LMFDB - Embedded newform 280.2.br.a.107.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.21
Character	$\chi$	$=$	280.107
Dual form			280.2.br.a.123.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0937676 + 1.41110i) q^{2} +(-2.51296 - 0.673346i) q^{3} +(-1.98242 - 0.264631i) q^{4} +(2.09775 + 0.774229i) q^{5} +(1.18579 - 3.48291i) q^{6} +(-0.419863 - 2.61222i) q^{7} +(0.559308 - 2.77258i) q^{8} +(3.26351 + 1.88419i) q^{9} +O(q^{10})$	\(q+(-0.0937676 + 1.41110i) q^{2} +(-2.51296 - 0.673346i) q^{3} +(-1.98242 - 0.264631i) q^{4} +(2.09775 + 0.774229i) q^{5} +(1.18579 - 3.48291i) q^{6} +(-0.419863 - 2.61222i) q^{7} +(0.559308 - 2.77258i) q^{8} +(3.26351 + 1.88419i) q^{9} +(-1.28922 + 2.88755i) q^{10} +(0.673124 + 1.16589i) q^{11} +(4.80355 + 1.99986i) q^{12} +(3.02874 + 3.02874i) q^{13} +(3.72548 - 0.347527i) q^{14} +(-4.75025 - 3.35812i) q^{15} +(3.85994 + 1.04922i) q^{16} +(1.09352 - 4.08108i) q^{17} +(-2.96479 + 4.42847i) q^{18} +(6.52363 + 3.76642i) q^{19} +(-3.95373 - 2.08997i) q^{20} +(-0.703832 + 6.84714i) q^{21} +(-1.70830 + 0.840524i) q^{22} +(-2.25799 + 0.605027i) q^{23} +(-3.27242 + 6.59077i) q^{24} +(3.80114 + 3.24828i) q^{25} +(-4.55785 + 3.98986i) q^{26} +(-1.41352 - 1.41352i) q^{27} +(0.141066 + 5.28962i) q^{28} -3.41296 q^{29} +(5.18407 - 6.38821i) q^{30} +(5.73934 - 3.31361i) q^{31} +(-1.84249 + 5.34839i) q^{32} +(-0.906492 - 3.38307i) q^{33} +(5.65627 + 1.92574i) q^{34} +(1.14169 - 5.80487i) q^{35} +(-5.97102 - 4.59887i) q^{36} +(-2.39958 - 8.95535i) q^{37} +(-5.92650 + 8.85233i) q^{38} +(-5.57171 - 9.65049i) q^{39} +(3.31990 - 5.38315i) q^{40} +9.58202 q^{41} +(-9.59601 - 1.63522i) q^{42} +(3.73207 - 3.73207i) q^{43} +(-1.02588 - 2.48940i) q^{44} +(5.38725 + 6.47927i) q^{45} +(-0.642028 - 3.24299i) q^{46} +(-0.998016 - 3.72465i) q^{47} +(-8.99340 - 5.23572i) q^{48} +(-6.64743 + 2.19355i) q^{49} +(-4.94008 + 5.05921i) q^{50} +(-5.49595 + 9.51927i) q^{51} +(-5.20271 - 6.80571i) q^{52} +(-0.0240790 + 0.0898639i) q^{53} +(2.12717 - 1.86208i) q^{54} +(0.509386 + 2.96689i) q^{55} +(-7.47742 - 0.296936i) q^{56} +(-13.8575 - 13.8575i) q^{57} +(0.320025 - 4.81603i) q^{58} +(0.663996 - 0.383358i) q^{59} +(8.52831 + 7.91426i) q^{60} +(-1.18730 - 0.685485i) q^{61} +(4.13768 + 8.40950i) q^{62} +(3.55170 - 9.31613i) q^{63} +(-7.37435 - 3.10145i) q^{64} +(4.00860 + 8.69848i) q^{65} +(4.85886 - 0.961929i) q^{66} +(-2.24546 + 8.38018i) q^{67} +(-3.24779 + 7.80101i) q^{68} +6.08164 q^{69} +(8.08421 + 2.15535i) q^{70} +1.47220i q^{71} +(7.04937 - 7.99449i) q^{72} +(0.914941 + 0.245158i) q^{73} +(12.8619 - 2.54633i) q^{74} +(-7.36490 - 10.7223i) q^{75} +(-11.9358 - 9.19296i) q^{76} +(2.76293 - 2.24786i) q^{77} +(14.1403 - 6.95735i) q^{78} +(-1.50999 + 2.61539i) q^{79} +(7.28487 + 5.18948i) q^{80} +(-3.05223 - 5.28661i) q^{81} +(-0.898484 + 13.5212i) q^{82} +(-7.12999 + 7.12999i) q^{83} +(3.20725 - 13.3876i) q^{84} +(5.45362 - 7.71445i) q^{85} +(4.91638 + 5.61628i) q^{86} +(8.57663 + 2.29810i) q^{87} +(3.60899 - 1.21420i) q^{88} +(-3.89233 - 2.24724i) q^{89} +(-9.64806 + 6.99441i) q^{90} +(6.64008 - 9.18339i) q^{91} +(4.63639 - 0.601879i) q^{92} +(-16.6540 + 4.46242i) q^{93} +(5.34944 - 1.05905i) q^{94} +(10.7689 + 12.9518i) q^{95} +(8.23143 - 12.1997i) q^{96} +(10.9372 + 10.9372i) q^{97} +(-2.47201 - 9.58588i) q^{98} +5.07317i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0937676	+	1.41110i	−0.0663037	+	0.997799i
$2$	−0.0937676	+	1.41110i	−0.0663037	+	0.997799i
$3$	−2.51296	−	0.673346i	−1.45086	−	0.388757i	−0.554537	−	0.832159i	$-0.687105\pi$
$3$	−2.51296	−	0.673346i	−1.45086	−	0.388757i	−0.896323	+	0.443402i	$0.853771\pi$
$4$	−1.98242	−	0.264631i	−0.991208	−	0.132316i
$5$	2.09775	+	0.774229i	0.938144	+	0.346246i
$5$	2.09775	+	0.774229i	0.938144	+	0.346246i
$6$	1.18579	−	3.48291i	0.484099	−	1.42189i
$7$	−0.419863	−	2.61222i	−0.158693	−	0.987328i
$7$	−0.419863	−	2.61222i	−0.158693	−	0.987328i
$8$	0.559308	−	2.77258i	0.197745	−	0.980253i
$9$	3.26351	+	1.88419i	1.08784	+	0.628063i
$10$	−1.28922	+	2.88755i	−0.407686	+	0.913122i
$11$	0.673124	+	1.16589i	0.202955	+	0.351528i	0.949479	−	0.313830i	$-0.101612\pi$
$11$	0.673124	+	1.16589i	0.202955	+	0.351528i	−0.746525	+	0.665358i	$0.768279\pi$
$12$	4.80355	+	1.99986i	1.38666	+	0.577310i
$13$	3.02874	+	3.02874i	0.840020	+	0.840020i	0.988861	−	0.148841i	$-0.0475543\pi$
$13$	3.02874	+	3.02874i	0.840020	+	0.840020i	−0.148841	+	0.988861i	$0.547554\pi$
$14$	3.72548	−	0.347527i	0.995677	−	0.0928805i
$15$	−4.75025	−	3.35812i	−1.22651	−	0.867064i
$16$	3.85994	+	1.04922i	0.964985	+	0.262305i
$17$	1.09352	−	4.08108i	0.265218	−	0.989806i	−0.696899	−	0.717169i	$-0.745438\pi$
$17$	1.09352	−	4.08108i	0.265218	−	0.989806i	0.962117	−	0.272637i	$-0.0878958\pi$
$18$	−2.96479	+	4.42847i	−0.698809	+	1.04380i
$19$	6.52363	+	3.76642i	1.49662	+	0.864075i	0.999992	−	0.00388708i	$-0.00123730\pi$
$19$	6.52363	+	3.76642i	1.49662	+	0.864075i	0.496630	+	0.867962i	$0.334571\pi$
$20$	−3.95373	−	2.08997i	−0.884082	−	0.467333i
$21$	−0.703832	+	6.84714i	−0.153589	+	1.49417i
$22$	−1.70830	+	0.840524i	−0.364211	+	0.179200i
$23$	−2.25799	+	0.605027i	−0.470824	+	0.126157i	−0.486427	−	0.873721i	$-0.661700\pi$
$23$	−2.25799	+	0.605027i	−0.470824	+	0.126157i	0.0156029	+	0.999878i	$0.495033\pi$
$24$	−3.27242	+	6.59077i	−0.667981	+	1.34534i
$25$	3.80114	+	3.24828i	0.760228	+	0.649657i
$26$	−4.55785	+	3.98986i	−0.893868	+	0.782475i
$27$	−1.41352	−	1.41352i	−0.272033	−	0.272033i
$28$	0.141066	+	5.28962i	0.0266591	+	0.999645i
$29$	−3.41296			−0.633770			−0.316885	−	0.948464i	$-0.602637\pi$
$29$	−3.41296			−0.633770			−0.316885	+	0.948464i	$0.602637\pi$
$30$	5.18407	−	6.38821i	0.946478	−	1.16632i
$31$	5.73934	−	3.31361i	1.03082	−	0.595142i	0.113598	−	0.993527i	$-0.463762\pi$
$31$	5.73934	−	3.31361i	1.03082	−	0.595142i	0.917218	+	0.398385i	$0.130429\pi$
$32$	−1.84249	+	5.34839i	−0.325709	+	0.945470i
$33$	−0.906492	−	3.38307i	−0.157800	−	0.588917i
$34$	5.65627	+	1.92574i	0.970043	+	0.330262i
$35$	1.14169	−	5.80487i	0.192981	−	0.981202i
$36$	−5.97102	−	4.59887i	−0.995170	−	0.766479i
$37$	−2.39958	−	8.95535i	−0.394488	−	1.47225i	−0.822650	−	0.568548i	$-0.807505\pi$
$37$	−2.39958	−	8.95535i	−0.394488	−	1.47225i	0.428162	−	0.903702i	$-0.359161\pi$
$38$	−5.92650	+	8.85233i	−0.961406	+	1.43604i
$39$	−5.57171	−	9.65049i	−0.892188	−	1.54531i
$40$	3.31990	−	5.38315i	0.524922	−	0.851150i
$41$	9.58202			1.49646			0.748230	−	0.663439i	$-0.230904\pi$
$41$	9.58202			1.49646			0.748230	+	0.663439i	$0.230904\pi$
$42$	−9.59601	−	1.63522i	−1.48070	−	0.252320i
$43$	3.73207	−	3.73207i	0.569135	−	0.569135i	−0.362751	−	0.931886i	$-0.618162\pi$
$43$	3.73207	−	3.73207i	0.569135	−	0.569135i	0.931886	+	0.362751i	$0.118162\pi$
$44$	−1.02588	−	2.48940i	−0.154658	−	0.375291i
$45$	5.38725	+	6.47927i	0.803084	+	0.965873i
$46$	−0.642028	−	3.24299i	−0.0946619	−	0.478152i
$47$	−0.998016	−	3.72465i	−0.145576	−	0.543296i	−0.999729	−	0.0232746i	$-0.992591\pi$
$47$	−0.998016	−	3.72465i	−0.145576	−	0.543296i	0.854153	−	0.520021i	$-0.174076\pi$
$48$	−8.99340	−	5.23572i	−1.29809	−	0.755712i
$49$	−6.64743	+	2.19355i	−0.949633	+	0.313365i
$50$	−4.94008	+	5.05921i	−0.698633	+	0.715480i
$51$	−5.49595	+	9.51927i	−0.769588	+	1.33296i
$52$	−5.20271	−	6.80571i	−0.721487	−	0.943782i
$53$	−0.0240790	+	0.0898639i	−0.00330750	+	0.0123438i	−0.967560	−	0.252642i	$-0.918701\pi$
$53$	−0.0240790	+	0.0898639i	−0.00330750	+	0.0123438i	0.964252	+	0.264986i	$0.0853672\pi$
$54$	2.12717	−	1.86208i	0.289471	−	0.253397i
$55$	0.509386	+	2.96689i	0.0686856	+	0.400056i
$56$	−7.47742	−	0.296936i	−0.999212	−	0.0396798i
$57$	−13.8575	−	13.8575i	−1.83547	−	1.83547i
$58$	0.320025	−	4.81603i	0.0420213	−	0.632375i
$59$	0.663996	−	0.383358i	0.0864449	−	0.0499090i	−0.456154	−	0.889901i	$-0.650774\pi$
$59$	0.663996	−	0.383358i	0.0864449	−	0.0499090i	0.542599	+	0.839992i	$0.317440\pi$
$60$	8.52831	+	7.91426i	1.10100	+	1.02173i
$61$	−1.18730	−	0.685485i	−0.152018	−	0.0877674i	0.422062	−	0.906567i	$-0.361307\pi$
$61$	−1.18730	−	0.685485i	−0.152018	−	0.0877674i	−0.574079	+	0.818800i	$0.694640\pi$
$62$	4.13768	+	8.40950i	0.525486	+	1.06801i
$63$	3.55170	−	9.31613i	0.447472	−	1.17372i
$64$	−7.37435	−	3.10145i	−0.921794	−	0.387681i
$65$	4.00860	+	8.69848i	0.497206	+	1.07891i
$66$	4.85886	−	0.961929i	0.598084	−	0.118405i
$67$	−2.24546	+	8.38018i	−0.274327	+	1.02380i	0.681964	+	0.731386i	$0.261126\pi$
$67$	−2.24546	+	8.38018i	−0.274327	+	1.02380i	−0.956291	+	0.292416i	$0.905541\pi$
$68$	−3.24779	+	7.80101i	−0.393853	+	0.946011i
$69$	6.08164			0.732144
$70$	8.08421	+	2.15535i	0.966248	+	0.257614i
$71$			1.47220i			0.174718i	0.996177	+	0.0873590i	$0.0278427\pi$
$71$			1.47220i			0.174718i	−0.996177	+	0.0873590i	$0.972157\pi$
$72$	7.04937	−	7.99449i	0.830776	−	0.942160i
$73$	0.914941	+	0.245158i	0.107086	+	0.0286935i	0.311964	−	0.950094i	$-0.399013\pi$
$73$	0.914941	+	0.245158i	0.107086	+	0.0286935i	−0.204878	+	0.978787i	$0.565680\pi$
$74$	12.8619	−	2.54633i	1.49517	−	0.296004i
$75$	−7.36490	−	10.7223i	−0.850425	−	1.23810i
$76$	−11.9358	−	9.19296i	−1.36913	−	1.05450i
$77$	2.76293	−	2.24786i	0.314866	−	0.256168i
$78$	14.1403	−	6.95735i	1.60107	−	0.787765i
$79$	−1.50999	+	2.61539i	−0.169888	+	0.294254i	−0.938380	−	0.345605i	$-0.887674\pi$
$79$	−1.50999	+	2.61539i	−0.169888	+	0.294254i	0.768493	+	0.639859i	$0.221007\pi$
$80$	7.28487	+	5.18948i	0.814473	+	0.580201i
$81$	−3.05223	−	5.28661i	−0.339136	−	0.587402i
$82$	−0.898484	+	13.5212i	−0.0992209	+	1.49317i
$83$	−7.12999	+	7.12999i	−0.782619	+	0.782619i	−0.980272	−	0.197653i	$-0.936668\pi$
$83$	−7.12999	+	7.12999i	−0.782619	+	0.782619i	0.197653	+	0.980272i	$0.436668\pi$
$84$	3.20725	−	13.3876i	0.349940	−	1.46071i
$85$	5.45362	−	7.71445i	0.591529	−	0.836750i
$86$	4.91638	+	5.61628i	0.530147	+	0.605619i
$87$	8.57663	+	2.29810i	0.919512	+	0.246382i
$88$	3.60899	−	1.21420i	0.384720	−	0.129434i
$89$	−3.89233	−	2.24724i	−0.412586	−	0.238207i	0.279314	−	0.960200i	$-0.409893\pi$
$89$	−3.89233	−	2.24724i	−0.412586	−	0.238207i	−0.691900	+	0.721993i	$0.743226\pi$
$90$	−9.64806	+	6.99441i	−1.01699	+	0.737275i
$91$	6.64008	−	9.18339i	0.696070	−	0.962681i
$92$	4.63639	−	0.601879i	0.483377	−	0.0627503i
$93$	−16.6540	+	4.46242i	−1.72694	+	0.462731i
$94$	5.34944	−	1.05905i	0.551752	−	0.109233i
$95$	10.7689	+	12.9518i	1.10486	+	1.32883i
$96$	8.23143	−	12.1997i	0.840117	−	1.24512i
$97$	10.9372	+	10.9372i	1.11050	+	1.11050i	0.993083	+	0.117417i	$0.0374614\pi$
$97$	10.9372	+	10.9372i	1.11050	+	1.11050i	0.117417	+	0.993083i	$0.462539\pi$
$98$	−2.47201	−	9.58588i	−0.249711	−	0.968320i
$99$			5.07317i			0.509873i
$100$	−6.67584	−	7.44535i	−0.667584	−	0.744535i
$101$	−10.7115	+	6.18426i	−1.06583	+	0.615357i	−0.927039	−	0.374964i	$-0.877655\pi$
$101$	−10.7115	+	6.18426i	−1.06583	+	0.615357i	−0.138791	+	0.990322i	$0.544322\pi$
$102$	−12.9173	−	8.64795i	−1.27901	−	0.856275i
$103$	−5.40781	+	1.44902i	−0.532848	+	0.142776i	−0.515203	−	0.857068i	$-0.672283\pi$
$103$	−5.40781	+	1.44902i	−0.532848	+	0.142776i	−0.0176448	+	0.999844i	$0.505617\pi$
$104$	10.0914	−	6.70340i	0.989543	−	0.657323i
$105$	−6.77772	+	13.8187i	−0.661438	+	1.34856i
$106$	−0.124549	−	0.0424042i	−0.0120973	−	0.00411866i
$107$	2.39905	−	0.642824i	0.231925	−	0.0621441i	−0.140985	−	0.990012i	$-0.545027\pi$
$107$	2.39905	−	0.642824i	0.231925	−	0.0621441i	0.372910	+	0.927868i	$0.378360\pi$
$108$	2.42813	+	3.17625i	0.233647	+	0.305635i
$109$	−1.16090	−	2.01074i	−0.111194	−	0.192594i	0.805058	−	0.593196i	$-0.202134\pi$
$109$	−1.16090	−	2.01074i	−0.111194	−	0.192594i	−0.916252	+	0.400602i	$0.868801\pi$
$110$	−4.23435	+	0.440597i	−0.403729	+	0.0420093i
$111$			24.1202i			2.28939i
$112$	1.12015	−	10.5236i	0.105844	−	0.994383i
$113$	−1.73042	+	1.73042i	−0.162784	+	0.162784i	−0.783799	−	0.621015i	$-0.786721\pi$
$113$	−1.73042	+	1.73042i	−0.162784	+	0.162784i	0.621015	+	0.783799i	$0.286721\pi$
$114$	20.8538	−	18.2550i	1.95313	−	1.70974i
$115$	−5.20514	−	0.479005i	−0.485382	−	0.0446675i
$116$	6.76590	+	0.903175i	0.628198	+	0.0838577i
$117$	4.17760	+	15.5910i	0.386220	+	1.44139i
$118$	0.478696	+	0.972912i	0.0440675	+	0.0895638i
$119$	−11.1198	−	1.14303i	−1.01935	−	0.104781i
$120$	−11.9675	+	11.2922i	−1.09248	+	1.03083i
$121$	4.59381	−	7.95671i	0.417619	−	0.723337i
$122$	1.07862	−	1.61112i	0.0976536	−	0.145864i
$123$	−24.0793	−	6.45202i	−2.17115	−	0.581759i
$124$	−12.2546	+	5.05014i	−1.10050	+	0.453516i
$125$	5.45893	+	9.75705i	0.488262	+	0.872697i
$126$	12.8130	+	5.88536i	1.14147	+	0.524309i
$127$	−2.84934	+	2.84934i	−0.252838	+	0.252838i	−0.822133	−	0.569295i	$-0.807216\pi$
$127$	−2.84934	+	2.84934i	−0.252838	+	0.252838i	0.569295	+	0.822133i	$0.307216\pi$
$128$	5.06793	−	10.1151i	0.447946	−	0.894061i
$129$	−11.8915	+	6.86558i	−1.04699	+	0.604480i
$130$	−12.6503	+	4.84091i	−1.10951	+	0.424576i
$131$	−7.16245	+	12.4057i	−0.625786	+	1.08389i	0.362603	+	0.931944i	$0.381888\pi$
$131$	−7.16245	+	12.4057i	−0.625786	+	1.08389i	−0.988388	+	0.151949i	$0.951445\pi$
$132$	0.901776	+	6.94654i	0.0784895	+	0.604619i
$133$	7.09970	−	18.6226i	0.615622	−	1.61478i
$134$	−11.6147	−	3.95436i	−1.00336	−	0.341605i
$135$	−1.87083	−	4.05961i	−0.161016	−	0.349396i
$136$	−10.7035	−	5.31445i	−0.917815	−	0.455710i
$137$	−0.766688	+	2.86132i	−0.0655026	+	0.244459i	−0.990912	−	0.134509i	$-0.957054\pi$
$137$	−0.766688	+	2.86132i	−0.0655026	+	0.244459i	0.925410	+	0.378968i	$0.123721\pi$
$138$	−0.570261	+	8.58181i	−0.0485438	+	0.730532i
$139$		−	22.6664i		−	1.92254i	−0.275607	−	0.961270i	$-0.588879\pi$
$139$		−	22.6664i		−	1.92254i	0.275607	−	0.961270i	$-0.411121\pi$
$140$	−3.79946	+	11.2055i	−0.321113	+	0.947041i
$141$			10.0319i			0.844839i
$142$	−2.07742	−	0.138045i	−0.174334	−	0.0115845i
$143$	−1.49244	+	5.56987i	−0.124804	+	0.465776i
$144$	10.6200	+	10.6970i	0.885003	+	0.891416i
$145$	−7.15954	−	2.64241i	−0.594567	−	0.219440i
$146$	−0.431734	+	1.26809i	−0.0357306	+	0.104948i
$147$	18.1818	−	1.03629i	1.49961	−	0.0854719i
$148$	2.38710	+	18.3882i	0.196218	+	1.51150i
$149$	−2.33400	+	4.04261i	−0.191209	+	0.331183i	−0.945651	−	0.325183i	$-0.894574\pi$
$149$	−2.33400	+	4.04261i	−0.191209	+	0.331183i	0.754442	+	0.656366i	$0.227907\pi$
$150$	15.8208	−	9.38722i	1.29177	−	0.766463i
$151$	1.59837	−	0.922821i	0.130074	−	0.0750981i	−0.433551	−	0.901129i	$-0.642740\pi$
$151$	1.59837	−	0.922821i	0.130074	−	0.0750981i	0.563625	+	0.826031i	$0.309406\pi$
$152$	14.0914	−	15.9807i	1.14296	−	1.29620i
$153$	11.2582	−	11.2582i	0.910175	−	0.910175i
$154$	2.91289	+	4.10956i	0.234727	+	0.331158i
$155$	14.6052	−	2.50757i	1.17312	−	0.201413i
$156$	8.49163	+	20.6057i	0.679874	+	1.64978i
$157$	3.10033	+	0.830732i	0.247434	+	0.0662996i	0.380404	−	0.924820i	$-0.375785\pi$
$157$	3.10033	+	0.830732i	0.247434	+	0.0662996i	−0.132971	+	0.991120i	$0.542452\pi$
$158$	−3.54899	−	2.37599i	−0.282342	−	0.189024i
$159$	0.121019	−	0.209611i	0.00959744	−	0.0166232i
$160$	−8.00597	+	9.79308i	−0.632927	+	0.774211i
$161$	2.52851	+	5.64435i	0.199275	+	0.444837i
$162$	7.74615	−	3.81129i	0.608595	−	0.299443i
$163$	3.29766	+	12.3070i	0.258293	+	0.963961i	0.966229	+	0.257685i	$0.0829596\pi$
$163$	3.29766	+	12.3070i	0.258293	+	0.963961i	−0.707936	+	0.706276i	$0.750374\pi$
$164$	−18.9956	−	2.53570i	−1.48330	−	0.198005i
$165$	0.717678	−	7.79868i	0.0558711	−	0.607127i
$166$	−9.39258	−	10.7297i	−0.729006	−	0.832787i
$167$	10.3330	−	10.3330i	0.799593	−	0.799593i	−0.183438	−	0.983031i	$-0.558723\pi$
$167$	10.3330	−	10.3330i	0.799593	−	0.799593i	0.983031	+	0.183438i	$0.0587227\pi$
$168$	18.5905	+	5.78108i	1.43429	+	0.446020i
$169$			5.34648i			0.411267i
$170$	10.3745	+	8.41898i	0.795688	+	0.645707i
$171$	14.1933	+	24.5835i	1.08539	+	1.87995i
$172$	−8.38613	+	6.41089i	−0.639437	+	0.488826i
$173$	−3.53568	+	0.947383i	−0.268813	+	0.0720282i	−0.390708	−	0.920515i	$-0.627770\pi$
$173$	−3.53568	+	0.947383i	−0.268813	+	0.0720282i	0.121895	+	0.992543i	$0.461103\pi$
$174$	−4.04707	+	11.8870i	−0.306807	+	0.901152i
$175$	6.88929	−	11.2933i	0.520781	−	0.853690i
$176$	1.37495	+	5.20650i	0.103641	+	0.392455i
$177$	−1.92673	+	0.516266i	−0.144822	+	0.0388049i
$178$	3.53606	−	5.28176i	0.265039	−	0.395885i
$179$	0.0344229	−	0.0198741i	0.00257289	−	0.00148546i	−0.498713	−	0.866767i	$-0.666194\pi$
$179$	0.0344229	−	0.0198741i	0.00257289	−	0.00148546i	0.501286	+	0.865282i	$0.332860\pi$
$180$	−8.96515	−	14.2702i	−0.668223	−	1.06364i
$181$		−	22.4617i		−	1.66957i	−0.550577	−	0.834784i	$-0.685592\pi$
$181$		−	22.4617i		−	1.66957i	0.550577	−	0.834784i	$-0.314408\pi$
$182$	12.3361	+	10.2309i	0.914410	+	0.758367i
$183$	2.52206	+	2.52206i	0.186436	+	0.186436i
$184$	0.414570	+	6.59885i	0.0305625	+	0.486473i
$185$	1.89977	−	20.6439i	0.139674	−	1.51777i
$186$	−4.73532	−	23.9189i	−0.347210	−	1.75382i
$187$	5.49414	−	1.47215i	0.401771	−	0.107654i
$188$	0.992824	+	7.64790i	0.0724092	+	0.557781i
$189$	−3.09895	+	4.28592i	−0.225416	+	0.311755i
$190$	−19.2861	+	13.9815i	−1.39916	+	1.01433i
$191$	−20.3885	−	11.7713i	−1.47526	−	0.851743i	−0.475651	−	0.879634i	$-0.657788\pi$
$191$	−20.3885	−	11.7713i	−1.47526	−	0.851743i	−0.999611	+	0.0278906i	$0.991121\pi$
$192$	16.4431	+	12.7593i	1.18668	+	0.920824i
$193$	−4.43408	−	1.18811i	−0.319172	−	0.0855218i	0.0956763	−	0.995413i	$-0.469499\pi$
$193$	−4.43408	−	1.18811i	−0.319172	−	0.0855218i	−0.414848	+	0.909891i	$0.636165\pi$
$194$	−16.4590	+	14.4079i	−1.18169	+	1.03443i
$195$	−4.21639	−	24.5581i	−0.301942	−	1.75864i
$196$	13.7584	−	2.58941i	0.982746	−	0.184958i
$197$	−15.8550	+	15.8550i	−1.12962	+	1.12962i	−0.139386	+	0.990238i	$0.544513\pi$
$197$	−15.8550	+	15.8550i	−1.12962	+	1.12962i	−0.990238	+	0.139386i	$0.955487\pi$
$198$	−7.15876	−	0.475700i	−0.508751	−	0.0338065i
$199$	1.70369	+	2.95087i	0.120771	+	0.209182i	0.920072	−	0.391749i	$-0.128130\pi$
$199$	1.70369	+	2.95087i	0.120771	+	0.209182i	−0.799301	+	0.600931i	$0.794797\pi$
$200$	11.1321	−	8.72215i	0.787160	−	0.616749i
$201$	11.2855	−	19.5471i	0.796020	−	1.37875i
$202$	−7.72224	−	15.6948i	−0.543335	−	1.10429i
$203$	1.43297	+	8.91541i	0.100575	+	0.625739i
$204$	13.4144	−	17.4168i	0.939193	−	1.21942i
$205$	20.1007	+	7.41868i	1.40390	+	0.518143i
$206$	−1.53764	−	7.76685i	−0.107132	−	0.541142i
$207$	−8.50897	−	2.27997i	−0.591414	−	0.158469i
$208$	8.51293	+	14.8685i	0.590266	+	1.03095i
$209$			10.1411i			0.701472i
$210$	−18.8640	−	10.8598i	−1.30174	−	0.749397i
$211$	1.03347			0.0711473			0.0355736	−	0.999367i	$-0.488674\pi$
$211$	1.03347			0.0711473			0.0355736	+	0.999367i	$0.488674\pi$
$212$	0.0715153	−	0.171775i	0.00491169	−	0.0117976i
$213$	0.991301	−	3.69958i	0.0679228	−	0.253491i
$214$	0.682136	+	3.44558i	0.0466299	+	0.235535i
$215$	10.7184	−	4.93948i	0.730991	−	0.336870i
$216$	−4.70969	+	3.12850i	−0.320454	+	0.212868i
$217$	−11.0656	−	13.6012i	−0.751184	−	0.923309i
$218$	2.94621	−	1.44961i	0.199543	−	0.0981798i
$219$	−2.13414	−	1.23214i	−0.144212	−	0.0832606i
$220$	−0.224682	−	6.01641i	−0.0151481	−	0.405626i
$221$	15.6725	−	9.04851i	1.05425	−	0.608669i
$222$	−34.0361	−	2.26169i	−2.28435	−	0.151795i
$223$	−11.4185	−	11.4185i	−0.764637	−	0.764637i	0.212519	−	0.977157i	$-0.431833\pi$
$223$	−11.4185	−	11.4185i	−0.764637	−	0.764637i	−0.977157	+	0.212519i	$0.931833\pi$
$224$	14.7448	+	2.56741i	0.985177	+	0.171542i
$225$	6.28468	+	17.7629i	0.418979	+	1.18419i
$226$	−2.27954	−	2.60406i	−0.151633	−	0.173219i
$227$	1.50910	−	5.63203i	0.100162	−	0.373811i	−0.897589	−	0.440833i	$-0.854683\pi$
$227$	1.50910	−	5.63203i	0.100162	−	0.373811i	0.997752	+	0.0670219i	$0.0213497\pi$
$228$	23.8042	+	31.1385i	1.57647	+	2.06220i
$229$	4.74804	−	8.22385i	0.313759	−	0.543447i	−0.665414	−	0.746475i	$-0.731745\pi$
$229$	4.74804	−	8.22385i	0.313759	−	0.543447i	0.979173	+	0.203028i	$0.0650781\pi$
$230$	1.16400	−	7.30006i	0.0767518	−	0.481352i
$231$	−8.45674	+	3.78839i	−0.556413	+	0.249258i
$232$	−1.90889	+	9.46268i	−0.125325	+	0.621255i
$233$	−0.122812	−	0.458341i	−0.00804569	−	0.0300269i	0.961786	−	0.273801i	$-0.0882810\pi$
$233$	−0.122812	−	0.458341i	−0.00804569	−	0.0300269i	−0.969832	+	0.243774i	$0.921614\pi$
$234$	−22.3922	+	4.43309i	−1.46383	+	0.289800i
$235$	0.790139	−	8.58608i	0.0515430	−	0.560094i
$236$	−1.41776	+	0.584261i	−0.0922886	+	0.0380321i
$237$	5.55562	−	5.55562i	0.360876	−	0.360876i
$238$	2.65561	−	15.5840i	0.172138	−	1.01016i
$239$	15.5439			1.00545			0.502724	−	0.864447i	$-0.332331\pi$
$239$	15.5439			1.00545			0.502724	+	0.864447i	$0.332331\pi$
$240$	−14.8123	−	17.9462i	−0.956129	−	1.15842i
$241$	10.3350	+	17.9007i	0.665735	+	1.15309i	0.979085	+	0.203450i	$0.0652154\pi$
$241$	10.3350	+	17.9007i	0.665735	+	1.15309i	−0.313350	+	0.949638i	$0.601451\pi$
$242$	10.7970	+	7.22841i	0.694056	+	0.464660i
$243$	5.66257	+	21.1330i	0.363254	+	1.35568i
$244$	2.17231	+	1.67311i	0.139068	+	0.107110i
$245$	−15.6430	−	0.545103i	−0.999393	−	0.0348254i
$246$	11.3623	−	33.3733i	0.724435	−	2.12780i
$247$	8.35086	+	31.1658i	0.531352	+	1.98303i
$248$	−5.97718	−	17.7661i	−0.379551	−	1.12815i
$249$	22.7184	−	13.1165i	1.43972	−	0.831222i
$250$	−14.2801	+	6.78822i	−0.903150	+	0.429324i
$251$	−18.3023			−1.15523			−0.577615	−	0.816310i	$-0.696016\pi$
$251$	−18.3023			−1.15523			−0.577615	+	0.816310i	$0.696016\pi$
$252$	−9.50628	+	17.5285i	−0.598839	+	1.10419i
$253$	−2.22530	−	2.22530i	−0.139903	−	0.139903i
$254$	−3.75354	−	4.28789i	−0.235518	−	0.269046i
$255$	−18.8993	+	15.7140i	−1.18352	+	0.984046i
$256$	13.7983	+	8.09984i	0.862393	+	0.506240i
$257$	−13.6246	+	3.65071i	−0.849882	+	0.227725i	−0.657369	−	0.753569i	$-0.728331\pi$
$257$	−13.6246	+	3.65071i	−0.849882	+	0.227725i	−0.192513	+	0.981294i	$0.561664\pi$
$258$	−8.57299	−	17.4239i	−0.533731	−	1.08477i
$259$	−22.3859	+	10.0283i	−1.39099	+	0.623125i
$260$	−5.64483	−	18.3048i	−0.350077	−	1.13522i
$261$	−11.1382	−	6.43066i	−0.689439	−	0.398048i
$262$	−16.8341	−	11.2702i	−1.04002	−	0.696275i
$263$	−3.65103	+	13.6258i	−0.225132	+	0.840205i	0.757219	+	0.653161i	$0.226557\pi$
$263$	−3.65103	+	13.6258i	−0.225132	+	0.840205i	−0.982351	+	0.187044i	$0.940109\pi$
$264$	−9.88683	+	0.621137i	−0.608492	+	0.0382283i
$265$	−0.120087	+	0.169870i	−0.00737688	+	0.0104350i
$266$	25.6126	+	11.7646i	1.57041	+	0.721333i
$267$	8.26812	+	8.26812i	0.506001	+	0.506001i
$268$	6.66910	−	16.0188i	0.407380	−	0.978502i
$269$	−10.4789	−	18.1500i	−0.638911	−	1.10663i	−0.985672	−	0.168673i	$-0.946052\pi$
$269$	−10.4789	−	18.1500i	−0.638911	−	1.10663i	0.346761	−	0.937953i	$-0.387281\pi$
$270$	5.90395	−	2.25927i	0.359303	−	0.137495i
$271$	19.6758	+	11.3598i	1.19522	+	0.690061i	0.959486	−	0.281756i	$-0.0909170\pi$
$271$	19.6758	+	11.3598i	1.19522	+	0.690061i	0.235735	+	0.971817i	$0.424250\pi$
$272$	8.50286	−	14.6054i	0.515562	−	0.885580i
$273$	−22.8699	+	18.6064i	−1.38415	+	1.12611i
$274$	−3.96572	−	1.35017i	−0.239578	−	0.0815670i
$275$	−1.22849	+	6.61819i	−0.0740806	+	0.399092i
$276$	−12.0563	−	1.60939i	−0.725706	−	0.0968740i
$277$	−7.75495	−	2.07793i	−0.465950	−	0.124851i	0.0182029	−	0.999834i	$-0.494206\pi$
$277$	−7.75495	−	2.07793i	−0.465950	−	0.124851i	−0.484153	+	0.874983i	$0.660872\pi$
$278$	31.9846	+	2.12538i	1.91831	+	0.127472i
$279$	24.9739			1.49515
$280$	−15.4559	−	6.41214i	−0.923666	−	0.383198i
$281$	−16.3703			−0.976567			−0.488284	−	0.872685i	$-0.662377\pi$
$281$	−16.3703			−0.976567			−0.488284	+	0.872685i	$0.662377\pi$
$282$	−14.1560	−	0.940668i	−0.842980	−	0.0560160i
$283$	19.1402	+	5.12860i	1.13777	+	0.304864i	0.778053	−	0.628199i	$-0.216207\pi$
$283$	19.1402	+	5.12860i	1.13777	+	0.304864i	0.359714	+	0.933062i	$0.382874\pi$
$284$	0.389590	−	2.91851i	0.0231179	−	0.173182i
$285$	−18.3408	−	39.7986i	−1.08641	−	2.35746i
$286$	−7.71971	−	2.62826i	−0.456476	−	0.155412i
$287$	−4.02314	−	25.0304i	−0.237478	−	1.47750i
$288$	−16.0904	+	13.9829i	−0.948134	+	0.823951i
$289$	−0.736955	−	0.425481i	−0.0433503	−	0.0250283i
$290$	4.40004	−	9.85507i	0.258379	−	0.578709i
$291$	−20.1202	−	34.8492i	−1.17947	−	2.04289i
$292$	−1.74892	−	0.728126i	−0.102348	−	0.0426104i
$293$	3.70370	+	3.70370i	0.216373	+	0.216373i	0.806968	−	0.590595i	$-0.201107\pi$
$293$	3.70370	+	3.70370i	0.216373	+	0.216373i	−0.590595	+	0.806968i	$0.701107\pi$
$294$	−0.242547	+	25.7535i	−0.0141457	+	1.50197i
$295$	1.68971	−	0.290106i	0.0983785	−	0.0168906i
$296$	−26.1715	+	1.64421i	−1.52119	+	0.0955680i
$297$	0.696529	−	2.59948i	0.0404167	−	0.150837i
$298$	−5.48567	−	3.67258i	−0.317777	−	0.212747i
$299$	−8.67132	−	5.00639i	−0.501476	−	0.289527i
$300$	11.7628	+	23.2050i	0.679128	+	1.33974i
$301$	−11.3160	−	8.18204i	−0.652241	−	0.471605i
$302$	1.15232	+	2.34200i	0.0663085	+	0.134767i
$303$	31.0817	−	8.32831i	1.78559	−	0.478449i
$304$	21.2290	+	21.3829i	1.21757	+	1.22639i
$305$	−1.95993	−	2.35722i	−0.112225	−	0.134974i
$306$	14.8309	+	16.9422i	0.847824	+	0.968520i
$307$	15.4323	+	15.4323i	0.880766	+	0.880766i	0.993612	−	0.112847i	$-0.0359969\pi$
$307$	15.4323	+	15.4323i	0.880766	+	0.880766i	−0.112847	+	0.993612i	$0.535997\pi$
$308$	−6.07214	+	3.72504i	−0.345992	+	0.212254i
$309$	14.5653			0.828593
$310$	2.16894	+	20.8446i	0.123188	+	1.18389i
$311$	−13.2913	+	7.67374i	−0.753681	+	0.435138i	−0.827022	−	0.562169i	$-0.809967\pi$
$311$	−13.2913	+	7.67374i	−0.753681	+	0.435138i	0.0733416	+	0.997307i	$0.476634\pi$
$312$	−29.8730	+	10.0504i	−1.69123	+	0.568992i
$313$	−1.54249	−	5.75664i	−0.0871866	−	0.325385i	0.908533	−	0.417814i	$-0.137204\pi$
$313$	−1.54249	−	5.75664i	−0.0871866	−	0.325385i	−0.995719	+	0.0924290i	$0.970537\pi$
$314$	−1.46296	+	4.29699i	−0.0825595	+	0.242493i
$315$	14.6634	−	16.7931i	0.826189	−	0.946184i
$316$	3.68555	−	4.78519i	0.207328	−	0.269188i
$317$	0.917983	+	3.42596i	0.0515591	+	0.192421i	0.986902	−	0.161321i	$-0.0515756\pi$
$317$	0.917983	+	3.42596i	0.0515591	+	0.192421i	−0.935343	+	0.353743i	$0.884909\pi$
$318$	0.284435	+	0.190425i	0.0159503	+	0.0106785i
$319$	−2.29734	−	3.97912i	−0.128627	−	0.222788i
$320$	−13.0683	−	12.2155i	−0.730542	−	0.682868i
$321$	−6.46157			−0.360650
$322$	−8.20184	+	3.03873i	−0.457071	+	0.169342i
$323$	22.5048	−	22.5048i	1.25220	−	1.25220i
$324$	4.65178	+	11.2880i	0.258432	+	0.627110i
$325$	1.67445	+	21.3508i	0.0928818	+	1.18433i
$326$	−17.6757	+	3.49933i	−0.978965	+	0.193810i
$327$	1.56338	+	5.83460i	0.0864550	+	0.322654i
$328$	5.35930	−	26.5669i	0.295918	−	1.46691i
$329$	−9.31058	+	4.17088i	−0.513309	+	0.229948i
$330$	10.9374	+	1.74398i	0.602086	+	0.0960030i
$331$	1.78672	−	3.09470i	0.0982072	−	0.170100i	−0.812735	−	0.582633i	$-0.802023\pi$
$331$	1.78672	−	3.09470i	0.0982072	−	0.170100i	0.910943	+	0.412533i	$0.135356\pi$
$332$	16.0214	−	12.2478i	0.879290	−	0.672185i
$333$	9.04252	−	33.7471i	0.495527	−	1.84933i
$334$	13.6120	+	15.5498i	0.744818	+	0.850850i
$335$	−11.1986	+	15.8410i	−0.611845	+	0.865489i
$336$	−9.90089	+	25.6911i	−0.540138	+	1.40156i
$337$	−13.4979	−	13.4979i	−0.735276	−	0.735276i	0.236384	−	0.971660i	$-0.424038\pi$
$337$	−13.4979	−	13.4979i	−0.735276	−	0.735276i	−0.971660	+	0.236384i	$0.924038\pi$
$338$	−7.54442	−	0.501326i	−0.410362	−	0.0272686i
$339$	5.51366	−	3.18331i	0.299461	−	0.172894i
$340$	−12.8528	+	13.8501i	−0.697043	+	0.751124i
$341$	7.72658	+	4.46094i	0.418418	+	0.241574i
$342$	−36.0207	+	17.7230i	−1.94778	+	0.958352i
$343$	8.52106	+	16.4436i	0.460094	+	0.887870i
$344$	−8.26007	−	12.4348i	−0.445353	−	0.670441i
$345$	12.7578	+	4.70858i	0.686856	+	0.253502i
$346$	−1.00532	−	5.07804i	−0.0540464	−	0.272997i
$347$	4.91159	−	18.3303i	0.263668	−	0.984022i	−0.699393	−	0.714738i	$-0.746546\pi$
$347$	4.91159	−	18.3303i	0.263668	−	0.984022i	0.963061	−	0.269285i	$-0.0867872\pi$
$348$	−16.3943	−	6.82544i	−0.878827	−	0.365882i
$349$	−34.4127			−1.84207			−0.921035	−	0.389480i	$-0.872655\pi$
$349$	−34.4127			−1.84207			−0.921035	+	0.389480i	$0.872655\pi$
$350$	15.2899	+	10.7804i	0.817282	+	0.576238i
$351$		−	8.56237i		−	0.457026i
$352$	−7.47583	+	1.45199i	−0.398463	+	0.0773916i
$353$	−5.69832	−	1.52686i	−0.303291	−	0.0812666i	0.103964	−	0.994581i	$-0.466847\pi$
$353$	−5.69832	−	1.52686i	−0.303291	−	0.0812666i	−0.407255	+	0.913314i	$0.633514\pi$
$354$	−0.547838	−	2.76722i	−0.0291173	−	0.147076i
$355$	−1.13982	+	3.08831i	−0.0604954	+	0.163911i
$356$	7.12153	+	5.48500i	0.377440	+	0.290704i
$357$	27.1740	+	10.3599i	1.43820	+	0.548303i
$358$	0.0248166	+	0.0504378i	0.00131160	+	0.00266572i
$359$	−7.06599	+	12.2387i	−0.372929	+	0.645931i	−0.990015	−	0.140964i	$-0.954980\pi$
$359$	−7.06599	+	12.2387i	−0.372929	+	0.645931i	0.617086	+	0.786896i	$0.288313\pi$
$360$	20.9774	−	11.3126i	1.10561	−	0.596229i
$361$	18.8718	+	32.6869i	0.993252	+	1.72036i
$362$	31.6958	+	2.10618i	1.66589	+	0.110699i
$363$	−16.9017	+	16.9017i	−0.887109	+	0.887109i
$364$	−15.5936	+	16.4481i	−0.817327	+	0.862116i
$365$	1.72951	+	1.22265i	0.0905268	+	0.0639966i
$366$	−3.79537	+	3.32240i	−0.198387	+	0.173664i
$367$	−17.0934	−	4.58016i	−0.892269	−	0.239083i	−0.216576	−	0.976266i	$-0.569489\pi$
$367$	−17.0934	−	4.58016i	−0.892269	−	0.239083i	−0.675693	+	0.737183i	$0.736155\pi$
$368$	−9.35052	−	0.0337575i	−0.487429	−	0.00175973i
$369$	31.2711	+	18.0544i	1.62791	+	0.939872i
$370$	28.9525	+	4.61650i	1.50517	+	0.240000i
$371$	0.244854	+	0.0251691i	0.0127122	+	0.00130672i
$372$	34.1960	−	4.43920i	1.77298	−	0.230162i
$373$	−20.1671	+	5.40375i	−1.04421	+	0.279795i	−0.739857	−	0.672764i	$-0.765107\pi$
$373$	−20.1671	+	5.40375i	−1.04421	+	0.279795i	−0.304353	+	0.952559i	$0.598440\pi$
$374$	1.56218	+	7.89083i	0.0807785	+	0.408025i
$375$	−7.14823	−	28.1949i	−0.369133	−	1.45598i
$376$	−10.8851	+	0.683850i	−0.561354	+	0.0352669i
$377$	−10.3369	−	10.3369i	−0.532380	−	0.532380i
$378$	−5.75729	−	4.77482i	−0.296123	−	0.245590i
$379$			8.01780i			0.411847i	0.978568	+	0.205923i	$0.0660198\pi$
$379$			8.01780i			0.411847i	−0.978568	+	0.205923i	$0.933980\pi$
$380$	−17.9210	−	28.5256i	−0.919326	−	1.46333i
$381$	9.07889	−	5.24170i	0.465126	−	0.268540i
$382$	18.5223	−	27.6665i	0.947684	−	1.41554i
$383$	30.6150	−	8.20325i	1.56435	−	0.419167i	0.630313	−	0.776341i	$-0.282926\pi$
$383$	30.6150	−	8.20325i	1.56435	−	0.419167i	0.934038	+	0.357174i	$0.116260\pi$
$384$	−19.5465	+	22.0065i	−0.997479	+	1.12301i
$385$	7.53632	−	2.57632i	0.384086	−	0.131301i
$386$	2.09231	−	6.14553i	0.106496	−	0.312799i
$387$	19.2116	−	5.14773i	0.976579	−	0.261674i
$388$	−18.7877	−	24.5763i	−0.953799	−	1.24767i
$389$	10.4742	+	18.1418i	0.531063	+	0.919828i	0.999343	+	0.0362475i	$0.0115405\pi$
$389$	10.4742	+	18.1418i	0.531063	+	0.919828i	−0.468280	+	0.883580i	$0.655126\pi$
$390$	35.0494	−	3.64699i	1.77479	−	0.184673i
$391$			9.87664i			0.499483i
$392$	2.36383	+	19.6574i	0.119391	+	0.992847i
$393$	26.3523	−	26.3523i	1.32930	−	1.32930i
$394$	−20.8864	−	23.8597i	−1.05224	−	1.20204i
$395$	−5.19250	+	4.31735i	−0.261263	+	0.217230i
$396$	1.34252	−	10.0571i	0.0674642	−	0.505390i
$397$	−1.00605	−	3.75465i	−0.0504924	−	0.188440i	0.936073	−	0.351805i	$-0.114432\pi$
$397$	−1.00605	−	3.75465i	−0.0504924	−	0.188440i	−0.986566	+	0.163365i	$0.947765\pi$
$398$	−4.32373	+	2.12738i	−0.216729	+	0.106636i
$399$	−30.3807	+	42.0172i	−1.52094	+	2.10349i
$400$	11.2640	+	16.5264i	0.563200	+	0.826320i
$401$	10.7819	−	18.6747i	0.538421	−	0.932572i	−0.460568	−	0.887624i	$-0.652354\pi$
$401$	10.7819	−	18.6747i	0.538421	−	0.932572i	0.998989	−	0.0449481i	$-0.0143122\pi$
$402$	26.5247	+	17.7579i	1.32293	+	0.885684i
$403$	27.4190	+	7.34690i	1.36584	+	0.365975i
$404$	22.8711	−	9.42519i	1.13788	−	0.468921i
$405$	−2.30977	−	13.4531i	−0.114773	−	0.668492i
$406$	−12.7149	+	1.18609i	−0.631030	+	0.0588649i
$407$	8.82569	−	8.82569i	0.437473	−	0.437473i
$408$	23.3190	+	20.5622i	1.15446	+	1.01798i
$409$	30.1987	−	17.4352i	1.49323	−	0.862116i	0.493258	−	0.869883i	$-0.335806\pi$
$409$	30.1987	−	17.4352i	1.49323	−	0.862116i	0.999970	+	0.00776728i	$0.00247243\pi$
$410$	−12.3533	+	27.6685i	−0.610087	+	1.36645i
$411$	3.85332	−	6.67415i	0.190070	−	0.329211i
$412$	11.1040	−	1.44148i	0.547054	−	0.0710167i
$413$	−1.28020	−	1.57355i	−0.0629947	−	0.0774292i
$414$	4.01514	−	11.7932i	0.197333	−	0.579606i
$415$	−20.4772	+	9.43672i	−1.00519	+	0.463230i
$416$	−21.7793	+	10.6184i	−1.06782	+	0.520611i
$417$	−15.2624	+	56.9599i	−0.747401	+	2.78934i
$418$	−14.3101	−	0.950904i	−0.699929	−	0.0465102i
$419$			1.80053i			0.0879618i	0.999032	+	0.0439809i	$0.0140041\pi$
$419$			1.80053i			0.0879618i	−0.999032	+	0.0439809i	$0.985996\pi$
$420$	17.0931	−	25.6008i	0.834058	−	1.24919i
$421$		−	7.84933i		−	0.382553i	−0.981536	−	0.191276i	$-0.938737\pi$
$421$		−	7.84933i		−	0.382553i	0.981536	−	0.191276i	$-0.0612627\pi$
$422$	−0.0969064	+	1.45834i	−0.00471733	+	0.0709907i
$423$	3.76090	−	14.0359i	0.182861	−	0.682448i
$424$	0.235687	+	0.117022i	0.0114460	+	0.00568311i
$425$	17.4131	−	11.9607i	0.844660	−	0.580177i
$426$	5.12754	+	1.74573i	0.248430	+	0.0845808i
$427$	−1.29214	+	3.38929i	−0.0625310	+	0.164019i
$428$	−4.92603	+	0.639480i	−0.238109	+	0.0309104i
$429$	7.50091	−	12.9920i	0.362147	−	0.627258i
$430$	5.96507	+	15.5880i	0.287661	+	0.751719i
$431$	25.2094	−	14.5547i	1.21430	−	0.701074i	0.250603	−	0.968090i	$-0.419371\pi$
$431$	25.2094	−	14.5547i	1.21430	−	0.701074i	0.963692	+	0.267016i	$0.0860377\pi$
$432$	−3.97302	−	6.93921i	−0.191152	−	0.333863i
$433$	10.4043	−	10.4043i	0.500000	−	0.500000i	−0.411438	−	0.911438i	$-0.634973\pi$
$433$	10.4043	−	10.4043i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$434$	20.2303	−	14.3394i	0.971083	−	0.688312i
$435$	16.2124	+	11.4611i	0.777325	+	0.549519i
$436$	1.76928	+	4.29333i	0.0847333	+	0.205613i
$437$	−17.0091	−	4.55757i	−0.813654	−	0.218018i
$438$	1.93879	−	2.89595i	0.0926391	−	0.138374i
$439$	−5.42804	+	9.40164i	−0.259066	+	0.448716i	−0.965992	−	0.258572i	$-0.916748\pi$
$439$	−5.42804	+	9.40164i	−0.259066	+	0.448716i	0.706926	+	0.707288i	$0.250081\pi$
$440$	8.51084	+	0.247095i	0.405738	+	0.0117798i
$441$	−25.8270	−	5.36633i	−1.22986	−	0.255540i
$442$	11.2988	+	22.9639i	0.537429	+	1.09228i
$443$	−4.17521	−	15.5821i	−0.198370	−	0.740327i	−0.991369	−	0.131104i	$-0.958148\pi$
$443$	−4.17521	−	15.5821i	−0.198370	−	0.740327i	0.792998	−	0.609224i	$-0.208519\pi$
$444$	6.38296	−	47.8163i	0.302922	−	2.26926i
$445$	−6.42528	−	7.72771i	−0.304587	−	0.366329i
$446$	17.1833	−	15.0419i	0.813653	−	0.712256i
$447$	8.58733	−	8.58733i	0.406167	−	0.406167i
$448$	−5.00546	+	20.5656i	−0.236486	+	0.971635i
$449$			35.3355i			1.66759i	0.552077	+	0.833793i	$0.313835\pi$
$449$			35.3355i			1.66759i	−0.552077	+	0.833793i	$0.686165\pi$
$450$	−25.6545	+	7.20274i	−1.20937	+	0.339540i
$451$	6.44989	+	11.1715i	0.303714	+	0.526047i
$452$	3.88834	−	2.97249i	0.182892	−	0.139814i
$453$	−4.63803	+	1.24276i	−0.217914	+	0.0583898i
$454$	7.80587	+	2.65759i	0.366348	+	0.124727i
$455$	21.0393	−	14.1235i	0.986338	−	0.662122i
$456$	−46.1717	+	30.6704i	−2.16219	+	1.43627i
$457$	−30.9202	+	8.28503i	−1.44638	+	0.387557i	−0.894764	−	0.446538i	$-0.852657\pi$
$457$	−30.9202	+	8.28503i	−1.44638	+	0.387557i	−0.551620	+	0.834096i	$0.685990\pi$
$458$	11.1595	+	7.47110i	0.521448	+	0.349102i
$459$	−7.31441	+	4.22298i	−0.341407	+	0.197112i
$460$	10.1920	+	2.32703i	0.475204	+	0.108498i
$461$			32.7954i			1.52743i	0.645551	+	0.763717i	$0.276628\pi$
$461$			32.7954i			1.52743i	−0.645551	+	0.763717i	$0.723372\pi$
$462$	−4.55283	−	12.2886i	−0.211817	−	0.571715i
$463$	−10.5490	−	10.5490i	−0.490253	−	0.490253i	0.418133	−	0.908386i	$-0.362685\pi$
$463$	−10.5490	−	10.5490i	−0.490253	−	0.490253i	−0.908386	+	0.418133i	$0.862685\pi$
$464$	−13.1738	−	3.58094i	−0.611579	−	0.166241i
$465$	−38.3908	−	3.53294i	−1.78033	−	0.163836i
$466$	0.658282	−	0.130323i	0.0304943	−	0.00603709i
$467$	−37.6580	+	10.0904i	−1.74261	+	0.466930i	−0.983023	−	0.183482i	$-0.941263\pi$
$467$	−37.6580	+	10.0904i	−1.74261	+	0.466930i	−0.759582	+	0.650412i	$0.774596\pi$
$468$	−4.15587	−	32.0134i	−0.192105	−	1.47982i
$469$	22.8337	+	2.34712i	1.05436	+	0.108380i
$470$	12.0417	+	1.92006i	0.555444	+	0.0885659i
$471$	−7.23165	−	4.17520i	−0.333217	−	0.192383i
$472$	−0.691511	−	2.05539i	−0.0318294	−	0.0946072i
$473$	6.86331	+	1.83902i	0.315575	+	0.0845582i
$474$	7.31860	+	8.36048i	0.336155	+	0.384010i
$475$	12.5628	+	35.5073i	0.576421	+	1.62918i
$476$	21.7416	+	5.20861i	0.996525	+	0.238736i
$477$	−0.247903	+	0.247903i	−0.0113507	+	0.0113507i
$478$	−1.45751	+	21.9340i	−0.0666650	+	1.00324i
$479$	−6.67440	−	11.5604i	−0.304961	−	0.528208i	0.672291	−	0.740287i	$-0.265310\pi$
$479$	−6.67440	−	11.5604i	−0.304961	−	0.528208i	−0.977253	+	0.212078i	$0.931977\pi$
$480$	26.7128	−	19.2189i	1.21927	−	0.877217i
$481$	19.8557	−	34.3911i	0.905342	−	1.56810i
$482$	−26.2288	+	12.9052i	−1.19469	+	0.587817i
$483$	−2.55346	−	15.8866i	−0.116186	−	0.722866i
$484$	−11.2124	+	14.5578i	−0.509656	+	0.661720i
$485$	14.4756	+	31.4113i	0.657303	+	1.42631i
$486$	−30.3518	+	6.00887i	−1.37678	+	0.272568i
$487$	−2.24272	−	0.600935i	−0.101627	−	0.0272310i	0.207647	−	0.978204i	$-0.433419\pi$
$487$	−2.24272	−	0.600935i	−0.101627	−	0.0272310i	−0.309274	+	0.950973i	$0.600086\pi$
$488$	−2.56462	+	2.90847i	−0.116095	+	0.131660i
$489$		−	33.1476i		−	1.49899i
$490$	2.23600	−	22.0227i	0.101012	−	0.994885i
$491$	−33.1377			−1.49548			−0.747742	−	0.663990i	$-0.768862\pi$
$491$	−33.1377			−1.49548			−0.747742	+	0.663990i	$0.768862\pi$
$492$	46.0277	+	19.1627i	2.07509	+	0.863922i
$493$	−3.73214	+	13.9285i	−0.168087	+	0.627309i
$494$	−44.7612	+	8.86156i	−2.01390	+	0.398700i
$495$	−3.92780	+	10.6423i	−0.176541	+	0.478334i
$496$	25.6302	−	6.76852i	1.15083	−	0.303915i
$497$	3.84572	−	0.618122i	0.172504	−	0.0277266i
$498$	16.3784	+	33.2878i	0.733934	+	1.49166i
$499$	−29.8457	−	17.2314i	−1.33608	−	0.771384i	−0.349852	−	0.936805i	$-0.613768\pi$
$499$	−29.8457	−	17.2314i	−1.33608	−	0.771384i	−0.986223	+	0.165421i	$0.947102\pi$
$500$	−8.23985	−	20.7871i	−0.368497	−	0.929629i
$501$	−32.9242	+	19.0088i	−1.47094	+	0.849250i
$502$	1.71616	−	25.8264i	0.0765960	−	1.15269i
$503$	−14.2936	−	14.2936i	−0.637319	−	0.637319i	0.312574	−	0.949893i	$-0.398809\pi$
$503$	−14.2936	−	14.2936i	−0.637319	−	0.637319i	−0.949893	+	0.312574i	$0.898809\pi$
$504$	−23.8432	−	15.0579i	−1.06206	−	0.670734i
$505$	−27.2580	+	4.67994i	−1.21297	+	0.208254i
$506$	3.34879	−	2.93146i	0.148872	−	0.130319i
$507$	3.60003	−	13.4355i	0.159883	−	0.596691i
$508$	6.40261	−	4.89456i	0.284070	−	0.217161i
$509$	−11.9053	+	20.6206i	−0.527692	+	0.913990i	0.471787	+	0.881713i	$0.343609\pi$
$509$	−11.9053	+	20.6206i	−0.527692	+	0.913990i	−0.999479	+	0.0322771i	$0.989724\pi$
$510$	−20.4019	−	28.1422i	−0.903409	−	1.24616i
$511$	0.256257	−	2.49296i	0.0113361	−	0.110282i
$512$	−12.7235	+	18.7113i	−0.562306	+	0.826929i
$513$	−3.89738	−	14.5452i	−0.172073	−	0.642187i
$514$	−3.87398	−	19.5681i	−0.170874	−	0.863111i
$515$	−12.4661	−	1.14720i	−0.549324	−	0.0505518i
$516$	25.3908	−	10.4636i	1.11777	−	0.460632i
$517$	3.67072	−	3.67072i	0.161438	−	0.161438i
$518$	−12.0518	−	32.5291i	−0.529526	−	1.42925i
$519$	9.52295			0.418011
$520$	26.3592	−	6.24903i	1.15593	−	0.274038i
$521$	6.41794	+	11.1162i	0.281175	+	0.487010i	0.971674	−	0.236323i	$-0.0759425\pi$
$521$	6.41794	+	11.1162i	0.281175	+	0.487010i	−0.690499	+	0.723333i	$0.742609\pi$
$522$	10.1187	−	15.1142i	0.442884	−	0.661530i
$523$	6.84585	+	25.5491i	0.299348	+	1.11718i	0.937702	+	0.347439i	$0.112949\pi$
$523$	6.84585	+	25.5491i	0.299348	+	1.11718i	−0.638354	+	0.769743i	$0.720385\pi$
$524$	17.4819	−	22.6979i	0.763700	−	0.991562i
$525$	−24.9168	+	23.7407i	−1.08746	+	1.03613i
$526$	−18.8851	−	6.42964i	−0.823429	−	0.280346i
$527$	−7.24700	−	27.0462i	−0.315684	−	1.17815i
$528$	0.0505778	−	14.0096i	0.00220112	−	0.609688i
$529$	−15.1861	+	8.76771i	−0.660266	+	0.381205i
$530$	−0.228443	−	0.185383i	−0.00992293	−	0.00805253i
$531$	2.88928			0.125384
$532$	−19.0027	+	35.0388i	−0.823870	+	1.51913i
$533$	29.0214	+	29.0214i	1.25706	+	1.25706i
$534$	−12.4424	+	10.8919i	−0.538437	+	0.471337i
$535$	5.53031	+	0.508930i	0.239096	+	0.0220030i
$536$	21.9788	+	10.9128i	0.949338	+	0.471362i
$537$	−0.0998857	+	0.0267643i	−0.00431039	+	0.00115496i
$538$	26.5941	−	13.0849i	1.14655	−	0.564131i
$539$	−7.03198	−	6.27361i	−0.302889	−	0.270223i
$540$	2.63446	+	8.54292i	0.113369	+	0.367629i
$541$	16.8313	+	9.71758i	0.723636	+	0.417791i	0.816089	−	0.577926i	$-0.196138\pi$
$541$	16.8313	+	9.71758i	0.723636	+	0.417791i	−0.0924536	+	0.995717i	$0.529471\pi$
$542$	−17.8748	+	26.6994i	−0.767790	+	1.14684i
$543$	−15.1245	+	56.4455i	−0.649056	+	2.42231i
$544$	19.8124	+	13.3679i	0.849448	+	0.573145i
$545$	−0.878511	−	5.11684i	−0.0376313	−	0.219181i
$546$	−24.1111	−	34.0164i	−1.03186	−	1.45577i
$547$	−5.98689	−	5.98689i	−0.255981	−	0.255981i	0.567436	−	0.823417i	$-0.307935\pi$
$547$	−5.98689	−	5.98689i	−0.255981	−	0.255981i	−0.823417	+	0.567436i	$0.807935\pi$
$548$	2.27709	−	5.46944i	0.0972725	−	0.233643i
$549$	−2.58317	−	4.47418i	−0.110247	−	0.190953i
$550$	−9.22375	−	2.35409i	−0.393302	−	0.100379i
$551$	−22.2648	−	12.8546i	−0.948514	−	0.547625i
$552$	3.40151	−	16.8618i	0.144778	−	0.717686i
$553$	7.46596	+	2.84634i	0.317485	+	0.121039i
$554$	3.65934	−	10.7482i	0.155470	−	0.456647i
$555$	−18.6746	+	50.5982i	−0.792691	+	2.14778i
$556$	−5.99824	+	44.9343i	−0.254382	+	1.90564i
$557$	38.2627	+	10.2524i	1.62124	+	0.434410i	0.951366	−	0.308064i	$-0.0996809\pi$
$557$	38.2627	+	10.2524i	1.62124	+	0.434410i	0.669875	+	0.742474i	$0.266348\pi$
$558$	−2.34174	+	35.2407i	−0.0991338	+	1.49186i
$559$	22.6069			0.956170
$560$	10.4974	−	21.2086i	0.443598	−	0.896226i
$561$	−14.7978			−0.624765
$562$	1.53500	−	23.1001i	0.0647501	−	0.974419i
$563$	−36.4705	−	9.77225i	−1.53705	−	0.411851i	−0.611739	−	0.791060i	$-0.709530\pi$
$563$	−36.4705	−	9.77225i	−1.53705	−	0.411851i	−0.925311	+	0.379209i	$0.876196\pi$
$564$	2.65476	−	19.8874i	0.111785	−	0.837411i
$565$	−4.96974	+	2.29025i	−0.209079	+	0.0963517i
$566$	−9.03171	+	26.5279i	−0.379631	+	1.11505i
$567$	−12.5283	+	10.1928i	−0.526139	+	0.428056i
$568$	4.08179	+	0.823413i	0.171268	+	0.0345497i
$569$	−5.44853	−	3.14571i	−0.228414	−	0.131875i	0.381426	−	0.924399i	$-0.375433\pi$
$569$	−5.44853	−	3.14571i	−0.228414	−	0.131875i	−0.609840	+	0.792524i	$0.708766\pi$
$570$	57.8796	−	22.1489i	2.42431	−	0.927714i
$571$	−17.2833	−	29.9355i	−0.723283	−	1.25276i	−0.959677	−	0.281105i	$-0.909299\pi$
$571$	−17.2833	−	29.9355i	−0.723283	−	1.25276i	0.236394	−	0.971657i	$-0.424034\pi$
$572$	4.43260	−	10.6469i	0.185337	−	0.445167i
$573$	43.3095	+	43.3095i	1.80928	+	1.80928i
$574$	35.6977	−	3.33001i	1.48999	−	0.138992i
$575$	−10.5482	−	5.03481i	−0.439892	−	0.209966i
$576$	−18.2226	−	24.0163i	−0.759273	−	1.00068i
$577$	3.52591	−	13.1589i	0.146785	−	0.547811i	−0.852884	−	0.522100i	$-0.825149\pi$
$577$	3.52591	−	13.1589i	0.146785	−	0.547811i	0.999669	−	0.0257102i	$-0.00818471\pi$
$578$	0.669500	−	1.00002i	0.0278475	−	0.0415954i
$579$	10.3427	+	5.97134i	0.429826	+	0.248160i
$580$	13.4939	+	7.13299i	0.560304	+	0.296181i
$581$	21.6188	+	15.6315i	0.896897	+	0.648505i
$582$	51.0623	−	25.1239i	2.11660	−	1.04142i
$583$	−0.120979	+	0.0324163i	−0.00501044	+	0.00134254i
$584$	1.19145	−	2.39962i	0.0493026	−	0.0992971i
$585$	−3.30745	+	35.9405i	−0.136746	+	1.48596i
$586$	−5.57359	+	4.87901i	−0.230243	+	0.201550i
$587$	15.9880	+	15.9880i	0.659893	+	0.659893i	0.955355	−	0.295461i	$-0.0954733\pi$
$587$	15.9880	+	15.9880i	0.659893	+	0.659893i	−0.295461	+	0.955355i	$0.595473\pi$
$588$	−36.3180	−	2.75710i	−1.49773	−	0.113701i
$589$	49.9218			2.05699
$590$	0.250929	+	2.41155i	0.0103306	+	0.0992819i
$591$	50.5190	−	29.1672i	2.07808	−	1.19978i
$592$	0.133885	−	37.0848i	0.00550263	−	1.52418i
$593$	−7.54158	−	28.1455i	−0.309695	−	1.15580i	−0.928828	−	0.370512i	$-0.879182\pi$
$593$	−7.54158	−	28.1455i	−0.309695	−	1.15580i	0.619132	−	0.785287i	$-0.287484\pi$
$594$	3.60282	+	1.22662i	0.147826	+	0.0503289i
$595$	−22.4417	−	11.0071i	−0.920018	−	0.451246i
$596$	5.69676	−	7.39647i	0.233348	−	0.302971i
$597$	−2.29434	−	8.56260i	−0.0939012	−	0.350444i
$598$	7.87762	−	11.7667i	0.322140	−	0.481175i
$599$	−19.2801	−	33.3941i	−0.787763	−	1.36445i	−0.927335	−	0.374233i	$-0.877906\pi$
$599$	−19.2801	−	33.3941i	−0.787763	−	1.36445i	0.139572	−	0.990212i	$-0.455427\pi$
$600$	−33.8476	+	14.4227i	−1.38182	+	0.588803i
$601$	−14.9274			−0.608900			−0.304450	−	0.952528i	$-0.598473\pi$
$601$	−14.9274			−0.608900			−0.304450	+	0.952528i	$0.598473\pi$
$602$	12.6068	−	15.2008i	0.513813	−	0.619537i
$603$	−23.1179	+	23.1179i	−0.941435	+	0.941435i
$604$	−3.41285	+	1.40643i	−0.138867	+	0.0572270i
$605$	15.7970	−	13.1346i	0.642239	−	0.533995i
$606$	8.83763	+	44.6403i	0.359004	+	1.81339i
$607$	−2.44316	−	9.11801i	−0.0991650	−	0.370089i	0.898453	−	0.439070i	$-0.144692\pi$
$607$	−2.44316	−	9.11801i	−0.0991650	−	0.370089i	−0.997618	+	0.0689810i	$0.978025\pi$
$608$	−32.1640	+	27.9513i	−1.30442	+	1.13357i
$609$	2.40215	−	23.3690i	0.0973399	−	0.946959i
$610$	3.51005	−	2.54463i	0.142118	−	0.103029i
$611$	8.25824	−	14.3037i	0.334093	−	0.578666i
$612$	−25.2978	+	19.3392i	−1.02260	+	0.781742i
$613$	−6.66205	+	24.8631i	−0.269078	+	1.00421i	0.690629	+	0.723209i	$0.257334\pi$
$613$	−6.66205	+	24.8631i	−0.269078	+	1.00421i	−0.959707	+	0.281003i	$0.909333\pi$
$614$	−23.2235	+	20.3294i	−0.937226	+	0.820430i
$615$	−45.5170	−	32.1776i	−1.83542	−	1.29753i
$616$	−4.68704	−	8.91769i	−0.188846	−	0.359304i
$617$	24.6497	+	24.6497i	0.992359	+	0.992359i	0.999971	−	0.00761213i	$-0.00242304\pi$
$617$	24.6497	+	24.6497i	0.992359	+	0.992359i	−0.00761213	+	0.999971i	$0.502423\pi$
$618$	−1.36576	+	20.5532i	−0.0549388	+	0.826769i
$619$	0.587745	−	0.339335i	0.0236235	−	0.0136390i	−0.488142	−	0.872764i	$-0.662325\pi$
$619$	0.587745	−	0.339335i	0.0236235	−	0.0136390i	0.511765	+	0.859125i	$0.328992\pi$
$620$	−29.6172	+	1.10605i	−1.18946	+	0.0444201i
$621$	4.04694	+	2.33650i	0.162398	+	0.0937606i
$622$	−9.58213	−	19.4749i	−0.384208	−	0.780873i
$623$	−4.23605	+	11.1112i	−0.169714	+	0.445160i
$624$	−11.3810	−	43.0963i	−0.455605	−	1.72523i
$625$	3.89730	+	24.6944i	0.155892	+	0.987774i
$626$	8.26784	−	1.63682i	0.330450	−	0.0654205i
$627$	6.82845	−	25.4841i	0.272702	−	1.01774i
$628$	−5.92631	−	2.46730i	−0.236486	−	0.0984560i
$629$	−39.1714			−1.56187
$630$	22.3218	+	22.2662i	0.889323	+	0.887107i
$631$		−	22.1330i		−	0.881099i	−0.897728	−	0.440550i	$-0.854784\pi$
$631$		−	22.1330i		−	0.881099i	0.897728	−	0.440550i	$-0.145216\pi$
$632$	6.40680	+	5.64938i	0.254849	+	0.224720i
$633$	−2.59708	−	0.695886i	−0.103225	−	0.0276590i
$634$	−4.92046	+	0.974124i	−0.195416	+	0.0386874i
$635$	−8.18326	+	3.77117i	−0.324743	+	0.149654i
$636$	−0.295380	+	0.383511i	−0.0117126	+	0.0152072i
$637$	−26.7770	−	13.4896i	−1.06094	−	0.534478i
$638$	5.83035	−	2.86867i	0.230826	−	0.113572i
$639$	−2.77390	+	4.80454i	−0.109734	+	0.190065i
$640$	18.4627	−	17.2953i	0.729803	−	0.683658i
$641$	9.20163	+	15.9377i	0.363443	+	0.629501i	0.988525	−	0.151058i	$-0.0482680\pi$
$641$	9.20163	+	15.9377i	0.363443	+	0.629501i	−0.625082	+	0.780559i	$0.714935\pi$
$642$	0.605886	−	9.11793i	0.0239124	−	0.359856i
$643$	10.4574	−	10.4574i	0.412399	−	0.412399i	−0.470174	−	0.882574i	$-0.655809\pi$
$643$	10.4574	−	10.4574i	0.412399	−	0.412399i	0.882574	+	0.470174i	$0.155809\pi$
$644$	−3.51889	−	11.8586i	−0.138664	−	0.467293i
$645$	−30.2610	+	5.19552i	−1.19153	+	0.204573i
$646$	29.6463	+	33.8667i	1.16642	+	1.33247i
$647$	19.0942	+	5.11628i	0.750671	+	0.201142i	0.613816	−	0.789449i	$-0.289634\pi$
$647$	19.0942	+	5.11628i	0.750671	+	0.201142i	0.136855	+	0.990591i	$0.456300\pi$
$648$	−16.3647	+	5.50569i	−0.642865	+	0.216284i
$649$	0.893903	+	0.516095i	0.0350888	+	0.0202585i
$650$	−30.2852	+	0.360802i	−1.18788	+	0.0141518i
$651$	18.6492	+	41.6303i	0.730920	+	1.63162i
$652$	−3.28050	−	25.2703i	−0.128474	−	0.989662i
$653$	−28.1197	+	7.53465i	−1.10041	+	0.294854i	−0.762931	−	0.646480i	$-0.776240\pi$
$653$	−28.1197	+	7.53465i	−1.10041	+	0.294854i	−0.337478	+	0.941333i	$0.609574\pi$
$654$	−8.37981	+	1.65899i	−0.327677	+	0.0648715i
$655$	−24.6299	+	20.4788i	−0.962370	+	0.800172i
$656$	36.9860	+	10.0536i	1.44406	+	0.392528i
$657$	2.52400	+	2.52400i	0.0984705	+	0.0984705i
$658$	−5.01251	−	13.5293i	−0.195408	−	0.527426i
$659$		−	31.0817i		−	1.21077i	−0.795932	−	0.605386i	$-0.793019\pi$
$659$		−	31.0817i		−	1.21077i	0.795932	−	0.605386i	$-0.206981\pi$
$660$	−3.48651	+	15.2703i	−0.135712	+	0.594396i
$661$	40.0158	−	23.1031i	1.55643	−	0.898608i	0.558841	−	0.829275i	$-0.311246\pi$
$661$	40.0158	−	23.1031i	1.55643	−	0.898608i	0.997594	−	0.0693333i	$-0.0220872\pi$
$662$	4.19939	+	2.81143i	0.163214	+	0.109269i
$663$	−45.4772	+	12.1856i	−1.76619	+	0.473248i
$664$	15.7806	+	23.7563i	0.612405	+	0.921924i
$665$	29.3115	−	33.5687i	1.13665	−	1.30174i
$666$	46.7728	+	15.9243i	1.81241	+	0.617054i
$667$	7.70642	−	2.06493i	0.298394	−	0.0799544i
$668$	−23.2188	+	17.7499i	−0.898361	+	0.686764i
$669$	21.0056	+	36.3828i	0.812124	+	1.40664i
$670$	−21.3033	−	17.2877i	−0.823017	−	0.667884i
$671$		−	1.84567i		−	0.0712512i
$672$	−35.3243	−	16.3801i	−1.36267	−	0.631878i
$673$	−13.8111	+	13.8111i	−0.532380	+	0.532380i	−0.921280	−	0.388900i	$-0.872855\pi$
$673$	−13.8111	+	13.8111i	−0.532380	+	0.532380i	0.388900	+	0.921280i	$0.372855\pi$
$674$	20.3125	−	17.7812i	0.782409	−	0.684906i
$675$	−0.781472	−	9.96452i	−0.0300789	−	0.383535i
$676$	1.41485	−	10.5989i	0.0544171	−	0.407651i
$677$	−1.51526	−	5.65504i	−0.0582363	−	0.217341i	0.930675	−	0.365846i	$-0.119220\pi$
$677$	−1.51526	−	5.65504i	−0.0582363	−	0.217341i	−0.988912	+	0.148505i	$0.952554\pi$
$678$	3.97497	+	8.07882i	0.152658	+	0.310265i
$679$	23.9782	−	33.1624i	0.920199	−	1.27266i
$680$	−18.3386	−	19.4353i	−0.703255	−	0.745311i
$681$	−7.58462	+	13.1369i	−0.290643	+	0.503409i
$682$	−7.01935	+	10.4847i	−0.268785	+	0.401480i
$683$	6.61451	+	1.77235i	0.253097	+	0.0678172i	0.383137	−	0.923692i	$-0.374844\pi$
$683$	6.61451	+	1.77235i	0.253097	+	0.0678172i	−0.130040	+	0.991509i	$0.541510\pi$
$684$	−21.6314	−	52.4907i	−0.827098	−	2.00703i
$685$	−3.82364	+	5.40875i	−0.146094	+	0.206658i
$686$	−24.0026	+	10.4822i	−0.916422	+	0.400212i
$687$	−17.4692	+	17.4692i	−0.666490	+	0.666490i
$688$	18.3213	−	10.4898i	0.698494	−	0.399920i
$689$	−0.345103	+	0.199245i	−0.0131474	+	0.00759064i
$690$	−7.84056	+	17.5610i	−0.298485	+	0.668536i
$691$	0.880585	−	1.52522i	0.0334990	−	0.0580220i	−0.848790	−	0.528730i	$-0.822668\pi$
$691$	0.880585	−	1.52522i	0.0334990	−	0.0580220i	0.882289	+	0.470708i	$0.156002\pi$
$692$	7.25989	−	0.942454i	0.275980	−	0.0358267i
$693$	13.2523	−	2.13004i	0.503412	−	0.0809135i
$694$	25.4054	+	8.64954i	0.964375	+	0.328332i
$695$	17.5490	−	47.5486i	0.665672	−	1.80362i
$696$	11.1686	−	22.4940i	0.423346	−	0.852633i
$697$	10.4781	−	39.1050i	0.396888	−	1.48121i
$698$	3.22680	−	48.5598i	0.122136	−	1.83802i
$699$			1.23449i			0.0466927i
$700$	−16.6460	+	20.5648i	−0.629159	+	0.777277i
$701$		−	33.6955i		−	1.27266i	−0.771416	−	0.636331i	$-0.780451\pi$
$701$		−	33.6955i		−	1.27266i	0.771416	−	0.636331i	$-0.219549\pi$
$702$	12.0824	+	0.802874i	0.456020	+	0.0303025i
$703$	18.0756	−	67.4591i	0.681735	−	2.54427i
$704$	−1.34792	−	10.6853i	−0.0508017	−	0.402718i
$705$	−7.76700	+	21.0445i	−0.292522	+	0.792581i
$706$	2.68887	−	7.89774i	0.101197	−	0.297235i
$707$	20.6520	+	25.3842i	0.776700	+	0.954671i
$708$	3.95620	−	0.513580i	0.148683	−	0.0193015i
$709$	17.6080	−	30.4979i	0.661281	−	1.14537i	−0.318998	−	0.947755i	$-0.603346\pi$
$709$	17.6080	−	30.4979i	0.661281	−	1.14537i	0.980279	−	0.197617i	$-0.0633202\pi$
$710$	−4.25104	−	1.89799i	−0.159539	−	0.0712301i
$711$	−9.85576	+	5.69023i	−0.369620	+	0.213400i
$712$	−8.40765	+	9.53489i	−0.315090	+	0.357335i
$713$	−10.9546	+	10.9546i	−0.410252	+	0.410252i
$714$	−17.1669	+	37.3739i	−0.642454	+	1.39868i
$715$	−7.44314	+	10.5287i	−0.278358	+	0.393752i
$716$	−0.0734999	+	0.0302893i	−0.00274682	+	0.00113196i
$717$	−39.0612	−	10.4664i	−1.45877	−	0.390875i
$718$	−16.6074	−	11.1184i	−0.619784	−	0.414936i
$719$	−1.99792	+	3.46050i	−0.0745098	+	0.129055i	−0.900873	−	0.434083i	$-0.857073\pi$
$719$	−1.99792	+	3.46050i	−0.0745098	+	0.129055i	0.826363	+	0.563138i	$0.190406\pi$
$720$	13.9963	+	30.6620i	0.521611	+	1.14271i
$721$	6.05571	+	13.5180i	0.225526	+	0.503438i
$722$	−47.8941	+	23.5650i	−1.78243	+	0.877000i
$723$	−13.9181	−	51.9429i	−0.517618	−	1.93178i
$724$	−5.94408	+	44.5285i	−0.220910	+	1.65489i
$725$	−12.9731	−	11.0862i	−0.481809	−	0.411733i
$726$	−22.2652	−	25.4348i	−0.826338	−	0.943975i
$727$	−21.1551	+	21.1551i	−0.784598	+	0.784598i	−0.980603	−	0.196005i	$-0.937203\pi$
$727$	−21.1551	+	21.1551i	−0.784598	+	0.784598i	0.196005	+	0.980603i	$0.437203\pi$
$728$	−21.7478	−	23.5465i	−0.806027	−	0.872690i
$729$		−	38.6059i		−	1.42985i
$730$	−1.88746	+	2.32587i	−0.0698581	+	0.0860843i
$731$	−11.1498	−	19.3120i	−0.412389	−	0.714278i
$732$	−4.33236	−	5.66719i	−0.160128	−	0.209465i
$733$	−20.4556	+	5.48107i	−0.755546	+	0.202448i	−0.615977	−	0.787764i	$-0.711238\pi$
$733$	−20.4556	+	5.48107i	−0.755546	+	0.202448i	−0.139569	+	0.990212i	$0.544572\pi$
$734$	8.06588	−	23.6911i	0.297717	−	0.874453i
$735$	38.9432	+	11.9030i	1.43644	+	0.439048i
$736$	0.924411	−	13.1914i	0.0340742	−	0.486240i
$737$	−11.2818	+	3.02295i	−0.415571	+	0.111352i
$738$	−28.4087	+	42.4337i	−1.04574	+	1.56201i
$739$	0.950273	−	0.548641i	0.0349564	−	0.0201821i	−0.482420	−	0.875940i	$-0.660242\pi$
$739$	0.950273	−	0.548641i	0.0349564	−	0.0201821i	0.517376	+	0.855758i	$0.326909\pi$
$740$	−9.22916	+	40.4221i	−0.339271	+	1.48595i
$741$		−	83.9416i		−	3.08367i
$742$	−0.0584756	+	0.343154i	−0.00214671	+	0.0125976i
$743$	5.20049	+	5.20049i	0.190787	+	0.190787i	0.796036	−	0.605249i	$-0.206926\pi$
$743$	5.20049	+	5.20049i	0.190787	+	0.190787i	−0.605249	+	0.796036i	$0.706926\pi$
$744$	3.05769	+	48.6702i	0.112100	+	1.78434i
$745$	−8.02606	+	6.67334i	−0.294052	+	0.244492i
$746$	−5.73422	−	28.9645i	−0.209945	−	1.06046i
$747$	−36.7031	+	9.83456i	−1.34290	+	0.359828i
$748$	−11.2812	+	1.46449i	−0.412483	+	0.0535471i
$749$	−2.68647	−	5.99696i	−0.0981616	−	0.219124i
$750$	40.4561	−	7.44311i	1.47725	−	0.271784i
$751$	23.6913	+	13.6782i	0.864510	+	0.499125i	0.865520	−	0.500875i	$-0.166988\pi$
$751$	23.6913	+	13.6782i	0.864510	+	0.499125i	−0.00101023	+	0.999999i	$0.500322\pi$
$752$	0.0556844	−	15.4241i	0.00203060	−	0.562457i
$753$	45.9929	+	12.3238i	1.67608	+	0.449103i
$754$	15.5557	−	13.6172i	0.566507	−	0.495909i
$755$	4.06747	−	0.698344i	0.148030	−	0.0254153i
$756$	7.27760	−	7.67640i	0.264684	−	0.279188i
$757$	−24.8295	+	24.8295i	−0.902444	+	0.902444i	−0.995647	−	0.0932031i	$-0.970289\pi$
$757$	−24.8295	+	24.8295i	−0.902444	+	0.902444i	0.0932031	+	0.995647i	$0.470289\pi$
$758$	−11.3139	−	0.751810i	−0.410941	−	0.0273070i
$759$	4.09370	+	7.09050i	0.148592	+	0.257369i
$760$	41.9330	−	22.6135i	1.52107	−	0.820278i
$761$	3.21147	−	5.56244i	0.116416	−	0.201638i	−0.801929	−	0.597419i	$-0.796193\pi$
$761$	3.21147	−	5.56244i	0.116416	−	0.201638i	0.918345	+	0.395781i	$0.129526\pi$
$762$	6.54526	+	13.3027i	0.237110	+	0.481907i
$763$	−4.76508	+	3.87677i	−0.172508	+	0.140348i
$764$	37.3035	+	28.7311i	1.34959	+	1.03945i
$765$	32.3335	−	14.9005i	1.16902	−	0.538730i
$766$	8.70493	+	43.9700i	0.314522	+	1.58870i
$767$	3.17216	+	0.849977i	0.114540	+	0.0306909i
$768$	−29.2206	−	29.6456i	−1.05441	−	1.06974i
$769$			34.2490i			1.23505i	0.786551	+	0.617525i	$0.211865\pi$
$769$			34.2490i			1.23505i	−0.786551	+	0.617525i	$0.788135\pi$
$770$	2.92879	+	10.8761i	0.105546	+	0.391947i
$771$	36.6964			1.32159
$772$	8.47577	+	3.52872i	0.305050	+	0.127001i
$773$	−3.70596	+	13.8308i	−0.133294	+	0.497461i	−0.999999	−	0.00136055i	$-0.999567\pi$
$773$	−3.70596	+	13.8308i	−0.133294	+	0.497461i	0.866705	+	0.498821i	$0.166234\pi$
$774$	5.46254	+	27.5922i	0.196347	+	0.991780i
$775$	32.5796	+	6.04752i	1.17029	+	0.217233i
$776$	36.4413	−	24.2068i	1.30817	−	0.868975i
$777$	63.0074	−	10.1272i	2.26038	−	0.363311i
$778$	−26.5821	+	13.0790i	−0.953015	+	0.468906i
$779$	62.5095	+	36.0899i	2.23964	+	1.29305i
$780$	1.85978	+	49.8002i	0.0665909	+	1.78313i
$781$	−1.71642	+	0.990973i	−0.0614182	+	0.0354598i
$782$	−13.9369	−	0.926109i	−0.498384	−	0.0331176i
$783$	4.82429	+	4.82429i	0.172406	+	0.172406i
$784$	−27.9602	+	1.49238i	−0.998579	+	0.0532992i
$785$	5.86056	+	4.14304i	0.209172	+	0.147871i
$786$	34.7148	+	39.6568i	1.23824	+	1.41451i
$787$	3.12306	−	11.6554i	0.111325	−	0.415471i	−0.887661	−	0.460498i	$-0.847671\pi$
$787$	3.12306	−	11.6554i	0.111325	−	0.415471i	0.998986	+	0.0450274i	$0.0143375\pi$
$788$	35.6270	−	27.2355i	1.26916	−	0.970225i
$789$	18.3498	−	31.7828i	0.653271	−	1.13150i
$790$	−5.60533	−	7.73197i	−0.199429	−	0.275091i
$791$	5.24679	+	3.79371i	0.186554	+	0.134889i
$792$	14.0658	+	2.83747i	0.499805	+	0.100825i
$793$	−1.51985	−	5.67216i	−0.0539715	−	0.201424i
$794$	5.39252	−	1.06758i	0.191373	−	0.0378870i
$795$	0.416155	−	0.346016i	0.0147595	−	0.0122719i
$796$	−2.59652	−	6.30070i	−0.0920312	−	0.223322i
$797$	−0.417606	+	0.417606i	−0.0147924	+	0.0147924i	−0.714464	−	0.699672i	$-0.753330\pi$
$797$	−0.417606	+	0.417606i	−0.0147924	+	0.0147924i	0.699672	+	0.714464i	$0.253330\pi$
$798$	−56.4419	−	46.8101i	−1.99802	−	1.65706i
$799$	−16.2919			−0.576367
$800$	−24.3766	+	14.3450i	−0.861844	+	0.507173i
$801$	−8.46845	−	14.6678i	−0.299218	−	0.518261i
$802$	25.3410	+	16.9654i	0.894821	+	0.599069i
$803$	0.330043	+	1.23174i	0.0116470	+	0.0434671i
$804$	−27.5454	+	35.7640i	−0.971451	+	1.26130i
$805$	0.934175	+	13.7981i	0.0329253	+	0.486319i
$806$	−12.9382	+	38.0021i	−0.455730	+	1.33857i
$807$	14.1119	+	52.6663i	0.496762	+	1.85394i
$808$	11.1553	+	33.1572i	0.392443	+	1.16647i
$809$	14.7536	−	8.51800i	0.518709	−	0.299477i	−0.217697	−	0.976016i	$-0.569855\pi$
$809$	14.7536	−	8.51800i	0.518709	−	0.299477i	0.736406	+	0.676540i	$0.236521\pi$
$810$	19.2003	−	1.99785i	0.674631	−	0.0701974i
$811$	4.67738			0.164245			0.0821226	−	0.996622i	$-0.473830\pi$
$811$	4.67738			0.164245			0.0821226	+	0.996622i	$0.473830\pi$
$812$	−0.481454	−	18.0532i	−0.0168957	−	0.633545i
$813$	−41.7955	−	41.7955i	−1.46583	−	1.46583i
$814$	11.6264	+	13.2815i	0.407505	+	0.465517i
$815$	−2.61079	+	28.3703i	−0.0914519	+	0.993767i
$816$	−31.2019	+	30.9774i	−1.09228	+	1.08442i
$817$	38.4032	−	10.2901i	1.34356	−	0.360005i
$818$	21.7712	+	44.2482i	0.761212	+	1.54710i
$819$	38.9732	−	17.4589i	1.36184	−	0.610064i
$820$	−37.8848	−	20.0262i	−1.32299	−	0.699345i
$821$	−42.5947	−	24.5921i	−1.48657	−	0.858269i	−0.486682	−	0.873579i	$-0.661793\pi$
$821$	−42.5947	−	24.5921i	−1.48657	−	0.858269i	−0.999883	+	0.0153104i	$0.995126\pi$
$822$	9.05658	+	6.06324i	0.315885	+	0.211480i
$823$	−6.20131	+	23.1436i	−0.216164	+	0.806736i	0.769589	+	0.638539i	$0.220461\pi$
$823$	−6.20131	+	23.1436i	−0.216164	+	0.806736i	−0.985753	+	0.168197i	$0.946206\pi$
$824$	0.992882	+	15.8040i	0.0345887	+	0.550559i
$825$	7.54348	−	15.8041i	0.262630	−	0.550227i
$826$	2.34048	−	1.65895i	0.0814356	−	0.0577223i
$827$	−12.4249	−	12.4249i	−0.432056	−	0.432056i	0.457271	−	0.889327i	$-0.348827\pi$
$827$	−12.4249	−	12.4249i	−0.432056	−	0.432056i	−0.889327	+	0.457271i	$0.848827\pi$
$828$	16.2650	+	6.77159i	0.565246	+	0.235329i
$829$	18.4502	+	31.9567i	0.640802	+	1.10990i	0.985254	+	0.171098i	$0.0547315\pi$
$829$	18.4502	+	31.9567i	0.640802	+	1.10990i	−0.344452	+	0.938804i	$0.611935\pi$
$830$	−11.3961	−	29.7803i	−0.395563	−	1.03369i
$831$	18.0887	+	10.4435i	0.627492	+	0.362282i
$832$	−12.9415	−	31.7284i	−0.448665	−	1.09998i
$833$	1.68295	+	29.5274i	0.0583107	+	1.02306i
$834$	−78.9451	−	26.8777i	−2.73364	−	0.930700i
$835$	29.6763	−	13.6760i	1.02699	−	0.473278i
$836$	2.68364	−	20.1038i	0.0928157	−	0.695305i
$837$	−12.7966	−	3.42883i	−0.442314	−	0.118518i
$838$	−2.54073	−	0.168832i	−0.0877682	−	0.00583219i
$839$	13.2988			0.459127			0.229563	−	0.973294i	$-0.426270\pi$
$839$	13.2988			0.459127			0.229563	+	0.973294i	$0.426270\pi$
$840$	34.5225	+	26.5206i	1.19114	+	0.915049i
$841$	−17.3517			−0.598336
$842$	11.0762	+	0.736013i	0.381711	+	0.0253647i
$843$	41.1378	+	11.0229i	1.41686	+	0.379647i
$844$	−2.04877	−	0.273490i	−0.0705217	−	0.00941390i
$845$	−4.13940	+	11.2156i	−0.142400	+	0.385828i
$846$	19.4534	+	6.62313i	0.668822	+	0.227708i
$847$	−22.7135	−	8.65933i	−0.780444	−	0.297538i
$848$	−0.187230	+	0.321605i	−0.00642951	+	0.0110440i
$849$	−44.6453	−	25.7760i	−1.53222	−	0.884630i
$850$	15.2449	+	25.6932i	0.522897	+	0.881269i
$851$	10.8365	+	18.7693i	0.371469	+	0.643403i
$852$	−2.94420	+	7.07178i	−0.100866	+	0.242275i
$853$	8.18730	+	8.18730i	0.280328	+	0.280328i	0.833240	−	0.552912i	$-0.186483\pi$
$853$	8.18730	+	8.18730i	0.280328	+	0.280328i	−0.552912	+	0.833240i	$0.686483\pi$
$854$	−4.66147	−	2.14115i	−0.159512	−	0.0732685i
$855$	10.7408	+	62.5590i	0.367326	+	2.13947i
$856$	−0.440469	−	7.01109i	−0.0150549	−	0.239634i
$857$	2.80662	−	10.4744i	0.0958722	−	0.357800i	−0.901278	−	0.433241i	$-0.857370\pi$
$857$	2.80662	−	10.4744i	0.0958722	−	0.357800i	0.997150	+	0.0754412i	$0.0240365\pi$
$858$	17.6296	+	11.8028i	0.601866	+	0.402940i
$859$	17.8737	+	10.3194i	0.609843	+	0.352093i	0.772904	−	0.634523i	$-0.218803\pi$
$859$	17.8737	+	10.3194i	0.609843	+	0.352093i	−0.163061	+	0.986616i	$0.552137\pi$
$860$	−22.5555	+	6.95567i	−0.769137	+	0.237187i
$861$	−6.74413	+	65.6094i	−0.229839	+	2.23596i
$862$	18.1743	+	36.9378i	0.619019	+	1.25811i
$863$	13.6046	−	3.64533i	0.463105	−	0.124089i	−0.0197198	−	0.999806i	$-0.506277\pi$
$863$	13.6046	−	3.64533i	0.463105	−	0.124089i	0.482825	+	0.875717i	$0.339611\pi$
$864$	10.1645	−	4.95566i	0.345802	−	0.168595i
$865$	−8.15048	−	0.750052i	−0.277124	−	0.0255025i
$866$	13.7060	+	15.6571i	0.465748	+	0.532051i
$867$	1.56544	+	1.56544i	0.0531653	+	0.0531653i
$868$	18.3374	+	29.8915i	0.622411	+	1.01458i
$869$	−4.06565			−0.137918
$870$	−17.6930	+	21.8027i	−0.599849	+	0.739179i
$871$	−32.1823	+	18.5804i	−1.09045	+	0.629574i
$872$	−6.22423	+	2.09406i	−0.210779	+	0.0709139i
$873$	15.0859	+	56.3012i	0.510579	+	1.90551i
$874$	8.02609	−	23.5742i	0.271487	−	0.797408i
$875$	23.1956	−	18.3566i	0.784154	−	0.620566i
$876$	3.90468	+	3.00738i	0.131927	+	0.101610i
$877$	−3.34102	−	12.4689i	−0.112818	−	0.421044i	0.886296	−	0.463119i	$-0.153270\pi$
$877$	−3.34102	−	12.4689i	−0.112818	−	0.421044i	−0.999114	+	0.0420751i	$0.986603\pi$
$878$	−12.7577	−	8.54109i	−0.430551	−	0.288248i
$879$	−6.81339	−	11.8011i	−0.229810	−	0.398043i
$880$	−1.14672	+	11.9865i	−0.0386558	+	0.404064i
$881$	−38.2543			−1.28882			−0.644410	−	0.764680i	$-0.722897\pi$
$881$	−38.2543			−1.28882			−0.644410	+	0.764680i	$0.722897\pi$
$882$	9.99418	−	35.9414i	0.336522	−	1.21021i
$883$	6.59194	−	6.59194i	0.221837	−	0.221837i	−0.587435	−	0.809271i	$-0.699862\pi$
$883$	6.59194	−	6.59194i	0.221837	−	0.221837i	0.809271	+	0.587435i	$0.199862\pi$
$884$	−33.4639	+	13.7905i	−1.12551	+	0.463824i
$885$	−4.44151	−	0.408732i	−0.149300	−	0.0137394i
$886$	22.3794	−	4.43055i	0.751851	−	0.148847i
$887$	−8.49782	−	31.7143i	−0.285329	−	1.06486i	−0.948599	−	0.316482i	$-0.897498\pi$
$887$	−8.49782	−	31.7143i	−0.285329	−	1.06486i	0.663270	−	0.748380i	$-0.269168\pi$
$888$	66.8751	+	13.4906i	2.24418	+	0.452716i
$889$	8.63945	+	6.24679i	0.289758	+	0.209511i
$890$	11.5071	−	8.34211i	0.385718	−	0.279628i
$891$	4.10906	−	7.11710i	0.137659	−	0.238432i
$892$	19.6145	+	25.6578i	0.656741	+	0.859088i
$893$	7.51789	−	28.0571i	0.251577	−	0.938897i
$894$	11.3124	+	12.9228i	0.378343	+	0.432203i
$895$	0.0875979	−	0.0150397i	0.00292808	−	0.000502722i
$896$	−28.5509	−	8.99160i	−0.953817	−	0.300388i
$897$	18.4197	+	18.4197i	0.615015	+	0.615015i
$898$	−49.8620	−	3.31333i	−1.66392	−	0.110567i
$899$	−19.5881	+	11.3092i	−0.653300	+	0.377183i
$900$	−7.75823	−	36.8765i	−0.258608	−	1.22922i
$901$	0.340410	+	0.196536i	0.0113407	+	0.00654757i
$902$	−16.3690	+	8.05392i	−0.545027	+	0.268166i
$903$	22.9272	+	28.1807i	0.762971	+	0.937796i
$904$	3.82989	+	5.76556i	0.127380	+	0.191760i
$905$	17.3905	−	47.1192i	0.578081	−	1.56630i
$906$	−1.31876	−	6.66126i	−0.0438128	−	0.221306i
$907$	−7.82991	+	29.2216i	−0.259988	+	0.970289i	0.705259	+	0.708950i	$0.250831\pi$
$907$	−7.82991	+	29.2216i	−0.259988	+	0.970289i	−0.965247	+	0.261339i	$0.915836\pi$
$908$	−4.48207	+	10.7657i	−0.148743	+	0.357271i
$909$	−46.6093			−1.54593
$910$	17.9569	+	31.0129i	0.595267	+	1.02807i
$911$		−	13.6579i		−	0.452506i	−0.974069	−	0.226253i	$-0.927352\pi$
$911$		−	13.6579i		−	0.452506i	0.974069	−	0.226253i	$-0.0726476\pi$
$912$	−38.9497	−	68.0288i	−1.28975	−	2.25266i
$913$	−13.1121	−	3.51338i	−0.433948	−	0.116276i
$914$	−8.79171	−	44.4084i	−0.290804	−	1.46890i
$915$	3.33801	+	7.24331i	0.110351	+	0.239457i
$916$	−11.5889	+	15.0466i	−0.382907	+	0.497154i
$917$	35.4138	+	13.5012i	1.16947	+	0.445849i
$918$	−5.27319	−	10.7174i	−0.174041	−	0.353725i
$919$	19.7817	−	34.2630i	0.652540	−	1.13023i	−0.329965	−	0.943993i	$-0.607037\pi$
$919$	19.7817	−	34.2630i	0.652540	−	1.13023i	0.982505	−	0.186238i	$-0.0596297\pi$
$920$	−4.23935	+	14.1637i	−0.139767	+	0.466964i
$921$	−28.3894	−	49.1720i	−0.935464	−	1.62027i
$922$	−46.2776	−	3.07515i	−1.52407	−	0.101275i
$923$	−4.45890	+	4.45890i	−0.146767	+	0.146767i
$924$	17.7673	−	5.27224i	0.584501	−	0.173444i
$925$	19.9684	−	41.8350i	0.656556	−	1.37553i
$926$	15.8748	−	13.8965i	0.521680	−	0.456668i
$927$	−20.3787	−	5.46046i	−0.669324	−	0.179345i
$928$	6.28834	−	18.2538i	0.206425	−	0.599210i
$929$	−0.204383	−	0.118001i	−0.00670560	−	0.00387148i	0.496643	−	0.867955i	$-0.334566\pi$
$929$	−0.204383	−	0.118001i	−0.00670560	−	0.00387148i	−0.503349	+	0.864083i	$0.667899\pi$
$930$	8.58515	−	53.8421i	0.281518	−	1.76555i
$931$	−51.6272	−	10.7271i	−1.69201	−	0.351566i
$932$	0.122173	+	0.941122i	0.00400192	+	0.0308275i
$933$	38.5676	−	10.3342i	1.26265	−	0.338325i
$934$	−10.7075	−	54.0854i	−0.350361	−	1.76973i
$935$	12.6651	+	1.16552i	0.414194	+	0.0381164i
$936$	45.5639	−	2.86253i	1.48930	−	0.0935648i
$937$	15.1895	+	15.1895i	0.496220	+	0.496220i	0.910259	−	0.414039i	$-0.135882\pi$
$937$	15.1895	+	15.1895i	0.496220	+	0.496220i	−0.414039	+	0.910259i	$0.635882\pi$
$938$	−5.45309	+	32.0006i	−0.178050	+	1.04486i
$939$			15.5049i			0.505982i
$940$	−3.83853	+	16.8121i	−0.125199	+	0.548350i
$941$	10.9201	−	6.30470i	0.355984	−	0.205527i	−0.311334	−	0.950301i	$-0.600776\pi$
$941$	10.9201	−	6.30470i	0.355984	−	0.205527i	0.667317	+	0.744773i	$0.267442\pi$
$942$	6.56972	−	9.81310i	0.214053	−	0.319728i
$943$	−21.6361	+	5.79738i	−0.704569	+	0.188789i
$944$	2.96521	−	0.783063i	0.0965094	−	0.0254865i
$945$	−9.81913	+	6.59151i	−0.319416	+	0.214422i
$946$	−3.23860	+	9.51239i	−0.105296	+	0.309274i
$947$	−49.3508	+	13.2235i	−1.60369	+	0.429706i	−0.946153	−	0.323719i	$-0.895067\pi$
$947$	−49.3508	+	13.2235i	−1.60369	+	0.429706i	−0.657533	+	0.753426i	$0.728400\pi$
$948$	−12.4837	+	9.54335i	−0.405453	+	0.309954i
$949$	2.02860	+	3.51363i	0.0658510	+	0.114057i
$950$	−51.2823	+	14.3980i	−1.66382	+	0.467132i
$951$		−	9.22743i		−	0.299220i
$952$	−9.38853	+	30.1912i	−0.304284	+	0.978503i
$953$	−0.903575	+	0.903575i	−0.0292697	+	0.0292697i	−0.721590	−	0.692320i	$-0.756588\pi$
$953$	−0.903575	+	0.903575i	−0.0292697	+	0.0292697i	0.692320	+	0.721590i	$0.256588\pi$
$954$	−0.326570	−	0.373061i	−0.0105731	−	0.0120783i
$955$	−33.6564	−	40.4787i	−1.08910	−	1.30986i
$956$	−30.8144	−	4.11339i	−0.996609	−	0.133037i
$957$	3.09382	+	11.5463i	0.100009	+	0.373238i
$958$	16.9387	−	8.33427i	0.547266	−	0.269268i
$959$	7.79631	+	0.801400i	0.251756	+	0.0258785i
$960$	24.6150	+	39.4966i	0.794445	+	1.27475i
$961$	6.46003	−	11.1891i	0.208388	−	0.360939i
$962$	46.6675	+	31.2432i	1.50462	+	1.00732i
$963$	9.04054	+	2.42240i	0.291327	+	0.0780609i
$964$	−15.7512	−	38.2217i	−0.507311	−	1.23104i
$965$	−8.38173	−	5.92535i	−0.269818	−	0.190744i
$966$	22.6571	−	2.11354i	0.728979	−	0.0680019i
$967$	7.22225	−	7.22225i	0.232252	−	0.232252i	−0.581380	−	0.813632i	$-0.697487\pi$
$967$	7.22225	−	7.22225i	0.232252	−	0.232252i	0.813632	+	0.581380i	$0.197487\pi$
$968$	−19.4912	−	17.1869i	−0.626472	−	0.552409i
$969$	−71.7071	+	41.4001i	−2.30356	+	1.32996i
$970$	−45.6819	+	17.4812i	−1.46676	+	0.561286i
$971$	−10.5245	+	18.2290i	−0.337747	+	0.584996i	−0.984009	−	0.178121i	$-0.942998\pi$
$971$	−10.5245	+	18.2290i	−0.337747	+	0.584996i	0.646261	+	0.763116i	$0.276332\pi$
$972$	−5.63311	−	43.3929i	−0.180682	−	1.39183i
$973$	−59.2098	+	9.51679i	−1.89818	+	0.305094i
$974$	1.05828	−	3.10836i	0.0339093	−	0.0995982i
$975$	10.1687	−	54.7813i	0.325658	−	1.75441i
$976$	−3.86367	−	3.89167i	−0.123673	−	0.124569i
$977$	2.50118	−	9.33452i	0.0800197	−	0.298638i	−0.914305	−	0.405027i	$-0.867262\pi$
$977$	2.50118	−	9.33452i	0.0800197	−	0.298638i	0.994325	+	0.106389i	$0.0339289\pi$
$978$	46.7746	+	3.10817i	1.49569	+	0.0993883i
$979$		−	6.05069i		−	0.193381i
$980$	30.8666	+	5.22024i	0.985998	+	0.166755i
$981$		−	8.74943i		−	0.279348i
$982$	3.10724	−	46.7607i	0.0991561	−	1.49219i
$983$	−4.19873	+	15.6699i	−0.133919	+	0.499792i	−1.00000		0.000111531i	$-0.999964\pi$
$983$	−4.19873	+	15.6699i	−0.133919	+	0.499792i	0.866081	+	0.499903i	$0.166631\pi$
$984$	−31.3564	+	63.1529i	−0.999607	+	2.01324i
$985$	−45.5354	+	20.9845i	−1.45088	+	0.668622i
$986$	−19.3046	−	6.57247i	−0.614784	−	0.209310i
$987$	26.2056	−	4.21203i	0.834133	−	0.134070i
$988$	−8.30741	−	63.9935i	−0.264294	−	2.03590i
$989$	−6.16898	+	10.6850i	−0.196162	+	0.339763i
$990$	−14.6490	−	6.54042i	−0.465576	−	0.207868i
$991$	−21.4275	+	12.3712i	−0.680666	+	0.392983i	−0.800106	−	0.599859i	$-0.795223\pi$
$991$	−21.4275	+	12.3712i	−0.680666	+	0.392983i	0.119440	+	0.992841i	$0.461890\pi$
$992$	7.14778	+	36.8015i	0.226942	+	1.16845i
$993$	−6.57377	+	6.57377i	−0.208612	+	0.208612i
$994$	0.511630	+	5.48466i	0.0162279	+	0.173963i
$995$	1.28926	+	7.50924i	0.0408724	+	0.238059i
$996$	−48.5083	+	19.9903i	−1.53704	+	0.633416i
$997$	−10.6155	−	2.84441i	−0.336195	−	0.0900833i	0.0867720	−	0.996228i	$-0.472345\pi$
$997$	−10.6155	−	2.84441i	−0.336195	−	0.0900833i	−0.422967	+	0.906145i	$0.639012\pi$
$998$	27.1138	−	40.4995i	0.858273	−	1.28199i
$999$	−9.26673	+	16.0504i	−0.293186	+	0.507814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.107.21	yes	176
5.3	odd	4	inner	280.2.br.a.163.43	yes	176
7.4	even	3	inner	280.2.br.a.67.9	✓	176
8.3	odd	2	inner	280.2.br.a.107.14	yes	176
35.18	odd	12	inner	280.2.br.a.123.14	yes	176
40.3	even	4	inner	280.2.br.a.163.9	yes	176
56.11	odd	6	inner	280.2.br.a.67.43	yes	176
280.123	even	12	inner	280.2.br.a.123.21	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.9	✓	176	7.4	even	3	inner
280.2.br.a.67.43	yes	176	56.11	odd	6	inner
280.2.br.a.107.14	yes	176	8.3	odd	2	inner
280.2.br.a.107.21	yes	176	1.1	even	1	trivial
280.2.br.a.123.14	yes	176	35.18	odd	12	inner
280.2.br.a.123.21	yes	176	280.123	even	12	inner
280.2.br.a.163.9	yes	176	40.3	even	4	inner
280.2.br.a.163.43	yes	176	5.3	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0937676 + 1.41110i) q^{2} +(-2.51296 - 0.673346i) q^{3} +(-1.98242 - 0.264631i) q^{4} +(2.09775 + 0.774229i) q^{5} +(1.18579 - 3.48291i) q^{6} +(-0.419863 - 2.61222i) q^{7} +(0.559308 - 2.77258i) q^{8} +(3.26351 + 1.88419i) q^{9} +O(q^{10})\)	\(q+(-0.0937676 + 1.41110i) q^{2} +(-2.51296 - 0.673346i) q^{3} +(-1.98242 - 0.264631i) q^{4} +(2.09775 + 0.774229i) q^{5} +(1.18579 - 3.48291i) q^{6} +(-0.419863 - 2.61222i) q^{7} +(0.559308 - 2.77258i) q^{8} +(3.26351 + 1.88419i) q^{9} +(-1.28922 + 2.88755i) q^{10} +(0.673124 + 1.16589i) q^{11} +(4.80355 + 1.99986i) q^{12} +(3.02874 + 3.02874i) q^{13} +(3.72548 - 0.347527i) q^{14} +(-4.75025 - 3.35812i) q^{15} +(3.85994 + 1.04922i) q^{16} +(1.09352 - 4.08108i) q^{17} +(-2.96479 + 4.42847i) q^{18} +(6.52363 + 3.76642i) q^{19} +(-3.95373 - 2.08997i) q^{20} +(-0.703832 + 6.84714i) q^{21} +(-1.70830 + 0.840524i) q^{22} +(-2.25799 + 0.605027i) q^{23} +(-3.27242 + 6.59077i) q^{24} +(3.80114 + 3.24828i) q^{25} +(-4.55785 + 3.98986i) q^{26} +(-1.41352 - 1.41352i) q^{27} +(0.141066 + 5.28962i) q^{28} -3.41296 q^{29} +(5.18407 - 6.38821i) q^{30} +(5.73934 - 3.31361i) q^{31} +(-1.84249 + 5.34839i) q^{32} +(-0.906492 - 3.38307i) q^{33} +(5.65627 + 1.92574i) q^{34} +(1.14169 - 5.80487i) q^{35} +(-5.97102 - 4.59887i) q^{36} +(-2.39958 - 8.95535i) q^{37} +(-5.92650 + 8.85233i) q^{38} +(-5.57171 - 9.65049i) q^{39} +(3.31990 - 5.38315i) q^{40} +9.58202 q^{41} +(-9.59601 - 1.63522i) q^{42} +(3.73207 - 3.73207i) q^{43} +(-1.02588 - 2.48940i) q^{44} +(5.38725 + 6.47927i) q^{45} +(-0.642028 - 3.24299i) q^{46} +(-0.998016 - 3.72465i) q^{47} +(-8.99340 - 5.23572i) q^{48} +(-6.64743 + 2.19355i) q^{49} +(-4.94008 + 5.05921i) q^{50} +(-5.49595 + 9.51927i) q^{51} +(-5.20271 - 6.80571i) q^{52} +(-0.0240790 + 0.0898639i) q^{53} +(2.12717 - 1.86208i) q^{54} +(0.509386 + 2.96689i) q^{55} +(-7.47742 - 0.296936i) q^{56} +(-13.8575 - 13.8575i) q^{57} +(0.320025 - 4.81603i) q^{58} +(0.663996 - 0.383358i) q^{59} +(8.52831 + 7.91426i) q^{60} +(-1.18730 - 0.685485i) q^{61} +(4.13768 + 8.40950i) q^{62} +(3.55170 - 9.31613i) q^{63} +(-7.37435 - 3.10145i) q^{64} +(4.00860 + 8.69848i) q^{65} +(4.85886 - 0.961929i) q^{66} +(-2.24546 + 8.38018i) q^{67} +(-3.24779 + 7.80101i) q^{68} +6.08164 q^{69} +(8.08421 + 2.15535i) q^{70} +1.47220i q^{71} +(7.04937 - 7.99449i) q^{72} +(0.914941 + 0.245158i) q^{73} +(12.8619 - 2.54633i) q^{74} +(-7.36490 - 10.7223i) q^{75} +(-11.9358 - 9.19296i) q^{76} +(2.76293 - 2.24786i) q^{77} +(14.1403 - 6.95735i) q^{78} +(-1.50999 + 2.61539i) q^{79} +(7.28487 + 5.18948i) q^{80} +(-3.05223 - 5.28661i) q^{81} +(-0.898484 + 13.5212i) q^{82} +(-7.12999 + 7.12999i) q^{83} +(3.20725 - 13.3876i) q^{84} +(5.45362 - 7.71445i) q^{85} +(4.91638 + 5.61628i) q^{86} +(8.57663 + 2.29810i) q^{87} +(3.60899 - 1.21420i) q^{88} +(-3.89233 - 2.24724i) q^{89} +(-9.64806 + 6.99441i) q^{90} +(6.64008 - 9.18339i) q^{91} +(4.63639 - 0.601879i) q^{92} +(-16.6540 + 4.46242i) q^{93} +(5.34944 - 1.05905i) q^{94} +(10.7689 + 12.9518i) q^{95} +(8.23143 - 12.1997i) q^{96} +(10.9372 + 10.9372i) q^{97} +(-2.47201 - 9.58588i) q^{98} +5.07317i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

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