LMFDB - Embedded newform 546.2.bi.e.257.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.17
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.72971 + 0.0900624i) q^{3} +1.00000 q^{4} +(-1.98183 - 1.14421i) q^{5} +(-1.72971 - 0.0900624i) q^{6} +(-0.877809 - 2.49589i) q^{7} -1.00000 q^{8} +(2.98378 + 0.311563i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.72971 + 0.0900624i) q^{3} +1.00000 q^{4} +(-1.98183 - 1.14421i) q^{5} +(-1.72971 - 0.0900624i) q^{6} +(-0.877809 - 2.49589i) q^{7} -1.00000 q^{8} +(2.98378 + 0.311563i) q^{9} +(1.98183 + 1.14421i) q^{10} +(-0.148570 + 0.257331i) q^{11} +(1.72971 + 0.0900624i) q^{12} +(3.20028 + 1.66078i) q^{13} +(0.877809 + 2.49589i) q^{14} +(-3.32494 - 2.15764i) q^{15} +1.00000 q^{16} +0.893327 q^{17} +(-2.98378 - 0.311563i) q^{18} +(-3.94533 - 6.83352i) q^{19} +(-1.98183 - 1.14421i) q^{20} +(-1.29357 - 4.39621i) q^{21} +(0.148570 - 0.257331i) q^{22} -7.81240i q^{23} +(-1.72971 - 0.0900624i) q^{24} +(0.118437 + 0.205138i) q^{25} +(-3.20028 - 1.66078i) q^{26} +(5.13300 + 0.807639i) q^{27} +(-0.877809 - 2.49589i) q^{28} +(-0.980947 + 0.566350i) q^{29} +(3.32494 + 2.15764i) q^{30} +(-0.839051 - 1.45328i) q^{31} -1.00000 q^{32} +(-0.280159 + 0.431727i) q^{33} -0.893327 q^{34} +(-1.11615 + 5.95083i) q^{35} +(2.98378 + 0.311563i) q^{36} -4.99903i q^{37} +(3.94533 + 6.83352i) q^{38} +(5.38598 + 3.16089i) q^{39} +(1.98183 + 1.14421i) q^{40} +(6.52086 - 3.76482i) q^{41} +(1.29357 + 4.39621i) q^{42} +(-1.94207 + 3.36377i) q^{43} +(-0.148570 + 0.257331i) q^{44} +(-5.55685 - 4.03154i) q^{45} +7.81240i q^{46} +(5.21062 + 3.00835i) q^{47} +(1.72971 + 0.0900624i) q^{48} +(-5.45890 + 4.38183i) q^{49} +(-0.118437 - 0.205138i) q^{50} +(1.54520 + 0.0804552i) q^{51} +(3.20028 + 1.66078i) q^{52} +(-6.28351 + 3.62779i) q^{53} +(-5.13300 - 0.807639i) q^{54} +(0.588883 - 0.339992i) q^{55} +(0.877809 + 2.49589i) q^{56} +(-6.20883 - 12.1753i) q^{57} +(0.980947 - 0.566350i) q^{58} +6.02418i q^{59} +(-3.32494 - 2.15764i) q^{60} +(7.31581 - 4.22379i) q^{61} +(0.839051 + 1.45328i) q^{62} +(-1.84156 - 7.72066i) q^{63} +1.00000 q^{64} +(-4.44214 - 6.95319i) q^{65} +(0.280159 - 0.431727i) q^{66} +(2.94347 + 1.69941i) q^{67} +0.893327 q^{68} +(0.703603 - 13.5132i) q^{69} +(1.11615 - 5.95083i) q^{70} +(-1.14995 + 1.99178i) q^{71} +(-2.98378 - 0.311563i) q^{72} +(6.16302 + 10.6747i) q^{73} +4.99903i q^{74} +(0.186386 + 0.365496i) q^{75} +(-3.94533 - 6.83352i) q^{76} +(0.772686 + 0.144927i) q^{77} +(-5.38598 - 3.16089i) q^{78} +(4.46469 - 7.73307i) q^{79} +(-1.98183 - 1.14421i) q^{80} +(8.80586 + 1.85927i) q^{81} +(-6.52086 + 3.76482i) q^{82} +1.54870i q^{83} +(-1.29357 - 4.39621i) q^{84} +(-1.77042 - 1.02215i) q^{85} +(1.94207 - 3.36377i) q^{86} +(-1.74776 + 0.891273i) q^{87} +(0.148570 - 0.257331i) q^{88} +14.3106i q^{89} +(5.55685 + 4.03154i) q^{90} +(1.33588 - 9.44539i) q^{91} -7.81240i q^{92} +(-1.32043 - 2.58932i) q^{93} +(-5.21062 - 3.00835i) q^{94} +18.0572i q^{95} +(-1.72971 - 0.0900624i) q^{96} +(-1.19346 + 2.06713i) q^{97} +(5.45890 - 4.38183i) q^{98} +(-0.523476 + 0.721530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.72971	+	0.0900624i	0.998647	+	0.0519975i
$3$	1.72971	+	0.0900624i	0.998647	+	0.0519975i
$4$	1.00000			0.500000
$5$	−1.98183	−	1.14421i	−0.886302	−	0.511707i	−0.0135708	−	0.999908i	$-0.504320\pi$
$5$	−1.98183	−	1.14421i	−0.886302	−	0.511707i	−0.872731	+	0.488201i	$0.837653\pi$
$6$	−1.72971	−	0.0900624i	−0.706150	−	0.0367678i
$7$	−0.877809	−	2.49589i	−0.331781	−	0.943357i
$7$	−0.877809	−	2.49589i	−0.331781	−	0.943357i
$8$	−1.00000			−0.353553
$9$	2.98378	+	0.311563i	0.994593	+	0.103854i
$10$	1.98183	+	1.14421i	0.626710	+	0.361831i
$11$	−0.148570	+	0.257331i	−0.0447956	+	0.0775883i	−0.887554	−	0.460704i	$-0.847597\pi$
$11$	−0.148570	+	0.257331i	−0.0447956	+	0.0775883i	0.842758	+	0.538292i	$0.180930\pi$
$12$	1.72971	+	0.0900624i	0.499324	+	0.0259988i
$13$	3.20028	+	1.66078i	0.887599	+	0.460618i
$13$	3.20028	+	1.66078i	0.887599	+	0.460618i
$14$	0.877809	+	2.49589i	0.234604	+	0.667054i
$15$	−3.32494	−	2.15764i	−0.858495	−	0.557100i
$16$	1.00000			0.250000
$17$	0.893327			0.216664			0.108332	−	0.994115i	$-0.465449\pi$
$17$	0.893327			0.216664			0.108332	+	0.994115i	$0.465449\pi$
$18$	−2.98378	−	0.311563i	−0.703283	−	0.0734362i
$19$	−3.94533	−	6.83352i	−0.905122	−	1.56772i	−0.820754	−	0.571282i	$-0.806446\pi$
$19$	−3.94533	−	6.83352i	−0.905122	−	1.56772i	−0.0843680	−	0.996435i	$-0.526887\pi$
$20$	−1.98183	−	1.14421i	−0.443151	−	0.255853i
$21$	−1.29357	−	4.39621i	−0.282280	−	0.959332i
$22$	0.148570	−	0.257331i	0.0316753	−	0.0548632i
$23$		−	7.81240i		−	1.62900i	−0.580165	−	0.814499i	$-0.697012\pi$
$23$		−	7.81240i		−	1.62900i	0.580165	−	0.814499i	$-0.302988\pi$
$24$	−1.72971	−	0.0900624i	−0.353075	−	0.0183839i
$25$	0.118437	+	0.205138i	0.0236873	+	0.0410277i
$26$	−3.20028	−	1.66078i	−0.627627	−	0.325706i
$27$	5.13300	+	0.807639i	0.987847	+	0.155430i
$28$	−0.877809	−	2.49589i	−0.165890	−	0.471678i
$29$	−0.980947	+	0.566350i	−0.182157	+	0.105169i	−0.588306	−	0.808639i	$-0.700205\pi$
$29$	−0.980947	+	0.566350i	−0.182157	+	0.105169i	0.406149	+	0.913807i	$0.366872\pi$
$30$	3.32494	+	2.15764i	0.607048	+	0.393929i
$31$	−0.839051	−	1.45328i	−0.150698	−	0.261017i	0.780786	−	0.624798i	$-0.214819\pi$
$31$	−0.839051	−	1.45328i	−0.150698	−	0.261017i	−0.931484	+	0.363782i	$0.881485\pi$
$32$	−1.00000			−0.176777
$33$	−0.280159	+	0.431727i	−0.0487694	+	0.0751541i
$34$	−0.893327			−0.153204
$35$	−1.11615	+	5.95083i	−0.188664	+	1.00587i
$36$	2.98378	+	0.311563i	0.497296	+	0.0519272i
$37$		−	4.99903i		−	0.821835i	−0.911673	−	0.410918i	$-0.865208\pi$
$37$		−	4.99903i		−	0.821835i	0.911673	−	0.410918i	$-0.134792\pi$
$38$	3.94533	+	6.83352i	0.640018	+	1.10854i
$39$	5.38598	+	3.16089i	0.862447	+	0.506148i
$40$	1.98183	+	1.14421i	0.313355	+	0.180916i
$41$	6.52086	−	3.76482i	1.01839	−	0.587966i	0.104751	−	0.994498i	$-0.466595\pi$
$41$	6.52086	−	3.76482i	1.01839	−	0.587966i	0.913636	+	0.406532i	$0.133262\pi$
$42$	1.29357	+	4.39621i	0.199602	+	0.678350i
$43$	−1.94207	+	3.36377i	−0.296163	+	0.512970i	−0.975255	−	0.221084i	$-0.929041\pi$
$43$	−1.94207	+	3.36377i	−0.296163	+	0.512970i	0.679092	+	0.734054i	$0.262374\pi$
$44$	−0.148570	+	0.257331i	−0.0223978	+	0.0387942i
$45$	−5.55685	−	4.03154i	−0.828366	−	0.600986i
$46$			7.81240i			1.15188i
$47$	5.21062	+	3.00835i	0.760047	+	0.438813i	0.829313	−	0.558785i	$-0.188732\pi$
$47$	5.21062	+	3.00835i	0.760047	+	0.438813i	−0.0692655	+	0.997598i	$0.522066\pi$
$48$	1.72971	+	0.0900624i	0.249662	+	0.0129994i
$49$	−5.45890	+	4.38183i	−0.779843	+	0.625975i
$50$	−0.118437	−	0.205138i	−0.0167495	−	0.0290109i
$51$	1.54520	+	0.0804552i	0.216371	+	0.0112660i
$52$	3.20028	+	1.66078i	0.443799	+	0.230309i
$53$	−6.28351	+	3.62779i	−0.863107	+	0.498315i	−0.865051	−	0.501683i	$-0.832714\pi$
$53$	−6.28351	+	3.62779i	−0.863107	+	0.498315i	0.00194455	+	0.999998i	$0.499381\pi$
$54$	−5.13300	−	0.807639i	−0.698513	−	0.109906i
$55$	0.588883	−	0.339992i	0.0794049	−	0.0458444i
$56$	0.877809	+	2.49589i	0.117302	+	0.333527i
$57$	−6.20883	−	12.1753i	−0.822380	−	1.61266i
$58$	0.980947	−	0.566350i	0.128805	−	0.0743654i
$59$			6.02418i			0.784281i	0.919905	+	0.392141i	$0.128265\pi$
$59$			6.02418i			0.784281i	−0.919905	+	0.392141i	$0.871735\pi$
$60$	−3.32494	−	2.15764i	−0.429248	−	0.278550i
$61$	7.31581	−	4.22379i	0.936694	−	0.540800i	0.0477714	−	0.998858i	$-0.484788\pi$
$61$	7.31581	−	4.22379i	0.936694	−	0.540800i	0.888922	+	0.458058i	$0.151455\pi$
$62$	0.839051	+	1.45328i	0.106560	+	0.184567i
$63$	−1.84156	−	7.72066i	−0.232015	−	0.972712i
$64$	1.00000			0.125000
$65$	−4.44214	−	6.95319i	−0.550979	−	0.862436i
$66$	0.280159	−	0.431727i	0.0344852	−	0.0531420i
$67$	2.94347	+	1.69941i	0.359602	+	0.207617i	0.668906	−	0.743347i	$-0.266763\pi$
$67$	2.94347	+	1.69941i	0.359602	+	0.207617i	−0.309304	+	0.950963i	$0.600096\pi$
$68$	0.893327			0.108332
$69$	0.703603	−	13.5132i	0.0847039	−	1.62679i
$70$	1.11615	−	5.95083i	0.133406	−	0.711260i
$71$	−1.14995	+	1.99178i	−0.136474	+	0.236381i	−0.926160	−	0.377131i	$-0.876910\pi$
$71$	−1.14995	+	1.99178i	−0.136474	+	0.236381i	0.789685	+	0.613512i	$0.210244\pi$
$72$	−2.98378	−	0.311563i	−0.351642	−	0.0367181i
$73$	6.16302	+	10.6747i	0.721327	+	1.24937i	0.960468	+	0.278390i	$0.0898007\pi$
$73$	6.16302	+	10.6747i	0.721327	+	1.24937i	−0.239141	+	0.970985i	$0.576866\pi$
$74$			4.99903i			0.581125i
$75$	0.186386	+	0.365496i	0.0215220	+	0.0422038i
$76$	−3.94533	−	6.83352i	−0.452561	−	0.783858i
$77$	0.772686	+	0.144927i	0.0880558	+	0.0165159i
$78$	−5.38598	−	3.16089i	−0.609842	−	0.357900i
$79$	4.46469	−	7.73307i	0.502317	−	0.870039i	−0.497679	−	0.867361i	$-0.665814\pi$
$79$	4.46469	−	7.73307i	0.502317	−	0.870039i	0.999996	−	0.00267764i	$-0.000852321\pi$
$80$	−1.98183	−	1.14421i	−0.221575	−	0.127927i
$81$	8.80586	+	1.85927i	0.978429	+	0.206586i
$82$	−6.52086	+	3.76482i	−0.720109	+	0.415755i
$83$			1.54870i			0.169992i	0.996381	+	0.0849962i	$0.0270878\pi$
$83$			1.54870i			0.169992i	−0.996381	+	0.0849962i	$0.972912\pi$
$84$	−1.29357	−	4.39621i	−0.141140	−	0.479666i
$85$	−1.77042	−	1.02215i	−0.192029	−	0.110868i
$86$	1.94207	−	3.36377i	0.209419	−	0.362725i
$87$	−1.74776	+	0.891273i	−0.187379	+	0.0955545i
$88$	0.148570	−	0.257331i	0.0158376	−	0.0274316i
$89$			14.3106i			1.51692i	0.651720	+	0.758460i	$0.274048\pi$
$89$			14.3106i			1.51692i	−0.651720	+	0.758460i	$0.725952\pi$
$90$	5.55685	+	4.03154i	0.585743	+	0.424961i
$91$	1.33588	−	9.44539i	0.140039	−	0.990146i
$92$		−	7.81240i		−	0.814499i
$93$	−1.32043	−	2.58932i	−0.136922	−	0.268500i
$94$	−5.21062	−	3.00835i	−0.537435	−	0.310288i
$95$			18.0572i			1.85263i
$96$	−1.72971	−	0.0900624i	−0.176538	−	0.00919195i
$97$	−1.19346	+	2.06713i	−0.121178	+	0.209886i	−0.920232	−	0.391373i	$-0.872000\pi$
$97$	−1.19346	+	2.06713i	−0.121178	+	0.209886i	0.799055	+	0.601258i	$0.205334\pi$
$98$	5.45890	−	4.38183i	0.551432	−	0.442631i
$99$	−0.523476	+	0.721530i	−0.0526113	+	0.0725165i
$100$	0.118437	+	0.205138i	0.0118437	+	0.0205138i
$101$	9.38860	−	16.2615i	0.934200	−	1.61808i	0.158146	−	0.987416i	$-0.449448\pi$
$101$	9.38860	−	16.2615i	0.934200	−	1.61808i	0.776054	−	0.630666i	$-0.217218\pi$
$102$	−1.54520	−	0.0804552i	−0.152997	−	0.00796625i
$103$	−12.3898	−	7.15323i	−1.22080	−	0.704828i	−0.255710	−	0.966753i	$-0.582309\pi$
$103$	−12.3898	−	7.15323i	−1.22080	−	0.704828i	−0.965088	+	0.261925i	$0.915643\pi$
$104$	−3.20028	−	1.66078i	−0.313813	−	0.162853i
$105$	−2.46656	+	10.1927i	−0.240712	+	0.994702i
$106$	6.28351	−	3.62779i	0.610309	−	0.352362i
$107$			16.6853i			1.61303i	0.591212	+	0.806516i	$0.298650\pi$
$107$			16.6853i			1.61303i	−0.591212	+	0.806516i	$0.701350\pi$
$108$	5.13300	+	0.807639i	0.493923	+	0.0777151i
$109$	−9.70354	+	5.60234i	−0.929431	+	0.536607i	−0.886632	−	0.462476i	$-0.846961\pi$
$109$	−9.70354	+	5.60234i	−0.929431	+	0.536607i	−0.0427994	+	0.999084i	$0.513628\pi$
$110$	−0.588883	+	0.339992i	−0.0561478	+	0.0324169i
$111$	0.450224	−	8.64686i	0.0427334	−	0.820723i
$112$	−0.877809	−	2.49589i	−0.0829452	−	0.235839i
$113$	−7.27033	−	4.19753i	−0.683935	−	0.394870i	0.117401	−	0.993085i	$-0.462544\pi$
$113$	−7.27033	−	4.19753i	−0.683935	−	0.394870i	−0.801336	+	0.598214i	$0.795877\pi$
$114$	6.20883	+	12.1753i	0.581510	+	1.14032i
$115$	−8.93903	+	15.4829i	−0.833569	+	1.44378i
$116$	−0.980947	+	0.566350i	−0.0910786	+	0.0525843i
$117$	9.03149	+	5.95249i	0.834962	+	0.550308i
$118$		−	6.02418i		−	0.554571i
$119$	−0.784171	−	2.22964i	−0.0718849	−	0.204391i
$120$	3.32494	+	2.15764i	0.303524	+	0.196965i
$121$	5.45585	+	9.44982i	0.495987	+	0.859074i
$122$	−7.31581	+	4.22379i	−0.662343	+	0.382404i
$123$	11.6183	−	5.92475i	1.04758	−	0.534217i
$124$	−0.839051	−	1.45328i	−0.0753490	−	0.130508i
$125$			10.9000i			0.974929i
$126$	1.84156	+	7.72066i	0.164059	+	0.687811i
$127$	2.63228	+	4.55924i	0.233577	+	0.404567i	0.958858	−	0.283886i	$-0.0916236\pi$
$127$	2.63228	+	4.55924i	0.233577	+	0.404567i	−0.725281	+	0.688453i	$0.758290\pi$
$128$	−1.00000			−0.0883883
$129$	−3.66217	+	5.64343i	−0.322436	+	0.496876i
$130$	4.44214	+	6.95319i	0.389601	+	0.609835i
$131$	0.386257	−	0.669016i	0.0337474	−	0.0584522i	−0.848658	−	0.528941i	$-0.822589\pi$
$131$	0.386257	−	0.669016i	0.0337474	−	0.0584522i	0.882406	+	0.470489i	$0.155922\pi$
$132$	−0.280159	+	0.431727i	−0.0243847	+	0.0375770i
$133$	−13.5924	+	15.8456i	−1.17861	+	1.37399i
$134$	−2.94347	−	1.69941i	−0.254277	−	0.146807i
$135$	−9.24864	−	7.47384i	−0.795996	−	0.643246i
$136$	−0.893327			−0.0766022
$137$	2.58684			0.221009			0.110505	−	0.993876i	$-0.464753\pi$
$137$	2.58684			0.221009			0.110505	+	0.993876i	$0.464753\pi$
$138$	−0.703603	+	13.5132i	−0.0598947	+	1.15032i
$139$	10.2034	+	5.89092i	0.865438	+	0.499661i	0.865830	−	0.500339i	$-0.166791\pi$
$139$	10.2034	+	5.89092i	0.865438	+	0.499661i	−0.000391380		1.00000i	$0.500125\pi$
$140$	−1.11615	+	5.95083i	−0.0943319	+	0.502937i
$141$	8.74191	+	5.67285i	0.736202	+	0.477740i
$142$	1.14995	−	1.99178i	0.0965020	−	0.167146i
$143$	−0.902838	+	0.576790i	−0.0754991	+	0.0482336i
$144$	2.98378	+	0.311563i	0.248648	+	0.0259636i
$145$	2.59209			0.215262
$146$	−6.16302	−	10.6747i	−0.510055	−	0.883441i
$147$	−9.83694	+	7.08764i	−0.811337	+	0.584578i
$148$		−	4.99903i		−	0.410918i
$149$	1.64375	+	2.84705i	0.134661	+	0.233240i	0.925468	−	0.378826i	$-0.123672\pi$
$149$	1.64375	+	2.84705i	0.134661	+	0.233240i	−0.790807	+	0.612066i	$0.790339\pi$
$150$	−0.186386	−	0.365496i	−0.0152183	−	0.0298426i
$151$	10.5899	−	6.11409i	0.861795	−	0.497557i	−0.00281814	−	0.999996i	$-0.500897\pi$
$151$	10.5899	−	6.11409i	0.861795	−	0.497557i	0.864613	+	0.502439i	$0.167564\pi$
$152$	3.94533	+	6.83352i	0.320009	+	0.554272i
$153$	2.66549	+	0.278328i	0.215492	+	0.0225015i
$154$	−0.772686	−	0.144927i	−0.0622648	−	0.0116785i
$155$			3.84021i			0.308453i
$156$	5.38598	+	3.16089i	0.431223	+	0.253074i
$157$	−15.4715	+	8.93248i	−1.23476	+	0.712889i	−0.968019	−	0.250879i	$-0.919280\pi$
$157$	−15.4715	+	8.93248i	−1.23476	+	0.712889i	−0.266742	+	0.963768i	$0.585947\pi$
$158$	−4.46469	+	7.73307i	−0.355192	+	0.615210i
$159$	−11.1954	+	5.70910i	−0.887851	+	0.452761i
$160$	1.98183	+	1.14421i	0.156678	+	0.0904578i
$161$	−19.4989	+	6.85779i	−1.53673	+	0.540470i
$162$	−8.80586	−	1.85927i	−0.691853	−	0.146078i
$163$	−2.00708	+	1.15879i	−0.157207	+	0.0907632i	−0.576540	−	0.817069i	$-0.695597\pi$
$163$	−2.00708	+	1.15879i	−0.157207	+	0.0907632i	0.419333	+	0.907833i	$0.362264\pi$
$164$	6.52086	−	3.76482i	0.509194	−	0.293983i
$165$	1.04922	−	0.535050i	0.0816813	−	0.0416536i
$166$		−	1.54870i		−	0.120203i
$167$	11.5588	−	6.67349i	0.894449	−	0.516410i	0.0190536	−	0.999818i	$-0.493935\pi$
$167$	11.5588	−	6.67349i	0.894449	−	0.516410i	0.875395	+	0.483408i	$0.160601\pi$
$168$	1.29357	+	4.39621i	0.0998009	+	0.339175i
$169$	7.48361	+	10.6299i	0.575662	+	0.817687i
$170$	1.77042	+	1.02215i	0.135785	+	0.0783957i
$171$	−9.64293	−	21.6189i	−0.737413	−	1.65324i
$172$	−1.94207	+	3.36377i	−0.148082	+	0.256485i
$173$	9.18090	+	15.9018i	0.698011	+	1.20899i	0.969155	+	0.246452i	$0.0792648\pi$
$173$	9.18090	+	15.9018i	0.698011	+	1.20899i	−0.271144	+	0.962539i	$0.587402\pi$
$174$	1.74776	−	0.891273i	0.132497	−	0.0675673i
$175$	0.408037	−	0.475677i	0.0308447	−	0.0359578i
$176$	−0.148570	+	0.257331i	−0.0111989	+	0.0193971i
$177$	−0.542552	+	10.4201i	−0.0407807	+	0.783220i
$178$		−	14.3106i		−	1.07262i
$179$	−8.93640	−	5.15943i	−0.667938	−	0.385634i	0.127357	−	0.991857i	$-0.459351\pi$
$179$	−8.93640	−	5.15943i	−0.667938	−	0.385634i	−0.795295	+	0.606223i	$0.792684\pi$
$180$	−5.55685	−	4.03154i	−0.414183	−	0.300493i
$181$			5.21743i			0.387809i	0.981020	+	0.193904i	$0.0621151\pi$
$181$			5.21743i			0.387809i	−0.981020	+	0.193904i	$0.937885\pi$
$182$	−1.33588	+	9.44539i	−0.0990223	+	0.700139i
$183$	13.0346	−	6.64704i	0.963547	−	0.491363i
$184$			7.81240i			0.575938i
$185$	−5.71994	+	9.90723i	−0.420538	+	0.728394i
$186$	1.32043	+	2.58932i	0.0968185	+	0.189858i
$187$	−0.132722	+	0.229881i	−0.00970559	+	0.0168106i
$188$	5.21062	+	3.00835i	0.380024	+	0.219407i
$189$	−2.49002	−	13.5203i	−0.181122	−	0.983461i
$190$		−	18.0572i		−	1.31001i
$191$	22.8395	−	13.1864i	1.65261	−	0.954135i	0.676616	−	0.736336i	$-0.263446\pi$
$191$	22.8395	−	13.1864i	1.65261	−	0.954135i	0.975994	−	0.217799i	$-0.0698877\pi$
$192$	1.72971	+	0.0900624i	0.124831	+	0.00649969i
$193$	2.77543	+	1.60239i	0.199780	+	0.115343i	0.596553	−	0.802574i	$-0.296537\pi$
$193$	2.77543	+	1.60239i	0.199780	+	0.115343i	−0.396773	+	0.917917i	$0.629870\pi$
$194$	1.19346	−	2.06713i	0.0856855	−	0.148412i
$195$	−7.05738	−	12.4270i	−0.505389	−	0.889919i
$196$	−5.45890	+	4.38183i	−0.389922	+	0.312988i
$197$	−12.9869	−	22.4940i	−0.925278	−	1.60263i	−0.791113	−	0.611670i	$-0.790498\pi$
$197$	−12.9869	−	22.4940i	−0.925278	−	1.60263i	−0.134165	−	0.990959i	$-0.542835\pi$
$198$	0.523476	−	0.721530i	0.0372018	−	0.0512769i
$199$		−	5.54735i		−	0.393241i	−0.980480	−	0.196621i	$-0.937003\pi$
$199$		−	5.54735i		−	0.393241i	0.980480	−	0.196621i	$-0.0629967\pi$
$200$	−0.118437	−	0.205138i	−0.00837474	−	0.0145055i
$201$	4.93829	+	3.20459i	0.348320	+	0.226034i
$202$	−9.38860	+	16.2615i	−0.660579	+	1.14416i
$203$	2.27463	+	1.95118i	0.159648	+	0.136946i
$204$	1.54520	+	0.0804552i	0.108185	+	0.00563299i
$205$	−17.2310			−1.20346
$206$	12.3898	+	7.15323i	0.863235	+	0.498389i
$207$	2.43406	−	23.3105i	0.169179	−	1.62019i
$208$	3.20028	+	1.66078i	0.221900	+	0.115154i
$209$	2.34464			0.162182
$210$	2.46656	−	10.1927i	0.170209	−	0.703361i
$211$	1.17040	+	2.02719i	0.0805736	+	0.139558i	0.903496	−	0.428596i	$-0.140991\pi$
$211$	1.17040	+	2.02719i	0.0805736	+	0.139558i	−0.822923	+	0.568153i	$0.807658\pi$
$212$	−6.28351	+	3.62779i	−0.431553	+	0.249158i
$213$	−2.16847	+	3.34163i	−0.148581	+	0.228965i
$214$		−	16.6853i		−	1.14059i
$215$	7.69772	−	4.44428i	0.524980	−	0.303097i
$216$	−5.13300	−	0.807639i	−0.349257	−	0.0549529i
$217$	−2.89069	+	3.36988i	−0.196233	+	0.228762i
$218$	9.70354	−	5.60234i	0.657207	−	0.379439i
$219$	9.69883	+	19.0191i	0.655387	+	1.28519i
$220$	0.588883	−	0.339992i	0.0397025	−	0.0229222i
$221$	2.85890	+	1.48362i	0.192310	+	0.0997992i
$222$	−0.450224	+	8.64686i	−0.0302171	+	0.580339i
$223$	0.746837	+	1.29356i	0.0500119	+	0.0866232i	0.889948	−	0.456063i	$-0.150741\pi$
$223$	0.746837	+	1.29356i	0.0500119	+	0.0866232i	−0.839936	+	0.542686i	$0.817407\pi$
$224$	0.877809	+	2.49589i	0.0586511	+	0.166763i
$225$	0.289475	+	0.648988i	0.0192983	+	0.0432658i
$226$	7.27033	+	4.19753i	0.483615	+	0.279215i
$227$		−	6.37084i		−	0.422848i	−0.977394	−	0.211424i	$-0.932190\pi$
$227$		−	6.37084i		−	0.422848i	0.977394	−	0.211424i	$-0.0678100\pi$
$228$	−6.20883	−	12.1753i	−0.411190	−	0.806330i
$229$	−3.93382	+	6.81358i	−0.259954	+	0.450254i	−0.966229	−	0.257684i	$-0.917041\pi$
$229$	−3.93382	+	6.81358i	−0.259954	+	0.450254i	0.706275	+	0.707937i	$0.250374\pi$
$230$	8.93903	−	15.4829i	0.589422	−	1.02091i
$231$	1.32347	+	0.320271i	0.0870779	+	0.0210723i
$232$	0.980947	−	0.566350i	0.0644023	−	0.0371827i
$233$	−8.04627	−	4.64552i	−0.527129	−	0.304338i	0.212718	−	0.977114i	$-0.431769\pi$
$233$	−8.04627	−	4.64552i	−0.527129	−	0.304338i	−0.739847	+	0.672776i	$0.765102\pi$
$234$	−9.03149	−	5.95249i	−0.590407	−	0.389127i
$235$	−6.88438	−	11.9241i	−0.449088	−	0.777842i
$236$			6.02418i			0.392141i
$237$	8.41907	−	12.9739i	0.546877	−	0.842743i
$238$	0.784171	+	2.22964i	0.0508303	+	0.144526i
$239$	−22.6067			−1.46230			−0.731152	−	0.682215i	$-0.761017\pi$
$239$	−22.6067			−1.46230			−0.731152	+	0.682215i	$0.761017\pi$
$240$	−3.32494	−	2.15764i	−0.214624	−	0.139275i
$241$	29.0874			1.87368			0.936842	−	0.349753i	$-0.113734\pi$
$241$	29.0874			1.87368			0.936842	+	0.349753i	$0.113734\pi$
$242$	−5.45585	−	9.44982i	−0.350716	−	0.607457i
$243$	15.0641	+	4.00907i	0.966363	+	0.257182i
$244$	7.31581	−	4.22379i	0.468347	−	0.270400i
$245$	15.8324	−	2.43790i	1.01149	−	0.155752i
$246$	−11.6183	+	5.92475i	−0.740753	+	0.377749i
$247$	−1.27720	−	28.4215i	−0.0812665	−	1.80842i
$248$	0.839051	+	1.45328i	0.0532798	+	0.0922834i
$249$	−0.139480	+	2.67881i	−0.00883919	+	0.169762i
$250$		−	10.9000i		−	0.689379i
$251$	6.89055	−	11.9348i	0.434928	−	0.753317i	−0.562362	−	0.826891i	$-0.690107\pi$
$251$	6.89055	−	11.9348i	0.434928	−	0.753317i	0.997290	+	0.0735742i	$0.0234406\pi$
$252$	−1.84156	−	7.72066i	−0.116007	−	0.486356i
$253$	2.01037	+	1.16069i	0.126391	+	0.0729720i
$254$	−2.63228	−	4.55924i	−0.165164	−	0.286072i
$255$	−2.97026	−	1.92748i	−0.186005	−	0.120703i
$256$	1.00000			0.0625000
$257$	−5.62443			−0.350843			−0.175421	−	0.984493i	$-0.556129\pi$
$257$	−5.62443			−0.350843			−0.175421	+	0.984493i	$0.556129\pi$
$258$	3.66217	−	5.64343i	0.227997	−	0.351345i
$259$	−12.4770	+	4.38819i	−0.775284	+	0.272669i
$260$	−4.44214	−	6.95319i	−0.275490	−	0.431218i
$261$	−3.10338	+	1.38424i	−0.192094	+	0.0856820i
$262$	−0.386257	+	0.669016i	−0.0238630	+	0.0413320i
$263$	−16.7851	−	9.69087i	−1.03501	−	0.597564i	−0.116595	−	0.993179i	$-0.537198\pi$
$263$	−16.7851	−	9.69087i	−1.03501	−	0.597564i	−0.918416	+	0.395615i	$0.870531\pi$
$264$	0.280159	−	0.431727i	0.0172426	−	0.0265710i
$265$	16.6038			1.01996
$266$	13.5924	−	15.8456i	0.833406	−	0.971558i
$267$	−1.28885	+	24.7531i	−0.0788761	+	1.51487i
$268$	2.94347	+	1.69941i	0.179801	+	0.103808i
$269$	27.9546			1.70442			0.852211	−	0.523199i	$-0.175261\pi$
$269$	27.9546			1.70442			0.852211	+	0.523199i	$0.175261\pi$
$270$	9.24864	+	7.47384i	0.562854	+	0.454844i
$271$	−20.4588			−1.24279			−0.621393	−	0.783499i	$-0.713433\pi$
$271$	−20.4588			−1.24279			−0.621393	+	0.783499i	$0.713433\pi$
$272$	0.893327			0.0541659
$273$	3.16136	−	16.2175i	0.191334	−	0.981525i
$274$	−2.58684			−0.156277
$275$	−0.0703847			−0.00424436
$276$	0.703603	−	13.5132i	0.0423519	−	0.813397i
$277$	6.51069			0.391190			0.195595	−	0.980685i	$-0.437336\pi$
$277$	6.51069			0.391190			0.195595	+	0.980685i	$0.437336\pi$
$278$	−10.2034	−	5.89092i	−0.611957	−	0.353314i
$279$	−2.05075	−	4.59768i	−0.122775	−	0.275256i
$280$	1.11615	−	5.95083i	0.0667028	−	0.355630i
$281$	−10.0287			−0.598262			−0.299131	−	0.954212i	$-0.596697\pi$
$281$	−10.0287			−0.598262			−0.299131	+	0.954212i	$0.596697\pi$
$282$	−8.74191	−	5.67285i	−0.520573	−	0.337814i
$283$	19.8164	+	11.4410i	1.17796	+	0.680097i	0.955542	−	0.294854i	$-0.0952712\pi$
$283$	19.8164	+	11.4410i	1.17796	+	0.680097i	0.222420	+	0.974951i	$0.428605\pi$
$284$	−1.14995	+	1.99178i	−0.0682372	+	0.118190i
$285$	−1.62627	+	31.2336i	−0.0963321	+	1.85012i
$286$	0.902838	−	0.576790i	0.0533859	−	0.0341063i
$287$	−15.1206	−	12.9705i	−0.892543	−	0.765626i
$288$	−2.98378	−	0.311563i	−0.175821	−	0.0183590i
$289$	−16.2020			−0.953057
$290$	−2.59209			−0.152213
$291$	−2.25051	+	3.46805i	−0.131927	+	0.203301i
$292$	6.16302	+	10.6747i	0.360663	+	0.624687i
$293$	−17.4353	−	10.0663i	−1.01858	−	0.588080i	−0.104890	−	0.994484i	$-0.533449\pi$
$293$	−17.4353	−	10.0663i	−1.01858	−	0.588080i	−0.913693	+	0.406404i	$0.866783\pi$
$294$	9.83694	−	7.08764i	0.573702	−	0.413359i
$295$	6.89293	−	11.9389i	0.401322	−	0.695110i
$296$			4.99903i			0.290563i
$297$	−0.970443	+	1.20089i	−0.0563108	+	0.0696828i
$298$	−1.64375	−	2.84705i	−0.0952198	−	0.164925i
$299$	12.9747	−	25.0019i	0.750345	−	1.44590i
$300$	0.186386	+	0.365496i	0.0107610	+	0.0211019i
$301$	10.1004	+	1.89445i	0.582175	+	0.109194i
$302$	−10.5899	+	6.11409i	−0.609381	+	0.351826i
$303$	17.7041	−	27.2821i	1.01707	−	1.56732i
$304$	−3.94533	−	6.83352i	−0.226280	−	0.391929i
$305$	−19.3316			−1.10692
$306$	−2.66549	−	0.278328i	−0.152376	−	0.0159110i
$307$	3.07801			0.175672			0.0878358	−	0.996135i	$-0.472005\pi$
$307$	3.07801			0.175672			0.0878358	+	0.996135i	$0.472005\pi$
$308$	0.772686	+	0.144927i	0.0440279	+	0.00825797i
$309$	−20.7864	−	13.4888i	−1.18250	−	0.767353i
$310$		−	3.84021i		−	0.218109i
$311$	7.75963	+	13.4401i	0.440008	+	0.762117i	0.997690	−	0.0679384i	$-0.0216421\pi$
$311$	7.75963	+	13.4401i	0.440008	+	0.762117i	−0.557681	+	0.830055i	$0.688309\pi$
$312$	−5.38598	−	3.16089i	−0.304921	−	0.178950i
$313$	13.7068	+	7.91361i	0.774752	+	0.447303i	0.834567	−	0.550906i	$-0.185718\pi$
$313$	13.7068	+	7.91361i	0.774752	+	0.447303i	−0.0598149	+	0.998209i	$0.519051\pi$
$314$	15.4715	−	8.93248i	0.873108	−	0.504089i
$315$	−5.18440	+	17.4082i	−0.292108	+	0.980840i
$316$	4.46469	−	7.73307i	0.251159	−	0.435019i
$317$	−6.47213	+	11.2101i	−0.363511	+	0.629619i	−0.988536	−	0.150985i	$-0.951755\pi$
$317$	−6.47213	+	11.2101i	−0.363511	+	0.629619i	0.625025	+	0.780605i	$0.285089\pi$
$318$	11.1954	−	5.70910i	0.627805	−	0.320151i
$319$		−	0.336571i		−	0.0188444i
$320$	−1.98183	−	1.14421i	−0.110788	−	0.0639633i
$321$	−1.50272	+	28.8608i	−0.0838737	+	1.61085i
$322$	19.4989	−	6.85779i	1.08663	−	0.382170i
$323$	−3.52448	−	6.10457i	−0.196107	−	0.339667i
$324$	8.80586	+	1.85927i	0.489214	+	0.103293i
$325$	0.0383409	+	0.853198i	0.00212677	+	0.0473269i
$326$	2.00708	−	1.15879i	0.111162	−	0.0641793i
$327$	−17.2889	+	8.81649i	−0.956076	+	0.487553i
$328$	−6.52086	+	3.76482i	−0.360054	+	0.207877i
$329$	2.93458	−	15.6459i	0.161789	−	0.862585i
$330$	−1.04922	+	0.535050i	−0.0577574	+	0.0294535i
$331$	7.76227	−	4.48155i	0.426653	−	0.246328i	−0.271267	−	0.962504i	$-0.587443\pi$
$331$	7.76227	−	4.48155i	0.426653	−	0.246328i	0.697920	+	0.716176i	$0.254109\pi$
$332$			1.54870i			0.0849962i
$333$	1.55751	−	14.9160i	0.0853512	−	0.817391i
$334$	−11.5588	+	6.67349i	−0.632471	+	0.365157i
$335$	−3.88898	−	6.73591i	−0.212477	−	0.368022i
$336$	−1.29357	−	4.39621i	−0.0705699	−	0.239833i
$337$	−7.76837			−0.423170			−0.211585	−	0.977360i	$-0.567863\pi$
$337$	−7.76837			−0.423170			−0.211585	+	0.977360i	$0.567863\pi$
$338$	−7.48361	−	10.6299i	−0.407055	−	0.578192i
$339$	−12.1975	−	7.91528i	−0.662478	−	0.429899i
$340$	−1.77042	−	1.02215i	−0.0960147	−	0.0554341i
$341$	0.498633			0.0270025
$342$	9.64293	+	21.6189i	0.521430	+	1.16902i
$343$	15.7284	+	9.77839i	0.849255	+	0.527984i
$344$	1.94207	−	3.36377i	0.104710	−	0.181362i
$345$	−16.8563	+	25.9757i	−0.907514	+	1.39849i
$346$	−9.18090	−	15.9018i	−0.493568	−	0.854886i
$347$		−	9.70091i		−	0.520772i	−0.965505	−	0.260386i	$-0.916150\pi$
$347$		−	9.70091i		−	0.520772i	0.965505	−	0.260386i	$-0.0838498\pi$
$348$	−1.74776	+	0.891273i	−0.0936897	+	0.0477773i
$349$	13.2526	+	22.9542i	0.709396	+	1.22871i	0.965081	+	0.261950i	$0.0843655\pi$
$349$	13.2526	+	22.9542i	0.709396	+	1.22871i	−0.255686	+	0.966760i	$0.582301\pi$
$350$	−0.408037	+	0.475677i	−0.0218105	+	0.0254260i
$351$	15.0857	+	11.1095i	0.805218	+	0.592980i
$352$	0.148570	−	0.257331i	0.00791882	−	0.0137158i
$353$	22.1838	+	12.8078i	1.18073	+	0.681693i	0.956183	−	0.292771i	$-0.0945774\pi$
$353$	22.1838	+	12.8078i	1.18073	+	0.681693i	0.224544	+	0.974464i	$0.427911\pi$
$354$	0.542552	−	10.4201i	0.0288363	−	0.553820i
$355$	4.55803	−	2.63158i	0.241915	−	0.139670i
$356$			14.3106i			0.758460i
$357$	−1.15558	−	3.92726i	−0.0611598	−	0.207852i
$358$	8.93640	+	5.15943i	0.472303	+	0.272684i
$359$	6.41408	−	11.1095i	0.338522	−	0.586338i	−0.645633	−	0.763648i	$-0.723406\pi$
$359$	6.41408	−	11.1095i	0.338522	−	0.586338i	0.984155	+	0.177310i	$0.0567396\pi$
$360$	5.55685	+	4.03154i	0.292872	+	0.212481i
$361$	−21.6313	+	37.4666i	−1.13849	+	1.97192i
$362$		−	5.21743i		−	0.274222i
$363$	8.58596	+	16.8368i	0.450646	+	0.883702i
$364$	1.33588	−	9.44539i	0.0700193	−	0.495073i
$365$		−	28.2072i		−	1.47643i
$366$	−13.0346	+	6.64704i	−0.681331	+	0.347446i
$367$	−21.2692	−	12.2798i	−1.11024	−	0.641000i	−0.171352	−	0.985210i	$-0.554813\pi$
$367$	−21.2692	−	12.2798i	−1.11024	−	0.641000i	−0.938893	+	0.344210i	$0.888147\pi$
$368$		−	7.81240i		−	0.407249i
$369$	20.6298	−	9.20173i	1.07394	−	0.479023i
$370$	5.71994	−	9.90723i	0.297366	−	0.515052i
$371$	14.5703	+	12.4984i	0.756451	+	0.648886i
$372$	−1.32043	−	2.58932i	−0.0684610	−	0.134250i
$373$	10.7383	+	18.5993i	0.556009	+	0.963036i	0.997824	+	0.0659297i	$0.0210013\pi$
$373$	10.7383	+	18.5993i	0.556009	+	0.963036i	−0.441815	+	0.897106i	$0.645665\pi$
$374$	0.132722	−	0.229881i	0.00686289	−	0.0118869i
$375$	−0.981684	+	18.8539i	−0.0506939	+	0.973611i
$376$	−5.21062	−	3.00835i	−0.268717	−	0.155144i
$377$	−4.07989	+	0.183342i	−0.210125	+	0.00944257i
$378$	2.49002	+	13.5203i	0.128073	+	0.695412i
$379$	−13.9171	+	8.03505i	−0.714874	+	0.412733i	−0.812863	−	0.582455i	$-0.802092\pi$
$379$	−13.9171	+	8.03505i	−0.714874	+	0.412733i	0.0979889	+	0.995188i	$0.468759\pi$
$380$			18.0572i			0.926314i
$381$	4.14246	+	8.12322i	0.212224	+	0.416165i
$382$	−22.8395	+	13.1864i	−1.16857	+	0.674675i
$383$	23.1968	−	13.3927i	1.18530	−	0.684335i	0.228068	−	0.973645i	$-0.426759\pi$
$383$	23.1968	−	13.3927i	1.18530	−	0.684335i	0.957235	+	0.289310i	$0.0934259\pi$
$384$	−1.72971	−	0.0900624i	−0.0882688	−	0.00459598i
$385$	−1.36551	−	1.17134i	−0.0695927	−	0.0596968i
$386$	−2.77543	−	1.60239i	−0.141266	−	0.0815597i
$387$	−6.84274	+	9.43166i	−0.347836	+	0.479438i
$388$	−1.19346	+	2.06713i	−0.0605888	+	0.104943i
$389$	−3.67405	+	2.12122i	−0.186282	+	0.107550i	−0.590241	−	0.807227i	$-0.700967\pi$
$389$	−3.67405	+	2.12122i	−0.186282	+	0.107550i	0.403959	+	0.914777i	$0.367634\pi$
$390$	7.05738	+	12.4270i	0.357364	+	0.629268i
$391$		−	6.97903i		−	0.352945i
$392$	5.45890	−	4.38183i	0.275716	−	0.221316i
$393$	0.728364	−	1.12242i	0.0367411	−	0.0566184i
$394$	12.9869	+	22.4940i	0.654270	+	1.13323i
$395$	−17.6965	+	10.2171i	−0.890409	+	0.514078i
$396$	−0.523476	+	0.721530i	−0.0263056	+	0.0362583i
$397$	−0.355073	−	0.615005i	−0.0178206	−	0.0308662i	0.856978	−	0.515354i	$-0.172339\pi$
$397$	−0.355073	−	0.615005i	−0.0178206	−	0.0308662i	−0.874798	+	0.484488i	$0.839006\pi$
$398$			5.54735i			0.278063i
$399$	−24.9380	+	26.1841i	−1.24846	+	1.31085i
$400$	0.118437	+	0.205138i	0.00592183	+	0.0102569i
$401$	−15.2330			−0.760701			−0.380351	−	0.924842i	$-0.624197\pi$
$401$	−15.2330			−0.760701			−0.380351	+	0.924842i	$0.624197\pi$
$402$	−4.93829	−	3.20459i	−0.246300	−	0.159830i
$403$	−0.271622	−	6.04439i	−0.0135305	−	0.301092i
$404$	9.38860	−	16.2615i	0.467100	−	0.809041i
$405$	−15.3243	−	13.7605i	−0.761472	−	0.683766i
$406$	−2.27463	−	1.95118i	−0.112888	−	0.0968357i
$407$	1.28641	+	0.742707i	0.0637648	+	0.0368146i
$408$	−1.54520	−	0.0804552i	−0.0764986	−	0.00398313i
$409$	26.0063			1.28593			0.642964	−	0.765896i	$-0.277704\pi$
$409$	26.0063			1.28593			0.642964	+	0.765896i	$0.277704\pi$
$410$	17.2310			0.850978
$411$	4.47448	+	0.232977i	0.220710	+	0.0114919i
$412$	−12.3898	−	7.15323i	−0.610399	−	0.352414i
$413$	15.0357	−	5.28808i	0.739857	−	0.260209i
$414$	−2.43406	+	23.3105i	−0.119627	+	1.14565i
$415$	1.77204	−	3.06927i	0.0869863	−	0.150665i
$416$	−3.20028	−	1.66078i	−0.156907	−	0.0814265i
$417$	17.1183	+	11.1085i	0.838286	+	0.543986i
$418$	−2.34464			−0.114680
$419$	−4.44170	−	7.69326i	−0.216991	−	0.375840i	0.736895	−	0.676007i	$-0.236291\pi$
$419$	−4.44170	−	7.69326i	−0.216991	−	0.375840i	−0.953887	+	0.300167i	$0.902958\pi$
$420$	−2.46656	+	10.1927i	−0.120356	+	0.497351i
$421$		−	11.9274i		−	0.581308i	−0.956828	−	0.290654i	$-0.906127\pi$
$421$		−	11.9274i		−	0.581308i	0.956828	−	0.290654i	$-0.0938729\pi$
$422$	−1.17040	−	2.02719i	−0.0569742	−	0.0986822i
$423$	14.6100	+	10.5997i	0.710365	+	0.515375i
$424$	6.28351	−	3.62779i	0.305154	−	0.176181i
$425$	0.105803	+	0.183256i	0.00513219	+	0.00888921i
$426$	2.16847	−	3.34163i	0.105063	−	0.161902i
$427$	−16.9640	−	14.5518i	−0.820945	−	0.704209i
$428$			16.6853i			0.806516i
$429$	−1.61359	+	0.916367i	−0.0779050	+	0.0442426i
$430$	−7.69772	+	4.44428i	−0.371217	+	0.214322i
$431$	9.74149	−	16.8728i	0.469231	−	0.812732i	−0.530150	−	0.847904i	$-0.677864\pi$
$431$	9.74149	−	16.8728i	0.469231	−	0.812732i	0.999381	+	0.0351717i	$0.0111978\pi$
$432$	5.13300	+	0.807639i	0.246962	+	0.0388576i
$433$	−15.8703	−	9.16273i	−0.762679	−	0.440333i	0.0675780	−	0.997714i	$-0.478473\pi$
$433$	−15.8703	−	9.16273i	−0.762679	−	0.440333i	−0.830257	+	0.557381i	$0.811806\pi$
$434$	2.89069	−	3.36988i	0.138758	−	0.161759i
$435$	4.48357	+	0.233450i	0.214971	+	0.0111931i
$436$	−9.70354	+	5.60234i	−0.464715	+	0.268304i
$437$	−53.3862	+	30.8225i	−2.55381	+	1.47444i
$438$	−9.69883	−	19.0191i	−0.463428	−	0.908768i
$439$		−	2.49215i		−	0.118944i	−0.998230	−	0.0594720i	$-0.981058\pi$
$439$		−	2.49215i		−	0.118944i	0.998230	−	0.0594720i	$-0.0189417\pi$
$440$	−0.588883	+	0.339992i	−0.0280739	+	0.0162085i
$441$	−17.6534	+	11.3736i	−0.840636	+	0.541600i
$442$	−2.85890	−	1.48362i	−0.135984	−	0.0705687i
$443$	−14.4424	−	8.33832i	−0.686179	−	0.396166i	0.116000	−	0.993249i	$-0.462993\pi$
$443$	−14.4424	−	8.33832i	−0.686179	−	0.396166i	−0.802179	+	0.597083i	$0.796326\pi$
$444$	0.450224	−	8.64686i	0.0213667	−	0.410362i
$445$	16.3743	−	28.3612i	0.776218	−	1.34445i
$446$	−0.746837	−	1.29356i	−0.0353638	−	0.0612519i
$447$	2.58679	+	5.07261i	0.122351	+	0.239926i
$448$	−0.877809	−	2.49589i	−0.0414726	−	0.117920i
$449$	18.5701	−	32.1643i	0.876375	−	1.51793i	0.0210850	−	0.999778i	$-0.493288\pi$
$449$	18.5701	−	32.1643i	0.876375	−	1.51793i	0.855290	−	0.518149i	$-0.173379\pi$
$450$	−0.289475	−	0.648988i	−0.0136460	−	0.0305936i
$451$			2.23736i			0.105353i
$452$	−7.27033	−	4.19753i	−0.341968	−	0.197435i
$453$	18.8681	−	9.62183i	0.886501	−	0.452073i
$454$			6.37084i			0.298998i
$455$	−13.4550	+	17.1906i	−0.630781	+	0.805910i
$456$	6.20883	+	12.1753i	0.290755	+	0.570161i
$457$		−	16.1075i		−	0.753476i	−0.926320	−	0.376738i	$-0.877046\pi$
$457$		−	16.1075i		−	0.753476i	0.926320	−	0.376738i	$-0.122954\pi$
$458$	3.93382	−	6.81358i	0.183815	−	0.318378i
$459$	4.58545	+	0.721486i	0.214031	+	0.0336761i
$460$	−8.93903	+	15.4829i	−0.416784	+	0.721892i
$461$	12.1978	+	7.04240i	0.568108	+	0.327997i	0.756393	−	0.654117i	$-0.226960\pi$
$461$	12.1978	+	7.04240i	0.568108	+	0.327997i	−0.188285	+	0.982114i	$0.560293\pi$
$462$	−1.32347	−	0.320271i	−0.0615734	−	0.0149004i
$463$		−	20.5027i		−	0.952843i	−0.879217	−	0.476421i	$-0.841934\pi$
$463$		−	20.5027i		−	0.952843i	0.879217	−	0.476421i	$-0.158066\pi$
$464$	−0.980947	+	0.566350i	−0.0455393	+	0.0262921i
$465$	−0.345858	+	6.64244i	−0.0160388	+	0.308036i
$466$	8.04627	+	4.64552i	0.372736	+	0.215199i
$467$	−2.86923	+	4.96965i	−0.132772	+	0.229968i	−0.924744	−	0.380589i	$-0.875721\pi$
$467$	−2.86923	+	4.96965i	−0.132772	+	0.229968i	0.791972	+	0.610557i	$0.209054\pi$
$468$	9.03149	+	5.95249i	0.417481	+	0.275154i
$469$	1.65774	−	8.83834i	0.0765473	−	0.408116i
$470$	6.88438	+	11.9241i	0.317553	+	0.550018i
$471$	−27.5657	+	14.0572i	−1.27016	+	0.647720i
$472$		−	6.02418i		−	0.277285i
$473$	−0.577069	−	0.999512i	−0.0265336	−	0.0459576i
$474$	−8.41907	+	12.9739i	−0.386701	+	0.595909i
$475$	0.934544	−	1.61868i	0.0428798	−	0.0742701i
$476$	−0.784171	−	2.22964i	−0.0359424	−	0.102196i
$477$	−19.8789	+	8.86680i	−0.910192	+	0.405983i
$478$	22.6067			1.03401
$479$	24.3944	+	14.0841i	1.11461	+	0.643519i	0.940019	−	0.341122i	$-0.110807\pi$
$479$	24.3944	+	14.0841i	1.11461	+	0.643519i	0.174589	+	0.984641i	$0.444140\pi$
$480$	3.32494	+	2.15764i	0.151762	+	0.0984823i
$481$	8.30229	−	15.9983i	0.378552	−	0.729460i
$482$	−29.0874			−1.32489
$483$	−34.3450	+	10.1059i	−1.56275	+	0.459833i
$484$	5.45585	+	9.44982i	0.247993	+	0.429537i
$485$	4.73047	−	2.73114i	0.214800	−	0.124015i
$486$	−15.0641	−	4.00907i	−0.683322	−	0.181855i
$487$			29.7095i			1.34627i	0.739521	+	0.673133i	$0.235052\pi$
$487$			29.7095i			1.34627i	−0.739521	+	0.673133i	$0.764948\pi$
$488$	−7.31581	+	4.22379i	−0.331171	+	0.191202i
$489$	−3.57602	+	1.82360i	−0.161713	+	0.0824661i
$490$	−15.8324	+	2.43790i	−0.715233	+	0.110133i
$491$	35.4120	−	20.4451i	1.59812	−	0.922676i	0.606272	−	0.795258i	$-0.292664\pi$
$491$	35.4120	−	20.4451i	1.59812	−	0.922676i	0.991849	−	0.127418i	$-0.0406690\pi$
$492$	11.6183	−	5.92475i	0.523791	−	0.267109i
$493$	−0.876307	+	0.505936i	−0.0394669	+	0.0227862i
$494$	1.27720	+	28.4215i	0.0574641	+	1.27874i
$495$	1.86302	−	0.830985i	0.0837367	−	0.0373500i
$496$	−0.839051	−	1.45328i	−0.0376745	−	0.0652542i
$497$	5.98070	+	1.12175i	0.268271	+	0.0503175i
$498$	0.139480	−	2.67881i	0.00625025	−	0.120040i
$499$	11.0351	+	6.37111i	0.493998	+	0.285210i	0.726232	−	0.687450i	$-0.241270\pi$
$499$	11.0351	+	6.37111i	0.493998	+	0.285210i	−0.232233	+	0.972660i	$0.574603\pi$
$500$			10.9000i			0.487465i
$501$	20.5944	−	10.5022i	0.920091	−	0.469202i
$502$	−6.89055	+	11.9348i	−0.307540	+	0.532675i
$503$	−20.5763	+	35.6392i	−0.917453	+	1.58908i	−0.114183	+	0.993460i	$0.536425\pi$
$503$	−20.5763	+	35.6392i	−0.917453	+	1.58908i	−0.803270	+	0.595615i	$0.796908\pi$
$504$	1.84156	+	7.72066i	0.0820297	+	0.343906i
$505$	−37.2132	+	21.4851i	−1.65597	+	0.956073i
$506$	−2.01037	−	1.16069i	−0.0893720	−	0.0515990i
$507$	11.9871	+	19.0607i	0.532366	+	0.846514i
$508$	2.63228	+	4.55924i	0.116788	+	0.202284i
$509$			17.9868i			0.797250i	0.917114	+	0.398625i	$0.130512\pi$
$509$			17.9868i			0.797250i	−0.917114	+	0.398625i	$0.869488\pi$
$510$	2.97026	+	1.92748i	0.131525	+	0.0853502i
$511$	21.2328	−	24.7525i	0.939283	−	1.09499i
$512$	−1.00000			−0.0441942
$513$	−14.7324	−	38.2629i	−0.650451	−	1.68935i
$514$	5.62443			0.248083
$515$	16.3696	+	28.3530i	0.721331	+	1.24938i
$516$	−3.66217	+	5.64343i	−0.161218	+	0.248438i
$517$	−1.54829	+	0.893904i	−0.0680936	+	0.0393139i
$518$	12.4770	−	4.38819i	0.548208	−	0.192806i
$519$	14.4481	+	28.3323i	0.634202	+	1.24365i
$520$	4.44214	+	6.95319i	0.194801	+	0.304917i
$521$	12.5794	+	21.7881i	0.551113	+	0.954555i	0.998195	+	0.0600622i	$0.0191299\pi$
$521$	12.5794	+	21.7881i	0.551113	+	0.954555i	−0.447082	+	0.894493i	$0.647537\pi$
$522$	3.10338	−	1.38424i	0.135831	−	0.0605863i
$523$		−	42.1093i		−	1.84131i	−0.390375	−	0.920656i	$-0.627655\pi$
$523$		−	42.1093i		−	1.84131i	0.390375	−	0.920656i	$-0.372345\pi$
$524$	0.386257	−	0.669016i	0.0168737	−	0.0292261i
$525$	0.748626	−	0.786033i	0.0326727	−	0.0343053i
$526$	16.7851	+	9.69087i	0.731864	+	0.422542i
$527$	−0.749548	−	1.29825i	−0.0326508	−	0.0565529i
$528$	−0.280159	+	0.431727i	−0.0121924	+	0.0187885i
$529$	−38.0335			−1.65363
$530$	−16.6038			−0.721224
$531$	−1.87691	+	17.9748i	−0.0814511	+	0.780040i
$532$	−13.5924	+	15.8456i	−0.589307	+	0.686995i
$533$	27.1211	−	1.21877i	1.17475	−	0.0527906i
$534$	1.28885	−	24.7531i	0.0557738	−	1.07117i
$535$	19.0915	−	33.0675i	0.825399	−	1.42963i
$536$	−2.94347	−	1.69941i	−0.127139	−	0.0734035i
$537$	−14.9927	−	9.72914i	−0.646982	−	0.419843i
$538$	−27.9546			−1.20521
$539$	−0.316550	−	2.05576i	−0.0136348	−	0.0885477i
$540$	−9.24864	−	7.47384i	−0.397998	−	0.321623i
$541$	−15.7491	−	9.09276i	−0.677107	−	0.390928i	0.121657	−	0.992572i	$-0.461179\pi$
$541$	−15.7491	−	9.09276i	−0.677107	−	0.390928i	−0.798764	+	0.601644i	$0.794513\pi$
$542$	20.4588			0.878782
$543$	−0.469894	+	9.02463i	−0.0201651	+	0.387284i
$544$	−0.893327			−0.0383011
$545$	25.6410			1.09834
$546$	−3.16136	+	16.2175i	−0.135294	+	0.694043i
$547$	7.61792			0.325719			0.162859	−	0.986649i	$-0.447928\pi$
$547$	7.61792			0.325719			0.162859	+	0.986649i	$0.447928\pi$
$548$	2.58684			0.110505
$549$	23.1447	−	10.3235i	0.987793	−	0.440596i
$550$	0.0703847			0.00300121
$551$	7.74033	+	4.46888i	0.329749	+	0.190381i
$552$	−0.703603	+	13.5132i	−0.0299473	+	0.575158i
$553$	−23.2200	−	4.35520i	−0.987416	−	0.185202i
$554$	−6.51069			−0.276613
$555$	−10.7861	+	16.6215i	−0.457844	+	0.705542i
$556$	10.2034	+	5.89092i	0.432719	+	0.249831i
$557$	−15.8600	+	27.4704i	−0.672011	+	1.16396i	0.305322	+	0.952249i	$0.401236\pi$
$557$	−15.8600	+	27.4704i	−0.672011	+	1.16396i	−0.977333	+	0.211708i	$0.932097\pi$
$558$	2.05075	+	4.59768i	0.0868154	+	0.194635i
$559$	−11.8017	+	7.53965i	−0.499157	+	0.318893i
$560$	−1.11615	+	5.95083i	−0.0471660	+	0.251468i
$561$	−0.250274	+	0.385674i	−0.0105666	+	0.0162832i
$562$	10.0287			0.423035
$563$	2.89827			0.122147			0.0610737	−	0.998133i	$-0.480548\pi$
$563$	2.89827			0.122147			0.0610737	+	0.998133i	$0.480548\pi$
$564$	8.74191	+	5.67285i	0.368101	+	0.238870i
$565$	9.60572	+	16.6376i	0.404115	+	0.699949i
$566$	−19.8164	−	11.4410i	−0.832945	−	0.480901i
$567$	−3.08933	−	23.6105i	−0.129740	−	0.991548i
$568$	1.14995	−	1.99178i	0.0482510	−	0.0835732i
$569$		−	37.8812i		−	1.58806i	−0.607878	−	0.794030i	$-0.707979\pi$
$569$		−	37.8812i		−	1.58806i	0.607878	−	0.794030i	$-0.292021\pi$
$570$	1.62627	−	31.2336i	0.0681171	−	1.30823i
$571$	−13.5869	−	23.5332i	−0.568594	−	0.984834i	−0.996705	−	0.0811082i	$-0.974154\pi$
$571$	−13.5869	−	23.5332i	−0.568594	−	0.984834i	0.428111	−	0.903726i	$-0.359179\pi$
$572$	−0.902838	+	0.576790i	−0.0377496	+	0.0241168i
$573$	40.6933	−	20.7516i	1.69999	−	0.866912i
$574$	15.1206	+	12.9705i	0.631123	+	0.541380i
$575$	1.60262	−	0.925274i	0.0668340	−	0.0385866i
$576$	2.98378	+	0.311563i	0.124324	+	0.0129818i
$577$	−19.0478	−	32.9918i	−0.792972	−	1.37347i	−0.924119	−	0.382105i	$-0.875199\pi$
$577$	−19.0478	−	32.9918i	−0.792972	−	1.37347i	0.131147	−	0.991363i	$-0.458134\pi$
$578$	16.2020			0.673913
$579$	4.65637	+	3.02164i	0.193512	+	0.125575i
$580$	2.59209			0.107631
$581$	3.86539	−	1.35947i	0.160363	−	0.0564002i
$582$	2.25051	−	3.46805i	0.0932866	−	0.143755i
$583$		−	2.15593i		−	0.0892894i
$584$	−6.16302	−	10.6747i	−0.255028	−	0.441721i
$585$	−11.0880	−	22.1308i	−0.458432	−	0.914994i
$586$	17.4353	+	10.0663i	0.720248	+	0.415835i
$587$	−19.1503	+	11.0565i	−0.790419	+	0.456349i	−0.840110	−	0.542416i	$-0.817510\pi$
$587$	−19.1503	+	11.0565i	−0.790419	+	0.456349i	0.0496910	+	0.998765i	$0.484176\pi$
$588$	−9.83694	+	7.08764i	−0.405669	+	0.292289i
$589$	−6.62068	+	11.4673i	−0.272800	+	0.472504i
$590$	−6.89293	+	11.9389i	−0.283777	+	0.491517i
$591$	−20.4377	−	40.0776i	−0.840694	−	1.64857i
$592$		−	4.99903i		−	0.205459i
$593$	−22.7957	−	13.1611i	−0.936109	−	0.540463i	−0.0473705	−	0.998877i	$-0.515084\pi$
$593$	−22.7957	−	13.1611i	−0.936109	−	0.540463i	−0.888738	+	0.458415i	$0.848417\pi$
$594$	0.970443	−	1.20089i	0.0398178	−	0.0492732i
$595$	−0.997088	+	5.31604i	−0.0408766	+	0.217936i
$596$	1.64375	+	2.84705i	0.0673305	+	0.116620i
$597$	0.499607	−	9.59529i	0.0204476	−	0.392709i
$598$	−12.9747	+	25.0019i	−0.530574	+	1.02240i
$599$	5.69118	−	3.28581i	0.232536	−	0.134254i	−0.379206	−	0.925312i	$-0.623803\pi$
$599$	5.69118	−	3.28581i	0.232536	−	0.134254i	0.611741	+	0.791058i	$0.290469\pi$
$600$	−0.186386	−	0.365496i	−0.00760916	−	0.0149213i
$601$	22.1774	−	12.8041i	0.904634	−	0.522291i	0.0259335	−	0.999664i	$-0.491744\pi$
$601$	22.1774	−	12.8041i	0.904634	−	0.522291i	0.878701	+	0.477373i	$0.158411\pi$
$602$	−10.1004	−	1.89445i	−0.411660	−	0.0772119i
$603$	8.25319	+	5.98775i	0.336096	+	0.243840i
$604$	10.5899	−	6.11409i	0.430897	−	0.248779i
$605$		−	24.9706i		−	1.01520i
$606$	−17.7041	+	27.2821i	−0.719179	+	1.10826i
$607$	36.9259	−	21.3192i	1.49878	−	0.865320i	0.498779	−	0.866729i	$-0.333782\pi$
$607$	36.9259	−	21.3192i	1.49878	−	0.865320i	0.999999	+	0.00140959i	$0.000448687\pi$
$608$	3.94533	+	6.83352i	0.160004	+	0.277136i
$609$	3.75872	+	3.57984i	0.152311	+	0.145062i
$610$	19.3316			0.782714
$611$	11.6792	+	18.2813i	0.472492	+	0.739582i
$612$	2.66549	+	0.278328i	0.107746	+	0.0112507i
$613$	−3.48038	−	2.00940i	−0.140571	−	0.0811588i	0.428065	−	0.903748i	$-0.359195\pi$
$613$	−3.48038	−	2.00940i	−0.140571	−	0.0811588i	−0.568636	+	0.822589i	$0.692529\pi$
$614$	−3.07801			−0.124219
$615$	−29.8046	−	1.55186i	−1.20184	−	0.0625772i
$616$	−0.772686	−	0.144927i	−0.0311324	−	0.00583927i
$617$	−12.9809	+	22.4837i	−0.522593	+	0.905158i	0.477061	+	0.878870i	$0.341702\pi$
$617$	−12.9809	+	22.4837i	−0.522593	+	0.905158i	−0.999654	+	0.0262879i	$0.991631\pi$
$618$	20.7864	+	13.4888i	0.836152	+	0.542601i
$619$	2.84282	+	4.92392i	0.114263	+	0.197909i	0.917485	−	0.397771i	$-0.130216\pi$
$619$	2.84282	+	4.92392i	0.114263	+	0.197909i	−0.803222	+	0.595680i	$0.796883\pi$
$620$			3.84021i			0.154226i
$621$	6.30960	−	40.1011i	0.253196	−	1.60920i
$622$	−7.75963	−	13.4401i	−0.311133	−	0.538898i
$623$	35.7176	−	12.5620i	1.43100	−	0.503285i
$624$	5.38598	+	3.16089i	0.215612	+	0.126537i
$625$	13.0641	−	22.6277i	0.522565	−	0.905109i
$626$	−13.7068	−	7.91361i	−0.547833	−	0.316291i
$627$	4.05554	+	0.211164i	0.161963	+	0.00843307i
$628$	−15.4715	+	8.93248i	−0.617380	+	0.356445i
$629$		−	4.46577i		−	0.178062i
$630$	5.18440	−	17.4082i	0.206552	−	0.693559i
$631$	11.9099	+	6.87621i	0.474128	+	0.273738i	0.717966	−	0.696078i	$-0.245073\pi$
$631$	11.9099	+	6.87621i	0.474128	+	0.273738i	−0.243838	+	0.969816i	$0.578407\pi$
$632$	−4.46469	+	7.73307i	−0.177596	+	0.307605i
$633$	1.84188	+	3.61186i	0.0732080	+	0.143558i
$634$	6.47213	−	11.2101i	0.257041	−	0.445208i
$635$		−	12.0475i		−	0.478092i
$636$	−11.1954	+	5.70910i	−0.443925	+	0.226381i
$637$	−24.7473	+	4.95704i	−0.980523	+	0.196405i
$638$			0.336571i			0.0133250i
$639$	−4.05177	+	5.58474i	−0.160286	+	0.220929i
$640$	1.98183	+	1.14421i	0.0783388	+	0.0452289i
$641$		−	6.28822i		−	0.248370i	−0.992259	−	0.124185i	$-0.960368\pi$
$641$		−	6.28822i		−	0.248370i	0.992259	−	0.124185i	$-0.0396316\pi$
$642$	1.50272	−	28.8608i	0.0593077	−	1.13904i
$643$	−17.3160	+	29.9922i	−0.682877	+	1.18278i	0.291222	+	0.956656i	$0.405938\pi$
$643$	−17.3160	+	29.9922i	−0.682877	+	1.18278i	−0.974099	+	0.226122i	$0.927395\pi$
$644$	−19.4989	+	6.85779i	−0.768363	+	0.270235i
$645$	13.7151	−	6.99403i	0.540030	−	0.275390i
$646$	3.52448	+	6.10457i	0.138669	+	0.240181i
$647$	−9.06347	+	15.6984i	−0.356322	+	0.617167i	−0.987343	−	0.158598i	$-0.949303\pi$
$647$	−9.06347	+	15.6984i	−0.356322	+	0.617167i	0.631022	+	0.775765i	$0.282636\pi$
$648$	−8.80586	−	1.85927i	−0.345927	−	0.0730391i
$649$	−1.55021	−	0.895014i	−0.0608511	−	0.0351324i
$650$	−0.0383409	−	0.853198i	−0.00150385	−	0.0334652i
$651$	−5.30356	+	5.56856i	−0.207863	+	0.218249i
$652$	−2.00708	+	1.15879i	−0.0786033	+	0.0453816i
$653$			40.1546i			1.57137i	0.618627	+	0.785685i	$0.287689\pi$
$653$			40.1546i			1.57137i	−0.618627	+	0.785685i	$0.712311\pi$
$654$	17.2889	−	8.81649i	0.676048	−	0.344752i
$655$	−1.53099	+	0.883918i	−0.0598208	+	0.0345375i
$656$	6.52086	−	3.76482i	0.254597	−	0.146992i
$657$	15.0632	+	33.7710i	0.587673	+	1.31753i
$658$	−2.93458	+	15.6459i	−0.114402	+	0.609940i
$659$	15.7627	+	9.10062i	0.614029	+	0.354510i	0.774541	−	0.632524i	$-0.217981\pi$
$659$	15.7627	+	9.10062i	0.614029	+	0.354510i	−0.160512	+	0.987034i	$0.551314\pi$
$660$	1.04922	−	0.535050i	0.0408406	−	0.0208268i
$661$	11.5569	−	20.0171i	0.449510	−	0.778575i	−0.548844	−	0.835925i	$-0.684932\pi$
$661$	11.5569	−	20.0171i	0.449510	−	0.778575i	0.998354	+	0.0573503i	$0.0182652\pi$
$662$	−7.76227	+	4.48155i	−0.301689	+	0.174180i
$663$	4.81144	+	2.82371i	0.186861	+	0.109664i
$664$		−	1.54870i		−	0.0601014i
$665$	45.0687	−	15.8508i	1.74769	−	0.614666i
$666$	−1.55751	+	14.9160i	−0.0603524	+	0.577983i
$667$	4.42455	+	7.66355i	0.171319	+	0.296734i
$668$	11.5588	−	6.67349i	0.447224	−	0.258205i
$669$	1.17531	+	2.30474i	0.0454401	+	0.0891065i
$670$	3.88898	+	6.73591i	0.150244	+	0.260231i
$671$			2.51012i			0.0969020i
$672$	1.29357	+	4.39621i	0.0499005	+	0.169588i
$673$	−18.1450	−	31.4281i	−0.699438	−	1.21146i	−0.968661	−	0.248385i	$-0.920100\pi$
$673$	−18.1450	−	31.4281i	−0.699438	−	1.21146i	0.269223	−	0.963078i	$-0.413233\pi$
$674$	7.76837			0.299226
$675$	0.442258	+	1.14863i	0.0170225	+	0.0442108i
$676$	7.48361	+	10.6299i	0.287831	+	0.408844i
$677$	−2.13681	+	3.70106i	−0.0821243	+	0.142243i	−0.904162	−	0.427189i	$-0.859504\pi$
$677$	−2.13681	+	3.70106i	−0.0821243	+	0.142243i	0.822038	+	0.569433i	$0.192837\pi$
$678$	12.1975	+	7.91528i	0.468443	+	0.303985i
$679$	6.20696	+	1.16419i	0.238201	+	0.0446776i
$680$	1.77042	+	1.02215i	0.0678927	+	0.0391978i
$681$	0.573773	−	11.0197i	0.0219870	−	0.422276i
$682$	−0.498633			−0.0190936
$683$	−30.0773			−1.15088			−0.575438	−	0.817846i	$-0.695168\pi$
$683$	−30.0773			−1.15088			−0.575438	+	0.817846i	$0.695168\pi$
$684$	−9.64293	−	21.6189i	−0.368706	−	0.826620i
$685$	−5.12669	−	2.95989i	−0.195881	−	0.113092i
$686$	−15.7284	−	9.77839i	−0.600514	−	0.373341i
$687$	−7.41801	+	11.4312i	−0.283015	+	0.436128i
$688$	−1.94207	+	3.36377i	−0.0740408	+	0.128242i
$689$	−26.1340	+	1.17441i	−0.995625	+	0.0447413i
$690$	16.8563	−	25.9757i	0.641709	−	0.988879i
$691$	−17.1832			−0.653679			−0.326840	−	0.945080i	$-0.605984\pi$
$691$	−17.1832			−0.653679			−0.326840	+	0.945080i	$0.605984\pi$
$692$	9.18090	+	15.9018i	0.349006	+	0.604495i
$693$	2.26037	+	0.673170i	0.0858644	+	0.0255716i
$694$			9.70091i			0.368241i
$695$	−13.4809	−	23.3496i	−0.511360	−	0.885701i
$696$	1.74776	−	0.891273i	0.0662486	−	0.0337836i
$697$	5.82526	−	3.36322i	0.220648	−	0.127391i
$698$	−13.2526	−	22.9542i	−0.501619	−	0.868829i
$699$	−13.4993	−	8.76006i	−0.510591	−	0.331336i
$700$	0.408037	−	0.475677i	0.0154224	−	0.0179789i
$701$			33.7755i			1.27568i	0.770167	+	0.637842i	$0.220173\pi$
$701$			33.7755i			1.27568i	−0.770167	+	0.637842i	$0.779827\pi$
$702$	−15.0857	−	11.1095i	−0.569375	−	0.419300i
$703$	−34.1610	+	19.7228i	−1.28840	+	0.743861i
$704$	−0.148570	+	0.257331i	−0.00559945	+	0.00969854i
$705$	−10.8341	−	21.2452i	−0.408034	−	0.800142i
$706$	−22.1838	−	12.8078i	−0.834900	−	0.482030i
$707$	−48.8283	−	9.15835i	−1.83638	−	0.344435i
$708$	−0.542552	+	10.4201i	−0.0203904	+	0.391610i
$709$	−1.05799	+	0.610834i	−0.0397338	+	0.0229403i	−0.519735	−	0.854327i	$-0.673969\pi$
$709$	−1.05799	+	0.610834i	−0.0397338	+	0.0229403i	0.480002	+	0.877268i	$0.340636\pi$
$710$	−4.55803	+	2.63158i	−0.171060	+	0.0987614i
$711$	15.7310	−	21.6827i	0.589958	−	0.813166i
$712$		−	14.3106i		−	0.536312i
$713$	−11.3536	+	6.55500i	−0.425196	+	0.245487i
$714$	1.15558	+	3.92726i	0.0432465	+	0.146974i
$715$	2.44924	−	0.110064i	0.0915965	−	0.00411615i
$716$	−8.93640	−	5.15943i	−0.333969	−	0.192817i
$717$	−39.1029	−	2.03601i	−1.46033	−	0.0760362i
$718$	−6.41408	+	11.1095i	−0.239371	+	0.414604i
$719$	−15.5184	−	26.8786i	−0.578738	−	1.00240i	−0.995624	−	0.0934449i	$-0.970212\pi$
$719$	−15.5184	−	26.8786i	−0.578738	−	1.00240i	0.416887	−	0.908959i	$-0.363121\pi$
$720$	−5.55685	−	4.03154i	−0.207092	−	0.150246i
$721$	−6.97780	+	37.2026i	−0.259867	+	1.38550i
$722$	21.6313	−	37.4666i	0.805035	−	1.39436i
$723$	50.3127	+	2.61968i	1.87115	+	0.0974270i
$724$			5.21743i			0.193904i
$725$	−0.232360	−	0.134153i	−0.00862964	−	0.00498232i
$726$	−8.58596	−	16.8368i	−0.318655	−	0.624872i
$727$			33.4726i			1.24143i	0.784036	+	0.620716i	$0.213158\pi$
$727$			33.4726i			1.24143i	−0.784036	+	0.620716i	$0.786842\pi$
$728$	−1.33588	+	9.44539i	−0.0495111	+	0.350069i
$729$	25.6954	+	8.29123i	0.951683	+	0.307083i
$730$			28.2072i			1.04399i
$731$	−1.73491	+	3.00495i	−0.0641678	+	0.111142i
$732$	13.0346	−	6.64704i	0.481773	−	0.245682i
$733$	−12.3342	+	21.3634i	−0.455573	+	0.789076i	−0.998721	−	0.0505610i	$-0.983899\pi$
$733$	−12.3342	+	21.3634i	−0.455573	+	0.789076i	0.543148	+	0.839637i	$0.317232\pi$
$734$	21.2692	+	12.2798i	0.785061	+	0.453255i
$735$	27.6049	−	2.79096i	1.01822	−	0.102946i
$736$			7.81240i			0.287969i
$737$	−0.874625	+	0.504965i	−0.0322172	+	0.0186006i
$738$	−20.6298	+	9.20173i	−0.759392	+	0.338720i
$739$	38.5610	+	22.2632i	1.41849	+	0.818964i	0.996166	−	0.0874820i	$-0.0278820\pi$
$739$	38.5610	+	22.2632i	1.41849	+	0.818964i	0.422321	+	0.906446i	$0.361215\pi$
$740$	−5.71994	+	9.90723i	−0.210269	+	0.364197i
$741$	0.350522	−	49.2760i	0.0128768	−	1.81020i
$742$	−14.5703	−	12.4984i	−0.534892	−	0.458832i
$743$	19.9258	+	34.5124i	0.731006	+	1.26614i	0.956454	+	0.291884i	$0.0942820\pi$
$743$	19.9258	+	34.5124i	0.731006	+	1.26614i	−0.225448	+	0.974255i	$0.572385\pi$
$744$	1.32043	+	2.58932i	0.0484092	+	0.0949289i
$745$		−	7.52318i		−	0.275628i
$746$	−10.7383	−	18.5993i	−0.393158	−	0.680969i
$747$	−0.482519	+	4.62099i	−0.0176545	+	0.169073i
$748$	−0.132722	+	0.229881i	−0.00485279	+	0.00840529i
$749$	41.6447	−	14.6465i	1.52166	−	0.535173i
$750$	0.981684	−	18.8539i	0.0358460	−	0.688447i
$751$	−17.9853			−0.656292			−0.328146	−	0.944627i	$-0.606424\pi$
$751$	−17.9853			−0.656292			−0.328146	+	0.944627i	$0.606424\pi$
$752$	5.21062	+	3.00835i	0.190012	+	0.109703i
$753$	12.9935	−	20.0231i	0.473510	−	0.729683i
$754$	4.07989	−	0.183342i	0.148581	−	0.00667691i
$755$	−27.9832			−1.01841
$756$	−2.49002	−	13.5203i	−0.0905612	−	0.491730i
$757$	20.2665	+	35.1027i	0.736600	+	1.27583i	0.954018	+	0.299750i	$0.0969034\pi$
$757$	20.2665	+	35.1027i	0.736600	+	1.27583i	−0.217417	+	0.976079i	$0.569763\pi$
$758$	13.9171	−	8.03505i	0.505492	−	0.291846i
$759$	3.37283	+	2.18871i	0.122426	+	0.0794453i
$760$		−	18.0572i		−	0.655003i
$761$	−1.19636	+	0.690718i	−0.0433680	+	0.0250385i	−0.521527	−	0.853235i	$-0.674638\pi$
$761$	−1.19636	+	0.690718i	−0.0433680	+	0.0250385i	0.478159	+	0.878273i	$0.341304\pi$
$762$	−4.14246	−	8.12322i	−0.150065	−	0.294273i
$763$	22.5007	+	19.3012i	0.814579	+	0.698749i
$764$	22.8395	−	13.1864i	0.826305	−	0.477067i
$765$	−4.96409	−	3.60148i	−0.179477	−	0.130212i
$766$	−23.1968	+	13.3927i	−0.838136	+	0.483898i
$767$	−10.0048	+	19.2791i	−0.361254	+	0.696127i
$768$	1.72971	+	0.0900624i	0.0624155	+	0.00324985i
$769$	−3.70242	−	6.41278i	−0.133513	−	0.231251i	0.791516	−	0.611149i	$-0.209292\pi$
$769$	−3.70242	−	6.41278i	−0.133513	−	0.231251i	−0.925028	+	0.379898i	$0.875959\pi$
$770$	1.36551	+	1.17134i	0.0492095	+	0.0422120i
$771$	−9.72863	−	0.506550i	−0.350368	−	0.0182430i
$772$	2.77543	+	1.60239i	0.0998899	+	0.0576714i
$773$			5.44545i			0.195859i	0.995193	+	0.0979297i	$0.0312220\pi$
$773$			5.44545i			0.195859i	−0.995193	+	0.0979297i	$0.968778\pi$
$774$	6.84274	−	9.43166i	0.245957	−	0.339014i
$775$	0.198749	−	0.344243i	0.00713927	−	0.0123656i
$776$	1.19346	−	2.06713i	0.0428427	−	0.0742058i
$777$	−21.9768	+	6.46658i	−0.788413	+	0.231987i
$778$	3.67405	−	2.12122i	0.131721	−	0.0760493i
$779$	−51.4539	−	29.7069i	−1.84353	−	1.06436i
$780$	−7.05738	−	12.4270i	−0.252695	−	0.444960i
$781$	−0.341698	−	0.591838i	−0.0122269	−	0.0211776i
$782$			6.97903i			0.249570i
$783$	−5.49261	+	2.11482i	−0.196290	+	0.0755777i
$784$	−5.45890	+	4.38183i	−0.194961	+	0.156494i
$785$	40.8825			1.45916
$786$	−0.728364	+	1.12242i	−0.0259799	+	0.0400352i
$787$	33.5494			1.19591			0.597953	−	0.801531i	$-0.295981\pi$
$787$	33.5494			1.19591			0.597953	+	0.801531i	$0.295981\pi$
$788$	−12.9869	−	22.4940i	−0.462639	−	0.801314i
$789$	−28.1605	−	18.2741i	−1.00254	−	0.650574i
$790$	17.6965	−	10.2171i	0.629614	−	0.363508i
$791$	−4.09459	+	21.8306i	−0.145587	+	0.776205i
$792$	0.523476	−	0.721530i	0.0186009	−	0.0256385i
$793$	30.4274	−	1.36735i	1.08051	−	0.0485558i
$794$	0.355073	+	0.615005i	0.0126011	+	0.0218257i
$795$	28.7198	+	1.49538i	1.01858	+	0.0530356i
$796$		−	5.54735i		−	0.196621i
$797$	−16.9758	+	29.4030i	−0.601315	+	1.04151i	0.391308	+	0.920260i	$0.372023\pi$
$797$	−16.9758	+	29.4030i	−0.601315	+	1.04151i	−0.992622	+	0.121248i	$0.961310\pi$
$798$	24.9380	−	26.1841i	0.882797	−	0.926909i
$799$	4.65479	+	2.68744i	0.164675	+	0.0950750i
$800$	−0.118437	−	0.205138i	−0.00418737	−	0.00725273i
$801$	−4.45865	+	42.6996i	−0.157539	+	1.50872i
$802$	15.2330			0.537897
$803$	−3.66257			−0.129249
$804$	4.93829	+	3.20459i	0.174160	+	0.113017i
$805$	46.4902	+	8.71981i	1.63856	+	0.307333i
$806$	0.271622	+	6.04439i	0.00956747	+	0.212904i
$807$	48.3533	+	2.51766i	1.70212	+	0.0886257i
$808$	−9.38860	+	16.2615i	−0.330290	+	0.572078i
$809$	21.4031	+	12.3571i	0.752494	+	0.434453i	0.826594	−	0.562798i	$-0.190275\pi$
$809$	21.4031	+	12.3571i	0.752494	+	0.434453i	−0.0741003	+	0.997251i	$0.523608\pi$
$810$	15.3243	+	13.7605i	0.538442	+	0.483495i
$811$	17.8537			0.626927			0.313464	−	0.949600i	$-0.398511\pi$
$811$	17.8537			0.626927			0.313464	+	0.949600i	$0.398511\pi$
$812$	2.27463	+	1.95118i	0.0798238	+	0.0684732i
$813$	−35.3878	−	1.84257i	−1.24110	−	0.0646218i
$814$	−1.28641	−	0.742707i	−0.0450885	−	0.0260319i
$815$	5.30359			0.185777
$816$	1.54520	+	0.0804552i	0.0540927	+	0.00281650i
$817$	30.6485			1.07226
$818$	−26.0063			−0.909289
$819$	6.92882	−	27.7667i	0.242112	−	0.970248i
$820$	−17.2310			−0.601732
$821$	32.4385			1.13211			0.566056	−	0.824367i	$-0.308469\pi$
$821$	32.4385			1.13211			0.566056	+	0.824367i	$0.308469\pi$
$822$	−4.47448	−	0.232977i	−0.156066	−	0.00812602i
$823$	23.5865			0.822175			0.411087	−	0.911596i	$-0.365149\pi$
$823$	23.5865			0.822175			0.411087	+	0.911596i	$0.365149\pi$
$824$	12.3898	+	7.15323i	0.431618	+	0.249194i
$825$	−0.121745	−	0.00633901i	−0.00423861	−	0.000220696i
$826$	−15.0357	+	5.28808i	−0.523158	+	0.183996i
$827$	−11.5185			−0.400539			−0.200269	−	0.979741i	$-0.564182\pi$
$827$	−11.5185			−0.400539			−0.200269	+	0.979741i	$0.564182\pi$
$828$	2.43406	−	23.3105i	0.0845893	−	0.810094i
$829$	−31.6004	−	18.2445i	−1.09753	−	0.633657i	−0.161956	−	0.986798i	$-0.551780\pi$
$829$	−31.6004	−	18.2445i	−1.09753	−	0.633657i	−0.935570	+	0.353141i	$0.885114\pi$
$830$	−1.77204	+	3.06927i	−0.0615086	+	0.106536i
$831$	11.2616	+	0.586369i	0.390660	+	0.0203409i
$832$	3.20028	+	1.66078i	0.110950	+	0.0575772i
$833$	−4.87659	+	3.91440i	−0.168964	+	0.135626i
$834$	−17.1183	−	11.1085i	−0.592758	−	0.384656i
$835$	−30.5435			−1.05700
$836$	2.34464			0.0810910
$837$	−3.13313	−	8.13734i	−0.108297	−	0.281268i
$838$	4.44170	+	7.69326i	0.153436	+	0.265759i
$839$	−27.0771	−	15.6330i	−0.934807	−	0.539711i	−0.0464780	−	0.998919i	$-0.514800\pi$
$839$	−27.0771	−	15.6330i	−0.934807	−	0.539711i	−0.888329	+	0.459209i	$0.848133\pi$
$840$	2.46656	−	10.1927i	0.0851044	−	0.351680i
$841$	−13.8585	+	24.0036i	−0.477879	+	0.827711i
$842$			11.9274i			0.411047i
$843$	−17.3467	−	0.903208i	−0.597452	−	0.0311081i
$844$	1.17040	+	2.02719i	0.0402868	+	0.0697788i
$845$	−2.66837	−	29.6296i	−0.0917947	−	1.01929i
$846$	−14.6100	−	10.5997i	−0.502304	−	0.364425i
$847$	18.7965	−	21.9123i	0.645854	−	0.752917i
$848$	−6.28351	+	3.62779i	−0.215777	+	0.124579i
$849$	33.2462	+	21.5743i	1.14100	+	0.740428i
$850$	−0.105803	−	0.183256i	−0.00362900	−	0.00628562i
$851$	−39.0544			−1.33877
$852$	−2.16847	+	3.34163i	−0.0742905	+	0.114482i
$853$	−33.1802			−1.13607			−0.568034	−	0.823005i	$-0.692296\pi$
$853$	−33.1802			−1.13607			−0.568034	+	0.823005i	$0.692296\pi$
$854$	16.9640	+	14.5518i	0.580495	+	0.497951i
$855$	−5.62595	+	53.8786i	−0.192403	+	1.84261i
$856$		−	16.6853i		−	0.570293i
$857$	−3.94184	−	6.82747i	−0.134651	−	0.233222i	0.790813	−	0.612058i	$-0.209658\pi$
$857$	−3.94184	−	6.82747i	−0.134651	−	0.233222i	−0.925464	+	0.378836i	$0.876325\pi$
$858$	1.61359	−	0.916367i	0.0550872	−	0.0312842i
$859$	−16.8815	−	9.74653i	−0.575989	−	0.332547i	0.183549	−	0.983011i	$-0.441241\pi$
$859$	−16.8815	−	9.74653i	−0.575989	−	0.332547i	−0.759538	+	0.650463i	$0.774575\pi$
$860$	7.69772	−	4.44428i	0.262490	−	0.151549i
$861$	−24.9861	−	23.7970i	−0.851525	−	0.811001i
$862$	−9.74149	+	16.8728i	−0.331796	+	0.574688i
$863$	−5.07880	+	8.79674i	−0.172884	+	0.299445i	−0.939427	−	0.342749i	$-0.888642\pi$
$863$	−5.07880	+	8.79674i	−0.172884	+	0.299445i	0.766543	+	0.642193i	$0.221975\pi$
$864$	−5.13300	−	0.807639i	−0.174628	−	0.0274765i
$865$		−	42.0196i		−	1.42871i
$866$	15.8703	+	9.16273i	0.539295	+	0.311362i
$867$	−28.0247	−	1.45919i	−0.951768	−	0.0495566i
$868$	−2.89069	+	3.36988i	−0.0981166	+	0.114381i
$869$	1.32664	+	2.29781i	0.0450032	+	0.0779479i
$870$	−4.48357	−	0.233450i	−0.152007	−	0.00791470i
$871$	6.59759	+	10.3271i	0.223551	+	0.349919i
$872$	9.70354	−	5.60234i	0.328603	−	0.189719i
$873$	−4.20506	+	5.79603i	−0.142320	+	0.196166i
$874$	53.3862	−	30.8225i	1.80581	−	1.04259i
$875$	27.2053	−	9.56816i	0.919706	−	0.323463i
$876$	9.69883	+	19.0191i	0.327693	+	0.642596i
$877$	7.28663	−	4.20694i	0.246052	−	0.142058i	−0.371903	−	0.928272i	$-0.621295\pi$
$877$	7.28663	−	4.20694i	0.246052	−	0.142058i	0.617955	+	0.786213i	$0.287961\pi$
$878$			2.49215i			0.0841061i
$879$	−29.2515	−	18.9820i	−0.986627	−	0.640248i
$880$	0.588883	−	0.339992i	0.0198512	−	0.0114611i
$881$	−3.40189	−	5.89224i	−0.114612	−	0.198515i	0.803012	−	0.595962i	$-0.203229\pi$
$881$	−3.40189	−	5.89224i	−0.114612	−	0.198515i	−0.917625	+	0.397448i	$0.869896\pi$
$882$	17.6534	−	11.3736i	0.594420	−	0.382969i
$883$	−8.76402			−0.294933			−0.147466	−	0.989067i	$-0.547112\pi$
$883$	−8.76402			−0.294933			−0.147466	+	0.989067i	$0.547112\pi$
$884$	2.85890	+	1.48362i	0.0961552	+	0.0498996i
$885$	12.9980	−	20.0300i	0.436923	−	0.673302i
$886$	14.4424	+	8.33832i	0.485202	+	0.280131i
$887$	−19.4033			−0.651499			−0.325749	−	0.945456i	$-0.605617\pi$
$887$	−19.4033			−0.651499			−0.325749	+	0.945456i	$0.605617\pi$
$888$	−0.450224	+	8.64686i	−0.0151085	+	0.290170i
$889$	9.06871	−	10.5720i	0.304155	−	0.354574i
$890$	−16.3743	+	28.3612i	−0.548869	+	0.950669i
$891$	−1.78674	+	1.98979i	−0.0598580	+	0.0666605i
$892$	0.746837	+	1.29356i	0.0250060	+	0.0433116i
$893$		−	47.4758i		−	1.58872i
$894$	−2.58679	−	5.07261i	−0.0865152	−	0.169654i
$895$	11.8070	+	20.4502i	0.394663	+	0.683576i
$896$	0.877809	+	2.49589i	0.0293256	+	0.0833817i
$897$	24.6941	−	42.0774i	0.824513	−	1.40492i
$898$	−18.5701	+	32.1643i	−0.619691	+	1.07334i
$899$	1.64613	+	0.950393i	0.0549015	+	0.0316974i
$900$	0.289475	+	0.648988i	0.00964917	+	0.0216329i
$901$	−5.61323	+	3.24080i	−0.187004	+	0.107967i
$902$		−	2.23736i		−	0.0744960i
$903$	17.3000	+	4.18650i	0.575709	+	0.139318i
$904$	7.27033	+	4.19753i	0.241808	+	0.139608i
$905$	5.96984	−	10.3401i	0.198444	−	0.343716i
$906$	−18.8681	+	9.62183i	−0.626851	+	0.319664i
$907$	8.31021	−	14.3937i	0.275936	−	0.477935i	−0.694435	−	0.719555i	$-0.744346\pi$
$907$	8.31021	−	14.3937i	0.275936	−	0.477935i	0.970371	+	0.241621i	$0.0776789\pi$
$908$		−	6.37084i		−	0.211424i
$909$	33.0800	−	45.5956i	1.09719	−	1.51231i
$910$	13.4550	−	17.1906i	0.446029	−	0.569864i
$911$		−	17.4495i		−	0.578127i	−0.957310	−	0.289063i	$-0.906656\pi$
$911$		−	17.4495i		−	0.578127i	0.957310	−	0.289063i	$-0.0933439\pi$
$912$	−6.20883	−	12.1753i	−0.205595	−	0.403165i
$913$	−0.398530	−	0.230092i	−0.0131894	−	0.00761492i
$914$			16.1075i			0.532788i
$915$	−33.4380	−	1.74105i	−1.10543	−	0.0575574i
$916$	−3.93382	+	6.81358i	−0.129977	+	0.225127i
$917$	−2.00885	−	0.376784i	−0.0663380	−	0.0124425i
$918$	−4.58545	−	0.721486i	−0.151342	−	0.0238126i
$919$	−8.08828	−	14.0093i	−0.266808	−	0.462125i	0.701228	−	0.712937i	$-0.252636\pi$
$919$	−8.08828	−	14.0093i	−0.266808	−	0.462125i	−0.968036	+	0.250813i	$0.919302\pi$
$920$	8.93903	−	15.4829i	0.294711	−	0.510454i
$921$	5.32406	+	0.277213i	0.175434	+	0.00913449i
$922$	−12.1978	−	7.04240i	−0.401713	−	0.231929i
$923$	−6.98809	+	4.46443i	−0.230016	+	0.146949i
$924$	1.32347	+	0.320271i	0.0435389	+	0.0105361i
$925$	1.02549	−	0.592068i	0.0337180	−	0.0194671i
$926$			20.5027i			0.673761i
$927$	−34.7396	−	25.2038i	−1.14100	−	0.827802i
$928$	0.980947	−	0.566350i	0.0322012	−	0.0185913i
$929$	−16.6028	+	9.58566i	−0.544722	+	0.314495i	−0.746990	−	0.664835i	$-0.768502\pi$
$929$	−16.6028	+	9.58566i	−0.544722	+	0.314495i	0.202269	+	0.979330i	$0.435169\pi$
$930$	0.345858	−	6.64244i	0.0113411	−	0.217814i
$931$	51.4805	+	20.0157i	1.68720	+	0.655989i
$932$	−8.04627	−	4.64552i	−0.263564	−	0.152169i
$933$	12.2115	+	23.9463i	0.399785	+	0.783965i
$934$	2.86923	−	4.96965i	0.0938840	−	0.162612i
$935$	0.526065	−	0.303724i	0.0172042	−	0.00993283i
$936$	−9.03149	−	5.95249i	−0.295204	−	0.194563i
$937$		−	38.4000i		−	1.25447i	−0.778828	−	0.627237i	$-0.784186\pi$
$937$		−	38.4000i		−	1.25447i	0.778828	−	0.627237i	$-0.215814\pi$
$938$	−1.65774	+	8.83834i	−0.0541271	+	0.288582i
$939$	22.9960	+	14.9227i	0.750446	+	0.486984i
$940$	−6.88438	−	11.9241i	−0.224544	−	0.388921i
$941$	6.21610	−	3.58887i	0.202639	−	0.116994i	−0.395247	−	0.918575i	$-0.629341\pi$
$941$	6.21610	−	3.58887i	0.202639	−	0.116994i	0.597886	+	0.801581i	$0.296008\pi$
$942$	27.5657	−	14.0572i	0.898138	−	0.458008i
$943$	−29.4123	−	50.9435i	−0.957795	−	1.65895i
$944$			6.02418i			0.196070i
$945$	−10.5353	+	29.6442i	−0.342714	+	0.964324i
$946$	0.577069	+	0.999512i	0.0187621	+	0.0324970i
$947$	−24.7971			−0.805799			−0.402899	−	0.915244i	$-0.631998\pi$
$947$	−24.7971			−0.805799			−0.402899	+	0.915244i	$0.631998\pi$
$948$	8.41907	−	12.9739i	0.273439	−	0.421371i
$949$	1.99512	+	44.3974i	0.0647644	+	1.44120i
$950$	−0.934544	+	1.61868i	−0.0303206	+	0.0525169i
$951$	−12.2045	+	18.8072i	−0.395758	+	0.609866i
$952$	0.784171	+	2.22964i	0.0254151	+	0.0722632i
$953$	−17.1692	−	9.91265i	−0.556165	−	0.321102i	0.195440	−	0.980716i	$-0.437387\pi$
$953$	−17.1692	−	9.91265i	−0.556165	−	0.321102i	−0.751605	+	0.659614i	$0.770720\pi$
$954$	19.8789	−	8.86680i	0.643603	−	0.287073i
$955$	−60.3521			−1.95295
$956$	−22.6067			−0.731152
$957$	0.0303124	−	0.582170i	0.000979861	−	0.0188189i
$958$	−24.3944	−	14.0841i	−0.788147	−	0.455037i
$959$	−2.27076	−	6.45647i	−0.0733265	−	0.208490i
$960$	−3.32494	−	2.15764i	−0.107312	−	0.0696375i
$961$	14.0920	−	24.4080i	0.454580	−	0.787356i
$962$	−8.30229	+	15.9983i	−0.267677	+	0.515806i
$963$	−5.19854	+	49.7853i	−0.167521	+	1.60431i
$964$	29.0874			0.936842
$965$	−3.66695	−	6.35135i	−0.118043	−	0.204457i
$966$	34.3450	−	10.1059i	1.10503	−	0.325151i
$967$			4.47698i			0.143970i	0.997406	+	0.0719849i	$0.0229333\pi$
$967$			4.47698i			0.143970i	−0.997406	+	0.0719849i	$0.977067\pi$
$968$	−5.45585	−	9.44982i	−0.175358	−	0.303729i
$969$	−5.54652	−	10.8765i	−0.178180	−	0.349405i
$970$	−4.73047	+	2.73114i	−0.151886	+	0.0876917i
$971$	−6.27077	−	10.8613i	−0.201239	−	0.348556i	0.747689	−	0.664049i	$-0.231163\pi$
$971$	−6.27077	−	10.8613i	−0.201239	−	0.348556i	−0.948928	+	0.315493i	$0.897830\pi$
$972$	15.0641	+	4.00907i	0.483181	+	0.128591i
$973$	5.74645	−	30.6375i	0.184223	−	0.982195i
$974$		−	29.7095i		−	0.951954i
$975$	−0.0105225	+	1.47924i	−0.000336989	+	0.0473735i
$976$	7.31581	−	4.22379i	0.234173	−	0.135200i
$977$	−27.3010	+	47.2868i	−0.873437	+	1.51284i	−0.0150192	+	0.999887i	$0.504781\pi$
$977$	−27.3010	+	47.2868i	−0.873437	+	1.51284i	−0.858418	+	0.512951i	$0.828552\pi$
$978$	3.57602	−	1.82360i	0.114349	−	0.0583123i
$979$	−3.68256	−	2.12613i	−0.117695	−	0.0679514i
$980$	15.8324	−	2.43790i	0.505746	−	0.0778760i
$981$	−30.6987	+	13.6929i	−0.980134	+	0.437180i
$982$	−35.4120	+	20.4451i	−1.13004	+	0.652430i
$983$	40.1578	−	23.1851i	1.28083	−	0.739490i	0.303833	−	0.952725i	$-0.401734\pi$
$983$	40.1578	−	23.1851i	1.28083	−	0.739490i	0.977001	+	0.213236i	$0.0684002\pi$
$984$	−11.6183	+	5.92475i	−0.370376	+	0.188874i
$985$			59.4390i			1.89388i
$986$	0.876307	−	0.505936i	0.0279073	−	0.0161123i
$987$	6.48507	−	26.7985i	0.206422	−	0.853006i
$988$	−1.27720	−	28.4215i	−0.0406332	−	0.904209i
$989$	26.2791	+	15.1722i	0.835627	+	0.482449i
$990$	−1.86302	+	0.830985i	−0.0592108	+	0.0264104i
$991$	−4.20625	+	7.28544i	−0.133616	+	0.231430i	−0.925068	−	0.379802i	$-0.875992\pi$
$991$	−4.20625	+	7.28544i	−0.133616	+	0.231430i	0.791452	+	0.611231i	$0.209326\pi$
$992$	0.839051	+	1.45328i	0.0266399	+	0.0461417i
$993$	13.8301	−	7.05268i	0.438884	−	0.223810i
$994$	−5.98070	−	1.12175i	−0.189696	−	0.0355798i
$995$	−6.34734	+	10.9939i	−0.201224	+	0.348530i
$996$	−0.139480	+	2.67881i	−0.00441959	+	0.0848812i
$997$			61.7989i			1.95719i	0.205796	+	0.978595i	$0.434022\pi$
$997$			61.7989i			1.95719i	−0.205796	+	0.978595i	$0.565978\pi$
$998$	−11.0351	−	6.37111i	−0.349310	−	0.201674i
$999$	4.03741	−	25.6600i	0.127738	−	0.811847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.257.17	yes	34
3.2	odd	2		546.2.bi.f.257.11	yes	34
7.3	odd	6		546.2.bn.f.101.11	yes	34
13.4	even	6		546.2.bn.e.173.7	yes	34
21.17	even	6		546.2.bn.e.101.7	yes	34
39.17	odd	6		546.2.bn.f.173.11	yes	34
91.17	odd	6		546.2.bi.f.17.11	yes	34
273.17	even	6	inner	546.2.bi.e.17.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.17	✓	34	273.17	even	6	inner
546.2.bi.e.257.17	yes	34	1.1	even	1	trivial
546.2.bi.f.17.11	yes	34	91.17	odd	6
546.2.bi.f.257.11	yes	34	3.2	odd	2
546.2.bn.e.101.7	yes	34	21.17	even	6
546.2.bn.e.173.7	yes	34	13.4	even	6
546.2.bn.f.101.11	yes	34	7.3	odd	6
546.2.bn.f.173.11	yes	34	39.17	odd	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.72971 + 0.0900624i) q^{3} +1.00000 q^{4} +(-1.98183 - 1.14421i) q^{5} +(-1.72971 - 0.0900624i) q^{6} +(-0.877809 - 2.49589i) q^{7} -1.00000 q^{8} +(2.98378 + 0.311563i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.72971 + 0.0900624i) q^{3} +1.00000 q^{4} +(-1.98183 - 1.14421i) q^{5} +(-1.72971 - 0.0900624i) q^{6} +(-0.877809 - 2.49589i) q^{7} -1.00000 q^{8} +(2.98378 + 0.311563i) q^{9} +(1.98183 + 1.14421i) q^{10} +(-0.148570 + 0.257331i) q^{11} +(1.72971 + 0.0900624i) q^{12} +(3.20028 + 1.66078i) q^{13} +(0.877809 + 2.49589i) q^{14} +(-3.32494 - 2.15764i) q^{15} +1.00000 q^{16} +0.893327 q^{17} +(-2.98378 - 0.311563i) q^{18} +(-3.94533 - 6.83352i) q^{19} +(-1.98183 - 1.14421i) q^{20} +(-1.29357 - 4.39621i) q^{21} +(0.148570 - 0.257331i) q^{22} -7.81240i q^{23} +(-1.72971 - 0.0900624i) q^{24} +(0.118437 + 0.205138i) q^{25} +(-3.20028 - 1.66078i) q^{26} +(5.13300 + 0.807639i) q^{27} +(-0.877809 - 2.49589i) q^{28} +(-0.980947 + 0.566350i) q^{29} +(3.32494 + 2.15764i) q^{30} +(-0.839051 - 1.45328i) q^{31} -1.00000 q^{32} +(-0.280159 + 0.431727i) q^{33} -0.893327 q^{34} +(-1.11615 + 5.95083i) q^{35} +(2.98378 + 0.311563i) q^{36} -4.99903i q^{37} +(3.94533 + 6.83352i) q^{38} +(5.38598 + 3.16089i) q^{39} +(1.98183 + 1.14421i) q^{40} +(6.52086 - 3.76482i) q^{41} +(1.29357 + 4.39621i) q^{42} +(-1.94207 + 3.36377i) q^{43} +(-0.148570 + 0.257331i) q^{44} +(-5.55685 - 4.03154i) q^{45} +7.81240i q^{46} +(5.21062 + 3.00835i) q^{47} +(1.72971 + 0.0900624i) q^{48} +(-5.45890 + 4.38183i) q^{49} +(-0.118437 - 0.205138i) q^{50} +(1.54520 + 0.0804552i) q^{51} +(3.20028 + 1.66078i) q^{52} +(-6.28351 + 3.62779i) q^{53} +(-5.13300 - 0.807639i) q^{54} +(0.588883 - 0.339992i) q^{55} +(0.877809 + 2.49589i) q^{56} +(-6.20883 - 12.1753i) q^{57} +(0.980947 - 0.566350i) q^{58} +6.02418i q^{59} +(-3.32494 - 2.15764i) q^{60} +(7.31581 - 4.22379i) q^{61} +(0.839051 + 1.45328i) q^{62} +(-1.84156 - 7.72066i) q^{63} +1.00000 q^{64} +(-4.44214 - 6.95319i) q^{65} +(0.280159 - 0.431727i) q^{66} +(2.94347 + 1.69941i) q^{67} +0.893327 q^{68} +(0.703603 - 13.5132i) q^{69} +(1.11615 - 5.95083i) q^{70} +(-1.14995 + 1.99178i) q^{71} +(-2.98378 - 0.311563i) q^{72} +(6.16302 + 10.6747i) q^{73} +4.99903i q^{74} +(0.186386 + 0.365496i) q^{75} +(-3.94533 - 6.83352i) q^{76} +(0.772686 + 0.144927i) q^{77} +(-5.38598 - 3.16089i) q^{78} +(4.46469 - 7.73307i) q^{79} +(-1.98183 - 1.14421i) q^{80} +(8.80586 + 1.85927i) q^{81} +(-6.52086 + 3.76482i) q^{82} +1.54870i q^{83} +(-1.29357 - 4.39621i) q^{84} +(-1.77042 - 1.02215i) q^{85} +(1.94207 - 3.36377i) q^{86} +(-1.74776 + 0.891273i) q^{87} +(0.148570 - 0.257331i) q^{88} +14.3106i q^{89} +(5.55685 + 4.03154i) q^{90} +(1.33588 - 9.44539i) q^{91} -7.81240i q^{92} +(-1.32043 - 2.58932i) q^{93} +(-5.21062 - 3.00835i) q^{94} +18.0572i q^{95} +(-1.72971 - 0.0900624i) q^{96} +(-1.19346 + 2.06713i) q^{97} +(5.45890 - 4.38183i) q^{98} +(-0.523476 + 0.721530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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