LMFDB - Embedded newform 350.2.r.a.83.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			83.13
Character	$\chi$	$=$	350.83
Dual form			350.2.r.a.97.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(-0.317364 + 2.00376i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.97984 + 1.03934i) q^{5} +(-1.19246 + 1.64128i) q^{6} +(2.06419 + 1.65503i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06116 - 0.344792i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(-0.317364 + 2.00376i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.97984 + 1.03934i) q^{5} +(-1.19246 + 1.64128i) q^{6} +(2.06419 + 1.65503i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06116 - 0.344792i) q^{9} +(1.29220 + 1.82489i) q^{10} +(-1.97473 - 6.07761i) q^{11} +(-1.80762 + 0.921027i) q^{12} +(-1.86308 - 3.65650i) q^{13} +(1.08784 + 2.41176i) q^{14} +(-2.71092 + 3.63727i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.583695 + 3.68530i) q^{17} +(-0.788968 - 0.788968i) q^{18} +(-4.00049 - 2.90653i) q^{19} +(0.322877 + 2.21263i) q^{20} +(-3.97138 + 3.61089i) q^{21} +(0.999675 - 6.31170i) q^{22} +(0.968792 - 1.90136i) q^{23} -2.02874 q^{24} +(2.83954 + 4.11546i) q^{25} -4.10379i q^{26} +(-1.73543 + 3.40597i) q^{27} +(-0.125644 + 2.64277i) q^{28} +(2.28482 + 3.14478i) q^{29} +(-4.06674 + 2.01010i) q^{30} +(2.56980 - 3.53702i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(12.8048 - 2.02808i) q^{33} +(-1.15302 + 3.54862i) q^{34} +(2.36663 + 5.42209i) q^{35} +(-0.344792 - 1.06116i) q^{36} +(-0.834231 - 1.63727i) q^{37} +(-2.24493 - 4.40592i) q^{38} +(7.91803 - 2.57272i) q^{39} +(-0.716830 + 2.11805i) q^{40} +(-9.86970 - 3.20686i) q^{41} +(-5.17783 + 1.41436i) q^{42} +(-7.82550 - 7.82550i) q^{43} +(3.75617 - 5.16992i) q^{44} +(-1.74257 - 1.78554i) q^{45} +(1.72640 - 1.25430i) q^{46} +(-2.56934 - 0.406944i) q^{47} +(-1.80762 - 0.921027i) q^{48} +(1.52177 + 6.83259i) q^{49} +(0.661669 + 4.95603i) q^{50} -7.56971 q^{51} +(1.86308 - 3.65650i) q^{52} +(11.9352 + 1.89036i) q^{53} +(-3.09255 + 2.24687i) q^{54} +(2.40705 - 14.0851i) q^{55} +(-1.31174 + 2.29768i) q^{56} +(7.09359 - 7.09359i) q^{57} +(0.608087 + 3.83931i) q^{58} +(0.397108 - 1.22217i) q^{59} +(-4.53606 - 0.0552440i) q^{60} +(2.46385 - 0.800554i) q^{61} +(3.89548 - 1.98485i) q^{62} +(-1.61980 - 2.46797i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.111749 - 9.17568i) q^{65} +(12.3299 + 4.00621i) q^{66} +(12.5273 - 1.98412i) q^{67} +(-2.63839 + 2.63839i) q^{68} +(3.50241 + 2.54465i) q^{69} +(-0.352893 + 5.90555i) q^{70} +(-5.66886 + 4.11867i) q^{71} +(0.174545 - 1.10203i) q^{72} +(6.88548 + 3.50833i) q^{73} -1.83755i q^{74} +(-9.14756 + 4.38365i) q^{75} -4.94488i q^{76} +(5.98238 - 15.8136i) q^{77} +(8.22301 + 1.30240i) q^{78} +(6.06836 + 8.35238i) q^{79} +(-1.60028 + 1.56177i) q^{80} +(-8.98200 - 6.52581i) q^{81} +(-7.33808 - 7.33808i) q^{82} +(-5.78468 + 0.916204i) q^{83} +(-5.25559 - 1.09048i) q^{84} +(-2.67467 + 7.90298i) q^{85} +(-3.41987 - 10.5253i) q^{86} +(-7.02651 + 3.58018i) q^{87} +(5.69386 - 2.90117i) q^{88} +(-0.170073 - 0.523432i) q^{89} +(-0.742025 - 2.38204i) q^{90} +(2.20586 - 10.6312i) q^{91} +(2.10768 - 0.333823i) q^{92} +(6.27178 + 6.27178i) q^{93} +(-2.10455 - 1.52905i) q^{94} +(-4.89946 - 9.91234i) q^{95} +(-1.19246 - 1.64128i) q^{96} +(9.85049 + 1.56016i) q^{97} +(-1.74602 + 6.77875i) q^{98} +7.13019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	−0.317364	+	2.00376i	−0.183230	+	1.15687i	0.708973	+	0.705236i	$0.249159\pi$
$3$	−0.317364	+	2.00376i	−0.183230	+	1.15687i	−0.892203	+	0.451635i	$0.850841\pi$
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	1.97984	+	1.03934i	0.885412	+	0.464807i
$5$	1.97984	+	1.03934i	0.885412	+	0.464807i
$6$	−1.19246	+	1.64128i	−0.486820	+	0.670051i
$7$	2.06419	+	1.65503i	0.780191	+	0.625542i
$7$	2.06419	+	1.65503i	0.780191	+	0.625542i
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−1.06116	−	0.344792i	−0.353720	−	0.114931i
$10$	1.29220	+	1.82489i	0.408630	+	0.577080i
$11$	−1.97473	−	6.07761i	−0.595405	−	1.83247i	−0.552701	−	0.833379i	$-0.686403\pi$
$11$	−1.97473	−	6.07761i	−0.595405	−	1.83247i	−0.0427033	−	0.999088i	$-0.513597\pi$
$12$	−1.80762	+	0.921027i	−0.521814	+	0.265878i
$13$	−1.86308	−	3.65650i	−0.516726	−	1.01413i	−0.991013	−	0.133762i	$-0.957294\pi$
$13$	−1.86308	−	3.65650i	−0.516726	−	1.01413i	0.474287	−	0.880370i	$-0.342706\pi$
$14$	1.08784	+	2.41176i	0.290738	+	0.644571i
$15$	−2.71092	+	3.63727i	−0.699956	+	0.939140i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.583695	+	3.68530i	0.141567	+	0.893818i	0.951579	+	0.307405i	$0.0994605\pi$
$17$	0.583695	+	3.68530i	0.141567	+	0.893818i	−0.810012	+	0.586413i	$0.800540\pi$
$18$	−0.788968	−	0.788968i	−0.185962	−	0.185962i
$19$	−4.00049	−	2.90653i	−0.917776	−	0.666803i	0.0251936	−	0.999683i	$-0.491980\pi$
$19$	−4.00049	−	2.90653i	−0.917776	−	0.666803i	−0.942969	+	0.332879i	$0.891980\pi$
$20$	0.322877	+	2.21263i	0.0721974	+	0.494760i
$21$	−3.97138	+	3.61089i	−0.866625	+	0.787962i
$22$	0.999675	−	6.31170i	0.213131	−	1.34566i
$23$	0.968792	−	1.90136i	0.202007	−	0.396461i	−0.767672	−	0.640843i	$-0.778585\pi$
$23$	0.968792	−	1.90136i	0.202007	−	0.396461i	0.969679	+	0.244382i	$0.0785850\pi$
$24$	−2.02874			−0.414114
$25$	2.83954	+	4.11546i	0.567908	+	0.823092i
$26$		−	4.10379i		−	0.804820i
$27$	−1.73543	+	3.40597i	−0.333983	+	0.655479i
$28$	−0.125644	+	2.64277i	−0.0237445	+	0.499436i
$29$	2.28482	+	3.14478i	0.424280	+	0.583972i	0.966629	−	0.256182i	$-0.0824647\pi$
$29$	2.28482	+	3.14478i	0.424280	+	0.583972i	−0.542348	+	0.840154i	$0.682465\pi$
$30$	−4.06674	+	2.01010i	−0.742481	+	0.366993i
$31$	2.56980	−	3.53702i	0.461549	−	0.635268i	−0.513280	−	0.858221i	$-0.671570\pi$
$31$	2.56980	−	3.53702i	0.461549	−	0.635268i	0.974829	+	0.222953i	$0.0715697\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	12.8048	−	2.02808i	2.22902	−	0.353043i
$34$	−1.15302	+	3.54862i	−0.197741	+	0.608584i
$35$	2.36663	+	5.42209i	0.400034	+	0.916500i
$36$	−0.344792	−	1.06116i	−0.0574653	−	0.176860i
$37$	−0.834231	−	1.63727i	−0.137147	−	0.269166i	0.812210	−	0.583365i	$-0.198264\pi$
$37$	−0.834231	−	1.63727i	−0.137147	−	0.269166i	−0.949357	+	0.314199i	$0.898264\pi$
$38$	−2.24493	−	4.40592i	−0.364175	−	0.714735i
$39$	7.91803	−	2.57272i	1.26790	−	0.411965i
$40$	−0.716830	+	2.11805i	−0.113341	+	0.334894i
$41$	−9.86970	−	3.20686i	−1.54139	−	0.500827i	−0.589629	−	0.807674i	$-0.700726\pi$
$41$	−9.86970	−	3.20686i	−1.54139	−	0.500827i	−0.951759	+	0.306847i	$0.900726\pi$
$42$	−5.17783	+	1.41436i	−0.798957	+	0.218241i
$43$	−7.82550	−	7.82550i	−1.19338	−	1.19338i	−0.976113	−	0.217265i	$-0.930286\pi$
$43$	−7.82550	−	7.82550i	−1.19338	−	1.19338i	−0.217265	−	0.976113i	$-0.569714\pi$
$44$	3.75617	−	5.16992i	0.566263	−	0.779395i
$45$	−1.74257	−	1.78554i	−0.259767	−	0.266173i
$46$	1.72640	−	1.25430i	0.254544	−	0.184937i
$47$	−2.56934	−	0.406944i	−0.374777	−	0.0593589i	−0.0337954	−	0.999429i	$-0.510759\pi$
$47$	−2.56934	−	0.406944i	−0.374777	−	0.0593589i	−0.340982	+	0.940070i	$0.610759\pi$
$48$	−1.80762	−	0.921027i	−0.260907	−	0.132939i
$49$	1.52177	+	6.83259i	0.217396	+	0.976084i
$50$	0.661669	+	4.95603i	0.0935741	+	0.700888i
$51$	−7.56971			−1.05997
$52$	1.86308	−	3.65650i	0.258363	−	0.507066i
$53$	11.9352	+	1.89036i	1.63943	+	0.259661i	0.906985	−	0.421163i	$-0.138378\pi$
$53$	11.9352	+	1.89036i	1.63943	+	0.259661i	0.732447	+	0.680824i	$0.238378\pi$
$54$	−3.09255	+	2.24687i	−0.420843	+	0.305760i
$55$	2.40705	−	14.0851i	0.324566	−	1.89924i
$56$	−1.31174	+	2.29768i	−0.175289	+	0.307040i
$57$	7.09359	−	7.09359i	0.939569	−	0.939569i
$58$	0.608087	+	3.83931i	0.0798457	+	0.504126i
$59$	0.397108	−	1.22217i	0.0516990	−	0.159113i	−0.921874	−	0.387491i	$-0.873342\pi$
$59$	0.397108	−	1.22217i	0.0516990	−	0.159113i	0.973573	+	0.228377i	$0.0733420\pi$
$60$	−4.53606	−	0.0552440i	−0.585602	−	0.00713197i
$61$	2.46385	−	0.800554i	0.315464	−	0.102500i	−0.147006	−	0.989136i	$-0.546964\pi$
$61$	2.46385	−	0.800554i	0.315464	−	0.102500i	0.462469	+	0.886635i	$0.346964\pi$
$62$	3.89548	−	1.98485i	0.494727	−	0.252076i
$63$	−1.61980	−	2.46797i	−0.204075	−	0.310934i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	0.111749	−	9.17568i	0.0138608	−	1.13810i
$66$	12.3299	+	4.00621i	1.51770	+	0.493131i
$67$	12.5273	−	1.98412i	1.53045	−	0.242399i	0.666319	−	0.745667i	$-0.267869\pi$
$67$	12.5273	−	1.98412i	1.53045	−	0.242399i	0.864131	+	0.503267i	$0.167869\pi$
$68$	−2.63839	+	2.63839i	−0.319951	+	0.319951i
$69$	3.50241	+	2.54465i	0.421641	+	0.306340i
$70$	−0.352893	+	5.90555i	−0.0421788	+	0.705848i
$71$	−5.66886	+	4.11867i	−0.672770	+	0.488796i	−0.870951	−	0.491370i	$-0.836496\pi$
$71$	−5.66886	+	4.11867i	−0.672770	+	0.488796i	0.198182	+	0.980165i	$0.436496\pi$
$72$	0.174545	−	1.10203i	0.0205703	−	0.129876i
$73$	6.88548	+	3.50833i	0.805885	+	0.410619i	0.807856	−	0.589379i	$-0.200628\pi$
$73$	6.88548	+	3.50833i	0.805885	+	0.410619i	−0.00197184	+	0.999998i	$0.500628\pi$
$74$		−	1.83755i		−	0.213611i
$75$	−9.14756	+	4.38365i	−1.05627	+	0.506181i
$76$		−	4.94488i		−	0.567217i
$77$	5.98238	−	15.8136i	0.681755	−	1.80212i
$78$	8.22301	+	1.30240i	0.931072	+	0.147467i
$79$	6.06836	+	8.35238i	0.682744	+	0.939716i	0.999963	−	0.00863630i	$-0.00274906\pi$
$79$	6.06836	+	8.35238i	0.682744	+	0.939716i	−0.317219	+	0.948352i	$0.602749\pi$
$80$	−1.60028	+	1.56177i	−0.178916	+	0.174611i
$81$	−8.98200	−	6.52581i	−0.998000	−	0.725090i
$82$	−7.33808	−	7.33808i	−0.810355	−	0.810355i
$83$	−5.78468	+	0.916204i	−0.634951	+	0.100566i	−0.465609	−	0.884991i	$-0.654165\pi$
$83$	−5.78468	+	0.916204i	−0.634951	+	0.100566i	−0.169343	+	0.985557i	$0.554165\pi$
$84$	−5.25559	−	1.09048i	−0.573432	−	0.118981i
$85$	−2.67467	+	7.90298i	−0.290108	+	0.857198i
$86$	−3.41987	−	10.5253i	−0.368774	−	1.13497i
$87$	−7.02651	+	3.58018i	−0.753321	+	0.383836i
$88$	5.69386	−	2.90117i	0.606968	−	0.309266i
$89$	−0.170073	−	0.523432i	−0.0180277	−	0.0554837i	0.941638	−	0.336627i	$-0.109286\pi$
$89$	−0.170073	−	0.523432i	−0.0180277	−	0.0554837i	−0.959666	+	0.281144i	$0.909286\pi$
$90$	−0.742025	−	2.38204i	−0.0782163	−	0.251089i
$91$	2.20586	−	10.6312i	0.231237	−	1.11445i
$92$	2.10768	−	0.333823i	0.219740	−	0.0348034i
$93$	6.27178	+	6.27178i	0.650354	+	0.650354i
$94$	−2.10455	−	1.52905i	−0.217068	−	0.157709i
$95$	−4.89946	−	9.91234i	−0.502674	−	1.01698i
$96$	−1.19246	−	1.64128i	−0.121705	−	0.167513i
$97$	9.85049	+	1.56016i	1.00017	+	0.158411i	0.634984	−	0.772525i	$-0.281007\pi$
$97$	9.85049	+	1.56016i	1.00017	+	0.158411i	0.365182	+	0.930936i	$0.381007\pi$
$98$	−1.74602	+	6.77875i	−0.176375	+	0.684757i
$99$			7.13019i			0.716611i
$100$	−1.66044	+	4.71624i	−0.166044	+	0.471624i
$101$			6.27358i			0.624245i	0.950042	+	0.312122i	$0.101040\pi$
$101$			6.27358i			0.624245i	−0.950042	+	0.312122i	$0.898960\pi$
$102$	−6.74466	−	3.43657i	−0.667821	−	0.340272i
$103$	−0.415865	+	2.62567i	−0.0409764	+	0.258715i	−0.999669	−	0.0257297i	$-0.991809\pi$
$103$	−0.415865	+	2.62567i	−0.0409764	+	0.258715i	0.958693	+	0.284444i	$0.0918091\pi$
$104$	3.32004	−	2.41215i	0.325556	−	0.236531i
$105$	−11.6156	+	3.02138i	−1.13357	+	0.294857i
$106$	9.77618	+	7.10281i	0.949546	+	0.689886i
$107$	−8.54361	+	8.54361i	−0.825942	+	0.825942i	−0.986953	−	0.161011i	$-0.948525\pi$
$107$	−8.54361	+	8.54361i	−0.825942	+	0.825942i	0.161011	+	0.986953i	$0.448525\pi$
$108$	−3.77554	+	0.597987i	−0.363302	+	0.0575414i
$109$	−1.44152	−	0.468379i	−0.138073	−	0.0448626i	0.239165	−	0.970979i	$-0.423126\pi$
$109$	−1.44152	−	0.468379i	−0.138073	−	0.0448626i	−0.377238	+	0.926116i	$0.623126\pi$
$110$	8.53920	−	11.4572i	0.814181	−	1.09240i
$111$	3.54545	−	1.15199i	0.336519	−	0.109342i
$112$	−2.21189	+	1.45173i	−0.209004	+	0.137176i
$113$	−6.57549	+	3.35038i	−0.618570	+	0.315177i	−0.735047	−	0.678016i	$-0.762840\pi$
$113$	−6.57549	+	3.35038i	−0.618570	+	0.315177i	0.116477	+	0.993193i	$0.462840\pi$
$114$	9.54086	−	3.10001i	0.893584	−	0.290343i
$115$	3.89422	−	2.75749i	0.363138	−	0.257137i
$116$	−1.20120	+	3.69692i	−0.111529	+	0.343250i
$117$	0.716296	+	4.52251i	0.0662216	+	0.418106i
$118$	0.908680	−	0.908680i	0.0836508	−	0.0836508i
$119$	−4.89442	+	8.57320i	−0.448671	+	0.785904i
$120$	−4.01657	−	2.10855i	−0.366661	−	0.192483i
$121$	−24.1385	+	17.5377i	−2.19441	+	1.59433i
$122$	2.55875	+	0.405266i	0.231658	+	0.0366911i
$123$	9.55806	−	18.7588i	0.861821	−	1.69142i
$124$	4.37200			0.392617
$125$	1.34447	+	11.0992i	0.120253	+	0.992743i
$126$	−0.322817	−	2.93435i	−0.0287588	−	0.261412i
$127$	−6.25343	−	3.18628i	−0.554902	−	0.282737i	0.153968	−	0.988076i	$-0.450795\pi$
$127$	−6.25343	−	3.18628i	−0.554902	−	0.282737i	−0.708870	+	0.705339i	$0.750795\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	18.1639	−	13.1969i	1.59925	−	1.16192i
$130$	4.26524	−	8.12485i	0.374086	−	0.712597i
$131$	−5.41558	+	7.45391i	−0.473161	+	0.651251i	−0.977173	−	0.212446i	$-0.931857\pi$
$131$	−5.41558	+	7.45391i	−0.473161	+	0.651251i	0.504011	+	0.863697i	$0.331857\pi$
$132$	9.16720	+	9.16720i	0.797902	+	0.797902i
$133$	−3.44740	−	12.6206i	−0.298927	−	1.09434i
$134$	12.0627	+	3.91939i	1.04205	+	0.338584i
$135$	−6.97583	+	4.93957i	−0.600384	+	0.425131i
$136$	−3.54862	+	1.15302i	−0.304292	+	0.0988704i
$137$	−1.92637	−	3.78071i	−0.164581	−	0.323008i	0.793957	−	0.607974i	$-0.208018\pi$
$137$	−1.92637	−	3.78071i	−0.164581	−	0.323008i	−0.958537	+	0.284966i	$0.908018\pi$
$138$	1.96542	+	3.85736i	0.167308	+	0.328360i
$139$	−3.24384	−	9.98353i	−0.275139	−	0.846792i	−0.989183	−	0.146690i	$-0.953138\pi$
$139$	−3.24384	−	9.98353i	−0.275139	−	0.846792i	0.714043	−	0.700102i	$-0.246862\pi$
$140$	−2.99549	+	5.10167i	−0.253165	+	0.431170i
$141$	1.63084	−	5.01919i	0.137341	−	0.422692i
$142$	−6.92082	+	1.09615i	−0.580783	+	0.0919869i
$143$	−18.5437	+	18.5437i	−1.55070	+	1.55070i
$144$	0.655833	−	0.902677i	0.0546528	−	0.0752231i
$145$	1.25508	+	8.60088i	0.104228	+	0.714264i
$146$	4.54226	+	6.25189i	0.375920	+	0.517410i
$147$	−14.1738	+	0.880839i	−1.16904	+	0.0726504i
$148$	0.834231	−	1.63727i	0.0685734	−	0.134583i
$149$		−	6.03684i		−	0.494557i	−0.968944	−	0.247278i	$-0.920464\pi$
$149$		−	6.03684i		−	0.494557i	0.968944	−	0.247278i	$-0.0795362\pi$
$150$	−10.1407	−	0.247040i	−0.827982	−	0.0201707i
$151$	3.59456			0.292521			0.146261	−	0.989246i	$-0.453276\pi$
$151$	3.59456			0.292521			0.146261	+	0.989246i	$0.453276\pi$
$152$	2.24493	−	4.40592i	0.182088	−	0.357367i
$153$	0.651269	−	4.11195i	0.0526520	−	0.332432i
$154$	12.5096	−	11.3741i	1.00805	−	0.916548i
$155$	8.76397	−	4.33185i	0.703939	−	0.347942i
$156$	6.73548	+	4.89361i	0.539270	+	0.391802i
$157$	−11.8953	−	11.8953i	−0.949352	−	0.949352i	0.0494261	−	0.998778i	$-0.484261\pi$
$157$	−11.8953	−	11.8953i	−0.949352	−	0.949352i	−0.998778	+	0.0494261i	$0.984261\pi$
$158$	1.61505	+	10.1970i	0.128486	+	0.811230i
$159$	−7.57564	+	23.3154i	−0.600787	+	1.84903i
$160$	−2.13488	+	0.665034i	−0.168777	+	0.0525755i
$161$	5.14658	−	2.32140i	0.405607	−	0.182952i
$162$	−5.04037	−	9.89228i	−0.396009	−	0.777211i
$163$	17.8323	−	9.08601i	1.39673	−	0.711671i	0.416430	−	0.909168i	$-0.363281\pi$
$163$	17.8323	−	9.08601i	1.39673	−	0.711671i	0.980304	+	0.197496i	$0.0632811\pi$
$164$	−3.20686	−	9.86970i	−0.250414	−	0.770694i
$165$	27.4593	+	9.29325i	2.13770	+	0.723479i
$166$	−5.57014	−	1.80985i	−0.432327	−	0.140471i
$167$	1.51820	+	9.58552i	0.117482	+	0.741749i	0.974153	+	0.225888i	$0.0725282\pi$
$167$	1.51820	+	9.58552i	0.117482	+	0.741749i	−0.856672	+	0.515862i	$0.827472\pi$
$168$	−4.18770	−	3.35761i	−0.323088	−	0.259046i
$169$	−2.25774	+	3.10752i	−0.173673	+	0.239040i
$170$	−5.97102	+	5.82733i	−0.457956	+	0.446936i
$171$	3.24302	+	4.46363i	0.248000	+	0.341342i
$172$	1.73125	−	10.9307i	0.132006	−	0.833456i
$173$	−2.07254	−	1.05601i	−0.157572	−	0.0802871i	0.373426	−	0.927660i	$-0.378183\pi$
$173$	−2.07254	−	1.05601i	−0.157572	−	0.0802871i	−0.530998	+	0.847373i	$0.678183\pi$
$174$	−7.88603			−0.597839
$175$	−0.949846	+	13.1946i	−0.0718016	+	0.997419i
$176$	6.39037			0.481692
$177$	2.32291	+	1.18358i	0.174601	+	0.0889634i
$178$	0.0860967	−	0.543593i	0.00645322	−	0.0407440i
$179$	4.77399	+	6.57083i	0.356825	+	0.491127i	0.949261	−	0.314490i	$-0.101834\pi$
$179$	4.77399	+	6.57083i	0.356825	+	0.491127i	−0.592436	+	0.805618i	$0.701834\pi$
$180$	0.420274	−	2.45928i	0.0313254	−	0.183304i
$181$	1.71406	−	2.35920i	0.127405	−	0.175358i	−0.740549	−	0.672002i	$-0.765435\pi$
$181$	1.71406	−	2.35920i	0.127405	−	0.175358i	0.867954	+	0.496644i	$0.165435\pi$
$182$	6.79189	−	8.47101i	0.503448	−	0.627913i
$183$	0.822178	+	5.19103i	0.0607772	+	0.383732i
$184$	2.02950	+	0.659426i	0.149617	+	0.0486135i
$185$	0.0500379	−	4.10859i	0.00367886	−	0.302069i
$186$	2.74087	+	8.43553i	0.200970	+	0.618523i
$187$	21.2452	−	10.8250i	1.55360	−	0.791600i
$188$	−1.18100	−	2.31784i	−0.0861331	−	0.169046i
$189$	−9.21922	+	4.15839i	−0.670600	+	0.302478i
$190$	0.134653	−	11.0563i	0.00976873	−	0.802106i
$191$	0.00657093	−	0.0202232i	0.000475456	−	0.00146330i	−0.950819	−	0.309749i	$-0.899755\pi$
$191$	0.00657093	−	0.0202232i	0.000475456	−	0.00146330i	0.951294	+	0.308285i	$0.0997551\pi$
$192$	−0.317364	−	2.00376i	−0.0229038	−	0.144609i
$193$	−7.62422	−	7.62422i	−0.548804	−	0.548804i	0.377291	−	0.926095i	$-0.376856\pi$
$193$	−7.62422	−	7.62422i	−0.548804	−	0.548804i	−0.926095	+	0.377291i	$0.876856\pi$
$194$	8.06855	+	5.86215i	0.579288	+	0.420878i
$195$	18.3504	+	3.13595i	1.31410	+	0.224570i
$196$	−4.63320	+	5.24723i	−0.330943	+	0.374802i
$197$	0.774385	−	4.88927i	0.0551726	−	0.348346i	−0.944624	−	0.328156i	$-0.893573\pi$
$197$	0.774385	−	4.88927i	0.0551726	−	0.348346i	0.999796	−	0.0201903i	$-0.00642721\pi$
$198$	−3.23704	+	6.35304i	−0.230046	+	0.451491i
$199$	−15.9421			−1.13011			−0.565054	−	0.825054i	$-0.691145\pi$
$199$	−15.9421			−1.13011			−0.565054	+	0.825054i	$0.691145\pi$
$200$	−3.62059	+	3.44838i	−0.256014	+	0.243837i
$201$			25.7313i			1.81495i
$202$	−2.84815	+	5.58980i	−0.200395	+	0.393297i
$203$	−0.488400	+	10.2729i	−0.0342790	+	0.721014i
$204$	−4.44936	−	6.12402i	−0.311518	−	0.428767i
$205$	−16.2074	−	16.6071i	−1.13197	−	1.15989i
$206$	−1.56257	+	2.15069i	−0.108869	+	0.149845i
$207$	−1.68362	+	1.68362i	−0.117019	+	0.117019i
$208$	4.05327	−	0.641974i	0.281043	−	0.0445129i
$209$	−9.76482	+	30.0530i	−0.675447	+	2.07881i
$210$	−11.7213	−	2.58132i	−0.808846	−	0.178128i
$211$	0.287839	+	0.885878i	0.0198157	+	0.0609864i	0.960475	−	0.278365i	$-0.0897925\pi$
$211$	0.287839	+	0.885878i	0.0198157	+	0.0609864i	−0.940660	+	0.339351i	$0.889792\pi$
$212$	5.48603	+	10.7669i	0.376782	+	0.739477i
$213$	−6.45372	−	12.6661i	−0.442202	−	0.867870i
$214$	−11.4911	+	3.73369i	−0.785518	+	0.255230i
$215$	−7.35988	−	23.6266i	−0.501940	−	1.61132i
$216$	−3.63551	−	1.18125i	−0.247365	−	0.0803739i
$217$	11.1584	−	3.04801i	0.757483	−	0.206912i
$218$	−1.07177	−	1.07177i	−0.0725892	−	0.0725892i
$219$	−9.21505	+	12.6834i	−0.622695	+	0.857066i
$220$	12.8099	−	6.33168i	0.863645	−	0.426882i
$221$	12.3879	−	9.00031i	0.833298	−	0.605426i
$222$	3.68201	+	0.583173i	0.247120	+	0.0391400i
$223$	3.81311	+	1.94287i	0.255344	+	0.130104i	0.576978	−	0.816760i	$-0.304232\pi$
$223$	3.81311	+	1.94287i	0.255344	+	0.130104i	−0.321633	+	0.946864i	$0.604232\pi$
$224$	−2.62988	+	0.289322i	−0.175717	+	0.0193312i
$225$	−1.59423	−	5.34621i	−0.106282	−	0.356414i
$226$	−7.37984			−0.490900
$227$	−5.58939	+	10.9698i	−0.370981	+	0.728091i	−0.998733	−	0.0503221i	$-0.983975\pi$
$227$	−5.58939	+	10.9698i	−0.370981	+	0.728091i	0.627752	+	0.778413i	$0.283975\pi$
$228$	9.90835	+	1.56933i	0.656196	+	0.103931i
$229$	10.3150	−	7.49430i	0.681636	−	0.495237i	−0.192264	−	0.981343i	$-0.561583\pi$
$229$	10.3150	−	7.49430i	0.681636	−	0.495237i	0.873900	+	0.486106i	$0.161583\pi$
$230$	4.72165	−	0.689002i	0.311336	−	0.0454314i
$231$	29.7880	+	17.0059i	1.95991	+	1.11891i
$232$	−2.74864	+	2.74864i	−0.180457	+	0.180457i
$233$	2.07732	+	13.1157i	0.136090	+	0.859237i	0.957402	+	0.288758i	$0.0932424\pi$
$233$	2.07732	+	13.1157i	0.136090	+	0.859237i	−0.821312	+	0.570479i	$0.806758\pi$
$234$	−1.41495	+	4.35478i	−0.0924984	+	0.284681i
$235$	−4.66394	−	3.47611i	−0.304242	−	0.226756i
$236$	1.22217	−	0.397108i	0.0795566	−	0.0258495i
$237$	−18.6620	+	9.50878i	−1.21223	+	0.617662i
$238$	−8.25312	+	5.41676i	−0.534970	+	0.351116i
$239$	−18.7340	+	6.08706i	−1.21180	+	0.393739i	−0.844091	−	0.536200i	$-0.819859\pi$
$239$	−18.7340	+	6.08706i	−1.21180	+	0.393739i	−0.367713	+	0.929939i	$0.619859\pi$
$240$	−2.62153	−	3.70222i	−0.169219	−	0.238977i
$241$	16.8449	+	5.47325i	1.08508	+	0.352563i	0.796342	−	0.604846i	$-0.206765\pi$
$241$	16.8449	+	5.47325i	1.08508	+	0.352563i	0.288735	+	0.957409i	$0.406765\pi$
$242$	−29.4695	+	4.66751i	−1.89437	+	0.300039i
$243$	7.81774	−	7.81774i	0.501508	−	0.501508i
$244$	2.09588	+	1.52274i	0.134175	+	0.0974836i
$245$	−4.08853	+	15.1091i	−0.261206	+	0.965283i
$246$	17.0326	−	12.3749i	1.08596	−	0.788995i
$247$	−3.17449	+	20.0429i	−0.201988	+	1.27530i
$248$	3.89548	+	1.98485i	0.247363	+	0.126038i
$249$		−	11.8819i		−	0.752984i
$250$	−3.84100	+	10.4998i	−0.242926	+	0.664068i
$251$		−	11.5734i		−	0.730507i	−0.930908	−	0.365253i	$-0.880982\pi$
$251$		−	11.5734i		−	0.730507i	0.930908	−	0.365253i	$-0.119018\pi$
$252$	1.04453	−	2.76108i	0.0657994	−	0.173932i
$253$	−13.4688	−	2.13325i	−0.846778	−	0.134116i
$254$	−4.12531	−	5.67800i	−0.258845	−	0.356269i
$255$	−14.9868	−	7.86751i	−0.938511	−	0.492682i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.769102	−	0.769102i	−0.0479752	−	0.0479752i	0.682712	−	0.730687i	$-0.260800\pi$
$257$	−0.769102	−	0.769102i	−0.0479752	−	0.0479752i	−0.730687	+	0.682712i	$0.760800\pi$
$258$	22.1755	−	3.51225i	1.38058	−	0.218663i
$259$	0.987715	−	4.76031i	0.0613736	−	0.295791i
$260$	7.48896	−	5.30292i	0.464446	−	0.328873i
$261$	−1.34026	−	4.12491i	−0.0829602	−	0.255325i
$262$	−8.20932	+	4.18286i	−0.507174	+	0.258418i
$263$	−26.1562	+	13.3273i	−1.61286	+	0.821793i	−0.613373	+	0.789794i	$0.710188\pi$
$263$	−26.1562	+	13.3273i	−1.61286	+	0.821793i	−0.999488	+	0.0319998i	$0.989812\pi$
$264$	4.00621	+	12.3299i	0.246565	+	0.758850i
$265$	21.6652	+	16.1474i	1.33088	+	0.991927i
$266$	2.65796	−	12.8101i	0.162970	−	0.785436i
$267$	1.10281	−	0.174667i	0.0674907	−	0.0106895i
$268$	8.96854	+	8.96854i	0.547840	+	0.547840i
$269$	−8.32215	−	6.04639i	−0.507410	−	0.368655i	0.304430	−	0.952535i	$-0.401534\pi$
$269$	−8.32215	−	6.04639i	−0.507410	−	0.368655i	−0.811840	+	0.583880i	$0.801534\pi$
$270$	−8.45803	+	1.23423i	−0.514739	+	0.0751129i
$271$	−17.7470	−	24.4267i	−1.07805	−	1.48381i	−0.861645	−	0.507511i	$-0.830566\pi$
$271$	−17.7470	−	24.4267i	−1.07805	−	1.48381i	−0.216409	−	0.976303i	$-0.569434\pi$
$272$	−3.68530	−	0.583695i	−0.223454	−	0.0353917i
$273$	20.6023	+	7.79396i	1.24691	+	0.471712i
$274$		−	4.24319i		−	0.256340i
$275$	19.4048	−	25.3845i	1.17015	−	1.53075i
$276$			4.32922i			0.260588i
$277$	26.5021	+	13.5035i	1.59235	+	0.811345i	0.999984	+	0.00567948i	$0.00180784\pi$
$277$	26.5021	+	13.5035i	1.59235	+	0.811345i	0.592371	+	0.805666i	$0.298192\pi$
$278$	1.64214	−	10.3681i	0.0984890	−	0.621835i
$279$	−3.94651	+	2.86730i	−0.236271	+	0.171661i
$280$	−4.98511	+	3.18570i	−0.297917	+	0.190382i
$281$	−10.8143	−	7.85707i	−0.645129	−	0.468714i	0.216479	−	0.976287i	$-0.430543\pi$
$281$	−10.8143	−	7.85707i	−0.645129	−	0.468714i	−0.861609	+	0.507573i	$0.830543\pi$
$282$	3.73175	−	3.73175i	0.222223	−	0.222223i
$283$	8.81553	−	1.39624i	0.524029	−	0.0829980i	0.111185	−	0.993800i	$-0.464535\pi$
$283$	8.81553	−	1.39624i	0.524029	−	0.0829980i	0.412844	+	0.910802i	$0.364535\pi$
$284$	−6.66414	−	2.16531i	−0.395444	−	0.128488i
$285$	21.4168	−	6.67152i	1.26862	−	0.395187i
$286$	−24.9412	+	8.10390i	−1.47481	+	0.479193i
$287$	−15.0655	−	22.9542i	−0.889288	−	1.35494i
$288$	0.994158	−	0.506549i	0.0585813	−	0.0298487i
$289$	2.92719	−	0.951102i	0.172188	−	0.0559472i
$290$	−2.78644	+	8.23323i	−0.163625	+	0.483472i
$291$	−6.25239	+	19.2429i	−0.366522	+	1.12804i
$292$	1.20889	+	7.63261i	0.0707448	+	0.446665i
$293$	4.09550	−	4.09550i	0.239262	−	0.239262i	−0.577283	−	0.816544i	$-0.695887\pi$
$293$	4.09550	−	4.09550i	0.239262	−	0.239262i	0.816544	+	0.577283i	$0.195887\pi$
$294$	−13.0288	−	5.64994i	−0.759858	−	0.329511i
$295$	2.05646	−	2.00698i	0.119732	−	0.116851i
$296$	1.48661	−	1.08009i	0.0864075	−	0.0627787i
$297$	24.1271	+	3.82136i	1.40000	+	0.221738i
$298$	2.74067	−	5.37886i	0.158763	−	0.311589i
$299$	−8.75728			−0.506446
$300$	−8.92325	−	4.82388i	−0.515184	−	0.278507i
$301$	−3.20191	−	29.1047i	−0.184555	−	1.67757i
$302$	3.20278	+	1.63190i	0.184299	+	0.0939051i
$303$	−12.5708	−	1.99101i	−0.722171	−	0.114381i
$304$	4.00049	−	2.90653i	0.229444	−	0.166701i
$305$	5.71008	+	0.975812i	0.326958	+	0.0558749i
$306$	2.44707	−	3.36811i	0.139890	−	0.192542i
$307$	12.6496	+	12.6496i	0.721951	+	0.721951i	0.969002	−	0.247051i	$-0.0794616\pi$
$307$	12.6496	+	12.6496i	0.721951	+	0.721951i	−0.247051	+	0.969002i	$0.579462\pi$
$308$	16.3098	−	4.45514i	0.929337	−	0.253855i
$309$	−5.12922	−	1.66658i	−0.291791	−	0.0948087i
$310$	9.77537	+	0.119053i	0.555204	+	0.00676175i
$311$	20.4476	−	6.64384i	1.15948	−	0.376737i	0.334772	−	0.942299i	$-0.391341\pi$
$311$	20.4476	−	6.64384i	1.15948	−	0.376737i	0.824706	+	0.565562i	$0.191341\pi$
$312$	3.77970	+	7.41808i	0.213983	+	0.419966i
$313$	−15.7295	−	30.8709i	−0.889084	−	1.74493i	−0.625375	−	0.780324i	$-0.715054\pi$
$313$	−15.7295	−	30.8709i	−0.889084	−	1.74493i	−0.263709	−	0.964602i	$-0.584946\pi$
$314$	−5.19846	−	15.9992i	−0.293366	−	0.902887i
$315$	−0.641883	−	6.56970i	−0.0361660	−	0.370161i
$316$	−3.19032	+	9.81881i	−0.179470	+	0.552351i
$317$	−15.8632	+	2.51248i	−0.890966	+	0.141115i	−0.585102	−	0.810960i	$-0.698945\pi$
$317$	−15.8632	+	2.51248i	−0.890966	+	0.141115i	−0.305864	+	0.952075i	$0.598945\pi$
$318$	−17.3349	+	17.3349i	−0.972094	+	0.972094i
$319$	14.6008	−	20.0963i	0.817491	−	1.12518i
$320$	−2.20411	−	0.376668i	−0.123214	−	0.0210564i
$321$	−14.4079	−	19.8308i	−0.804171	−	1.10685i
$322$	5.63952	+	0.268118i	0.314278	+	0.0149417i
$323$	8.37637	−	16.4396i	0.466074	−	0.914721i
$324$		−	11.1024i		−	0.616798i
$325$	9.75790	−	18.0502i	0.541271	−	1.00125i
$326$	20.0137			1.10845
$327$	1.39601	−	2.73982i	0.0771994	−	0.151512i
$328$	1.62342	−	10.2498i	0.0896382	−	0.565953i
$329$	−4.63011	−	5.09234i	−0.255266	−	0.280750i
$330$	20.2473	+	20.7466i	1.11458	+	1.14206i
$331$	2.75931	+	2.00475i	0.151665	+	0.110191i	0.661030	−	0.750360i	$-0.270120\pi$
$331$	2.75931	+	2.00475i	0.151665	+	0.110191i	−0.509365	+	0.860551i	$0.670120\pi$
$332$	−4.14138	−	4.14138i	−0.227288	−	0.227288i
$333$	0.320735	+	2.02504i	0.0175762	+	0.110972i
$334$	−2.99901	+	9.23000i	−0.164099	+	0.505043i
$335$	26.8642	+	9.09186i	1.46775	+	0.496741i
$336$	−2.20694	−	4.89283i	−0.120399	−	0.266926i
$337$	8.77744	+	17.2267i	0.478138	+	0.938398i	0.996528	+	0.0832543i	$0.0265314\pi$
$337$	8.77744	+	17.2267i	0.478138	+	0.938398i	−0.518391	+	0.855144i	$0.673469\pi$
$338$	−3.42245	+	1.74382i	−0.186157	+	0.0948515i
$339$	−4.62653	−	14.2390i	−0.251278	−	0.773356i
$340$	−7.96577	+	2.48140i	−0.432005	+	0.134573i
$341$	−26.5713	−	8.63354i	−1.43892	−	0.467533i
$342$	0.863103	+	5.44942i	0.0466713	+	0.294671i
$343$	−8.16689	+	16.6223i	−0.440971	+	0.897521i
$344$	6.50498	−	8.95333i	0.350725	−	0.482731i
$345$	4.28946	+	8.67820i	0.230937	+	0.467219i
$346$	−1.36723	−	1.88183i	−0.0735026	−	0.101168i
$347$	−4.50760	+	28.4599i	−0.241981	+	1.52781i	0.505093	+	0.863065i	$0.331458\pi$
$347$	−4.50760	+	28.4599i	−0.241981	+	1.52781i	−0.747074	+	0.664741i	$0.768542\pi$
$348$	−7.02651	−	3.58018i	−0.376660	−	0.191918i
$349$	−18.1836			−0.973346			−0.486673	−	0.873584i	$-0.661790\pi$
$349$	−18.1836			−0.973346			−0.486673	+	0.873584i	$0.661790\pi$
$350$	−6.83655	+	11.3253i	−0.365429	+	0.605361i
$351$	15.6872			0.837319
$352$	5.69386	+	2.90117i	0.303484	+	0.154633i
$353$	−2.82575	+	17.8411i	−0.150400	+	0.949586i	0.790883	+	0.611967i	$0.209622\pi$
$353$	−2.82575	+	17.8411i	−0.150400	+	0.949586i	−0.941283	+	0.337619i	$0.890378\pi$
$354$	1.53239	+	2.10916i	0.0814458	+	0.112100i
$355$	−15.5041	+	2.26243i	−0.822874	+	0.120077i
$356$	0.323499	−	0.445258i	0.0171454	−	0.0235986i
$357$	−15.6253	−	12.5281i	−0.826980	−	0.663056i
$358$	1.27056	+	8.02200i	0.0671512	+	0.423976i
$359$	12.6557	+	4.11209i	0.667943	+	0.217028i	0.623309	−	0.781976i	$-0.285788\pi$
$359$	12.6557	+	4.11209i	0.667943	+	0.217028i	0.0446340	+	0.999003i	$0.485788\pi$
$360$	1.49096	−	2.00044i	0.0785804	−	0.105432i
$361$	1.68471	+	5.18500i	0.0886689	+	0.272895i
$362$	2.59829	−	1.32390i	0.136563	−	0.0695824i
$363$	−27.4806	−	53.9336i	−1.44236	−	2.83078i
$364$	9.89737	−	4.46427i	0.518763	−	0.233991i
$365$	9.98581	+	14.1023i	0.522681	+	0.738148i
$366$	−1.62411	+	4.99850i	−0.0848937	+	0.261276i
$367$	−4.27556	−	26.9948i	−0.223182	−	1.40912i	−0.803780	−	0.594927i	$-0.797181\pi$
$367$	−4.27556	−	26.9948i	−0.223182	−	1.40912i	0.580597	−	0.814191i	$-0.302819\pi$
$368$	1.50893	+	1.50893i	0.0786584	+	0.0786584i
$369$	9.36763	+	6.80598i	0.487659	+	0.354305i
$370$	1.90984	−	3.63806i	0.0992880	−	0.189134i
$371$	21.5080	+	23.6552i	1.11664	+	1.22812i
$372$	−1.38752	+	8.76044i	−0.0719394	+	0.454208i
$373$	−8.35865	+	16.4048i	−0.432794	+	0.849407i	0.566878	+	0.823802i	$0.308151\pi$
$373$	−8.35865	+	16.4048i	−0.432794	+	0.849407i	−0.999672	+	0.0256049i	$0.991849\pi$
$374$	23.8440			1.23295
$375$	−22.6668	−	0.828496i	−1.17051	−	0.0427833i
$376$		−	2.60137i		−	0.134155i
$377$	7.24211	−	14.2134i	0.372988	−	0.732030i
$378$	−10.1023	−	0.480289i	−0.519604	−	0.0247034i
$379$	−8.41697	−	11.5850i	−0.432351	−	0.595080i	0.536140	−	0.844129i	$-0.319882\pi$
$379$	−8.41697	−	11.5850i	−0.432351	−	0.595080i	−0.968491	+	0.249049i	$0.919882\pi$
$380$	5.13942	−	9.79008i	0.263647	−	0.502220i
$381$	8.36916	−	11.5192i	0.428765	−	0.590144i
$382$	0.0150359	−	0.0150359i	0.000769303	−	0.000769303i
$383$	27.4839	−	4.35302i	1.40436	−	0.222429i	0.592167	−	0.805815i	$-0.298272\pi$
$383$	27.4839	−	4.35302i	1.40436	−	0.222429i	0.812195	+	0.583386i	$0.198272\pi$
$384$	0.626914	−	1.92944i	0.0319921	−	0.0984615i
$385$	28.2799	−	25.0906i	1.44127	−	1.27874i
$386$	−3.33191	−	10.2546i	−0.169590	−	0.521943i
$387$	5.60594	+	11.0023i	0.284966	+	0.559277i
$388$	4.52778	+	8.88626i	0.229863	+	0.451131i
$389$	3.29671	−	1.07117i	0.167150	−	0.0543103i	−0.224247	−	0.974532i	$-0.571992\pi$
$389$	3.29671	−	1.07117i	0.167150	−	0.0543103i	0.391396	+	0.920222i	$0.371992\pi$
$390$	14.9266	+	11.1250i	0.755838	+	0.563339i
$391$	7.57257	+	2.46048i	0.382962	+	0.124432i
$392$	−6.51041	+	2.57188i	−0.328825	+	0.129900i
$393$	−13.2171	−	13.2171i	−0.666716	−	0.666716i
$394$	2.90967	−	4.00481i	0.146587	−	0.201760i
$395$	3.33341	+	22.8435i	0.167722	+	1.14938i
$396$	−5.76844	+	4.19102i	−0.289875	+	0.210607i
$397$	−6.74654	−	1.06855i	−0.338599	−	0.0536288i	−0.0151803	−	0.999885i	$-0.504832\pi$
$397$	−6.74654	−	1.06855i	−0.338599	−	0.0536288i	−0.323419	+	0.946256i	$0.604832\pi$
$398$	−14.2046	−	7.23758i	−0.712010	−	0.362787i
$399$	26.3826	−	2.90244i	1.32078	−	0.145304i
$400$	−4.79150	+	1.42882i	−0.239575	+	0.0714408i
$401$	27.6912			1.38283			0.691416	−	0.722457i	$-0.256987\pi$
$401$	27.6912			1.38283			0.691416	+	0.722457i	$0.256987\pi$
$402$	−11.6818	+	22.9268i	−0.582634	+	1.14348i
$403$	−17.7209	−	2.80671i	−0.882741	−	0.139812i
$404$	−5.07544	+	3.68752i	−0.252512	+	0.183461i
$405$	−11.0004	−	22.2554i	−0.546614	−	1.10588i
$406$	−5.09895	+	8.93147i	−0.253057	+	0.443261i
$407$	−8.30330	+	8.30330i	−0.411579	+	0.411579i
$408$	−1.18416	−	7.47651i	−0.0586248	−	0.370142i
$409$	6.14260	−	18.9050i	0.303732	−	0.934791i	−0.676415	−	0.736520i	$-0.736468\pi$
$409$	6.14260	−	18.9050i	0.303732	−	0.934791i	0.980147	−	0.198270i	$-0.0635324\pi$
$410$	−6.90146	−	22.1550i	−0.340839	−	1.09416i
$411$	8.18698	−	2.66011i	0.403834	−	0.131214i
$412$	−2.36865	+	1.20689i	−0.116695	+	0.0594590i
$413$	2.84243	−	1.86557i	0.139867	−	0.0917988i
$414$	−2.26446	+	0.735768i	−0.111292	+	0.0361610i
$415$	−12.4050	−	4.19832i	−0.608937	−	0.206087i
$416$	3.90294	+	1.26814i	0.191357	+	0.0621757i
$417$	21.0341	−	3.33147i	1.03004	−	0.163143i
$418$	−22.3443	+	22.3443i	−1.09290	+	1.09290i
$419$	−12.9124	−	9.38140i	−0.630812	−	0.458312i	0.225870	−	0.974158i	$-0.427478\pi$
$419$	−12.9124	−	9.38140i	−0.630812	−	0.458312i	−0.856681	+	0.515846i	$0.827478\pi$
$420$	−9.27185	−	7.62133i	−0.452420	−	0.371883i
$421$	−7.91922	+	5.75365i	−0.385959	+	0.280416i	−0.763798	−	0.645456i	$-0.776668\pi$
$421$	−7.91922	+	5.75365i	−0.385959	+	0.280416i	0.377838	+	0.925872i	$0.376668\pi$
$422$	−0.145714	+	0.919999i	−0.00709323	+	0.0447849i
$423$	2.58617	+	1.31772i	0.125744	+	0.0640698i
$424$			12.0840i			0.586852i
$425$	−13.5093	+	12.8667i	−0.655297	+	0.624129i
$426$		−	14.2155i		−	0.688745i
$427$	6.41080	+	2.42524i	0.310240	+	0.117366i
$428$	−11.9337	−	1.89012i	−0.576839	−	0.0913623i
$429$	−31.2720	−	43.0422i	−1.50983	−	2.07810i
$430$	4.16855	−	24.3928i	0.201026	−	1.17632i
$431$	−22.1382	−	16.0843i	−1.06636	−	0.774756i	−0.0911053	−	0.995841i	$-0.529040\pi$
$431$	−22.1382	−	16.0843i	−1.06636	−	0.774756i	−0.975254	+	0.221086i	$0.929040\pi$
$432$	−2.70299	−	2.70299i	−0.130048	−	0.130048i
$433$	0.679946	−	0.107693i	0.0326761	−	0.00517539i	−0.140075	−	0.990141i	$-0.544734\pi$
$433$	0.679946	−	0.107693i	0.0326761	−	0.00517539i	0.172751	+	0.984966i	$0.444734\pi$
$434$	11.3260	+	2.35003i	0.543665	+	0.112805i
$435$	−17.6324	−	0.214743i	−0.845409	−	0.0102961i
$436$	−0.468379	−	1.44152i	−0.0224313	−	0.0690364i
$437$	−9.40200	+	4.79056i	−0.449759	+	0.229164i
$438$	−13.9688	+	7.11747i	−0.667456	+	0.340086i
$439$	−5.59521	−	17.2203i	−0.267045	−	0.821880i	−0.991215	−	0.132258i	$-0.957777\pi$
$439$	−5.59521	−	17.2203i	−0.267045	−	0.821880i	0.724170	−	0.689621i	$-0.242223\pi$
$440$	14.2882	+	0.174015i	0.681166	+	0.00829582i
$441$	0.740979	−	7.77516i	0.0352847	−	0.370246i
$442$	15.1237	−	2.39536i	0.719362	−	0.113936i
$443$	6.52649	+	6.52649i	0.310083	+	0.310083i	0.844942	−	0.534859i	$-0.179635\pi$
$443$	6.52649	+	6.52649i	0.310083	+	0.310083i	−0.534859	+	0.844942i	$0.679635\pi$
$444$	3.01594	+	2.19121i	0.143130	+	0.103990i
$445$	0.207306	−	1.21308i	0.00982726	−	0.0575054i
$446$	2.51546	+	3.46223i	0.119110	+	0.163941i
$447$	12.0964	+	1.91588i	0.572138	+	0.0906178i
$448$	−2.47459	−	0.936155i	−0.116914	−	0.0442291i
$449$		−	7.52635i		−	0.355191i	−0.984104	−	0.177595i	$-0.943168\pi$
$449$		−	7.52635i		−	0.355191i	0.984104	−	0.177595i	$-0.0568318\pi$
$450$	1.00666	−	5.48728i	0.0474544	−	0.258673i
$451$			66.3168i			3.12274i
$452$	−6.57549	−	3.35038i	−0.309285	−	0.157589i
$453$	−1.14079	+	7.20263i	−0.0535988	+	0.338409i
$454$	−9.96037	+	7.23663i	−0.467463	+	0.339632i
$455$	15.4167	−	18.7554i	0.722744	−	0.879267i
$456$	8.11594	+	5.89658i	0.380064	+	0.276133i
$457$	4.52366	−	4.52366i	0.211608	−	0.211608i	−0.593342	−	0.804950i	$-0.702192\pi$
$457$	4.52366	−	4.52366i	0.211608	−	0.211608i	0.804950	+	0.593342i	$0.202192\pi$
$458$	12.5931	−	1.99455i	0.588436	−	0.0931992i
$459$	−13.5650	−	4.40753i	−0.633159	−	0.205726i
$460$	4.51982	+	1.52968i	0.210738	+	0.0713216i
$461$	−29.1683	+	9.47735i	−1.35850	+	0.441404i	−0.895543	−	0.444975i	$-0.853213\pi$
$461$	−29.1683	+	9.47735i	−1.35850	+	0.441404i	−0.462960	+	0.886379i	$0.653213\pi$
$462$	18.8208	+	28.6758i	0.875622	+	1.33412i
$463$	1.25301	−	0.638442i	0.0582324	−	0.0296709i	−0.424632	−	0.905366i	$-0.639596\pi$
$463$	1.25301	−	0.638442i	0.0582324	−	0.0296709i	0.482864	+	0.875695i	$0.339596\pi$
$464$	−3.69692	+	1.20120i	−0.171625	+	0.0557643i
$465$	5.89861	+	18.9357i	0.273541	+	0.878120i
$466$	−4.10349	+	12.6292i	−0.190091	+	0.585039i
$467$	3.92625	+	24.7894i	0.181685	+	1.14711i	0.894932	+	0.446202i	$0.147224\pi$
$467$	3.92625	+	24.7894i	0.181685	+	1.14711i	−0.713247	+	0.700912i	$0.752776\pi$
$468$	−3.23776	+	3.23776i	−0.149666	+	0.149666i
$469$	29.1425	+	16.6374i	1.34567	+	0.768242i
$470$	−2.57748	−	5.21462i	−0.118890	−	0.240532i
$471$	27.6106	−	20.0602i	1.27223	−	0.924327i
$472$	1.26925	+	0.201029i	0.0584218	+	0.00925310i
$473$	−32.1070	+	63.0136i	−1.47628	+	2.89737i
$474$	−20.9449			−0.962031
$475$	0.602141	−	24.7171i	0.0276281	−	1.13410i
$476$	−9.81274	+	1.07953i	−0.449766	+	0.0494803i
$477$	−12.0134	−	6.12115i	−0.550057	−	0.280268i
$478$	−19.4556	−	3.08147i	−0.889879	−	0.140943i
$479$	21.6960	−	15.7631i	0.991317	−	0.720234i	0.0311079	−	0.999516i	$-0.490096\pi$
$479$	21.6960	−	15.7631i	0.991317	−	0.720234i	0.960209	+	0.279282i	$0.0900965\pi$
$480$	−0.655032	−	4.48885i	−0.0298980	−	0.204887i
$481$	−4.43245	+	6.10074i	−0.202102	+	0.278170i
$482$	12.5241	+	12.5241i	0.570459	+	0.570459i
$483$	3.01818	+	11.0492i	0.137332	+	0.502757i
$484$	−28.3765	−	9.22010i	−1.28984	−	0.419095i
$485$	17.8809	+	13.3269i	0.811928	+	0.605143i
$486$	10.5148	−	3.41648i	0.476963	−	0.154975i
$487$	2.17522	+	4.26911i	0.0985686	+	0.193452i	0.935025	−	0.354582i	$-0.115377\pi$
$487$	2.17522	+	4.26911i	0.0985686	+	0.193452i	−0.836456	+	0.548033i	$0.815377\pi$
$488$	1.17613	+	2.30828i	0.0532408	+	0.104491i
$489$	12.5468	+	38.6152i	0.567388	+	1.74624i
$490$	−10.5023	+	11.6061i	−0.474445	+	0.524311i
$491$	11.2305	−	34.5638i	0.506824	−	1.55984i	−0.290859	−	0.956766i	$-0.593941\pi$
$491$	11.2305	−	34.5638i	0.506824	−	1.55984i	0.797683	−	0.603077i	$-0.206059\pi$
$492$	20.7942	−	3.29348i	0.937477	−	0.148482i
$493$	−10.2558	+	10.2558i	−0.461900	+	0.461900i
$494$	−11.9278	+	16.4172i	−0.536656	+	0.738644i
$495$	−7.41069	+	14.1166i	−0.333086	+	0.634495i
$496$	2.56980	+	3.53702i	0.115387	+	0.158817i
$497$	−18.5181	−	0.880401i	−0.830651	−	0.0394914i
$498$	5.39426	−	10.5868i	0.241723	−	0.474407i
$499$			14.3000i			0.640156i	0.947391	+	0.320078i	$0.103709\pi$
$499$			14.3000i			0.640156i	−0.947391	+	0.320078i	$0.896291\pi$
$500$	−8.18919	+	7.61165i	−0.366232	+	0.340403i
$501$	−19.6889			−0.879634
$502$	5.25422	−	10.3120i	0.234507	−	0.460246i
$503$	−3.05787	+	19.3067i	−0.136344	+	0.860841i	0.820797	+	0.571219i	$0.193529\pi$
$503$	−3.05787	+	19.3067i	−0.136344	+	0.860841i	−0.957141	+	0.289622i	$0.906471\pi$
$504$	2.18419	−	1.98593i	0.0972915	−	0.0884603i
$505$	−6.52039	+	12.4207i	−0.290154	+	0.552714i
$506$	−11.0323	−	8.01546i	−0.490447	−	0.356331i
$507$	−5.51019	−	5.51019i	−0.244716	−	0.244716i
$508$	−1.09792	−	6.93198i	−0.0487122	−	0.307557i
$509$	4.72839	−	14.5525i	0.209582	−	0.645028i	−0.789912	−	0.613221i	$-0.789874\pi$
$509$	4.72839	−	14.5525i	0.209582	−	0.645028i	0.999494	−	0.0318076i	$-0.0101264\pi$
$510$	−9.78158	−	13.8139i	−0.433135	−	0.611688i
$511$	8.40657	+	18.6375i	0.371885	+	0.824475i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	16.8421	−	8.58148i	0.743597	−	0.378881i
$514$	−0.336110	−	1.03444i	−0.0148252	−	0.0456272i
$515$	−3.55231	+	4.76618i	−0.156533	+	0.210023i
$516$	21.3530	+	6.93801i	0.940014	+	0.305429i
$517$	2.60052	+	16.4191i	0.114371	+	0.722110i
$518$	3.04120	−	3.79306i	0.133623	−	0.166657i
$519$	2.77374	−	3.81773i	0.121754	−	0.167580i
$520$	9.08019	−	1.32502i	0.398193	−	0.0581059i
$521$	5.75677	+	7.92351i	0.252209	+	0.347135i	0.916283	−	0.400531i	$-0.131174\pi$
$521$	5.75677	+	7.92351i	0.252209	+	0.347135i	−0.664075	+	0.747666i	$0.731174\pi$
$522$	0.678485	−	4.28379i	0.0296965	−	0.187496i
$523$	29.2535	+	14.9054i	1.27917	+	0.651767i	0.955664	−	0.294460i	$-0.0951399\pi$
$523$	29.2535	+	14.9054i	1.27917	+	0.651767i	0.323502	+	0.946228i	$0.395140\pi$
$524$	−9.21354			−0.402495
$525$	−26.1374	−	6.09076i	−1.14073	−	0.265823i
$526$	−29.3558			−1.27997
$527$	14.5350	+	7.40595i	0.633154	+	0.322608i
$528$	−2.02808	+	12.8048i	−0.0882607	+	0.557256i
$529$	10.8424	+	14.9233i	0.471411	+	0.648841i
$530$	11.9730	+	24.2232i	0.520075	+	1.05219i
$531$	−0.842790	+	1.16000i	−0.0365740	+	0.0503397i
$532$	8.18391	−	10.2072i	0.354818	−	0.442537i
$533$	6.66216	+	42.0632i	0.288570	+	1.82196i
$534$	1.06191	+	0.345034i	0.0459532	+	0.0149311i
$535$	−25.7947	+	8.03526i	−1.11520	+	0.347395i
$536$	3.91939	+	12.0627i	0.169292	+	0.521027i
$537$	−14.6815	+	7.48058i	−0.633552	+	0.322811i
$538$	−4.67008	−	9.16555i	−0.201342	−	0.395155i
$539$	38.5207	−	22.7412i	1.65920	−	0.979535i
$540$	−8.09649	−	2.74016i	−0.348417	−	0.117918i
$541$	−0.884493	+	2.72219i	−0.0380273	+	0.117036i	−0.968268	−	0.249913i	$-0.919598\pi$
$541$	−0.884493	+	2.72219i	−0.0380273	+	0.117036i	0.930241	+	0.366950i	$0.119598\pi$
$542$	−4.72323	−	29.8213i	−0.202880	−	1.28093i
$543$	4.18329	+	4.18329i	0.179522	+	0.179522i
$544$	−3.01864	−	2.19317i	−0.129423	−	0.0940314i
$545$	−2.36718	−	2.42555i	−0.101399	−	0.103899i
$546$	14.8184	+	16.2977i	0.634167	+	0.697477i
$547$	−2.64493	+	16.6994i	−0.113089	+	0.714015i	0.864365	+	0.502865i	$0.167721\pi$
$547$	−2.64493	+	16.6994i	−0.113089	+	0.714015i	−0.977454	+	0.211150i	$0.932279\pi$
$548$	1.92637	−	3.78071i	0.0822903	−	0.161504i
$549$	−2.89056			−0.123366
$550$	28.8142	−	13.8082i	1.22864	−	0.588783i
$551$		−	19.2216i		−	0.818866i
$552$	−1.96542	+	3.85736i	−0.0836540	+	0.164180i
$553$	−1.29717	+	27.2842i	−0.0551611	+	1.16024i
$554$	17.4831	+	24.0634i	0.742784	+	1.02235i
$555$	8.21673	+	1.40418i	0.348781	+	0.0596042i
$556$	6.17016	−	8.49249i	0.261673	−	0.360162i
$557$	−6.63724	+	6.63724i	−0.281229	+	0.281229i	−0.833599	−	0.552370i	$-0.813724\pi$
$557$	−6.63724	+	6.63724i	−0.281229	+	0.281229i	0.552370	+	0.833599i	$0.313724\pi$
$558$	−4.81809	+	0.763111i	−0.203966	+	0.0323050i
$559$	−14.0344	+	43.1935i	−0.593593	+	1.82689i
$560$	−5.88804	+	0.575283i	−0.248815	+	0.0243101i
$561$	14.9482	+	46.0057i	0.631112	+	1.94236i
$562$	−6.06861	−	11.9103i	−0.255989	−	0.502406i
$563$	−3.56479	−	6.99630i	−0.150238	−	0.294859i	0.803606	−	0.595162i	$-0.202912\pi$
$563$	−3.56479	−	6.99630i	−0.150238	−	0.294859i	−0.953844	+	0.300303i	$0.902912\pi$
$564$	5.01919	−	1.63084i	0.211346	−	0.0686706i
$565$	−16.5006	−	0.200959i	−0.694186	−	0.00845439i
$566$	8.48857	+	2.75811i	0.356801	+	0.115932i
$567$	−7.74018	−	28.3360i	−0.325057	−	1.19000i
$568$	−4.95476	−	4.95476i	−0.207897	−	0.207897i
$569$	14.3402	−	19.7376i	0.601172	−	0.827442i	−0.394643	−	0.918834i	$-0.629132\pi$
$569$	14.3402	−	19.7376i	0.601172	−	0.827442i	0.995815	+	0.0913925i	$0.0291318\pi$
$570$	22.1114	+	3.77868i	0.926143	+	0.158271i
$571$	31.6199	−	22.9732i	1.32325	−	0.961399i	0.323367	−	0.946274i	$-0.395185\pi$
$571$	31.6199	−	22.9732i	1.32325	−	0.961399i	0.999886	−	0.0151252i	$-0.00481469\pi$
$572$	−25.9019	−	4.10246i	−1.08301	−	0.171532i
$573$	0.0384371	+	0.0195847i	0.00160573	+	0.000818162i
$574$	−3.00248	−	27.2919i	−0.125321	−	1.13914i
$575$	10.5759	−	1.41197i	0.441046	−	0.0588831i
$576$	1.11577			0.0464904
$577$	−13.5555	+	26.6043i	−0.564325	+	1.10755i	0.415853	+	0.909432i	$0.363483\pi$
$577$	−13.5555	+	26.6043i	−0.564325	+	1.10755i	−0.980178	+	0.198118i	$0.936517\pi$
$578$	3.03994	+	0.481479i	0.126445	+	0.0200269i
$579$	17.6968	−	12.8574i	0.735452	−	0.534337i
$580$	−6.22054	+	6.07085i	−0.258294	+	0.252078i
$581$	−13.4570	−	7.68259i	−0.558292	−	0.318727i
$582$	−14.3070	+	14.3070i	−0.593044	+	0.593044i
$583$	−12.0801	−	76.2707i	−0.500306	−	3.15881i
$584$	−2.38801	+	7.34953i	−0.0988165	+	0.304126i
$585$	−3.28228	+	9.69833i	−0.135706	+	0.400977i
$586$	5.50844	−	1.78980i	0.227552	−	0.0739360i
$587$	7.68078	−	3.91355i	0.317020	−	0.161530i	−0.288239	−	0.957559i	$-0.593070\pi$
$587$	7.68078	−	3.91355i	0.317020	−	0.161530i	0.605259	+	0.796029i	$0.293070\pi$
$588$	−9.04377	−	10.9491i	−0.372959	−	0.451534i
$589$	−20.5609	+	6.68065i	−0.847198	+	0.275271i
$590$	2.74347	−	0.854613i	0.112947	−	0.0351839i
$591$	9.55117	+	3.10336i	0.392882	+	0.127655i
$592$	1.81493	−	0.287456i	0.0745931	−	0.0118144i
$593$	−4.28367	+	4.28367i	−0.175909	+	0.175909i	−0.789570	−	0.613661i	$-0.789696\pi$
$593$	−4.28367	+	4.28367i	−0.175909	+	0.175909i	0.613661	+	0.789570i	$0.289696\pi$
$594$	19.7626	+	14.3583i	0.810868	+	0.589130i
$595$	−18.6007	+	11.8866i	−0.762553	+	0.487303i
$596$	4.88390	−	3.54836i	0.200052	−	0.145347i
$597$	5.05947	−	31.9442i	0.207070	−	1.30739i
$598$	−7.80279	−	3.97572i	−0.319080	−	0.162579i
$599$		−	4.59205i		−	0.187626i	−0.995590	−	0.0938129i	$-0.970094\pi$
$599$		−	4.59205i		−	0.187626i	0.995590	−	0.0938129i	$-0.0299056\pi$
$600$	−5.76068	−	8.34918i	−0.235179	−	0.340854i
$601$			21.8349i			0.890666i	0.895365	+	0.445333i	$0.146915\pi$
$601$			21.8349i			0.890666i	−0.895365	+	0.445333i	$0.853085\pi$
$602$	10.3604	−	27.3862i	0.422257	−	1.11618i
$603$	−13.9776	−	2.21383i	−0.569210	−	0.0901540i
$604$	2.11283	+	2.90806i	0.0859698	+	0.118327i
$605$	−66.0181	+	9.63363i	−2.68402	+	0.391663i
$606$	−10.2967	−	7.48101i	−0.418276	−	0.303895i
$607$	21.1752	+	21.1752i	0.859477	+	0.859477i	0.991276	−	0.131800i	$-0.0420755\pi$
$607$	21.1752	+	21.1752i	0.859477	+	0.859477i	−0.131800	+	0.991276i	$0.542076\pi$
$608$	4.88400	−	0.773550i	0.198072	−	0.0313716i
$609$	−20.4294	−	4.23888i	−0.827839	−	0.171768i
$610$	4.64471	+	3.46178i	0.188059	+	0.140163i
$611$	3.29890	+	10.1530i	0.133459	+	0.410746i
$612$	3.70945	−	1.89006i	0.149945	−	0.0764010i
$613$	10.1857	−	5.18988i	0.411397	−	0.209617i	−0.236028	−	0.971746i	$-0.575846\pi$
$613$	10.1857	−	5.18988i	0.411397	−	0.209617i	0.647425	+	0.762129i	$0.275846\pi$
$614$	5.52808	+	17.0137i	0.223095	+	0.686617i
$615$	38.4202	−	27.2053i	1.54925	−	1.09702i
$616$	16.5547	+	3.43494i	0.667009	+	0.138397i
$617$	0.0586443	−	0.00928835i	0.00236093	−	0.000373935i	−0.155254	−	0.987875i	$-0.549620\pi$
$617$	0.0586443	−	0.00928835i	0.00236093	−	0.000373935i	0.157615	+	0.987501i	$0.449620\pi$
$618$	−3.81356	−	3.81356i	−0.153404	−	0.153404i
$619$	20.3533	+	14.7875i	0.818067	+	0.594361i	0.916158	−	0.400817i	$-0.131274\pi$
$619$	20.3533	+	14.7875i	0.818067	+	0.594361i	−0.0980910	+	0.995177i	$0.531274\pi$
$620$	8.65587	+	4.54400i	0.347628	+	0.182492i
$621$	4.79471	+	6.59935i	0.192405	+	0.264823i
$622$	21.2352	+	3.36333i	0.851454	+	0.134857i
$623$	0.515231	−	1.36194i	0.0206423	−	0.0545650i
$624$			8.32551i			0.333287i
$625$	−8.87402	+	23.3720i	−0.354961	+	0.934881i
$626$		−	34.6472i		−	1.38478i
$627$	−57.1200	−	29.1041i	−2.28115	−	1.16231i
$628$	2.63163	−	16.6154i	0.105013	−	0.663028i
$629$	5.54690	−	4.03006i	0.221170	−	0.160689i
$630$	2.41066	−	6.14506i	0.0960430	−	0.244825i
$631$	2.33814	+	1.69876i	0.0930799	+	0.0676265i	0.633352	−	0.773864i	$-0.281679\pi$
$631$	2.33814	+	1.69876i	0.0930799	+	0.0676265i	−0.540272	+	0.841491i	$0.681679\pi$
$632$	−7.30025	+	7.30025i	−0.290388	+	0.290388i
$633$	−1.86644	+	0.295614i	−0.0741842	+	0.0117496i
$634$	−15.2749	−	4.96310i	−0.606642	−	0.197110i
$635$	−9.06916	−	12.8078i	−0.359899	−	0.508261i
$636$	−23.3154	+	7.57564i	−0.924517	+	0.300394i
$637$	22.1482	−	18.2940i	0.877544	−	0.724836i
$638$	22.1330	−	11.2773i	0.876254	−	0.446474i
$639$	7.43565	−	2.41599i	0.294150	−	0.0955750i
$640$	−1.79288	−	1.33626i	−0.0708697	−	0.0528203i
$641$	−6.94639	+	21.3788i	−0.274366	+	0.844411i	0.715021	+	0.699103i	$0.246417\pi$
$641$	−6.94639	+	21.3788i	−0.274366	+	0.844411i	−0.989387	+	0.145308i	$0.953583\pi$
$642$	−3.83455	−	24.2104i	−0.151338	−	0.955508i
$643$	13.2775	−	13.2775i	0.523615	−	0.523615i	−0.395046	−	0.918661i	$-0.629271\pi$
$643$	13.2775	−	13.2775i	0.523615	−	0.523615i	0.918661	+	0.395046i	$0.129271\pi$
$644$	4.90313	+	2.79919i	0.193210	+	0.110303i
$645$	49.6778	−	7.24919i	1.95606	−	0.285436i
$646$	14.9268	−	10.8450i	0.587287	−	0.426689i
$647$	15.6379	+	2.47680i	0.614790	+	0.0973731i	0.456060	−	0.889949i	$-0.349260\pi$
$647$	15.6379	+	2.47680i	0.614790	+	0.0973731i	0.158729	+	0.987322i	$0.449260\pi$
$648$	5.04037	−	9.89228i	0.198004	−	0.388606i
$649$	−8.21206			−0.322352
$650$	16.8890	−	11.6529i	0.662441	−	0.457064i
$651$	2.56618	+	23.3261i	0.100577	+	0.914223i
$652$	17.8323	+	9.08601i	0.698367	+	0.355836i
$653$	6.75109	+	1.06927i	0.264191	+	0.0418437i	0.287124	−	0.957893i	$-0.407301\pi$
$653$	6.75109	+	1.06927i	0.264191	+	0.0418437i	−0.0229338	+	0.999737i	$0.507301\pi$
$654$	2.48770	−	1.80742i	0.0972769	−	0.0706758i
$655$	−18.4691	+	9.12892i	−0.721649	+	0.356696i
$656$	6.09981	−	8.39567i	0.238158	−	0.327796i
$657$	−6.09696	−	6.09696i	−0.237865	−	0.237865i
$658$	−1.81358	−	6.63934i	−0.0707009	−	0.258828i
$659$	20.8326	+	6.76891i	0.811522	+	0.263679i	0.685242	−	0.728315i	$-0.259696\pi$
$659$	20.8326	+	6.76891i	0.811522	+	0.263679i	0.126279	+	0.991995i	$0.459696\pi$
$660$	8.62175	+	27.6774i	0.335601	+	1.07734i
$661$	−6.11820	+	1.98792i	−0.237970	+	0.0773212i	−0.425574	−	0.904924i	$-0.639928\pi$
$661$	−6.11820	+	1.98792i	−0.237970	+	0.0773212i	0.187604	+	0.982245i	$0.439928\pi$
$662$	1.54842	+	3.03895i	0.0601811	+	0.118112i
$663$	14.1030	+	27.6787i	0.547715	+	1.07495i
$664$	−1.80985	−	5.57014i	−0.0702357	−	0.216163i
$665$	6.29176	−	28.5697i	0.243984	−	1.10789i
$666$	−0.633573	+	1.94994i	−0.0245504	+	0.0755585i
$667$	8.19288	−	1.29763i	0.317230	−	0.0502443i
$668$	−6.86247	+	6.86247i	−0.265517	+	0.265517i
$669$	−5.10320	+	7.02395i	−0.197301	+	0.271561i
$670$	19.8085	+	20.2970i	0.765271	+	0.784141i
$671$	−9.73090	−	13.3934i	−0.375657	−	0.517048i
$672$	0.254899	−	5.36148i	0.00983295	−	0.206823i
$673$	−8.58061	+	16.8404i	−0.330758	+	0.649150i	−0.995165	−	0.0982218i	$-0.968685\pi$
$673$	−8.58061	+	16.8404i	−0.330758	+	0.649150i	0.664406	+	0.747372i	$0.268685\pi$
$674$			19.3340i			0.744717i
$675$	−18.9449	+	2.52930i	−0.729191	+	0.0973528i
$676$	−3.84110			−0.147735
$677$	2.55836	−	5.02107i	0.0983258	−	0.192975i	−0.836604	−	0.547808i	$-0.815462\pi$
$677$	2.55836	−	5.02107i	0.0983258	−	0.192975i	0.934930	+	0.354833i	$0.115462\pi$
$678$	2.34210	−	14.7874i	0.0899478	−	0.567908i
$679$	17.7512	+	19.5233i	0.681228	+	0.749236i
$680$	−8.22409	−	1.40544i	−0.315379	−	0.0538961i
$681$	−20.2070	−	14.6812i	−0.774333	−	0.562586i
$682$	−19.7557	−	19.7557i	−0.756483	−	0.756483i
$683$	−3.64031	−	22.9840i	−0.139293	−	0.879458i	−0.954048	−	0.299654i	$-0.903129\pi$
$683$	−3.64031	−	22.9840i	−0.139293	−	0.879458i	0.814755	−	0.579805i	$-0.196871\pi$
$684$	−1.70495	+	5.24731i	−0.0651906	+	0.200636i
$685$	0.115545	−	9.48735i	0.00441475	−	0.362493i
$686$	−14.8231	+	11.1029i	−0.565950	+	0.423911i
$687$	11.7432	+	23.0472i	0.448029	+	0.879307i
$688$	9.86071	−	5.02428i	0.375936	−	0.191549i
$689$	−15.3242	−	47.1632i	−0.583807	−	1.79677i
$690$	−0.117888	+	9.67970i	−0.00448791	+	0.368500i
$691$	−33.4885	−	10.8811i	−1.27396	−	0.413936i	−0.407513	−	0.913199i	$-0.633604\pi$
$691$	−33.4885	−	10.8811i	−1.27396	−	0.413936i	−0.866450	+	0.499263i	$0.833604\pi$
$692$	−0.363877	−	2.29743i	−0.0138325	−	0.0873351i
$693$	−11.8007	+	14.7181i	−0.448270	+	0.559093i
$694$	−16.9368	+	23.3115i	−0.642913	+	0.884893i
$695$	3.95399	−	23.1373i	0.149984	−	0.877646i
$696$	−4.63529	−	6.37994i	−0.175700	−	0.241831i
$697$	6.05736	−	38.2447i	0.229439	−	1.44862i
$698$	−16.2017	−	8.25518i	−0.613244	−	0.312463i
$699$	−26.9399			−1.01896
$700$	−11.2330	+	6.98716i	−0.424566	+	0.264090i
$701$	−46.5278			−1.75733			−0.878666	−	0.477437i	$-0.841566\pi$
$701$	−46.5278			−1.75733			−0.878666	+	0.477437i	$0.841566\pi$
$702$	13.9774	+	7.12183i	0.527542	+	0.268796i
$703$	−1.42144	+	8.97460i	−0.0536105	+	0.338483i
$704$	3.75617	+	5.16992i	0.141566	+	0.194849i
$705$	8.44545	−	8.24221i	0.318074	−	0.310420i
$706$	−10.6175	+	14.6137i	−0.399593	+	0.549993i
$707$	−10.3830	+	12.9499i	−0.390491	+	0.487030i
$708$	0.407834	+	2.57496i	0.0153274	+	0.0967731i
$709$	−5.60354	−	1.82070i	−0.210445	−	0.0683779i	0.201897	−	0.979407i	$-0.435289\pi$
$709$	−5.60354	−	1.82070i	−0.210445	−	0.0683779i	−0.412343	+	0.911029i	$0.635289\pi$
$710$	−14.8414	−	5.02289i	−0.556988	−	0.188506i
$711$	−3.55967	−	10.9555i	−0.133498	−	0.410865i
$712$	0.490383	−	0.249862i	0.0183779	−	0.00936399i
$713$	−4.23556	−	8.31276i	−0.158623	−	0.311315i
$714$	−8.23464	−	18.2563i	−0.308173	−	0.683226i
$715$	−55.9868	+	17.4403i	−2.09379	+	0.652232i
$716$	−2.50984	+	7.72448i	−0.0937969	+	0.288677i
$717$	−6.25148	−	39.4703i	−0.233466	−	1.47405i
$718$	9.40948	+	9.40948i	0.351159	+	0.351159i
$719$	15.6427	+	11.3651i	0.583375	+	0.423846i	0.839939	−	0.542681i	$-0.182591\pi$
$719$	15.6427	+	11.3651i	0.583375	+	0.423846i	−0.256564	+	0.966527i	$0.582591\pi$
$720$	2.23663	−	1.10552i	0.0833544	−	0.0412004i
$721$	−5.20397	+	4.73161i	−0.193806	+	0.176214i
$722$	−0.852855	+	5.38471i	−0.0317400	+	0.200398i
$723$	−16.3130	+	32.0162i	−0.606689	+	1.19069i
$724$	2.91613			0.108377
$725$	−6.45440	+	18.3328i	−0.239710	+	0.680864i
$726$		−	60.5311i		−	2.24652i
$727$	−11.2398	+	22.0594i	−0.416862	+	0.818138i	0.583121	+	0.812385i	$0.301831\pi$
$727$	−11.2398	+	22.0594i	−0.416862	+	0.818138i	−0.999983	+	0.00575318i	$0.998169\pi$
$728$	10.8454	+	0.515618i	0.401956	+	0.0191101i
$729$	−6.39363	−	8.80007i	−0.236801	−	0.325929i
$730$	2.49511	+	17.0987i	0.0923482	+	0.632851i
$731$	24.2716	−	33.4071i	0.897719	−	1.23560i
$732$	−3.71637	+	3.71637i	−0.137361	+	0.137361i
$733$	8.17849	−	1.29535i	0.302079	−	0.0478447i	−0.00355486	−	0.999994i	$-0.501132\pi$
$733$	8.17849	−	1.29535i	0.302079	−	0.0478447i	0.305634	+	0.952149i	$0.401132\pi$
$734$	8.44584	−	25.9936i	0.311742	−	0.959442i
$735$	−28.9774	−	12.9875i	−1.06885	−	0.479051i
$736$	0.659426	+	2.02950i	0.0243068	+	0.0748085i
$737$	−36.7968	−	72.2177i	−1.35543	−	2.66017i
$738$	5.25677	+	10.3170i	0.193504	+	0.379774i
$739$	−24.1159	+	7.83574i	−0.887119	+	0.288242i	−0.716910	−	0.697166i	$-0.754444\pi$
$739$	−24.1159	+	7.83574i	−0.887119	+	0.288242i	−0.170209	+	0.985408i	$0.554444\pi$
$740$	3.35333	−	2.37448i	0.123271	−	0.0872878i
$741$	−39.1537	−	12.7218i	−1.43835	−	0.467347i
$742$	8.42456	+	30.8414i	0.309275	+	1.13222i
$743$	28.4071	+	28.4071i	1.04216	+	1.04216i	0.999071	+	0.0430849i	$0.0137186\pi$
$743$	28.4071	+	28.4071i	1.04216	+	1.04216i	0.0430849	+	0.999071i	$0.486281\pi$
$744$	−5.21344	+	7.17569i	−0.191134	+	0.263074i
$745$	6.27433	−	11.9520i	0.229874	−	0.437886i
$746$	−14.8952	+	10.8220i	−0.545353	+	0.396222i
$747$	6.45437	+	1.02227i	0.236153	+	0.0374030i
$748$	21.2452	+	10.8250i	0.776801	+	0.395800i
$749$	−31.7756	+	3.49573i	−1.16105	+	0.127731i
$750$	−19.8202	−	11.0287i	−0.723730	−	0.402712i
$751$	34.3321			1.25280			0.626399	−	0.779503i	$-0.284528\pi$
$751$	34.3321			1.25280			0.626399	+	0.779503i	$0.284528\pi$
$752$	1.18100	−	2.31784i	0.0430665	−	0.0845229i
$753$	23.1903	+	3.67298i	0.845102	+	0.133851i
$754$	12.9055	−	9.37642i	0.469992	−	0.341469i
$755$	7.11666	+	3.73598i	0.259002	+	0.135966i
$756$	−8.78313	−	5.01427i	−0.319439	−	0.182367i
$757$	16.2296	−	16.2296i	0.589876	−	0.589876i	−0.347722	−	0.937598i	$-0.613045\pi$
$757$	16.2296	−	16.2296i	0.589876	−	0.589876i	0.937598	+	0.347722i	$0.113045\pi$
$758$	−2.24011	−	14.1435i	−0.0813645	−	0.513715i
$759$	8.54905	−	26.3113i	0.310311	−	0.955039i
$760$	9.02385	−	6.38977i	0.327330	−	0.231781i
$761$	30.3692	−	9.86755i	1.10088	−	0.357698i	0.298440	−	0.954428i	$-0.403534\pi$
$761$	30.3692	−	9.86755i	1.10088	−	0.357698i	0.802442	+	0.596730i	$0.203534\pi$
$762$	12.6866	−	6.46412i	0.459586	−	0.234171i
$763$	−2.20040	−	3.35258i	−0.0796598	−	0.121372i
$764$	0.0202232	−	0.00657093i	0.000731651	−	0.000237728i
$765$	5.56313	−	7.46412i	0.201135	−	0.269866i
$766$	26.4646	+	8.59886i	0.956204	+	0.310690i
$767$	−5.20872	+	0.824980i	−0.188076	+	0.0297883i
$768$	1.43453	−	1.43453i	0.0517643	−	0.0517643i
$769$	5.31683	+	3.86290i	0.191730	+	0.139300i	0.679509	−	0.733667i	$-0.262193\pi$
$769$	5.31683	+	3.86290i	0.191730	+	0.139300i	−0.487779	+	0.872967i	$0.662193\pi$
$770$	36.5884	−	9.51714i	1.31856	−	0.342974i
$771$	1.78518	−	1.29701i	0.0642917	−	0.0467106i
$772$	1.68672	−	10.6495i	0.0607064	−	0.383285i
$773$	−9.55486	−	4.86844i	−0.343664	−	0.175106i	0.273636	−	0.961833i	$-0.411774\pi$
$773$	−9.55486	−	4.86844i	−0.343664	−	0.175106i	−0.617300	+	0.786728i	$0.711774\pi$
$774$			12.3481i			0.443845i
$775$	21.8535	+	0.532381i	0.785002	+	0.0191237i
$776$			9.97328i			0.358020i
$777$	9.22506	+	3.48990i	0.330947	+	0.125199i
$778$	3.42369	+	0.542259i	0.122745	+	0.0194409i
$779$	30.1628	+	41.5156i	1.08070	+	1.48745i
$780$	8.24904	+	16.6890i	0.295363	+	0.597563i
$781$	36.2261	+	26.3198i	1.29627	+	0.941797i
$782$	5.63018	+	5.63018i	0.201335	+	0.201335i
$783$	−14.6762	+	2.32448i	−0.524483	+	0.0830700i
$784$	−6.96843	−	0.664097i	−0.248872	−	0.0237177i
$785$	−11.1876	−	35.9142i	−0.399301	−	1.28183i
$786$	−5.77609	−	17.7770i	−0.206026	−	0.634084i
$787$	0.181619	−	0.0925394i	0.00647401	−	0.00329867i	−0.450750	−	0.892650i	$-0.648844\pi$
$787$	0.181619	−	0.0925394i	0.00647401	−	0.00329867i	0.457225	+	0.889351i	$0.348844\pi$
$788$	4.41068	−	2.24735i	0.157124	−	0.0800586i
$789$	−18.4036	−	56.6403i	−0.655184	−	2.01645i
$790$	−7.40063	+	21.8670i	−0.263302	+	0.777994i
$791$	−19.1180	−	3.96679i	−0.679759	−	0.141043i
$792$	−7.04240	+	1.11541i	−0.250241	+	0.0396343i
$793$	−7.51758	−	7.51758i	−0.266957	−	0.266957i
$794$	−5.52610	−	4.01494i	−0.196114	−	0.142485i
$795$	−39.2312	+	38.2872i	−1.39139	+	1.35791i
$796$	−9.37055	−	12.8975i	−0.332131	−	0.457138i
$797$	30.3574	+	4.80815i	1.07532	+	0.170313i	0.668883	−	0.743367i	$-0.266773\pi$
$797$	30.3574	+	4.80815i	1.07532	+	0.170313i	0.406433	+	0.913681i	$0.366773\pi$
$798$	24.8248	+	9.39137i	0.878787	+	0.332451i
$799$		−	9.70634i		−	0.343386i
$800$	−4.91793	−	0.902212i	−0.173875	−	0.0318980i
$801$			0.614085i			0.0216976i
$802$	24.6730	+	12.5715i	0.871235	+	0.443916i
$803$	7.72524	−	48.7753i	0.272618	−	1.72124i
$804$	−20.8171	+	15.1245i	−0.734162	+	0.533400i
$805$	12.6021	+	0.753055i	0.444167	+	0.0265417i
$806$	−14.5152	−	10.5459i	−0.511276	−	0.371464i
$807$	14.7567	−	14.7567i	0.519459	−	0.519459i
$808$	−6.19635	+	0.981405i	−0.217987	+	0.0345257i
$809$	2.47745	+	0.804973i	0.0871026	+	0.0283013i	0.352244	−	0.935908i	$-0.385419\pi$
$809$	2.47745	+	0.804973i	0.0871026	+	0.0283013i	−0.265142	+	0.964209i	$0.585419\pi$
$810$	0.302326	−	24.8238i	0.0106226	−	0.872220i
$811$	6.48215	−	2.10618i	0.227619	−	0.0739579i	−0.192987	−	0.981201i	$-0.561818\pi$
$811$	6.48215	−	2.10618i	0.227619	−	0.0739579i	0.420606	+	0.907243i	$0.361818\pi$
$812$	−8.59800	+	5.64312i	−0.301731	+	0.198035i
$813$	54.5774	−	27.8086i	1.91411	−	0.975289i
$814$	−11.1679	+	3.62868i	−0.391435	+	0.127185i
$815$	44.7486	+	0.544987i	1.56747	+	0.0190900i
$816$	2.33917	−	7.19922i	0.0818873	−	0.252023i
$817$	8.56082	+	54.0509i	0.299505	+	1.89100i
$818$	14.0558	−	14.0558i	0.491449	−	0.491449i
$819$	−6.00631	+	10.5208i	−0.209878	+	0.367627i
$820$	3.90891	−	22.8735i	0.136505	−	0.798776i
$821$	36.5139	−	26.5289i	1.27434	−	0.925865i	0.274978	−	0.961451i	$-0.411329\pi$
$821$	36.5139	−	26.5289i	1.27434	−	0.925865i	0.999367	+	0.0355851i	$0.0113295\pi$
$822$	8.50232	+	1.34664i	0.296553	+	0.0469693i
$823$	11.2337	−	22.0474i	0.391582	−	0.768523i	−0.608097	−	0.793863i	$-0.708067\pi$
$823$	11.2337	−	22.0474i	0.391582	−	0.768523i	0.999679	+	0.0253396i	$0.00806672\pi$
$824$	−2.65839			−0.0926096
$825$	44.7061	+	46.9387i	1.55647	+	1.63420i
$826$	3.37958	−	0.371799i	0.117591	−	0.0129365i
$827$	−31.2832	−	15.9396i	−1.08782	−	0.554274i	−0.184325	−	0.982865i	$-0.559010\pi$
$827$	−31.2832	−	15.9396i	−1.08782	−	0.554274i	−0.903498	+	0.428592i	$0.859010\pi$
$828$	−2.35168	−	0.372470i	−0.0817265	−	0.0129442i
$829$	−42.6284	+	30.9713i	−1.48054	+	1.07568i	−0.503163	+	0.864191i	$0.667830\pi$
$829$	−42.6284	+	30.9713i	−1.48054	+	1.07568i	−0.977381	+	0.211487i	$0.932170\pi$
$830$	−9.14694	−	9.37248i	−0.317495	−	0.325324i
$831$	−35.4685	+	48.8182i	−1.23039	+	1.69349i
$832$	2.90182	+	2.90182i	0.100602	+	0.100602i
$833$	−24.2919	+	9.59633i	−0.841665	+	0.332493i
$834$	20.2539	+	6.58090i	0.701337	+	0.227878i
$835$	−6.95683	+	20.5557i	−0.240751	+	0.711360i
$836$	−30.0530	+	9.76482i	−1.03941	+	0.337723i
$837$	7.58729	+	14.8909i	0.262255	+	0.514705i
$838$	−7.24596	−	14.2210i	−0.250308	−	0.491256i
$839$	16.3563	+	50.3396i	0.564683	+	1.73792i	0.668891	+	0.743360i	$0.266769\pi$
$839$	16.3563	+	50.3396i	0.564683	+	1.73792i	−0.104208	+	0.994555i	$0.533231\pi$
$840$	−4.80127	−	11.0000i	−0.165660	−	0.379536i
$841$	4.29223	−	13.2101i	0.148008	−	0.455521i
$842$	−9.66818	+	1.53129i	−0.333188	+	0.0527717i
$843$	19.1758	−	19.1758i	0.660448	−	0.660448i
$844$	−0.547503	+	0.753573i	−0.0188458	+	0.0259390i
$845$	−7.69974	+	3.80582i	−0.264879	+	0.130924i
$846$	1.70606	+	2.34820i	0.0586557	+	0.0807327i
$847$	−78.8519	−	3.74883i	−2.70938	−	0.128811i
$848$	−5.48603	+	10.7669i	−0.188391	+	0.369738i
$849$			18.1073i			0.621441i
$850$	−17.8783	+	5.33126i	−0.613219	+	0.182861i
$851$	−3.92124			−0.134418
$852$	6.45372	−	12.6661i	0.221101	−	0.433935i
$853$	5.96748	−	37.6772i	0.204323	−	1.29004i	−0.645820	−	0.763490i	$-0.723484\pi$
$853$	5.96748	−	37.6772i	0.204323	−	1.29004i	0.850142	−	0.526553i	$-0.176516\pi$
$854$	4.61102	+	5.07135i	0.157786	+	0.173538i
$855$	1.78142	+	12.2079i	0.0609234	+	0.417500i
$856$	−9.77494	−	7.10191i	−0.334101	−	0.242738i
$857$	16.2758	+	16.2758i	0.555969	+	0.555969i	0.928157	−	0.372188i	$-0.121392\pi$
$857$	16.2758	+	16.2758i	0.555969	+	0.555969i	−0.372188	+	0.928157i	$0.621392\pi$
$858$	−8.32280	−	52.5481i	−0.284136	−	1.79396i
$859$	1.50280	−	4.62515i	0.0512750	−	0.157808i	−0.922140	−	0.386856i	$-0.873561\pi$
$859$	1.50280	−	4.62515i	0.0512750	−	0.157808i	0.973415	+	0.229048i	$0.0735611\pi$
$860$	14.7883	−	19.8416i	0.504277	−	0.676594i
$861$	50.7759	−	22.9028i	1.73044	−	0.780525i
$862$	−12.4231	−	24.3818i	−0.423134	−	0.830447i
$863$	15.7768	−	8.03869i	0.537049	−	0.273640i	−0.164358	−	0.986401i	$-0.552555\pi$
$863$	15.7768	−	8.03869i	0.537049	−	0.273640i	0.701408	+	0.712760i	$0.252555\pi$
$864$	−1.18125	−	3.63551i	−0.0401869	−	0.123683i
$865$	−3.00574	−	4.24481i	−0.102198	−	0.144328i
$866$	0.654727	+	0.212734i	0.0222485	+	0.00722899i
$867$	0.976793	+	6.16723i	0.0331736	+	0.209450i
$868$	9.02465	+	7.23578i	0.306317	+	0.245599i
$869$	38.7791	−	53.3748i	1.31549	−	1.81062i
$870$	−15.6131	−	8.19628i	−0.529333	−	0.277880i
$871$	−30.5943	−	42.1094i	−1.03665	−	1.42682i
$872$	0.237109	−	1.49705i	0.00802952	−	0.0506964i
$873$	−9.91502	−	5.05195i	−0.335573	−	0.170983i
$874$	−10.5521			−0.356931
$875$	−15.5942	+	25.1360i	−0.527182	+	0.849753i
$876$	−15.6776			−0.529696
$877$	−31.8933	−	16.2505i	−1.07696	−	0.548739i	−0.176778	−	0.984251i	$-0.556568\pi$
$877$	−31.8933	−	16.2505i	−1.07696	−	0.548739i	−0.900183	+	0.435512i	$0.856568\pi$
$878$	2.83248	−	17.8836i	0.0955915	−	0.603541i
$879$	6.90664	+	9.50617i	0.232955	+	0.320635i
$880$	12.6519	+	6.64178i	0.426496	+	0.223894i
$881$	21.7226	−	29.8986i	0.731852	−	1.00731i	−0.267194	−	0.963643i	$-0.586096\pi$
$881$	21.7226	−	29.8986i	0.731852	−	1.00731i	0.999046	−	0.0436655i	$-0.0139036\pi$
$882$	4.19007	−	6.59132i	0.141087	−	0.221941i
$883$	4.65855	+	29.4129i	0.156773	+	0.989824i	0.933132	+	0.359534i	$0.117064\pi$
$883$	4.65855	+	29.4129i	0.156773	+	0.989824i	−0.776359	+	0.630290i	$0.782936\pi$
$884$	14.5628	+	4.73174i	0.489800	+	0.159146i
$885$	3.36885	+	4.75760i	0.113243	+	0.159925i
$886$	2.85218	+	8.77811i	0.0958209	+	0.294906i
$887$	8.67025	−	4.41771i	0.291118	−	0.148332i	−0.302332	−	0.953203i	$-0.597765\pi$
$887$	8.67025	−	4.41771i	0.291118	−	0.148332i	0.593451	+	0.804870i	$0.297765\pi$
$888$	1.69243	+	3.32159i	0.0567944	+	0.111465i
$889$	−7.63489	−	16.9267i	−0.256066	−	0.567703i
$890$	0.735437	−	0.986744i	0.0246519	−	0.0330757i
$891$	−21.9242	+	67.4758i	−0.734489	+	2.26052i
$892$	0.669469	+	4.22686i	0.0224155	+	0.141526i
$893$	9.09584	+	9.09584i	0.304381	+	0.304381i
$894$	9.90815	+	7.19869i	0.331378	+	0.240760i
$895$	2.62240	+	17.9710i	0.0876573	+	0.600705i
$896$	−1.77987	−	1.95756i	−0.0594614	−	0.0653976i
$897$	2.77925	−	17.5475i	0.0927963	−	0.585893i
$898$	3.41689	−	6.70603i	0.114023	−	0.223783i
$899$	16.9947			0.566805
$900$	3.38811	−	4.43218i	0.112937	−	0.147739i
$901$			45.0884i			1.50211i
$902$	−30.1072	+	59.0887i	−1.00246	+	1.96744i
$903$	59.3351	+	2.82095i	1.97455	+	0.0938753i
$904$	−4.33776	−	5.97042i	−0.144272	−	0.198573i
$905$	5.84558	−	2.88935i	0.194314	−	0.0960452i
$906$	−4.28637	+	5.89969i	−0.142405	+	0.196004i
$907$	−4.44344	+	4.44344i	−0.147542	+	0.147542i	−0.777019	−	0.629477i	$-0.783269\pi$
$907$	−4.44344	+	4.44344i	−0.147542	+	0.147542i	0.629477	+	0.777019i	$0.283269\pi$
$908$	−12.1601	+	1.92597i	−0.403548	+	0.0639157i
$909$	2.16308	−	6.65728i	0.0717449	−	0.220808i
$910$	22.2511	−	9.71216i	0.737618	−	0.321955i
$911$	−1.24685	−	3.83741i	−0.0413100	−	0.127139i	0.928275	−	0.371895i	$-0.121292\pi$
$911$	−1.24685	−	3.83741i	−0.0413100	−	0.127139i	−0.969585	+	0.244756i	$0.921292\pi$
$912$	4.55437	+	8.93845i	0.150810	+	0.295982i
$913$	16.9915	+	33.3478i	0.562338	+	1.10365i
$914$	6.08431	−	1.97691i	0.201251	−	0.0653904i
$915$	−3.76747	+	11.1319i	−0.124549	+	0.368010i
$916$	12.1260	+	3.93999i	0.400655	+	0.130181i
$917$	−23.5152	+	6.42335i	−0.776541	+	0.212118i
$918$	−10.0855	−	10.0855i	−0.332872	−	0.332872i
$919$	−31.4198	+	43.2456i	−1.03644	+	1.42654i	−0.136445	+	0.990648i	$0.543568\pi$
$919$	−31.4198	+	43.2456i	−1.03644	+	1.42654i	−0.899998	+	0.435894i	$0.856432\pi$
$920$	3.33273	+	3.41491i	0.109877	+	0.112586i
$921$	−29.3613	+	21.3322i	−0.967488	+	0.702921i
$922$	−30.2918	−	4.79775i	−0.997606	−	0.158005i
$923$	25.6215	+	13.0548i	0.843341	+	0.429704i
$924$	3.75088	+	34.0948i	0.123395	+	1.12164i
$925$	4.36929	−	8.08234i	0.143661	−	0.265746i
$926$	1.40629			0.0462135
$927$	1.34661	−	2.64287i	0.0442284	−	0.0868031i
$928$	−3.83931	−	0.608087i	−0.126031	−	0.0199614i
$929$	−47.7383	+	34.6839i	−1.56624	+	1.13794i	−0.635596	+	0.772022i	$0.719246\pi$
$929$	−47.7383	+	34.6839i	−1.56624	+	1.13794i	−0.930646	+	0.365920i	$0.880754\pi$
$930$	−3.34091	+	19.5497i	−0.109553	+	0.641060i
$931$	13.7713	−	31.7568i	0.451335	−	1.04079i
$932$	−9.38980	+	9.38980i	−0.307573	+	0.307573i
$933$	6.82330	+	43.0806i	0.223385	+	1.41040i
$934$	−7.75582	+	23.8700i	−0.253778	+	0.781049i
$935$	53.3129	+	0.649290i	1.74352	+	0.0212341i
$936$	−4.35478	+	1.41495i	−0.142340	+	0.0462492i
$937$	−5.41083	+	2.75696i	−0.176764	+	0.0900658i	−0.540134	−	0.841579i	$-0.681626\pi$
$937$	−5.41083	+	2.75696i	−0.176764	+	0.0900658i	0.363369	+	0.931645i	$0.381626\pi$
$938$	18.4129	+	28.0544i	0.601203	+	0.916009i
$939$	66.8498	−	21.7208i	2.18156	−	0.708832i
$940$	0.0708372	−	5.81641i	0.00231046	−	0.189710i
$941$	37.0881	+	12.0507i	1.20904	+	0.392840i	0.843078	−	0.537791i	$-0.180741\pi$
$941$	37.0881	+	12.0507i	1.20904	+	0.392840i	0.365959	+	0.930631i	$0.380741\pi$
$942$	33.7083	−	5.33888i	1.09828	−	0.173950i
$943$	−15.6591	+	15.6591i	−0.509930	+	0.509930i
$944$	1.03964	+	0.755344i	0.0338374	+	0.0245843i
$945$	−22.5746	−	1.34897i	−0.734351	−	0.0438820i
$946$	−57.2151	+	41.5692i	−1.86022	+	1.35153i
$947$	3.32039	−	20.9641i	0.107898	−	0.681242i	−0.873146	−	0.487458i	$-0.837924\pi$
$947$	3.32039	−	20.9641i	0.107898	−	0.681242i	0.981044	−	0.193783i	$-0.0620759\pi$
$948$	−18.6620	−	9.50878i	−0.606115	−	0.308831i
$949$		−	31.7131i		−	1.02945i
$950$	11.7578	−	21.7497i	0.381474	−	0.705653i
$951$		−	32.5834i		−	1.05659i
$952$	−9.23331	−	3.49302i	−0.299253	−	0.113209i
$953$	24.0767	+	3.81337i	0.779920	+	0.123527i	0.533686	−	0.845683i	$-0.320807\pi$
$953$	24.0767	+	3.81337i	0.779920	+	0.123527i	0.246235	+	0.969210i	$0.420807\pi$
$954$	−7.92510	−	10.9080i	−0.256585	−	0.353158i
$955$	0.0340282	−	0.0332093i	0.00110113	−	0.00107463i
$956$	−15.9361	−	11.5783i	−0.515411	−	0.374468i
$957$	35.6344	+	35.6344i	1.15190	+	1.15190i
$958$	26.4876	−	4.19522i	0.855775	−	0.135542i
$959$	2.28079	−	10.9923i	0.0736504	−	0.354960i
$960$	1.45426	−	4.29697i	0.0469360	−	0.138684i
$961$	3.67285	+	11.3039i	0.118479	+	0.364641i
$962$	−6.71902	+	3.42351i	−0.216630	+	0.110378i
$963$	12.0119	−	6.12037i	0.387078	−	0.197226i
$964$	5.47325	+	16.8449i	0.176281	+	0.542538i
$965$	−7.17058	−	23.0189i	−0.230829	−	0.741005i
$966$	−2.32703	+	11.2152i	−0.0748709	+	0.360842i
$967$	−56.4736	+	8.94453i	−1.81607	+	0.287637i	−0.969580	−	0.244773i	$-0.921287\pi$
$967$	−56.4736	+	8.94453i	−1.81607	+	0.287637i	−0.846487	+	0.532410i	$0.821287\pi$
$968$	−21.0979	−	21.0979i	−0.678111	−	0.678111i
$969$	30.2825	+	22.0016i	0.972816	+	0.706792i
$970$	9.88168	+	19.9921i	0.317282	+	0.641908i
$971$	31.1093	+	42.8183i	0.998345	+	1.37410i	0.926335	+	0.376700i	$0.122941\pi$
$971$	31.1093	+	42.8183i	0.998345	+	1.37410i	0.0720098	+	0.997404i	$0.477059\pi$
$972$	10.9198	+	1.72953i	0.350254	+	0.0554748i
$973$	9.82709	−	25.9766i	0.315042	−	0.832770i
$974$			4.79133i			0.153524i
$975$	33.0715	+	25.2810i	1.05914	+	0.809639i
$976$			2.59065i			0.0829245i
$977$	−3.61378	−	1.84131i	−0.115615	−	0.0589089i	0.395226	−	0.918584i	$-0.370666\pi$
$977$	−3.61378	−	1.84131i	−0.115615	−	0.0589089i	−0.510842	+	0.859675i	$0.670666\pi$
$978$	−6.35162	+	40.1025i	−0.203102	+	1.28234i
$979$	−2.84536	+	2.06728i	−0.0909383	+	0.0660705i
$980$	−14.6267	+	5.57320i	−0.467232	+	0.178029i
$981$	1.36819	+	0.994051i	0.0436831	+	0.0317376i
$982$	25.6981	−	25.6981i	0.820058	−	0.820058i
$983$	17.8950	−	2.83429i	0.570761	−	0.0903997i	0.135618	−	0.990761i	$-0.456698\pi$
$983$	17.8950	−	2.83429i	0.570761	−	0.0903997i	0.435143	+	0.900361i	$0.356698\pi$
$984$	20.0230	+	6.50587i	0.638310	+	0.207400i
$985$	6.61478	−	8.87514i	0.210765	−	0.282785i
$986$	−13.7941	+	4.48197i	−0.439293	+	0.142735i
$987$	11.6733	−	7.66150i	0.371564	−	0.243868i
$988$	−18.0810	+	9.21272i	−0.575232	+	0.293096i
$989$	−22.4604	+	7.29782i	−0.714199	+	0.232057i
$990$	−13.0118	+	9.21363i	−0.413542	+	0.292828i
$991$	11.5405	−	35.5180i	0.366596	−	1.12827i	−0.582380	−	0.812917i	$-0.697878\pi$
$991$	11.5405	−	35.5180i	0.366596	−	1.12827i	0.948976	−	0.315349i	$-0.102122\pi$
$992$	0.683932	+	4.31818i	0.0217149	+	0.137102i
$993$	−4.89275	+	4.89275i	−0.155267	+	0.155267i
$994$	−16.1001	−	9.19149i	−0.510663	−	0.291536i
$995$	−31.5629	−	16.5693i	−1.00061	−	0.525283i
$996$	9.61264	−	6.98399i	0.304588	−	0.221296i
$997$	−12.2676	−	1.94300i	−0.388519	−	0.0615354i	−0.0408806	−	0.999164i	$-0.513016\pi$
$997$	−12.2676	−	1.94300i	−0.388519	−	0.0615354i	−0.347638	+	0.937629i	$0.613016\pi$
$998$	−6.49207	+	12.7414i	−0.205503	+	0.403322i
$999$	7.02423			0.222237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.83.13	✓	160
7.6	odd	2	inner	350.2.r.a.83.18	yes	160
25.22	odd	20	inner	350.2.r.a.97.18	yes	160
175.97	even	20	inner	350.2.r.a.97.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.83.13	✓	160	1.1	even	1	trivial
350.2.r.a.83.18	yes	160	7.6	odd	2	inner
350.2.r.a.97.13	yes	160	175.97	even	20	inner
350.2.r.a.97.18	yes	160	25.22	odd	20	inner

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(-0.317364 + 2.00376i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.97984 + 1.03934i) q^{5} +(-1.19246 + 1.64128i) q^{6} +(2.06419 + 1.65503i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06116 - 0.344792i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(-0.317364 + 2.00376i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.97984 + 1.03934i) q^{5} +(-1.19246 + 1.64128i) q^{6} +(2.06419 + 1.65503i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.06116 - 0.344792i) q^{9} +(1.29220 + 1.82489i) q^{10} +(-1.97473 - 6.07761i) q^{11} +(-1.80762 + 0.921027i) q^{12} +(-1.86308 - 3.65650i) q^{13} +(1.08784 + 2.41176i) q^{14} +(-2.71092 + 3.63727i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.583695 + 3.68530i) q^{17} +(-0.788968 - 0.788968i) q^{18} +(-4.00049 - 2.90653i) q^{19} +(0.322877 + 2.21263i) q^{20} +(-3.97138 + 3.61089i) q^{21} +(0.999675 - 6.31170i) q^{22} +(0.968792 - 1.90136i) q^{23} -2.02874 q^{24} +(2.83954 + 4.11546i) q^{25} -4.10379i q^{26} +(-1.73543 + 3.40597i) q^{27} +(-0.125644 + 2.64277i) q^{28} +(2.28482 + 3.14478i) q^{29} +(-4.06674 + 2.01010i) q^{30} +(2.56980 - 3.53702i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(12.8048 - 2.02808i) q^{33} +(-1.15302 + 3.54862i) q^{34} +(2.36663 + 5.42209i) q^{35} +(-0.344792 - 1.06116i) q^{36} +(-0.834231 - 1.63727i) q^{37} +(-2.24493 - 4.40592i) q^{38} +(7.91803 - 2.57272i) q^{39} +(-0.716830 + 2.11805i) q^{40} +(-9.86970 - 3.20686i) q^{41} +(-5.17783 + 1.41436i) q^{42} +(-7.82550 - 7.82550i) q^{43} +(3.75617 - 5.16992i) q^{44} +(-1.74257 - 1.78554i) q^{45} +(1.72640 - 1.25430i) q^{46} +(-2.56934 - 0.406944i) q^{47} +(-1.80762 - 0.921027i) q^{48} +(1.52177 + 6.83259i) q^{49} +(0.661669 + 4.95603i) q^{50} -7.56971 q^{51} +(1.86308 - 3.65650i) q^{52} +(11.9352 + 1.89036i) q^{53} +(-3.09255 + 2.24687i) q^{54} +(2.40705 - 14.0851i) q^{55} +(-1.31174 + 2.29768i) q^{56} +(7.09359 - 7.09359i) q^{57} +(0.608087 + 3.83931i) q^{58} +(0.397108 - 1.22217i) q^{59} +(-4.53606 - 0.0552440i) q^{60} +(2.46385 - 0.800554i) q^{61} +(3.89548 - 1.98485i) q^{62} +(-1.61980 - 2.46797i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.111749 - 9.17568i) q^{65} +(12.3299 + 4.00621i) q^{66} +(12.5273 - 1.98412i) q^{67} +(-2.63839 + 2.63839i) q^{68} +(3.50241 + 2.54465i) q^{69} +(-0.352893 + 5.90555i) q^{70} +(-5.66886 + 4.11867i) q^{71} +(0.174545 - 1.10203i) q^{72} +(6.88548 + 3.50833i) q^{73} -1.83755i q^{74} +(-9.14756 + 4.38365i) q^{75} -4.94488i q^{76} +(5.98238 - 15.8136i) q^{77} +(8.22301 + 1.30240i) q^{78} +(6.06836 + 8.35238i) q^{79} +(-1.60028 + 1.56177i) q^{80} +(-8.98200 - 6.52581i) q^{81} +(-7.33808 - 7.33808i) q^{82} +(-5.78468 + 0.916204i) q^{83} +(-5.25559 - 1.09048i) q^{84} +(-2.67467 + 7.90298i) q^{85} +(-3.41987 - 10.5253i) q^{86} +(-7.02651 + 3.58018i) q^{87} +(5.69386 - 2.90117i) q^{88} +(-0.170073 - 0.523432i) q^{89} +(-0.742025 - 2.38204i) q^{90} +(2.20586 - 10.6312i) q^{91} +(2.10768 - 0.333823i) q^{92} +(6.27178 + 6.27178i) q^{93} +(-2.10455 - 1.52905i) q^{94} +(-4.89946 - 9.91234i) q^{95} +(-1.19246 - 1.64128i) q^{96} +(9.85049 + 1.56016i) q^{97} +(-1.74602 + 6.77875i) q^{98} +7.13019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

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