LMFDB - Embedded newform 950.2.u.a.899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			899.2
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	950.899
Dual form			950.2.u.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.76604 + 0.642788i) q^{6} +(-0.300767 - 0.173648i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.407604 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.76604 + 0.642788i) q^{6} +(-0.300767 - 0.173648i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.407604 - 0.342020i) q^{9} +(2.97178 + 5.14728i) q^{11} +(-1.62760 - 0.939693i) q^{12} +(1.12554 + 3.09240i) q^{13} +(-0.0603074 - 0.342020i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-3.55596 - 4.23783i) q^{17} -0.532089i q^{18} +(4.11721 + 1.43128i) q^{19} +(0.500000 - 0.419550i) q^{21} +(-2.03282 + 5.58512i) q^{22} +(-2.79439 - 0.492726i) q^{23} +(-0.326352 - 1.85083i) q^{24} +(-1.64543 + 2.84997i) q^{26} +(-4.01676 + 2.31908i) q^{27} +(0.223238 - 0.266044i) q^{28} +(-5.46064 - 4.58202i) q^{29} +(-1.52094 + 2.63435i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-11.0005 + 1.93969i) q^{33} +(0.960637 - 5.44804i) q^{34} +(0.407604 - 0.342020i) q^{36} -1.82295i q^{37} +(1.55007 + 4.07398i) q^{38} -6.18479 q^{39} +(6.41147 + 2.33359i) q^{41} +(0.642788 + 0.113341i) q^{42} +(-0.524005 + 0.0923963i) q^{43} +(-5.58512 + 2.03282i) q^{44} +(-1.41875 - 2.45734i) q^{46} +(-2.99070 + 3.56418i) q^{47} +(1.20805 - 1.43969i) q^{48} +(-3.43969 - 5.95772i) q^{49} +(9.76991 - 3.55596i) q^{51} +(-3.24086 + 0.571452i) q^{52} +(3.05888 + 0.539363i) q^{53} +(-4.35844 - 1.58634i) q^{54} +0.347296 q^{56} +(-5.17420 + 6.35117i) q^{57} -7.12836i q^{58} +(2.10741 - 1.76833i) q^{59} +(-2.14156 + 12.1454i) q^{61} +(-2.99568 + 0.528218i) q^{62} +(0.0632028 + 0.173648i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-8.55690 - 7.18009i) q^{66} +(3.24086 - 3.86231i) q^{67} +(4.79093 - 2.76604i) q^{68} +(2.66637 - 4.61830i) q^{69} +(-2.26991 - 12.8733i) q^{71} +(0.524005 + 0.0923963i) q^{72} +(-0.752219 + 2.06670i) q^{73} +(1.39646 - 1.17177i) q^{74} +(-2.12449 + 3.80612i) q^{76} -2.06418i q^{77} +(-3.97551 - 4.73783i) q^{78} +(-0.939693 - 0.342020i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(2.33359 + 6.41147i) q^{82} +(8.10170 + 4.67752i) q^{83} +(0.326352 + 0.565258i) q^{84} +(-0.407604 - 0.342020i) q^{86} +(11.6021 - 6.69846i) q^{87} +(-5.14728 - 2.97178i) q^{88} +(10.6493 - 3.87603i) q^{89} +(0.198463 - 1.12554i) q^{91} +(0.970481 - 2.66637i) q^{92} +(-3.67474 - 4.37939i) q^{93} -4.65270 q^{94} +1.87939 q^{96} +(-3.67799 - 4.38326i) q^{97} +(2.35289 - 6.46451i) q^{98} +(0.549163 - 3.11446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^6 - 12 * q^9	$ 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) $ 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	−0.642788	+	1.76604i	−0.371114	+	1.01963i	0.603818	+	0.797122i	$0.293645\pi$
$3$	−0.642788	+	1.76604i	−0.371114	+	1.01963i	−0.974932	+	0.222504i	$0.928577\pi$
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	−1.76604	+	0.642788i	−0.720985	+	0.262417i
$7$	−0.300767	−	0.173648i	−0.113679	−	0.0656328i	0.442082	−	0.896975i	$-0.354240\pi$
$7$	−0.300767	−	0.173648i	−0.113679	−	0.0656328i	−0.555762	+	0.831342i	$0.687573\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.407604	−	0.342020i	−0.135868	−	0.114007i
$10$		0			0
$11$	2.97178	+	5.14728i	0.896026	+	1.55196i	0.832530	+	0.553980i	$0.186892\pi$
$11$	2.97178	+	5.14728i	0.896026	+	1.55196i	0.0634960	+	0.997982i	$0.479775\pi$
$12$	−1.62760	−	0.939693i	−0.469846	−	0.271266i
$13$	1.12554	+	3.09240i	0.312169	+	0.857676i	0.992218	+	0.124510i	$0.0397360\pi$
$13$	1.12554	+	3.09240i	0.312169	+	0.857676i	−0.680050	+	0.733166i	$0.738042\pi$
$14$	−0.0603074	−	0.342020i	−0.0161178	−	0.0914087i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.55596	−	4.23783i	−0.862447	−	1.02782i	−0.999307	−	0.0372334i	$-0.988146\pi$
$17$	−3.55596	−	4.23783i	−0.862447	−	1.02782i	0.136860	−	0.990590i	$-0.456299\pi$
$18$		−	0.532089i		−	0.125415i
$19$	4.11721	+	1.43128i	0.944553	+	0.328359i
$19$	4.11721	+	1.43128i	0.944553	+	0.328359i
$20$		0			0
$21$	0.500000	−	0.419550i	0.109109	−	0.0915533i
$22$	−2.03282	+	5.58512i	−0.433398	+	1.19075i
$23$	−2.79439	−	0.492726i	−0.582670	−	0.102740i	−0.125459	−	0.992099i	$-0.540040\pi$
$23$	−2.79439	−	0.492726i	−0.582670	−	0.102740i	−0.457211	+	0.889358i	$0.651152\pi$
$24$	−0.326352	−	1.85083i	−0.0666163	−	0.377800i
$25$		0			0
$26$	−1.64543	+	2.84997i	−0.322695	+	0.558925i
$27$	−4.01676	+	2.31908i	−0.773026	+	0.446307i
$28$	0.223238	−	0.266044i	0.0421880	−	0.0502777i
$29$	−5.46064	−	4.58202i	−1.01401	−	0.850859i	−0.0251512	−	0.999684i	$-0.508007\pi$
$29$	−5.46064	−	4.58202i	−1.01401	−	0.850859i	−0.988864	+	0.148824i	$0.952451\pi$
$30$		0			0
$31$	−1.52094	+	2.63435i	−0.273170	+	0.473144i	−0.969672	−	0.244411i	$-0.921405\pi$
$31$	−1.52094	+	2.63435i	−0.273170	+	0.473144i	0.696502	+	0.717555i	$0.254739\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	−11.0005	+	1.93969i	−1.91495	+	0.337657i
$34$	0.960637	−	5.44804i	0.164748	−	0.934332i
$35$		0			0
$36$	0.407604	−	0.342020i	0.0679340	−	0.0570034i
$37$		−	1.82295i		−	0.299691i	−0.988709	−	0.149845i	$-0.952122\pi$
$37$		−	1.82295i		−	0.299691i	0.988709	−	0.149845i	$-0.0478776\pi$
$38$	1.55007	+	4.07398i	0.251454	+	0.660886i
$39$	−6.18479			−0.990359
$40$		0			0
$41$	6.41147	+	2.33359i	1.00130	+	0.364445i	0.790087	−	0.612994i	$-0.210035\pi$
$41$	6.41147	+	2.33359i	1.00130	+	0.364445i	0.211217	+	0.977439i	$0.432257\pi$
$42$	0.642788	+	0.113341i	0.0991843	+	0.0174889i
$43$	−0.524005	+	0.0923963i	−0.0799101	+	0.0140903i	−0.213460	−	0.976952i	$-0.568473\pi$
$43$	−0.524005	+	0.0923963i	−0.0799101	+	0.0140903i	0.133550	+	0.991042i	$0.457362\pi$
$44$	−5.58512	+	2.03282i	−0.841989	+	0.306459i
$45$		0			0
$46$	−1.41875	−	2.45734i	−0.209183	−	0.362316i
$47$	−2.99070	+	3.56418i	−0.436238	+	0.519889i	−0.938711	−	0.344704i	$-0.887979\pi$
$47$	−2.99070	+	3.56418i	−0.436238	+	0.519889i	0.502473	+	0.864593i	$0.332424\pi$
$48$	1.20805	−	1.43969i	0.174366	−	0.207802i
$49$	−3.43969	−	5.95772i	−0.491385	−	0.851103i
$50$		0			0
$51$	9.76991	−	3.55596i	1.36806	−	0.497934i
$52$	−3.24086	+	0.571452i	−0.449427	+	0.0792461i
$53$	3.05888	+	0.539363i	0.420169	+	0.0740872i	0.379736	−	0.925095i	$-0.376015\pi$
$53$	3.05888	+	0.539363i	0.420169	+	0.0740872i	0.0404337	+	0.999182i	$0.487126\pi$
$54$	−4.35844	−	1.58634i	−0.593109	−	0.215874i
$55$		0			0
$56$	0.347296			0.0464094
$57$	−5.17420	+	6.35117i	−0.685340	+	0.841233i
$58$		−	7.12836i		−	0.935999i
$59$	2.10741	−	1.76833i	0.274362	−	0.230217i	−0.495216	−	0.868770i	$-0.664911\pi$
$59$	2.10741	−	1.76833i	0.274362	−	0.230217i	0.769578	+	0.638553i	$0.220467\pi$
$60$		0			0
$61$	−2.14156	+	12.1454i	−0.274199	+	1.55506i	0.467297	+	0.884100i	$0.345228\pi$
$61$	−2.14156	+	12.1454i	−0.274199	+	1.55506i	−0.741496	+	0.670957i	$0.765883\pi$
$62$	−2.99568	+	0.528218i	−0.380451	+	0.0670838i
$63$	0.0632028	+	0.173648i	0.00796280	+	0.0218776i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−8.55690	−	7.18009i	−1.05328	−	0.883809i
$67$	3.24086	−	3.86231i	0.395935	−	0.471856i	−0.530841	−	0.847471i	$-0.678124\pi$
$67$	3.24086	−	3.86231i	0.395935	−	0.471856i	0.926776	+	0.375615i	$0.122568\pi$
$68$	4.79093	−	2.76604i	0.580986	−	0.335432i
$69$	2.66637	−	4.61830i	0.320994	−	0.555977i
$70$		0			0
$71$	−2.26991	−	12.8733i	−0.269389	−	1.52778i	−0.756238	−	0.654297i	$-0.772965\pi$
$71$	−2.26991	−	12.8733i	−0.269389	−	1.52778i	0.486849	−	0.873486i	$-0.338146\pi$
$72$	0.524005	+	0.0923963i	0.0617546	+	0.0108890i
$73$	−0.752219	+	2.06670i	−0.0880405	+	0.241889i	−0.975897	−	0.218231i	$-0.929971\pi$
$73$	−0.752219	+	2.06670i	−0.0880405	+	0.241889i	0.887857	+	0.460120i	$0.152194\pi$
$74$	1.39646	−	1.17177i	0.162335	−	0.136215i
$75$		0			0
$76$	−2.12449	+	3.80612i	−0.243695	+	0.436592i
$77$		−	2.06418i		−	0.235235i
$78$	−3.97551	−	4.73783i	−0.450138	−	0.536453i
$79$	−0.939693	−	0.342020i	−0.105724	−	0.0384803i	0.288617	−	0.957445i	$-0.406805\pi$
$79$	−0.939693	−	0.342020i	−0.105724	−	0.0384803i	−0.394340	+	0.918964i	$0.629027\pi$
$80$		0			0
$81$	−1.79086	−	10.1565i	−0.198984	−	1.12850i
$82$	2.33359	+	6.41147i	0.257701	+	0.708029i
$83$	8.10170	+	4.67752i	0.889277	+	0.513424i	0.873706	−	0.486454i	$-0.161710\pi$
$83$	8.10170	+	4.67752i	0.889277	+	0.513424i	0.0155711	+	0.999879i	$0.495043\pi$
$84$	0.326352	+	0.565258i	0.0356079	+	0.0616747i
$85$		0			0
$86$	−0.407604	−	0.342020i	−0.0439530	−	0.0368810i
$87$	11.6021	−	6.69846i	1.24387	−	0.718151i
$88$	−5.14728	−	2.97178i	−0.548702	−	0.316793i
$89$	10.6493	−	3.87603i	1.12882	−	0.410858i	0.290959	−	0.956736i	$-0.406026\pi$
$89$	10.6493	−	3.87603i	1.12882	−	0.410858i	0.837865	+	0.545877i	$0.183804\pi$
$90$		0			0
$91$	0.198463	−	1.12554i	0.0208046	−	0.117989i
$92$	0.970481	−	2.66637i	0.101180	−	0.277989i
$93$	−3.67474	−	4.37939i	−0.381053	−	0.454121i
$94$	−4.65270			−0.479890
$95$		0			0
$96$	1.87939			0.191814
$97$	−3.67799	−	4.38326i	−0.373443	−	0.445052i	0.546290	−	0.837596i	$-0.316040\pi$
$97$	−3.67799	−	4.38326i	−0.373443	−	0.445052i	−0.919733	+	0.392544i	$0.871595\pi$
$98$	2.35289	−	6.46451i	0.237678	−	0.653014i
$99$	0.549163	−	3.11446i	0.0551930	−	0.313015i
$100$		0			0
$101$	−4.45336	+	1.62089i	−0.443126	+	0.161285i	−0.553940	−	0.832556i	$-0.686876\pi$
$101$	−4.45336	+	1.62089i	−0.443126	+	0.161285i	0.110814	+	0.993841i	$0.464654\pi$
$102$	9.00400	+	5.19846i	0.891529	+	0.514725i
$103$	2.74551	−	1.58512i	0.270523	−	0.156187i	−0.358602	−	0.933491i	$-0.616747\pi$
$103$	2.74551	−	1.58512i	0.270523	−	0.156187i	0.629125	+	0.777304i	$0.283413\pi$
$104$	−2.52094	−	2.11532i	−0.247199	−	0.207425i
$105$		0			0
$106$	1.55303	+	2.68993i	0.150844	+	0.261269i
$107$	11.6021	+	6.69846i	1.12162	+	0.647565i	0.941813	−	0.336138i	$-0.109121\pi$
$107$	11.6021	+	6.69846i	1.12162	+	0.647565i	0.179802	+	0.983703i	$0.442454\pi$
$108$	−1.58634	−	4.35844i	−0.152646	−	0.419391i
$109$	2.37551	+	13.4722i	0.227533	+	1.29040i	0.857783	+	0.514012i	$0.171841\pi$
$109$	2.37551	+	13.4722i	0.227533	+	1.29040i	−0.630250	+	0.776392i	$0.717048\pi$
$110$		0			0
$111$	3.21941	+	1.17177i	0.305573	+	0.111219i
$112$	0.223238	+	0.266044i	0.0210940	+	0.0251388i
$113$			13.5202i			1.27188i	0.771740	+	0.635938i	$0.219387\pi$
$113$			13.5202i			1.27188i	−0.771740	+	0.635938i	$0.780613\pi$
$114$	−8.19119	+	0.118782i	−0.767175	+	0.0111250i
$115$		0			0
$116$	5.46064	−	4.58202i	0.507007	−	0.425430i
$117$	0.598887	−	1.64543i	0.0553672	−	0.152120i
$118$	2.70924	+	0.477711i	0.249405	+	0.0439769i
$119$	0.333626	+	1.89209i	0.0305834	+	0.173447i
$120$		0			0
$121$	−12.1630	+	21.0669i	−1.10572	+	1.91517i
$122$	−10.6805	+	6.16637i	−0.966965	+	0.558277i
$123$	−8.24243	+	9.82295i	−0.743195	+	0.885705i
$124$	−2.33022	−	1.95529i	−0.209260	−	0.175590i
$125$		0			0
$126$	−0.0923963	+	0.160035i	−0.00823131	+	0.0142571i
$127$	6.61311	+	18.1694i	0.586819	+	1.61227i	0.776284	+	0.630383i	$0.217102\pi$
$127$	6.61311	+	18.1694i	0.586819	+	1.61227i	−0.189466	+	0.981887i	$0.560676\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	0.173648	−	0.984808i	0.0152889	−	0.0867075i
$130$		0			0
$131$	13.0817	−	10.9769i	1.14296	−	0.959053i	0.143424	−	0.989661i	$-0.454189\pi$
$131$	13.0817	−	10.9769i	1.14296	−	0.959053i	0.999531	+	0.0306082i	$0.00974442\pi$
$132$		−	11.1702i		−	0.972245i
$133$	−0.989783	−	1.14543i	−0.0858251	−	0.0993213i
$134$	5.04189			0.435553
$135$		0			0
$136$	5.19846	+	1.89209i	0.445765	+	0.162245i
$137$	−15.1218	−	2.66637i	−1.29194	−	0.227804i	−0.514897	−	0.857252i	$-0.672170\pi$
$137$	−15.1218	−	2.66637i	−1.29194	−	0.227804i	−0.777042	+	0.629448i	$0.783281\pi$
$138$	5.25173	−	0.926022i	0.447057	−	0.0788282i
$139$	4.84477	−	1.76335i	0.410928	−	0.149566i	−0.128280	−	0.991738i	$-0.540946\pi$
$139$	4.84477	−	1.76335i	0.410928	−	0.149566i	0.539208	+	0.842172i	$0.318724\pi$
$140$		0			0
$141$	−4.37211	−	7.57272i	−0.368198	−	0.637738i
$142$	8.40247	−	10.0137i	0.705119	−	0.840329i
$143$	−12.5726	+	14.9834i	−1.05137	+	1.25297i
$144$	0.266044	+	0.460802i	0.0221704	+	0.0384002i
$145$		0			0
$146$	−2.06670	+	0.752219i	−0.171042	+	0.0622541i
$147$	12.7326	−	2.24510i	1.05017	−	0.185173i
$148$	1.79525	+	0.316552i	0.147569	+	0.0260204i
$149$	10.9829	+	3.99746i	0.899756	+	0.327485i	0.750155	−	0.661262i	$-0.229979\pi$
$149$	10.9829	+	3.99746i	0.899756	+	0.327485i	0.149601	+	0.988746i	$0.452201\pi$
$150$		0			0
$151$	−7.14290			−0.581281			−0.290641	−	0.956832i	$-0.593868\pi$
$151$	−7.14290			−0.581281			−0.290641	+	0.956832i	$0.593868\pi$
$152$	−4.28125	+	0.819078i	−0.347255	+	0.0664360i
$153$			2.94356i			0.237973i
$154$	1.58125	−	1.32683i	0.127421	−	0.106919i
$155$		0			0
$156$	1.07398	−	6.09083i	0.0859871	−	0.487657i
$157$	−3.02525	+	0.533433i	−0.241441	+	0.0425726i	−0.293059	−	0.956094i	$-0.594673\pi$
$157$	−3.02525	+	0.533433i	−0.241441	+	0.0425726i	0.0516180	+	0.998667i	$0.483562\pi$
$158$	−0.342020	−	0.939693i	−0.0272097	−	0.0747579i
$159$	−2.91875	+	5.05542i	−0.231472	+	0.400921i
$160$		0			0
$161$	0.754900	+	0.633436i	0.0594945	+	0.0499218i
$162$	6.62916	−	7.90033i	0.520836	−	0.620709i
$163$	16.5144	−	9.53462i	1.29351	−	0.746809i	0.314236	−	0.949345i	$-0.398252\pi$
$163$	16.5144	−	9.53462i	1.29351	−	0.746809i	0.979275	+	0.202536i	$0.0649184\pi$
$164$	−3.41147	+	5.90885i	−0.266391	+	0.461403i
$165$		0			0
$166$	1.62449	+	9.21291i	0.126085	+	0.715061i
$167$	13.0696	+	2.30453i	1.01136	+	0.178330i	0.654687	−	0.755900i	$-0.272800\pi$
$167$	13.0696	+	2.30453i	1.01136	+	0.178330i	0.356672	+	0.934230i	$0.383911\pi$
$168$	−0.223238	+	0.613341i	−0.0172232	+	0.0473203i
$169$	1.66250	−	1.39501i	0.127885	−	0.107308i
$170$		0			0
$171$	−1.18866	−	1.99157i	−0.0908993	−	0.152299i
$172$		−	0.532089i		−	0.0405714i
$173$	−0.669713	−	0.798133i	−0.0509174	−	0.0606810i	0.739985	−	0.672624i	$-0.234833\pi$
$173$	−0.669713	−	0.798133i	−0.0509174	−	0.0606810i	−0.790902	+	0.611943i	$0.790388\pi$
$174$	12.5890	+	4.58202i	0.954369	+	0.347362i
$175$		0			0
$176$	−1.03209	−	5.85327i	−0.0777966	−	0.441207i
$177$	1.76833	+	4.85844i	0.132916	+	0.365183i
$178$	9.81445	+	5.66637i	0.735624	+	0.424713i
$179$	6.48293	+	11.2288i	0.484557	+	0.839277i	0.999843	−	0.0177416i	$-0.00564762\pi$
$179$	6.48293	+	11.2288i	0.484557	+	0.839277i	−0.515286	+	0.857018i	$0.672314\pi$
$180$		0			0
$181$	14.2456	+	11.9534i	1.05886	+	0.888493i	0.993998	−	0.109401i	$-0.0348933\pi$
$181$	14.2456	+	11.9534i	1.05886	+	0.888493i	0.0648669	+	0.997894i	$0.479338\pi$
$182$	0.989783	−	0.571452i	0.0733676	−	0.0423588i
$183$	−20.0727	−	11.5890i	−1.48382	−	0.856683i
$184$	2.66637	−	0.970481i	0.196568	−	0.0715448i
$185$		0			0
$186$	0.992726	−	5.63003i	0.0727902	−	0.412814i
$187$	11.2457	−	30.8974i	0.822369	−	2.25944i
$188$	−2.99070	−	3.56418i	−0.218119	−	0.259944i
$189$	1.61081			0.117170
$190$		0			0
$191$	−23.5645			−1.70507			−0.852533	−	0.522673i	$-0.824935\pi$
$191$	−23.5645			−1.70507			−0.852533	+	0.522673i	$0.824935\pi$
$192$	1.20805	+	1.43969i	0.0871832	+	0.103901i
$193$	1.43036	−	3.92989i	0.102960	−	0.282880i	−0.877507	−	0.479564i	$-0.840795\pi$
$193$	1.43036	−	3.92989i	0.102960	−	0.282880i	0.980467	+	0.196684i	$0.0630172\pi$
$194$	0.993603	−	5.63500i	0.0713366	−	0.404570i
$195$		0			0
$196$	6.46451	−	2.35289i	0.461751	−	0.168063i
$197$	−22.2589	−	12.8512i	−1.58588	−	0.915608i	−0.993976	−	0.109599i	$-0.965043\pi$
$197$	−22.2589	−	12.8512i	−1.58588	−	0.915608i	−0.591903	−	0.806009i	$-0.701623\pi$
$198$	2.73881	−	1.58125i	0.194639	−	0.112375i
$199$	20.0385	+	16.8143i	1.42049	+	1.19193i	0.951077	+	0.308955i	$0.0999792\pi$
$199$	20.0385	+	16.8143i	1.42049	+	1.19193i	0.469414	+	0.882978i	$0.344465\pi$
$200$		0			0
$201$	4.73783	+	8.20616i	0.334180	+	0.578818i
$202$	−4.10424	−	2.36959i	−0.288773	−	0.166723i
$203$	0.846723	+	2.32635i	0.0594283	+	0.163278i
$204$	1.80541	+	10.2390i	0.126404	+	0.716872i
$205$		0			0
$206$	2.97906	+	1.08429i	0.207561	+	0.0755459i
$207$	0.970481	+	1.15657i	0.0674531	+	0.0803875i
$208$		−	3.29086i		−	0.228180i
$209$	4.86824	+	25.4459i	0.336743	+	1.76013i
$210$		0			0
$211$	5.03983	−	4.22892i	0.346956	−	0.291131i	−0.452610	−	0.891708i	$-0.649507\pi$
$211$	5.03983	−	4.22892i	0.346956	−	0.291131i	0.799566	+	0.600578i	$0.205063\pi$
$212$	−1.06234	+	2.91875i	−0.0729616	+	0.200460i
$213$	24.1939	+	4.26604i	1.65774	+	0.292305i
$214$	2.32635	+	13.1934i	0.159026	+	0.901882i
$215$		0			0
$216$	2.31908	−	4.01676i	0.157793	−	0.273306i
$217$	0.914901	−	0.528218i	0.0621075	−	0.0358578i
$218$	−8.79336	+	10.4795i	−0.595562	+	0.709763i
$219$	−3.16637	−	2.65690i	−0.213964	−	0.179537i
$220$		0			0
$221$	9.10266	−	15.7663i	0.612311	−	1.06055i
$222$	1.17177	+	3.21941i	0.0786440	+	0.216072i
$223$	20.8200	−	3.67112i	1.39421	−	0.245837i	0.574447	−	0.818542i	$-0.305217\pi$
$223$	20.8200	−	3.67112i	1.39421	−	0.245837i	0.819761	+	0.572705i	$0.194106\pi$
$224$	−0.0603074	+	0.342020i	−0.00402946	+	0.0228522i
$225$		0			0
$226$	−10.3571	+	8.69064i	−0.688944	+	0.578092i
$227$			3.24216i			0.215190i	0.994195	+	0.107595i	$0.0343150\pi$
$227$			3.24216i			0.215190i	−0.994195	+	0.107595i	$0.965685\pi$
$228$	−5.35619	−	6.19846i	−0.354722	−	0.410503i
$229$	−8.56717			−0.566135			−0.283067	−	0.959100i	$-0.591352\pi$
$229$	−8.56717			−0.566135			−0.283067	+	0.959100i	$0.591352\pi$
$230$		0			0
$231$	3.64543	+	1.32683i	0.239852	+	0.0872989i
$232$	7.02006	+	1.23783i	0.460890	+	0.0812673i
$233$	−1.09861	+	0.193715i	−0.0719726	+	0.0126907i	−0.209519	−	0.977805i	$-0.567190\pi$
$233$	−1.09861	+	0.193715i	−0.0719726	+	0.0126907i	0.137546	+	0.990495i	$0.456079\pi$
$234$	1.64543	−	0.598887i	0.107565	−	0.0391505i
$235$		0			0
$236$	1.37551	+	2.38246i	0.0895384	+	0.155085i
$237$	1.20805	−	1.43969i	0.0784710	−	0.0935181i
$238$	−1.23497	+	1.47178i	−0.0800513	+	0.0954014i
$239$	2.09879	+	3.63522i	0.135760	+	0.235143i	0.925887	−	0.377800i	$-0.123319\pi$
$239$	2.09879	+	3.63522i	0.135760	+	0.235143i	−0.790128	+	0.612942i	$0.789986\pi$
$240$		0			0
$241$	−14.5842	+	5.30823i	−0.939454	+	0.341933i	−0.765950	−	0.642900i	$-0.777731\pi$
$241$	−14.5842	+	5.30823i	−0.939454	+	0.341933i	−0.173504	+	0.984833i	$0.555509\pi$
$242$	−23.9564	+	4.22416i	−1.53997	+	0.271539i
$243$	5.38484	+	0.949493i	0.345438	+	0.0609100i
$244$	−11.5890	−	4.21805i	−0.741909	−	0.270033i
$245$		0			0
$246$	−12.8229			−0.817561
$247$	0.207991	+	14.3430i	0.0132342	+	0.912624i
$248$		−	3.04189i		−	0.193160i
$249$	−13.4684	+	11.3013i	−0.853524	+	0.716191i
$250$		0			0
$251$	1.27244	−	7.21637i	0.0803158	−	0.455493i	−0.917954	−	0.396688i	$-0.870160\pi$
$251$	1.27244	−	7.21637i	0.0803158	−	0.455493i	0.998269	−	0.0588058i	$-0.0187293\pi$
$252$	−0.181985	+	0.0320889i	−0.0114640	+	0.00202141i
$253$	−5.76811	−	15.8478i	−0.362638	−	0.996340i
$254$	−9.66772	+	16.7450i	−0.606607	+	1.05067i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	20.0853	−	23.9368i	1.25289	−	1.49313i	0.454799	−	0.890594i	$-0.349711\pi$
$257$	20.0853	−	23.9368i	1.25289	−	1.49313i	0.798089	−	0.602540i	$-0.205845\pi$
$258$	0.866025	−	0.500000i	0.0539164	−	0.0311286i
$259$	−0.316552	+	0.548284i	−0.0196696	+	0.0340687i
$260$		0			0
$261$	0.658633	+	3.73530i	0.0407684	+	0.231209i
$262$	16.8175	+	2.96538i	1.03899	+	0.183202i
$263$	7.48757	−	20.5719i	0.461703	−	1.26852i	−0.462501	−	0.886619i	$-0.653048\pi$
$263$	7.48757	−	20.5719i	0.461703	−	1.26852i	0.924204	−	0.381900i	$-0.124730\pi$
$264$	8.55690	−	7.18009i	0.526641	−	0.441904i
$265$		0			0
$266$	0.241230	−	1.49449i	0.0147907	−	0.0916328i
$267$			21.2986i			1.30345i
$268$	3.24086	+	3.86231i	0.197967	+	0.235928i
$269$	−19.1411	−	6.96681i	−1.16706	−	0.424774i	−0.315443	−	0.948944i	$-0.602153\pi$
$269$	−19.1411	−	6.96681i	−1.16706	−	0.424774i	−0.851613	+	0.524171i	$0.824375\pi$
$270$		0			0
$271$	−3.93835	−	22.3355i	−0.239238	−	1.35678i	−0.833503	−	0.552515i	$-0.813668\pi$
$271$	−3.93835	−	22.3355i	−0.239238	−	1.35678i	0.594265	−	0.804269i	$-0.297443\pi$
$272$	1.89209	+	5.19846i	0.114725	+	0.315203i
$273$	1.86018	+	1.07398i	0.112583	+	0.0650001i
$274$	−7.67752	−	13.2979i	−0.463816	−	0.803353i
$275$		0			0
$276$	4.08512	+	3.42782i	0.245895	+	0.206331i
$277$	−18.0265	+	10.4076i	−1.08311	+	0.625332i	−0.931733	−	0.363144i	$-0.881703\pi$
$277$	−18.0265	+	10.4076i	−1.08311	+	0.625332i	−0.151374	+	0.988477i	$0.548370\pi$
$278$	4.46496	+	2.57785i	0.267791	+	0.154609i
$279$	1.52094	−	0.553579i	0.0910566	−	0.0331419i
$280$		0			0
$281$	3.16028	−	17.9229i	0.188527	−	1.06919i	−0.732813	−	0.680430i	$-0.761793\pi$
$281$	3.16028	−	17.9229i	0.188527	−	1.06919i	0.921340	−	0.388758i	$-0.127096\pi$
$282$	2.99070	−	8.21688i	0.178094	−	0.489308i
$283$	11.6989	+	13.9422i	0.695428	+	0.828779i	0.992001	−	0.126231i	$-0.0402882\pi$
$283$	11.6989	+	13.9422i	0.695428	+	0.828779i	−0.296573	+	0.955010i	$0.595844\pi$
$284$	13.0719			0.775676
$285$		0			0
$286$	−19.5594			−1.15657
$287$	−1.52314	−	1.81521i	−0.0899081	−	0.107148i
$288$	−0.181985	+	0.500000i	−0.0107236	+	0.0294628i
$289$	−2.36231	+	13.3973i	−0.138959	+	0.788078i
$290$		0			0
$291$	10.1052	−	3.67799i	0.592377	−	0.215607i
$292$	−1.90468	−	1.09967i	−0.111463	−	0.0643533i
$293$	25.8081	−	14.9003i	1.50773	−	0.870487i	0.507767	−	0.861494i	$-0.330471\pi$
$293$	25.8081	−	14.9003i	1.50773	−	0.870487i	0.999960	−	0.00899234i	$-0.00286239\pi$
$294$	9.90420	+	8.31061i	0.577625	+	0.484685i
$295$		0			0
$296$	0.911474	+	1.57872i	0.0529784	+	0.0917612i
$297$	−23.8739	−	13.7836i	−1.38530	−	0.799805i
$298$	3.99746	+	10.9829i	0.231567	+	0.636224i
$299$	−1.62149	−	9.19594i	−0.0937733	−	0.531815i
$300$		0			0
$301$	0.173648	+	0.0632028i	0.0100089	+	0.00364295i
$302$	−4.59137	−	5.47178i	−0.264204	−	0.314866i
$303$		−	8.90673i		−	0.511678i
$304$	−3.37939	−	2.75314i	−0.193821	−	0.157903i
$305$		0			0
$306$	−2.25490	+	1.89209i	−0.128904	+	0.108163i
$307$	1.59224	−	4.37464i	0.0908738	−	0.249674i	−0.885927	−	0.463825i	$-0.846476\pi$
$307$	1.59224	−	4.37464i	0.0908738	−	0.249674i	0.976800	+	0.214152i	$0.0686987\pi$
$308$	2.03282	+	0.358441i	0.115831	+	0.0204241i
$309$	1.03462	+	5.86759i	0.0588572	+	0.333796i
$310$		0			0
$311$	−7.02869	+	12.1740i	−0.398560	+	0.690326i	−0.993549	−	0.113408i	$-0.963823\pi$
$311$	−7.02869	+	12.1740i	−0.398560	+	0.690326i	0.594988	+	0.803734i	$0.297157\pi$
$312$	5.35619	−	3.09240i	0.303234	−	0.175072i
$313$	4.72600	−	5.63223i	0.267129	−	0.318352i	−0.615760	−	0.787934i	$-0.711151\pi$
$313$	4.72600	−	5.63223i	0.267129	−	0.318352i	0.882889	+	0.469582i	$0.155595\pi$
$314$	−2.35323	−	1.97459i	−0.132800	−	0.111433i
$315$		0			0
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	1.84911	+	5.08037i	0.103856	+	0.285342i	0.980727	−	0.195384i	$-0.0625953\pi$
$317$	1.84911	+	5.08037i	0.103856	+	0.285342i	−0.876871	+	0.480726i	$0.840373\pi$
$318$	−5.74881	+	1.01367i	−0.322377	+	0.0568438i
$319$	7.35710	−	41.7242i	0.411918	−	2.33610i
$320$		0			0
$321$	−19.2875	+	16.1841i	−1.07652	+	0.903308i
$322$			0.985452i			0.0549171i
$323$	−8.57510	−	22.5376i	−0.477131	−	1.25403i
$324$	10.3131			0.572953
$325$		0			0
$326$	17.9192	+	6.52206i	0.992454	+	0.361224i
$327$	−25.3195	−	4.46451i	−1.40017	−	0.246888i
$328$	−6.71929	+	1.18479i	−0.371011	+	0.0654192i
$329$	1.51842	−	0.552659i	0.0837131	−	0.0304691i
$330$		0			0
$331$	12.8562	+	22.2676i	0.706642	+	1.22394i	0.966096	+	0.258184i	$0.0831240\pi$
$331$	12.8562	+	22.2676i	0.706642	+	1.22394i	−0.259454	+	0.965755i	$0.583543\pi$
$332$	−6.01330	+	7.16637i	−0.330023	+	0.393306i
$333$	−0.623485	+	0.743041i	−0.0341668	+	0.0407184i
$334$	6.63563	+	11.4932i	0.363085	+	0.628883i
$335$		0			0
$336$	−0.613341	+	0.223238i	−0.0334605	+	0.0121786i
$337$	17.6104	−	3.10519i	0.959300	−	0.169150i	0.327990	−	0.944681i	$-0.393629\pi$
$337$	17.6104	−	3.10519i	0.959300	−	0.169150i	0.631310	+	0.775531i	$0.282518\pi$
$338$	2.13727	+	0.376859i	0.116252	+	0.0204984i
$339$	−23.8773	−	8.69064i	−1.29684	−	0.472011i
$340$		0			0
$341$	−18.0797			−0.979068
$342$	0.761570	−	2.19072i	0.0411810	−	0.118461i
$343$			4.82026i			0.260270i
$344$	0.407604	−	0.342020i	0.0219765	−	0.0184405i
$345$		0			0
$346$	0.180922	−	1.02606i	0.00972643	−	0.0551614i
$347$	−13.5793	+	2.39440i	−0.728976	+	0.128538i	−0.525805	−	0.850605i	$-0.676236\pi$
$347$	−13.5793	+	2.39440i	−0.728976	+	0.128538i	−0.203171	+	0.979143i	$0.565125\pi$
$348$	4.58202	+	12.5890i	0.245622	+	0.674841i
$349$	−4.40760	+	7.63419i	−0.235934	+	0.408649i	−0.959544	−	0.281560i	$-0.909148\pi$
$349$	−4.40760	+	7.63419i	−0.235934	+	0.408649i	0.723610	+	0.690209i	$0.242481\pi$
$350$		0			0
$351$	−11.6925	−	9.81120i	−0.624101	−	0.523683i
$352$	3.82045	−	4.55303i	0.203631	−	0.242677i
$353$	−0.531028	+	0.306589i	−0.0282638	+	0.0163181i	−0.514065	−	0.857751i	$-0.671861\pi$
$353$	−0.531028	+	0.306589i	−0.0282638	+	0.0163181i	0.485802	+	0.874069i	$0.338528\pi$
$354$	−2.58512	+	4.47756i	−0.137398	+	0.237980i
$355$		0			0
$356$	1.96791	+	11.1606i	0.104299	+	0.591509i
$357$	−3.55596	−	0.627011i	−0.188201	−	0.0331850i
$358$	−4.43458	+	12.1839i	−0.234375	+	0.643940i
$359$	11.9834	−	10.0553i	0.632459	−	0.530696i	−0.269233	−	0.963075i	$-0.586770\pi$
$359$	11.9834	−	10.0553i	0.632459	−	0.530696i	0.901692	+	0.432379i	$0.142326\pi$
$360$		0			0
$361$	14.9029	+	11.7858i	0.784361	+	0.620305i
$362$			18.5963i			0.977398i
$363$	−29.3868	−	35.0219i	−1.54241	−	1.83817i
$364$	1.07398	+	0.390896i	0.0562917	+	0.0204885i
$365$		0			0
$366$	−4.02481	−	22.8259i	−0.210380	−	1.19313i
$367$	11.9906	+	32.9440i	0.625907	+	1.71966i	0.692045	+	0.721854i	$0.256710\pi$
$367$	11.9906	+	32.9440i	0.625907	+	1.71966i	−0.0661388	+	0.997810i	$0.521068\pi$
$368$	2.45734	+	1.41875i	0.128098	+	0.0739574i
$369$	−1.81521	−	3.14403i	−0.0944959	−	0.163672i
$370$		0			0
$371$	−0.826352	−	0.693392i	−0.0429020	−	0.0359991i
$372$	4.95096	−	2.85844i	0.256696	−	0.148203i
$373$	−22.3834	−	12.9231i	−1.15897	−	0.669132i	−0.207914	−	0.978147i	$-0.566667\pi$
$373$	−22.3834	−	12.9231i	−1.15897	−	0.669132i	−0.951057	+	0.309015i	$0.900001\pi$
$374$	30.8974	−	11.2457i	1.59767	−	0.581503i
$375$		0			0
$376$	0.807934	−	4.58202i	0.0416660	−	0.236300i
$377$	8.02325	−	22.0437i	0.413218	−	1.13531i
$378$	1.03541	+	1.23396i	0.0532558	+	0.0634678i
$379$	−4.44562			−0.228356			−0.114178	−	0.993460i	$-0.536423\pi$
$379$	−4.44562			−0.228356			−0.114178	+	0.993460i	$0.536423\pi$
$380$		0			0
$381$	−36.3387			−1.86169
$382$	−15.1470	−	18.0514i	−0.774986	−	0.923592i
$383$	−9.38759	+	25.7922i	−0.479684	+	1.31792i	0.430079	+	0.902791i	$0.358486\pi$
$383$	−9.38759	+	25.7922i	−0.479684	+	1.31792i	−0.909763	+	0.415129i	$0.863737\pi$
$384$	−0.326352	+	1.85083i	−0.0166541	+	0.0944499i
$385$		0			0
$386$	3.92989	−	1.43036i	0.200026	−	0.0728036i
$387$	0.245188	+	0.141559i	0.0124636	+	0.00719586i
$388$	4.95534	−	2.86097i	0.251569	−	0.145244i
$389$	−17.6250	−	14.7891i	−0.893621	−	0.749837i	0.0753125	−	0.997160i	$-0.476005\pi$
$389$	−17.6250	−	14.7891i	−0.893621	−	0.749837i	−0.968933	+	0.247323i	$0.920449\pi$
$390$		0			0
$391$	7.84864	+	13.5942i	0.396923	+	0.687490i
$392$	5.95772	+	3.43969i	0.300910	+	0.173731i
$393$	10.9769	+	30.1587i	0.553710	+	1.52130i
$394$	−4.46316	−	25.3119i	−0.224851	−	1.27519i
$395$		0			0
$396$	2.97178	+	1.08164i	0.149338	+	0.0543545i
$397$	23.5386	+	28.0522i	1.18137	+	1.40790i	0.892809	+	0.450435i	$0.148731\pi$
$397$	23.5386	+	28.0522i	1.18137	+	1.40790i	0.288557	+	0.957463i	$0.406825\pi$
$398$			26.1584i			1.31120i
$399$	2.65910	−	1.01173i	0.133122	−	0.0506500i
$400$		0			0
$401$	27.1195	−	22.7560i	1.35428	−	1.13638i	0.376580	−	0.926384i	$-0.377100\pi$
$401$	27.1195	−	22.7560i	1.35428	−	1.13638i	0.977703	−	0.209994i	$-0.0673444\pi$
$402$	−3.24086	+	8.90420i	−0.161640	+	0.444101i
$403$	−9.85835	−	1.73829i	−0.491079	−	0.0865905i
$404$	−0.822948	−	4.66717i	−0.0409432	−	0.232200i
$405$		0			0
$406$	−1.23783	+	2.14398i	−0.0614323	+	0.106404i
$407$	9.38322	−	5.41740i	0.465109	−	0.268531i
$408$	−6.68302	+	7.96451i	−0.330859	+	0.394302i
$409$	−1.28833	−	1.08104i	−0.0637040	−	0.0534540i	0.610380	−	0.792109i	$-0.291017\pi$
$409$	−1.28833	−	1.08104i	−0.0637040	−	0.0534540i	−0.674084	+	0.738655i	$0.735461\pi$
$410$		0			0
$411$	14.4290	−	24.9918i	0.711731	−	1.23275i
$412$	1.08429	+	2.97906i	0.0534190	+	0.146768i
$413$	−0.940908	+	0.165907i	−0.0462990	+	0.00816377i
$414$	−0.262174	+	1.48686i	−0.0128852	+	0.0730753i
$415$		0			0
$416$	2.52094	−	2.11532i	0.123599	−	0.103712i
$417$			9.68954i			0.474499i
$418$	−16.3634	+	20.0856i	−0.800362	+	0.982418i
$419$	−33.7033			−1.64651			−0.823256	−	0.567670i	$-0.807845\pi$
$419$	−33.7033			−1.64651			−0.823256	+	0.567670i	$0.807845\pi$
$420$		0			0
$421$	−6.71941	−	2.44566i	−0.327484	−	0.119194i	0.173046	−	0.984914i	$-0.444639\pi$
$421$	−6.71941	−	2.44566i	−0.327484	−	0.119194i	−0.500530	+	0.865719i	$0.666861\pi$
$422$	6.47908	+	1.14244i	0.315397	+	0.0556129i
$423$	2.43804	−	0.429892i	0.118542	−	0.0209021i
$424$	−2.91875	+	1.06234i	−0.141747	+	0.0515917i
$425$		0			0
$426$	12.2836	+	21.2758i	0.595142	+	1.03082i
$427$	2.75314	−	3.28106i	0.133234	−	0.158782i
$428$	−8.61138	+	10.2626i	−0.416247	+	0.496063i
$429$	−18.3799	−	31.8348i	−0.887388	−	1.53700i
$430$		0			0
$431$	21.2738	−	7.74302i	1.02472	−	0.372968i	0.225653	−	0.974208i	$-0.427548\pi$
$431$	21.2738	−	7.74302i	1.02472	−	0.372968i	0.799069	+	0.601239i	$0.205326\pi$
$432$	4.56769	−	0.805407i	0.219763	−	0.0387502i
$433$	4.69410	+	0.827696i	0.225584	+	0.0397765i	0.285297	−	0.958439i	$-0.407908\pi$
$433$	4.69410	+	0.827696i	0.225584	+	0.0397765i	−0.0597135	+	0.998216i	$0.519019\pi$
$434$	0.992726	+	0.361323i	0.0476524	+	0.0173440i
$435$		0			0
$436$	−13.6800			−0.655155
$437$	−10.7999	−	6.02822i	−0.516627	−	0.288369i
$438$		−	4.13341i		−	0.197502i
$439$	4.68866	−	3.93426i	0.223778	−	0.187772i	−0.524005	−	0.851715i	$-0.675563\pi$
$439$	4.68866	−	3.93426i	0.223778	−	0.187772i	0.747783	+	0.663943i	$0.231118\pi$
$440$		0			0
$441$	−0.635630	+	3.60483i	−0.0302681	+	0.171659i
$442$	17.9287	−	3.16132i	0.852784	−	0.150369i
$443$	−8.48092	−	23.3011i	−0.402940	−	1.10707i	−0.960826	−	0.277152i	$-0.910609\pi$
$443$	−8.48092	−	23.3011i	−0.402940	−	1.10707i	0.557886	−	0.829918i	$-0.311613\pi$
$444$	−1.71301	+	2.96702i	−0.0812959	+	0.140809i
$445$		0			0
$446$	16.1951	+	13.5893i	0.766858	+	0.643471i
$447$	−14.1194	+	16.8268i	−0.667824	+	0.795881i
$448$	−0.300767	+	0.173648i	−0.0142099	+	0.00820411i
$449$	−0.333626	+	0.577857i	−0.0157448	+	0.0272707i	−0.873790	−	0.486303i	$-0.838345\pi$
$449$	−0.333626	+	0.577857i	−0.0157448	+	0.0272707i	0.858046	+	0.513573i	$0.171679\pi$
$450$		0			0
$451$	7.04189	+	39.9365i	0.331590	+	1.88054i
$452$	−13.3148	−	2.34776i	−0.626277	−	0.110429i
$453$	4.59137	−	12.6147i	0.215721	−	0.592690i
$454$	−2.48364	+	2.08402i	−0.116563	+	0.0978080i
$455$		0			0
$456$	1.30541	−	8.08737i	0.0611313	−	0.378726i
$457$			13.1967i			0.617313i	0.951174	+	0.308657i	$0.0998794\pi$
$457$			13.1967i			0.617313i	−0.951174	+	0.308657i	$0.900121\pi$
$458$	−5.50687	−	6.56283i	−0.257319	−	0.306661i
$459$	24.1113	+	8.77579i	1.12542	+	0.409619i
$460$		0			0
$461$	−2.50346	−	14.1978i	−0.116598	−	0.661259i	−0.985947	−	0.167060i	$-0.946573\pi$
$461$	−2.50346	−	14.1978i	−0.116598	−	0.661259i	0.869349	−	0.494199i	$-0.164538\pi$
$462$	1.32683	+	3.64543i	0.0617296	+	0.169601i
$463$	5.65463	+	3.26470i	0.262793	+	0.151723i	0.625608	−	0.780138i	$-0.284851\pi$
$463$	5.65463	+	3.26470i	0.262793	+	0.151723i	−0.362815	+	0.931861i	$0.618184\pi$
$464$	3.56418	+	6.17334i	0.165463	+	0.286590i
$465$		0			0
$466$	−0.854570	−	0.717070i	−0.0395872	−	0.0332176i
$467$	21.8048	−	12.5890i	1.00900	−	0.582549i	0.0981046	−	0.995176i	$-0.468722\pi$
$467$	21.8048	−	12.5890i	1.00900	−	0.582549i	0.910900	+	0.412627i	$0.135389\pi$
$468$	1.51644	+	0.875515i	0.0700973	+	0.0404707i
$469$	−1.64543	+	0.598887i	−0.0759789	+	0.0276541i
$470$		0			0
$471$	1.00253	−	5.68561i	0.0461940	−	0.261979i
$472$	−0.940908	+	2.58512i	−0.0433088	+	0.118990i
$473$	−2.03282	−	2.42262i	−0.0934691	−	0.111392i
$474$	1.87939			0.0863230
$475$		0			0
$476$	−1.92127			−0.0880615
$477$	−1.06234	−	1.26604i	−0.0486411	−	0.0579682i
$478$	−1.43566	+	3.94444i	−0.0656655	+	0.180415i
$479$	1.61246	−	9.14473i	0.0736753	−	0.417834i	−0.925555	−	0.378613i	$-0.876401\pi$
$479$	1.61246	−	9.14473i	0.0736753	−	0.417834i	0.999231	−	0.0392210i	$-0.0124876\pi$
$480$		0			0
$481$	5.63728	−	2.05180i	0.257038	−	0.0935541i
$482$	−13.4409	−	7.76011i	−0.612217	−	0.353464i
$483$	−1.60392	+	0.926022i	−0.0729808	+	0.0421355i
$484$	−18.6348	−	15.6364i	−0.847034	−	0.710746i
$485$		0			0
$486$	2.73396	+	4.73535i	0.124015	+	0.214800i
$487$	−13.7973	−	7.96585i	−0.625214	−	0.360967i	0.153682	−	0.988120i	$-0.450887\pi$
$487$	−13.7973	−	7.96585i	−0.625214	−	0.360967i	−0.778896	+	0.627153i	$0.784220\pi$
$488$	−4.21805	−	11.5890i	−0.190942	−	0.524609i
$489$	6.22328	+	35.2940i	0.281426	+	1.59605i
$490$		0			0
$491$	−1.50640	−	0.548284i	−0.0679827	−	0.0247437i	0.307805	−	0.951449i	$-0.400406\pi$
$491$	−1.50640	−	0.548284i	−0.0679827	−	0.0247437i	−0.375788	+	0.926706i	$0.622628\pi$
$492$	−8.24243	−	9.82295i	−0.371598	−	0.442853i
$493$			39.4347i			1.77605i
$494$	−10.8537	+	9.37884i	−0.488331	+	0.421974i
$495$		0			0
$496$	2.33022	−	1.95529i	0.104630	−	0.0877950i
$497$	−1.55271	+	4.26604i	−0.0696487	+	0.191358i
$498$	−17.3146	−	3.05303i	−0.775886	−	0.136810i
$499$	−5.78652	−	32.8170i	−0.259040	−	1.46909i	−0.785485	−	0.618881i	$-0.787586\pi$
$499$	−5.78652	−	32.8170i	−0.259040	−	1.46909i	0.526444	−	0.850210i	$-0.323525\pi$
$500$		0			0
$501$	−12.4709	+	21.6002i	−0.557159	+	0.965028i
$502$	6.34597	−	3.66385i	0.283235	−	0.163526i
$503$	−23.1108	+	27.5424i	−1.03046	+	1.22805i	−0.0571949	+	0.998363i	$0.518216\pi$
$503$	−23.1108	+	27.5424i	−1.03046	+	1.22805i	−0.973264	+	0.229690i	$0.926229\pi$
$504$	−0.141559	−	0.118782i	−0.00630555	−	0.00529099i
$505$		0			0
$506$	8.43242	−	14.6054i	0.374867	−	0.649288i
$507$	1.39501	+	3.83275i	0.0619544	+	0.170218i
$508$	−19.0417	+	3.35756i	−0.844838	+	0.148968i
$509$	0.504337	−	2.86024i	0.0223544	−	0.126778i	−0.971588	−	0.236677i	$-0.923942\pi$
$509$	0.504337	−	2.86024i	0.0223544	−	0.126778i	0.993943	+	0.109899i	$0.0350528\pi$
$510$		0			0
$511$	0.585122	−	0.490976i	0.0258843	−	0.0217195i
$512$			1.00000i			0.0441942i
$513$	−19.8571	+	3.79901i	−0.876713	+	0.167730i
$514$	31.2472			1.37826
$515$		0			0
$516$	0.939693	+	0.342020i	0.0413677	+	0.0150566i
$517$	−27.2335	−	4.80200i	−1.19773	−	0.211192i
$518$	−0.623485	+	0.109937i	−0.0273944	+	0.00483036i
$519$	1.84002	−	0.669713i	0.0807680	−	0.0293972i
$520$		0			0
$521$	3.43330	+	5.94664i	0.150415	+	0.260527i	0.931380	−	0.364048i	$-0.118606\pi$
$521$	3.43330	+	5.94664i	0.150415	+	0.260527i	−0.780965	+	0.624575i	$0.785272\pi$
$522$	−2.43804	+	2.90554i	−0.106710	+	0.127172i
$523$	21.5590	−	25.6930i	0.942709	−	1.12348i	−0.0494856	−	0.998775i	$-0.515758\pi$
$523$	21.5590	−	25.6930i	0.942709	−	1.12348i	0.992194	−	0.124702i	$-0.0397974\pi$
$524$	8.53849	+	14.7891i	0.373005	+	0.646064i
$525$		0			0
$526$	20.5719	−	7.48757i	0.896978	−	0.326473i
$527$	16.5723	−	2.92215i	0.721903	−	0.127291i
$528$	11.0005	+	1.93969i	0.478737	+	0.0844143i
$529$	−14.0471	−	5.11273i	−0.610744	−	0.222293i
$530$		0			0
$531$	−1.46379			−0.0635232
$532$	1.29990	−	0.775845i	0.0563579	−	0.0336371i
$533$			22.4534i			0.972563i
$534$	−16.3157	+	13.6905i	−0.706048	+	0.592445i
$535$		0			0
$536$	−0.875515	+	4.96529i	−0.0378165	+	0.214468i
$537$	−23.9976	+	4.23143i	−1.03557	+	0.182600i
$538$	−6.96681	−	19.1411i	−0.300360	−	0.825234i
$539$	20.4440	−	35.4101i	0.880587	−	1.52522i
$540$		0			0
$541$	−24.3744	−	20.4525i	−1.04794	−	0.879323i	−0.0550617	−	0.998483i	$-0.517536\pi$
$541$	−24.3744	−	20.4525i	−1.04794	−	0.879323i	−0.992875	+	0.119160i	$0.961980\pi$
$542$	14.5785	−	17.3739i	0.626198	−	0.746274i
$543$	−30.2672	+	17.4748i	−1.29889	+	0.749914i
$544$	−2.76604	+	4.79093i	−0.118593	+	0.205409i
$545$		0			0
$546$	0.372989	+	2.11532i	0.0159624	+	0.0905275i
$547$	5.82634	+	1.02734i	0.249116	+	0.0439259i	0.296812	−	0.954936i	$-0.404077\pi$
$547$	5.82634	+	1.02734i	0.249116	+	0.0439259i	−0.0476955	+	0.998862i	$0.515188\pi$
$548$	5.25173	−	14.4290i	0.224343	−	0.616377i
$549$	5.02687	−	4.21805i	0.214542	−	0.180022i
$550$		0			0
$551$	−15.9244	−	26.6809i	−0.678404	−	1.13664i
$552$			5.33275i			0.226977i
$553$	0.223238	+	0.266044i	0.00949304	+	0.0113134i
$554$	−19.5599	−	7.11922i	−0.831020	−	0.302467i
$555$		0			0
$556$	0.895277	+	5.07737i	0.0379682	+	0.215328i
$557$	−8.75677	−	24.0590i	−0.371036	−	1.01941i	−0.974962	−	0.222373i	$-0.928620\pi$
$557$	−8.75677	−	24.0590i	−0.371036	−	1.01941i	0.603926	−	0.797041i	$-0.293602\pi$
$558$	1.40171	+	0.809278i	0.0593391	+	0.0342595i
$559$	−0.875515	−	1.51644i	−0.0370303	−	0.0641384i
$560$		0			0
$561$	47.3376	+	39.7209i	1.99859	+	1.67702i
$562$	15.7611	−	9.09967i	0.664842	−	0.383846i
$563$	−18.9193	−	10.9231i	−0.797355	−	0.460353i	0.0451904	−	0.998978i	$-0.485611\pi$
$563$	−18.9193	−	10.9231i	−0.797355	−	0.460353i	−0.842545	+	0.538625i	$0.818944\pi$
$564$	8.21688	−	2.99070i	0.345993	−	0.125931i
$565$		0			0
$566$	−3.16044	+	17.9238i	−0.132843	+	0.753392i
$567$	−1.22502	+	3.36571i	−0.0514460	+	0.141347i
$568$	8.40247	+	10.0137i	0.352560	+	0.420164i
$569$	15.5175			0.650529			0.325265	−	0.945623i	$-0.394547\pi$
$569$	15.5175			0.650529			0.325265	+	0.945623i	$0.394547\pi$
$570$		0			0
$571$	−37.2317			−1.55810			−0.779050	−	0.626962i	$-0.784298\pi$
$571$	−37.2317			−1.55810			−0.779050	+	0.626962i	$0.784298\pi$
$572$	−12.5726	−	14.9834i	−0.525685	−	0.626487i
$573$	15.1470	−	41.6159i	0.632773	−	1.73853i
$574$	0.411474	−	2.33359i	0.0171746	−	0.0974020i
$575$		0			0
$576$	−0.500000	+	0.181985i	−0.0208333	+	0.00758271i
$577$	24.6480	+	14.2306i	1.02611	+	0.592426i	0.915868	−	0.401479i	$-0.131504\pi$
$577$	24.6480	+	14.2306i	1.02611	+	0.592426i	0.110243	+	0.993905i	$0.464837\pi$
$578$	−11.7814	+	6.80200i	−0.490042	+	0.282926i
$579$	6.02094	+	5.05217i	0.250222	+	0.209961i
$580$		0			0
$581$	−1.62449	−	2.81369i	−0.0673950	−	0.116732i
$582$	9.31299	+	5.37686i	0.386036	+	0.222878i
$583$	6.31407	+	17.3478i	0.261502	+	0.718471i
$584$	−0.381911	−	2.16593i	−0.0158036	−	0.0896267i
$585$		0			0
$586$	28.0035	+	10.1924i	1.15681	+	0.421045i
$587$	18.0191	+	21.4743i	0.743727	+	0.886340i	0.996703	−	0.0811330i	$-0.0258539\pi$
$587$	18.0191	+	21.4743i	0.743727	+	0.886340i	−0.252976	+	0.967473i	$0.581409\pi$
$588$			12.9290i			0.533184i
$589$	−10.0326	+	8.66929i	−0.413384	+	0.357212i
$590$		0			0
$591$	37.0035	−	31.0496i	1.52212	−	1.27721i
$592$	−0.623485	+	1.71301i	−0.0256251	+	0.0704043i
$593$	−23.5108	−	4.14559i	−0.965474	−	0.170239i	−0.331382	−	0.943497i	$-0.607515\pi$
$593$	−23.5108	−	4.14559i	−0.965474	−	0.170239i	−0.634092	+	0.773258i	$0.718626\pi$
$594$	−4.78699	−	27.1484i	−0.196413	−	1.11391i
$595$		0			0
$596$	−5.84389	+	10.1219i	−0.239375	+	0.414610i
$597$	−42.5753	+	24.5808i	−1.74249	+	1.00603i
$598$	6.00222	−	7.15317i	0.245449	−	0.292515i
$599$	−30.3182	−	25.4400i	−1.23877	−	1.03945i	−0.997619	−	0.0689617i	$-0.978031\pi$
$599$	−30.3182	−	25.4400i	−1.23877	−	1.03945i	−0.241149	−	0.970488i	$-0.577524\pi$
$600$		0			0
$601$	−18.2083	+	31.5376i	−0.742731	+	1.28645i	0.208517	+	0.978019i	$0.433136\pi$
$601$	−18.2083	+	31.5376i	−0.742731	+	1.28645i	−0.951248	+	0.308428i	$0.900197\pi$
$602$	0.0632028	+	0.173648i	0.00257595	+	0.00707737i
$603$	−2.64198	+	0.465852i	−0.107590	+	0.0189709i
$604$	1.24035	−	7.03439i	0.0504692	−	0.286225i
$605$		0			0
$606$	6.82295	−	5.72513i	0.277163	−	0.232568i
$607$			8.97266i			0.364189i	0.983281	+	0.182094i	$0.0582877\pi$
$607$			8.97266i			0.364189i	−0.983281	+	0.182094i	$0.941712\pi$
$608$	−0.0632028	−	4.35844i	−0.00256321	−	0.176758i
$609$	−4.65270			−0.188537
$610$		0			0
$611$	−14.3880	−	5.23680i	−0.582076	−	0.211858i
$612$	−2.89884	−	0.511144i	−0.117179	−	0.0206618i
$613$	26.9614	−	4.75402i	1.08896	−	0.192013i	0.399786	−	0.916608i	$-0.369084\pi$
$613$	26.9614	−	4.75402i	1.08896	−	0.192013i	0.689175	+	0.724595i	$0.257973\pi$
$614$	4.37464	−	1.59224i	0.176546	−	0.0642575i
$615$		0			0
$616$	1.03209	+	1.78763i	0.0415840	+	0.0720257i
$617$	−13.5474	+	16.1452i	−0.545398	+	0.649981i	−0.966389	−	0.257085i	$-0.917238\pi$
$617$	−13.5474	+	16.1452i	−0.545398	+	0.649981i	0.420991	+	0.907065i	$0.361683\pi$
$618$	−3.82980	+	4.56418i	−0.154057	+	0.183598i
$619$	−17.0064	−	29.4559i	−0.683545	−	1.18393i	−0.973892	−	0.227013i	$-0.927104\pi$
$619$	−17.0064	−	29.4559i	−0.683545	−	1.18393i	0.290347	−	0.956921i	$-0.406229\pi$
$620$		0			0
$621$	12.3671	−	4.50124i	0.496273	−	0.180629i
$622$	−13.8438	+	2.44104i	−0.555086	+	0.0978767i
$623$	−3.87603	−	0.683448i	−0.155290	−	0.0273818i
$624$	5.81180	+	2.11532i	0.232658	+	0.0846807i
$625$		0			0
$626$	7.35235			0.293859
$627$	−48.0678	−	7.75877i	−1.91964	−	0.309855i
$628$		−	3.07192i		−	0.122583i
$629$	−7.72534	+	6.48233i	−0.308029	+	0.258467i
$630$		0			0
$631$	−2.68551	+	15.2303i	−0.106908	+	0.606308i	0.883533	+	0.468370i	$0.155158\pi$
$631$	−2.68551	+	15.2303i	−0.106908	+	0.606308i	−0.990441	+	0.137938i	$0.955953\pi$
$632$	0.984808	−	0.173648i	0.0391735	−	0.00690735i
$633$	4.22892	+	11.6189i	0.168084	+	0.461808i
$634$	−2.70321	+	4.68210i	−0.107358	+	0.185950i
$635$		0			0
$636$	−4.47178	−	3.75227i	−0.177318	−	0.148787i
$637$	14.5521	−	17.3425i	0.576576	−	0.687137i
$638$	36.6916	−	21.1839i	1.45264	−	0.838679i
$639$	−3.47771	+	6.02357i	−0.137576	+	0.238289i
$640$		0			0
$641$	−6.35545	−	36.0435i	−0.251025	−	1.42363i	−0.806073	−	0.591816i	$-0.798411\pi$
$641$	−6.35545	−	36.0435i	−0.251025	−	1.42363i	0.555048	−	0.831818i	$-0.312700\pi$
$642$	−24.7955	−	4.37211i	−0.978599	−	0.172553i
$643$	−8.36711	+	22.9884i	−0.329967	+	0.906576i	0.658152	+	0.752885i	$0.271338\pi$
$643$	−8.36711	+	22.9884i	−0.329967	+	0.906576i	−0.988119	+	0.153691i	$0.950884\pi$
$644$	−0.754900	+	0.633436i	−0.0297472	+	0.0249609i
$645$		0			0
$646$	11.7528	−	21.0558i	0.462409	−	0.828430i
$647$			17.2787i			0.679295i	0.940553	+	0.339647i	$0.110308\pi$
$647$			17.2787i			0.679295i	−0.940553	+	0.339647i	$0.889692\pi$
$648$	6.62916	+	7.90033i	0.260418	+	0.310354i
$649$	15.3648	+	5.59234i	0.603123	+	0.219519i
$650$		0			0
$651$	0.344770	+	1.95529i	0.0135126	+	0.0766338i
$652$	6.52206	+	17.9192i	0.255424	+	0.701771i
$653$	7.35121	+	4.24422i	0.287675	+	0.166089i	0.636893	−	0.770952i	$-0.280219\pi$
$653$	7.35121	+	4.24422i	0.287675	+	0.166089i	−0.349218	+	0.937042i	$0.613553\pi$
$654$	−12.8550	−	22.2656i	−0.502672	−	0.870653i
$655$		0			0
$656$	−5.22668	−	4.38571i	−0.204068	−	0.171233i
$657$	1.01346	−	0.585122i	0.0395389	−	0.0228278i
$658$	1.39938	+	0.807934i	0.0545536	+	0.0314965i
$659$	−29.8859	+	10.8776i	−1.16419	+	0.423731i	−0.850593	−	0.525825i	$-0.823757\pi$
$659$	−29.8859	+	10.8776i	−1.16419	+	0.423731i	−0.313598	+	0.949556i	$0.601535\pi$
$660$		0			0
$661$	−3.88114	+	22.0110i	−0.150959	+	0.856130i	0.811429	+	0.584451i	$0.198690\pi$
$661$	−3.88114	+	22.0110i	−0.150959	+	0.856130i	−0.962388	+	0.271679i	$0.912421\pi$
$662$	−8.79417	+	24.1618i	−0.341795	+	0.939075i
$663$	21.9929	+	26.2101i	0.854132	+	1.01791i
$664$	−9.35504			−0.363046
$665$		0			0
$666$	−0.969971			−0.0375856
$667$	13.0015	+	15.4945i	0.503419	+	0.599951i
$668$	−4.53904	+	12.4709i	−0.175621	+	0.482514i
$669$	−6.89945	+	39.1287i	−0.266748	+	1.51280i
$670$		0			0
$671$	−68.8799	+	25.0702i	−2.65908	+	0.967826i
$672$	−0.565258	−	0.326352i	−0.0218053	−	0.0125893i
$673$	36.4169	−	21.0253i	1.40377	−	0.810465i	0.408990	−	0.912539i	$-0.365881\pi$
$673$	36.4169	−	21.0253i	1.40377	−	0.810465i	0.994777	+	0.102074i	$0.0325478\pi$
$674$	13.6985	+	11.4944i	0.527645	+	0.442747i
$675$		0			0
$676$	1.08512	+	1.87949i	0.0417355	+	0.0722880i
$677$	10.6170	+	6.12970i	0.408043	+	0.235583i	0.689948	−	0.723859i	$-0.257633\pi$
$677$	10.6170	+	6.12970i	0.408043	+	0.235583i	−0.281906	+	0.959442i	$0.590967\pi$
$678$	−8.69064	−	23.8773i	−0.333762	−	0.917003i
$679$	0.345075	+	1.95702i	0.0132428	+	0.0751034i
$680$		0			0
$681$	−5.72580	−	2.08402i	−0.219413	−	0.0798599i
$682$	−11.6214	−	13.8498i	−0.445006	−	0.530337i
$683$		−	10.1652i		−	0.388960i	−0.980906	−	0.194480i	$-0.937698\pi$
$683$		−	10.1652i		−	0.388960i	0.980906	−	0.194480i	$-0.0623020\pi$
$684$	2.16772	−	0.824773i	0.0828848	−	0.0315360i
$685$		0			0
$686$	−3.69253	+	3.09840i	−0.140982	+	0.118298i
$687$	5.50687	−	15.1300i	0.210100	−	0.577246i
$688$	0.524005	+	0.0923963i	0.0199775	+	0.00352257i
$689$	1.77497	+	10.0663i	0.0676209	+	0.383497i
$690$		0			0
$691$	0.740763	−	1.28304i	0.0281799	−	0.0488091i	−0.851592	−	0.524206i	$-0.824362\pi$
$691$	0.740763	−	1.28304i	0.0281799	−	0.0488091i	0.879771	+	0.475397i	$0.157696\pi$
$692$	0.902302	−	0.520945i	0.0343004	−	0.0198033i
$693$	−0.705990	+	0.841367i	−0.0268184	+	0.0319609i
$694$	−10.5628	−	8.86327i	−0.400960	−	0.336445i
$695$		0			0
$696$	−6.69846	+	11.6021i	−0.253905	+	0.439776i
$697$	−12.9096	−	35.4688i	−0.488986	−	1.34348i
$698$	−8.68128	+	1.53074i	−0.328591	+	0.0579395i
$699$	0.364066	−	2.06472i	0.0137702	−	0.0780949i
$700$		0			0
$701$	−21.7101	+	18.2169i	−0.819978	+	0.688043i	−0.952967	−	0.303074i	$-0.901987\pi$
$701$	−21.7101	+	18.2169i	−0.819978	+	0.688043i	0.132989	+	0.991118i	$0.457543\pi$
$702$		−	15.2635i		−	0.576084i
$703$	2.60916	−	7.50546i	0.0984062	−	0.283074i
$704$	5.94356			0.224006
$705$		0			0
$706$	−0.576199	−	0.209719i	−0.0216856	−	0.00789290i
$707$	1.62089	+	0.285807i	0.0609599	+	0.0107489i
$708$	−5.09170	+	0.897804i	−0.191358	+	0.0337415i
$709$	−12.2852	+	4.47146i	−0.461382	+	0.167929i	−0.562244	−	0.826971i	$-0.690062\pi$
$709$	−12.2852	+	4.47146i	−0.461382	+	0.167929i	0.100863	+	0.994900i	$0.467840\pi$
$710$		0			0
$711$	0.266044	+	0.460802i	0.00997745	+	0.0172814i
$712$	−7.28455	+	8.68139i	−0.273000	+	0.325349i
$713$	5.54812	−	6.61200i	0.207779	−	0.247621i
$714$	−1.80541	−	3.12706i	−0.0675657	−	0.117027i
$715$		0			0
$716$	−12.1839	+	4.43458i	−0.455334	+	0.165728i
$717$	−7.76903	+	1.36989i	−0.290140	+	0.0511595i
$718$	15.4056	+	2.71641i	0.574930	+	0.101376i
$719$	26.4722	+	9.63511i	0.987248	+	0.359329i	0.784654	−	0.619934i	$-0.212841\pi$
$719$	26.4722	+	9.63511i	0.987248	+	0.359329i	0.202594	+	0.979263i	$0.435063\pi$
$720$		0			0
$721$	−1.10101			−0.0410039
$722$	0.550931	+	18.9920i	0.0205035	+	0.706809i
$723$		−	29.1685i		−	1.08479i
$724$	−14.2456	+	11.9534i	−0.529432	+	0.444246i
$725$		0			0
$726$	7.93882	−	45.0233i	0.294637	−	1.67097i
$727$	−33.4162	+	5.89218i	−1.23934	+	0.218529i	−0.754632	−	0.656148i	$-0.772185\pi$
$727$	−33.4162	+	5.89218i	−1.23934	+	0.218529i	−0.484706	+	0.874677i	$0.661074\pi$
$728$	0.390896	+	1.07398i	0.0144876	+	0.0398043i
$729$	10.3316	−	17.8948i	0.382651	−	0.662770i
$730$		0			0
$731$	2.25490	+	1.89209i	0.0834005	+	0.0699813i
$732$	14.8985	−	17.7554i	0.550665	−	0.656257i
$733$	30.4331	−	17.5706i	1.12407	−	0.648984i	0.181636	−	0.983366i	$-0.441861\pi$
$733$	30.4331	−	17.5706i	1.12407	−	0.648984i	0.942438	+	0.334382i	$0.108528\pi$
$734$	−17.5292	+	30.3614i	−0.647013	+	1.12066i
$735$		0			0
$736$	0.492726	+	2.79439i	0.0181621	+	0.103003i
$737$	29.5115	+	5.20368i	1.08707	+	0.191680i
$738$	1.24168	−	3.41147i	0.0457067	−	0.125578i
$739$	−12.6511	+	10.6155i	−0.465379	+	0.390499i	−0.845105	−	0.534600i	$-0.820462\pi$
$739$	−12.6511	+	10.6155i	−0.465379	+	0.390499i	0.379727	+	0.925099i	$0.376018\pi$
$740$		0			0
$741$	−25.4641	−	8.85219i	−0.935447	−	0.325193i
$742$		−	1.07873i		−	0.0396013i
$743$	−24.5992	−	29.3161i	−0.902456	−	1.07550i	−0.996798	−	0.0799651i	$-0.974519\pi$
$743$	−24.5992	−	29.3161i	−0.902456	−	1.07550i	0.0943419	−	0.995540i	$-0.469925\pi$
$744$	5.37211	+	1.95529i	0.196951	+	0.0716844i
$745$		0			0
$746$	−4.48814	−	25.4535i	−0.164322	−	0.931919i
$747$	−1.70248	−	4.67752i	−0.0622904	−	0.171141i
$748$	28.4752	+	16.4402i	1.04116	+	0.601112i
$749$	−2.32635	−	4.02936i	−0.0850030	−	0.147230i
$750$		0			0
$751$	8.77972	+	7.36706i	0.320376	+	0.268828i	0.788765	−	0.614695i	$-0.210721\pi$
$751$	8.77972	+	7.36706i	0.320376	+	0.268828i	−0.468389	+	0.883523i	$0.655165\pi$
$752$	4.02936	−	2.32635i	0.146936	−	0.0848333i
$753$	11.9265	+	6.88578i	0.434627	+	0.250932i
$754$	22.0437	−	8.02325i	0.802784	−	0.292190i
$755$		0			0
$756$	−0.279715	+	1.58634i	−0.0101731	+	0.0576947i
$757$	6.63943	−	18.2417i	0.241314	−	0.663006i	−0.758620	−	0.651534i	$-0.774126\pi$
$757$	6.63943	−	18.2417i	0.241314	−	0.663006i	0.999934	−	0.0114722i	$-0.00365180\pi$
$758$	−2.85759	−	3.40554i	−0.103792	−	0.123695i
$759$	31.6955			1.15047
$760$		0			0
$761$	14.6441			0.530850			0.265425	−	0.964132i	$-0.414488\pi$
$761$	14.6441			0.530850			0.265425	+	0.964132i	$0.414488\pi$
$762$	−23.3581	−	27.8371i	−0.846174	−	1.00843i
$763$	1.62495	−	4.46451i	0.0588271	−	0.161626i
$764$	4.09193	−	23.2065i	0.148041	−	0.839581i
$765$		0			0
$766$	−25.7922	+	9.38759i	−0.931910	+	0.339188i
$767$	7.84035	+	4.52663i	0.283098	+	0.163447i
$768$	−1.62760	+	0.939693i	−0.0587308	+	0.0339082i
$769$	31.6024	+	26.5176i	1.13961	+	0.956248i	0.999426	−	0.0338770i	$-0.0107854\pi$
$769$	31.6024	+	26.5176i	1.13961	+	0.956248i	0.140186	+	0.990125i	$0.455230\pi$
$770$		0			0
$771$	29.3628	+	50.8578i	1.05747	+	1.83160i
$772$	3.62181	+	2.09105i	0.130352	+	0.0752586i
$773$	−6.85646	−	18.8380i	−0.246610	−	0.677554i	−0.999805	−	0.0197573i	$-0.993711\pi$
$773$	−6.85646	−	18.8380i	−0.246610	−	0.677554i	0.753195	−	0.657797i	$-0.228512\pi$
$774$	0.0491630	+	0.278817i	0.00176713	+	0.0100219i
$775$		0			0
$776$	5.37686	+	1.95702i	0.193018	+	0.0702528i
$777$	−0.764818	−	0.911474i	−0.0274377	−	0.0326990i
$778$		−	23.0077i		−	0.824867i
$779$	23.0574	+	18.7845i	0.826116	+	0.673025i
$780$		0			0
$781$	59.5169	−	49.9406i	2.12968	−	1.78701i
$782$	−5.36879	+	14.7506i	−0.191987	+	0.527481i
$783$	32.5601	+	5.74123i	1.16360	+	0.205175i
$784$	1.19459	+	6.77487i	0.0426640	+	0.241960i
$785$		0			0
$786$	−16.0471	+	27.7944i	−0.572381	+	0.991393i
$787$	30.2093	−	17.4413i	1.07684	−	0.621717i	0.146801	−	0.989166i	$-0.453102\pi$
$787$	30.2093	−	17.4413i	1.07684	−	0.621717i	0.930044	+	0.367449i	$0.119769\pi$
$788$	16.5211	−	19.6891i	0.588541	−	0.701396i
$789$	31.5180	+	26.4467i	1.12207	+	0.941529i
$790$		0			0
$791$	2.34776	−	4.06645i	0.0834768	−	0.144586i
$792$	1.08164	+	2.97178i	0.0384344	+	0.105598i
$793$	−39.9688	+	7.04757i	−1.41933	+	0.250267i
$794$	−6.35891	+	36.0632i	−0.225669	+	1.27983i
$795$		0			0
$796$	−20.0385	+	16.8143i	−0.710245	+	0.595967i
$797$			42.3979i			1.50181i	0.660411	+	0.750905i	$0.270382\pi$
$797$			42.3979i			1.50181i	−0.660411	+	0.750905i	$0.729618\pi$
$798$	2.48427	+	1.38666i	0.0879422	+	0.0490872i
$799$	25.7392			0.910586
$800$		0			0
$801$	−5.66637	−	2.06239i	−0.200211	−	0.0728710i
$802$	34.8641	+	6.14749i	1.23110	+	0.217075i
$803$	−12.8733	+	2.26991i	−0.454290	+	0.0801036i
$804$	−8.90420	+	3.24086i	−0.314027	+	0.114296i
$805$		0			0
$806$	−5.00521	−	8.66929i	−0.176301	−	0.305363i
$807$	24.6074	−	29.3259i	0.866221	−	1.03232i
$808$	3.04628	−	3.63041i	0.107168	−	0.127718i
$809$	3.97384	+	6.88289i	0.139713	+	0.241990i	0.927388	−	0.374101i	$-0.122049\pi$
$809$	3.97384	+	6.88289i	0.139713	+	0.241990i	−0.787675	+	0.616091i	$0.788715\pi$
$810$		0			0
$811$	−2.68510	+	0.977295i	−0.0942865	+	0.0343175i	−0.388733	−	0.921351i	$-0.627087\pi$
$811$	−2.68510	+	0.977295i	−0.0942865	+	0.0343175i	0.294446	+	0.955668i	$0.404865\pi$
$812$	−2.43804	+	0.429892i	−0.0855585	+	0.0150863i
$813$	41.9770	+	7.40167i	1.47220	+	0.259588i
$814$	10.1814	+	3.70572i	0.356857	+	0.129886i
$815$		0			0
$816$	−10.3969			−0.363965
$817$	−2.28969	−	0.369585i	−0.0801060	−	0.0129301i
$818$		−	1.68180i		−	0.0588027i
$819$	−0.465852	+	0.390896i	−0.0162782	+	0.0136590i
$820$		0			0
$821$	6.34183	−	35.9663i	0.221332	−	1.25523i	−0.648244	−	0.761433i	$-0.724496\pi$
$821$	6.34183	−	35.9663i	0.221332	−	1.25523i	0.869575	−	0.493800i	$-0.164393\pi$
$822$	28.4196	−	5.01114i	0.991248	−	0.174784i
$823$	12.8171	+	35.2148i	0.446778	+	1.22751i	0.934955	+	0.354767i	$0.115440\pi$
$823$	12.8171	+	35.2148i	0.446778	+	1.22751i	−0.488177	+	0.872745i	$0.662338\pi$
$824$	−1.58512	+	2.74551i	−0.0552204	+	0.0956445i
$825$		0			0
$826$	−0.731896	−	0.614134i	−0.0254659	−	0.0213684i
$827$	11.9111	−	14.1951i	0.414188	−	0.493611i	−0.518103	−	0.855318i	$-0.673362\pi$
$827$	11.9111	−	14.1951i	0.414188	−	0.493611i	0.932292	+	0.361708i	$0.117806\pi$
$828$	−1.30753	+	0.754900i	−0.0454396	+	0.0262346i
$829$	−0.458578	+	0.794280i	−0.0159271	+	0.0275865i	−0.873879	−	0.486143i	$-0.838403\pi$
$829$	−0.458578	+	0.794280i	−0.0159271	+	0.0275865i	0.857952	+	0.513730i	$0.171737\pi$
$830$		0			0
$831$	−6.79308	−	38.5255i	−0.235649	−	1.33643i
$832$	3.24086	+	0.571452i	0.112357	+	0.0198115i
$833$	−13.0164	+	35.7622i	−0.450991	+	1.23909i
$834$	−7.42262	+	6.22832i	−0.257024	+	0.215669i
$835$		0			0
$836$	−25.9047	+	0.375650i	−0.895932	+	0.0129921i
$837$		−	14.1088i		−	0.487670i
$838$	−21.6640	−	25.8182i	−0.748372	−	0.891875i
$839$	−25.5462	−	9.29807i	−0.881954	−	0.321005i	−0.138956	−	0.990299i	$-0.544375\pi$
$839$	−25.5462	−	9.29807i	−0.881954	−	0.321005i	−0.742998	+	0.669294i	$0.766597\pi$
$840$		0			0
$841$	3.78787	+	21.4821i	0.130616	+	0.740761i
$842$	−2.44566	−	6.71941i	−0.0842832	−	0.231566i
$843$	29.6212	+	17.1018i	1.02021	+	0.589017i
$844$	3.28952	+	5.69761i	0.113230	+	0.196120i
$845$		0			0
$846$	1.89646	+	1.59132i	0.0652016	+	0.0547107i
$847$	7.31645	−	4.22416i	0.251396	−	0.145144i
$848$	−2.68993	−	1.55303i	−0.0923727	−	0.0533314i
$849$	−32.1425	+	11.6989i	−1.10313	+	0.401506i
$850$		0			0
$851$	−0.898214	+	5.09403i	−0.0307904	+	0.174621i
$852$	−8.40247	+	23.0856i	−0.287864	+	0.790899i
$853$	−8.74946	−	10.4272i	−0.299576	−	0.357021i	0.595167	−	0.803602i	$-0.297086\pi$
$853$	−8.74946	−	10.4272i	−0.299576	−	0.357021i	−0.894743	+	0.446581i	$0.852641\pi$
$854$	4.28312			0.146565
$855$		0			0
$856$	−13.3969			−0.457898
$857$	−4.56942	−	5.44562i	−0.156088	−	0.186019i	0.682333	−	0.731042i	$-0.260965\pi$
$857$	−4.56942	−	5.44562i	−0.156088	−	0.186019i	−0.838421	+	0.545023i	$0.816521\pi$
$858$	12.5726	−	34.5428i	0.429220	−	1.17927i
$859$	−2.95605	+	16.7646i	−0.100859	+	0.572001i	0.891935	+	0.452165i	$0.149348\pi$
$859$	−2.95605	+	16.7646i	−0.100859	+	0.572001i	−0.992794	+	0.119836i	$0.961763\pi$
$860$		0			0
$861$	4.18479	−	1.52314i	0.142617	−	0.0519085i
$862$	19.6060	+	11.3195i	0.667784	+	0.385545i
$863$	−9.41236	+	5.43423i	−0.320401	+	0.184983i	−0.651571	−	0.758588i	$-0.725890\pi$
$863$	−9.41236	+	5.43423i	−0.320401	+	0.184983i	0.331171	+	0.943571i	$0.392556\pi$
$864$	3.55303	+	2.98135i	0.120877	+	0.101428i
$865$		0			0
$866$	2.38326	+	4.12792i	0.0809863	+	0.140272i
$867$	−22.1418	−	12.7836i	−0.751976	−	0.434153i
$868$	0.361323	+	0.992726i	0.0122641	+	0.0336953i
$869$	−1.03209	−	5.85327i	−0.0350112	−	0.198558i
$870$		0			0
$871$	15.5915	+	5.67485i	0.528298	+	0.192285i
$872$	−8.79336	−	10.4795i	−0.297781	−	0.354881i
$873$			3.04458i			0.103043i
$874$	−2.32413	−	12.1480i	−0.0786149	−	0.410913i
$875$		0			0
$876$	3.16637	−	2.65690i	0.106982	−	0.0897684i
$877$	4.29201	−	11.7922i	0.144931	−	0.398194i	−0.845893	−	0.533352i	$-0.820932\pi$
$877$	4.29201	−	11.7922i	0.144931	−	0.398194i	0.990824	+	0.135158i	$0.0431542\pi$
$878$	6.02763	+	1.06283i	0.203423	+	0.0358689i
$879$	9.72550	+	55.1560i	0.328033	+	1.86037i
$880$		0			0
$881$	−17.7408	+	30.7280i	−0.597703	+	1.03525i	0.395456	+	0.918485i	$0.370587\pi$
$881$	−17.7408	+	30.7280i	−0.597703	+	1.03525i	−0.993159	+	0.116768i	$0.962747\pi$
$882$	−3.17004	+	1.83022i	−0.106741	+	0.0616268i
$883$	−10.8499	+	12.9304i	−0.365127	+	0.435141i	−0.917061	−	0.398746i	$-0.869445\pi$
$883$	−10.8499	+	12.9304i	−0.365127	+	0.435141i	0.551934	+	0.833888i	$0.313890\pi$
$884$	13.9461	+	11.7022i	0.469058	+	0.393586i
$885$		0			0
$886$	12.3983	−	21.4744i	0.416528	−	0.721448i
$887$	−19.9624	−	54.8462i	−0.670271	−	1.84155i	−0.522730	−	0.852498i	$-0.675086\pi$
$887$	−19.9624	−	54.8462i	−0.670271	−	1.84155i	−0.147541	−	0.989056i	$-0.547136\pi$
$888$	−3.37397	+	0.594922i	−0.113223	+	0.0199643i
$889$	1.16607	−	6.61311i	0.0391087	−	0.221797i
$890$		0			0
$891$	46.9561	−	39.4009i	1.57309	−	1.31998i
$892$			21.1411i			0.707858i
$893$	−17.4147	+	10.3939i	−0.582760	+	0.347820i
$894$	−21.9659			−0.734648
$895$		0			0
$896$	−0.326352	−	0.118782i	−0.0109026	−	0.00396824i
$897$	17.2827	+	3.04741i	0.577053	+	0.101750i
$898$	−0.657115	+	0.115867i	−0.0219282	+	0.00386653i
$899$	20.3760	−	7.41625i	0.679577	−	0.247346i
$900$		0			0
$901$	−8.59152	−	14.8809i	−0.286225	−	0.495756i
$902$	−26.0667	+	31.0651i	−0.867927	+	1.03436i
$903$	−0.223238	+	0.266044i	−0.00742889	+	0.00885340i
$904$	−6.76011	−	11.7089i	−0.224838	−	0.389431i
$905$		0			0
$906$	12.6147	−	4.59137i	0.419095	−	0.152538i
$907$	1.60565	−	0.283119i	0.0533146	−	0.00940080i	−0.146927	−	0.989147i	$-0.546938\pi$
$907$	1.60565	−	0.283119i	0.0533146	−	0.00940080i	0.200242	+	0.979747i	$0.435827\pi$
$908$	−3.19291	−	0.562996i	−0.105960	−	0.0186837i
$909$	2.36959	+	0.862458i	0.0785942	+	0.0286059i
$910$		0			0
$911$	21.6016			0.715694			0.357847	−	0.933780i	$-0.383511\pi$
$911$	21.6016			0.715694			0.357847	+	0.933780i	$0.383511\pi$
$912$	7.03439	−	4.19846i	0.232932	−	0.139025i
$913$			55.6023i			1.84017i
$914$	−10.1092	+	8.48264i	−0.334383	+	0.280581i
$915$		0			0
$916$	1.48767	−	8.43702i	0.0491541	−	0.278767i
$917$	−5.84067	+	1.02987i	−0.192876	+	0.0340092i
$918$	8.77579	+	24.1113i	0.289644	+	0.795791i
$919$	17.8152	−	30.8568i	0.587669	−	1.01787i	−0.406867	−	0.913487i	$-0.633379\pi$
$919$	17.8152	−	30.8568i	0.587669	−	1.01787i	0.994537	−	0.104386i	$-0.0332878\pi$
$920$		0			0
$921$	6.70233	+	5.62393i	0.220849	+	0.185315i
$922$	9.26697	−	11.0439i	0.305192	−	0.363713i
$923$	37.2545	−	21.5089i	1.22625	−	0.707975i
$924$	−1.93969	+	3.35965i	−0.0638112	+	0.110524i
$925$		0			0
$926$	1.13382	+	6.43020i	0.0372596	+	0.211310i
$927$	−1.66122	−	0.292919i	−0.0545618	−	0.00962071i
$928$	−2.43804	+	6.69846i	−0.0800326	+	0.219888i
$929$	−22.0271	+	18.4829i	−0.722685	+	0.606405i	−0.928127	−	0.372264i	$-0.878581\pi$
$929$	−22.0271	+	18.4829i	−0.722685	+	0.606405i	0.205441	+	0.978669i	$0.434137\pi$
$930$		0			0
$931$	−5.63475	−	29.4524i	−0.184672	−	0.965263i
$932$		−	1.11556i		−	0.0365415i
$933$	−16.9819	−	20.2383i	−0.555964	−	0.662572i
$934$	23.6596	+	8.61138i	0.774165	+	0.281773i
$935$		0			0
$936$	0.304063	+	1.72443i	0.00993861	+	0.0563647i
$937$	−12.3507	−	33.9334i	−0.403481	−	1.10855i	−0.960555	−	0.278091i	$-0.910298\pi$
$937$	−12.3507	−	33.9334i	−0.403481	−	1.10855i	0.557074	−	0.830463i	$-0.311924\pi$
$938$	−1.51644	−	0.875515i	−0.0495134	−	0.0285866i
$939$	6.90895	+	11.9666i	0.225465	+	0.390517i
$940$		0			0
$941$	35.1018	+	29.4539i	1.14429	+	0.960170i	0.999571	−	0.0293038i	$-0.00932903\pi$
$941$	35.1018	+	29.4539i	1.14429	+	0.960170i	0.144715	+	0.989473i	$0.453773\pi$
$942$	4.99984	−	2.88666i	0.162904	−	0.0940524i
$943$	−16.7663	−	9.68004i	−0.545987	−	0.315226i
$944$	−2.58512	+	0.940908i	−0.0841386	+	0.0306239i
$945$		0			0
$946$	0.549163	−	3.11446i	0.0178548	−	0.101260i
$947$	−7.54590	+	20.7322i	−0.245209	+	0.673706i	0.754637	+	0.656143i	$0.227813\pi$
$947$	−7.54590	+	20.7322i	−0.245209	+	0.673706i	−0.999846	+	0.0175633i	$0.994409\pi$
$948$	1.20805	+	1.43969i	0.0392355	+	0.0467590i
$949$	−7.23772			−0.234946
$950$		0			0
$951$	−10.1607			−0.329485
$952$	−1.23497	−	1.47178i	−0.0400257	−	0.0477007i
$953$	−18.4940	+	50.8119i	−0.599080	+	1.64596i	0.154033	+	0.988066i	$0.450774\pi$
$953$	−18.4940	+	50.8119i	−0.599080	+	1.64596i	−0.753112	+	0.657892i	$0.771448\pi$
$954$	0.286989	−	1.62760i	0.00929161	−	0.0526953i
$955$		0			0
$956$	−3.94444	+	1.43566i	−0.127572	+	0.0464325i
$957$	68.9577	+	39.8127i	2.22909	+	1.28696i
$958$	8.04174	−	4.64290i	0.259817	−	0.150005i
$959$	4.08512	+	3.42782i	0.131915	+	0.110690i
$960$		0			0
$961$	10.8735	+	18.8334i	0.350757	+	0.607528i
$962$	5.19534	+	2.99953i	0.167505	+	0.0967088i
$963$	−2.43804	−	6.69846i	−0.0785648	−	0.215855i
$964$	−2.69506	−	15.2844i	−0.0868020	−	0.492279i
$965$		0			0
$966$	−1.74035	−	0.633436i	−0.0559949	−	0.0203805i
$967$	1.01957	+	1.21507i	0.0327870	+	0.0390740i	0.782189	−	0.623042i	$-0.214103\pi$
$967$	1.01957	+	1.21507i	0.0327870	+	0.0390740i	−0.749402	+	0.662116i	$0.769659\pi$
$968$		−	24.3259i		−	0.781865i
$969$	45.3144	−	0.657115i	1.45571	−	0.0211096i
$970$		0			0
$971$	8.74944	−	7.34165i	0.280783	−	0.235605i	−0.491509	−	0.870872i	$-0.663555\pi$
$971$	8.74944	−	7.34165i	0.280783	−	0.235605i	0.772292	+	0.635268i	$0.219110\pi$
$972$	−1.87014	+	5.13816i	−0.0599846	+	0.164806i
$973$	−1.76335	−	0.310927i	−0.0565305	−	0.00996785i
$974$	−2.76651	−	15.6897i	−0.0886447	−	0.502729i
$975$		0			0
$976$	6.16637	−	10.6805i	0.197381	−	0.341874i
$977$	39.5503	−	22.8344i	1.26533	−	0.730537i	0.291227	−	0.956654i	$-0.405936\pi$
$977$	39.5503	−	22.8344i	1.26533	−	0.730537i	0.974100	+	0.226117i	$0.0726031\pi$
$978$	−23.0365	+	27.4538i	−0.736626	+	0.877877i
$979$	51.5984	+	43.2962i	1.64909	+	1.38375i
$980$		0			0
$981$	3.63950	−	6.30380i	0.116200	−	0.201265i
$982$	−0.548284	−	1.50640i	−0.0174964	−	0.0480710i
$983$	22.0271	−	3.88397i	0.702555	−	0.123879i	0.189052	−	0.981967i	$-0.439459\pi$
$983$	22.0271	−	3.88397i	0.702555	−	0.123879i	0.513503	+	0.858088i	$0.328347\pi$
$984$	2.22668	−	12.6281i	0.0709840	−	0.402570i
$985$		0			0
$986$	−30.2087	+	25.3481i	−0.962042	+	0.807249i
$987$			3.03684i			0.0966636i
$988$	−14.1612	−	2.28581i	−0.450529	−	0.0727212i
$989$	1.50980			0.0480089
$990$		0			0
$991$	28.2511	+	10.2826i	0.897425	+	0.326636i	0.749221	−	0.662321i	$-0.230428\pi$
$991$	28.2511	+	10.2826i	0.897425	+	0.326636i	0.148205	+	0.988957i	$0.452651\pi$
$992$	2.99568	+	0.528218i	0.0951128	+	0.0167710i
$993$	−47.5894	+	8.39130i	−1.51021	+	0.266290i
$994$	−4.26604	+	1.55271i	−0.135311	+	0.0492491i
$995$		0			0
$996$	−8.79086	−	15.2262i	−0.278549	−	0.482461i
$997$	11.9456	−	14.2362i	0.378322	−	0.450866i	−0.542962	−	0.839757i	$-0.682697\pi$
$997$	11.9456	−	14.2362i	0.378322	−	0.450866i	0.921284	+	0.388891i	$0.127142\pi$
$998$	21.4198	−	25.5271i	0.678031	−	0.808046i
$999$	4.22756	+	7.32235i	0.133754	+	0.231669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.a.899.2		12
5.2	odd	4		950.2.l.f.101.1	yes	6
5.3	odd	4		950.2.l.a.101.1	✓	6
5.4	even	2	inner	950.2.u.a.899.1		12
19.16	even	9	inner	950.2.u.a.149.1		12
95.54	even	18	inner	950.2.u.a.149.2		12
95.73	odd	36		950.2.l.a.301.1	yes	6
95.92	odd	36		950.2.l.f.301.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.a.101.1	✓	6	5.3	odd	4
950.2.l.a.301.1	yes	6	95.73	odd	36
950.2.l.f.101.1	yes	6	5.2	odd	4
950.2.l.f.301.1	yes	6	95.92	odd	36
950.2.u.a.149.1		12	19.16	even	9	inner
950.2.u.a.149.2		12	95.54	even	18	inner
950.2.u.a.899.1		12	5.4	even	2	inner
950.2.u.a.899.2		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.76604 + 0.642788i) q^{6} +(-0.300767 - 0.173648i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.407604 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.76604 + 0.642788i) q^{6} +(-0.300767 - 0.173648i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.407604 - 0.342020i) q^{9} +(2.97178 + 5.14728i) q^{11} +(-1.62760 - 0.939693i) q^{12} +(1.12554 + 3.09240i) q^{13} +(-0.0603074 - 0.342020i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-3.55596 - 4.23783i) q^{17} -0.532089i q^{18} +(4.11721 + 1.43128i) q^{19} +(0.500000 - 0.419550i) q^{21} +(-2.03282 + 5.58512i) q^{22} +(-2.79439 - 0.492726i) q^{23} +(-0.326352 - 1.85083i) q^{24} +(-1.64543 + 2.84997i) q^{26} +(-4.01676 + 2.31908i) q^{27} +(0.223238 - 0.266044i) q^{28} +(-5.46064 - 4.58202i) q^{29} +(-1.52094 + 2.63435i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-11.0005 + 1.93969i) q^{33} +(0.960637 - 5.44804i) q^{34} +(0.407604 - 0.342020i) q^{36} -1.82295i q^{37} +(1.55007 + 4.07398i) q^{38} -6.18479 q^{39} +(6.41147 + 2.33359i) q^{41} +(0.642788 + 0.113341i) q^{42} +(-0.524005 + 0.0923963i) q^{43} +(-5.58512 + 2.03282i) q^{44} +(-1.41875 - 2.45734i) q^{46} +(-2.99070 + 3.56418i) q^{47} +(1.20805 - 1.43969i) q^{48} +(-3.43969 - 5.95772i) q^{49} +(9.76991 - 3.55596i) q^{51} +(-3.24086 + 0.571452i) q^{52} +(3.05888 + 0.539363i) q^{53} +(-4.35844 - 1.58634i) q^{54} +0.347296 q^{56} +(-5.17420 + 6.35117i) q^{57} -7.12836i q^{58} +(2.10741 - 1.76833i) q^{59} +(-2.14156 + 12.1454i) q^{61} +(-2.99568 + 0.528218i) q^{62} +(0.0632028 + 0.173648i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-8.55690 - 7.18009i) q^{66} +(3.24086 - 3.86231i) q^{67} +(4.79093 - 2.76604i) q^{68} +(2.66637 - 4.61830i) q^{69} +(-2.26991 - 12.8733i) q^{71} +(0.524005 + 0.0923963i) q^{72} +(-0.752219 + 2.06670i) q^{73} +(1.39646 - 1.17177i) q^{74} +(-2.12449 + 3.80612i) q^{76} -2.06418i q^{77} +(-3.97551 - 4.73783i) q^{78} +(-0.939693 - 0.342020i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(2.33359 + 6.41147i) q^{82} +(8.10170 + 4.67752i) q^{83} +(0.326352 + 0.565258i) q^{84} +(-0.407604 - 0.342020i) q^{86} +(11.6021 - 6.69846i) q^{87} +(-5.14728 - 2.97178i) q^{88} +(10.6493 - 3.87603i) q^{89} +(0.198463 - 1.12554i) q^{91} +(0.970481 - 2.66637i) q^{92} +(-3.67474 - 4.37939i) q^{93} -4.65270 q^{94} +1.87939 q^{96} +(-3.67799 - 4.38326i) q^{97} +(2.35289 - 6.46451i) q^{98} +(0.549163 - 3.11446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^6 - 12 * q^9	\( 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) \) 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * q^99

Introduction

L-functions

Modular forms

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