903431i	$-0.641040\pi$
$359$	9.74960	−	10.8280i	0.514564	−	0.571481i	0.943297	+	0.331950i	$0.107707\pi$
$360$	−1.98694	−	17.7501i	−0.104721	−	0.935513i
$361$	−11.4758	−	12.7451i	−0.603988	−	0.670797i
$362$	−35.1962	−	31.6908i	−1.84987	−	1.66563i
$363$	0.0254066	−	0.00825511i	0.00133350	−	0.000433281i
$364$	−54.0698	−	62.1697i	−2.83403	−	3.25858i
$365$	−22.4631	−	16.0897i	−1.17577	−	0.842171i
$366$	14.8303	−	16.4708i	0.775194	−	0.860940i
$367$	−3.81659	+	0.401140i	−0.199225	+	0.0209393i	−0.203615	−	0.979051i	$-0.565269\pi$
$367$	−3.81659	+	0.401140i	−0.199225	+	0.0209393i	0.00439052	+	0.999990i	$0.498602\pi$
$368$	−81.0406	−	46.7888i	−4.22453	−	2.43904i
$369$	−4.34351	−	1.93386i	−0.226114	−	0.100672i
$370$	21.0259	+	6.67504i	1.09309	+	0.347019i
$371$	−20.8373	+	8.85087i	−1.08182	+	0.459514i
$372$	13.5900	−	18.7051i	0.704610	−	0.969812i
$373$	−1.00875	−	4.74579i	−0.0522310	−	0.245728i	0.944285	−	0.329129i	$-0.106755\pi$
$373$	−1.00875	−	4.74579i	−0.0522310	−	0.245728i	−0.996516	+	0.0834012i	$0.973422\pi$
$374$	29.1622	−	50.5104i	1.50794	−	2.61183i
$375$	5.39280	−	9.79376i	0.278483	−	0.505747i
$376$	−4.86266	−	8.42237i	−0.250772	−	0.434351i
$377$	16.6132	+	5.39796i	0.855623	+	0.278009i
$378$	6.95581	+	0.852352i	0.357768	+	0.0438402i
$379$	25.9067	+	18.8223i	1.33074	+	0.966837i	0.999731	+	0.0232081i	$0.00738802\pi$
$379$	25.9067	+	18.8223i	1.33074	+	0.966837i	0.331006	+	0.943629i	$0.392612\pi$
$380$	−3.27210	−	14.8984i	−0.167855	−	0.764272i
$381$	−0.423400	−	4.02838i	−0.0216914	−	0.206380i
$382$	24.7582	+	14.2942i	1.26674	+	0.731353i
$383$	−10.6206	+	23.8543i	−0.542689	+	1.21890i	0.409197	+	0.912446i	$0.365809\pi$
$383$	−10.6206	+	23.8543i	−0.542689	+	1.21890i	−0.951886	+	0.306453i	$0.900858\pi$
$384$	2.70116	+	8.31333i	0.137843	+	0.424238i
$385$	−15.7335	−	11.6843i	−0.801852	−	0.595487i
$386$	−2.11344	+	6.50451i	−0.107571	+	0.331071i
$387$	−1.07009	−	0.963511i	−0.0543956	−	0.0489780i
$388$	−4.99119	+	23.4817i	−0.253389	+	1.19210i
$389$	17.3935	+	19.3174i	0.881883	+	0.979430i	0.999908	−	0.0135803i	$-0.00432288\pi$
$389$	17.3935	+	19.3174i	0.881883	+	0.979430i	−0.118025	+	0.993011i	$0.537656\pi$
$390$	−33.6943	−	14.7297i	−1.70618	−	0.745868i
$391$	17.2772	+	53.1739i	0.873747	+	2.68912i
$392$	−31.2891	−	46.3394i	−1.58034	−	2.34049i
$393$		−	14.4930i		−	0.731074i
$394$	−45.0586	−	20.0614i	−2.27002	−	1.01068i
$395$	−24.2745	+	2.71727i	−1.22138	+	0.136721i
$396$	−15.1785	+	6.75790i	−0.762748	+	0.339597i
$397$	−15.7958	−	1.66021i	−0.792769	−	0.0833234i	−0.300517	−	0.953776i	$-0.597159\pi$
$397$	−15.7958	−	1.66021i	−0.792769	−	0.0833234i	−0.492252	+	0.870453i	$0.663826\pi$
$398$	−17.5550	−	5.70398i	−0.879954	−	0.285915i
$399$	3.59782	+	0.0619264i	0.180116	+	0.00310020i
$400$	−16.4738	+	53.1332i	−0.823689	+	2.65666i
$401$	0.477313	+	0.826730i	0.0238359	+	0.0412849i	0.877697	−	0.479215i	$-0.159079\pi$
$401$	0.477313	+	0.826730i	0.0238359	+	0.0412849i	−0.853861	+	0.520500i	$0.825745\pi$
$402$	5.45710	−	4.91359i	0.272175	−	0.245068i
$403$	−11.6412	−	26.1465i	−0.579888	−	1.30245i
$404$	6.71865	−	63.9237i	0.334265	−	3.18032i
$405$	2.12191	−	0.705334i	0.105439	−	0.0350483i
$406$	17.8708	+	8.32801i	0.886913	+	0.413312i
$407$		−	12.3383i		−	0.611586i
$408$	21.5964	−	48.5062i	1.06918	−	2.40141i
$409$	−16.8361	−	3.57861i	−0.832489	−	0.176951i	−0.228098	−	0.973638i	$-0.573251\pi$
$409$	−16.8361	−	3.57861i	−0.832489	−	0.176951i	−0.604392	+	0.796687i	$0.706584\pi$
$410$	18.9836	+	20.7991i	0.937532	+	1.02719i
$411$	0.0899832	−	0.0191265i	0.00443854	−	0.000943441i
$412$	−47.2083	+	15.3389i	−2.32579	+	0.755694i
$413$	1.33429	−	5.78586i	0.0656562	−	0.284703i
$414$	6.88434	−	21.1878i	0.338347	−	1.04132i
$415$	4.50077	−	5.06704i	0.220934	−	0.248731i
$416$	81.9479	+	17.4186i	4.01783	+	0.854015i
$417$	−3.42117	+	0.359580i	−0.167535	+	0.0176087i
$418$	−10.3345	+	5.96661i	−0.505475	+	0.291836i
$419$	12.7977	−	9.29809i	0.625210	−	0.454241i	−0.229528	−	0.973302i	$-0.573718\pi$
$419$	12.7977	−	9.29809i	0.625210	−	0.454241i	0.854737	+	0.519061i	$0.173718\pi$
$420$	−25.5412	−	15.1044i	−1.24628	−	0.737021i
$421$	17.4340	+	12.6665i	0.849681	+	0.617330i	0.925058	−	0.379825i	$-0.124016\pi$
$421$	17.4340	+	12.6665i	0.849681	+	0.617330i	−0.0753768	+	0.997155i	$0.524016\pi$
$422$	21.5270	+	2.26258i	1.04792	+	0.110140i
$423$	0.904809	−	0.814694i	0.0439933	−	0.0396118i
$424$	34.1744	−	59.1918i	1.65965	−	2.87461i
$425$	28.5566	−	17.0057i	1.38520	−	0.824897i
$426$	−19.8476			−0.961620
$427$	−4.22956	−	21.7310i	−0.204683	−	1.05164i
$428$	−10.1377	+	13.9533i	−0.490024	+	0.674460i
$429$	−2.14988	+	20.4548i	−0.103797	+	0.987565i
$430$	3.52135	+	7.76743i	0.169815	+	0.374579i
$431$	0.938668	+	8.93083i	0.0452141	+	0.430183i	0.993591	+	0.113037i	$0.0360579\pi$
$431$	0.938668	+	8.93083i	0.0452141	+	0.430183i	−0.948377	+	0.317146i	$0.897275\pi$
$432$	−9.63513	+	5.56285i	−0.463570	+	0.267643i
$433$	13.1631	+	18.1175i	0.632579	+	0.870670i	0.998193	−	0.0600963i	$-0.0191408\pi$
$433$	13.1631	+	18.1175i	0.632579	+	0.870670i	−0.365613	+	0.930767i	$0.619141\pi$
$434$	−9.45226	−	30.8901i	−0.453723	−	1.48277i
$435$	6.29087	−	0.0424992i	0.301624	−	0.00203768i
$436$	−31.7130	+	6.74081i	−1.51878	+	0.322826i
$437$	2.37836	−	11.1893i	0.113773	−	0.535258i
$438$	−6.80494	+	32.0147i	−0.325152	+	1.52972i
$439$	35.4775	−	7.54098i	1.69325	−	0.359911i	0.742493	−	0.669854i	$-0.233643\pi$
$439$	35.4775	−	7.54098i	1.69325	−	0.359911i	0.950755	+	0.309942i	$0.100310\pi$
$440$	59.1648	−	0.399700i	2.82057	−	0.0190549i
$441$	4.86016	−	5.03774i	0.231436	−	0.239892i
$442$	−64.2558	−	88.4405i	−3.05633	−	4.20668i
$443$	−26.0615	+	15.0466i	−1.23822	+	0.714887i	−0.968730	−	0.248116i	$-0.920189\pi$
$443$	−26.0615	+	15.0466i	−1.23822	+	0.714887i	−0.269491	+	0.963003i	$0.586855\pi$
$444$	−1.95277	−	18.5793i	−0.0926743	−	0.881737i
$445$	−1.65571	−	3.65219i	−0.0784882	−	0.173130i
$446$	0.236814	−	2.25313i	0.0112135	−	0.106689i
$447$	0.0909806	−	0.125224i	0.00430323	−	0.00592289i
$448$	33.7465	+	11.6107i	1.59437	+	0.548554i
$449$	−20.8070			−0.981942			−0.490971	−	0.871176i	$-0.663358\pi$
$449$	−20.8070			−0.981942			−0.490971	+	0.871176i	$0.663358\pi$
$450$	−13.1885	−	1.20625i	−0.621713	−	0.0568633i
$451$	7.87497	−	13.6399i	0.370818	−	0.642276i
$452$	−48.0672	+	43.2799i	−2.26089	+	2.03571i
$453$	−8.64069	−	0.908173i	−0.405975	−	0.0426697i
$454$	−28.5996	−	20.7788i	−1.34224	−	0.975197i
$455$	−32.0012	+	18.0325i	−1.50024	+	0.845375i
$456$	−8.78885	+	6.38547i	−0.411576	+	0.299027i
$457$	−17.0452	+	9.84103i	−0.797339	+	0.460344i	−0.842540	−	0.538634i	$-0.818941\pi$
$457$	−17.0452	+	9.84103i	−0.797339	+	0.460344i	0.0452007	+	0.998978i	$0.485607\pi$
$458$	75.9986	−	7.98777i	3.55118	−	0.373244i
$459$	6.50206	+	1.38206i	0.303490	+	0.0645089i
$460$	−62.6455	+	70.5273i	−2.92086	+	3.28835i
$461$	4.01807	−	12.3663i	0.187140	−	0.575958i	−0.812839	−	0.582489i	$-0.802079\pi$
$461$	4.01807	−	12.3663i	0.187140	−	0.575958i	0.999979	+	0.00653107i	$0.00207892\pi$
$462$	−5.21655	+	22.6204i	−0.242696	+	1.05240i
$463$	21.6431	−	7.03228i	1.00584	−	0.326818i	0.240644	−	0.970613i	$-0.422641\pi$
$463$	21.6431	−	7.03228i	1.00584	−	0.326818i	0.765197	+	0.643796i	$0.222641\pi$
$464$	−30.6173	+	6.50791i	−1.42137	+	0.302122i
$465$	−6.94871	−	7.61326i	−0.322239	−	0.353056i
$466$	46.7609	+	9.93935i	2.16616	+	0.460431i
$467$	−12.0789	+	27.1297i	−0.558946	+	1.25541i	0.384266	+	0.923222i	$0.374455\pi$
$467$	−12.0789	+	27.1297i	−0.558946	+	1.25541i	−0.943212	+	0.332191i	$0.892212\pi$
$468$			31.1416i			1.43952i
$469$	−0.641065	−	7.30697i	−0.0296016	−	0.337405i
$470$	−6.84298	+	2.27464i	−0.315643	+	0.104921i
$471$	0.967593	−	9.20603i	0.0445843	−	0.424191i
$472$	7.29128	+	16.3765i	0.335609	+	0.753789i
$473$	3.54476	−	3.19172i	0.162988	−	0.146755i
$474$	14.4669	+	25.0573i	0.664484	+	1.15092i
$475$	−6.79962	+	0.0918765i	−0.311988	+	0.00421558i
$476$	−42.7846	−	77.1412i	−1.96103	−	3.53576i
$477$	8.13798	+	2.64419i	0.372613	+	0.121069i
$478$	71.5553	+	7.52077i	3.27286	+	0.343992i
$479$	−0.960887	+	0.427815i	−0.0439041	+	0.0195473i	−0.428571	−	0.903508i	$-0.640983\pi$
$479$	−0.960887	+	0.427815i	−0.0439041	+	0.0195473i	0.384667	+	0.923055i	$0.374316\pi$
$480$	29.9849	−	3.35649i	1.36862	−	0.153202i
$481$	−21.1265	−	9.40613i	−0.963286	−	0.428883i
$482$			3.97918i			0.181247i
$483$	−12.7684	−	18.2257i	−0.580982	−	0.829299i
$484$	0.0414050	+	0.127431i	0.00188205	+	0.00579234i
$485$	9.80629	+	4.28690i	0.445281	+	0.194658i
$486$	−1.77233	−	1.96838i	−0.0803947	−	0.0892874i
$487$	−0.391238	+	1.84063i	−0.0177287	+	0.0834068i	−0.986123	−	0.166019i	$-0.946909\pi$
$487$	−0.391238	+	1.84063i	−0.0177287	+	0.0834068i	0.968394	+	0.249426i	$0.0802420\pi$
$488$	49.6705	+	44.7236i	2.24848	+	2.02454i
$489$	5.56175	−	17.1173i	0.251511	−	0.774071i
$490$	−38.3266	+	15.8087i	−1.73142	+	0.714165i
$491$	−11.3988	−	35.0820i	−0.514423	−	1.58323i	−0.784330	−	0.620344i	$-0.786993\pi$
$491$	−11.3988	−	35.0820i	−0.514423	−	1.58323i	0.269908	−	0.962886i	$-0.413007\pi$
$492$	9.69960	−	21.7857i	0.437292	−	0.982174i
$493$	16.1962	+	9.35088i	0.729440	+	0.421142i
$494$	2.33795	+	22.2441i	0.105189	+	1.00081i
$495$	1.58895	+	7.23475i	0.0714181	+	0.325178i
$496$	41.4912	+	30.1451i	1.86301	+	1.35356i
$497$	−11.9274	+	15.8362i	−0.535017	+	0.710350i
$498$	−7.63507	−	2.48078i	−0.342136	−	0.111167i
$499$	4.64734	+	8.04942i	0.208043	+	0.360342i	0.951098	−	0.308889i	$-0.0999571\pi$
$499$	4.64734	+	8.04942i	0.208043	+	0.360342i	−0.743055	+	0.669231i	$0.766624\pi$
$500$	49.1224	+	27.0486i	2.19682	+	1.20965i
$501$	4.02417	−	6.97006i	0.179786	−	0.311399i
$502$	1.99235	+	9.37325i	0.0889228	+	0.418349i
$503$	−5.21306	+	7.17516i	−0.232439	+	0.319924i	−0.909265	−	0.416219i	$-0.863355\pi$
$503$	−5.21306	+	7.17516i	−0.232439	+	0.319924i	0.676826	+	0.736143i	$0.263355\pi$
$504$	−2.57042	+	20.9765i	−0.114496	+	0.934367i
$505$	−27.3119	−	8.67062i	−1.21536	−	0.385837i
$506$	67.4184	+	30.0166i	2.99711	+	1.33440i
$507$	22.1268	+	12.7749i	0.982688	+	0.567355i
$508$	20.2051	−	2.12364i	0.896455	−	0.0942212i
$509$	−4.02236	+	4.46728i	−0.178288	+	0.198009i	−0.825664	−	0.564162i	$-0.809199\pi$
$509$	−4.02236	+	4.46728i	−0.178288	+	0.198009i	0.647377	+	0.762170i	$0.275866\pi$
$510$	−32.0067	−	22.9255i	−1.41728	−	1.01516i
$511$	21.4547	+	24.6688i	0.949102	+	1.09128i
$512$	26.2617	−	8.53294i	1.16061	−	0.377106i
$513$	−1.01071	−	0.910050i	−0.0446241	−	0.0401797i
$514$	−1.18938	−	1.32095i	−0.0524615	−	0.0582644i
$515$	2.46176	+	21.9919i	0.108478	+	0.969080i
$516$	4.83266	−	5.36721i	0.212746	−	0.236278i
$517$	2.37067	+	3.26294i	0.104262	+	0.143504i
$518$	−22.3769	−	13.4380i	−0.983183	−	0.590431i
$519$	2.45946	−	1.78690i	0.107958	−	0.0784363i
$520$	44.4201	−	101.611i	1.94795	−	4.45594i
$521$	−36.3707	+	16.1933i	−1.59343	+	0.709441i	−0.995733	−	0.0922801i	$-0.970584\pi$
$521$	−36.3707	+	16.1933i	−1.59343	+	0.709441i	−0.597698	+	0.801721i	$0.703918\pi$
$522$	−3.03098	−	6.80770i	−0.132663	−	0.297965i
$523$	4.33248	+	20.3827i	0.189446	+	0.891273i	0.965459	+	0.260556i	$0.0839059\pi$
$523$	4.33248	+	20.3827i	0.189446	+	0.891273i	−0.776013	+	0.630717i	$0.782761\pi$
$524$	72.6922			3.17557
$525$	−8.88807	+	9.79807i	−0.387907	+	0.427623i
$526$	11.2126			0.488893
$527$	−6.37085	−	29.9725i	−0.277519	−	1.30562i
$528$	−14.9902	−	33.6686i	−0.652367	−	1.46524i
$529$	−43.6164	+	19.4193i	−1.89637	+	0.844316i
$530$	−37.8903	−	33.6558i	−1.64585	−	1.46192i
$531$	−1.81563	+	1.31913i	−0.0787918	+	0.0572456i
$532$	−0.310603	+	18.0455i	−0.0134664	+	0.782371i
$533$	−17.3517	−	23.8825i	−0.751584	−	1.03447i
$534$	−3.17835	+	3.52991i	−0.137541	+	0.152754i
$535$	5.18349	+	5.67922i	0.224102	+	0.245534i
$536$	14.8178	+	16.4569i	0.640033	+	0.710828i
$537$	6.53437	+	5.88357i	0.281979	+	0.253895i
$538$	−55.1991	+	17.9353i	−2.37980	+	0.773244i
$539$	14.9137	+	17.7559i	0.642378	+	0.764802i
$540$	3.53773	+	10.6428i	0.152240	+	0.457994i
$541$	−5.37361	+	5.96800i	−0.231030	+	0.256585i	−0.847502	−	0.530792i	$-0.821895\pi$
$541$	−5.37361	+	5.96800i	−0.231030	+	0.256585i	0.616472	+	0.787377i	$0.288561\pi$
$542$	−21.9169	+	2.30356i	−0.941412	+	0.0989463i
$543$	15.4853	+	8.94042i	0.664536	+	0.383670i
$544$	81.9406	+	36.4823i	3.51317	+	1.56417i
$545$	0.0976446	+	14.4537i	0.00418264	+	0.619127i
$546$	34.7555	+	26.1769i	1.48740	+	1.12027i
$547$	3.91188	−	5.38425i	0.167260	−	0.230214i	−0.717156	−	0.696912i	$-0.754557\pi$
$547$	3.91188	−	5.38425i	0.167260	−	0.230214i	0.884416	+	0.466699i	$0.154557\pi$
$548$	0.0959325	+	0.451327i	0.00409803	+	0.0192797i
$549$	−4.18384	+	7.24663i	−0.178562	+	0.309278i
$550$	8.54060	−	43.0312i	0.364172	−	1.83486i
$551$	−1.91320	−	3.31375i	−0.0815049	−	0.141171i
$552$	63.8957	+	20.7610i	2.71958	+	0.883646i
$553$	28.6868	+	3.51522i	1.21989	+	0.149483i
$554$	3.34861	+	2.43291i	0.142269	+	0.103364i
$555$	−8.28865	−	0.814599i	−0.351834	−	0.0345778i
$556$	−1.80354	−	17.1595i	−0.0764870	−	0.727725i
$557$	−35.2033	−	20.3247i	−1.49161	−	0.861183i	−0.491659	−	0.870788i	$-0.663610\pi$
$557$	−35.2033	−	20.3247i	−1.49161	−	0.861183i	−0.999954	+	0.00960422i	$0.996943\pi$
$558$	−4.96615	+	11.1542i	−0.210234	+	0.472193i
$559$	−2.76274	−	8.50283i	−0.116851	−	0.359631i
$560$	33.5044	−	56.6550i	1.41582	−	2.39411i
$561$	−6.80452	+	20.9422i	−0.287287	+	0.884179i
$562$	−4.68802	−	4.22111i	−0.197752	−	0.178057i
$563$	−0.764237	+	3.59545i	−0.0322088	+	0.151530i	−0.991313	−	0.131522i	$-0.958014\pi$
$563$	−0.764237	+	3.59545i	−0.0322088	+	0.151530i	0.959105	+	0.283052i	$0.0913470\pi$
$564$	4.08624	+	4.53823i	0.172062	+	0.191094i
$565$	14.5862	+	24.8745i	0.613647	+	1.04648i
$566$	23.2346	+	71.5087i	0.976623	+	3.00574i
$567$	−2.63563	+	0.231232i	−0.110686	+	0.00971084i
$568$		−	59.8540i		−	2.51142i
$569$	−38.8537	−	17.2988i	−1.62883	−	0.725202i	−0.630146	−	0.776477i	$-0.717005\pi$
$569$	−38.8537	−	17.2988i	−1.62883	−	0.725202i	−0.998685	+	0.0512746i	$0.983672\pi$
$570$	3.32597	+	7.33645i	0.139309	+	0.307290i
$571$	6.07538	−	2.70494i	0.254247	−	0.113198i	−0.275656	−	0.961256i	$-0.588895\pi$
$571$	6.07538	−	2.70494i	0.254247	−	0.113198i	0.529903	+	0.848058i	$0.322228\pi$
$572$	−102.595	−	10.7831i	−4.28969	−	0.450865i
$573$	−10.2650	−	3.33531i	−0.428828	−	0.139335i
$574$	−16.1605	−	29.1377i	−0.674528	−	1.21618i
$575$	25.1766	+	33.6859i	1.04994	+	1.40480i
$576$	−6.74440	−	11.6817i	−0.281017	−	0.486735i
$577$	−28.0291	+	25.2376i	−1.16687	+	1.05065i	−0.168986	+	0.985619i	$0.554049\pi$
$577$	−28.0291	+	25.2376i	−1.16687	+	1.05065i	−0.997883	+	0.0650348i	$0.979284\pi$
$578$	−29.2892	−	65.7847i	−1.21827	−	2.73628i
$579$	0.269903	−	2.56796i	0.0112168	−	0.106721i
$580$	0.213162	+	31.5530i	0.00885108	+	1.31017i
$581$	−6.56767	+	4.60111i	−0.272473	+	0.190886i
$582$		−	12.6774i		−	0.525495i
$583$	−11.5290	+	25.8946i	−0.477483	+	1.07244i
$584$	−96.5461	−	20.5215i	−3.99511	−	0.849186i
$585$	13.5992	+	2.79472i	0.562259	+	0.115547i
$586$	−24.9405	+	5.30127i	−1.03028	+	0.218993i
$587$	35.3082	−	11.4723i	1.45733	−	0.473514i	0.530074	−	0.847952i	$-0.322164\pi$
$587$	35.3082	−	11.4723i	1.45733	−	0.473514i	0.927252	+	0.374438i	$0.122164\pi$
$588$	25.2677	+	24.3770i	1.04202	+	1.00529i
$589$	−1.93735	+	5.96255i	−0.0798272	+	0.245683i
$590$	12.9826	−	2.85133i	0.534484	−	0.117387i
$591$	18.2145	+	3.87161i	0.749243	+	0.159257i
$592$	41.2124	−	4.33160i	1.69382	−	0.178027i
$593$	−3.06907	+	1.77193i	−0.126032	+	0.0727644i	−0.561690	−	0.827348i	$-0.689849\pi$
$593$	−3.06907	+	1.77193i	−0.126032	+	0.0727644i	0.435659	+	0.900112i	$0.356515\pi$
$594$	7.09841	−	5.15729i	0.291251	−	0.211606i
$595$	−37.5264	+	11.7607i	−1.53843	+	0.482144i
$596$	0.628084	+	0.456330i	0.0257273	+	0.0186920i
$597$	6.93066	+	0.728442i	0.283653	+	0.0298132i
$598$	102.793	−	92.5555i	4.20353	−	3.78488i
$599$	−18.3769	+	31.8298i	−0.750860	+	1.30053i	0.196546	+	0.980495i	$0.437028\pi$
$599$	−18.3769	+	31.8298i	−0.750860	+	1.30053i	−0.947406	+	0.320034i	$0.896306\pi$
$600$	3.63767	−	39.7724i	0.148507	−	1.62370i
$601$	−3.40034			−0.138703			−0.0693514	−	0.997592i	$-0.522093\pi$
$601$	−3.40034			−0.138703			−0.0693514	+	0.997592i	$0.522093\pi$
$602$	−1.92784	−	9.90503i	−0.0785728	−	0.403699i
$603$	−1.62957	+	2.24291i	−0.0663611	+	0.0913382i
$604$	4.55510	−	43.3389i	0.185345	−	1.76344i
$605$	0.0593638	−	0.00664514i	0.00241348	−	0.000270164i
$606$	3.54803	+	33.7572i	0.144129	+	1.37129i
$607$	16.7406	−	9.66520i	0.679480	−	0.392298i	−0.120179	−	0.992752i	$-0.538347\pi$
$607$	16.7406	−	9.66520i	0.679480	−	0.392298i	0.799659	+	0.600454i	$0.205013\pi$
$608$	−10.7869	−	14.8468i	−0.437465	−	0.602119i
$609$	−7.25325	−	1.67269i	−0.293917	−	0.0677808i
$610$	39.8966	−	29.4004i	1.61537	−	1.19039i
$611$	7.39434	−	1.57172i	0.299143	−	0.0635848i
$612$	−6.93195	+	32.6123i	−0.280208	+	1.31827i
$613$	−5.50653	+	25.9062i	−0.222406	+	1.04634i	0.715275	+	0.698843i	$0.246302\pi$
$613$	−5.50653	+	25.9062i	−0.222406	+	1.04634i	−0.937681	+	0.347497i	$0.887032\pi$
$614$	−41.5670	+	8.83534i	−1.67751	+	0.356565i
$615$	−8.64311	−	6.19081i	−0.348524	−	0.249637i
$616$	−68.2159	−	15.7314i	−2.74850	−	0.633838i
$617$	24.9078	+	34.2826i	1.00275	+	1.38017i	0.923623	+	0.383302i	$0.125213\pi$
$617$	24.9078	+	34.2826i	1.00275	+	1.38017i	0.0791268	+	0.996865i	$0.474787\pi$
$618$	22.7011	−	13.1065i	0.913174	−	0.527221i
$619$	−3.71277	−	35.3246i	−0.149229	−	1.41982i	−0.771109	−	0.636704i	$-0.780298\pi$
$619$	−3.71277	−	35.3246i	−0.149229	−	1.41982i	0.621880	−	0.783113i	$-0.286369\pi$
$620$	38.1857	−	34.8525i	1.53357	−	1.39971i
$621$	−0.879184	+	8.36487i	−0.0352804	+	0.335671i
$622$	−0.0864571	+	0.118998i	−0.00346661	+	0.00477138i
$623$	0.906454	+	4.65726i	0.0363163	+	0.186589i
$624$	−69.0778			−2.76533
$625$	16.2202	−	19.0238i	0.648807	−	0.760953i
$626$	−28.3515	+	49.1063i	−1.13315	+	1.96268i
$627$	3.34808	−	3.01463i	0.133710	−	0.120393i
$628$	46.1745	+	4.85314i	1.84256	+	0.193661i
$629$	−20.0305	−	14.5530i	−0.798667	−	0.580265i
$630$	14.8516	+	4.99784i	0.591702	+	0.199119i
$631$	22.6133	−	16.4295i	0.900223	−	0.654050i	−0.0383005	−	0.999266i	$-0.512194\pi$
$631$	22.6133	−	16.4295i	0.900223	−	0.654050i	0.938523	+	0.345216i	$0.112194\pi$
$632$	−75.5649	+	43.6274i	−3.00581	+	1.73540i
$633$	−8.12733	+	0.854217i	−0.323032	+	0.0339521i
$634$	1.90563	+	0.405055i	0.0756823	+	0.0160868i
$635$	0.885877	−	9.01393i	0.0351550	−	0.357707i
$636$	−13.2624	+	40.8175i	−0.525889	+	1.61852i
$637$	41.7725	−	12.0000i	1.65509	−	0.475459i
$638$	23.4771	−	7.62818i	0.929469	−	0.302003i
$639$	7.32956	−	1.55795i	0.289953	−	0.0616314i
$640$	2.17436	+	19.4245i	0.0859493	+	0.767820i
$641$	−43.9645	−	9.34493i	−1.73649	−	0.369103i	−0.772496	−	0.635020i	$-0.780992\pi$
$641$	−43.9645	−	9.34493i	−1.73649	−	0.369103i	−0.963996	+	0.265917i	$0.914325\pi$
$642$	3.70458	−	8.32061i	0.146208	−	0.328388i
$643$		−	25.0623i		−	0.988359i	−0.869360	−	0.494179i	$-0.835469\pi$
$643$		−	25.0623i		−	0.988359i	0.869360	−	0.494179i	$-0.164531\pi$
$644$	91.4144	−	64.0421i	3.60223	−	2.52361i
$645$	−1.91011	−	2.59204i	−0.0752106	−	0.102061i
$646$	−2.50306	+	23.8150i	−0.0984814	+	0.936988i
$647$	5.12757	+	11.5167i	0.201586	+	0.452769i	0.985844	−	0.167666i	$-0.0536229\pi$
$647$	5.12757	+	11.5167i	0.201586	+	0.452769i	−0.784258	+	0.620435i	$0.786956\pi$
$648$	5.93600	−	5.34480i	0.233188	−	0.209963i
$649$	−3.71714	−	6.43827i	−0.145910	−	0.252724i
$650$	−67.1703	−	47.4288i	−2.63464	−	1.86031i
$651$	5.91537	+	10.6655i	0.231842	+	0.418014i
$652$	85.8549	+	27.8959i	3.36234	+	1.09249i
$653$	18.4614	+	1.94037i	0.722450	+	0.0759326i	0.458615	−	0.888635i	$-0.348346\pi$
$653$	18.4614	+	1.94037i	0.722450	+	0.0759326i	0.263835	+	0.964568i	$0.415012\pi$
$654$	15.6411	−	6.96388i	0.611617	−	0.272309i
$655$	6.52356	−	31.7439i	0.254896	−	1.24034i
$656$	48.3246	+	21.5155i	1.88676	+	0.840038i
$657$		−	12.3569i		−	0.482089i
$658$	8.49968	−	0.745705i	0.331352	−	0.0290706i
$659$	12.3805	+	38.1032i	0.482276	+	1.48429i	0.835888	+	0.548900i	$0.184953\pi$
$659$	12.3805	+	38.1032i	0.482276	+	1.48429i	−0.353613	+	0.935392i	$0.615047\pi$
$660$	−36.2872	+	7.96968i	−1.41248	+	0.310219i
$661$	−26.2235	−	29.1241i	−1.01997	−	1.13280i	−0.991087	−	0.133214i	$-0.957470\pi$
$661$	−26.2235	−	29.1241i	−1.01997	−	1.13280i	−0.0288871	−	0.999583i	$-0.509196\pi$
$662$	−10.6596	+	50.1496i	−0.414298	+	1.94912i
$663$	30.6713	+	27.6165i	1.19117	+	1.07254i
$664$	7.48125	−	23.0249i	0.290329	−	0.893541i
$665$	7.85241	+	1.75508i	0.304503	+	0.0680591i
$666$	3.04862	+	9.38269i	0.118132	+	0.363572i
$667$	−9.62485	+	21.6178i	−0.372676	+	0.837043i
$668$	34.9596	+	20.1839i	1.35263	+	0.780940i
$669$	0.0894071	+	0.850652i	0.00345668	+	0.0328881i
$670$	14.1644	−	8.30588i	0.547217	−	0.320884i
$671$	−22.4249	−	16.2927i	−0.865705	−	0.628972i
$672$	−35.4352	−	4.34216i	−1.36694	−	0.167502i
$673$	−30.3784	−	9.87055i	−1.17100	−	0.380482i	−0.341985	−	0.939705i	$-0.611099\pi$
$673$	−30.3784	−	9.87055i	−1.17100	−	0.380482i	−0.829017	+	0.559224i	$0.811099\pi$
$674$	26.0700	+	45.1545i	1.00418	+	1.73929i
$675$	4.96509	−	0.589778i	0.191107	−	0.0227006i
$676$	−64.0750	+	110.981i	−2.46442	+	4.26851i
$677$	−6.13271	−	28.8521i	−0.235699	−	1.10888i	−0.923685	−	0.383153i	$-0.874838\pi$
$677$	−6.13271	−	28.8521i	−0.235699	−	1.10888i	0.687986	−	0.725724i	$-0.258495\pi$
$678$	20.0770	−	27.6336i	0.771053	−	1.06126i
$679$	−10.1151	−	7.61846i	−0.388184	−	0.292370i
$680$	69.1359	−	96.5220i	2.65124	−	3.70145i
$681$	12.1926	+	5.42850i	0.467222	+	0.208021i
$682$	−35.0272	−	20.2230i	−1.34126	−	0.774378i
$683$	10.1234	−	1.06401i	0.387361	−	0.0407133i	0.0911536	−	0.995837i	$-0.470945\pi$
$683$	10.1234	−	1.06401i	0.387361	−	0.0407133i	0.296208	+	0.955124i	$0.404278\pi$
$684$	4.56452	−	5.06941i	0.174529	−	0.193834i
$685$	0.205699	−	0.00138964i	0.00785935	−	5.30954e-5i
$686$	48.4453	−	7.70915i	1.84965	−	0.294337i
$687$	−27.4386	+	8.91536i	−1.04685	+	0.340142i
$688$	11.9055	+	10.7197i	0.453891	+	0.408686i
$689$	35.5494	+	39.4817i	1.35433	+	1.50413i
$690$	24.6158	−	43.3088i	0.937106	−	1.64874i
$691$	15.2282	−	16.9127i	0.579309	−	0.643388i	−0.380254	−	0.924882i	$-0.624163\pi$
$691$	15.2282	−	16.9127i	0.579309	−	0.643388i	0.959563	+	0.281494i	$0.0908301\pi$
$692$	8.96253	+	12.3359i	0.340704	+	0.468939i
$693$	0.150831	−	8.76300i	0.00572959	−	0.332879i
$694$	−25.3790	+	18.4389i	−0.963374	+	0.699932i
$695$	−7.65523	−	0.752346i	−0.290379	−	0.0285381i
$696$	20.5299	−	9.14048i	0.778182	−	0.346469i
$697$	−12.8550	−	28.8727i	−0.486917	−	1.09363i
$698$	6.94505	+	32.6739i	0.262874	+	1.23673i
$699$	−18.0486			−0.682662
$700$	−49.1440	−	44.5797i	−1.85747	−	1.68496i
$701$	3.76283			0.142120			0.0710601	−	0.997472i	$-0.477362\pi$
$701$	3.76283			0.142120			0.0710601	+	0.997472i	$0.477362\pi$
$702$	−3.41921	−	16.0861i	−0.129050	−	0.607131i
$703$	2.06041	+	4.62776i	0.0777099	+	0.174539i
$704$	40.8199	−	18.1742i	1.53846	−	0.684966i
$705$	2.34851	−	1.37715i	0.0884499	−	0.0518664i
$706$	29.7051	−	21.5820i	1.11797	−	0.812250i
$707$	29.0667	+	17.4554i	1.09317	+	0.656479i
$708$	−6.61636	−	9.10664i	−0.248658	−	0.342248i
$709$	−13.0638	+	14.5089i	−0.490622	+	0.544891i	−0.936714	−	0.350096i	$-0.886149\pi$
$709$	−13.0638	+	14.5089i	−0.490622	+	0.544891i	0.446091	+	0.894987i	$0.352816\pi$
$710$	−43.4721	−	8.93377i	−1.63148	−	0.335278i
$711$	−7.30937	−	8.11788i	−0.274123	−	0.304444i
$712$	−10.6451	−	9.58489i	−0.398942	−	0.359209i
$713$	36.8742	−	11.9812i	1.38095	−	0.448698i
$714$	30.5700	+	35.1495i	1.14405	+	1.31544i
$715$	−13.9159	+	43.8342i	−0.520426	+	1.63931i
$716$	−29.5101	+	32.7743i	−1.10284	+	1.22483i
$717$	−27.0151	+	2.83940i	−1.00890	+	0.106040i
$718$	−33.4227	−	19.2966i	−1.24732	−	0.720142i
$719$	−20.2511	−	9.01637i	−0.755238	−	0.336254i	−0.00725702	−	0.999974i	$-0.502310\pi$
$719$	−20.2511	−	9.01637i	−0.755238	−	0.336254i	−0.747981	+	0.663720i	$0.768977\pi$
$720$	−23.6077	+	7.84733i	−0.879808	+	0.292453i
$721$	3.18468	−	25.9893i	0.118604	−	0.967893i
$722$	−26.7008	+	36.7505i	−0.993701	+	1.36771i
$723$	−0.312347	−	1.46948i	−0.0116163	−	0.0546505i
$724$	−44.8423	+	77.6691i	−1.66655	+	2.88655i
$725$	13.7980	+	2.73855i	0.512444	+	0.101707i
$726$	−0.0353790	−	0.0612782i	−0.00131304	−	0.00227425i
$727$	−11.7563	−	3.81985i	−0.436016	−	0.141670i	0.0827805	−	0.996568i	$-0.473620\pi$
$727$	−11.7563	−	3.81985i	−0.436016	−	0.141670i	−0.518797	+	0.854897i	$0.673620\pi$
$728$	−78.9412	+	104.811i	−2.92576	+	3.88457i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−29.3152	+	67.0586i	−1.08501	+	2.48195i
$731$	−1.00052	−	9.51934i	−0.0370057	−	0.352085i
$732$	−36.3468	−	20.9848i	−1.34342	−	0.775621i
$733$	14.1996	−	31.8929i	0.524476	−	1.17799i	−0.436081	−	0.899907i	$-0.643634\pi$
$733$	14.1996	−	31.8929i	0.524476	−	1.17799i	0.960557	−	0.278084i	$-0.0896994\pi$
$734$	3.14108	+	9.66725i	0.115939	+	0.356825i
$735$	12.9128	−	8.84649i	0.476295	−	0.326308i
$736$	−35.0711	+	107.938i	−1.29274	+	3.97864i
$737$	−6.82488	−	6.14515i	−0.251398	−	0.226360i
$738$	−2.61833	+	12.3183i	−0.0963821	+	0.453442i
$739$	−27.9767	−	31.0713i	−1.02914	−	1.14298i	−0.989613	−	0.143757i	$-0.954082\pi$
$739$	−27.9767	−	31.0713i	−1.02914	−	1.14298i	−0.0395270	−	0.999219i	$-0.512585\pi$
$740$	4.08577	−	41.5732i	0.150196	−	1.52826i
$741$	−2.60945	−	8.03105i	−0.0958604	−	0.295028i
$742$	34.4062	+	49.1117i	1.26309	+	1.80295i
$743$			14.7117i			0.539720i	0.962900	+	0.269860i	$0.0869774\pi$
$743$			14.7117i			0.539720i	−0.962900	+	0.269860i	$0.913023\pi$
$744$	−33.6374	−	14.9763i	−1.23321	−	0.549059i
$745$	0.255640	−	0.233326i	0.00936593	−	0.00854839i
$746$	−11.7400	+	5.22700i	−0.429833	+	0.191374i
$747$	3.01430	+	0.316815i	0.110287	+	0.0115917i
$748$	−105.039	−	34.1293i	−3.84061	−	1.24789i
$749$	−4.41266	−	7.95610i	−0.161235	−	0.290709i
$750$	−28.3438	−	8.57844i	−1.03497	−	0.313240i
$751$	−21.7600	−	37.6895i	−0.794035	−	1.37531i	−0.923450	−	0.383718i	$-0.874644\pi$
$751$	−21.7600	−	37.6895i	−0.794035	−	1.37531i	0.129416	−	0.991590i	$-0.458690\pi$
$752$	−10.0666	+	9.06403i	−0.367092	+	0.330531i
$753$	−1.47151	−	3.30507i	−0.0536249	−	0.120444i
$754$	4.83634	−	46.0147i	0.176129	−	1.67576i
$755$	−18.5169	−	5.87850i	−0.673898	−	0.213940i
$756$	−1.15979	−	13.2195i	−0.0421811	−	0.480787i
$757$			47.4408i			1.72427i	0.506682	+	0.862133i	$0.330872\pi$
$757$			47.4408i			1.72427i	−0.506682	+	0.862133i	$0.669128\pi$
$758$	34.4987	−	77.4853i	1.25305	−	2.81439i
$759$	−27.2532	−	5.79285i	−0.989229	−	0.210267i
$760$	−22.1244	+	10.0301i	−0.802536	+	0.363828i
$761$	−2.99021	+	0.635588i	−0.108395	+	0.0230400i	−0.261790	−	0.965125i	$-0.584313\pi$
$761$	−2.99021	+	0.635588i	−0.108395	+	0.0230400i	0.153395	+	0.988165i	$0.450979\pi$
$762$	−10.2037	+	3.31538i	−0.369641	+	0.120104i
$763$	3.84311	−	16.6648i	0.139130	−	0.603307i
$764$	16.7288	−	51.4861i	0.605228	−	1.86270i
$765$	13.6194	+	5.95381i	0.492409	+	0.215260i
$766$	67.6513	+	14.3797i	2.44434	+	0.519561i
$767$	−13.8579	+	1.45652i	−0.500379	+	0.0525919i
$768$	−3.31240	+	1.91241i	−0.119526	+	0.0690083i
$769$	−2.45532	+	1.78389i	−0.0885410	+	0.0643288i	−0.631175	−	0.775640i	$-0.717427\pi$
$769$	−2.45532	+	1.78389i	−0.0885410	+	0.0643288i	0.542634	+	0.839969i	$0.317427\pi$
$770$	−21.6076	+	47.1973i	−0.778686	+	1.70087i
$771$	0.542918	+	0.394453i	0.0195527	+	0.0142059i
$772$	12.8801	+	1.35375i	0.463563	+	0.0487225i
$773$	−0.745746	+	0.671473i	−0.0268226	+	0.0241512i	−0.682433	−	0.730948i	$-0.739078\pi$
$773$	−0.745746	+	0.671473i	−0.0268226	+	0.0241512i	0.655610	+	0.755099i	$0.272411\pi$
$774$	−1.90700	+	3.30302i	−0.0685457	+	0.118725i
$775$	−11.7929	−	19.8030i	−0.423612	−	0.711345i
$776$	38.2310			1.37241
$777$	9.31841	+	3.20605i	0.334296	+	0.115017i
$778$	40.4696	−	55.7016i	1.45090	−	1.99700i
$779$	−0.675927	+	6.43101i	−0.0242176	+	0.230415i
$780$	−14.0174	+	68.2094i	−0.501904	+	2.44229i
$781$	2.59463	+	24.6863i	0.0928433	+	0.883345i
$782$	128.250	−	74.0452i	4.58621	−	2.64785i
$783$	1.65369	+	2.27611i	0.0590981	+	0.0813415i
$784$	−54.0727	+	56.0483i	−1.93117	+	2.00173i
$785$	6.26312	−	19.7284i	0.223540	−	0.704136i
$786$	−37.5489	+	7.98126i	−1.33932	+	0.284682i
$787$	0.313088	−	1.47296i	0.0111604	−	0.0525055i	−0.972215	−	0.234090i	$-0.924789\pi$
$787$	0.313088	−	1.47296i	0.0111604	−	0.0525055i	0.983375	+	0.181584i	$0.0581224\pi$
$788$	−19.4187	+	91.3580i	−0.691764	+	3.25449i
$789$	−4.14073	+	0.880139i	−0.147414	+	0.0313338i
$790$	20.4079	+	61.3947i	0.726081	+	2.18433i
$791$	−9.98330	−	32.6256i	−0.354965	−	1.16003i
$792$	15.5528	+	21.4065i	0.552643	+	0.760648i
$793$	−44.9933	+	25.9769i	−1.59776	+	0.922466i
$794$	4.39741	+	41.8386i	0.156058	+	1.48480i
$795$	16.6344	+	9.45461i	0.589961	+	0.335321i
$796$	−3.65363	+	34.7620i	−0.129500	+	1.23211i
$797$	5.74655	−	7.90945i	0.203553	−	0.280167i	−0.695020	−	0.718990i	$-0.744605\pi$
$797$	5.74655	−	7.90945i	0.203553	−	0.280167i	0.898573	+	0.438823i	$0.144605\pi$
$798$	−1.82087	−	9.35544i	−0.0644581	−	0.331179i
$799$	8.09339			0.286323
$800$	67.1867	+	6.14505i	2.37541	+	0.217260i
$801$	0.896656	−	1.55305i	0.0316818	−	0.0548744i
$802$	1.87906	−	1.69192i	0.0663520	−	0.0597436i
$803$	40.7092	+	4.27871i	1.43660	+	0.150992i
$804$	−11.2497	−	8.17338i	−0.396746	−	0.288253i
$805$	−19.7628	−	45.6670i	−0.696547	−	1.60955i
$806$	−61.3304	+	44.5591i	−2.16027	+	1.56953i
$807$	18.9767	−	10.9562i	0.668012	−	0.385677i
$808$	−101.801	+	10.6997i	−3.58135	+	0.376415i
$809$	34.8088	+	7.39883i	1.22381	+	0.260129i	0.774111	−	0.633050i	$-0.218197\pi$
$809$	34.8088	+	7.39883i	1.22381	+	0.260129i	0.449701	+	0.893179i	$0.351531\pi$
$810$	−2.99593	−	5.10909i	−0.105266	−	0.179515i
$811$	−7.94105	+	24.4400i	−0.278848	+	0.858206i	0.709328	+	0.704879i	$0.248999\pi$
$811$	−7.94105	+	24.4400i	−0.278848	+	0.858206i	−0.988176	+	0.153327i	$0.951001\pi$
$812$	8.38968	−	36.3800i	0.294420	−	1.27669i
$813$	7.91291	−	2.57106i	0.277518	−	0.0901710i
$814$	−31.9664	+	6.79467i	−1.12042	+	0.238153i
$815$	19.8867	−	34.9885i	0.696600	−	1.22559i
$816$	−72.3400	−	15.3763i	−2.53241	−	0.538279i
$817$	−0.796550	+	1.78908i	−0.0278678	+	0.0625920i
$818$			45.5901i			1.59402i
$819$	−14.8897	−	6.93877i	−0.520288	−	0.242460i
$820$	31.0511	−	43.3511i	1.08435	−	1.51388i
$821$	2.22216	−	21.1424i	0.0775539	−	0.737876i	−0.884781	−	0.466008i	$-0.845692\pi$
$821$	2.22216	−	21.1424i	0.0775539	−	0.737876i	0.962335	−	0.271868i	$-0.0876414\pi$
$822$	−0.0991072	−	0.222598i	−0.00345676	−	0.00776401i
$823$	13.4597	−	12.1192i	0.469177	−	0.422449i	−0.400329	−	0.916372i	$-0.631104\pi$
$823$	13.4597	−	12.1192i	0.469177	−	0.422449i	0.869506	+	0.493923i	$0.164437\pi$
$824$	39.5250	+	68.4594i	1.37692	+	2.38490i
$825$	0.223779	+	16.5615i	0.00779097	+	0.576596i
$826$	−15.7250	−	0.270662i	−0.547142	−	0.00941753i
$827$	−36.7810	−	11.9509i	−1.27900	−	0.415573i	−0.410773	−	0.911738i	$-0.634741\pi$
$827$	−36.7810	−	11.9509i	−1.27900	−	0.415573i	−0.868228	+	0.496165i	$0.834741\pi$
$828$	−41.9555	−	4.40970i	−1.45806	−	0.153248i
$829$	36.2522	−	16.1405i	1.25909	−	0.560583i	0.334806	−	0.942287i	$-0.391329\pi$
$829$	36.2522	−	16.1405i	1.25909	−	0.560583i	0.924285	+	0.381704i	$0.124663\pi$
$830$	−15.6064	−	8.87034i	−0.541706	−	0.307894i
$831$	−1.42758	−	0.635601i	−0.0495224	−	0.0220488i
$832$		−	83.7501i		−	2.90351i
$833$	46.4163	−	3.26839i	1.60823	−	0.113243i
$834$	2.81564	+	8.66566i	0.0974978	+	0.300067i
$835$	11.9515	−	13.4551i	0.413597	−	0.465634i
$836$	15.1204	+	16.7929i	0.522950	+	0.580795i
$837$	0.958408	−	4.50896i	0.0331274	−	0.155852i
$838$	−31.1375	−	28.0363i	−1.07563	−	0.968498i
$839$	2.32772	−	7.16399i	0.0803619	−	0.247328i	−0.902801	−	0.430058i	$-0.858493\pi$
$839$	2.32772	−	7.16399i	0.0803619	−	0.247328i	0.983163	+	0.182729i	$0.0584932\pi$
$840$	−15.0719	+	44.7877i	−0.520029	+	1.54532i
$841$	−6.51551	−	20.0527i	−0.224673	−	0.691472i
$842$	23.2160	−	52.1440i	0.800077	−	1.79700i
$843$	2.06258	+	1.19083i	0.0710391	+	0.0410145i
$844$	−4.28448	−	40.7641i	−0.147478	−	1.40316i
$845$	42.7141	+	37.9406i	1.46941	+	1.30520i
$846$	−2.60901	−	1.89556i	−0.0896997	−	0.0651706i
$847$	−0.0701541	−	0.00859655i	−0.00241052	−	0.000295381i
$848$	−90.5407	−	29.4184i	−3.10918	−	1.01023i
$849$	−14.1934	−	24.5838i	−0.487118	−	0.843712i
$850$	−59.7850	−	64.6204i	−2.05061	−	2.21646i
$851$	15.6640	−	27.1308i	0.536953	−	0.930031i
$852$	7.81416	+	36.7627i	0.267709	+	1.25947i
$853$	−18.6080	+	25.6117i	−0.637125	+	0.876928i	−0.998458	−	0.0555093i	$-0.982322\pi$
$853$	−18.6080	+	25.6117i	−0.637125	+	0.876928i	0.361333	+	0.932437i	$0.382322\pi$
$854$	−53.9722	+	22.9253i	−1.84689	+	0.784488i
$855$	−1.80413	−	2.44822i	−0.0616999	−	0.0837273i
$856$	25.0923	+	11.1718i	0.857638	+	0.381845i
$857$	−28.3133	−	16.3467i	−0.967164	−	0.558392i	−0.0687933	−	0.997631i	$-0.521915\pi$
$857$	−28.3133	−	16.3467i	−0.967164	−	0.558392i	−0.898370	+	0.439239i	$0.855248\pi$
$858$	54.1788	−	5.69442i	1.84963	−	0.194404i
$859$	10.1599	−	11.2837i	0.346650	−	0.384994i	−0.544456	−	0.838790i	$-0.683264\pi$
$859$	10.1599	−	11.2837i	0.346650	−	0.384994i	0.891106	+	0.453796i	$0.149930\pi$
$860$	13.0008	−	9.58051i	0.443325	−	0.326693i
$861$	8.25513	+	9.49179i	0.281334	+	0.323479i
$862$	22.6214	−	7.35013i	0.770487	−	0.250346i
$863$	39.8658	+	35.8953i	1.35705	+	1.22189i	0.951437	+	0.307843i	$0.0996072\pi$
$863$	39.8658	+	35.8953i	1.35705	+	1.22189i	0.405609	+	0.914047i	$0.367059\pi$
$864$	9.02886	+	10.0276i	0.307168	+	0.341145i
$865$	6.19126	−	2.80680i	0.210509	−	0.0954339i
$866$	39.6904	−	44.0807i	1.34874	−	1.49792i
$867$	15.9801	+	21.9947i	0.542712	+	0.746978i
$868$	−53.4948	+	29.6696i	−1.81573	+	1.00705i
$869$	29.2749	−	21.2694i	0.993082	−	0.721516i
$870$	−3.57448	−	16.2752i	−0.121186	−	0.551780i
$871$	−15.7252	+	7.00129i	−0.532827	+	0.237230i
$872$	21.0008	+	47.1687i	0.711178	+	1.59733i
$873$	0.995117	+	4.68166i	0.0336796	+	0.158450i
$874$	−30.2994			−1.02489
$875$	−23.8778	+	17.4600i	−0.807217	+	0.590255i
$876$	61.9784			2.09405
$877$	−2.01743	−	9.49125i	−0.0681237	−	0.320497i	0.930870	−	0.365351i	$-0.119051\pi$
$877$	−2.01743	−	9.49125i	−0.0681237	−	0.320497i	−0.998994	+	0.0448543i	$0.985718\pi$
$878$	−39.0748	−	87.7634i	−1.31871	−	2.96187i
$879$	8.79420	−	3.91543i	0.296621	−	0.132064i
$880$	−17.6782	−	80.4916i	−0.595932	−	2.71337i
$881$	−3.76011	+	2.73188i	−0.126681	+	0.0920393i	−0.649322	−	0.760514i	$-0.724947\pi$
$881$	−3.76011	+	2.73188i	−0.126681	+	0.0920393i	0.522640	+	0.852553i	$0.324947\pi$
$882$	−15.7284	−	9.81759i	−0.529603	−	0.330576i
$883$	−11.3432	−	15.6126i	−0.381729	−	0.525405i	0.574312	−	0.818636i	$-0.305269\pi$
$883$	−11.3432	−	15.6126i	−0.381729	−	0.525405i	−0.956042	+	0.293231i	$0.905269\pi$
$884$	−138.516	+	153.837i	−4.65879	+	5.17411i
$885$	−4.57054	+	2.07204i	−0.153637	+	0.0696510i
$886$	53.3354	+	59.2349i	1.79184	+	1.99004i
$887$	−9.06981	−	8.16649i	−0.304534	−	0.274204i	0.502667	−	0.864480i	$-0.332352\pi$
$887$	−9.06981	−	8.16649i	−0.304534	−	0.274204i	−0.807201	+	0.590276i	$0.799019\pi$
$888$	−28.2952	+	9.19367i	−0.949525	+	0.308519i
$889$	−3.48659	+	10.1338i	−0.116936	+	0.339876i
$890$	−8.55040	+	6.30092i	−0.286610	+	0.211207i
$891$	−2.21656	+	2.46174i	−0.0742575	+	0.0824713i
$892$	−4.26660	+	0.448438i	−0.142856	+	0.0150148i
$893$	−1.43406	−	0.827957i	−0.0479891	−	0.0277065i
$894$	−0.374537	−	0.166755i	−0.0125264	−	0.00557711i
$895$	11.6639	+	15.8280i	0.389881	+	0.529072i
$896$	2.81289	−	22.9552i	0.0939720	−	0.766879i
$897$	−30.6955	+	42.2488i	−1.02489	+	1.41065i
$898$	11.4584	+	53.9074i	0.382371	+	1.79891i
$899$	6.48451	−	11.2315i	0.216271	−	0.374592i
$900$	2.95814	+	24.9033i	0.0986047	+	0.830111i
$901$	28.4398	+	49.2593i	0.947469	+	1.64106i
$902$	−39.6753	−	12.8913i	−1.32104	−	0.429233i
$903$	1.48943	+	3.50652i	0.0495652	+	0.116690i
$904$	83.3342	+	60.5458i	2.77165	+	2.01372i
$905$	29.8930	+	26.5523i	0.993678	+	0.882630i
$906$	2.40549	+	22.8867i	0.0799170	+	0.760360i
$907$	38.2465	+	22.0816i	1.26995	+	0.733208i	0.974979	−	0.222298i	$-0.0713557\pi$
$907$	38.2465	+	22.0816i	1.26995	+	0.733208i	0.294974	+	0.955505i	$0.404689\pi$
$908$	−27.2276	+	61.1543i	−0.903581	+	2.02948i
$909$	−3.96004	−	12.1878i	−0.131346	−	0.404243i
$910$	64.3421	+	72.9793i	2.13292	+	2.41924i
$911$	8.61252	−	26.5066i	0.285345	−	0.878203i	−0.700950	−	0.713211i	$-0.747240\pi$
$911$	8.61252	−	26.5066i	0.285345	−	0.878203i	0.986295	−	0.164992i	$-0.0527598\pi$
$912$	11.2449	+	10.1249i	0.372355	+	0.335270i
$913$	−2.08746	+	9.82075i	−0.0690850	+	0.325019i
$914$	34.8832	+	38.7417i	1.15383	+	1.28146i
$915$	−12.4257	+	13.9890i	−0.410781	+	0.462463i
$916$	−44.7166	−	137.623i	−1.47748	−	4.54721i
$917$	−16.1968	+	34.7562i	−0.534865	+	1.14775i
$918$		−	17.6069i		−	0.581113i
$919$	44.7579	+	19.9275i	1.47643	+	0.657347i	0.977813	−	0.209478i	$-0.0671764\pi$
$919$	44.7579	+	19.9275i	1.47643	+	0.657347i	0.498613	+	0.866825i	$0.333843\pi$
$920$	130.606	+	74.2333i	4.30594	+	2.44740i
$921$	14.6568	−	6.52563i	0.482958	−	0.215027i
$922$	−34.2519	−	3.60002i	−1.12802	−	0.118560i
$923$	44.2477	+	14.3770i	1.45643	+	0.473224i
$924$	43.9524	+	0.756519i	1.44593	+	0.0248877i
$925$	−17.7879	−	5.51509i	−0.584864	−	0.181335i
$926$	−30.1383	−	52.2010i	−0.990405	−	1.71543i
$927$	−7.35454	+	6.62206i	−0.241555	+	0.217497i
$928$	15.4408	+	34.6807i	0.506870	+	1.13845i
$929$	−0.925689	+	8.80734i	−0.0303709	+	0.288960i	0.968786	+	0.247899i	$0.0797402\pi$
$929$	−0.925689	+	8.80734i	−0.0303709	+	0.288960i	−0.999157	+	0.0410602i	$0.986926\pi$
$930$	−15.8980	+	22.1955i	−0.521317	+	0.727821i
$931$	−8.55885	−	4.16929i	−0.280505	−	0.136643i
$932$		−	90.5261i		−	2.96528i
$933$	0.0225871	−	0.0507314i	0.000739468	−	0.00166087i
$934$	76.9404	+	16.3542i	2.51757	+	0.535125i
$935$	−24.3304	+	42.8067i	−0.795688	+	1.39993i
$936$	48.5105	−	10.3112i	1.58562	−	0.337033i
$937$	15.9737	−	5.19019i	0.521840	−	0.169556i	−0.0362404	−	0.999343i	$-0.511538\pi$
$937$	15.9737	−	5.19019i	0.521840	−	0.169556i	0.558080	+	0.829787i	$0.311538\pi$
$938$	−18.5781	+	5.68483i	−0.606597	+	0.185616i
$939$	6.61536	−	20.3600i	0.215884	−	0.664423i
$940$	6.90734	+	11.7794i	0.225293	+	0.384200i
$941$	34.1531	+	7.25946i	1.11336	+	0.236652i	0.727636	−	0.685963i	$-0.240619\pi$
$941$	34.1531	+	7.25946i	1.11336	+	0.236652i	0.385722	+	0.922615i	$0.373952\pi$
$942$	−24.3841	+	2.56288i	−0.794478	+	0.0835030i
$943$	34.6327	−	19.9952i	1.12780	−	0.651133i
$944$	20.2002	−	14.6763i	0.657460	−	0.477672i
$945$	−5.87688	−	0.679877i	−0.191175	−	0.0221164i
$946$	−10.2213	−	7.42622i	−0.332323	−	0.241447i
$947$	−42.7552	−	4.49376i	−1.38936	−	0.146027i	−0.619878	−	0.784698i	$-0.712818\pi$
$947$	−42.7552	−	4.49376i	−1.38936	−	0.146027i	−0.769480	+	0.638670i	$0.779485\pi$
$948$	40.7167	−	36.6615i	1.32242	−	1.19071i
$949$	38.3612	−	66.4435i	1.24526	−	2.15685i
$950$	3.98258	+	17.5661i	0.129212	+	0.569919i
$951$	−0.735529			−0.0238512
$952$	−106.000	+	92.1893i	−3.43547	+	2.98787i
$953$	−29.6246	+	40.7748i	−0.959636	+	1.32083i	−0.0125241	+	0.999922i	$0.503987\pi$
$953$	−29.6246	+	40.7748i	−0.959636	+	1.32083i	−0.947112	+	0.320904i	$0.896013\pi$
$954$	2.36908	−	22.5403i	0.0767018	−	0.729769i
$955$	−20.9822	−	11.9258i	−0.678967	−	0.385909i
$956$	−14.2415	−	135.499i	−0.460605	−	4.38236i
$957$	−8.07113	+	4.65987i	−0.260903	+	0.150632i
$958$	1.63755	+	2.25390i	0.0529070	+	0.0728202i
$959$	−0.237167	−	0.0546937i	−0.00765852	−	0.00176615i
$960$	−9.51411	−	28.6220i	−0.307067	−	0.923773i
$961$	9.53768	−	2.02730i	0.307667	−	0.0653967i
$962$	−12.7354	+	59.9152i	−0.410605	+	1.93174i
$963$	−0.714939	+	3.36352i	−0.0230386	+	0.108388i
$964$	7.37043	−	1.56663i	0.237386	−	0.0504579i
$965$	1.74705	−	5.50310i	0.0562396	−	0.177151i
$966$	−40.1883	+	43.1176i	−1.29304	+	1.38729i
$967$	−27.5048	−	37.8571i	−0.884495	−	1.21740i	−0.975156	−	0.221521i	$-0.928898\pi$
$967$	−27.5048	−	37.8571i	−0.884495	−	1.21740i	0.0906611	−	0.995882i	$-0.471102\pi$
$968$	0.184795	−	0.106692i	0.00593955	−	0.00342920i
$969$	−0.945008	−	8.99115i	−0.0303580	−	0.288838i
$970$	5.70633	−	27.7672i	0.183219	−	0.891552i
$971$	−2.36887	+	22.5383i	−0.0760206	+	0.723287i	0.888428	+	0.459016i	$0.151798\pi$
$971$	−2.36887	+	22.5383i	−0.0760206	+	0.723287i	−0.964448	+	0.264271i	$0.914869\pi$
$972$	−2.94814	+	4.05777i	−0.0945617	+	0.130153i
$973$	8.60629	+	2.96105i	0.275905	+	0.0949268i
$974$	4.98421			0.159704
$975$	28.5284	+	12.2425i	0.913639	+	0.392074i
$976$	46.5481	−	80.6237i	1.48997	−	2.58070i
$977$	43.8374	−	39.4713i	1.40248	−	1.26280i	0.479724	−	0.877419i	$-0.340737\pi$
$977$	43.8374	−	39.4713i	1.40248	−	1.26280i	0.922758	−	0.385381i	$-0.125930\pi$
$978$	−47.4109	−	4.98309i	−1.51603	−	0.159342i
$979$	4.80598	+	3.49175i	0.153600	+	0.111597i
$980$	44.3712	+	64.7663i	1.41738	+	2.06888i
$981$	−5.22951	+	3.79946i	−0.166965	+	0.121307i
$982$	−84.6143	+	48.8521i	−2.70015	+	1.55893i
$983$	27.0893	−	2.84720i	0.864014	−	0.0908116i	0.337856	−	0.941198i	$-0.390298\pi$
$983$	27.0893	−	2.84720i	0.864014	−	0.0908116i	0.526159	+	0.850386i	$0.323632\pi$
$984$	−37.1480	−	7.89605i	−1.18423	−	0.251717i
$985$	38.1524	+	16.6786i	1.21564	+	0.531425i
$986$	15.3073	−	47.1111i	0.487485	−	1.50032i
$987$	−3.08033	+	0.942568i	−0.0980478	+	0.0300023i
$988$	40.2812	−	13.0881i	1.28151	−	0.416389i
$989$	11.8466	−	2.51808i	0.376701	−	0.0800703i
$990$	17.8690	−	8.10088i	0.567914	−	0.257463i
$991$	−20.5421	−	4.36637i	−0.652543	−	0.138702i	−0.130267	−	0.991479i	$-0.541583\pi$
$991$	−20.5421	−	4.36637i	−0.652543	−	0.138702i	−0.522276	+	0.852777i	$0.674917\pi$
$992$	25.2992	−	56.8230i	0.803251	−	1.80413i
$993$		−	19.3566i		−	0.614262i
$994$	47.5973	+	22.1809i	1.50969	+	0.703536i
$995$	14.8523	+	4.71512i	0.470850	+	0.149479i
$996$	−1.58905	+	15.1188i	−0.0503508	+	0.479056i
$997$	2.98069	+	6.69474i	0.0943994	+	0.212024i	0.954573	−	0.297976i	$-0.0963117\pi$
$997$	2.98069	+	6.69474i	0.0943994	+	0.212024i	−0.860174	+	0.510001i	$0.829645\pi$
$998$	18.2954	−	16.4733i	0.579132	−	0.521452i
$999$	−1.86233	−	3.22565i	−0.0589215	−	0.102055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.4.3	✓	320
7.2	even	3	inner	525.2.bo.a.79.3	yes	320
25.19	even	10	inner	525.2.bo.a.319.3	yes	320
175.44	even	30	inner	525.2.bo.a.394.3	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.3	✓	320	1.1	even	1	trivial
525.2.bo.a.79.3	yes	320	7.2	even	3	inner
525.2.bo.a.319.3	yes	320	25.19	even	10	inner
525.2.bo.a.394.3	yes	320	175.44	even	30	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550698 - 2.59083i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-4.58205 + 2.04006i) q^{4} +(0.479670 + 2.18401i) q^{5} +(2.14285 - 1.55687i) q^{6} +(0.0455325 - 2.64536i) q^{7} +(4.69504 + 6.46216i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.550698 - 2.59083i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-4.58205 + 2.04006i) q^{4} +(0.479670 + 2.18401i) q^{5} +(2.14285 - 1.55687i) q^{6} +(0.0455325 - 2.64536i) q^{7} +(4.69504 + 6.46216i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(5.39426 - 2.44548i) q^{10} +(-2.21656 - 2.46174i) q^{11} +(-3.72738 - 3.35615i) q^{12} +(-5.90497 + 1.91864i) q^{13} +(-6.87876 + 1.33883i) q^{14} +(-1.80010 + 1.32652i) q^{15} +(7.44454 - 8.26800i) q^{16} +(-6.61091 + 0.694835i) q^{17} +(2.29385 + 1.32436i) q^{18} +(1.24247 + 0.553181i) q^{19} +(-6.65339 - 9.02871i) q^{20} +(2.43518 - 1.03437i) q^{21} +(-5.15729 + 7.09841i) q^{22} +(-1.74873 - 8.22715i) q^{23} +(-3.99384 + 6.91753i) q^{24} +(-4.53983 + 2.09521i) q^{25} +(8.22274 + 14.2422i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(5.18806 + 12.2141i) q^{28} +(-2.27611 - 1.65369i) q^{29} +(4.42810 + 3.93324i) q^{30} +(0.481844 + 4.58444i) q^{31} +(-11.6856 - 6.74671i) q^{32} +(1.34735 - 3.02621i) q^{33} +(5.44082 + 16.7451i) q^{34} +(5.79934 - 1.16946i) q^{35} +(1.54993 - 4.77020i) q^{36} +(2.76796 + 2.49228i) q^{37} +(0.748976 - 3.52366i) q^{38} +(-4.15454 - 4.61408i) q^{39} +(-11.8614 + 13.3537i) q^{40} +(1.46924 + 4.52186i) q^{41} +(-4.02092 - 5.73951i) q^{42} +1.43994i q^{43} +(15.1785 + 6.75790i) q^{44} +(-1.94400 - 1.10493i) q^{45} +(-20.3521 + 9.06136i) q^{46} +(-1.21087 - 0.127268i) q^{47} +(10.5812 + 3.43803i) q^{48} +(-6.99585 - 0.240900i) q^{49} +(7.92842 + 10.6081i) q^{50} +(-3.32366 - 5.75675i) q^{51} +(23.1427 - 20.8378i) q^{52} +(-3.48036 - 7.81701i) q^{53} +(-0.276866 + 2.63420i) q^{54} +(4.31325 - 6.02182i) q^{55} +(17.3085 - 12.1258i) q^{56} +1.36005i q^{57} +(-3.03098 + 6.80770i) q^{58} +(2.19520 + 0.466605i) q^{59} +(5.54196 - 9.75049i) q^{60} +(8.18483 - 1.73974i) q^{61} +(11.6122 - 3.77302i) q^{62} +(1.93542 + 1.80393i) q^{63} +(-4.16827 + 12.8286i) q^{64} +(-7.02278 - 11.9762i) q^{65} +(-8.58238 - 1.82424i) q^{66} +(2.75720 - 0.289793i) q^{67} +(28.8740 - 16.6704i) q^{68} +(6.80460 - 4.94383i) q^{69} +(-6.22355 - 14.3811i) q^{70} +(-6.06221 - 4.40445i) q^{71} +(-7.94392 - 0.834939i) q^{72} +(-9.18298 + 8.26839i) q^{73} +(4.93277 - 8.54381i) q^{74} +(-3.76059 - 3.29515i) q^{75} -6.82157 q^{76} +(-6.61311 + 5.75151i) q^{77} +(-9.66641 + 13.3047i) q^{78} +(-1.14184 + 10.8638i) q^{79} +(21.6283 + 12.2931i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(10.9063 - 6.29674i) q^{82} +(-1.78152 - 2.45205i) q^{83} +(-9.04793 + 9.70744i) q^{84} +(-4.68858 - 14.1050i) q^{85} +(3.73065 - 0.792975i) q^{86} +(0.584944 - 2.75195i) q^{87} +(5.50133 - 25.8817i) q^{88} +(-1.75412 + 0.372850i) q^{89} +(-1.79212 + 5.64506i) q^{90} +(4.80663 + 15.7081i) q^{91} +(24.7967 + 34.1297i) q^{92} +(-3.99211 + 2.30484i) q^{93} +(0.337095 + 3.20725i) q^{94} +(-0.612183 + 2.97891i) q^{95} +(1.41045 - 13.4195i) q^{96} +(2.81329 - 3.87215i) q^{97} +(3.22847 + 18.2577i) q^{98} +3.31260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

L-functions

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