LMFDB - Embedded newform 950.2.u.d.549.2

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			549.2
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	950.549
Dual form			950.2.u.d.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.565258 - 0.673648i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.673648 - 0.565258i) q^{6} +(0.460802 - 0.266044i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.386659 + 2.19285i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.565258 - 0.673648i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.673648 - 0.565258i) q^{6} +(0.460802 - 0.266044i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.386659 + 2.19285i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.761570 - 0.439693i) q^{12} +(-0.419550 - 0.500000i) q^{13} +(0.500000 - 0.181985i) q^{14} +(0.766044 + 0.642788i) q^{16} +(3.82045 + 0.673648i) q^{17} +2.22668i q^{18} +(4.21688 + 1.10359i) q^{19} +(0.0812519 - 0.460802i) q^{21} +(0.642788 - 0.766044i) q^{22} +(1.55007 - 4.25877i) q^{23} +(0.826352 - 0.300767i) q^{24} +(-0.326352 - 0.565258i) q^{26} +(3.98048 + 2.29813i) q^{27} +(0.524005 - 0.0923963i) q^{28} +(0.773318 + 4.38571i) q^{29} +(-1.37939 - 2.38917i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-0.300767 - 0.826352i) q^{33} +(3.64543 + 1.32683i) q^{34} +(-0.386659 + 2.19285i) q^{36} -0.958111i q^{37} +(3.96118 + 1.81908i) q^{38} -0.573978 q^{39} +(-4.78699 - 4.01676i) q^{41} +(0.160035 - 0.439693i) q^{42} +(-1.71275 - 4.70574i) q^{43} +(0.766044 - 0.642788i) q^{44} +(2.26604 - 3.92490i) q^{46} +(-0.761570 + 0.134285i) q^{47} +(0.866025 - 0.152704i) q^{48} +(-3.35844 + 5.81699i) q^{49} +(2.61334 - 2.19285i) q^{51} +(-0.223238 - 0.613341i) q^{52} +(1.31920 - 3.62449i) q^{53} +(3.52094 + 2.95442i) q^{54} +0.532089 q^{56} +(3.12706 - 2.21688i) q^{57} +4.45336i q^{58} +(-1.08853 + 6.17334i) q^{59} +(-4.62449 - 1.68317i) q^{61} +(-0.943555 - 2.59240i) q^{62} +(0.761570 + 0.907604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.152704 - 0.866025i) q^{66} +(-1.32683 + 0.233956i) q^{67} +(3.35965 + 1.93969i) q^{68} +(-1.99273 - 3.45150i) q^{69} +(-5.33275 + 1.94096i) q^{71} +(-0.761570 + 2.09240i) q^{72} +(4.80526 - 5.72668i) q^{73} +(0.166374 - 0.943555i) q^{74} +(3.58512 + 2.47929i) q^{76} -0.532089i q^{77} +(-0.565258 - 0.0996702i) q^{78} +(0.543233 + 0.455827i) q^{79} +(-2.47906 + 0.902302i) q^{81} +(-4.01676 - 4.78699i) q^{82} +(9.15144 - 5.28359i) q^{83} +(0.233956 - 0.405223i) q^{84} +(-0.869585 - 4.93166i) q^{86} +(3.39155 + 1.95811i) q^{87} +(0.866025 - 0.500000i) q^{88} +(-3.75877 + 3.15398i) q^{89} +(-0.326352 - 0.118782i) q^{91} +(2.91317 - 3.47178i) q^{92} +(-2.38917 - 0.421274i) q^{93} -0.773318 q^{94} +0.879385 q^{96} +(0.0994798 + 0.0175410i) q^{97} +(-4.31753 + 5.14543i) q^{98} +(2.09240 + 0.761570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 + 18 * q^9	$ 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.565258	−	0.673648i	0.326352	−	0.388931i	−0.577774	−	0.816197i	$-0.696079\pi$
$3$	0.565258	−	0.673648i	0.326352	−	0.388931i	0.904126	+	0.427266i	$0.140523\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	0.673648	−	0.565258i	0.275016	−	0.230766i
$7$	0.460802	−	0.266044i	0.174167	−	0.100555i	−0.410382	−	0.911914i	$-0.634605\pi$
$7$	0.460802	−	0.266044i	0.174167	−	0.100555i	0.584549	+	0.811358i	$0.301271\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.386659	+	2.19285i	0.128886	+	0.730951i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	0.761570	−	0.439693i	0.219846	−	0.126928i
$13$	−0.419550	−	0.500000i	−0.116362	−	0.138675i	0.704719	−	0.709487i	$-0.251073\pi$
$13$	−0.419550	−	0.500000i	−0.116362	−	0.138675i	−0.821081	+	0.570812i	$0.806629\pi$
$14$	0.500000	−	0.181985i	0.133631	−	0.0486376i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.82045	+	0.673648i	0.926595	+	0.163384i	0.616530	−	0.787332i	$-0.288538\pi$
$17$	3.82045	+	0.673648i	0.926595	+	0.163384i	0.310065	+	0.950715i	$0.399649\pi$
$18$			2.22668i			0.524834i
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$20$		0			0
$21$	0.0812519	−	0.460802i	0.0177306	−	0.100555i
$22$	0.642788	−	0.766044i	0.137043	−	0.163321i
$23$	1.55007	−	4.25877i	0.323211	−	0.888015i	−0.666573	−	0.745440i	$-0.732239\pi$
$23$	1.55007	−	4.25877i	0.323211	−	0.888015i	0.989784	−	0.142575i	$-0.0455383\pi$
$24$	0.826352	−	0.300767i	0.168678	−	0.0613939i
$25$		0			0
$26$	−0.326352	−	0.565258i	−0.0640029	−	0.110856i
$27$	3.98048	+	2.29813i	0.766044	+	0.442276i
$28$	0.524005	−	0.0923963i	0.0990277	−	0.0174613i
$29$	0.773318	+	4.38571i	0.143602	+	0.814405i	0.968479	+	0.249094i	$0.0801328\pi$
$29$	0.773318	+	4.38571i	0.143602	+	0.814405i	−0.824878	+	0.565311i	$0.808756\pi$
$30$		0			0
$31$	−1.37939	−	2.38917i	−0.247745	−	0.429107i	0.715155	−	0.698966i	$-0.246356\pi$
$31$	−1.37939	−	2.38917i	−0.247745	−	0.429107i	−0.962900	+	0.269859i	$0.913023\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−0.300767	−	0.826352i	−0.0523569	−	0.143849i
$34$	3.64543	+	1.32683i	0.625186	+	0.227549i
$35$		0			0
$36$	−0.386659	+	2.19285i	−0.0644432	+	0.365476i
$37$		−	0.958111i		−	0.157512i	−0.996894	−	0.0787562i	$-0.974905\pi$
$37$		−	0.958111i		−	0.157512i	0.996894	−	0.0787562i	$-0.0250949\pi$
$38$	3.96118	+	1.81908i	0.642588	+	0.295093i
$39$	−0.573978			−0.0919100
$40$		0			0
$41$	−4.78699	−	4.01676i	−0.747602	−	0.627313i	0.187265	−	0.982309i	$-0.440038\pi$
$41$	−4.78699	−	4.01676i	−0.747602	−	0.627313i	−0.934868	+	0.354997i	$0.884482\pi$
$42$	0.160035	−	0.439693i	0.0246939	−	0.0678460i
$43$	−1.71275	−	4.70574i	−0.261192	−	0.717618i	−0.999088	−	0.0427039i	$-0.986403\pi$
$43$	−1.71275	−	4.70574i	−0.261192	−	0.717618i	0.737896	−	0.674914i	$-0.235819\pi$
$44$	0.766044	−	0.642788i	0.115486	−	0.0969039i
$45$		0			0
$46$	2.26604	−	3.92490i	0.334110	−	0.578696i
$47$	−0.761570	+	0.134285i	−0.111086	+	0.0195875i	−0.228915	−	0.973446i	$-0.573518\pi$
$47$	−0.761570	+	0.134285i	−0.111086	+	0.0195875i	0.117829	+	0.993034i	$0.462407\pi$
$48$	0.866025	−	0.152704i	0.125000	−	0.0220409i
$49$	−3.35844	+	5.81699i	−0.479777	+	0.830999i
$50$		0			0
$51$	2.61334	−	2.19285i	0.365941	−	0.307061i
$52$	−0.223238	−	0.613341i	−0.0309575	−	0.0850551i
$53$	1.31920	−	3.62449i	0.181207	−	0.497861i	−0.815518	−	0.578732i	$-0.803548\pi$
$53$	1.31920	−	3.62449i	0.181207	−	0.497861i	0.996725	+	0.0808705i	$0.0257700\pi$
$54$	3.52094	+	2.95442i	0.479140	+	0.402046i
$55$		0			0
$56$	0.532089			0.0711034
$57$	3.12706	−	2.21688i	0.414189	−	0.293633i
$58$			4.45336i			0.584755i
$59$	−1.08853	+	6.17334i	−0.141714	+	0.803700i	0.828233	+	0.560384i	$0.189346\pi$
$59$	−1.08853	+	6.17334i	−0.141714	+	0.803700i	−0.969947	+	0.243316i	$0.921765\pi$
$60$		0			0
$61$	−4.62449	−	1.68317i	−0.592105	−	0.215508i	0.0285502	−	0.999592i	$-0.490911\pi$
$61$	−4.62449	−	1.68317i	−0.592105	−	0.215508i	−0.620655	+	0.784084i	$0.713133\pi$
$62$	−0.943555	−	2.59240i	−0.119832	−	0.329235i
$63$	0.761570	+	0.907604i	0.0959488	+	0.114347i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−0.152704	−	0.866025i	−0.0187965	−	0.106600i
$67$	−1.32683	+	0.233956i	−0.162098	+	0.0285822i	−0.254108	−	0.967176i	$-0.581782\pi$
$67$	−1.32683	+	0.233956i	−0.162098	+	0.0285822i	0.0920102	+	0.995758i	$0.470671\pi$
$68$	3.35965	+	1.93969i	0.407417	+	0.235222i
$69$	−1.99273	−	3.45150i	−0.239896	−	0.415512i
$70$		0			0
$71$	−5.33275	+	1.94096i	−0.632881	+	0.230350i	−0.638485	−	0.769635i	$-0.720438\pi$
$71$	−5.33275	+	1.94096i	−0.632881	+	0.230350i	0.00560389	+	0.999984i	$0.498216\pi$
$72$	−0.761570	+	2.09240i	−0.0897519	+	0.246591i
$73$	4.80526	−	5.72668i	0.562413	−	0.670257i	−0.407643	−	0.913142i	$-0.633649\pi$
$73$	4.80526	−	5.72668i	0.562413	−	0.670257i	0.970055	+	0.242884i	$0.0780935\pi$
$74$	0.166374	−	0.943555i	0.0193406	−	0.109686i
$75$		0			0
$76$	3.58512	+	2.47929i	0.411242	+	0.284395i
$77$		−	0.532089i		−	0.0606372i
$78$	−0.565258	−	0.0996702i	−0.0640029	−	0.0112854i
$79$	0.543233	+	0.455827i	0.0611185	+	0.0512845i	0.672835	−	0.739792i	$-0.265076\pi$
$79$	0.543233	+	0.455827i	0.0611185	+	0.0512845i	−0.611717	+	0.791077i	$0.709521\pi$
$80$		0			0
$81$	−2.47906	+	0.902302i	−0.275451	+	0.100256i
$82$	−4.01676	−	4.78699i	−0.443577	−	0.528634i
$83$	9.15144	−	5.28359i	1.00450	−	0.579949i	0.0949240	−	0.995485i	$-0.469739\pi$
$83$	9.15144	−	5.28359i	1.00450	−	0.579949i	0.909577	+	0.415536i	$0.136406\pi$
$84$	0.233956	−	0.405223i	0.0255266	−	0.0442134i
$85$		0			0
$86$	−0.869585	−	4.93166i	−0.0937698	−	0.531795i
$87$	3.39155	+	1.95811i	0.363612	+	0.209932i
$88$	0.866025	−	0.500000i	0.0923186	−	0.0533002i
$89$	−3.75877	+	3.15398i	−0.398429	+	0.334322i	−0.819886	−	0.572527i	$-0.805963\pi$
$89$	−3.75877	+	3.15398i	−0.398429	+	0.334322i	0.421457	+	0.906848i	$0.361519\pi$
$90$		0			0
$91$	−0.326352	−	0.118782i	−0.0342110	−	0.0124518i
$92$	2.91317	−	3.47178i	0.303719	−	0.361958i
$93$	−2.38917	−	0.421274i	−0.247745	−	0.0436841i
$94$	−0.773318			−0.0797617
$95$		0			0
$96$	0.879385			0.0897519
$97$	0.0994798	+	0.0175410i	0.0101006	+	0.00178102i	0.178696	−	0.983904i	$-0.442812\pi$
$97$	0.0994798	+	0.0175410i	0.0101006	+	0.00178102i	−0.168596	+	0.985685i	$0.553923\pi$
$98$	−4.31753	+	5.14543i	−0.436136	+	0.519767i
$99$	2.09240	+	0.761570i	0.210294	+	0.0765407i
$100$		0			0
$101$	−10.9816	+	9.21464i	−1.09271	+	0.916891i	−0.996913	−	0.0785100i	$-0.974984\pi$
$101$	−10.9816	+	9.21464i	−1.09271	+	0.916891i	−0.0957949	+	0.995401i	$0.530539\pi$
$102$	2.95442	−	1.70574i	0.292531	−	0.168893i
$103$	−5.35619	−	3.09240i	−0.527761	−	0.304703i	0.212343	−	0.977195i	$-0.431890\pi$
$103$	−5.35619	−	3.09240i	−0.527761	−	0.304703i	−0.740104	+	0.672492i	$0.765224\pi$
$104$	−0.113341	−	0.642788i	−0.0111140	−	0.0630305i
$105$		0			0
$106$	1.92855	−	3.34034i	0.187317	−	0.324443i
$107$	−8.47065	+	4.89053i	−0.818888	+	0.472785i	−0.850033	−	0.526730i	$-0.823418\pi$
$107$	−8.47065	+	4.89053i	−0.818888	+	0.472785i	0.0311447	+	0.999515i	$0.490085\pi$
$108$	2.95442	+	3.52094i	0.284290	+	0.338803i
$109$	−12.0360	+	4.38073i	−1.15284	+	0.419598i	−0.846533	−	0.532336i	$-0.821314\pi$
$109$	−12.0360	+	4.38073i	−1.15284	+	0.419598i	−0.306303	+	0.951934i	$0.599092\pi$
$110$		0			0
$111$	−0.645430	−	0.541580i	−0.0612615	−	0.0514045i
$112$	0.524005	+	0.0923963i	0.0495138	+	0.00873063i
$113$			5.47565i			0.515106i	0.966264	+	0.257553i	$0.0829162\pi$
$113$			5.47565i			0.515106i	−0.966264	+	0.257553i	$0.917084\pi$
$114$	3.46451	−	1.64019i	0.324481	−	0.153618i
$115$		0			0
$116$	−0.773318	+	4.38571i	−0.0718008	+	0.407203i
$117$	0.934204	−	1.11334i	0.0863672	−	0.102928i
$118$	−2.14398	+	5.89053i	−0.197369	+	0.542267i
$119$	1.93969	−	0.705990i	0.177811	−	0.0647180i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−4.26195	−	2.46064i	−0.385859	−	0.222776i
$123$	−5.41177	+	0.954241i	−0.487963	+	0.0860410i
$124$	−0.479055	−	2.71686i	−0.0430205	−	0.243981i
$125$		0			0
$126$	0.592396	+	1.02606i	0.0527749	+	0.0914087i
$127$	−6.61046	−	7.87804i	−0.586584	−	0.699063i	0.388362	−	0.921507i	$-0.373041\pi$
$127$	−6.61046	−	7.87804i	−0.586584	−	0.699063i	−0.974946	+	0.222444i	$0.928597\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−4.13816	−	1.50617i	−0.364344	−	0.132610i
$130$		0			0
$131$	−1.46404	+	8.30299i	−0.127914	+	0.725435i	0.851621	+	0.524159i	$0.175620\pi$
$131$	−1.46404	+	8.30299i	−0.127914	+	0.725435i	−0.979534	+	0.201277i	$0.935491\pi$
$132$		−	0.879385i		−	0.0765407i
$133$	2.23675	−	0.613341i	0.193951	−	0.0531834i
$134$	−1.34730			−0.116389
$135$		0			0
$136$	2.97178	+	2.49362i	0.254828	+	0.213826i
$137$	2.72621	−	7.49020i	0.232916	−	0.639931i	−0.767083	−	0.641548i	$-0.778293\pi$
$137$	2.72621	−	7.49020i	0.232916	−	0.639931i	0.999999	+	0.00161707i	$0.000514729\pi$
$138$	−1.36310	−	3.74510i	−0.116035	−	0.318804i
$139$	4.83409	−	4.05629i	0.410022	−	0.344050i	−0.414330	−	0.910127i	$-0.635984\pi$
$139$	4.83409	−	4.05629i	0.410022	−	0.344050i	0.824352	+	0.566077i	$0.191540\pi$
$140$		0			0
$141$	−0.340022	+	0.588936i	−0.0286351	+	0.0495974i
$142$	−5.58878	+	0.985452i	−0.469000	+	0.0826973i
$143$	−0.642788	+	0.113341i	−0.0537526	+	0.00947803i
$144$	−1.11334	+	1.92836i	−0.0927784	+	0.160697i
$145$		0			0
$146$	5.72668	−	4.80526i	0.473944	−	0.397686i
$147$	2.02022	+	5.55051i	0.166625	+	0.457798i
$148$	0.327693	−	0.900330i	0.0269362	−	0.0740067i
$149$	−13.8589	−	11.6290i	−1.13537	−	0.952685i	−0.136089	−	0.990697i	$-0.543453\pi$
$149$	−13.8589	−	11.6290i	−1.13537	−	0.952685i	−0.999277	+	0.0380115i	$0.987898\pi$
$150$		0			0
$151$	10.2071			0.830640			0.415320	−	0.909675i	$-0.363670\pi$
$151$	10.2071			0.830640			0.415320	+	0.909675i	$0.363670\pi$
$152$	3.10013	+	3.06418i	0.251454	+	0.248538i
$153$			8.63816i			0.698353i
$154$	0.0923963	−	0.524005i	0.00744550	−	0.0422255i
$155$		0			0
$156$	−0.539363	−	0.196312i	−0.0431836	−	0.0157175i
$157$	−5.45475	−	14.9868i	−0.435336	−	1.19608i	−0.942494	−	0.334223i	$-0.891526\pi$
$157$	−5.45475	−	14.9868i	−0.435336	−	1.19608i	0.507158	−	0.861853i	$-0.330696\pi$
$158$	0.455827	+	0.543233i	0.0362636	+	0.0432173i
$159$	−1.69594	−	2.93745i	−0.134497	−	0.232955i
$160$		0			0
$161$	−0.418748	−	2.37484i	−0.0330020	−	0.187163i
$162$	−2.59808	+	0.458111i	−0.204124	+	0.0359926i
$163$	−14.3113	−	8.26264i	−1.12095	−	0.647180i	−0.179306	−	0.983793i	$-0.557385\pi$
$163$	−14.3113	−	8.26264i	−1.12095	−	0.647180i	−0.941643	+	0.336613i	$0.890718\pi$
$164$	−3.12449	−	5.41177i	−0.243981	−	0.422588i
$165$		0			0
$166$	9.92989	−	3.61419i	0.770709	−	0.280515i
$167$	−8.13533	+	22.3516i	−0.629531	+	1.72962i	0.0528278	+	0.998604i	$0.483177\pi$
$167$	−8.13533	+	22.3516i	−0.629531	+	1.72962i	−0.682359	+	0.731018i	$0.739046\pi$
$168$	0.300767	−	0.358441i	0.0232047	−	0.0276543i
$169$	2.18345	−	12.3830i	0.167958	−	0.952535i
$170$		0			0
$171$	−0.789515	+	9.67372i	−0.0603757	+	0.739768i
$172$		−	5.00774i		−	0.381837i
$173$	3.02525	+	0.533433i	0.230005	+	0.0405562i	0.287463	−	0.957792i	$-0.407188\pi$
$173$	3.02525	+	0.533433i	0.230005	+	0.0405562i	−0.0574574	+	0.998348i	$0.518299\pi$
$174$	3.00000	+	2.51730i	0.227429	+	0.190836i
$175$		0			0
$176$	0.939693	−	0.342020i	0.0708320	−	0.0257807i
$177$	3.54336	+	4.22281i	0.266335	+	0.317406i
$178$	−4.24935	+	2.45336i	−0.318502	+	0.183887i
$179$	7.98680	−	13.8335i	0.596961	−	1.03397i	−0.396306	−	0.918119i	$-0.629708\pi$
$179$	7.98680	−	13.8335i	0.596961	−	1.03397i	0.993267	−	0.115848i	$-0.0369587\pi$
$180$		0			0
$181$	−1.69728	−	9.62576i	−0.126158	−	0.715477i	−0.980613	−	0.195952i	$-0.937220\pi$
$181$	−1.69728	−	9.62576i	−0.126158	−	0.715477i	0.854455	−	0.519525i	$-0.173891\pi$
$182$	−0.300767	−	0.173648i	−0.0222944	−	0.0128717i
$183$	−3.74789	+	2.16385i	−0.277052	+	0.159956i
$184$	3.47178	−	2.91317i	0.255943	−	0.214762i
$185$		0			0
$186$	−2.27972	−	0.829748i	−0.167157	−	0.0608401i
$187$	2.49362	−	2.97178i	0.182352	−	0.217318i
$188$	−0.761570	−	0.134285i	−0.0555432	−	0.00979376i
$189$	2.44562			0.177893
$190$		0			0
$191$	7.52023			0.544145			0.272072	−	0.962277i	$-0.412291\pi$
$191$	7.52023			0.544145			0.272072	+	0.962277i	$0.412291\pi$
$192$	0.866025	+	0.152704i	0.0625000	+	0.0110204i
$193$	−15.7739	+	18.7986i	−1.13543	+	1.35315i	−0.208454	+	0.978032i	$0.566843\pi$
$193$	−15.7739	+	18.7986i	−1.13543	+	1.35315i	−0.926976	+	0.375121i	$0.877601\pi$
$194$	0.0949225	+	0.0345490i	0.00681504	+	0.00248047i
$195$		0			0
$196$	−5.14543	+	4.31753i	−0.367531	+	0.308395i
$197$	−12.4740	+	7.20187i	−0.888736	+	0.513112i	−0.873529	−	0.486773i	$-0.838174\pi$
$197$	−12.4740	+	7.20187i	−0.888736	+	0.513112i	−0.0152069	+	0.999884i	$0.504841\pi$
$198$	1.92836	+	1.11334i	0.137043	+	0.0791217i
$199$	0.771097	+	4.37311i	0.0546616	+	0.310001i	0.999864	−	0.0164832i	$-0.00524699\pi$
$199$	0.771097	+	4.37311i	0.0546616	+	0.310001i	−0.945203	+	0.326485i	$0.894136\pi$
$200$		0			0
$201$	−0.592396	+	1.02606i	−0.0417844	+	0.0723727i
$202$	−12.4149	+	7.16772i	−0.873506	+	0.504319i
$203$	1.52314	+	1.81521i	0.106903	+	0.127403i
$204$	3.20574	−	1.16679i	0.224446	−	0.0816918i
$205$		0			0
$206$	−4.73783	−	3.97551i	−0.330100	−	0.276987i
$207$	9.93821	+	1.75237i	0.690753	+	0.121798i
$208$		−	0.652704i		−	0.0452569i
$209$	3.06418	−	3.10013i	0.211954	−	0.214441i
$210$		0			0
$211$	−1.95218	+	11.0714i	−0.134394	+	0.762185i	0.840886	+	0.541212i	$0.182034\pi$
$211$	−1.95218	+	11.0714i	−0.134394	+	0.762185i	−0.975280	+	0.220973i	$0.929077\pi$
$212$	2.47929	−	2.95471i	0.170279	−	0.202930i
$213$	−1.70685	+	4.68954i	−0.116952	+	0.321322i
$214$	−9.19119	+	3.34532i	−0.628297	+	0.228681i
$215$		0			0
$216$	2.29813	+	3.98048i	0.156368	+	0.270838i
$217$	−1.27125	−	0.733956i	−0.0862980	−	0.0498241i
$218$	−12.6138	+	2.22416i	−0.854315	+	0.150639i
$219$	−1.14156	−	6.47410i	−0.0771394	−	0.437479i
$220$		0			0
$221$	−1.26604	−	2.19285i	−0.0851634	−	0.147507i
$222$	−0.541580	−	0.645430i	−0.0363485	−	0.0433184i
$223$	−4.10597	−	11.2811i	−0.274956	−	0.755436i	−0.997915	−	0.0645444i	$-0.979441\pi$
$223$	−4.10597	−	11.2811i	−0.274956	−	0.755436i	0.722959	−	0.690891i	$-0.242782\pi$
$224$	0.500000	+	0.181985i	0.0334077	+	0.0121594i
$225$		0			0
$226$	−0.950837	+	5.39246i	−0.0632487	+	0.358701i
$227$			25.8871i			1.71819i	0.511817	+	0.859094i	$0.328973\pi$
$227$			25.8871i			1.71819i	−0.511817	+	0.859094i	$0.671027\pi$
$228$	3.69669	−	1.01367i	0.244819	−	0.0671320i
$229$	−11.1138			−0.734421			−0.367211	−	0.930138i	$-0.619687\pi$
$229$	−11.1138			−0.734421			−0.367211	+	0.930138i	$0.619687\pi$
$230$		0			0
$231$	−0.358441	−	0.300767i	−0.0235837	−	0.0197890i
$232$	−1.52314	+	4.18479i	−0.0999990	+	0.274745i
$233$	0.433877	+	1.19207i	0.0284242	+	0.0780949i	0.953093	−	0.302677i	$-0.0978804\pi$
$233$	0.433877	+	1.19207i	0.0284242	+	0.0780949i	−0.924669	+	0.380772i	$0.875658\pi$
$234$	1.11334	−	0.934204i	0.0727814	−	0.0610708i
$235$		0			0
$236$	−3.13429	+	5.42874i	−0.204025	+	0.353381i
$237$	0.614134	−	0.108288i	0.0398923	−	0.00703408i
$238$	2.03282	−	0.358441i	0.131768	−	0.0232343i
$239$	2.13429	−	3.69669i	0.138055	−	0.239119i	−0.788705	−	0.614772i	$-0.789248\pi$
$239$	2.13429	−	3.69669i	0.138055	−	0.239119i	0.926761	+	0.375653i	$0.122581\pi$
$240$		0			0
$241$	22.5214	−	18.8977i	1.45073	−	1.21731i	0.518687	−	0.854964i	$-0.326421\pi$
$241$	22.5214	−	18.8977i	1.45073	−	1.21731i	0.932044	−	0.362344i	$-0.118024\pi$
$242$	3.42020	+	9.39693i	0.219859	+	0.604057i
$243$	−5.50952	+	15.1373i	−0.353436	+	0.971057i
$244$	−3.76991	−	3.16333i	−0.241344	−	0.202512i
$245$		0			0
$246$	−5.49525			−0.350364
$247$	−1.21740	−	2.57145i	−0.0774611	−	0.163618i
$248$		−	2.75877i		−	0.175182i
$249$	1.61365	−	9.15144i	0.102261	−	0.579949i
$250$		0			0
$251$	−9.14290	−	3.32774i	−0.577095	−	0.210045i	0.0369491	−	0.999317i	$-0.488236\pi$
$251$	−9.14290	−	3.32774i	−0.577095	−	0.210045i	−0.614044	+	0.789272i	$0.710458\pi$
$252$	0.405223	+	1.11334i	0.0255266	+	0.0701339i
$253$	−2.91317	−	3.47178i	−0.183149	−	0.218269i
$254$	−5.14203	−	8.90625i	−0.322639	−	0.558828i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	4.44393	−	0.783585i	0.277205	−	0.0488787i	−0.0333173	−	0.999445i	$-0.510607\pi$
$257$	4.44393	−	0.783585i	0.277205	−	0.0488787i	0.310522	+	0.950566i	$0.399496\pi$
$258$	−3.81374	−	2.20187i	−0.237433	−	0.137082i
$259$	−0.254900	−	0.441500i	−0.0158387	−	0.0274335i
$260$		0			0
$261$	−9.31820	+	3.39155i	−0.576782	+	0.209932i
$262$	−2.88360	+	7.92262i	−0.178149	+	0.489461i
$263$	19.3618	−	23.0744i	1.19390	−	1.42283i	0.312850	−	0.949802i	$-0.398716\pi$
$263$	19.3618	−	23.0744i	1.19390	−	1.42283i	0.881047	−	0.473029i	$-0.156839\pi$
$264$	0.152704	−	0.866025i	0.00939826	−	0.0533002i
$265$		0			0
$266$	2.30928	−	0.215615i	0.141591	−	0.0132202i
$267$			4.31490i			0.264068i
$268$	−1.32683	−	0.233956i	−0.0810489	−	0.0142911i
$269$	3.31315	+	2.78006i	0.202006	+	0.169503i	0.738179	−	0.674605i	$-0.235686\pi$
$269$	3.31315	+	2.78006i	0.202006	+	0.169503i	−0.536173	+	0.844108i	$0.680130\pi$
$270$		0			0
$271$	25.3491	−	9.22632i	1.53985	−	0.560459i	0.573840	−	0.818968i	$-0.305453\pi$
$271$	25.3491	−	9.22632i	1.53985	−	0.560459i	0.966009	+	0.258509i	$0.0832310\pi$
$272$	2.49362	+	2.97178i	0.151198	+	0.180191i
$273$	−0.264490	+	0.152704i	−0.0160077	+	0.00924205i
$274$	3.98545	−	6.90301i	0.240770	−	0.417026i
$275$		0			0
$276$	−0.692066	−	3.92490i	−0.0416575	−	0.236251i
$277$	−1.90906	−	1.10220i	−0.114704	−	0.0662246i	0.441550	−	0.897237i	$-0.354429\pi$
$277$	−1.90906	−	1.10220i	−0.114704	−	0.0662246i	−0.556255	+	0.831012i	$0.687762\pi$
$278$	5.46502	−	3.15523i	0.327770	−	0.189238i
$279$	4.70574	−	3.94858i	0.281725	−	0.236395i
$280$		0			0
$281$	−17.8341	−	6.49108i	−1.06389	−	0.387225i	−0.250003	−	0.968245i	$-0.580432\pi$
$281$	−17.8341	−	6.49108i	−1.06389	−	0.387225i	−0.813889	+	0.581020i	$0.802654\pi$
$282$	−0.437124	+	0.520945i	−0.0260304	+	0.0310218i
$283$	−14.3189	−	2.52481i	−0.851172	−	0.150085i	−0.268990	−	0.963143i	$-0.586690\pi$
$283$	−14.3189	−	2.52481i	−0.851172	−	0.150085i	−0.582182	+	0.813058i	$0.697801\pi$
$284$	−5.67499			−0.336749
$285$		0			0
$286$	−0.652704			−0.0385952
$287$	−3.27449	−	0.577382i	−0.193287	−	0.0340818i
$288$	−1.43128	+	1.70574i	−0.0843392	+	0.100512i
$289$	−1.83275	−	0.667066i	−0.107809	−	0.0392392i
$290$		0			0
$291$	0.0680482	−	0.0570992i	0.00398905	−	0.00334721i
$292$	6.47410	−	3.73783i	0.378868	−	0.218740i
$293$	5.42285	+	3.13088i	0.316806	+	0.182908i	0.649968	−	0.759962i	$-0.274782\pi$
$293$	5.42285	+	3.13088i	0.316806	+	0.182908i	−0.333162	+	0.942870i	$0.608116\pi$
$294$	1.02569	+	5.81699i	0.0598196	+	0.339254i
$295$		0			0
$296$	0.479055	−	0.829748i	0.0278445	−	0.0482281i
$297$	3.98048	−	2.29813i	0.230971	−	0.133351i
$298$	−11.6290	−	13.8589i	−0.673650	−	0.802825i
$299$	−2.77972	+	1.01173i	−0.160755	+	0.0585101i
$300$		0			0
$301$	−2.04117	−	1.71275i	−0.117651	−	0.0987212i
$302$	10.0520	+	1.77244i	0.578428	+	0.101993i
$303$			12.6064i			0.724217i
$304$	2.52094	+	3.55596i	0.144586	+	0.203948i
$305$		0			0
$306$	−1.50000	+	8.50692i	−0.0857493	+	0.486308i
$307$	−5.00097	+	5.95992i	−0.285420	+	0.340151i	−0.889636	−	0.456670i	$-0.849042\pi$
$307$	−5.00097	+	5.95992i	−0.285420	+	0.340151i	0.604216	+	0.796821i	$0.293486\pi$
$308$	0.181985	−	0.500000i	0.0103696	−	0.0284901i
$309$	−5.11081	+	1.86018i	−0.290744	+	0.105822i
$310$		0			0
$311$	15.5189	+	26.8795i	0.879995	+	1.52420i	0.851345	+	0.524607i	$0.175788\pi$
$311$	15.5189	+	26.8795i	0.879995	+	1.52420i	0.0286507	+	0.999589i	$0.490879\pi$
$312$	−0.497079	−	0.286989i	−0.0281416	−	0.0162476i
$313$	−9.08651	+	1.60220i	−0.513600	+	0.0905615i	−0.424440	−	0.905456i	$-0.639529\pi$
$313$	−9.08651	+	1.60220i	−0.513600	+	0.0905615i	−0.0891594	+	0.996017i	$0.528418\pi$
$314$	−2.76945	−	15.7063i	−0.156289	−	0.886359i
$315$		0			0
$316$	0.354570	+	0.614134i	0.0199461	+	0.0345477i
$317$	−15.4308	−	18.3897i	−0.866677	−	1.03287i	−0.999131	−	0.0416766i	$-0.986730\pi$
$317$	−15.4308	−	18.3897i	−0.866677	−	1.03287i	0.132454	−	0.991189i	$-0.457714\pi$
$318$	−1.16009	−	3.18732i	−0.0650546	−	0.178736i
$319$	4.18479	+	1.52314i	0.234303	+	0.0852795i
$320$		0			0
$321$	−1.49360	+	8.47065i	−0.0833648	+	0.472785i
$322$		−	2.41147i		−	0.134386i
$323$	15.3669	+	7.05690i	0.855040	+	0.392657i
$324$	−2.63816			−0.146564
$325$		0			0
$326$	−12.6591	−	10.6222i	−0.701123	−	0.588312i
$327$	−3.85235	+	10.5842i	−0.213035	+	0.585310i
$328$	−2.13727	−	5.87211i	−0.118011	−	0.324233i
$329$	−0.315207	+	0.264490i	−0.0173780	+	0.0145818i
$330$		0			0
$331$	12.2724	−	21.2565i	0.674554	−	1.16836i	−0.302045	−	0.953294i	$-0.597669\pi$
$331$	12.2724	−	21.2565i	0.674554	−	1.16836i	0.976599	−	0.215069i	$-0.0689975\pi$
$332$	10.4066	−	1.83497i	0.571138	−	0.100707i
$333$	2.10100	−	0.370462i	0.115134	−	0.0203012i
$334$	−11.8931	+	20.5994i	−0.650759	+	1.12715i
$335$		0			0
$336$	0.358441	−	0.300767i	0.0195545	−	0.0164082i
$337$	−10.4842	−	28.8050i	−0.571109	−	1.56911i	−0.802756	−	0.596308i	$-0.796634\pi$
$337$	−10.4842	−	28.8050i	−0.571109	−	1.56911i	0.231647	−	0.972800i	$-0.425589\pi$
$338$	4.30055	−	11.8157i	0.233919	−	0.642688i
$339$	3.68866	+	3.09516i	0.200341	+	0.168106i
$340$		0			0
$341$	−2.75877			−0.149396
$342$	−2.45734	+	9.38965i	−0.132878	+	0.507734i
$343$			7.29860i			0.394087i
$344$	0.869585	−	4.93166i	0.0468849	−	0.265897i
$345$		0			0
$346$	2.88666	+	1.05066i	0.155188	+	0.0564837i
$347$	−2.65366	−	7.29086i	−0.142456	−	0.391394i	0.847861	−	0.530218i	$-0.177890\pi$
$347$	−2.65366	−	7.29086i	−0.142456	−	0.391394i	−0.990317	+	0.138824i	$0.955668\pi$
$348$	2.51730	+	3.00000i	0.134941	+	0.160817i
$349$	−6.37551	−	11.0427i	−0.341273	−	0.591103i	0.643396	−	0.765534i	$-0.277525\pi$
$349$	−6.37551	−	11.0427i	−0.341273	−	0.591103i	−0.984669	+	0.174431i	$0.944192\pi$
$350$		0			0
$351$	−0.520945	−	2.95442i	−0.0278060	−	0.157695i
$352$	0.984808	−	0.173648i	0.0524904	−	0.00925548i
$353$	−8.19275	−	4.73009i	−0.436056	−	0.251757i	0.265867	−	0.964010i	$-0.414342\pi$
$353$	−8.19275	−	4.73009i	−0.436056	−	0.251757i	−0.701923	+	0.712253i	$0.747675\pi$
$354$	2.75624	+	4.77396i	0.146493	+	0.253733i
$355$		0			0
$356$	−4.61081	+	1.67820i	−0.244373	+	0.0889444i
$357$	0.620838	−	1.70574i	0.0328582	−	0.0902772i
$358$	10.2676	−	12.2365i	0.542661	−	0.646718i
$359$	0.181799	−	1.03104i	0.00959501	−	0.0544160i	−0.979634	−	0.200790i	$-0.935649\pi$
$359$	0.181799	−	1.03104i	0.00959501	−	0.0544160i	0.989229	+	0.146374i	$0.0467603\pi$
$360$		0			0
$361$	16.5642	+	9.30742i	0.871799	+	0.489864i
$362$		−	9.77425i		−	0.513723i
$363$	8.66025	+	1.52704i	0.454545	+	0.0801486i
$364$	−0.266044	−	0.223238i	−0.0139445	−	0.0117008i
$365$		0			0
$366$	−4.06670	+	1.48016i	−0.212570	+	0.0773692i
$367$	6.35359	+	7.57192i	0.331655	+	0.395251i	0.905941	−	0.423404i	$-0.139165\pi$
$367$	6.35359	+	7.57192i	0.331655	+	0.395251i	−0.574286	+	0.818655i	$0.694720\pi$
$368$	3.92490	−	2.26604i	0.204600	−	0.118126i
$369$	6.95723	−	12.0503i	0.362179	−	0.627313i
$370$		0			0
$371$	−0.356381	−	2.02114i	−0.0185024	−	0.104932i
$372$	−2.10100	−	1.21301i	−0.108932	−	0.0628917i
$373$	24.0079	−	13.8610i	1.24308	−	0.717694i	0.273361	−	0.961911i	$-0.411864\pi$
$373$	24.0079	−	13.8610i	1.24308	−	0.717694i	0.969720	+	0.244218i	$0.0785312\pi$
$374$	2.97178	−	2.49362i	0.153667	−	0.128942i
$375$		0			0
$376$	−0.726682	−	0.264490i	−0.0374757	−	0.0136401i
$377$	1.86841	−	2.22668i	0.0962279	−	0.114680i
$378$	2.40847	+	0.424678i	0.123878	+	0.0218431i
$379$	13.0787			0.671809			0.335905	−	0.941896i	$-0.390958\pi$
$379$	13.0787			0.671809			0.335905	+	0.941896i	$0.390958\pi$
$380$		0			0
$381$	−9.04364			−0.463320
$382$	7.40598	+	1.30587i	0.378923	+	0.0668143i
$383$	−6.40268	+	7.63041i	−0.327162	+	0.389896i	−0.904404	−	0.426677i	$-0.859684\pi$
$383$	−6.40268	+	7.63041i	−0.327162	+	0.389896i	0.577243	+	0.816573i	$0.304129\pi$
$384$	0.826352	+	0.300767i	0.0421696	+	0.0153485i
$385$		0			0
$386$	−18.7986	+	15.7739i	−0.956824	+	0.802870i
$387$	9.65674	−	5.57532i	0.490880	−	0.283410i
$388$	0.0874810	+	0.0505072i	0.00444118	+	0.00256411i
$389$	4.18850	+	23.7542i	0.212365	+	1.20438i	0.885420	+	0.464791i	$0.153871\pi$
$389$	4.18850	+	23.7542i	0.212365	+	1.20438i	−0.673055	+	0.739593i	$0.735018\pi$
$390$		0			0
$391$	8.79086	−	15.2262i	0.444573	−	0.770023i
$392$	−5.81699	+	3.35844i	−0.293802	+	0.169627i
$393$	4.76573	+	5.67958i	0.240399	+	0.286497i
$394$	−13.5351	+	4.92637i	−0.681888	+	0.248187i
$395$		0			0
$396$	1.70574	+	1.43128i	0.0857165	+	0.0719247i
$397$	24.9842	+	4.40538i	1.25392	+	0.221100i	0.760872	−	0.648902i	$-0.224772\pi$
$397$	24.9842	+	4.40538i	1.25392	+	0.221100i	0.493048	+	0.870002i	$0.335883\pi$
$398$			4.44057i			0.222586i
$399$	0.851167	−	1.85348i	0.0426116	−	0.0927901i
$400$		0			0
$401$	−4.30810	+	24.4324i	−0.215136	+	1.22010i	0.665534	+	0.746367i	$0.268204\pi$
$401$	−4.30810	+	24.4324i	−0.215136	+	1.22010i	−0.880670	+	0.473730i	$0.842907\pi$
$402$	−0.761570	+	0.907604i	−0.0379837	+	0.0452672i
$403$	−0.615862	+	1.69207i	−0.0306783	+	0.0842878i
$404$	−13.4709	+	4.90301i	−0.670203	+	0.243934i
$405$		0			0
$406$	1.18479	+	2.05212i	0.0588003	+	0.101845i
$407$	−0.829748	−	0.479055i	−0.0411291	−	0.0237459i
$408$	3.35965	−	0.592396i	0.166327	−	0.0293280i
$409$	5.20692	+	29.5299i	0.257466	+	1.46016i	0.789664	+	0.613540i	$0.210255\pi$
$409$	5.20692	+	29.5299i	0.257466	+	1.46016i	−0.532198	+	0.846620i	$0.678634\pi$
$410$		0			0
$411$	−3.50475	−	6.07040i	−0.172876	−	0.299431i
$412$	−3.97551	−	4.73783i	−0.195859	−	0.233416i
$413$	1.14079	+	3.13429i	0.0561344	+	0.154228i
$414$	9.48293	+	3.45150i	0.466060	+	0.169632i
$415$		0			0
$416$	0.113341	−	0.642788i	0.00555699	−	0.0315153i
$417$		−	5.54933i		−	0.271752i
$418$	3.55596	−	2.52094i	0.173928	−	0.123303i
$419$	17.7196			0.865658			0.432829	−	0.901476i	$-0.357515\pi$
$419$	17.7196			0.865658			0.432829	+	0.901476i	$0.357515\pi$
$420$		0			0
$421$	−9.22462	−	7.74038i	−0.449581	−	0.377243i	0.389700	−	0.920942i	$-0.372579\pi$
$421$	−9.22462	−	7.74038i	−0.449581	−	0.377243i	−0.839280	+	0.543699i	$0.817023\pi$
$422$	−3.84505	+	10.5642i	−0.187174	+	0.514256i
$423$	−0.588936	−	1.61809i	−0.0286351	−	0.0786742i
$424$	2.95471	−	2.47929i	0.143493	−	0.120405i
$425$		0			0
$426$	−2.49525	+	4.32190i	−0.120895	+	0.209397i
$427$	−2.57877	+	0.454707i	−0.124796	+	0.0220048i
$428$	−9.63246	+	1.69846i	−0.465603	+	0.0820983i
$429$	−0.286989	+	0.497079i	−0.0138560	+	0.0239992i
$430$		0			0
$431$	27.0913	−	22.7323i	1.30494	−	1.09498i	0.315672	−	0.948868i	$-0.397770\pi$
$431$	27.0913	−	22.7323i	1.30494	−	1.09498i	0.989269	−	0.146107i	$-0.0466743\pi$
$432$	1.57202	+	4.31908i	0.0756336	+	0.207802i
$433$	−9.16496	+	25.1805i	−0.440440	+	1.21010i	0.498764	+	0.866738i	$0.333787\pi$
$433$	−9.16496	+	25.1805i	−0.440440	+	1.21010i	−0.939204	+	0.343360i	$0.888435\pi$
$434$	−1.12449	−	0.943555i	−0.0539770	−	0.0452921i
$435$		0			0
$436$	−12.8084			−0.613411
$437$	11.2364	−	16.2481i	0.537509	−	0.777252i
$438$		−	6.57398i		−	0.314117i
$439$	−4.14244	+	23.4929i	−0.197708	+	1.12126i	0.710802	+	0.703392i	$0.248332\pi$
$439$	−4.14244	+	23.4929i	−0.197708	+	1.12126i	−0.908510	+	0.417864i	$0.862779\pi$
$440$		0			0
$441$	−14.0544	−	5.11538i	−0.669256	−	0.243589i
$442$	−0.866025	−	2.37939i	−0.0411926	−	0.113176i
$443$	21.6640	+	25.8182i	1.02929	+	1.22666i	0.973612	+	0.228211i	$0.0732876\pi$
$443$	21.6640	+	25.8182i	1.02929	+	1.22666i	0.0556780	+	0.998449i	$0.482268\pi$
$444$	−0.421274	−	0.729669i	−0.0199928	−	0.0346285i
$445$		0			0
$446$	−2.08466	−	11.8227i	−0.0987113	−	0.559820i
$447$	−15.6677	+	2.76264i	−0.741057	+	0.130668i
$448$	0.460802	+	0.266044i	0.0217709	+	0.0125694i
$449$	6.45605	+	11.1822i	0.304680	+	0.527721i	0.977190	−	0.212367i	$-0.0681172\pi$
$449$	6.45605	+	11.1822i	0.304680	+	0.527721i	−0.672510	+	0.740088i	$0.734784\pi$
$450$		0			0
$451$	−5.87211	+	2.13727i	−0.276507	+	0.100640i
$452$	−1.87278	+	5.14543i	−0.0880883	+	0.242021i
$453$	5.76963	−	6.87598i	0.271081	−	0.323062i
$454$	−4.49525	+	25.4938i	−0.210973	+	1.19649i
$455$		0			0
$456$	3.81655	−	0.356347i	0.178726	−	0.0166875i
$457$		−	36.0779i		−	1.68765i	−0.536616	−	0.843827i	$-0.680298\pi$
$457$		−	36.0779i		−	1.68765i	0.536616	−	0.843827i	$-0.319702\pi$
$458$	−10.9450	−	1.92989i	−0.511425	−	0.0901780i
$459$	13.6591	+	11.4613i	0.637552	+	0.534970i
$460$		0			0
$461$	0.0530334	−	0.0193026i	0.00247001	−	0.000899011i	−0.340785	−	0.940141i	$-0.610693\pi$
$461$	0.0530334	−	0.0193026i	0.00247001	−	0.000899011i	0.343255	+	0.939242i	$0.388471\pi$
$462$	−0.300767	−	0.358441i	−0.0139930	−	0.0166762i
$463$	24.3792	−	14.0753i	1.13300	−	0.654136i	0.188310	−	0.982110i	$-0.439699\pi$
$463$	24.3792	−	14.0753i	1.13300	−	0.654136i	0.944687	+	0.327974i	$0.106366\pi$
$464$	−2.22668	+	3.85673i	−0.103371	+	0.179044i
$465$		0			0
$466$	0.220285	+	1.24930i	0.0102045	+	0.0578726i
$467$	0.266819	+	0.154048i	0.0123469	+	0.00712848i	0.506161	−	0.862439i	$-0.331064\pi$
$467$	0.266819	+	0.154048i	0.0123469	+	0.00712848i	−0.493814	+	0.869568i	$0.664398\pi$
$468$	1.25865	−	0.726682i	0.0581811	−	0.0335909i
$469$	−0.549163	+	0.460802i	−0.0253580	+	0.0212779i
$470$		0			0
$471$	−13.1792	−	4.79682i	−0.607264	−	0.221026i
$472$	−4.02936	+	4.80200i	−0.185466	+	0.221030i
$473$	−4.93166	−	0.869585i	−0.226758	−	0.0399836i
$474$	0.623608			0.0286433
$475$		0			0
$476$	2.06418			0.0946114
$477$	8.45805	+	1.49138i	0.387267	+	0.0682857i
$478$	2.74378	−	3.26991i	0.125498	−	0.149562i
$479$	28.4021	+	10.3375i	1.29773	+	0.472334i	0.896256	−	0.443538i	$-0.146277\pi$
$479$	28.4021	+	10.3375i	1.29773	+	0.472334i	0.401471	+	0.915872i	$0.368499\pi$
$480$		0			0
$481$	−0.479055	+	0.401975i	−0.0218430	+	0.0183285i
$482$	25.4608	−	14.6998i	1.15971	−	0.669558i
$483$	−1.83651	−	1.06031i	−0.0835639	−	0.0482457i
$484$	1.73648	+	9.84808i	0.0789310	+	0.447640i
$485$		0			0
$486$	−8.05438	+	13.9506i	−0.365354	+	0.632812i
$487$	25.8956	−	14.9508i	1.17344	−	0.677487i	0.218954	−	0.975735i	$-0.429736\pi$
$487$	25.8956	−	14.9508i	1.17344	−	0.677487i	0.954488	+	0.298248i	$0.0964023\pi$
$488$	−3.16333	−	3.76991i	−0.143197	−	0.170656i
$489$	−13.6557	+	4.97027i	−0.617532	+	0.224763i
$490$		0			0
$491$	−2.98680	−	2.50622i	−0.134792	−	0.113104i	0.572899	−	0.819626i	$-0.305819\pi$
$491$	−2.98680	−	2.50622i	−0.134792	−	0.113104i	−0.707691	+	0.706522i	$0.750263\pi$
$492$	−5.41177	−	0.954241i	−0.243981	−	0.0430205i
$493$			17.2763i			0.778086i
$494$	−0.752374	−	2.74378i	−0.0338509	−	0.123449i
$495$		0			0
$496$	0.479055	−	2.71686i	0.0215102	−	0.121991i
$497$	−1.94096	+	2.31315i	−0.0870640	+	0.103759i
$498$	3.17826	−	8.73220i	0.142421	−	0.391299i
$499$	−22.9231	+	8.34332i	−1.02618	+	0.373498i	−0.799625	−	0.600500i	$-0.794968\pi$
$499$	−22.9231	+	8.34332i	−1.02618	+	0.373498i	−0.226554	+	0.973999i	$0.572746\pi$
$500$		0			0
$501$	10.4586	+	18.1148i	0.467255	+	0.809309i
$502$	−8.42615	−	4.86484i	−0.376077	−	0.217128i
$503$	−13.4283	+	2.36777i	−0.598739	+	0.105574i	−0.464800	−	0.885416i	$-0.653874\pi$
$503$	−13.4283	+	2.36777i	−0.598739	+	0.105574i	−0.133939	+	0.990990i	$0.542763\pi$
$504$	0.205737	+	1.16679i	0.00916426	+	0.0519731i
$505$		0			0
$506$	−2.26604	−	3.92490i	−0.100738	−	0.174483i
$507$	−7.10754	−	8.47044i	−0.315657	−	0.376185i
$508$	−3.51735	−	9.66385i	−0.156057	−	0.428764i
$509$	−7.18004	−	2.61332i	−0.318250	−	0.115833i	0.177956	−	0.984038i	$-0.443052\pi$
$509$	−7.18004	−	2.61332i	−0.318250	−	0.115833i	−0.496206	+	0.868205i	$0.665274\pi$
$510$		0			0
$511$	0.690722	−	3.91728i	0.0305558	−	0.173290i
$512$			1.00000i			0.0441942i
$513$	14.2490	+	14.0838i	0.629110	+	0.621814i
$514$	4.51249			0.199037
$515$		0			0
$516$	−3.37346	−	2.83067i	−0.148508	−	0.124613i
$517$	−0.264490	+	0.726682i	−0.0116323	+	0.0319594i
$518$	−0.174362	−	0.479055i	−0.00766102	−	0.0210485i
$519$	2.06939	−	1.73643i	0.0908362	−	0.0762207i
$520$		0			0
$521$	−6.52734	+	11.3057i	−0.285968	+	0.495311i	−0.972843	−	0.231464i	$-0.925648\pi$
$521$	−6.52734	+	11.3057i	−0.285968	+	0.495311i	0.686875	+	0.726775i	$0.258982\pi$
$522$	−9.76557	+	1.72193i	−0.427427	+	0.0753670i
$523$	17.5065	−	3.08688i	0.765508	−	0.134980i	0.222758	−	0.974874i	$-0.428494\pi$
$523$	17.5065	−	3.08688i	0.765508	−	0.134980i	0.542750	+	0.839894i	$0.317383\pi$
$524$	−4.21554	+	7.30152i	−0.184157	+	0.318969i
$525$		0			0
$526$	23.0744	−	19.3618i	1.00609	−	0.844213i
$527$	−3.66041	−	10.0569i	−0.159450	−	0.438086i
$528$	0.300767	−	0.826352i	0.0130892	−	0.0359623i
$529$	1.88460	+	1.58137i	0.0819391	+	0.0687551i
$530$		0			0
$531$	−13.9581			−0.605730
$532$	2.31164	+	0.188663i	0.100222	+	0.00817958i
$533$			4.07873i			0.176669i
$534$	−0.749275	+	4.24935i	−0.0324243	+	0.183887i
$535$		0			0
$536$	−1.26604	−	0.460802i	−0.0546848	−	0.0199036i
$537$	−4.80434	−	13.1998i	−0.207322	−	0.569614i
$538$	2.78006	+	3.31315i	0.119857	+	0.142840i
$539$	3.35844	+	5.81699i	0.144658	+	0.250555i
$540$		0			0
$541$	−6.67008	−	37.8279i	−0.286769	−	1.62635i	−0.698896	−	0.715223i	$-0.746325\pi$
$541$	−6.67008	−	37.8279i	−0.286769	−	1.62635i	0.412127	−	0.911126i	$-0.364786\pi$
$542$	26.5661	−	4.68433i	1.14111	−	0.201209i
$543$	−7.44378	−	4.29767i	−0.319443	−	0.184431i
$544$	1.93969	+	3.35965i	0.0831636	+	0.144044i
$545$		0			0
$546$	−0.286989	+	0.104455i	−0.0122820	+	0.00447028i
$547$	−9.24076	+	25.3888i	−0.395106	+	1.08555i	0.569532	+	0.821969i	$0.307124\pi$
$547$	−9.24076	+	25.3888i	−0.395106	+	1.08555i	−0.964638	+	0.263577i	$0.915098\pi$
$548$	5.12360	−	6.10607i	0.218869	−	0.260838i
$549$	1.90286	−	10.7916i	0.0812119	−	0.460576i
$550$		0			0
$551$	−1.57903	+	19.3474i	−0.0672690	+	0.824228i
$552$		−	3.98545i		−	0.169632i
$553$	0.371593	+	0.0655219i	0.0158018	+	0.00278628i
$554$	−1.68866	−	1.41696i	−0.0717444	−	0.0602007i
$555$		0			0
$556$	5.92989	−	2.15830i	0.251483	−	0.0915325i
$557$	7.72016	+	9.20052i	0.327113	+	0.389839i	0.904388	−	0.426712i	$-0.140328\pi$
$557$	7.72016	+	9.20052i	0.327113	+	0.389839i	−0.577274	+	0.816550i	$0.695884\pi$
$558$	5.31991	−	3.07145i	0.225210	−	0.130025i
$559$	−1.63429	+	2.83067i	−0.0691229	+	0.119724i
$560$		0			0
$561$	−0.592396	−	3.35965i	−0.0250110	−	0.141844i
$562$	−16.4360	−	9.48932i	−0.693310	−	0.400283i
$563$	12.7815	−	7.37939i	0.538675	−	0.311004i	−0.205867	−	0.978580i	$-0.566001\pi$
$563$	12.7815	−	7.37939i	0.538675	−	0.311004i	0.744542	+	0.667576i	$0.232668\pi$
$564$	−0.520945	+	0.437124i	−0.0219357	+	0.0184063i
$565$		0			0
$566$	−13.6630	−	4.97291i	−0.574297	−	0.209027i
$567$	−0.902302	+	1.07532i	−0.0378931	+	0.0451593i
$568$	−5.58878	−	0.985452i	−0.234500	−	0.0413487i
$569$	41.7570			1.75055			0.875273	−	0.483630i	$-0.160682\pi$
$569$	41.7570			1.75055			0.875273	+	0.483630i	$0.160682\pi$
$570$		0			0
$571$	29.2431			1.22379			0.611893	−	0.790941i	$-0.290408\pi$
$571$	29.2431			1.22379			0.611893	+	0.790941i	$0.290408\pi$
$572$	−0.642788	−	0.113341i	−0.0268763	−	0.00473902i
$573$	4.25087	−	5.06599i	0.177583	−	0.211635i
$574$	−3.12449	−	1.13722i	−0.130413	−	0.0474666i
$575$		0			0
$576$	−1.70574	+	1.43128i	−0.0710724	+	0.0596368i
$577$	1.06029	−	0.612159i	0.0441405	−	0.0254845i	−0.477767	−	0.878486i	$-0.658554\pi$
$577$	1.06029	−	0.612159i	0.0441405	−	0.0254845i	0.521908	+	0.853002i	$0.325220\pi$
$578$	−1.68907	−	0.975185i	−0.0702561	−	0.0405624i
$579$	3.74732	+	21.2521i	0.155733	+	0.883208i
$580$		0			0
$581$	2.81134	−	4.86938i	0.116634	−	0.202016i
$582$	0.0769295	−	0.0444153i	0.00318883	−	0.00184107i
$583$	−2.47929	−	2.95471i	−0.102682	−	0.122371i
$584$	7.02481	−	2.55682i	0.290689	−	0.105802i
$585$		0			0
$586$	4.79679	+	4.02498i	0.198154	+	0.166271i
$587$	27.3868	+	4.82904i	1.13038	+	0.199316i	0.707392	−	0.706821i	$-0.249872\pi$
$587$	27.3868	+	4.82904i	1.13038	+	0.199316i	0.422984	+	0.906137i	$0.360983\pi$
$588$			5.90673i			0.243589i
$589$	−3.18004	−	11.5971i	−0.131031	−	0.477850i
$590$		0			0
$591$	−2.19950	+	12.4740i	−0.0904754	+	0.513112i
$592$	0.615862	−	0.733956i	0.0253118	−	0.0301654i
$593$	−10.3596	+	28.4628i	−0.425418	+	1.16883i	0.523147	+	0.852242i	$0.324758\pi$
$593$	−10.3596	+	28.4628i	−0.425418	+	1.16883i	−0.948565	+	0.316583i	$0.897464\pi$
$594$	4.31908	−	1.57202i	0.177214	−	0.0645006i
$595$		0			0
$596$	−9.04576	−	15.6677i	−0.370529	−	0.641775i
$597$	3.38180	+	1.95249i	0.138408	+	0.0799099i
$598$	−2.91317	+	0.513671i	−0.119128	+	0.0210056i
$599$	2.09105	+	11.8589i	0.0854381	+	0.484543i	0.997261	+	0.0739602i	$0.0235638\pi$
$599$	2.09105	+	11.8589i	0.0854381	+	0.484543i	−0.911823	+	0.410583i	$0.865325\pi$
$600$		0			0
$601$	−7.05572	−	12.2209i	−0.287809	−	0.498500i	0.685478	−	0.728094i	$-0.259593\pi$
$601$	−7.05572	−	12.2209i	−0.287809	−	0.498500i	−0.973286	+	0.229594i	$0.926260\pi$
$602$	−1.71275	−	2.04117i	−0.0698064	−	0.0831920i
$603$	−1.02606	−	2.81908i	−0.0417844	−	0.114802i
$604$	9.59152	+	3.49103i	0.390273	+	0.142048i
$605$		0			0
$606$	−2.18907	+	12.4149i	−0.0889250	+	0.504319i
$607$			5.31727i			0.215821i	0.994161	+	0.107911i	$0.0344160\pi$
$607$			5.31727i			0.215821i	−0.994161	+	0.107911i	$0.965584\pi$
$608$	1.86516	+	3.93969i	0.0756422	+	0.159776i
$609$	2.08378			0.0844390
$610$		0			0
$611$	0.386659	+	0.324446i	0.0156426	+	0.0131257i
$612$	−2.95442	+	8.11721i	−0.119425	+	0.328119i
$613$	−14.3961	−	39.5531i	−0.581455	−	1.59753i	−0.785695	−	0.618614i	$-0.787695\pi$
$613$	−14.3961	−	39.5531i	−0.581455	−	1.59753i	0.204241	−	0.978921i	$-0.434528\pi$
$614$	−5.95992	+	5.00097i	−0.240523	+	0.201823i
$615$		0			0
$616$	0.266044	−	0.460802i	0.0107192	−	0.0185663i
$617$	−15.3617	+	2.70867i	−0.618437	+	0.109047i	−0.474085	−	0.880479i	$-0.657221\pi$
$617$	−15.3617	+	2.70867i	−0.618437	+	0.109047i	−0.144352	+	0.989526i	$0.546110\pi$
$618$	−5.35619	+	0.944440i	−0.215457	+	0.0379910i
$619$	11.1853	−	19.3734i	0.449574	−	0.778684i	−0.548785	−	0.835964i	$-0.684909\pi$
$619$	11.1853	−	19.3734i	0.449574	−	0.778684i	0.998358	+	0.0572796i	$0.0182426\pi$
$620$		0			0
$621$	15.9572	−	13.3897i	0.640342	−	0.537311i
$622$	10.6155	+	29.1660i	0.425644	+	1.16945i
$623$	−0.892951	+	2.45336i	−0.0357753	+	0.0982919i
$624$	−0.439693	−	0.368946i	−0.0176018	−	0.0147697i
$625$		0			0
$626$	−9.22668			−0.368772
$627$	−0.356347	−	3.81655i	−0.0142311	−	0.152418i
$628$		−	15.9486i		−	0.636419i
$629$	0.645430	−	3.66041i	0.0257350	−	0.145950i
$630$		0			0
$631$	−4.58260	−	1.66793i	−0.182430	−	0.0663992i	0.249190	−	0.968455i	$-0.419836\pi$
$631$	−4.58260	−	1.66793i	−0.182430	−	0.0663992i	−0.431620	+	0.902055i	$0.642058\pi$
$632$	0.242540	+	0.666374i	0.00964774	+	0.0265069i
$633$	6.35472	+	7.57326i	0.252578	+	0.301010i
$634$	−12.0030	−	20.7898i	−0.476700	−	0.825668i
$635$		0			0
$636$	−0.588993	−	3.34034i	−0.0233551	−	0.132453i
$637$	4.31753	−	0.761297i	0.171067	−	0.0301637i
$638$	3.85673	+	2.22668i	0.152689	+	0.0881552i
$639$	−6.31820	−	10.9434i	−0.249944	−	0.432916i
$640$		0			0
$641$	1.32635	−	0.482753i	0.0523877	−	0.0190676i	−0.315693	−	0.948861i	$-0.602237\pi$
$641$	1.32635	−	0.482753i	0.0523877	−	0.0190676i	0.368081	+	0.929794i	$0.380015\pi$
$642$	−2.94182	+	8.08260i	−0.116105	+	0.318995i
$643$	5.25346	−	6.26083i	0.207176	−	0.246903i	−0.652444	−	0.757837i	$-0.726256\pi$
$643$	5.25346	−	6.26083i	0.207176	−	0.246903i	0.859620	+	0.510934i	$0.170700\pi$
$644$	0.418748	−	2.37484i	0.0165010	−	0.0935817i
$645$		0			0
$646$	13.9081	+	9.61814i	0.547206	+	0.378421i
$647$			31.3773i			1.23357i	0.787132	+	0.616785i	$0.211565\pi$
$647$			31.3773i			1.23357i	−0.787132	+	0.616785i	$0.788435\pi$
$648$	−2.59808	−	0.458111i	−0.102062	−	0.0179963i
$649$	4.80200	+	4.02936i	0.188495	+	0.158166i
$650$		0			0
$651$	−1.21301	+	0.441500i	−0.0475417	+	0.0173037i
$652$	−10.6222	−	12.6591i	−0.415999	−	0.495769i
$653$	33.6780	−	19.4440i	1.31792	−	0.760904i	0.334530	−	0.942385i	$-0.391423\pi$
$653$	33.6780	−	19.4440i	1.31792	−	0.760904i	0.983394	+	0.181482i	$0.0580893\pi$
$654$	−5.63176	+	9.75449i	−0.220219	+	0.381431i
$655$		0			0
$656$	−1.08512	−	6.15403i	−0.0423669	−	0.240275i
$657$	14.4158	+	8.32295i	0.562413	+	0.324709i
$658$	−0.356347	+	0.205737i	−0.0138919	+	0.00802047i
$659$	−9.69047	+	8.13127i	−0.377487	+	0.316749i	−0.811715	−	0.584054i	$-0.801466\pi$
$659$	−9.69047	+	8.13127i	−0.377487	+	0.316749i	0.434228	+	0.900803i	$0.357021\pi$
$660$		0			0
$661$	−41.7708	−	15.2033i	−1.62470	−	0.591342i	−0.640429	−	0.768018i	$-0.721243\pi$
$661$	−41.7708	−	15.2033i	−1.62470	−	0.591342i	−0.984269	+	0.176676i	$0.943466\pi$
$662$	15.7771	−	18.8025i	0.613196	−	0.730779i
$663$	−2.19285	−	0.386659i	−0.0851634	−	0.0150166i
$664$	10.5672			0.410086
$665$		0			0
$666$	2.13341			0.0826679
$667$	19.8764	+	3.50475i	0.769618	+	0.135704i
$668$	−15.2894	+	18.2212i	−0.591565	+	0.705000i
$669$	−9.92040	−	3.61073i	−0.383545	−	0.139599i
$670$		0			0
$671$	−3.76991	+	3.16333i	−0.145536	+	0.122119i
$672$	0.405223	−	0.233956i	0.0156318	−	0.00902503i
$673$	16.8909	+	9.75196i	0.651096	+	0.375911i	0.788876	−	0.614552i	$-0.210663\pi$
$673$	16.8909	+	9.75196i	0.651096	+	0.375911i	−0.137780	+	0.990463i	$0.543997\pi$
$674$	−5.32295	−	30.1879i	−0.205032	−	1.16280i
$675$		0			0
$676$	6.28699	−	10.8894i	0.241807	−	0.418822i
$677$	−6.08738	+	3.51455i	−0.233957	+	0.135075i	−0.612396	−	0.790551i	$-0.709794\pi$
$677$	−6.08738	+	3.51455i	−0.233957	+	0.135075i	0.378439	+	0.925626i	$0.376461\pi$
$678$	3.09516	+	3.68866i	0.118869	+	0.141662i
$679$	0.0505072	−	0.0183831i	0.00193829	−	0.000705479i
$680$		0			0
$681$	17.4388	+	14.6329i	0.668257	+	0.560734i
$682$	−2.71686	−	0.479055i	−0.104034	−	0.0183440i
$683$		−	0.386821i		−	0.0148013i	−0.999973	−	0.00740065i	$-0.997644\pi$
$683$		−	0.386821i		−	0.0148013i	0.999973	−	0.00740065i	$-0.00235572\pi$
$684$	−4.05051	+	8.82029i	−0.154875	+	0.337252i
$685$		0			0
$686$	−1.26739	+	7.18772i	−0.0483891	+	0.274428i
$687$	−6.28217	+	7.48680i	−0.239680	+	0.285639i
$688$	1.71275	−	4.70574i	0.0652979	−	0.179405i
$689$	−2.36571	+	0.861050i	−0.0901266	+	0.0328034i
$690$		0			0
$691$	21.2260	+	36.7645i	0.807474	+	1.39859i	0.914608	+	0.404341i	$0.132499\pi$
$691$	21.2260	+	36.7645i	0.807474	+	1.39859i	−0.107134	+	0.994245i	$0.534168\pi$
$692$	2.66036	+	1.53596i	0.101132	+	0.0583884i
$693$	1.16679	−	0.205737i	0.0443228	−	0.00781530i
$694$	−1.34730	−	7.64090i	−0.0511427	−	0.290044i
$695$		0			0
$696$	1.95811	+	3.39155i	0.0742220	+	0.128556i
$697$	−15.5826	−	18.5706i	−0.590232	−	0.703411i
$698$	−4.36111	−	11.9820i	−0.165070	−	0.453527i
$699$	1.04829	+	0.381545i	0.0396498	+	0.0144313i
$700$		0			0
$701$	−5.96497	+	33.8291i	−0.225294	+	1.27771i	0.636828	+	0.771006i	$0.280246\pi$
$701$	−5.96497	+	33.8291i	−0.225294	+	1.27771i	−0.862122	+	0.506700i	$0.830865\pi$
$702$		−	3.00000i		−	0.113228i
$703$	1.05736	−	4.04024i	0.0398792	−	0.152381i
$704$	1.00000			0.0376889
$705$		0			0
$706$	−7.24691	−	6.08088i	−0.272741	−	0.228857i
$707$	−2.60884	+	7.16772i	−0.0981154	+	0.269570i
$708$	1.88538	+	5.18004i	0.0708570	+	0.194678i
$709$	7.38144	−	6.19377i	0.277216	−	0.232612i	−0.493570	−	0.869706i	$-0.664308\pi$
$709$	7.38144	−	6.19377i	0.277216	−	0.232612i	0.770786	+	0.637094i	$0.219864\pi$
$710$		0			0
$711$	−0.789515	+	1.36748i	−0.0296091	+	0.0512845i
$712$	−4.83218	+	0.852044i	−0.181094	+	0.0319317i
$713$	−12.3130	+	2.17112i	−0.461127	+	0.0813092i
$714$	0.907604	−	1.57202i	0.0339662	−	0.0588312i
$715$		0			0
$716$	12.2365	−	10.2676i	0.457299	−	0.383719i
$717$	−1.28385	−	3.52734i	−0.0479462	−	0.131731i
$718$	0.358075	−	0.983803i	0.0133632	−	0.0367152i
$719$	−35.3542	−	29.6657i	−1.31849	−	1.10634i	−0.986624	−	0.163015i	$-0.947878\pi$
$719$	−35.3542	−	29.6657i	−1.31849	−	1.10634i	−0.331864	−	0.943327i	$-0.607678\pi$
$720$		0			0
$721$	−3.29086			−0.122558
$722$	14.6963	+	12.0424i	0.546940	+	0.448170i
$723$		−	25.8536i		−	0.961505i
$724$	1.69728	−	9.62576i	0.0630790	−	0.357739i
$725$		0			0
$726$	8.26352	+	3.00767i	0.306688	+	0.111625i
$727$	1.12879	+	3.10132i	0.0418644	+	0.115022i	0.958863	−	0.283868i	$-0.0916178\pi$
$727$	1.12879	+	3.10132i	0.0418644	+	0.115022i	−0.916999	+	0.398890i	$0.869396\pi$
$728$	−0.223238	−	0.266044i	−0.00827374	−	0.00986026i
$729$	3.12567	+	5.41381i	0.115765	+	0.200512i
$730$		0			0
$731$	−3.37346	−	19.1318i	−0.124772	−	0.707616i
$732$	−4.26195	+	0.751497i	−0.157526	+	0.0277761i
$733$	−37.5450	−	21.6766i	−1.38676	−	0.800645i	−0.393809	−	0.919192i	$-0.628843\pi$
$733$	−37.5450	−	21.6766i	−1.38676	−	0.800645i	−0.992948	+	0.118547i	$0.962176\pi$
$734$	4.94222	+	8.56017i	0.182421	+	0.315962i
$735$		0			0
$736$	4.25877	−	1.55007i	0.156980	−	0.0571362i
$737$	−0.460802	+	1.26604i	−0.0169739	+	0.0466353i
$738$	8.94405	−	10.6591i	0.329235	−	0.392367i
$739$	0.427204	−	2.42279i	0.0157150	−	0.0891239i	−0.975942	−	0.218032i	$-0.930036\pi$
$739$	0.427204	−	2.42279i	0.0157150	−	0.0891239i	0.991657	+	0.128908i	$0.0411473\pi$
$740$		0			0
$741$	−2.42040	−	0.633436i	−0.0889155	−	0.0232699i
$742$		−	2.05232i		−	0.0753430i
$743$	−8.28104	−	1.46017i	−0.303802	−	0.0535685i	0.0196692	−	0.999807i	$-0.493739\pi$
$743$	−8.28104	−	1.46017i	−0.303802	−	0.0535685i	−0.323471	+	0.946238i	$0.604850\pi$
$744$	−1.85844	−	1.55942i	−0.0681337	−	0.0571710i
$745$		0			0
$746$	26.0501	−	9.48146i	0.953762	−	0.347141i
$747$	15.1246	+	18.0248i	0.553381	+	0.659493i
$748$	3.35965	−	1.93969i	0.122841	−	0.0709222i
$749$	−2.60220	+	4.50714i	−0.0950822	+	0.164687i
$750$		0			0
$751$	−1.14502	−	6.49373i	−0.0417823	−	0.236959i	0.956764	−	0.290867i	$-0.0939436\pi$
$751$	−1.14502	−	6.49373i	−0.0417823	−	0.236959i	−0.998546	+	0.0539072i	$0.982832\pi$
$752$	−0.669713	−	0.386659i	−0.0244219	−	0.0141000i
$753$	−7.40983	+	4.27807i	−0.270029	+	0.155901i
$754$	2.22668	−	1.86841i	0.0810910	−	0.0680434i
$755$		0			0
$756$	2.29813	+	0.836452i	0.0835823	+	0.0304215i
$757$	1.66772	−	1.98751i	0.0606143	−	0.0722373i	−0.734885	−	0.678191i	$-0.762764\pi$
$757$	1.66772	−	1.98751i	0.0606143	−	0.0722373i	0.795500	+	0.605954i	$0.207208\pi$
$758$	12.8800	+	2.27110i	0.467824	+	0.0824900i
$759$	−3.98545			−0.144663
$760$		0			0
$761$	35.9454			1.30302			0.651510	−	0.758640i	$-0.274136\pi$
$761$	35.9454			1.30302			0.651510	+	0.758640i	$0.274136\pi$
$762$	−8.90625	−	1.57041i	−0.322639	−	0.0568900i
$763$	−4.38073	+	5.22075i	−0.158593	+	0.189004i
$764$	7.06670	+	2.57207i	0.255664	+	0.0930542i
$765$		0			0
$766$	−7.63041	+	6.40268i	−0.275698	+	0.231338i
$767$	3.54336	−	2.04576i	0.127943	−	0.0738681i
$768$	0.761570	+	0.439693i	0.0274808	+	0.0158660i
$769$	−3.00815	−	17.0601i	−0.108477	−	0.615202i	−0.989775	−	0.142641i	$-0.954441\pi$
$769$	−3.00815	−	17.0601i	−0.108477	−	0.615202i	0.881298	−	0.472561i	$-0.156670\pi$
$770$		0			0
$771$	1.98411	−	3.43658i	0.0714559	−	0.123765i
$772$	−21.2521	+	12.2699i	−0.764880	+	0.441604i
$773$	−23.1790	−	27.6236i	−0.833689	−	0.993552i	−0.999972	−	0.00747402i	$-0.997621\pi$
$773$	−23.1790	−	27.6236i	−0.833689	−	0.993552i	0.166283	−	0.986078i	$-0.446824\pi$
$774$	10.4782	−	3.81374i	0.376630	−	0.137082i
$775$		0			0
$776$	0.0773815	+	0.0649308i	0.00277783	+	0.00233088i
$777$	−0.441500	−	0.0778483i	−0.0158387	−	0.00279279i
$778$			24.1206i			0.864766i
$779$	−15.7533	−	22.2211i	−0.564421	−	0.796153i
$780$		0			0
$781$	−0.985452	+	5.58878i	−0.0352622	+	0.199982i
$782$	11.3013	−	13.4684i	0.404134	−	0.481628i
$783$	−7.00076	+	19.2344i	−0.250187	+	0.687382i
$784$	−6.31180	+	2.29731i	−0.225422	+	0.0820467i
$785$		0			0
$786$	3.70708	+	6.42085i	0.132227	+	0.229024i
$787$	10.0380	+	5.79544i	0.357816	+	0.206585i	0.668122	−	0.744051i	$-0.267098\pi$
$787$	10.0380	+	5.79544i	0.357816	+	0.206585i	−0.310306	+	0.950637i	$0.600432\pi$
$788$	−14.1849	+	2.50118i	−0.505316	+	0.0891009i
$789$	−4.59967	−	26.0860i	−0.163753	−	0.928687i
$790$		0			0
$791$	1.45677	+	2.52319i	0.0517967	+	0.0897145i
$792$	1.43128	+	1.70574i	0.0508584	+	0.0606107i
$793$	1.09861	+	3.01842i	0.0390129	+	0.107187i
$794$	23.8396	+	8.67691i	0.846036	+	0.307932i
$795$		0			0
$796$	−0.771097	+	4.37311i	−0.0273308	+	0.155001i
$797$			45.0634i			1.59623i	0.602508	+	0.798113i	$0.294168\pi$
$797$			45.0634i			1.59623i	−0.602508	+	0.798113i	$0.705832\pi$
$798$	1.16009	−	1.67752i	0.0410667	−	0.0593835i
$799$	−3.00000			−0.106132
$800$		0			0
$801$	−8.36959	−	7.02292i	−0.295725	−	0.248143i
$802$	−8.48529	+	23.3131i	−0.299626	+	0.823216i
$803$	−2.55682	−	7.02481i	−0.0902283	−	0.247900i
$804$	−0.907604	+	0.761570i	−0.0320087	+	0.0268585i
$805$		0			0
$806$	−0.900330	+	1.55942i	−0.0317128	+	0.0549281i
$807$	3.74557	−	0.660444i	0.131850	−	0.0232487i
$808$	−14.1176	+	2.48932i	−0.496657	+	0.0875741i
$809$	−2.82841	+	4.89895i	−0.0994416	+	0.172238i	−0.911454	−	0.411403i	$-0.865039\pi$
$809$	−2.82841	+	4.89895i	−0.0994416	+	0.172238i	0.812012	+	0.583641i	$0.198372\pi$
$810$		0			0
$811$	21.2781	−	17.8545i	0.747176	−	0.626955i	−0.187578	−	0.982250i	$-0.560064\pi$
$811$	21.2781	−	17.8545i	0.747176	−	0.626955i	0.934754	+	0.355295i	$0.115619\pi$
$812$	0.810446	+	2.22668i	0.0284411	+	0.0781412i
$813$	8.11349	−	22.2916i	0.284553	−	0.781802i
$814$	−0.733956	−	0.615862i	−0.0257251	−	0.0215859i
$815$		0			0
$816$	3.41147			0.119425
$817$	−2.02925	−	21.7337i	−0.0709945	−	0.760366i
$818$			29.9855i			1.04842i
$819$	0.134285	−	0.761570i	0.00469231	−	0.0266114i
$820$		0			0
$821$	−36.1450	−	13.1557i	−1.26147	−	0.459137i	−0.377208	−	0.926129i	$-0.623116\pi$
$821$	−36.1450	−	13.1557i	−1.26147	−	0.459137i	−0.884262	+	0.466991i	$0.845338\pi$
$822$	−2.39739	−	6.58677i	−0.0836185	−	0.229740i
$823$	−6.00833	−	7.16044i	−0.209437	−	0.249597i	0.651092	−	0.758999i	$-0.274311\pi$
$823$	−6.00833	−	7.16044i	−0.209437	−	0.249597i	−0.860529	+	0.509402i	$0.829867\pi$
$824$	−3.09240	−	5.35619i	−0.107729	−	0.186592i
$825$		0			0
$826$	0.579193	+	3.28476i	0.0201527	+	0.114292i
$827$	−45.1237	+	7.95652i	−1.56910	+	0.276675i	−0.889511	−	0.456914i	$-0.848955\pi$
$827$	−45.1237	+	7.95652i	−1.56910	+	0.276675i	−0.679593	+	0.733590i	$0.737843\pi$
$828$	8.73951	+	5.04576i	0.303719	+	0.175352i
$829$	−20.7699	−	35.9745i	−0.721369	−	1.24945i	−0.960451	−	0.278448i	$-0.910180\pi$
$829$	−20.7699	−	35.9745i	−0.721369	−	1.24945i	0.239082	−	0.970999i	$-0.423153\pi$
$830$		0			0
$831$	−1.82160	+	0.663010i	−0.0631907	+	0.0229996i
$832$	0.223238	−	0.613341i	0.00773938	−	0.0212638i
$833$	−16.7494	+	19.9611i	−0.580331	+	0.691611i
$834$	0.963630	−	5.46502i	0.0333678	−	0.189238i
$835$		0			0
$836$	3.93969	−	1.86516i	0.136257	−	0.0645079i
$837$		−	12.6800i		−	0.438286i
$838$	17.4504	+	3.07697i	0.602813	+	0.106292i
$839$	18.0458	+	15.1422i	0.623009	+	0.522766i	0.898748	−	0.438466i	$-0.144478\pi$
$839$	18.0458	+	15.1422i	0.623009	+	0.522766i	−0.275739	+	0.961233i	$0.588923\pi$
$840$		0			0
$841$	8.61468	−	3.13549i	0.297058	−	0.108120i
$842$	−7.74038	−	9.22462i	−0.266751	−	0.317901i
$843$	−14.4536	+	8.34477i	−0.497807	+	0.287409i
$844$	−5.62108	+	9.73600i	−0.193486	+	0.335127i
$845$		0			0
$846$	−0.299011	−	1.69577i	−0.0102802	−	0.0583019i
$847$	4.60802	+	2.66044i	0.158334	+	0.0914140i
$848$	3.34034	−	1.92855i	0.114708	−	0.0662266i
$849$	−9.79473	+	8.21875i	−0.336154	+	0.282067i
$850$		0			0
$851$	−4.08037	−	1.48513i	−0.139873	−	0.0509098i
$852$	−3.20783	+	3.82295i	−0.109899	+	0.130972i
$853$	15.4840	+	2.73025i	0.530162	+	0.0934819i	0.432320	−	0.901720i	$-0.357695\pi$
$853$	15.4840	+	2.73025i	0.530162	+	0.0934819i	0.0978418	+	0.995202i	$0.468806\pi$
$854$	−2.61856			−0.0896051
$855$		0			0
$856$	−9.78106			−0.334310
$857$	2.57705	+	0.454403i	0.0880302	+	0.0155221i	0.217490	−	0.976063i	$-0.430213\pi$
$857$	2.57705	+	0.454403i	0.0880302	+	0.0155221i	−0.129460	+	0.991585i	$0.541324\pi$
$858$	−0.368946	+	0.439693i	−0.0125956	+	0.0150109i
$859$	−20.7729	−	7.56072i	−0.708762	−	0.257968i	−0.0376150	−	0.999292i	$-0.511976\pi$
$859$	−20.7729	−	7.56072i	−0.708762	−	0.257968i	−0.671147	+	0.741324i	$0.734198\pi$
$860$		0			0
$861$	−2.23989	+	1.87949i	−0.0763351	+	0.0640527i
$862$	30.6271	−	17.6826i	1.04316	−	0.602271i
$863$	2.76990	+	1.59920i	0.0942885	+	0.0544375i	0.546403	−	0.837522i	$-0.315997\pi$
$863$	2.76990	+	1.59920i	0.0942885	+	0.0544375i	−0.452114	+	0.891960i	$0.649330\pi$
$864$	0.798133	+	4.52644i	0.0271530	+	0.153993i
$865$		0			0
$866$	−13.3983	+	23.2065i	−0.455292	+	0.788588i
$867$	−1.48534	+	0.857563i	−0.0504449	+	0.0291244i
$868$	−0.943555	−	1.12449i	−0.0320263	−	0.0381675i
$869$	0.666374	−	0.242540i	0.0226052	−	0.00822762i
$870$		0			0
$871$	0.673648	+	0.565258i	0.0228257	+	0.0191530i
$872$	−12.6138	−	2.22416i	−0.427158	−	0.0753194i
$873$			0.224927i			0.00761262i
$874$	13.8871	−	14.0501i	0.469739	−	0.475251i
$875$		0			0
$876$	1.14156	−	6.47410i	0.0385697	−	0.218740i
$877$	−34.8227	+	41.5001i	−1.17588	+	1.40136i	−0.278305	+	0.960493i	$0.589773\pi$
$877$	−34.8227	+	41.5001i	−1.17588	+	1.40136i	−0.897574	+	0.440865i	$0.854672\pi$
$878$	−8.15901	+	22.4167i	−0.275353	+	0.756527i
$879$	5.17442	−	1.88333i	0.174529	−	0.0635233i
$880$		0			0
$881$	25.2670	+	43.7637i	0.851266	+	1.47444i	0.880066	+	0.474851i	$0.157498\pi$
$881$	25.2670	+	43.7637i	0.851266	+	1.47444i	−0.0288001	+	0.999585i	$0.509169\pi$
$882$	−12.9526	−	7.47818i	−0.436136	−	0.251803i
$883$	−44.4756	+	7.84224i	−1.49672	+	0.263913i	−0.861238	−	0.508201i	$-0.830311\pi$
$883$	−44.4756	+	7.84224i	−1.49672	+	0.263913i	−0.635484	+	0.772114i	$0.719199\pi$
$884$	−0.439693	−	2.49362i	−0.0147885	−	0.0838695i
$885$		0			0
$886$	16.8516	+	29.1879i	0.566142	+	0.980586i
$887$	−34.7430	−	41.4051i	−1.16656	−	1.39025i	−0.905189	−	0.425009i	$-0.860271\pi$
$887$	−34.7430	−	41.4051i	−1.16656	−	1.39025i	−0.261368	−	0.965239i	$-0.584174\pi$
$888$	−0.288169	−	0.791737i	−0.00967030	−	0.0265689i
$889$	−5.14203	−	1.87154i	−0.172458	−	0.0627696i
$890$		0			0
$891$	−0.458111	+	2.59808i	−0.0153473	+	0.0870388i
$892$		−	12.0051i		−	0.401959i
$893$	−3.35965	−	0.274196i	−0.112426	−	0.00917561i
$894$	−15.9094			−0.532090
$895$		0			0
$896$	0.407604	+	0.342020i	0.0136171	+	0.0114261i
$897$	−0.889704	+	2.44444i	−0.0297063	+	0.0816175i
$898$	4.41620	+	12.1334i	0.147370	+	0.404897i
$899$	9.41147	−	7.89716i	0.313890	−	0.263385i
$900$		0			0
$901$	7.48158	−	12.9585i	0.249248	−	0.431710i
$902$	−6.15403	+	1.08512i	−0.204907	+	0.0361306i
$903$	−2.30758	+	0.406889i	−0.0767914	+	0.0135404i
$904$	−2.73783	+	4.74205i	−0.0910587	+	0.157718i
$905$		0			0
$906$	6.87598	−	5.76963i	0.228439	−	0.191683i
$907$	−7.39744	−	20.3243i	−0.245628	−	0.674857i	−0.999834	−	0.0182193i	$-0.994200\pi$
$907$	−7.39744	−	20.3243i	−0.245628	−	0.674857i	0.754206	−	0.656638i	$-0.228022\pi$
$908$	−8.85392	+	24.3259i	−0.293828	+	0.807285i
$909$	−24.4525	−	20.5181i	−0.811038	−	0.680541i
$910$		0			0
$911$	−38.0529			−1.26075			−0.630375	−	0.776291i	$-0.717099\pi$
$911$	−38.0529			−1.26075			−0.630375	+	0.776291i	$0.717099\pi$
$912$	3.82045	+	0.311804i	0.126508	+	0.0103249i
$913$		−	10.5672i		−	0.349722i
$914$	6.26486	−	35.5298i	0.207223	−	1.17522i
$915$		0			0
$916$	−10.4436	−	3.80115i	−0.345065	−	0.125593i
$917$	1.53433	+	4.21554i	0.0506680	+	0.139209i
$918$	11.4613	+	13.6591i	0.378281	+	0.450817i
$919$	−10.7255	−	18.5771i	−0.353802	−	0.612802i	0.633111	−	0.774061i	$-0.281778\pi$
$919$	−10.7255	−	18.5771i	−0.353802	−	0.612802i	−0.986912	+	0.161259i	$0.948445\pi$
$920$		0			0
$921$	1.18805	+	6.73779i	0.0391477	+	0.222018i
$922$	0.0555796	−	0.00980018i	0.00183042	−	0.000322752i
$923$	3.20783	+	1.85204i	0.105587	+	0.0609608i
$924$	−0.233956	−	0.405223i	−0.00769657	−	0.0133309i
$925$		0			0
$926$	26.4530	−	9.62809i	0.869298	−	0.316399i
$927$	4.71015	−	12.9410i	0.154702	−	0.425039i
$928$	−2.86257	+	3.41147i	−0.0939684	+	0.111987i
$929$	−3.81093	+	21.6128i	−0.125032	+	0.709094i	0.856256	+	0.516551i	$0.172785\pi$
$929$	−3.81093	+	21.6128i	−0.125032	+	0.709094i	−0.981289	+	0.192543i	$0.938327\pi$
$930$		0			0
$931$	−20.5817	+	20.8232i	−0.674539	+	0.682453i
$932$			1.26857i			0.0415534i
$933$	26.8795	+	4.73958i	0.879995	+	0.155167i
$934$	0.236015	+	0.198040i	0.00772265	+	0.00648007i
$935$		0			0
$936$	1.36571	−	0.497079i	0.0446398	−	0.0162476i
$937$	30.9934	+	36.9365i	1.01251	+	1.20666i	0.978288	+	0.207249i	$0.0664510\pi$
$937$	30.9934	+	36.9365i	1.01251	+	1.20666i	0.0342223	+	0.999414i	$0.489105\pi$
$938$	−0.620838	+	0.358441i	−0.0202711	+	0.0117035i
$939$	−4.05690	+	7.02676i	−0.132392	+	0.229310i
$940$		0			0
$941$	2.49004	+	14.1217i	0.0811729	+	0.460354i	0.998117	+	0.0613388i	$0.0195370\pi$
$941$	2.49004	+	14.1217i	0.0811729	+	0.460354i	−0.916944	+	0.399016i	$0.869352\pi$
$942$	−12.1460	−	7.01249i	−0.395738	−	0.228479i
$943$	−24.5266	+	14.1604i	−0.798696	+	0.461128i
$944$	−4.80200	+	4.02936i	−0.156292	+	0.131144i
$945$		0			0
$946$	−4.70574	−	1.71275i	−0.152997	−	0.0556862i
$947$	−15.1025	+	17.9984i	−0.490764	+	0.584870i	−0.953412	−	0.301673i	$-0.902455\pi$
$947$	−15.1025	+	17.9984i	−0.490764	+	0.584870i	0.462648	+	0.886542i	$0.346900\pi$
$948$	0.614134	+	0.108288i	0.0199461	+	0.00351704i
$949$	−4.87939			−0.158392
$950$		0			0
$951$	−21.1105			−0.684555
$952$	2.03282	+	0.358441i	0.0658840	+	0.0116171i
$953$	−27.4216	+	32.6798i	−0.888273	+	1.05860i	0.109636	+	0.993972i	$0.465031\pi$
$953$	−27.4216	+	32.6798i	−0.888273	+	1.05860i	−0.997909	+	0.0646307i	$0.979413\pi$
$954$	8.07057	+	2.93745i	0.261294	+	0.0951034i
$955$		0			0
$956$	3.26991	−	2.74378i	0.105757	−	0.0887403i
$957$	3.39155	−	1.95811i	0.109633	−	0.0632967i
$958$	26.1756	+	15.1125i	0.845694	+	0.488262i
$959$	−0.736482	−	4.17680i	−0.0237822	−	0.134876i
$960$		0			0
$961$	11.6946	−	20.2556i	0.377245	−	0.653407i
$962$	−0.541580	+	0.312681i	−0.0174612	+	0.0100812i
$963$	−13.9995	−	16.6839i	−0.451127	−	0.537632i
$964$	27.6266	−	10.0553i	0.889793	−	0.323858i
$965$		0			0
$966$	−1.62449	−	1.36310i	−0.0522670	−	0.0438572i
$967$	−17.7757	−	3.13434i	−0.571629	−	0.100794i	−0.119640	−	0.992817i	$-0.538174\pi$
$967$	−17.7757	−	3.13434i	−0.571629	−	0.100794i	−0.451989	+	0.892024i	$0.649285\pi$
$968$			10.0000i			0.321412i
$969$	13.4402	−	6.36295i	0.431760	−	0.204407i
$970$		0			0
$971$	−3.87346	+	21.9675i	−0.124305	+	0.704969i	0.857413	+	0.514629i	$0.172070\pi$
$971$	−3.87346	+	21.9675i	−0.124305	+	0.704969i	−0.981718	+	0.190340i	$0.939041\pi$
$972$	−10.3545	+	12.3400i	−0.332121	+	0.395806i
$973$	1.14841	−	3.15523i	0.0368163	−	0.101152i
$974$	28.0984	−	10.2270i	0.900330	−	0.327693i
$975$		0			0
$976$	−2.46064	−	4.26195i	−0.0787631	−	0.136422i
$977$	6.45918	+	3.72921i	0.206647	+	0.119308i	0.599752	−	0.800186i	$-0.295266\pi$
$977$	6.45918	+	3.72921i	0.206647	+	0.119308i	−0.393105	+	0.919494i	$0.628599\pi$
$978$	−14.3113	+	2.52347i	−0.457625	+	0.0806917i
$979$	0.852044	+	4.83218i	0.0272314	+	0.154437i
$980$		0			0
$981$	−14.2601	−	24.6992i	−0.455290	−	0.788586i
$982$	−2.50622	−	2.98680i	−0.0799767	−	0.0953125i
$983$	2.39354	+	6.57620i	0.0763421	+	0.209748i	0.971993	−	0.235009i	$-0.0755121\pi$
$983$	2.39354	+	6.57620i	0.0763421	+	0.209748i	−0.895651	+	0.444758i	$0.853290\pi$
$984$	−5.16385	−	1.87949i	−0.164617	−	0.0599159i
$985$		0			0
$986$	−3.00000	+	17.0138i	−0.0955395	+	0.541831i
$987$			0.361844i			0.0115176i
$988$	−0.264490	−	2.83275i	−0.00841456	−	0.0901217i
$989$	−22.6955			−0.721676
$990$		0			0
$991$	7.77900	+	6.52736i	0.247108	+	0.207348i	0.757926	−	0.652341i	$-0.226213\pi$
$991$	7.77900	+	6.52736i	0.247108	+	0.207348i	−0.510818	+	0.859689i	$0.670657\pi$
$992$	0.943555	−	2.59240i	0.0299579	−	0.0823087i
$993$	−7.38230	−	20.2827i	−0.234270	−	0.643652i
$994$	−2.31315	+	1.94096i	−0.0733686	+	0.0615636i
$995$		0			0
$996$	4.64631	−	8.04764i	0.147224	−	0.254999i
$997$	−53.8731	+	9.49928i	−1.70618	+	0.300845i	−0.939846	−	0.341598i	$-0.889032\pi$
$997$	−53.8731	+	9.49928i	−1.70618	+	0.300845i	−0.766333	+	0.642444i	$0.777921\pi$
$998$	−24.0236	+	4.23601i	−0.760455	+	0.134089i
$999$	2.20187	−	3.81374i	0.0696640	−	0.120662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.d.549.2		12
5.2	odd	4		950.2.l.b.701.1	yes	6
5.3	odd	4		950.2.l.e.701.1	yes	6
5.4	even	2	inner	950.2.u.d.549.1		12
19.9	even	9	inner	950.2.u.d.199.1		12
95.9	even	18	inner	950.2.u.d.199.2		12
95.28	odd	36		950.2.l.e.351.1	yes	6
95.47	odd	36		950.2.l.b.351.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.b.351.1	✓	6	95.47	odd	36
950.2.l.b.701.1	yes	6	5.2	odd	4
950.2.l.e.351.1	yes	6	95.28	odd	36
950.2.l.e.701.1	yes	6	5.3	odd	4
950.2.u.d.199.1		12	19.9	even	9	inner
950.2.u.d.199.2		12	95.9	even	18	inner
950.2.u.d.549.1		12	5.4	even	2	inner
950.2.u.d.549.2		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)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.565258 - 0.673648i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.673648 - 0.565258i) q^{6} +(0.460802 - 0.266044i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.386659 + 2.19285i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.565258 - 0.673648i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.673648 - 0.565258i) q^{6} +(0.460802 - 0.266044i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.386659 + 2.19285i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.761570 - 0.439693i) q^{12} +(-0.419550 - 0.500000i) q^{13} +(0.500000 - 0.181985i) q^{14} +(0.766044 + 0.642788i) q^{16} +(3.82045 + 0.673648i) q^{17} +2.22668i q^{18} +(4.21688 + 1.10359i) q^{19} +(0.0812519 - 0.460802i) q^{21} +(0.642788 - 0.766044i) q^{22} +(1.55007 - 4.25877i) q^{23} +(0.826352 - 0.300767i) q^{24} +(-0.326352 - 0.565258i) q^{26} +(3.98048 + 2.29813i) q^{27} +(0.524005 - 0.0923963i) q^{28} +(0.773318 + 4.38571i) q^{29} +(-1.37939 - 2.38917i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-0.300767 - 0.826352i) q^{33} +(3.64543 + 1.32683i) q^{34} +(-0.386659 + 2.19285i) q^{36} -0.958111i q^{37} +(3.96118 + 1.81908i) q^{38} -0.573978 q^{39} +(-4.78699 - 4.01676i) q^{41} +(0.160035 - 0.439693i) q^{42} +(-1.71275 - 4.70574i) q^{43} +(0.766044 - 0.642788i) q^{44} +(2.26604 - 3.92490i) q^{46} +(-0.761570 + 0.134285i) q^{47} +(0.866025 - 0.152704i) q^{48} +(-3.35844 + 5.81699i) q^{49} +(2.61334 - 2.19285i) q^{51} +(-0.223238 - 0.613341i) q^{52} +(1.31920 - 3.62449i) q^{53} +(3.52094 + 2.95442i) q^{54} +0.532089 q^{56} +(3.12706 - 2.21688i) q^{57} +4.45336i q^{58} +(-1.08853 + 6.17334i) q^{59} +(-4.62449 - 1.68317i) q^{61} +(-0.943555 - 2.59240i) q^{62} +(0.761570 + 0.907604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.152704 - 0.866025i) q^{66} +(-1.32683 + 0.233956i) q^{67} +(3.35965 + 1.93969i) q^{68} +(-1.99273 - 3.45150i) q^{69} +(-5.33275 + 1.94096i) q^{71} +(-0.761570 + 2.09240i) q^{72} +(4.80526 - 5.72668i) q^{73} +(0.166374 - 0.943555i) q^{74} +(3.58512 + 2.47929i) q^{76} -0.532089i q^{77} +(-0.565258 - 0.0996702i) q^{78} +(0.543233 + 0.455827i) q^{79} +(-2.47906 + 0.902302i) q^{81} +(-4.01676 - 4.78699i) q^{82} +(9.15144 - 5.28359i) q^{83} +(0.233956 - 0.405223i) q^{84} +(-0.869585 - 4.93166i) q^{86} +(3.39155 + 1.95811i) q^{87} +(0.866025 - 0.500000i) q^{88} +(-3.75877 + 3.15398i) q^{89} +(-0.326352 - 0.118782i) q^{91} +(2.91317 - 3.47178i) q^{92} +(-2.38917 - 0.421274i) q^{93} -0.773318 q^{94} +0.879385 q^{96} +(0.0994798 + 0.0175410i) q^{97} +(-4.31753 + 5.14543i) q^{98} +(2.09240 + 0.761570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 + 18 * q^9	\( 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more