LMFDB - Embedded newform 208.2.n.a.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(53,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("208.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40847 - 0.127312i) q^{2} +(-2.17257 - 2.17257i) q^{3} +(1.96758 + 0.358630i) q^{4} +(-2.25200 + 2.25200i) q^{5} +(2.78341 + 3.33660i) q^{6} -2.10748i q^{7} +(-2.72563 - 0.755616i) q^{8} +6.44015i q^{9} +O(q^{10})$	\(q+(-1.40847 - 0.127312i) q^{2} +(-2.17257 - 2.17257i) q^{3} +(1.96758 + 0.358630i) q^{4} +(-2.25200 + 2.25200i) q^{5} +(2.78341 + 3.33660i) q^{6} -2.10748i q^{7} +(-2.72563 - 0.755616i) q^{8} +6.44015i q^{9} +(3.45858 - 2.88517i) q^{10} +(-0.970496 + 0.970496i) q^{11} +(-3.49557 - 5.05387i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.268307 + 2.96833i) q^{14} +9.78527 q^{15} +(3.74277 + 1.41127i) q^{16} +5.32671 q^{17} +(0.819906 - 9.07076i) q^{18} +(4.19124 + 4.19124i) q^{19} +(-5.23863 + 3.62336i) q^{20} +(-4.57866 + 4.57866i) q^{21} +(1.49047 - 1.24336i) q^{22} +4.81340i q^{23} +(4.27999 + 7.56326i) q^{24} -5.14301i q^{25} +(-0.905917 - 1.08596i) q^{26} +(7.47397 - 7.47397i) q^{27} +(0.755805 - 4.14664i) q^{28} +(-3.09404 - 3.09404i) q^{29} +(-13.7823 - 1.24578i) q^{30} -4.15745 q^{31} +(-5.09191 - 2.46423i) q^{32} +4.21695 q^{33} +(-7.50252 - 0.678153i) q^{34} +(4.74605 + 4.74605i) q^{35} +(-2.30963 + 12.6715i) q^{36} +(-6.92773 + 6.92773i) q^{37} +(-5.36964 - 6.43683i) q^{38} -3.07248i q^{39} +(7.83976 - 4.43647i) q^{40} +9.94083i q^{41} +(7.03182 - 5.86599i) q^{42} +(-1.27996 + 1.27996i) q^{43} +(-2.25758 + 1.56148i) q^{44} +(-14.5032 - 14.5032i) q^{45} +(0.612802 - 6.77953i) q^{46} +0.528901 q^{47} +(-5.06536 - 11.1975i) q^{48} +2.55853 q^{49} +(-0.654765 + 7.24378i) q^{50} +(-11.5727 - 11.5727i) q^{51} +(1.13770 + 1.64488i) q^{52} +(-0.242187 + 0.242187i) q^{53} +(-11.4784 + 9.57535i) q^{54} -4.37111i q^{55} +(-1.59245 + 5.74421i) q^{56} -18.2115i q^{57} +(3.96395 + 4.75177i) q^{58} +(-1.95896 + 1.95896i) q^{59} +(19.2533 + 3.50929i) q^{60} +(5.73782 + 5.73782i) q^{61} +(5.85565 + 0.529292i) q^{62} +13.5725 q^{63} +(6.85809 + 4.11906i) q^{64} -3.18481 q^{65} +(-5.93945 - 0.536867i) q^{66} +(-6.99447 - 6.99447i) q^{67} +(10.4808 + 1.91032i) q^{68} +(10.4575 - 10.4575i) q^{69} +(-6.08044 - 7.28890i) q^{70} +1.27496i q^{71} +(4.86628 - 17.5534i) q^{72} +3.73380i q^{73} +(10.6395 - 8.87552i) q^{74} +(-11.1736 + 11.1736i) q^{75} +(6.74351 + 9.74971i) q^{76} +(2.04530 + 2.04530i) q^{77} +(-0.391163 + 4.32750i) q^{78} -10.1429 q^{79} +(-11.6069 + 5.25054i) q^{80} -13.1551 q^{81} +(1.26558 - 14.0014i) q^{82} +(10.0243 + 10.0243i) q^{83} +(-10.6509 + 7.36684i) q^{84} +(-11.9958 + 11.9958i) q^{85} +(1.96573 - 1.63983i) q^{86} +13.4440i q^{87} +(3.37853 - 1.91189i) q^{88} -9.75665i q^{89} +(18.5809 + 22.2738i) q^{90} +(1.49021 - 1.49021i) q^{91} +(-1.72623 + 9.47076i) q^{92} +(9.03236 + 9.03236i) q^{93} +(-0.744942 - 0.0673353i) q^{94} -18.8773 q^{95} +(5.70883 + 16.4163i) q^{96} +4.87230 q^{97} +(-3.60361 - 0.325730i) q^{98} +(-6.25013 - 6.25013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 4 * q^4 - 12 * q^8	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.40847	−	0.127312i	−0.995940	−	0.0900230i
$2$	−1.40847	−	0.127312i	−0.995940	−	0.0900230i
$3$	−2.17257	−	2.17257i	−1.25434	−	1.25434i	−0.953757	−	0.300579i	$-0.902820\pi$
$3$	−2.17257	−	2.17257i	−1.25434	−	1.25434i	−0.300579	−	0.953757i	$-0.597180\pi$
$4$	1.96758	+	0.358630i	0.983792	+	0.179315i
$5$	−2.25200	+	2.25200i	−1.00713	+	1.00713i	−0.00715062	+	0.999974i	$0.502276\pi$
$5$	−2.25200	+	2.25200i	−1.00713	+	1.00713i	−0.999974	+	0.00715062i	$0.997724\pi$
$6$	2.78341	+	3.33660i	1.13632	+	1.36216i
$7$		−	2.10748i		−	0.796553i	−0.917265	−	0.398276i	$-0.869608\pi$
$7$		−	2.10748i		−	0.796553i	0.917265	−	0.398276i	$-0.130392\pi$
$8$	−2.72563	−	0.755616i	−0.963655	−	0.267151i
$9$			6.44015i			2.14672i
$10$	3.45858	−	2.88517i	1.09370	−	0.912371i
$11$	−0.970496	+	0.970496i	−0.292615	+	0.292615i	−0.838113	−	0.545497i	$-0.816341\pi$
$11$	−0.970496	+	0.970496i	−0.292615	+	0.292615i	0.545497	+	0.838113i	$0.316341\pi$
$12$	−3.49557	−	5.05387i	−1.00908	−	1.45893i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	−0.268307	+	2.96833i	−0.0717080	+	0.793319i
$15$	9.78527			2.52655
$16$	3.74277	+	1.41127i	0.935692	+	0.352817i
$17$	5.32671			1.29192			0.645959	−	0.763372i	$-0.276458\pi$
$17$	5.32671			1.29192			0.645959	+	0.763372i	$0.276458\pi$
$18$	0.819906	−	9.07076i	0.193254	−	2.13800i
$19$	4.19124	+	4.19124i	0.961536	+	0.961536i	0.999287	−	0.0377516i	$-0.0120196\pi$
$19$	4.19124	+	4.19124i	0.961536	+	0.961536i	−0.0377516	+	0.999287i	$0.512020\pi$
$20$	−5.23863	+	3.62336i	−1.17139	+	0.810209i
$21$	−4.57866	+	4.57866i	−0.999144	+	0.999144i
$22$	1.49047	−	1.24336i	0.317769	−	0.265085i
$23$			4.81340i			1.00366i	0.864966	+	0.501831i	$0.167340\pi$
$23$			4.81340i			1.00366i	−0.864966	+	0.501831i	$0.832660\pi$
$24$	4.27999	+	7.56326i	0.873650	+	1.54384i
$25$		−	5.14301i		−	1.02860i
$26$	−0.905917	−	1.08596i	−0.177665	−	0.212975i
$27$	7.47397	−	7.47397i	1.43837	−	1.43837i
$28$	0.755805	−	4.14664i	0.142834	−	0.783642i
$29$	−3.09404	−	3.09404i	−0.574548	−	0.574548i	0.358848	−	0.933396i	$-0.383170\pi$
$29$	−3.09404	−	3.09404i	−0.574548	−	0.574548i	−0.933396	+	0.358848i	$0.883170\pi$
$30$	−13.7823	−	1.24578i	−2.51629	−	0.227447i
$31$	−4.15745			−0.746700			−0.373350	−	0.927691i	$-0.621791\pi$
$31$	−4.15745			−0.746700			−0.373350	+	0.927691i	$0.621791\pi$
$32$	−5.09191	−	2.46423i	−0.900131	−	0.435618i
$33$	4.21695			0.734076
$34$	−7.50252	−	0.678153i	−1.28667	−	0.116302i
$35$	4.74605	+	4.74605i	0.802228	+	0.802228i
$36$	−2.30963	+	12.6715i	−0.384938	+	2.11192i
$37$	−6.92773	+	6.92773i	−1.13891	+	1.13891i	−0.150266	+	0.988646i	$0.548013\pi$
$37$	−6.92773	+	6.92773i	−1.13891	+	1.13891i	−0.988646	+	0.150266i	$0.951987\pi$
$38$	−5.36964	−	6.43683i	−0.871071	−	1.04419i
$39$		−	3.07248i		−	0.491991i
$40$	7.83976	−	4.43647i	1.23958	−	0.701467i
$41$			9.94083i			1.55250i	0.630427	+	0.776248i	$0.282880\pi$
$41$			9.94083i			1.55250i	−0.630427	+	0.776248i	$0.717120\pi$
$42$	7.03182	−	5.86599i	1.08503	−	0.905142i
$43$	−1.27996	+	1.27996i	−0.195191	+	0.195191i	−0.797935	−	0.602744i	$-0.794074\pi$
$43$	−1.27996	+	1.27996i	−0.195191	+	0.195191i	0.602744	+	0.797935i	$0.294074\pi$
$44$	−2.25758	+	1.56148i	−0.340343	+	0.235402i
$45$	−14.5032	−	14.5032i	−2.16201	−	2.16201i
$46$	0.612802	−	6.77953i	0.0903527	−	0.999587i
$47$	0.528901			0.0771482			0.0385741	−	0.999256i	$-0.487718\pi$
$47$	0.528901			0.0771482			0.0385741	+	0.999256i	$0.487718\pi$
$48$	−5.06536	−	11.1975i	−0.731121	−	1.61622i
$49$	2.55853			0.365504
$50$	−0.654765	+	7.24378i	−0.0925978	+	1.02443i
$51$	−11.5727	−	11.5727i	−1.62050	−	1.62050i
$52$	1.13770	+	1.64488i	0.157771	+	0.228104i
$53$	−0.242187	+	0.242187i	−0.0332669	+	0.0332669i	−0.723545	−	0.690278i	$-0.757488\pi$
$53$	−0.242187	+	0.242187i	−0.0332669	+	0.0332669i	0.690278	+	0.723545i	$0.257488\pi$
$54$	−11.4784	+	9.57535i	−1.56201	+	1.30304i
$55$		−	4.37111i		−	0.589401i
$56$	−1.59245	+	5.74421i	−0.212800	+	0.767602i
$57$		−	18.2115i		−	2.41218i
$58$	3.96395	+	4.75177i	0.520493	+	0.623938i
$59$	−1.95896	+	1.95896i	−0.255036	+	0.255036i	−0.823031	−	0.567996i	$-0.807719\pi$
$59$	−1.95896	+	1.95896i	−0.255036	+	0.255036i	0.567996	+	0.823031i	$0.307719\pi$
$60$	19.2533	+	3.50929i	2.48559	+	0.453047i
$61$	5.73782	+	5.73782i	0.734652	+	0.734652i	0.971538	−	0.236885i	$-0.0761265\pi$
$61$	5.73782	+	5.73782i	0.734652	+	0.734652i	−0.236885	+	0.971538i	$0.576127\pi$
$62$	5.85565	+	0.529292i	0.743668	+	0.0672201i
$63$	13.5725			1.70997
$64$	6.85809	+	4.11906i	0.857261	+	0.514882i
$65$	−3.18481			−0.395027
$66$	−5.93945	−	0.536867i	−0.731095	−	0.0660837i
$67$	−6.99447	−	6.99447i	−0.854510	−	0.854510i	0.136174	−	0.990685i	$-0.456519\pi$
$67$	−6.99447	−	6.99447i	−0.854510	−	0.854510i	−0.990685	+	0.136174i	$0.956519\pi$
$68$	10.4808	+	1.91032i	1.27098	+	0.231660i
$69$	10.4575	−	10.4575i	1.25893	−	1.25893i
$70$	−6.08044	−	7.28890i	−0.726752	−	0.871190i
$71$			1.27496i			0.151310i	0.997134	+	0.0756548i	$0.0241047\pi$
$71$			1.27496i			0.151310i	−0.997134	+	0.0756548i	$0.975895\pi$
$72$	4.86628	−	17.5534i	0.573497	−	2.06869i
$73$			3.73380i			0.437008i	0.975836	+	0.218504i	$0.0701177\pi$
$73$			3.73380i			0.437008i	−0.975836	+	0.218504i	$0.929882\pi$
$74$	10.6395	−	8.87552i	1.23682	−	1.03176i
$75$	−11.1736	+	11.1736i	−1.29021	+	1.29021i
$76$	6.74351	+	9.74971i	0.773533	+	1.11837i
$77$	2.04530	+	2.04530i	0.233084	+	0.233084i
$78$	−0.391163	+	4.32750i	−0.0442905	+	0.489993i
$79$	−10.1429			−1.14117			−0.570584	−	0.821239i	$-0.693283\pi$
$79$	−10.1429			−1.14117			−0.570584	+	0.821239i	$0.693283\pi$
$80$	−11.6069	+	5.25054i	−1.29769	+	0.587028i
$81$	−13.1551			−1.46167
$82$	1.26558	−	14.0014i	0.139760	−	1.54619i
$83$	10.0243	+	10.0243i	1.10031	+	1.10031i	0.994373	+	0.105936i	$0.0337840\pi$
$83$	10.0243	+	10.0243i	1.10031	+	1.10031i	0.105936	+	0.994373i	$0.466216\pi$
$84$	−10.6509	+	7.36684i	−1.16211	+	0.803789i
$85$	−11.9958	+	11.9958i	−1.30112	+	1.30112i
$86$	1.96573	−	1.63983i	0.211970	−	0.176827i
$87$			13.4440i			1.44135i
$88$	3.37853	−	1.91189i	0.360153	−	0.203808i
$89$		−	9.75665i		−	1.03420i	−0.855924	−	0.517101i	$-0.827011\pi$
$89$		−	9.75665i		−	1.03420i	0.855924	−	0.517101i	$-0.172989\pi$
$90$	18.5809	+	22.2738i	1.95860	+	2.34786i
$91$	1.49021	−	1.49021i	0.156217	−	0.156217i
$92$	−1.72623	+	9.47076i	−0.179972	+	0.987395i
$93$	9.03236	+	9.03236i	0.936612	+	0.936612i
$94$	−0.744942	−	0.0673353i	−0.0768349	−	0.00694511i
$95$	−18.8773			−1.93677
$96$	5.70883	+	16.4163i	0.582655	+	1.67548i
$97$	4.87230			0.494707			0.247354	−	0.968925i	$-0.420439\pi$
$97$	4.87230			0.494707			0.247354	+	0.968925i	$0.420439\pi$
$98$	−3.60361	−	0.325730i	−0.364020	−	0.0329037i
$99$	−6.25013	−	6.25013i	−0.628162	−	0.628162i
$100$	1.84444	−	10.1193i	0.184444	−	1.01193i
$101$	5.53810	−	5.53810i	0.551061	−	0.551061i	−0.375686	−	0.926747i	$-0.622593\pi$
$101$	5.53810	−	5.53810i	0.551061	−	0.551061i	0.926747	+	0.375686i	$0.122593\pi$
$102$	14.8264	+	17.7731i	1.46804	+	1.75980i
$103$			7.20492i			0.709922i	0.934881	+	0.354961i	$0.115506\pi$
$103$			7.20492i			0.709922i	−0.934881	+	0.354961i	$0.884494\pi$
$104$	−1.39301	−	2.46161i	−0.136596	−	0.241381i
$105$		−	20.6223i		−	2.01253i
$106$	0.371947	−	0.310280i	0.0361266	−	0.0301371i
$107$	0.630896	−	0.630896i	0.0609910	−	0.0609910i	−0.675953	−	0.736944i	$-0.736268\pi$
$107$	0.630896	−	0.630896i	0.0609910	−	0.0609910i	0.736944	+	0.675953i	$0.236268\pi$
$108$	17.3860	−	12.0253i	1.67297	−	1.15713i
$109$	11.3972	+	11.3972i	1.09166	+	1.09166i	0.995352	+	0.0963041i	$0.0307021\pi$
$109$	11.3972	+	11.3972i	1.09166	+	1.09166i	0.0963041	+	0.995352i	$0.469298\pi$
$110$	−0.556494	+	6.15659i	−0.0530596	+	0.587008i
$111$	30.1020			2.85715
$112$	2.97422	−	7.88781i	0.281037	−	0.745328i
$113$	−13.6842			−1.28730			−0.643651	−	0.765319i	$-0.722581\pi$
$113$	−13.6842			−1.28730			−0.643651	+	0.765319i	$0.722581\pi$
$114$	−2.31854	+	25.6504i	−0.217151	+	2.40238i
$115$	−10.8398	−	10.8398i	−1.01081	−	1.01081i
$116$	−4.97816	−	7.19739i	−0.462211	−	0.668261i
$117$	−4.55387	+	4.55387i	−0.421006	+	0.421006i
$118$	3.00855	−	2.50975i	0.276959	−	0.231041i
$119$		−	11.2259i		−	1.02908i
$120$	−26.6710	−	7.39391i	−2.43472	−	0.674968i
$121$			9.11628i			0.828752i
$122$	−7.35106	−	8.81204i	−0.665534	−	0.797805i
$123$	21.5972	−	21.5972i	1.94735	−	1.94735i
$124$	−8.18012	−	1.49098i	−0.734597	−	0.133894i
$125$	0.322056	+	0.322056i	0.0288055	+	0.0288055i
$126$	−19.1165	−	1.72794i	−1.70303	−	0.153937i
$127$	−6.92702			−0.614673			−0.307337	−	0.951601i	$-0.599438\pi$
$127$	−6.92702			−0.614673			−0.307337	+	0.951601i	$0.599438\pi$
$128$	−9.13502	−	6.67469i	−0.807429	−	0.589965i
$129$	5.56159			0.489671
$130$	4.48571	+	0.405463i	0.393423	+	0.0355615i
$131$	−8.15576	−	8.15576i	−0.712572	−	0.712572i	0.254501	−	0.967073i	$-0.418089\pi$
$131$	−8.15576	−	8.15576i	−0.712572	−	0.712572i	−0.967073	+	0.254501i	$0.918089\pi$
$132$	8.29719	+	1.51232i	0.722178	+	0.131631i
$133$	8.83295	−	8.83295i	0.765914	−	0.765914i
$134$	8.96103	+	10.7420i	0.774115	+	0.927966i
$135$			33.6628i			2.89723i
$136$	−14.5186	−	4.02495i	−1.24496	−	0.345137i
$137$		−	1.06220i		−	0.0907497i	−0.998970	−	0.0453748i	$-0.985552\pi$
$137$		−	1.06220i		−	0.0907497i	0.998970	−	0.0453748i	$-0.0144482\pi$
$138$	−16.0604	+	13.3977i	−1.36715	+	1.14049i
$139$	16.2546	−	16.2546i	1.37869	−	1.37869i	0.531865	−	0.846829i	$-0.321491\pi$
$139$	16.2546	−	16.2546i	1.37869	−	1.37869i	0.846829	−	0.531865i	$-0.178509\pi$
$140$	7.63617	+	11.0403i	0.645374	+	0.933077i
$141$	−1.14908	−	1.14908i	−0.0967697	−	0.0967697i
$142$	0.162317	−	1.79574i	0.0136213	−	0.150695i
$143$	−1.37249			−0.114773
$144$	−9.08877	+	24.1040i	−0.757398	+	2.00867i
$145$	13.9355			1.15728
$146$	0.475356	−	5.25895i	0.0393408	−	0.435234i
$147$	−5.55858	−	5.55858i	−0.458464	−	0.458464i
$148$	−16.1154	+	11.1464i	−1.32468	+	0.916228i
$149$	6.61207	−	6.61207i	0.541682	−	0.541682i	−0.382340	−	0.924022i	$-0.624882\pi$
$149$	6.61207	−	6.61207i	0.541682	−	0.541682i	0.924022	+	0.382340i	$0.124882\pi$
$150$	17.1602	−	14.3151i	1.40112	−	1.16882i
$151$		−	2.96276i		−	0.241106i	−0.992707	−	0.120553i	$-0.961533\pi$
$151$		−	2.96276i		−	0.241106i	0.992707	−	0.120553i	$-0.0384668\pi$
$152$	−8.25678	−	14.5907i	−0.669713	−	1.18346i
$153$			34.3048i			2.77338i
$154$	−2.62036	−	3.14114i	−0.211154	−	0.253120i
$155$	9.36257	−	9.36257i	0.752020	−	0.752020i
$156$	1.10188	−	6.04537i	0.0882213	−	0.484017i
$157$	2.12351	+	2.12351i	0.169475	+	0.169475i	0.786748	−	0.617274i	$-0.211763\pi$
$157$	2.12351	+	2.12351i	0.169475	+	0.169475i	−0.617274	+	0.786748i	$0.711763\pi$
$158$	14.2860	+	1.29131i	1.13653	+	0.102731i
$159$	1.05234			0.0834558
$160$	17.0164	−	5.91754i	1.34527	−	0.467823i
$161$	10.1441			0.799470
$162$	18.5285	+	1.67479i	1.45574	+	0.131584i
$163$	0.340117	+	0.340117i	0.0266400	+	0.0266400i	0.720301	−	0.693661i	$-0.244004\pi$
$163$	0.340117	+	0.340117i	0.0266400	+	0.0266400i	−0.693661	+	0.720301i	$0.744004\pi$
$164$	−3.56508	+	19.5594i	−0.278386	+	1.52733i
$165$	−9.49656	+	9.49656i	−0.739306	+	0.739306i
$166$	−12.8427	−	15.3951i	−0.996789	−	1.19489i
$167$			11.2979i			0.874257i	0.899399	+	0.437129i	$0.144005\pi$
$167$			11.2979i			0.874257i	−0.899399	+	0.437129i	$0.855995\pi$
$168$	15.9394	−	9.02000i	1.22975	−	0.695908i
$169$			1.00000i			0.0769231i
$170$	18.4229	−	15.3685i	1.41297	−	1.17871i
$171$	−26.9922	+	26.9922i	−2.06414	+	2.06414i
$172$	−2.97745	+	2.05939i	−0.227028	+	0.157027i
$173$	−3.03931	−	3.03931i	−0.231075	−	0.231075i	0.582067	−	0.813141i	$-0.302244\pi$
$173$	−3.03931	−	3.03931i	−0.231075	−	0.231075i	−0.813141	+	0.582067i	$0.802244\pi$
$174$	1.71158	−	18.9355i	0.129755	−	1.43550i
$175$	−10.8388			−0.819336
$176$	−5.00197	+	2.26271i	−0.377038	+	0.170558i
$177$	8.51199			0.639800
$178$	−1.24214	+	13.7420i	−0.0931020	+	1.03000i
$179$	5.39500	+	5.39500i	0.403241	+	0.403241i	0.879374	−	0.476132i	$-0.157962\pi$
$179$	5.39500	+	5.39500i	0.403241	+	0.403241i	−0.476132	+	0.879374i	$0.657962\pi$
$180$	−23.3350	−	33.7376i	−1.73929	−	2.51465i
$181$	−7.44553	+	7.44553i	−0.553422	+	0.553422i	−0.927427	−	0.374005i	$-0.877984\pi$
$181$	−7.44553	+	7.44553i	−0.553422	+	0.553422i	0.374005	+	0.927427i	$0.377984\pi$
$182$	−2.28865	+	1.90920i	−0.169646	+	0.141519i
$183$		−	24.9317i		−	1.84300i
$184$	3.63708	−	13.1195i	0.268129	−	0.967184i
$185$		−	31.2025i		−	2.29405i
$186$	−11.5719	−	13.8717i	−0.848492	−	1.01713i
$187$	−5.16955	+	5.16955i	−0.378035	+	0.378035i
$188$	1.04066	+	0.189680i	0.0758978	+	0.0138338i
$189$	−15.7512	−	15.7512i	−1.14573	−	1.14573i
$190$	26.5882	+	2.40331i	1.92891	+	0.174354i
$191$	−8.62098			−0.623792			−0.311896	−	0.950116i	$-0.600964\pi$
$191$	−8.62098			−0.623792			−0.311896	+	0.950116i	$0.600964\pi$
$192$	−5.95075	−	23.8486i	−0.429458	−	1.72113i
$193$	−11.5232			−0.829458			−0.414729	−	0.909945i	$-0.636124\pi$
$193$	−11.5232			−0.829458			−0.414729	+	0.909945i	$0.636124\pi$
$194$	−6.86250	−	0.620301i	−0.492699	−	0.0445350i
$195$	6.91923	+	6.91923i	0.495496	+	0.495496i
$196$	5.03411	+	0.917564i	0.359580	+	0.0655403i
$197$	3.30426	−	3.30426i	0.235419	−	0.235419i	−0.579531	−	0.814950i	$-0.696764\pi$
$197$	3.30426	−	3.30426i	0.235419	−	0.235419i	0.814950	+	0.579531i	$0.196764\pi$
$198$	8.00742	+	9.59885i	0.569063	+	0.682161i
$199$			21.9279i			1.55443i	0.629236	+	0.777214i	$0.283368\pi$
$199$			21.9279i			1.55443i	−0.629236	+	0.777214i	$0.716632\pi$
$200$	−3.88614	+	14.0179i	−0.274792	+	0.991217i
$201$			30.3920i			2.14369i
$202$	−8.50532	+	7.09519i	−0.598432	+	0.499216i
$203$	−6.52062	+	6.52062i	−0.457658	+	0.457658i
$204$	−18.6199	−	26.9205i	−1.30365	−	1.88481i
$205$	−22.3868	−	22.3868i	−1.56356	−	1.56356i
$206$	0.917271	−	10.1479i	0.0639093	−	0.707039i
$207$	−30.9990			−2.15458
$208$	1.64862	+	3.64445i	0.114311	+	0.252697i
$209$	−8.13515			−0.562720
$210$	−2.62546	+	29.0459i	−0.181174	+	2.00436i
$211$	6.31619	+	6.31619i	0.434824	+	0.434824i	0.890266	−	0.455441i	$-0.150519\pi$
$211$	6.31619	+	6.31619i	0.434824	+	0.434824i	−0.455441	+	0.890266i	$0.650519\pi$
$212$	−0.563378	+	0.389668i	−0.0386930	+	0.0267625i
$213$	2.76994	−	2.76994i	0.189793	−	0.189793i
$214$	−0.968920	+	0.808279i	−0.0662340	+	0.0552528i
$215$		−	5.76492i		−	0.393164i
$216$	−26.0187	+	14.7238i	−1.77035	+	1.00183i
$217$			8.76174i			0.594786i
$218$	−14.6017	−	17.5037i	−0.988949	−	1.18550i
$219$	8.11195	−	8.11195i	0.548155	−	0.548155i
$220$	1.56761	−	8.60053i	0.105688	−	0.579848i
$221$	3.76655	+	3.76655i	0.253366	+	0.253366i
$222$	−42.3978	−	3.83233i	−2.84555	−	0.257209i
$223$	−6.40174			−0.428692			−0.214346	−	0.976758i	$-0.568762\pi$
$223$	−6.40174			−0.428692			−0.214346	+	0.976758i	$0.568762\pi$
$224$	−5.19332	+	10.7311i	−0.346993	+	0.717002i
$225$	33.1217			2.20812
$226$	19.2738	+	1.74216i	1.28207	+	0.115887i
$227$	4.22527	+	4.22527i	0.280441	+	0.280441i	0.833285	−	0.552844i	$-0.186457\pi$
$227$	4.22527	+	4.22527i	0.280441	+	0.280441i	−0.552844	+	0.833285i	$0.686457\pi$
$228$	6.53120	−	35.8327i	0.432539	−	2.37308i
$229$	19.1442	−	19.1442i	1.26509	−	1.26509i	0.316491	−	0.948595i	$-0.397495\pi$
$229$	19.1442	−	19.1442i	1.26509	−	1.26509i	0.948595	−	0.316491i	$-0.102505\pi$
$230$	13.8875	+	16.6475i	0.915713	+	1.09771i
$231$		−	8.88713i		−	0.584730i
$232$	6.09528	+	10.7711i	0.400175	+	0.707157i
$233$		−	10.7872i		−	0.706693i	−0.935493	−	0.353346i	$-0.885044\pi$
$233$		−	10.7872i		−	0.706693i	0.935493	−	0.353346i	$-0.114956\pi$
$234$	6.99376	−	5.83424i	0.457196	−	0.381396i
$235$	−1.19109	+	1.19109i	−0.0776979	+	0.0776979i
$236$	−4.55697	+	3.15188i	−0.296634	+	0.205170i
$237$	22.0362	+	22.0362i	1.43141	+	1.43141i
$238$	−1.42919	+	15.8114i	−0.0926409	+	1.02490i
$239$	−0.732989			−0.0474131			−0.0237066	−	0.999719i	$-0.507547\pi$
$239$	−0.732989			−0.0474131			−0.0237066	+	0.999719i	$0.507547\pi$
$240$	36.6240	+	13.8096i	2.36407	+	0.891408i
$241$	−16.0923			−1.03660			−0.518299	−	0.855200i	$-0.673434\pi$
$241$	−16.0923			−1.03660			−0.518299	+	0.855200i	$0.673434\pi$
$242$	1.16061	−	12.8400i	0.0746068	−	0.825387i
$243$	6.15840	+	6.15840i	0.395061	+	0.395061i
$244$	9.23188	+	13.3474i	0.591011	+	0.854479i
$245$	−5.76180	+	5.76180i	−0.368108	+	0.368108i
$246$	−33.1686	+	27.6694i	−2.11475	+	1.76414i
$247$			5.92730i			0.377145i
$248$	11.3317	+	3.14143i	0.719561	+	0.199481i
$249$		−	43.5570i		−	2.76031i
$250$	−0.412605	−	0.494608i	−0.0260954	−	0.0312817i
$251$	−15.5752	+	15.5752i	−0.983100	+	0.983100i	−0.999860	−	0.0167595i	$-0.994665\pi$
$251$	−15.5752	+	15.5752i	−0.983100	+	0.983100i	0.0167595	+	0.999860i	$0.494665\pi$
$252$	26.7050	+	4.86750i	1.68226	+	0.306624i
$253$	−4.67138	−	4.67138i	−0.293687	−	0.293687i
$254$	9.75651	+	0.881890i	0.612178	+	0.0553347i
$255$	52.1233			3.26409
$256$	12.0166	+	10.5641i	0.751040	+	0.660256i
$257$	26.6179			1.66038			0.830191	−	0.557479i	$-0.188231\pi$
$257$	26.6179			1.66038			0.830191	+	0.557479i	$0.188231\pi$
$258$	−7.83334	−	0.708056i	−0.487683	−	0.0440816i
$259$	14.6000	+	14.6000i	0.907203	+	0.907203i
$260$	−6.26638	−	1.14217i	−0.388624	−	0.0708342i
$261$	19.9260	−	19.9260i	1.23339	−	1.23339i
$262$	10.4488	+	12.5255i	0.645531	+	0.773826i
$263$		−	2.82970i		−	0.174487i	−0.996187	−	0.0872434i	$-0.972194\pi$
$263$		−	2.82970i		−	0.174487i	0.996187	−	0.0872434i	$-0.0278058\pi$
$264$	−11.4938	−	3.18639i	−0.707396	−	0.196109i
$265$		−	1.09081i		−	0.0670079i
$266$	−13.5655	+	11.3164i	−0.831754	+	0.693854i
$267$	−21.1970	+	21.1970i	−1.29724	+	1.29724i
$268$	−11.2538	−	16.2706i	−0.687434	−	0.993887i
$269$	8.69674	+	8.69674i	0.530250	+	0.530250i	0.920647	−	0.390397i	$-0.127662\pi$
$269$	8.69674	+	8.69674i	0.530250	+	0.530250i	−0.390397	+	0.920647i	$0.627662\pi$
$270$	4.28566	−	47.4130i	0.260817	−	2.88547i
$271$	−18.7456			−1.13871			−0.569357	−	0.822090i	$-0.692808\pi$
$271$	−18.7456			−1.13871			−0.569357	+	0.822090i	$0.692808\pi$
$272$	19.9367	+	7.51742i	1.20884	+	0.455811i
$273$	−6.47520			−0.391897
$274$	−0.135230	+	1.49607i	−0.00816955	+	0.0903812i
$275$	4.99127	+	4.99127i	0.300985	+	0.300985i
$276$	24.3263	−	16.8256i	1.46427	−	1.01278i
$277$	−15.5450	+	15.5450i	−0.934006	+	0.934006i	−0.997953	−	0.0639475i	$-0.979631\pi$
$277$	−15.5450	+	15.5450i	−0.934006	+	0.934006i	0.0639475	+	0.997953i	$0.479631\pi$
$278$	−24.9635	+	20.8247i	−1.49721	+	1.24898i
$279$		−	26.7746i		−	1.60295i
$280$	−9.34976	−	16.5221i	−0.558755	−	0.987387i
$281$			9.00560i			0.537229i	0.963248	+	0.268615i	$0.0865658\pi$
$281$			9.00560i			0.537229i	−0.963248	+	0.268615i	$0.913434\pi$
$282$	1.47215	+	1.76473i	0.0876653	+	0.105088i
$283$	−16.7031	+	16.7031i	−0.992895	+	0.992895i	−0.999975	−	0.00708040i	$-0.997746\pi$
$283$	−16.7031	+	16.7031i	−0.992895	+	0.992895i	0.00708040	+	0.999975i	$0.497746\pi$
$284$	−0.457238	+	2.50859i	−0.0271321	+	0.148857i
$285$	41.0124	+	41.0124i	2.42936	+	2.42936i
$286$	1.93311	+	0.174734i	0.114307	+	0.0103322i
$287$	20.9501			1.23665
$288$	15.8700	−	32.7927i	0.935149	−	1.93233i
$289$	11.3739			0.669051
$290$	−19.6278	−	1.77416i	−1.15258	−	0.104182i
$291$	−10.5854	−	10.5854i	−0.620529	−	0.620529i
$292$	−1.33905	+	7.34656i	−0.0783621	+	0.429925i
$293$	1.80399	−	1.80399i	0.105390	−	0.105390i	−0.652446	−	0.757836i	$-0.726257\pi$
$293$	1.80399	−	1.80399i	0.105390	−	0.105390i	0.757836	+	0.652446i	$0.226257\pi$
$294$	7.12143	+	8.53678i	0.415330	+	0.497875i
$295$		−	8.82318i		−	0.513705i
$296$	24.1171	−	13.6477i	1.40178	−	0.793256i
$297$			14.5069i			0.841776i
$298$	−10.1547	+	8.47112i	−0.588246	+	0.490719i
$299$	−3.40358	+	3.40358i	−0.196834	+	0.196834i
$300$	−25.9921	+	17.9777i	−1.50065	+	1.03795i
$301$	2.69748	+	2.69748i	0.155480	+	0.155480i
$302$	−0.377194	+	4.17296i	−0.0217051	+	0.240127i
$303$	−24.0638			−1.38243
$304$	9.77187	+	21.6018i	0.560455	+	1.23895i
$305$	−25.8431			−1.47977
$306$	4.36740	−	48.3173i	0.249668	−	2.76212i
$307$	0.122376	+	0.122376i	0.00698439	+	0.00698439i	0.710590	−	0.703606i	$-0.248428\pi$
$307$	0.122376	+	0.122376i	0.00698439	+	0.00698439i	−0.703606	+	0.710590i	$0.748428\pi$
$308$	3.29079	+	4.75781i	0.187510	+	0.271101i
$309$	15.6532	−	15.6532i	0.890480	−	0.890480i
$310$	−14.3789	+	11.9949i	−0.816665	+	0.681267i
$311$		−	0.0182004i		−	0.00103205i	−1.00000		0.000516026i	$-0.999836\pi$
$311$		−	0.0182004i		−	0.00103205i	1.00000		0.000516026i	$-0.000164256\pi$
$312$	−2.32162	+	8.37444i	−0.131436	+	0.474109i
$313$		−	8.17496i		−	0.462076i	−0.972945	−	0.231038i	$-0.925788\pi$
$313$		−	8.17496i		−	0.462076i	0.972945	−	0.231038i	$-0.0742122\pi$
$314$	−2.72056	−	3.26126i	−0.153530	−	0.184043i
$315$	−30.5652	+	30.5652i	−1.72216	+	1.72216i
$316$	−19.9571	−	3.63756i	−1.12267	−	0.204628i
$317$	−16.2814	−	16.2814i	−0.914452	−	0.914452i	0.0821668	−	0.996619i	$-0.473816\pi$
$317$	−16.2814	−	16.2814i	−0.914452	−	0.914452i	−0.996619	+	0.0821668i	$0.973816\pi$
$318$	−1.48219	−	0.133975i	−0.0831169	−	0.00751294i
$319$	6.00550			0.336243
$320$	−24.7205	+	6.16830i	−1.38192	+	0.344818i
$321$	−2.74134			−0.153006
$322$	−14.2877	−	1.29147i	−0.796224	−	0.0719707i
$323$	22.3255	+	22.3255i	1.24222	+	1.24222i
$324$	−25.8837	−	4.71779i	−1.43798	−	0.262100i
$325$	3.63666	−	3.63666i	0.201725	−	0.201725i
$326$	−0.435744	−	0.522346i	−0.0241336	−	0.0289301i
$327$		−	49.5226i		−	2.73861i
$328$	7.51145	−	27.0950i	0.414751	−	1.49607i
$329$		−	1.11465i		−	0.0614526i
$330$	14.5847	−	12.1666i	0.802859	−	0.669750i
$331$	7.82355	−	7.82355i	0.430021	−	0.430021i	−0.458614	−	0.888635i	$-0.651654\pi$
$331$	7.82355	−	7.82355i	0.430021	−	0.430021i	0.888635	+	0.458614i	$0.151654\pi$
$332$	16.1286	+	23.3186i	0.885173	+	1.27978i
$333$	−44.6156	−	44.6156i	−2.44492	−	2.44492i
$334$	1.43835	−	15.9128i	0.0787032	−	0.870708i
$335$	31.5031			1.72120
$336$	−23.5986	+	10.6751i	−1.28741	+	0.582377i
$337$	12.6209			0.687504			0.343752	−	0.939060i	$-0.388302\pi$
$337$	12.6209			0.687504			0.343752	+	0.939060i	$0.388302\pi$
$338$	0.127312	−	1.40847i	0.00692484	−	0.0766107i
$339$	29.7299	+	29.7299i	1.61471	+	1.61471i
$340$	−27.9047	+	19.3006i	−1.51334	+	1.04672i
$341$	4.03478	−	4.03478i	0.218496	−	0.218496i
$342$	41.4541	−	34.5813i	2.24158	−	1.86994i
$343$		−	20.1444i		−	1.08770i
$344$	4.45584	−	2.52153i	0.240243	−	0.135952i
$345$			47.1004i			2.53580i
$346$	3.89385	+	4.66773i	0.209334	+	0.250938i
$347$	18.5373	−	18.5373i	0.995134	−	0.995134i	−0.00485438	−	0.999988i	$-0.501545\pi$
$347$	18.5373	−	18.5373i	0.995134	−	0.995134i	0.999988	+	0.00485438i	$0.00154520\pi$
$348$	−4.82143	+	26.4523i	−0.258456	+	1.41799i
$349$	−6.75273	−	6.75273i	−0.361465	−	0.361465i	0.502887	−	0.864352i	$-0.332271\pi$
$349$	−6.75273	−	6.75273i	−0.361465	−	0.361465i	−0.864352	+	0.502887i	$0.832271\pi$
$350$	15.2661	+	1.37990i	0.816009	+	0.0737590i
$351$	10.5698			0.564174
$352$	7.33320	−	2.55016i	0.390861	−	0.135924i
$353$	−27.6231			−1.47023			−0.735114	−	0.677943i	$-0.762872\pi$
$353$	−27.6231			−1.47023			−0.735114	+	0.677943i	$0.762872\pi$
$354$	−11.9889	−	1.08368i	−0.637202	−	0.0575967i
$355$	−2.87120	−	2.87120i	−0.152388	−	0.152388i
$356$	3.49902	−	19.1970i	0.185448	−	1.01744i
$357$	−24.3892	+	24.3892i	−1.29081	+	1.29081i
$358$	−6.91186	−	8.28555i	−0.365303	−	0.437905i
$359$		−	11.3853i		−	0.600892i	−0.953799	−	0.300446i	$-0.902865\pi$
$359$		−	11.3853i		−	0.600892i	0.953799	−	0.300446i	$-0.0971354\pi$
$360$	28.5715	+	50.4892i	1.50585	+	2.66101i
$361$			16.1329i			0.849101i
$362$	11.4347	−	9.53891i	0.600995	−	0.501354i
$363$	19.8058	−	19.8058i	1.03953	−	1.03953i
$364$	3.46656	−	2.39768i	0.181697	−	0.125673i
$365$	−8.40851	−	8.40851i	−0.440122	−	0.440122i
$366$	−3.17409	+	35.1155i	−0.165912	+	1.83552i
$367$	−4.28074			−0.223453			−0.111726	−	0.993739i	$-0.535638\pi$
$367$	−4.28074			−0.223453			−0.111726	+	0.993739i	$0.535638\pi$
$368$	−6.79299	+	18.0154i	−0.354109	+	0.939119i
$369$	−64.0204			−3.33277
$370$	−3.97244	+	43.9478i	−0.206517	+	2.28474i
$371$	0.510404	+	0.510404i	0.0264989	+	0.0264989i
$372$	14.5326	+	21.0112i	0.753482	+	1.08938i
$373$	−12.0993	+	12.0993i	−0.626475	+	0.626475i	−0.947179	−	0.320704i	$-0.896081\pi$
$373$	−12.0993	+	12.0993i	−0.626475	+	0.626475i	0.320704	+	0.947179i	$0.396081\pi$
$374$	7.93931	−	6.62302i	0.410532	−	0.342468i
$375$		−	1.39938i		−	0.0722636i
$376$	−1.44159	−	0.399646i	−0.0743442	−	0.0206102i
$377$		−	4.37563i		−	0.225356i
$378$	20.1799	+	24.1905i	1.03794	+	1.24422i
$379$	2.78595	−	2.78595i	0.143105	−	0.143105i	−0.631925	−	0.775030i	$-0.717735\pi$
$379$	2.78595	−	2.78595i	0.143105	−	0.143105i	0.775030	+	0.631925i	$0.217735\pi$
$380$	−37.1427	−	6.76997i	−1.90538	−	0.347292i
$381$	15.0495	+	15.0495i	0.771007	+	0.771007i
$382$	12.1424	+	1.09755i	0.621259	+	0.0561556i
$383$	27.0365			1.38150			0.690752	−	0.723092i	$-0.257280\pi$
$383$	27.0365			1.38150			0.690752	+	0.723092i	$0.257280\pi$
$384$	5.34524	+	34.3477i	0.272773	+	1.75280i
$385$	−9.21204			−0.469489
$386$	16.2301	+	1.46704i	0.826090	+	0.0746703i
$387$	−8.24310	−	8.24310i	−0.419020	−	0.419020i
$388$	9.58666	+	1.74735i	0.486689	+	0.0887084i
$389$	7.47600	−	7.47600i	0.379048	−	0.379048i	−0.491711	−	0.870759i	$-0.663628\pi$
$389$	7.47600	−	7.47600i	0.379048	−	0.379048i	0.870759	+	0.491711i	$0.163628\pi$
$390$	−8.86464	−	10.6264i	−0.448878	−	0.538091i
$391$			25.6396i			1.29665i
$392$	−6.97359	−	1.93326i	−0.352219	−	0.0976446i
$393$			35.4380i			1.78761i
$394$	−5.07463	+	4.23329i	−0.255656	+	0.213270i
$395$	22.8419	−	22.8419i	1.14930	−	1.14930i
$396$	−10.0562	−	14.5391i	−0.505342	−	0.730620i
$397$	−6.13080	−	6.13080i	−0.307696	−	0.307696i	0.536319	−	0.844015i	$-0.319814\pi$
$397$	−6.13080	−	6.13080i	−0.307696	−	0.307696i	−0.844015	+	0.536319i	$0.819814\pi$
$398$	2.79168	−	30.8848i	0.139934	−	1.54812i
$399$	−38.3805			−1.92143
$400$	7.25816	−	19.2491i	0.362908	−	0.962455i
$401$	37.9903			1.89715			0.948573	−	0.316560i	$-0.102528\pi$
$401$	37.9903			1.89715			0.948573	+	0.316560i	$0.102528\pi$
$402$	3.86926	−	42.8063i	0.192981	−	2.13498i
$403$	−2.93976	−	2.93976i	−0.146440	−	0.146440i
$404$	12.8828	−	8.91054i	0.640943	−	0.443316i
$405$	29.6252	−	29.6252i	1.47209	−	1.47209i
$406$	10.0143	−	8.35396i	0.496999	−	0.414600i
$407$		−	13.4467i		−	0.666526i
$408$	22.7983	+	40.2873i	1.12868	+	1.99452i
$409$		−	25.6645i		−	1.26903i	−0.772912	−	0.634514i	$-0.781200\pi$
$409$		−	25.6645i		−	1.26903i	0.772912	−	0.634514i	$-0.218800\pi$
$410$	28.6810	+	34.3812i	1.41645	+	1.69797i
$411$	−2.30770	+	2.30770i	−0.113831	+	0.113831i
$412$	−2.58390	+	14.1763i	−0.127300	+	0.698415i
$413$	4.12848	+	4.12848i	0.203149	+	0.203149i
$414$	43.6612	+	3.94653i	2.14583	+	0.193961i
$415$	−45.1494			−2.21630
$416$	−1.85805	−	5.34300i	−0.0910985	−	0.261962i
$417$	−70.6285			−3.45869
$418$	11.4581	+	1.03570i	0.560436	+	0.0506578i
$419$	−12.8767	−	12.8767i	−0.629068	−	0.629068i	0.318766	−	0.947834i	$-0.396732\pi$
$419$	−12.8767	−	12.8767i	−0.629068	−	0.629068i	−0.947834	+	0.318766i	$0.896732\pi$
$420$	7.39576	−	40.5760i	0.360876	−	1.97991i
$421$	5.33511	−	5.33511i	0.260017	−	0.260017i	−0.565044	−	0.825061i	$-0.691141\pi$
$421$	5.33511	−	5.33511i	0.260017	−	0.260017i	0.825061	+	0.565044i	$0.191141\pi$
$422$	−8.09204	−	9.70029i	−0.393915	−	0.472203i
$423$			3.40620i			0.165615i
$424$	0.843112	−	0.477111i	0.0409451	−	0.0231706i
$425$		−	27.3953i		−	1.32887i
$426$	−4.25402	+	3.54873i	−0.206108	+	0.171937i
$427$	12.0923	−	12.0923i	0.585189	−	0.585189i
$428$	1.46760	−	1.01508i	0.0709391	−	0.0490659i
$429$	2.98183	+	2.98183i	0.143964	+	0.143964i
$430$	−0.733942	+	8.11972i	−0.0353938	+	0.391568i
$431$	−17.6891			−0.852055			−0.426028	−	0.904710i	$-0.640087\pi$
$431$	−17.6891			−0.852055			−0.426028	+	0.904710i	$0.640087\pi$
$432$	38.5211	−	17.4256i	1.85335	−	0.838388i
$433$	24.1349			1.15985			0.579924	−	0.814671i	$-0.303082\pi$
$433$	24.1349			1.15985			0.579924	+	0.814671i	$0.303082\pi$
$434$	1.11547	−	12.3407i	0.0535444	−	0.592371i
$435$	−30.2760	−	30.2760i	−1.45162	−	1.45162i
$436$	18.3376	+	26.5124i	0.878212	+	1.26971i
$437$	−20.1741	+	20.1741i	−0.965057	+	0.965057i
$438$	−12.4582	+	10.3927i	−0.595276	+	0.496583i
$439$		−	29.8384i		−	1.42411i	−0.702125	−	0.712054i	$-0.747765\pi$
$439$		−	29.8384i		−	1.42411i	0.702125	−	0.712054i	$-0.252235\pi$
$440$	−3.30288	+	11.9140i	−0.157459	+	0.567979i
$441$			16.4773i			0.784632i
$442$	−4.82556	−	5.78461i	−0.229528	−	0.275146i
$443$	7.51004	−	7.51004i	0.356813	−	0.356813i	−0.505824	−	0.862637i	$-0.668811\pi$
$443$	7.51004	−	7.51004i	0.356813	−	0.356813i	0.862637	+	0.505824i	$0.168811\pi$
$444$	59.2282	+	10.7955i	2.81084	+	0.512330i
$445$	21.9720	+	21.9720i	1.04157	+	1.04157i
$446$	9.01666	+	0.815016i	0.426951	+	0.0385921i
$447$	−28.7304			−1.35890
$448$	8.68083	−	14.4533i	0.410131	−	0.682854i
$449$	3.69242			0.174256			0.0871281	−	0.996197i	$-0.472231\pi$
$449$	3.69242			0.174256			0.0871281	+	0.996197i	$0.472231\pi$
$450$	−46.6510	−	4.21678i	−2.19915	−	0.198781i
$451$	−9.64753	−	9.64753i	−0.454285	−	0.454285i
$452$	−26.9248	−	4.90756i	−1.26644	−	0.230832i
$453$	−6.43681	+	6.43681i	−0.302428	+	0.302428i
$454$	−5.41325	−	6.48910i	−0.254056	−	0.304549i
$455$			6.71192i			0.314660i
$456$	−13.7609	+	49.6379i	−0.644415	+	2.32451i
$457$			12.5264i			0.585962i	0.956118	+	0.292981i	$0.0946472\pi$
$457$			12.5264i			0.585962i	−0.956118	+	0.292981i	$0.905353\pi$
$458$	−29.4014	+	24.5268i	−1.37384	+	1.14606i
$459$	39.8117	−	39.8117i	1.85825	−	1.85825i
$460$	−17.4407	−	25.2156i	−0.813176	−	1.17568i
$461$	−6.50133	−	6.50133i	−0.302797	−	0.302797i	0.539310	−	0.842107i	$-0.318685\pi$
$461$	−6.50133	−	6.50133i	−0.302797	−	0.302797i	−0.842107	+	0.539310i	$0.818685\pi$
$462$	−1.13144	+	12.5173i	−0.0526392	+	0.582356i
$463$	−6.25758			−0.290814			−0.145407	−	0.989372i	$-0.546449\pi$
$463$	−6.25758			−0.290814			−0.145407	+	0.989372i	$0.546449\pi$
$464$	−7.21375	−	15.9468i	−0.334890	−	0.740311i
$465$	−40.6817			−1.88657
$466$	−1.37334	+	15.1935i	−0.0636186	+	0.703824i
$467$	25.9176	+	25.9176i	1.19932	+	1.19932i	0.974369	+	0.224956i	$0.0722238\pi$
$467$	25.9176	+	25.9176i	1.19932	+	1.19932i	0.224956	+	0.974369i	$0.427776\pi$
$468$	−10.5933	+	7.32697i	−0.489674	+	0.338689i
$469$	−14.7407	+	14.7407i	−0.680663	+	0.680663i
$470$	1.82925	−	1.52597i	0.0843770	−	0.0703878i
$471$		−	9.22697i		−	0.425157i
$472$	6.81963	−	3.85918i	0.313899	−	0.177633i
$473$		−	2.48438i		−	0.114232i
$474$	−28.2319	−	33.8429i	−1.29674	−	1.55446i
$475$	21.5556	−	21.5556i	0.989037	−	0.989037i
$476$	4.02596	−	22.0880i	0.184529	−	1.01240i
$477$	−1.55972	−	1.55972i	−0.0714146	−	0.0714146i
$478$	1.03239	+	0.0933181i	0.0472206	+	0.00426827i
$479$	28.9350			1.32207			0.661037	−	0.750353i	$-0.270117\pi$
$479$	28.9350			1.32207			0.661037	+	0.750353i	$0.270117\pi$
$480$	−49.8257	−	24.1131i	−2.27422	−	1.10061i
$481$	−9.79728			−0.446718
$482$	22.6656	+	2.04874i	1.03239	+	0.0933176i
$483$	−22.0389	−	22.0389i	−1.00280	−	1.00280i
$484$	−3.26937	+	17.9370i	−0.148608	+	0.815320i
$485$	−10.9724	+	10.9724i	−0.498232	+	0.498232i
$486$	−7.88989	−	9.45796i	−0.357893	−	0.429022i
$487$			15.4687i			0.700953i	0.936572	+	0.350477i	$0.113980\pi$
$487$			15.4687i			0.700953i	−0.936572	+	0.350477i	$0.886020\pi$
$488$	−11.3036	−	19.9747i	−0.511688	−	0.904214i
$489$		−	1.47786i		−	0.0668310i
$490$	8.84888	−	7.38179i	0.399751	−	0.333475i
$491$	−21.1392	+	21.1392i	−0.954000	+	0.954000i	−0.998988	−	0.0449878i	$-0.985675\pi$
$491$	−21.1392	+	21.1392i	−0.954000	+	0.954000i	0.0449878	+	0.998988i	$0.485675\pi$
$492$	50.2396	−	34.7489i	2.26498	−	1.56660i
$493$	−16.4810	−	16.4810i	−0.742269	−	0.742269i
$494$	0.754615	−	8.34844i	0.0339517	−	0.375614i
$495$	28.1506			1.26528
$496$	−15.5604	−	5.86727i	−0.698681	−	0.263448i
$497$	2.68695			0.120526
$498$	−5.54532	+	61.3488i	−0.248492	+	2.74911i
$499$	21.0952	+	21.0952i	0.944349	+	0.944349i	0.998531	−	0.0541823i	$-0.0172552\pi$
$499$	21.0952	+	21.0952i	0.944349	+	0.944349i	−0.0541823	+	0.998531i	$0.517255\pi$
$500$	0.518173	+	0.749170i	0.0231734	+	0.0335039i
$501$	24.5455	−	24.5455i	1.09661	−	1.09661i
$502$	23.9202	−	19.9544i	1.06761	−	0.890607i
$503$			32.7628i			1.46082i	0.683009	+	0.730410i	$0.260671\pi$
$503$			32.7628i			1.46082i	−0.683009	+	0.730410i	$0.739329\pi$
$504$	−36.9935	−	10.2556i	−1.64782	−	0.456820i
$505$			24.9436i			1.10998i
$506$	5.98478	+	7.17423i	0.266056	+	0.318933i
$507$	2.17257	−	2.17257i	0.0964874	−	0.0964874i
$508$	−13.6295	−	2.48424i	−0.604711	−	0.110220i
$509$	16.7060	+	16.7060i	0.740483	+	0.740483i	0.972671	−	0.232188i	$-0.0745885\pi$
$509$	16.7060	+	16.7060i	0.740483	+	0.740483i	−0.232188	+	0.972671i	$0.574589\pi$
$510$	−73.4142	−	6.63591i	−3.25084	−	0.293843i
$511$	7.86891			0.348100
$512$	−15.5802	−	16.4091i	−0.688553	−	0.725186i
$513$	62.6503			2.76608
$514$	−37.4906	−	3.38878i	−1.65364	−	0.149473i
$515$	−16.2255	−	16.2255i	−0.714980	−	0.714980i
$516$	10.9429	+	1.99455i	0.481734	+	0.0878053i
$517$	−0.513297	+	0.513297i	−0.0225748	+	0.0225748i
$518$	−18.7050	−	22.4225i	−0.821850	−	0.985188i
$519$			13.2063i			0.579690i
$520$	8.68060	+	2.40649i	0.380670	+	0.105532i
$521$		−	22.9611i		−	1.00595i	−0.864302	−	0.502973i	$-0.832240\pi$
$521$		−	22.9611i		−	1.00595i	0.864302	−	0.502973i	$-0.167760\pi$
$522$	−30.6021	+	25.5284i	−1.33942	+	1.11735i
$523$	12.0775	−	12.0775i	0.528112	−	0.528112i	−0.391897	−	0.920009i	$-0.628181\pi$
$523$	12.0775	−	12.0775i	0.528112	−	0.528112i	0.920009	+	0.391897i	$0.128181\pi$
$524$	−13.1222	−	18.9720i	−0.573248	−	0.828797i
$525$	23.5481	+	23.5481i	1.02772	+	1.02772i
$526$	−0.360254	+	3.98555i	−0.0157078	+	0.173778i
$527$	−22.1455			−0.964674
$528$	15.7831	+	5.95124i	0.686869	+	0.258995i
$529$	−0.168776			−0.00733807
$530$	−0.138873	+	1.53637i	−0.00603225	+	0.0667358i
$531$	−12.6160	−	12.6160i	−0.547489	−	0.547489i
$532$	20.5473	−	14.2118i	0.890839	−	0.616160i
$533$	−7.02923	+	7.02923i	−0.304470	+	0.304470i
$534$	32.5540	−	27.1568i	1.40875	−	1.17519i
$535$			2.84156i			0.122851i
$536$	13.7792	+	24.3495i	0.595170	+	1.05174i
$537$		−	23.4421i		−	1.01160i
$538$	−11.1419	−	13.3563i	−0.480362	−	0.575832i
$539$	−2.48304	+	2.48304i	−0.106952	+	0.106952i
$540$	−12.0725	+	66.2343i	−0.519516	+	2.85027i
$541$	−20.4582	−	20.4582i	−0.879567	−	0.879567i	0.113923	−	0.993490i	$-0.463658\pi$
$541$	−20.4582	−	20.4582i	−0.879567	−	0.879567i	−0.993490	+	0.113923i	$0.963658\pi$
$542$	26.4026	+	2.38653i	1.13409	+	0.102510i
$543$	32.3519			1.38835
$544$	−27.1232	−	13.1262i	−1.16290	−	0.562783i
$545$	−51.3331			−2.19887
$546$	9.12013	+	0.824368i	0.390305	+	0.0352797i
$547$	14.3574	+	14.3574i	0.613880	+	0.613880i	0.943955	−	0.330075i	$-0.107074\pi$
$547$	14.3574	+	14.3574i	0.613880	+	0.613880i	−0.330075	+	0.943955i	$0.607074\pi$
$548$	0.380936	−	2.08996i	0.0162728	−	0.0892788i
$549$	−36.9524	+	36.9524i	−1.57709	+	1.57709i
$550$	−6.39461	−	7.66551i	−0.272667	−	0.326858i
$551$		−	25.9357i		−	1.10490i
$552$	−36.4049	+	20.6013i	−1.54950	+	0.876849i
$553$			21.3760i			0.909001i
$554$	23.8737	−	19.9156i	1.01430	−	0.846131i
$555$	−67.7897	+	67.7897i	−2.87751	+	2.87751i
$556$	37.8116	−	26.1528i	1.60357	−	1.10913i
$557$	18.0279	+	18.0279i	0.763866	+	0.763866i	0.977019	−	0.213153i	$-0.0683734\pi$
$557$	18.0279	+	18.0279i	0.763866	+	0.763866i	−0.213153	+	0.977019i	$0.568373\pi$
$558$	−3.40872	+	37.7112i	−0.144302	+	1.59644i
$559$	−1.81013			−0.0765603
$560$	11.0654	+	24.4613i	0.467599	+	1.03368i
$561$	22.4625			0.948366
$562$	1.14652	−	12.6841i	0.0483630	−	0.535048i
$563$	−5.75900	−	5.75900i	−0.242713	−	0.242713i	0.575259	−	0.817972i	$-0.304901\pi$
$563$	−5.75900	−	5.75900i	−0.242713	−	0.242713i	−0.817972	+	0.575259i	$0.804901\pi$
$564$	−1.84881	−	2.67300i	−0.0778490	−	0.112554i
$565$	30.8168	−	30.8168i	1.29647	−	1.29647i
$566$	25.6523	−	21.3993i	1.07825	−	0.899480i
$567$			27.7240i			1.16430i
$568$	0.963379	−	3.47506i	0.0404225	−	0.145810i
$569$		−	16.2145i		−	0.679747i	−0.940471	−	0.339873i	$-0.889616\pi$
$569$		−	16.2145i		−	0.679747i	0.940471	−	0.339873i	$-0.110384\pi$
$570$	−52.5434	−	62.9861i	−2.20080	−	2.63820i
$571$	−16.6894	+	16.6894i	−0.698429	+	0.698429i	−0.964072	−	0.265643i	$-0.914416\pi$
$571$	−16.6894	+	16.6894i	−0.698429	+	0.698429i	0.265643	+	0.964072i	$0.414416\pi$
$572$	−2.70049	−	0.492215i	−0.112913	−	0.0205806i
$573$	18.7297	+	18.7297i	0.782445	+	0.782445i
$574$	−29.5076	−	2.66719i	−1.23162	−	0.111327i
$575$	24.7553			1.03237
$576$	−26.5273	+	44.1671i	−1.10531	+	1.84030i
$577$	16.8486			0.701418			0.350709	−	0.936484i	$-0.385941\pi$
$577$	16.8486			0.701418			0.350709	+	0.936484i	$0.385941\pi$
$578$	−16.0198	−	1.44803i	−0.666334	−	0.0602299i
$579$	25.0350	+	25.0350i	1.04042	+	1.04042i
$580$	27.4193	+	4.99770i	1.13853	+	0.207518i
$581$	21.1260	−	21.1260i	0.876454	−	0.876454i
$582$	13.5616	+	16.2569i	0.562147	+	0.673871i
$583$		−	0.470083i		−	0.0194688i
$584$	2.82132	−	10.1769i	0.116747	−	0.421125i
$585$		−	20.5106i		−	0.848011i
$586$	−2.77053	+	2.31119i	−0.114450	+	0.0954746i
$587$	−16.8873	+	16.8873i	−0.697015	+	0.697015i	−0.963766	−	0.266750i	$-0.914050\pi$
$587$	−16.8873	+	16.8873i	−0.697015	+	0.697015i	0.266750	+	0.963766i	$0.414050\pi$
$588$	−8.94350	−	12.9305i	−0.368824	−	0.533243i
$589$	−17.4248	−	17.4248i	−0.717978	−	0.717978i
$590$	−1.12329	+	12.4272i	−0.0462453	+	0.511620i
$591$	−14.3575			−0.590589
$592$	−35.7058	+	16.1520i	−1.46750	+	0.663843i
$593$	9.05420			0.371812			0.185906	−	0.982568i	$-0.440478\pi$
$593$	9.05420			0.371812			0.185906	+	0.982568i	$0.440478\pi$
$594$	1.84690	−	20.4326i	0.0757792	−	0.838359i
$595$	25.2808	+	25.2808i	1.03641	+	1.03641i
$596$	15.3811	−	10.6385i	0.630034	−	0.435770i
$597$	47.6400	−	47.6400i	1.94977	−	1.94977i
$598$	5.22717	−	4.36054i	0.213755	−	0.178316i
$599$			10.0219i			0.409483i	0.978816	+	0.204742i	$0.0656354\pi$
$599$			10.0219i			0.409483i	−0.978816	+	0.204742i	$0.934365\pi$
$600$	38.8979	−	22.0120i	1.58800	−	0.898638i
$601$			12.0888i			0.493113i	0.969128	+	0.246556i	$0.0792991\pi$
$601$			12.0888i			0.493113i	−0.969128	+	0.246556i	$0.920701\pi$
$602$	−3.45590	−	4.14275i	−0.140852	−	0.168846i
$603$	45.0454	−	45.0454i	1.83439	−	1.83439i
$604$	1.06253	−	5.82948i	0.0432339	−	0.237198i
$605$	−20.5299	−	20.5299i	−0.834657	−	0.834657i
$606$	33.8932	+	3.06361i	1.37682	+	0.124451i
$607$	42.6071			1.72937			0.864684	−	0.502316i	$-0.167518\pi$
$607$	42.6071			1.72937			0.864684	+	0.502316i	$0.167518\pi$
$608$	−11.0132	−	31.6696i	−0.446646	−	1.28437i
$609$	28.3330			1.14811
$610$	36.3993	+	3.29013i	1.47377	+	0.133214i
$611$	0.373990	+	0.373990i	0.0151300	+	0.0151300i
$612$	−12.3027	+	67.4976i	−0.497308	+	2.72843i
$613$	8.25930	−	8.25930i	0.333590	−	0.333590i	−0.520358	−	0.853948i	$-0.674202\pi$
$613$	8.25930	−	8.25930i	0.333590	−	0.333590i	0.853948	+	0.520358i	$0.174202\pi$
$614$	−0.156784	−	0.187944i	−0.00632728	−	0.00758479i
$615$			97.2737i			3.92245i
$616$	−4.02927	−	7.12019i	−0.162344	−	0.286881i
$617$		−	29.6176i		−	1.19236i	−0.802851	−	0.596180i	$-0.796685\pi$
$617$		−	29.6176i		−	1.19236i	0.802851	−	0.596180i	$-0.203315\pi$
$618$	−24.0399	+	20.0543i	−0.967028	+	0.806701i
$619$	10.6479	−	10.6479i	0.427975	−	0.427975i	−0.459963	−	0.887938i	$-0.652137\pi$
$619$	10.6479	−	10.6479i	0.427975	−	0.427975i	0.887938	+	0.459963i	$0.152137\pi$
$620$	21.7793	−	15.0639i	0.874679	−	0.604982i
$621$	35.9752	+	35.9752i	1.44363	+	1.44363i
$622$	−0.00231713	+	0.0256348i	−9.29084e−5	+	0.00102786i
$623$	−20.5619			−0.823797
$624$	4.33610	−	11.4996i	0.173583	−	0.460352i
$625$	24.2645			0.970580
$626$	−1.04077	+	11.5142i	−0.0415975	+	0.460200i
$627$	17.6742	+	17.6742i	0.705840	+	0.705840i
$628$	3.41663	+	4.93974i	0.136339	+	0.197117i
$629$	−36.9020	+	36.9020i	−1.47138	+	1.47138i
$630$	46.9416	−	39.1589i	1.87020	−	1.56013i
$631$			0.482730i			0.0192172i	0.999954	+	0.00960859i	$0.00305856\pi$
$631$			0.482730i			0.0192172i	−0.999954	+	0.00960859i	$0.996941\pi$
$632$	27.6458	+	7.66416i	1.09969	+	0.304864i
$633$		−	27.4448i		−	1.09083i
$634$	20.8590	+	25.0046i	0.828417	+	0.993061i
$635$	15.5996	−	15.5996i	0.619053	−	0.619053i
$636$	2.07056	+	0.377400i	0.0821031	+	0.0149649i
$637$	1.80915	+	1.80915i	0.0716812	+	0.0716812i
$638$	−8.45857	−	0.764570i	−0.334878	−	0.0302696i
$639$	−8.21091			−0.324819
$640$	35.6035	−	5.54066i	1.40735	−	0.219014i
$641$	−41.3538			−1.63338			−0.816688	−	0.577079i	$-0.804192\pi$
$641$	−41.3538			−1.63338			−0.816688	+	0.577079i	$0.804192\pi$
$642$	3.86109	+	0.349004i	0.152385	+	0.0137741i
$643$	5.83914	+	5.83914i	0.230273	+	0.230273i	0.812807	−	0.582534i	$-0.197939\pi$
$643$	5.83914	+	5.83914i	0.230273	+	0.230273i	−0.582534	+	0.812807i	$0.697939\pi$
$644$	19.9594	+	3.63799i	0.786512	+	0.143357i
$645$	−12.5247	+	12.5247i	−0.493160	+	0.493160i
$646$	−28.6025	−	34.2871i	−1.12535	−	1.34901i
$647$			5.51605i			0.216858i	0.994104	+	0.108429i	$0.0345820\pi$
$647$			5.51605i			0.216858i	−0.994104	+	0.108429i	$0.965418\pi$
$648$	35.8558	+	9.94017i	1.40855	+	0.390487i
$649$		−	3.80233i		−	0.149255i
$650$	−5.58512	+	4.65914i	−0.219066	+	0.182746i
$651$	19.0355	−	19.0355i	0.746061	−	0.746061i
$652$	0.547232	+	0.791184i	0.0214313	+	0.0309852i
$653$	14.8803	+	14.8803i	0.582312	+	0.582312i	0.935538	−	0.353226i	$-0.114915\pi$
$653$	14.8803	+	14.8803i	0.582312	+	0.582312i	−0.353226	+	0.935538i	$0.614915\pi$
$654$	−6.30481	+	69.7512i	−0.246537	+	2.72749i
$655$	36.7335			1.43530
$656$	−14.0292	+	37.2062i	−0.547747	+	1.45266i
$657$	−24.0462			−0.938132
$658$	−0.141908	+	1.56995i	−0.00553215	+	0.0612031i
$659$	6.83395	+	6.83395i	0.266213	+	0.266213i	0.827572	−	0.561359i	$-0.189721\pi$
$659$	6.83395	+	6.83395i	0.266213	+	0.266213i	−0.561359	+	0.827572i	$0.689721\pi$
$660$	−22.0910	+	15.2795i	−0.859892	+	0.594755i
$661$	29.5201	−	29.5201i	1.14820	−	1.14820i	0.161291	−	0.986907i	$-0.448434\pi$
$661$	29.5201	−	29.5201i	1.14820	−	1.14820i	0.986907	−	0.161291i	$-0.0515658\pi$
$662$	−12.0153	+	10.0232i	−0.466987	+	0.389563i
$663$		−	16.3662i		−	0.635612i
$664$	−19.7480	−	34.8970i	−0.766370	−	1.35427i
$665$			39.7836i			1.54274i
$666$	57.1597	+	68.5198i	2.21489	+	2.65509i
$667$	14.8928	−	14.8928i	0.576652	−	0.576652i
$668$	−4.05176	+	22.2296i	−0.156767	+	0.860087i
$669$	13.9082	+	13.9082i	0.537724	+	0.537724i
$670$	−44.3712	−	4.01071i	−1.71421	−	0.154947i
$671$	−11.1371			−0.429941
$672$	34.5970	−	12.0313i	1.33461	−	0.464116i
$673$	−28.7023			−1.10639			−0.553196	−	0.833051i	$-0.686592\pi$
$673$	−28.7023			−1.10639			−0.553196	+	0.833051i	$0.686592\pi$
$674$	−17.7762	−	1.60679i	−0.684713	−	0.0618912i
$675$	−38.4387	−	38.4387i	−1.47951	−	1.47951i
$676$	−0.358630	+	1.96758i	−0.0137935	+	0.0756763i
$677$	−26.6965	+	26.6965i	−1.02603	+	1.02603i	−0.0263779	+	0.999652i	$0.508397\pi$
$677$	−26.6965	+	26.6965i	−1.02603	+	1.02603i	−0.999652	+	0.0263779i	$0.991603\pi$
$678$	−38.0888	−	45.6587i	−1.46279	−	1.75351i
$679$		−	10.2683i		−	0.394060i
$680$	41.7602	−	23.6318i	1.60143	−	0.906237i
$681$		−	18.3594i		−	0.703534i
$682$	−6.19655	+	5.16920i	−0.237278	+	0.197939i
$683$	−23.9019	+	23.9019i	−0.914579	+	0.914579i	−0.996628	−	0.0820492i	$-0.973854\pi$
$683$	−23.9019	+	23.9019i	−0.914579	+	0.914579i	0.0820492	+	0.996628i	$0.473854\pi$
$684$	−62.7896	+	43.4292i	−2.40082	+	1.66056i
$685$	2.39207	+	2.39207i	0.0913963	+	0.0913963i
$686$	−2.56462	+	28.3728i	−0.0979176	+	1.08328i
$687$	−83.1845			−3.17369
$688$	−6.59694	+	2.98422i	−0.251506	+	0.113772i
$689$	−0.342504			−0.0130484
$690$	5.99643	−	66.3395i	0.228280	−	2.52550i
$691$	−20.6492	−	20.6492i	−0.785531	−	0.785531i	0.195227	−	0.980758i	$-0.437456\pi$
$691$	−20.6492	−	20.6492i	−0.785531	−	0.785531i	−0.980758	+	0.195227i	$0.937456\pi$
$692$	−4.89011	−	7.07009i	−0.185894	−	0.268764i
$693$	−13.1720	+	13.1720i	−0.500364	+	0.500364i
$694$	−28.4693	+	23.7492i	−1.08068	+	0.901508i
$695$			73.2106i			2.77704i
$696$	10.1585	−	36.6434i	0.385058	−	1.38897i
$697$			52.9519i			2.00570i
$698$	8.65132	+	10.3707i	0.327457	+	0.392538i
$699$	−23.4360	+	23.4360i	−0.886430	+	0.886430i
$700$	−21.3262	−	3.88711i	−0.806056	−	0.146919i
$701$	−6.84513	−	6.84513i	−0.258537	−	0.258537i	0.565922	−	0.824459i	$-0.308520\pi$
$701$	−6.84513	−	6.84513i	−0.258537	−	0.258537i	−0.824459	+	0.565922i	$0.808520\pi$
$702$	−14.8872	−	1.34566i	−0.561883	−	0.0507886i
$703$	−58.0715			−2.19021
$704$	−10.6533	+	2.65822i	−0.401510	+	0.100185i
$705$	5.17544			0.194918
$706$	38.9063	+	3.51674i	1.46426	+	0.132354i
$707$	−11.6714	−	11.6714i	−0.438949	−	0.438949i
$708$	16.7480	+	3.05265i	0.629430	+	0.114726i
$709$	−3.86607	+	3.86607i	−0.145193	+	0.145193i	−0.775967	−	0.630774i	$-0.782738\pi$
$709$	−3.86607	+	3.86607i	−0.145193	+	0.145193i	0.630774	+	0.775967i	$0.282738\pi$
$710$	3.67847	+	4.40955i	0.138051	+	0.165487i
$711$		−	65.3219i		−	2.44976i
$712$	−7.37228	+	26.5930i	−0.276288	+	0.996614i
$713$		−	20.0114i		−	0.749434i
$714$	37.4565	−	31.2464i	1.40177	−	1.16937i
$715$	3.09084	−	3.09084i	0.115591	−	0.115591i
$716$	8.68031	+	12.5499i	0.324398	+	0.469013i
$717$	1.59247	+	1.59247i	0.0594720	+	0.0594720i
$718$	−1.44948	+	16.0358i	−0.0540940	+	0.598452i
$719$	51.8131			1.93230			0.966151	−	0.257976i	$-0.0830557\pi$
$719$	51.8131			1.93230			0.966151	+	0.257976i	$0.0830557\pi$
$720$	−33.8143	−	74.7501i	−1.26018	−	2.78577i
$721$	15.1842			0.565490
$722$	2.05391	−	22.7228i	0.0764386	−	0.845654i
$723$	34.9617	+	34.9617i	1.30024	+	1.30024i
$724$	−17.3199	+	11.9795i	−0.643689	+	0.445215i
$725$	−15.9127	+	15.9127i	−0.590981	+	0.590981i
$726$	−30.4174	+	25.3744i	−1.12889	+	0.941731i
$727$		−	22.7810i		−	0.844901i	−0.906386	−	0.422450i	$-0.861170\pi$
$727$		−	22.7810i		−	0.844901i	0.906386	−	0.422450i	$-0.138830\pi$
$728$	−5.18780	+	2.93574i	−0.192273	+	0.108806i
$729$			12.7060i			0.470593i
$730$	10.7726	+	12.9137i	0.398714	+	0.477956i
$731$	−6.81795	+	6.81795i	−0.252171	+	0.252171i
$732$	8.94124	−	49.0551i	0.330478	−	1.81313i
$733$	−27.2233	−	27.2233i	−1.00552	−	1.00552i	−0.999985	−	0.00553157i	$-0.998239\pi$
$733$	−27.2233	−	27.2233i	−1.00552	−	1.00552i	−0.00553157	−	0.999985i	$-0.501761\pi$
$734$	6.02930	+	0.544988i	0.222545	+	0.0201159i
$735$	25.0359			0.923462
$736$	11.8613	−	24.5094i	0.437214	−	0.903428i
$737$	13.5762			0.500086
$738$	90.1709	+	8.15055i	3.31924	+	0.300026i
$739$	−25.0118	−	25.0118i	−0.920073	−	0.920073i	0.0769614	−	0.997034i	$-0.475478\pi$
$739$	−25.0118	−	25.0118i	−0.920073	−	0.920073i	−0.997034	+	0.0769614i	$0.975478\pi$
$740$	11.1901	−	61.3935i	0.411358	−	2.25687i
$741$	12.8775	−	12.8775i	0.473067	−	0.473067i
$742$	−0.653909	−	0.783870i	−0.0240058	−	0.0287768i
$743$		−	29.8672i		−	1.09572i	−0.836570	−	0.547860i	$-0.815443\pi$
$743$		−	29.8672i		−	1.09572i	0.836570	−	0.547860i	$-0.184557\pi$
$744$	−17.7938	−	31.4438i	−0.652354	−	1.15279i
$745$			29.7808i			1.09108i
$746$	18.5818	−	15.5011i	0.680329	−	0.567535i
$747$	−64.5579	+	64.5579i	−2.36205	+	2.36205i
$748$	−12.0255	+	8.31757i	−0.439695	+	0.304120i
$749$	−1.32960	−	1.32960i	−0.0485826	−	0.0485826i
$750$	−0.178157	+	1.97099i	−0.00650539	+	0.0719702i
$751$	25.9522			0.947009			0.473505	−	0.880791i	$-0.342989\pi$
$751$	25.9522			0.947009			0.473505	+	0.880791i	$0.342989\pi$
$752$	1.97956	+	0.746422i	0.0721870	+	0.0272192i
$753$	67.6767			2.46627
$754$	−0.557069	+	6.16295i	−0.0202872	+	0.224441i
$755$	6.67213	+	6.67213i	0.242824	+	0.242824i
$756$	−25.3430	−	36.6408i	−0.921717	−	1.33261i
$757$	18.1373	−	18.1373i	0.659212	−	0.659212i	−0.295981	−	0.955194i	$-0.595647\pi$
$757$	18.1373	−	18.1373i	0.659212	−	0.659212i	0.955194	+	0.295981i	$0.0956466\pi$
$758$	−4.27862	+	3.56925i	−0.155406	+	0.129641i
$759$			20.2978i			0.736764i
$760$	51.4526	+	14.2640i	1.86638	+	0.517410i
$761$		−	21.2499i		−	0.770307i	−0.922853	−	0.385153i	$-0.874149\pi$
$761$		−	21.2499i		−	0.770307i	0.922853	−	0.385153i	$-0.125851\pi$
$762$	−19.2808	−	23.1127i	−0.698468	−	0.837285i
$763$	24.0194	−	24.0194i	0.869562	−	0.869562i
$764$	−16.9625	−	3.09174i	−0.613681	−	0.111855i
$765$	−77.2544	−	77.2544i	−2.79314	−	2.79314i
$766$	−38.0802	−	3.44207i	−1.37589	−	0.124367i
$767$	−2.77039			−0.100033
$768$	−3.15575	−	49.0583i	−0.113873	−	1.77024i
$769$	14.8930			0.537055			0.268527	−	0.963272i	$-0.413463\pi$
$769$	14.8930			0.537055			0.268527	+	0.963272i	$0.413463\pi$
$770$	12.9749	+	1.17280i	0.467583	+	0.0422648i
$771$	−57.8294	−	57.8294i	−2.08268	−	2.08268i
$772$	−22.6728	−	4.13256i	−0.816014	−	0.148734i
$773$	10.2923	−	10.2923i	0.370188	−	0.370188i	−0.497358	−	0.867545i	$-0.665696\pi$
$773$	10.2923	−	10.2923i	0.370188	−	0.370188i	0.867545	+	0.497358i	$0.165696\pi$
$774$	10.5607	+	12.6596i	0.379597	+	0.455040i
$775$			21.3818i			0.768056i
$776$	−13.2801	−	3.68159i	−0.476727	−	0.132161i
$777$		−	63.4393i		−	2.27587i
$778$	−11.4815	+	9.57795i	−0.411632	+	0.343386i
$779$	−41.6644	+	41.6644i	−1.49278	+	1.49278i
$780$	11.1327	+	16.0956i	0.398615	+	0.576315i
$781$	−1.23734	−	1.23734i	−0.0442755	−	0.0442755i
$782$	3.26422	−	36.1126i	0.116728	−	1.29138i
$783$	−46.2495			−1.65282
$784$	9.57597	+	3.61077i	0.341999	+	0.128956i
$785$	−9.56430			−0.341365
$786$	4.51167	−	49.9134i	0.160926	−	1.78035i
$787$	35.3458	+	35.3458i	1.25994	+	1.25994i	0.951120	+	0.308821i	$0.0999346\pi$
$787$	35.3458	+	35.3458i	1.25994	+	1.25994i	0.308821	+	0.951120i	$0.400065\pi$
$788$	7.68642	−	5.31640i	0.273817	−	0.189389i
$789$	−6.14773	+	6.14773i	−0.218865	+	0.218865i
$790$	−35.0802	+	29.2641i	−1.24810	+	1.04117i
$791$			28.8392i			1.02540i
$792$	12.3128	+	21.7582i	0.437518	+	0.773145i
$793$			8.11450i			0.288154i
$794$	7.85453	+	9.41558i	0.278747	+	0.334146i
$795$	−2.36986	+	2.36986i	−0.0840504	+	0.0840504i
$796$	−7.86400	+	43.1450i	−0.278732	+	1.52923i
$797$	2.67413	+	2.67413i	0.0947224	+	0.0947224i	0.752880	−	0.658158i	$-0.228664\pi$
$797$	2.67413	+	2.67413i	0.0947224	+	0.0947224i	−0.658158	+	0.752880i	$0.728664\pi$
$798$	54.0578	+	4.88628i	1.91362	+	0.172972i
$799$	2.81731			0.0996691
$800$	−12.6736	+	26.1878i	−0.448078	+	0.925877i
$801$	62.8342			2.22014
$802$	−53.5083	−	4.83661i	−1.88944	−	0.170787i
$803$	−3.62364	−	3.62364i	−0.127875	−	0.127875i
$804$	−10.8995	+	59.7988i	−0.384395	+	2.10894i
$805$	−22.8446	+	22.8446i	−0.805166	+	0.805166i
$806$	3.76630	+	4.51483i	0.132662	+	0.159028i
$807$		−	37.7886i		−	1.33022i
$808$	−19.2795	+	10.9101i	−0.678249	+	0.383816i
$809$			35.1719i			1.23658i	0.785951	+	0.618288i	$0.212174\pi$
$809$			35.1719i			1.23658i	−0.785951	+	0.618288i	$0.787826\pi$
$810$	−45.4978	+	37.9546i	−1.59863	+	1.33359i
$811$	22.3671	−	22.3671i	0.785415	−	0.785415i	−0.195324	−	0.980739i	$-0.562576\pi$
$811$	22.3671	−	22.3671i	0.785415	−	0.785415i	0.980739	+	0.195324i	$0.0625758\pi$
$812$	−15.1684	+	10.4914i	−0.532305	+	0.368175i
$813$	40.7262	+	40.7262i	1.42833	+	1.42833i
$814$	−1.71192	+	18.9392i	−0.0600027	+	0.663820i
$815$	−1.53189			−0.0536596
$816$	−26.9817	−	59.6460i	−0.944548	−	2.08803i
$817$	−10.7292			−0.375367
$818$	−3.26739	+	36.1477i	−0.114242	+	1.26387i
$819$	9.59720	+	9.59720i	0.335353	+	0.335353i
$820$	−36.0192	−	52.0764i	−1.25785	−	1.81859i
$821$	18.1445	−	18.1445i	0.633248	−	0.633248i	−0.315633	−	0.948881i	$-0.602217\pi$
$821$	18.1445	−	18.1445i	0.633248	−	0.633248i	0.948881	+	0.315633i	$0.102217\pi$
$822$	3.54413	−	2.95653i	0.123616	−	0.103121i
$823$		−	22.5033i		−	0.784416i	−0.919876	−	0.392208i	$-0.871711\pi$
$823$		−	22.5033i		−	0.784416i	0.919876	−	0.392208i	$-0.128289\pi$
$824$	5.44415	−	19.6379i	0.189656	−	0.684119i
$825$		−	21.6878i		−	0.755072i
$826$	−5.28924	−	6.34045i	−0.184036	−	0.220612i
$827$	−5.03676	+	5.03676i	−0.175145	+	0.175145i	−0.789236	−	0.614090i	$-0.789523\pi$
$827$	−5.03676	+	5.03676i	−0.175145	+	0.175145i	0.614090	+	0.789236i	$0.289523\pi$
$828$	−60.9931	−	11.1172i	−2.11966	−	0.386348i
$829$	−29.9034	−	29.9034i	−1.03859	−	1.03859i	−0.999225	−	0.0393644i	$-0.987467\pi$
$829$	−29.9034	−	29.9034i	−1.03859	−	1.03859i	−0.0393644	−	0.999225i	$-0.512533\pi$
$830$	63.5917	+	5.74805i	2.20730	+	0.199518i
$831$	67.5451			2.34311
$832$	1.93679	+	7.76201i	0.0671460	+	0.269099i
$833$	13.6285			0.472201
$834$	99.4782	+	8.99183i	3.44465	+	0.311362i
$835$	−25.4429	−	25.4429i	−0.880486	−	0.880486i
$836$	−16.0066	−	2.91751i	−0.553600	−	0.100904i
$837$	−31.0726	+	31.0726i	−1.07403	+	1.07403i
$838$	16.4971	+	19.7758i	0.569883	+	0.683144i
$839$			24.7130i			0.853188i	0.904443	+	0.426594i	$0.140287\pi$
$839$			24.7130i			0.853188i	−0.904443	+	0.426594i	$0.859713\pi$
$840$	−15.5825	+	56.2086i	−0.537648	+	1.93938i
$841$		−	9.85388i		−	0.339789i
$842$	−8.19357	+	6.83513i	−0.282369	+	0.235554i
$843$	19.5653	−	19.5653i	0.673866	−	0.673866i
$844$	10.1625	+	14.6928i	0.349806	+	0.505747i
$845$	−2.25200	−	2.25200i	−0.0774712	−	0.0774712i
$846$	0.433649	−	4.79754i	0.0149092	−	0.164943i
$847$	19.2124			0.660145
$848$	−1.24824	+	0.564659i	−0.0428648	+	0.0193905i
$849$	72.5773			2.49085
$850$	−3.48775	+	38.5855i	−0.119629	+	1.32347i
$851$	−33.3459	−	33.3459i	−1.14308	−	1.14308i
$852$	6.44347	−	4.45670i	0.220750	−	0.152684i
$853$	−11.7189	+	11.7189i	−0.401247	+	0.401247i	−0.878672	−	0.477425i	$-0.841570\pi$
$853$	−11.7189	+	11.7189i	−0.401247	+	0.401247i	0.477425	+	0.878672i	$0.341570\pi$
$854$	−18.5712	+	15.4922i	−0.635494	+	0.530133i
$855$		−	121.573i		−	4.15770i
$856$	−2.19630	+	1.24287i	−0.0750681	+	0.0424805i
$857$		−	18.1025i		−	0.618371i	−0.951002	−	0.309186i	$-0.899944\pi$
$857$		−	18.1025i		−	0.618371i	0.951002	−	0.309186i	$-0.100056\pi$
$858$	−3.82020	−	4.57945i	−0.130420	−	0.156340i
$859$	−34.1865	+	34.1865i	−1.16643	+	1.16643i	−0.183389	+	0.983040i	$0.558707\pi$
$859$	−34.1865	+	34.1865i	−1.16643	+	1.16643i	−0.983040	+	0.183389i	$0.941293\pi$
$860$	2.06747	−	11.3430i	0.0705002	−	0.386792i
$861$	−45.5156	−	45.5156i	−1.55117	−	1.55117i
$862$	24.9146	+	2.25203i	0.848596	+	0.0767045i
$863$	9.58703			0.326346			0.163173	−	0.986597i	$-0.447827\pi$
$863$	9.58703			0.326346			0.163173	+	0.986597i	$0.447827\pi$
$864$	−56.4744	+	19.6392i	−1.92130	+	0.668140i
$865$	13.6891			0.465442
$866$	−33.9933	−	3.07265i	−1.15514	−	0.104413i
$867$	−24.7105	−	24.7105i	−0.839214	−	0.839214i
$868$	−3.14222	+	17.2395i	−0.106654	+	0.585145i
$869$	9.84367	−	9.84367i	0.333923	−	0.333923i
$870$	38.7884	+	46.4973i	1.31505	+	1.57641i
$871$		−	9.89167i		−	0.335167i
$872$	−22.4527	−	39.6765i	−0.760343	−	1.34362i
$873$			31.3783i			1.06200i
$874$	30.9830	−	25.8462i	1.04802	−	0.874261i
$875$	0.678726	−	0.678726i	0.0229451	−	0.0229451i
$876$	18.8701	−	13.0518i	0.637562	−	0.440978i
$877$	28.0650	+	28.0650i	0.947689	+	0.947689i	0.998698	−	0.0510094i	$-0.0162438\pi$
$877$	28.0650	+	28.0650i	0.947689	+	0.947689i	−0.0510094	+	0.998698i	$0.516244\pi$
$878$	−3.79877	+	42.0265i	−0.128202	+	1.41833i
$879$	−7.83858			−0.264389
$880$	6.16881	−	16.3601i	0.207951	−	0.551498i
$881$	−16.5130			−0.556336			−0.278168	−	0.960532i	$-0.589727\pi$
$881$	−16.5130			−0.556336			−0.278168	+	0.960532i	$0.589727\pi$
$882$	2.09775	−	23.2078i	0.0706349	−	0.781447i
$883$	−29.7641	−	29.7641i	−1.00164	−	1.00164i	−0.999999	−	0.00164200i	$-0.999477\pi$
$883$	−29.7641	−	29.7641i	−1.00164	−	1.00164i	−0.00164200	−	0.999999i	$-0.500523\pi$
$884$	6.06021	+	8.76181i	0.203827	+	0.294692i
$885$	−19.1690	+	19.1690i	−0.644359	+	0.644359i
$886$	−11.5338	+	9.62156i	−0.387485	+	0.323243i
$887$		−	36.9810i		−	1.24170i	−0.783929	−	0.620850i	$-0.786788\pi$
$887$		−	36.9810i		−	1.24170i	0.783929	−	0.620850i	$-0.213212\pi$
$888$	−82.0468	−	22.7455i	−2.75331	−	0.763291i
$889$			14.5986i			0.489620i
$890$	−28.1496	−	33.7442i	−0.943577	−	1.13111i
$891$	12.7669	−	12.7669i	0.427708	−	0.427708i
$892$	−12.5959	−	2.29585i	−0.421744	−	0.0768709i
$893$	2.21675	+	2.21675i	0.0741807	+	0.0741807i
$894$	40.4660	+	3.65772i	1.35338	+	0.122332i
$895$	−24.2991			−0.812229
$896$	−14.0668	+	19.2519i	−0.469938	+	0.643160i
$897$	14.7891			0.493793
$898$	−5.20067	−	0.470089i	−0.173549	−	0.0156871i
$899$	12.8633	+	12.8633i	0.429015	+	0.429015i
$900$	65.1698	+	11.8784i	2.17233	+	0.395948i
$901$	−1.29006	+	1.29006i	−0.0429781	+	0.0429781i
$902$	12.3600	+	14.8165i	0.411544	+	0.493336i
$903$		−	11.7209i		−	0.390049i
$904$	37.2980	+	10.3400i	1.24051	+	0.343903i
$905$		−	33.5347i		−	1.11473i
$906$	9.88555	−	8.24658i	0.328425	−	0.273974i
$907$	33.0589	−	33.0589i	1.09770	−	1.09770i	0.103023	−	0.994679i	$-0.467148\pi$
$907$	33.0589	−	33.0589i	1.09770	−	1.09770i	0.994679	−	0.103023i	$-0.0328516\pi$
$908$	6.79826	+	9.82888i	0.225608	+	0.326183i
$909$	35.6662	+	35.6662i	1.18297	+	1.18297i
$910$	0.854506	−	9.45355i	0.0283266	−	0.313382i
$911$	57.4072			1.90199			0.950993	−	0.309212i	$-0.100065\pi$
$911$	57.4072			1.90199			0.950993	+	0.309212i	$0.100065\pi$
$912$	25.7014	−	68.1616i	0.851057	−	2.25706i
$913$	−19.4571			−0.643935
$914$	1.59476	−	17.6431i	0.0527500	−	0.583582i
$915$	56.1461	+	56.1461i	1.85613	+	1.85613i
$916$	44.5336	−	30.8022i	1.47143	−	1.01773i
$917$	−17.1881	+	17.1881i	−0.567601	+	0.567601i
$918$	−61.1421	+	51.0051i	−2.01799	+	1.68342i
$919$			50.5966i			1.66903i	0.550987	+	0.834514i	$0.314251\pi$
$919$			50.5966i			1.66903i	−0.550987	+	0.834514i	$0.685749\pi$
$920$	21.3545	+	37.7359i	0.704036	+	1.24411i
$921$		−	0.531743i		−	0.0175215i
$922$	8.32925	+	9.98464i	0.274309	+	0.328826i
$923$	−0.901531	+	0.901531i	−0.0296743	+	0.0296743i
$924$	3.18719	−	17.4862i	0.104851	−	0.575253i
$925$	35.6294	+	35.6294i	1.17149	+	1.17149i
$926$	8.81362	+	0.796663i	0.289633	+	0.0261800i
$927$	−46.4007			−1.52400
$928$	8.13015	+	23.3790i	0.266885	+	0.767452i
$929$	−36.1591			−1.18634			−0.593171	−	0.805076i	$-0.702124\pi$
$929$	−36.1591			−1.18634			−0.593171	+	0.805076i	$0.702124\pi$
$930$	57.2991	+	5.17926i	1.87891	+	0.169835i
$931$	10.7234	+	10.7234i	0.351445	+	0.351445i
$932$	3.86861	−	21.2247i	0.126721	−	0.695239i
$933$	−0.0395418	+	0.0395418i	−0.00129454	+	0.00129454i
$934$	−33.2046	−	39.8039i	−1.08649	−	1.30242i
$935$		−	23.2837i		−	0.761457i
$936$	15.8531	−	8.97118i	0.518176	−	0.293232i
$937$		−	13.2813i		−	0.433880i	−0.976185	−	0.216940i	$-0.930392\pi$
$937$		−	13.2813i		−	0.433880i	0.976185	−	0.216940i	$-0.0696075\pi$
$938$	22.6385	−	18.8852i	0.739174	−	0.616624i
$939$	−17.7607	+	17.7607i	−0.579599	+	0.579599i
$940$	−2.77072	+	1.91640i	−0.0903709	+	0.0625061i
$941$	2.51043	+	2.51043i	0.0818377	+	0.0818377i	0.746841	−	0.665003i	$-0.231570\pi$
$941$	2.51043	+	2.51043i	0.0818377	+	0.0818377i	−0.665003	+	0.746841i	$0.731570\pi$
$942$	−1.17470	+	12.9959i	−0.0382739	+	0.423430i
$943$	−47.8491			−1.55818
$944$	−10.0966	+	4.56733i	−0.328616	+	0.148654i
$945$	70.9436			2.30780
$946$	−0.316291	+	3.49918i	−0.0102835	+	0.113768i
$947$	−22.6495	−	22.6495i	−0.736009	−	0.736009i	0.235794	−	0.971803i	$-0.424231\pi$
$947$	−22.6495	−	22.6495i	−0.736009	−	0.736009i	−0.971803	+	0.235794i	$0.924231\pi$
$948$	35.4553	+	51.2610i	1.15153	+	1.66488i
$949$	−2.64019	+	2.64019i	−0.0857043	+	0.0857043i
$950$	−33.1047	+	27.6161i	−1.07406	+	0.895985i
$951$			70.7448i			2.29406i
$952$	−8.48250	+	30.5977i	−0.274920	+	0.991678i
$953$			50.2836i			1.62884i	0.580273	+	0.814422i	$0.302946\pi$
$953$			50.2836i			1.62884i	−0.580273	+	0.814422i	$0.697054\pi$
$954$	1.99825	+	2.39539i	0.0646957	+	0.0775536i
$955$	19.4144	−	19.4144i	0.628237	−	0.628237i
$956$	−1.44222	−	0.262872i	−0.0466446	−	0.00850188i
$957$	−13.0474	−	13.0474i	−0.421762	−	0.421762i
$958$	−40.7541	−	3.68376i	−1.31671	−	0.119017i
$959$	−2.23856			−0.0722869
$960$	67.1082	+	40.3061i	2.16591	+	1.30087i
$961$	−13.7156			−0.442440
$962$	13.7992	+	1.24731i	0.444904	+	0.0402149i
$963$	4.06306	+	4.06306i	0.130930	+	0.130930i
$964$	−31.6630	−	5.77118i	−1.01980	−	0.185877i
$965$	25.9502	−	25.9502i	0.835368	−	0.835368i
$966$	28.2353	+	33.8469i	0.908457	+	1.08901i
$967$			9.82663i			0.316003i	0.987439	+	0.158002i	$0.0505051\pi$
$967$			9.82663i			0.316003i	−0.987439	+	0.158002i	$0.949495\pi$
$968$	6.88841	−	24.8476i	0.221402	−	0.798631i
$969$		−	97.0076i		−	3.11633i
$970$	16.8513	−	14.0574i	0.541061	−	0.451357i
$971$	−29.7421	+	29.7421i	−0.954470	+	0.954470i	−0.999008	−	0.0445373i	$-0.985819\pi$
$971$	−29.7421	+	29.7421i	−0.954470	+	0.954470i	0.0445373	+	0.999008i	$0.485819\pi$
$972$	9.90857	+	14.3257i	0.317818	+	0.459498i
$973$	−34.2562	−	34.2562i	−1.09820	−	1.09820i
$974$	1.96934	−	21.7872i	0.0631019	−	0.698107i
$975$	−15.8018			−0.506063
$976$	13.3777	+	29.5729i	0.428211	+	0.946606i
$977$	4.18274			0.133818			0.0669089	−	0.997759i	$-0.478686\pi$
$977$	4.18274			0.133818			0.0669089	+	0.997759i	$0.478686\pi$
$978$	−0.188149	+	2.08152i	−0.00601633	+	0.0665597i
$979$	9.46878	+	9.46878i	0.302624	+	0.302624i
$980$	−13.4032	+	9.27047i	−0.428149	+	0.296134i
$981$	−73.3998	+	73.3998i	−2.34348	+	2.34348i
$982$	32.4653	−	27.0827i	1.03601	−	0.864244i
$983$			29.1666i			0.930270i	0.885240	+	0.465135i	$0.153994\pi$
$983$			29.1666i			0.930270i	−0.885240	+	0.465135i	$0.846006\pi$
$984$	−75.1850	+	42.5467i	−2.39681	+	1.35634i
$985$			14.8824i			0.474192i
$986$	21.1148	+	25.3113i	0.672434	+	0.806076i
$987$	−2.42166	+	2.42166i	−0.0770822	+	0.0770822i
$988$	−2.12571	+	11.6625i	−0.0676278	+	0.371032i
$989$	−6.16093	−	6.16093i	−0.195906	−	0.195906i
$990$	−39.6493	−	3.58390i	−1.26014	−	0.113904i
$991$	12.2046			0.387691			0.193845	−	0.981032i	$-0.437904\pi$
$991$	12.2046			0.387691			0.193845	+	0.981032i	$0.437904\pi$
$992$	21.1694	+	10.2449i	0.672128	+	0.325276i
$993$	−33.9945			−1.07878
$994$	−3.78449	−	0.342080i	−0.120037	−	0.0108501i
$995$	−49.3816	−	49.3816i	−1.56550	−	1.56550i
$996$	15.6208	−	85.7021i	0.494966	−	2.71557i
$997$	23.7017	−	23.7017i	0.750641	−	0.750641i	−0.223958	−	0.974599i	$-0.571898\pi$
$997$	23.7017	−	23.7017i	0.750641	−	0.750641i	0.974599	+	0.223958i	$0.0718978\pi$
$998$	−27.0263	−	32.3976i	−0.855501	−	1.02553i
$999$			103.555i			3.27634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.2	yes	48
4.3	odd	2		832.2.n.a.209.24		48
8.3	odd	2		1664.2.n.a.417.1		48
8.5	even	2		1664.2.n.b.417.24		48
16.3	odd	4		1664.2.n.a.1249.1		48
16.5	even	4	inner	208.2.n.a.53.2	✓	48
16.11	odd	4		832.2.n.a.625.24		48
16.13	even	4		1664.2.n.b.1249.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.2	✓	48	16.5	even	4	inner
208.2.n.a.157.2	yes	48	1.1	even	1	trivial
832.2.n.a.209.24		48	4.3	odd	2
832.2.n.a.625.24		48	16.11	odd	4
1664.2.n.a.417.1		48	8.3	odd	2
1664.2.n.a.1249.1		48	16.3	odd	4
1664.2.n.b.417.24		48	8.5	even	2
1664.2.n.b.1249.24		48	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40847 - 0.127312i) q^{2} +(-2.17257 - 2.17257i) q^{3} +(1.96758 + 0.358630i) q^{4} +(-2.25200 + 2.25200i) q^{5} +(2.78341 + 3.33660i) q^{6} -2.10748i q^{7} +(-2.72563 - 0.755616i) q^{8} +6.44015i q^{9} +O(q^{10})\)	\(q+(-1.40847 - 0.127312i) q^{2} +(-2.17257 - 2.17257i) q^{3} +(1.96758 + 0.358630i) q^{4} +(-2.25200 + 2.25200i) q^{5} +(2.78341 + 3.33660i) q^{6} -2.10748i q^{7} +(-2.72563 - 0.755616i) q^{8} +6.44015i q^{9} +(3.45858 - 2.88517i) q^{10} +(-0.970496 + 0.970496i) q^{11} +(-3.49557 - 5.05387i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.268307 + 2.96833i) q^{14} +9.78527 q^{15} +(3.74277 + 1.41127i) q^{16} +5.32671 q^{17} +(0.819906 - 9.07076i) q^{18} +(4.19124 + 4.19124i) q^{19} +(-5.23863 + 3.62336i) q^{20} +(-4.57866 + 4.57866i) q^{21} +(1.49047 - 1.24336i) q^{22} +4.81340i q^{23} +(4.27999 + 7.56326i) q^{24} -5.14301i q^{25} +(-0.905917 - 1.08596i) q^{26} +(7.47397 - 7.47397i) q^{27} +(0.755805 - 4.14664i) q^{28} +(-3.09404 - 3.09404i) q^{29} +(-13.7823 - 1.24578i) q^{30} -4.15745 q^{31} +(-5.09191 - 2.46423i) q^{32} +4.21695 q^{33} +(-7.50252 - 0.678153i) q^{34} +(4.74605 + 4.74605i) q^{35} +(-2.30963 + 12.6715i) q^{36} +(-6.92773 + 6.92773i) q^{37} +(-5.36964 - 6.43683i) q^{38} -3.07248i q^{39} +(7.83976 - 4.43647i) q^{40} +9.94083i q^{41} +(7.03182 - 5.86599i) q^{42} +(-1.27996 + 1.27996i) q^{43} +(-2.25758 + 1.56148i) q^{44} +(-14.5032 - 14.5032i) q^{45} +(0.612802 - 6.77953i) q^{46} +0.528901 q^{47} +(-5.06536 - 11.1975i) q^{48} +2.55853 q^{49} +(-0.654765 + 7.24378i) q^{50} +(-11.5727 - 11.5727i) q^{51} +(1.13770 + 1.64488i) q^{52} +(-0.242187 + 0.242187i) q^{53} +(-11.4784 + 9.57535i) q^{54} -4.37111i q^{55} +(-1.59245 + 5.74421i) q^{56} -18.2115i q^{57} +(3.96395 + 4.75177i) q^{58} +(-1.95896 + 1.95896i) q^{59} +(19.2533 + 3.50929i) q^{60} +(5.73782 + 5.73782i) q^{61} +(5.85565 + 0.529292i) q^{62} +13.5725 q^{63} +(6.85809 + 4.11906i) q^{64} -3.18481 q^{65} +(-5.93945 - 0.536867i) q^{66} +(-6.99447 - 6.99447i) q^{67} +(10.4808 + 1.91032i) q^{68} +(10.4575 - 10.4575i) q^{69} +(-6.08044 - 7.28890i) q^{70} +1.27496i q^{71} +(4.86628 - 17.5534i) q^{72} +3.73380i q^{73} +(10.6395 - 8.87552i) q^{74} +(-11.1736 + 11.1736i) q^{75} +(6.74351 + 9.74971i) q^{76} +(2.04530 + 2.04530i) q^{77} +(-0.391163 + 4.32750i) q^{78} -10.1429 q^{79} +(-11.6069 + 5.25054i) q^{80} -13.1551 q^{81} +(1.26558 - 14.0014i) q^{82} +(10.0243 + 10.0243i) q^{83} +(-10.6509 + 7.36684i) q^{84} +(-11.9958 + 11.9958i) q^{85} +(1.96573 - 1.63983i) q^{86} +13.4440i q^{87} +(3.37853 - 1.91189i) q^{88} -9.75665i q^{89} +(18.5809 + 22.2738i) q^{90} +(1.49021 - 1.49021i) q^{91} +(-1.72623 + 9.47076i) q^{92} +(9.03236 + 9.03236i) q^{93} +(-0.744942 - 0.0673353i) q^{94} -18.8773 q^{95} +(5.70883 + 16.4163i) q^{96} +4.87230 q^{97} +(-3.60361 - 0.325730i) q^{98} +(-6.25013 - 6.25013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 4 * q^4 - 12 * q^8	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

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