LMFDB - Embedded newform 275.2.z.a.124.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, 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("275.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (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:	$2.19588605559$
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} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.2
Root			$-0.701538 - 0.227943i$ of defining polynomial
Character	$\chi$	$=$	275.124
Dual form			275.2.z.a.224.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433574 - 0.596764i) q^{2} +(2.67395 - 0.868820i) q^{3} +(0.449894 - 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.980901 - 0.318714i) q^{7} +(-2.42443 + 0.787747i) q^{8} +(3.96813 - 2.88301i) q^{9} +O(q^{10})$	\(q+(-0.433574 - 0.596764i) q^{2} +(2.67395 - 0.868820i) q^{3} +(0.449894 - 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.980901 - 0.318714i) q^{7} +(-2.42443 + 0.787747i) q^{8} +(3.96813 - 2.88301i) q^{9} +(1.93675 + 2.69240i) q^{11} -4.09331i q^{12} +(-2.02726 - 2.79029i) q^{13} +(0.235096 + 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(-1.40964 + 1.94020i) q^{17} +(-3.44095 - 1.11803i) q^{18} +(2.36979 + 7.29347i) q^{19} -2.89979 q^{21} +(0.767001 - 2.32313i) q^{22} +2.45589i q^{23} +(-5.79842 + 4.21280i) q^{24} +(-0.786174 + 2.41960i) q^{26} +(3.14799 - 4.33283i) q^{27} +(-0.882602 + 1.21480i) q^{28} +(1.83998 - 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919i q^{32} +(7.51798 + 5.51666i) q^{33} +1.76902 q^{34} +(-2.20667 - 6.79144i) q^{36} +(-5.66694 - 1.84130i) q^{37} +(3.32500 - 4.57646i) q^{38} +(-7.84507 - 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +(1.25727 + 1.73049i) q^{42} -7.64941i q^{43} +(4.59931 - 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(5.55697 - 1.80557i) q^{47} +(-2.75786 - 0.896084i) q^{48} +(-4.80253 - 3.48924i) q^{49} +(-2.08362 + 6.41272i) q^{51} +(-4.77558 + 1.55168i) q^{52} +(6.96410 + 9.58526i) q^{53} -3.95056 q^{54} +2.62920 q^{56} +(12.6734 + 17.4435i) q^{57} +(-4.17718 + 1.35725i) q^{58} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-2.58741 - 0.840701i) q^{62} +(-4.81120 + 1.56325i) q^{63} +(1.82774 - 1.32793i) q^{64} +(0.0325397 - 6.87834i) q^{66} +6.14702i q^{67} +(2.05227 + 2.82471i) q^{68} +(2.13372 + 6.56693i) q^{69} +(-1.63676 - 1.18918i) q^{71} +(-7.34938 + 10.1156i) q^{72} +(-0.785446 - 0.255207i) q^{73} +(1.35822 + 4.18017i) q^{74} +11.1649 q^{76} +(-1.04165 - 3.25824i) q^{77} +7.15293i q^{78} +(-9.77146 + 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(1.70666 - 2.34901i) q^{82} +(0.946345 - 1.30253i) q^{83} +(-1.30460 + 4.01513i) q^{84} +(-4.56489 + 3.31659i) q^{86} -16.7409i q^{87} +(-6.81645 - 5.00188i) q^{88} -8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(3.40050 + 1.10489i) q^{92} +(6.09510 - 8.38919i) q^{93} +(-3.48685 - 2.53335i) q^{94} +(5.09058 + 15.6672i) q^{96} +(1.43583 + 1.97625i) q^{97} +4.37882i q^{98} +(15.4475 + 5.10011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44} + 6 q^{46} - 2 q^{49} + 2 q^{51} - 32 q^{54} + 44 q^{56} + 54 q^{59} + 12 q^{61} + 52 q^{64} + 26 q^{66} + 2 q^{69} - 40 q^{71} - 40 q^{74} - 74 q^{79} + 16 q^{81} - 56 q^{84} - 6 q^{86} + 32 q^{89} + 88 q^{91} - 34 q^{94} - 34 q^{96} + 40 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−0.433574	−	0.596764i	−0.306583	−	0.421976i	0.627729	−	0.778432i	$-0.283985\pi$
$2$	−0.433574	−	0.596764i	−0.306583	−	0.421976i	−0.934312	+	0.356457i	$0.883985\pi$
$3$	2.67395	−	0.868820i	1.54381	−	0.501614i	0.591384	−	0.806390i	$-0.298582\pi$
$3$	2.67395	−	0.868820i	1.54381	−	0.501614i	0.952424	+	0.304777i	$0.0985818\pi$
$4$	0.449894	−	1.38463i	0.224947	−	0.692315i
$5$		0			0
$5$		0			0
$6$	−1.67784	−	1.21902i	−0.684974	−	0.497663i
$7$	−0.980901	−	0.318714i	−0.370746	−	0.120463i	0.117717	−	0.993047i	$-0.462442\pi$
$7$	−0.980901	−	0.318714i	−0.370746	−	0.120463i	−0.488463	+	0.872585i	$0.662442\pi$
$8$	−2.42443	+	0.787747i	−0.857167	+	0.278510i
$9$	3.96813	−	2.88301i	1.32271	−	0.961005i
$10$		0			0
$11$	1.93675	+	2.69240i	0.583951	+	0.811789i
$11$	1.93675	+	2.69240i	0.583951	+	0.811789i
$12$		−	4.09331i		−	1.18164i
$13$	−2.02726	−	2.79029i	−0.562262	−	0.773887i	0.429350	−	0.903138i	$-0.358743\pi$
$13$	−2.02726	−	2.79029i	−0.562262	−	0.773887i	−0.991612	+	0.129251i	$0.958743\pi$
$14$	0.235096	+	0.723552i	0.0628321	+	0.193377i
$15$		0			0
$16$	−0.834404	−	0.606230i	−0.208601	−	0.151557i
$17$	−1.40964	+	1.94020i	−0.341887	+	0.470567i	−0.944991	−	0.327095i	$-0.893930\pi$
$17$	−1.40964	+	1.94020i	−0.341887	+	0.470567i	0.603105	+	0.797662i	$0.293930\pi$
$18$	−3.44095	−	1.11803i	−0.811041	−	0.263523i
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	0.724137	+	0.689656i	$0.242238\pi$
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	−0.180470	+	0.983581i	$0.557762\pi$
$20$		0			0
$21$	−2.89979			−0.632786
$22$	0.767001	−	2.32313i	0.163525	−	0.495294i
$23$			2.45589i			0.512088i	0.966665	+	0.256044i	$0.0824192\pi$
$23$			2.45589i			0.512088i	−0.966665	+	0.256044i	$0.917581\pi$
$24$	−5.79842	+	4.21280i	−1.18360	+	0.859933i
$25$		0			0
$26$	−0.786174	+	2.41960i	−0.154181	+	0.474522i
$27$	3.14799	−	4.33283i	0.605830	−	0.833854i
$28$	−0.882602	+	1.21480i	−0.166796	+	0.229575i
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	−0.621663	−	0.783285i	$-0.713542\pi$
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	0.963339	−	0.268287i	$-0.0864575\pi$
$30$		0			0
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	−0.286654	−	0.958034i	$-0.592543\pi$
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	0.822564	+	0.568673i	$0.192543\pi$
$32$			5.85919i			1.03577i
$33$	7.51798	+	5.51666i	1.30871	+	0.960328i
$34$	1.76902			0.303384
$35$		0			0
$36$	−2.20667	−	6.79144i	−0.367779	−	1.13191i
$37$	−5.66694	−	1.84130i	−0.931640	−	0.302708i	−0.196407	−	0.980523i	$-0.562927\pi$
$37$	−5.66694	−	1.84130i	−0.931640	−	0.302708i	−0.735233	+	0.677814i	$0.762927\pi$
$38$	3.32500	−	4.57646i	0.539386	−	0.742401i
$39$	−7.84507	−	5.69978i	−1.25622	−	0.912695i
$40$		0			0
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	0.999999	−	0.00173135i	$-0.000551106\pi$
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	−0.810033	+	0.586384i	$0.800551\pi$
$42$	1.25727	+	1.73049i	0.194001	+	0.267020i
$43$		−	7.64941i		−	1.16652i	−0.812284	−	0.583262i	$-0.801776\pi$
$43$		−	7.64941i		−	1.16652i	0.812284	−	0.583262i	$-0.198224\pi$
$44$	4.59931	−	1.47039i	0.693372	−	0.221669i
$45$		0			0
$46$	1.46558	−	1.06481i	0.216089	−	0.156998i
$47$	5.55697	−	1.80557i	0.810567	−	0.263369i	0.125729	−	0.992065i	$-0.459873\pi$
$47$	5.55697	−	1.80557i	0.810567	−	0.263369i	0.684838	+	0.728695i	$0.259873\pi$
$48$	−2.75786	−	0.896084i	−0.398063	−	0.129339i
$49$	−4.80253	−	3.48924i	−0.686076	−	0.498463i
$50$		0			0
$51$	−2.08362	+	6.41272i	−0.291765	+	0.897960i
$52$	−4.77558	+	1.55168i	−0.662253	+	0.215179i
$53$	6.96410	+	9.58526i	0.956592	+	1.31664i	0.948536	+	0.316669i	$0.102564\pi$
$53$	6.96410	+	9.58526i	0.956592	+	1.31664i	0.00805607	+	0.999968i	$0.497436\pi$
$54$	−3.95056			−0.537603
$55$		0			0
$56$	2.62920			0.351341
$57$	12.6734	+	17.4435i	1.67864	+	2.31044i
$58$	−4.17718	+	1.35725i	−0.548490	+	0.178215i
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	−0.992667	−	0.120880i	$-0.961428\pi$
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	0.874136	+	0.485681i	$0.161428\pi$
$60$		0			0
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	0.451864	−	0.892087i	$-0.350759\pi$
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	−0.708791	+	0.705419i	$0.750759\pi$
$62$	−2.58741	−	0.840701i	−0.328602	−	0.106769i
$63$	−4.81120	+	1.56325i	−0.606154	+	0.196951i
$64$	1.82774	−	1.32793i	0.228468	−	0.165992i
$65$		0			0
$66$	0.0325397	−	6.87834i	0.00400536	−	0.846665i
$67$			6.14702i			0.750978i	0.926827	+	0.375489i	$0.122525\pi$
$67$			6.14702i			0.750978i	−0.926827	+	0.375489i	$0.877475\pi$
$68$	2.05227	+	2.82471i	0.248874	+	0.342546i
$69$	2.13372	+	6.56693i	0.256870	+	0.790565i
$70$		0			0
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	0.486410	−	0.873731i	$-0.338306\pi$
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	−0.680658	+	0.732601i	$0.738306\pi$
$72$	−7.34938	+	10.1156i	−0.866133	+	1.19213i
$73$	−0.785446	−	0.255207i	−0.0919295	−	0.0298697i	0.262691	−	0.964880i	$-0.415390\pi$
$73$	−0.785446	−	0.255207i	−0.0919295	−	0.0298697i	−0.354621	+	0.935010i	$0.615390\pi$
$74$	1.35822	+	4.18017i	0.157890	+	0.485934i
$75$		0			0
$76$	11.1649			1.28070
$77$	−1.04165	−	3.25824i	−0.118707	−	0.371311i
$78$			7.15293i			0.809910i
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.980958	−	0.194221i	$-0.937782\pi$
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.118417	+	0.992964i	$0.537782\pi$
$80$		0			0
$81$	0.106048	−	0.326382i	0.0117831	−	0.0362647i
$82$	1.70666	−	2.34901i	0.188469	−	0.259405i
$83$	0.946345	−	1.30253i	0.103875	−	0.142971i	−0.753915	−	0.656972i	$-0.771837\pi$
$83$	0.946345	−	1.30253i	0.103875	−	0.142971i	0.857790	+	0.514000i	$0.171837\pi$
$84$	−1.30460	+	4.01513i	−0.142343	+	0.438087i
$85$		0			0
$86$	−4.56489	+	3.31659i	−0.492245	+	0.357637i
$87$		−	16.7409i		−	1.79481i
$88$	−6.81645	−	5.00188i	−0.726636	−	0.533202i
$89$	−8.16116			−0.865081			−0.432541	−	0.901614i	$-0.642383\pi$
$89$	−8.16116			−0.865081			−0.432541	+	0.901614i	$0.642383\pi$
$90$		0			0
$91$	1.09924	+	3.38312i	0.115232	+	0.354647i
$92$	3.40050	+	1.10489i	0.354526	+	0.115193i
$93$	6.09510	−	8.38919i	0.632032	−	0.869918i
$94$	−3.48685	−	2.53335i	−0.359642	−	0.261295i
$95$		0			0
$96$	5.09058	+	15.6672i	0.519555	+	1.59903i
$97$	1.43583	+	1.97625i	0.145787	+	0.200658i	0.875665	−	0.482919i	$-0.160423\pi$
$97$	1.43583	+	1.97625i	0.145787	+	0.200658i	−0.729879	+	0.683577i	$0.760423\pi$
$98$			4.37882i			0.442328i
$99$	15.4475	+	5.10011i	1.55253	+	0.512580i
$100$		0			0
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	−0.242222	−	0.970221i	$-0.577876\pi$
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	0.847884	+	0.530182i	$0.177876\pi$
$102$	4.73028	−	1.53696i	0.468367	−	0.152182i
$103$	−9.01821	−	2.93020i	−0.888591	−	0.288721i	−0.171071	−	0.985259i	$-0.554723\pi$
$103$	−9.01821	−	2.93020i	−0.888591	−	0.288721i	−0.717520	+	0.696538i	$0.754723\pi$
$104$	7.11301	+	5.16791i	0.697488	+	0.506755i
$105$		0			0
$106$	2.70068	−	8.31184i	0.262313	−	0.807317i
$107$	−4.41935	+	1.43593i	−0.427235	+	0.138817i	−0.514739	−	0.857347i	$-0.672111\pi$
$107$	−4.41935	+	1.43593i	−0.427235	+	0.138817i	0.0875039	+	0.996164i	$0.472111\pi$
$108$	−4.58311	−	6.30811i	−0.441010	−	0.606998i
$109$	5.32826			0.510355			0.255178	−	0.966894i	$-0.417866\pi$
$109$	5.32826			0.510355			0.255178	+	0.966894i	$0.417866\pi$
$110$		0			0
$111$	−16.7529			−1.59012
$112$	0.625253	+	0.860587i	0.0590809	+	0.0813179i
$113$	−0.289978	+	0.0942195i	−0.0272788	+	0.00886342i	−0.322625	−	0.946527i	$-0.604565\pi$
$113$	−0.289978	+	0.0942195i	−0.0272788	+	0.00886342i	0.295346	+	0.955390i	$0.404565\pi$
$114$	4.91476	−	15.1261i	0.460310	−	1.41669i
$115$		0			0
$116$	−7.01321	−	5.09540i	−0.651160	−	0.473096i
$117$	−16.0889	−	5.22760i	−1.48742	−	0.483292i
$118$	2.06694	−	0.671589i	0.190277	−	0.0618248i
$119$	2.00108	−	1.45387i	0.183439	−	0.133276i
$120$		0			0
$121$	−3.49802	+	10.4290i	−0.318001	+	0.948090i
$122$			1.82962i			0.165646i
$123$	6.50503	+	8.95341i	0.586539	+	0.807302i
$124$	−1.65930	−	5.10680i	−0.149009	−	0.458604i
$125$		0			0
$126$	3.01890	+	2.19336i	0.268945	+	0.195400i
$127$	7.00050	−	9.63536i	0.621194	−	0.855000i	−0.376245	−	0.926520i	$-0.622785\pi$
$127$	7.00050	−	9.63536i	0.621194	−	0.855000i	0.997439	+	0.0715199i	$0.0227850\pi$
$128$	9.55992	+	3.10621i	0.844985	+	0.274552i
$129$	−6.64596	−	20.4542i	−0.585145	−	1.80089i
$130$		0			0
$131$	−11.1875			−0.977452			−0.488726	−	0.872437i	$-0.662538\pi$
$131$	−11.1875			−0.977452			−0.488726	+	0.872437i	$0.662538\pi$
$132$	11.0208	−	7.92772i	0.959240	−	0.690019i
$133$		−	7.90945i		−	0.685837i
$134$	3.66832	−	2.66519i	0.316894	−	0.230237i
$135$		0			0
$136$	1.88919	−	5.81432i	0.161996	−	0.498573i
$137$	2.51645	−	3.46360i	0.214995	−	0.295915i	−0.687875	−	0.725829i	$-0.741456\pi$
$137$	2.51645	−	3.46360i	0.214995	−	0.295915i	0.902870	+	0.429914i	$0.141456\pi$
$138$	2.99378	−	4.12058i	0.254847	−	0.350767i
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	−0.842228	−	0.539121i	$-0.818757\pi$
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	0.998264	+	0.0588913i	$0.0187565\pi$
$140$		0			0
$141$	13.2904	−	9.65601i	1.11925	−	0.813183i
$142$			1.49235i			0.125236i
$143$	3.58627	−	10.8623i	0.299899	−	0.908351i
$144$	−5.05879			−0.421566
$145$		0			0
$146$	0.188251	+	0.579377i	0.0155798	+	0.0479495i
$147$	−15.8733	−	5.15754i	−1.30921	−	0.425387i
$148$	−5.09905	+	7.01823i	−0.419139	+	0.576895i
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	0.455269	−	0.890354i	$-0.349543\pi$
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	−0.706091	+	0.708121i	$0.749543\pi$
$150$		0			0
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.433159	−	0.901317i	$-0.642601\pi$
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.179348	−	0.983786i	$-0.557399\pi$
$152$	−11.4908	−	15.8157i	−0.932028	−	1.28283i
$153$			11.7629i			0.950978i
$154$	−1.49277	+	2.03431i	−0.120291	+	0.163929i
$155$		0			0
$156$	−11.4215	+	8.29823i	−0.914455	+	0.664390i
$157$	6.87813	−	2.23484i	0.548935	−	0.178360i	−0.0214015	−	0.999771i	$-0.506813\pi$
$157$	6.87813	−	2.23484i	0.548935	−	0.178360i	0.570336	+	0.821411i	$0.306813\pi$
$158$	8.47330	+	2.75314i	0.674100	+	0.219028i
$159$	26.9495	+	19.5800i	2.13724	+	1.55279i
$160$		0			0
$161$	0.782725	−	2.40898i	0.0616874	−	0.189854i
$162$	−0.240753	+	0.0782252i	−0.0189153	+	0.00614596i
$163$	−10.9852	−	15.1198i	−0.860428	−	1.18428i	−0.981467	−	0.191630i	$-0.938623\pi$
$163$	−10.9852	−	15.1198i	−0.860428	−	1.18428i	0.121039	−	0.992648i	$-0.461377\pi$
$164$	5.73074			0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	4.61604	+	6.35343i	0.357200	+	0.491644i	0.949366	−	0.314172i	$-0.101727\pi$
$167$	4.61604	+	6.35343i	0.357200	+	0.491644i	−0.592166	+	0.805816i	$0.701727\pi$
$168$	7.03035	−	2.28430i	0.542403	−	0.176237i
$169$	0.341302	−	1.05042i	0.0262540	−	0.0808014i
$170$		0			0
$171$	30.4308	+	22.1093i	2.32710	+	1.69074i
$172$	−10.5916	−	3.44142i	−0.807603	−	0.262406i
$173$	−10.6563	+	3.46244i	−0.810183	+	0.263244i	−0.684675	−	0.728848i	$-0.740056\pi$
$173$	−10.6563	+	3.46244i	−0.810183	+	0.263244i	−0.125508	+	0.992093i	$0.540056\pi$
$174$	−9.99037	+	7.25843i	−0.757368	+	0.550260i
$175$		0			0
$176$	0.0161823	−	3.42066i	0.00121979	−	0.257842i
$177$			8.28370i			0.622641i
$178$	3.53847	+	4.87028i	0.265219	+	0.365043i
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	0.932716	−	0.360611i	$-0.117432\pi$
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	−0.966545	+	0.256497i	$0.917432\pi$
$180$		0			0
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	0.272357	−	0.962196i	$-0.412197\pi$
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	−0.830940	+	0.556362i	$0.812197\pi$
$182$	1.54232	−	2.12282i	0.114324	−	0.157354i
$183$	−6.63239	−	2.15499i	−0.490280	−	0.159302i
$184$	−1.93462	−	5.95414i	−0.142622	−	0.438945i
$185$		0			0
$186$	−7.64904			−0.560855
$187$	−7.95389	−	0.0376278i	−0.581646	−	0.00275162i
$188$		−	8.50666i		−	0.620412i
$189$	−4.46880	+	3.24677i	−0.325057	+	0.236168i
$190$		0			0
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	−0.988528	−	0.151038i	$-0.951738\pi$
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	0.888514	+	0.458850i	$0.151738\pi$
$192$	3.73357	−	5.13881i	0.269447	−	0.370862i
$193$	−13.3227	+	18.3372i	−0.958992	+	1.31994i	−0.0115772	+	0.999933i	$0.503685\pi$
$193$	−13.3227	+	18.3372i	−0.958992	+	1.31994i	−0.947415	+	0.320007i	$0.896315\pi$
$194$	0.556816	−	1.71370i	0.0399771	−	0.123037i
$195$		0			0
$196$	−6.99194	+	5.07994i	−0.499424	+	0.362853i
$197$			11.2080i			0.798535i	0.916835	+	0.399267i	$0.130735\pi$
$197$			11.2080i			0.798535i	−0.916835	+	0.399267i	$0.869265\pi$
$198$	−3.65407	−	11.4298i	−0.259683	−	0.812278i
$199$	7.81979			0.554330			0.277165	−	0.960822i	$-0.410605\pi$
$199$	7.81979			0.554330			0.277165	+	0.960822i	$0.410605\pi$
$200$		0			0
$201$	5.34065	+	16.4368i	0.376701	+	1.15937i
$202$	−5.27818	−	1.71499i	−0.371372	−	0.120666i
$203$	−3.60968	+	4.96830i	−0.253350	+	0.348707i
$204$	7.94184	+	5.77008i	0.556040	+	0.403987i
$205$		0			0
$206$	2.16143	+	6.65220i	0.150594	+	0.463481i
$207$	7.08035	+	9.74527i	0.492119	+	0.677343i
$208$			3.55722i			0.246649i
$209$	−15.0472	+	20.5060i	−1.04084	+	1.41843i
$210$		0			0
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.268887	−	0.963172i	$-0.413344\pi$
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.999121	+	0.0419098i	$0.0133442\pi$
$212$	16.4051	−	5.33035i	1.12671	−	0.366090i
$213$	−5.40980	−	1.75775i	−0.370673	−	0.120439i
$214$	2.77303	+	2.01472i	0.189560	+	0.137724i
$215$		0			0
$216$	−4.21891	+	12.9845i	−0.287061	+	0.883482i
$217$	−3.61776	+	1.17548i	−0.245589	+	0.0797969i
$218$	−2.31020	−	3.17971i	−0.156466	−	0.215357i
$219$	−2.32197			−0.156905
$220$		0			0
$221$	8.27142			0.556396
$222$	7.26363	+	9.99752i	0.487503	+	0.670990i
$223$	15.2575	−	4.95746i	1.02172	−	0.331976i	0.250207	−	0.968192i	$-0.419501\pi$
$223$	15.2575	−	4.95746i	1.02172	−	0.331976i	0.771511	+	0.636216i	$0.219501\pi$
$224$	1.86741	−	5.74728i	0.124771	−	0.384006i
$225$		0			0
$226$	0.181954	+	0.132197i	0.0121034	+	0.00879361i
$227$	22.9739	+	7.46468i	1.52483	+	0.495448i	0.947144	−	0.320809i	$-0.103955\pi$
$227$	22.9739	+	7.46468i	1.52483	+	0.495448i	0.577689	+	0.816257i	$0.303955\pi$
$228$	29.8545	−	9.70030i	1.97716	−	0.642418i
$229$	−12.1468	+	8.82517i	−0.802684	+	0.583184i	−0.911700	−	0.410856i	$-0.865230\pi$
$229$	−12.1468	+	8.82517i	−0.802684	+	0.583184i	0.109017	+	0.994040i	$0.465230\pi$
$230$		0			0
$231$	−5.61616	−	7.80738i	−0.369516	−	0.513688i
$232$			15.1787i			0.996534i
$233$	−6.71600	−	9.24378i	−0.439980	−	0.605580i	0.530228	−	0.847855i	$-0.322106\pi$
$233$	−6.71600	−	9.24378i	−0.439980	−	0.605580i	−0.970208	+	0.242275i	$0.922106\pi$
$234$	3.85609	+	11.8678i	0.252080	+	0.775823i
$235$		0			0
$236$	3.47026	+	2.52129i	0.225895	+	0.164122i
$237$	−19.9603	+	27.4730i	−1.29656	+	1.78457i
$238$	−1.73523	−	0.563811i	−0.112478	−	0.0365465i
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	−0.714181	−	0.699961i	$-0.753201\pi$
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	0.166358	−	0.986065i	$-0.446799\pi$
$240$		0			0
$241$	10.9387			0.704624			0.352312	−	0.935883i	$-0.385396\pi$
$241$	10.9387			0.704624			0.352312	+	0.935883i	$0.385396\pi$
$242$	7.74029	−	2.43425i	0.497565	−	0.156480i
$243$			15.1022i			0.968804i
$244$	−2.92147	+	2.12257i	−0.187028	+	0.135884i
$245$		0			0
$246$	2.52265	−	7.76393i	0.160839	−	0.495010i
$247$	15.5467	−	21.3982i	0.989213	−	1.36154i
$248$	−5.52634	+	7.60635i	−0.350923	+	0.483004i
$249$	1.39882	−	4.30511i	0.0886463	−	0.272825i
$250$		0			0
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	−0.933225	−	0.359291i	$-0.883018\pi$
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	0.0533238	+	0.998577i	$0.483018\pi$
$252$			7.36503i			0.463953i
$253$	−6.61222	+	4.75643i	−0.415707	+	0.299034i
$254$	−8.78527			−0.551237
$255$		0			0
$256$	−3.68753	−	11.3491i	−0.230471	−	0.709316i
$257$	−17.5902	−	5.71540i	−1.09725	−	0.356517i	−0.296204	−	0.955125i	$-0.595721\pi$
$257$	−17.5902	−	5.71540i	−1.09725	−	0.356517i	−0.801042	+	0.598608i	$0.795721\pi$
$258$	−9.32479	+	12.8345i	−0.580536	+	0.799039i
$259$	4.97186	+	3.61227i	0.308936	+	0.224455i
$260$		0			0
$261$	−9.02489	−	27.7758i	−0.558627	−	1.71928i
$262$	4.85059	+	6.67626i	0.299670	+	0.412461i
$263$			3.69135i			0.227618i	0.993503	+	0.113809i	$0.0363052\pi$
$263$			3.69135i			0.227618i	−0.993503	+	0.113809i	$0.963695\pi$
$264$	−22.5726	−	7.45252i	−1.38925	−	0.458671i
$265$		0			0
$266$	−4.72007	+	3.42933i	−0.289406	+	0.210266i
$267$	−21.8226	+	7.09058i	−1.33552	+	0.433937i
$268$	8.51135	+	2.76550i	0.519913	+	0.168930i
$269$	−8.04575	−	5.84558i	−0.490558	−	0.356411i	0.314841	−	0.949145i	$-0.398049\pi$
$269$	−8.04575	−	5.84558i	−0.490558	−	0.356411i	−0.805399	+	0.592733i	$0.798049\pi$
$270$		0			0
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	−0.938600	−	0.345006i	$-0.887877\pi$
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	0.962133	+	0.272580i	$0.0878768\pi$
$272$	2.35241	−	0.764345i	0.142636	−	0.0463452i
$273$	5.87864	+	8.09125i	0.355791	+	0.489705i
$274$	−3.15802			−0.190783
$275$		0			0
$276$	10.0527			0.605102
$277$	−4.75713	−	6.54763i	−0.285828	−	0.393409i	0.641825	−	0.766851i	$-0.278177\pi$
$277$	−4.75713	−	6.54763i	−0.285828	−	0.393409i	−0.927654	+	0.373442i	$0.878177\pi$
$278$	−4.17639	+	1.35699i	−0.250483	+	0.0813870i
$279$	5.59017	−	17.2048i	0.334675	−	1.03002i
$280$		0			0
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.227958	−	0.973671i	$-0.573205\pi$
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.996459	+	0.0840804i	$0.973205\pi$
$282$	−11.5247	−	3.74461i	−0.686286	−	0.222988i
$283$	19.4419	−	6.31705i	1.15570	−	0.375510i	0.332412	−	0.943134i	$-0.392137\pi$
$283$	19.4419	−	6.31705i	1.15570	−	0.375510i	0.823288	+	0.567624i	$0.192137\pi$
$284$	−2.38294	+	1.73131i	−0.141401	+	0.102734i
$285$		0			0
$286$	−8.03714	+	2.56945i	−0.475246	+	0.151935i
$287$		−	4.05977i		−	0.239641i
$288$	16.8921	+	23.2500i	0.995378	+	1.37002i
$289$	3.47600	+	10.6980i	0.204470	+	0.629295i
$290$		0			0
$291$	5.55635	+	4.03693i	0.325719	+	0.236649i
$292$	−0.706734	+	0.972737i	−0.0413585	+	0.0569251i
$293$	2.42431	+	0.787705i	0.141630	+	0.0460182i	0.378974	−	0.925407i	$-0.376277\pi$
$293$	2.42431	+	0.787705i	0.141630	+	0.0460182i	−0.237344	+	0.971426i	$0.576277\pi$
$294$	3.80441	+	11.7088i	0.221878	+	0.682869i
$295$		0			0
$296$	15.1896			0.882878
$297$	17.7626	+	0.0840302i	1.03069	+	0.00487593i
$298$			2.79156i			0.161711i
$299$	6.85264	−	4.97873i	0.396298	−	0.287928i
$300$		0			0
$301$	−2.43797	+	7.50331i	−0.140523	+	0.432484i
$302$	−10.5604	+	14.5352i	−0.607683	+	0.836404i
$303$	12.4337	−	17.1135i	0.714296	−	0.983144i
$304$	2.44416	−	7.52234i	0.140182	−	0.431436i
$305$		0			0
$306$	7.01970	−	5.10011i	0.401289	−	0.291554i
$307$		−	8.99273i		−	0.513242i	−0.966512	−	0.256621i	$-0.917391\pi$
$307$		−	8.99273i		−	0.513242i	0.966512	−	0.256621i	$-0.0826092\pi$
$308$	−4.98010	−	0.0235596i	−0.283767	−	0.00134243i
$309$	−26.6601			−1.51664
$310$		0			0
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	−0.957380	−	0.288830i	$-0.906734\pi$
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	0.604767	−	0.796402i	$-0.293266\pi$
$312$	23.5098	+	7.63881i	1.33098	+	0.432463i
$313$	4.17611	−	5.74792i	0.236048	−	0.324892i	−0.674516	−	0.738260i	$-0.735648\pi$
$313$	4.17611	−	5.74792i	0.236048	−	0.324892i	0.910564	+	0.413368i	$0.135648\pi$
$314$	−4.31585	−	3.13565i	−0.243558	−	0.176955i
$315$		0			0
$316$	5.43390	+	16.7238i	0.305681	+	0.940789i
$317$	1.34793	+	1.85526i	0.0757071	+	0.104202i	0.845191	−	0.534464i	$-0.179487\pi$
$317$	1.34793	+	1.85526i	0.0757071	+	0.104202i	−0.769484	+	0.638666i	$0.779487\pi$
$318$		−	24.5719i		−	1.37792i
$319$	18.8103	−	6.01362i	1.05318	−	0.336698i
$320$		0			0
$321$	−10.5696	+	7.67924i	−0.589936	+	0.428613i
$322$	−1.77696	+	0.577370i	−0.0990262	+	0.0321756i
$323$	−17.4913	−	5.68327i	−0.973242	−	0.316226i
$324$	−0.404208	−	0.293674i	−0.0224560	−	0.0163152i
$325$		0			0
$326$	−4.26007	+	13.1111i	−0.235943	+	0.726159i
$327$	14.2475	−	4.62930i	0.787890	−	0.256001i
$328$	−5.89802	−	8.11793i	−0.325664	−	0.448237i
$329$	−6.02629			−0.332240
$330$		0			0
$331$	15.3951			0.846192			0.423096	−	0.906085i	$-0.360943\pi$
$331$	15.3951			0.846192			0.423096	+	0.906085i	$0.360943\pi$
$332$	−1.37777	−	1.89634i	−0.0756150	−	0.104075i
$333$	−27.7957	+	9.03136i	−1.52319	+	0.494915i
$334$	1.79010	−	5.50937i	0.0979501	−	0.301459i
$335$		0			0
$336$	2.41959	+	1.75794i	0.132000	+	0.0959034i
$337$	18.5426	+	6.02485i	1.01008	+	0.328195i	0.766886	−	0.641783i	$-0.221805\pi$
$337$	18.5426	+	6.02485i	1.01008	+	0.328195i	0.243193	+	0.969978i	$0.421805\pi$
$338$	−0.774831	+	0.251758i	−0.0421453	+	0.0136938i
$339$	−0.693527	+	0.503877i	−0.0376672	+	0.0273668i
$340$		0			0
$341$	11.6157	+	3.83501i	0.629024	+	0.207677i
$342$		−	27.7460i		−	1.50033i
$343$	7.84234	+	10.7941i	0.423447	+	0.582825i
$344$	6.02580	+	18.5455i	0.324889	+	0.999907i
$345$		0			0
$346$	6.68655	+	4.85806i	0.359471	+	0.261171i
$347$	1.27493	−	1.75479i	0.0684420	−	0.0942023i	−0.773424	−	0.633889i	$-0.781457\pi$
$347$	1.27493	−	1.75479i	0.0684420	−	0.0942023i	0.841866	+	0.539687i	$0.181457\pi$
$348$	−23.1800	−	7.53163i	−1.24258	−	0.403738i
$349$	7.74150	+	23.8259i	0.414393	+	1.27537i	0.912793	+	0.408423i	$0.133921\pi$
$349$	7.74150	+	23.8259i	0.414393	+	1.27537i	−0.498400	+	0.866947i	$0.666079\pi$
$350$		0			0
$351$	−18.4717			−0.985944
$352$	−15.7753	+	11.3478i	−0.840825	+	0.604838i
$353$		−	23.2532i		−	1.23764i	−0.785532	−	0.618821i	$-0.787611\pi$
$353$		−	23.2532i		−	1.23764i	0.785532	−	0.618821i	$-0.212389\pi$
$354$	4.94341	−	3.59160i	0.262739	−	0.190891i
$355$		0			0
$356$	−3.67166	+	11.3002i	−0.194597	+	0.598909i
$357$	4.08764	−	5.62616i	0.216341	−	0.297768i
$358$	−0.635025	+	0.874037i	−0.0335621	+	0.0461943i
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	−0.999043	−	0.0437429i	$-0.986072\pi$
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	0.833954	+	0.551834i	$0.186072\pi$
$360$		0			0
$361$	−32.2075	+	23.4001i	−1.69513	+	1.23158i
$362$			6.85194i			0.360130i
$363$	−0.292611	+	30.9258i	−0.0153581	+	1.62318i
$364$	5.17891			0.271448
$365$		0			0
$366$	1.58961	+	4.89232i	0.0830903	+	0.255726i
$367$	−3.52770	−	1.14622i	−0.184145	−	0.0598322i	0.215493	−	0.976505i	$-0.430864\pi$
$367$	−3.52770	−	1.14622i	−0.184145	−	0.0598322i	−0.399638	+	0.916673i	$0.630864\pi$
$368$	1.48883	−	2.04920i	0.0776107	−	0.106822i
$369$	15.6196	+	11.3483i	0.813122	+	0.590768i
$370$		0			0
$371$	−3.77613	−	11.6217i	−0.196047	−	0.603371i
$372$	−8.87378	−	12.2137i	−0.460084	−	0.633251i
$373$		−	9.34017i		−	0.483616i	−0.970324	−	0.241808i	$-0.922260\pi$
$373$		−	9.34017i		−	0.483616i	0.970324	−	0.241808i	$-0.0777403\pi$
$374$	3.42615	+	4.76291i	0.177162	+	0.246284i
$375$		0			0
$376$	−12.0502	+	8.75496i	−0.621440	+	0.451503i
$377$	−19.5312	+	6.34609i	−1.00591	+	0.326840i
$378$	3.87511	+	1.25910i	0.199314	+	0.0647611i
$379$	−7.93783	−	5.76717i	−0.407739	−	0.296240i	0.364947	−	0.931028i	$-0.381087\pi$
$379$	−7.93783	−	5.76717i	−0.407739	−	0.296240i	−0.772686	+	0.634789i	$0.781087\pi$
$380$		0			0
$381$	10.3476	−	31.8467i	0.530124	−	1.63156i
$382$	3.13795	−	1.01958i	0.160552	−	0.0521663i
$383$	10.6076	+	14.6002i	0.542025	+	0.746034i	0.988903	−	0.148561i	$-0.0474642\pi$
$383$	10.6076	+	14.6002i	0.542025	+	0.746034i	−0.446878	+	0.894595i	$0.647464\pi$
$384$	28.2615			1.44221
$385$		0			0
$386$	16.7194			0.850993
$387$	−22.0534	−	30.3539i	−1.12104	−	1.54297i
$388$	3.38235	−	1.09899i	0.171713	−	0.0557929i
$389$	−9.63871	+	29.6649i	−0.488702	+	1.50407i	0.337844	+	0.941202i	$0.390302\pi$
$389$	−9.63871	+	29.6649i	−0.488702	+	1.50407i	−0.826546	+	0.562869i	$0.809698\pi$
$390$		0			0
$391$	−4.76490	−	3.46191i	−0.240972	−	0.175076i
$392$	14.3921	+	4.67626i	0.726909	+	0.236187i
$393$	−29.9147	+	9.71989i	−1.50900	+	0.490303i
$394$	6.68851	−	4.85948i	0.336962	−	0.244817i
$395$		0			0
$396$	14.0115	−	19.0946i	0.704104	−	0.959537i
$397$			10.6212i			0.533062i	0.963826	+	0.266531i	$0.0858774\pi$
$397$			10.6212i			0.533062i	−0.963826	+	0.266531i	$0.914123\pi$
$398$	−3.39046	−	4.66657i	−0.169948	−	0.233914i
$399$	−6.87189	−	21.1495i	−0.344025	−	1.05880i
$400$		0			0
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.983251	−	0.182258i	$-0.0583407\pi$
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.130503	+	0.991448i	$0.458341\pi$
$402$	7.49334	−	10.3137i	0.373734	−	0.514400i
$403$	−12.0980	−	3.93087i	−0.602643	−	0.195811i
$404$	−3.38488	−	10.4176i	−0.168404	−	0.518295i
$405$		0			0
$406$	4.52997			0.224818
$407$	−6.01792	−	18.8238i	−0.298297	−	0.933061i
$408$		−	17.1886i		−	0.850961i
$409$	11.6241	−	8.44540i	0.574774	−	0.417598i	−0.262062	−	0.965051i	$-0.584402\pi$
$409$	11.6241	−	8.44540i	0.574774	−	0.417598i	0.836836	+	0.547453i	$0.184402\pi$
$410$		0			0
$411$	3.71963	−	11.4478i	0.183476	−	0.564681i
$412$	−8.11448	+	11.1686i	−0.399772	+	0.550238i
$413$	1.78613	−	2.45840i	0.0878899	−	0.120970i
$414$	2.74576	−	8.45060i	0.134947	−	0.415324i
$415$		0			0
$416$	16.3488	−	11.8781i	0.801568	−	0.582373i
$417$		−	16.7378i		−	0.819652i
$418$	18.7613	+	0.0887552i	0.917647	+	0.00434116i
$419$	31.4707			1.53744			0.768722	−	0.639584i	$-0.220893\pi$
$419$	31.4707			1.53744			0.768722	+	0.639584i	$0.220893\pi$
$420$		0			0
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	0.924856	+	0.380318i	$0.124185\pi$
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	−0.524679	+	0.851300i	$0.675815\pi$
$422$	−15.9719	−	5.18959i	−0.777500	−	0.252625i
$423$	16.8453	−	23.1855i	0.819045	−	1.12732i
$424$	−24.4348	−	17.7529i	−1.18666	−	0.862156i
$425$		0			0
$426$	1.29659	+	3.99049i	0.0628199	+	0.193340i
$427$	1.50367	+	2.06963i	0.0727679	+	0.100156i
$428$			6.76518i			0.327008i
$429$	0.152146	−	32.1611i	0.00734568	−	1.55275i
$430$		0			0
$431$	3.12984	−	2.27397i	0.150759	−	0.109533i	−0.509849	−	0.860264i	$-0.670299\pi$
$431$	3.12984	−	2.27397i	0.150759	−	0.109533i	0.660608	+	0.750731i	$0.270299\pi$
$432$	−5.25338	+	1.70693i	−0.252754	+	0.0821246i
$433$	38.1743	+	12.4036i	1.83454	+	0.596077i	0.998905	+	0.0467895i	$0.0148990\pi$
$433$	38.1743	+	12.4036i	1.83454	+	0.596077i	0.835633	+	0.549288i	$0.185101\pi$
$434$	2.27005	+	1.64929i	0.108966	+	0.0791684i
$435$		0			0
$436$	2.39715	−	7.37768i	0.114803	−	0.353327i
$437$	−17.9119	+	5.81994i	−0.856844	+	0.278406i
$438$	1.00675	+	1.38567i	0.0481043	+	0.0662099i
$439$	−1.02336			−0.0488425			−0.0244212	−	0.999702i	$-0.507774\pi$
$439$	−1.02336			−0.0488425			−0.0244212	+	0.999702i	$0.507774\pi$
$440$		0			0
$441$	−29.1166			−1.38650
$442$	−3.58627	−	4.93608i	−0.170582	−	0.234785i
$443$	15.2862	−	4.96678i	0.726268	−	0.235979i	0.0775295	−	0.996990i	$-0.475297\pi$
$443$	15.2862	−	4.96678i	0.726268	−	0.235979i	0.648739	+	0.761011i	$0.275297\pi$
$444$	−7.53703	+	23.1966i	−0.357691	+	1.10086i
$445$		0			0
$446$	−9.57368	−	6.95569i	−0.453327	−	0.329361i
$447$	−10.1194	−	3.28800i	−0.478633	−	0.155517i
$448$	−2.21607	+	0.720043i	−0.104699	+	0.0340188i
$449$	28.9969	−	21.0675i	1.36845	−	0.994235i	0.370590	−	0.928797i	$-0.379156\pi$
$449$	28.9969	−	21.0675i	1.36845	−	0.994235i	0.997857	−	0.0654379i	$-0.0208444\pi$
$450$		0			0
$451$	−7.72346	+	10.5254i	−0.363684	+	0.495620i
$452$			0.443901i			0.0208793i
$453$	−40.2516	−	55.4016i	−1.89119	−	2.60299i
$454$	−5.50625	−	16.9465i	−0.258421	−	0.795338i
$455$		0			0
$456$	−44.4669	−	32.3071i	−2.08235	−	1.51292i
$457$	14.7842	−	20.3488i	0.691578	−	0.951875i	−0.308422	−	0.951250i	$-0.599801\pi$
$457$	14.7842	−	20.3488i	0.691578	−	0.951875i	1.00000		0.000625413i	$-0.000199075\pi$
$458$	10.5331	+	3.42241i	0.492179	+	0.159919i
$459$	3.96903	+	12.2154i	0.185259	+	0.570167i
$460$		0			0
$461$	6.65631			0.310015			0.155008	−	0.987913i	$-0.450460\pi$
$461$	6.65631			0.310015			0.155008	+	0.987913i	$0.450460\pi$
$462$	−2.22414	+	6.73660i	−0.103476	+	0.313415i
$463$			38.7730i			1.80194i	0.433886	+	0.900968i	$0.357142\pi$
$463$			38.7730i			1.80194i	−0.433886	+	0.900968i	$0.642858\pi$
$464$	−4.96830	+	3.60968i	−0.230648	+	0.167575i
$465$		0			0
$466$	−2.60447	+	8.01573i	−0.120650	+	0.371321i
$467$	−13.2542	+	18.2429i	−0.613332	+	0.844179i	−0.996846	−	0.0793559i	$-0.974714\pi$
$467$	−13.2542	+	18.2429i	−0.613332	+	0.844179i	0.383514	+	0.923535i	$0.374714\pi$
$468$	−14.4766	+	19.9253i	−0.669180	+	0.921048i
$469$	1.95914	−	6.02961i	0.0904647	−	0.278422i
$470$		0			0
$471$	16.4501	−	11.9517i	0.757982	−	0.550706i
$472$		−	7.51071i		−	0.345708i
$473$	20.5953	−	14.8150i	0.946971	−	0.681194i
$474$	25.0492			1.15055
$475$		0			0
$476$	−1.11280	−	3.42484i	−0.0510051	−	0.156977i
$477$	55.2689	+	17.9579i	2.53059	+	0.822238i
$478$	−11.8828	+	16.3553i	−0.543509	+	0.748075i
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	0.557216	−	0.830368i	$-0.311870\pi$
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	−0.617538	+	0.786541i	$0.711870\pi$
$480$		0			0
$481$	6.35063	+	19.5452i	0.289564	+	0.891186i
$482$	−4.74274	−	6.52782i	−0.216026	−	0.297334i
$483$		−	7.12155i		−	0.324042i
$484$	12.8666	+	9.53540i	0.584844	+	0.433427i
$485$		0			0
$486$	9.01242	−	6.54790i	0.408811	−	0.297019i
$487$	0.998894	−	0.324560i	0.0452642	−	0.0147072i	−0.286297	−	0.958141i	$-0.592425\pi$
$487$	0.998894	−	0.324560i	0.0452642	−	0.0147072i	0.331562	+	0.943434i	$0.392425\pi$
$488$	6.01349	+	1.95390i	0.272218	+	0.0884490i
$489$	−42.5104	−	30.8856i	−1.92239	−	1.39669i
$490$		0			0
$491$	−4.29969	+	13.2331i	−0.194042	+	0.597201i	0.805944	+	0.591992i	$0.201658\pi$
$491$	−4.29969	+	13.2331i	−0.194042	+	0.597201i	−0.999986	+	0.00520928i	$0.998342\pi$
$492$	15.3237	−	4.97898i	0.690847	−	0.224470i
$493$	8.39341	+	11.5525i	0.378020	+	0.520300i
$494$	−19.5103			−0.877811
$495$		0			0
$496$	−3.80394			−0.170802
$497$	1.22649	+	1.68812i	0.0550157	+	0.0757226i
$498$	−3.17562	+	1.03182i	−0.142303	+	0.0462371i
$499$	−5.36679	+	16.5173i	−0.240250	+	0.739415i	0.756131	+	0.654420i	$0.227087\pi$
$499$	−5.36679	+	16.5173i	−0.240250	+	0.739415i	−0.996381	+	0.0849943i	$0.972913\pi$
$500$		0			0
$501$	17.8631	+	12.9783i	0.798063	+	0.579827i
$502$	12.0883	+	3.92772i	0.539526	+	0.175303i
$503$	−34.0988	+	11.0794i	−1.52039	+	0.494005i	−0.945887	−	0.324498i	$-0.894805\pi$
$503$	−34.0988	+	11.0794i	−1.52039	+	0.494005i	−0.574503	+	0.818502i	$0.694805\pi$
$504$	10.4330	−	7.58000i	0.464722	−	0.337640i
$505$		0			0
$506$	5.70536	+	1.88367i	0.253634	+	0.0837393i
$507$		−	3.10530i		−	0.137911i
$508$	−10.1919	−	14.0280i	−0.452194	−	0.622392i
$509$	−0.660921	−	2.03410i	−0.0292948	−	0.0901601i	0.935340	−	0.353750i	$-0.115094\pi$
$509$	−0.660921	−	2.03410i	−0.0292948	−	0.0901601i	−0.964635	+	0.263590i	$0.915094\pi$
$510$		0			0
$511$	0.689106	+	0.500665i	0.0304843	+	0.0221481i
$512$	6.64282	−	9.14306i	0.293574	−	0.404070i
$513$	39.0614	+	12.6918i	1.72461	+	0.560358i
$514$	4.21591	+	12.9752i	0.185956	+	0.572313i
$515$		0			0
$516$	−31.3115			−1.37841
$517$	15.6238	+	11.4646i	0.687132	+	0.504214i
$518$		−	4.53321i		−	0.199178i
$519$	−25.4862	+	18.5168i	−1.11872	+	0.812797i
$520$		0			0
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	−0.999506	−	0.0314326i	$-0.989993\pi$
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	0.827093	+	0.562065i	$0.189993\pi$
$522$	−12.6626	+	17.4286i	−0.554227	+	0.762828i
$523$	14.0532	−	19.3426i	0.614504	−	0.845793i	−0.382434	−	0.923983i	$-0.624914\pi$
$523$	14.0532	−	19.3426i	0.614504	−	0.845793i	0.996938	+	0.0781901i	$0.0249141\pi$
$524$	−5.03317	+	15.4905i	−0.219875	+	0.676705i
$525$		0			0
$526$	2.20286	−	1.60047i	0.0960493	−	0.0697839i
$527$			8.84510i			0.385299i
$528$	−2.92867	−	9.16075i	−0.127454	−	0.398670i
$529$	16.9686			0.737766
$530$		0			0
$531$	4.46567	+	13.7439i	0.193794	+	0.596436i
$532$	−10.9517	−	3.55841i	−0.474815	−	0.154277i
$533$	7.97983	−	10.9833i	0.345645	−	0.475739i
$534$	13.6931	+	9.94862i	0.592558	+	0.430519i
$535$		0			0
$536$	−4.84229	−	14.9030i	−0.209155	−	0.643713i
$537$	−2.42044	−	3.33145i	−0.104450	−	0.143763i
$538$			7.33590i			0.316273i
$539$	0.0931395	−	19.6881i	0.00401180	−	0.848027i
$540$		0			0
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	−0.610491	−	0.792023i	$-0.709028\pi$
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	0.564606	+	0.825360i	$0.309028\pi$
$542$	−0.879484	+	0.285762i	−0.0377771	+	0.0122745i
$543$	−24.8384	−	8.07047i	−1.06592	−	0.346337i
$544$	−11.3680	−	8.25932i	−0.487398	−	0.354116i
$545$		0			0
$546$	2.27974	−	7.01631i	0.0975638	−	0.300270i
$547$	8.86507	−	2.88044i	0.379043	−	0.123159i	−0.113298	−	0.993561i	$-0.536141\pi$
$547$	8.86507	−	2.88044i	0.379043	−	0.123159i	0.492341	+	0.870403i	$0.336141\pi$
$548$	−3.66367	−	5.04261i	−0.156504	−	0.215410i
$549$	−12.1659			−0.519228
$550$		0			0
$551$	45.6625			1.94529
$552$	−10.3461	−	14.2403i	−0.440361	−	0.606105i
$553$	11.8475	−	3.84949i	0.503807	−	0.163697i
$554$	−1.84482	+	5.67776i	−0.0783788	+	0.241225i
$555$		0			0
$556$	−7.01190	−	5.09444i	−0.297371	−	0.216052i
$557$	−37.3929	−	12.1497i	−1.58439	−	0.514798i	−0.621205	−	0.783648i	$-0.713356\pi$
$557$	−37.3929	−	12.1497i	−1.58439	−	0.514798i	−0.963182	+	0.268850i	$0.913356\pi$
$558$	−12.6909	+	4.12353i	−0.537250	+	0.174563i
$559$	−21.3441	+	15.5074i	−0.902759	+	0.655893i
$560$		0			0
$561$	−21.3010	+	6.80989i	−0.899330	+	0.287514i
$562$			18.7141i			0.789407i
$563$	−11.7445	−	16.1649i	−0.494972	−	0.681271i	0.486323	−	0.873779i	$-0.338338\pi$
$563$	−11.7445	−	16.1649i	−0.494972	−	0.681271i	−0.981295	+	0.192508i	$0.938338\pi$
$564$	−7.39076	−	22.7464i	−0.311207	−	0.957797i
$565$		0			0
$566$	−12.1993	−	8.86330i	−0.512774	−	0.372552i
$567$	−0.208045	+	0.286349i	−0.00873707	+	0.0120255i
$568$	4.90499	+	1.59373i	0.205809	+	0.0668713i
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	0.879412	+	0.476061i	$0.157936\pi$
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	−0.431637	+	0.902047i	$0.642064\pi$
$570$		0			0
$571$	3.15090			0.131861			0.0659306	−	0.997824i	$-0.478998\pi$
$571$	3.15090			0.131861			0.0659306	+	0.997824i	$0.478998\pi$
$572$	−13.4268	−	9.85254i	−0.561404	−	0.411955i
$573$			12.5760i			0.525370i
$574$	−2.42273	+	1.76021i	−0.101123	+	0.0734699i
$575$		0			0
$576$	3.42427	−	10.5388i	0.142678	−	0.439117i
$577$	−16.0598	+	22.1044i	−0.668579	+	0.920220i	−0.999727	−	0.0233590i	$-0.992564\pi$
$577$	−16.0598	+	22.1044i	−0.668579	+	0.920220i	0.331148	+	0.943579i	$0.392564\pi$
$578$	4.87709	−	6.71273i	0.202860	−	0.279213i
$579$	−19.6927	+	60.6079i	−0.818400	+	2.51878i
$580$		0			0
$581$	−1.34340	+	0.976041i	−0.0557338	+	0.0404930i
$582$		−	5.06614i		−	0.209998i
$583$	−12.3196	+	37.3143i	−0.510227	+	1.54540i
$584$	2.10530			0.0871180
$585$		0			0
$586$	−0.581043	−	1.78827i	−0.0240027	−	0.0738726i
$587$	43.9082	+	14.2667i	1.81229	+	0.588848i	0.999984	+	0.00561158i	$0.00178623\pi$
$587$	43.9082	+	14.2667i	1.81229	+	0.588848i	0.812303	+	0.583236i	$0.198214\pi$
$588$	−14.2826	+	19.6583i	−0.589003	+	0.810694i
$589$	22.8823	+	16.6250i	0.942850	+	0.685020i
$590$		0			0
$591$	9.73771	+	29.9696i	0.400556	+	1.23278i
$592$	3.61227	+	4.97186i	0.148463	+	0.204342i
$593$			39.4265i			1.61905i	0.587085	+	0.809525i	$0.300275\pi$
$593$			39.4265i			1.61905i	−0.587085	+	0.809525i	$0.699725\pi$
$594$	−7.65124	−	10.6365i	−0.313934	−	0.436420i
$595$		0			0
$596$	−4.45746	+	3.23853i	−0.182585	+	0.132656i
$597$	20.9098	−	6.79399i	0.855780	−	0.278060i
$598$	−5.94225	−	1.93075i	−0.242997	−	0.0789544i
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	0.604984	−	0.796238i	$-0.293180\pi$
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	−0.570317	+	0.821425i	$0.693180\pi$
$600$		0			0
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	−0.618904	−	0.785466i	$-0.712423\pi$
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	0.962390	−	0.271673i	$-0.0875768\pi$
$602$	5.53475	−	1.79835i	0.225579	−	0.0732952i
$603$	17.7219	+	24.3921i	0.721693	+	0.993325i
$604$	−35.4605			−1.44287
$605$		0			0
$606$	−15.6036			−0.633854
$607$	12.8852	+	17.7350i	0.522996	+	0.719842i	0.986043	−	0.166492i	$-0.0532438\pi$
$607$	12.8852	+	17.7350i	0.522996	+	0.719842i	−0.463047	+	0.886334i	$0.653244\pi$
$608$	−42.7338	+	13.8851i	−1.73309	+	0.563114i
$609$	−5.33556	+	16.4212i	−0.216208	+	0.665420i
$610$		0			0
$611$	−16.3035	−	11.8452i	−0.659569	−	0.479205i
$612$	16.2873	+	5.29208i	0.658377	+	0.213920i
$613$	−10.0736	+	3.27313i	−0.406871	+	0.132200i	−0.505300	−	0.862944i	$-0.668618\pi$
$613$	−10.0736	+	3.27313i	−0.406871	+	0.132200i	0.0984293	+	0.995144i	$0.468618\pi$
$614$	−5.36653	+	3.89901i	−0.216576	+	0.157351i
$615$		0			0
$616$	5.09209	+	7.07884i	0.205166	+	0.285215i
$617$		−	4.60402i		−	0.185351i	−0.995696	−	0.0926755i	$-0.970458\pi$
$617$		−	4.60402i		−	0.185351i	0.995696	−	0.0926755i	$-0.0295419\pi$
$618$	11.5591	+	15.9098i	0.464976	+	0.639985i
$619$	−11.4348	−	35.1926i	−0.459603	−	1.41451i	−0.865645	−	0.500657i	$-0.833092\pi$
$619$	−11.4348	−	35.1926i	−0.459603	−	1.41451i	0.406043	−	0.913854i	$-0.366908\pi$
$620$		0			0
$621$	10.6409	+	7.73110i	0.427006	+	0.310238i
$622$	−8.72489	+	12.0088i	−0.349836	+	0.481508i
$623$	8.00529	+	2.60108i	0.320725	+	0.104210i
$624$	3.09058	+	9.51183i	0.123722	+	0.380778i
$625$		0			0
$626$	−5.24081			−0.209465
$627$	−22.4195	+	67.9055i	−0.895350	+	2.71189i
$628$		−	10.5291i		−	0.420157i
$629$	11.5608	−	8.39942i	0.460960	−	0.334907i
$630$		0			0
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	0.673875	+	0.738845i	$0.264628\pi$
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	−0.979459	+	0.201644i	$0.935372\pi$
$632$	18.0977	−	24.9094i	0.719890	−	0.990843i
$633$	37.6246	−	51.7858i	1.49544	−	2.05830i
$634$	0.522727	−	1.60879i	0.0207601	−	0.0638931i
$635$		0			0
$636$	39.2355	−	28.5062i	1.55579	−	1.13035i
$637$			20.4741i			0.811213i
$638$	−11.7444	−	8.61798i	−0.464965	−	0.341189i
$639$	−9.92328			−0.392559
$640$		0			0
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	−0.727374	−	0.686241i	$-0.759260\pi$
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	0.185096	−	0.982720i	$-0.440740\pi$
$642$	9.16538	+	2.97801i	0.361729	+	0.117533i
$643$	15.2007	−	20.9220i	0.599457	−	0.825082i	−0.396201	−	0.918164i	$-0.629672\pi$
$643$	15.2007	−	20.9220i	0.599457	−	0.825082i	0.995658	+	0.0930818i	$0.0296718\pi$
$644$	−2.98341	−	2.16757i	−0.117563	−	0.0854143i
$645$		0			0
$646$	4.19221	+	12.9023i	0.164940	+	0.507634i
$647$	11.4539	+	15.7649i	0.450298	+	0.619782i	0.972462	−	0.233063i	$-0.0748749\pi$
$647$	11.4539	+	15.7649i	0.450298	+	0.619782i	−0.522163	+	0.852845i	$0.674875\pi$
$648$			0.874831i			0.0343666i
$649$	−9.30768	+	2.97564i	−0.365358	+	0.116804i
$650$		0			0
$651$	−8.65244	+	6.28636i	−0.339116	+	0.246382i
$652$	−25.8776	+	8.40814i	−1.01344	+	0.329288i
$653$	−15.9110	−	5.16979i	−0.622645	−	0.202310i	−0.0193305	−	0.999813i	$-0.506153\pi$
$653$	−15.9110	−	5.16979i	−0.622645	−	0.202310i	−0.603314	+	0.797504i	$0.706153\pi$
$654$	−8.93996	−	6.49526i	−0.349580	−	0.253985i
$655$		0			0
$656$	1.25454	−	3.86108i	0.0489815	−	0.150750i
$657$	−3.85251	+	1.25176i	−0.150301	+	0.0488357i
$658$	2.61284	+	3.59627i	0.101859	+	0.140197i
$659$	1.66127			0.0647137			0.0323569	−	0.999476i	$-0.489699\pi$
$659$	1.66127			0.0647137			0.0323569	+	0.999476i	$0.489699\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$	−6.67492	−	9.18724i	−0.259428	−	0.357072i
$663$	22.1174	−	7.18637i	0.858968	−	0.279096i
$664$	−1.26829	+	3.90338i	−0.0492190	+	0.151481i
$665$		0			0
$666$	17.4411	+	12.6717i	0.675827	+	0.491017i
$667$	13.9074	+	4.51879i	0.538497	+	0.174968i
$668$	10.8739	−	3.53314i	0.420723	−	0.136701i
$669$	36.4907	−	26.5120i	1.41081	−	1.02501i
$670$		0			0
$671$	0.0389168	−	8.22636i	0.00150237	−	0.317575i
$672$		−	16.9904i		−	0.655419i
$673$	22.6855	+	31.2239i	0.874462	+	1.20359i	0.977924	+	0.208961i	$0.0670080\pi$
$673$	22.6855	+	31.2239i	0.874462	+	1.20359i	−0.103462	+	0.994633i	$0.532992\pi$
$674$	−4.44417	−	13.6778i	−0.171183	−	0.526848i
$675$		0			0
$676$	−1.30089	−	0.945154i	−0.0500343	−	0.0363521i
$677$	22.6878	−	31.2271i	0.871964	−	1.20016i	−0.106619	−	0.994300i	$-0.534002\pi$
$677$	22.6878	−	31.2271i	0.871964	−	1.20016i	0.978582	−	0.205855i	$-0.0659976\pi$
$678$	0.601391	+	0.195404i	0.0230963	+	0.00750443i
$679$	−0.778549	−	2.39613i	−0.0298780	−	0.0919549i
$680$		0			0
$681$	67.9167			2.60257
$682$	−2.74766	−	8.59457i	−0.105213	−	0.329103i
$683$		−	0.748158i		−	0.0286275i	−0.999898	−	0.0143137i	$-0.995444\pi$
$683$		−	0.748158i		−	0.0286275i	0.999898	−	0.0143137i	$-0.00455636\pi$
$684$	44.3038	−	32.1886i	1.69400	−	1.23076i
$685$		0			0
$686$	3.04126	−	9.36005i	0.116116	−	0.357368i
$687$	−24.8125	+	34.1515i	−0.946656	+	1.30296i
$688$	−4.63730	+	6.38270i	−0.176796	+	0.243338i
$689$	12.6276	−	38.8637i	0.481073	−	1.48059i
$690$		0			0
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	−0.665234	−	0.746635i	$-0.731668\pi$
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	0.504524	+	0.863398i	$0.331668\pi$
$692$			16.3128i			0.620118i
$693$	−13.5270	−	9.92603i	−0.513847	−	0.377059i
$694$	−1.59998			−0.0607342
$695$		0			0
$696$	13.1876	+	40.5873i	0.499875	+	1.53846i
$697$	−8.97796	−	2.91712i	−0.340065	−	0.110494i
$698$	10.8619	−	14.9501i	0.411129	−	0.565871i
$699$	−25.9895	−	18.8824i	−0.983011	−	0.714200i
$700$		0			0
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	0.833811	−	0.552051i	$-0.186155\pi$
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	−0.999054	+	0.0434831i	$0.986155\pi$
$702$	8.00883	+	11.0232i	0.302274	+	0.416044i
$703$		−	45.6952i		−	1.72343i
$704$	7.11520	+	2.34914i	0.268164	+	0.0885366i
$705$		0			0
$706$	−13.8766	+	10.0820i	−0.522255	+	0.379440i
$707$	−7.38004	+	2.39792i	−0.277555	+	0.0901830i
$708$	11.4699	+	3.72678i	0.431064	+	0.140061i
$709$	−13.9267	−	10.1183i	−0.523028	−	0.380002i	0.294715	−	0.955585i	$-0.404775\pi$
$709$	−13.9267	−	10.1183i	−0.523028	−	0.380002i	−0.817744	+	0.575583i	$0.804775\pi$
$710$		0			0
$711$	−18.3068	+	56.3425i	−0.686558	+	2.11301i
$712$	19.7862	−	6.42893i	0.741519	−	0.240934i
$713$	5.32404	+	7.32792i	0.199387	+	0.274433i
$714$	−5.12978			−0.191977
$715$		0			0
$716$	−2.13233			−0.0796891
$717$	−45.2922	−	62.3393i	−1.69147	−	2.32811i
$718$	7.10123	−	2.30733i	0.265015	−	0.0861087i
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	−0.673246	−	0.739419i	$-0.735100\pi$
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	0.979287	−	0.202478i	$-0.0648996\pi$
$720$		0			0
$721$	7.91208	+	5.74846i	0.294661	+	0.214084i
$722$	27.9286	+	9.07457i	1.03940	+	0.337720i
$723$	29.2496	−	9.50377i	1.08780	−	0.353449i
$724$	−10.9409	+	7.94905i	−0.406617	+	0.295424i
$725$		0			0
$726$	18.5823	−	13.2340i	0.689652	−	0.491160i
$727$		−	44.1917i		−	1.63898i	−0.573094	−	0.819490i	$-0.694257\pi$
$727$		−	44.1917i		−	1.63898i	0.573094	−	0.819490i	$-0.305743\pi$
$728$	−5.33007	−	7.33622i	−0.197546	−	0.271898i
$729$	13.4392	+	41.3616i	0.497748	+	1.53191i
$730$		0			0
$731$	14.8414	+	10.7829i	0.548928	+	0.398819i
$732$	−5.96774	+	8.21389i	−0.220574	+	0.303594i
$733$	23.7388	+	7.71320i	0.876812	+	0.284894i	0.712633	−	0.701537i	$-0.247502\pi$
$733$	23.7388	+	7.71320i	0.876812	+	0.284894i	0.164179	+	0.986431i	$0.447502\pi$
$734$	0.845498	+	2.60218i	0.0312079	+	0.0960480i
$735$		0			0
$736$	−14.3895			−0.530404
$737$	−16.5502	+	11.9052i	−0.609635	+	0.438534i
$738$		−	14.2415i		−	0.524237i
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	−0.225135	−	0.974327i	$-0.572282\pi$
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	0.857070	+	0.515200i	$0.172282\pi$
$740$		0			0
$741$	22.9800	−	70.7251i	0.844190	−	2.59815i
$742$	−5.29820	+	7.29234i	−0.194503	+	0.267710i
$743$	−18.0172	+	24.7986i	−0.660988	+	0.909772i	−0.999514	−	0.0311852i	$-0.990072\pi$
$743$	−18.0172	+	24.7986i	−0.660988	+	0.909772i	0.338526	+	0.940957i	$0.390072\pi$
$744$	−8.16862	+	25.1404i	−0.299476	+	0.921693i
$745$		0			0
$746$	−5.57387	+	4.04965i	−0.204074	+	0.148268i
$747$		−	7.89694i		−	0.288934i
$748$	−3.63051	+	10.9963i	−0.132744	+	0.402064i
$749$	4.79259			0.175118
$750$		0			0
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	−0.963300	−	0.268427i	$-0.913496\pi$
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	0.621549	−	0.783375i	$-0.286504\pi$
$752$	−5.73134	−	1.86223i	−0.209001	−	0.0679084i
$753$	−28.4760	+	39.1939i	−1.03772	+	1.42831i
$754$	12.2554	+	8.90404i	0.446314	+	0.324266i
$755$		0			0
$756$	2.48509	+	7.64833i	0.0903820	+	0.278167i
$757$	−20.4957	−	28.2099i	−0.744929	−	1.02531i	−0.998320	−	0.0579427i	$-0.981546\pi$
$757$	−20.4957	−	28.2099i	−0.744929	−	1.02531i	0.253391	−	0.967364i	$-0.418454\pi$
$758$			7.23750i			0.262878i
$759$	−13.5483	+	18.4633i	−0.491772	+	0.670176i
$760$		0			0
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	−0.547646	−	0.836710i	$-0.684476\pi$
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	0.626527	+	0.779400i	$0.284476\pi$
$762$	−23.4914	+	7.63282i	−0.851004	+	0.276508i
$763$	−5.22650	−	1.69819i	−0.189212	−	0.0614787i
$764$	5.26842	+	3.82773i	0.190605	+	0.138482i
$765$		0			0
$766$	4.11365	−	12.6605i	0.148632	−	0.457443i
$767$	9.66440	−	3.14015i	0.348961	−	0.113384i
$768$	−19.7206	−	27.1431i	−0.711605	−	0.979441i
$769$	32.5735			1.17463			0.587315	−	0.809359i	$-0.300185\pi$
$769$	32.5735			1.17463			0.587315	+	0.809359i	$0.300185\pi$
$770$		0			0
$771$	−52.0010			−1.87277
$772$	19.3964	+	26.6969i	0.698092	+	0.960841i
$773$	−39.6246	+	12.8748i	−1.42520	+	0.463074i	−0.917249	−	0.398314i	$-0.869595\pi$
$773$	−39.6246	+	12.8748i	−1.42520	+	0.463074i	−0.507947	+	0.861388i	$0.669595\pi$
$774$	−8.55230	+	26.3213i	−0.307406	+	0.946099i
$775$		0			0
$776$	−5.03787	−	3.66022i	−0.180849	−	0.131394i
$777$	16.4329	+	5.33938i	0.589528	+	0.191549i
$778$	21.8820	−	7.10990i	0.784509	−	0.254902i
$779$	−24.4213	+	17.7431i	−0.874984	+	0.635713i
$780$		0			0
$781$	0.0317431	−	6.70994i	0.00113586	−	0.240101i
$782$			4.34451i			0.155359i
$783$	−18.7441	−	25.7990i	−0.669860	−	0.921983i
$784$	1.89197	+	5.82288i	0.0675703	+	0.207960i
$785$		0			0
$786$	18.7707	+	13.6377i	0.669530	+	0.486442i
$787$	21.1137	−	29.0605i	0.752622	−	1.03589i	−0.245170	−	0.969480i	$-0.578844\pi$
$787$	21.1137	−	29.0605i	0.752622	−	1.03589i	0.997792	−	0.0664148i	$-0.0211561\pi$
$788$	15.5189	+	5.04239i	0.552838	+	0.179628i
$789$	3.20712	+	9.87049i	0.114176	+	0.351399i
$790$		0			0
$791$	0.314468			0.0111812
$792$	−41.4690	−	0.196179i	−1.47354	−	0.00697093i
$793$			8.55476i			0.303789i
$794$	6.33833	−	4.60507i	0.224939	−	0.163428i
$795$		0			0
$796$	3.51808	−	10.8275i	0.124695	−	0.383771i
$797$	18.6444	−	25.6618i	0.660418	−	0.908987i	−0.339077	−	0.940759i	$-0.610115\pi$
$797$	18.6444	−	25.6618i	0.660418	−	0.908987i	0.999495	+	0.0317713i	$0.0101148\pi$
$798$	−9.64178	+	13.2708i	−0.341315	+	0.469780i
$799$	−4.33014	+	13.3268i	−0.153189	+	0.471468i
$800$		0			0
$801$	−32.3845	+	23.5287i	−1.14425	+	0.831347i
$802$		−	20.3352i		−	0.718061i
$803$	−0.834092	−	2.60900i	−0.0294345	−	0.0920698i
$804$	25.1617			0.887384
$805$		0			0
$806$	2.89957	+	8.92396i	0.102133	+	0.314333i
$807$	−26.5927	−	8.64050i	−0.936108	−	0.304160i
$808$	−11.2734	+	15.5166i	−0.396598	+	0.545870i
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	0.460053	−	0.887891i	$-0.347830\pi$
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	−0.702270	+	0.711910i	$0.747830\pi$
$810$		0			0
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	0.988021	−	0.154320i	$-0.0493186\pi$
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	−0.890033	+	0.455897i	$0.849319\pi$
$812$	5.25529	+	7.23329i	0.184425	+	0.253839i
$813$		−	3.52472i		−	0.123617i
$814$	−8.62415	+	11.7528i	−0.302276	+	0.411935i
$815$		0			0
$816$	5.62616	−	4.08764i	0.196955	−	0.143096i
$817$	55.7908	−	18.1275i	1.95187	−	0.634202i
$818$	−10.0798	−	3.27513i	−0.352432	−	0.114512i
$819$	14.1155	+	10.2555i	0.493235	+	0.358356i
$820$		0			0
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	0.00994979	+	0.999950i	$0.496833\pi$
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	−0.595806	+	0.803129i	$0.703167\pi$
$822$	−8.44439	+	2.74375i	−0.294532	+	0.0956993i
$823$	−10.4975	−	14.4486i	−0.365920	−	0.503646i	0.585866	−	0.810408i	$-0.300755\pi$
$823$	−10.4975	−	14.4486i	−0.365920	−	0.503646i	−0.951786	+	0.306762i	$0.900755\pi$
$824$	24.1723			0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−30.5351	−	42.0280i	−1.06181	−	1.46146i	−0.878102	−	0.478474i	$-0.841190\pi$
$827$	−30.5351	−	42.0280i	−1.06181	−	1.46146i	−0.183708	−	0.982981i	$-0.558810\pi$
$828$	16.6790	−	5.41934i	0.579636	−	0.188335i
$829$	6.10185	−	18.7796i	0.211926	−	0.652241i	−0.787431	−	0.616402i	$-0.788590\pi$
$829$	6.10185	−	18.7796i	0.211926	−	0.652241i	0.999358	−	0.0358392i	$-0.0114104\pi$
$830$		0			0
$831$	−18.4091	−	13.3750i	−0.638603	−	0.463972i
$832$	−7.41064	−	2.40786i	−0.256918	−	0.0834776i
$833$	13.5396	−	4.39930i	0.469121	−	0.152427i
$834$	−9.98849	+	7.25707i	−0.345873	+	0.251292i
$835$		0			0
$836$	21.6236	+	30.0604i	0.747869	+	1.03966i
$837$		−	19.7528i		−	0.682757i
$838$	−13.6449	−	18.7806i	−0.471354	−	0.648763i
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	0.970611	−	0.240655i	$-0.0773623\pi$
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	−0.926694	+	0.375817i	$0.877362\pi$
$840$		0			0
$841$	−5.22128	−	3.79348i	−0.180044	−	0.130810i
$842$	11.5206	−	15.8567i	0.397025	−	0.546458i
$843$	−67.8389	−	22.0422i	−2.33649	−	0.759173i
$844$	−10.2427	−	31.5239i	−0.352569	−	1.08510i
$845$		0			0
$846$	−21.1400			−0.726807
$847$	6.75507	−	9.11494i	0.232107	−	0.313193i
$848$		−	12.2198i		−	0.419630i
$849$	46.4983	−	33.7830i	1.59582	−	1.15943i
$850$		0			0
$851$	4.52203	−	13.9174i	0.155013	−	0.477081i
$852$	−4.86767	+	6.69978i	−0.166764	+	0.229531i
$853$	3.23449	−	4.45190i	0.110747	−	0.152430i	−0.750046	−	0.661386i	$-0.769968\pi$
$853$	3.23449	−	4.45190i	0.110747	−	0.152430i	0.860792	+	0.508956i	$0.169968\pi$
$854$	0.583125	−	1.79468i	0.0199541	−	0.0614125i
$855$		0			0
$856$	9.58327	−	6.96265i	0.327549	−	0.237979i
$857$			26.9281i			0.919847i	0.887959	+	0.459924i	$0.152123\pi$
$857$			26.9281i			0.919847i	−0.887959	+	0.459924i	$0.847877\pi$
$858$	−19.2585	+	13.8534i	−0.657476	+	0.472948i
$859$	−19.1519			−0.653456			−0.326728	−	0.945118i	$-0.605946\pi$
$859$	−19.1519			−0.653456			−0.326728	+	0.945118i	$0.605946\pi$
$860$		0			0
$861$	−3.52721	−	10.8556i	−0.120207	−	0.369960i
$862$	−2.71404	−	0.881845i	−0.0924405	−	0.0300358i
$863$	2.91630	−	4.01394i	0.0992720	−	0.136636i	−0.756491	−	0.654004i	$-0.773088\pi$
$863$	2.91630	−	4.01394i	0.0992720	−	0.136636i	0.855763	+	0.517368i	$0.173088\pi$
$864$	25.3869	+	18.4447i	0.863679	+	0.627500i
$865$		0			0
$866$	−9.14937	−	28.1589i	−0.310908	−	0.956877i
$867$	18.5893	+	25.5860i	0.631326	+	0.868946i
$868$			5.53810i			0.187975i
$869$	−38.0392	−	12.5589i	−1.29039	−	0.426033i
$870$		0			0
$871$	17.1520	−	12.4616i	0.581172	−	0.422246i
$872$	−12.9180	+	4.19732i	−0.437460	+	0.142139i
$873$	11.3951	+	3.70250i	0.385667	+	0.125311i
$874$	11.2393	+	8.16581i	0.380174	+	0.276213i
$875$		0			0
$876$	−1.04464	+	3.21508i	−0.0352952	+	0.108627i
$877$	−25.8738	+	8.40691i	−0.873696	+	0.283881i	−0.711338	−	0.702851i	$-0.751910\pi$
$877$	−25.8738	+	8.40691i	−0.873696	+	0.283881i	−0.162359	+	0.986732i	$0.551910\pi$
$878$	0.443704	+	0.610706i	0.0149743	+	0.0206103i
$879$	7.16686			0.241732
$880$		0			0
$881$	10.3570			0.348935			0.174467	−	0.984663i	$-0.444180\pi$
$881$	10.3570			0.348935			0.174467	+	0.984663i	$0.444180\pi$
$882$	12.6242	+	17.3757i	0.425079	+	0.585071i
$883$	−7.03296	+	2.28515i	−0.236678	+	0.0769014i	−0.424954	−	0.905215i	$-0.639710\pi$
$883$	−7.03296	+	2.28515i	−0.236678	+	0.0769014i	0.188276	+	0.982116i	$0.439710\pi$
$884$	3.72126	−	11.4529i	0.125159	−	0.385201i
$885$		0			0
$886$	−9.59168	−	6.96877i	−0.322239	−	0.234120i
$887$	17.1752	+	5.58054i	0.576685	+	0.187376i	0.582815	−	0.812605i	$-0.301951\pi$
$887$	17.1752	+	5.58054i	0.576685	+	0.187376i	−0.00612989	+	0.999981i	$0.501951\pi$
$888$	40.6163	−	13.1970i	1.36299	−	0.442864i
$889$	−9.93772	+	7.22018i	−0.333300	+	0.242157i
$890$		0			0
$891$	1.08414	−	0.346596i	0.0363200	−	0.0116114i
$892$		−	23.3563i		−	0.782027i
$893$	26.3377	+	36.2507i	0.881358	+	1.21309i
$894$	2.42536	+	7.46450i	0.0811163	+	0.249650i
$895$		0			0
$896$	−8.38734	−	6.09376i	−0.280201	−	0.203578i
$897$	13.9980	−	19.2666i	0.467380	−	0.643293i
$898$	−25.1446	−	8.16997i	−0.839085	−	0.272635i
$899$	−6.78623	−	20.8859i	−0.226334	−	0.696583i
$900$		0			0
$901$	−28.4141			−0.946612
$902$	9.62985	+	0.0455564i	0.320639	+	0.00151686i
$903$			22.1817i			0.738160i
$904$	0.628811	−	0.456858i	0.0209139	−	0.0151949i
$905$		0			0
$906$	−15.6096	+	48.0414i	−0.518594	+	1.59607i
$907$	−15.4570	+	21.2748i	−0.513242	+	0.706417i	−0.984462	−	0.175599i	$-0.943814\pi$
$907$	−15.4570	+	21.2748i	−0.513242	+	0.706417i	0.471220	+	0.882016i	$0.343814\pi$
$908$	20.6716	−	28.4521i	0.686013	−	0.944215i
$909$	11.4036	−	35.0968i	0.378235	−	1.16409i
$910$		0			0
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	−0.901324	−	0.433146i	$-0.857403\pi$
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	0.133422	+	0.991059i	$0.457403\pi$
$912$		−	22.2379i		−	0.736371i
$913$	5.33976	+	0.0252611i	0.176720	+	0.000836020i
$914$	−18.5535			−0.613694
$915$		0			0
$916$	6.75483	+	20.7892i	0.223186	+	0.686896i
$917$	10.9738	+	3.56560i	0.362386	+	0.117746i
$918$	5.56885	−	7.66487i	0.183799	−	0.252978i
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.969692	−	0.244330i	$-0.0785681\pi$
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.0672794	+	0.997734i	$0.478568\pi$
$920$		0			0
$921$	−7.81306	−	24.0461i	−0.257449	−	0.792347i
$922$	−2.88600	−	3.97224i	−0.0950455	−	0.130819i
$923$			6.97781i			0.229677i
$924$	−13.3370	+	4.26381i	−0.438756	+	0.140269i
$925$		0			0
$926$	23.1383	−	16.8110i	0.760373	−	0.552443i
$927$	−44.2332	+	14.3722i	−1.45281	+	0.472046i
$928$	33.1799	+	10.7808i	1.08919	+	0.353898i
$929$	6.00397	+	4.36214i	0.196984	+	0.143117i	0.681905	−	0.731441i	$-0.261152\pi$
$929$	6.00397	+	4.36214i	0.196984	+	0.143117i	−0.484921	+	0.874558i	$0.661152\pi$
$930$		0			0
$931$	14.0677	−	43.2959i	0.461050	−	1.41897i
$932$	−15.8207	+	5.14046i	−0.518224	+	0.168381i
$933$	−33.2554	−	45.7722i	−1.08873	−	1.49851i
$934$	16.6334			0.544260
$935$		0			0
$936$	43.1245			1.40957
$937$	−8.77914	−	12.0834i	−0.286802	−	0.394749i	0.641170	−	0.767399i	$-0.278449\pi$
$937$	−8.77914	−	12.0834i	−0.286802	−	0.394749i	−0.927972	+	0.372650i	$0.878449\pi$
$938$	−4.44768	+	1.44514i	−0.145222	+	0.0471855i
$939$	6.17282	−	18.9980i	0.201442	−	0.619975i
$940$		0			0
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.996843	+	0.0793986i	$0.0253000\pi$
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.383554	+	0.923518i	$0.374700\pi$
$942$	−14.2647	−	4.63488i	−0.464769	−	0.151013i
$943$	−9.19386	+	2.98727i	−0.299393	+	0.0972788i
$944$	2.45840	−	1.78613i	0.0800142	−	0.0581337i
$945$		0			0
$946$	−17.7706	−	5.86711i	−0.577773	−	0.190756i
$947$			3.69553i			0.120088i	0.998196	+	0.0600442i	$0.0191242\pi$
$947$			3.69553i			0.120088i	−0.998196	+	0.0600442i	$0.980876\pi$
$948$	29.0600	+	39.9976i	0.943825	+	1.29906i
$949$	0.880206	+	2.70899i	0.0285727	+	0.0879377i
$950$		0			0
$951$	5.21618	+	3.78978i	0.169146	+	0.122892i
$952$	−3.70621	+	5.10116i	−0.120119	+	0.165329i
$953$	41.0406	+	13.3349i	1.32943	+	0.431959i	0.885724	−	0.464211i	$-0.153662\pi$
$953$	41.0406	+	13.3349i	1.32943	+	0.431959i	0.443709	+	0.896171i	$0.353662\pi$
$954$	−13.2465	−	40.7685i	−0.428871	−	1.31993i
$955$		0			0
$956$	−39.9011			−1.29049
$957$	45.0732	−	32.4229i	1.45701	−	1.04808i
$958$			1.20373i			0.0388907i
$959$	−3.57229	+	2.59542i	−0.115355	+	0.0838104i
$960$		0			0
$961$	−5.37602	+	16.5457i	−0.173420	+	0.533732i
$962$	8.91041	−	12.2641i	0.287283	−	0.395411i
$963$	−13.3967	+	18.4390i	−0.431704	+	0.594189i
$964$	4.92126	−	15.1461i	0.158503	−	0.487822i
$965$		0			0
$966$	−4.24988	+	3.08772i	−0.136738	+	0.0993457i
$967$			29.2144i			0.939471i	0.882807	+	0.469736i	$0.155651\pi$
$967$			29.2144i			0.939471i	−0.882807	+	0.469736i	$0.844349\pi$
$968$	0.265306	−	28.0400i	0.00852725	−	0.901238i
$969$	−51.7087			−1.66112
$970$		0			0
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	−0.992402	−	0.123035i	$-0.960737\pi$
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	0.730552	−	0.682857i	$-0.239263\pi$
$972$	20.9109	+	6.79437i	0.670718	+	0.217929i
$973$	−3.60901	+	4.96737i	−0.115699	+	0.159247i
$974$	−0.626780	−	0.455382i	−0.0200833	−	0.0145914i
$975$		0			0
$976$	0.790528	+	2.43300i	0.0253042	+	0.0778783i
$977$	−9.31251	−	12.8176i	−0.297934	−	0.410070i	0.633637	−	0.773630i	$-0.281561\pi$
$977$	−9.31251	−	12.8176i	−0.297934	−	0.410070i	−0.931571	+	0.363560i	$0.881561\pi$
$978$			38.7598i			1.23940i
$979$	−15.8061	−	21.9731i	−0.505166	−	0.702263i
$980$		0			0
$981$	21.1432	−	15.3615i	0.675051	−	0.490454i
$982$	9.76126	−	3.17163i	0.311494	−	0.101211i
$983$	33.3858	+	10.8477i	1.06484	+	0.345988i	0.788477	−	0.615064i	$-0.210870\pi$
$983$	33.3858	+	10.8477i	1.06484	+	0.345988i	0.276365	+	0.961053i	$0.410870\pi$
$984$	−22.8240	−	16.5826i	−0.727604	−	0.528635i
$985$		0			0
$986$	3.25497	−	10.0178i	0.103659	−	0.319031i
$987$	−16.1140	+	5.23576i	−0.512915	+	0.166656i
$988$	−22.6342	−	31.1534i	−0.720091	−	0.991120i
$989$	18.7861			0.597363
$990$		0			0
$991$	18.9700			0.602600			0.301300	−	0.953529i	$-0.402579\pi$
$991$	18.9700			0.602600			0.301300	+	0.953529i	$0.402579\pi$
$992$	12.7020	+	17.4828i	0.403288	+	0.555078i
$993$	41.1658	−	13.3756i	1.30636	−	0.424461i
$994$	0.475634	−	1.46385i	0.0150862	−	0.0464306i
$995$		0			0
$996$	−5.33167	−	3.87369i	−0.168940	−	0.122742i
$997$	−28.6598	−	9.31213i	−0.907665	−	0.294918i	−0.182268	−	0.983249i	$-0.558344\pi$
$997$	−28.6598	−	9.31213i	−0.907665	−	0.294918i	−0.725397	+	0.688331i	$0.758344\pi$
$998$	12.1838	−	3.95876i	0.385672	−	0.125312i
$999$	−25.8175	+	18.7575i	−0.816830	+	0.593462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.a.124.2		16
5.2	odd	4		55.2.g.b.36.2	yes	8
5.3	odd	4		275.2.h.a.201.1		8
5.4	even	2	inner	275.2.z.a.124.3		16
11.4	even	5	inner	275.2.z.a.224.3		16
15.2	even	4		495.2.n.e.91.1		8
20.7	even	4		880.2.bo.h.641.2		8
55.2	even	20		605.2.a.k.1.3		4
55.4	even	10	inner	275.2.z.a.224.2		16
55.7	even	20		605.2.g.k.81.1		8
55.13	even	20		3025.2.a.w.1.2		4
55.17	even	20		605.2.g.e.251.2		8
55.27	odd	20		605.2.g.m.251.1		8
55.32	even	4		605.2.g.k.366.1		8
55.37	odd	20		55.2.g.b.26.2	✓	8
55.42	odd	20		605.2.a.j.1.2		4
55.47	odd	20		605.2.g.m.511.1		8
55.48	odd	20		275.2.h.a.26.1		8
55.52	even	20		605.2.g.e.511.2		8
55.53	odd	20		3025.2.a.bd.1.3		4
165.2	odd	20		5445.2.a.bi.1.2		4
165.92	even	20		495.2.n.e.136.1		8
165.152	even	20		5445.2.a.bp.1.3		4
220.147	even	20		880.2.bo.h.81.2		8
220.167	odd	20		9680.2.a.cm.1.4		4
220.207	even	20		9680.2.a.cn.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	55.37	odd	20
55.2.g.b.36.2	yes	8	5.2	odd	4
275.2.h.a.26.1		8	55.48	odd	20
275.2.h.a.201.1		8	5.3	odd	4
275.2.z.a.124.2		16	1.1	even	1	trivial
275.2.z.a.124.3		16	5.4	even	2	inner
275.2.z.a.224.2		16	55.4	even	10	inner
275.2.z.a.224.3		16	11.4	even	5	inner
495.2.n.e.91.1		8	15.2	even	4
495.2.n.e.136.1		8	165.92	even	20
605.2.a.j.1.2		4	55.42	odd	20
605.2.a.k.1.3		4	55.2	even	20
605.2.g.e.251.2		8	55.17	even	20
605.2.g.e.511.2		8	55.52	even	20
605.2.g.k.81.1		8	55.7	even	20
605.2.g.k.366.1		8	55.32	even	4
605.2.g.m.251.1		8	55.27	odd	20
605.2.g.m.511.1		8	55.47	odd	20
880.2.bo.h.81.2		8	220.147	even	20
880.2.bo.h.641.2		8	20.7	even	4
3025.2.a.w.1.2		4	55.13	even	20
3025.2.a.bd.1.3		4	55.53	odd	20
5445.2.a.bi.1.2		4	165.2	odd	20
5445.2.a.bp.1.3		4	165.152	even	20
9680.2.a.cm.1.4		4	220.167	odd	20
9680.2.a.cn.1.4		4	220.207	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433574 - 0.596764i) q^{2} +(2.67395 - 0.868820i) q^{3} +(0.449894 - 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.980901 - 0.318714i) q^{7} +(-2.42443 + 0.787747i) q^{8} +(3.96813 - 2.88301i) q^{9} +O(q^{10})\)	\(q+(-0.433574 - 0.596764i) q^{2} +(2.67395 - 0.868820i) q^{3} +(0.449894 - 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.980901 - 0.318714i) q^{7} +(-2.42443 + 0.787747i) q^{8} +(3.96813 - 2.88301i) q^{9} +(1.93675 + 2.69240i) q^{11} -4.09331i q^{12} +(-2.02726 - 2.79029i) q^{13} +(0.235096 + 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(-1.40964 + 1.94020i) q^{17} +(-3.44095 - 1.11803i) q^{18} +(2.36979 + 7.29347i) q^{19} -2.89979 q^{21} +(0.767001 - 2.32313i) q^{22} +2.45589i q^{23} +(-5.79842 + 4.21280i) q^{24} +(-0.786174 + 2.41960i) q^{26} +(3.14799 - 4.33283i) q^{27} +(-0.882602 + 1.21480i) q^{28} +(1.83998 - 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919i q^{32} +(7.51798 + 5.51666i) q^{33} +1.76902 q^{34} +(-2.20667 - 6.79144i) q^{36} +(-5.66694 - 1.84130i) q^{37} +(3.32500 - 4.57646i) q^{38} +(-7.84507 - 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +(1.25727 + 1.73049i) q^{42} -7.64941i q^{43} +(4.59931 - 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(5.55697 - 1.80557i) q^{47} +(-2.75786 - 0.896084i) q^{48} +(-4.80253 - 3.48924i) q^{49} +(-2.08362 + 6.41272i) q^{51} +(-4.77558 + 1.55168i) q^{52} +(6.96410 + 9.58526i) q^{53} -3.95056 q^{54} +2.62920 q^{56} +(12.6734 + 17.4435i) q^{57} +(-4.17718 + 1.35725i) q^{58} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-2.58741 - 0.840701i) q^{62} +(-4.81120 + 1.56325i) q^{63} +(1.82774 - 1.32793i) q^{64} +(0.0325397 - 6.87834i) q^{66} +6.14702i q^{67} +(2.05227 + 2.82471i) q^{68} +(2.13372 + 6.56693i) q^{69} +(-1.63676 - 1.18918i) q^{71} +(-7.34938 + 10.1156i) q^{72} +(-0.785446 - 0.255207i) q^{73} +(1.35822 + 4.18017i) q^{74} +11.1649 q^{76} +(-1.04165 - 3.25824i) q^{77} +7.15293i q^{78} +(-9.77146 + 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(1.70666 - 2.34901i) q^{82} +(0.946345 - 1.30253i) q^{83} +(-1.30460 + 4.01513i) q^{84} +(-4.56489 + 3.31659i) q^{86} -16.7409i q^{87} +(-6.81645 - 5.00188i) q^{88} -8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(3.40050 + 1.10489i) q^{92} +(6.09510 - 8.38919i) q^{93} +(-3.48685 - 2.53335i) q^{94} +(5.09058 + 15.6672i) q^{96} +(1.43583 + 1.97625i) q^{97} +4.37882i q^{98} +(15.4475 + 5.10011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44} + 6 q^{46} - 2 q^{49} + 2 q^{51} - 32 q^{54} + 44 q^{56} + 54 q^{59} + 12 q^{61} + 52 q^{64} + 26 q^{66} + 2 q^{69} - 40 q^{71} - 40 q^{74} - 74 q^{79} + 16 q^{81} - 56 q^{84} - 6 q^{86} + 32 q^{89} + 88 q^{91} - 34 q^{94} - 34 q^{96} + 40 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

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