LMFDB - Embedded newform 930.2.r.a.119.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.12
Character	$\chi$	$=$	930.119
Dual form			930.2.r.a.719.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.581525 + 1.63151i) q^{3} +1.00000 q^{4} +(1.92892 - 1.13105i) q^{5} +(0.581525 - 1.63151i) q^{6} +(-0.996061 - 0.575076i) q^{7} -1.00000 q^{8} +(-2.32366 - 1.89753i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.581525 + 1.63151i) q^{3} +1.00000 q^{4} +(1.92892 - 1.13105i) q^{5} +(0.581525 - 1.63151i) q^{6} +(-0.996061 - 0.575076i) q^{7} -1.00000 q^{8} +(-2.32366 - 1.89753i) q^{9} +(-1.92892 + 1.13105i) q^{10} +(1.18492 + 2.05235i) q^{11} +(-0.581525 + 1.63151i) q^{12} +(-2.12245 - 3.67620i) q^{13} +(0.996061 + 0.575076i) q^{14} +(0.723613 + 3.80478i) q^{15} +1.00000 q^{16} +(0.282061 + 0.162848i) q^{17} +(2.32366 + 1.89753i) q^{18} +(2.95296 - 5.11467i) q^{19} +(1.92892 - 1.13105i) q^{20} +(1.51748 - 1.29066i) q^{21} +(-1.18492 - 2.05235i) q^{22} -3.91946i q^{23} +(0.581525 - 1.63151i) q^{24} +(2.44143 - 4.36342i) q^{25} +(2.12245 + 3.67620i) q^{26} +(4.44711 - 2.68761i) q^{27} +(-0.996061 - 0.575076i) q^{28} -6.15260 q^{29} +(-0.723613 - 3.80478i) q^{30} +(-5.18162 - 2.03737i) q^{31} -1.00000 q^{32} +(-4.03749 + 0.739723i) q^{33} +(-0.282061 - 0.162848i) q^{34} +(-2.57176 + 0.0173251i) q^{35} +(-2.32366 - 1.89753i) q^{36} +(-2.70854 + 4.69134i) q^{37} +(-2.95296 + 5.11467i) q^{38} +(7.23202 - 1.32500i) q^{39} +(-1.92892 + 1.13105i) q^{40} +(-6.40890 + 3.70018i) q^{41} +(-1.51748 + 1.29066i) q^{42} +(2.92261 - 5.06211i) q^{43} +(1.18492 + 2.05235i) q^{44} +(-6.62835 - 1.03200i) q^{45} +3.91946i q^{46} +9.74464 q^{47} +(-0.581525 + 1.63151i) q^{48} +(-2.83858 - 4.91656i) q^{49} +(-2.44143 + 4.36342i) q^{50} +(-0.429714 + 0.365486i) q^{51} +(-2.12245 - 3.67620i) q^{52} +(5.94982 - 3.43513i) q^{53} +(-4.44711 + 2.68761i) q^{54} +(4.60693 + 2.61859i) q^{55} +(0.996061 + 0.575076i) q^{56} +(6.62742 + 7.79210i) q^{57} +6.15260 q^{58} +(6.72767 + 3.88422i) q^{59} +(0.723613 + 3.80478i) q^{60} -7.88942i q^{61} +(5.18162 + 2.03737i) q^{62} +(1.22328 + 3.22633i) q^{63} +1.00000 q^{64} +(-8.25201 - 4.69047i) q^{65} +(4.03749 - 0.739723i) q^{66} +(5.51167 - 3.18217i) q^{67} +(0.282061 + 0.162848i) q^{68} +(6.39464 + 2.27926i) q^{69} +(2.57176 - 0.0173251i) q^{70} +(5.90885 - 3.41147i) q^{71} +(2.32366 + 1.89753i) q^{72} +(-7.91524 - 13.7096i) q^{73} +(2.70854 - 4.69134i) q^{74} +(5.69920 + 6.52066i) q^{75} +(2.95296 - 5.11467i) q^{76} -2.72568i q^{77} +(-7.23202 + 1.32500i) q^{78} +(-1.66882 - 0.963496i) q^{79} +(1.92892 - 1.13105i) q^{80} +(1.79876 + 8.81842i) q^{81} +(6.40890 - 3.70018i) q^{82} +(-4.70315 + 2.71537i) q^{83} +(1.51748 - 1.29066i) q^{84} +(0.728262 - 0.00490607i) q^{85} +(-2.92261 + 5.06211i) q^{86} +(3.57789 - 10.0380i) q^{87} +(-1.18492 - 2.05235i) q^{88} +6.10143 q^{89} +(6.62835 + 1.03200i) q^{90} +4.88229i q^{91} -3.91946i q^{92} +(6.33723 - 7.26908i) q^{93} -9.74464 q^{94} +(-0.0889628 - 13.2057i) q^{95} +(0.581525 - 1.63151i) q^{96} +12.1521i q^{97} +(2.83858 + 4.91656i) q^{98} +(1.14104 - 7.01738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.581525	+	1.63151i	−0.335744	+	0.941953i
$3$	−0.581525	+	1.63151i	−0.335744	+	0.941953i
$4$	1.00000			0.500000
$5$	1.92892	−	1.13105i	0.862637	−	0.505823i
$5$	1.92892	−	1.13105i	0.862637	−	0.505823i
$6$	0.581525	−	1.63151i	0.237407	−	0.666062i
$7$	−0.996061	−	0.575076i	−0.376476	−	0.217358i	0.299808	−	0.954000i	$-0.403077\pi$
$7$	−0.996061	−	0.575076i	−0.376476	−	0.217358i	−0.676284	+	0.736641i	$0.736411\pi$
$8$	−1.00000			−0.353553
$9$	−2.32366	−	1.89753i	−0.774552	−	0.632510i
$10$	−1.92892	+	1.13105i	−0.609977	+	0.357671i
$11$	1.18492	+	2.05235i	0.357268	+	0.618806i	0.987503	−	0.157598i	$-0.0503750\pi$
$11$	1.18492	+	2.05235i	0.357268	+	0.618806i	−0.630235	+	0.776404i	$0.717042\pi$
$12$	−0.581525	+	1.63151i	−0.167872	+	0.470977i
$13$	−2.12245	−	3.67620i	−0.588663	−	1.01959i	−0.994408	−	0.105608i	$-0.966321\pi$
$13$	−2.12245	−	3.67620i	−0.588663	−	1.01959i	0.405745	−	0.913986i	$-0.367012\pi$
$14$	0.996061	+	0.575076i	0.266208	+	0.153696i
$15$	0.723613	+	3.80478i	0.186836	+	0.982391i
$16$	1.00000			0.250000
$17$	0.282061	+	0.162848i	0.0684099	+	0.0394965i	0.533815	−	0.845601i	$-0.320758\pi$
$17$	0.282061	+	0.162848i	0.0684099	+	0.0394965i	−0.465405	+	0.885098i	$0.654091\pi$
$18$	2.32366	+	1.89753i	0.547691	+	0.447252i
$19$	2.95296	−	5.11467i	0.677455	−	1.17339i	−0.298290	−	0.954475i	$-0.596416\pi$
$19$	2.95296	−	5.11467i	0.677455	−	1.17339i	0.975745	−	0.218911i	$-0.0702505\pi$
$20$	1.92892	−	1.13105i	0.431319	−	0.252911i
$21$	1.51748	−	1.29066i	0.331141	−	0.281646i
$22$	−1.18492	−	2.05235i	−0.252627	−	0.437562i
$23$		−	3.91946i		−	0.817263i	−0.912699	−	0.408632i	$-0.866006\pi$
$23$		−	3.91946i		−	0.817263i	0.912699	−	0.408632i	$-0.133994\pi$
$24$	0.581525	−	1.63151i	0.118703	−	0.333031i
$25$	2.44143	−	4.36342i	0.488287	−	0.872683i
$26$	2.12245	+	3.67620i	0.416247	+	0.720962i
$27$	4.44711	−	2.68761i	0.855846	−	0.517231i
$28$	−0.996061	−	0.575076i	−0.188238	−	0.108679i
$29$	−6.15260			−1.14251			−0.571254	−	0.820773i	$-0.693543\pi$
$29$	−6.15260			−1.14251			−0.571254	+	0.820773i	$0.693543\pi$
$30$	−0.723613	−	3.80478i	−0.132113	−	0.694655i
$31$	−5.18162	−	2.03737i	−0.930646	−	0.365922i
$31$	−5.18162	−	2.03737i	−0.930646	−	0.365922i
$32$	−1.00000			−0.176777
$33$	−4.03749	+	0.739723i	−0.702837	+	0.128769i
$34$	−0.282061	−	0.162848i	−0.0483731	−	0.0279282i
$35$	−2.57176	+	0.0173251i	−0.434707	+	0.00292848i
$36$	−2.32366	−	1.89753i	−0.387276	−	0.316255i
$37$	−2.70854	+	4.69134i	−0.445282	+	0.771251i	−0.998072	−	0.0620698i	$-0.980230\pi$
$37$	−2.70854	+	4.69134i	−0.445282	+	0.771251i	0.552790	+	0.833321i	$0.313563\pi$
$38$	−2.95296	+	5.11467i	−0.479033	+	0.829709i
$39$	7.23202	−	1.32500i	1.15805	−	0.212171i
$40$	−1.92892	+	1.13105i	−0.304988	+	0.178835i
$41$	−6.40890	+	3.70018i	−1.00090	+	0.577871i	−0.908515	−	0.417853i	$-0.862783\pi$
$41$	−6.40890	+	3.70018i	−1.00090	+	0.577871i	−0.0923864	+	0.995723i	$0.529450\pi$
$42$	−1.51748	+	1.29066i	−0.234152	+	0.199154i
$43$	2.92261	−	5.06211i	0.445694	−	0.771965i	−0.552406	−	0.833575i	$-0.686290\pi$
$43$	2.92261	−	5.06211i	0.445694	−	0.771965i	0.998100	+	0.0616100i	$0.0196235\pi$
$44$	1.18492	+	2.05235i	0.178634	+	0.309403i
$45$	−6.62835	−	1.03200i	−0.988096	−	0.153841i
$46$			3.91946i			0.577892i
$47$	9.74464			1.42140			0.710701	−	0.703495i	$-0.248378\pi$
$47$	9.74464			1.42140			0.710701	+	0.703495i	$0.248378\pi$
$48$	−0.581525	+	1.63151i	−0.0839360	+	0.235488i
$49$	−2.83858	−	4.91656i	−0.405511	−	0.702365i
$50$	−2.44143	+	4.36342i	−0.345271	+	0.617080i
$51$	−0.429714	+	0.365486i	−0.0601720	+	0.0511782i
$52$	−2.12245	−	3.67620i	−0.294331	−	0.509797i
$53$	5.94982	−	3.43513i	0.817271	−	0.471852i	−0.0322036	−	0.999481i	$-0.510252\pi$
$53$	5.94982	−	3.43513i	0.817271	−	0.471852i	0.849474	+	0.527630i	$0.176919\pi$
$54$	−4.44711	+	2.68761i	−0.605175	+	0.365737i
$55$	4.60693	+	2.61859i	0.621199	+	0.353091i
$56$	0.996061	+	0.575076i	0.133104	+	0.0768478i
$57$	6.62742	+	7.79210i	0.877824	+	1.03209i
$58$	6.15260			0.807875
$59$	6.72767	+	3.88422i	0.875868	+	0.505683i	0.869294	−	0.494296i	$-0.164574\pi$
$59$	6.72767	+	3.88422i	0.875868	+	0.505683i	0.00657435	+	0.999978i	$0.497907\pi$
$60$	0.723613	+	3.80478i	0.0934180	+	0.491196i
$61$		−	7.88942i		−	1.01014i	−0.863079	−	0.505069i	$-0.831467\pi$
$61$		−	7.88942i		−	1.01014i	0.863079	−	0.505069i	$-0.168533\pi$
$62$	5.18162	+	2.03737i	0.658066	+	0.258746i
$63$	1.22328	+	3.22633i	0.154119	+	0.406480i
$64$	1.00000			0.125000
$65$	−8.25201	−	4.69047i	−1.02354	−	0.581781i
$66$	4.03749	−	0.739723i	0.496981	−	0.0910537i
$67$	5.51167	−	3.18217i	0.673358	−	0.388764i	−0.123990	−	0.992284i	$-0.539569\pi$
$67$	5.51167	−	3.18217i	0.673358	−	0.388764i	0.797348	+	0.603520i	$0.206236\pi$
$68$	0.282061	+	0.162848i	0.0342049	+	0.0197482i
$69$	6.39464	+	2.27926i	0.769824	+	0.274391i
$70$	2.57176	−	0.0173251i	0.307384	−	0.00207075i
$71$	5.90885	−	3.41147i	0.701251	−	0.404867i	−0.106562	−	0.994306i	$-0.533984\pi$
$71$	5.90885	−	3.41147i	0.701251	−	0.404867i	0.807813	+	0.589439i	$0.200651\pi$
$72$	2.32366	+	1.89753i	0.273846	+	0.223626i
$73$	−7.91524	−	13.7096i	−0.926409	−	1.60459i	−0.789280	−	0.614034i	$-0.789546\pi$
$73$	−7.91524	−	13.7096i	−0.926409	−	1.60459i	−0.137129	−	0.990553i	$-0.543788\pi$
$74$	2.70854	−	4.69134i	0.314862	−	0.545357i
$75$	5.69920	+	6.52066i	0.658087	+	0.752941i
$76$	2.95296	−	5.11467i	0.338727	−	0.586693i
$77$		−	2.72568i		−	0.310621i
$78$	−7.23202	+	1.32500i	−0.818865	+	0.150027i
$79$	−1.66882	−	0.963496i	−0.187757	−	0.108402i	0.403175	−	0.915123i	$-0.367907\pi$
$79$	−1.66882	−	0.963496i	−0.187757	−	0.108402i	−0.590932	+	0.806721i	$0.701240\pi$
$80$	1.92892	−	1.13105i	0.215659	−	0.126456i
$81$	1.79876	+	8.81842i	0.199862	+	0.979824i
$82$	6.40890	−	3.70018i	0.707744	−	0.408616i
$83$	−4.70315	+	2.71537i	−0.516238	+	0.298050i	−0.735394	−	0.677640i	$-0.763003\pi$
$83$	−4.70315	+	2.71537i	−0.516238	+	0.298050i	0.219156	+	0.975690i	$0.429670\pi$
$84$	1.51748	−	1.29066i	0.165570	−	0.140823i
$85$	0.728262	−	0.00490607i	0.0789911	−	0.000532138i
$86$	−2.92261	+	5.06211i	−0.315154	+	0.545862i
$87$	3.57789	−	10.0380i	0.383590	−	1.07619i
$88$	−1.18492	−	2.05235i	−0.126313	−	0.218781i
$89$	6.10143			0.646751			0.323375	−	0.946271i	$-0.395182\pi$
$89$	6.10143			0.646751			0.323375	+	0.946271i	$0.395182\pi$
$90$	6.62835	+	1.03200i	0.698689	+	0.108782i
$91$			4.88229i			0.511803i
$92$		−	3.91946i		−	0.408632i
$93$	6.33723	−	7.26908i	0.657140	−	0.753769i
$94$	−9.74464			−1.00508
$95$	−0.0889628	−	13.2057i	−0.00912739	−	1.35488i
$96$	0.581525	−	1.63151i	0.0593517	−	0.166515i
$97$			12.1521i			1.23385i	0.787020	+	0.616927i	$0.211623\pi$
$97$			12.1521i			1.23385i	−0.787020	+	0.616927i	$0.788377\pi$
$98$	2.83858	+	4.91656i	0.286739	+	0.496647i
$99$	1.14104	−	7.01738i	0.114679	−	0.705273i
$100$	2.44143	−	4.36342i	0.244143	−	0.436342i
$101$			9.75329i			0.970489i	0.874379	+	0.485244i	$0.161269\pi$
$101$			9.75329i			0.970489i	−0.874379	+	0.485244i	$0.838731\pi$
$102$	0.429714	−	0.365486i	0.0425480	−	0.0361885i
$103$	2.47328	−	1.42795i	0.243700	−	0.140700i	−0.373176	−	0.927760i	$-0.621731\pi$
$103$	2.47328	−	1.42795i	0.243700	−	0.140700i	0.616876	+	0.787060i	$0.288398\pi$
$104$	2.12245	+	3.67620i	0.208124	+	0.360481i
$105$	1.46728	−	4.20593i	0.143192	−	0.410457i
$106$	−5.94982	+	3.43513i	−0.577898	+	0.333649i
$107$	8.09940	−	14.0286i	0.782999	−	1.35619i	−0.147188	−	0.989108i	$-0.547022\pi$
$107$	8.09940	−	14.0286i	0.782999	−	1.35619i	0.930187	−	0.367085i	$-0.119644\pi$
$108$	4.44711	−	2.68761i	0.427923	−	0.258615i
$109$	11.4068			1.09257			0.546286	−	0.837599i	$-0.316041\pi$
$109$	11.4068			1.09257			0.546286	+	0.837599i	$0.316041\pi$
$110$	−4.60693	−	2.61859i	−0.439254	−	0.249673i
$111$	−6.07888	−	7.14715i	−0.576982	−	0.678377i
$112$	−0.996061	−	0.575076i	−0.0941189	−	0.0543396i
$113$	5.70370	+	9.87909i	0.536559	+	0.929347i	0.999086	+	0.0427418i	$0.0136093\pi$
$113$	5.70370	+	9.87909i	0.536559	+	0.929347i	−0.462528	+	0.886605i	$0.653057\pi$
$114$	−6.62742	−	7.79210i	−0.620715	−	0.729797i
$115$	−4.43312	−	7.56030i	−0.413390	−	0.705002i
$116$	−6.15260			−0.571254
$117$	−2.04384	+	12.5696i	−0.188953	+	1.16206i
$118$	−6.72767	−	3.88422i	−0.619332	−	0.357572i
$119$	−0.187300	−	0.324413i	−0.0171698	−	0.0297389i
$120$	−0.723613	−	3.80478i	−0.0660565	−	0.347328i
$121$	2.69191	−	4.66253i	0.244719	−	0.423866i
$122$			7.88942i			0.714275i
$123$	−2.30994	−	12.6079i	−0.208281	−	1.13682i
$124$	−5.18162	−	2.03737i	−0.465323	−	0.182961i
$125$	−0.225936	−	11.1781i	−0.0202084	−	0.999796i
$126$	−1.22328	−	3.22633i	−0.108978	−	0.287425i
$127$	−6.22733	+	10.7860i	−0.552586	+	0.957107i	0.445501	+	0.895281i	$0.353026\pi$
$127$	−6.22733	+	10.7860i	−0.552586	+	0.957107i	−0.998087	+	0.0618254i	$0.980308\pi$
$128$	−1.00000			−0.0883883
$129$	6.55932	+	7.71202i	0.577516	+	0.679006i
$130$	8.25201	+	4.69047i	0.723749	+	0.411381i
$131$	11.2712	+	6.50743i	0.984770	+	0.568557i	0.903707	−	0.428152i	$-0.140835\pi$
$131$	11.2712	+	6.50743i	0.984770	+	0.568557i	0.0810631	+	0.996709i	$0.474168\pi$
$132$	−4.03749	+	0.739723i	−0.351419	+	0.0643847i
$133$	−5.88265	+	3.39635i	−0.510091	+	0.294501i
$134$	−5.51167	+	3.18217i	−0.476136	+	0.274897i
$135$	5.53827	−	10.2141i	0.476658	−	0.879089i
$136$	−0.282061	−	0.162848i	−0.0241865	−	0.0139641i
$137$	−4.03169	+	2.32769i	−0.344450	+	0.198868i	−0.662238	−	0.749293i	$-0.730393\pi$
$137$	−4.03169	+	2.32769i	−0.344450	+	0.198868i	0.317788	+	0.948162i	$0.397060\pi$
$138$	−6.39464	−	2.27926i	−0.544348	−	0.194024i
$139$			13.6026i			1.15376i	0.816828	+	0.576881i	$0.195730\pi$
$139$			13.6026i			1.15376i	−0.816828	+	0.576881i	$0.804270\pi$
$140$	−2.57176	+	0.0173251i	−0.217353	+	0.00146424i
$141$	−5.66675	+	15.8985i	−0.477227	+	1.33889i
$142$	−5.90885	+	3.41147i	−0.495859	+	0.286285i
$143$	5.02989	−	8.71203i	0.420621	−	0.728536i
$144$	−2.32366	−	1.89753i	−0.193638	−	0.158128i
$145$	−11.8678	+	6.95892i	−0.985570	+	0.577907i
$146$	7.91524	+	13.7096i	0.655070	+	1.13461i
$147$	9.67212	−	1.77206i	0.797743	−	0.146157i
$148$	−2.70854	+	4.69134i	−0.222641	+	0.385625i
$149$	−20.5556	−	11.8678i	−1.68398	−	0.972247i	−0.958969	−	0.283510i	$-0.908501\pi$
$149$	−20.5556	−	11.8678i	−1.68398	−	0.972247i	−0.725012	−	0.688737i	$-0.758166\pi$
$150$	−5.69920	−	6.52066i	−0.465338	−	0.532410i
$151$			8.61990i			0.701478i	0.936473	+	0.350739i	$0.114069\pi$
$151$			8.61990i			0.701478i	−0.936473	+	0.350739i	$0.885931\pi$
$152$	−2.95296	+	5.11467i	−0.239516	+	0.414855i
$153$	−0.346404	−	0.913622i	−0.0280051	−	0.0738620i
$154$			2.72568i			0.219642i
$155$	−12.2993	+	1.93078i	−0.987901	+	0.155084i
$156$	7.23202	−	1.32500i	0.579025	−	0.106085i
$157$		−	16.1601i		−	1.28972i	−0.764301	−	0.644860i	$-0.776916\pi$
$157$		−	16.1601i		−	1.28972i	0.764301	−	0.644860i	$-0.223084\pi$
$158$	1.66882	+	0.963496i	0.132765	+	0.0766517i
$159$	2.14448	+	11.7048i	0.170068	+	0.928252i
$160$	−1.92892	+	1.13105i	−0.152494	+	0.0894177i
$161$	−2.25399	+	3.90402i	−0.177639	+	0.307680i
$162$	−1.79876	−	8.81842i	−0.141324	−	0.692840i
$163$		−	15.1298i		−	1.18506i	−0.805550	−	0.592528i	$-0.798130\pi$
$163$		−	15.1298i		−	1.18506i	0.805550	−	0.592528i	$-0.201870\pi$
$164$	−6.40890	+	3.70018i	−0.500451	+	0.288935i
$165$	−6.95131	+	5.99348i	−0.541159	+	0.466592i
$166$	4.70315	−	2.71537i	0.365035	−	0.210753i
$167$	−12.3209	−	7.11348i	−0.953420	−	0.550458i	−0.0592786	−	0.998241i	$-0.518880\pi$
$167$	−12.3209	−	7.11348i	−0.953420	−	0.550458i	−0.894142	+	0.447784i	$0.852213\pi$
$168$	−1.51748	+	1.29066i	−0.117076	+	0.0995768i
$169$	−2.50962	+	4.34679i	−0.193048	+	0.334369i
$170$	−0.728262	+	0.00490607i	−0.0558552	+	0.000376279i
$171$	−16.5669	+	6.28142i	−1.26690	+	0.480352i
$172$	2.92261	−	5.06211i	0.222847	−	0.385983i
$173$	1.11273	+	1.92730i	0.0845989	+	0.146530i	0.905220	−	0.424943i	$-0.139706\pi$
$173$	1.11273	+	1.92730i	0.0845989	+	0.146530i	−0.820621	+	0.571472i	$0.806372\pi$
$174$	−3.57789	+	10.0380i	−0.271239	+	0.760981i
$175$	−4.94111	+	2.94222i	−0.373513	+	0.222411i
$176$	1.18492	+	2.05235i	0.0893170	+	0.154702i
$177$	−10.2495	+	8.71750i	−0.770397	+	0.655247i
$178$	−6.10143			−0.457322
$179$	4.88016	−	8.45268i	0.364760	−	0.631783i	−0.623978	−	0.781442i	$-0.714484\pi$
$179$	4.88016	−	8.45268i	0.364760	−	0.631783i	0.988738	+	0.149659i	$0.0478177\pi$
$180$	−6.62835	−	1.03200i	−0.494048	−	0.0769205i
$181$	2.88528	−	1.66582i	0.214461	−	0.123819i	−0.388922	−	0.921271i	$-0.627152\pi$
$181$	2.88528	−	1.66582i	0.214461	−	0.123819i	0.603383	+	0.797452i	$0.293819\pi$
$182$		−	4.88229i		−	0.361899i
$183$	12.8717	+	4.58790i	0.951502	+	0.339147i
$184$			3.91946i			0.288946i
$185$	0.0815994	+	12.1127i	0.00599931	+	0.890544i
$186$	−6.33723	+	7.26908i	−0.464668	+	0.532995i
$187$			0.771850i			0.0564433i
$188$	9.74464			0.710701
$189$	−5.97517	+	0.119597i	−0.434630	+	0.00869944i
$190$	0.0889628	+	13.2057i	0.00645404	+	0.958044i
$191$	−4.71452	+	2.72193i	−0.341130	+	0.196952i	−0.660772	−	0.750587i	$-0.729771\pi$
$191$	−4.71452	+	2.72193i	−0.341130	+	0.196952i	0.319641	+	0.947539i	$0.396438\pi$
$192$	−0.581525	+	1.63151i	−0.0419680	+	0.117744i
$193$	−0.398168	−	0.229882i	−0.0286607	−	0.0165473i	0.485601	−	0.874180i	$-0.338601\pi$
$193$	−0.398168	−	0.229882i	−0.0286607	−	0.0165473i	−0.514262	+	0.857633i	$0.671934\pi$
$194$		−	12.1521i		−	0.872467i
$195$	12.4513	−	10.7356i	0.891657	−	0.768794i
$196$	−2.83858	−	4.91656i	−0.202755	−	0.351183i
$197$	−12.8639	+	7.42698i	−0.916515	+	0.529150i	−0.882522	−	0.470272i	$-0.844156\pi$
$197$	−12.8639	+	7.42698i	−0.916515	+	0.529150i	−0.0339935	+	0.999422i	$0.510823\pi$
$198$	−1.14104	+	7.01738i	−0.0810900	+	0.498703i
$199$	−8.34879	+	4.82018i	−0.591830	+	0.341693i	−0.765821	−	0.643054i	$-0.777667\pi$
$199$	−8.34879	+	4.82018i	−0.591830	+	0.341693i	0.173991	+	0.984747i	$0.444334\pi$
$200$	−2.44143	+	4.36342i	−0.172635	+	0.308540i
$201$	1.98656	+	10.8429i	0.140121	+	0.764797i
$202$		−	9.75329i		−	0.686239i
$203$	6.12836	+	3.53821i	0.430126	+	0.248334i
$204$	−0.429714	+	0.365486i	−0.0300860	+	0.0255891i
$205$	−8.17712	+	14.3861i	−0.571115	+	1.00477i
$206$	−2.47328	+	1.42795i	−0.172322	+	0.0994900i
$207$	−7.43729	+	9.10747i	−0.516927	+	0.633013i
$208$	−2.12245	−	3.67620i	−0.147166	−	0.254898i
$209$	13.9961			0.968132
$210$	−1.46728	+	4.20593i	−0.101252	+	0.290237i
$211$	−11.6563	+	20.1893i	−0.802452	+	1.38989i	0.115546	+	0.993302i	$0.463138\pi$
$211$	−11.6563	+	20.1893i	−0.802452	+	1.38989i	−0.917998	+	0.396585i	$0.870195\pi$
$212$	5.94982	−	3.43513i	0.408635	−	0.235926i
$213$	2.12971	+	11.6242i	0.145926	+	0.796478i
$214$	−8.09940	+	14.0286i	−0.553664	+	0.958974i
$215$	−0.0880486	−	13.0700i	−0.00600487	−	0.891368i
$216$	−4.44711	+	2.68761i	−0.302587	+	0.182869i
$217$	3.98956	+	5.00916i	0.270829	+	0.340044i
$218$	−11.4068			−0.772565
$219$	26.9703	−	4.94132i	1.82248	−	0.333904i
$220$	4.60693	+	2.61859i	0.310599	+	0.176546i
$221$		−	1.38255i		−	0.0930004i
$222$	6.07888	+	7.14715i	0.407988	+	0.479685i
$223$	−3.51266	+	6.08411i	−0.235225	+	0.407422i	−0.959338	−	0.282260i	$-0.908916\pi$
$223$	−3.51266	+	6.08411i	−0.235225	+	0.407422i	0.724113	+	0.689681i	$0.242249\pi$
$224$	0.996061	+	0.575076i	0.0665521	+	0.0384239i
$225$	−13.9528	+	5.50638i	−0.930185	+	0.367092i
$226$	−5.70370	−	9.87909i	−0.379404	−	0.657147i
$227$	1.06064	+	1.83708i	0.0703972	+	0.121931i	0.899075	−	0.437794i	$-0.144240\pi$
$227$	1.06064	+	1.83708i	0.0703972	+	0.121931i	−0.828678	+	0.559725i	$0.810907\pi$
$228$	6.62742	+	7.79210i	0.438912	+	0.516044i
$229$	−16.2859	−	9.40267i	−1.07620	−	0.621346i	−0.146334	−	0.989235i	$-0.546747\pi$
$229$	−16.2859	−	9.40267i	−1.07620	−	0.621346i	−0.929870	+	0.367889i	$0.880081\pi$
$230$	4.43312	+	7.56030i	0.292311	+	0.498512i
$231$	4.44698	+	1.58505i	0.292590	+	0.104289i
$232$	6.15260			0.403938
$233$	16.5941			1.08711			0.543556	−	0.839373i	$-0.317077\pi$
$233$	16.5941			1.08711			0.543556	+	0.839373i	$0.317077\pi$
$234$	2.04384	−	12.5696i	0.133610	−	0.821703i
$235$	18.7966	−	11.0217i	1.22615	−	0.718977i
$236$	6.72767	+	3.88422i	0.437934	+	0.252841i
$237$	2.54242	−	2.16241i	0.165148	−	0.140464i
$238$	0.187300	+	0.324413i	0.0121409	+	0.0210286i
$239$	−5.63430	−	9.75890i	−0.364453	−	0.631251i	0.624236	−	0.781236i	$-0.285411\pi$
$239$	−5.63430	−	9.75890i	−0.364453	−	0.631251i	−0.988688	+	0.149986i	$0.952077\pi$
$240$	0.723613	+	3.80478i	0.0467090	+	0.245598i
$241$	19.8736	+	11.4740i	1.28017	+	0.739106i	0.976879	−	0.213792i	$-0.0685816\pi$
$241$	19.8736	+	11.4740i	1.28017	+	0.739106i	0.303290	+	0.952898i	$0.401915\pi$
$242$	−2.69191	+	4.66253i	−0.173043	+	0.299719i
$243$	−15.4334	−	2.19344i	−0.990051	−	0.140709i
$244$		−	7.88942i		−	0.505069i
$245$	−11.0363	−	6.27304i	−0.705081	−	0.400770i
$246$	2.30994	+	12.6079i	0.147277	+	0.803852i
$247$	−25.0701			−1.59517
$248$	5.18162	+	2.03737i	0.329033	+	0.129373i
$249$	−1.69515	−	9.25230i	−0.107426	−	0.586341i
$250$	0.225936	+	11.1781i	0.0142895	+	0.706962i
$251$	−8.16084	+	14.1350i	−0.515108	+	0.892193i	0.484739	+	0.874659i	$0.338915\pi$
$251$	−8.16084	+	14.1350i	−0.515108	+	0.892193i	−0.999846	+	0.0175335i	$0.994419\pi$
$252$	1.22328	+	3.22633i	0.0770593	+	0.203240i
$253$	8.04409	−	4.64426i	0.505728	−	0.291982i
$254$	6.22733	−	10.7860i	0.390737	−	0.676777i
$255$	−0.415499	+	1.19102i	−0.0260195	+	0.0745846i
$256$	1.00000			0.0625000
$257$	−1.66337	−	2.88103i	−0.103758	−	0.179714i	0.809472	−	0.587158i	$-0.199753\pi$
$257$	−1.66337	−	2.88103i	−0.103758	−	0.179714i	−0.913230	+	0.407444i	$0.866420\pi$
$258$	−6.55932	−	7.71202i	−0.408366	−	0.480130i
$259$	5.39575	−	3.11524i	0.335276	−	0.193571i
$260$	−8.25201	−	4.69047i	−0.511768	−	0.290890i
$261$	14.2965	+	11.6747i	0.884932	+	0.722648i
$262$	−11.2712	−	6.50743i	−0.696337	−	0.402031i
$263$			3.51416i			0.216692i	0.994113	+	0.108346i	$0.0345555\pi$
$263$			3.51416i			0.216692i	−0.994113	+	0.108346i	$0.965444\pi$
$264$	4.03749	−	0.739723i	0.248490	−	0.0455268i
$265$	7.59139	−	13.3556i	0.466335	−	0.820431i
$266$	5.88265	−	3.39635i	0.360688	−	0.208244i
$267$	−3.54814	+	9.95456i	−0.217143	+	0.609209i
$268$	5.51167	−	3.18217i	0.336679	−	0.194382i
$269$	−14.5882	−	25.2676i	−0.889461	−	1.54059i	−0.840514	−	0.541790i	$-0.817747\pi$
$269$	−14.5882	−	25.2676i	−0.889461	−	1.54059i	−0.0489471	−	0.998801i	$-0.515587\pi$
$270$	−5.53827	+	10.2141i	−0.337048	+	0.621610i
$271$			17.4293i			1.05876i	0.848386	+	0.529378i	$0.177575\pi$
$271$			17.4293i			1.05876i	−0.848386	+	0.529378i	$0.822425\pi$
$272$	0.282061	+	0.162848i	0.0171025	+	0.00987411i
$273$	−7.96551	−	2.83918i	−0.482095	−	0.171835i
$274$	4.03169	−	2.32769i	0.243563	−	0.140621i
$275$	11.8482	−	0.159642i	0.714471	−	0.00962677i
$276$	6.39464	+	2.27926i	0.384912	+	0.137196i
$277$	−3.05552			−0.183588			−0.0917942	−	0.995778i	$-0.529260\pi$
$277$	−3.05552			−0.183588			−0.0917942	+	0.995778i	$0.529260\pi$
$278$		−	13.6026i		−	0.815833i
$279$	8.17433	+	14.5664i	0.489384	+	0.872068i
$280$	2.57176	−	0.0173251i	0.153692	−	0.00103537i
$281$		−	13.7415i		−	0.819749i	−0.912142	−	0.409874i	$-0.865573\pi$
$281$		−	13.7415i		−	0.819749i	0.912142	−	0.409874i	$-0.134427\pi$
$282$	5.66675	−	15.8985i	0.337450	−	0.946741i
$283$			5.87010i			0.348941i	0.984662	+	0.174471i	$0.0558214\pi$
$283$			5.87010i			0.348941i	−0.984662	+	0.174471i	$0.944179\pi$
$284$	5.90885	−	3.41147i	0.350626	−	0.202434i
$285$	21.5970	+	7.53432i	1.27930	+	0.446295i
$286$	−5.02989	+	8.71203i	−0.297424	+	0.515153i
$287$	8.51153			0.502420
$288$	2.32366	+	1.89753i	0.136923	+	0.111813i
$289$	−8.44696	−	14.6306i	−0.496880	−	0.860622i
$290$	11.8678	−	6.95892i	0.696904	−	0.408642i
$291$	−19.8262	−	7.06673i	−1.16223	−	0.414259i
$292$	−7.91524	−	13.7096i	−0.463204	−	0.802294i
$293$	−16.3181	+	28.2638i	−0.953313	+	1.65119i	−0.215130	+	0.976585i	$0.569018\pi$
$293$	−16.3181	+	28.2638i	−0.953313	+	1.65119i	−0.738183	+	0.674601i	$0.764316\pi$
$294$	−9.67212	+	1.77206i	−0.564089	+	0.103349i
$295$	17.3704	−	0.117019i	1.01134	−	0.00681309i
$296$	2.70854	−	4.69134i	0.157431	−	0.272678i
$297$	10.7854	+	5.94240i	0.625832	+	0.344813i
$298$	20.5556	+	11.8678i	1.19075	+	0.687482i
$299$	−14.4087	+	8.31887i	−0.833277	+	0.481092i
$300$	5.69920	+	6.52066i	0.329044	+	0.376471i
$301$	−5.82220	+	3.36145i	−0.335586	+	0.193751i
$302$		−	8.61990i		−	0.496020i
$303$	−15.9126	−	5.67179i	−0.914155	−	0.325836i
$304$	2.95296	−	5.11467i	0.169364	−	0.293347i
$305$	−8.92336	−	15.2180i	−0.510950	−	0.871382i
$306$	0.346404	+	0.913622i	0.0198026	+	0.0522283i
$307$	8.09277	+	4.67236i	0.461879	+	0.266666i	0.712834	−	0.701333i	$-0.247411\pi$
$307$	8.09277	+	4.67236i	0.461879	+	0.266666i	−0.250955	+	0.967999i	$0.580745\pi$
$308$		−	2.72568i		−	0.155310i
$309$	0.891440	+	4.86558i	0.0507123	+	0.276793i
$310$	12.2993	−	1.93078i	0.698552	−	0.109661i
$311$			11.9460i			0.677393i	0.940896	+	0.338697i	$0.109986\pi$
$311$			11.9460i			0.677393i	−0.940896	+	0.338697i	$0.890014\pi$
$312$	−7.23202	+	1.32500i	−0.409432	+	0.0750136i
$313$	−5.17715	+	8.96708i	−0.292630	+	0.506849i	−0.974431	−	0.224688i	$-0.927864\pi$
$313$	−5.17715	+	8.96708i	−0.292630	+	0.506849i	0.681801	+	0.731538i	$0.261197\pi$
$314$			16.1601i			0.911970i
$315$	6.00876	+	4.83973i	0.338555	+	0.272688i
$316$	−1.66882	−	0.963496i	−0.0938787	−	0.0542009i
$317$	−17.1526	+	29.7092i	−0.963387	+	1.66864i	−0.249500	+	0.968375i	$0.580266\pi$
$317$	−17.1526	+	29.7092i	−0.963387	+	1.66864i	−0.713888	+	0.700260i	$0.753067\pi$
$318$	−2.14448	−	11.7048i	−0.120257	−	0.656373i
$319$	−7.29036	−	12.6273i	−0.408182	−	0.706991i
$320$	1.92892	−	1.13105i	0.107830	−	0.0632278i
$321$	18.1778	+	21.3722i	1.01458	+	1.19288i
$322$	2.25399	−	3.90402i	0.125610	−	0.217562i
$323$	1.66583	−	0.961767i	0.0926892	−	0.0535141i
$324$	1.79876	+	8.81842i	0.0999310	+	0.489912i
$325$	−21.2226	+	0.285953i	−1.17722	+	0.0158618i
$326$			15.1298i			0.837962i
$327$	−6.63333	+	18.6103i	−0.366824	+	1.02915i
$328$	6.40890	−	3.70018i	0.353872	−	0.204308i
$329$	−9.70625	−	5.60391i	−0.535123	−	0.308953i
$330$	6.95131	−	5.99348i	0.382657	−	0.329930i
$331$	15.4178	−	8.90148i	0.847440	−	0.489270i	−0.0123462	−	0.999924i	$-0.503930\pi$
$331$	15.4178	−	8.90148i	0.847440	−	0.489270i	0.859786	+	0.510654i	$0.170597\pi$
$332$	−4.70315	+	2.71537i	−0.258119	+	0.149025i
$333$	15.1957	−	5.76151i	0.832718	−	0.315729i
$334$	12.3209	+	7.11348i	0.674170	+	0.389232i
$335$	7.03236	−	12.3721i	0.384219	−	0.675962i
$336$	1.51748	−	1.29066i	0.0827852	−	0.0704114i
$337$	17.1276			0.932999			0.466500	−	0.884521i	$-0.345515\pi$
$337$	17.1276			0.932999			0.466500	+	0.884521i	$0.345515\pi$
$338$	2.50962	−	4.34679i	0.136505	−	0.236434i
$339$	−19.4347	+	3.56070i	−1.05555	+	0.193391i
$340$	0.728262	−	0.00490607i	0.0394956	−	0.000266069i
$341$	−1.95843	−	13.0486i	−0.106055	−	0.706621i
$342$	16.5669	−	6.28142i	0.895836	−	0.339660i
$343$			14.5806i			0.787281i
$344$	−2.92261	+	5.06211i	−0.157577	+	0.272931i
$345$	14.9127	−	2.83617i	0.802872	−	0.152694i
$346$	−1.11273	−	1.92730i	−0.0598205	−	0.103612i
$347$	−2.68079	−	1.54776i	−0.143912	−	0.0830879i	0.426315	−	0.904575i	$-0.359812\pi$
$347$	−2.68079	−	1.54776i	−0.143912	−	0.0830879i	−0.570227	+	0.821487i	$0.693145\pi$
$348$	3.57789	−	10.0380i	0.191795	−	0.538095i
$349$	5.53280			0.296164			0.148082	−	0.988975i	$-0.452690\pi$
$349$	5.53280			0.296164			0.148082	+	0.988975i	$0.452690\pi$
$350$	4.94111	−	2.94222i	0.264114	−	0.157268i
$351$	−19.3190	−	10.6441i	−1.03117	−	0.568141i
$352$	−1.18492	−	2.05235i	−0.0631566	−	0.109391i
$353$	−10.3291	−	5.96353i	−0.549765	−	0.317407i	0.199262	−	0.979946i	$-0.436145\pi$
$353$	−10.3291	−	5.96353i	−0.549765	−	0.317407i	−0.749027	+	0.662539i	$0.769479\pi$
$354$	10.2495	−	8.71750i	0.544753	−	0.463330i
$355$	7.53911	−	13.2637i	0.400134	−	0.703963i
$356$	6.10143			0.323375
$357$	0.638203	−	0.116928i	0.0337773	−	0.00618846i
$358$	−4.88016	+	8.45268i	−0.257924	+	0.446738i
$359$	6.38325	−	3.68537i	0.336895	−	0.194507i	−0.322003	−	0.946739i	$-0.604356\pi$
$359$	6.38325	−	3.68537i	0.336895	−	0.194507i	0.658898	+	0.752232i	$0.271023\pi$
$360$	6.62835	+	1.03200i	0.349345	+	0.0543910i
$361$	−7.93992	−	13.7523i	−0.417890	−	0.723807i
$362$	−2.88528	+	1.66582i	−0.151647	+	0.0875534i
$363$	6.04155	+	7.10326i	0.317099	+	0.372825i
$364$			4.88229i			0.255901i
$365$	−30.7741	−	17.4921i	−1.61079	−	0.915578i
$366$	−12.8717	−	4.58790i	−0.672813	−	0.239813i
$367$	−2.44646	−	4.23739i	−0.127704	−	0.221190i	0.795083	−	0.606501i	$-0.207427\pi$
$367$	−2.44646	−	4.23739i	−0.127704	−	0.221190i	−0.922787	+	0.385311i	$0.874094\pi$
$368$		−	3.91946i		−	0.204316i
$369$	21.9133	+	3.56313i	1.14076	+	0.185489i
$370$	−0.0815994	−	12.1127i	−0.00424215	−	0.629709i
$371$	−7.90185			−0.410243
$372$	6.33723	−	7.26908i	0.328570	−	0.376884i
$373$		−	25.5466i		−	1.32276i	−0.750053	−	0.661378i	$-0.769972\pi$
$373$		−	25.5466i		−	1.32276i	0.750053	−	0.661378i	$-0.230028\pi$
$374$		−	0.771850i		−	0.0399114i
$375$	18.3685	+	6.13171i	0.948546	+	0.316640i
$376$	−9.74464			−0.502541
$377$	13.0586	+	22.6182i	0.672552	+	1.16489i
$378$	5.97517	−	0.119597i	0.307329	−	0.00615143i
$379$	0.132403	−	0.229328i	0.00680108	−	0.0117798i	−0.862605	−	0.505878i	$-0.831168\pi$
$379$	0.132403	−	0.229328i	0.00680108	−	0.0117798i	0.869406	+	0.494099i	$0.164502\pi$
$380$	−0.0889628	−	13.2057i	−0.00456370	−	0.677440i
$381$	−13.9762	−	16.4323i	−0.716023	−	0.841853i
$382$	4.71452	−	2.72193i	0.241216	−	0.139266i
$383$	33.2231	−	19.1814i	1.69762	−	0.980122i	0.749612	−	0.661878i	$-0.230240\pi$
$383$	33.2231	−	19.1814i	1.69762	−	0.980122i	0.948009	−	0.318244i	$-0.103093\pi$
$384$	0.581525	−	1.63151i	0.0296758	−	0.0832577i
$385$	−3.08290	−	5.25762i	−0.157119	−	0.267953i
$386$	0.398168	+	0.229882i	0.0202662	+	0.0117007i
$387$	−16.3967	+	6.21687i	−0.833489	+	0.316021i
$388$			12.1521i			0.616927i
$389$	−7.96052	+	13.7880i	−0.403614	+	0.699080i	−0.994159	−	0.107924i	$-0.965580\pi$
$389$	−7.96052	+	13.7880i	−0.403614	+	0.699080i	0.590545	+	0.807005i	$0.298913\pi$
$390$	−12.4513	+	10.7356i	−0.630496	+	0.543620i
$391$	0.638276	−	1.10553i	0.0322790	−	0.0559089i
$392$	2.83858	+	4.91656i	0.143370	+	0.248324i
$393$	−17.1714	+	14.6049i	−0.866185	+	0.736718i
$394$	12.8639	−	7.42698i	0.648074	−	0.374166i
$395$	−4.30879	+	0.0290269i	−0.216799	+	0.00146050i
$396$	1.14104	−	7.01738i	0.0573393	−	0.352637i
$397$	16.2347	+	9.37313i	0.814798	+	0.470424i	0.848619	−	0.529004i	$-0.177434\pi$
$397$	16.2347	+	9.37313i	0.814798	+	0.470424i	−0.0338214	+	0.999428i	$0.510768\pi$
$398$	8.34879	−	4.82018i	0.418487	−	0.241614i
$399$	−2.12027	−	11.5727i	−0.106146	−	0.579358i
$400$	2.44143	−	4.36342i	0.122072	−	0.218171i
$401$	−7.69817			−0.384428			−0.192214	−	0.981353i	$-0.561567\pi$
$401$	−7.69817			−0.384428			−0.192214	+	0.981353i	$0.561567\pi$
$402$	−1.98656	−	10.8429i	−0.0990807	−	0.540793i
$403$	3.50798	+	23.3729i	0.174745	+	1.16429i
$404$			9.75329i			0.485244i
$405$	13.4438	+	14.9755i	0.668026	+	0.744138i
$406$	−6.12836	−	3.53821i	−0.304145	−	0.175598i
$407$	−12.8377			−0.636340
$408$	0.429714	−	0.365486i	0.0212740	−	0.0180942i
$409$	−1.71414	−	0.989662i	−0.0847590	−	0.0489356i	0.457021	−	0.889456i	$-0.348916\pi$
$409$	−1.71414	−	0.989662i	−0.0847590	−	0.0489356i	−0.541780	+	0.840520i	$0.682250\pi$
$410$	8.17712	−	14.3861i	0.403839	−	0.710481i
$411$	−1.45313	−	7.93135i	−0.0716777	−	0.391225i
$412$	2.47328	−	1.42795i	0.121850	−	0.0703501i
$413$	−4.46745	−	7.73784i	−0.219829	−	0.380754i
$414$	7.43729	−	9.10747i	0.365523	−	0.447608i
$415$	−6.00076	+	10.5572i	−0.294566	+	0.518234i
$416$	2.12245	+	3.67620i	0.104062	+	0.180240i
$417$	−22.1929	−	7.91029i	−1.08679	−	0.387368i
$418$	−13.9961			−0.684572
$419$		−	3.70987i		−	0.181239i	−0.995886	−	0.0906196i	$-0.971115\pi$
$419$		−	3.70987i		−	0.181239i	0.995886	−	0.0906196i	$-0.0288847\pi$
$420$	1.46728	−	4.20593i	0.0715958	−	0.205228i
$421$	2.92363	+	5.06387i	0.142489	+	0.246798i	0.928433	−	0.371499i	$-0.121156\pi$
$421$	2.92363	+	5.06387i	0.142489	+	0.246798i	−0.785944	+	0.618297i	$0.787823\pi$
$422$	11.6563	−	20.1893i	0.567419	−	0.982799i
$423$	−22.6432	−	18.4907i	−1.10095	−	0.899051i
$424$	−5.94982	+	3.43513i	−0.288949	+	0.166825i
$425$	1.39921	−	0.833167i	0.0678715	−	0.0404145i
$426$	−2.12971	−	11.6242i	−0.103185	−	0.563195i
$427$	−4.53702	+	7.85834i	−0.219562	+	0.380292i
$428$	8.09940	−	14.0286i	0.391499	−	0.678097i
$429$	11.2888	+	13.2726i	0.545026	+	0.640807i
$430$	0.0880486	+	13.0700i	0.00424608	+	0.630293i
$431$	−0.535714	−	0.309295i	−0.0258044	−	0.0148982i	0.487042	−	0.873378i	$-0.338076\pi$
$431$	−0.535714	−	0.309295i	−0.0258044	−	0.0148982i	−0.512847	+	0.858480i	$0.671409\pi$
$432$	4.44711	−	2.68761i	0.213962	−	0.129308i
$433$	−19.8014			−0.951597			−0.475798	−	0.879554i	$-0.657841\pi$
$433$	−19.8014			−0.951597			−0.475798	+	0.879554i	$0.657841\pi$
$434$	−3.98956	−	5.00916i	−0.191505	−	0.240448i
$435$	−4.45210	−	23.4093i	−0.213462	−	1.12239i
$436$	11.4068			0.546286
$437$	−20.0467	−	11.5740i	−0.958966	−	0.553659i
$438$	−26.9703	+	4.94132i	−1.28869	+	0.236105i
$439$	−17.6243	−	30.5262i	−0.841161	−	1.45693i	−0.888914	−	0.458075i	$-0.848539\pi$
$439$	−17.6243	−	30.5262i	−0.841161	−	1.45693i	0.0477523	−	0.998859i	$-0.484794\pi$
$440$	−4.60693	−	2.61859i	−0.219627	−	0.124837i
$441$	−2.73344	+	16.8107i	−0.130164	+	0.800508i
$442$			1.38255i			0.0657612i
$443$	10.2043	+	17.6744i	0.484822	+	0.839736i	0.999848	−	0.0174385i	$-0.00555114\pi$
$443$	10.2043	+	17.6744i	0.484822	+	0.839736i	−0.515026	+	0.857174i	$0.672218\pi$
$444$	−6.07888	−	7.14715i	−0.288491	−	0.339189i
$445$	11.7692	−	6.90105i	0.557911	−	0.327141i
$446$	3.51266	−	6.08411i	0.166329	−	0.288091i
$447$	31.3160	−	26.6353i	1.48120	−	1.25981i
$448$	−0.996061	−	0.575076i	−0.0470595	−	0.0271698i
$449$	32.2841			1.52358			0.761791	−	0.647823i	$-0.224320\pi$
$449$	32.2841			1.52358			0.761791	+	0.647823i	$0.224320\pi$
$450$	13.9528	−	5.50638i	0.657740	−	0.259573i
$451$	−15.1881	−	8.76885i	−0.715180	−	0.412909i
$452$	5.70370	+	9.87909i	0.268279	+	0.464673i
$453$	−14.0635	−	5.01269i	−0.660759	−	0.235517i
$454$	−1.06064	−	1.83708i	−0.0497783	−	0.0862186i
$455$	5.52213	+	9.41753i	0.258882	+	0.441500i
$456$	−6.62742	−	7.79210i	−0.310358	−	0.364898i
$457$	0.447328			0.0209251			0.0104626	−	0.999945i	$-0.496670\pi$
$457$	0.447328			0.0209251			0.0104626	+	0.999945i	$0.496670\pi$
$458$	16.2859	+	9.40267i	0.760991	+	0.439358i
$459$	1.69203	−	0.0338672i	0.0789771	−	0.00158079i
$460$	−4.43312	−	7.56030i	−0.206695	−	0.352501i
$461$	−5.05183			−0.235287			−0.117644	−	0.993056i	$-0.537534\pi$
$461$	−5.05183			−0.235287			−0.117644	+	0.993056i	$0.537534\pi$
$462$	−4.44698	−	1.58505i	−0.206892	−	0.0737434i
$463$	13.8424			0.643310			0.321655	−	0.946857i	$-0.395761\pi$
$463$	13.8424			0.643310			0.321655	+	0.946857i	$0.395761\pi$
$464$	−6.15260			−0.285627
$465$	4.00225	−	21.1892i	0.185600	−	0.982625i
$466$	−16.5941			−0.768705
$467$	−16.8843			−0.781315			−0.390657	−	0.920536i	$-0.627752\pi$
$467$	−16.8843			−0.781315			−0.390657	+	0.920536i	$0.627752\pi$
$468$	−2.04384	+	12.5696i	−0.0944767	+	0.581032i
$469$	−7.31995			−0.338004
$470$	−18.7966	+	11.0217i	−0.867022	+	0.508393i
$471$	26.3655	+	9.39754i	1.21486	+	0.433016i
$472$	−6.72767	−	3.88422i	−0.309666	−	0.178786i
$473$	13.8523			0.636929
$474$	−2.54242	+	2.16241i	−0.116777	+	0.0993227i
$475$	−15.1080	−	25.3721i	−0.693202	−	1.16415i
$476$	−0.187300	−	0.324413i	−0.00858488	−	0.0148695i
$477$	−20.3436	−	3.30790i	−0.931470	−	0.151458i
$478$	5.63430	+	9.75890i	0.257707	+	0.446362i
$479$	12.1074	+	6.99019i	0.553200	+	0.319390i	0.750412	−	0.660971i	$-0.229855\pi$
$479$	12.1074	+	6.99019i	0.553200	+	0.319390i	−0.197212	+	0.980361i	$0.563189\pi$
$480$	−0.723613	−	3.80478i	−0.0330283	−	0.173664i
$481$	22.9950			1.04848
$482$	−19.8736	−	11.4740i	−0.905216	−	0.522627i
$483$	−5.05870	−	5.94769i	−0.230179	−	0.270629i
$484$	2.69191	−	4.66253i	0.122360	−	0.211933i
$485$	13.7446	+	23.4403i	0.624111	+	1.06437i
$486$	15.4334	+	2.19344i	0.700072	+	0.0994965i
$487$	2.36047	+	4.08845i	0.106963	+	0.185265i	0.914538	−	0.404499i	$-0.132554\pi$
$487$	2.36047	+	4.08845i	0.106963	+	0.185265i	−0.807576	+	0.589764i	$0.799221\pi$
$488$			7.88942i			0.357137i
$489$	24.6844	+	8.79836i	1.11627	+	0.397876i
$490$	11.0363	+	6.27304i	0.498568	+	0.283387i
$491$	−5.00068	−	8.66143i	−0.225677	−	0.390885i	0.730845	−	0.682543i	$-0.239126\pi$
$491$	−5.00068	−	8.66143i	−0.225677	−	0.390885i	−0.956522	+	0.291659i	$0.905793\pi$
$492$	−2.30994	−	12.6079i	−0.104140	−	0.568409i
$493$	−1.73541	−	1.00194i	−0.0781588	−	0.0451250i
$494$	25.0701			1.12796
$495$	−5.73607	−	14.8265i	−0.257817	−	0.666402i
$496$	−5.18162	−	2.03737i	−0.232661	−	0.0914804i
$497$	−7.84743			−0.352005
$498$	1.69515	+	9.25230i	0.0759614	+	0.414605i
$499$	31.3741	+	18.1139i	1.40450	+	0.810888i	0.994850	−	0.101355i	$-0.0323177\pi$
$499$	31.3741	+	18.1139i	1.40450	+	0.810888i	0.409649	+	0.912243i	$0.365651\pi$
$500$	−0.225936	−	11.1781i	−0.0101042	−	0.499898i
$501$	18.7706	−	15.9650i	0.838610	−	0.713265i
$502$	8.16084	−	14.1350i	0.364236	−	0.630875i
$503$	0.284981	−	0.493601i	0.0127067	−	0.0220086i	−0.859602	−	0.510964i	$-0.829289\pi$
$503$	0.284981	−	0.493601i	0.0127067	−	0.0220086i	0.872309	+	0.488955i	$0.162622\pi$
$504$	−1.22328	−	3.22633i	−0.0544892	−	0.143712i
$505$	11.0315	+	18.8133i	0.490895	+	0.837180i
$506$	−8.04409	+	4.64426i	−0.357603	+	0.206462i
$507$	−5.63243	−	6.62225i	−0.250145	−	0.294104i
$508$	−6.22733	+	10.7860i	−0.276293	+	0.478553i
$509$	−10.3917	−	17.9989i	−0.460603	−	0.797788i	0.538388	−	0.842697i	$-0.319034\pi$
$509$	−10.3917	−	17.9989i	−0.460603	−	0.797788i	−0.998991	+	0.0449089i	$0.985700\pi$
$510$	0.415499	−	1.19102i	0.0183986	−	0.0527393i
$511$			18.2075i			0.805451i
$512$	−1.00000			−0.0441942
$513$	−0.614121	−	30.6819i	−0.0271141	−	1.35464i
$514$	1.66337	+	2.88103i	0.0733679	+	0.127077i
$515$	3.15567	−	5.55181i	0.139055	−	0.244642i
$516$	6.55932	+	7.71202i	0.288758	+	0.339503i
$517$	11.5466	+	19.9994i	0.507821	+	0.879572i
$518$	−5.39575	+	3.11524i	−0.237076	+	0.136876i
$519$	−3.79148	+	0.694652i	−0.166428	+	0.0304918i
$520$	8.25201	+	4.69047i	0.361875	+	0.205691i
$521$	21.4810	+	12.4021i	0.941102	+	0.543345i	0.890306	−	0.455364i	$-0.150491\pi$
$521$	21.4810	+	12.4021i	0.941102	+	0.543345i	0.0507962	+	0.998709i	$0.483824\pi$
$522$	−14.2965	−	11.6747i	−0.625742	−	0.510989i
$523$	−8.92818			−0.390402			−0.195201	−	0.980763i	$-0.562536\pi$
$523$	−8.92818			−0.390402			−0.195201	+	0.980763i	$0.562536\pi$
$524$	11.2712	+	6.50743i	0.492385	+	0.284279i
$525$	−1.92688	−	9.77245i	−0.0840958	−	0.426505i
$526$		−	3.51416i		−	0.153225i
$527$	−1.12975	−	1.41848i	−0.0492127	−	0.0617899i
$528$	−4.03749	+	0.739723i	−0.175709	+	0.0321923i
$529$	7.63786			0.332081
$530$	−7.59139	+	13.3556i	−0.329749	+	0.580132i
$531$	−8.26237	−	21.7916i	−0.358556	−	0.945673i
$532$	−5.88265	+	3.39635i	−0.255045	+	0.147250i
$533$	27.2052	+	15.7069i	1.17839	+	0.680342i
$534$	3.54814	−	9.95456i	0.153543	−	0.430776i
$535$	−0.244008	−	36.2208i	−0.0105494	−	1.56596i
$536$	−5.51167	+	3.18217i	−0.238068	+	0.137449i
$537$	10.9527	+	12.8775i	0.472644	+	0.555704i
$538$	14.5882	+	25.2676i	0.628944	+	1.08936i
$539$	6.72699	−	11.6515i	0.289752	−	0.501865i
$540$	5.53827	−	10.2141i	0.238329	−	0.439544i
$541$	20.8884	−	36.1798i	0.898062	−	1.55549i	0.0680933	−	0.997679i	$-0.478308\pi$
$541$	20.8884	−	36.1798i	0.898062	−	1.55549i	0.829969	−	0.557810i	$-0.188358\pi$
$542$		−	17.4293i		−	0.748654i
$543$	1.03993	+	5.67608i	0.0446279	+	0.243584i
$544$	−0.282061	−	0.162848i	−0.0120933	−	0.00698205i
$545$	22.0027	−	12.9017i	0.942493	−	0.552647i
$546$	7.96551	+	2.83918i	0.340892	+	0.121505i
$547$	−16.7262	+	9.65685i	−0.715159	+	0.412897i	−0.812968	−	0.582308i	$-0.802150\pi$
$547$	−16.7262	+	9.65685i	−0.715159	+	0.412897i	0.0978095	+	0.995205i	$0.468816\pi$
$548$	−4.03169	+	2.32769i	−0.172225	+	0.0994342i
$549$	−14.9704	+	18.3323i	−0.638922	+	0.782404i
$550$	−11.8482	+	0.159642i	−0.505207	+	0.00680715i
$551$	−18.1684	+	31.4685i	−0.773998	+	1.34060i
$552$	−6.39464	−	2.27926i	−0.272174	−	0.0970119i
$553$	1.10817	+	1.91940i	0.0471241	+	0.0816213i
$554$	3.05552			0.129817
$555$	−19.8095	−	6.91071i	−0.840865	−	0.293343i
$556$			13.6026i			0.576881i
$557$		−	5.32274i		−	0.225532i	−0.993622	−	0.112766i	$-0.964029\pi$
$557$		−	5.32274i		−	0.225532i	0.993622	−	0.112766i	$-0.0359710\pi$
$558$	−8.17433	−	14.5664i	−0.346047	−	0.616645i
$559$	−24.8125			−1.04945
$560$	−2.57176	+	0.0173251i	−0.108677	+	0.000732120i
$561$	−1.25928	−	0.448850i	−0.0531669	−	0.0189505i
$562$			13.7415i			0.579650i
$563$	15.2215	+	26.3644i	0.641510	+	1.11113i	0.985096	+	0.172006i	$0.0550249\pi$
$563$	15.2215	+	26.3644i	0.641510	+	1.11113i	−0.343586	+	0.939121i	$0.611642\pi$
$564$	−5.66675	+	15.8985i	−0.238613	+	0.669447i
$565$	22.1757	+	12.6047i	0.932940	+	0.530286i
$566$		−	5.87010i		−	0.246739i
$567$	3.27959	−	9.81810i	0.137730	−	0.412322i
$568$	−5.90885	+	3.41147i	−0.247930	+	0.143142i
$569$	20.1762	+	34.9463i	0.845832	+	1.46502i	0.884897	+	0.465787i	$0.154229\pi$
$569$	20.1762	+	34.9463i	0.845832	+	1.46502i	−0.0390654	+	0.999237i	$0.512438\pi$
$570$	−21.5970	−	7.53432i	−0.904600	−	0.315578i
$571$	25.4693	−	14.7047i	1.06586	−	0.615372i	0.138809	−	0.990319i	$-0.455673\pi$
$571$	25.4693	−	14.7047i	1.06586	−	0.615372i	0.927046	+	0.374948i	$0.122339\pi$
$572$	5.02989	−	8.71203i	0.210310	−	0.364268i
$573$	−1.69924	−	9.27465i	−0.0709869	−	0.387454i
$574$	−8.51153			−0.355265
$575$	−17.1022	−	9.56910i	−0.713212	−	0.399059i
$576$	−2.32366	−	1.89753i	−0.0968190	−	0.0790638i
$577$	9.45915	+	5.46124i	0.393790	+	0.227355i	0.683801	−	0.729669i	$-0.260326\pi$
$577$	9.45915	+	5.46124i	0.393790	+	0.227355i	−0.290011	+	0.957023i	$0.593659\pi$
$578$	8.44696	+	14.6306i	0.351347	+	0.608551i
$579$	0.606600	−	0.515933i	0.0252094	−	0.0214414i
$580$	−11.8678	+	6.95892i	−0.492785	+	0.288953i
$581$	6.24617			0.259135
$582$	19.8262	+	7.06673i	0.821823	+	0.292925i
$583$	14.1002	+	8.14074i	0.583969	+	0.337155i
$584$	7.91524	+	13.7096i	0.327535	+	0.567307i
$585$	10.2745	+	26.5575i	0.424800	+	1.09802i
$586$	16.3181	−	28.2638i	0.674094	−	1.16757i
$587$			26.1714i			1.08021i	0.841598	+	0.540104i	$0.181615\pi$
$587$			26.1714i			1.08021i	−0.841598	+	0.540104i	$0.818385\pi$
$588$	9.67212	−	1.77206i	0.398871	−	0.0730787i
$589$	−25.7216	+	20.4860i	−1.05984	+	0.844111i
$590$	−17.3704	+	0.117019i	−0.715127	+	0.00481759i
$591$	−4.63651	−	25.3066i	−0.190720	−	1.04097i
$592$	−2.70854	+	4.69134i	−0.111320	+	0.192813i
$593$	−4.63363			−0.190280			−0.0951402	−	0.995464i	$-0.530330\pi$
$593$	−4.63363			−0.190280			−0.0951402	+	0.995464i	$0.530330\pi$
$594$	−10.7854	−	5.94240i	−0.442530	−	0.243820i
$595$	−0.728215	−	0.413919i	−0.0298539	−	0.0169690i
$596$	−20.5556	−	11.8678i	−0.841990	−	0.486123i
$597$	−3.00914	−	16.4242i	−0.123156	−	0.672198i
$598$	14.4087	−	8.31887i	0.589216	−	0.340184i
$599$	20.4399	−	11.8010i	0.835152	−	0.482175i	−0.0204614	−	0.999791i	$-0.506514\pi$
$599$	20.4399	−	11.8010i	0.835152	−	0.482175i	0.855613	+	0.517615i	$0.173180\pi$
$600$	−5.69920	−	6.52066i	−0.232669	−	0.266205i
$601$	−11.3744	−	6.56699i	−0.463970	−	0.267873i	0.249742	−	0.968312i	$-0.419654\pi$
$601$	−11.3744	−	6.56699i	−0.463970	−	0.267873i	−0.713712	+	0.700439i	$0.752987\pi$
$602$	5.82220	−	3.36145i	0.237295	−	0.137002i
$603$	−18.8455	−	3.06431i	−0.767448	−	0.124788i
$604$			8.61990i			0.350739i
$605$	−0.0810984	−	12.0383i	−0.00329712	−	0.489427i
$606$	15.9126	+	5.67179i	0.646405	+	0.230401i
$607$	34.9531	−	20.1802i	1.41870	−	0.819088i	0.422516	−	0.906355i	$-0.361147\pi$
$607$	34.9531	−	20.1802i	1.41870	−	0.819088i	0.996185	+	0.0872676i	$0.0278135\pi$
$608$	−2.95296	+	5.11467i	−0.119758	+	0.207427i
$609$	−9.33642	+	7.94093i	−0.378331	+	0.321783i
$610$	8.92336	+	15.2180i	0.361296	+	0.616160i
$611$	−20.6825	−	35.8232i	−0.836726	−	1.44925i
$612$	−0.346404	−	0.913622i	−0.0140026	−	0.0369310i
$613$	−14.1359	+	24.4841i	−0.570944	+	0.988903i	0.425526	+	0.904946i	$0.360089\pi$
$613$	−14.1359	+	24.4841i	−0.570944	+	0.988903i	−0.996469	+	0.0839570i	$0.973244\pi$
$614$	−8.09277	−	4.67236i	−0.326597	−	0.188561i
$615$	−18.7159	−	21.7070i	−0.754699	−	0.875309i
$616$			2.72568i			0.109821i
$617$	−7.37685	+	12.7771i	−0.296981	+	0.514386i	−0.975444	−	0.220249i	$-0.929313\pi$
$617$	−7.37685	+	12.7771i	−0.296981	+	0.514386i	0.678463	+	0.734635i	$0.262646\pi$
$618$	−0.891440	−	4.86558i	−0.0358590	−	0.195722i
$619$		−	29.8573i		−	1.20007i	−0.799975	−	0.600033i	$-0.795154\pi$
$619$		−	29.8573i		−	1.20007i	0.799975	−	0.600033i	$-0.204846\pi$
$620$	−12.2993	+	1.93078i	−0.493951	+	0.0775419i
$621$	−10.5340	−	17.4302i	−0.422713	−	0.699452i
$622$		−	11.9460i		−	0.478989i
$623$	−6.07740	−	3.50879i	−0.243486	−	0.140577i
$624$	7.23202	−	1.32500i	0.289512	−	0.0530426i
$625$	−13.0788	−	21.3060i	−0.523152	−	0.852239i
$626$	5.17715	−	8.96708i	0.206920	−	0.358397i
$627$	−8.13910	+	22.8348i	−0.325044	+	0.911935i
$628$		−	16.1601i		−	0.644860i
$629$	−1.52795	+	0.882162i	−0.0609234	+	0.0351741i
$630$	−6.00876	−	4.83973i	−0.239395	−	0.192820i
$631$	28.4375	−	16.4184i	1.13208	−	0.653606i	0.187622	−	0.982241i	$-0.439922\pi$
$631$	28.4375	−	16.4184i	1.13208	−	0.653606i	0.944457	+	0.328636i	$0.106589\pi$
$632$	1.66882	+	0.963496i	0.0663823	+	0.0383258i
$633$	−26.1606	−	30.7579i	−1.03979	−	1.22252i
$634$	17.1526	−	29.7092i	0.681218	−	1.17990i
$635$	0.187609	+	27.8488i	0.00744502	+	1.10515i
$636$	2.14448	+	11.7048i	0.0850342	+	0.464126i
$637$	−12.0495	+	20.8703i	−0.477418	+	0.826913i
$638$	7.29036	+	12.6273i	0.288628	+	0.499918i
$639$	−20.2035	−	3.28512i	−0.799238	−	0.129957i
$640$	−1.92892	+	1.13105i	−0.0762471	+	0.0447088i
$641$	15.4302	+	26.7259i	0.609456	+	1.05561i	0.991330	+	0.131395i	$0.0419456\pi$
$641$	15.4302	+	26.7259i	0.609456	+	1.05561i	−0.381874	+	0.924214i	$0.624721\pi$
$642$	−18.1778	−	21.3722i	−0.717419	−	0.843495i
$643$	38.0016			1.49864			0.749318	−	0.662210i	$-0.230381\pi$
$643$	38.0016			1.49864			0.749318	+	0.662210i	$0.230381\pi$
$644$	−2.25399	+	3.90402i	−0.0888195	+	0.153840i
$645$	21.3751	+	7.45690i	0.841644	+	0.293615i
$646$	−1.66583	+	0.961767i	−0.0655412	+	0.0378402i
$647$		−	48.3294i		−	1.90003i	−0.312209	−	0.950013i	$-0.601069\pi$
$647$		−	48.3294i		−	1.90003i	0.312209	−	0.950013i	$-0.398931\pi$
$648$	−1.79876	−	8.81842i	−0.0706619	−	0.346420i
$649$			18.4100i			0.722657i
$650$	21.2226	−	0.285953i	0.832419	−	0.0112160i
$651$	−10.4925	+	3.59606i	−0.411235	+	0.140941i
$652$		−	15.1298i		−	0.592528i
$653$	6.14945			0.240647			0.120323	−	0.992735i	$-0.461607\pi$
$653$	6.14945			0.240647			0.120323	+	0.992735i	$0.461607\pi$
$654$	6.63333	−	18.6103i	0.259384	−	0.727720i
$655$	29.1015	−	0.196047i	1.13709	−	0.00766021i
$656$	−6.40890	+	3.70018i	−0.250225	+	0.144468i
$657$	−7.62208	+	46.8758i	−0.297366	+	1.82880i
$658$	9.70625	+	5.60391i	0.378389	+	0.218463i
$659$			5.11790i			0.199365i	0.995019	+	0.0996825i	$0.0317827\pi$
$659$			5.11790i			0.199365i	−0.995019	+	0.0996825i	$0.968217\pi$
$660$	−6.95131	+	5.99348i	−0.270580	+	0.233296i
$661$	−0.623086	−	1.07922i	−0.0242353	−	0.0419767i	0.853653	−	0.520841i	$-0.174382\pi$
$661$	−0.623086	−	1.07922i	−0.0242353	−	0.0419767i	−0.877889	+	0.478865i	$0.841048\pi$
$662$	−15.4178	+	8.90148i	−0.599231	+	0.345966i
$663$	2.25565	+	0.803988i	0.0876020	+	0.0312243i
$664$	4.70315	−	2.71537i	0.182518	−	0.105377i
$665$	−7.50569	+	13.2049i	−0.291058	+	0.512063i
$666$	−15.1957	+	5.76151i	−0.588821	+	0.223254i
$667$			24.1148i			0.933730i
$668$	−12.3209	−	7.11348i	−0.476710	−	0.275229i
$669$	−7.88358	−	9.26901i	−0.304797	−	0.358360i
$670$	−7.03236	+	12.3721i	−0.271684	+	0.477977i
$671$	16.1918	−	9.34836i	0.625079	−	0.360890i
$672$	−1.51748	+	1.29066i	−0.0585380	+	0.0497884i
$673$	9.47126	+	16.4047i	0.365090	+	0.632355i	0.988791	−	0.149309i	$-0.0477048\pi$
$673$	9.47126	+	16.4047i	0.365090	+	0.632355i	−0.623700	+	0.781663i	$0.714371\pi$
$674$	−17.1276			−0.659730
$675$	−0.869836	−	25.9662i	−0.0334800	−	0.999439i
$676$	−2.50962	+	4.34679i	−0.0965239	+	0.167184i
$677$	19.0799	−	11.0158i	0.733299	−	0.423370i	−0.0863292	−	0.996267i	$-0.527514\pi$
$677$	19.0799	−	11.0158i	0.733299	−	0.423370i	0.819628	+	0.572897i	$0.194180\pi$
$678$	19.4347	−	3.56070i	0.746385	−	0.136748i
$679$	6.98835	−	12.1042i	0.268188	−	0.464516i
$680$	−0.728262	+	0.00490607i	−0.0279276	+	0.000188139i
$681$	−3.61401	+	0.662136i	−0.138489	+	0.0253731i
$682$	1.95843	+	13.0486i	0.0749923	+	0.499657i
$683$	−15.0523			−0.575960			−0.287980	−	0.957636i	$-0.592984\pi$
$683$	−15.0523			−0.575960			−0.287980	+	0.957636i	$0.592984\pi$
$684$	−16.5669	+	6.28142i	−0.633451	+	0.240176i
$685$	−5.14403	+	9.04998i	−0.196543	+	0.345782i
$686$		−	14.5806i		−	0.556692i
$687$	24.8112	−	21.1027i	0.946608	−	0.805120i
$688$	2.92261	−	5.06211i	0.111424	−	0.192991i
$689$	−25.2564	−	14.5818i	−0.962194	−	0.555523i
$690$	−14.9127	+	2.83617i	−0.567716	+	0.107971i
$691$	7.32478	+	12.6869i	0.278648	+	0.482632i	0.971049	−	0.238881i	$-0.0767805\pi$
$691$	7.32478	+	12.6869i	0.278648	+	0.482632i	−0.692401	+	0.721513i	$0.743447\pi$
$692$	1.11273	+	1.92730i	0.0422995	+	0.0732648i
$693$	−5.17207	+	6.33355i	−0.196471	+	0.240592i
$694$	2.68079	+	1.54776i	0.101761	+	0.0587520i
$695$	15.3853	+	26.2384i	0.583599	+	0.995278i
$696$	−3.57789	+	10.0380i	−0.135620	+	0.380490i
$697$	−2.41027			−0.0912954
$698$	−5.53280			−0.209419
$699$	−9.64987	+	27.0734i	−0.364991	+	1.02401i
$700$	−4.94111	+	2.94222i	−0.186757	+	0.111205i
$701$	6.92391	+	3.99752i	0.261513	+	0.150984i	0.625024	−	0.780605i	$-0.285089\pi$
$701$	6.92391	+	3.99752i	0.261513	+	0.150984i	−0.363512	+	0.931590i	$0.618422\pi$
$702$	19.3190	+	10.6441i	0.729147	+	0.401736i
$703$	15.9964	+	27.7066i	0.603317	+	1.04498i
$704$	1.18492	+	2.05235i	0.0446585	+	0.0773508i
$705$	7.05135	+	37.0762i	0.265569	+	1.39637i
$706$	10.3291	+	5.96353i	0.388742	+	0.224441i
$707$	5.60888	−	9.71487i	0.210944	−	0.365365i
$708$	−10.2495	+	8.71750i	−0.385198	+	0.327624i
$709$			15.2414i			0.572404i	0.958169	+	0.286202i	$0.0923928\pi$
$709$			15.2414i			0.572404i	−0.958169	+	0.286202i	$0.907607\pi$
$710$	−7.53911	+	13.2637i	−0.282938	+	0.497777i
$711$	2.04951	+	5.40548i	0.0768627	+	0.202721i
$712$	−6.10143			−0.228661
$713$	−7.98537	+	20.3091i	−0.299054	+	0.760582i
$714$	−0.638203	+	0.116928i	−0.0238842	+	0.00437590i
$715$	−0.151534	−	22.4938i	−0.00566705	−	0.841222i
$716$	4.88016	−	8.45268i	0.182380	−	0.315891i
$717$	19.1982	−	3.51738i	0.716971	−	0.131359i
$718$	−6.38325	+	3.68537i	−0.238221	+	0.137537i
$719$	−22.2214	+	38.4886i	−0.828718	+	1.43538i	0.0703260	+	0.997524i	$0.477596\pi$
$719$	−22.2214	+	38.4886i	−0.828718	+	1.43538i	−0.899044	+	0.437858i	$0.855737\pi$
$720$	−6.62835	−	1.03200i	−0.247024	−	0.0384602i
$721$	−3.28472			−0.122329
$722$	7.93992	+	13.7523i	0.295493	+	0.511809i
$723$	−30.2770	+	25.7515i	−1.12601	+	0.957709i
$724$	2.88528	−	1.66582i	0.107231	−	0.0619096i
$725$	−15.0212	+	26.8463i	−0.557872	+	0.997048i
$726$	−6.04155	−	7.10326i	−0.224223	−	0.263627i
$727$	15.5130	+	8.95646i	0.575347	+	0.332177i	0.759282	−	0.650762i	$-0.225550\pi$
$727$	15.5130	+	8.95646i	0.575347	+	0.332177i	−0.183935	+	0.982938i	$0.558884\pi$
$728$		−	4.88229i		−	0.180950i
$729$	12.5535	−	23.9042i	0.464945	−	0.885340i
$730$	30.7741	+	17.4921i	1.13900	+	0.647412i
$731$	1.64871	−	0.951884i	0.0609798	−	0.0352067i
$732$	12.8717	+	4.58790i	0.475751	+	0.169574i
$733$	33.6135	−	19.4068i	1.24154	−	0.716805i	0.272135	−	0.962259i	$-0.412270\pi$
$733$	33.6135	−	19.4068i	1.24154	−	0.716805i	0.969408	+	0.245454i	$0.0789370\pi$
$734$	2.44646	+	4.23739i	0.0903004	+	0.156405i
$735$	16.6524	−	14.3579i	0.614233	−	0.529597i
$736$			3.91946i			0.144473i
$737$	13.0618	+	7.54125i	0.481139	+	0.277785i
$738$	−21.9133	−	3.56313i	−0.806639	−	0.131161i
$739$	−26.1751	+	15.1122i	−0.962868	+	0.555912i	−0.897054	−	0.441920i	$-0.854297\pi$
$739$	−26.1751	+	15.1122i	−0.962868	+	0.555912i	−0.0658132	+	0.997832i	$0.520964\pi$
$740$	0.0815994	+	12.1127i	0.00299966	+	0.445272i
$741$	14.5789	−	40.9021i	0.535569	−	1.50258i
$742$	7.90185			0.290086
$743$			14.3870i			0.527807i	0.964549	+	0.263904i	$0.0850101\pi$
$743$			14.3870i			0.527807i	−0.964549	+	0.263904i	$0.914990\pi$
$744$	−6.33723	+	7.26908i	−0.232334	+	0.266497i
$745$	−53.0731	+	0.357537i	−1.94445	+	0.0130991i
$746$			25.5466i			0.935329i
$747$	16.0810	+	2.61480i	0.588373	+	0.0956704i
$748$			0.771850i			0.0282216i
$749$	−16.1350	+	9.31554i	−0.589560	+	0.340383i
$750$	−18.3685	−	6.13171i	−0.670723	−	0.223898i
$751$	−17.8664	+	30.9455i	−0.651954	+	1.12922i	0.330694	+	0.943738i	$0.392717\pi$
$751$	−17.8664	+	30.9455i	−0.651954	+	1.12922i	−0.982648	+	0.185480i	$0.940616\pi$
$752$	9.74464			0.355350
$753$	−18.3157	−	21.5344i	−0.667460	−	0.784756i
$754$	−13.0586	−	22.6182i	−0.475566	−	0.823705i
$755$	9.74957	+	16.6271i	0.354823	+	0.605121i
$756$	−5.97517	+	0.119597i	−0.217315	+	0.00434972i
$757$	13.4198	+	23.2438i	0.487751	+	0.844810i	0.999901	−	0.0140863i	$-0.00448397\pi$
$757$	13.4198	+	23.2438i	0.487751	+	0.844810i	−0.512150	+	0.858896i	$0.671151\pi$
$758$	−0.132403	+	0.229328i	−0.00480909	+	0.00832958i
$759$	2.89931	+	15.8248i	0.105238	+	0.574403i
$760$	0.0889628	+	13.2057i	0.00322702	+	0.479022i
$761$	18.3229	−	31.7361i	0.664203	−	1.15043i	−0.315298	−	0.948993i	$-0.602104\pi$
$761$	18.3229	−	31.7361i	0.664203	−	1.15043i	0.979501	−	0.201441i	$-0.0645623\pi$
$762$	13.9762	+	16.4323i	0.506304	+	0.595280i
$763$	−11.3618	−	6.55976i	−0.411326	−	0.237479i
$764$	−4.71452	+	2.72193i	−0.170565	+	0.0984758i
$765$	−1.70154	−	1.37050i	−0.0615193	−	0.0495505i
$766$	−33.2231	+	19.1814i	−1.20040	+	0.693051i
$767$		−	32.9763i		−	1.19071i
$768$	−0.581525	+	1.63151i	−0.0209840	+	0.0588721i
$769$	2.03601	−	3.52648i	0.0734205	−	0.127168i	−0.826978	−	0.562235i	$-0.809942\pi$
$769$	2.03601	−	3.52648i	0.0734205	−	0.127168i	0.900398	+	0.435067i	$0.143275\pi$
$770$	3.08290	+	5.25762i	0.111100	+	0.189471i
$771$	5.66773	−	1.03840i	0.204118	−	0.0373972i
$772$	−0.398168	−	0.229882i	−0.0143304	−	0.00827365i
$773$			37.5422i			1.35030i	0.737681	+	0.675149i	$0.235921\pi$
$773$			37.5422i			1.35030i	−0.737681	+	0.675149i	$0.764079\pi$
$774$	16.3967	−	6.21687i	0.589366	−	0.223461i
$775$	−21.5404	+	17.6354i	−0.773756	+	0.633484i
$776$		−	12.1521i		−	0.436233i
$777$	1.94478	+	10.6148i	0.0697685	+	0.380804i
$778$	7.96052	−	13.7880i	0.285398	−	0.494324i
$779$			43.7059i			1.56593i
$780$	12.4513	−	10.7356i	0.445828	−	0.384397i
$781$	14.0031	+	8.08467i	0.501069	+	0.289292i
$782$	−0.638276	+	1.10553i	−0.0228247	+	0.0395335i
$783$	−27.3612	+	16.5358i	−0.977811	+	0.590940i
$784$	−2.83858	−	4.91656i	−0.101378	−	0.175591i
$785$	−18.2780	−	31.1716i	−0.652370	−	1.11256i
$786$	17.1714	−	14.6049i	0.612485	−	0.520938i
$787$	10.7430	−	18.6075i	0.382948	−	0.663286i	−0.608534	−	0.793528i	$-0.708242\pi$
$787$	10.7430	−	18.6075i	0.382948	−	0.663286i	0.991482	+	0.130242i	$0.0415755\pi$
$788$	−12.8639	+	7.42698i	−0.458258	+	0.264575i
$789$	−5.73339	−	2.04357i	−0.204114	−	0.0727532i
$790$	4.30879	−	0.0290269i	0.153300	−	0.00103273i
$791$		−	13.1202i		−	0.466502i
$792$	−1.14104	+	7.01738i	−0.0405450	+	0.249352i
$793$	−29.0031	+	16.7449i	−1.02993	+	0.594630i
$794$	−16.2347	−	9.37313i	−0.576149	−	0.332640i
$795$	17.3753	+	20.1521i	0.616238	+	0.714721i
$796$	−8.34879	+	4.82018i	−0.295915	+	0.170847i
$797$	17.7187	−	10.2299i	0.627628	−	0.362361i	−0.152205	−	0.988349i	$-0.548637\pi$
$797$	17.7187	−	10.2299i	0.627628	−	0.362361i	0.779833	+	0.625988i	$0.215304\pi$
$798$	2.12027	+	11.5727i	0.0750568	+	0.409668i
$799$	2.74858	+	1.58690i	0.0972379	+	0.0561403i
$800$	−2.44143	+	4.36342i	−0.0863177	+	0.154270i
$801$	−14.1776	−	11.5777i	−0.500942	−	0.409076i
$802$	7.69817			0.271832
$803$	18.7579	−	32.4897i	0.661952	−	1.14653i
$804$	1.98656	+	10.8429i	0.0700606	+	0.382399i
$805$	0.0679051	+	10.0799i	0.00239334	+	0.355270i
$806$	−3.50798	−	23.3729i	−0.123563	−	0.823274i
$807$	49.7078	−	9.10714i	1.74980	−	0.320587i
$808$		−	9.75329i		−	0.343120i
$809$	6.68909	−	11.5858i	0.235176	−	0.407337i	−0.724148	−	0.689645i	$-0.757767\pi$
$809$	6.68909	−	11.5858i	0.235176	−	0.407337i	0.959324	+	0.282308i	$0.0911000\pi$
$810$	−13.4438	−	14.9755i	−0.472365	−	0.526185i
$811$	12.3459	+	21.3837i	0.433524	+	0.750885i	0.997174	−	0.0751287i	$-0.0239368\pi$
$811$	12.3459	+	21.3837i	0.433524	+	0.750885i	−0.563650	+	0.826014i	$0.690603\pi$
$812$	6.12836	+	3.53821i	0.215063	+	0.124167i
$813$	−28.4362	−	10.1356i	−0.997299	−	0.355471i
$814$	12.8377			0.449960
$815$	−17.1126	−	29.1841i	−0.599429	−	1.02227i
$816$	−0.429714	+	0.365486i	−0.0150430	+	0.0127946i
$817$	−17.2607	−	29.8964i	−0.603876	−	1.04594i
$818$	1.71414	+	0.989662i	0.0599337	+	0.0346027i
$819$	9.26429	−	11.3448i	0.323721	−	0.396418i
$820$	−8.17712	+	14.3861i	−0.285557	+	0.502386i
$821$	−20.6876			−0.722004			−0.361002	−	0.932565i	$-0.617565\pi$
$821$	−20.6876			−0.722004			−0.361002	+	0.932565i	$0.617565\pi$
$822$	1.45313	+	7.93135i	0.0506838	+	0.276638i
$823$	6.00138	−	10.3947i	0.209195	−	0.362337i	−0.742266	−	0.670105i	$-0.766249\pi$
$823$	6.00138	−	10.3947i	0.209195	−	0.362337i	0.951461	+	0.307769i	$0.0995823\pi$
$824$	−2.47328	+	1.42795i	−0.0861609	+	0.0497450i
$825$	−6.62955	+	19.4232i	−0.230811	+	0.676230i
$826$	4.46745	+	7.73784i	0.155442	+	0.269234i
$827$	−48.4395	+	27.9666i	−1.68441	+	0.972493i	−0.725738	+	0.687971i	$0.758502\pi$
$827$	−48.4395	+	27.9666i	−1.68441	+	0.972493i	−0.958669	+	0.284522i	$0.908165\pi$
$828$	−7.43729	+	9.10747i	−0.258464	+	0.316506i
$829$			33.5302i			1.16455i	0.812991	+	0.582277i	$0.197838\pi$
$829$			33.5302i			1.16455i	−0.812991	+	0.582277i	$0.802162\pi$
$830$	6.00076	−	10.5572i	0.208289	−	0.366447i
$831$	1.77686	−	4.98512i	0.0616387	−	0.172932i
$832$	−2.12245	−	3.67620i	−0.0735829	−	0.127449i
$833$		−	1.84903i		−	0.0640650i
$834$	22.1929	+	7.91029i	0.768476	+	0.273911i
$835$	−31.8117	+	0.214306i	−1.10089	+	0.00741635i
$836$	13.9961			0.484066
$837$	−28.5188	+	4.86577i	−0.985755	+	0.168186i
$838$			3.70987i			0.128155i
$839$		−	7.25474i		−	0.250462i	−0.992128	−	0.125231i	$-0.960033\pi$
$839$		−	7.25474i		−	0.250462i	0.992128	−	0.125231i	$-0.0399671\pi$
$840$	−1.46728	+	4.20593i	−0.0506259	+	0.145118i
$841$	8.85443			0.305325
$842$	−2.92363	−	5.06387i	−0.100755	−	0.174512i
$843$	22.4194	+	7.99103i	0.772165	+	0.275226i
$844$	−11.6563	+	20.1893i	−0.401226	+	0.694944i
$845$	0.0756066	+	11.2231i	0.00260095	+	0.386087i
$846$	22.6432	+	18.4907i	0.778489	+	0.635725i
$847$	−5.36262	+	3.09611i	−0.184262	+	0.106384i
$848$	5.94982	−	3.43513i	0.204318	−	0.117963i
$849$	−9.57713	−	3.41361i	−0.328686	−	0.117155i
$850$	−1.39921	+	0.833167i	−0.0479924	+	0.0285774i
$851$	18.3875	+	10.6160i	0.630315	+	0.363912i
$852$	2.12971	+	11.6242i	0.0729628	+	0.398239i
$853$		−	36.3991i		−	1.24628i	−0.782109	−	0.623141i	$-0.785856\pi$
$853$		−	36.3991i		−	1.24628i	0.782109	−	0.623141i	$-0.214144\pi$
$854$	4.53702	−	7.85834i	0.155254	−	0.268907i
$855$	−24.8516	+	30.8544i	−0.849905	+	1.05520i
$856$	−8.09940	+	14.0286i	−0.276832	+	0.479487i
$857$	−28.8592	−	49.9856i	−0.985811	−	1.70748i	−0.638274	−	0.769809i	$-0.720351\pi$
$857$	−28.8592	−	49.9856i	−0.985811	−	1.70748i	−0.347537	−	0.937666i	$-0.612982\pi$
$858$	−11.2888	−	13.2726i	−0.385392	−	0.453119i
$859$	−29.8935	+	17.2590i	−1.01995	+	0.588870i	−0.914090	−	0.405511i	$-0.867094\pi$
$859$	−29.8935	+	17.2590i	−1.01995	+	0.588870i	−0.105862	+	0.994381i	$0.533760\pi$
$860$	−0.0880486	−	13.0700i	−0.00300243	−	0.445684i
$861$	−4.94967	+	13.8867i	−0.168684	+	0.473256i
$862$	0.535714	+	0.309295i	0.0182465	+	0.0105346i
$863$	12.1829	−	7.03381i	0.414711	−	0.239434i	−0.278101	−	0.960552i	$-0.589705\pi$
$863$	12.1829	−	7.03381i	0.414711	−	0.239434i	0.692812	+	0.721118i	$0.256372\pi$
$864$	−4.44711	+	2.68761i	−0.151294	+	0.0914343i
$865$	4.32623	+	2.45904i	0.147096	+	0.0836099i
$866$	19.8014			0.672880
$867$	28.7821	−	5.27326i	0.977490	−	0.179089i
$868$	3.98956	+	5.00916i	0.135415	+	0.170022i
$869$		−	4.56668i		−	0.154914i
$870$	4.45210	+	23.4093i	0.150940	+	0.793650i
$871$	−23.3966	−	13.5080i	−0.792762	−	0.457701i
$872$	−11.4068			−0.386282
$873$	23.0589	−	28.2372i	0.780425	−	0.955684i
$874$	20.0467	+	11.5740i	0.678091	+	0.391496i
$875$	−6.20319	+	11.2640i	−0.209706	+	0.380791i
$876$	26.9703	−	4.94132i	0.911241	−	0.166952i
$877$	−21.8930	+	12.6399i	−0.739274	+	0.426820i	−0.821805	−	0.569768i	$-0.807033\pi$
$877$	−21.8930	+	12.6399i	−0.739274	+	0.426820i	0.0825311	+	0.996588i	$0.473700\pi$
$878$	17.6243	+	30.5262i	0.594791	+	1.03021i
$879$	−36.6232	−	43.0592i	−1.23527	−	1.45235i
$880$	4.60693	+	2.61859i	0.155300	+	0.0882728i
$881$	−28.8559	−	49.9798i	−0.972179	−	1.68386i	−0.688947	−	0.724812i	$-0.741927\pi$
$881$	−28.8559	−	49.9798i	−0.972179	−	1.68386i	−0.283232	−	0.959051i	$-0.591407\pi$
$882$	2.73344	−	16.8107i	0.0920398	−	0.566045i
$883$	−33.2470			−1.11885			−0.559425	−	0.828881i	$-0.688978\pi$
$883$	−33.2470			−1.11885			−0.559425	+	0.828881i	$0.688978\pi$
$884$		−	1.38255i		−	0.0465002i
$885$	−9.91040	+	28.4080i	−0.333134	+	0.954925i
$886$	−10.2043	−	17.6744i	−0.342821	−	0.593783i
$887$	8.24124	−	14.2742i	0.276714	−	0.479282i	−0.693852	−	0.720117i	$-0.744088\pi$
$887$	8.24124	−	14.2742i	0.276714	−	0.479282i	0.970566	+	0.240835i	$0.0774213\pi$
$888$	6.07888	+	7.14715i	0.203994	+	0.239843i
$889$	12.4056	−	7.16237i	0.416070	−	0.240218i
$890$	−11.7692	+	6.90105i	−0.394503	+	0.231324i
$891$	−15.9671	+	14.1408i	−0.534917	+	0.473736i
$892$	−3.51266	+	6.08411i	−0.117613	+	0.203711i
$893$	28.7755	−	49.8406i	0.962935	−	1.66785i
$894$	−31.3160	+	26.6353i	−1.04736	+	0.890817i
$895$	−0.147023	−	21.8242i	−0.00491443	−	0.729504i
$896$	0.996061	+	0.575076i	0.0332761	+	0.0192119i
$897$	−5.19330	−	28.3456i	−0.173399	−	0.946432i
$898$	−32.2841			−1.07734
$899$	31.8804	+	12.5351i	1.06327	+	0.418069i
$900$	−13.9528	+	5.50638i	−0.465092	+	0.183546i
$901$	2.23762			0.0745459
$902$	15.1881	+	8.76885i	0.505708	+	0.291971i
$903$	−2.09848	−	11.4538i	−0.0698332	−	0.381157i
$904$	−5.70370	−	9.87909i	−0.189702	−	0.328574i
$905$	3.68133	−	6.47662i	0.122372	−	0.215290i
$906$	14.0635	+	5.01269i	0.467227	+	0.166536i
$907$			43.5648i			1.44655i	0.690562	+	0.723274i	$0.257363\pi$
$907$			43.5648i			1.44655i	−0.690562	+	0.723274i	$0.742637\pi$
$908$	1.06064	+	1.83708i	0.0351986	+	0.0609657i
$909$	18.5072	−	22.6633i	0.613844	−	0.751694i
$910$	−5.52213	−	9.41753i	−0.183057	−	0.312188i
$911$	−0.529754	+	0.917560i	−0.0175515	+	0.0304001i	−0.874668	−	0.484723i	$-0.838920\pi$
$911$	−0.529754	+	0.917560i	−0.0175515	+	0.0304001i	0.857116	+	0.515123i	$0.172254\pi$
$912$	6.62742	+	7.79210i	0.219456	+	0.258022i
$913$	−11.1458	−	6.43500i	−0.368871	−	0.212967i
$914$	−0.447328			−0.0147963
$915$	30.0176	−	5.70889i	0.992350	−	0.188730i
$916$	−16.2859	−	9.40267i	−0.538102	−	0.310673i
$917$	−7.48454	−	12.9636i	−0.247161	−	0.428096i
$918$	−1.69203	+	0.0338672i	−0.0558452	+	0.00111778i
$919$	−9.67021	−	16.7493i	−0.318991	−	0.552508i	0.661287	−	0.750133i	$-0.270011\pi$
$919$	−9.67021	−	16.7493i	−0.318991	−	0.552508i	−0.980278	+	0.197625i	$0.936677\pi$
$920$	4.43312	+	7.56030i	0.146156	+	0.249256i
$921$	−12.3292	+	10.4863i	−0.406260	+	0.345537i
$922$	5.05183			0.166373
$923$	−25.0825	−	14.4814i	−0.825601	−	0.476661i
$924$	4.44698	+	1.58505i	0.146295	+	0.0521445i
$925$	13.8575	+	23.2721i	0.455632	+	0.765182i
$926$	−13.8424			−0.454889
$927$	−8.45664	−	1.37506i	−0.277752	−	0.0451630i
$928$	6.15260			0.201969
$929$	−6.90820			−0.226651			−0.113325	−	0.993558i	$-0.536150\pi$
$929$	−6.90820			−0.226651			−0.113325	+	0.993558i	$0.536150\pi$
$930$	−4.00225	+	21.1892i	−0.131239	+	0.694821i
$931$	−33.5288			−1.09886
$932$	16.5941			0.543556
$933$	−19.4900	−	6.94688i	−0.638073	−	0.227431i
$934$	16.8843			0.552473
$935$	0.873004	+	1.48883i	0.0285503	+	0.0486901i
$936$	2.04384	−	12.5696i	0.0668051	−	0.410852i
$937$	−9.60104	−	5.54316i	−0.313652	−	0.181087i	0.334907	−	0.942251i	$-0.391295\pi$
$937$	−9.60104	−	5.54316i	−0.313652	−	0.181087i	−0.648560	+	0.761164i	$0.724628\pi$
$938$	7.31995			0.239005
$939$	−11.6192	−	13.6612i	−0.379180	−	0.445815i
$940$	18.7966	−	11.0217i	0.613077	−	0.359488i
$941$	−5.61701	−	9.72894i	−0.183109	−	0.317154i	0.759829	−	0.650124i	$-0.225283\pi$
$941$	−5.61701	−	9.72894i	−0.183109	−	0.317154i	−0.942938	+	0.332969i	$0.891950\pi$
$942$	−26.3655	−	9.39754i	−0.859033	−	0.306188i
$943$	14.5027	+	25.1194i	0.472272	+	0.818000i
$944$	6.72767	+	3.88422i	0.218967	+	0.126421i
$945$	−11.3903	+	6.98893i	−0.370527	+	0.227350i
$946$	−13.8523			−0.450377
$947$	35.7758	+	20.6552i	1.16256	+	0.671203i	0.951916	−	0.306360i	$-0.0991113\pi$
$947$	35.7758	+	20.6552i	1.16256	+	0.671203i	0.210642	+	0.977563i	$0.432445\pi$
$948$	2.54242	−	2.16241i	0.0825739	−	0.0702318i
$949$	−33.5995	+	58.1960i	−1.09068	+	1.88912i
$950$	15.1080	+	25.3721i	0.490168	+	0.823180i
$951$	−38.4962	−	45.2613i	−1.24833	−	1.46770i
$952$	0.187300	+	0.324413i	0.00607043	+	0.0105143i
$953$		−	1.55758i		−	0.0504550i	−0.999682	−	0.0252275i	$-0.991969\pi$
$953$		−	1.55758i		−	0.0504550i	0.999682	−	0.0252275i	$-0.00803101\pi$
$954$	20.3436	+	3.30790i	0.658649	+	0.107097i
$955$	−6.01526	+	10.5827i	−0.194649	+	0.342449i
$956$	−5.63430	−	9.75890i	−0.182226	−	0.315625i
$957$	24.8410	−	4.55122i	0.802997	−	0.147120i
$958$	−12.1074	−	6.99019i	−0.391171	−	0.225843i
$959$	5.35440			0.172903
$960$	0.723613	+	3.80478i	0.0233545	+	0.122799i
$961$	22.6983	+	21.1137i	0.732203	+	0.681087i
$962$	−22.9950			−0.741390
$963$	−45.4399	+	17.2287i	−1.46428	+	0.555188i
$964$	19.8736	+	11.4740i	0.640085	+	0.369553i
$965$	−1.02804	+	0.00692559i	−0.0330938	+	0.000222943i
$966$	5.05870	+	5.94769i	0.162761	+	0.191364i
$967$	12.5116	−	21.6708i	0.402347	−	0.696885i	−0.591662	−	0.806186i	$-0.701528\pi$
$967$	12.5116	−	21.6708i	0.402347	−	0.696885i	0.994009	+	0.109301i	$0.0348614\pi$
$968$	−2.69191	+	4.66253i	−0.0865213	+	0.149859i
$969$	0.600411	+	3.27711i	0.0192880	+	0.105276i
$970$	−13.7446	−	23.4403i	−0.441313	−	0.752622i
$971$	48.1883	−	27.8215i	1.54644	−	0.892836i	0.548028	−	0.836460i	$-0.315379\pi$
$971$	48.1883	−	27.8215i	1.54644	−	0.892836i	0.998410	−	0.0563756i	$-0.0179544\pi$
$972$	−15.4334	−	2.19344i	−0.495025	−	0.0703546i
$973$	7.82256	−	13.5491i	0.250780	−	0.434363i
$974$	−2.36047	−	4.08845i	−0.0756342	−	0.131002i
$975$	11.8750	−	34.7912i	0.380303	−	1.11421i
$976$		−	7.88942i		−	0.252534i
$977$	58.0437			1.85698			0.928491	−	0.371356i	$-0.121107\pi$
$977$	58.0437			1.85698			0.928491	+	0.371356i	$0.121107\pi$
$978$	−24.6844	−	8.79836i	−0.789321	−	0.281340i
$979$	7.22973	+	12.5223i	0.231063	+	0.400213i
$980$	−11.0363	−	6.27304i	−0.352541	−	0.200385i
$981$	−26.5054	−	21.6447i	−0.846253	−	0.691062i
$982$	5.00068	+	8.66143i	0.159578	+	0.276397i
$983$	16.8719	−	9.74099i	0.538130	−	0.310689i	−0.206191	−	0.978512i	$-0.566107\pi$
$983$	16.8719	−	9.74099i	0.538130	−	0.310689i	0.744321	+	0.667822i	$0.232773\pi$
$984$	2.30994	+	12.6079i	0.0736383	+	0.401926i
$985$	−16.4131	+	28.8758i	−0.522964	+	0.920059i
$986$	1.73541	+	1.00194i	0.0552666	+	0.0319082i
$987$	14.7873	−	12.5770i	0.470684	−	0.400332i
$988$	−25.0701			−0.797585
$989$	−19.8407	−	11.4551i	−0.630899	−	0.364250i
$990$	5.73607	+	14.8265i	0.182304	+	0.471217i
$991$			8.39172i			0.266572i	0.991078	+	0.133286i	$0.0425528\pi$
$991$			8.39172i			0.266572i	−0.991078	+	0.133286i	$0.957447\pi$
$992$	5.18162	+	2.03737i	0.164516	+	0.0646864i
$993$	5.55701	+	30.3308i	0.176346	+	0.962518i
$994$	7.84743			0.248905
$995$	−10.6522	+	18.7407i	−0.337699	+	0.594119i
$996$	−1.69515	−	9.25230i	−0.0537128	−	0.293170i
$997$	−53.4544	+	30.8619i	−1.69292	+	0.977407i	−0.740775	+	0.671753i	$0.765542\pi$
$997$	−53.4544	+	30.8619i	−1.69292	+	0.977407i	−0.952143	+	0.305654i	$0.901125\pi$
$998$	−31.3741	−	18.1139i	−0.993131	−	0.573385i
$999$	0.563291	+	28.1424i	0.0178217	+	0.890385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.a.119.12	✓	64
3.2	odd	2		930.2.r.b.119.9	yes	64
5.4	even	2		930.2.r.b.119.21	yes	64
15.14	odd	2	inner	930.2.r.a.119.24	yes	64
31.6	odd	6	inner	930.2.r.a.719.24	yes	64
93.68	even	6		930.2.r.b.719.21	yes	64
155.99	odd	6		930.2.r.b.719.9	yes	64
465.254	even	6	inner	930.2.r.a.719.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.12	✓	64	1.1	even	1	trivial
930.2.r.a.119.24	yes	64	15.14	odd	2	inner
930.2.r.a.719.12	yes	64	465.254	even	6	inner
930.2.r.a.719.24	yes	64	31.6	odd	6	inner
930.2.r.b.119.9	yes	64	3.2	odd	2
930.2.r.b.119.21	yes	64	5.4	even	2
930.2.r.b.719.9	yes	64	155.99	odd	6
930.2.r.b.719.21	yes	64	93.68	even	6

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.581525 + 1.63151i) q^{3} +1.00000 q^{4} +(1.92892 - 1.13105i) q^{5} +(0.581525 - 1.63151i) q^{6} +(-0.996061 - 0.575076i) q^{7} -1.00000 q^{8} +(-2.32366 - 1.89753i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.581525 + 1.63151i) q^{3} +1.00000 q^{4} +(1.92892 - 1.13105i) q^{5} +(0.581525 - 1.63151i) q^{6} +(-0.996061 - 0.575076i) q^{7} -1.00000 q^{8} +(-2.32366 - 1.89753i) q^{9} +(-1.92892 + 1.13105i) q^{10} +(1.18492 + 2.05235i) q^{11} +(-0.581525 + 1.63151i) q^{12} +(-2.12245 - 3.67620i) q^{13} +(0.996061 + 0.575076i) q^{14} +(0.723613 + 3.80478i) q^{15} +1.00000 q^{16} +(0.282061 + 0.162848i) q^{17} +(2.32366 + 1.89753i) q^{18} +(2.95296 - 5.11467i) q^{19} +(1.92892 - 1.13105i) q^{20} +(1.51748 - 1.29066i) q^{21} +(-1.18492 - 2.05235i) q^{22} -3.91946i q^{23} +(0.581525 - 1.63151i) q^{24} +(2.44143 - 4.36342i) q^{25} +(2.12245 + 3.67620i) q^{26} +(4.44711 - 2.68761i) q^{27} +(-0.996061 - 0.575076i) q^{28} -6.15260 q^{29} +(-0.723613 - 3.80478i) q^{30} +(-5.18162 - 2.03737i) q^{31} -1.00000 q^{32} +(-4.03749 + 0.739723i) q^{33} +(-0.282061 - 0.162848i) q^{34} +(-2.57176 + 0.0173251i) q^{35} +(-2.32366 - 1.89753i) q^{36} +(-2.70854 + 4.69134i) q^{37} +(-2.95296 + 5.11467i) q^{38} +(7.23202 - 1.32500i) q^{39} +(-1.92892 + 1.13105i) q^{40} +(-6.40890 + 3.70018i) q^{41} +(-1.51748 + 1.29066i) q^{42} +(2.92261 - 5.06211i) q^{43} +(1.18492 + 2.05235i) q^{44} +(-6.62835 - 1.03200i) q^{45} +3.91946i q^{46} +9.74464 q^{47} +(-0.581525 + 1.63151i) q^{48} +(-2.83858 - 4.91656i) q^{49} +(-2.44143 + 4.36342i) q^{50} +(-0.429714 + 0.365486i) q^{51} +(-2.12245 - 3.67620i) q^{52} +(5.94982 - 3.43513i) q^{53} +(-4.44711 + 2.68761i) q^{54} +(4.60693 + 2.61859i) q^{55} +(0.996061 + 0.575076i) q^{56} +(6.62742 + 7.79210i) q^{57} +6.15260 q^{58} +(6.72767 + 3.88422i) q^{59} +(0.723613 + 3.80478i) q^{60} -7.88942i q^{61} +(5.18162 + 2.03737i) q^{62} +(1.22328 + 3.22633i) q^{63} +1.00000 q^{64} +(-8.25201 - 4.69047i) q^{65} +(4.03749 - 0.739723i) q^{66} +(5.51167 - 3.18217i) q^{67} +(0.282061 + 0.162848i) q^{68} +(6.39464 + 2.27926i) q^{69} +(2.57176 - 0.0173251i) q^{70} +(5.90885 - 3.41147i) q^{71} +(2.32366 + 1.89753i) q^{72} +(-7.91524 - 13.7096i) q^{73} +(2.70854 - 4.69134i) q^{74} +(5.69920 + 6.52066i) q^{75} +(2.95296 - 5.11467i) q^{76} -2.72568i q^{77} +(-7.23202 + 1.32500i) q^{78} +(-1.66882 - 0.963496i) q^{79} +(1.92892 - 1.13105i) q^{80} +(1.79876 + 8.81842i) q^{81} +(6.40890 - 3.70018i) q^{82} +(-4.70315 + 2.71537i) q^{83} +(1.51748 - 1.29066i) q^{84} +(0.728262 - 0.00490607i) q^{85} +(-2.92261 + 5.06211i) q^{86} +(3.57789 - 10.0380i) q^{87} +(-1.18492 - 2.05235i) q^{88} +6.10143 q^{89} +(6.62835 + 1.03200i) q^{90} +4.88229i q^{91} -3.91946i q^{92} +(6.33723 - 7.26908i) q^{93} -9.74464 q^{94} +(-0.0889628 - 13.2057i) q^{95} +(0.581525 - 1.63151i) q^{96} +12.1521i q^{97} +(2.83858 + 4.91656i) q^{98} +(1.14104 - 7.01738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more