LMFDB - Embedded newform 550.2.ba.f.449.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(49,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("550.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 75x^{12} - 554x^{10} + 2019x^{8} - 3874x^{6} + 9670x^{4} - 16456x^{2} + 14641 $ x^16 - x^14 + 75x^12 - 554x^10 + 2019x^8 - 3874x^6 + 9670x^4 - 16456x^2 + 14641
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			449.4
Root			$1.20306 + 0.390899i$ of defining polynomial
Character	$\chi$	$=$	550.449
Dual form			550.2.ba.f.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.155750 + 0.214371i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.0818824 + 0.252008i) q^{6} +(2.53438 - 3.48828i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.905354 - 2.78639i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.155750 + 0.214371i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.0818824 + 0.252008i) q^{6} +(2.53438 - 3.48828i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.905354 - 2.78639i) q^{9} +(-1.42705 - 2.99391i) q^{11} +0.264977i q^{12} +(1.15129 + 0.374078i) q^{13} +(3.48828 - 2.53438i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-6.81513 + 2.21437i) q^{17} +(1.72209 - 2.37025i) q^{18} +(2.19992 - 1.59833i) q^{19} +1.14252 q^{21} +(-0.432036 - 3.28837i) q^{22} +7.01787i q^{23} +(-0.0818824 + 0.252008i) q^{24} +(0.979348 + 0.711538i) q^{26} +(1.49436 - 0.485545i) q^{27} +(4.10072 - 1.33240i) q^{28} +(8.54782 + 6.21036i) q^{29} +(1.11908 - 3.44417i) q^{31} +1.00000i q^{32} +(0.419546 - 0.772220i) q^{33} -7.16586 q^{34} +(2.37025 - 1.72209i) q^{36} +(-1.24556 + 1.71437i) q^{37} +(2.58616 - 0.840293i) q^{38} +(0.0991220 + 0.305066i) q^{39} +(-2.22713 + 1.61811i) q^{41} +(1.08660 + 0.353057i) q^{42} +6.59251i q^{43} +(0.605270 - 3.26093i) q^{44} +(-2.16864 + 6.67439i) q^{46} +(3.37418 + 4.64416i) q^{47} +(-0.155750 + 0.214371i) q^{48} +(-3.58188 - 11.0239i) q^{49} +(-1.53615 - 1.11608i) q^{51} +(0.711538 + 0.979348i) q^{52} +(-5.58779 - 1.81558i) q^{53} +1.57126 q^{54} +4.31175 q^{56} +(0.685272 + 0.222659i) q^{57} +(6.21036 + 8.54782i) q^{58} +(-4.77117 - 3.46646i) q^{59} +(-1.89879 - 5.84387i) q^{61} +(2.12861 - 2.92979i) q^{62} +(-7.42521 - 10.2199i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.637641 - 0.604778i) q^{66} +1.63381i q^{67} +(-6.81513 - 2.21437i) q^{68} +(-1.50443 + 1.09303i) q^{69} +(2.29862 + 7.07443i) q^{71} +(2.78639 - 0.905354i) q^{72} +(-4.34501 + 5.98039i) q^{73} +(-1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-14.0603 - 2.60978i) q^{77} +0.320766i q^{78} +(-2.16376 + 6.65938i) q^{79} +(-6.77391 - 4.92153i) q^{81} +(-2.61815 + 0.850690i) q^{82} +(1.51655 - 0.492758i) q^{83} +(0.924315 + 0.671554i) q^{84} +(-2.03720 + 6.26985i) q^{86} +2.79967i q^{87} +(1.58333 - 2.91429i) q^{88} -1.24711 q^{89} +(4.22271 - 3.06798i) q^{91} +(-4.12500 + 5.67757i) q^{92} +(0.912627 - 0.296530i) q^{93} +(1.77391 + 5.45954i) q^{94} +(-0.214371 + 0.155750i) q^{96} +(6.57491 + 2.13632i) q^{97} -11.5912i q^{98} +(-9.63421 + 1.26577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9	$ 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9} + 4 q^{11} - 2 q^{14} - 4 q^{16} + 14 q^{19} + 64 q^{21} + 2 q^{24} - 12 q^{26} + 44 q^{29} - 52 q^{31} - 4 q^{34} - 2 q^{36} + 96 q^{39} - 30 q^{41} - 14 q^{44} - 12 q^{46} - 54 q^{49} - 10 q^{51} + 48 q^{54} + 12 q^{56} - 78 q^{59} - 40 q^{61} + 4 q^{64} + 72 q^{66} + 20 q^{69} + 4 q^{71} - 16 q^{74} + 16 q^{76} - 28 q^{79} - 62 q^{81} + 36 q^{84} + 34 q^{86} - 64 q^{89} + 106 q^{91} - 18 q^{94} + 8 q^{96} - 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9 + 4 * q^11 - 2 * q^14 - 4 * q^16 + 14 * q^19 + 64 * q^21 + 2 * q^24 - 12 * q^26 + 44 * q^29 - 52 * q^31 - 4 * q^34 - 2 * q^36 + 96 * q^39 - 30 * q^41 - 14 * q^44 - 12 * q^46 - 54 * q^49 - 10 * q^51 + 48 * q^54 + 12 * q^56 - 78 * q^59 - 40 * q^61 + 4 * q^64 + 72 * q^66 + 20 * q^69 + 4 * q^71 - 16 * q^74 + 16 * q^76 - 28 * q^79 - 62 * q^81 + 36 * q^84 + 34 * q^86 - 64 * q^89 + 106 * q^91 - 18 * q^94 + 8 * q^96 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.155750	+	0.214371i	0.0899221	+	0.123767i	0.851608	−	0.524180i	$-0.175628\pi$
$3$	0.155750	+	0.214371i	0.0899221	+	0.123767i	−0.761686	+	0.647947i	$0.775628\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	0.0818824	+	0.252008i	0.0334284	+	0.102882i
$7$	2.53438	−	3.48828i	0.957907	−	1.31845i	0.00998336	−	0.999950i	$-0.496822\pi$
$7$	2.53438	−	3.48828i	0.957907	−	1.31845i	0.947924	−	0.318496i	$-0.103178\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.905354	−	2.78639i	0.301785	−	0.928798i
$10$		0			0
$11$	−1.42705	−	2.99391i	−0.430272	−	0.902699i
$11$	−1.42705	−	2.99391i	−0.430272	−	0.902699i
$12$			0.264977i			0.0764923i
$13$	1.15129	+	0.374078i	0.319311	+	0.103750i	0.464287	−	0.885685i	$-0.346311\pi$
$13$	1.15129	+	0.374078i	0.319311	+	0.103750i	−0.144976	+	0.989435i	$0.546311\pi$
$14$	3.48828	−	2.53438i	0.932282	−	0.677343i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.81513	+	2.21437i	−1.65291	+	0.537064i	−0.979368	−	0.202083i	$-0.935229\pi$
$17$	−6.81513	+	2.21437i	−1.65291	+	0.537064i	−0.673544	+	0.739147i	$0.735229\pi$
$18$	1.72209	−	2.37025i	0.405899	−	0.558673i
$19$	2.19992	−	1.59833i	0.504695	−	0.366683i	−0.306112	−	0.951995i	$-0.599028\pi$
$19$	2.19992	−	1.59833i	0.504695	−	0.366683i	0.810808	+	0.585313i	$0.199028\pi$
$20$		0			0
$21$	1.14252			0.249317
$22$	−0.432036	−	3.28837i	−0.0921103	−	0.701082i
$23$			7.01787i			1.46333i	0.681666	+	0.731663i	$0.261256\pi$
$23$			7.01787i			1.46333i	−0.681666	+	0.731663i	$0.738744\pi$
$24$	−0.0818824	+	0.252008i	−0.0167142	+	0.0514410i
$25$		0			0
$26$	0.979348	+	0.711538i	0.192066	+	0.139544i
$27$	1.49436	−	0.485545i	0.287589	−	0.0934433i
$28$	4.10072	−	1.33240i	0.774963	−	0.251801i
$29$	8.54782	+	6.21036i	1.58729	+	1.15323i	0.907682	+	0.419659i	$0.137850\pi$
$29$	8.54782	+	6.21036i	1.58729	+	1.15323i	0.679609	+	0.733575i	$0.262150\pi$
$30$		0			0
$31$	1.11908	−	3.44417i	0.200993	−	0.618591i	−0.798862	−	0.601515i	$-0.794564\pi$
$31$	1.11908	−	3.44417i	0.200993	−	0.618591i	0.999854	−	0.0170766i	$-0.00543592\pi$
$32$			1.00000i			0.176777i
$33$	0.419546	−	0.772220i	0.0730336	−	0.134426i
$34$	−7.16586			−1.22893
$35$		0			0
$36$	2.37025	−	1.72209i	0.395041	−	0.287014i
$37$	−1.24556	+	1.71437i	−0.204769	+	0.281841i	−0.899034	−	0.437879i	$-0.855730\pi$
$37$	−1.24556	+	1.71437i	−0.204769	+	0.281841i	0.694265	+	0.719720i	$0.255730\pi$
$38$	2.58616	−	0.840293i	0.419530	−	0.136314i
$39$	0.0991220	+	0.305066i	0.0158722	+	0.0488497i
$40$		0			0
$41$	−2.22713	+	1.61811i	−0.347820	+	0.252706i	−0.747954	−	0.663751i	$-0.768964\pi$
$41$	−2.22713	+	1.61811i	−0.347820	+	0.252706i	0.400134	+	0.916457i	$0.368964\pi$
$42$	1.08660	+	0.353057i	0.167666	+	0.0544779i
$43$			6.59251i			1.00535i	0.864476	+	0.502674i	$0.167650\pi$
$43$			6.59251i			1.00535i	−0.864476	+	0.502674i	$0.832350\pi$
$44$	0.605270	−	3.26093i	0.0912480	−	0.491603i
$45$		0			0
$46$	−2.16864	+	6.67439i	−0.319749	+	0.984085i
$47$	3.37418	+	4.64416i	0.492175	+	0.677420i	0.980787	−	0.195081i	$-0.0624969\pi$
$47$	3.37418	+	4.64416i	0.492175	+	0.677420i	−0.488613	+	0.872501i	$0.662497\pi$
$48$	−0.155750	+	0.214371i	−0.0224805	+	0.0309418i
$49$	−3.58188	−	11.0239i	−0.511697	−	1.57484i
$50$		0			0
$51$	−1.53615	−	1.11608i	−0.215104	−	0.156282i
$52$	0.711538	+	0.979348i	0.0986726	+	0.135811i
$53$	−5.58779	−	1.81558i	−0.767542	−	0.249390i	−0.101030	−	0.994883i	$-0.532214\pi$
$53$	−5.58779	−	1.81558i	−0.767542	−	0.249390i	−0.666512	+	0.745494i	$0.732214\pi$
$54$	1.57126			0.213821
$55$		0			0
$56$	4.31175			0.576182
$57$	0.685272	+	0.222659i	0.0907666	+	0.0294918i
$58$	6.21036	+	8.54782i	0.815460	+	1.12238i
$59$	−4.77117	−	3.46646i	−0.621154	−	0.451295i	0.232170	−	0.972675i	$-0.425417\pi$
$59$	−4.77117	−	3.46646i	−0.621154	−	0.451295i	−0.853324	+	0.521380i	$0.825417\pi$
$60$		0			0
$61$	−1.89879	−	5.84387i	−0.243115	−	0.748231i	−0.995941	−	0.0900109i	$-0.971310\pi$
$61$	−1.89879	−	5.84387i	−0.243115	−	0.748231i	0.752826	−	0.658220i	$-0.228690\pi$
$62$	2.12861	−	2.92979i	0.270334	−	0.372083i
$63$	−7.42521	−	10.2199i	−0.935488	−	1.28759i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		0			0
$66$	0.637641	−	0.604778i	0.0784881	−	0.0744430i
$67$			1.63381i			0.199602i	0.995007	+	0.0998009i	$0.0318206\pi$
$67$			1.63381i			0.199602i	−0.995007	+	0.0998009i	$0.968179\pi$
$68$	−6.81513	−	2.21437i	−0.826456	−	0.268532i
$69$	−1.50443	+	1.09303i	−0.181112	+	0.131585i
$70$		0			0
$71$	2.29862	+	7.07443i	0.272796	+	0.839580i	0.989794	+	0.142505i	$0.0455156\pi$
$71$	2.29862	+	7.07443i	0.272796	+	0.839580i	−0.716998	+	0.697075i	$0.754484\pi$
$72$	2.78639	−	0.905354i	0.328380	−	0.106697i
$73$	−4.34501	+	5.98039i	−0.508545	+	0.699952i	−0.983673	−	0.179965i	$-0.942402\pi$
$73$	−4.34501	+	5.98039i	−0.508545	+	0.699952i	0.475128	+	0.879917i	$0.342402\pi$
$74$	−1.71437	+	1.24556i	−0.199292	+	0.144794i
$75$		0			0
$76$	2.71925			0.311919
$77$	−14.0603	−	2.60978i	−1.60232	−	0.297412i
$78$			0.320766i			0.0363196i
$79$	−2.16376	+	6.65938i	−0.243443	+	0.749239i	0.752446	+	0.658654i	$0.228874\pi$
$79$	−2.16376	+	6.65938i	−0.243443	+	0.749239i	−0.995889	+	0.0905854i	$0.971126\pi$
$80$		0			0
$81$	−6.77391	−	4.92153i	−0.752657	−	0.546837i
$82$	−2.61815	+	0.850690i	−0.289127	+	0.0939430i
$83$	1.51655	−	0.492758i	0.166463	−	0.0540872i	−0.224600	−	0.974451i	$-0.572107\pi$
$83$	1.51655	−	0.492758i	0.166463	−	0.0540872i	0.391063	+	0.920364i	$0.372107\pi$
$84$	0.924315	+	0.671554i	0.100851	+	0.0732726i
$85$		0			0
$86$	−2.03720	+	6.26985i	−0.219677	+	0.676095i
$87$			2.79967i			0.300156i
$88$	1.58333	−	2.91429i	0.168783	−	0.310664i
$89$	−1.24711			−0.132193			−0.0660967	−	0.997813i	$-0.521055\pi$
$89$	−1.24711			−0.132193			−0.0660967	+	0.997813i	$0.521055\pi$
$90$		0			0
$91$	4.22271	−	3.06798i	0.442660	−	0.321611i
$92$	−4.12500	+	5.67757i	−0.430061	+	0.591928i
$93$	0.912627	−	0.296530i	0.0946350	−	0.0307488i
$94$	1.77391	+	5.45954i	0.182965	+	0.563108i
$95$		0			0
$96$	−0.214371	+	0.155750i	−0.0218791	+	0.0158961i
$97$	6.57491	+	2.13632i	0.667581	+	0.216910i	0.623150	−	0.782102i	$-0.285853\pi$
$97$	6.57491	+	2.13632i	0.667581	+	0.216910i	0.0444310	+	0.999012i	$0.485853\pi$
$98$		−	11.5912i		−	1.17089i
$99$	−9.63421	+	1.26577i	−0.968275	+	0.127215i
$100$		0			0
$101$	1.00000	−	3.07768i	0.0995037	−	0.306241i	−0.888897	−	0.458106i	$-0.848528\pi$
$101$	1.00000	−	3.07768i	0.0995037	−	0.306241i	0.988401	+	0.151865i	$0.0485280\pi$
$102$	−1.11608	−	1.53615i	−0.110508	−	0.152102i
$103$	3.39518	−	4.67307i	0.334537	−	0.460451i	−0.608299	−	0.793708i	$-0.708148\pi$
$103$	3.39518	−	4.67307i	0.334537	−	0.460451i	0.942836	+	0.333257i	$0.108148\pi$
$104$	0.374078	+	1.15129i	0.0366813	+	0.112894i
$105$		0			0
$106$	−4.75326	−	3.45344i	−0.461677	−	0.335428i
$107$	0.100761	+	0.138686i	0.00974095	+	0.0134073i	0.813860	−	0.581061i	$-0.197362\pi$
$107$	0.100761	+	0.138686i	0.00974095	+	0.0134073i	−0.804119	+	0.594469i	$0.797362\pi$
$108$	1.49436	+	0.485545i	0.143794	+	0.0467216i
$109$	2.32753			0.222937			0.111468	−	0.993768i	$-0.464445\pi$
$109$	2.32753			0.222937			0.111468	+	0.993768i	$0.464445\pi$
$110$		0			0
$111$	−0.561508			−0.0532959
$112$	4.10072	+	1.33240i	0.387482	+	0.125900i
$113$	−2.53240	−	3.48555i	−0.238228	−	0.327893i	0.673117	−	0.739536i	$-0.264955\pi$
$113$	−2.53240	−	3.48555i	−0.238228	−	0.327893i	−0.911345	+	0.411643i	$0.864955\pi$
$114$	0.582928	+	0.423522i	0.0545962	+	0.0396664i
$115$		0			0
$116$	3.26498	+	10.0486i	0.303146	+	0.932986i
$117$	2.08466	−	2.86928i	0.192726	−	0.265265i
$118$	−3.46646	−	4.77117i	−0.319114	−	0.439222i
$119$	−9.54782	+	29.3852i	−0.875247	+	2.69373i
$120$		0			0
$121$	−6.92705	+	8.54494i	−0.629732	+	0.776813i
$122$		−	6.14461i		−	0.556307i
$123$	−0.693751	−	0.225413i	−0.0625534	−	0.0203248i
$124$	2.92979	−	2.12861i	0.263103	−	0.191155i
$125$		0			0
$126$	−3.90366	−	12.0142i	−0.347766	−	1.07031i
$127$	10.3058	−	3.34855i	0.914490	−	0.297136i	0.186285	−	0.982496i	$-0.440355\pi$
$127$	10.3058	−	3.34855i	0.914490	−	0.297136i	0.728205	+	0.685360i	$0.240355\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−1.41324	+	1.02678i	−0.124429	+	0.0904030i
$130$		0			0
$131$	5.78518			0.505454			0.252727	−	0.967538i	$-0.418673\pi$
$131$	5.78518			0.505454			0.252727	+	0.967538i	$0.418673\pi$
$132$	0.793319	−	0.378136i	0.0690496	−	0.0329125i
$133$		−	11.7247i		−	1.01666i
$134$	−0.504875	+	1.55385i	−0.0436146	+	0.134232i
$135$		0			0
$136$	−5.79730	−	4.21198i	−0.497114	−	0.361175i
$137$	8.22695	−	2.67310i	0.702876	−	0.228378i	0.0642926	−	0.997931i	$-0.479521\pi$
$137$	8.22695	−	2.67310i	0.702876	−	0.228378i	0.638583	+	0.769553i	$0.279521\pi$
$138$	−1.76856	+	0.574640i	−0.150550	+	0.0489166i
$139$	10.3135	+	7.49318i	0.874777	+	0.635563i	0.931865	−	0.362806i	$-0.118181\pi$
$139$	10.3135	+	7.49318i	0.874777	+	0.635563i	−0.0570872	+	0.998369i	$0.518181\pi$
$140$		0			0
$141$	−0.470046	+	1.44665i	−0.0395850	+	0.121830i
$142$			7.43849i			0.624224i
$143$	−0.522997	−	3.98070i	−0.0437352	−	0.332883i
$144$	2.92979			0.244149
$145$		0			0
$146$	−5.98039	+	4.34501i	−0.494941	+	0.359596i
$147$	1.80533	−	2.48482i	0.148901	−	0.204945i
$148$	−2.01536	+	0.654831i	−0.165662	+	0.0538268i
$149$	−2.04339	−	6.28892i	−0.167401	−	0.515208i	0.831804	−	0.555070i	$-0.187308\pi$
$149$	−2.04339	−	6.28892i	−0.167401	−	0.515208i	−0.999205	+	0.0398613i	$0.987308\pi$
$150$		0			0
$151$	−16.9064	+	12.2832i	−1.37582	+	0.999591i	−0.378562	+	0.925576i	$0.623581\pi$
$151$	−16.9064	+	12.2832i	−1.37582	+	0.999591i	−0.997257	+	0.0740153i	$0.976419\pi$
$152$	2.58616	+	0.840293i	0.209765	+	0.0681568i
$153$			20.9944i			1.69730i
$154$	−12.5657	−	6.82692i	−1.01257	−	0.550129i
$155$		0			0
$156$	−0.0991220	+	0.305066i	−0.00793611	+	0.0244248i
$157$	−11.8904	−	16.3657i	−0.948957	−	1.30613i	−0.951989	−	0.306131i	$-0.900965\pi$
$157$	−11.8904	−	16.3657i	−0.948957	−	1.30613i	0.00303254	−	0.999995i	$-0.499035\pi$
$158$	−4.11573	+	5.66481i	−0.327430	+	0.450668i
$159$	−0.481088	−	1.48064i	−0.0381528	−	0.117422i
$160$		0			0
$161$	24.4803	+	17.7860i	1.92932	+	1.40173i
$162$	−4.92153	−	6.77391i	−0.386672	−	0.532209i
$163$	−7.68564	−	2.49721i	−0.601986	−	0.195597i	−0.00785979	−	0.999969i	$-0.502502\pi$
$163$	−7.68564	−	2.49721i	−0.601986	−	0.195597i	−0.594126	+	0.804372i	$0.702502\pi$
$164$	−2.75289			−0.214965
$165$		0			0
$166$	1.59460			0.123765
$167$	−16.4272	−	5.33751i	−1.27117	−	0.413029i	−0.405709	−	0.914002i	$-0.632975\pi$
$167$	−16.4272	−	5.33751i	−1.27117	−	0.413029i	−0.865463	+	0.500973i	$0.832975\pi$
$168$	0.671554	+	0.924315i	0.0518115	+	0.0713124i
$169$	−9.33168	−	6.77986i	−0.717822	−	0.521528i
$170$		0			0
$171$	−2.46188	−	7.57689i	−0.188265	−	0.579419i
$172$	−3.87498	+	5.33345i	−0.295464	+	0.406672i
$173$	−8.44868	−	11.6286i	−0.642341	−	0.884107i	0.356397	−	0.934335i	$-0.384005\pi$
$173$	−8.44868	−	11.6286i	−0.642341	−	0.884107i	−0.998738	+	0.0502280i	$0.984005\pi$
$174$	−0.865144	+	2.66264i	−0.0655864	+	0.201854i
$175$		0			0
$176$	2.40640	−	2.28238i	0.181389	−	0.172041i
$177$		−	1.56270i		−	0.117460i
$178$	−1.18607	−	0.385378i	−0.0888999	−	0.0288853i
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.152953	−	0.988233i	$-0.451122\pi$
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.987131	+	0.159914i	$0.0511216\pi$
$180$		0			0
$181$	−4.04887	−	12.4611i	−0.300950	−	0.926228i	−0.981158	−	0.193209i	$-0.938110\pi$
$181$	−4.04887	−	12.4611i	−0.300950	−	0.926228i	0.680208	−	0.733019i	$-0.261890\pi$
$182$	4.96409	−	1.61293i	0.367963	−	0.119558i
$183$	0.957020	−	1.31723i	0.0707450	−	0.0973721i
$184$	−5.67757	+	4.12500i	−0.418556	+	0.304099i
$185$		0			0
$186$	0.959592			0.0703607
$187$	16.3552	+	17.2439i	1.19601	+	1.26100i
$188$			5.74050i			0.418669i
$189$	2.09355	−	6.44329i	0.152283	−	0.468680i
$190$		0			0
$191$	9.11908	+	6.62540i	0.659833	+	0.479397i	0.866607	−	0.498992i	$-0.166296\pi$
$191$	9.11908	+	6.62540i	0.659833	+	0.479397i	−0.206773	+	0.978389i	$0.566296\pi$
$192$	−0.252008	+	0.0818824i	−0.0181871	+	0.00590936i
$193$	−6.60440	+	2.14590i	−0.475395	+	0.154465i	−0.536907	−	0.843641i	$-0.680408\pi$
$193$	−6.60440	+	2.14590i	−0.475395	+	0.154465i	0.0615126	+	0.998106i	$0.480408\pi$
$194$	5.59295	+	4.06352i	0.401551	+	0.291744i
$195$		0			0
$196$	3.58188	−	11.0239i	0.255849	−	0.787421i
$197$			13.4389i			0.957485i	0.877955	+	0.478743i	$0.158907\pi$
$197$			13.4389i			0.957485i	−0.877955	+	0.478743i	$0.841093\pi$
$198$	−9.55382	−	1.77331i	−0.678961	−	0.126024i
$199$	19.4427			1.37825			0.689127	−	0.724640i	$-0.257994\pi$
$199$	19.4427			1.37825			0.689127	+	0.724640i	$0.257994\pi$
$200$		0			0
$201$	−0.350242	+	0.254465i	−0.0247041	+	0.0179486i
$202$	1.90211	−	2.61803i	0.133832	−	0.184204i
$203$	43.3269	−	14.0778i	3.04095	−	0.988066i
$204$	−0.586758	−	1.80585i	−0.0410813	−	0.126435i
$205$		0			0
$206$	4.67307	−	3.39518i	0.325588	−	0.236554i
$207$	19.5545	+	6.35365i	1.35913	+	0.441609i
$208$			1.21054i			0.0839359i
$209$	−7.92467	−	4.30546i	−0.548161	−	0.297815i
$210$		0			0
$211$	−0.728826	+	2.24309i	−0.0501744	+	0.154421i	−0.973004	−	0.230786i	$-0.925870\pi$
$211$	−0.728826	+	2.24309i	−0.0501744	+	0.154421i	0.922830	+	0.385207i	$0.125870\pi$
$212$	−3.45344	−	4.75326i	−0.237184	−	0.326455i
$213$	−1.15854	+	1.59460i	−0.0793820	+	0.109260i
$214$	0.0529733	+	0.163035i	0.00362118	+	0.0111448i
$215$		0			0
$216$	1.27117	+	0.923562i	0.0864925	+	0.0628405i
$217$	−9.17806	−	12.6325i	−0.623047	−	0.857551i
$218$	2.21361	+	0.719246i	0.149925	+	0.0487135i
$219$	−1.95876			−0.132361
$220$		0			0
$221$	−8.67456			−0.583514
$222$	−0.534025	−	0.173515i	−0.0358414	−	0.0116456i
$223$	8.57978	+	11.8090i	0.574544	+	0.790792i	0.993084	−	0.117406i	$-0.0374579\pi$
$223$	8.57978	+	11.8090i	0.574544	+	0.790792i	−0.418540	+	0.908198i	$0.637458\pi$
$224$	3.48828	+	2.53438i	0.233071	+	0.169336i
$225$		0			0
$226$	−1.33136	−	4.09750i	−0.0885607	−	0.272562i
$227$	−1.75730	+	2.41871i	−0.116636	+	0.160536i	−0.863343	−	0.504617i	$-0.831634\pi$
$227$	−1.75730	+	2.41871i	−0.116636	+	0.160536i	0.746707	+	0.665153i	$0.231634\pi$
$228$	0.423522	+	0.582928i	0.0280484	+	0.0386053i
$229$	−0.487913	+	1.50164i	−0.0322422	+	0.0992312i	−0.965883	−	0.258981i	$-0.916613\pi$
$229$	−0.487913	+	1.50164i	−0.0322422	+	0.0992312i	0.933640	+	0.358212i	$0.116613\pi$
$230$		0			0
$231$	−1.63043	−	3.42060i	−0.107274	−	0.225059i
$232$			10.5657i			0.693671i
$233$	0.480967	+	0.156276i	0.0315092	+	0.0102380i	0.324729	−	0.945807i	$-0.394727\pi$
$233$	0.480967	+	0.156276i	0.0315092	+	0.0102380i	−0.293220	+	0.956045i	$0.594727\pi$
$234$	2.86928	−	2.08466i	0.187571	−	0.136278i
$235$		0			0
$236$	−1.82243	−	5.60885i	−0.118630	−	0.365105i
$237$	−1.76458	+	0.573348i	−0.114622	+	0.0372430i
$238$	−18.1610	+	24.9965i	−1.17721	+	1.62028i
$239$	−13.5444	+	9.84061i	−0.876117	+	0.636536i	−0.932221	−	0.361889i	$-0.882132\pi$
$239$	−13.5444	+	9.84061i	−0.876117	+	0.636536i	0.0561044	+	0.998425i	$0.482132\pi$
$240$		0			0
$241$	−15.2947			−0.985217			−0.492609	−	0.870251i	$-0.663957\pi$
$241$	−15.2947			−0.985217			−0.492609	+	0.870251i	$0.663957\pi$
$242$	−9.22855	+	5.98614i	−0.593234	+	0.384804i
$243$		−	6.93243i		−	0.444716i
$244$	1.89879	−	5.84387i	0.121557	−	0.374115i
$245$		0			0
$246$	−0.590140	−	0.428762i	−0.0376259	−	0.0273368i
$247$	3.13065	−	1.01721i	0.199198	−	0.0647235i
$248$	3.44417	−	1.11908i	0.218705	−	0.0710616i
$249$	0.341835	+	0.248358i	0.0216629	+	0.0157390i
$250$		0			0
$251$	−0.132071	+	0.406472i	−0.00833623	+	0.0256563i	−0.955138	−	0.296161i	$-0.904294\pi$
$251$	−0.132071	+	0.406472i	−0.00833623	+	0.0256563i	0.946802	+	0.321817i	$0.104294\pi$
$252$		−	12.6325i		−	0.795774i
$253$	21.0109	−	10.0149i	1.32094	−	0.629628i
$254$	10.8361			0.679920
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−10.5068	+	14.4614i	−0.655397	+	0.902076i	−0.999318	−	0.0369221i	$-0.988245\pi$
$257$	−10.5068	+	14.4614i	−0.655397	+	0.902076i	0.343921	+	0.938998i	$0.388245\pi$
$258$	−1.66137	+	0.539811i	−0.103432	+	0.0336071i
$259$	2.82347	+	8.68975i	0.175442	+	0.539955i
$260$		0			0
$261$	25.0433	−	18.1950i	1.55014	−	1.12624i
$262$	5.50203	+	1.78772i	0.339917	+	0.110446i
$263$			14.4977i			0.893964i	0.894543	+	0.446982i	$0.147501\pi$
$263$			14.4977i			0.893964i	−0.894543	+	0.446982i	$0.852499\pi$
$264$	0.871342	−	0.114480i	0.0536274	−	0.00704573i
$265$		0			0
$266$	3.62314	−	11.1509i	0.222149	−	0.683704i
$267$	−0.194237	−	0.267344i	−0.0118871	−	0.0163612i
$268$	−0.960330	+	1.32178i	−0.0586615	+	0.0807406i
$269$	−8.63326	−	26.5704i	−0.526379	−	1.62003i	−0.761573	−	0.648079i	$-0.775573\pi$
$269$	−8.63326	−	26.5704i	−0.526379	−	1.62003i	0.235194	−	0.971948i	$-0.424427\pi$
$270$		0			0
$271$	−8.40531	−	6.10681i	−0.510586	−	0.370962i	0.302460	−	0.953162i	$-0.402192\pi$
$271$	−8.40531	−	6.10681i	−0.510586	−	0.370962i	−0.813046	+	0.582200i	$0.802192\pi$
$272$	−4.21198	−	5.79730i	−0.255389	−	0.351513i
$273$	1.31537	+	0.427390i	0.0796098	+	0.0258668i
$274$	8.65033			0.522585
$275$		0			0
$276$	−1.85957			−0.111933
$277$	0.597585	+	0.194167i	0.0359054	+	0.0116664i	0.326915	−	0.945054i	$-0.393991\pi$
$277$	0.597585	+	0.194167i	0.0359054	+	0.0116664i	−0.291009	+	0.956720i	$0.593991\pi$
$278$	7.49318	+	10.3135i	0.449411	+	0.618561i
$279$	−8.58365	−	6.23639i	−0.513890	−	0.373363i
$280$		0			0
$281$	9.30347	+	28.6331i	0.554998	+	1.70811i	0.695948	+	0.718092i	$0.254984\pi$
$281$	9.30347	+	28.6331i	0.554998	+	1.70811i	−0.140950	+	0.990017i	$0.545016\pi$
$282$	−0.894080	+	1.23060i	−0.0532417	+	0.0732809i
$283$	9.46599	+	13.0288i	0.562694	+	0.774482i	0.991666	−	0.128836i	$-0.0411239\pi$
$283$	9.46599	+	13.0288i	0.562694	+	0.774482i	−0.428972	+	0.903318i	$0.641124\pi$
$284$	−2.29862	+	7.07443i	−0.136398	+	0.419790i
$285$		0			0
$286$	0.732705	−	3.94749i	0.0433257	−	0.233420i
$287$			11.8698i			0.700651i
$288$	2.78639	+	0.905354i	0.164190	+	0.0533485i
$289$	27.7893	−	20.1901i	1.63467	−	1.18765i
$290$		0			0
$291$	0.566076	+	1.74220i	0.0331839	+	0.102130i
$292$	−7.03037	+	2.28431i	−0.411422	+	0.133679i
$293$	−2.33941	+	3.21992i	−0.136670	+	0.188110i	−0.871866	−	0.489745i	$-0.837090\pi$
$293$	−2.33941	+	3.21992i	−0.136670	+	0.188110i	0.735196	+	0.677854i	$0.237090\pi$
$294$	2.48482	−	1.80533i	0.144918	−	0.105289i
$295$		0			0
$296$	−2.11908			−0.123169
$297$	−3.58620	−	3.78107i	−0.208093	−	0.219400i
$298$		−	6.61256i		−	0.383055i
$299$	−2.62523	+	8.07962i	−0.151821	+	0.467256i
$300$		0			0
$301$	22.9965	+	16.7079i	1.32550	+	0.963030i
$302$	−19.8746	+	6.45765i	−1.14366	+	0.371596i
$303$	0.815516	−	0.264977i	0.0468502	−	0.0152225i
$304$	2.19992	+	1.59833i	0.126174	+	0.0916707i
$305$		0			0
$306$	−6.48764	+	19.9669i	−0.370873	+	1.14143i
$307$		−	17.6055i		−	1.00480i	−0.864635	−	0.502401i	$-0.832450\pi$
$307$		−	17.6055i		−	1.00480i	0.864635	−	0.502401i	$-0.167550\pi$
$308$	−9.84104	−	10.3758i	−0.560746	−	0.591216i
$309$	1.53057			0.0870710
$310$		0			0
$311$	18.3117	−	13.3042i	1.03836	−	0.754412i	0.0683942	−	0.997658i	$-0.478212\pi$
$311$	18.3117	−	13.3042i	1.03836	−	0.754412i	0.969964	+	0.243247i	$0.0782124\pi$
$312$	−0.188541	+	0.259505i	−0.0106741	+	0.0146916i
$313$	11.9925	−	3.89659i	0.677855	−	0.220248i	0.0501989	−	0.998739i	$-0.484014\pi$
$313$	11.9925	−	3.89659i	0.677855	−	0.220248i	0.627656	+	0.778491i	$0.284014\pi$
$314$	−6.25115	−	19.2391i	−0.352773	−	1.08572i
$315$		0			0
$316$	−5.66481	+	4.11573i	−0.318670	+	0.231528i
$317$	−24.9822	−	8.11722i	−1.40314	−	0.455908i	−0.492936	−	0.870065i	$-0.664076\pi$
$317$	−24.9822	−	8.11722i	−1.40314	−	0.455908i	−0.910205	+	0.414157i	$0.864076\pi$
$318$		−	1.55683i		−	0.0873029i
$319$	6.39510	−	34.4539i	0.358057	−	1.92905i
$320$		0			0
$321$	−0.0140367	+	0.0432005i	−0.000783453	+	0.00241122i
$322$	17.7860	+	24.4803i	0.991174	+	1.36423i
$323$	−11.4534	+	15.7643i	−0.637285	+	0.877148i
$324$	−2.58740	−	7.96321i	−0.143745	−	0.442401i
$325$		0			0
$326$	−6.53779	−	4.74999i	−0.362095	−	0.263077i
$327$	0.362512	+	0.498955i	0.0200470	+	0.0275923i
$328$	−2.61815	−	0.850690i	−0.144563	−	0.0469715i
$329$	24.7516			1.36460
$330$		0			0
$331$	12.7406			0.700284			0.350142	−	0.936697i	$-0.386133\pi$
$331$	12.7406			0.700284			0.350142	+	0.936697i	$0.386133\pi$
$332$	1.51655	+	0.492758i	0.0832316	+	0.0270436i
$333$	3.64924	+	5.02274i	0.199977	+	0.275245i
$334$	−13.9738	−	10.1525i	−0.764611	−	0.555522i
$335$		0			0
$336$	0.353057	+	1.08660i	0.0192608	+	0.0592787i
$337$	11.2014	−	15.4174i	0.610180	−	0.839841i	−0.386412	−	0.922326i	$-0.626286\pi$
$337$	11.2014	−	15.4174i	0.610180	−	0.839841i	0.996592	+	0.0824856i	$0.0262858\pi$
$338$	−6.77986	−	9.33168i	−0.368776	−	0.507576i
$339$	0.352780	−	1.08574i	0.0191604	−	0.0589696i
$340$		0			0
$341$	−11.9085	+	1.56458i	−0.644884	+	0.0847268i
$342$		−	7.96681i		−	0.430796i
$343$	−18.8273	−	6.11736i	−1.01658	−	0.330306i
$344$	−5.33345	+	3.87498i	−0.287560	+	0.208925i
$345$		0			0
$346$	−4.44173	−	13.6703i	−0.238789	−	0.734917i
$347$	17.9017	−	5.81663i	0.961016	−	0.312253i	0.213832	−	0.976870i	$-0.431405\pi$
$347$	17.9017	−	5.81663i	0.961016	−	0.312253i	0.747184	+	0.664617i	$0.231405\pi$
$348$	−1.64560	+	2.26498i	−0.0882135	+	0.121416i
$349$	−22.0200	+	15.9984i	−1.17870	+	0.856377i	−0.992025	−	0.126045i	$-0.959772\pi$
$349$	−22.0200	+	15.9984i	−1.17870	+	0.856377i	−0.186677	+	0.982421i	$0.559772\pi$
$350$		0			0
$351$	1.90207			0.101525
$352$	2.99391	−	1.42705i	0.159576	−	0.0760621i
$353$			25.6380i			1.36457i	0.731085	+	0.682286i	$0.239014\pi$
$353$			25.6380i			1.36457i	−0.731085	+	0.682286i	$0.760986\pi$
$354$	0.482901	−	1.48622i	0.0256659	−	0.0789916i
$355$		0			0
$356$	−1.00893	−	0.733033i	−0.0534734	−	0.0388507i
$357$	−7.78640	+	2.52995i	−0.412100	+	0.133899i
$358$	17.9313	−	5.82624i	0.947700	−	0.307926i
$359$	7.82857	+	5.68779i	0.413176	+	0.300190i	0.774886	−	0.632100i	$-0.217807\pi$
$359$	7.82857	+	5.68779i	0.413176	+	0.300190i	−0.361710	+	0.932291i	$0.617807\pi$
$360$		0			0
$361$	−3.58636	+	11.0377i	−0.188756	+	0.580930i
$362$		−	13.1024i		−	0.688647i
$363$	−2.91067	−	0.154088i	−0.152771	−	0.00808751i
$364$	5.21955			0.273579
$365$		0			0
$366$	1.31723	−	0.957020i	0.0688525	−	0.0500243i
$367$	12.1692	−	16.7495i	0.635229	−	0.874317i	−0.363121	−	0.931742i	$-0.618289\pi$
$367$	12.1692	−	16.7495i	0.635229	−	0.874317i	0.998350	+	0.0574247i	$0.0182889\pi$
$368$	−6.67439	+	2.16864i	−0.347927	+	0.113048i
$369$	2.49234	+	7.67063i	0.129746	+	0.399317i
$370$		0			0
$371$	−20.4949	+	14.8904i	−1.06404	+	0.773071i
$372$	0.912627	+	0.296530i	0.0473175	+	0.0153744i
$373$		−	16.1463i		−	0.836021i	−0.908442	−	0.418011i	$-0.862727\pi$
$373$		−	16.1463i		−	0.836021i	0.908442	−	0.418011i	$-0.137273\pi$
$374$	10.2260	+	21.4540i	0.528776	+	1.10936i
$375$		0			0
$376$	−1.77391	+	5.45954i	−0.0914825	+	0.281554i
$377$	7.51789	+	10.3475i	0.387191	+	0.532923i
$378$	3.98217	−	5.48099i	0.204821	−	0.281912i
$379$	0.0709811	+	0.218457i	0.00364605	+	0.0112214i	0.952863	−	0.303401i	$-0.0981221\pi$
$379$	0.0709811	+	0.218457i	0.00364605	+	0.0112214i	−0.949217	+	0.314622i	$0.898122\pi$
$380$		0			0
$381$	2.32295	+	1.68772i	0.119009	+	0.0864648i
$382$	6.62540	+	9.11908i	0.338985	+	0.466573i
$383$	12.3847	+	4.02403i	0.632829	+	0.205619i	0.607828	−	0.794069i	$-0.292041\pi$
$383$	12.3847	+	4.02403i	0.632829	+	0.205619i	0.0250010	+	0.999687i	$0.492041\pi$
$384$	−0.264977			−0.0135221
$385$		0			0
$386$	−6.94427			−0.353454
$387$	18.3693	+	5.96855i	0.933765	+	0.303399i
$388$	4.06352	+	5.59295i	0.206294	+	0.283939i
$389$	23.9676	+	17.4135i	1.21521	+	0.882899i	0.995693	−	0.0927106i	$-0.0295532\pi$
$389$	23.9676	+	17.4135i	1.21521	+	0.882899i	0.219513	+	0.975610i	$0.429553\pi$
$390$		0			0
$391$	−15.5402	−	47.8277i	−0.785900	−	2.41875i
$392$	6.81315	−	9.37749i	0.344116	−	0.473635i
$393$	0.901040	+	1.24018i	0.0454515	+	0.0625586i
$394$	−4.15286	+	12.7812i	−0.209218	+	0.643908i
$395$		0			0
$396$	−8.53824	−	4.63882i	−0.429063	−	0.233109i
$397$		−	2.18665i		−	0.109745i	−0.998493	−	0.0548724i	$-0.982525\pi$
$397$		−	2.18665i		−	0.109745i	0.998493	−	0.0548724i	$-0.0174752\pi$
$398$	18.4911	+	6.00812i	0.926874	+	0.301160i
$399$	2.51344	−	1.82612i	0.125829	−	0.0914204i
$400$		0			0
$401$	−4.04638	−	12.4535i	−0.202066	−	0.621896i	−0.999821	−	0.0189143i	$-0.993979\pi$
$401$	−4.04638	−	12.4535i	−0.202066	−	0.621896i	0.797755	−	0.602982i	$-0.206021\pi$
$402$	−0.411734	+	0.133780i	−0.0205354	+	0.00667236i
$403$	2.57678	−	3.54663i	0.128358	−	0.176670i
$404$	2.61803	−	1.90211i	0.130252	−	0.0946337i
$405$		0			0
$406$	45.5566			2.26094
$407$	6.91016	+	1.28262i	0.342524	+	0.0635769i
$408$		−	1.89879i		−	0.0940040i
$409$	−9.40299	+	28.9394i	−0.464948	+	1.43096i	0.394100	+	0.919067i	$0.371056\pi$
$409$	−9.40299	+	28.9394i	−0.464948	+	1.43096i	−0.859048	+	0.511895i	$0.828944\pi$
$410$		0			0
$411$	1.85438	+	1.34729i	0.0914698	+	0.0664567i
$412$	5.49352	−	1.78495i	0.270646	−	0.0879383i
$413$	−24.1840	+	7.85785i	−1.19002	+	0.386660i
$414$	16.6341	+	12.0854i	0.817521	+	0.593963i
$415$		0			0
$416$	−0.374078	+	1.15129i	−0.0183407	+	0.0564468i
$417$			3.37797i			0.165420i
$418$	−6.20634	−	6.54359i	−0.303562	−	0.320058i
$419$	−26.7473			−1.30669			−0.653346	−	0.757059i	$-0.726635\pi$
$419$	−26.7473			−1.30669			−0.653346	+	0.757059i	$0.726635\pi$
$420$		0			0
$421$	24.5477	−	17.8350i	1.19638	−	0.869223i	0.202459	−	0.979291i	$-0.435107\pi$
$421$	24.5477	−	17.8350i	1.19638	−	0.869223i	0.993924	+	0.110068i	$0.0351068\pi$
$422$	−1.38631	+	1.90809i	−0.0674844	+	0.0928844i
$423$	15.9953	−	5.19718i	0.777717	−	0.252696i
$424$	−1.81558	−	5.58779i	−0.0881725	−	0.271367i
$425$		0			0
$426$	−1.59460	+	1.15854i	−0.0772585	+	0.0561316i
$427$	−25.1973	−	8.18710i	−1.21938	−	0.396202i
$428$			0.171425i			0.00828615i
$429$	0.771890	−	0.732108i	0.0372672	−	0.0353465i
$430$		0			0
$431$	−3.65506	+	11.2491i	−0.176058	+	0.541851i	−0.999680	−	0.0252880i	$-0.991950\pi$
$431$	−3.65506	+	11.2491i	−0.176058	+	0.541851i	0.823622	+	0.567139i	$0.191950\pi$
$432$	0.923562	+	1.27117i	0.0444349	+	0.0611594i
$433$	19.1578	−	26.3685i	0.920665	−	1.26719i	−0.0427255	−	0.999087i	$-0.513604\pi$
$433$	19.1578	−	26.3685i	0.920665	−	1.26719i	0.963391	−	0.268100i	$-0.0863959\pi$
$434$	−4.82519	−	14.8504i	−0.231617	−	0.712843i
$435$		0			0
$436$	1.88301	+	1.36809i	0.0901799	+	0.0655195i
$437$	11.2169	+	15.4387i	0.536576	+	0.738534i
$438$	−1.86289	−	0.605289i	−0.0890122	−	0.0289218i
$439$	−5.09564			−0.243202			−0.121601	−	0.992579i	$-0.538803\pi$
$439$	−5.09564			−0.243202			−0.121601	+	0.992579i	$0.538803\pi$
$440$		0			0
$441$	−33.9598			−1.61713
$442$	−8.25000	−	2.68059i	−0.392412	−	0.127503i
$443$	−14.5061	−	19.9660i	−0.689207	−	0.948612i	0.310791	−	0.950478i	$-0.399406\pi$
$443$	−14.5061	−	19.9660i	−0.689207	−	0.948612i	−0.999998	+	0.00186632i	$0.999406\pi$
$444$	−0.454269	−	0.330046i	−0.0215587	−	0.0156633i
$445$		0			0
$446$	4.51065	+	13.8824i	0.213586	+	0.657349i
$447$	1.02990	−	1.41754i	0.0487128	−	0.0670474i
$448$	2.53438	+	3.48828i	0.119738	+	0.164806i
$449$	5.86154	−	18.0400i	0.276623	−	0.851359i	−0.712162	−	0.702015i	$-0.752284\pi$
$449$	5.86154	−	18.0400i	0.276623	−	0.851359i	0.988785	−	0.149344i	$-0.0477161\pi$
$450$		0			0
$451$	8.02271	+	4.35873i	0.377775	+	0.205245i
$452$		−	4.30837i		−	0.202649i
$453$	−5.26632	−	1.71113i	−0.247433	−	0.0803959i
$454$	−2.41871	+	1.75730i	−0.113516	+	0.0824741i
$455$		0			0
$456$	0.222659	+	0.685272i	0.0104269	+	0.0320908i
$457$	−27.1185	+	8.81134i	−1.26855	+	0.412177i	−0.864534	−	0.502575i	$-0.832386\pi$
$457$	−27.1185	+	8.81134i	−1.26855	+	0.412177i	−0.404016	+	0.914752i	$0.632386\pi$
$458$	−0.928065	+	1.27737i	−0.0433656	+	0.0596877i
$459$	−9.10905	+	6.61811i	−0.425174	+	0.308907i
$460$		0			0
$461$	−35.3117			−1.64463			−0.822315	−	0.569032i	$-0.807318\pi$
$461$	−35.3117			−1.64463			−0.822315	+	0.569032i	$0.807318\pi$
$462$	−0.493608	−	3.75701i	−0.0229647	−	0.174792i
$463$			3.89605i			0.181065i	0.995894	+	0.0905323i	$0.0288568\pi$
$463$			3.89605i			0.181065i	−0.995894	+	0.0905323i	$0.971143\pi$
$464$	−3.26498	+	10.0486i	−0.151573	+	0.466493i
$465$		0			0
$466$	0.409135	+	0.297254i	0.0189528	+	0.0137700i
$467$	−11.2727	+	3.66272i	−0.521638	+	0.169490i	−0.557989	−	0.829849i	$-0.688427\pi$
$467$	−11.2727	+	3.66272i	−0.521638	+	0.169490i	0.0363506	+	0.999339i	$0.488427\pi$
$468$	3.37304	−	1.09597i	0.155919	−	0.0506611i
$469$	5.69919	+	4.14070i	0.263164	+	0.191200i
$470$		0			0
$471$	1.65641	−	5.09791i	0.0763234	−	0.234899i
$472$		−	5.89750i		−	0.271454i
$473$	19.7374	−	9.40784i	0.907527	−	0.432573i
$474$	−1.85539			−0.0852211
$475$		0			0
$476$	−24.9965	+	18.1610i	−1.14571	+	0.832410i
$477$	−10.1179	+	13.9260i	−0.463265	+	0.637629i
$478$	−15.9224	+	5.17352i	−0.728276	+	0.236631i
$479$	−3.22158	−	9.91501i	−0.147198	−	0.453029i	0.850089	−	0.526639i	$-0.176548\pi$
$479$	−3.22158	−	9.91501i	−0.147198	−	0.453029i	−0.997287	+	0.0736102i	$0.976548\pi$
$480$		0			0
$481$	−2.07532	+	1.50781i	−0.0946263	+	0.0687500i
$482$	−14.5461	−	4.72632i	−0.662557	−	0.215278i
$483$			8.01803i			0.364833i
$484$	−10.6267	+	2.84138i	−0.483031	+	0.129154i
$485$		0			0
$486$	2.14224	−	6.59313i	0.0971739	−	0.299071i
$487$	−14.4604	−	19.9030i	−0.655261	−	0.901890i	0.344052	−	0.938951i	$-0.388200\pi$
$487$	−14.4604	−	19.9030i	−0.655261	−	0.901890i	−0.999313	+	0.0370611i	$0.988200\pi$
$488$	3.61171	−	4.97109i	0.163494	−	0.225031i
$489$	−0.661705	−	2.03652i	−0.0299233	−	0.0920945i
$490$		0			0
$491$	18.7305	+	13.6085i	0.845296	+	0.614143i	0.923845	−	0.382767i	$-0.125029\pi$
$491$	18.7305	+	13.6085i	0.845296	+	0.614143i	−0.0785493	+	0.996910i	$0.525029\pi$
$492$	−0.428762	−	0.590140i	−0.0193301	−	0.0266056i
$493$	−72.0066	−	23.3964i	−3.24301	−	1.05372i
$494$	3.29176			0.148103
$495$		0			0
$496$	3.62142			0.162606
$497$	30.5032	+	9.91108i	1.36825	+	0.444573i
$498$	0.248358	+	0.341835i	0.0111292	+	0.0153180i
$499$	18.3406	+	13.3253i	0.821040	+	0.596520i	0.917010	−	0.398864i	$-0.130595\pi$
$499$	18.3406	+	13.3253i	0.821040	+	0.596520i	−0.0959702	+	0.995384i	$0.530595\pi$
$500$		0			0
$501$	−1.41432	−	4.35282i	−0.0631871	−	0.194470i
$502$	−0.251213	+	0.345766i	−0.0112122	+	0.0154323i
$503$	−12.7318	−	17.5238i	−0.567682	−	0.781347i	0.424596	−	0.905383i	$-0.360416\pi$
$503$	−12.7318	−	17.5238i	−0.567682	−	0.781347i	−0.992278	+	0.124036i	$0.960416\pi$
$504$	3.90366	−	12.0142i	0.173883	−	0.535157i
$505$		0			0
$506$	23.0773	−	3.03197i	1.02591	−	0.134787i
$507$		−	3.05640i		−	0.135740i
$508$	10.3058	+	3.34855i	0.457245	+	0.148568i
$509$	−12.4590	+	9.05200i	−0.552236	+	0.401223i	−0.828609	−	0.559828i	$-0.810867\pi$
$509$	−12.4590	+	9.05200i	−0.552236	+	0.401223i	0.276373	+	0.961050i	$0.410867\pi$
$510$		0			0
$511$	9.84937	+	30.3132i	0.435710	+	1.34098i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	2.51139	−	3.45664i	0.110881	−	0.152614i
$514$	−14.4614	+	10.5068i	−0.637864	+	0.463436i
$515$		0			0
$516$	−1.74686			−0.0769014
$517$	9.08909	−	16.7295i	0.399738	−	0.735760i
$518$			9.13695i			0.401454i
$519$	1.17696	−	3.62230i	0.0516627	−	0.159001i
$520$		0			0
$521$	−23.3132	−	16.9380i	−1.02137	−	0.742069i	−0.0548065	−	0.998497i	$-0.517454\pi$
$521$	−23.3132	−	16.9380i	−1.02137	−	0.742069i	−0.966563	+	0.256428i	$0.917454\pi$
$522$	29.4402	−	9.56569i	1.28856	−	0.418679i
$523$	−34.1267	+	11.0884i	−1.49226	+	0.484863i	−0.937748	−	0.347316i	$-0.887093\pi$
$523$	−34.1267	+	11.0884i	−1.49226	+	0.484863i	−0.554507	+	0.832179i	$0.687093\pi$
$524$	4.68031	+	3.40044i	0.204460	+	0.148549i
$525$		0			0
$526$	−4.48002	+	13.7881i	−0.195338	+	0.601190i
$527$			25.9505i			1.13042i
$528$	0.864071	+	0.160383i	0.0376039	+	0.00697977i
$529$	−26.2505			−1.14132
$530$		0			0
$531$	−13.9785	+	10.1560i	−0.606616	+	0.440733i
$532$	6.89162	−	9.48550i	0.298789	−	0.411248i
$533$	−3.16938	+	1.02979i	−0.137281	+	0.0446054i
$534$	−0.102116	−	0.314282i	−0.00441901	−	0.0136003i
$535$		0			0
$536$	−1.32178	+	0.960330i	−0.0570922	+	0.0414799i
$537$	4.75139	+	1.54382i	0.205038	+	0.0666207i
$538$		−	27.9378i		−	1.20448i
$539$	−27.8931	+	26.4555i	−1.20144	+	1.13952i
$540$		0			0
$541$	2.17819	−	6.70378i	0.0936477	−	0.288218i	−0.893251	−	0.449558i	$-0.851582\pi$
$541$	2.17819	−	6.70378i	0.0936477	−	0.288218i	0.986899	+	0.161340i	$0.0515816\pi$
$542$	−6.10681	−	8.40531i	−0.262310	−	0.361039i
$543$	2.04070	−	2.80878i	0.0875746	−	0.120536i
$544$	−2.21437	−	6.81513i	−0.0949404	−	0.292196i
$545$		0			0
$546$	1.11892	+	0.812944i	0.0478854	+	0.0347908i
$547$	8.91181	+	12.2661i	0.381041	+	0.524459i	0.955860	−	0.293822i	$-0.0949274\pi$
$547$	8.91181	+	12.2661i	0.381041	+	0.524459i	−0.574819	+	0.818281i	$0.694927\pi$
$548$	8.22695	+	2.67310i	0.351438	+	0.114189i
$549$	−18.0024			−0.768323
$550$		0			0
$551$	28.7307			1.22397
$552$	−1.76856	−	0.574640i	−0.0752749	−	0.0244583i
$553$	17.7460	+	24.4253i	0.754636	+	1.03867i
$554$	0.508336	+	0.369328i	0.0215971	+	0.0156912i
$555$		0			0
$556$	3.93940	+	12.1242i	0.167068	+	0.514181i
$557$	6.77793	−	9.32902i	0.287190	−	0.395283i	−0.640909	−	0.767617i	$-0.721442\pi$
$557$	6.77793	−	9.32902i	0.287190	−	0.395283i	0.928099	+	0.372334i	$0.121442\pi$
$558$	−6.23639	−	8.58365i	−0.264007	−	0.363375i
$559$	−2.46611	+	7.58991i	−0.104305	+	0.321019i
$560$		0			0
$561$	−1.14928	+	6.19181i	−0.0485226	+	0.261418i
$562$			30.1066i			1.26997i
$563$	−32.4519	−	10.5443i	−1.36769	−	0.444388i	−0.469084	−	0.883154i	$-0.655416\pi$
$563$	−32.4519	−	10.5443i	−1.36769	−	0.444388i	−0.898601	+	0.438766i	$0.855416\pi$
$564$	−1.23060	+	0.894080i	−0.0518174	+	0.0376476i
$565$		0			0
$566$	4.97656	+	15.3163i	0.209181	+	0.643792i
$567$	−34.3354	+	11.1562i	−1.44195	+	0.468518i
$568$	−4.37224	+	6.01787i	−0.183455	+	0.252504i
$569$	−6.45701	+	4.69129i	−0.270692	+	0.196669i	−0.714847	−	0.699281i	$-0.753504\pi$
$569$	−6.45701	+	4.69129i	−0.270692	+	0.196669i	0.444155	+	0.895950i	$0.353504\pi$
$570$		0			0
$571$	−3.62605			−0.151746			−0.0758728	−	0.997118i	$-0.524174\pi$
$571$	−3.62605			−0.151746			−0.0758728	+	0.997118i	$0.524174\pi$
$572$	1.91668	−	3.52786i	0.0801406	−	0.147507i
$573$			2.98677i			0.124774i
$574$	−3.66796	+	11.2888i	−0.153098	+	0.471187i
$575$		0			0
$576$	2.37025	+	1.72209i	0.0987603	+	0.0717536i
$577$	−3.48094	+	1.13103i	−0.144913	+	0.0470852i	−0.380576	−	0.924750i	$-0.624274\pi$
$577$	−3.48094	+	1.13103i	−0.144913	+	0.0470852i	0.235662	+	0.971835i	$0.424274\pi$
$578$	32.6683	−	10.6146i	1.35882	−	0.441508i
$579$	−1.48865	−	1.08157i	−0.0618662	−	0.0449484i
$580$		0			0
$581$	2.12465	−	6.53900i	0.0881453	−	0.271283i
$582$			1.83186i			0.0759330i
$583$	2.53836	+	19.3203i	0.105128	+	0.800165i
$584$	−7.39217			−0.305890
$585$		0			0
$586$	−3.21992	+	2.33941i	−0.133014	+	0.0966402i
$587$	10.4798	−	14.4242i	0.432547	−	0.595350i	−0.535988	−	0.844225i	$-0.680061\pi$
$587$	10.4798	−	14.4242i	0.432547	−	0.595350i	0.968536	+	0.248875i	$0.0800610\pi$
$588$	2.92108	−	0.949117i	0.120463	−	0.0391409i
$589$	−3.04305	−	9.36555i	−0.125387	−	0.385901i
$590$		0			0
$591$	−2.88092	+	2.09311i	−0.118505	+	0.0860991i
$592$	−2.01536	−	0.654831i	−0.0828309	−	0.0269134i
$593$			23.0006i			0.944523i	0.881458	+	0.472262i	$0.156562\pi$
$593$			23.0006i			0.944523i	−0.881458	+	0.472262i	$0.843438\pi$
$594$	−2.24227	−	4.70421i	−0.0920013	−	0.193016i
$595$		0			0
$596$	2.04339	−	6.28892i	0.0837007	−	0.257604i
$597$	3.02819	+	4.16795i	0.123936	+	0.170583i
$598$	−4.99348	+	6.87293i	−0.204199	+	0.281055i
$599$	−1.03235	−	3.17725i	−0.0421807	−	0.129819i	0.927749	−	0.373206i	$-0.121742\pi$
$599$	−1.03235	−	3.17725i	−0.0421807	−	0.129819i	−0.969929	+	0.243387i	$0.921742\pi$
$600$		0			0
$601$	−28.2605	−	20.5324i	−1.15277	−	0.837535i	−0.163921	−	0.986473i	$-0.552414\pi$
$601$	−28.2605	−	20.5324i	−1.15277	−	0.837535i	−0.988846	+	0.148939i	$0.952414\pi$
$602$	16.7079	+	22.9965i	0.680965	+	0.937268i
$603$	4.55244	+	1.47918i	0.185390	+	0.0602367i
$604$	−20.8974			−0.850303
$605$		0			0
$606$	0.857484			0.0348329
$607$	−11.9913	−	3.89620i	−0.486711	−	0.158142i	0.0553739	−	0.998466i	$-0.482365\pi$
$607$	−11.9913	−	3.89620i	−0.486711	−	0.158142i	−0.542085	+	0.840324i	$0.682365\pi$
$608$	1.59833	+	2.19992i	0.0648210	+	0.0892184i
$609$	9.76602	+	7.09543i	0.395739	+	0.287521i
$610$		0			0
$611$	2.14739	+	6.60899i	0.0868742	+	0.267371i
$612$	−12.3402	+	16.9849i	−0.498824	+	0.686572i
$613$	−5.03320	−	6.92760i	−0.203289	−	0.279803i	0.695184	−	0.718832i	$-0.255323\pi$
$613$	−5.03320	−	6.92760i	−0.203289	−	0.279803i	−0.898473	+	0.439028i	$0.855323\pi$
$614$	5.44041	−	16.7439i	0.219557	−	0.675727i
$615$		0			0
$616$	−6.15309	−	12.9090i	−0.247915	−	0.520119i
$617$		−	1.77165i		−	0.0713241i	−0.999364	−	0.0356620i	$-0.988646\pi$
$617$		−	1.77165i		−	0.0713241i	0.999364	−	0.0356620i	$-0.0113540\pi$
$618$	1.45566	+	0.472972i	0.0585551	+	0.0190257i
$619$	−15.6706	+	11.3854i	−0.629855	+	0.457616i	−0.856350	−	0.516396i	$-0.827273\pi$
$619$	−15.6706	+	11.3854i	−0.629855	+	0.457616i	0.226495	+	0.974012i	$0.427273\pi$
$620$		0			0
$621$	3.40749	+	10.4872i	0.136738	+	0.420836i
$622$	21.5266	−	6.99443i	0.863140	−	0.280451i
$623$	−3.16066	+	4.35027i	−0.126629	+	0.174290i
$624$	−0.259505	+	0.188541i	−0.0103885	+	0.00754769i
$625$		0			0
$626$	12.6096			0.503982
$627$	−0.311298	−	2.36939i	−0.0124320	−	0.0946244i
$628$		−	20.2291i		−	0.807231i
$629$	4.69243	−	14.4418i	0.187099	−	0.575833i
$630$		0			0
$631$	−22.1727	−	16.1094i	−0.882680	−	0.641305i	0.0512788	−	0.998684i	$-0.483670\pi$
$631$	−22.1727	−	16.1094i	−0.882680	−	0.641305i	−0.933959	+	0.357379i	$0.883670\pi$
$632$	−6.65938	+	2.16376i	−0.264896	+	0.0860699i
$633$	−0.594369	+	0.193122i	−0.0236240	+	0.00767591i
$634$	−21.2511	−	15.4399i	−0.843991	−	0.613195i
$635$		0			0
$636$	0.481088	−	1.48064i	0.0190764	−	0.0587111i
$637$		−	14.0316i		−	0.555954i
$638$	16.7290	−	30.7915i	0.662306	−	1.21905i
$639$	21.7932			0.862126
$640$		0			0
$641$	19.3094	−	14.0291i	0.762676	−	0.554117i	−0.137054	−	0.990564i	$-0.543763\pi$
$641$	19.3094	−	14.0291i	0.762676	−	0.554117i	0.899730	+	0.436447i	$0.143763\pi$
$642$	−0.0266994	+	0.0367486i	−0.00105374	+	0.00145035i
$643$	−11.8726	+	3.85766i	−0.468211	+	0.152131i	−0.533614	−	0.845728i	$-0.679167\pi$
$643$	−11.8726	+	3.85766i	−0.468211	+	0.152131i	0.0654032	+	0.997859i	$0.479167\pi$
$644$	9.35064	+	28.7783i	0.368467	+	1.13402i
$645$		0			0
$646$	−15.7643	+	11.4534i	−0.620237	+	0.450629i
$647$	−6.71040	−	2.18034i	−0.263813	−	0.0857180i	0.174124	−	0.984724i	$-0.444291\pi$
$647$	−6.71040	−	2.18034i	−0.263813	−	0.0857180i	−0.437937	+	0.899006i	$0.644291\pi$
$648$		−	8.37301i		−	0.328923i
$649$	−3.56958	+	19.2313i	−0.140118	+	0.754895i
$650$		0			0
$651$	1.27857	−	3.93502i	0.0501109	−	0.154226i
$652$	−4.74999	−	6.53779i	−0.186024	−	0.256040i
$653$	1.57315	−	2.16526i	0.0615622	−	0.0847331i	−0.777126	−	0.629345i	$-0.783323\pi$
$653$	1.57315	−	2.16526i	0.0615622	−	0.0847331i	0.838688	+	0.544612i	$0.183323\pi$
$654$	0.190584	+	0.586557i	0.00745242	+	0.0229362i
$655$		0			0
$656$	−2.22713	−	1.61811i	−0.0869550	−	0.0631765i
$657$	12.7300	+	17.5213i	0.496643	+	0.683570i
$658$	23.5402	+	7.64866i	0.917691	+	0.298176i
$659$	36.5069			1.42211			0.711053	−	0.703138i	$-0.248219\pi$
$659$	36.5069			1.42211			0.711053	+	0.703138i	$0.248219\pi$
$660$		0			0
$661$	40.3521			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$661$	40.3521			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$662$	12.1170	+	3.93705i	0.470940	+	0.153018i
$663$	−1.35106	−	1.85957i	−0.0524708	−	0.0722199i
$664$	1.29006	+	0.937281i	0.0500639	+	0.0363735i
$665$		0			0
$666$	1.91852	+	5.90459i	0.0743410	+	0.228798i
$667$	−43.5834	+	59.9875i	−1.68756	+	2.32272i
$668$	−10.1525	−	13.9738i	−0.392814	−	0.540662i
$669$	−1.19522	+	3.67851i	−0.0462099	+	0.142219i
$670$		0			0
$671$	−14.7864	+	14.0243i	−0.570822	+	0.541402i
$672$			1.14252i			0.0440735i
$673$	12.1340	+	3.94257i	0.467731	+	0.151975i	0.533394	−	0.845867i	$-0.320916\pi$
$673$	12.1340	+	3.94257i	0.467731	+	0.151975i	−0.0656634	+	0.997842i	$0.520916\pi$
$674$	15.4174	−	11.2014i	0.593857	−	0.431462i
$675$		0			0
$676$	−3.56438	−	10.9700i	−0.137092	−	0.421925i
$677$	−11.8707	+	3.85703i	−0.456228	+	0.148238i	−0.528111	−	0.849175i	$-0.677099\pi$
$677$	−11.8707	+	3.85703i	−0.456228	+	0.148238i	0.0718823	+	0.997413i	$0.477099\pi$
$678$	0.671027	−	0.923590i	0.0257706	−	0.0354703i
$679$	24.1154	−	17.5209i	0.925466	−	0.672390i
$680$		0			0
$681$	−0.792201			−0.0303572
$682$	−11.8092	−	2.19194i	−0.452197	−	0.0839336i
$683$			5.10260i			0.195246i	0.995223	+	0.0976228i	$0.0311239\pi$
$683$			5.10260i			0.195246i	−0.995223	+	0.0976228i	$0.968876\pi$
$684$	2.46188	−	7.57689i	0.0941324	−	0.289710i
$685$		0			0
$686$	−16.0155	−	11.6359i	−0.611473	−	0.444261i
$687$	−0.397900	+	0.129286i	−0.0151808	+	0.00493256i
$688$	−6.26985	+	2.03720i	−0.239036	+	0.0776674i
$689$	−5.75401	−	4.18054i	−0.219210	−	0.159266i
$690$		0			0
$691$	3.68372	−	11.3373i	0.140135	−	0.431292i	−0.856218	−	0.516615i	$-0.827192\pi$
$691$	3.68372	−	11.3373i	0.140135	−	0.431292i	0.996353	+	0.0853223i	$0.0271920\pi$
$692$		−	14.3738i		−	0.546408i
$693$	−20.0014	+	36.8148i	−0.759791	+	1.39848i
$694$	18.8230			0.714511
$695$		0			0
$696$	−2.26498	+	1.64560i	−0.0858537	+	0.0623764i
$697$	11.5951	−	15.9593i	0.439197	−	0.604502i
$698$	−25.8860	+	8.41088i	−0.979800	+	0.318356i
$699$	0.0414095	+	0.127445i	0.00156625	+	0.00482043i
$700$		0			0
$701$	9.19138	−	6.67793i	0.347154	−	0.252222i	−0.400520	−	0.916288i	$-0.631171\pi$
$701$	9.19138	−	6.67793i	0.347154	−	0.252222i	0.747674	+	0.664066i	$0.231171\pi$
$702$	1.80898	+	0.587773i	0.0682755	+	0.0221840i
$703$			5.76230i			0.217329i
$704$	3.28837	−	0.432036i	0.123935	−	0.0162830i
$705$		0			0
$706$	−7.92257	+	24.3832i	−0.298170	+	0.917673i
$707$	−8.20144	−	11.2883i	−0.308447	−	0.424541i
$708$	0.918533	−	1.26425i	0.0345206	−	0.0475135i
$709$	−3.75791	−	11.5656i	−0.141131	−	0.434357i	0.855362	−	0.518031i	$-0.173335\pi$
$709$	−3.75791	−	11.5656i	−0.141131	−	0.434357i	−0.996493	+	0.0836737i	$0.973335\pi$
$710$		0			0
$711$	16.5967	+	12.0582i	0.622424	+	0.452218i
$712$	−0.733033	−	1.00893i	−0.0274716	−	0.0378114i
$713$	24.1707	+	7.85355i	0.905201	+	0.294118i
$714$	−8.18710			−0.306395
$715$		0			0
$716$	18.8541			0.704611
$717$	−4.21908	−	1.37086i	−0.157565	−	0.0511958i
$718$	5.68779	+	7.82857i	0.212267	+	0.292160i
$719$	−27.9662	−	20.3186i	−1.04296	−	0.757756i	−0.0721003	−	0.997397i	$-0.522970\pi$
$719$	−27.9662	−	20.3186i	−1.04296	−	0.757756i	−0.970862	+	0.239641i	$0.922970\pi$
$720$		0			0
$721$	−7.69628	−	23.6867i	−0.286624	−	0.882139i
$722$	−6.82166	+	9.38921i	−0.253876	+	0.349430i
$723$	−2.38214	−	3.27874i	−0.0885928	−	0.121938i
$724$	4.04887	−	12.4611i	0.150475	−	0.463114i
$725$		0			0
$726$	−2.72060	−	1.04599i	−0.100971	−	0.0388205i
$727$		−	46.4273i		−	1.72189i	−0.508695	−	0.860947i	$-0.669872\pi$
$727$		−	46.4273i		−	1.72189i	0.508695	−	0.860947i	$-0.330128\pi$
$728$	4.96409	+	1.61293i	0.183981	+	0.0597792i
$729$	−18.8356	+	13.6849i	−0.697616	+	0.506847i
$730$		0			0
$731$	−14.5983	−	44.9288i	−0.539936	−	1.66175i
$732$	1.54849	−	0.503135i	0.0572339	−	0.0185964i
$733$	8.59151	−	11.8252i	0.317334	−	0.436773i	−0.620317	−	0.784352i	$-0.712996\pi$
$733$	8.59151	−	11.8252i	0.317334	−	0.436773i	0.937651	+	0.347578i	$0.112996\pi$
$734$	16.7495	−	12.1692i	0.618236	−	0.449174i
$735$		0			0
$736$	−7.01787			−0.258682
$737$	4.89149	−	2.33153i	0.180180	−	0.0858830i
$738$			8.06538i			0.296891i
$739$	12.8330	−	39.4959i	0.472070	−	1.45288i	−0.377800	−	0.925887i	$-0.623319\pi$
$739$	12.8330	−	39.4959i	0.472070	−	1.45288i	0.849869	−	0.526994i	$-0.176681\pi$
$740$		0			0
$741$	0.705658	+	0.512690i	0.0259230	+	0.0188341i
$742$	−24.0932	+	7.82835i	−0.884488	+	0.287388i
$743$	38.0571	−	12.3655i	1.39618	−	0.453646i	0.488226	−	0.872717i	$-0.337644\pi$
$743$	38.0571	−	12.3655i	1.39618	−	0.453646i	0.907953	+	0.419071i	$0.137644\pi$
$744$	0.776327	+	0.564034i	0.0284615	+	0.0206785i
$745$		0			0
$746$	4.98947	−	15.3560i	0.182677	−	0.562223i
$747$		−	4.67183i		−	0.170933i
$748$	3.09590	+	23.5639i	0.113197	+	0.861583i
$749$	0.739143			0.0270077
$750$		0			0
$751$	−11.5210	+	8.37050i	−0.420407	+	0.305444i	−0.777802	−	0.628510i	$-0.783665\pi$
$751$	−11.5210	+	8.37050i	−0.420407	+	0.305444i	0.357394	+	0.933954i	$0.383665\pi$
$752$	−3.37418	+	4.64416i	−0.123044	+	0.169355i
$753$	−0.107706	+	0.0349957i	−0.00392502	+	0.00127531i
$754$	3.95239	+	12.1642i	0.143937	+	0.442994i
$755$		0			0
$756$	5.48099	−	3.98217i	0.199342	−	0.144830i
$757$	28.3439	+	9.20948i	1.03017	+	0.334724i	0.774859	−	0.632134i	$-0.217821\pi$
$757$	28.3439	+	9.20948i	1.03017	+	0.334724i	0.255316	+	0.966858i	$0.417821\pi$
$758$			0.229700i			0.00834306i
$759$	5.41933	+	2.94432i	0.196709	+	0.106872i
$760$		0			0
$761$	−4.10031	+	12.6195i	−0.148636	+	0.457455i	−0.997461	−	0.0712199i	$-0.977311\pi$
$761$	−4.10031	+	12.6195i	−0.148636	+	0.457455i	0.848825	+	0.528675i	$0.177311\pi$
$762$	1.68772	+	2.32295i	0.0611398	+	0.0841517i
$763$	5.89886	−	8.11908i	0.213553	−	0.293930i
$764$	3.48318	+	10.7201i	0.126017	+	0.387840i
$765$		0			0
$766$	10.5351	+	7.65417i	0.380647	+	0.276556i
$767$	−4.19629	−	5.77570i	−0.151519	−	0.208548i
$768$	−0.252008	−	0.0818824i	−0.00909356	−	0.00295468i
$769$	46.3160			1.67020			0.835099	−	0.550099i	$-0.185410\pi$
$769$	46.3160			1.67020			0.835099	+	0.550099i	$0.185410\pi$
$770$		0			0
$771$	−4.73653			−0.170582
$772$	−6.60440	−	2.14590i	−0.237697	−	0.0772326i
$773$	−30.0645	−	41.3802i	−1.08134	−	1.48834i	−0.858032	−	0.513596i	$-0.828313\pi$
$773$	−30.0645	−	41.3802i	−1.08134	−	1.48834i	−0.223312	−	0.974747i	$-0.571687\pi$
$774$	15.6259	+	11.3529i	0.561660	+	0.408070i
$775$		0			0
$776$	2.13632	+	6.57491i	0.0766894	+	0.236026i
$777$	−1.42308	+	1.95870i	−0.0510526	+	0.0702678i
$778$	17.4135	+	23.9676i	0.624304	+	0.859280i
$779$	−2.31323	+	7.11940i	−0.0828802	+	0.255079i
$780$		0			0
$781$	17.9000	−	16.9774i	0.640512	−	0.607501i
$782$		−	50.2890i		−	1.79833i
$783$	15.7889	+	5.13012i	0.564249	+	0.183336i
$784$	9.37749	−	6.81315i	0.334910	−	0.243327i
$785$		0			0
$786$	0.473705	+	1.45791i	0.0168965	+	0.0520020i
$787$	33.0022	−	10.7231i	1.17640	−	0.382236i	0.345374	−	0.938465i	$-0.387752\pi$
$787$	33.0022	−	10.7231i	1.17640	−	0.382236i	0.831029	+	0.556229i	$0.187752\pi$
$788$	−7.89922	+	10.8723i	−0.281398	+	0.387311i
$789$	−3.10788	+	2.25801i	−0.110643	+	0.0803871i
$790$		0			0
$791$	−18.5766			−0.660509
$792$	−6.68688	−	7.05024i	−0.237608	−	0.250519i
$793$		−	7.43830i		−	0.264142i
$794$	0.675711	−	2.07963i	0.0239801	−	0.0738032i
$795$		0			0
$796$	15.7295	+	11.4281i	0.557516	+	0.405059i
$797$	42.4885	−	13.8054i	1.50502	−	0.489011i	0.563544	−	0.826086i	$-0.309438\pi$
$797$	42.4885	−	13.8054i	1.50502	−	0.489011i	0.941478	+	0.337075i	$0.109438\pi$
$798$	2.95473	−	0.960049i	0.104596	−	0.0339853i
$799$	−33.2794	−	24.1789i	−1.17734	−	0.855387i
$800$		0			0
$801$	−1.12908	+	3.47494i	−0.0398939	+	0.122781i
$802$		−	13.0944i		−	0.462378i
$803$	24.1053	+	4.47426i	0.850659	+	0.157893i
$804$	−0.432922			−0.0152680
$805$		0			0
$806$	3.54663	−	2.57678i	0.124925	−	0.0907630i
$807$	4.35130	−	5.98906i	0.153173	−	0.210825i
$808$	3.07768	−	1.00000i	0.108273	−	0.0351799i
$809$	4.04819	+	12.4590i	0.142327	+	0.438037i	0.996658	−	0.0816929i	$-0.0260327\pi$
$809$	4.04819	+	12.4590i	0.142327	+	0.438037i	−0.854331	+	0.519730i	$0.826033\pi$
$810$		0			0
$811$	6.33646	−	4.60371i	0.222503	−	0.161658i	−0.470949	−	0.882160i	$-0.656089\pi$
$811$	6.33646	−	4.60371i	0.222503	−	0.161658i	0.693453	+	0.720502i	$0.256089\pi$
$812$	43.3269	+	14.0778i	1.52048	+	0.494033i
$813$		−	2.75299i		−	0.0965515i
$814$	6.17561	+	3.35520i	0.216455	+	0.117600i
$815$		0			0
$816$	0.586758	−	1.80585i	0.0205406	−	0.0632176i
$817$	10.5370	+	14.5030i	0.368644	+	0.507394i
$818$	−17.8855	+	24.6173i	−0.625353	+	0.860725i
$819$	−4.72554	−	14.5437i	−0.165124	−	0.508199i
$820$		0			0
$821$	19.4432	+	14.1263i	0.678573	+	0.493012i	0.872884	−	0.487928i	$-0.162247\pi$
$821$	19.4432	+	14.1263i	0.678573	+	0.493012i	−0.194311	+	0.980940i	$0.562247\pi$
$822$	1.34729	+	1.85438i	0.0469920	+	0.0646789i
$823$	11.4813	+	3.73052i	0.400215	+	0.130038i	0.502207	−	0.864748i	$-0.332522\pi$
$823$	11.4813	+	3.73052i	0.400215	+	0.130038i	−0.101992	+	0.994785i	$0.532522\pi$
$824$	5.77623			0.201224
$825$		0			0
$826$	−25.4285			−0.884772
$827$	−33.5158	−	10.8899i	−1.16546	−	0.378680i	−0.338512	−	0.940962i	$-0.609924\pi$
$827$	−33.5158	−	10.8899i	−1.16546	−	0.378680i	−0.826946	+	0.562282i	$0.809924\pi$
$828$	12.0854	+	16.6341i	0.419996	+	0.578074i
$829$	19.6457	+	14.2734i	0.682322	+	0.495736i	0.874127	−	0.485697i	$-0.161434\pi$
$829$	19.6457	+	14.2734i	0.682322	+	0.495736i	−0.191805	+	0.981433i	$0.561434\pi$
$830$		0			0
$831$	0.0514499	+	0.158346i	0.00178478	+	0.00549298i
$832$	−0.711538	+	0.979348i	−0.0246681	+	0.0339528i
$833$	48.8220	+	67.1977i	1.69158	+	2.32826i
$834$	−1.04385	+	3.21264i	−0.0361456	+	0.111245i
$835$		0			0
$836$	−3.88050	−	8.14119i	−0.134210	−	0.281569i
$837$		−	5.69018i		−	0.196681i
$838$	−25.4382	−	8.26538i	−0.878748	−	0.285523i
$839$	12.3220	−	8.95243i	0.425401	−	0.309072i	−0.354406	−	0.935092i	$-0.615317\pi$
$839$	12.3220	−	8.95243i	0.425401	−	0.309072i	0.779807	+	0.626019i	$0.215317\pi$
$840$		0			0
$841$	25.5352	+	78.5894i	0.880525	+	2.70998i
$842$	28.8576	−	9.37640i	0.994498	−	0.323132i
$843$	−4.68910	+	6.45399i	−0.161501	+	0.222287i
$844$	−1.90809	+	1.38631i	−0.0656792	+	0.0477187i
$845$		0			0
$846$	16.8184			0.578229
$847$	12.2513	+	45.8197i	0.420961	+	1.57438i
$848$		−	5.87535i		−	0.201760i
$849$	−1.31868	+	4.05847i	−0.0452568	+	0.139286i
$850$		0			0
$851$	−12.0312	−	8.74120i	−0.412425	−	0.299644i
$852$	−1.87456	+	0.609082i	−0.0642214	+	0.0208668i
$853$	6.56839	−	2.13420i	0.224897	−	0.0730736i	−0.194401	−	0.980922i	$-0.562276\pi$
$853$	6.56839	−	2.13420i	0.224897	−	0.0730736i	0.419298	+	0.907849i	$0.362276\pi$
$854$	−21.4341	−	15.5728i	−0.733460	−	0.532890i
$855$		0			0
$856$	−0.0529733	+	0.163035i	−0.00181059	+	0.00557242i
$857$			1.68576i			0.0575845i	0.999585	+	0.0287922i	$0.00916612\pi$
$857$			1.68576i			0.0575845i	−0.999585	+	0.0287922i	$0.990834\pi$
$858$	0.960345	−	0.457749i	0.0327856	−	0.0156273i
$859$	52.7330			1.79923			0.899613	−	0.436688i	$-0.143849\pi$
$859$	52.7330			1.79923			0.899613	+	0.436688i	$0.143849\pi$
$860$		0			0
$861$	−2.54454	+	1.84871i	−0.0867176	+	0.0630040i
$862$	−6.95234	+	9.56907i	−0.236798	+	0.325924i
$863$	−28.0504	+	9.11412i	−0.954846	+	0.310248i	−0.744683	−	0.667418i	$-0.767399\pi$
$863$	−28.0504	+	9.11412i	−0.954846	+	0.310248i	−0.210163	+	0.977666i	$0.567399\pi$
$864$	0.485545	+	1.49436i	0.0165186	+	0.0508390i
$865$		0			0
$866$	26.3685	−	19.1578i	0.896037	−	0.651009i
$867$	8.65635	+	2.81262i	0.293985	+	0.0955216i
$868$		−	15.6147i		−	0.529996i
$869$	23.0254	−	3.02515i	0.781084	−	0.102621i
$870$		0			0
$871$	−0.611172	+	1.88099i	−0.0207088	+	0.0637351i
$872$	1.36809	+	1.88301i	0.0463293	+	0.0637668i
$873$	11.9052	−	16.3862i	0.402932	−	0.554588i
$874$	5.89707	+	18.1493i	0.199471	+	0.613909i
$875$		0			0
$876$	−1.58467	−	1.15133i	−0.0535410	−	0.0388998i
$877$	−16.4715	−	22.6710i	−0.556202	−	0.765547i	0.434635	−	0.900607i	$-0.356877\pi$
$877$	−16.4715	−	22.6710i	−0.556202	−	0.765547i	−0.990837	+	0.135060i	$0.956877\pi$
$878$	−4.84624	−	1.57464i	−0.163553	−	0.0531415i
$879$	−1.05462			−0.0355715
$880$		0			0
$881$	−28.1345			−0.947875			−0.473937	−	0.880559i	$-0.657168\pi$
$881$	−28.1345			−0.947875			−0.473937	+	0.880559i	$0.657168\pi$
$882$	−32.2977	−	10.4942i	−1.08752	−	0.353357i
$883$	−23.8191	−	32.7842i	−0.801578	−	1.10328i	−0.992569	−	0.121686i	$-0.961170\pi$
$883$	−23.8191	−	32.7842i	−0.801578	−	1.10328i	0.190991	−	0.981592i	$-0.438830\pi$
$884$	−7.01787	−	5.09878i	−0.236036	−	0.171490i
$885$		0			0
$886$	−7.62632	−	23.4714i	−0.256211	−	0.788537i
$887$	−8.37825	+	11.5317i	−0.281314	+	0.387196i	−0.926169	−	0.377110i	$-0.876918\pi$
$887$	−8.37825	+	11.5317i	−0.281314	+	0.387196i	0.644854	+	0.764305i	$0.276918\pi$
$888$	−0.330046	−	0.454269i	−0.0110756	−	0.0152443i
$889$	14.4381	−	44.4360i	0.484239	−	1.49033i
$890$		0			0
$891$	−5.06794	+	27.3038i	−0.169782	+	0.914711i
$892$			14.5968i			0.488737i
$893$	14.8458	+	4.82370i	0.496796	+	0.161419i
$894$	1.41754	−	1.02990i	0.0474097	−	0.0344451i
$895$		0			0
$896$	1.33240	+	4.10072i	0.0445125	+	0.136995i
$897$	−2.14091	+	0.695625i	−0.0714831	+	0.0232263i
$898$	11.1493	−	15.3457i	0.372057	−	0.512093i
$899$	30.9552	−	22.4903i	1.03241	−	0.750093i
$900$		0			0
$901$	42.1019			1.40262
$902$	6.28313	+	6.62455i	0.209205	+	0.220573i
$903$			7.53204i			0.250651i
$904$	1.33136	−	4.09750i	0.0442804	−	0.136281i
$905$		0			0
$906$	−4.47980	−	3.25476i	−0.148831	−	0.108132i
$907$	−41.2401	+	13.3997i	−1.36936	+	0.444931i	−0.899156	−	0.437629i	$-0.855818\pi$
$907$	−41.2401	+	13.3997i	−1.36936	+	0.444931i	−0.470200	+	0.882560i	$0.655818\pi$
$908$	−2.84337	+	0.923867i	−0.0943605	+	0.0306596i
$909$	−7.67028	−	5.57279i	−0.254407	−	0.184838i
$910$		0			0
$911$	7.33435	−	22.5728i	0.242998	−	0.747871i	−0.752961	−	0.658065i	$-0.771375\pi$
$911$	7.33435	−	22.5728i	0.242998	−	0.747871i	0.995959	−	0.0898061i	$-0.0286247\pi$
$912$			0.720538i			0.0238594i
$913$	−3.63947	−	3.83724i	−0.120449	−	0.126994i
$914$	−28.5141			−0.943162
$915$		0			0
$916$	−1.27737	+	0.928065i	−0.0422055	+	0.0306641i
$917$	14.6619	−	20.1803i	0.484178	−	0.666414i
$918$	−10.7083	+	3.47935i	−0.353428	+	0.114836i
$919$	4.34410	+	13.3698i	0.143299	+	0.441028i	0.996788	−	0.0800817i	$-0.0255181\pi$
$919$	4.34410	+	13.3698i	0.143299	+	0.441028i	−0.853490	+	0.521110i	$0.825518\pi$
$920$		0			0
$921$	3.77412	−	2.74206i	0.124361	−	0.0903538i
$922$	−33.5834	−	10.9119i	−1.10601	−	0.359365i
$923$			9.00460i			0.296390i
$924$	0.691531	−	3.72566i	0.0227497	−	0.122565i
$925$		0			0
$926$	−1.20394	+	3.70536i	−0.0395641	+	0.121766i
$927$	−9.94716	−	13.6911i	−0.326708	−	0.449674i
$928$	−6.21036	+	8.54782i	−0.203865	+	0.280596i
$929$	17.2507	+	53.0922i	0.565977	+	1.74190i	0.665030	+	0.746816i	$0.268419\pi$
$929$	17.2507	+	53.0922i	0.565977	+	1.74190i	−0.0990531	+	0.995082i	$0.531581\pi$
$930$		0			0
$931$	−25.4997	−	18.5266i	−0.835719	−	0.607185i
$932$	0.297254	+	0.409135i	0.00973688	+	0.0134017i
$933$	5.70407	+	1.85336i	0.186743	+	0.0606764i
$934$	−11.8528			−0.387836
$935$		0			0
$936$	3.54663			0.115925
$937$	11.8183	+	3.84000i	0.386088	+	0.125447i	0.495628	−	0.868535i	$-0.334938\pi$
$937$	11.8183	+	3.84000i	0.386088	+	0.125447i	−0.109540	+	0.993982i	$0.534938\pi$
$938$	4.14070	+	5.69919i	0.135199	+	0.186085i
$939$	2.70314	+	1.96395i	0.0882136	+	0.0640910i
$940$		0			0
$941$	−4.50996	−	13.8802i	−0.147020	−	0.452483i	0.850245	−	0.526387i	$-0.176454\pi$
$941$	−4.50996	−	13.8802i	−0.147020	−	0.452483i	−0.997265	+	0.0739049i	$0.976454\pi$
$942$	3.15068	−	4.33654i	0.102655	−	0.141292i
$943$	−11.3557	−	15.6297i	−0.369791	−	0.508974i
$944$	1.82243	−	5.60885i	0.0593149	−	0.182553i
$945$		0			0
$946$	21.6786	−	2.84820i	0.704831	−	0.0926029i
$947$		−	38.1184i		−	1.23868i	−0.785123	−	0.619340i	$-0.787400\pi$
$947$		−	38.1184i		−	1.23868i	0.785123	−	0.619340i	$-0.212600\pi$
$948$	−1.76458	−	0.573348i	−0.0573110	−	0.0186215i
$949$	−7.23951	+	5.25981i	−0.235004	+	0.170741i
$950$		0			0
$951$	−2.15088	−	6.61972i	−0.0697470	−	0.214659i
$952$	−29.3852	+	9.54782i	−0.952379	+	0.309447i
$953$	0.277189	−	0.381518i	0.00897903	−	0.0123586i	−0.804504	−	0.593947i	$-0.797569\pi$
$953$	0.277189	−	0.381518i	0.00897903	−	0.0123586i	0.813483	+	0.581589i	$0.197569\pi$
$954$	−13.9260	+	10.1179i	−0.450872	+	0.327578i
$955$		0			0
$956$	−16.7418			−0.541470
$957$	8.38196	−	3.99527i	0.270950	−	0.129149i
$958$		−	10.4253i		−	0.336825i
$959$	11.5257	−	35.4726i	0.372185	−	1.14547i
$960$		0			0
$961$	14.4695	+	10.5127i	0.466760	+	0.339121i
$962$	−2.43968	+	0.792700i	−0.0786585	+	0.0255577i
$963$	0.477658	−	0.155200i	0.0153923	−	0.00500126i
$964$	−12.3737	−	8.98999i	−0.398529	−	0.289548i
$965$		0			0
$966$	−2.47771	+	7.62559i	−0.0797189	+	0.245349i
$967$			29.1678i			0.937975i	0.883205	+	0.468987i	$0.155381\pi$
$967$			29.1678i			0.937975i	−0.883205	+	0.468987i	$0.844619\pi$
$968$	−10.9846	−	0.581513i	−0.353059	−	0.0186906i
$969$	−5.16327			−0.165868
$970$		0			0
$971$	12.8033	−	9.30216i	0.410878	−	0.298520i	−0.363079	−	0.931758i	$-0.618275\pi$
$971$	12.8033	−	9.30216i	0.410878	−	0.298520i	0.773957	+	0.633238i	$0.218275\pi$
$972$	4.07478	−	5.60845i	0.130699	−	0.179891i
$973$	52.2766	−	16.9857i	1.67591	−	0.544537i
$974$	−7.60226	−	23.3973i	−0.243592	−	0.749699i
$975$		0			0
$976$	4.97109	−	3.61171i	0.159121	−	0.115608i
$977$	−39.7961	−	12.9305i	−1.27319	−	0.413684i	−0.407013	−	0.913423i	$-0.633429\pi$
$977$	−39.7961	−	12.9305i	−1.27319	−	0.413684i	−0.866176	+	0.499738i	$0.833429\pi$
$978$		−	2.14132i		−	0.0684719i
$979$	1.77969	+	3.73374i	0.0568791	+	0.119331i
$980$		0			0
$981$	2.10724	−	6.48541i	0.0672789	−	0.207063i
$982$	13.6085	+	18.7305i	0.434265	+	0.597714i
$983$	2.99693	−	4.12492i	0.0955872	−	0.131565i	−0.758545	−	0.651621i	$-0.774089\pi$
$983$	2.99693	−	4.12492i	0.0955872	−	0.131565i	0.854132	+	0.520057i	$0.174089\pi$
$984$	−0.225413	−	0.693751i	−0.00718591	−	0.0221160i
$985$		0			0
$986$	−61.2524	−	44.5025i	−1.95068	−	1.41725i
$987$	3.85505	+	5.30602i	0.122708	+	0.168893i
$988$	3.13065	+	1.01721i	0.0995992	+	0.0323617i
$989$	−46.2653			−1.47115
$990$		0			0
$991$	−14.8133			−0.470560			−0.235280	−	0.971928i	$-0.575601\pi$
$991$	−14.8133			−0.470560			−0.235280	+	0.971928i	$0.575601\pi$
$992$	3.44417	+	1.11908i	0.109353	+	0.0355308i
$993$	1.98434	+	2.73121i	0.0629710	+	0.0866722i
$994$	25.9476	+	18.8520i	0.823007	+	0.597949i
$995$		0			0
$996$	0.130569	+	0.401852i	0.00413725	+	0.0127332i
$997$	34.1374	−	46.9861i	1.08114	−	1.48807i	0.222886	−	0.974844i	$-0.428452\pi$
$997$	34.1374	−	46.9861i	1.08114	−	1.48807i	0.858257	−	0.513221i	$-0.171548\pi$
$998$	13.3253	+	18.3406i	0.421804	+	0.580563i
$999$	−1.02891	+	3.16666i	−0.0325532	+	0.100189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.f.449.4		16
5.2	odd	4		110.2.g.c.31.2	✓	8
5.3	odd	4		550.2.h.l.251.1		8
5.4	even	2	inner	550.2.ba.f.449.1		16
11.5	even	5	inner	550.2.ba.f.49.1		16
15.2	even	4		990.2.n.j.361.2		8
20.7	even	4		880.2.bo.g.801.1		8
55.7	even	20		1210.2.a.v.1.2		4
55.18	even	20		6050.2.a.cy.1.3		4
55.27	odd	20		110.2.g.c.71.2	yes	8
55.37	odd	20		1210.2.a.u.1.2		4
55.38	odd	20		550.2.h.l.401.1		8
55.48	odd	20		6050.2.a.dh.1.3		4
55.49	even	10	inner	550.2.ba.f.49.4		16
165.137	even	20		990.2.n.j.181.2		8
220.7	odd	20		9680.2.a.ci.1.3		4
220.27	even	20		880.2.bo.g.401.1		8
220.147	even	20		9680.2.a.cj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.2	✓	8	5.2	odd	4
110.2.g.c.71.2	yes	8	55.27	odd	20
550.2.h.l.251.1		8	5.3	odd	4
550.2.h.l.401.1		8	55.38	odd	20
550.2.ba.f.49.1		16	11.5	even	5	inner
550.2.ba.f.49.4		16	55.49	even	10	inner
550.2.ba.f.449.1		16	5.4	even	2	inner
550.2.ba.f.449.4		16	1.1	even	1	trivial
880.2.bo.g.401.1		8	220.27	even	20
880.2.bo.g.801.1		8	20.7	even	4
990.2.n.j.181.2		8	165.137	even	20
990.2.n.j.361.2		8	15.2	even	4
1210.2.a.u.1.2		4	55.37	odd	20
1210.2.a.v.1.2		4	55.7	even	20
6050.2.a.cy.1.3		4	55.18	even	20
6050.2.a.dh.1.3		4	55.48	odd	20
9680.2.a.ci.1.3		4	220.7	odd	20
9680.2.a.cj.1.3		4	220.147	even	20

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.155750 + 0.214371i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.0818824 + 0.252008i) q^{6} +(2.53438 - 3.48828i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.905354 - 2.78639i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.155750 + 0.214371i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.0818824 + 0.252008i) q^{6} +(2.53438 - 3.48828i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.905354 - 2.78639i) q^{9} +(-1.42705 - 2.99391i) q^{11} +0.264977i q^{12} +(1.15129 + 0.374078i) q^{13} +(3.48828 - 2.53438i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-6.81513 + 2.21437i) q^{17} +(1.72209 - 2.37025i) q^{18} +(2.19992 - 1.59833i) q^{19} +1.14252 q^{21} +(-0.432036 - 3.28837i) q^{22} +7.01787i q^{23} +(-0.0818824 + 0.252008i) q^{24} +(0.979348 + 0.711538i) q^{26} +(1.49436 - 0.485545i) q^{27} +(4.10072 - 1.33240i) q^{28} +(8.54782 + 6.21036i) q^{29} +(1.11908 - 3.44417i) q^{31} +1.00000i q^{32} +(0.419546 - 0.772220i) q^{33} -7.16586 q^{34} +(2.37025 - 1.72209i) q^{36} +(-1.24556 + 1.71437i) q^{37} +(2.58616 - 0.840293i) q^{38} +(0.0991220 + 0.305066i) q^{39} +(-2.22713 + 1.61811i) q^{41} +(1.08660 + 0.353057i) q^{42} +6.59251i q^{43} +(0.605270 - 3.26093i) q^{44} +(-2.16864 + 6.67439i) q^{46} +(3.37418 + 4.64416i) q^{47} +(-0.155750 + 0.214371i) q^{48} +(-3.58188 - 11.0239i) q^{49} +(-1.53615 - 1.11608i) q^{51} +(0.711538 + 0.979348i) q^{52} +(-5.58779 - 1.81558i) q^{53} +1.57126 q^{54} +4.31175 q^{56} +(0.685272 + 0.222659i) q^{57} +(6.21036 + 8.54782i) q^{58} +(-4.77117 - 3.46646i) q^{59} +(-1.89879 - 5.84387i) q^{61} +(2.12861 - 2.92979i) q^{62} +(-7.42521 - 10.2199i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.637641 - 0.604778i) q^{66} +1.63381i q^{67} +(-6.81513 - 2.21437i) q^{68} +(-1.50443 + 1.09303i) q^{69} +(2.29862 + 7.07443i) q^{71} +(2.78639 - 0.905354i) q^{72} +(-4.34501 + 5.98039i) q^{73} +(-1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-14.0603 - 2.60978i) q^{77} +0.320766i q^{78} +(-2.16376 + 6.65938i) q^{79} +(-6.77391 - 4.92153i) q^{81} +(-2.61815 + 0.850690i) q^{82} +(1.51655 - 0.492758i) q^{83} +(0.924315 + 0.671554i) q^{84} +(-2.03720 + 6.26985i) q^{86} +2.79967i q^{87} +(1.58333 - 2.91429i) q^{88} -1.24711 q^{89} +(4.22271 - 3.06798i) q^{91} +(-4.12500 + 5.67757i) q^{92} +(0.912627 - 0.296530i) q^{93} +(1.77391 + 5.45954i) q^{94} +(-0.214371 + 0.155750i) q^{96} +(6.57491 + 2.13632i) q^{97} -11.5912i q^{98} +(-9.63421 + 1.26577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9	\( 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9} + 4 q^{11} - 2 q^{14} - 4 q^{16} + 14 q^{19} + 64 q^{21} + 2 q^{24} - 12 q^{26} + 44 q^{29} - 52 q^{31} - 4 q^{34} - 2 q^{36} + 96 q^{39} - 30 q^{41} - 14 q^{44} - 12 q^{46} - 54 q^{49} - 10 q^{51} + 48 q^{54} + 12 q^{56} - 78 q^{59} - 40 q^{61} + 4 q^{64} + 72 q^{66} + 20 q^{69} + 4 q^{71} - 16 q^{74} + 16 q^{76} - 28 q^{79} - 62 q^{81} + 36 q^{84} + 34 q^{86} - 64 q^{89} + 106 q^{91} - 18 q^{94} + 8 q^{96} - 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9 + 4 * q^11 - 2 * q^14 - 4 * q^16 + 14 * q^19 + 64 * q^21 + 2 * q^24 - 12 * q^26 + 44 * q^29 - 52 * q^31 - 4 * q^34 - 2 * q^36 + 96 * q^39 - 30 * q^41 - 14 * q^44 - 12 * q^46 - 54 * q^49 - 10 * q^51 + 48 * q^54 + 12 * q^56 - 78 * q^59 - 40 * q^61 + 4 * q^64 + 72 * q^66 + 20 * q^69 + 4 * q^71 - 16 * q^74 + 16 * q^76 - 28 * q^79 - 62 * q^81 + 36 * q^84 + 34 * q^86 - 64 * q^89 + 106 * q^91 - 18 * q^94 + 8 * q^96 - 72 * q^99

Introduction

L-functions

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