LMFDB - Embedded newform 546.2.bi.e.17.17

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			17.17
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.17

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	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	−0.872731	−	0.488201i	$-0.837653\pi$
$5$	−1.98183	+	1.14421i	−0.886302	+	0.511707i	−0.0135708	+	0.999908i	$0.504320\pi$
$6$	−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	0.842758	−	0.538292i	$-0.180930\pi$
$11$	−0.148570	−	0.257331i	−0.0447956	−	0.0775883i	−0.887554	+	0.460704i	$0.847597\pi$
$12$	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	−0.0843680	+	0.996435i	$0.526887\pi$
$19$	−3.94533	+	6.83352i	−0.905122	+	1.56772i	−0.820754	+	0.571282i	$0.806446\pi$
$20$	−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	$0.302988\pi$
$23$			7.81240i			1.62900i	−0.580165	+	0.814499i	$0.697012\pi$
$24$	−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	0.406149	−	0.913807i	$-0.366872\pi$
$29$	−0.980947	−	0.566350i	−0.182157	−	0.105169i	−0.588306	+	0.808639i	$0.700205\pi$
$30$	3.32494	−	2.15764i	0.607048	−	0.393929i
$31$	−0.839051	+	1.45328i	−0.150698	+	0.261017i	−0.931484	−	0.363782i	$-0.881485\pi$
$31$	−0.839051	+	1.45328i	−0.150698	+	0.261017i	0.780786	+	0.624798i	$0.214819\pi$
$32$	−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	$0.134792\pi$
$37$			4.99903i			0.821835i	−0.911673	+	0.410918i	$0.865208\pi$
$38$	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	0.913636	−	0.406532i	$-0.133262\pi$
$41$	6.52086	+	3.76482i	1.01839	+	0.587966i	0.104751	+	0.994498i	$0.466595\pi$
$42$	1.29357	−	4.39621i	0.199602	−	0.678350i
$43$	−1.94207	−	3.36377i	−0.296163	−	0.512970i	0.679092	−	0.734054i	$-0.262374\pi$
$43$	−1.94207	−	3.36377i	−0.296163	−	0.512970i	−0.975255	+	0.221084i	$0.929041\pi$
$44$	−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	−0.0692655	−	0.997598i	$-0.522066\pi$
$47$	5.21062	−	3.00835i	0.760047	−	0.438813i	0.829313	+	0.558785i	$0.188732\pi$
$48$	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	0.00194455	−	0.999998i	$-0.499381\pi$
$53$	−6.28351	−	3.62779i	−0.863107	−	0.498315i	−0.865051	+	0.501683i	$0.832714\pi$
$54$	−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	$-0.871735\pi$
$59$		−	6.02418i		−	0.784281i	0.919905	−	0.392141i	$-0.128265\pi$
$60$	−3.32494	+	2.15764i	−0.429248	+	0.278550i
$61$	7.31581	+	4.22379i	0.936694	+	0.540800i	0.888922	−	0.458058i	$-0.151455\pi$
$61$	7.31581	+	4.22379i	0.936694	+	0.540800i	0.0477714	+	0.998858i	$0.484788\pi$
$62$	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	−0.309304	−	0.950963i	$-0.600096\pi$
$67$	2.94347	−	1.69941i	0.359602	−	0.207617i	0.668906	+	0.743347i	$0.266763\pi$
$68$	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	0.789685	−	0.613512i	$-0.210244\pi$
$71$	−1.14995	−	1.99178i	−0.136474	−	0.236381i	−0.926160	+	0.377131i	$0.876910\pi$
$72$	−2.98378	+	0.311563i	−0.351642	+	0.0367181i
$73$	6.16302	−	10.6747i	0.721327	−	1.24937i	−0.239141	−	0.970985i	$-0.576866\pi$
$73$	6.16302	−	10.6747i	0.721327	−	1.24937i	0.960468	−	0.278390i	$-0.0898007\pi$
$74$		−	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	0.999996	+	0.00267764i	$0.000852321\pi$
$79$	4.46469	+	7.73307i	0.502317	+	0.870039i	−0.497679	+	0.867361i	$0.665814\pi$
$80$	−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	$-0.972912\pi$
$83$		−	1.54870i		−	0.169992i	0.996381	−	0.0849962i	$-0.0270878\pi$
$84$	−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	$-0.725952\pi$
$89$		−	14.3106i		−	1.51692i	0.651720	−	0.758460i	$-0.274048\pi$
$90$	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	0.799055	−	0.601258i	$-0.205334\pi$
$97$	−1.19346	−	2.06713i	−0.121178	−	0.209886i	−0.920232	+	0.391373i	$0.872000\pi$
$98$	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	0.776054	+	0.630666i	$0.217218\pi$
$101$	9.38860	+	16.2615i	0.934200	+	1.61808i	0.158146	+	0.987416i	$0.449448\pi$
$102$	−1.54520	+	0.0804552i	−0.152997	+	0.00796625i
$103$	−12.3898	+	7.15323i	−1.22080	+	0.704828i	−0.965088	−	0.261925i	$-0.915643\pi$
$103$	−12.3898	+	7.15323i	−1.22080	+	0.704828i	−0.255710	+	0.966753i	$0.582309\pi$
$104$	−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	$-0.701350\pi$
$107$		−	16.6853i		−	1.61303i	0.591212	−	0.806516i	$-0.298650\pi$
$108$	5.13300	−	0.807639i	0.493923	−	0.0777151i
$109$	−9.70354	−	5.60234i	−0.929431	−	0.536607i	−0.0427994	−	0.999084i	$-0.513628\pi$
$109$	−9.70354	−	5.60234i	−0.929431	−	0.536607i	−0.886632	+	0.462476i	$0.846961\pi$
$110$	−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	−0.801336	−	0.598214i	$-0.795877\pi$
$113$	−7.27033	+	4.19753i	−0.683935	+	0.394870i	0.117401	+	0.993085i	$0.462544\pi$
$114$	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	−0.725281	−	0.688453i	$-0.758290\pi$
$127$	2.63228	−	4.55924i	0.233577	−	0.404567i	0.958858	+	0.283886i	$0.0916236\pi$
$128$	−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	0.882406	−	0.470489i	$-0.155922\pi$
$131$	0.386257	+	0.669016i	0.0337474	+	0.0584522i	−0.848658	+	0.528941i	$0.822589\pi$
$132$	−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	−0.000391380	−	1.00000i	$-0.500125\pi$
$139$	10.2034	−	5.89092i	0.865438	−	0.499661i	0.865830	+	0.500339i	$0.166791\pi$
$140$	−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	−0.790807	−	0.612066i	$-0.790339\pi$
$149$	1.64375	−	2.84705i	0.134661	−	0.233240i	0.925468	+	0.378826i	$0.123672\pi$
$150$	−0.186386	+	0.365496i	−0.0152183	+	0.0298426i
$151$	10.5899	+	6.11409i	0.861795	+	0.497557i	0.864613	−	0.502439i	$-0.167564\pi$
$151$	10.5899	+	6.11409i	0.861795	+	0.497557i	−0.00281814	+	0.999996i	$0.500897\pi$
$152$	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	−0.266742	−	0.963768i	$-0.585947\pi$
$157$	−15.4715	−	8.93248i	−1.23476	−	0.712889i	−0.968019	+	0.250879i	$0.919280\pi$
$158$	−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	0.419333	−	0.907833i	$-0.362264\pi$
$163$	−2.00708	−	1.15879i	−0.157207	−	0.0907632i	−0.576540	+	0.817069i	$0.695597\pi$
$164$	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	0.875395	−	0.483408i	$-0.160601\pi$
$167$	11.5588	+	6.67349i	0.894449	+	0.516410i	0.0190536	+	0.999818i	$0.493935\pi$
$168$	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	−0.271144	−	0.962539i	$-0.587402\pi$
$173$	9.18090	−	15.9018i	0.698011	−	1.20899i	0.969155	−	0.246452i	$-0.0792648\pi$
$174$	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	−0.795295	−	0.606223i	$-0.792684\pi$
$179$	−8.93640	+	5.15943i	−0.667938	+	0.385634i	0.127357	+	0.991857i	$0.459351\pi$
$180$	−5.55685	+	4.03154i	−0.414183	+	0.300493i
$181$		−	5.21743i		−	0.387809i	−0.981020	−	0.193904i	$-0.937885\pi$
$181$		−	5.21743i		−	0.387809i	0.981020	−	0.193904i	$-0.0621151\pi$
$182$	−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	0.975994	+	0.217799i	$0.0698877\pi$
$191$	22.8395	+	13.1864i	1.65261	+	0.954135i	0.676616	+	0.736336i	$0.263446\pi$
$192$	1.72971	−	0.0900624i	0.124831	−	0.00649969i
$193$	2.77543	−	1.60239i	0.199780	−	0.115343i	−0.396773	−	0.917917i	$-0.629870\pi$
$193$	2.77543	−	1.60239i	0.199780	−	0.115343i	0.596553	+	0.802574i	$0.296537\pi$
$194$	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	−0.134165	+	0.990959i	$0.542835\pi$
$197$	−12.9869	+	22.4940i	−0.925278	+	1.60263i	−0.791113	+	0.611670i	$0.790498\pi$
$198$	0.523476	+	0.721530i	0.0372018	+	0.0512769i
$199$			5.54735i			0.393241i	0.980480	+	0.196621i	$0.0629967\pi$
$199$			5.54735i			0.393241i	−0.980480	+	0.196621i	$0.937003\pi$
$200$	−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	−0.822923	−	0.568153i	$-0.807658\pi$
$211$	1.17040	−	2.02719i	0.0805736	−	0.139558i	0.903496	+	0.428596i	$0.140991\pi$
$212$	−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	−0.839936	−	0.542686i	$-0.817407\pi$
$223$	0.746837	−	1.29356i	0.0500119	−	0.0866232i	0.889948	+	0.456063i	$0.150741\pi$
$224$	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	$0.0678100\pi$
$227$			6.37084i			0.422848i	−0.977394	+	0.211424i	$0.932190\pi$
$228$	−6.20883	+	12.1753i	−0.411190	+	0.806330i
$229$	−3.93382	−	6.81358i	−0.259954	−	0.450254i	0.706275	−	0.707937i	$-0.250374\pi$
$229$	−3.93382	−	6.81358i	−0.259954	−	0.450254i	−0.966229	+	0.257684i	$0.917041\pi$
$230$	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	−0.739847	−	0.672776i	$-0.765102\pi$
$233$	−8.04627	+	4.64552i	−0.527129	+	0.304338i	0.212718	+	0.977114i	$0.431769\pi$
$234$	−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	0.997290	−	0.0735742i	$-0.0234406\pi$
$251$	6.89055	+	11.9348i	0.434928	+	0.753317i	−0.562362	+	0.826891i	$0.690107\pi$
$252$	−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	−0.918416	−	0.395615i	$-0.870531\pi$
$263$	−16.7851	+	9.69087i	−1.03501	+	0.597564i	−0.116595	+	0.993179i	$0.537198\pi$
$264$	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	0.222420	−	0.974951i	$-0.428605\pi$
$283$	19.8164	−	11.4410i	1.17796	−	0.680097i	0.955542	+	0.294854i	$0.0952712\pi$
$284$	−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	−0.913693	−	0.406404i	$-0.866783\pi$
$293$	−17.4353	+	10.0663i	−1.01858	+	0.588080i	−0.104890	+	0.994484i	$0.533449\pi$
$294$	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	−0.557681	−	0.830055i	$-0.688309\pi$
$311$	7.75963	−	13.4401i	0.440008	−	0.762117i	0.997690	+	0.0679384i	$0.0216421\pi$
$312$	−5.38598	+	3.16089i	−0.304921	+	0.178950i
$313$	13.7068	−	7.91361i	0.774752	−	0.447303i	−0.0598149	−	0.998209i	$-0.519051\pi$
$313$	13.7068	−	7.91361i	0.774752	−	0.447303i	0.834567	+	0.550906i	$0.185718\pi$
$314$	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	0.625025	−	0.780605i	$-0.285089\pi$
$317$	−6.47213	−	11.2101i	−0.363511	−	0.629619i	−0.988536	+	0.150985i	$0.951755\pi$
$318$	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	0.697920	−	0.716176i	$-0.254109\pi$
$331$	7.76227	+	4.48155i	0.426653	+	0.246328i	−0.271267	+	0.962504i	$0.587443\pi$
$332$		−	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	$0.0838498\pi$
$347$			9.70091i			0.520772i	−0.965505	+	0.260386i	$0.916150\pi$
$348$	−1.74776	−	0.891273i	−0.0936897	−	0.0477773i
$349$	13.2526	−	22.9542i	0.709396	−	1.22871i	−0.255686	−	0.966760i	$-0.582301\pi$
$349$	13.2526	−	22.9542i	0.709396	−	1.22871i	0.965081	−	0.261950i	$-0.0843655\pi$
$350$	−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	0.224544	−	0.974464i	$-0.427911\pi$
$353$	22.1838	−	12.8078i	1.18073	−	0.681693i	0.956183	+	0.292771i	$0.0945774\pi$
$354$	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	0.984155	−	0.177310i	$-0.0567396\pi$
$359$	6.41408	+	11.1095i	0.338522	+	0.586338i	−0.645633	+	0.763648i	$0.723406\pi$
$360$	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	−0.938893	−	0.344210i	$-0.888147\pi$
$367$	−21.2692	+	12.2798i	−1.11024	+	0.641000i	−0.171352	+	0.985210i	$0.554813\pi$
$368$			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	−0.441815	−	0.897106i	$-0.645665\pi$
$373$	10.7383	−	18.5993i	0.556009	−	0.963036i	0.997824	−	0.0659297i	$-0.0210013\pi$
$374$	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	0.0979889	−	0.995188i	$-0.468759\pi$
$379$	−13.9171	−	8.03505i	−0.714874	−	0.412733i	−0.812863	+	0.582455i	$0.802092\pi$
$380$		−	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	0.957235	−	0.289310i	$-0.0934259\pi$
$383$	23.1968	+	13.3927i	1.18530	+	0.684335i	0.228068	+	0.973645i	$0.426759\pi$
$384$	−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	0.403959	−	0.914777i	$-0.367634\pi$
$389$	−3.67405	−	2.12122i	−0.186282	−	0.107550i	−0.590241	+	0.807227i	$0.700967\pi$
$390$	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	−0.874798	−	0.484488i	$-0.839006\pi$
$397$	−0.355073	+	0.615005i	−0.0178206	+	0.0308662i	0.856978	+	0.515354i	$0.172339\pi$
$398$		−	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	−0.953887	−	0.300167i	$-0.902958\pi$
$419$	−4.44170	+	7.69326i	−0.216991	+	0.375840i	0.736895	+	0.676007i	$0.236291\pi$
$420$	−2.46656	−	10.1927i	−0.120356	−	0.497351i
$421$			11.9274i			0.581308i	0.956828	+	0.290654i	$0.0938729\pi$
$421$			11.9274i			0.581308i	−0.956828	+	0.290654i	$0.906127\pi$
$422$	−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	0.999381	−	0.0351717i	$-0.0111978\pi$
$431$	9.74149	+	16.8728i	0.469231	+	0.812732i	−0.530150	+	0.847904i	$0.677864\pi$
$432$	5.13300	−	0.807639i	0.246962	−	0.0388576i
$433$	−15.8703	+	9.16273i	−0.762679	+	0.440333i	−0.830257	−	0.557381i	$-0.811806\pi$
$433$	−15.8703	+	9.16273i	−0.762679	+	0.440333i	0.0675780	+	0.997714i	$0.478473\pi$
$434$	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	$0.0189417\pi$
$439$			2.49215i			0.118944i	−0.998230	+	0.0594720i	$0.981058\pi$
$440$	−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	−0.802179	−	0.597083i	$-0.796326\pi$
$443$	−14.4424	+	8.33832i	−0.686179	+	0.396166i	0.116000	+	0.993249i	$0.462993\pi$
$444$	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	0.855290	+	0.518149i	$0.173379\pi$
$449$	18.5701	+	32.1643i	0.876375	+	1.51793i	0.0210850	+	0.999778i	$0.493288\pi$
$450$	−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	$0.122954\pi$
$457$			16.1075i			0.753476i	−0.926320	+	0.376738i	$0.877046\pi$
$458$	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	−0.188285	−	0.982114i	$-0.560293\pi$
$461$	12.1978	−	7.04240i	0.568108	−	0.327997i	0.756393	+	0.654117i	$0.226960\pi$
$462$	−1.32347	+	0.320271i	−0.0615734	+	0.0149004i
$463$			20.5027i			0.952843i	0.879217	+	0.476421i	$0.158066\pi$
$463$			20.5027i			0.952843i	−0.879217	+	0.476421i	$0.841934\pi$
$464$	−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	0.791972	−	0.610557i	$-0.209054\pi$
$467$	−2.86923	−	4.96965i	−0.132772	−	0.229968i	−0.924744	+	0.380589i	$0.875721\pi$
$468$	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	0.174589	−	0.984641i	$-0.444140\pi$
$479$	24.3944	−	14.0841i	1.11461	−	0.643519i	0.940019	+	0.341122i	$0.110807\pi$
$480$	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	$-0.764948\pi$
$487$		−	29.7095i		−	1.34627i	0.739521	−	0.673133i	$-0.235052\pi$
$488$	−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	0.991849	+	0.127418i	$0.0406690\pi$
$491$	35.4120	+	20.4451i	1.59812	+	0.922676i	0.606272	+	0.795258i	$0.292664\pi$
$492$	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	−0.232233	−	0.972660i	$-0.574603\pi$
$499$	11.0351	−	6.37111i	0.493998	−	0.285210i	0.726232	+	0.687450i	$0.241270\pi$
$500$		−	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	−0.803270	−	0.595615i	$-0.796908\pi$
$503$	−20.5763	−	35.6392i	−0.917453	−	1.58908i	−0.114183	−	0.993460i	$-0.536425\pi$
$504$	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	$-0.869488\pi$
$509$		−	17.9868i		−	0.797250i	0.917114	−	0.398625i	$-0.130512\pi$
$510$	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	−0.447082	−	0.894493i	$-0.647537\pi$
$521$	12.5794	−	21.7881i	0.551113	−	0.954555i	0.998195	−	0.0600622i	$-0.0191299\pi$
$522$	3.10338	+	1.38424i	0.135831	+	0.0605863i
$523$			42.1093i			1.84131i	0.390375	+	0.920656i	$0.372345\pi$
$523$			42.1093i			1.84131i	−0.390375	+	0.920656i	$0.627655\pi$
$524$	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	−0.798764	−	0.601644i	$-0.794513\pi$
$541$	−15.7491	+	9.09276i	−0.677107	+	0.390928i	0.121657	+	0.992572i	$0.461179\pi$
$542$	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	−0.977333	−	0.211708i	$-0.932097\pi$
$557$	−15.8600	−	27.4704i	−0.672011	−	1.16396i	0.305322	−	0.952249i	$-0.401236\pi$
$558$	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	$0.292021\pi$
$569$			37.8812i			1.58806i	−0.607878	+	0.794030i	$0.707979\pi$
$570$	1.62627	+	31.2336i	0.0681171	+	1.30823i
$571$	−13.5869	+	23.5332i	−0.568594	+	0.984834i	0.428111	+	0.903726i	$0.359179\pi$
$571$	−13.5869	+	23.5332i	−0.568594	+	0.984834i	−0.996705	+	0.0811082i	$0.974154\pi$
$572$	−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	0.131147	+	0.991363i	$0.458134\pi$
$577$	−19.0478	+	32.9918i	−0.792972	+	1.37347i	−0.924119	+	0.382105i	$0.875199\pi$
$578$	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	0.0496910	−	0.998765i	$-0.484176\pi$
$587$	−19.1503	−	11.0565i	−0.790419	−	0.456349i	−0.840110	+	0.542416i	$0.817510\pi$
$588$	−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	−0.888738	−	0.458415i	$-0.848417\pi$
$593$	−22.7957	+	13.1611i	−0.936109	+	0.540463i	−0.0473705	+	0.998877i	$0.515084\pi$
$594$	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	0.611741	−	0.791058i	$-0.290469\pi$
$599$	5.69118	+	3.28581i	0.232536	+	0.134254i	−0.379206	+	0.925312i	$0.623803\pi$
$600$	−0.186386	+	0.365496i	−0.00760916	+	0.0149213i
$601$	22.1774	+	12.8041i	0.904634	+	0.522291i	0.878701	−	0.477373i	$-0.158411\pi$
$601$	22.1774	+	12.8041i	0.904634	+	0.522291i	0.0259335	+	0.999664i	$0.491744\pi$
$602$	−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	0.999999	−	0.00140959i	$-0.000448687\pi$
$607$	36.9259	+	21.3192i	1.49878	+	0.865320i	0.498779	+	0.866729i	$0.333782\pi$
$608$	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	−0.568636	−	0.822589i	$-0.692529\pi$
$613$	−3.48038	+	2.00940i	−0.140571	+	0.0811588i	0.428065	+	0.903748i	$0.359195\pi$
$614$	−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	−0.999654	−	0.0262879i	$-0.991631\pi$
$617$	−12.9809	−	22.4837i	−0.522593	−	0.905158i	0.477061	−	0.878870i	$-0.341702\pi$
$618$	20.7864	−	13.4888i	0.836152	−	0.542601i
$619$	2.84282	−	4.92392i	0.114263	−	0.197909i	−0.803222	−	0.595680i	$-0.796883\pi$
$619$	2.84282	−	4.92392i	0.114263	−	0.197909i	0.917485	+	0.397771i	$0.130216\pi$
$620$		−	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	−0.243838	−	0.969816i	$-0.578407\pi$
$631$	11.9099	−	6.87621i	0.474128	−	0.273738i	0.717966	+	0.696078i	$0.245073\pi$
$632$	−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	$0.0396316\pi$
$641$			6.28822i			0.248370i	−0.992259	+	0.124185i	$0.960368\pi$
$642$	1.50272	+	28.8608i	0.0593077	+	1.13904i
$643$	−17.3160	−	29.9922i	−0.682877	−	1.18278i	−0.974099	−	0.226122i	$-0.927395\pi$
$643$	−17.3160	−	29.9922i	−0.682877	−	1.18278i	0.291222	−	0.956656i	$-0.405938\pi$
$644$	−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	0.631022	−	0.775765i	$-0.282636\pi$
$647$	−9.06347	−	15.6984i	−0.356322	−	0.617167i	−0.987343	+	0.158598i	$0.949303\pi$
$648$	−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	$-0.712311\pi$
$653$		−	40.1546i		−	1.57137i	0.618627	−	0.785685i	$-0.287689\pi$
$654$	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	−0.160512	−	0.987034i	$-0.551314\pi$
$659$	15.7627	−	9.10062i	0.614029	−	0.354510i	0.774541	+	0.632524i	$0.217981\pi$
$660$	1.04922	+	0.535050i	0.0408406	+	0.0208268i
$661$	11.5569	+	20.0171i	0.449510	+	0.778575i	0.998354	−	0.0573503i	$-0.0182652\pi$
$661$	11.5569	+	20.0171i	0.449510	+	0.778575i	−0.548844	+	0.835925i	$0.684932\pi$
$662$	−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	0.269223	+	0.963078i	$0.413233\pi$
$673$	−18.1450	+	31.4281i	−0.699438	+	1.21146i	−0.968661	+	0.248385i	$0.920100\pi$
$674$	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	0.822038	−	0.569433i	$-0.192837\pi$
$677$	−2.13681	−	3.70106i	−0.0821243	−	0.142243i	−0.904162	+	0.427189i	$0.859504\pi$
$678$	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	$-0.779827\pi$
$701$		−	33.7755i		−	1.27568i	0.770167	−	0.637842i	$-0.220173\pi$
$702$	−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	0.480002	−	0.877268i	$-0.340636\pi$
$709$	−1.05799	−	0.610834i	−0.0397338	−	0.0229403i	−0.519735	+	0.854327i	$0.673969\pi$
$710$	−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	0.416887	+	0.908959i	$0.363121\pi$
$719$	−15.5184	+	26.8786i	−0.578738	+	1.00240i	−0.995624	+	0.0934449i	$0.970212\pi$
$720$	−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	$-0.786842\pi$
$727$		−	33.4726i		−	1.24143i	0.784036	−	0.620716i	$-0.213158\pi$
$728$	−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	0.543148	−	0.839637i	$-0.317232\pi$
$733$	−12.3342	−	21.3634i	−0.455573	−	0.789076i	−0.998721	+	0.0505610i	$0.983899\pi$
$734$	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	0.422321	−	0.906446i	$-0.361215\pi$
$739$	38.5610	−	22.2632i	1.41849	−	0.818964i	0.996166	+	0.0874820i	$0.0278820\pi$
$740$	−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	−0.225448	−	0.974255i	$-0.572385\pi$
$743$	19.9258	−	34.5124i	0.731006	−	1.26614i	0.956454	−	0.291884i	$-0.0942820\pi$
$744$	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	−0.217417	−	0.976079i	$-0.569763\pi$
$757$	20.2665	−	35.1027i	0.736600	−	1.27583i	0.954018	−	0.299750i	$-0.0969034\pi$
$758$	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	0.478159	−	0.878273i	$-0.341304\pi$
$761$	−1.19636	−	0.690718i	−0.0433680	−	0.0250385i	−0.521527	+	0.853235i	$0.674638\pi$
$762$	−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	−0.925028	−	0.379898i	$-0.875959\pi$
$769$	−3.70242	+	6.41278i	−0.133513	+	0.231251i	0.791516	+	0.611149i	$0.209292\pi$
$770$	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	$-0.968778\pi$
$773$		−	5.44545i		−	0.195859i	0.995193	−	0.0979297i	$-0.0312220\pi$
$774$	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	−0.992622	−	0.121248i	$-0.961310\pi$
$797$	−16.9758	−	29.4030i	−0.601315	−	1.04151i	0.391308	−	0.920260i	$-0.372023\pi$
$798$	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	−0.0741003	−	0.997251i	$-0.523608\pi$
$809$	21.4031	−	12.3571i	0.752494	−	0.434453i	0.826594	+	0.562798i	$0.190275\pi$
$810$	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	−0.935570	−	0.353141i	$-0.885114\pi$
$829$	−31.6004	+	18.2445i	−1.09753	+	0.633657i	−0.161956	+	0.986798i	$0.551780\pi$
$830$	−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	−0.888329	−	0.459209i	$-0.848133\pi$
$839$	−27.0771	+	15.6330i	−0.934807	+	0.539711i	−0.0464780	+	0.998919i	$0.514800\pi$
$840$	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	−0.925464	−	0.378836i	$-0.876325\pi$
$857$	−3.94184	+	6.82747i	−0.134651	+	0.233222i	0.790813	+	0.612058i	$0.209658\pi$
$858$	1.61359	+	0.916367i	0.0550872	+	0.0312842i
$859$	−16.8815	+	9.74653i	−0.575989	+	0.332547i	−0.759538	−	0.650463i	$-0.774575\pi$
$859$	−16.8815	+	9.74653i	−0.575989	+	0.332547i	0.183549	+	0.983011i	$0.441241\pi$
$860$	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	0.766543	−	0.642193i	$-0.221975\pi$
$863$	−5.07880	−	8.79674i	−0.172884	−	0.299445i	−0.939427	+	0.342749i	$0.888642\pi$
$864$	−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	0.617955	−	0.786213i	$-0.287961\pi$
$877$	7.28663	+	4.20694i	0.246052	+	0.142058i	−0.371903	+	0.928272i	$0.621295\pi$
$878$		−	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	−0.917625	−	0.397448i	$-0.869896\pi$
$881$	−3.40189	+	5.89224i	−0.114612	+	0.198515i	0.803012	+	0.595962i	$0.203229\pi$
$882$	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	0.970371	−	0.241621i	$-0.0776789\pi$
$907$	8.31021	+	14.3937i	0.275936	+	0.477935i	−0.694435	+	0.719555i	$0.744346\pi$
$908$			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	$0.0933439\pi$
$911$			17.4495i			0.578127i	−0.957310	+	0.289063i	$0.906656\pi$
$912$	−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	−0.968036	−	0.250813i	$-0.919302\pi$
$919$	−8.08828	+	14.0093i	−0.266808	+	0.462125i	0.701228	+	0.712937i	$0.252636\pi$
$920$	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	0.202269	−	0.979330i	$-0.435169\pi$
$929$	−16.6028	−	9.58566i	−0.544722	−	0.314495i	−0.746990	+	0.664835i	$0.768502\pi$
$930$	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	$0.215814\pi$
$937$			38.4000i			1.25447i	−0.778828	+	0.627237i	$0.784186\pi$
$938$	−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	0.597886	−	0.801581i	$-0.296008\pi$
$941$	6.21610	+	3.58887i	0.202639	+	0.116994i	−0.395247	+	0.918575i	$0.629341\pi$
$942$	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	−0.751605	−	0.659614i	$-0.770720\pi$
$953$	−17.1692	+	9.91265i	−0.556165	+	0.321102i	0.195440	+	0.980716i	$0.437387\pi$
$954$	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	$-0.977067\pi$
$967$		−	4.47698i		−	0.143970i	0.997406	−	0.0719849i	$-0.0229333\pi$
$968$	−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	−0.948928	−	0.315493i	$-0.897830\pi$
$971$	−6.27077	+	10.8613i	−0.201239	+	0.348556i	0.747689	+	0.664049i	$0.231163\pi$
$972$	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	−0.858418	−	0.512951i	$-0.828552\pi$
$977$	−27.3010	−	47.2868i	−0.873437	−	1.51284i	−0.0150192	−	0.999887i	$-0.504781\pi$
$978$	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	0.977001	−	0.213236i	$-0.0684002\pi$
$983$	40.1578	+	23.1851i	1.28083	+	0.739490i	0.303833	+	0.952725i	$0.401734\pi$
$984$	−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	0.791452	−	0.611231i	$-0.209326\pi$
$991$	−4.20625	−	7.28544i	−0.133616	−	0.231430i	−0.925068	+	0.379802i	$0.875992\pi$
$992$	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	$-0.565978\pi$
$997$		−	61.7989i		−	1.95719i	0.205796	−	0.978595i	$-0.434022\pi$
$998$	−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.17.17	✓	34
3.2	odd	2		546.2.bi.f.17.11	yes	34
7.5	odd	6		546.2.bn.f.173.11	yes	34
13.10	even	6		546.2.bn.e.101.7	yes	34
21.5	even	6		546.2.bn.e.173.7	yes	34
39.23	odd	6		546.2.bn.f.101.11	yes	34
91.75	odd	6		546.2.bi.f.257.11	yes	34
273.257	even	6	inner	546.2.bi.e.257.17	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.17	✓	34	1.1	even	1	trivial
546.2.bi.e.257.17	yes	34	273.257	even	6	inner
546.2.bi.f.17.11	yes	34	3.2	odd	2
546.2.bi.f.257.11	yes	34	91.75	odd	6
546.2.bn.e.101.7	yes	34	13.10	even	6
546.2.bn.e.173.7	yes	34	21.5	even	6
546.2.bn.f.101.11	yes	34	39.23	odd	6
546.2.bn.f.173.11	yes	34	7.5	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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