LMFDB - Embedded newform 805.2.bi.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(43,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([33, 0, 10]))

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

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

chi := DirichletCharacter("805.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.bi (of order $44$, degree $20$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$1440$
Relative dimension:	$72$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	805.43
Dual form			805.2.bi.a.337.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02354 - 1.51480i) q^{2} +(2.86191 - 1.06744i) q^{3} +(1.23661 + 4.21152i) q^{4} +(0.167422 + 2.22979i) q^{5} +(-7.40814 - 2.17523i) q^{6} +(-0.977147 - 0.212565i) q^{7} +(2.11059 - 5.65871i) q^{8} +(4.78387 - 4.14525i) q^{9} +O(q^{10})$	\(q+(-2.02354 - 1.51480i) q^{2} +(2.86191 - 1.06744i) q^{3} +(1.23661 + 4.21152i) q^{4} +(0.167422 + 2.22979i) q^{5} +(-7.40814 - 2.17523i) q^{6} +(-0.977147 - 0.212565i) q^{7} +(2.11059 - 5.65871i) q^{8} +(4.78387 - 4.14525i) q^{9} +(3.03890 - 4.76567i) q^{10} +(-0.0389563 - 0.00560107i) q^{11} +(8.03462 + 10.7330i) q^{12} +(1.37302 + 6.31169i) q^{13} +(1.65530 + 1.91032i) q^{14} +(2.85931 + 6.20275i) q^{15} +(-5.45762 + 3.50740i) q^{16} +(1.50712 + 2.76008i) q^{17} +(-15.9596 + 1.14145i) q^{18} +(4.36521 - 1.28174i) q^{19} +(-9.18378 + 3.46249i) q^{20} +(-3.02341 + 0.434701i) q^{21} +(0.0703449 + 0.0703449i) q^{22} +(-4.77532 - 0.443044i) q^{23} -18.4477i q^{24} +(-4.94394 + 0.746632i) q^{25} +(6.78258 - 14.8518i) q^{26} +(4.87462 - 8.92720i) q^{27} +(-0.313130 - 4.37814i) q^{28} +(-1.64600 + 5.60577i) q^{29} +(3.61002 - 16.8828i) q^{30} +(3.37973 + 7.40058i) q^{31} +(4.30846 + 0.308147i) q^{32} +(-0.117468 + 0.0255536i) q^{33} +(1.13126 - 7.86811i) q^{34} +(0.310381 - 2.21442i) q^{35} +(23.3736 + 15.0213i) q^{36} +(0.441435 - 6.17207i) q^{37} +(-10.7748 - 4.01878i) q^{38} +(10.6668 + 16.5979i) q^{39} +(12.9711 + 3.75879i) q^{40} +(1.87203 - 2.16044i) q^{41} +(6.77646 + 3.70023i) q^{42} +(0.750035 + 2.01092i) q^{43} +(-0.0245849 - 0.170991i) q^{44} +(10.0440 + 9.97302i) q^{45} +(8.99192 + 8.13018i) q^{46} +(1.31423 - 1.31423i) q^{47} +(-11.8753 + 15.8635i) q^{48} +(0.909632 + 0.415415i) q^{49} +(11.1352 + 5.97825i) q^{50} +(7.25946 + 6.29035i) q^{51} +(-24.8839 + 13.5876i) q^{52} +(0.333891 - 1.53487i) q^{53} +(-23.3869 + 10.6804i) q^{54} +(0.00596708 - 0.0878021i) q^{55} +(-3.26520 + 5.08076i) q^{56} +(11.1247 - 8.32783i) q^{57} +(11.8224 - 8.85011i) q^{58} +(2.46014 - 3.82806i) q^{59} +(-22.5872 + 19.7125i) q^{60} +(6.83568 - 3.12175i) q^{61} +(4.37139 - 20.0950i) q^{62} +(-5.55568 + 3.03363i) q^{63} +(1.55428 + 1.34679i) q^{64} +(-13.8439 + 4.11827i) q^{65} +(0.276410 + 0.126232i) q^{66} +(-1.48340 + 1.98159i) q^{67} +(-9.76042 + 9.76042i) q^{68} +(-14.1395 + 3.82941i) q^{69} +(-3.98247 + 4.01080i) q^{70} +(-1.88642 - 13.1203i) q^{71} +(-13.3600 - 35.8195i) q^{72} +(-8.30665 - 4.53577i) q^{73} +(-10.2427 + 11.8207i) q^{74} +(-13.3521 + 7.41414i) q^{75} +(10.7962 + 16.7992i) q^{76} +(0.0368754 + 0.0137538i) q^{77} +(3.55780 - 49.7445i) q^{78} +(13.4304 + 8.63119i) q^{79} +(-8.73449 - 11.5821i) q^{80} +(1.71896 - 11.9556i) q^{81} +(-7.06077 + 1.53598i) q^{82} +(0.539353 + 0.0385753i) q^{83} +(-5.56954 - 12.1956i) q^{84} +(-5.90208 + 3.82266i) q^{85} +(1.52842 - 5.20533i) q^{86} +(1.27310 + 17.8002i) q^{87} +(-0.113916 + 0.208621i) q^{88} +(7.33009 - 16.0506i) q^{89} +(-5.21717 - 35.3954i) q^{90} -6.45930i q^{91} +(-4.03934 - 20.6592i) q^{92} +(17.5722 + 17.5722i) q^{93} +(-4.65019 + 0.668596i) q^{94} +(3.58885 + 9.51893i) q^{95} +(12.6594 - 3.71713i) q^{96} +(17.0383 - 1.21860i) q^{97} +(-1.21140 - 2.21852i) q^{98} +(-0.209579 + 0.134689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1440 q - 8 q^{3} + 16 q^{6}+O(q^{10}) $ 1440 * q - 8 * q^3 + 16 * q^6	$ 1440 q - 8 q^{3} + 16 q^{6} - 32 q^{12} + 16 q^{13} + 192 q^{16} - 72 q^{18} - 36 q^{23} + 8 q^{25} - 8 q^{27} + 40 q^{32} - 44 q^{33} - 208 q^{36} - 88 q^{37} - 32 q^{41} + 80 q^{46} - 192 q^{47} - 24 q^{48} + 56 q^{50} + 64 q^{52} - 56 q^{55} - 88 q^{57} + 24 q^{62} - 352 q^{66} + 16 q^{70} - 344 q^{71} + 48 q^{72} - 32 q^{73} - 144 q^{75} - 352 q^{76} - 40 q^{78} - 16 q^{81} + 96 q^{82} - 16 q^{85} + 16 q^{87} - 836 q^{90} - 112 q^{92} + 8 q^{93} - 56 q^{95} - 96 q^{96} + 132 q^{97}+O(q^{100}) $ 1440 * q - 8 * q^3 + 16 * q^6 - 32 * q^12 + 16 * q^13 + 192 * q^16 - 72 * q^18 - 36 * q^23 + 8 * q^25 - 8 * q^27 + 40 * q^32 - 44 * q^33 - 208 * q^36 - 88 * q^37 - 32 * q^41 + 80 * q^46 - 192 * q^47 - 24 * q^48 + 56 * q^50 + 64 * q^52 - 56 * q^55 - 88 * q^57 + 24 * q^62 - 352 * q^66 + 16 * q^70 - 344 * q^71 + 48 * q^72 - 32 * q^73 - 144 * q^75 - 352 * q^76 - 40 * q^78 - 16 * q^81 + 96 * q^82 - 16 * q^85 + 16 * q^87 - 836 * q^90 - 112 * q^92 + 8 * q^93 - 56 * q^95 - 96 * q^96 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{22}\right)$	$1$

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 $

$2$	−2.02354	−	1.51480i	−1.43086	−	1.07113i	−0.984326	−	0.176357i	$-0.943569\pi$
$2$	−2.02354	−	1.51480i	−1.43086	−	1.07113i	−0.446530	−	0.894769i	$-0.647340\pi$
$3$	2.86191	−	1.06744i	1.65233	−	0.616286i	0.661320	−	0.750104i	$-0.269997\pi$
$3$	2.86191	−	1.06744i	1.65233	−	0.616286i	0.991006	+	0.133818i	$0.0427239\pi$
$4$	1.23661	+	4.21152i	0.618307	+	2.10576i
$5$	0.167422	+	2.22979i	0.0748733	+	0.997193i
$5$	0.167422	+	2.22979i	0.0748733	+	0.997193i
$6$	−7.40814	−	2.17523i	−3.02436	−	0.888032i
$7$	−0.977147	−	0.212565i	−0.369327	−	0.0803421i
$7$	−0.977147	−	0.212565i	−0.369327	−	0.0803421i
$8$	2.11059	−	5.65871i	0.746207	−	2.00066i
$9$	4.78387	−	4.14525i	1.59462	−	1.38175i
$10$	3.03890	−	4.76567i	0.960986	−	1.50704i
$11$	−0.0389563	−	0.00560107i	−0.0117458	−	0.00168878i	0.136439	−	0.990648i	$-0.456434\pi$
$11$	−0.0389563	−	0.00560107i	−0.0117458	−	0.00168878i	−0.148185	+	0.988960i	$0.547343\pi$
$12$	8.03462	+	10.7330i	2.31939	+	3.09835i
$13$	1.37302	+	6.31169i	0.380808	+	1.75055i	0.624814	+	0.780774i	$0.285175\pi$
$13$	1.37302	+	6.31169i	0.380808	+	1.75055i	−0.244006	+	0.969774i	$0.578462\pi$
$14$	1.65530	+	1.91032i	0.442397	+	0.510553i
$15$	2.85931	+	6.20275i	0.738271	+	1.60154i
$16$	−5.45762	+	3.50740i	−1.36440	+	0.876850i
$17$	1.50712	+	2.76008i	0.365530	+	0.669418i	0.994116	−	0.108322i	$-0.0345478\pi$
$17$	1.50712	+	2.76008i	0.365530	+	0.669418i	−0.628586	+	0.777740i	$0.716366\pi$
$18$	−15.9596	+	1.14145i	−3.76170	+	0.269042i
$19$	4.36521	−	1.28174i	1.00145	−	0.294052i	0.260398	−	0.965501i	$-0.416146\pi$
$19$	4.36521	−	1.28174i	1.00145	−	0.294052i	0.741051	+	0.671449i	$0.234328\pi$
$20$	−9.18378	+	3.46249i	−2.05356	+	0.774237i
$21$	−3.02341	+	0.434701i	−0.659762	+	0.0948594i
$22$	0.0703449	+	0.0703449i	0.0149976	+	0.0149976i
$23$	−4.77532	−	0.443044i	−0.995724	−	0.0923811i
$23$	−4.77532	−	0.443044i	−0.995724	−	0.0923811i
$24$		−	18.4477i		−	3.76561i
$25$	−4.94394	+	0.746632i	−0.988788	+	0.149326i
$26$	6.78258	−	14.8518i	1.33017	−	2.91268i
$27$	4.87462	−	8.92720i	0.938121	−	1.71804i
$28$	−0.313130	−	4.37814i	−0.0591761	−	0.827390i
$29$	−1.64600	+	5.60577i	−0.305655	+	1.04096i	0.653228	+	0.757161i	$0.273414\pi$
$29$	−1.64600	+	5.60577i	−0.305655	+	1.04096i	−0.958883	+	0.283803i	$0.908404\pi$
$30$	3.61002	−	16.8828i	0.659096	−	3.08236i
$31$	3.37973	+	7.40058i	0.607018	+	1.32918i	0.924595	+	0.380951i	$0.124403\pi$
$31$	3.37973	+	7.40058i	0.607018	+	1.32918i	−0.317578	+	0.948232i	$0.602869\pi$
$32$	4.30846	+	0.308147i	0.761636	+	0.0544733i
$33$	−0.117468	+	0.0255536i	−0.0204486	+	0.00444832i
$34$	1.13126	−	7.86811i	0.194010	−	1.34937i
$35$	0.310381	−	2.21442i	0.0524639	−	0.374306i
$36$	23.3736	+	15.0213i	3.89560	+	2.50355i
$37$	0.441435	−	6.17207i	0.0725715	−	1.01468i	−0.822502	−	0.568763i	$-0.807422\pi$
$37$	0.441435	−	6.17207i	0.0725715	−	1.01468i	0.895073	−	0.445919i	$-0.147123\pi$
$38$	−10.7748	−	4.01878i	−1.74790	−	0.651932i
$39$	10.6668	+	16.5979i	1.70806	+	2.65779i
$40$	12.9711	+	3.75879i	2.05091	+	0.594316i
$41$	1.87203	−	2.16044i	0.292363	−	0.337405i	−0.590498	−	0.807039i	$-0.701069\pi$
$41$	1.87203	−	2.16044i	0.292363	−	0.337405i	0.882861	+	0.469634i	$0.155614\pi$
$42$	6.77646	+	3.70023i	1.04563	+	0.570958i
$43$	0.750035	+	2.01092i	0.114379	+	0.306663i	0.981508	−	0.191422i	$-0.0613097\pi$
$43$	0.750035	+	2.01092i	0.114379	+	0.306663i	−0.867129	+	0.498084i	$0.834037\pi$
$44$	−0.0245849	−	0.170991i	−0.00370631	−	0.0257779i
$45$	10.0440	+	9.97302i	1.49726	+	1.48669i
$46$	8.99192	+	8.13018i	1.32579	+	1.19873i
$47$	1.31423	−	1.31423i	0.191700	−	0.191700i	−0.604730	−	0.796430i	$-0.706719\pi$
$47$	1.31423	−	1.31423i	0.191700	−	0.191700i	0.796430	+	0.604730i	$0.206719\pi$
$48$	−11.8753	+	15.8635i	−1.71405	+	2.28970i
$49$	0.909632	+	0.415415i	0.129947	+	0.0593450i
$50$	11.1352	+	5.97825i	1.57476	+	0.845452i
$51$	7.25946	+	6.29035i	1.01653	+	0.880826i
$52$	−24.8839	+	13.5876i	−3.45078	+	1.88427i
$53$	0.333891	−	1.53487i	0.0458635	−	0.210831i	−0.948512	−	0.316740i	$-0.897412\pi$
$53$	0.333891	−	1.53487i	0.0458635	−	0.210831i	0.994376	+	0.105909i	$0.0337753\pi$
$54$	−23.3869	+	10.6804i	−3.18255	+	1.45342i
$55$	0.00596708	−	0.0878021i	0.000804601	−	0.0118392i
$56$	−3.26520	+	5.08076i	−0.436331	+	0.678945i
$57$	11.1247	−	8.32783i	1.47350	−	1.10305i
$58$	11.8224	−	8.85011i	1.55235	−	1.16208i
$59$	2.46014	−	3.82806i	0.320283	−	0.498371i	−0.643359	−	0.765564i	$-0.722460\pi$
$59$	2.46014	−	3.82806i	0.320283	−	0.498371i	0.963643	+	0.267193i	$0.0860963\pi$
$60$	−22.5872	+	19.7125i	−2.91599	+	2.54487i
$61$	6.83568	−	3.12175i	0.875219	−	0.399699i	0.0734259	−	0.997301i	$-0.476607\pi$
$61$	6.83568	−	3.12175i	0.875219	−	0.399699i	0.801793	+	0.597601i	$0.203879\pi$
$62$	4.37139	−	20.0950i	0.555167	−	2.55206i
$63$	−5.55568	+	3.03363i	−0.699950	+	0.382201i
$64$	1.55428	+	1.34679i	0.194285	+	0.168349i
$65$	−13.8439	+	4.11827i	−1.71712	+	0.510809i
$66$	0.276410	+	0.126232i	0.0340237	+	0.0155381i
$67$	−1.48340	+	1.98159i	−0.181226	+	0.242090i	−0.881950	−	0.471343i	$-0.843770\pi$
$67$	−1.48340	+	1.98159i	−0.181226	+	0.242090i	0.700724	+	0.713432i	$0.252860\pi$
$68$	−9.76042	+	9.76042i	−1.18362	+	1.18362i
$69$	−14.1395	+	3.82941i	−1.70219	+	0.461007i
$70$	−3.98247	+	4.01080i	−0.475997	+	0.479382i
$71$	−1.88642	−	13.1203i	−0.223876	−	1.55709i	−0.723176	−	0.690664i	$-0.757318\pi$
$71$	−1.88642	−	13.1203i	−0.223876	−	1.55709i	0.499299	−	0.866430i	$-0.333591\pi$
$72$	−13.3600	−	35.8195i	−1.57449	−	4.22136i
$73$	−8.30665	−	4.53577i	−0.972220	−	0.530872i	−0.0870819	−	0.996201i	$-0.527754\pi$
$73$	−8.30665	−	4.53577i	−0.972220	−	0.530872i	−0.885138	+	0.465329i	$0.845936\pi$
$74$	−10.2427	+	11.8207i	−1.19069	+	1.37413i
$75$	−13.3521	+	7.41414i	−1.54177	+	0.856112i
$76$	10.7962	+	16.7992i	1.23841	+	1.92700i
$77$	0.0368754	+	0.0137538i	0.00420234	+	0.00156739i
$78$	3.55780	−	49.7445i	0.402841	−	5.63246i
$79$	13.4304	+	8.63119i	1.51104	+	0.971085i	0.993302	+	0.115544i	$0.0368613\pi$
$79$	13.4304	+	8.63119i	1.51104	+	0.971085i	0.517736	+	0.855541i	$0.326775\pi$
$80$	−8.73449	−	11.5821i	−0.976546	−	1.29492i
$81$	1.71896	−	11.9556i	0.190995	−	1.32840i
$82$	−7.06077	+	1.53598i	−0.779732	+	0.169620i
$83$	0.539353	+	0.0385753i	0.0592016	+	0.00423418i	0.100909	−	0.994896i	$-0.467825\pi$
$83$	0.539353	+	0.0385753i	0.0592016	+	0.00423418i	−0.0417069	+	0.999130i	$0.513280\pi$
$84$	−5.56954	−	12.1956i	−0.607687	−	1.33065i
$85$	−5.90208	+	3.82266i	−0.640171	+	0.414625i
$86$	1.52842	−	5.20533i	0.164814	−	0.561305i
$87$	1.27310	+	17.8002i	0.136490	+	1.90838i
$88$	−0.113916	+	0.208621i	−0.0121434	+	0.0222391i
$89$	7.33009	−	16.0506i	0.776988	−	1.70137i	0.0663612	−	0.997796i	$-0.478861\pi$
$89$	7.33009	−	16.0506i	0.776988	−	1.70137i	0.710626	−	0.703570i	$-0.248412\pi$
$90$	−5.21717	−	35.3954i	−0.549938	−	3.73100i
$91$		−	6.45930i		−	0.677119i
$92$	−4.03934	−	20.6592i	−0.421130	−	2.15388i
$93$	17.5722	+	17.5722i	1.82215	+	1.82215i
$94$	−4.65019	+	0.668596i	−0.479630	+	0.0689604i
$95$	3.58885	+	9.51893i	0.368208	+	0.976621i
$96$	12.6594	−	3.71713i	1.29204	−	0.379378i
$97$	17.0383	−	1.21860i	1.72998	−	0.123730i	0.829464	−	0.558561i	$-0.188646\pi$
$97$	17.0383	−	1.21860i	1.72998	−	0.123730i	0.900512	+	0.434830i	$0.143192\pi$
$98$	−1.21140	−	2.21852i	−0.122370	−	0.224104i
$99$	−0.209579	+	0.134689i	−0.0210635	+	0.0135367i
$100$	−9.25820	−	19.8982i	−0.925820	−	1.98982i
$101$	3.15394	+	3.63984i	0.313829	+	0.362178i	0.890647	−	0.454695i	$-0.150252\pi$
$101$	3.15394	+	3.63984i	0.313829	+	0.362178i	−0.576819	+	0.816872i	$0.695706\pi$
$102$	−5.16114	−	23.7254i	−0.511029	−	2.34916i
$103$	−3.87781	−	5.18015i	−0.382092	−	0.510416i	0.567726	−	0.823218i	$-0.307823\pi$
$103$	−3.87781	−	5.18015i	−0.382092	−	0.510416i	−0.949818	+	0.312802i	$0.898732\pi$
$104$	38.6139	+	5.55185i	3.78641	+	0.544403i
$105$	−1.47548	−	6.66879i	−0.143992	−	0.650808i
$106$	−3.00067	+	2.60009i	−0.291450	+	0.252543i
$107$	−1.03708	+	2.78052i	−0.100258	+	0.268803i	−0.977389	−	0.211448i	$-0.932182\pi$
$107$	−1.03708	+	2.78052i	−0.100258	+	0.268803i	0.877131	+	0.480252i	$0.159455\pi$
$108$	43.6251	+	9.49006i	4.19783	+	0.913182i
$109$	−6.77090	−	1.98812i	−0.648535	−	0.190427i	−0.0591114	−	0.998251i	$-0.518827\pi$
$109$	−6.77090	−	1.98812i	−0.648535	−	0.190427i	−0.589423	+	0.807824i	$0.700645\pi$
$110$	−0.145077	+	0.168632i	−0.0138326	+	0.0160784i
$111$	−5.32495	−	18.1351i	−0.505422	−	1.72131i
$112$	6.07845	−	2.26714i	0.574359	−	0.214225i
$113$	−10.8167	−	8.09726i	−1.01755	−	0.761726i	−0.0460887	−	0.998937i	$-0.514676\pi$
$113$	−10.8167	−	8.09726i	−1.01755	−	0.761726i	−0.971458	+	0.237211i	$0.923767\pi$
$114$	−35.1262			−3.28987
$115$	0.188403	−	10.7222i	0.0175687	−	0.999846i
$116$	−25.6443			−2.38101
$117$	32.7319	+	24.5028i	3.02606	+	2.26528i
$118$	−10.7769	+	4.01959i	−0.992097	+	0.370033i
$119$	−0.885979	−	3.01737i	−0.0812175	−	0.276601i
$120$	41.1345	−	3.08854i	3.75504	−	0.281944i
$121$	−10.5529	−	3.09862i	−0.959358	−	0.281693i
$122$	−18.5611	−	4.03771i	−1.68044	−	0.365558i
$123$	3.05146	−	8.18128i	0.275141	−	0.737681i
$124$	−26.9883	+	23.3855i	−2.42362	+	2.10008i
$125$	−2.49256	−	10.8990i	−0.222941	−	0.974832i
$126$	15.8375	+	2.27708i	1.41091	+	0.202859i
$127$	2.56515	+	3.42664i	0.227620	+	0.304065i	0.899782	−	0.436339i	$-0.143725\pi$
$127$	2.56515	+	3.42664i	0.227620	+	0.304065i	−0.672162	+	0.740404i	$0.734634\pi$
$128$	−2.94136	−	13.5212i	−0.259982	−	1.19512i
$129$	4.29307	+	4.95447i	0.377984	+	0.436216i
$130$	34.2519	+	12.6372i	3.00409	+	1.10836i
$131$	−7.46116	+	4.79500i	−0.651885	+	0.418941i	−0.824354	−	0.566074i	$-0.808462\pi$
$131$	−7.46116	+	4.79500i	−0.651885	+	0.418941i	0.172470	+	0.985015i	$0.444825\pi$
$132$	−0.252883	−	0.463120i	−0.0220106	−	0.0403094i
$133$	−4.53791	+	0.324558i	−0.393487	+	0.0281427i
$134$	6.00343	−	1.76277i	0.518617	−	0.152280i
$135$	20.7219	+	9.37478i	1.78346	+	0.806853i
$136$	18.7994	−	2.70295i	1.61204	−	0.231776i
$137$	−12.5835	−	12.5835i	−1.07508	−	1.07508i	−0.996942	−	0.0781396i	$-0.975102\pi$
$137$	−12.5835	−	12.5835i	−1.07508	−	1.07508i	−0.0781396	−	0.996942i	$-0.524898\pi$
$138$	34.4125	+	13.6695i	2.92939	+	1.16363i
$139$			8.77269i			0.744090i	0.928215	+	0.372045i	$0.121343\pi$
$139$			8.77269i			0.744090i	−0.928215	+	0.372045i	$0.878657\pi$
$140$	9.70990	−	1.43121i	0.820637	−	0.120959i
$141$	2.35835	−	5.16407i	0.198609	−	0.434893i
$142$	−16.0574	+	29.4070i	−1.34751	+	2.46778i
$143$	−0.0181357	−	0.253570i	−0.00151658	−	0.0212046i
$144$	−11.5695	+	39.4021i	−0.964125	+	3.28351i
$145$	−12.7753	−	2.73171i	−1.06093	−	0.226856i
$146$	9.93801	+	21.7612i	0.822476	+	1.80097i
$147$	3.04672	+	0.217905i	0.251289	+	0.0179725i
$148$	26.5397	−	5.77335i	2.18155	−	0.474567i
$149$	−0.0501711	+	0.348948i	−0.00411018	+	0.0285869i	−0.991773	−	0.128007i	$-0.959142\pi$
$149$	−0.0501711	+	0.348948i	−0.00411018	+	0.0285869i	0.987663	+	0.156593i	$0.0500512\pi$
$150$	38.2495	+	5.22303i	3.12306	+	0.426459i
$151$	1.53160	+	0.984302i	0.124640	+	0.0801014i	0.601475	−	0.798891i	$-0.294580\pi$
$151$	1.53160	+	0.984302i	0.124640	+	0.0801014i	−0.476835	+	0.878993i	$0.658216\pi$
$152$	1.96017	−	27.4067i	0.158991	−	2.22298i
$153$	18.6511	+	6.95649i	1.50785	+	0.562399i
$154$	−0.0537844	−	0.0836902i	−0.00433407	−	0.00674395i
$155$	−15.9359	+	8.77511i	−1.28000	+	0.704834i
$156$	−56.7116	+	65.4487i	−4.54056	+	5.24009i
$157$	−4.34736	−	2.37384i	−0.346957	−	0.189453i	0.296316	−	0.955090i	$-0.404242\pi$
$157$	−4.34736	−	2.37384i	−0.346957	−	0.189453i	−0.643272	+	0.765637i	$0.722424\pi$
$158$	−14.1024	−	37.8099i	−1.12192	−	3.00799i
$159$	−0.682814	−	4.74908i	−0.0541507	−	0.376626i
$160$	0.0342265	+	9.65857i	0.00270584	+	0.763577i
$161$	4.57202	+	1.44799i	0.360325	+	0.114117i
$162$	−21.5887	+	21.5887i	−1.69617	+	1.69617i
$163$	0.793204	−	1.05960i	0.0621286	−	0.0829940i	−0.768401	−	0.639969i	$-0.778947\pi$
$163$	0.793204	−	1.05960i	0.0621286	−	0.0829940i	0.830529	+	0.556975i	$0.188038\pi$
$164$	11.4137	+	5.21248i	0.891263	+	0.407026i
$165$	−0.0766460	−	0.257651i	−0.00596689	−	0.0200581i
$166$	−1.03297	−	0.895070i	−0.0801737	−	0.0694709i
$167$	−13.7769	+	7.52276i	−1.06609	+	0.582129i	−0.913782	−	0.406204i	$-0.866852\pi$
$167$	−13.7769	+	7.52276i	−1.06609	+	0.582129i	−0.152307	+	0.988333i	$0.548670\pi$
$168$	−3.92133	+	18.0261i	−0.302537	+	1.39074i
$169$	−26.1270	+	11.9318i	−2.00977	+	0.917831i
$170$	17.7336	+	1.20519i	1.36011	+	0.0924337i
$171$	15.5695	−	24.2266i	1.19063	−	1.85265i
$172$	−7.54154	+	5.64552i	−0.575037	+	0.430467i
$173$	10.5341	−	7.88575i	0.800895	−	0.599543i	−0.118466	−	0.992958i	$-0.537798\pi$
$173$	10.5341	−	7.88575i	0.800895	−	0.599543i	0.919361	+	0.393416i	$0.128707\pi$
$174$	24.3876	−	37.9479i	1.84882	−	2.87682i
$175$	4.98966	+	0.321341i	0.377183	+	0.0242911i
$176$	0.232254	−	0.106067i	0.0175068	−	0.00799508i
$177$	2.95450	−	13.5816i	0.222074	−	1.02086i
$178$	−39.1462	+	21.3755i	−2.93413	+	1.60216i
$179$	−8.81897	−	7.64168i	−0.659161	−	0.571166i	0.259728	−	0.965682i	$-0.416367\pi$
$179$	−8.81897	−	7.64168i	−0.659161	−	0.571166i	−0.918889	+	0.394516i	$0.870912\pi$
$180$	−29.5811	+	54.6331i	−2.20485	+	4.07211i
$181$	−1.13834	−	0.519863i	−0.0846123	−	0.0386411i	0.372659	−	0.927968i	$-0.378446\pi$
$181$	−1.13834	−	0.519863i	−0.0846123	−	0.0386411i	−0.457272	+	0.889327i	$0.651173\pi$
$182$	−9.78455	+	13.0706i	−0.725279	+	0.968860i
$183$	16.2308	−	16.2308i	1.19982	−	1.19982i
$184$	−12.5858	+	26.0871i	−0.927839	+	1.92317i
$185$	13.8363	−	0.0490310i	1.01727	−	0.00360483i
$186$	−8.93959	−	62.1762i	−0.655482	−	4.55898i
$187$	−0.0432523	−	0.115964i	−0.00316292	−	0.00848012i
$188$	7.16010	+	3.90971i	0.522204	+	0.285145i
$189$	−6.66083	+	7.68701i	−0.484504	+	0.559148i
$190$	7.15710	−	24.6983i	0.519231	−	1.79180i
$191$	5.86939	+	9.13295i	0.424694	+	0.660837i	0.985995	−	0.166775i	$-0.0533352\pi$
$191$	5.86939	+	9.13295i	0.424694	+	0.660837i	−0.561301	+	0.827612i	$0.689699\pi$
$192$	5.88582	+	2.19530i	0.424772	+	0.158432i
$193$	−1.07379	+	15.0135i	−0.0772929	+	1.08070i	0.799766	+	0.600312i	$0.204957\pi$
$193$	−1.07379	+	15.0135i	−0.0772929	+	1.08070i	−0.877059	+	0.480383i	$0.840498\pi$
$194$	−36.3235	−	23.3437i	−2.60788	−	1.67598i
$195$	−35.2240	+	26.5636i	−2.52244	+	1.90226i
$196$	−0.624665	+	4.34464i	−0.0446189	+	0.310332i
$197$	−20.7579	+	4.51561i	−1.47894	+	0.321724i	−0.878422	−	0.477886i	$-0.841403\pi$
$197$	−20.7579	+	4.51561i	−1.47894	+	0.321724i	−0.600520	+	0.799610i	$0.705040\pi$
$198$	0.628118	+	0.0449239i	0.0446384	+	0.00319260i
$199$	−0.743537	−	1.62812i	−0.0527079	−	0.115414i	0.881446	−	0.472285i	$-0.156571\pi$
$199$	−0.743537	−	1.62812i	−0.0527079	−	0.115414i	−0.934154	+	0.356871i	$0.883844\pi$
$200$	−6.20966	+	29.5522i	−0.439089	+	2.08965i
$201$	−2.13014	+	7.25458i	−0.150248	+	0.511698i
$202$	−0.868480	−	12.1429i	−0.0611060	−	0.854374i
$203$	2.79998	−	5.12777i	0.196520	−	0.359899i
$204$	−17.5148	+	38.3521i	−1.22628	+	2.68518i
$205$	5.13076	+	3.81254i	0.358348	+	0.266279i
$206$			16.3563i			1.13960i
$207$	−24.6810	+	17.6754i	−1.71545	+	1.22853i
$208$	−29.6311	−	29.6311i	−2.05454	−	2.05454i
$209$	−0.177232	+	0.0254821i	−0.0122594	+	0.00176263i
$210$	−7.11621	+	15.7296i	−0.491065	+	1.08545i
$211$	25.2394	−	7.41094i	1.73755	−	0.510190i	0.749193	−	0.662352i	$-0.230441\pi$
$211$	25.2394	−	7.41094i	1.73755	−	0.510190i	0.988356	+	0.152161i	$0.0486233\pi$
$212$	6.87704	−	0.491856i	0.472317	−	0.0337808i
$213$	−19.4039	−	35.5355i	−1.32953	−	2.43485i
$214$	6.31051	−	4.05552i	0.431377	−	0.277229i
$215$	−4.35836	+	2.00909i	−0.297238	+	0.137019i
$216$	−40.2282	−	46.4258i	−2.73718	−	3.15887i
$217$	−1.72939	−	7.94986i	−0.117398	−	0.539672i
$218$	10.6896	+	14.2796i	0.723989	+	0.967136i
$219$	−28.6146	−	4.11415i	−1.93359	−	0.278009i
$220$	0.377159	−	0.0834468i	0.0254281	−	0.00562598i
$221$	−15.3515	+	13.3021i	−1.03265	+	0.894797i
$222$	−16.6959	+	44.7633i	−1.12055	+	3.00432i
$223$	7.46609	+	1.62415i	0.499966	+	0.108761i	0.455475	−	0.890249i	$-0.349470\pi$
$223$	7.46609	+	1.62415i	0.499966	+	0.108761i	0.0444916	+	0.999010i	$0.485833\pi$
$224$	−4.14450	−	1.21694i	−0.276916	−	0.0813099i
$225$	−20.5562	+	24.0656i	−1.37041	+	1.60438i
$226$	9.62220	+	32.7702i	0.640059	+	2.17984i
$227$	23.7167	−	8.84585i	1.57413	−	0.587120i	0.597466	−	0.801894i	$-0.296174\pi$
$227$	23.7167	−	8.84585i	1.57413	−	0.587120i	0.976664	+	0.214774i	$0.0689016\pi$
$228$	48.8298	+	36.5535i	3.23383	+	2.42082i
$229$	−22.2568			−1.47077			−0.735384	−	0.677650i	$-0.762998\pi$
$229$	−22.2568			−1.47077			−0.735384	+	0.677650i	$0.762998\pi$
$230$	−16.6232	+	21.4113i	−1.09610	+	1.41182i
$231$	0.120216			0.00790960
$232$	28.2474	+	21.1457i	1.85453	+	1.38829i
$233$	−9.87011	+	3.68136i	−0.646612	+	0.241174i	−0.651306	−	0.758815i	$-0.725779\pi$
$233$	−9.87011	+	3.68136i	−0.646612	+	0.241174i	0.00469381	+	0.999989i	$0.498506\pi$
$234$	−29.1173	−	99.1645i	−1.90346	−	6.48258i
$235$	3.15049	+	2.71043i	0.205515	+	0.176809i
$236$	19.1642	+	5.62712i	1.24748	+	0.366294i
$237$	47.6499	+	10.3656i	3.09519	+	0.673318i
$238$	−2.77790	+	7.44783i	−0.180064	+	0.482771i
$239$	8.68791	−	7.52812i	0.561974	−	0.486953i	−0.326929	−	0.945049i	$-0.606014\pi$
$239$	8.68791	−	7.52812i	0.561974	−	0.486953i	0.888903	+	0.458096i	$0.151468\pi$
$240$	−37.3606	−	23.8235i	−2.41161	−	1.53780i
$241$	−12.1176	−	1.74225i	−0.780563	−	0.112228i	−0.259496	−	0.965744i	$-0.583557\pi$
$241$	−12.1176	−	1.74225i	−0.780563	−	0.112228i	−0.521066	+	0.853516i	$0.674466\pi$
$242$	16.6605	+	22.2558i	1.07097	+	1.43065i
$243$	−1.35613	−	6.23403i	−0.0869958	−	0.399913i
$244$	21.6004	+	24.9282i	1.38282	+	1.59587i
$245$	−0.773997	+	2.09784i	−0.0494488	+	0.134026i
$246$	−18.5677	+	11.9328i	−1.18384	+	0.760805i
$247$	14.0835	+	25.7920i	0.896112	+	1.64111i
$248$	49.0110	−	3.50533i	3.11220	−	0.222589i
$249$	1.58476	−	0.465326i	0.100430	−	0.0294889i
$250$	−11.4660	+	25.8302i	−0.725171	+	1.63364i
$251$	22.8467	−	3.28486i	1.44207	−	0.207339i	0.623536	−	0.781795i	$-0.285695\pi$
$251$	22.8467	−	3.28486i	1.44207	−	0.207339i	0.818535	+	0.574456i	$0.194786\pi$
$252$	−19.6464	−	19.6464i	−1.23761	−	1.23761i
$253$	0.183547	+	0.0440063i	0.0115395	+	0.00276665i
$254$		−	10.8196i		−	0.678882i
$255$	−12.8108	+	17.2402i	−0.802243	+	1.07962i
$256$	−12.8213	+	28.0747i	−0.801331	+	1.75467i
$257$	−5.15656	+	9.44353i	−0.321657	+	0.589071i	−0.987611	−	0.156922i	$-0.949843\pi$
$257$	−5.15656	+	9.44353i	−0.321657	+	0.589071i	0.665954	+	0.745993i	$0.268025\pi$
$258$	−1.18215	−	16.5287i	−0.0735977	−	1.02903i
$259$	−1.74331	+	5.93718i	−0.108324	+	0.368919i
$260$	−34.4637	−	53.2111i	−2.13735	−	3.30001i
$261$	15.3630	+	33.6403i	0.950947	+	2.08228i
$262$	22.3614	+	1.59932i	1.38149	+	0.0988062i
$263$	−13.4261	+	2.92068i	−0.827891	+	0.180097i	−0.606495	−	0.795087i	$-0.707425\pi$
$263$	−13.4261	+	2.92068i	−0.827891	+	0.180097i	−0.221396	+	0.975184i	$0.571061\pi$
$264$	−0.103327	+	0.718652i	−0.00635931	+	0.0442300i
$265$	3.47835	+	0.487536i	0.213673	+	0.0299491i
$266$	9.67427	+	6.21727i	0.593167	+	0.381205i
$267$	3.84499	−	53.7600i	0.235309	−	3.29006i
$268$	−10.1799	−	3.79691i	−0.621837	−	0.231933i
$269$	17.4923	+	27.2186i	1.06653	+	1.65955i	0.671763	+	0.740766i	$0.265537\pi$
$269$	17.4923	+	27.2186i	1.06653	+	1.65955i	0.394764	+	0.918783i	$0.370826\pi$
$270$	−27.7306	−	50.3598i	−1.68763	−	3.06480i
$271$	2.43888	−	2.81462i	0.148151	−	0.170976i	−0.676823	−	0.736146i	$-0.736644\pi$
$271$	2.43888	−	2.81462i	0.148151	−	0.170976i	0.824975	+	0.565170i	$0.191189\pi$
$272$	−17.9060	−	9.77741i	−1.08571	−	0.592842i
$273$	−6.89491	−	18.4860i	−0.417299	−	1.11882i
$274$	6.40169	+	44.5247i	0.386740	+	2.68984i
$275$	0.196779	−	0.00139465i	0.0118662	−	8.41005e-5i
$276$	−33.6127	−	54.8132i	−2.02325	−	3.29937i
$277$	−4.27972	+	4.27972i	−0.257144	+	0.257144i	−0.823891	−	0.566748i	$-0.808201\pi$
$277$	−4.27972	+	4.27972i	−0.257144	+	0.257144i	0.566748	+	0.823891i	$0.308201\pi$
$278$	13.2889	−	17.7519i	0.797014	−	1.06469i
$279$	46.8454	+	21.3936i	2.80456	+	1.28080i
$280$	−11.8757	−	6.43009i	−0.709708	−	0.384272i
$281$	−18.6873	−	16.1926i	−1.11479	−	0.965972i	−0.115165	−	0.993346i	$-0.536740\pi$
$281$	−18.6873	−	16.1926i	−1.11479	−	0.965972i	−0.999625	+	0.0273747i	$0.991285\pi$
$282$	−12.5947	+	6.87725i	−0.750006	+	0.409534i
$283$	2.11027	−	9.70078i	0.125443	−	0.576651i	−0.870919	−	0.491427i	$-0.836476\pi$
$283$	2.11027	−	9.70078i	0.125443	−	0.576651i	0.996362	−	0.0852247i	$-0.0271608\pi$
$284$	52.9237	−	24.1694i	3.14044	−	1.43419i
$285$	20.4318	+	23.4115i	1.21028	+	1.38677i
$286$	−0.347410	+	0.540580i	−0.0205428	+	0.0319652i
$287$	−2.28849	+	1.71314i	−0.135085	+	0.101123i
$288$	21.8885	−	16.3855i	1.28979	−	0.965525i
$289$	3.84425	−	5.98177i	0.226132	−	0.351869i
$290$	21.7132	+	24.8797i	1.27504	+	1.46099i
$291$	47.4613	−	21.6748i	2.78223	−	1.27060i
$292$	8.83039	−	40.5926i	0.516759	−	2.37550i
$293$	−8.99620	+	4.91230i	−0.525564	+	0.286980i	−0.720046	−	0.693927i	$-0.755879\pi$
$293$	−8.99620	+	4.91230i	−0.525564	+	0.286980i	0.194482	+	0.980906i	$0.437697\pi$
$294$	−5.83506	−	5.05611i	−0.340308	−	0.294878i
$295$	8.94765	+	4.84471i	0.520953	+	0.282070i
$296$	−33.9943	−	15.5247i	−1.97588	−	0.902353i
$297$	−0.239899	+	0.320467i	−0.0139203	+	0.0185954i
$298$	0.630109	−	0.630109i	0.0365013	−	0.0365013i
$299$	−3.76027	−	30.7487i	−0.217462	−	1.77824i
$300$	−47.7363	−	47.0644i	−2.75605	−	2.71726i
$301$	−0.305442	−	2.12440i	−0.0176054	−	0.122448i
$302$	−1.60823	−	4.31184i	−0.0925435	−	0.248119i
$303$	12.9116	+	7.05027i	0.741752	+	0.405027i
$304$	−19.3281	+	22.3058i	−1.10854	+	1.27933i
$305$	8.10529	+	14.7195i	0.464108	+	0.842836i
$306$	−27.2034	−	42.3294i	−1.55512	−	2.41981i
$307$	−1.43334	−	0.534610i	−0.0818053	−	0.0305118i	0.308228	−	0.951312i	$-0.400264\pi$
$307$	−1.43334	−	0.534610i	−0.0818053	−	0.0305118i	−0.390034	+	0.920801i	$0.627537\pi$
$308$	−0.0123238	+	0.172310i	−0.000702216	+	0.00981826i
$309$	−16.6275	−	10.6858i	−0.945903	−	0.607895i
$310$	45.5394	+	6.38295i	2.58647	+	0.362527i
$311$	−1.28096	+	8.90928i	−0.0726367	+	0.505199i	0.920729	+	0.390202i	$0.127595\pi$
$311$	−1.28096	+	8.90928i	−0.0726367	+	0.505199i	−0.993366	+	0.114997i	$0.963314\pi$
$312$	116.436	−	25.3291i	6.59189	−	1.43398i
$313$	−7.31017	−	0.522833i	−0.413195	−	0.0295523i	−0.136805	−	0.990598i	$-0.543683\pi$
$313$	−7.31017	−	0.522833i	−0.413195	−	0.0295523i	−0.276390	+	0.961046i	$0.589138\pi$
$314$	5.20114	+	11.3889i	0.293518	+	0.642714i
$315$	−7.69450	−	11.8801i	−0.433536	−	0.669368i
$316$	−19.7422	+	67.2359i	−1.11059	+	3.78231i
$317$	−1.75601	−	24.5522i	−0.0986272	−	1.37899i	−0.770083	−	0.637944i	$-0.779785\pi$
$317$	−1.75601	−	24.5522i	−0.0986272	−	1.37899i	0.671455	−	0.741045i	$-0.265669\pi$
$318$	−5.81221	+	10.6443i	−0.325932	+	0.596900i
$319$	0.0955203	−	0.209160i	0.00534811	−	0.0117107i
$320$	−2.74284	+	3.69120i	−0.153329	+	0.206344i
$321$			9.06463i			0.505938i
$322$	−7.05823	−	9.85575i	−0.393340	−	0.549239i
$323$	10.1166	+	10.1166i	0.562903	+	0.562903i
$324$	52.4770	−	7.54506i	2.91539	−	0.419170i
$325$	−11.5007	−	30.1795i	−0.637941	−	1.67406i
$326$	−3.21016	+	0.942587i	−0.177794	+	0.0522051i
$327$	−21.4999	+	1.53770i	−1.18895	+	0.0850352i
$328$	−8.27423	−	15.1531i	−0.456868	−	0.836691i
$329$	−1.56356	+	1.00484i	−0.0862016	+	0.0553984i
$330$	−0.235194	+	0.637470i	−0.0129470	+	0.0350916i
$331$	0.359232	+	0.414575i	0.0197452	+	0.0227871i	0.765536	−	0.643393i	$-0.222474\pi$
$331$	0.359232	+	0.414575i	0.0197452	+	0.0227871i	−0.745791	+	0.666180i	$0.767928\pi$
$332$	0.504510	+	2.31920i	0.0276886	+	0.127282i
$333$	−23.4730	−	31.3562i	−1.28631	−	1.71831i
$334$	39.2736	+	5.64669i	2.14895	+	0.308973i
$335$	−4.66689	−	2.97591i	−0.254979	−	0.162591i
$336$	14.9759	−	12.9767i	0.817005	−	0.707939i
$337$	8.65115	−	23.1946i	0.471258	−	1.26349i	−0.456304	−	0.889824i	$-0.650827\pi$
$337$	8.65115	−	23.1946i	0.471258	−	1.26349i	0.927563	−	0.373668i	$-0.121900\pi$
$338$	70.9432	+	15.4328i	3.85880	+	0.839431i
$339$	−39.5997	−	11.6275i	−2.15076	−	0.631520i
$340$	−23.3978	−	20.1296i	−1.26892	−	1.09168i
$341$	−0.0902106	−	0.307229i	−0.00488518	−	0.0166374i
$342$	−68.2038	+	25.4387i	−3.68804	+	1.37557i
$343$	−0.800541	−	0.599278i	−0.0432252	−	0.0323580i
$344$	12.9623			0.698878
$345$	−10.9060	−	30.8870i	−0.587161	−	1.66290i
$346$	−33.2615			−1.78815
$347$	6.40769	+	4.79674i	0.343983	+	0.257502i	0.757275	−	0.653096i	$-0.226530\pi$
$347$	6.40769	+	4.79674i	0.343983	+	0.257502i	−0.413292	+	0.910598i	$0.635621\pi$
$348$	−73.3916	+	27.3737i	−3.93420	+	1.46738i
$349$	−2.30005	−	7.83326i	−0.123119	−	0.419305i	0.874748	−	0.484577i	$-0.161027\pi$
$349$	−2.30005	−	7.83326i	−0.123119	−	0.419305i	−0.997867	+	0.0652724i	$0.979208\pi$
$350$	−9.61000	−	8.20859i	−0.513676	−	0.438768i
$351$	63.0387	+	18.5098i	3.36476	+	0.987981i
$352$	−0.166116	−	0.0361363i	−0.00885400	−	0.00192607i
$353$	−8.73775	+	23.4268i	−0.465064	+	1.24688i	0.466893	+	0.884314i	$0.345373\pi$
$353$	−8.73775	+	23.4268i	−0.465064	+	1.24688i	−0.931957	+	0.362570i	$0.881899\pi$
$354$	−26.5520	+	23.0074i	−1.41122	+	1.22283i
$355$	28.9397	−	6.40294i	1.53596	−	0.339833i
$356$	76.6621	+	11.0224i	4.06308	+	0.584183i
$357$	−5.75644	−	7.68971i	−0.304663	−	0.406983i
$358$	6.26989	+	28.8222i	0.331374	+	1.52330i
$359$	15.2160	+	17.5602i	0.803068	+	0.926790i	0.998545	−	0.0539184i	$-0.0171711\pi$
$359$	15.2160	+	17.5602i	0.803068	+	0.926790i	−0.195477	+	0.980708i	$0.562626\pi$
$360$	77.6332	−	35.7869i	4.09163	−	1.88614i
$361$	1.42842	−	0.917989i	0.0751799	−	0.0483152i
$362$	1.51599	+	2.77632i	0.0796785	+	0.145920i
$363$	−33.5092	+	2.39662i	−1.75877	+	0.125790i
$364$	27.2035	−	7.98767i	1.42585	−	0.418667i
$365$	8.72311	−	19.2815i	0.456589	−	1.00924i
$366$	−57.4302	+	8.25721i	−3.00192	+	0.431611i
$367$	−4.75126	−	4.75126i	−0.248014	−	0.248014i	0.572141	−	0.820155i	$-0.306113\pi$
$367$	−4.75126	−	4.75126i	−0.248014	−	0.248014i	−0.820155	+	0.572141i	$0.806113\pi$
$368$	27.6158	−	14.3310i	1.43957	−	0.747055i
$369$		−	18.0953i		−	0.942005i
$370$	−28.0726	−	20.8601i	−1.45942	−	1.08446i
$371$	−0.652521	+	1.42882i	−0.0338772	+	0.0741808i
$372$	−52.2755	+	95.7354i	−2.71036	+	4.96365i
$373$	−2.45283	−	34.2950i	−0.127003	−	1.77573i	−0.518043	−	0.855354i	$-0.673339\pi$
$373$	−2.45283	−	34.2950i	−0.127003	−	1.77573i	0.391041	−	0.920373i	$-0.372115\pi$
$374$	−0.0881396	+	0.300176i	−0.00455759	+	0.0155217i
$375$	−18.7674	−	28.5312i	−0.969146	−	1.47334i
$376$	−4.66305	−	10.2107i	−0.240478	−	0.526574i
$377$	−37.6418	−	2.69220i	−1.93865	−	0.138655i
$378$	25.1227	−	5.46511i	1.29217	−	0.281095i
$379$	2.60521	−	18.1196i	0.133821	−	0.930742i	−0.806689	−	0.590976i	$-0.798743\pi$
$379$	2.60521	−	18.1196i	0.133821	−	0.930742i	0.940510	−	0.339767i	$-0.110348\pi$
$380$	−35.6511	+	26.8858i	−1.82886	+	1.37921i
$381$	10.9989	+	7.06859i	0.563493	+	0.362135i
$382$	1.95767	−	27.3718i	0.100163	−	1.40046i
$383$	−8.70923	−	3.24837i	−0.445021	−	0.165984i	0.116956	−	0.993137i	$-0.462686\pi$
$383$	−8.70923	−	3.24837i	−0.445021	−	0.165984i	−0.561977	+	0.827153i	$0.689959\pi$
$384$	−22.8510	−	35.5568i	−1.16611	−	1.81450i
$385$	−0.0244944	+	0.0845271i	−0.00124835	+	0.00430790i
$386$	24.9153	−	28.7538i	1.26816	−	1.46353i
$387$	11.9238	+	6.51091i	0.606123	+	0.330968i
$388$	26.2020	+	70.2502i	1.33020	+	3.56641i
$389$	−0.458584	−	3.18952i	−0.0232511	−	0.161715i	0.974888	−	0.222697i	$-0.0714860\pi$
$389$	−0.458584	−	3.18952i	−0.0232511	−	0.161715i	−0.998139	+	0.0609816i	$0.980577\pi$
$390$	111.516	−	0.395171i	5.64681	−	0.0200103i
$391$	−5.97414	−	13.8480i	−0.302125	−	0.700324i
$392$	4.27058	−	4.27058i	0.215697	−	0.215697i
$393$	−16.2348	+	21.6872i	−0.818939	+	1.09397i
$394$	48.8447	+	22.3066i	2.46076	+	1.12379i
$395$	−16.9972	+	31.3920i	−0.855223	+	1.57950i
$396$	−0.826412	−	0.716090i	−0.0415288	−	0.0359849i
$397$	30.2265	−	16.5049i	1.51703	−	0.828359i	0.517401	−	0.855743i	$-0.326900\pi$
$397$	30.2265	−	16.5049i	1.51703	−	0.828359i	0.999625	+	0.0273845i	$0.00871784\pi$
$398$	−0.961700	+	4.42087i	−0.0482057	+	0.221598i
$399$	−12.6407	+	5.77279i	−0.632824	+	0.289001i
$400$	24.3634	−	21.4152i	1.21817	−	1.07076i
$401$	−8.01997	+	12.4793i	−0.400498	+	0.623187i	−0.981669	−	0.190594i	$-0.938958\pi$
$401$	−8.01997	+	12.4793i	−0.400498	+	0.623187i	0.581171	+	0.813782i	$0.302595\pi$
$402$	15.2996	−	11.4532i	0.763077	−	0.571232i
$403$	−42.0697	+	31.4930i	−2.09564	+	1.56878i
$404$	−11.4291	+	17.7840i	−0.568617	+	0.884785i
$405$	26.9463	+	1.83129i	1.33897	+	0.0909974i
$406$	−13.4334	+	6.13483i	−0.666689	+	0.304467i
$407$	−0.0517668	+	0.237968i	−0.00256599	+	0.0117956i
$408$	50.9171	−	27.8028i	2.52077	−	1.37644i
$409$	11.7844	+	10.2112i	0.582700	+	0.504913i	0.895592	−	0.444876i	$-0.146752\pi$
$409$	11.7844	+	10.2112i	0.582700	+	0.504913i	−0.312892	+	0.949789i	$0.601298\pi$
$410$	−4.60703	−	15.4869i	−0.227525	−	0.764843i
$411$	−49.4450	−	22.5808i	−2.43894	−	1.11383i
$412$	17.0210	−	22.7373i	0.838563	−	1.12019i
$413$	−3.21763	+	3.21763i	−0.158329	+	0.158329i
$414$	76.7177	+	1.62000i	3.77047	+	0.0796186i
$415$	0.00428462	+	1.20910i	0.000210324	+	0.0593525i
$416$	3.97069	+	27.6168i	0.194679	+	1.35402i
$417$	9.36430	+	25.1067i	0.458572	+	1.22948i
$418$	0.397235	+	0.216907i	0.0194294	+	0.0106092i
$419$	0.0786721	−	0.0907925i	0.00384338	−	0.00443550i	−0.753825	−	0.657076i	$-0.771793\pi$
$419$	0.0786721	−	0.0907925i	0.00384338	−	0.00443550i	0.757668	+	0.652640i	$0.226339\pi$
$420$	26.2612	−	14.4607i	1.28141	−	0.705611i
$421$	−7.94049	−	12.3556i	−0.386996	−	0.602177i	0.592029	−	0.805916i	$-0.298327\pi$
$421$	−7.94049	−	12.3556i	−0.386996	−	0.602177i	−0.979025	+	0.203739i	$0.934691\pi$
$422$	−62.2989	−	23.2363i	−3.03266	−	1.13112i
$423$	0.839297	−	11.7349i	0.0408080	−	0.570571i
$424$	−7.98070	−	5.12888i	−0.387577	−	0.249081i
$425$	−9.51187	−	12.5204i	−0.461393	−	0.607329i
$426$	−14.5648	+	101.300i	−0.705667	+	4.90802i
$427$	−7.34304	+	1.59738i	−0.355355	+	0.0773027i
$428$	−12.9927	−	0.929256i	−0.628026	−	0.0449173i
$429$	−0.322573	−	0.706337i	−0.0155740	−	0.0341023i
$430$	11.8627	+	2.53658i	0.572069	+	0.122325i
$431$	2.12191	−	7.22655i	0.102209	−	0.348091i	−0.892471	−	0.451104i	$-0.851030\pi$
$431$	2.12191	−	7.22655i	0.102209	−	0.348091i	0.994680	+	0.103013i	$0.0328485\pi$
$432$	4.70743	+	65.8185i	0.226486	+	3.16669i
$433$	−12.1141	+	22.1853i	−0.582167	+	1.06616i	0.406159	+	0.913803i	$0.366868\pi$
$433$	−12.1141	+	22.1853i	−0.582167	+	1.06616i	−0.988326	+	0.152356i	$0.951314\pi$
$434$	−8.54298	+	18.7065i	−0.410076	+	0.897942i
$435$	−39.4776	+	5.81888i	−1.89281	+	0.278994i
$436$		−	30.9743i		−	1.48340i
$437$	−21.4132	+	4.18675i	−1.02433	+	0.200280i
$438$	51.6705	+	51.6705i	2.46891	+	2.46891i
$439$	−27.0118	+	3.88371i	−1.28920	+	0.185359i	−0.752601	−	0.658477i	$-0.771201\pi$
$439$	−27.0118	+	3.88371i	−1.28920	+	0.185359i	−0.536601	+	0.843836i	$0.680292\pi$
$440$	−0.484253	−	0.219080i	−0.0230859	−	0.0104442i
$441$	6.07356	−	1.78336i	0.289217	−	0.0849218i
$442$	51.2143	−	3.66292i	2.43602	−	0.174227i
$443$	6.53067	+	11.9600i	0.310282	+	0.568238i	0.985560	−	0.169324i	$-0.0541585\pi$
$443$	6.53067	+	11.9600i	0.310282	+	0.568238i	−0.675279	+	0.737563i	$0.735977\pi$
$444$	69.7915	−	44.8523i	3.31216	−	2.12860i
$445$	37.0168	+	13.6573i	1.75477	+	0.647420i
$446$	−12.6476	−	14.5962i	−0.598883	−	0.691148i
$447$	0.228895	+	1.05221i	0.0108264	+	0.0497679i
$448$	−1.23248	−	1.64640i	−0.0582290	−	0.0777849i
$449$	33.3245	+	4.79134i	1.57268	+	0.226117i	0.872776	−	0.488121i	$-0.162317\pi$
$449$	33.3245	+	4.79134i	1.57268	+	0.226117i	0.699903	+	0.714238i	$0.253226\pi$
$450$	78.0508	−	17.5592i	3.67935	−	0.827747i
$451$	−0.0850283	+	0.0736774i	−0.00400382	+	0.00346933i
$452$	20.7257	−	55.5678i	0.974856	−	2.61369i
$453$	5.43400	+	1.18209i	0.255311	+	0.0555396i
$454$	−61.3912	−	18.0261i	−2.88123	−	0.846006i
$455$	14.4029	−	1.08143i	0.675218	−	0.0506981i
$456$	−23.6452	−	80.5280i	−1.10729	−	3.77107i
$457$	22.2269	−	8.29019i	1.03973	−	0.387799i	0.229127	−	0.973397i	$-0.426413\pi$
$457$	22.2269	−	8.29019i	1.03973	−	0.387799i	0.810602	+	0.585598i	$0.199140\pi$
$458$	45.0374	+	33.7146i	2.10446	+	1.57538i
$459$	31.9864			1.49300
$460$	45.3895	−	12.4657i	2.11630	−	0.581216i
$461$	−1.87647			−0.0873959			−0.0436980	−	0.999045i	$-0.513914\pi$
$461$	−1.87647			−0.0873959			−0.0436980	+	0.999045i	$0.513914\pi$
$462$	−0.243260	−	0.182102i	−0.0113175	−	0.00847217i
$463$	−3.35787	+	1.25242i	−0.156054	+	0.0582050i	−0.426277	−	0.904593i	$-0.640175\pi$
$463$	−3.35787	+	1.25242i	−0.156054	+	0.0582050i	0.270224	+	0.962798i	$0.412902\pi$
$464$	−10.6784	−	36.3673i	−0.495733	−	1.68831i
$465$	−36.2403	+	42.1242i	−1.68060	+	1.95346i
$466$	25.5491	+	7.50188i	1.18354	+	0.347518i
$467$	−1.11554	−	0.242671i	−0.0516210	−	0.0112295i	0.186681	−	0.982421i	$-0.440227\pi$
$467$	−1.11554	−	0.242671i	−0.0516210	−	0.0112295i	−0.238302	+	0.971191i	$0.576591\pi$
$468$	−62.7172	+	168.151i	−2.89910	+	7.77280i
$469$	1.87072	−	1.62099i	0.0863817	−	0.0748502i
$470$	−2.26937	−	10.2570i	−0.104678	−	0.473121i
$471$	−14.9757	−	2.15318i	−0.690042	−	0.0992131i
$472$	−16.4695	−	22.0007i	−0.758072	−	1.01267i
$473$	−0.0179553	−	0.0825390i	−0.000825584	−	0.00379515i
$474$	−80.7195	−	93.1552i	−3.70757	−	4.27876i
$475$	−20.6244	+	9.59607i	−0.946311	+	0.440298i
$476$	11.6121	−	7.46263i	0.532239	−	0.342049i
$477$	−4.76513	−	8.72669i	−0.218180	−	0.399568i
$478$	−28.9839	+	2.07297i	−1.32569	+	0.0948154i
$479$	−1.25711	+	0.369119i	−0.0574386	+	0.0168655i	−0.310326	−	0.950630i	$-0.600438\pi$
$479$	−1.25711	+	0.369119i	−0.0574386	+	0.0168655i	0.252887	+	0.967496i	$0.418620\pi$
$480$	10.4079	+	27.6054i	0.475052	+	1.26001i
$481$	39.5623	−	5.68820i	1.80388	−	0.259359i
$482$	21.8812	+	21.8812i	0.996663	+	0.996663i
$483$	14.6303	−	0.736331i	0.665704	−	0.0335042i
$484$		−	48.2757i		−	2.19435i
$485$	5.56981	+	37.7878i	0.252912	+	1.71586i
$486$	−6.69913	+	14.6690i	−0.303879	+	0.665402i
$487$	−6.71283	+	12.2936i	−0.304187	+	0.557077i	−0.984402	−	0.175936i	$-0.943705\pi$
$487$	−6.71283	+	12.2936i	−0.304187	+	0.557077i	0.680214	+	0.733013i	$0.261887\pi$
$488$	−3.23777	−	45.2699i	−0.146567	−	2.04927i
$489$	1.13903	−	3.87917i	0.0515086	−	0.175422i
$490$	4.74402	−	3.07260i	0.214313	−	0.138806i
$491$	−13.0714	−	28.6224i	−0.589905	−	1.29171i	−0.935499	−	0.353328i	$-0.885050\pi$
$491$	−13.0714	−	28.6224i	−0.589905	−	1.29171i	0.345594	−	0.938384i	$-0.387677\pi$
$492$	38.2291	+	2.73420i	1.72350	+	0.123267i
$493$	−17.9531	+	3.90546i	−0.808566	+	0.175893i
$494$	10.5713	−	73.5248i	0.475624	−	3.30804i
$495$	−0.335416	−	0.444769i	−0.0150758	−	0.0199909i
$496$	−44.4021	−	28.5355i	−1.99371	−	1.28128i
$497$	−0.945617	+	13.2215i	−0.0424167	+	0.593063i
$498$	−3.91169	−	1.45898i	−0.175287	−	0.0653787i
$499$	−20.6799	−	32.1785i	−0.925757	−	1.44051i	−0.897554	−	0.440904i	$-0.854658\pi$
$499$	−20.6799	−	32.1785i	−0.925757	−	1.44051i	−0.0282033	−	0.999602i	$-0.508979\pi$
$500$	42.8188	−	23.9753i	1.91492	−	1.07221i
$501$	−31.3982	+	36.2355i	−1.40277	+	1.61888i
$502$	−51.2071	−	27.9612i	−2.28548	−	1.24797i
$503$	−2.92684	−	7.84716i	−0.130501	−	0.349888i	0.855222	−	0.518262i	$-0.173421\pi$
$503$	−2.92684	−	7.84716i	−0.130501	−	0.349888i	−0.985723	+	0.168375i	$0.946148\pi$
$504$	5.44068	+	37.8407i	0.242347	+	1.68556i
$505$	−7.58805	+	7.64202i	−0.337664	+	0.340065i
$506$	−0.304754	−	0.367086i	−0.0135480	−	0.0163189i
$507$	−62.0367	+	62.0367i	−2.75515	+	2.75515i
$508$	−11.2592	+	15.0406i	−0.499548	+	0.667318i
$509$	7.15546	+	3.26779i	0.317160	+	0.144842i	0.567634	−	0.823281i	$-0.307859\pi$
$509$	7.15546	+	3.26779i	0.317160	+	0.144842i	−0.250473	+	0.968123i	$0.580586\pi$
$510$	52.0386	−	15.4804i	2.30431	−	0.685485i
$511$	7.15267	+	6.19782i	0.316415	+	0.274176i
$512$	44.1823	−	24.1254i	1.95260	−	1.06620i
$513$	9.83639	−	45.2172i	0.434287	−	1.99639i
$514$	24.7395	−	11.2982i	1.09121	−	0.498341i
$515$	10.9014	−	9.51399i	0.480374	−	0.419236i
$516$	−15.5570	+	24.2071i	−0.684857	+	1.06566i
$517$	−0.0585586	+	0.0438364i	−0.00257540	+	0.00192792i
$518$	12.5213	−	9.37333i	0.550155	−	0.411841i
$519$	21.7302	−	33.8129i	0.953850	−	1.48422i
$520$	−5.91464	+	87.0305i	−0.259374	+	3.81654i
$521$	2.74054	−	1.25156i	0.120065	−	0.0548319i	−0.354477	−	0.935065i	$-0.615341\pi$
$521$	2.74054	−	1.25156i	0.120065	−	0.0548319i	0.474542	+	0.880233i	$0.342614\pi$
$522$	19.8707	−	91.3443i	0.869719	−	3.99803i
$523$	14.5458	−	7.94260i	0.636043	−	0.347306i	−0.128660	−	0.991689i	$-0.541068\pi$
$523$	14.5458	−	7.94260i	0.636043	−	0.347306i	0.764703	+	0.644383i	$0.222886\pi$
$524$	−29.4208	−	25.4933i	−1.28525	−	1.11368i
$525$	14.6230	−	4.40651i	0.638200	−	0.192316i
$526$	31.5925	+	14.4278i	1.37750	+	0.629083i
$527$	−15.3325	+	20.4819i	−0.667896	+	0.892205i
$528$	0.551470	−	0.551470i	0.0239996	−	0.0239996i
$529$	22.6074	+	4.23136i	0.982931	+	0.183972i
$530$	−6.30004	−	6.25555i	−0.273656	−	0.271724i
$531$	−4.09924	−	28.5108i	−0.177892	−	1.23726i
$532$	−6.97853	−	18.7102i	−0.302557	−	0.811188i
$533$	16.2064	+	8.84936i	0.701977	+	0.383308i
$534$	−89.2161	+	102.961i	−3.86076	+	4.45555i
$535$	−6.37361	−	1.84695i	−0.275555	−	0.0798508i
$536$	8.08240	+	12.5765i	0.349107	+	0.543221i
$537$	−33.3961	−	12.4561i	−1.44115	−	0.537521i
$538$	5.83438	−	81.5753i	0.251538	−	3.51696i
$539$	−0.0331091	−	0.0212779i	−0.00142611	−	0.000916505i
$540$	−13.8571	+	98.8638i	−0.596313	+	4.25442i
$541$	4.36783	−	30.3789i	0.187788	−	1.30609i	−0.649932	−	0.759992i	$-0.725203\pi$
$541$	4.36783	−	30.3789i	0.187788	−	1.30609i	0.837720	−	0.546100i	$-0.183888\pi$
$542$	−9.19875	+	2.00107i	−0.395120	+	0.0859531i
$543$	−3.81276	−	0.272694i	−0.163621	−	0.0117024i
$544$	5.64285	+	12.3561i	0.241935	+	0.529765i
$545$	3.29949	−	15.4305i	0.141334	−	0.660972i
$546$	−14.0504	+	47.8514i	−0.601303	+	2.04785i
$547$	0.175053	+	2.44756i	0.00748473	+	0.104650i	0.999821	−	0.0189159i	$-0.00602146\pi$
$547$	0.175053	+	2.44756i	0.00748473	+	0.104650i	−0.992336	+	0.123566i	$0.960567\pi$
$548$	37.4348	−	68.5567i	1.59913	−	2.92860i
$549$	19.7606	−	43.2696i	0.843361	−	1.84670i
$550$	−0.400303	−	0.295259i	−0.0170690	−	0.0125899i
$551$			26.5801i			1.13235i
$552$	−8.17314	+	88.0936i	−0.347872	+	3.74951i
$553$	−11.2888	−	11.2888i	−0.480048	−	0.480048i
$554$	15.1431	−	2.17725i	0.643369	−	0.0925025i
$555$	39.5460	−	14.9097i	1.67864	−	0.632884i
$556$	−36.9464	+	10.8484i	−1.56687	+	0.460076i
$557$	−1.34079	+	0.0958950i	−0.0568110	+	0.00406320i	−0.0997157	−	0.995016i	$-0.531793\pi$
$557$	−1.34079	+	0.0958950i	−0.0568110	+	0.00406320i	0.0429048	+	0.999079i	$0.486339\pi$
$558$	−62.3864	−	114.252i	−2.64103	−	4.83668i
$559$	−11.6625	+	7.49503i	−0.493271	+	0.317006i
$560$	6.07292	+	13.1741i	0.256628	+	0.556707i
$561$	−0.247569	−	0.285709i	−0.0104524	−	0.0120627i
$562$	13.2858	+	61.0739i	0.560428	+	2.57625i
$563$	1.37261	+	1.83360i	0.0578487	+	0.0772768i	0.828533	−	0.559941i	$-0.189176\pi$
$563$	1.37261	+	1.83360i	0.0578487	+	0.0772768i	−0.770684	+	0.637218i	$0.780085\pi$
$564$	24.6650	+	3.54629i	1.03858	+	0.149326i
$565$	16.2442	−	25.4746i	0.683401	−	1.07172i
$566$	−18.9650	+	16.4332i	−0.797157	+	0.690740i
$567$	−4.22102	+	11.3170i	−0.177266	+	0.475269i
$568$	−78.2255	−	17.0169i	−3.28227	−	0.714014i
$569$	8.15786	+	2.39536i	0.341995	+	0.100419i	0.448220	−	0.893923i	$-0.352058\pi$
$569$	8.15786	+	2.39536i	0.341995	+	0.100419i	−0.106225	+	0.994342i	$0.533876\pi$
$570$	−5.88089	−	78.3241i	−0.246323	−	3.28064i
$571$	−1.69013	−	5.75606i	−0.0707298	−	0.240884i	0.916539	−	0.399946i	$-0.130971\pi$
$571$	−1.69013	−	5.75606i	−0.0707298	−	0.240884i	−0.987269	+	0.159062i	$0.949153\pi$
$572$	1.04549	−	0.389947i	0.0437141	−	0.0163045i
$573$	26.5466	+	19.8725i	1.10900	+	0.830186i
$574$	7.22590			0.301603
$575$	23.9397	−	1.37502i	0.998355	−	0.0573424i
$576$	13.0182			0.542426
$577$	−30.2727	−	22.6618i	−1.26027	−	0.943425i	−0.260511	−	0.965471i	$-0.583891\pi$
$577$	−30.2727	−	22.6618i	−1.26027	−	0.943425i	−0.999757	+	0.0220460i	$0.992982\pi$
$578$	−16.8402	+	6.28106i	−0.700459	+	0.261258i
$579$	12.9529	+	44.1135i	0.538304	+	1.83330i
$580$	−4.29341	−	57.1814i	−0.178274	−	2.37433i
$581$	−0.518827	−	0.152341i	−0.0215246	−	0.00632018i
$582$	−128.873	−	28.0345i	−5.34195	−	1.16207i
$583$	−0.0216041	+	0.0579228i	−0.000894749	+	0.00239892i
$584$	−43.1986	+	37.4318i	−1.78757	+	1.54894i
$585$	−49.1560	+	77.0875i	−2.03235	+	3.18718i
$586$	25.6453	+	3.68724i	1.05940	+	0.152318i
$587$	23.4462	+	31.3204i	0.967727	+	1.29273i	0.956174	+	0.292798i	$0.0945865\pi$
$587$	23.4462	+	31.3204i	0.967727	+	1.29273i	0.0115526	+	0.999933i	$0.496323\pi$
$588$	2.84990	+	13.1008i	0.117528	+	0.540267i
$589$	24.2389	+	27.9732i	0.998746	+	1.15261i
$590$	−10.7671	−	23.3573i	−0.443276	−	0.961607i
$591$	−54.5872	+	35.0811i	−2.24542	+	1.44304i
$592$	19.2387	+	35.2331i	0.790707	+	1.44807i
$593$	9.76150	−	0.698156i	0.400857	−	0.0286698i	0.130544	−	0.991442i	$-0.458328\pi$
$593$	9.76150	−	0.698156i	0.400857	−	0.0286698i	0.270312	+	0.962773i	$0.412873\pi$
$594$	0.970888	−	0.285078i	0.0398360	−	0.0116969i
$595$	6.57976	−	2.48072i	0.269744	−	0.101700i
$596$	−1.53164	+	0.220217i	−0.0627386	+	0.00902044i
$597$	−3.86585	−	3.86585i	−0.158219	−	0.158219i
$598$	−38.9690	+	67.9171i	−1.59356	+	2.77734i
$599$			33.7414i			1.37864i	0.724459	+	0.689318i	$0.242090\pi$
$599$			33.7414i			1.37864i	−0.724459	+	0.689318i	$0.757910\pi$
$600$	13.7736	+	91.2042i	0.562305	+	3.72339i
$601$	−9.84497	+	21.5575i	−0.401585	+	0.879348i	0.595522	+	0.803339i	$0.296945\pi$
$601$	−9.84497	+	21.5575i	−0.401585	+	0.879348i	−0.997107	+	0.0760093i	$0.975782\pi$
$602$	−2.59996	+	4.76148i	−0.105967	+	0.194063i
$603$	1.11779	+	15.6287i	0.0455199	+	0.636451i
$604$	−2.25141	+	7.66758i	−0.0916084	+	0.311990i
$605$	5.14249	−	24.0496i	0.209072	−	0.977756i
$606$	−15.4473	−	33.8250i	−0.627506	−	1.37405i
$607$	−2.40935	−	0.172320i	−0.0977927	−	0.00699427i	0.0223571	−	0.999750i	$-0.492883\pi$
$607$	−2.40935	−	0.172320i	−0.0977927	−	0.00699427i	−0.120150	+	0.992756i	$0.538337\pi$
$608$	19.2023	−	4.17721i	0.778758	−	0.169408i
$609$	2.53971	−	17.6640i	0.102914	−	0.715783i
$610$	5.89573	−	42.0633i	0.238711	−	1.70309i
$611$	10.0995	+	6.49054i	0.408581	+	0.262579i
$612$	−6.23322	+	87.1519i	−0.251963	+	3.52291i
$613$	−4.08523	−	1.52371i	−0.165001	−	0.0615421i	0.265606	−	0.964082i	$-0.414428\pi$
$613$	−4.08523	−	1.52371i	−0.165001	−	0.0615421i	−0.430607	+	0.902539i	$0.641701\pi$
$614$	2.09060	+	3.25303i	0.0843696	+	0.131282i
$615$	18.7534	+	5.43439i	0.756211	+	0.219136i
$616$	0.155658	−	0.179639i	0.00627163	−	0.00723785i
$617$	6.76671	+	3.69490i	0.272417	+	0.148751i	0.609651	−	0.792670i	$-0.291309\pi$
$617$	6.76671	+	3.69490i	0.272417	+	0.148751i	−0.337234	+	0.941421i	$0.609491\pi$
$618$	17.4594	+	46.8104i	0.702319	+	1.88299i
$619$	−1.32133	−	9.19002i	−0.0531086	−	0.369378i	−0.998993	−	0.0448736i	$-0.985712\pi$
$619$	−1.32133	−	9.19002i	−0.0531086	−	0.369378i	0.945884	−	0.324505i	$-0.105198\pi$
$620$	−56.6631	−	56.2630i	−2.27565	−	2.25958i
$621$	−27.2330	+	40.4706i	−1.09282	+	1.62403i
$622$	16.0879	−	16.0879i	0.645064	−	0.645064i
$623$	−10.5744	+	14.1257i	−0.423654	+	0.565935i
$624$	−116.431	−	53.1722i	−4.66096	−	2.12859i
$625$	23.8851	−	7.38260i	0.955403	−	0.295304i
$626$	14.0004	+	12.1314i	0.559568	+	0.484869i
$627$	−0.480021	+	0.262111i	−0.0191702	+	0.0104677i
$628$	4.62146	−	21.2445i	0.184416	−	0.847748i
$629$	17.7007	−	8.08364i	0.705773	−	0.322316i
$630$	−2.42588	+	35.6955i	−0.0966495	+	1.42214i
$631$	2.44033	−	3.79722i	0.0971479	−	0.151165i	−0.789277	−	0.614037i	$-0.789545\pi$
$631$	2.44033	−	3.79722i	0.0971479	−	0.151165i	0.886425	+	0.462872i	$0.153181\pi$
$632$	77.1875	−	57.7819i	3.07036	−	2.29844i
$633$	64.3221	−	48.1509i	2.55657	−	1.91383i
$634$	−33.6383	+	52.3423i	−1.33595	+	2.07878i
$635$	−7.21122	+	6.29344i	−0.286169	+	0.249747i
$636$	19.1565	−	8.74846i	0.759603	−	0.346899i
$637$	−1.37302	+	6.31169i	−0.0544012	+	0.250078i
$638$	−0.510125	+	0.278549i	−0.0201960	+	0.0110279i
$639$	−63.4112	−	54.9462i	−2.50851	−	2.17364i
$640$	29.6570	−	8.82236i	1.17230	−	0.348734i
$641$	−25.3831	−	11.5921i	−1.00257	−	0.457859i	−0.154643	−	0.987970i	$-0.549423\pi$
$641$	−25.3831	−	11.5921i	−1.00257	−	0.457859i	−0.847928	+	0.530112i	$0.822150\pi$
$642$	13.7311	−	18.3426i	0.541923	−	0.723925i
$643$	−6.20620	+	6.20620i	−0.244749	+	0.244749i	−0.818811	−	0.574063i	$-0.805367\pi$
$643$	−6.20620	+	6.20620i	−0.244749	+	0.244749i	0.574063	+	0.818811i	$0.305367\pi$
$644$	−0.444409	+	21.0457i	−0.0175122	+	0.829318i
$645$	−10.3287	+	10.4021i	−0.406691	+	0.409584i
$646$	−5.14668	−	35.7960i	−0.202494	−	1.40837i
$647$	−6.79880	−	18.2283i	−0.267289	−	0.716628i	−0.999373	−	0.0354141i	$-0.988725\pi$
$647$	−6.79880	−	18.2283i	−0.267289	−	0.716628i	0.732084	−	0.681214i	$-0.238548\pi$
$648$	−64.0254	−	34.9605i	−2.51516	−	1.37338i
$649$	−0.117279	+	0.135347i	−0.00460361	+	0.00531285i
$650$	−22.4439	+	78.4904i	−0.880321	+	3.07865i
$651$	−13.4353	−	20.9058i	−0.526573	−	0.819363i
$652$	5.44340	+	2.03028i	0.213180	+	0.0795121i
$653$	0.901324	−	12.6022i	0.0352716	−	0.493161i	−0.948857	−	0.315705i	$-0.897759\pi$
$653$	0.901324	−	12.6022i	0.0352716	−	0.493161i	0.984129	−	0.177455i	$-0.0567866\pi$
$654$	45.8352	+	29.4565i	1.79230	+	1.15184i
$655$	−11.9410	−	15.8340i	−0.466574	−	0.618687i
$656$	−2.63932	+	18.3568i	−0.103048	+	0.716715i
$657$	−58.5398	+	12.7346i	−2.28386	+	0.496822i
$658$	4.68604	+	0.335152i	0.182681	+	0.0130656i
$659$	13.0156	+	28.5002i	0.507015	+	1.11021i	0.974125	+	0.226009i	$0.0725680\pi$
$659$	13.0156	+	28.5002i	0.507015	+	1.11021i	−0.467110	+	0.884199i	$0.654705\pi$
$660$	0.990323	−	0.641412i	0.0385483	−	0.0249669i
$661$	2.14838	−	7.31671i	0.0835623	−	0.284587i	−0.907102	−	0.420911i	$-0.861711\pi$
$661$	2.14838	−	7.31671i	0.0835623	−	0.284587i	0.990664	+	0.136324i	$0.0435287\pi$
$662$	−0.0989193	−	1.38307i	−0.00384461	−	0.0537546i
$663$	−29.7354	+	54.4562i	−1.15483	+	2.11490i
$664$	1.35664	−	2.97063i	0.0526478	−	0.115283i
$665$	−1.48344	−	10.0643i	−0.0575254	−	0.390275i
$666$			99.0073i			3.83646i
$667$	10.3438	−	26.0401i	0.400513	−	1.00828i
$668$	−48.7190	−	48.7190i	−1.88500	−	1.88500i
$669$	23.1010	−	3.32142i	0.893135	−	0.128413i
$670$	4.93570	+	13.0913i	0.190683	+	0.505760i
$671$	−0.283778	+	0.0833247i	−0.0109551	+	0.00321671i
$672$	−13.1602	+	0.941236i	−0.507666	+	0.0363090i
$673$	−18.7868	−	34.4055i	−0.724178	−	1.32623i	−0.937065	−	0.349156i	$-0.886468\pi$
$673$	−18.7868	−	34.4055i	−0.724178	−	1.32623i	0.212886	−	0.977077i	$-0.431714\pi$
$674$	−52.6411	+	33.8304i	−2.02766	+	1.30310i
$675$	−17.4345	+	47.7751i	−0.671054	+	1.83886i
$676$	−82.5600	−	95.2794i	−3.17539	−	3.66459i
$677$	2.93003	+	13.4691i	0.112610	+	0.517661i	0.998549	+	0.0538577i	$0.0171517\pi$
$677$	2.93003	+	13.4691i	0.112610	+	0.517661i	−0.885938	+	0.463803i	$0.846485\pi$
$678$	62.5180	+	83.5143i	2.40099	+	3.20735i
$679$	−16.9079	−	2.43099i	−0.648867	−	0.0932930i
$680$	9.17445	+	41.4663i	0.351824	+	1.59016i
$681$	58.4326	−	50.6321i	2.23914	−	1.94023i
$682$	−0.282846	+	0.758340i	−0.0108307	+	0.0290383i
$683$	−21.2516	−	4.62301i	−0.813170	−	0.176894i	−0.213295	−	0.976988i	$-0.568420\pi$
$683$	−21.2516	−	4.62301i	−0.813170	−	0.176894i	−0.599875	+	0.800093i	$0.704783\pi$
$684$	121.284	+	35.6122i	4.63742	+	1.36167i
$685$	25.9519	−	30.1654i	0.991569	−	1.15256i
$686$	0.712138	+	2.42532i	0.0271896	+	0.0925992i
$687$	−63.6969	+	23.7577i	−2.43019	+	0.906414i
$688$	−11.1465	−	8.34418i	−0.424957	−	0.318119i
$689$	10.1461			0.386535
$690$	−24.7188	+	79.0214i	−0.941029	+	3.00829i
$691$	−2.50024			−0.0951134			−0.0475567	−	0.998869i	$-0.515143\pi$
$691$	−2.50024			−0.0951134			−0.0475567	+	0.998869i	$0.515143\pi$
$692$	46.2377	+	34.6131i	1.75769	+	1.31579i
$693$	0.233420	−	0.0870612i	0.00886689	−	0.00330718i
$694$	−5.70010	−	19.4127i	−0.216373	−	0.736898i
$695$	−19.5613	+	1.46874i	−0.742001	+	0.0557125i
$696$	103.413	+	30.3649i	3.91987	+	1.15098i
$697$	8.78438	+	1.91092i	0.332732	+	0.0723814i
$698$	−7.21159	+	19.3350i	−0.272963	+	0.731841i
$699$	−24.3178	+	21.0715i	−0.919782	+	0.796996i
$700$	4.81695	+	21.4114i	0.182064	+	0.809277i
$701$	−25.7482	−	3.70203i	−0.972496	−	0.139824i	−0.362289	−	0.932066i	$-0.618005\pi$
$701$	−25.7482	−	3.70203i	−0.972496	−	0.139824i	−0.610207	+	0.792242i	$0.708914\pi$
$702$	−99.5224	−	132.946i	−3.75623	−	5.01774i
$703$	−5.98405	−	27.5082i	−0.225693	−	1.03749i
$704$	−0.0530054	−	0.0611715i	−0.00199772	−	0.00230549i
$705$	11.9096	+	4.39405i	0.448543	+	0.165490i
$706$	53.1681	−	34.1691i	2.00101	−	1.28597i
$707$	−2.30816	−	4.22708i	−0.0868072	−	0.158976i
$708$	60.8528	−	4.35228i	2.28699	−	0.163569i
$709$	4.23404	−	1.24323i	0.159013	−	0.0466904i	−0.201257	−	0.979538i	$-0.564503\pi$
$709$	4.23404	−	1.24323i	0.159013	−	0.0466904i	0.360270	+	0.932848i	$0.382685\pi$
$710$	−68.2597	−	30.8813i	−2.56174	−	1.15896i
$711$	100.028	−	14.3818i	3.75133	−	0.539360i
$712$	−75.3552	−	75.3552i	−2.82406	−	2.82406i
$713$	−12.8605	−	36.8375i	−0.481630	−	1.37958i
$714$			24.2803i			0.908666i
$715$	0.562372	−	0.0828920i	0.0210315	−	0.00309999i
$716$	21.2774	−	46.5911i	0.795175	−	1.74119i
$717$	16.8282	−	30.8186i	0.628462	−	1.15094i
$718$	−4.18992	−	58.5828i	−0.156367	−	2.18629i
$719$	4.28609	−	14.5971i	0.159844	−	0.544379i	−0.840154	−	0.542348i	$-0.817535\pi$
$719$	4.28609	−	14.5971i	0.159844	−	0.544379i	0.999998	−	0.00203089i	$-0.000646452\pi$
$720$	−89.7955	−	19.2008i	−3.34648	−	0.715572i
$721$	2.68807	+	5.88606i	0.100109	+	0.219208i
$722$	−4.28103	−	0.306185i	−0.159323	−	0.0113950i
$723$	−36.5392	+	7.94862i	−1.35891	+	0.295612i
$724$	0.781726	−	5.43702i	0.0290526	−	0.202065i
$725$	3.95229	−	28.9435i	0.146784	−	1.07494i
$726$	71.4374	+	45.9100i	2.65129	+	1.70388i
$727$	1.12115	−	15.6758i	0.0415813	−	0.581383i	−0.933363	−	0.358934i	$-0.883140\pi$
$727$	1.12115	−	15.6758i	0.0415813	−	0.581383i	0.974944	−	0.222449i	$-0.0714051\pi$
$728$	−36.5514	−	13.6329i	−1.35468	−	0.505271i
$729$	9.05492	+	14.0897i	0.335368	+	0.521842i
$730$	−46.8591	+	25.8030i	−1.73433	+	0.955012i
$731$	−4.41992	+	5.10086i	−0.163477	+	0.188662i
$732$	88.4278	+	48.2852i	3.26839	+	1.78467i
$733$	−14.1700	−	37.9914i	−0.523383	−	1.40324i	−0.882660	−	0.470012i	$-0.844250\pi$
$733$	−14.1700	−	37.9914i	−0.523383	−	1.40324i	0.359277	−	0.933231i	$-0.383023\pi$
$734$	2.41714	+	16.8116i	0.0892182	+	0.620526i
$735$	0.0242032	+	6.83002i	0.000892747	+	0.251929i
$736$	−20.4378	−	3.38034i	−0.753347	−	0.124601i
$737$	0.0688868	−	0.0688868i	0.00253748	−	0.00253748i
$738$	−27.4108	+	36.6165i	−1.00901	+	1.34787i
$739$	4.08055	+	1.86353i	0.150106	+	0.0685509i	0.489051	−	0.872255i	$-0.337343\pi$
$739$	4.08055	+	1.86353i	0.150106	+	0.0685509i	−0.338946	+	0.940806i	$0.610070\pi$
$740$	17.3167	+	58.2114i	0.636574	+	2.13989i
$741$	67.8371	+	58.7812i	2.49206	+	2.15938i
$742$	3.48478	−	1.90283i	0.127930	−	0.0698552i
$743$	−8.33034	+	38.2940i	−0.305611	+	1.40487i	0.526460	+	0.850200i	$0.323519\pi$
$743$	−8.33034	+	38.2940i	−0.305611	+	1.40487i	−0.832071	+	0.554670i	$0.812845\pi$
$744$	136.523	−	62.3482i	5.00519	−	2.28579i
$745$	−0.786481	−	0.0534497i	−0.0288144	−	0.00195824i
$746$	−46.9867	+	73.1127i	−1.72031	+	2.67685i
$747$	2.74010	−	2.05121i	0.100255	−	0.0750498i
$748$	0.434898	−	0.325561i	0.0159015	−	0.0119037i
$749$	1.60442	−	2.49653i	0.0586243	−	0.0912213i
$750$	−5.24248	+	86.1628i	−0.191428	+	3.14622i
$751$	37.3188	−	17.0429i	1.36178	−	0.621905i	0.405431	−	0.914125i	$-0.367121\pi$
$751$	37.3188	−	17.0429i	1.36178	−	0.621905i	0.956351	+	0.292220i	$0.0943940\pi$
$752$	−2.56304	+	11.7821i	−0.0934644	+	0.429649i
$753$	61.8789	−	33.7884i	2.25499	−	1.23132i
$754$	72.0915	+	62.4676i	2.62542	+	2.27494i
$755$	−1.93836	+	3.57995i	−0.0705443	+	0.130288i
$756$	−40.6109	−	18.5464i	−1.47700	−	0.674525i
$757$	4.15400	−	5.54909i	0.150980	−	0.201685i	−0.718675	−	0.695347i	$-0.755251\pi$
$757$	4.15400	−	5.54909i	0.150980	−	0.201685i	0.869654	+	0.493661i	$0.164342\pi$
$758$	−32.7193	+	32.7193i	−1.18842	+	1.18842i
$759$	0.572270	−	0.0699833i	0.0207721	−	0.00254023i
$760$	61.4395	−	0.217719i	2.22864	−	0.00789752i
$761$	6.89930	+	47.9857i	0.250100	+	1.73948i	0.597594	+	0.801799i	$0.296123\pi$
$761$	6.89930	+	47.9857i	0.250100	+	1.73948i	−0.347495	+	0.937682i	$0.612968\pi$
$762$	−11.5493	−	30.9648i	−0.418385	−	1.12173i
$763$	6.19356	+	3.38194i	0.224222	+	0.122434i
$764$	−31.2055	+	36.0130i	−1.12897	+	1.30291i
$765$	−12.3889	+	42.7527i	−0.447923	+	1.54573i
$766$	12.7028	+	19.7659i	0.458971	+	0.714173i
$767$	27.5393	+	10.2716i	0.994388	+	0.370888i
$768$	−6.72540	+	94.0333i	−0.242682	+	3.39314i
$769$	−44.8602	−	28.8299i	−1.61770	−	1.03963i	−0.957454	−	0.288585i	$-0.906815\pi$
$769$	−44.8602	−	28.8299i	−1.61770	−	1.03963i	−0.660247	−	0.751048i	$-0.729548\pi$
$770$	0.177607	−	0.133940i	0.00640051	−	0.00482685i
$771$	−4.67723	+	32.5308i	−0.168446	+	1.17157i
$772$	−64.5575	+	14.0436i	−2.32348	+	0.505441i
$773$	41.5521	+	2.97186i	1.49452	+	0.106890i	0.794515	−	0.607244i	$-0.207725\pi$
$773$	41.5521	+	2.97186i	1.49452	+	0.106890i	0.700008	+	0.714135i	$0.253180\pi$
$774$	−14.2656	−	31.2373i	−0.512766	−	1.12280i
$775$	−22.2347	−	34.0646i	−0.798694	−	1.22364i
$776$	29.0651	−	98.9868i	1.04338	−	3.55342i
$777$	1.34836	+	18.8526i	0.0483723	+	0.676332i
$778$	−3.90353	+	7.14878i	−0.139948	+	0.256296i
$779$	5.40270	−	11.8303i	0.193572	−	0.423863i
$780$	−155.432	−	115.497i	−5.56534	−	4.13547i
$781$			0.521684i			0.0186673i
$782$	−8.88807	+	37.0716i	−0.317837	+	1.32568i
$783$	42.0202	+	42.0202i	1.50168	+	1.50168i
$784$	−6.42145	+	0.923265i	−0.229338	+	0.0329738i
$785$	4.56532	−	10.0911i	0.162943	−	0.360168i
$786$	65.7035	−	19.2923i	2.34357	−	0.688133i
$787$	24.3263	−	1.73985i	0.867140	−	0.0620191i	0.369323	−	0.929301i	$-0.379590\pi$
$787$	24.3263	−	1.73985i	0.867140	−	0.0620191i	0.497817	+	0.867282i	$0.334135\pi$
$788$	−44.6872	−	81.8384i	−1.59191	−	2.91537i
$789$	−35.3068	+	22.6903i	−1.25695	+	0.807796i
$790$	81.9472	−	37.7755i	2.91555	−	1.34399i
$791$	8.84828	+	10.2115i	0.314609	+	0.363078i
$792$	0.319827	+	1.47022i	0.0113646	+	0.0522421i
$793$	29.0891	+	38.8584i	1.03298	+	1.37990i
$794$	−86.1661	−	12.3888i	−3.05792	−	0.439663i
$795$	10.4751	−	2.31763i	0.371515	−	0.0821980i
$796$	5.93739	−	5.14477i	0.210445	−	0.182352i
$797$	2.77845	−	7.44932i	0.0984178	−	0.263868i	−0.878405	−	0.477916i	$-0.841392\pi$
$797$	2.77845	−	7.44932i	0.0984178	−	0.263868i	0.976823	+	0.214048i	$0.0686649\pi$
$798$	34.3235	+	7.46661i	1.21504	+	0.264315i
$799$	5.60808	+	1.64668i	0.198400	+	0.0582554i
$800$	−21.5309	+	1.69337i	−0.761231	+	0.0598698i
$801$	−31.4677	−	107.169i	−1.11186	−	3.78664i
$802$	35.1324	−	13.1037i	1.24057	−	0.462708i
$803$	0.298191	+	0.223223i	0.0105229	+	0.00787736i
$804$	−33.1870			−1.17041
$805$	−2.46325	+	10.4371i	−0.0868183	+	0.367858i
$806$	132.835			4.67892
$807$	79.1157	+	59.2253i	2.78501	+	2.08483i
$808$	27.2535	−	10.1650i	0.958775	−	0.357604i
$809$	2.96708	+	10.1050i	0.104317	+	0.355271i	0.995065	−	0.0992266i	$-0.0316369\pi$
$809$	2.96708	+	10.1050i	0.104317	+	0.355271i	−0.890748	+	0.454498i	$0.849819\pi$
$810$	−51.7528	−	44.5240i	−1.81841	−	1.56441i
$811$	−38.6294	−	11.3426i	−1.35646	−	0.398293i	−0.478948	−	0.877843i	$-0.658982\pi$
$811$	−38.6294	−	11.3426i	−1.35646	−	0.398293i	−0.877515	+	0.479550i	$0.840800\pi$
$812$	25.0582	+	5.45108i	0.879371	+	0.191295i
$813$	3.97543	−	10.6585i	0.139424	−	0.373811i
$814$	0.465226	−	0.403121i	0.0163062	−	0.0141294i
$815$	2.49548	+	1.59128i	0.0874129	+	0.0557401i
$816$	−61.6821	−	8.86855i	−2.15931	−	0.310461i
$817$	5.85155	+	7.81675i	0.204720	+	0.273474i
$818$	−8.37816	−	38.5138i	−0.292936	−	1.34660i
$819$	−26.7754	−	30.9005i	−0.935608	−	1.07975i
$820$	−9.71183	+	26.3229i	−0.339152	+	0.919237i
$821$	−5.47328	+	3.51746i	−0.191019	+	0.122760i	−0.632655	−	0.774434i	$-0.718035\pi$
$821$	−5.47328	+	3.51746i	−0.191019	+	0.122760i	0.441636	+	0.897194i	$0.354398\pi$
$822$	65.8484	+	120.592i	2.29673	+	4.20614i
$823$	−1.09176	+	0.0780844i	−0.0380565	+	0.00272185i	−0.0903544	−	0.995910i	$-0.528800\pi$
$823$	−1.09176	+	0.0780844i	−0.0380565	+	0.00272185i	0.0522980	+	0.998632i	$0.483345\pi$
$824$	−37.4975	+	11.0103i	−1.30629	+	0.383560i
$825$	0.561677	−	0.214041i	0.0195551	−	0.00745196i
$826$	11.3851	−	1.63693i	0.396137	−	0.0569559i
$827$	32.8410	+	32.8410i	1.14199	+	1.14199i	0.988085	+	0.153908i	$0.0491860\pi$
$827$	32.8410	+	32.8410i	1.14199	+	1.14199i	0.153908	+	0.988085i	$0.450814\pi$
$828$	−104.961	−	82.0871i	−3.64766	−	2.85272i
$829$			31.2372i			1.08491i	0.840084	+	0.542456i	$0.182505\pi$
$829$			31.2372i			1.08491i	−0.840084	+	0.542456i	$0.817495\pi$
$830$	1.82288	−	2.45315i	0.0632730	−	0.0851502i
$831$	−7.67986	+	16.8165i	−0.266411	+	0.583359i
$832$	−6.36645	+	11.6593i	−0.220717	+	0.404213i
$833$	0.224344	+	3.13674i	0.00777306	+	0.108682i
$834$	19.0826	−	64.9893i	0.660776	−	2.25040i
$835$	−19.0808	−	29.4602i	−0.660317	−	1.01951i
$836$	−0.326485	−	0.714903i	−0.0112917	−	0.0247254i
$837$	82.5414	+	5.90347i	2.85305	+	0.204054i
$838$	−0.296728	+	0.0645493i	−0.0102503	+	0.00222982i
$839$	1.06172	−	7.38440i	0.0366545	−	0.254938i	−0.963252	−	0.268599i	$-0.913439\pi$
$839$	1.06172	−	7.38440i	0.0366545	−	0.254938i	0.999907	+	0.0136609i	$0.00434854\pi$
$840$	−40.8509	−	5.72580i	−1.40949	−	0.197559i
$841$	−4.31893	−	2.77561i	−0.148929	−	0.0957106i
$842$	−2.64846	+	37.0304i	−0.0912721	+	1.27615i
$843$	−70.7660	−	26.3944i	−2.43731	−	0.909070i
$844$	62.4227	+	97.1316i	2.14868	+	3.34341i
$845$	−30.9797	−	56.2601i	−1.06573	−	1.93541i
$846$	−19.4744	+	22.4746i	−0.669543	+	0.772694i
$847$	9.65311	+	5.27100i	0.331685	+	0.181114i
$848$	3.56116	+	9.54784i	0.122291	+	0.327874i
$849$	−4.31556	−	30.0154i	−0.148110	−	1.03012i
$850$	0.281681	+	39.7441i	0.00966158	+	1.36321i
$851$	−4.84250	+	29.2780i	−0.165999	+	1.00364i
$852$	125.664	−	125.664i	4.30516	−	4.30516i
$853$	−16.4777	+	22.0116i	−0.564186	+	0.753664i	−0.988396	−	0.151900i	$-0.951461\pi$
$853$	−16.4777	+	22.0116i	−0.564186	+	0.753664i	0.424210	+	0.905564i	$0.360552\pi$
$854$	17.2786	+	7.89088i	0.591262	+	0.270020i
$855$	56.6269	+	30.6606i	1.93660	+	1.04857i
$856$	13.5453	+	11.7371i	0.462970	+	0.401166i
$857$	35.2980	−	19.2742i	1.20576	−	0.658394i	0.254584	−	0.967051i	$-0.418061\pi$
$857$	35.2980	−	19.2742i	1.20576	−	0.658394i	0.951173	+	0.308657i	$0.0998795\pi$
$858$	−0.417221	+	1.91793i	−0.0142437	+	0.0654771i
$859$	34.7375	−	15.8641i	1.18523	−	0.541276i	0.277456	−	0.960738i	$-0.410509\pi$
$859$	34.7375	−	15.8641i	1.18523	−	0.541276i	0.907773	+	0.419463i	$0.137782\pi$
$860$	−13.8510	−	15.8709i	−0.472314	−	0.541192i
$861$	−4.72078	+	7.34568i	−0.160884	+	0.250340i
$862$	−15.2405	+	11.4089i	−0.519095	+	0.388589i
$863$	11.9771	−	8.96593i	0.407705	−	0.305204i	−0.375670	−	0.926753i	$-0.622587\pi$
$863$	11.9771	−	8.96593i	0.407705	−	0.305204i	0.783375	+	0.621550i	$0.213497\pi$
$864$	23.7530	−	36.9604i	0.808094	−	1.25742i
$865$	19.3472	+	22.1687i	0.657825	+	0.753757i
$866$	58.1197	−	26.5424i	1.97499	−	0.901946i
$867$	4.61674	−	21.2228i	0.156793	−	0.720764i
$868$	31.3424	−	17.1143i	1.06383	−	0.580896i
$869$	−0.474854	−	0.411464i	−0.0161083	−	0.0139579i
$870$	88.6988	+	48.0260i	3.00717	+	1.62823i
$871$	−14.5439	−	6.64199i	−0.492802	−	0.225055i
$872$	−25.5408	+	34.1185i	−0.864920	+	1.15540i
$873$	76.4575	−	76.4575i	2.58769	−	2.58769i
$874$	49.6724	+	23.9646i	1.68020	+	0.810616i
$875$	0.118855	+	11.1797i	0.00401802	+	0.377943i
$876$	−18.0583	−	125.598i	−0.610134	−	4.24358i
$877$	3.22647	+	8.65049i	0.108950	+	0.292106i	0.979971	−	0.199139i	$-0.0638146\pi$
$877$	3.22647	+	8.65049i	0.108950	+	0.292106i	−0.871021	+	0.491245i	$0.836542\pi$
$878$	60.5424	+	33.0586i	2.04321	+	1.11567i
$879$	−20.5028	+	23.6615i	−0.691541	+	0.798081i
$880$	0.275391	+	0.500119i	0.00928343	+	0.0168590i
$881$	−2.23427	−	3.47658i	−0.0752743	−	0.117129i	0.801575	−	0.597894i	$-0.203996\pi$
$881$	−2.23427	−	3.47658i	−0.0752743	−	0.117129i	−0.876850	+	0.480765i	$0.840359\pi$
$882$	−14.9915	−	5.59154i	−0.504790	−	0.188277i
$883$	−3.43090	+	47.9702i	−0.115459	+	1.61433i	0.528272	+	0.849075i	$0.322840\pi$
$883$	−3.43090	+	47.9702i	−0.115459	+	1.61433i	−0.643731	+	0.765252i	$0.722614\pi$
$884$	−75.0060	−	48.2034i	−2.52272	−	1.62126i
$885$	30.7788	+	4.31406i	1.03462	+	0.145016i
$886$	4.90201	−	34.0942i	0.164686	−	1.14542i
$887$	−36.4350	+	7.92596i	−1.22337	+	0.266128i	−0.777449	−	0.628945i	$-0.783487\pi$
$887$	−36.4350	+	7.92596i	−1.22337	+	0.266128i	−0.445919	+	0.895073i	$0.647123\pi$
$888$	−113.860	−	8.14345i	−3.82090	−	0.273276i
$889$	−1.77814	−	3.89359i	−0.0596370	−	0.130587i
$890$	−54.2167	−	83.7092i	−1.81735	−	2.80594i
$891$	−0.133928	+	0.456118i	−0.00448677	+	0.0152805i
$892$	2.39254	+	33.4520i	0.0801080	+	1.12006i
$893$	4.05239	−	7.42140i	0.135608	−	0.248348i
$894$	1.13071	−	2.47592i	0.0378168	−	0.0828072i
$895$	15.5629	−	20.9439i	0.520209	−	0.700076i
$896$			13.8374i			0.462276i
$897$	−43.5839	−	83.9861i	−1.45522	−	2.80421i
$898$	−60.1754	−	60.1754i	−2.00808	−	2.00808i
$899$	−47.0489	+	6.76462i	−1.56917	+	0.225613i
$900$	−126.773	−	56.8129i	−4.22577	−	1.89376i
$901$	4.73959	−	1.39167i	0.157899	−	0.0463632i
$902$	0.283664	−	0.0202881i	0.00944499	−	0.000675519i
$903$	−3.14181	−	5.75380i	−0.104553	−	0.191474i
$904$	−68.6496	+	44.1184i	−2.28325	+	1.46736i
$905$	0.968604	−	2.62530i	0.0321975	−	0.0872680i
$906$	−9.20525	−	10.6234i	−0.305824	−	0.352940i
$907$	0.497193	+	2.28556i	0.0165090	+	0.0758907i	0.984664	−	0.174460i	$-0.0558178\pi$
$907$	0.497193	+	2.28556i	0.0165090	+	0.0758907i	−0.968155	+	0.250350i	$0.919454\pi$
$908$	66.5828	+	88.9443i	2.20963	+	2.95172i
$909$	30.1761	+	4.33866i	1.00088	+	0.143904i
$910$	−30.7829	−	19.6292i	−1.02044	−	0.650702i
$911$	13.0177	−	11.2799i	0.431296	−	0.373720i	−0.411987	−	0.911190i	$-0.635165\pi$
$911$	13.0177	−	11.2799i	0.431296	−	0.373720i	0.843283	+	0.537469i	$0.180620\pi$
$912$	−31.5052	+	84.4688i	−1.04324	+	2.79704i
$913$	−0.0207951	−	0.00452370i	−0.000688217	−	0.000149713i
$914$	−57.5349	−	16.8938i	−1.90308	−	0.558796i
$915$	38.9088	+	33.4740i	1.28628	+	1.10662i
$916$	−27.5230	−	93.7349i	−0.909387	−	3.09709i
$917$	8.30990	−	3.09943i	0.274417	−	0.102352i
$918$	−64.7257	−	48.4531i	−2.13627	−	1.59919i
$919$	−16.5065			−0.544500			−0.272250	−	0.962227i	$-0.587768\pi$
$919$	−16.5065			−0.544500			−0.272250	+	0.962227i	$0.587768\pi$
$920$	−60.2759	−	23.6962i	−1.98724	−	0.781240i
$921$	−4.67277			−0.153973
$922$	3.79711	+	2.84248i	0.125051	+	0.0936120i
$923$	80.2212	−	29.9210i	2.64051	−	0.984860i
$924$	0.148660	+	0.506290i	0.00489056	+	0.0166557i
$925$	2.42583	+	30.8439i	0.0797609	+	1.01414i
$926$	8.69194	+	2.55218i	0.285635	+	0.0838700i
$927$	−40.0240	−	8.70668i	−1.31456	−	0.285965i
$928$	−8.81914	+	23.6450i	−0.289502	+	0.776186i
$929$	29.7755	−	25.8006i	0.976902	−	0.846490i	−0.0112550	−	0.999937i	$-0.503583\pi$
$929$	29.7755	−	25.8006i	0.976902	−	0.846490i	0.988157	+	0.153446i	$0.0490372\pi$
$930$	137.143	−	30.3431i	4.49710	−	0.994988i
$931$	4.50319	+	0.647462i	0.147586	+	0.0212197i
$932$	−27.7096	−	37.0158i	−0.907660	−	1.21249i
$933$	5.84411	+	26.8649i	0.191328	+	0.879518i
$934$	1.88974	+	2.18087i	0.0618340	+	0.0713603i
$935$	0.251334	−	0.115859i	0.00821950	−	0.00378898i
$936$	207.738	−	133.505i	6.79012	−	4.36375i
$937$	13.0799	+	23.9541i	0.427303	+	0.782547i	0.999288	−	0.0377167i	$-0.0120084\pi$
$937$	13.0799	+	23.9541i	0.427303	+	0.782547i	−0.571985	+	0.820264i	$0.693827\pi$
$938$	−6.24093	+	0.446360i	−0.203774	+	0.0145742i
$939$	−21.4791	+	6.30685i	−0.700945	+	0.205816i
$940$	−7.51909	+	16.6201i	−0.245246	+	0.542088i
$941$	16.9750	−	2.44063i	0.553368	−	0.0795623i	0.140042	−	0.990146i	$-0.455276\pi$
$941$	16.9750	−	2.44063i	0.553368	−	0.0795623i	0.413326	+	0.910583i	$0.364367\pi$
$942$	27.0422	+	27.0422i	0.881082	+	0.881082i
$943$	−9.89674	+	9.48742i	−0.322282	+	0.308953i
$944$			29.5208i			0.960820i
$945$	−18.2556	−	13.5653i	−0.593855	−	0.441279i
$946$	−0.0886970	+	0.194219i	−0.00288379	+	0.00631461i
$947$	5.79551	−	10.6137i	0.188329	−	0.344898i	−0.766406	−	0.642356i	$-0.777957\pi$
$947$	5.79551	−	10.6137i	0.188329	−	0.344898i	0.954735	+	0.297458i	$0.0961388\pi$
$948$	15.2696	+	213.497i	0.495933	+	6.93405i
$949$	17.2232	−	58.6567i	0.559087	−	1.90408i
$950$	56.2703	+	11.8238i	1.82565	+	0.383615i
$951$	−31.2335	−	68.3918i	−1.01282	−	2.21776i
$952$	−18.9444	−	1.35493i	−0.613990	−	0.0439134i
$953$	−7.80602	+	1.69810i	−0.252862	+	0.0550067i	−0.337209	−	0.941430i	$-0.609483\pi$
$953$	−7.80602	+	1.69810i	−0.252862	+	0.0550067i	0.0843476	+	0.996436i	$0.473119\pi$
$954$	−3.57677	+	24.8770i	−0.115802	+	0.805422i
$955$	−19.3819	+	14.6166i	−0.627184	+	0.472981i
$956$	42.4484	+	27.2799i	1.37288	+	0.882296i
$957$	0.0501051	−	0.700560i	0.00161967	−	0.0226459i
$958$	3.10294	+	1.15734i	0.100251	+	0.0373919i
$959$	9.62112	+	14.9708i	0.310682	+	0.483431i
$960$	−3.90964	+	13.4917i	−0.126183	+	0.435442i
$961$	−23.0453	+	26.5957i	−0.743396	+	0.857925i
$962$	−88.6722	−	48.4187i	−2.85891	−	1.56108i
$963$	6.56469	+	17.6006i	0.211544	+	0.567172i
$964$	−7.64728	−	53.1880i	−0.246302	−	1.71307i
$965$	−33.6567	+	0.119267i	−1.08345	+	0.00383935i
$966$	−30.7204	−	20.6721i	−0.988414	−	0.665113i
$967$	17.5098	−	17.5098i	0.563076	−	0.563076i	−0.367104	−	0.930180i	$-0.619651\pi$
$967$	17.5098	−	17.5098i	0.563076	−	0.563076i	0.930180	+	0.367104i	$0.119651\pi$
$968$	−39.8072	+	53.1761i	−1.27945	+	1.70915i
$969$	39.7517	+	18.1540i	1.27701	+	0.583190i
$970$	45.9703	−	84.9021i	1.47602	−	2.72604i
$971$	−38.6835	−	33.5194i	−1.24141	−	1.07569i	−0.994291	−	0.106705i	$-0.965970\pi$
$971$	−38.6835	−	33.5194i	−1.24141	−	1.07569i	−0.247121	−	0.968985i	$-0.579485\pi$
$972$	24.5777	−	13.4205i	0.788331	−	0.430461i
$973$	1.86477	−	8.57221i	0.0597818	−	0.274812i
$974$	32.2060	−	14.7080i	1.03195	−	0.471275i
$975$	−65.1286	−	74.0947i	−2.08578	−	2.37293i
$976$	−26.3573	+	41.0128i	−0.843677	+	1.31279i
$977$	0.00452286	−	0.00338577i	0.000144699	−	0.000108321i	−0.599205	−	0.800595i	$-0.704517\pi$
$977$	0.00452286	−	0.00338577i	0.000144699	−	0.000108321i	0.599350	+	0.800487i	$0.295426\pi$
$978$	−8.18103	+	6.12424i	−0.261601	+	0.195832i
$979$	−0.375454	+	0.584217i	−0.0119995	+	0.0186717i
$980$	−9.79223	−	0.665485i	−0.312801	−	0.0212581i
$981$	−40.6323	+	18.5562i	−1.29729	+	0.592453i
$982$	−16.9068	+	77.7191i	−0.539516	+	2.48012i
$983$	−1.08299	+	0.591359i	−0.0345421	+	0.0188614i	−0.496427	−	0.868078i	$-0.665355\pi$
$983$	−1.08299	+	0.591359i	−0.0345421	+	0.0188614i	0.461885	+	0.886940i	$0.347173\pi$
$984$	−39.8551	−	34.5347i	−1.27054	−	1.10093i
$985$	−13.5442	−	45.5299i	−0.431554	−	1.45070i
$986$	42.2447	+	19.2925i	1.34535	+	0.614399i
$987$	−3.40216	+	4.54475i	−0.108292	+	0.144661i
$988$	−91.2077	+	91.2077i	−2.90170	+	2.90170i
$989$	−2.69073	−	9.93510i	−0.0855603	−	0.315918i
$990$	0.00498978	+	1.40809i	0.000158585	+	0.0447521i
$991$	2.34533	+	16.3121i	0.0745018	+	0.518171i	0.992563	+	0.121733i	$0.0388450\pi$
$991$	2.34533	+	16.3121i	0.0745018	+	0.518171i	−0.918061	+	0.396439i	$0.870246\pi$
$992$	12.2810	+	32.9266i	0.389921	+	1.04542i
$993$	1.47062	+	0.803021i	0.0466688	+	0.0254831i
$994$	21.9413	−	25.3217i	0.695937	−	0.803154i
$995$	3.50588	−	1.93051i	0.111144	−	0.0612014i
$996$	3.91946	+	6.09881i	0.124193	+	0.193248i
$997$	16.5630	+	6.17766i	0.524554	+	0.195649i	0.597770	−	0.801668i	$-0.296054\pi$
$997$	16.5630	+	6.17766i	0.524554	+	0.195649i	−0.0732160	+	0.997316i	$0.523326\pi$
$998$	−6.89754	+	96.4402i	−0.218338	+	3.05276i
$999$	−52.9475	−	34.0273i	−1.67518	−	1.07658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.bi.a.43.5	✓	1440
5.2	odd	4	inner	805.2.bi.a.687.68	yes	1440
23.15	odd	22	inner	805.2.bi.a.498.68	yes	1440
115.107	even	44	inner	805.2.bi.a.337.5	yes	1440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.bi.a.43.5	✓	1440	1.1	even	1	trivial
805.2.bi.a.337.5	yes	1440	115.107	even	44	inner
805.2.bi.a.498.68	yes	1440	23.15	odd	22	inner
805.2.bi.a.687.68	yes	1440	5.2	odd	4	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bi (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02354 - 1.51480i) q^{2} +(2.86191 - 1.06744i) q^{3} +(1.23661 + 4.21152i) q^{4} +(0.167422 + 2.22979i) q^{5} +(-7.40814 - 2.17523i) q^{6} +(-0.977147 - 0.212565i) q^{7} +(2.11059 - 5.65871i) q^{8} +(4.78387 - 4.14525i) q^{9} +O(q^{10})\)	\(q+(-2.02354 - 1.51480i) q^{2} +(2.86191 - 1.06744i) q^{3} +(1.23661 + 4.21152i) q^{4} +(0.167422 + 2.22979i) q^{5} +(-7.40814 - 2.17523i) q^{6} +(-0.977147 - 0.212565i) q^{7} +(2.11059 - 5.65871i) q^{8} +(4.78387 - 4.14525i) q^{9} +(3.03890 - 4.76567i) q^{10} +(-0.0389563 - 0.00560107i) q^{11} +(8.03462 + 10.7330i) q^{12} +(1.37302 + 6.31169i) q^{13} +(1.65530 + 1.91032i) q^{14} +(2.85931 + 6.20275i) q^{15} +(-5.45762 + 3.50740i) q^{16} +(1.50712 + 2.76008i) q^{17} +(-15.9596 + 1.14145i) q^{18} +(4.36521 - 1.28174i) q^{19} +(-9.18378 + 3.46249i) q^{20} +(-3.02341 + 0.434701i) q^{21} +(0.0703449 + 0.0703449i) q^{22} +(-4.77532 - 0.443044i) q^{23} -18.4477i q^{24} +(-4.94394 + 0.746632i) q^{25} +(6.78258 - 14.8518i) q^{26} +(4.87462 - 8.92720i) q^{27} +(-0.313130 - 4.37814i) q^{28} +(-1.64600 + 5.60577i) q^{29} +(3.61002 - 16.8828i) q^{30} +(3.37973 + 7.40058i) q^{31} +(4.30846 + 0.308147i) q^{32} +(-0.117468 + 0.0255536i) q^{33} +(1.13126 - 7.86811i) q^{34} +(0.310381 - 2.21442i) q^{35} +(23.3736 + 15.0213i) q^{36} +(0.441435 - 6.17207i) q^{37} +(-10.7748 - 4.01878i) q^{38} +(10.6668 + 16.5979i) q^{39} +(12.9711 + 3.75879i) q^{40} +(1.87203 - 2.16044i) q^{41} +(6.77646 + 3.70023i) q^{42} +(0.750035 + 2.01092i) q^{43} +(-0.0245849 - 0.170991i) q^{44} +(10.0440 + 9.97302i) q^{45} +(8.99192 + 8.13018i) q^{46} +(1.31423 - 1.31423i) q^{47} +(-11.8753 + 15.8635i) q^{48} +(0.909632 + 0.415415i) q^{49} +(11.1352 + 5.97825i) q^{50} +(7.25946 + 6.29035i) q^{51} +(-24.8839 + 13.5876i) q^{52} +(0.333891 - 1.53487i) q^{53} +(-23.3869 + 10.6804i) q^{54} +(0.00596708 - 0.0878021i) q^{55} +(-3.26520 + 5.08076i) q^{56} +(11.1247 - 8.32783i) q^{57} +(11.8224 - 8.85011i) q^{58} +(2.46014 - 3.82806i) q^{59} +(-22.5872 + 19.7125i) q^{60} +(6.83568 - 3.12175i) q^{61} +(4.37139 - 20.0950i) q^{62} +(-5.55568 + 3.03363i) q^{63} +(1.55428 + 1.34679i) q^{64} +(-13.8439 + 4.11827i) q^{65} +(0.276410 + 0.126232i) q^{66} +(-1.48340 + 1.98159i) q^{67} +(-9.76042 + 9.76042i) q^{68} +(-14.1395 + 3.82941i) q^{69} +(-3.98247 + 4.01080i) q^{70} +(-1.88642 - 13.1203i) q^{71} +(-13.3600 - 35.8195i) q^{72} +(-8.30665 - 4.53577i) q^{73} +(-10.2427 + 11.8207i) q^{74} +(-13.3521 + 7.41414i) q^{75} +(10.7962 + 16.7992i) q^{76} +(0.0368754 + 0.0137538i) q^{77} +(3.55780 - 49.7445i) q^{78} +(13.4304 + 8.63119i) q^{79} +(-8.73449 - 11.5821i) q^{80} +(1.71896 - 11.9556i) q^{81} +(-7.06077 + 1.53598i) q^{82} +(0.539353 + 0.0385753i) q^{83} +(-5.56954 - 12.1956i) q^{84} +(-5.90208 + 3.82266i) q^{85} +(1.52842 - 5.20533i) q^{86} +(1.27310 + 17.8002i) q^{87} +(-0.113916 + 0.208621i) q^{88} +(7.33009 - 16.0506i) q^{89} +(-5.21717 - 35.3954i) q^{90} -6.45930i q^{91} +(-4.03934 - 20.6592i) q^{92} +(17.5722 + 17.5722i) q^{93} +(-4.65019 + 0.668596i) q^{94} +(3.58885 + 9.51893i) q^{95} +(12.6594 - 3.71713i) q^{96} +(17.0383 - 1.21860i) q^{97} +(-1.21140 - 2.21852i) q^{98} +(-0.209579 + 0.134689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1440 q - 8 q^{3} + 16 q^{6}+O(q^{10}) \) 1440 * q - 8 * q^3 + 16 * q^6	\( 1440 q - 8 q^{3} + 16 q^{6} - 32 q^{12} + 16 q^{13} + 192 q^{16} - 72 q^{18} - 36 q^{23} + 8 q^{25} - 8 q^{27} + 40 q^{32} - 44 q^{33} - 208 q^{36} - 88 q^{37} - 32 q^{41} + 80 q^{46} - 192 q^{47} - 24 q^{48} + 56 q^{50} + 64 q^{52} - 56 q^{55} - 88 q^{57} + 24 q^{62} - 352 q^{66} + 16 q^{70} - 344 q^{71} + 48 q^{72} - 32 q^{73} - 144 q^{75} - 352 q^{76} - 40 q^{78} - 16 q^{81} + 96 q^{82} - 16 q^{85} + 16 q^{87} - 836 q^{90} - 112 q^{92} + 8 q^{93} - 56 q^{95} - 96 q^{96} + 132 q^{97}+O(q^{100}) \) 1440 * q - 8 * q^3 + 16 * q^6 - 32 * q^12 + 16 * q^13 + 192 * q^16 - 72 * q^18 - 36 * q^23 + 8 * q^25 - 8 * q^27 + 40 * q^32 - 44 * q^33 - 208 * q^36 - 88 * q^37 - 32 * q^41 + 80 * q^46 - 192 * q^47 - 24 * q^48 + 56 * q^50 + 64 * q^52 - 56 * q^55 - 88 * q^57 + 24 * q^62 - 352 * q^66 + 16 * q^70 - 344 * q^71 + 48 * q^72 - 32 * q^73 - 144 * q^75 - 352 * q^76 - 40 * q^78 - 16 * q^81 + 96 * q^82 - 16 * q^85 + 16 * q^87 - 836 * q^90 - 112 * q^92 + 8 * q^93 - 56 * q^95 - 96 * q^96 + 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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