LMFDB - Embedded newform 240.2.s.b.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.3
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.b.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.635665 + 1.26330i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.443806 + 1.34277i) q^{6} +1.41421i q^{7} +(-2.78658 - 0.484753i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.635665 + 1.26330i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.443806 + 1.34277i) q^{6} +1.41421i q^{7} +(-2.78658 - 0.484753i) q^{8} +1.00000i q^{9} +(-1.34277 - 0.443806i) q^{10} +(1.11239 - 1.11239i) q^{11} +(-1.97844 + 0.292893i) q^{12} +(-0.271330 - 0.271330i) q^{13} +(-1.78658 + 0.898966i) q^{14} -1.00000 q^{15} +(-1.15894 - 3.82843i) q^{16} +0.744728 q^{17} +(-1.26330 + 0.635665i) q^{18} +(5.21215 + 5.21215i) q^{19} +(-0.292893 - 1.97844i) q^{20} +(-1.00000 + 1.00000i) q^{21} +(2.11239 + 0.698175i) q^{22} -4.76744i q^{23} +(-1.62764 - 2.31318i) q^{24} -1.00000i q^{25} +(0.170297 - 0.515247i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.27133 - 1.68554i) q^{28} +(-1.21215 - 1.21215i) q^{29} +(-0.635665 - 1.26330i) q^{30} +7.75481 q^{31} +(4.09976 - 3.89769i) q^{32} +1.57316 q^{33} +(0.473398 + 0.940816i) q^{34} +(-1.00000 - 1.00000i) q^{35} +(-1.60607 - 1.19186i) q^{36} +(-5.32453 + 5.32453i) q^{37} +(-3.27133 + 9.89769i) q^{38} -0.383719i q^{39} +(2.31318 - 1.62764i) q^{40} -7.33897i q^{41} +(-1.89897 - 0.627636i) q^{42} +(6.78530 - 6.78530i) q^{43} +(0.460766 + 3.11239i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(6.02271 - 3.03049i) q^{46} -0.735321 q^{47} +(1.88761 - 3.52660i) q^{48} +5.00000 q^{49} +(1.26330 - 0.635665i) q^{50} +(0.526602 + 0.526602i) q^{51} +(0.759164 - 0.112389i) q^{52} +(-9.55274 + 9.55274i) q^{53} +(-1.34277 - 0.443806i) q^{54} +1.57316i q^{55} +(0.685544 - 3.94082i) q^{56} +7.37109i q^{57} +(0.760787 - 2.30182i) q^{58} +(1.62293 - 1.62293i) q^{59} +(1.19186 - 1.60607i) q^{60} +(-5.70160 - 5.70160i) q^{61} +(4.92946 + 9.79666i) q^{62} -1.41421 q^{63} +(7.53003 + 2.70160i) q^{64} +0.383719 q^{65} +(1.00000 + 1.98737i) q^{66} +(5.59587 + 5.59587i) q^{67} +(-0.887611 + 1.19609i) q^{68} +(3.37109 - 3.37109i) q^{69} +(0.627636 - 1.89897i) q^{70} -8.60365i q^{71} +(0.484753 - 2.78658i) q^{72} -4.28577i q^{73} +(-10.1111 - 3.34187i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-14.5832 + 2.15894i) q^{76} +(1.57316 + 1.57316i) q^{77} +(0.484753 - 0.243917i) q^{78} -1.01263 q^{79} +(3.52660 + 1.88761i) q^{80} -1.00000 q^{81} +(9.27133 - 4.66513i) q^{82} +(1.68212 + 1.68212i) q^{83} +(-0.414214 - 2.79793i) q^{84} +(-0.526602 + 0.526602i) q^{85} +(12.8851 + 4.25870i) q^{86} -1.71423i q^{87} +(-3.63899 + 2.56052i) q^{88} -10.3990i q^{89} +(0.443806 - 1.34277i) q^{90} +(0.383719 - 0.383719i) q^{91} +(7.65685 + 5.68212i) q^{92} +(5.48348 + 5.48348i) q^{93} +(-0.467418 - 0.928932i) q^{94} -7.37109 q^{95} +(5.65505 + 0.142883i) q^{96} -16.9670 q^{97} +(3.17833 + 6.31651i) q^{98} +(1.11239 + 1.11239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8	$ 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} + 8 q^{17} - 4 q^{18} + 8 q^{19} - 8 q^{20} - 8 q^{21} + 16 q^{22} - 12 q^{24} - 20 q^{26} - 8 q^{28} + 24 q^{29} + 8 q^{31} - 8 q^{33} + 16 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{37} - 16 q^{38} - 4 q^{40} - 4 q^{42} - 16 q^{44} + 24 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 16 q^{56} + 8 q^{59} + 4 q^{60} - 16 q^{61} + 28 q^{62} + 8 q^{64} - 8 q^{65} + 8 q^{66} - 8 q^{68} - 16 q^{69} + 4 q^{70} + 4 q^{72} - 36 q^{74} - 40 q^{76} - 8 q^{77} + 4 q^{78} - 40 q^{79} + 16 q^{80} - 8 q^{81} + 64 q^{82} + 32 q^{83} + 8 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{88} + 4 q^{90} - 8 q^{91} + 16 q^{92} + 32 q^{94} - 16 q^{95} + 24 q^{96} - 48 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 8 * q^15 + 8 * q^17 - 4 * q^18 + 8 * q^19 - 8 * q^20 - 8 * q^21 + 16 * q^22 - 12 * q^24 - 20 * q^26 - 8 * q^28 + 24 * q^29 + 8 * q^31 - 8 * q^33 + 16 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^37 - 16 * q^38 - 4 * q^40 - 4 * q^42 - 16 * q^44 + 24 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 16 * q^56 + 8 * q^59 + 4 * q^60 - 16 * q^61 + 28 * q^62 + 8 * q^64 - 8 * q^65 + 8 * q^66 - 8 * q^68 - 16 * q^69 + 4 * q^70 + 4 * q^72 - 36 * q^74 - 40 * q^76 - 8 * q^77 + 4 * q^78 - 40 * q^79 + 16 * q^80 - 8 * q^81 + 64 * q^82 + 32 * q^83 + 8 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^88 + 4 * q^90 - 8 * q^91 + 16 * q^92 + 32 * q^94 - 16 * q^95 + 24 * q^96 - 48 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.635665	+	1.26330i	0.449483	+	0.893289i
$2$	0.635665	+	1.26330i	0.449483	+	0.893289i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.19186	+	1.60607i	−0.595930	+	0.803037i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.443806	+	1.34277i	−0.181183	+	0.548184i
$7$			1.41421i			0.534522i	0.963624	+	0.267261i	$0.0861187\pi$
$7$			1.41421i			0.534522i	−0.963624	+	0.267261i	$0.913881\pi$
$8$	−2.78658	−	0.484753i	−0.985204	−	0.171386i
$9$			1.00000i			0.333333i
$10$	−1.34277	−	0.443806i	−0.424622	−	0.140344i
$11$	1.11239	−	1.11239i	0.335398	−	0.335398i	−0.519234	−	0.854632i	$-0.673783\pi$
$11$	1.11239	−	1.11239i	0.335398	−	0.335398i	0.854632	+	0.519234i	$0.173783\pi$
$12$	−1.97844	+	0.292893i	−0.571126	+	0.0845510i
$13$	−0.271330	−	0.271330i	−0.0752535	−	0.0752535i	0.668478	−	0.743732i	$-0.266946\pi$
$13$	−0.271330	−	0.271330i	−0.0752535	−	0.0752535i	−0.743732	+	0.668478i	$0.766946\pi$
$14$	−1.78658	+	0.898966i	−0.477483	+	0.240259i
$15$	−1.00000			−0.258199
$16$	−1.15894	−	3.82843i	−0.289735	−	0.957107i
$17$	0.744728			0.180623			0.0903115	−	0.995914i	$-0.471214\pi$
$17$	0.744728			0.180623			0.0903115	+	0.995914i	$0.471214\pi$
$18$	−1.26330	+	0.635665i	−0.297763	+	0.149828i
$19$	5.21215	+	5.21215i	1.19575	+	1.19575i	0.975427	+	0.220321i	$0.0707105\pi$
$19$	5.21215	+	5.21215i	1.19575	+	1.19575i	0.220321	+	0.975427i	$0.429290\pi$
$20$	−0.292893	−	1.97844i	−0.0654929	−	0.442392i
$21$	−1.00000	+	1.00000i	−0.218218	+	0.218218i
$22$	2.11239	+	0.698175i	0.450363	+	0.148851i
$23$		−	4.76744i		−	0.994080i	−0.867728	−	0.497040i	$-0.834420\pi$
$23$		−	4.76744i		−	0.994080i	0.867728	−	0.497040i	$-0.165580\pi$
$24$	−1.62764	−	2.31318i	−0.332240	−	0.472176i
$25$		−	1.00000i		−	0.200000i
$26$	0.170297	−	0.515247i	0.0333979	−	0.101048i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.27133	−	1.68554i	−0.429241	−	0.318538i
$29$	−1.21215	−	1.21215i	−0.225090	−	0.225090i	0.585548	−	0.810638i	$-0.300879\pi$
$29$	−1.21215	−	1.21215i	−0.225090	−	0.225090i	−0.810638	+	0.585548i	$0.800879\pi$
$30$	−0.635665	−	1.26330i	−0.116056	−	0.230646i
$31$	7.75481			1.39280			0.696402	−	0.717652i	$-0.254783\pi$
$31$	7.75481			1.39280			0.696402	+	0.717652i	$0.254783\pi$
$32$	4.09976	−	3.89769i	0.724742	−	0.689021i
$33$	1.57316			0.273851
$34$	0.473398	+	0.940816i	0.0811870	+	0.161349i
$35$	−1.00000	−	1.00000i	−0.169031	−	0.169031i
$36$	−1.60607	−	1.19186i	−0.267679	−	0.198643i
$37$	−5.32453	+	5.32453i	−0.875348	+	0.875348i	−0.993049	−	0.117701i	$-0.962448\pi$
$37$	−5.32453	+	5.32453i	−0.875348	+	0.875348i	0.117701	+	0.993049i	$0.462448\pi$
$38$	−3.27133	+	9.89769i	−0.530680	+	1.60562i
$39$		−	0.383719i		−	0.0614442i
$40$	2.31318	−	1.62764i	0.365746	−	0.257352i
$41$		−	7.33897i		−	1.14615i	−0.819501	−	0.573077i	$-0.805749\pi$
$41$		−	7.33897i		−	1.14615i	0.819501	−	0.573077i	$-0.194251\pi$
$42$	−1.89897	−	0.627636i	−0.293017	−	0.0968463i
$43$	6.78530	−	6.78530i	1.03475	−	1.03475i	0.0353746	−	0.999374i	$-0.488738\pi$
$43$	6.78530	−	6.78530i	1.03475	−	1.03475i	0.999374	−	0.0353746i	$-0.0112624\pi$
$44$	0.460766	+	3.11239i	0.0694632	+	0.469210i
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$	6.02271	−	3.03049i	0.888000	−	0.446822i
$47$	−0.735321			−0.107258			−0.0536288	−	0.998561i	$-0.517079\pi$
$47$	−0.735321			−0.107258			−0.0536288	+	0.998561i	$0.517079\pi$
$48$	1.88761	−	3.52660i	0.272453	−	0.509021i
$49$	5.00000			0.714286
$50$	1.26330	−	0.635665i	0.178658	−	0.0898966i
$51$	0.526602	+	0.526602i	0.0737391	+	0.0737391i
$52$	0.759164	−	0.112389i	0.105277	−	0.0155855i
$53$	−9.55274	+	9.55274i	−1.31217	+	1.31217i	−0.392356	+	0.919813i	$0.628340\pi$
$53$	−9.55274	+	9.55274i	−1.31217	+	1.31217i	−0.919813	+	0.392356i	$0.871660\pi$
$54$	−1.34277	−	0.443806i	−0.182728	−	0.0603943i
$55$			1.57316i			0.212124i
$56$	0.685544	−	3.94082i	0.0916097	−	0.526614i
$57$			7.37109i			0.976324i
$58$	0.760787	−	2.30182i	0.0998962	−	0.302244i
$59$	1.62293	−	1.62293i	0.211288	−	0.211288i	−0.593527	−	0.804814i	$-0.702265\pi$
$59$	1.62293	−	1.62293i	0.211288	−	0.211288i	0.804814	+	0.593527i	$0.202265\pi$
$60$	1.19186	−	1.60607i	0.153868	−	0.207343i
$61$	−5.70160	−	5.70160i	−0.730015	−	0.730015i	0.240607	−	0.970623i	$-0.422653\pi$
$61$	−5.70160	−	5.70160i	−0.730015	−	0.730015i	−0.970623	+	0.240607i	$0.922653\pi$
$62$	4.92946	+	9.79666i	0.626042	+	1.24418i
$63$	−1.41421			−0.178174
$64$	7.53003	+	2.70160i	0.941254	+	0.337700i
$65$	0.383719			0.0475945
$66$	1.00000	+	1.98737i	0.123091	+	0.244628i
$67$	5.59587	+	5.59587i	0.683644	+	0.683644i	0.960819	−	0.277176i	$-0.0893984\pi$
$67$	5.59587	+	5.59587i	0.683644	+	0.683644i	−0.277176	+	0.960819i	$0.589398\pi$
$68$	−0.887611	+	1.19609i	−0.107639	+	0.145047i
$69$	3.37109	−	3.37109i	0.405831	−	0.405831i
$70$	0.627636	−	1.89897i	0.0750168	−	0.226970i
$71$		−	8.60365i		−	1.02107i	−0.859858	−	0.510533i	$-0.829448\pi$
$71$		−	8.60365i		−	1.02107i	0.859858	−	0.510533i	$-0.170552\pi$
$72$	0.484753	−	2.78658i	0.0571287	−	0.328401i
$73$		−	4.28577i		−	0.501611i	−0.968037	−	0.250806i	$-0.919305\pi$
$73$		−	4.28577i		−	0.501611i	0.968037	−	0.250806i	$-0.0806955\pi$
$74$	−10.1111	−	3.34187i	−1.17539	−	0.388484i
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$	−14.5832	+	2.15894i	−1.67281	+	0.247648i
$77$	1.57316	+	1.57316i	0.179278	+	0.179278i
$78$	0.484753	−	0.243917i	0.0548874	−	0.0276181i
$79$	−1.01263			−0.113930			−0.0569650	−	0.998376i	$-0.518142\pi$
$79$	−1.01263			−0.113930			−0.0569650	+	0.998376i	$0.518142\pi$
$80$	3.52660	+	1.88761i	0.394286	+	0.211041i
$81$	−1.00000			−0.111111
$82$	9.27133	−	4.66513i	1.02385	−	0.515177i
$83$	1.68212	+	1.68212i	0.184636	+	0.184636i	0.793373	−	0.608736i	$-0.208323\pi$
$83$	1.68212	+	1.68212i	0.184636	+	0.184636i	−0.608736	+	0.793373i	$0.708323\pi$
$84$	−0.414214	−	2.79793i	−0.0451944	−	0.305279i
$85$	−0.526602	+	0.526602i	−0.0571180	+	0.0571180i
$86$	12.8851	+	4.25870i	1.38943	+	0.459227i
$87$		−	1.71423i		−	0.183785i
$88$	−3.63899	+	2.56052i	−0.387918	+	0.272953i
$89$		−	10.3990i		−	1.10229i	−0.834408	−	0.551147i	$-0.814190\pi$
$89$		−	10.3990i		−	1.10229i	0.834408	−	0.551147i	$-0.185810\pi$
$90$	0.443806	−	1.34277i	0.0467812	−	0.141541i
$91$	0.383719	−	0.383719i	0.0402247	−	0.0402247i
$92$	7.65685	+	5.68212i	0.798282	+	0.592402i
$93$	5.48348	+	5.48348i	0.568610	+	0.568610i
$94$	−0.467418	−	0.928932i	−0.0482105	−	0.0958120i
$95$	−7.37109			−0.756258
$96$	5.65505	+	0.142883i	0.577166	+	0.0145830i
$97$	−16.9670			−1.72273			−0.861367	−	0.507984i	$-0.830391\pi$
$97$	−16.9670			−1.72273			−0.861367	+	0.507984i	$0.830391\pi$
$98$	3.17833	+	6.31651i	0.321059	+	0.638063i
$99$	1.11239	+	1.11239i	0.111799	+	0.111799i
$100$	1.60607	+	1.19186i	0.160607	+	0.119186i
$101$	−5.35322	+	5.35322i	−0.532666	+	0.532666i	−0.921365	−	0.388699i	$-0.872925\pi$
$101$	−5.35322	+	5.35322i	−0.532666	+	0.532666i	0.388699	+	0.921365i	$0.372925\pi$
$102$	−0.330515	+	1.00000i	−0.0327258	+	0.0990148i
$103$		−	10.5807i		−	1.04255i	−0.853390	−	0.521273i	$-0.825457\pi$
$103$		−	10.5807i		−	1.04255i	0.853390	−	0.521273i	$-0.174543\pi$
$104$	0.624555	+	0.887611i	0.0612427	+	0.0870374i
$105$		−	1.41421i		−	0.138013i
$106$	−18.1403	−	5.99564i	−1.76194	−	0.582348i
$107$	−10.7422	+	10.7422i	−1.03849	+	1.03849i	−0.0392561	+	0.999229i	$0.512499\pi$
$107$	−10.7422	+	10.7422i	−1.03849	+	1.03849i	−0.999229	+	0.0392561i	$0.987501\pi$
$108$	−0.292893	−	1.97844i	−0.0281837	−	0.190375i
$109$	−1.47682	−	1.47682i	−0.141454	−	0.141454i	0.632834	−	0.774288i	$-0.281892\pi$
$109$	−1.47682	−	1.47682i	−0.141454	−	0.141454i	−0.774288	+	0.632834i	$0.781892\pi$
$110$	−1.98737	+	1.00000i	−0.189488	+	0.0953463i
$111$	−7.53003			−0.714719
$112$	5.41421	−	1.63899i	0.511595	−	0.154870i
$113$	0.472265			0.0444270			0.0222135	−	0.999753i	$-0.492929\pi$
$113$	0.472265			0.0444270			0.0222135	+	0.999753i	$0.492929\pi$
$114$	−9.31190	+	4.68554i	−0.872140	+	0.438841i
$115$	3.37109	+	3.37109i	0.314356	+	0.314356i
$116$	3.39150	−	0.502087i	0.314893	−	0.0466176i
$117$	0.271330	−	0.271330i	0.0250845	−	0.0250845i
$118$	3.08189	+	1.01861i	0.283711	+	0.0937707i
$119$			1.05320i			0.0965471i
$120$	2.78658	+	0.484753i	0.254379	+	0.0442517i
$121$			8.52518i			0.775017i
$122$	3.57853	−	10.8272i	0.323985	−	0.980244i
$123$	5.18944	−	5.18944i	0.467916	−	0.467916i
$124$	−9.24264	+	12.4548i	−0.830014	+	1.11847i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.898966	−	1.78658i	−0.0800863	−	0.159161i
$127$	−14.7532			−1.30913			−0.654567	−	0.756004i	$-0.727149\pi$
$127$	−14.7532			−1.30913			−0.654567	+	0.756004i	$0.727149\pi$
$128$	1.37364	+	11.2300i	0.121414	+	0.992602i
$129$	9.59587			0.844869
$130$	0.243917	+	0.484753i	0.0213929	+	0.0425156i
$131$	−12.6830	−	12.6830i	−1.10812	−	1.10812i	−0.993398	−	0.114720i	$-0.963403\pi$
$131$	−12.6830	−	12.6830i	−1.10812	−	1.10812i	−0.114720	−	0.993398i	$-0.536597\pi$
$132$	−1.87498	+	2.52660i	−0.163196	+	0.219913i
$133$	−7.37109	+	7.37109i	−0.639154	+	0.639154i
$134$	−3.51217	+	10.6264i	−0.303405	+	0.917978i
$135$		−	1.00000i		−	0.0860663i
$136$	−2.07524	−	0.361009i	−0.177951	−	0.0309563i
$137$		−	1.59842i		−	0.136562i	−0.997666	−	0.0682810i	$-0.978249\pi$
$137$		−	1.59842i		−	0.136562i	0.997666	−	0.0682810i	$-0.0217514\pi$
$138$	6.40158	+	2.11582i	0.544939	+	0.180110i
$139$	−11.8528	+	11.8528i	−1.00534	+	1.00534i	−0.00535228	+	0.999986i	$0.501704\pi$
$139$	−11.8528	+	11.8528i	−1.00534	+	1.00534i	−0.999986	+	0.00535228i	$0.998296\pi$
$140$	2.79793	−	0.414214i	0.236468	−	0.0350074i
$141$	−0.519951	−	0.519951i	−0.0437877	−	0.0437877i
$142$	10.8690	−	5.46904i	0.912106	−	0.458952i
$143$	−0.603650			−0.0504797
$144$	3.82843	−	1.15894i	0.319036	−	0.0965785i
$145$	1.71423			0.142359
$146$	5.41421	−	2.72431i	0.448084	−	0.225466i
$147$	3.53553	+	3.53553i	0.291606	+	0.291606i
$148$	−2.20549	−	14.8977i	−0.181291	−	1.22458i
$149$	8.70160	−	8.70160i	0.712863	−	0.712863i	−0.254270	−	0.967133i	$-0.581835\pi$
$149$	8.70160	−	8.70160i	0.712863	−	0.712863i	0.967133	+	0.254270i	$0.0818352\pi$
$150$	1.34277	+	0.443806i	0.109637	+	0.0362366i
$151$			9.49791i			0.772929i	0.922304	+	0.386465i	$0.126304\pi$
$151$			9.49791i			0.772929i	−0.922304	+	0.386465i	$0.873696\pi$
$152$	−11.9974	−	17.0507i	−0.973122	−	1.38299i
$153$			0.744728i			0.0602077i
$154$	−0.987369	+	2.98737i	−0.0795644	+	0.240729i
$155$	−5.48348	+	5.48348i	−0.440443	+	0.440443i
$156$	0.616281	+	0.457339i	0.0493420	+	0.0366164i
$157$	−10.8750	−	10.8750i	−0.867918	−	0.867918i	0.124324	−	0.992242i	$-0.460324\pi$
$157$	−10.8750	−	10.8750i	−0.867918	−	0.867918i	−0.992242	+	0.124324i	$0.960324\pi$
$158$	−0.643694	−	1.27926i	−0.0512096	−	0.101772i
$159$	−13.5096			−1.07138
$160$	−0.142883	+	5.65505i	−0.0112959	+	0.447071i
$161$	6.74218			0.531358
$162$	−0.635665	−	1.26330i	−0.0499426	−	0.0992543i
$163$	11.0422	+	11.0422i	0.864892	+	0.864892i	0.991901	−	0.127010i	$-0.0405380\pi$
$163$	11.0422	+	11.0422i	0.864892	+	0.864892i	−0.127010	+	0.991901i	$0.540538\pi$
$164$	11.7869	+	8.74702i	0.920404	+	0.683028i
$165$	−1.11239	+	1.11239i	−0.0865993	+	0.0865993i
$166$	−1.05576	+	3.19428i	−0.0819426	+	0.247924i
$167$		−	5.00778i		−	0.387514i	−0.981050	−	0.193757i	$-0.937933\pi$
$167$		−	5.00778i		−	0.387514i	0.981050	−	0.193757i	$-0.0620673\pi$
$168$	3.27133	−	2.30182i	0.252389	−	0.177590i
$169$		−	12.8528i		−	0.988674i
$170$	−1.00000	−	0.330515i	−0.0766965	−	0.0253493i
$171$	−5.21215	+	5.21215i	−0.398583	+	0.398583i
$172$	2.81056	+	18.9848i	0.214303	+	1.44758i
$173$	16.9621	+	16.9621i	1.28961	+	1.28961i	0.935026	+	0.354579i	$0.115376\pi$
$173$	16.9621	+	16.9621i	1.28961	+	1.28961i	0.354579	+	0.935026i	$0.384624\pi$
$174$	2.16559	−	1.08968i	0.164173	−	0.0826083i
$175$	1.41421			0.106904
$176$	−5.54789	−	2.96951i	−0.418188	−	0.223835i
$177$	2.29517			0.172516
$178$	13.1371	−	6.61030i	0.984668	−	0.495463i
$179$	2.54447	+	2.54447i	0.190182	+	0.190182i	0.795775	−	0.605593i	$-0.207064\pi$
$179$	2.54447	+	2.54447i	0.190182	+	0.190182i	−0.605593	+	0.795775i	$0.707064\pi$
$180$	1.97844	−	0.292893i	0.147464	−	0.0218310i
$181$	3.09795	−	3.09795i	0.230269	−	0.230269i	−0.582536	−	0.812805i	$-0.697939\pi$
$181$	3.09795	−	3.09795i	0.230269	−	0.230269i	0.812805	+	0.582536i	$0.197939\pi$
$182$	0.728670	+	0.240836i	0.0540126	+	0.0178519i
$183$		−	8.06328i		−	0.596055i
$184$	−2.31103	+	13.2848i	−0.170371	+	0.979371i
$185$		−	7.53003i		−	0.553619i
$186$	−3.44163	+	10.4129i	−0.252352	+	0.763514i
$187$	0.828427	−	0.828427i	0.0605806	−	0.0605806i
$188$	0.876400	−	1.18098i	0.0639180	−	0.0861318i
$189$	−1.00000	−	1.00000i	−0.0727393	−	0.0727393i
$190$	−4.68554	−	9.31190i	−0.339925	−	0.675556i
$191$	23.6637			1.71225			0.856123	−	0.516772i	$-0.172867\pi$
$191$	23.6637			1.71225			0.856123	+	0.516772i	$0.172867\pi$
$192$	3.41421	+	7.23486i	0.246400	+	0.522131i
$193$	2.61695			0.188372			0.0941862	−	0.995555i	$-0.469975\pi$
$193$	2.61695			0.188372			0.0941862	+	0.995555i	$0.469975\pi$
$194$	−10.7853	−	21.4344i	−0.774340	−	1.53890i
$195$	0.271330	+	0.271330i	0.0194304	+	0.0194304i
$196$	−5.95930	+	8.03037i	−0.425664	+	0.573598i
$197$	5.15116	−	5.15116i	0.367005	−	0.367005i	−0.499379	−	0.866384i	$-0.666438\pi$
$197$	5.15116	−	5.15116i	0.367005	−	0.367005i	0.866384	+	0.499379i	$0.166438\pi$
$198$	−0.698175	+	2.11239i	−0.0496171	+	0.150121i
$199$		−	0.0947078i		−	0.00671366i	−0.999994	−	0.00335683i	$-0.998931\pi$
$199$		−	0.0947078i		−	0.00671366i	0.999994	−	0.00335683i	$-0.00106851\pi$
$200$	−0.484753	+	2.78658i	−0.0342772	+	0.197041i
$201$			7.91375i			0.558193i
$202$	−10.1656	−	3.35988i	−0.715249	−	0.236400i
$203$	1.71423	−	1.71423i	0.120316	−	0.120316i
$204$	−1.47340	+	0.218126i	−0.103158	+	0.0152719i
$205$	5.18944	+	5.18944i	0.362446	+	0.362446i
$206$	13.3666	−	6.72577i	0.931294	−	0.468607i
$207$	4.76744			0.331360
$208$	−0.724312	+	1.35322i	−0.0502220	+	0.0938292i
$209$	11.5959			0.802103
$210$	1.78658	−	0.898966i	0.123286	−	0.0620346i
$211$	6.72202	+	6.72202i	0.462763	+	0.462763i	0.899560	−	0.436797i	$-0.143887\pi$
$211$	6.72202	+	6.72202i	0.462763	+	0.462763i	−0.436797	+	0.899560i	$0.643887\pi$
$212$	−3.95687	−	26.7279i	−0.271759	−	1.83568i
$213$	6.08370	−	6.08370i	0.416848	−	0.416848i
$214$	−20.3990	−	6.74218i	−1.39445	−	0.460886i
$215$			9.59587i			0.654433i
$216$	2.31318	−	1.62764i	0.157392	−	0.110747i
$217$			10.9670i			0.744485i
$218$	0.926908	−	2.80444i	0.0627782	−	0.189941i
$219$	3.03049	−	3.03049i	0.204782	−	0.204782i
$220$	−2.52660	−	1.87498i	−0.170343	−	0.126411i
$221$	−0.202067	−	0.202067i	−0.0135925	−	0.0135925i
$222$	−4.78658	−	9.51269i	−0.321254	−	0.638450i
$223$	−21.4091			−1.43366			−0.716830	−	0.697248i	$-0.754408\pi$
$223$	−21.4091			−1.43366			−0.716830	+	0.697248i	$0.754408\pi$
$224$	5.51217	+	5.79793i	0.368297	+	0.387391i
$225$	1.00000			0.0666667
$226$	0.300202	+	0.596613i	0.0199692	+	0.0396861i
$227$	−10.8486	−	10.8486i	−0.720046	−	0.720046i	0.248568	−	0.968614i	$-0.420040\pi$
$227$	−10.8486	−	10.8486i	−0.720046	−	0.720046i	−0.968614	+	0.248568i	$0.920040\pi$
$228$	−11.8385	−	8.78530i	−0.784024	−	0.581821i
$229$	20.2323	−	20.2323i	1.33699	−	1.33699i	0.438026	−	0.898962i	$-0.355678\pi$
$229$	20.2323	−	20.2323i	1.33699	−	1.33699i	0.898962	−	0.438026i	$-0.144322\pi$
$230$	−2.11582	+	6.40158i	−0.139513	+	0.422108i
$231$			2.22478i			0.146380i
$232$	2.79015	+	3.96533i	0.183182	+	0.260337i
$233$		−	15.8048i		−	1.03541i	−0.855560	−	0.517703i	$-0.826787\pi$
$233$		−	15.8048i		−	1.03541i	0.855560	−	0.517703i	$-0.173213\pi$
$234$	0.515247	+	0.170297i	0.0336828	+	0.0111326i
$235$	0.519951	−	0.519951i	0.0339178	−	0.0339178i
$236$	0.672241	+	4.54086i	0.0437591	+	0.295585i
$237$	−0.716038	−	0.716038i	−0.0465117	−	0.0465117i
$238$	−1.33051	+	0.669485i	−0.0862444	+	0.0433963i
$239$	12.6848			0.820511			0.410256	−	0.911971i	$-0.365439\pi$
$239$	12.6848			0.820511			0.410256	+	0.911971i	$0.365439\pi$
$240$	1.15894	+	3.82843i	0.0748094	+	0.247124i
$241$	12.7830			0.823426			0.411713	−	0.911314i	$-0.364931\pi$
$241$	12.7830			0.823426			0.411713	+	0.911314i	$0.364931\pi$
$242$	−10.7699	+	5.41916i	−0.692314	+	0.348357i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	15.9527	−	2.36168i	1.02127	−	0.151191i
$245$	−3.53553	+	3.53553i	−0.225877	+	0.225877i
$246$	9.85456	+	3.25708i	0.628304	+	0.207664i
$247$		−	2.82843i		−	0.179969i
$248$	−21.6094	−	3.75916i	−1.37220	−	0.238707i
$249$			2.37887i			0.150755i
$250$	−0.443806	+	1.34277i	−0.0280687	+	0.0849244i
$251$	−10.8876	+	10.8876i	−0.687220	+	0.687220i	−0.961617	−	0.274397i	$-0.911522\pi$
$251$	−10.8876	+	10.8876i	−0.687220	+	0.687220i	0.274397	+	0.961617i	$0.411522\pi$
$252$	1.68554	−	2.27133i	0.106179	−	0.143080i
$253$	−5.30324	−	5.30324i	−0.333412	−	0.333412i
$254$	−9.37809	−	18.6377i	−0.588433	−	1.16943i
$255$	−0.744728			−0.0466367
$256$	−13.3137	+	8.87385i	−0.832107	+	0.554615i
$257$	23.6135			1.47297			0.736484	−	0.676455i	$-0.236485\pi$
$257$	23.6135			1.47297			0.736484	+	0.676455i	$0.236485\pi$
$258$	6.09976	+	12.1225i	0.379754	+	0.754712i
$259$	−7.53003	−	7.53003i	−0.467893	−	0.467893i
$260$	−0.457339	+	0.616281i	−0.0283630	+	0.0382201i
$261$	1.21215	−	1.21215i	0.0750300	−	0.0750300i
$262$	7.96030	−	24.0846i	0.491789	−	1.48795i
$263$			0.372018i			0.0229396i	0.999934	+	0.0114698i	$0.00365103\pi$
$263$			0.372018i			0.0229396i	−0.999934	+	0.0114698i	$0.996349\pi$
$264$	−4.38372	−	0.762591i	−0.269799	−	0.0469343i
$265$		−	13.5096i		−	0.829889i
$266$	−13.9974	−	4.62636i	−0.858239	−	0.283660i
$267$	7.35322	−	7.35322i	0.450010	−	0.450010i
$268$	−15.6569	+	2.31788i	−0.956395	+	0.141587i
$269$	7.10574	+	7.10574i	0.433244	+	0.433244i	0.889731	−	0.456486i	$-0.150892\pi$
$269$	7.10574	+	7.10574i	0.433244	+	0.433244i	−0.456486	+	0.889731i	$0.650892\pi$
$270$	1.26330	−	0.635665i	0.0768821	−	0.0386854i
$271$	11.7094			0.711295			0.355647	−	0.934620i	$-0.384260\pi$
$271$	11.7094			0.711295			0.355647	+	0.934620i	$0.384260\pi$
$272$	−0.863096	−	2.85114i	−0.0523329	−	0.172876i
$273$	0.542661			0.0328433
$274$	2.01928	−	1.01606i	0.121989	−	0.0613823i
$275$	−1.11239	−	1.11239i	−0.0670796	−	0.0670796i
$276$	1.39635	+	9.43208i	0.0840504	+	0.567744i
$277$	7.83508	−	7.83508i	0.470764	−	0.470764i	−0.431398	−	0.902162i	$-0.641979\pi$
$277$	7.83508	−	7.83508i	0.470764	−	0.470764i	0.902162	+	0.431398i	$0.141979\pi$
$278$	−22.5080	−	7.43922i	−1.34994	−	0.446175i
$279$			7.75481i			0.464268i
$280$	2.30182	+	3.27133i	0.137560	+	0.195499i
$281$			26.8486i			1.60165i	0.598897	+	0.800826i	$0.295606\pi$
$281$			26.8486i			1.60165i	−0.598897	+	0.800826i	$0.704394\pi$
$282$	0.326340	−	0.987369i	0.0194332	−	0.0587970i
$283$	20.2926	−	20.2926i	1.20627	−	1.20627i	0.234045	−	0.972226i	$-0.424804\pi$
$283$	20.2926	−	20.2926i	1.20627	−	1.20627i	0.972226	−	0.234045i	$-0.0751965\pi$
$284$	13.8181	+	10.2543i	0.819953	+	0.608483i
$285$	−5.21215	−	5.21215i	−0.308741	−	0.308741i
$286$	−0.383719	−	0.762591i	−0.0226898	−	0.0450930i
$287$	10.3789			0.612645
$288$	3.89769	+	4.09976i	0.229674	+	0.241581i
$289$	−16.4454			−0.967375
$290$	1.08968	+	2.16559i	0.0639881	+	0.127168i
$291$	−11.9974	−	11.9974i	−0.703303	−	0.703303i
$292$	6.88325	+	5.10803i	0.402812	+	0.298925i
$293$	−22.2722	+	22.2722i	−1.30116	+	1.30116i	−0.373543	+	0.927613i	$0.621857\pi$
$293$	−22.2722	+	22.2722i	−1.30116	+	1.30116i	−0.927613	+	0.373543i	$0.878143\pi$
$294$	−2.21903	+	6.71386i	−0.129416	+	0.391560i
$295$			2.29517i			0.133630i
$296$	17.4183	−	12.2561i	1.01242	−	0.712374i
$297$			1.57316i			0.0912837i
$298$	16.5240	+	5.46144i	0.957213	+	0.316373i
$299$	−1.29355	+	1.29355i	−0.0748080	+	0.0748080i
$300$	0.292893	+	1.97844i	0.0169102	+	0.114225i
$301$	9.59587	+	9.59587i	0.553096	+	0.553096i
$302$	−11.9987	+	6.03749i	−0.690449	+	0.347419i
$303$	−7.57060			−0.434920
$304$	13.9137	−	25.9949i	0.798008	−	1.49091i
$305$	8.06328			0.461702
$306$	−0.940816	+	0.473398i	−0.0537829	+	0.0270623i
$307$	−17.9747	−	17.9747i	−1.02587	−	1.02587i	−0.999656	−	0.0262162i	$-0.991654\pi$
$307$	−17.9747	−	17.9747i	−1.02587	−	1.02587i	−0.0262162	−	0.999656i	$-0.508346\pi$
$308$	−4.40158	+	0.651622i	−0.250803	+	0.0371296i
$309$	7.48167	−	7.48167i	0.425617	−	0.425617i
$310$	−10.4129	−	3.44163i	−0.591415	−	0.195471i
$311$			11.3555i			0.643912i	0.946755	+	0.321956i	$0.104340\pi$
$311$			11.3555i			0.643912i	−0.946755	+	0.321956i	$0.895660\pi$
$312$	−0.186009	+	1.06926i	−0.0105307	+	0.0605351i
$313$			11.7023i			0.661452i	0.943727	+	0.330726i	$0.107294\pi$
$313$			11.7023i			0.661452i	−0.943727	+	0.330726i	$0.892706\pi$
$314$	6.82553	−	20.6512i	0.385187	−	1.16542i
$315$	1.00000	−	1.00000i	0.0563436	−	0.0563436i
$316$	1.20691	−	1.62636i	0.0678942	−	0.0914899i
$317$	12.7827	+	12.7827i	0.717951	+	0.717951i	0.968185	−	0.250235i	$-0.0805077\pi$
$317$	12.7827	+	12.7827i	0.717951	+	0.717951i	−0.250235	+	0.968185i	$0.580508\pi$
$318$	−8.58759	−	17.0667i	−0.481568	−	0.957054i
$319$	−2.69676			−0.150989
$320$	−7.23486	+	3.41421i	−0.404441	+	0.190860i
$321$	−15.1917			−0.847920
$322$	4.28577	+	8.51740i	0.238836	+	0.474656i
$323$	3.88163	+	3.88163i	0.215980	+	0.215980i
$324$	1.19186	−	1.60607i	0.0662144	−	0.0892263i
$325$	−0.271330	+	0.271330i	−0.0150507	+	0.0150507i
$326$	−6.93048	+	20.9688i	−0.383844	+	1.16135i
$327$		−	2.08855i		−	0.115497i
$328$	−3.55759	+	20.4506i	−0.196435	+	1.12920i
$329$		−	1.03990i		−	0.0573316i
$330$	−2.11239	−	0.698175i	−0.116283	−	0.0384333i
$331$	14.0775	−	14.0775i	0.773771	−	0.773771i	−0.204992	−	0.978764i	$-0.565717\pi$
$331$	14.0775	−	14.0775i	0.773771	−	0.773771i	0.978764	+	0.204992i	$0.0657169\pi$
$332$	−4.70645	+	0.696756i	−0.258300	+	0.0382394i
$333$	−5.32453	−	5.32453i	−0.291783	−	0.291783i
$334$	6.32634	−	3.18327i	0.346162	−	0.174181i
$335$	−7.91375			−0.432374
$336$	4.98737	+	2.66949i	0.272083	+	0.145632i
$337$	−9.19859			−0.501079			−0.250539	−	0.968106i	$-0.580608\pi$
$337$	−9.19859			−0.501079			−0.250539	+	0.968106i	$0.580608\pi$
$338$	16.2369	−	8.17005i	0.883171	−	0.444392i
$339$	0.333942	+	0.333942i	0.0181372	+	0.0181372i
$340$	−0.218126	−	1.47340i	−0.0118295	−	0.0799062i
$341$	8.62636	−	8.62636i	0.467144	−	0.467144i
$342$	−9.89769	−	3.27133i	−0.535206	−	0.176893i
$343$			16.9706i			0.916324i
$344$	−22.1970	+	15.6186i	−1.19678	+	0.842097i
$345$			4.76744i			0.256670i
$346$	−10.6460	+	32.2105i	−0.572334	+	1.73165i
$347$	−4.94680	+	4.94680i	−0.265558	+	0.265558i	−0.827307	−	0.561749i	$-0.810128\pi$
$347$	−4.94680	+	4.94680i	−0.265558	+	0.265558i	0.561749	+	0.827307i	$0.310128\pi$
$348$	2.75318	+	2.04313i	0.147586	+	0.109523i
$349$	−7.82358	−	7.82358i	−0.418787	−	0.418787i	0.465999	−	0.884785i	$-0.345695\pi$
$349$	−7.82358	−	7.82358i	−0.418787	−	0.418787i	−0.884785	+	0.465999i	$0.845695\pi$
$350$	0.898966	+	1.78658i	0.0480518	+	0.0954966i
$351$	0.383719			0.0204814
$352$	0.224777	−	8.89627i	0.0119807	−	0.474173i
$353$	−33.1080			−1.76216			−0.881081	−	0.472965i	$-0.843184\pi$
$353$	−33.1080			−1.76216			−0.881081	+	0.472965i	$0.843184\pi$
$354$	1.45896	+	2.89949i	0.0775429	+	0.154106i
$355$	6.08370	+	6.08370i	0.322889	+	0.322889i
$356$	16.7016	+	12.3942i	0.885183	+	0.656890i
$357$	−0.744728	+	0.744728i	−0.0394152	+	0.0394152i
$358$	−1.59700	+	4.83185i	−0.0844040	+	0.255371i
$359$			29.5655i			1.56041i	0.625526	+	0.780204i	$0.284885\pi$
$359$			29.5655i			1.56041i	−0.625526	+	0.780204i	$0.715115\pi$
$360$	1.62764	+	2.31318i	0.0857839	+	0.121915i
$361$			35.3329i			1.85963i
$362$	5.88291	+	1.94439i	0.309199	+	0.102195i
$363$	−6.02821	+	6.02821i	−0.316399	+	0.316399i
$364$	0.158942	+	1.07362i	0.00833081	+	0.0562730i
$365$	3.03049	+	3.03049i	0.158623	+	0.158623i
$366$	10.1864	−	5.12555i	0.532449	−	0.267917i
$367$	25.0270			1.30640			0.653199	−	0.757186i	$-0.273426\pi$
$367$	25.0270			1.30640			0.653199	+	0.757186i	$0.273426\pi$
$368$	−18.2518	+	5.52518i	−0.951440	+	0.288020i
$369$	7.33897			0.382052
$370$	9.51269	−	4.78658i	0.494541	−	0.248842i
$371$	−13.5096	−	13.5096i	−0.701384	−	0.701384i
$372$	−15.3424	+	2.27133i	−0.795466	+	0.117763i
$373$	7.50389	−	7.50389i	0.388537	−	0.388537i	−0.485628	−	0.874165i	$-0.661409\pi$
$373$	7.50389	−	7.50389i	0.388537	−	0.388537i	0.874165	+	0.485628i	$0.161409\pi$
$374$	1.57316	+	0.519951i	0.0813459	+	0.0268860i
$375$			1.00000i			0.0516398i
$376$	2.04903	+	0.356449i	0.105671	+	0.0183825i
$377$			0.657784i			0.0338776i
$378$	0.627636	−	1.89897i	0.0322821	−	0.0976723i
$379$	−23.5181	+	23.5181i	−1.20804	+	1.20804i	−0.236382	+	0.971660i	$0.575962\pi$
$379$	−23.5181	+	23.5181i	−1.20804	+	1.20804i	−0.971660	+	0.236382i	$0.924038\pi$
$380$	8.78530	−	11.8385i	0.450676	−	0.607303i
$381$	−10.4321	−	10.4321i	−0.534451	−	0.534451i
$382$	15.0422	+	29.8944i	0.769626	+	1.52953i
$383$	4.04542			0.206711			0.103356	−	0.994644i	$-0.467042\pi$
$383$	4.04542			0.206711			0.103356	+	0.994644i	$0.467042\pi$
$384$	−6.96951	+	8.91213i	−0.355661	+	0.454795i
$385$	−2.22478			−0.113385
$386$	1.66351	+	3.30600i	0.0846702	+	0.168271i
$387$	6.78530	+	6.78530i	0.344916	+	0.344916i
$388$	20.2222	−	27.2502i	1.02663	−	1.38342i
$389$	−25.3734	+	25.3734i	−1.28648	+	1.28648i	−0.349572	+	0.936909i	$0.613673\pi$
$389$	−25.3734	+	25.3734i	−1.28648	+	1.28648i	−0.936909	+	0.349572i	$0.886327\pi$
$390$	−0.170297	+	0.515247i	−0.00862331	+	0.0260906i
$391$		−	3.55045i		−	0.179554i
$392$	−13.9329	−	2.42376i	−0.703717	−	0.122419i
$393$		−	17.9365i		−	0.904775i
$394$	9.78187	+	3.23305i	0.492804	+	0.162879i
$395$	0.716038	−	0.716038i	0.0360278	−	0.0360278i
$396$	−3.11239	+	0.460766i	−0.156403	+	0.0231544i
$397$	−9.36026	−	9.36026i	−0.469778	−	0.469778i	0.432065	−	0.901843i	$-0.357785\pi$
$397$	−9.36026	−	9.36026i	−0.469778	−	0.469778i	−0.901843	+	0.432065i	$0.857785\pi$
$398$	0.119644	−	0.0602025i	0.00599724	−	0.00301768i
$399$	−10.4243			−0.521867
$400$	−3.82843	+	1.15894i	−0.191421	+	0.0579471i
$401$	−26.3582			−1.31627			−0.658133	−	0.752902i	$-0.728653\pi$
$401$	−26.3582			−1.31627			−0.658133	+	0.752902i	$0.728653\pi$
$402$	−9.99745	+	5.03049i	−0.498627	+	0.250898i
$403$	−2.10411	−	2.10411i	−0.104813	−	0.104813i
$404$	−2.21738	−	14.9780i	−0.110319	−	0.745181i
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$	3.25527	+	1.07591i	0.161556	+	0.0533967i
$407$			11.8459i			0.587180i
$408$	−1.21215	−	1.72269i	−0.0600102	−	0.0852859i
$409$		−	4.71691i		−	0.233236i	−0.993177	−	0.116618i	$-0.962795\pi$
$409$		−	4.71691i		−	0.233236i	0.993177	−	0.116618i	$-0.0372054\pi$
$410$	−3.25708	+	9.85456i	−0.160856	+	0.486682i
$411$	1.13025	−	1.13025i	0.0557512	−	0.0557512i
$412$	16.9933	+	12.6107i	0.837202	+	0.621284i
$413$	2.29517	+	2.29517i	0.112938	+	0.112938i
$414$	3.03049	+	6.02271i	0.148941	+	0.296000i
$415$	−2.37887			−0.116774
$416$	−2.16995	−	0.0548270i	−0.106391	−	0.00268812i
$417$	−16.7623			−0.820855
$418$	7.37109	+	14.6491i	0.360532	+	0.716509i
$419$	−6.97386	−	6.97386i	−0.340695	−	0.340695i	0.515933	−	0.856629i	$-0.327445\pi$
$419$	−6.97386	−	6.97386i	−0.340695	−	0.340695i	−0.856629	+	0.515933i	$0.827445\pi$
$420$	2.27133	+	1.68554i	0.110830	+	0.0822461i
$421$	10.8933	−	10.8933i	0.530909	−	0.530909i	−0.389934	−	0.920843i	$-0.627502\pi$
$421$	10.8933	−	10.8933i	0.530909	−	0.530909i	0.920843	+	0.389934i	$0.127502\pi$
$422$	−4.21898	+	12.7649i	−0.205377	+	0.621385i
$423$		−	0.735321i		−	0.0357525i
$424$	31.2502	−	21.9887i	1.51764	−	1.06787i
$425$		−	0.744728i		−	0.0361246i
$426$	11.5527	+	3.81835i	0.559732	+	0.185000i
$427$	8.06328	−	8.06328i	0.390210	−	0.390210i
$428$	−4.44955	−	30.0559i	−0.215077	−	1.45281i
$429$	−0.426845	−	0.426845i	−0.0206083	−	0.0206083i
$430$	−12.1225	+	6.09976i	−0.584597	+	0.294156i
$431$	22.0151			1.06043			0.530214	−	0.847864i	$-0.322112\pi$
$431$	22.0151			1.06043			0.530214	+	0.847864i	$0.322112\pi$
$432$	3.52660	+	1.88761i	0.169674	+	0.0908177i
$433$	2.39218			0.114961			0.0574803	−	0.998347i	$-0.481693\pi$
$433$	2.39218			0.114961			0.0574803	+	0.998347i	$0.481693\pi$
$434$	−13.8546	+	6.97131i	−0.665040	+	0.334634i
$435$	1.21215	+	1.21215i	0.0581180	+	0.0581180i
$436$	4.13206	−	0.611721i	0.197890	−	0.0292961i
$437$	24.8486	−	24.8486i	1.18867	−	1.18867i
$438$	5.75481	+	1.90205i	0.274975	+	0.0908833i
$439$		−	4.41259i		−	0.210601i	−0.994440	−	0.105301i	$-0.966419\pi$
$439$		−	4.41259i		−	0.210601i	0.994440	−	0.105301i	$-0.0335805\pi$
$440$	0.762591	−	4.38372i	0.0363551	−	0.208986i
$441$			5.00000i			0.238095i
$442$	0.126825	−	0.383719i	0.00603244	−	0.0182517i
$443$	19.9206	−	19.9206i	0.946456	−	0.946456i	−0.0521812	−	0.998638i	$-0.516617\pi$
$443$	19.9206	−	19.9206i	0.946456	−	0.946456i	0.998638	+	0.0521812i	$0.0166173\pi$
$444$	8.97474	−	12.0938i	0.425922	−	0.573945i
$445$	7.35322	+	7.35322i	0.348576	+	0.348576i
$446$	−13.6090	−	27.0462i	−0.644406	−	1.28067i
$447$	12.3059			0.582050
$448$	−3.82064	+	10.6491i	−0.180508	+	0.503121i
$449$	−34.0760			−1.60815			−0.804074	−	0.594529i	$-0.797338\pi$
$449$	−34.0760			−1.60815			−0.804074	+	0.594529i	$0.797338\pi$
$450$	0.635665	+	1.26330i	0.0299655	+	0.0595526i
$451$	−8.16379	−	8.16379i	−0.384418	−	0.384418i
$452$	−0.562874	+	0.758492i	−0.0264753	+	0.0356765i
$453$	−6.71604	+	6.71604i	−0.315547	+	0.315547i
$454$	6.80896	−	20.6011i	0.319560	−	0.966857i
$455$			0.542661i			0.0254403i
$456$	3.57316	−	20.5401i	0.167328	−	0.961879i
$457$			15.1881i			0.710470i	0.934777	+	0.355235i	$0.115599\pi$
$457$			15.1881i			0.710470i	−0.934777	+	0.355235i	$0.884401\pi$
$458$	38.4205	+	12.6985i	1.79527	+	0.593363i
$459$	−0.526602	+	0.526602i	−0.0245797	+	0.0245797i
$460$	−9.43208	+	1.39635i	−0.439773	+	0.0651052i
$461$	−12.4194	−	12.4194i	−0.578431	−	0.578431i	0.356040	−	0.934471i	$-0.384127\pi$
$461$	−12.4194	−	12.4194i	−0.578431	−	0.578431i	−0.934471	+	0.356040i	$0.884127\pi$
$462$	−2.81056	+	1.41421i	−0.130759	+	0.0657952i
$463$	−19.7711			−0.918839			−0.459420	−	0.888219i	$-0.651943\pi$
$463$	−19.7711			−0.918839			−0.459420	+	0.888219i	$0.651943\pi$
$464$	−3.23581	+	6.04542i	−0.150219	+	0.280652i
$465$	−7.75481			−0.359621
$466$	19.9662	−	10.0466i	0.924917	−	0.465398i
$467$	−6.56282	−	6.56282i	−0.303691	−	0.303691i	0.538765	−	0.842456i	$-0.318891\pi$
$467$	−6.56282	−	6.56282i	−0.303691	−	0.303691i	−0.842456	+	0.538765i	$0.818891\pi$
$468$	0.112389	+	0.759164i	0.00519517	+	0.0350924i
$469$	−7.91375	+	7.91375i	−0.365423	+	0.365423i
$470$	0.987369	+	0.326340i	0.0455439	+	0.0150529i
$471$		−	15.3795i		−	0.708652i
$472$	−5.30915	+	3.73571i	−0.244373	+	0.171950i
$473$		−	15.0958i		−	0.694105i
$474$	0.449411	−	1.35973i	0.0206422	−	0.0624546i
$475$	5.21215	−	5.21215i	0.239150	−	0.239150i
$476$	−1.69152	−	1.25527i	−0.0775309	−	0.0575353i
$477$	−9.55274	−	9.55274i	−0.437390	−	0.437390i
$478$	8.06328	+	16.0247i	0.368806	+	0.732954i
$479$	22.9871			1.05031			0.525154	−	0.851007i	$-0.324008\pi$
$479$	22.9871			1.05031			0.525154	+	0.851007i	$0.324008\pi$
$480$	−4.09976	+	3.89769i	−0.187127	+	0.177904i
$481$	2.88942			0.131746
$482$	8.12571	+	16.1488i	0.370116	+	0.735557i
$483$	4.76744	+	4.76744i	0.216926	+	0.216926i
$484$	−13.6921	−	10.1608i	−0.622367	−	0.461855i
$485$	11.9974	−	11.9974i	0.544776	−	0.544776i
$486$	0.443806	−	1.34277i	0.0201314	−	0.0609094i
$487$		−	12.1110i		−	0.548800i	−0.961616	−	0.274400i	$-0.911521\pi$
$487$		−	12.1110i		−	0.548800i	0.961616	−	0.274400i	$-0.0884793\pi$
$488$	13.1241	+	18.6518i	0.594100	+	0.844328i
$489$			15.6160i			0.706181i
$490$	−6.71386	−	2.21903i	−0.303301	−	0.100245i
$491$	−12.9555	+	12.9555i	−0.584671	+	0.584671i	−0.936183	−	0.351512i	$-0.885668\pi$
$491$	−12.9555	+	12.9555i	−0.584671	+	0.584671i	0.351512	+	0.936183i	$0.385668\pi$
$492$	2.14953	+	14.5197i	0.0969085	+	0.654598i
$493$	−0.902719	−	0.902719i	−0.0406564	−	0.0406564i
$494$	3.57316	−	1.79793i	0.160764	−	0.0808928i
$495$	−1.57316			−0.0707081
$496$	−8.98737	−	29.6887i	−0.403545	−	1.33306i
$497$	12.1674			0.545782
$498$	−3.00523	+	1.51217i	−0.134668	+	0.0677618i
$499$	−19.7344	−	19.7344i	−0.883433	−	0.883433i	0.110449	−	0.993882i	$-0.464771\pi$
$499$	−19.7344	−	19.7344i	−0.883433	−	0.883433i	−0.993882	+	0.110449i	$0.964771\pi$
$500$	−1.97844	+	0.292893i	−0.0884784	+	0.0130986i
$501$	3.54104	−	3.54104i	0.158202	−	0.158202i
$502$	−20.6752	−	6.83346i	−0.922780	−	0.304992i
$503$		−	9.75641i		−	0.435017i	−0.976058	−	0.217508i	$-0.930207\pi$
$503$		−	9.75641i		−	0.435017i	0.976058	−	0.217508i	$-0.0697929\pi$
$504$	3.94082	+	0.685544i	0.175538	+	0.0305366i
$505$		−	7.57060i		−	0.336887i
$506$	3.32851	−	10.0707i	0.147970	−	0.447696i
$507$	9.08827	−	9.08827i	0.403624	−	0.403624i
$508$	17.5837	−	23.6947i	0.780152	−	1.05128i
$509$	−27.9449	−	27.9449i	−1.23864	−	1.23864i	−0.960558	−	0.278078i	$-0.910303\pi$
$509$	−27.9449	−	27.9449i	−1.23864	−	1.23864i	−0.278078	−	0.960558i	$-0.589697\pi$
$510$	−0.473398	−	0.940816i	−0.0209624	−	0.0416600i
$511$	6.06099			0.268122
$512$	−19.6734	−	11.1784i	−0.869450	−	0.494021i
$513$	−7.37109			−0.325441
$514$	15.0103	+	29.8309i	0.662074	+	1.31579i
$515$	7.48167	+	7.48167i	0.329682	+	0.329682i
$516$	−11.4369	+	15.4117i	−0.503482	+	0.678461i
$517$	−0.817963	+	0.817963i	−0.0359740	+	0.0359740i
$518$	4.72612	−	14.2993i	0.207654	−	0.628274i
$519$			23.9880i			1.05296i
$520$	−1.06926	−	0.186009i	−0.0468903	−	0.00815703i
$521$		−	26.7169i		−	1.17049i	−0.810857	−	0.585245i	$-0.800998\pi$
$521$		−	26.7169i		−	1.17049i	0.810857	−	0.585245i	$-0.199002\pi$
$522$	2.30182	+	0.760787i	0.100748	+	0.0332987i
$523$	2.76514	−	2.76514i	0.120911	−	0.120911i	−0.644062	−	0.764973i	$-0.722752\pi$
$523$	2.76514	−	2.76514i	0.120911	−	0.120911i	0.764973	+	0.644062i	$0.222752\pi$
$524$	35.4862	−	5.25347i	1.55022	−	0.229499i
$525$	1.00000	+	1.00000i	0.0436436	+	0.0436436i
$526$	−0.469970	+	0.236479i	−0.0204917	+	0.0103110i
$527$	5.77522			0.251573
$528$	−1.82320	−	6.02271i	−0.0793444	−	0.262105i
$529$	0.271533			0.0118058
$530$	17.0667	−	8.58759i	0.741331	−	0.373021i
$531$	1.62293	+	1.62293i	0.0704293	+	0.0704293i
$532$	−3.05320	−	20.6238i	−0.132373	−	0.894155i
$533$	−1.99129	+	1.99129i	−0.0862522	+	0.0862522i
$534$	13.9635	+	4.61515i	0.604261	+	0.199717i
$535$		−	15.1917i		−	0.656796i
$536$	−12.8807	−	18.3059i	−0.556362	−	0.790695i
$537$			3.59842i			0.155283i
$538$	−4.45982	+	13.4936i	−0.192276	+	0.581748i
$539$	5.56194	−	5.56194i	0.239570	−	0.239570i
$540$	1.60607	+	1.19186i	0.0691144	+	0.0512895i
$541$	−11.0337	−	11.0337i	−0.474377	−	0.474377i	0.428951	−	0.903328i	$-0.358883\pi$
$541$	−11.0337	−	11.0337i	−0.474377	−	0.474377i	−0.903328	+	0.428951i	$0.858883\pi$
$542$	7.44325	+	14.7925i	0.319715	+	0.635391i
$543$	4.38117			0.188014
$544$	3.05320	−	2.90272i	0.130905	−	0.124453i
$545$	2.08855			0.0894635
$546$	0.344951	+	0.685544i	0.0147625	+	0.0293386i
$547$	−3.06746	−	3.06746i	−0.131155	−	0.131155i	0.638482	−	0.769637i	$-0.279563\pi$
$547$	−3.06746	−	3.06746i	−0.131155	−	0.131155i	−0.769637	+	0.638482i	$0.779563\pi$
$548$	2.56718	+	1.90509i	0.109664	+	0.0813814i
$549$	5.70160	−	5.70160i	0.243338	−	0.243338i
$550$	0.698175	−	2.11239i	0.0297703	−	0.0900726i
$551$		−	12.6358i		−	0.538302i
$552$	−11.0279	+	7.75965i	−0.469380	+	0.330273i
$553$		−	1.43208i		−	0.0608981i
$554$	14.8786	+	4.91758i	0.632129	+	0.208928i
$555$	5.32453	−	5.32453i	0.226014	−	0.226014i
$556$	−4.90957	−	33.1632i	−0.208212	−	1.40643i
$557$	10.3516	+	10.3516i	0.438611	+	0.438611i	0.891545	−	0.452933i	$-0.149622\pi$
$557$	10.3516	+	10.3516i	0.438611	+	0.438611i	−0.452933	+	0.891545i	$0.649622\pi$
$558$	−9.79666	+	4.92946i	−0.414726	+	0.208681i
$559$	−3.68212			−0.155737
$560$	−2.66949	+	4.98737i	−0.112806	+	0.210755i
$561$	1.17157			0.0494638
$562$	−33.9178	+	17.0667i	−1.43074	+	0.719916i
$563$	11.8022	+	11.8022i	0.497405	+	0.497405i	0.910629	−	0.413224i	$-0.135597\pi$
$563$	11.8022	+	11.8022i	0.497405	+	0.497405i	−0.413224	+	0.910629i	$0.635597\pi$
$564$	1.45479	−	0.215371i	0.0612576	−	0.00906874i
$565$	−0.333942	+	0.333942i	−0.0140490	+	0.0140490i
$566$	38.5350	+	12.7364i	1.61975	+	0.535350i
$567$		−	1.41421i		−	0.0593914i
$568$	−4.17064	+	23.9747i	−0.174996	+	1.00596i
$569$			37.3371i			1.56525i	0.622491	+	0.782627i	$0.286121\pi$
$569$			37.3371i			1.56525i	−0.622491	+	0.782627i	$0.713879\pi$
$570$	3.27133	−	9.89769i	0.137021	−	0.414569i
$571$	−8.89627	+	8.89627i	−0.372297	+	0.372297i	−0.868313	−	0.496016i	$-0.834796\pi$
$571$	−8.89627	+	8.89627i	−0.372297	+	0.372297i	0.496016	+	0.868313i	$0.334796\pi$
$572$	0.719466	−	0.969506i	0.0300824	−	0.0405371i
$573$	16.7328	+	16.7328i	0.699021	+	0.699021i
$574$	6.59749	+	13.1116i	0.275374	+	0.547269i
$575$	−4.76744			−0.198816
$576$	−2.70160	+	7.53003i	−0.112567	+	0.313751i
$577$	−16.7807			−0.698591			−0.349296	−	0.937013i	$-0.613579\pi$
$577$	−16.7807			−0.698591			−0.349296	+	0.937013i	$0.613579\pi$
$578$	−10.4538	−	20.7755i	−0.434819	−	0.864146i
$579$	1.85047	+	1.85047i	0.0769027	+	0.0769027i
$580$	−2.04313	+	2.75318i	−0.0848362	+	0.114320i
$581$	−2.37887	+	2.37887i	−0.0986923	+	0.0986923i
$582$	7.53003	−	22.7827i	0.312130	−	0.944375i
$583$			21.2527i			0.880198i
$584$	−2.07754	+	11.9426i	−0.0859691	+	0.494189i
$585$			0.383719i			0.0158648i
$586$	−42.2942	−	13.9788i	−1.74716	−	0.577460i
$587$	3.26468	−	3.26468i	0.134748	−	0.134748i	−0.636516	−	0.771264i	$-0.719625\pi$
$587$	3.26468	−	3.26468i	0.134748	−	0.134748i	0.771264	+	0.636516i	$0.219625\pi$
$588$	−9.89219	+	1.46447i	−0.407947	+	0.0603936i
$589$	40.4192	+	40.4192i	1.66544	+	1.66544i
$590$	−2.89949	+	1.45896i	−0.119370	+	0.0600645i
$591$	7.28484			0.299658
$592$	26.5554	+	14.2138i	1.09142	+	0.584182i
$593$	6.83422			0.280648			0.140324	−	0.990106i	$-0.455186\pi$
$593$	6.83422			0.280648			0.140324	+	0.990106i	$0.455186\pi$
$594$	−1.98737	+	1.00000i	−0.0815427	+	0.0410305i
$595$	−0.744728	−	0.744728i	−0.0305309	−	0.0305309i
$596$	3.60432	+	24.3465i	0.147639	+	0.997271i
$597$	0.0669685	−	0.0669685i	0.00274084	−	0.00274084i
$598$	−2.45641	−	0.811879i	−0.100450	−	0.0332002i
$599$		−	16.8317i		−	0.687723i	−0.939020	−	0.343862i	$-0.888265\pi$
$599$		−	16.8317i		−	0.687723i	0.939020	−	0.343862i	$-0.111735\pi$
$600$	−2.31318	+	1.62764i	−0.0944352	+	0.0664480i
$601$			22.7422i			0.927673i	0.885921	+	0.463836i	$0.153527\pi$
$601$			22.7422i			0.927673i	−0.885921	+	0.463836i	$0.846473\pi$
$602$	−6.02271	+	18.2222i	−0.245467	+	0.742682i
$603$	−5.59587	+	5.59587i	−0.227881	+	0.227881i
$604$	−15.2543	−	11.3202i	−0.620690	−	0.460612i
$605$	−6.02821	−	6.02821i	−0.245082	−	0.245082i
$606$	−4.81237	−	9.56395i	−0.195489	−	0.388509i
$607$	11.9702			0.485855			0.242927	−	0.970045i	$-0.421892\pi$
$607$	11.9702			0.485855			0.242927	+	0.970045i	$0.421892\pi$
$608$	41.6839	+	1.05320i	1.69050	+	0.0427131i
$609$	2.42429			0.0982373
$610$	5.12555	+	10.1864i	0.207527	+	0.412433i
$611$	0.199515	+	0.199515i	0.00807151	+	0.00807151i
$612$	−1.19609	−	0.887611i	−0.0483490	−	0.0358796i
$613$	−27.1488	+	27.1488i	−1.09653	+	1.09653i	−0.101716	+	0.994814i	$0.532433\pi$
$613$	−27.1488	+	27.1488i	−1.09653	+	1.09653i	−0.994814	+	0.101716i	$0.967567\pi$
$614$	11.2816	−	34.1334i	0.455288	−	1.37751i
$615$			7.33897i			0.295936i
$616$	−3.62113	−	5.14631i	−0.145899	−	0.207351i
$617$		−	8.75442i		−	0.352440i	−0.984351	−	0.176220i	$-0.943613\pi$
$617$		−	8.75442i		−	0.352440i	0.984351	−	0.176220i	$-0.0563870\pi$
$618$	14.2074	+	4.69577i	0.571507	+	0.188891i
$619$	−8.64222	+	8.64222i	−0.347360	+	0.347360i	−0.859125	−	0.511765i	$-0.828992\pi$
$619$	−8.64222	+	8.64222i	−0.347360	+	0.347360i	0.511765	+	0.859125i	$0.328992\pi$
$620$	−2.27133	−	15.3424i	−0.0912188	−	0.616166i
$621$	3.37109	+	3.37109i	0.135277	+	0.135277i
$622$	−14.3454	+	7.21831i	−0.575200	+	0.289428i
$623$	14.7064			0.589201
$624$	−1.46904	+	0.444708i	−0.0588087	+	0.0178026i
$625$	−1.00000			−0.0400000
$626$	−14.7835	+	7.43873i	−0.590867	+	0.297311i
$627$	8.19951	+	8.19951i	0.327457	+	0.327457i
$628$	30.4275	−	4.50456i	1.21419	−	0.179752i
$629$	−3.96533	+	3.96533i	−0.158108	+	0.158108i
$630$	1.89897	+	0.627636i	0.0756566	+	0.0250056i
$631$			2.55473i			0.101702i	0.998706	+	0.0508510i	$0.0161934\pi$
$631$			2.55473i			0.101702i	−0.998706	+	0.0508510i	$0.983807\pi$
$632$	2.82178	+	0.490876i	0.112244	+	0.0195260i
$633$			9.50637i			0.377844i
$634$	−8.02291	+	24.2740i	−0.318631	+	0.964044i
$635$	10.4321	−	10.4321i	0.413984	−	0.413984i
$636$	16.1016	−	21.6974i	0.638468	−	0.860359i
$637$	−1.35665	−	1.35665i	−0.0537525	−	0.0537525i
$638$	−1.71423	−	3.40681i	−0.0678672	−	0.134877i
$639$	8.60365			0.340355
$640$	−8.91213	−	6.96951i	−0.352283	−	0.275494i
$641$	−41.7867			−1.65047			−0.825237	−	0.564787i	$-0.808959\pi$
$641$	−41.7867			−1.65047			−0.825237	+	0.564787i	$0.808959\pi$
$642$	−9.65685	−	19.1917i	−0.381126	−	0.757437i
$643$	4.73988	+	4.73988i	0.186923	+	0.186923i	0.794364	−	0.607442i	$-0.207804\pi$
$643$	4.73988	+	4.73988i	0.186923	+	0.186923i	−0.607442	+	0.794364i	$0.707804\pi$
$644$	−8.03573	+	10.8284i	−0.316652	+	0.426700i
$645$	−6.78530	+	6.78530i	−0.267171	+	0.267171i
$646$	−2.43625	+	7.37109i	−0.0958530	+	0.290012i
$647$			8.79956i			0.345946i	0.984927	+	0.172973i	$0.0553374\pi$
$647$			8.79956i			0.345946i	−0.984927	+	0.172973i	$0.944663\pi$
$648$	2.78658	+	0.484753i	0.109467	+	0.0190429i
$649$		−	3.61066i		−	0.141731i
$650$	−0.515247	−	0.170297i	−0.0202097	−	0.00667959i
$651$	−7.75481	+	7.75481i	−0.303935	+	0.303935i
$652$	−30.8953	+	4.57383i	−1.20995	+	0.179125i
$653$	6.41839	+	6.41839i	0.251171	+	0.251171i	0.821451	−	0.570280i	$-0.193165\pi$
$653$	6.41839	+	6.41839i	0.251171	+	0.251171i	−0.570280	+	0.821451i	$0.693165\pi$
$654$	2.63846	−	1.32762i	0.103172	−	0.0519139i
$655$	17.9365			0.700835
$656$	−28.0967	+	8.50544i	−1.09699	+	0.332082i
$657$	4.28577			0.167204
$658$	1.31371	−	0.661029i	0.0512137	−	0.0257696i
$659$	25.9729	+	25.9729i	1.01176	+	1.01176i	0.999930	+	0.0118318i	$0.00376627\pi$
$659$	25.9729	+	25.9729i	1.01176	+	1.01176i	0.0118318	+	0.999930i	$0.496234\pi$
$660$	−0.460766	−	3.11239i	−0.0179353	−	0.121150i
$661$	33.3534	−	33.3534i	1.29730	−	1.29730i	0.367122	−	0.930173i	$-0.380343\pi$
$661$	33.3534	−	33.3534i	1.29730	−	1.29730i	0.930173	−	0.367122i	$-0.119657\pi$
$662$	26.7328	+	8.83557i	1.03900	+	0.343404i
$663$		−	0.285766i		−	0.0110982i
$664$	−3.87194	−	5.50276i	−0.150260	−	0.213548i
$665$		−	10.4243i		−	0.404237i
$666$	3.34187	−	10.1111i	0.129495	−	0.391798i
$667$	−5.77883	+	5.77883i	−0.223757	+	0.223757i
$668$	8.04287	+	5.96858i	0.311188	+	0.230931i
$669$	−15.1385	−	15.1385i	−0.585289	−	0.585289i
$670$	−5.03049	−	9.99745i	−0.194345	−	0.386235i
$671$	−12.6848			−0.489691
$672$	−0.202067	+	7.99745i	−0.00779492	+	0.308508i
$673$	39.3958			1.51860			0.759299	−	0.650742i	$-0.225542\pi$
$673$	39.3958			1.51860			0.759299	+	0.650742i	$0.225542\pi$
$674$	−5.84722	−	11.6206i	−0.225227	−	0.447608i
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$	20.6425	+	15.3187i	0.793941	+	0.589180i
$677$	−7.02565	+	7.02565i	−0.270018	+	0.270018i	−0.829107	−	0.559090i	$-0.811151\pi$
$677$	−7.02565	+	7.02565i	−0.270018	+	0.270018i	0.559090	+	0.829107i	$0.311151\pi$
$678$	−0.209594	+	0.634144i	−0.00804940	+	0.0243542i
$679$		−	23.9949i		−	0.920840i
$680$	1.72269	−	1.21215i	0.0660621	−	0.0464837i
$681$		−	15.3422i		−	0.587915i
$682$	16.3812	+	5.41421i	0.627267	+	0.207321i
$683$	−16.9060	+	16.9060i	−0.646889	+	0.646889i	−0.952240	−	0.305351i	$-0.901226\pi$
$683$	−16.9060	+	16.9060i	−0.646889	+	0.646889i	0.305351	+	0.952240i	$0.401226\pi$
$684$	−2.15894	−	14.5832i	−0.0825492	−	0.557604i
$685$	1.13025	+	1.13025i	0.0431847	+	0.0431847i
$686$	−21.4389	+	10.7876i	−0.818542	+	0.411872i
$687$	28.6128			1.09165
$688$	−33.8408	−	18.1133i	−1.29017	−	0.690562i
$689$	5.18390			0.197491
$690$	−6.02271	+	3.03049i	−0.229281	+	0.115369i
$691$	−18.9047	−	18.9047i	−0.719170	−	0.719170i	0.249265	−	0.968435i	$-0.419811\pi$
$691$	−18.9047	−	18.9047i	−0.719170	−	0.719170i	−0.968435	+	0.249265i	$0.919811\pi$
$692$	−47.4588	+	7.02593i	−1.80411	+	0.267086i
$693$	−1.57316	+	1.57316i	−0.0597592	+	0.0597592i
$694$	−9.39380	−	3.10479i	−0.356584	−	0.117856i
$695$		−	16.7623i		−	0.635832i
$696$	−0.830979	+	4.77685i	−0.0314982	+	0.181066i
$697$		−	5.46554i		−	0.207022i
$698$	4.91036	−	14.8567i	0.185860	−	0.562335i
$699$	11.1757	−	11.1757i	0.422703	−	0.422703i
$700$	−1.68554	+	2.27133i	−0.0637076	+	0.0858482i
$701$	−1.94357	−	1.94357i	−0.0734077	−	0.0734077i	0.669450	−	0.742857i	$-0.266530\pi$
$701$	−1.94357	−	1.94357i	−0.0734077	−	0.0734077i	−0.742857	+	0.669450i	$0.766530\pi$
$702$	0.243917	+	0.484753i	0.00920605	+	0.0182958i
$703$	−55.5045			−2.09339
$704$	11.3816	−	5.37109i	0.428958	−	0.202430i
$705$	0.735321			0.0276938
$706$	−21.0456	−	41.8254i	−0.792062	−	1.57412i
$707$	−7.57060	−	7.57060i	−0.284722	−	0.284722i
$708$	−2.73552	+	3.68622i	−0.102807	+	0.138536i
$709$	−12.3374	+	12.3374i	−0.463340	+	0.463340i	−0.899748	−	0.436409i	$-0.856250\pi$
$709$	−12.3374	+	12.3374i	−0.463340	+	0.463340i	0.436409	+	0.899748i	$0.356250\pi$
$710$	−3.81835	+	11.5527i	−0.143300	+	0.433567i
$711$		−	1.01263i		−	0.0379766i
$712$	−5.04096	+	28.9777i	−0.188918	+	1.08599i
$713$		−	36.9706i		−	1.38456i
$714$	−1.41421	−	0.467418i	−0.0529256	−	0.0174927i
$715$	0.426845	−	0.426845i	0.0159631	−	0.0159631i
$716$	−7.11924	+	1.05395i	−0.266059	+	0.0393880i
$717$	8.96951	+	8.96951i	0.334972	+	0.334972i
$718$	−37.3501	+	18.7938i	−1.39389	+	0.701377i
$719$	−16.0811			−0.599726			−0.299863	−	0.953982i	$-0.596941\pi$
$719$	−16.0811			−0.599726			−0.299863	+	0.953982i	$0.596941\pi$
$720$	−1.88761	+	3.52660i	−0.0703471	+	0.131429i
$721$	14.9633			0.557264
$722$	−44.6361	+	22.4599i	−1.66119	+	0.835872i
$723$	9.03895	+	9.03895i	0.336162	+	0.336162i
$724$	1.28321	+	8.66786i	0.0476903	+	0.322139i
$725$	−1.21215	+	1.21215i	−0.0450180	+	0.0450180i
$726$	−11.4474	−	3.78352i	−0.424852	−	0.140420i
$727$			34.6164i			1.28385i	0.766767	+	0.641926i	$0.221864\pi$
$727$			34.6164i			1.28385i	−0.766767	+	0.641926i	$0.778136\pi$
$728$	−1.25527	+	0.883254i	−0.0465235	+	0.0327356i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.90205	+	5.75481i	−0.0703979	+	0.212995i
$731$	5.05320	−	5.05320i	0.186900	−	0.186900i
$732$	12.9502	+	9.61030i	0.478654	+	0.355207i
$733$	15.2419	+	15.2419i	0.562972	+	0.562972i	0.930151	−	0.367178i	$-0.119676\pi$
$733$	15.2419	+	15.2419i	0.562972	+	0.562972i	−0.367178	+	0.930151i	$0.619676\pi$
$734$	15.9088	+	31.6166i	0.587204	+	1.16699i
$735$	−5.00000			−0.184428
$736$	−18.5820	−	19.5453i	−0.684941	−	0.720451i
$737$	12.4496			0.458585
$738$	4.66513	+	9.27133i	0.171726	+	0.341282i
$739$	2.53942	+	2.53942i	0.0934139	+	0.0934139i	0.752269	−	0.658856i	$-0.228959\pi$
$739$	2.53942	+	2.53942i	0.0934139	+	0.0934139i	−0.658856	+	0.752269i	$0.728959\pi$
$740$	12.0938	+	8.97474i	0.444576	+	0.329918i
$741$	2.00000	−	2.00000i	0.0734718	−	0.0734718i
$742$	8.47912	−	25.6543i	0.311278	−	0.941799i
$743$			2.48394i			0.0911268i	0.998961	+	0.0455634i	$0.0145083\pi$
$743$			2.48394i			0.0911268i	−0.998961	+	0.0455634i	$0.985492\pi$
$744$	−12.6220	−	17.9383i	−0.462745	−	0.657649i
$745$			12.3059i			0.450854i
$746$	14.2496	+	4.70971i	0.521716	+	0.172435i
$747$	−1.68212	+	1.68212i	−0.0615454	+	0.0615454i
$748$	0.343146	+	2.31788i	0.0125467	+	0.0847502i
$749$	−15.1917	−	15.1917i	−0.555094	−	0.555094i
$750$	−1.26330	+	0.635665i	−0.0461292	+	0.0232112i
$751$	4.96211			0.181070			0.0905349	−	0.995893i	$-0.471142\pi$
$751$	4.96211			0.181070			0.0905349	+	0.995893i	$0.471142\pi$
$752$	0.852194	+	2.81512i	0.0310763	+	0.102657i
$753$	−15.3974			−0.561113
$754$	−0.830979	+	0.418130i	−0.0302625	+	0.0152274i
$755$	−6.71604	−	6.71604i	−0.244422	−	0.244422i
$756$	2.79793	−	0.414214i	0.101760	−	0.0150648i
$757$	−10.3456	+	10.3456i	−0.376018	+	0.376018i	−0.869663	−	0.493645i	$-0.835664\pi$
$757$	−10.3456	+	10.3456i	−0.376018	+	0.376018i	0.493645	+	0.869663i	$0.335664\pi$
$758$	−44.6600	−	14.7608i	−1.62213	−	0.536136i
$759$		−	7.49992i		−	0.272230i
$760$	20.5401	+	3.57316i	0.745068	+	0.129612i
$761$			32.4957i			1.17797i	0.808144	+	0.588985i	$0.200472\pi$
$761$			32.4957i			1.17797i	−0.808144	+	0.588985i	$0.799528\pi$
$762$	6.54755	−	19.8102i	0.237193	−	0.717646i
$763$	2.08855	−	2.08855i	0.0756104	−	0.0756104i
$764$	−28.2038	+	38.0056i	−1.02038	+	1.37500i
$765$	−0.526602	−	0.526602i	−0.0190393	−	0.0190393i
$766$	2.57153	+	5.11058i	0.0929133	+	0.184653i
$767$	−0.880702			−0.0318003
$768$	−15.6890	−	3.13946i	−0.566127	−	0.113285i
$769$	−26.1220			−0.941983			−0.470991	−	0.882138i	$-0.656104\pi$
$769$	−26.1220			−0.941983			−0.470991	+	0.882138i	$0.656104\pi$
$770$	−1.41421	−	2.81056i	−0.0509647	−	0.101286i
$771$	16.6972	+	16.6972i	0.601337	+	0.601337i
$772$	−3.11904	+	4.20302i	−0.112257	+	0.151270i
$773$	15.8479	−	15.8479i	0.570010	−	0.570010i	−0.362121	−	0.932131i	$-0.617947\pi$
$773$	15.8479	−	15.8479i	0.570010	−	0.570010i	0.932131	+	0.362121i	$0.117947\pi$
$774$	−4.25870	+	12.8851i	−0.153076	+	0.463144i
$775$		−	7.75481i		−	0.278561i
$776$	47.2797	+	8.22478i	1.69724	+	0.295252i
$777$		−	10.6491i		−	0.382033i
$778$	−48.1832	−	15.9252i	−1.72745	−	0.570948i
$779$	38.2518	−	38.2518i	1.37051	−	1.37051i
$780$	−0.759164	+	0.112389i	−0.0271824	+	0.00402416i
$781$	−9.57060	−	9.57060i	−0.342463	−	0.342463i
$782$	4.48528	−	2.25689i	0.160393	−	0.0807064i
$783$	1.71423			0.0612617
$784$	−5.79471	−	19.1421i	−0.206954	−	0.683648i
$785$	15.3795			0.548919
$786$	22.6591	−	11.4016i	0.808225	−	0.406681i
$787$	14.3610	+	14.3610i	0.511915	+	0.511915i	0.915113	−	0.403198i	$-0.132101\pi$
$787$	14.3610	+	14.3610i	0.511915	+	0.511915i	−0.403198	+	0.915113i	$0.632101\pi$
$788$	2.13368	+	14.4126i	0.0760092	+	0.513427i
$789$	−0.263056	+	0.263056i	−0.00936505	+	0.00936505i
$790$	1.35973	+	0.449411i	0.0483771	+	0.0159893i
$791$			0.667884i			0.0237472i
$792$	−2.56052	−	3.63899i	−0.0909843	−	0.129306i
$793$			3.09404i			0.109872i
$794$	5.87484	−	17.7748i	0.208490	−	0.630805i
$795$	9.55274	−	9.55274i	0.338801	−	0.338801i
$796$	0.152108	+	0.112878i	0.00539131	+	0.00400087i
$797$	−11.1379	−	11.1379i	−0.394523	−	0.394523i	0.481773	−	0.876296i	$-0.339993\pi$
$797$	−11.1379	−	11.1379i	−0.394523	−	0.394523i	−0.876296	+	0.481773i	$0.839993\pi$
$798$	−6.62636	−	13.1690i	−0.234571	−	0.466178i
$799$	−0.547614			−0.0193732
$800$	−3.89769	−	4.09976i	−0.137804	−	0.144948i
$801$	10.3990			0.367432
$802$	−16.7550	−	33.2983i	−0.591639	−	1.17581i
$803$	−4.76744	−	4.76744i	−0.168239	−	0.168239i
$804$	−12.7101	−	9.43208i	−0.448249	−	0.332644i
$805$	−4.76744	+	4.76744i	−0.168030	+	0.168030i
$806$	1.32062	−	3.99564i	0.0465168	−	0.140741i
$807$			10.0490i			0.353743i
$808$	17.5122	−	12.3222i	0.616076	−	0.433493i
$809$			27.3981i			0.963266i	0.876373	+	0.481633i	$0.159956\pi$
$809$			27.3981i			0.963266i	−0.876373	+	0.481633i	$0.840044\pi$
$810$	1.34277	+	0.443806i	0.0471802	+	0.0155937i
$811$	−7.86957	+	7.86957i	−0.276338	+	0.276338i	−0.831645	−	0.555307i	$-0.812601\pi$
$811$	−7.86957	+	7.86957i	−0.276338	+	0.276338i	0.555307	+	0.831645i	$0.312601\pi$
$812$	0.710059	+	4.79631i	0.0249182	+	0.168317i
$813$	8.27979	+	8.27979i	0.290385	+	0.290385i
$814$	−14.9649	+	7.53003i	−0.524521	+	0.263927i
$815$	−15.6160			−0.547005
$816$	1.40576	−	2.62636i	0.0492113	−	0.0919410i
$817$	70.7320			2.47460
$818$	5.95888	−	2.99838i	0.208347	−	0.104836i
$819$	0.383719	+	0.383719i	0.0134082	+	0.0134082i
$820$	−14.5197	+	2.14953i	−0.507050	+	0.0750650i
$821$	13.3438	−	13.3438i	0.465702	−	0.465702i	−0.434817	−	0.900519i	$-0.643187\pi$
$821$	13.3438	−	13.3438i	0.465702	−	0.465702i	0.900519	+	0.434817i	$0.143187\pi$
$822$	2.14631	+	0.709387i	0.0748612	+	0.0247427i
$823$		−	12.9881i		−	0.452735i	−0.974042	−	0.226368i	$-0.927315\pi$
$823$		−	12.9881i		−	0.452735i	0.974042	−	0.226368i	$-0.0726851\pi$
$824$	−5.12901	+	29.4839i	−0.178678	+	1.02712i
$825$		−	1.57316i		−	0.0547702i
$826$	−1.44053	+	4.35846i	−0.0501226	+	0.151650i
$827$	−31.1830	+	31.1830i	−1.08434	+	1.08434i	−0.0882405	+	0.996099i	$0.528124\pi$
$827$	−31.1830	+	31.1830i	−1.08434	+	1.08434i	−0.996099	+	0.0882405i	$0.971876\pi$
$828$	−5.68212	+	7.65685i	−0.197467	+	0.266094i
$829$	34.0024	+	34.0024i	1.18095	+	1.18095i	0.979498	+	0.201455i	$0.0645670\pi$
$829$	34.0024	+	34.0024i	1.18095	+	1.18095i	0.201455	+	0.979498i	$0.435433\pi$
$830$	−1.51217	−	3.00523i	−0.0524881	−	0.104313i
$831$	11.0805			0.384377
$832$	−1.31010	−	2.77615i	−0.0454195	−	0.0962458i
$833$	3.72364			0.129016
$834$	−10.6552	−	21.1759i	−0.368961	−	0.733261i
$835$	3.54104	+	3.54104i	0.122543	+	0.122543i
$836$	−13.8206	+	18.6238i	−0.477997	+	0.644118i
$837$	−5.48348	+	5.48348i	−0.189537	+	0.189537i
$838$	4.37705	−	13.2431i	0.151203	−	0.457476i
$839$		−	23.3371i		−	0.805687i	−0.915269	−	0.402843i	$-0.868022\pi$
$839$		−	23.3371i		−	0.805687i	0.915269	−	0.402843i	$-0.131978\pi$
$840$	−0.685544	+	3.94082i	−0.0236535	+	0.135971i
$841$		−	26.0614i		−	0.898669i
$842$	20.6861	+	6.83705i	0.712889	+	0.235620i
$843$	−18.9848	+	18.9848i	−0.653872	+	0.653872i
$844$	−18.8078	+	2.78435i	−0.647390	+	0.0958413i
$845$	9.08827	+	9.08827i	0.312646	+	0.312646i
$846$	0.928932	−	0.467418i	0.0319373	−	0.0160702i
$847$	−12.0564			−0.414264
$848$	47.6430	+	25.5009i	1.63607	+	0.875704i
$849$	28.6981			0.984916
$850$	0.940816	−	0.473398i	0.0322697	−	0.0162374i
$851$	25.3844	+	25.3844i	0.870166	+	0.870166i
$852$	2.51995	+	17.0218i	0.0863321	+	0.583157i
$853$	7.81306	−	7.81306i	0.267514	−	0.267514i	−0.560584	−	0.828098i	$-0.689423\pi$
$853$	7.81306	−	7.81306i	0.267514	−	0.267514i	0.828098	+	0.560584i	$0.189423\pi$
$854$	15.3119	+	5.06081i	0.523963	+	0.173177i
$855$		−	7.37109i		−	0.252086i
$856$	35.1412	−	24.7266i	1.20110	−	0.845138i
$857$			3.95527i			0.135110i	0.997716	+	0.0675548i	$0.0215197\pi$
$857$			3.95527i			0.135110i	−0.997716	+	0.0675548i	$0.978480\pi$
$858$	0.267903	−	0.810564i	0.00914606	−	0.0276722i
$859$	−15.8814	+	15.8814i	−0.541865	+	0.541865i	−0.924075	−	0.382210i	$-0.875163\pi$
$859$	−15.8814	+	15.8814i	−0.541865	+	0.541865i	0.382210	+	0.924075i	$0.375163\pi$
$860$	−15.4117	−	11.4369i	−0.525533	−	0.389996i
$861$	7.33897	+	7.33897i	0.250111	+	0.250111i
$862$	13.9942	+	27.8116i	0.476644	+	0.947268i
$863$	−2.02165			−0.0688179			−0.0344089	−	0.999408i	$-0.510955\pi$
$863$	−2.02165			−0.0688179			−0.0344089	+	0.999408i	$0.510955\pi$
$864$	−0.142883	+	5.65505i	−0.00486098	+	0.192389i
$865$	−23.9880			−0.815618
$866$	1.52062	+	3.02204i	0.0516729	+	0.102693i
$867$	−11.6286	−	11.6286i	−0.394929	−	0.394929i
$868$	−17.6137	−	13.0711i	−0.597849	−	0.443661i
$869$	−1.12644	+	1.12644i	−0.0382118	+	0.0382118i
$870$	−0.760787	+	2.30182i	−0.0257931	+	0.0780392i
$871$		−	3.03666i		−	0.102893i
$872$	3.39939	+	4.83118i	0.115118	+	0.163604i
$873$		−	16.9670i		−	0.574244i
$874$	47.1866	+	15.5959i	1.59611	+	0.527538i
$875$	−1.00000	+	1.00000i	−0.0338062	+	0.0338062i
$876$	1.25527	+	8.47912i	0.0424117	+	0.286483i
$877$	3.82178	+	3.82178i	0.129052	+	0.129052i	0.768683	−	0.639630i	$-0.220913\pi$
$877$	3.82178	+	3.82178i	0.129052	+	0.129052i	−0.639630	+	0.768683i	$0.720913\pi$
$878$	5.57443	−	2.80493i	0.188128	−	0.0946618i
$879$	−31.4977			−1.06239
$880$	6.02271	−	1.82320i	0.203026	−	0.0614599i
$881$	38.0591			1.28224			0.641122	−	0.767439i	$-0.278469\pi$
$881$	38.0591			1.28224			0.641122	+	0.767439i	$0.278469\pi$
$882$	−6.31651	+	3.17833i	−0.212688	+	0.107020i
$883$	−7.33668	−	7.33668i	−0.246899	−	0.246899i	0.572798	−	0.819697i	$-0.305858\pi$
$883$	−7.33668	−	7.33668i	−0.246899	−	0.246899i	−0.819697	+	0.572798i	$0.805858\pi$
$884$	0.565371	−	0.0836990i	0.0190155	−	0.00281510i
$885$	−1.62293	+	1.62293i	−0.0545543	+	0.0545543i
$886$	37.8286	+	12.5029i	1.27088	+	0.420043i
$887$			17.3996i			0.584221i	0.956385	+	0.292111i	$0.0943575\pi$
$887$			17.3996i			0.584221i	−0.956385	+	0.292111i	$0.905642\pi$
$888$	20.9830	+	3.65020i	0.704144	+	0.122493i
$889$		−	20.8642i		−	0.699761i
$890$	−4.61515	+	13.9635i	−0.154700	+	0.468058i
$891$	−1.11239	+	1.11239i	−0.0372664	+	0.0372664i
$892$	25.5167	−	34.3846i	0.854361	−	1.15128i
$893$	−3.83260	−	3.83260i	−0.128253	−	0.128253i
$894$	7.82245	+	15.5461i	0.261622	+	0.519939i
$895$	−3.59842			−0.120282
$896$	−15.8816	+	1.94262i	−0.530568	+	0.0648984i
$897$	−1.82936			−0.0610805
$898$	−21.6610	−	43.0483i	−0.722835	−	1.43654i
$899$	−9.39996	−	9.39996i	−0.313506	−	0.313506i
$900$	−1.19186	+	1.60607i	−0.0397287	+	0.0535358i
$901$	−7.11419	+	7.11419i	−0.237008	+	0.237008i
$902$	5.12389	−	15.5028i	0.170607	−	0.516185i
$903$			13.5706i			0.451601i
$904$	−1.31600	−	0.228932i	−0.0437696	−	0.00761416i
$905$			4.38117i			0.145635i
$906$	−12.7535	−	4.21523i	−0.423708	−	0.140042i
$907$	25.1454	−	25.1454i	0.834938	−	0.834938i	−0.153250	−	0.988188i	$-0.548974\pi$
$907$	25.1454	−	25.1454i	0.834938	−	0.834938i	0.988188	+	0.153250i	$0.0489738\pi$
$908$	30.3536	−	4.49363i	1.00732	−	0.149126i
$909$	−5.35322	−	5.35322i	−0.177555	−	0.177555i
$910$	−0.685544	+	0.344951i	−0.0227256	+	0.0114350i
$911$	−38.8402			−1.28683			−0.643417	−	0.765516i	$-0.722484\pi$
$911$	−38.8402			−1.28683			−0.643417	+	0.765516i	$0.722484\pi$
$912$	28.2197	−	8.54266i	0.934447	−	0.282876i
$913$	3.74234			0.123853
$914$	−19.1872	+	9.65456i	−0.634655	+	0.319344i
$915$	5.70160	+	5.70160i	0.188489	+	0.188489i
$916$	8.38049	+	56.6086i	0.276899	+	1.87040i
$917$	17.9365	−	17.9365i	0.592314	−	0.592314i
$918$	−1.00000	−	0.330515i	−0.0330049	−	0.0109086i
$919$			7.49146i			0.247121i	0.992337	+	0.123560i	$0.0394312\pi$
$919$			7.49146i			0.247121i	−0.992337	+	0.123560i	$0.960569\pi$
$920$	−7.75965	−	11.0279i	−0.255828	−	0.363580i
$921$		−	25.4201i		−	0.837621i
$922$	7.79489	−	23.5841i	0.256711	−	0.776701i
$923$	−2.33443	+	2.33443i	−0.0768387	+	0.0768387i
$924$	−3.57316	−	2.65162i	−0.117548	−	0.0872320i
$925$	5.32453	+	5.32453i	0.175070	+	0.175070i
$926$	−12.5678	−	24.9768i	−0.413003	−	0.820789i
$927$	10.5807			0.347515
$928$	−9.69408	−	0.244935i	−0.318224	−	0.00804039i
$929$	−1.01974			−0.0334567			−0.0167284	−	0.999860i	$-0.505325\pi$
$929$	−1.01974			−0.0334567			−0.0167284	+	0.999860i	$0.505325\pi$
$930$	−4.92946	−	9.79666i	−0.161643	−	0.321245i
$931$	26.0607	+	26.0607i	0.854106	+	0.854106i
$932$	25.3836	+	18.8371i	0.831469	+	0.617029i
$933$	−8.02956	+	8.02956i	−0.262876	+	0.262876i
$934$	4.11906	−	12.4626i	0.134780	−	0.407788i
$935$			1.17157i			0.0383145i
$936$	−0.887611	+	0.624555i	−0.0290125	+	0.0204142i
$937$		−	23.4440i		−	0.765883i	−0.923773	−	0.382942i	$-0.874911\pi$
$937$		−	23.4440i		−	0.765883i	0.923773	−	0.382942i	$-0.125089\pi$
$938$	−15.0279	−	4.96695i	−0.490680	−	0.162177i
$939$	−8.27476	+	8.27476i	−0.270037	+	0.270037i
$940$	0.215371	+	1.45479i	0.00702461	+	0.0474499i
$941$	−5.81324	−	5.81324i	−0.189506	−	0.189506i	0.605976	−	0.795483i	$-0.292783\pi$
$941$	−5.81324	−	5.81324i	−0.189506	−	0.189506i	−0.795483	+	0.605976i	$0.792783\pi$
$942$	19.4290	−	9.77624i	0.633031	−	0.318527i
$943$	−34.9881			−1.13937
$944$	−8.09416	−	4.33239i	−0.263443	−	0.141007i
$945$	1.41421			0.0460044
$946$	19.0705	−	9.59587i	0.620036	−	0.311988i
$947$	−12.9757	−	12.9757i	−0.421653	−	0.421653i	0.464120	−	0.885772i	$-0.346371\pi$
$947$	−12.9757	−	12.9757i	−0.421653	−	0.421653i	−0.885772	+	0.464120i	$0.846371\pi$
$948$	2.00343	−	0.296593i	0.0650683	−	0.00963289i
$949$	−1.16286	+	1.16286i	−0.0377480	+	0.0377480i
$950$	9.89769	+	3.27133i	0.321123	+	0.106136i
$951$			18.0775i			0.586204i
$952$	0.510544	−	2.93484i	0.0165468	−	0.0951186i
$953$		−	10.3704i		−	0.335932i	−0.985793	−	0.167966i	$-0.946280\pi$
$953$		−	10.3704i		−	0.335932i	0.985793	−	0.167966i	$-0.0537198\pi$
$954$	5.99564	−	18.1403i	0.194116	−	0.587315i
$955$	−16.7328	+	16.7328i	−0.541460	+	0.541460i
$956$	−15.1185	+	20.3727i	−0.488967	+	0.658901i
$957$	−1.90689	−	1.90689i	−0.0616411	−	0.0616411i
$958$	14.6121	+	29.0396i	0.472096	+	0.938228i
$959$	2.26050			0.0729955
$960$	−7.53003	−	2.70160i	−0.243031	−	0.0871938i
$961$	29.1370			0.939904
$962$	1.83670	+	3.65020i	0.0592176	+	0.117687i
$963$	−10.7422	−	10.7422i	−0.346162	−	0.346162i
$964$	−15.2355	+	20.5304i	−0.490704	+	0.661241i
$965$	−1.85047	+	1.85047i	−0.0595686	+	0.0595686i
$966$	−2.99222	+	9.05320i	−0.0962730	+	0.291282i
$967$		−	50.7669i		−	1.63255i	−0.577661	−	0.816277i	$-0.696035\pi$
$967$		−	50.7669i		−	1.63255i	0.577661	−	0.816277i	$-0.303965\pi$
$968$	4.13261	−	23.7561i	0.132827	−	0.763549i
$969$			5.48946i			0.176347i
$970$	22.7827	+	7.53003i	0.731510	+	0.241775i
$971$	−8.66742	+	8.66742i	−0.278151	+	0.278151i	−0.832370	−	0.554220i	$-0.813017\pi$
$971$	−8.66742	+	8.66742i	−0.278151	+	0.278151i	0.554220	+	0.832370i	$0.313017\pi$
$972$	1.97844	−	0.292893i	0.0634584	−	0.00939455i
$973$	−16.7623	−	16.7623i	−0.537376	−	0.537376i
$974$	15.2998	−	7.69852i	0.490237	−	0.246677i
$975$	−0.383719			−0.0122888
$976$	−15.2203	+	28.4360i	−0.487191	+	0.910214i
$977$	2.79339			0.0893686			0.0446843	−	0.999001i	$-0.485772\pi$
$977$	2.79339			0.0893686			0.0446843	+	0.999001i	$0.485772\pi$
$978$	−19.7277	+	9.92656i	−0.630824	+	0.317416i
$979$	−11.5678	−	11.5678i	−0.369707	−	0.369707i
$980$	−1.46447	−	9.89219i	−0.0467807	−	0.315994i
$981$	1.47682	−	1.47682i	0.0471514	−	0.0471514i
$982$	−24.6020	−	8.13131i	−0.785080	−	0.259481i
$983$		−	39.4811i		−	1.25925i	−0.776898	−	0.629626i	$-0.783208\pi$
$983$		−	39.4811i		−	1.25925i	0.776898	−	0.629626i	$-0.216792\pi$
$984$	−16.9764	+	11.9452i	−0.541187	+	0.380798i
$985$			7.28484i			0.232114i
$986$	0.566579	−	1.71423i	0.0180436	−	0.0545923i
$987$	0.735321	−	0.735321i	0.0234055	−	0.0234055i
$988$	4.54266	+	3.37109i	0.144521	+	0.107249i
$989$	−32.3485	−	32.3485i	−1.02862	−	1.02862i
$990$	−1.00000	−	1.98737i	−0.0317821	−	0.0631627i
$991$	−32.7708			−1.04100			−0.520499	−	0.853862i	$-0.674254\pi$
$991$	−32.7708			−1.04100			−0.520499	+	0.853862i	$0.674254\pi$
$992$	31.7928	−	30.2258i	1.00942	−	0.959671i
$993$	19.9086			0.631782
$994$	7.73439	+	15.3711i	0.245320	+	0.487541i
$995$	0.0669685	+	0.0669685i	0.00212305	+	0.00212305i
$996$	−3.82064	−	2.83528i	−0.121062	−	0.0898393i
$997$	−21.7103	+	21.7103i	−0.687571	+	0.687571i	−0.961694	−	0.274124i	$-0.911612\pi$
$997$	−21.7103	+	21.7103i	−0.687571	+	0.687571i	0.274124	+	0.961694i	$0.411612\pi$
$998$	12.3860	−	37.4749i	0.392072	−	1.18625i
$999$		−	7.53003i		−	0.238240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.b.61.3	✓	8
3.2	odd	2		720.2.t.b.541.2		8
4.3	odd	2		960.2.s.b.721.1		8
8.3	odd	2		1920.2.s.d.1441.4		8
8.5	even	2		1920.2.s.c.1441.1		8
12.11	even	2		2880.2.t.b.721.4		8
16.3	odd	4		1920.2.s.d.481.4		8
16.5	even	4	inner	240.2.s.b.181.3	yes	8
16.11	odd	4		960.2.s.b.241.1		8
16.13	even	4		1920.2.s.c.481.1		8
48.5	odd	4		720.2.t.b.181.2		8
48.11	even	4		2880.2.t.b.2161.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.b.61.3	✓	8	1.1	even	1	trivial
240.2.s.b.181.3	yes	8	16.5	even	4	inner
720.2.t.b.181.2		8	48.5	odd	4
720.2.t.b.541.2		8	3.2	odd	2
960.2.s.b.241.1		8	16.11	odd	4
960.2.s.b.721.1		8	4.3	odd	2
1920.2.s.c.481.1		8	16.13	even	4
1920.2.s.c.1441.1		8	8.5	even	2
1920.2.s.d.481.4		8	16.3	odd	4
1920.2.s.d.1441.4		8	8.3	odd	2
2880.2.t.b.721.4		8	12.11	even	2
2880.2.t.b.2161.4		8	48.11	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.635665 + 1.26330i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.443806 + 1.34277i) q^{6} +1.41421i q^{7} +(-2.78658 - 0.484753i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.635665 + 1.26330i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.443806 + 1.34277i) q^{6} +1.41421i q^{7} +(-2.78658 - 0.484753i) q^{8} +1.00000i q^{9} +(-1.34277 - 0.443806i) q^{10} +(1.11239 - 1.11239i) q^{11} +(-1.97844 + 0.292893i) q^{12} +(-0.271330 - 0.271330i) q^{13} +(-1.78658 + 0.898966i) q^{14} -1.00000 q^{15} +(-1.15894 - 3.82843i) q^{16} +0.744728 q^{17} +(-1.26330 + 0.635665i) q^{18} +(5.21215 + 5.21215i) q^{19} +(-0.292893 - 1.97844i) q^{20} +(-1.00000 + 1.00000i) q^{21} +(2.11239 + 0.698175i) q^{22} -4.76744i q^{23} +(-1.62764 - 2.31318i) q^{24} -1.00000i q^{25} +(0.170297 - 0.515247i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.27133 - 1.68554i) q^{28} +(-1.21215 - 1.21215i) q^{29} +(-0.635665 - 1.26330i) q^{30} +7.75481 q^{31} +(4.09976 - 3.89769i) q^{32} +1.57316 q^{33} +(0.473398 + 0.940816i) q^{34} +(-1.00000 - 1.00000i) q^{35} +(-1.60607 - 1.19186i) q^{36} +(-5.32453 + 5.32453i) q^{37} +(-3.27133 + 9.89769i) q^{38} -0.383719i q^{39} +(2.31318 - 1.62764i) q^{40} -7.33897i q^{41} +(-1.89897 - 0.627636i) q^{42} +(6.78530 - 6.78530i) q^{43} +(0.460766 + 3.11239i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(6.02271 - 3.03049i) q^{46} -0.735321 q^{47} +(1.88761 - 3.52660i) q^{48} +5.00000 q^{49} +(1.26330 - 0.635665i) q^{50} +(0.526602 + 0.526602i) q^{51} +(0.759164 - 0.112389i) q^{52} +(-9.55274 + 9.55274i) q^{53} +(-1.34277 - 0.443806i) q^{54} +1.57316i q^{55} +(0.685544 - 3.94082i) q^{56} +7.37109i q^{57} +(0.760787 - 2.30182i) q^{58} +(1.62293 - 1.62293i) q^{59} +(1.19186 - 1.60607i) q^{60} +(-5.70160 - 5.70160i) q^{61} +(4.92946 + 9.79666i) q^{62} -1.41421 q^{63} +(7.53003 + 2.70160i) q^{64} +0.383719 q^{65} +(1.00000 + 1.98737i) q^{66} +(5.59587 + 5.59587i) q^{67} +(-0.887611 + 1.19609i) q^{68} +(3.37109 - 3.37109i) q^{69} +(0.627636 - 1.89897i) q^{70} -8.60365i q^{71} +(0.484753 - 2.78658i) q^{72} -4.28577i q^{73} +(-10.1111 - 3.34187i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-14.5832 + 2.15894i) q^{76} +(1.57316 + 1.57316i) q^{77} +(0.484753 - 0.243917i) q^{78} -1.01263 q^{79} +(3.52660 + 1.88761i) q^{80} -1.00000 q^{81} +(9.27133 - 4.66513i) q^{82} +(1.68212 + 1.68212i) q^{83} +(-0.414214 - 2.79793i) q^{84} +(-0.526602 + 0.526602i) q^{85} +(12.8851 + 4.25870i) q^{86} -1.71423i q^{87} +(-3.63899 + 2.56052i) q^{88} -10.3990i q^{89} +(0.443806 - 1.34277i) q^{90} +(0.383719 - 0.383719i) q^{91} +(7.65685 + 5.68212i) q^{92} +(5.48348 + 5.48348i) q^{93} +(-0.467418 - 0.928932i) q^{94} -7.37109 q^{95} +(5.65505 + 0.142883i) q^{96} -16.9670 q^{97} +(3.17833 + 6.31651i) q^{98} +(1.11239 + 1.11239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8	\( 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} + 8 q^{17} - 4 q^{18} + 8 q^{19} - 8 q^{20} - 8 q^{21} + 16 q^{22} - 12 q^{24} - 20 q^{26} - 8 q^{28} + 24 q^{29} + 8 q^{31} - 8 q^{33} + 16 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{37} - 16 q^{38} - 4 q^{40} - 4 q^{42} - 16 q^{44} + 24 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 16 q^{56} + 8 q^{59} + 4 q^{60} - 16 q^{61} + 28 q^{62} + 8 q^{64} - 8 q^{65} + 8 q^{66} - 8 q^{68} - 16 q^{69} + 4 q^{70} + 4 q^{72} - 36 q^{74} - 40 q^{76} - 8 q^{77} + 4 q^{78} - 40 q^{79} + 16 q^{80} - 8 q^{81} + 64 q^{82} + 32 q^{83} + 8 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{88} + 4 q^{90} - 8 q^{91} + 16 q^{92} + 32 q^{94} - 16 q^{95} + 24 q^{96} - 48 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 8 * q^15 + 8 * q^17 - 4 * q^18 + 8 * q^19 - 8 * q^20 - 8 * q^21 + 16 * q^22 - 12 * q^24 - 20 * q^26 - 8 * q^28 + 24 * q^29 + 8 * q^31 - 8 * q^33 + 16 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^37 - 16 * q^38 - 4 * q^40 - 4 * q^42 - 16 * q^44 + 24 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 16 * q^56 + 8 * q^59 + 4 * q^60 - 16 * q^61 + 28 * q^62 + 8 * q^64 - 8 * q^65 + 8 * q^66 - 8 * q^68 - 16 * q^69 + 4 * q^70 + 4 * q^72 - 36 * q^74 - 40 * q^76 - 8 * q^77 + 4 * q^78 - 40 * q^79 + 16 * q^80 - 8 * q^81 + 64 * q^82 + 32 * q^83 + 8 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^88 + 4 * q^90 - 8 * q^91 + 16 * q^92 + 32 * q^94 - 16 * q^95 + 24 * q^96 - 48 * q^97 + 8 * q^99

Introduction

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