LMFDB - Embedded newform 930.2.be.b.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.08483 + 0.808396i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.0488226 + 0.182208i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.08483 + 0.808396i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.0488226 + 0.182208i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.04582 - 0.902572i) q^{10} +(-5.38881 - 3.11123i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.35977 - 0.364350i) q^{13} +(-0.163364 + 0.0943180i) q^{14} +(-0.241258 - 2.22301i) q^{15} -1.00000 q^{16} +(6.65872 + 1.78420i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-5.32398 + 3.07380i) q^{19} +(-0.808396 - 2.08483i) q^{20} +(-0.163364 - 0.0943180i) q^{21} +(-1.61049 - 6.01044i) q^{22} +(-6.32132 - 6.32132i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.69299 - 3.37073i) q^{25} +(1.21914 + 0.703869i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.182208 - 0.0488226i) q^{28} -7.80882 q^{29} +(1.40131 - 1.74250i) q^{30} +(4.39001 - 3.42459i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.39995 - 4.39995i) q^{33} +(3.44680 + 5.97004i) q^{34} +(-0.0455100 - 0.419341i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.10501 - 1.09993i) q^{37} +(-5.93813 - 1.59112i) q^{38} +1.40774i q^{39} +(0.902572 - 2.04582i) q^{40} +(0.781646 - 1.35385i) q^{41} +(-0.0488226 - 0.182208i) q^{42} +(-0.471798 + 1.76077i) q^{43} +(3.11123 - 5.38881i) q^{44} +(2.20971 + 0.342321i) q^{45} -8.93969i q^{46} +(-1.40611 - 1.40611i) q^{47} +(0.258819 - 0.965926i) q^{48} +(6.03136 + 3.48221i) q^{49} +(4.99480 + 0.227875i) q^{50} +(-3.44680 + 5.97004i) q^{51} +(0.364350 + 1.35977i) q^{52} +(-0.133993 + 0.0359033i) q^{53} +1.00000 q^{54} +(13.7498 + 2.13008i) q^{55} +(-0.0943180 - 0.163364i) q^{56} +(-1.59112 - 5.93813i) q^{57} +(-5.52167 - 5.52167i) q^{58} +(0.717723 - 0.414378i) q^{59} +(2.22301 - 0.241258i) q^{60} +10.5848i q^{61} +(5.52576 + 0.682652i) q^{62} +(0.133386 - 0.133386i) q^{63} -1.00000i q^{64} +(-2.54035 + 1.85884i) q^{65} +6.22247 q^{66} +(-3.81463 + 1.02213i) q^{67} +(-1.78420 + 6.65872i) q^{68} +(7.74200 - 4.46985i) q^{69} +(0.264338 - 0.328699i) q^{70} +(3.11180 - 5.38980i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-14.8216 + 3.97143i) q^{73} +(-2.12491 - 3.68045i) q^{74} +(2.30006 + 4.43957i) q^{75} +(-3.07380 - 5.32398i) q^{76} +(0.829989 - 0.829989i) q^{77} +(-0.995422 + 0.995422i) q^{78} +(-1.50657 - 2.60946i) q^{79} +(2.08483 - 0.808396i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.51002 - 0.404610i) q^{82} +(-14.9953 + 4.01797i) q^{83} +(0.0943180 - 0.163364i) q^{84} +(-15.3246 + 1.66314i) q^{85} +(-1.57867 + 0.911443i) q^{86} +(2.02107 - 7.54274i) q^{87} +(6.01044 - 1.61049i) q^{88} -5.85821 q^{89} +(1.32044 + 1.80456i) q^{90} +0.265550i q^{91} +(6.32132 - 6.32132i) q^{92} +(2.17168 + 5.12677i) q^{93} -1.98853i q^{94} +(8.61472 - 10.7122i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-11.8573 - 11.8573i) q^{97} +(1.80252 + 6.72711i) q^{98} +(3.11123 + 5.38881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−2.08483	+	0.808396i	−0.932362	+	0.361526i
$5$	−2.08483	+	0.808396i	−0.932362	+	0.361526i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.0488226	+	0.182208i	−0.0184532	+	0.0688683i	−0.974538	−	0.224220i	$-0.928016\pi$
$7$	−0.0488226	+	0.182208i	−0.0184532	+	0.0688683i	0.956085	+	0.293089i	$0.0946831\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−2.04582	−	0.902572i	−0.646944	−	0.285418i
$11$	−5.38881	−	3.11123i	−1.62479	−	0.938072i	−0.985614	−	0.169010i	$-0.945943\pi$
$11$	−5.38881	−	3.11123i	−1.62479	−	0.938072i	−0.639174	−	0.769062i	$-0.720724\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	1.35977	−	0.364350i	0.377133	−	0.101052i	−0.0652730	−	0.997867i	$-0.520792\pi$
$13$	1.35977	−	0.364350i	0.377133	−	0.101052i	0.442406	+	0.896815i	$0.354125\pi$
$14$	−0.163364	+	0.0943180i	−0.0436608	+	0.0252076i
$15$	−0.241258	−	2.22301i	−0.0622926	−	0.573980i
$16$	−1.00000			−0.250000
$17$	6.65872	+	1.78420i	1.61498	+	0.432731i	0.949520	−	0.313706i	$-0.101571\pi$
$17$	6.65872	+	1.78420i	1.61498	+	0.432731i	0.665456	+	0.746437i	$0.268237\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−5.32398	+	3.07380i	−1.22141	+	0.705179i	−0.965217	−	0.261449i	$-0.915800\pi$
$19$	−5.32398	+	3.07380i	−1.22141	+	0.705179i	−0.256188	+	0.966627i	$0.582466\pi$
$20$	−0.808396	−	2.08483i	−0.180763	−	0.466181i
$21$	−0.163364	−	0.0943180i	−0.0356489	−	0.0205819i
$22$	−1.61049	−	6.01044i	−0.343358	−	1.28143i
$23$	−6.32132	−	6.32132i	−1.31809	−	1.31809i	−0.915290	−	0.402797i	$-0.868038\pi$
$23$	−6.32132	−	6.32132i	−1.31809	−	1.31809i	−0.402797	−	0.915290i	$-0.631962\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	3.69299	−	3.37073i	0.738598	−	0.674146i
$26$	1.21914	+	0.703869i	0.239093	+	0.138040i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.182208	−	0.0488226i	−0.0344342	−	0.00922661i
$29$	−7.80882			−1.45006			−0.725030	−	0.688717i	$-0.758174\pi$
$29$	−7.80882			−1.45006			−0.725030	+	0.688717i	$0.758174\pi$
$30$	1.40131	−	1.74250i	0.255844	−	0.318136i
$31$	4.39001	−	3.42459i	0.788469	−	0.615075i
$31$	4.39001	−	3.42459i	0.788469	−	0.615075i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.39995	−	4.39995i	0.765933	−	0.765933i
$34$	3.44680	+	5.97004i	0.591122	+	1.02385i
$35$	−0.0455100	−	0.419341i	−0.00769259	−	0.0708815i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−4.10501	−	1.09993i	−0.674860	−	0.180828i	−0.0949167	−	0.995485i	$-0.530258\pi$
$37$	−4.10501	−	1.09993i	−0.674860	−	0.180828i	−0.579943	+	0.814657i	$0.696925\pi$
$38$	−5.93813	−	1.59112i	−0.963292	−	0.258113i
$39$			1.40774i			0.225419i
$40$	0.902572	−	2.04582i	0.142709	−	0.323472i
$41$	0.781646	−	1.35385i	0.122073	−	0.211436i	−0.798512	−	0.601979i	$-0.794379\pi$
$41$	0.781646	−	1.35385i	0.122073	−	0.211436i	0.920585	+	0.390543i	$0.127713\pi$
$42$	−0.0488226	−	0.182208i	−0.00753349	−	0.0281154i
$43$	−0.471798	+	1.76077i	−0.0719484	+	0.268515i	−0.992524	−	0.122049i	$-0.961053\pi$
$43$	−0.471798	+	1.76077i	−0.0719484	+	0.268515i	0.920576	+	0.390564i	$0.127720\pi$
$44$	3.11123	−	5.38881i	0.469036	−	0.812394i
$45$	2.20971	+	0.342321i	0.329404	+	0.0510302i
$46$		−	8.93969i		−	1.31809i
$47$	−1.40611	−	1.40611i	−0.205102	−	0.205102i	0.597080	−	0.802182i	$-0.296327\pi$
$47$	−1.40611	−	1.40611i	−0.205102	−	0.205102i	−0.802182	+	0.597080i	$0.796327\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	6.03136	+	3.48221i	0.861623	+	0.497458i
$50$	4.99480	+	0.227875i	0.706372	+	0.0322264i
$51$	−3.44680	+	5.97004i	−0.482649	+	0.835973i
$52$	0.364350	+	1.35977i	0.0505262	+	0.188566i
$53$	−0.133993	+	0.0359033i	−0.0184053	+	0.00493169i	−0.268010	−	0.963416i	$-0.586366\pi$
$53$	−0.133993	+	0.0359033i	−0.0184053	+	0.00493169i	0.249605	+	0.968348i	$0.419699\pi$
$54$	1.00000			0.136083
$55$	13.7498	+	2.13008i	1.85403	+	0.287220i
$56$	−0.0943180	−	0.163364i	−0.0126038	−	0.0218304i
$57$	−1.59112	−	5.93813i	−0.210749	−	0.786524i
$58$	−5.52167	−	5.52167i	−0.725030	−	0.725030i
$59$	0.717723	−	0.414378i	0.0934396	−	0.0539474i	−0.452552	−	0.891738i	$-0.649486\pi$
$59$	0.717723	−	0.414378i	0.0934396	−	0.0539474i	0.545992	+	0.837791i	$0.316153\pi$
$60$	2.22301	−	0.241258i	0.286990	−	0.0311463i
$61$			10.5848i			1.35524i	0.735412	+	0.677620i	$0.236989\pi$
$61$			10.5848i			1.35524i	−0.735412	+	0.677620i	$0.763011\pi$
$62$	5.52576	+	0.682652i	0.701772	+	0.0866969i
$63$	0.133386	−	0.133386i	0.0168050	−	0.0168050i
$64$		−	1.00000i		−	0.125000i
$65$	−2.54035	+	1.85884i	−0.315091	+	0.230561i
$66$	6.22247			0.765933
$67$	−3.81463	+	1.02213i	−0.466031	+	0.124873i	−0.484191	−	0.874963i	$-0.660886\pi$
$67$	−3.81463	+	1.02213i	−0.466031	+	0.124873i	0.0181598	+	0.999835i	$0.494219\pi$
$68$	−1.78420	+	6.65872i	−0.216366	+	0.807488i
$69$	7.74200	−	4.46985i	0.932028	−	0.538106i
$70$	0.264338	−	0.328699i	0.0315945	−	0.0392871i
$71$	3.11180	−	5.38980i	0.369303	−	0.639652i	−0.620154	−	0.784480i	$-0.712930\pi$
$71$	3.11180	−	5.38980i	0.369303	−	0.639652i	0.989457	+	0.144829i	$0.0462631\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−14.8216	+	3.97143i	−1.73474	+	0.464821i	−0.981266	−	0.192660i	$-0.938289\pi$
$73$	−14.8216	+	3.97143i	−1.73474	+	0.464821i	−0.753471	+	0.657481i	$0.771622\pi$
$74$	−2.12491	−	3.68045i	−0.247016	−	0.427844i
$75$	2.30006	+	4.43957i	0.265588	+	0.512637i
$76$	−3.07380	−	5.32398i	−0.352589	−	0.610703i
$77$	0.829989	−	0.829989i	0.0945860	−	0.0945860i
$78$	−0.995422	+	0.995422i	−0.112709	+	0.112709i
$79$	−1.50657	−	2.60946i	−0.169503	−	0.293587i	0.768742	−	0.639558i	$-0.220883\pi$
$79$	−1.50657	−	2.60946i	−0.169503	−	0.293587i	−0.938245	+	0.345971i	$0.887549\pi$
$80$	2.08483	−	0.808396i	0.233091	−	0.0903814i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.51002	−	0.404610i	0.166754	−	0.0446817i
$83$	−14.9953	+	4.01797i	−1.64595	+	0.441030i	−0.958474	−	0.285181i	$-0.907946\pi$
$83$	−14.9953	+	4.01797i	−1.64595	+	0.441030i	−0.687472	+	0.726211i	$0.741280\pi$
$84$	0.0943180	−	0.163364i	0.0102909	−	0.0178244i
$85$	−15.3246	+	1.66314i	−1.66219	+	0.180393i
$86$	−1.57867	+	0.911443i	−0.170232	+	0.0982834i
$87$	2.02107	−	7.54274i	0.216682	−	0.808666i
$88$	6.01044	−	1.61049i	0.640715	−	0.171679i
$89$	−5.85821			−0.620969			−0.310484	−	0.950578i	$-0.600491\pi$
$89$	−5.85821			−0.620969			−0.310484	+	0.950578i	$0.600491\pi$
$90$	1.32044	+	1.80456i	0.139187	+	0.190217i
$91$			0.265550i			0.0278372i
$92$	6.32132	−	6.32132i	0.659043	−	0.659043i
$93$	2.17168	+	5.12677i	0.225193	+	0.531621i
$94$		−	1.98853i		−	0.205102i
$95$	8.61472	−	10.7122i	0.883852	−	1.09905i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−11.8573	−	11.8573i	−1.20393	−	1.20393i	−0.972961	−	0.230970i	$-0.925810\pi$
$97$	−11.8573	−	11.8573i	−1.20393	−	1.20393i	−0.230970	−	0.972961i	$-0.574190\pi$
$98$	1.80252	+	6.72711i	0.182082	+	0.679541i
$99$	3.11123	+	5.38881i	0.312691	+	0.541596i
$100$	3.37073	+	3.69299i	0.337073	+	0.369299i
$101$	−1.86845			−0.185918			−0.0929590	−	0.995670i	$-0.529633\pi$
$101$	−1.86845			−0.185918			−0.0929590	+	0.995670i	$0.529633\pi$
$102$	−6.65872	+	1.78420i	−0.659311	+	0.176662i
$103$	3.52661	+	13.1615i	0.347487	+	1.29684i	0.889680	+	0.456585i	$0.150927\pi$
$103$	3.52661	+	13.1615i	0.347487	+	1.29684i	−0.542193	+	0.840254i	$0.682406\pi$
$104$	−0.703869	+	1.21914i	−0.0690201	+	0.119546i
$105$	0.416831	+	0.0645741i	0.0406785	+	0.00630179i
$106$	−0.120135	−	0.0693598i	−0.0116685	−	0.00673682i
$107$	0.376471	−	1.40501i	0.0363948	−	0.135827i	−0.945338	−	0.326092i	$-0.894268\pi$
$107$	0.376471	−	1.40501i	0.0363948	−	0.135827i	0.981733	+	0.190265i	$0.0609347\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	10.3806i		−	0.994285i	−0.867669	−	0.497142i	$-0.834383\pi$
$109$		−	10.3806i		−	0.994285i	0.867669	−	0.497142i	$-0.165617\pi$
$110$	8.21641	+	11.2288i	0.783404	+	1.07062i
$111$	2.12491	−	3.68045i	0.201688	−	0.349333i
$112$	0.0488226	−	0.182208i	0.00461330	−	0.0172171i
$113$	3.81922	+	14.2535i	0.359282	+	1.34086i	0.875009	+	0.484106i	$0.160855\pi$
$113$	3.81922	+	14.2535i	0.359282	+	1.34086i	−0.515727	+	0.856753i	$0.672478\pi$
$114$	3.07380	−	5.32398i	0.287888	−	0.498637i
$115$	18.2890	+	8.06872i	1.70546	+	0.752412i
$116$		−	7.80882i		−	0.725030i
$117$	−1.35977	−	0.364350i	−0.125711	−	0.0336841i
$118$	0.800516	+	0.214498i	0.0736935	+	0.0197461i
$119$	−0.650192	+	1.12617i	−0.0596030	+	0.103235i
$120$	1.74250	+	1.40131i	0.159068	+	0.127922i
$121$	13.8595	+	24.0054i	1.25996	+	2.18231i
$122$	−7.48456	+	7.48456i	−0.677620	+	0.677620i
$123$	1.10541	+	1.10541i	0.0996719	+	0.0996719i
$124$	3.42459	+	4.39001i	0.307537	+	0.394234i
$125$	−4.97436	+	10.0128i	−0.444920	+	0.895570i
$126$	0.188636			0.0168050
$127$	−0.446194	−	0.119557i	−0.0395933	−	0.0106090i	0.238968	−	0.971027i	$-0.423191\pi$
$127$	−0.446194	−	0.119557i	−0.0395933	−	0.0106090i	−0.278561	+	0.960418i	$0.589858\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.57867	−	0.911443i	−0.138994	−	0.0802481i
$130$	−3.11069	−	0.481899i	−0.272826	−	0.0422653i
$131$	3.09020	+	5.35238i	0.269992	+	0.467639i	0.968859	−	0.247612i	$-0.0796457\pi$
$131$	3.09020	+	5.35238i	0.269992	+	0.467639i	−0.698868	+	0.715251i	$0.746312\pi$
$132$	4.39995	+	4.39995i	0.382966	+	0.382966i
$133$	−0.300142	−	1.12015i	−0.0260256	−	0.0971289i
$134$	−3.42010	−	1.97460i	−0.295452	−	0.170579i
$135$	−0.902572	+	2.04582i	−0.0776810	+	0.176076i
$136$	−5.97004	+	3.44680i	−0.511927	+	0.295561i
$137$	−1.66367	−	6.20889i	−0.142137	−	0.530461i	−0.999866	−	0.0163600i	$-0.994792\pi$
$137$	−1.66367	−	6.20889i	−0.142137	−	0.530461i	0.857729	−	0.514101i	$-0.171874\pi$
$138$	8.63508	+	2.31376i	0.735067	+	0.196961i
$139$	−0.244065			−0.0207013			−0.0103507	−	0.999946i	$-0.503295\pi$
$139$	−0.244065			−0.0207013			−0.0103507	+	0.999946i	$0.503295\pi$
$140$	0.419341	−	0.0455100i	0.0354408	−	0.00384629i
$141$	1.72212	−	0.994267i	0.145029	−	0.0837324i
$142$	6.01154	−	1.61079i	0.504477	−	0.135174i
$143$	−8.46113	−	2.26715i	−0.707555	−	0.189589i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	16.2800	−	6.31262i	1.35198	−	0.524234i
$146$	−13.2887	−	7.67222i	−1.09978	−	0.634958i
$147$	−4.92459	+	4.92459i	−0.406173	+	0.406173i
$148$	1.09993	−	4.10501i	0.0904140	−	0.337430i
$149$	−14.8665	+	8.58317i	−1.21791	+	0.703161i	−0.964471	−	0.264190i	$-0.914895\pi$
$149$	−14.8665	+	8.58317i	−1.21791	+	0.703161i	−0.253440	+	0.967351i	$0.581562\pi$
$150$	−1.51286	+	4.76563i	−0.123525	+	0.389112i
$151$			3.07386i			0.250147i	0.992147	+	0.125073i	$0.0399167\pi$
$151$			3.07386i			0.250147i	−0.992147	+	0.125073i	$0.960083\pi$
$152$	1.59112	−	5.93813i	0.129057	−	0.481646i
$153$	−4.87452	−	4.87452i	−0.394081	−	0.394081i
$154$	1.17378			0.0945860
$155$	−6.38397	+	10.6885i	−0.512773	+	0.858524i
$156$	−1.40774			−0.112709
$157$	11.4349	+	11.4349i	0.912602	+	0.912602i	0.996476	−	0.0838739i	$-0.0267293\pi$
$157$	11.4349	+	11.4349i	0.912602	+	0.912602i	−0.0838739	+	0.996476i	$0.526729\pi$
$158$	0.779859	−	2.91047i	0.0620423	−	0.231545i
$159$		−	0.138720i		−	0.0110012i
$160$	2.04582	+	0.902572i	0.161736	+	0.0713546i
$161$	1.46042	−	0.843175i	0.115097	−	0.0664515i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	7.20110	−	7.20110i	0.564034	−	0.564034i	−0.366417	−	0.930451i	$-0.619416\pi$
$163$	7.20110	−	7.20110i	0.564034	−	0.564034i	0.930451	+	0.366417i	$0.119416\pi$
$164$	1.35385	+	0.781646i	0.105718	+	0.0610363i
$165$	−5.61622	+	12.7300i	−0.437222	+	0.991031i
$166$	−13.4444	−	7.76213i	−1.04349	−	0.602458i
$167$	−11.0768	−	2.96801i	−0.857147	−	0.229672i	−0.196625	−	0.980479i	$-0.562998\pi$
$167$	−11.0768	−	2.96801i	−0.857147	−	0.229672i	−0.660522	+	0.750807i	$0.729665\pi$
$168$	0.182208	−	0.0488226i	0.0140577	−	0.00376675i
$169$	−9.54210	+	5.50914i	−0.734008	+	0.423780i
$170$	−12.0121	−	9.66011i	−0.921289	−	0.740897i
$171$	6.14760			0.470119
$172$	−1.76077	−	0.471798i	−0.134258	−	0.0359742i
$173$	−3.16909	−	11.8272i	−0.240941	−	0.899205i	−0.975380	−	0.220530i	$-0.929221\pi$
$173$	−3.16909	−	11.8272i	−0.240941	−	0.899205i	0.734439	−	0.678675i	$-0.237445\pi$
$174$	6.76263	−	3.90441i	0.512674	−	0.295992i
$175$	0.433874	+	0.837462i	0.0327978	+	0.0633062i
$176$	5.38881	+	3.11123i	0.406197	+	0.234518i
$177$	0.214498	+	0.800516i	0.0161226	+	0.0601705i
$178$	−4.14238	−	4.14238i	−0.310484	−	0.310484i
$179$	−0.548295	−	0.949674i	−0.0409815	−	0.0709820i	0.844807	−	0.535071i	$-0.179715\pi$
$179$	−0.548295	−	0.949674i	−0.0409815	−	0.0709820i	−0.885789	+	0.464089i	$0.846382\pi$
$180$	−0.342321	+	2.20971i	−0.0255151	+	0.164702i
$181$	19.2505	+	11.1143i	1.43088	+	0.826118i	0.997188	−	0.0749433i	$-0.0238776\pi$
$181$	19.2505	+	11.1143i	1.43088	+	0.826118i	0.433691	+	0.901062i	$0.357211\pi$
$182$	−0.187772	+	0.187772i	−0.0139186	+	0.0139186i
$183$	−10.2241	−	2.73954i	−0.755787	−	0.202513i
$184$	8.93969			0.659043
$185$	9.44741	−	1.02530i	0.694588	−	0.0753818i
$186$	−2.08956	+	5.16079i	−0.153214	+	0.378407i
$187$	−30.3315	−	30.3315i	−2.21806	−	2.21806i
$188$	1.40611	−	1.40611i	0.102551	−	0.102551i
$189$	0.0943180	+	0.163364i	0.00686063	+	0.0118830i
$190$	13.6662	−	1.48316i	0.991451	−	0.107600i
$191$	−5.88081	+	10.1859i	−0.425521	+	0.737023i	−0.996469	−	0.0839627i	$-0.973242\pi$
$191$	−5.88081	+	10.1859i	−0.425521	+	0.737023i	0.570948	+	0.820986i	$0.306576\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	−1.60792	−	0.430840i	−0.115740	−	0.0310125i	0.200484	−	0.979697i	$-0.435749\pi$
$193$	−1.60792	−	0.430840i	−0.115740	−	0.0310125i	−0.316224	+	0.948684i	$0.602415\pi$
$194$		−	16.7688i		−	1.20393i
$195$	−1.13801	−	2.93489i	−0.0814946	−	0.210172i
$196$	−3.48221	+	6.03136i	−0.248729	+	0.430812i
$197$	0.586574	+	2.18912i	0.0417917	+	0.155969i	0.983668	−	0.179990i	$-0.0576065\pi$
$197$	0.586574	+	2.18912i	0.0417917	+	0.155969i	−0.941877	+	0.335958i	$0.890940\pi$
$198$	−1.61049	+	6.01044i	−0.114453	+	0.427143i
$199$	−7.10193	+	12.3009i	−0.503442	+	0.871988i	0.496550	+	0.868008i	$0.334600\pi$
$199$	−7.10193	+	12.3009i	−0.503442	+	0.871988i	−0.999992	+	0.00397949i	$0.998733\pi$
$200$	−0.227875	+	4.99480i	−0.0161132	+	0.353186i
$201$		−	3.94919i		−	0.278555i
$202$	−1.32120	−	1.32120i	−0.0929590	−	0.0929590i
$203$	0.381247	−	1.42283i	0.0267583	−	0.0998633i
$204$	−5.97004	−	3.44680i	−0.417986	−	0.241325i
$205$	−0.535148	+	3.45442i	−0.0373764	+	0.241267i
$206$	−6.81288	+	11.8003i	−0.474676	+	0.822163i
$207$	2.31376	+	8.63508i	0.160818	+	0.600180i
$208$	−1.35977	+	0.364350i	−0.0942832	+	0.0252631i
$209$	38.2533			2.64603
$210$	0.249083	+	0.340405i	0.0171884	+	0.0234902i
$211$	−3.80480	−	6.59011i	−0.261933	−	0.453682i	0.704822	−	0.709384i	$-0.251027\pi$
$211$	−3.80480	−	6.59011i	−0.261933	−	0.453682i	−0.966756	+	0.255702i	$0.917693\pi$
$212$	−0.0359033	−	0.133993i	−0.00246585	−	0.00920266i
$213$	4.40075	+	4.40075i	0.301535	+	0.301535i
$214$	1.25970	−	0.727285i	0.0861110	−	0.0497162i
$215$	−0.439786	−	4.05230i	−0.0299931	−	0.276365i
$216$			1.00000i			0.0680414i
$217$	0.409658	+	0.967094i	0.0278094	+	0.0656506i
$218$	7.34022	−	7.34022i	0.497142	−	0.497142i
$219$		−	15.3444i		−	1.03688i
$220$	−2.13008	+	13.7498i	−0.143610	+	0.927014i
$221$	9.70440			0.652789
$222$	4.10501	−	1.09993i	0.275510	−	0.0738228i
$223$	5.33486	−	19.9100i	0.357249	−	1.33327i	−0.520382	−	0.853933i	$-0.674211\pi$
$223$	5.33486	−	19.9100i	0.357249	−	1.33327i	0.877631	−	0.479337i	$-0.159123\pi$
$224$	0.163364	−	0.0943180i	0.0109152	−	0.00630189i
$225$	−4.88359	+	1.07264i	−0.325573	+	0.0715094i
$226$	−7.37817	+	12.7794i	−0.490789	+	0.850071i
$227$	11.7141	−	3.13879i	0.777495	−	0.208329i	0.151815	−	0.988409i	$-0.451488\pi$
$227$	11.7141	−	3.13879i	0.777495	−	0.208329i	0.625680	+	0.780080i	$0.284822\pi$
$228$	5.93813	−	1.59112i	0.393262	−	0.105374i
$229$	2.85015	+	4.93661i	0.188343	+	0.326220i	0.944698	−	0.327941i	$-0.106355\pi$
$229$	2.85015	+	4.93661i	0.188343	+	0.326220i	−0.756355	+	0.654162i	$0.773022\pi$
$230$	7.22681	+	18.6377i	0.476522	+	1.22893i
$231$	0.586891	+	1.01652i	0.0386146	+	0.0668824i
$232$	5.52167	−	5.52167i	0.362515	−	0.362515i
$233$	−12.7639	+	12.7639i	−0.836193	+	0.836193i	−0.988355	−	0.152163i	$-0.951376\pi$
$233$	−12.7639	+	12.7639i	−0.836193	+	0.836193i	0.152163	+	0.988355i	$0.451376\pi$
$234$	−0.703869	−	1.21914i	−0.0460134	−	0.0796975i
$235$	4.06817	+	1.79479i	0.265378	+	0.117079i
$236$	0.414378	+	0.717723i	0.0269737	+	0.0467198i
$237$	2.91047	−	0.779859i	0.189056	−	0.0506573i
$238$	−1.25607	+	0.336564i	−0.0814192	+	0.0218162i
$239$	−10.4545	+	18.1076i	−0.676242	+	1.17129i	0.299862	+	0.953983i	$0.403060\pi$
$239$	−10.4545	+	18.1076i	−0.676242	+	1.17129i	−0.976104	+	0.217304i	$0.930274\pi$
$240$	0.241258	+	2.22301i	0.0155731	+	0.143495i
$241$	6.12396	−	3.53567i	0.394479	−	0.227752i	−0.289620	−	0.957142i	$-0.593529\pi$
$241$	6.12396	−	3.53567i	0.394479	−	0.227752i	0.684099	+	0.729389i	$0.260196\pi$
$242$	−7.17423	+	26.7746i	−0.461177	+	1.72113i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−10.5848			−0.677620
$245$	−15.3893	−	2.38407i	−0.983189	−	0.152312i
$246$			1.56329i			0.0996719i
$247$	−6.11946	+	6.11946i	−0.389372	+	0.389372i
$248$	−0.682652	+	5.52576i	−0.0433485	+	0.350886i
$249$		−	15.5243i		−	0.983810i
$250$	−10.5975	+	3.56270i	−0.670245	+	0.225325i
$251$	−10.4646	+	6.04173i	−0.660519	+	0.381351i	−0.792475	−	0.609905i	$-0.791208\pi$
$251$	−10.4646	+	6.04173i	−0.660519	+	0.381351i	0.131956	+	0.991256i	$0.457874\pi$
$252$	0.133386	+	0.133386i	0.00840252	+	0.00840252i
$253$	14.3973	+	53.7315i	0.905151	+	3.37807i
$254$	−0.230967	−	0.400047i	−0.0144922	−	0.0251012i
$255$	2.35983	−	15.2329i	0.147778	−	0.953920i
$256$	1.00000			0.0625000
$257$	−0.227443	+	0.0609432i	−0.0141875	+	0.00380153i	−0.265906	−	0.963999i	$-0.585671\pi$
$257$	−0.227443	+	0.0609432i	−0.0141875	+	0.00380153i	0.251718	+	0.967801i	$0.419004\pi$
$258$	−0.471798	−	1.76077i	−0.0293728	−	0.109621i
$259$	0.400835	−	0.694266i	0.0249067	−	0.0431396i
$260$	−1.85884	−	2.54035i	−0.115280	−	0.157546i
$261$	6.76263	+	3.90441i	0.418597	+	0.241677i
$262$	−1.59960	+	5.96980i	−0.0988239	+	0.368816i
$263$	−12.0278	−	12.0278i	−0.741665	−	0.741665i	0.231233	−	0.972898i	$-0.425724\pi$
$263$	−12.0278	−	12.0278i	−0.741665	−	0.741665i	−0.972898	+	0.231233i	$0.925724\pi$
$264$			6.22247i			0.382966i
$265$	0.250328	−	0.183171i	0.0153775	−	0.0112521i
$266$	0.579830	−	1.00429i	0.0355517	−	0.0615773i
$267$	1.51622	−	5.65860i	0.0927909	−	0.346300i
$268$	−1.02213	−	3.81463i	−0.0624363	−	0.233015i
$269$	12.9037	−	22.3498i	0.786751	−	1.36269i	−0.141197	−	0.989982i	$-0.545095\pi$
$269$	12.9037	−	22.3498i	0.786751	−	1.36269i	0.927948	−	0.372711i	$-0.121572\pi$
$270$	−2.08483	+	0.808396i	−0.126878	+	0.0491974i
$271$		−	12.6080i		−	0.765880i	−0.923773	−	0.382940i	$-0.874912\pi$
$271$		−	12.6080i		−	0.765880i	0.923773	−	0.382940i	$-0.125088\pi$
$272$	−6.65872	−	1.78420i	−0.403744	−	0.108183i
$273$	−0.256502	−	0.0687295i	−0.0155242	−	0.00415970i
$274$	3.21396	−	5.56674i	0.194162	−	0.336299i
$275$	−30.3880	+	6.67447i	−1.83246	+	0.402486i
$276$	4.46985	+	7.74200i	0.269053	+	0.466014i
$277$	10.1919	−	10.1919i	0.612373	−	0.612373i	−0.331191	−	0.943564i	$-0.607450\pi$
$277$	10.1919	−	10.1919i	0.612373	−	0.612373i	0.943564	+	0.331191i	$0.107450\pi$
$278$	−0.172580	−	0.172580i	−0.0103507	−	0.0103507i
$279$	−5.51415	+	0.770779i	−0.330124	+	0.0461454i
$280$	0.328699	+	0.264338i	0.0196435	+	0.0157972i
$281$	21.5446			1.28524			0.642621	−	0.766184i	$-0.277847\pi$
$281$	21.5446			1.28524			0.642621	+	0.766184i	$0.277847\pi$
$282$	1.92078	+	0.514670i	0.114381	+	0.0306482i
$283$	2.45921	−	2.45921i	0.146185	−	0.146185i	−0.630227	−	0.776411i	$-0.717038\pi$
$283$	2.45921	−	2.45921i	0.146185	−	0.146185i	0.776411	+	0.630227i	$0.217038\pi$
$284$	5.38980	+	3.11180i	0.319826	+	0.184652i
$285$	8.11756	+	11.0937i	0.480843	+	0.657135i
$286$	−4.37980	−	7.58604i	−0.258983	−	0.448572i
$287$	0.208521	+	0.208521i	0.0123086	+	0.0123086i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	26.4327	+	15.2609i	1.55486	+	0.897702i
$290$	15.9754	+	7.04802i	0.938108	+	0.413874i
$291$	14.5222	−	8.38441i	0.851308	−	0.491503i
$292$	−3.97143	−	14.8216i	−0.232411	−	0.867368i
$293$	19.6576	+	5.26723i	1.14841	+	0.307715i	0.782327	−	0.622868i	$-0.214033\pi$
$293$	19.6576	+	5.26723i	1.14841	+	0.307715i	0.366081	+	0.930583i	$0.380699\pi$
$294$	−6.96442			−0.406173
$295$	−1.16135	+	1.44411i	−0.0676162	+	0.0840793i
$296$	3.68045	−	2.12491i	0.213922	−	0.123508i
$297$	−6.01044	+	1.61049i	−0.348761	+	0.0934503i
$298$	−16.5814	−	4.44298i	−0.960536	−	0.257375i
$299$	−10.8987	−	6.29238i	−0.630289	−	0.363898i
$300$	−4.43957	+	2.30006i	−0.256318	+	0.132794i
$301$	−0.297793	−	0.171931i	−0.0171645	−	0.00990994i
$302$	−2.17355	+	2.17355i	−0.125073	+	0.125073i
$303$	0.483591	−	1.80479i	0.0277816	−	0.103682i
$304$	5.32398	−	3.07380i	0.305351	−	0.176295i
$305$	−8.55668	−	22.0674i	−0.489954	−	1.26358i
$306$		−	6.89361i		−	0.394081i
$307$	3.14342	−	11.7314i	0.179404	−	0.669546i	−0.816355	−	0.577550i	$-0.804009\pi$
$307$	3.14342	−	11.7314i	0.179404	−	0.669546i	0.995759	−	0.0919958i	$-0.0293247\pi$
$308$	0.829989	+	0.829989i	0.0472930	+	0.0472930i
$309$	−13.6258			−0.775142
$310$	−12.0721	+	3.04379i	−0.685649	+	0.172876i
$311$	−0.711379			−0.0403386			−0.0201693	−	0.999797i	$-0.506421\pi$
$311$	−0.711379			−0.0403386			−0.0201693	+	0.999797i	$0.506421\pi$
$312$	−0.995422	−	0.995422i	−0.0563547	−	0.0563547i
$313$	4.43922	−	16.5674i	0.250919	−	0.936444i	−0.719396	−	0.694600i	$-0.755581\pi$
$313$	4.43922	−	16.5674i	0.250919	−	0.936444i	0.970315	−	0.241844i	$-0.0777521\pi$
$314$			16.1714i			0.912602i
$315$	−0.170258	+	0.385915i	−0.00959293	+	0.0217438i
$316$	2.60946	−	1.50657i	0.146794	−	0.0847513i
$317$	2.58970	−	9.66488i	0.145452	−	0.542834i	−0.854283	−	0.519808i	$-0.826003\pi$
$317$	2.58970	−	9.66488i	0.145452	−	0.542834i	0.999735	−	0.0230257i	$-0.00732996\pi$
$318$	0.0980895	−	0.0980895i	0.00550059	−	0.00550059i
$319$	42.0803	+	24.2950i	2.35604	+	1.36026i
$320$	0.808396	+	2.08483i	0.0451907	+	0.116545i
$321$	1.25970	+	0.727285i	0.0703093	+	0.0405931i
$322$	1.62889	+	0.436459i	0.0907744	+	0.0243229i
$323$	−40.9351	+	10.9685i	−2.27769	+	0.610306i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	3.79350	−	5.92896i	0.210426	−	0.328880i
$326$	10.1839			0.564034
$327$	10.0269	+	2.68671i	0.554490	+	0.148575i
$328$	0.404610	+	1.51002i	0.0223408	+	0.0833772i
$329$	0.324854	−	0.187555i	0.0179098	−	0.0103402i
$330$	−12.9728	+	5.03022i	−0.714127	+	0.276904i
$331$	29.1055	+	16.8041i	1.59978	+	0.923636i	0.991528	+	0.129895i	$0.0414640\pi$
$331$	29.1055	+	16.8041i	1.59978	+	0.923636i	0.608256	+	0.793741i	$0.291869\pi$
$332$	−4.01797	−	14.9953i	−0.220515	−	0.822973i
$333$	3.00508	+	3.00508i	0.164677	+	0.164677i
$334$	−5.73376	−	9.93116i	−0.313737	−	0.543409i
$335$	7.12655	−	5.21468i	0.389365	−	0.284909i
$336$	0.163364	+	0.0943180i	0.00891222	+	0.00514547i
$337$	−14.4522	+	14.4522i	−0.787263	+	0.787263i	−0.981045	−	0.193781i	$-0.937925\pi$
$337$	−14.4522	+	14.4522i	−0.787263	+	0.787263i	0.193781	+	0.981045i	$0.437925\pi$
$338$	−10.6428	−	2.85174i	−0.578894	−	0.155114i
$339$	−14.7563			−0.801454
$340$	−1.66314	−	15.3246i	−0.0901964	−	0.831093i
$341$	−34.3116	+	4.79615i	−1.85808	+	0.259726i
$342$	4.34701	+	4.34701i	0.235060	+	0.235060i
$343$	−1.86266	+	1.86266i	−0.100574	+	0.100574i
$344$	−0.911443	−	1.57867i	−0.0491417	−	0.0851159i
$345$	−12.5273	+	15.5775i	−0.674448	+	0.838662i
$346$	6.12221	−	10.6040i	0.329132	−	0.570073i
$347$	9.87245	+	2.64531i	0.529981	+	0.142008i	0.513879	−	0.857862i	$-0.328208\pi$
$347$	9.87245	+	2.64531i	0.529981	+	0.142008i	0.0161013	+	0.999870i	$0.494875\pi$
$348$	7.54274	+	2.02107i	0.404333	+	0.108341i
$349$		−	22.3271i		−	1.19514i	−0.801815	−	0.597572i	$-0.796132\pi$
$349$		−	22.3271i		−	1.19514i	0.801815	−	0.597572i	$-0.203868\pi$
$350$	−0.285380	+	0.898970i	−0.0152542	+	0.0480520i
$351$	0.703869	−	1.21914i	0.0375698	−	0.0650728i
$352$	1.61049	+	6.01044i	0.0858395	+	0.320358i
$353$	−8.70807	+	32.4990i	−0.463484	+	1.72974i	0.198384	+	0.980124i	$0.436431\pi$
$353$	−8.70807	+	32.4990i	−0.463484	+	1.72974i	−0.661868	+	0.749620i	$0.730236\pi$
$354$	−0.414378	+	0.717723i	−0.0220239	+	0.0381466i
$355$	−2.13047	+	13.7524i	−0.113074	+	0.729900i
$356$		−	5.85821i		−	0.310484i
$357$	−0.919510	−	0.919510i	−0.0486656	−	0.0486656i
$358$	0.283818	−	1.05922i	0.0150003	−	0.0559817i
$359$	−13.9156	−	8.03416i	−0.734436	−	0.424027i	0.0856068	−	0.996329i	$-0.472717\pi$
$359$	−13.9156	−	8.03416i	−0.734436	−	0.424027i	−0.820043	+	0.572302i	$0.806050\pi$
$360$	−1.80456	+	1.32044i	−0.0951086	+	0.0695935i
$361$	9.39652	−	16.2752i	0.494554	−	0.856592i
$362$	5.75318	+	21.4712i	0.302380	+	1.12850i
$363$	−26.7746	+	7.17423i	−1.40530	+	0.376549i
$364$	−0.265550			−0.0139186
$365$	27.6899	−	20.2615i	1.44936	−	1.06053i
$366$	−5.29238	−	9.16668i	−0.276637	−	0.479150i
$367$	−8.85890	−	33.0619i	−0.462431	−	1.72582i	−0.665270	−	0.746603i	$-0.731683\pi$
$367$	−8.85890	−	33.0619i	−0.462431	−	1.72582i	0.202839	−	0.979212i	$-0.434983\pi$
$368$	6.32132	+	6.32132i	0.329522	+	0.329522i
$369$	−1.35385	+	0.781646i	−0.0704787	+	0.0406909i
$370$	7.40533	+	5.95533i	0.384985	+	0.309603i
$371$		−	0.0261675i		−	0.00135855i
$372$	−5.12677	+	2.17168i	−0.265811	+	0.112597i
$373$	5.32825	−	5.32825i	0.275886	−	0.275886i	−0.555578	−	0.831464i	$-0.687503\pi$
$373$	5.32825	−	5.32825i	0.275886	−	0.275886i	0.831464	+	0.555578i	$0.187503\pi$
$374$		−	42.8953i		−	2.21806i
$375$	−8.38414	−	7.39636i	−0.432955	−	0.381946i
$376$	1.98853			0.102551
$377$	−10.6182	+	2.84514i	−0.546865	+	0.146532i
$378$	−0.0488226	+	0.182208i	−0.00251116	+	0.00937179i
$379$	−0.429018	+	0.247693i	−0.0220372	+	0.0127232i	−0.510978	−	0.859594i	$-0.670717\pi$
$379$	−0.429018	+	0.247693i	−0.0220372	+	0.0127232i	0.488941	+	0.872317i	$0.337383\pi$
$380$	10.7122	+	8.61472i	0.549526	+	0.441926i
$381$	0.230967	−	0.400047i	0.0118328	−	0.0204950i
$382$	−11.3609	+	3.04413i	−0.581272	+	0.155751i
$383$	14.4594	−	3.87438i	0.738839	−	0.197971i	0.130277	−	0.991478i	$-0.458413\pi$
$383$	14.4594	−	3.87438i	0.738839	−	0.197971i	0.608562	+	0.793506i	$0.291747\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−1.05942	+	2.40134i	−0.0539932	+	0.122384i
$386$	−0.832318	−	1.44162i	−0.0423639	−	0.0733764i
$387$	1.28897	−	1.28897i	0.0655223	−	0.0655223i
$388$	11.8573	−	11.8573i	0.601966	−	0.601966i
$389$	−15.5647	−	26.9588i	−0.789160	−	1.36687i	−0.926482	−	0.376339i	$-0.877183\pi$
$389$	−15.5647	−	26.9588i	−0.789160	−	1.36687i	0.137322	−	0.990526i	$-0.456151\pi$
$390$	1.27059	−	2.87998i	0.0643386	−	0.145833i
$391$	−30.8134	−	53.3703i	−1.55830	−	2.69905i
$392$	−6.72711	+	1.80252i	−0.339770	+	0.0910412i
$393$	−5.96980	+	1.59960i	−0.301137	+	0.0806893i
$394$	−1.13317	+	1.96272i	−0.0570885	+	0.0988802i
$395$	5.25042	+	4.22236i	0.264177	+	0.212450i
$396$	−5.38881	+	3.11123i	−0.270798	+	0.156345i
$397$	0.947543	−	3.53628i	0.0475558	−	0.177481i	−0.938063	−	0.346465i	$-0.887382\pi$
$397$	0.947543	−	3.53628i	0.0475558	−	0.177481i	0.985619	+	0.168984i	$0.0540487\pi$
$398$	−13.7199	+	3.67623i	−0.687715	+	0.184273i
$399$	1.15966			0.0580556
$400$	−3.69299	+	3.37073i	−0.184650	+	0.168536i
$401$			0.605773i			0.0302508i	0.999886	+	0.0151254i	$0.00481476\pi$
$401$			0.605773i			0.0302508i	−0.999886	+	0.0151254i	$0.995185\pi$
$402$	2.79250	−	2.79250i	0.139277	−	0.139277i
$403$	4.72166	−	6.25616i	0.235203	−	0.311642i
$404$		−	1.86845i		−	0.0929590i
$405$	−1.74250	−	1.40131i	−0.0865857	−	0.0696318i
$406$	1.27568	−	0.736512i	0.0633108	−	0.0365525i
$407$	18.6990	+	18.6990i	0.926874	+	0.926874i
$408$	−1.78420	−	6.65872i	−0.0883309	−	0.329656i
$409$	−7.24538	−	12.5494i	−0.358261	−	0.620526i	0.629409	−	0.777074i	$-0.283297\pi$
$409$	−7.24538	−	12.5494i	−0.358261	−	0.620526i	−0.987670	+	0.156548i	$0.949964\pi$
$410$	−2.82105	+	2.06424i	−0.139322	+	0.101945i
$411$	6.42792			0.317066
$412$	−13.1615	+	3.52661i	−0.648419	+	0.173743i
$413$	0.0404620	+	0.151006i	0.00199100	+	0.00743053i
$414$	−4.46985	+	7.74200i	−0.219681	+	0.380499i
$415$	28.0144	−	20.4989i	1.37517	−	1.00625i
$416$	−1.21914	−	0.703869i	−0.0597731	−	0.0345100i
$417$	0.0631687	−	0.235749i	0.00309338	−	0.0115447i
$418$	27.0491	+	27.0491i	1.32302	+	1.32302i
$419$			26.6613i			1.30249i	0.758869	+	0.651244i	$0.225752\pi$
$419$			26.6613i			1.30249i	−0.758869	+	0.651244i	$0.774248\pi$
$420$	−0.0645741	+	0.416831i	−0.00315089	+	0.0203393i
$421$	−14.6537	+	25.3809i	−0.714176	+	1.23699i	0.249100	+	0.968478i	$0.419865\pi$
$421$	−14.6537	+	25.3809i	−0.714176	+	1.23699i	−0.963276	+	0.268512i	$0.913468\pi$
$422$	1.96951	−	7.35031i	0.0958743	−	0.357808i
$423$	0.514670	+	1.92078i	0.0250241	+	0.0933913i
$424$	0.0693598	−	0.120135i	0.00336841	−	0.00583426i
$425$	30.6046	−	15.8557i	1.48454	−	0.769114i
$426$			6.22361i			0.301535i
$427$	−1.92863	−	0.516776i	−0.0933332	−	0.0250085i
$428$	1.40501	+	0.376471i	0.0679136	+	0.0181974i
$429$	4.37980	−	7.58604i	0.211459	−	0.366258i
$430$	2.55443	−	3.17639i	0.123186	−	0.153179i
$431$	16.2962	+	28.2259i	0.784961	+	1.35959i	0.929022	+	0.370024i	$0.120651\pi$
$431$	16.2962	+	28.2259i	0.784961	+	1.35959i	−0.144061	+	0.989569i	$0.546016\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−1.36516	−	1.36516i	−0.0656053	−	0.0656053i	0.673543	−	0.739148i	$-0.264772\pi$
$433$	−1.36516	−	1.36516i	−0.0656053	−	0.0656053i	−0.739148	+	0.673543i	$0.764772\pi$
$434$	−0.394167	+	0.973511i	−0.0189206	+	0.0467300i
$435$	1.88394	+	17.3591i	0.0903280	+	0.832306i
$436$	10.3806			0.497142
$437$	53.0851	+	14.2241i	2.53940	+	0.680431i
$438$	10.8502	−	10.8502i	0.518441	−	0.518441i
$439$	−25.7990	−	14.8950i	−1.23132	−	0.710902i	−0.264013	−	0.964519i	$-0.585046\pi$
$439$	−25.7990	−	14.8950i	−1.23132	−	0.710902i	−0.967305	+	0.253618i	$0.918380\pi$
$440$	−11.2288	+	8.21641i	−0.535312	+	0.391702i
$441$	−3.48221	−	6.03136i	−0.165819	−	0.287208i
$442$	6.86205	+	6.86205i	0.326394	+	0.326394i
$443$	−4.62780	−	17.2712i	−0.219873	−	0.820579i	−0.984394	−	0.175979i	$-0.943691\pi$
$443$	−4.62780	−	17.2712i	−0.219873	−	0.820579i	0.764521	−	0.644599i	$-0.222976\pi$
$444$	3.68045	+	2.12491i	0.174667	+	0.100844i
$445$	12.2133	−	4.73575i	0.578968	−	0.224496i
$446$	17.8508	−	10.3062i	0.845260	−	0.488011i
$447$	−4.44298	−	16.5814i	−0.210146	−	0.784274i
$448$	0.182208	+	0.0488226i	0.00860854	+	0.00230665i
$449$	30.5766			1.44300			0.721499	−	0.692416i	$-0.243454\pi$
$449$	30.5766			1.44300			0.721499	+	0.692416i	$0.243454\pi$
$450$	−4.21169	−	2.69475i	−0.198541	−	0.127032i
$451$	−8.42429	+	4.86377i	−0.396684	+	0.229026i
$452$	−14.2535	+	3.81922i	−0.670430	+	0.179641i
$453$	−2.96912	−	0.795573i	−0.139501	−	0.0373793i
$454$	10.5026	+	6.06369i	0.492912	+	0.284583i
$455$	−0.214670	−	0.553626i	−0.0100639	−	0.0259544i
$456$	5.32398	+	3.07380i	0.249318	+	0.143944i
$457$	−1.70234	+	1.70234i	−0.0796321	+	0.0796321i	−0.745801	−	0.666169i	$-0.767933\pi$
$457$	−1.70234	+	1.70234i	−0.0796321	+	0.0796321i	0.666169	+	0.745801i	$0.267933\pi$
$458$	−1.47535	+	5.50607i	−0.0689385	+	0.257282i
$459$	5.97004	−	3.44680i	0.278658	−	0.160883i
$460$	−8.06872	+	18.2890i	−0.376206	+	0.852728i
$461$		−	18.1435i		−	0.845025i	−0.906357	−	0.422513i	$-0.861148\pi$
$461$		−	18.1435i		−	0.845025i	0.906357	−	0.422513i	$-0.138852\pi$
$462$	−0.303797	+	1.13379i	−0.0141339	+	0.0527485i
$463$	5.70937	+	5.70937i	0.265337	+	0.265337i	0.827218	−	0.561881i	$-0.189922\pi$
$463$	5.70937	+	5.70937i	0.265337	+	0.265337i	−0.561881	+	0.827218i	$0.689922\pi$
$464$	7.80882			0.362515
$465$	−8.67204	−	8.93284i	−0.402156	−	0.414251i
$466$	−18.0509			−0.836193
$467$	−7.70792	−	7.70792i	−0.356680	−	0.356680i	0.505908	−	0.862588i	$-0.331158\pi$
$467$	−7.70792	−	7.70792i	−0.356680	−	0.356680i	−0.862588	+	0.505908i	$0.831158\pi$
$468$	0.364350	−	1.35977i	0.0168421	−	0.0628555i
$469$		−	0.744960i		−	0.0343991i
$470$	1.60752	+	4.14575i	0.0741495	+	0.191229i
$471$	−14.0048	+	8.08568i	−0.645307	+	0.372568i
$472$	−0.214498	+	0.800516i	−0.00987305	+	0.0368467i
$473$	8.02060	−	8.02060i	0.368788	−	0.368788i
$474$	2.60946	+	1.50657i	0.119856	+	0.0691992i
$475$	−9.30047	+	29.2972i	−0.426735	+	1.34425i
$476$	−1.12617	−	0.650192i	−0.0516177	−	0.0298015i
$477$	0.133993	+	0.0359033i	0.00613511	+	0.00164390i
$478$	−20.1965	+	5.41162i	−0.923764	+	0.247522i
$479$	21.4429	−	12.3801i	0.979751	−	0.565659i	0.0775559	−	0.996988i	$-0.475288\pi$
$479$	21.4429	−	12.3801i	0.979751	−	0.565659i	0.902195	+	0.431329i	$0.141955\pi$
$480$	−1.40131	+	1.74250i	−0.0639609	+	0.0795341i
$481$	−5.98264			−0.272785
$482$	6.83038	+	1.83020i	0.311116	+	0.0833631i
$483$	0.436459	+	1.62889i	0.0198596	+	0.0741170i
$484$	−24.0054	+	13.8595i	−1.09116	+	0.629979i
$485$	34.3059	+	15.1351i	1.55775	+	0.687248i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−8.39529	−	31.3316i	−0.380427	−	1.41977i	−0.845251	−	0.534369i	$-0.820549\pi$
$487$	−8.39529	−	31.3316i	−0.380427	−	1.41977i	0.464825	−	0.885403i	$-0.346117\pi$
$488$	−7.48456	−	7.48456i	−0.338810	−	0.338810i
$489$	5.09195	+	8.81951i	0.230266	+	0.398832i
$490$	−9.19611	−	12.5677i	−0.415438	−	0.567751i
$491$	−11.1587	−	6.44248i	−0.503585	−	0.290745i	0.226608	−	0.973986i	$-0.427237\pi$
$491$	−11.1587	−	6.44248i	−0.503585	−	0.290745i	−0.730193	+	0.683241i	$0.760570\pi$
$492$	−1.10541	+	1.10541i	−0.0498359	+	0.0498359i
$493$	−51.9967	−	13.9325i	−2.34181	−	0.627487i
$494$	−8.65422			−0.389372
$495$	−10.8427	−	8.71963i	−0.487342	−	0.391918i
$496$	−4.39001	+	3.42459i	−0.197117	+	0.153769i
$497$	0.830141	+	0.830141i	0.0372369	+	0.0372369i
$498$	10.9773	−	10.9773i	0.491905	−	0.491905i
$499$	0.898485	+	1.55622i	0.0402217	+	0.0696660i	0.885435	−	0.464762i	$-0.153860\pi$
$499$	0.898485	+	1.55622i	0.0402217	+	0.0696660i	−0.845214	+	0.534428i	$0.820527\pi$
$500$	−10.0128	−	4.97436i	−0.447785	−	0.222460i
$501$	5.73376	−	9.93116i	0.256166	−	0.443692i
$502$	−11.6717	−	3.12743i	−0.520935	−	0.139584i
$503$	10.7502	+	2.88051i	0.479328	+	0.128436i	0.490390	−	0.871503i	$-0.336854\pi$
$503$	10.7502	+	2.88051i	0.479328	+	0.128436i	−0.0110615	+	0.999939i	$0.503521\pi$
$504$			0.188636i			0.00840252i
$505$	3.89540	−	1.51045i	0.173343	−	0.0672141i
$506$	−27.8135	+	48.1743i	−1.23646	+	2.14161i
$507$	−2.85174	−	10.6428i	−0.126650	−	0.472665i
$508$	0.119557	−	0.446194i	0.00530450	−	0.0197967i
$509$	14.4760	−	25.0732i	0.641639	−	1.11135i	−0.343428	−	0.939179i	$-0.611588\pi$
$509$	14.4760	−	25.0732i	0.641639	−	1.11135i	0.985067	−	0.172172i	$-0.0550785\pi$
$510$	12.4399	−	9.10262i	0.550849	−	0.403071i
$511$		−	2.89452i		−	0.128046i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.59112	+	5.93813i	−0.0702495	+	0.262175i
$514$	−0.203920	−	0.117733i	−0.00899452	−	0.00519299i
$515$	−17.9920	−	24.5885i	−0.792824	−	1.08350i
$516$	0.911443	−	1.57867i	0.0401240	−	0.0694969i
$517$	3.20252	+	11.9520i	0.140847	+	0.525647i
$518$	0.774353	−	0.207487i	0.0340231	−	0.00911647i
$519$	12.2444			0.537470
$520$	0.481899	−	3.11069i	0.0211327	−	0.136413i
$521$	−5.77032	−	9.99448i	−0.252802	−	0.437866i	0.711494	−	0.702692i	$-0.248019\pi$
$521$	−5.77032	−	9.99448i	−0.252802	−	0.437866i	−0.964296	+	0.264826i	$0.914686\pi$
$522$	2.02107	+	7.54274i	0.0884599	+	0.330137i
$523$	−20.2124	−	20.2124i	−0.883826	−	0.883826i	0.110095	−	0.993921i	$-0.464884\pi$
$523$	−20.2124	−	20.2124i	−0.883826	−	0.883826i	−0.993921	+	0.110095i	$0.964884\pi$
$524$	−5.35238	+	3.09020i	−0.233820	+	0.134996i
$525$	−0.921221	+	0.202339i	−0.0402054	+	0.00883078i
$526$		−	17.0099i		−	0.741665i
$527$	35.3420	−	14.9707i	1.53952	−	0.652136i
$528$	−4.39995	+	4.39995i	−0.191483	+	0.191483i
$529$			56.9181i			2.47470i
$530$	0.306530	+	0.0474866i	0.0133148	+	0.00206269i
$531$	−0.828755			−0.0359649
$532$	1.12015	−	0.300142i	0.0485645	−	0.0130128i
$533$	0.569585	−	2.12572i	0.0246715	−	0.0920752i
$534$	5.07336	−	2.92910i	0.219546	−	0.126755i
$535$	0.350927	+	3.23353i	0.0151719	+	0.139798i
$536$	1.97460	−	3.42010i	0.0852896	−	0.147726i
$537$	1.05922	−	0.283818i	0.0457089	−	0.0122477i
$538$	24.9280	−	6.67943i	1.07472	−	0.287971i
$539$	−21.6679	−	37.5299i	−0.933303	−	1.61653i
$540$	−2.04582	−	0.902572i	−0.0880379	−	0.0388405i
$541$	−7.02031	−	12.1595i	−0.301827	−	0.522779i	0.674723	−	0.738071i	$-0.264263\pi$
$541$	−7.02031	−	12.1595i	−0.301827	−	0.522779i	−0.976550	+	0.215292i	$0.930930\pi$
$542$	8.91519	−	8.91519i	0.382940	−	0.382940i
$543$	−15.7180	+	15.7180i	−0.674523	+	0.674523i
$544$	−3.44680	−	5.97004i	−0.147781	−	0.255963i
$545$	8.39167	+	21.6418i	0.359459	+	0.927034i
$546$	−0.132775	−	0.229973i	−0.00568225	−	0.00984195i
$547$	−13.7924	+	3.69566i	−0.589720	+	0.158015i	−0.541325	−	0.840813i	$-0.682077\pi$
$547$	−13.7924	+	3.69566i	−0.589720	+	0.158015i	−0.0483948	+	0.998828i	$0.515411\pi$
$548$	6.20889	−	1.66367i	0.265231	−	0.0710683i
$549$	5.29238	−	9.16668i	0.225873	−	0.391224i
$550$	−26.2071	−	16.7680i	−1.11747	−	0.714989i
$551$	41.5740	−	24.0028i	1.77111	−	1.02255i
$552$	−2.31376	+	8.63508i	−0.0984803	+	0.367534i
$553$	0.549021	−	0.147110i	0.0233467	−	0.00625574i
$554$	14.4135			0.612373
$555$	−1.45480	+	9.39087i	−0.0617530	+	0.398620i
$556$		−	0.244065i		−	0.0103507i
$557$	−15.8491	+	15.8491i	−0.671547	+	0.671547i	−0.958073	−	0.286525i	$-0.907500\pi$
$557$	−15.8491	+	15.8491i	−0.671547	+	0.671547i	0.286525	+	0.958073i	$0.407500\pi$
$558$	−4.44412	−	3.35407i	−0.188135	−	0.141989i
$559$			2.56615i			0.108536i
$560$	0.0455100	+	0.419341i	0.00192315	+	0.0177204i
$561$	37.1484	−	21.4476i	1.56841	−	0.905519i
$562$	15.2343	+	15.2343i	0.642621	+	0.642621i
$563$	7.96704	+	29.7334i	0.335771	+	1.25311i	0.903031	+	0.429575i	$0.141337\pi$
$563$	7.96704	+	29.7334i	0.335771	+	1.25311i	−0.567261	+	0.823538i	$0.691997\pi$
$564$	0.994267	+	1.72212i	0.0418662	+	0.0725144i
$565$	−19.4849	−	26.6287i	−0.819736	−	1.12028i
$566$	3.47784			0.146185
$567$	−0.182208	+	0.0488226i	−0.00765204	+	0.00205036i
$568$	1.61079	+	6.01154i	0.0675871	+	0.252239i
$569$	2.36534	−	4.09689i	0.0991604	−	0.171751i	−0.812177	−	0.583411i	$-0.801718\pi$
$569$	2.36534	−	4.09689i	0.0991604	−	0.171751i	0.911337	+	0.411660i	$0.135051\pi$
$570$	−2.10446	+	13.5844i	−0.0881459	+	0.568989i
$571$	1.70018	+	0.981599i	0.0711503	+	0.0410786i	0.535153	−	0.844755i	$-0.320254\pi$
$571$	1.70018	+	0.981599i	0.0711503	+	0.0410786i	−0.464003	+	0.885834i	$0.653587\pi$
$572$	2.26715	−	8.46113i	0.0947944	−	0.353778i
$573$	−8.31672	−	8.31672i	−0.347436	−	0.347436i
$574$			0.294893i			0.0123086i
$575$	−44.6520	−	2.03713i	−1.86212	−	0.0849543i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.38695	+	27.5685i	−0.307523	+	1.14769i	0.623229	+	0.782039i	$0.285820\pi$
$577$	−7.38695	+	27.5685i	−0.307523	+	1.14769i	−0.930752	+	0.365651i	$0.880846\pi$
$578$	7.89964	+	29.4818i	0.328582	+	1.22628i
$579$	0.832318	−	1.44162i	0.0345900	−	0.0599116i
$580$	6.31262	+	16.2800i	0.262117	+	0.675991i
$581$		−	2.92843i		−	0.121492i
$582$	16.1974	+	4.34009i	0.671405	+	0.179903i
$583$	0.833766	+	0.223407i	0.0345310	+	0.00925257i
$584$	7.67222	−	13.2887i	0.317479	−	0.549889i
$585$	3.12942	−	0.339628i	0.129386	−	0.0140419i
$586$	10.1755	+	17.6245i	0.420346	+	0.728061i
$587$	−11.0267	+	11.0267i	−0.455121	+	0.455121i	−0.897050	−	0.441929i	$-0.854294\pi$
$587$	−11.0267	+	11.0267i	−0.455121	+	0.455121i	0.441929	+	0.897050i	$0.354294\pi$
$588$	−4.92459	−	4.92459i	−0.203087	−	0.203087i
$589$	−12.8458	+	31.7265i	−0.529302	+	1.30727i
$590$	−1.84234	+	0.199944i	−0.0758477	+	0.00823156i
$591$	−2.26635			−0.0932251
$592$	4.10501	+	1.09993i	0.168715	+	0.0452070i
$593$	26.2255	−	26.2255i	1.07695	−	1.07695i	0.0801694	−	0.996781i	$-0.474454\pi$
$593$	26.2255	−	26.2255i	1.07695	−	1.07695i	0.996781	−	0.0801694i	$-0.0255461\pi$
$594$	−5.38881	−	3.11123i	−0.221106	−	0.127655i
$595$	0.445149	−	2.87347i	0.0182493	−	0.117801i
$596$	−8.58317	−	14.8665i	−0.351580	−	0.608955i
$597$	−10.0436	−	10.0436i	−0.411059	−	0.411059i
$598$	−3.25717	−	12.1559i	−0.133196	−	0.497093i
$599$	5.83850	+	3.37086i	0.238555	+	0.137730i	0.614512	−	0.788907i	$-0.289353\pi$
$599$	5.83850	+	3.37086i	0.238555	+	0.137730i	−0.375958	+	0.926637i	$0.622686\pi$
$600$	−4.76563	−	1.51286i	−0.194556	−	0.0617623i
$601$	−31.3849	+	18.1201i	−1.28022	+	0.739133i	−0.976888	−	0.213753i	$-0.931431\pi$
$601$	−31.3849	+	18.1201i	−1.28022	+	0.739133i	−0.303328	+	0.952886i	$0.598098\pi$
$602$	−0.0889980	−	0.332145i	−0.00362729	−	0.0135372i
$603$	3.81463	+	1.02213i	0.155344	+	0.0416242i
$604$	−3.07386			−0.125073
$605$	−48.3006	−	38.8431i	−1.96370	−	1.57920i
$606$	1.61813	−	0.934226i	0.0657319	−	0.0379504i
$607$	−3.73751	+	1.00146i	−0.151701	+	0.0406482i	−0.333870	−	0.942619i	$-0.608355\pi$
$607$	−3.73751	+	1.00146i	−0.151701	+	0.0406482i	0.182169	+	0.983267i	$0.441688\pi$
$608$	5.93813	+	1.59112i	0.240823	+	0.0645283i
$609$	1.27568	+	0.736512i	0.0516930	+	0.0298450i
$610$	9.55351	−	21.6545i	0.386810	−	0.876765i
$611$	−2.42430	−	1.39967i	−0.0980765	−	0.0566245i
$612$	4.87452	−	4.87452i	0.197041	−	0.197041i
$613$	10.5781	−	39.4782i	0.427247	−	1.59451i	−0.331719	−	0.943378i	$-0.607629\pi$
$613$	10.5781	−	39.4782i	0.427247	−	1.59451i	0.758966	−	0.651130i	$-0.225705\pi$
$614$	10.5181	−	6.07262i	0.424475	−	0.245071i
$615$	−3.19821	−	1.41098i	−0.128964	−	0.0568964i
$616$			1.17378i			0.0472930i
$617$	−6.05988	+	22.6158i	−0.243962	+	0.910477i	0.729941	+	0.683510i	$0.239548\pi$
$617$	−6.05988	+	22.6158i	−0.243962	+	0.910477i	−0.973902	+	0.226967i	$0.927119\pi$
$618$	−9.63487	−	9.63487i	−0.387571	−	0.387571i
$619$	36.5558			1.46930			0.734651	−	0.678445i	$-0.237346\pi$
$619$	36.5558			1.46930			0.734651	+	0.678445i	$0.237346\pi$
$620$	−10.6885	−	6.38397i	−0.429262	−	0.256387i
$621$	−8.93969			−0.358738
$622$	−0.503021	−	0.503021i	−0.0201693	−	0.0201693i
$623$	0.286013	−	1.06742i	0.0114589	−	0.0427651i
$624$		−	1.40774i		−	0.0563547i
$625$	2.27638	−	24.8961i	0.0910553	−	0.995846i
$626$	14.8539	−	8.57591i	0.593682	−	0.342762i
$627$	−9.90067	+	36.9498i	−0.395395	+	1.47563i
$628$	−11.4349	+	11.4349i	−0.456301	+	0.456301i
$629$	−25.3716	−	14.6483i	−1.01163	−	0.584066i
$630$	−0.393273	+	0.152493i	−0.0156684	+	0.00607545i
$631$	30.5268	+	17.6247i	1.21525	+	0.701628i	0.963899	−	0.266267i	$-0.0857904\pi$
$631$	30.5268	+	17.6247i	1.21525	+	0.701628i	0.251355	+	0.967895i	$0.419124\pi$
$632$	2.91047	+	0.779859i	0.115772	+	0.0310211i
$633$	7.35031	−	1.96951i	0.292149	−	0.0782810i
$634$	8.66530	−	5.00291i	0.344143	−	0.198691i
$635$	1.02689	−	0.111445i	0.0407507	−	0.00442257i
$636$	0.138720			0.00550059
$637$	9.47001	+	2.53748i	0.375216	+	0.100539i
$638$	12.5760	+	46.9344i	0.497890	+	1.85815i
$639$	−5.38980	+	3.11180i	−0.213217	+	0.123101i
$640$	−0.902572	+	2.04582i	−0.0356773	+	0.0808680i
$641$	17.4670	+	10.0846i	0.689906	+	0.398317i	0.803577	−	0.595201i	$-0.202928\pi$
$641$	17.4670	+	10.0846i	0.689906	+	0.398317i	−0.113671	+	0.993518i	$0.536261\pi$
$642$	0.376471	+	1.40501i	0.0148581	+	0.0554512i
$643$	−28.0879	−	28.0879i	−1.10768	−	1.10768i	−0.993455	−	0.114224i	$-0.963562\pi$
$643$	−28.0879	−	28.0879i	−1.10768	−	1.10768i	−0.114224	−	0.993455i	$-0.536438\pi$
$644$	0.843175	+	1.46042i	0.0332257	+	0.0575487i
$645$	4.02805	+	0.624012i	0.158604	+	0.0245705i
$646$	−36.7014	−	21.1896i	−1.44400	−	0.833693i
$647$	−2.75453	+	2.75453i	−0.108292	+	0.108292i	−0.759176	−	0.650885i	$-0.774398\pi$
$647$	−2.75453	+	2.75453i	−0.108292	+	0.108292i	0.650885	+	0.759176i	$0.274398\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−5.15690			−0.202426
$650$	6.87482	−	1.51000i	0.269653	−	0.0592270i
$651$	−1.04017	+	0.145397i	−0.0407674	+	0.00569855i
$652$	7.20110	+	7.20110i	0.282017	+	0.282017i
$653$	18.1791	−	18.1791i	0.711402	−	0.711402i	−0.255427	−	0.966828i	$-0.582216\pi$
$653$	18.1791	−	18.1791i	0.711402	−	0.711402i	0.966828	+	0.255427i	$0.0822159\pi$
$654$	5.19032	+	8.98990i	0.202958	+	0.351533i
$655$	−10.7694	−	8.66067i	−0.420794	−	0.338400i
$656$	−0.781646	+	1.35385i	−0.0305182	+	0.0528590i
$657$	14.8216	+	3.97143i	0.578245	+	0.154940i
$658$	0.362328	+	0.0970854i	0.0141250	+	0.00378478i
$659$			0.723146i			0.0281698i	0.999901	+	0.0140849i	$0.00448351\pi$
$659$			0.723146i			0.0281698i	−0.999901	+	0.0140849i	$0.995516\pi$
$660$	−12.7300	−	5.61622i	−0.495515	−	0.218611i
$661$	5.11287	−	8.85575i	0.198868	−	0.344449i	−0.749294	−	0.662238i	$-0.769607\pi$
$661$	5.11287	−	8.85575i	0.198868	−	0.344449i	0.948162	+	0.317789i	$0.102940\pi$
$662$	8.69843	+	32.4630i	0.338074	+	1.26171i
$663$	−2.51168	+	9.37373i	−0.0975457	+	0.364046i
$664$	7.76213	−	13.4444i	0.301229	−	0.521744i
$665$	1.53126	+	2.09267i	0.0593799	+	0.0811504i
$666$			4.24982i			0.164677i
$667$	49.3620	+	49.3620i	1.91131	+	1.91131i
$668$	2.96801	−	11.0768i	0.114836	−	0.428573i
$669$	17.8508	+	10.3062i	0.690152	+	0.398459i
$670$	8.72657	+	1.35189i	0.337137	+	0.0522282i
$671$	32.9317	−	57.0393i	1.27131	−	2.20198i
$672$	0.0488226	+	0.182208i	0.00188337	+	0.00702884i
$673$	−35.2483	+	9.44475i	−1.35872	+	0.364068i	−0.863347	−	0.504611i	$-0.831636\pi$
$673$	−35.2483	+	9.44475i	−1.35872	+	0.364068i	−0.495374	+	0.868680i	$0.664969\pi$
$674$	−20.4385			−0.787263
$675$	0.227875	−	4.99480i	0.00877091	−	0.192250i
$676$	−5.50914	−	9.54210i	−0.211890	−	0.367004i
$677$	2.95239	+	11.0185i	0.113470	+	0.423474i	0.999168	−	0.0407872i	$-0.0129866\pi$
$677$	2.95239	+	11.0185i	0.113470	+	0.423474i	−0.885698	+	0.464261i	$0.846320\pi$
$678$	−10.4343	−	10.4343i	−0.400727	−	0.400727i
$679$	2.73942	−	1.58160i	0.105129	−	0.0606963i
$680$	9.66011	−	12.0121i	0.370448	−	0.460645i
$681$			12.1274i			0.464722i
$682$	−27.6534	−	20.8706i	−1.05890	−	0.799177i
$683$	−5.33508	+	5.33508i	−0.204141	+	0.204141i	−0.801772	−	0.597631i	$-0.796109\pi$
$683$	−5.33508	+	5.33508i	−0.204141	+	0.204141i	0.597631	+	0.801772i	$0.296109\pi$
$684$			6.14760i			0.235060i
$685$	8.48770	+	11.5995i	0.324298	+	0.443196i
$686$	−2.63419			−0.100574
$687$	−5.50607	+	1.47535i	−0.210070	+	0.0562880i
$688$	0.471798	−	1.76077i	0.0179871	−	0.0671288i
$689$	−0.169118	+	0.0976405i	−0.00644289	+	0.00371981i
$690$	−19.8731	+	2.15677i	−0.756555	+	0.0821069i
$691$	−19.5776	+	33.9094i	−0.744767	+	1.28997i	0.205536	+	0.978650i	$0.434106\pi$
$691$	−19.5776	+	33.9094i	−0.744767	+	1.28997i	−0.950303	+	0.311325i	$0.899227\pi$
$692$	11.8272	−	3.16909i	0.449603	−	0.120471i
$693$	−1.13379	+	0.303797i	−0.0430690	+	0.0115403i
$694$	5.11035	+	8.85139i	0.193986	+	0.335994i
$695$	0.508833	−	0.197301i	0.0193011	−	0.00748406i
$696$	3.90441	+	6.76263i	0.147996	+	0.256337i
$697$	7.62030	−	7.62030i	0.288639	−	0.288639i
$698$	15.7877	−	15.7877i	0.597572	−	0.597572i
$699$	−9.02546	−	15.6326i	−0.341374	−	0.591277i
$700$	−0.837462	+	0.433874i	−0.0316531	+	0.0163989i
$701$	4.03093	+	6.98178i	0.152246	+	0.263698i	0.932053	−	0.362322i	$-0.118016\pi$
$701$	4.03093	+	6.98178i	0.152246	+	0.263698i	−0.779807	+	0.626020i	$0.784683\pi$
$702$	1.35977	−	0.364350i	0.0513213	−	0.0137515i
$703$	25.2360	−	6.76196i	0.951793	−	0.255032i
$704$	−3.11123	+	5.38881i	−0.117259	+	0.203099i
$705$	−2.78656	+	3.46503i	−0.104948	+	0.130500i
$706$	−29.1378	+	16.8227i	−1.09661	+	0.633131i
$707$	0.0912228	−	0.340448i	0.00343078	−	0.0128039i
$708$	−0.800516	+	0.214498i	−0.0300852	+	0.00806131i
$709$	−15.0466			−0.565086			−0.282543	−	0.959255i	$-0.591178\pi$
$709$	−15.0466			−0.565086			−0.282543	+	0.959255i	$0.591178\pi$
$710$	−11.2309	+	8.21792i	−0.421487	+	0.308413i
$711$			3.01315i			0.113002i
$712$	4.14238	−	4.14238i	0.155242	−	0.155242i
$713$	−49.3986	−	6.10270i	−1.84999	−	0.228548i
$714$		−	1.30038i		−	0.0486656i
$715$	19.4727	−	2.11333i	0.728239	−	0.0790339i
$716$	0.949674	−	0.548295i	0.0354910	−	0.0204907i
$717$	−14.7848	−	14.7848i	−0.552150	−	0.552150i
$718$	−4.15879	−	15.5208i	−0.155205	−	0.579231i
$719$	12.7430	+	22.0716i	0.475235	+	0.823132i	0.999598	−	0.0283633i	$-0.00902953\pi$
$719$	12.7430	+	22.0716i	0.475235	+	0.823132i	−0.524362	+	0.851495i	$0.675696\pi$
$720$	−2.20971	−	0.342321i	−0.0823510	−	0.0127576i
$721$	−2.57031			−0.0957234
$722$	18.1527	−	4.86399i	0.675573	−	0.181019i
$723$	1.83020	+	6.83038i	0.0680657	+	0.254025i
$724$	−11.1143	+	19.2505i	−0.413059	+	0.715439i
$725$	−28.8379	+	26.3214i	−1.07101	+	0.977552i
$726$	−24.0054	−	13.8595i	−0.890925	−	0.514376i
$727$	3.33350	−	12.4408i	0.123633	−	0.461404i	−0.876154	−	0.482030i	$-0.839899\pi$
$727$	3.33350	−	12.4408i	0.123633	−	0.461404i	0.999787	+	0.0206267i	$0.00656615\pi$
$728$	−0.187772	−	0.187772i	−0.00695931	−	0.00695931i
$729$		−	1.00000i		−	0.0370370i
$730$	33.9068	+	5.25273i	1.25495	+	0.194412i
$731$	−6.28313	+	10.8827i	−0.232390	+	0.402511i
$732$	2.73954	−	10.2241i	0.101256	−	0.377894i
$733$	0.892727	+	3.33170i	0.0329736	+	0.123059i	0.980451	−	0.196764i	$-0.0630432\pi$
$733$	0.892727	+	3.33170i	0.0329736	+	0.123059i	−0.947477	+	0.319823i	$0.896377\pi$
$734$	17.1141	−	29.6425i	0.631692	−	1.09412i
$735$	6.28589	−	14.2479i	0.231858	−	0.525542i
$736$			8.93969i			0.329522i
$737$	23.7364	+	6.36014i	0.874341	+	0.234279i
$738$	−1.51002	−	0.404610i	−0.0555848	−	0.0148939i
$739$	−18.6089	+	32.2315i	−0.684538	+	1.18565i	0.289044	+	0.957316i	$0.406663\pi$
$739$	−18.6089	+	32.2315i	−0.684538	+	1.18565i	−0.973582	+	0.228338i	$0.926671\pi$
$740$	1.02530	+	9.44741i	0.0376909	+	0.347294i
$741$	−4.32711	−	7.49478i	−0.158960	−	0.275327i
$742$	0.0185032	−	0.0185032i	0.000679275	−	0.000679275i
$743$	−11.6094	−	11.6094i	−0.425907	−	0.425907i	0.461325	−	0.887231i	$-0.347374\pi$
$743$	−11.6094	−	11.6094i	−0.425907	−	0.425907i	−0.887231	+	0.461325i	$0.847374\pi$
$744$	−5.16079	−	2.08956i	−0.189204	−	0.0766071i
$745$	24.0554	−	29.9124i	0.881323	−	1.09591i
$746$	7.53528			0.275886
$747$	14.9953	+	4.01797i	0.548649	+	0.147010i
$748$	30.3315	−	30.3315i	1.10903	−	1.10903i
$749$	0.237624	+	0.137192i	0.00868259	+	0.00501290i
$750$	−0.698467	−	11.1585i	−0.0255044	−	0.407451i
$751$	1.04840	+	1.81588i	0.0382565	+	0.0662622i	0.884520	−	0.466503i	$-0.154486\pi$
$751$	1.04840	+	1.81588i	0.0382565	+	0.0662622i	−0.846263	+	0.532765i	$0.821153\pi$
$752$	1.40611	+	1.40611i	0.0512754	+	0.0512754i
$753$	−3.12743	−	11.6717i	−0.113970	−	0.425341i
$754$	−9.52002	−	5.49639i	−0.346699	−	0.200167i
$755$	−2.48489	−	6.40846i	−0.0904346	−	0.233228i
$756$	−0.163364	+	0.0943180i	−0.00594148	+	0.00343031i
$757$	−2.52265	−	9.41467i	−0.0916874	−	0.342182i	0.904809	−	0.425818i	$-0.140013\pi$
$757$	−2.52265	−	9.41467i	−0.0916874	−	0.342182i	−0.996496	+	0.0836357i	$0.973347\pi$
$758$	−0.478507	−	0.128216i	−0.0173802	−	0.00465700i
$759$	−55.6269			−2.01913
$760$	1.48316	+	13.6662i	0.0537998	+	0.495726i
$761$	−15.9127	+	9.18721i	−0.576835	+	0.333036i	−0.759875	−	0.650070i	$-0.774740\pi$
$761$	−15.9127	+	9.18721i	−0.576835	+	0.333036i	0.183039	+	0.983106i	$0.441406\pi$
$762$	0.446194	−	0.119557i	0.0161639	−	0.00433111i
$763$	1.89144	+	0.506810i	0.0684747	+	0.0183478i
$764$	−10.1859	−	5.88081i	−0.368512	−	0.212760i
$765$	14.1031	+	6.22198i	0.509897	+	0.224956i
$766$	12.9639	+	7.48472i	0.468405	+	0.270434i
$767$	0.824961	−	0.824961i	0.0297876	−	0.0297876i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−37.2454	+	21.5036i	−1.34310	+	0.775441i	−0.987262	−	0.159105i	$-0.949139\pi$
$769$	−37.2454	+	21.5036i	−1.34310	+	0.775441i	−0.355842	+	0.934546i	$0.615806\pi$
$770$	−2.44713	+	0.948880i	−0.0881884	+	0.0341953i
$771$		−	0.235466i		−	0.00848012i
$772$	0.430840	−	1.60792i	0.0155063	−	0.0578701i
$773$	3.60681	+	3.60681i	0.129728	+	0.129728i	0.768989	−	0.639262i	$-0.220760\pi$
$773$	3.60681	+	3.60681i	0.129728	+	0.129728i	−0.639262	+	0.768989i	$0.720760\pi$
$774$	1.82289			0.0655223
$775$	4.66890	−	27.4445i	0.167712	−	0.985836i
$776$	16.7688			0.601966
$777$	0.566866	+	0.566866i	0.0203362	+	0.0203362i
$778$	8.05687	−	30.0686i	0.288853	−	1.07801i
$779$			9.61050i			0.344332i
$780$	2.93489	−	1.13801i	0.105086	−	0.0407473i
$781$	−33.5378	+	19.3631i	−1.20008	+	0.692866i
$782$	15.9502	−	59.5269i	0.570377	−	2.12868i
$783$	−5.52167	+	5.52167i	−0.197328	+	0.197328i
$784$	−6.03136	−	3.48221i	−0.215406	−	0.124365i
$785$	−33.0836	−	14.5958i	−1.18081	−	0.520947i
$786$	−5.35238	−	3.09020i	−0.190913	−	0.110224i
$787$	−45.8617	−	12.2886i	−1.63479	−	0.438041i	−0.679493	−	0.733682i	$-0.737800\pi$
$787$	−45.8617	−	12.2886i	−1.63479	−	0.438041i	−0.955299	+	0.295641i	$0.904467\pi$
$788$	−2.18912	+	0.586574i	−0.0779843	+	0.0208958i
$789$	14.7310	−	8.50493i	0.524436	−	0.302783i
$790$	0.726945	+	6.69827i	0.0258636	+	0.238314i
$791$	−2.78358			−0.0989727
$792$	−6.01044	−	1.61049i	−0.213572	−	0.0572264i
$793$	3.85656	+	14.3929i	0.136950	+	0.511106i
$794$	3.17054	−	1.83051i	0.112518	−	0.0649624i
$795$	0.112140	+	0.289206i	0.00397721	+	0.0102571i
$796$	−12.3009	−	7.10193i	−0.435994	−	0.251721i
$797$	−9.02302	−	33.6744i	−0.319612	−	1.19281i	−0.919618	−	0.392813i	$-0.871502\pi$
$797$	−9.02302	−	33.6744i	−0.319612	−	1.19281i	0.600007	−	0.799995i	$-0.295165\pi$
$798$	0.820003	+	0.820003i	0.0290278	+	0.0290278i
$799$	−6.85409	−	11.8716i	−0.242480	−	0.419988i
$800$	−4.99480	−	0.227875i	−0.176593	−	0.00805660i
$801$	5.07336	+	2.92910i	0.179258	+	0.103495i
$802$	−0.428346	+	0.428346i	−0.0151254	+	0.0151254i
$803$	92.2269	+	24.7121i	3.25462	+	0.872072i
$804$	3.94919			0.139277
$805$	−2.36310	+	2.93847i	−0.0832885	+	0.103567i
$806$	7.76249	−	1.08506i	0.273422	−	0.0382195i
$807$	18.2485	+	18.2485i	0.642379	+	0.642379i
$808$	1.32120	−	1.32120i	0.0464795	−	0.0464795i
$809$	3.13899	+	5.43689i	0.110361	+	0.191151i	0.915916	−	0.401370i	$-0.131466\pi$
$809$	3.13899	+	5.43689i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$810$	−0.241258	−	2.22301i	−0.00847694	−	0.0781088i
$811$	−18.4037	+	31.8761i	−0.646240	+	1.11932i	0.337774	+	0.941227i	$0.390326\pi$
$811$	−18.4037	+	31.8761i	−0.646240	+	1.11932i	−0.984014	+	0.178093i	$0.943007\pi$
$812$	1.42283	+	0.381247i	0.0499316	+	0.0133791i
$813$	12.1784	+	3.26319i	0.427114	+	0.114445i
$814$			26.4444i			0.926874i
$815$	−9.19170	+	20.8344i	−0.321971	+	0.729797i
$816$	3.44680	−	5.97004i	0.120662	−	0.208993i
$817$	−2.90042	−	10.8245i	−0.101473	−	0.378702i
$818$	3.75049	−	13.9970i	0.131133	−	0.489394i
$819$	0.132775	−	0.229973i	0.00463954	−	0.00803592i
$820$	−3.45442	−	0.535148i	−0.120634	−	0.0186882i
$821$			16.5313i			0.576946i	0.957488	+	0.288473i	$0.0931475\pi$
$821$			16.5313i			0.576946i	−0.957488	+	0.288473i	$0.906853\pi$
$822$	4.54522	+	4.54522i	0.158533	+	0.158533i
$823$	−12.0842	+	45.0987i	−0.421227	+	1.57204i	0.350799	+	0.936451i	$0.385910\pi$
$823$	−12.0842	+	45.0987i	−0.421227	+	1.57204i	−0.772026	+	0.635591i	$0.780757\pi$
$824$	−11.8003	−	6.81288i	−0.411081	−	0.237338i
$825$	1.41794	−	31.0800i	0.0493665	−	1.08207i
$826$	−0.0781666	+	0.135388i	−0.00271976	+	0.00471077i
$827$	−0.610483	−	2.27835i	−0.0212286	−	0.0792261i	0.954499	−	0.298214i	$-0.0963910\pi$
$827$	−0.610483	−	2.27835i	−0.0212286	−	0.0792261i	−0.975727	+	0.218988i	$0.929724\pi$
$828$	−8.63508	+	2.31376i	−0.300090	+	0.0804088i
$829$	−24.4046			−0.847608			−0.423804	−	0.905754i	$-0.639305\pi$
$829$	−24.4046			−0.847608			−0.423804	+	0.905754i	$0.639305\pi$
$830$	34.3041	+	5.31428i	1.19071	+	0.184461i
$831$	7.20677	+	12.4825i	0.250000	+	0.433013i
$832$	−0.364350	−	1.35977i	−0.0126316	−	0.0471416i
$833$	33.9482	+	33.9482i	1.17623	+	1.17623i
$834$	0.211367	−	0.122033i	0.00731903	−	0.00422564i
$835$	25.4925	−	2.76663i	0.882203	−	0.0957432i
$836$			38.2533i			1.32302i
$837$	0.682652	−	5.52576i	0.0235959	−	0.190998i
$838$	−18.8524	+	18.8524i	−0.651244	+	0.651244i
$839$			24.4766i			0.845027i	0.906357	+	0.422513i	$0.138852\pi$
$839$			24.4766i			0.845027i	−0.906357	+	0.422513i	$0.861148\pi$
$840$	−0.340405	+	0.249083i	−0.0117451	+	0.00859419i
$841$	31.9776			1.10268
$842$	−28.3087	+	7.58530i	−0.975583	+	0.261407i
$843$	−5.57615	+	20.8105i	−0.192053	+	0.716751i
$844$	6.59011	−	3.80480i	0.226841	−	0.130967i
$845$	15.4401	−	19.1994i	0.531154	−	0.660479i
$846$	−0.994267	+	1.72212i	−0.0341836	+	0.0592077i
$847$	−5.05065	+	1.35332i	−0.173542	+	0.0465006i
$848$	0.133993	−	0.0359033i	0.00460133	−	0.00123292i
$849$	1.73892	+	3.01190i	0.0596796	+	0.103368i
$850$	32.8524	+	10.4291i	1.12683	+	0.357714i
$851$	18.9960	+	32.9021i	0.651176	+	1.12787i
$852$	−4.40075	+	4.40075i	−0.150767	+	0.150767i
$853$	0.392117	−	0.392117i	0.0134258	−	0.0134258i	−0.700362	−	0.713788i	$-0.746978\pi$
$853$	0.392117	−	0.392117i	0.0134258	−	0.0134258i	0.713788	+	0.700362i	$0.246978\pi$
$854$	−0.998335	−	1.72917i	−0.0341623	−	0.0591709i
$855$	−12.8167	+	4.96970i	−0.438321	+	0.169960i
$856$	0.727285	+	1.25970i	0.0248581	+	0.0430555i
$857$	−32.5181	+	8.71319i	−1.11080	+	0.297637i	−0.767153	−	0.641464i	$-0.778327\pi$
$857$	−32.5181	+	8.71319i	−1.11080	+	0.297637i	−0.343642	+	0.939101i	$0.611661\pi$
$858$	8.46113	−	2.26715i	0.288858	−	0.0773993i
$859$	−1.29633	+	2.24532i	−0.0442304	+	0.0766092i	−0.887293	−	0.461206i	$-0.847417\pi$
$859$	−1.29633	+	2.24532i	−0.0442304	+	0.0766092i	0.843063	+	0.537815i	$0.180750\pi$
$860$	4.05230	−	0.439786i	0.138182	−	0.0149966i
$861$	−0.255385	+	0.147447i	−0.00870350	+	0.00502497i
$862$	−8.43555	+	31.4819i	−0.287316	+	1.07228i
$863$	−14.7483	+	3.95179i	−0.502037	+	0.134520i	−0.500945	−	0.865479i	$-0.667014\pi$
$863$	−14.7483	+	3.95179i	−0.502037	+	0.134520i	−0.00109163	+	0.999999i	$0.500347\pi$
$864$	−1.00000			−0.0340207
$865$	16.1681	+	22.0958i	0.549730	+	0.751279i
$866$		−	1.93063i		−	0.0656053i
$867$	−21.5822	+	21.5822i	−0.732970	+	0.732970i
$868$	−0.967094	+	0.409658i	−0.0328253	+	0.0139047i
$869$			18.7492i			0.636023i
$870$	−10.9426	+	13.6069i	−0.370989	+	0.461317i
$871$	−4.81461	+	2.77972i	−0.163137	+	0.0941871i
$872$	7.34022	+	7.34022i	0.248571	+	0.248571i
$873$	4.34009	+	16.1974i	0.146890	+	0.548200i
$874$	27.4789	+	47.5948i	0.929486	+	1.60992i
$875$	−1.58155	−	1.39522i	−0.0534662	−	0.0471671i
$876$	15.3444			0.518441
$877$	−8.09351	+	2.16865i	−0.273298	+	0.0732301i	−0.392865	−	0.919596i	$-0.628516\pi$
$877$	−8.09351	+	2.16865i	−0.273298	+	0.0732301i	0.119567	+	0.992826i	$0.461849\pi$
$878$	−7.71024	−	28.7750i	−0.260208	−	0.971110i
$879$	−10.1755	+	17.6245i	−0.343211	+	0.594459i
$880$	−13.7498	−	2.13008i	−0.463507	−	0.0718050i
$881$	34.1266	+	19.7030i	1.14976	+	0.663812i	0.948828	−	0.315794i	$-0.102271\pi$
$881$	34.1266	+	19.7030i	1.14976	+	0.663812i	0.200928	+	0.979606i	$0.435604\pi$
$882$	1.80252	−	6.72711i	0.0606941	−	0.226514i
$883$	−13.0011	−	13.0011i	−0.437522	−	0.437522i	0.453656	−	0.891177i	$-0.350120\pi$
$883$	−13.0011	−	13.0011i	−0.437522	−	0.437522i	−0.891177	+	0.453656i	$0.850120\pi$
$884$			9.70440i			0.326394i
$885$	−1.09432	−	1.49554i	−0.0367853	−	0.0502719i
$886$	8.94022	−	15.4849i	0.300353	−	0.520226i
$887$	4.51469	−	16.8491i	0.151589	−	0.565736i	−0.847785	−	0.530340i	$-0.822064\pi$
$887$	4.51469	−	16.8491i	0.151589	−	0.565736i	0.999373	−	0.0353959i	$-0.0112692\pi$
$888$	1.09993	+	4.10501i	0.0369114	+	0.137755i
$889$	0.0435687	−	0.0754632i	0.00146125	−	0.00253096i
$890$	11.9848	+	5.28745i	0.401732	+	0.177236i
$891$		−	6.22247i		−	0.208460i
$892$	19.9100	+	5.33486i	0.666635	+	0.178624i
$893$	11.8082	+	3.16399i	0.395145	+	0.105879i
$894$	8.58317	−	14.8665i	0.287064	−	0.497210i
$895$	1.91081	+	1.53667i	0.0638714	+	0.0513651i
$896$	0.0943180	+	0.163364i	0.00315094	+	0.00545760i
$897$	8.89877	−	8.89877i	0.297121	−	0.297121i
$898$	21.6209	+	21.6209i	0.721499	+	0.721499i
$899$	−34.2808	+	26.7420i	−1.14333	+	0.891896i
$900$	−1.07264	−	4.88359i	−0.0357547	−	0.162786i
$901$	−0.956279			−0.0318583
$902$	−9.39608	−	2.51767i	−0.312855	−	0.0838293i
$903$	0.243147	−	0.243147i	0.00809143	−	0.00809143i
$904$	−12.7794	−	7.37817i	−0.425035	−	0.245394i
$905$	−49.1187	−	7.60931i	−1.63276	−	0.252942i
$906$	−1.53693	−	2.66204i	−0.0510610	−	0.0884403i
$907$	21.9667	+	21.9667i	0.729393	+	0.729393i	0.970499	−	0.241106i	$-0.0775101\pi$
$907$	21.9667	+	21.9667i	0.729393	+	0.729393i	−0.241106	+	0.970499i	$0.577510\pi$
$908$	3.13879	+	11.7141i	0.104165	+	0.388747i
$909$	1.61813	+	0.934226i	0.0536699	+	0.0309863i
$910$	0.239678	−	0.543267i	0.00794526	−	0.0180091i
$911$	−9.26403	+	5.34859i	−0.306931	+	0.177207i	−0.645552	−	0.763716i	$-0.723373\pi$
$911$	−9.26403	+	5.34859i	−0.306931	+	0.177207i	0.338621	+	0.940923i	$0.390039\pi$
$912$	1.59112	+	5.93813i	0.0526871	+	0.196631i
$913$	93.3076	+	25.0017i	3.08803	+	0.827436i
$914$	−2.40747			−0.0796321
$915$	23.5301	−	2.55366i	0.777881	−	0.0844214i
$916$	−4.93661	+	2.85015i	−0.163110	+	0.0941717i
$917$	−1.12612	+	0.301743i	−0.0371878	+	0.00996443i
$918$	6.65872	+	1.78420i	0.219770	+	0.0588873i
$919$	20.2032	+	11.6643i	0.666443	+	0.384771i	0.794728	−	0.606966i	$-0.207614\pi$
$919$	20.2032	+	11.6643i	0.666443	+	0.384771i	−0.128284	+	0.991737i	$0.540947\pi$
$920$	−18.6377	+	7.22681i	−0.614467	+	0.238261i
$921$	10.5181	+	6.07262i	0.346583	+	0.200100i
$922$	12.8294	−	12.8294i	0.422513	−	0.422513i
$923$	2.26757	−	8.46268i	0.0746379	−	0.278553i
$924$	−1.01652	+	0.586891i	−0.0334412	+	0.0193073i
$925$	−18.8674	+	9.77483i	−0.620355	+	0.321394i
$926$			8.07427i			0.265337i
$927$	3.52661	−	13.1615i	0.115829	−	0.432280i
$928$	5.52167	+	5.52167i	0.181258	+	0.181258i
$929$	12.9140			0.423694			0.211847	−	0.977303i	$-0.432052\pi$
$929$	12.9140			0.423694			0.211847	+	0.977303i	$0.432052\pi$
$930$	0.184413	−	12.4485i	0.00604715	−	0.408204i
$931$	−42.8145			−1.40319
$932$	−12.7639	−	12.7639i	−0.418096	−	0.418096i
$933$	0.184118	−	0.687139i	0.00602777	−	0.0224959i
$934$		−	10.9006i		−	0.356680i
$935$	87.7558	+	38.7160i	2.86992	+	1.26615i
$936$	1.21914	−	0.703869i	0.0398488	−	0.0230067i
$937$	−8.73878	+	32.6136i	−0.285483	+	1.06544i	0.663002	+	0.748618i	$0.269282\pi$
$937$	−8.73878	+	32.6136i	−0.285483	+	1.06544i	−0.948485	+	0.316821i	$0.897385\pi$
$938$	0.526766	−	0.526766i	0.0171995	−	0.0171995i
$939$	14.8539	+	8.57591i	0.484739	+	0.279864i
$940$	−1.79479	+	4.06817i	−0.0585397	+	0.132689i
$941$	45.9840	+	26.5489i	1.49904	+	0.865469i	0.999999	−	0.00111196i	$-0.000353949\pi$
$941$	45.9840	+	26.5489i	1.49904	+	0.865469i	0.499037	+	0.866581i	$0.333687\pi$
$942$	−15.6203	−	4.18546i	−0.508938	−	0.136369i
$943$	−13.4992	+	3.61709i	−0.439593	+	0.117789i
$944$	−0.717723	+	0.414378i	−0.0233599	+	0.0134868i
$945$	−0.328699	−	0.264338i	−0.0106926	−	0.00859893i
$946$	11.3428			0.368788
$947$	−34.7867	−	9.32106i	−1.13041	−	0.302894i	−0.355323	−	0.934743i	$-0.615629\pi$
$947$	−34.7867	−	9.32106i	−1.13041	−	0.302894i	−0.775091	+	0.631850i	$0.782296\pi$
$948$	0.779859	+	2.91047i	0.0253287	+	0.0945278i
$949$	−18.7070	+	10.8005i	−0.607255	+	0.350599i
$950$	−27.2927	+	14.1398i	−0.885492	+	0.458757i
$951$	8.66530	+	5.00291i	0.280992	+	0.162231i
$952$	−0.336564	−	1.25607i	−0.0109081	−	0.0407096i
$953$	−22.4667	−	22.4667i	−0.727767	−	0.727767i	0.242408	−	0.970174i	$-0.422063\pi$
$953$	−22.4667	−	22.4667i	−0.727767	−	0.727767i	−0.970174	+	0.242408i	$0.922063\pi$
$954$	0.0693598	+	0.120135i	0.00224561	+	0.00388950i
$955$	4.02625	−	25.9898i	0.130286	−	0.841009i
$956$	−18.1076	−	10.4545i	−0.585643	−	0.338121i
$957$	−34.3584	+	34.3584i	−1.11065	+	1.11065i
$958$	23.9164	+	6.40839i	0.772705	+	0.207046i
$959$	1.21254			0.0391549
$960$	−2.22301	+	0.241258i	−0.0717475	+	0.00778657i
$961$	7.54434	−	30.0680i	0.243366	−	0.969935i
$962$	−4.23036	−	4.23036i	−0.136392	−	0.136392i
$963$	−1.02854	+	1.02854i	−0.0331441	+	0.0331441i
$964$	3.53567	+	6.12396i	0.113876	+	0.197239i
$965$	3.70051	−	0.401607i	0.119124	−	0.0129282i
$966$	−0.843175	+	1.46042i	−0.0271287	+	0.0469883i
$967$	−29.2038	−	7.82515i	−0.939132	−	0.251640i	−0.243388	−	0.969929i	$-0.578259\pi$
$967$	−29.2038	−	7.82515i	−0.939132	−	0.251640i	−0.695745	+	0.718289i	$0.744925\pi$
$968$	−26.7746	−	7.17423i	−0.860567	−	0.230588i
$969$		−	42.3792i		−	1.36142i
$970$	13.5558	+	34.9601i	0.435252	+	1.12250i
$971$	−17.4407	+	30.2081i	−0.559698	+	0.969425i	0.437823	+	0.899061i	$0.355750\pi$
$971$	−17.4407	+	30.2081i	−0.559698	+	0.969425i	−0.997521	+	0.0703644i	$0.977584\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	0.0119159	−	0.0444707i	0.000382006	−	0.00142567i
$974$	16.2184	−	28.0912i	0.519673	−	0.900099i
$975$	4.74511	+	5.19877i	0.151965	+	0.166494i
$976$		−	10.5848i		−	0.338810i
$977$	−5.99628	−	5.99628i	−0.191838	−	0.191838i	0.604652	−	0.796490i	$-0.293312\pi$
$977$	−5.99628	−	5.99628i	−0.191838	−	0.191838i	−0.796490	+	0.604652i	$0.793312\pi$
$978$	−2.63579	+	9.83689i	−0.0842832	+	0.314549i
$979$	31.5688	+	18.2263i	1.00894	+	0.582514i
$980$	2.38407	−	15.3893i	0.0761562	−	0.491594i
$981$	−5.19032	+	8.98990i	−0.165714	+	0.287025i
$982$	−3.33487	−	12.4459i	−0.106420	−	0.397165i
$983$	55.4388	−	14.8548i	1.76822	−	0.473794i	0.779866	−	0.625947i	$-0.215287\pi$
$983$	55.4388	−	14.8548i	1.76822	−	0.473794i	0.988357	+	0.152153i	$0.0486205\pi$
$984$	−1.56329			−0.0498359
$985$	−2.99258	−	4.08976i	−0.0953516	−	0.130311i
$986$	−26.9155	−	46.6190i	−0.857163	−	1.48465i
$987$	0.0970854	+	0.362328i	0.00309026	+	0.0115330i
$988$	−6.11946	−	6.11946i	−0.194686	−	0.194686i
$989$	14.1128	−	8.14802i	0.448760	−	0.259092i
$990$	−1.50122	−	13.8326i	−0.0477119	−	0.439630i
$991$		−	46.0870i		−	1.46400i	−0.681303	−	0.732001i	$-0.738586\pi$
$991$		−	46.0870i		−	1.46400i	0.681303	−	0.732001i	$-0.261414\pi$
$992$	−5.52576	−	0.682652i	−0.175443	−	0.0216742i
$993$	−23.7646	+	23.7646i	−0.754145	+	0.754145i
$994$			1.17400i			0.0372369i
$995$	4.86228	−	31.3864i	0.154145	−	0.995016i
$996$	15.5243			0.491905
$997$	5.86359	−	1.57114i	0.185702	−	0.0497586i	−0.164770	−	0.986332i	$-0.552688\pi$
$997$	5.86359	−	1.57114i	0.185702	−	0.0497586i	0.350471	+	0.936573i	$0.386021\pi$
$998$	−0.465090	+	1.73574i	−0.0147222	+	0.0549439i
$999$	−3.68045	+	2.12491i	−0.116444	+	0.0672292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.9	yes	64
5.3	odd	4		930.2.be.a.223.13	✓	64
31.26	odd	6		930.2.be.a.367.13	yes	64
155.88	even	12	inner	930.2.be.b.553.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.13	✓	64	5.3	odd	4
930.2.be.a.367.13	yes	64	31.26	odd	6
930.2.be.b.37.9	yes	64	1.1	even	1	trivial
930.2.be.b.553.9	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.08483 + 0.808396i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.0488226 + 0.182208i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.08483 + 0.808396i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.0488226 + 0.182208i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.04582 - 0.902572i) q^{10} +(-5.38881 - 3.11123i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.35977 - 0.364350i) q^{13} +(-0.163364 + 0.0943180i) q^{14} +(-0.241258 - 2.22301i) q^{15} -1.00000 q^{16} +(6.65872 + 1.78420i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-5.32398 + 3.07380i) q^{19} +(-0.808396 - 2.08483i) q^{20} +(-0.163364 - 0.0943180i) q^{21} +(-1.61049 - 6.01044i) q^{22} +(-6.32132 - 6.32132i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.69299 - 3.37073i) q^{25} +(1.21914 + 0.703869i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.182208 - 0.0488226i) q^{28} -7.80882 q^{29} +(1.40131 - 1.74250i) q^{30} +(4.39001 - 3.42459i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.39995 - 4.39995i) q^{33} +(3.44680 + 5.97004i) q^{34} +(-0.0455100 - 0.419341i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.10501 - 1.09993i) q^{37} +(-5.93813 - 1.59112i) q^{38} +1.40774i q^{39} +(0.902572 - 2.04582i) q^{40} +(0.781646 - 1.35385i) q^{41} +(-0.0488226 - 0.182208i) q^{42} +(-0.471798 + 1.76077i) q^{43} +(3.11123 - 5.38881i) q^{44} +(2.20971 + 0.342321i) q^{45} -8.93969i q^{46} +(-1.40611 - 1.40611i) q^{47} +(0.258819 - 0.965926i) q^{48} +(6.03136 + 3.48221i) q^{49} +(4.99480 + 0.227875i) q^{50} +(-3.44680 + 5.97004i) q^{51} +(0.364350 + 1.35977i) q^{52} +(-0.133993 + 0.0359033i) q^{53} +1.00000 q^{54} +(13.7498 + 2.13008i) q^{55} +(-0.0943180 - 0.163364i) q^{56} +(-1.59112 - 5.93813i) q^{57} +(-5.52167 - 5.52167i) q^{58} +(0.717723 - 0.414378i) q^{59} +(2.22301 - 0.241258i) q^{60} +10.5848i q^{61} +(5.52576 + 0.682652i) q^{62} +(0.133386 - 0.133386i) q^{63} -1.00000i q^{64} +(-2.54035 + 1.85884i) q^{65} +6.22247 q^{66} +(-3.81463 + 1.02213i) q^{67} +(-1.78420 + 6.65872i) q^{68} +(7.74200 - 4.46985i) q^{69} +(0.264338 - 0.328699i) q^{70} +(3.11180 - 5.38980i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-14.8216 + 3.97143i) q^{73} +(-2.12491 - 3.68045i) q^{74} +(2.30006 + 4.43957i) q^{75} +(-3.07380 - 5.32398i) q^{76} +(0.829989 - 0.829989i) q^{77} +(-0.995422 + 0.995422i) q^{78} +(-1.50657 - 2.60946i) q^{79} +(2.08483 - 0.808396i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.51002 - 0.404610i) q^{82} +(-14.9953 + 4.01797i) q^{83} +(0.0943180 - 0.163364i) q^{84} +(-15.3246 + 1.66314i) q^{85} +(-1.57867 + 0.911443i) q^{86} +(2.02107 - 7.54274i) q^{87} +(6.01044 - 1.61049i) q^{88} -5.85821 q^{89} +(1.32044 + 1.80456i) q^{90} +0.265550i q^{91} +(6.32132 - 6.32132i) q^{92} +(2.17168 + 5.12677i) q^{93} -1.98853i q^{94} +(8.61472 - 10.7122i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-11.8573 - 11.8573i) q^{97} +(1.80252 + 6.72711i) q^{98} +(3.11123 + 5.38881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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