LMFDB - Embedded newform 300.3.f.c.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(199,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$16$
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} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 14x^13 + 23x^12 - 26x^11 + 18x^10 - 10x^9 + 9x^8 - 20x^7 + 72x^6 - 208x^5 + 368x^4 - 448x^3 + 512x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$-0.485936 + 1.32811i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99209 + 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 - 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.99209 + 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 - 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +3.00000 q^{9} -8.22072i q^{11} +(-6.81884 + 1.22614i) q^{12} +11.1863i q^{13} +(2.38058 - 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} -20.9256i q^{17} +(-5.97628 + 0.533041i) q^{18} +27.9657i q^{19} +2.06983 q^{21} +(1.46066 + 16.3764i) q^{22} -9.48564 q^{23} +(13.3659 - 3.65415i) q^{24} +(-1.98759 - 22.2842i) q^{26} -5.19615 q^{27} +(-4.70460 + 0.845964i) q^{28} -40.4205 q^{29} -55.3130i q^{31} +(-28.8865 + 13.7685i) q^{32} +14.2387i q^{33} +(3.71807 + 41.6858i) q^{34} +(11.8106 - 2.12373i) q^{36} -50.1890i q^{37} +(-4.96895 - 55.7102i) q^{38} -19.3753i q^{39} -73.6361 q^{41} +(-4.12328 + 0.367767i) q^{42} -19.0843 q^{43} +(-5.81954 - 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598 q^{47} +(-25.9768 + 9.65427i) q^{48} -47.5719 q^{49} +36.2442i q^{51} +(7.91894 + 44.0391i) q^{52} -57.2212i q^{53} +(10.3512 - 0.923254i) q^{54} +(9.22169 - 2.52115i) q^{56} -48.4380i q^{57} +(80.5213 - 7.18193i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(9.82804 + 110.189i) q^{62} -3.58504 q^{63} +(55.0981 - 32.5607i) q^{64} +(-2.52994 - 28.3648i) q^{66} -9.68679 q^{67} +(-14.8135 - 82.3812i) q^{68} +16.4296 q^{69} +68.6944i q^{71} +(-23.1504 + 6.32918i) q^{72} +84.7825i q^{73} +(8.91760 + 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} +9.82388i q^{77} +(3.44261 + 38.5974i) q^{78} +23.2903i q^{79} +9.00000 q^{81} +(146.690 - 13.0837i) q^{82} +93.2595 q^{83} +(8.14861 - 1.46525i) q^{84} +(38.0177 - 3.39091i) q^{86} +70.0104 q^{87} +(17.3435 + 63.4377i) q^{88} -62.9898 q^{89} -13.3678i q^{91} +(-37.3436 + 6.71499i) q^{92} +95.8049i q^{93} +(35.9767 - 3.20887i) q^{94} +(50.0328 - 23.8478i) q^{96} -91.3962i q^{97} +(94.7677 - 8.45260i) q^{98} -24.6622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.99209	+	0.177680i	−0.996046	+	0.0888402i
$2$	−1.99209	+	0.177680i	−0.996046	+	0.0888402i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	3.93686	−	0.707911i	0.984215	−	0.176978i
$5$		0			0
$5$		0			0
$6$	3.45040	−	0.307751i	0.575067	−	0.0512919i
$7$	−1.19501			−0.170716			−0.0853582	−	0.996350i	$-0.527203\pi$
$7$	−1.19501			−0.170716			−0.0853582	+	0.996350i	$0.527203\pi$
$8$	−7.71680	+	2.10973i	−0.964600	+	0.263716i
$9$	3.00000			0.333333
$10$		0			0
$11$		−	8.22072i		−	0.747338i	−0.927562	−	0.373669i	$-0.878100\pi$
$11$		−	8.22072i		−	0.747338i	0.927562	−	0.373669i	$-0.121900\pi$
$12$	−6.81884	+	1.22614i	−0.568237	+	0.102178i
$13$			11.1863i			0.860488i	0.902713	+	0.430244i	$0.141572\pi$
$13$			11.1863i			0.860488i	−0.902713	+	0.430244i	$0.858428\pi$
$14$	2.38058	−	0.212331i	0.170041	−	0.0151665i
$15$		0			0
$16$	14.9977	−	5.57389i	0.937358	−	0.348368i
$17$		−	20.9256i		−	1.23092i	−0.788169	−	0.615459i	$-0.788970\pi$
$17$		−	20.9256i		−	1.23092i	0.788169	−	0.615459i	$-0.211030\pi$
$18$	−5.97628	+	0.533041i	−0.332015	+	0.0296134i
$19$			27.9657i			1.47188i	0.677048	+	0.735939i	$0.263259\pi$
$19$			27.9657i			1.47188i	−0.677048	+	0.735939i	$0.736741\pi$
$20$		0			0
$21$	2.06983			0.0985631
$22$	1.46066	+	16.3764i	0.0663937	+	0.744383i
$23$	−9.48564			−0.412419			−0.206209	−	0.978508i	$-0.566113\pi$
$23$	−9.48564			−0.412419			−0.206209	+	0.978508i	$0.566113\pi$
$24$	13.3659	−	3.65415i	0.556912	−	0.152256i
$25$		0			0
$26$	−1.98759	−	22.2842i	−0.0764459	−	0.857085i
$27$	−5.19615			−0.192450
$28$	−4.70460	+	0.845964i	−0.168022	+	0.0302130i
$29$	−40.4205			−1.39381			−0.696905	−	0.717163i	$-0.745440\pi$
$29$	−40.4205			−1.39381			−0.696905	+	0.717163i	$0.745440\pi$
$30$		0			0
$31$		−	55.3130i		−	1.78429i	−0.451748	−	0.892145i	$-0.649200\pi$
$31$		−	55.3130i		−	1.78429i	0.451748	−	0.892145i	$-0.350800\pi$
$32$	−28.8865	+	13.7685i	−0.902702	+	0.430266i
$33$			14.2387i			0.431476i
$34$	3.71807	+	41.6858i	0.109355	+	1.22605i
$35$		0			0
$36$	11.8106	−	2.12373i	0.328072	−	0.0589926i
$37$		−	50.1890i		−	1.35646i	−0.734850	−	0.678230i	$-0.762747\pi$
$37$		−	50.1890i		−	1.35646i	0.734850	−	0.678230i	$-0.237253\pi$
$38$	−4.96895	−	55.7102i	−0.130762	−	1.46606i
$39$		−	19.3753i		−	0.496803i
$40$		0			0
$41$	−73.6361			−1.79600			−0.898001	−	0.439994i	$-0.854981\pi$
$41$	−73.6361			−1.79600			−0.898001	+	0.439994i	$0.854981\pi$
$42$	−4.12328	+	0.367767i	−0.0981734	+	0.00875637i
$43$	−19.0843			−0.443822			−0.221911	−	0.975067i	$-0.571229\pi$
$43$	−19.0843			−0.443822			−0.221911	+	0.975067i	$0.571229\pi$
$44$	−5.81954	−	32.3638i	−0.132262	−	0.735541i
$45$		0			0
$46$	18.8963	−	1.68541i	0.410788	−	0.0366394i
$47$	−18.0598			−0.384251			−0.192125	−	0.981370i	$-0.561538\pi$
$47$	−18.0598			−0.384251			−0.192125	+	0.981370i	$0.561538\pi$
$48$	−25.9768	+	9.65427i	−0.541184	+	0.201131i
$49$	−47.5719			−0.970856
$50$		0			0
$51$			36.2442i			0.710671i
$52$	7.91894	+	44.0391i	0.152287	+	0.846905i
$53$		−	57.2212i		−	1.07965i	−0.841779	−	0.539823i	$-0.818491\pi$
$53$		−	57.2212i		−	1.07965i	0.841779	−	0.539823i	$-0.181509\pi$
$54$	10.3512	−	0.923254i	0.191689	−	0.0170973i
$55$		0			0
$56$	9.22169	−	2.52115i	0.164673	−	0.0450206i
$57$		−	48.4380i		−	0.849789i
$58$	80.5213	−	7.18193i	1.38830	−	0.123826i
$59$		−	60.6645i		−	1.02821i	−0.857727	−	0.514106i	$-0.828124\pi$
$59$		−	60.6645i		−	1.02821i	0.857727	−	0.514106i	$-0.171876\pi$
$60$		0			0
$61$	−21.3518			−0.350030			−0.175015	−	0.984566i	$-0.555997\pi$
$61$	−21.3518			−0.350030			−0.175015	+	0.984566i	$0.555997\pi$
$62$	9.82804	+	110.189i	0.158517	+	1.77724i
$63$	−3.58504			−0.0569054
$64$	55.0981	−	32.5607i	0.860908	−	0.508761i
$65$		0			0
$66$	−2.52994	−	28.3648i	−0.0383324	−	0.429770i
$67$	−9.68679			−0.144579			−0.0722895	−	0.997384i	$-0.523031\pi$
$67$	−9.68679			−0.144579			−0.0722895	+	0.997384i	$0.523031\pi$
$68$	−14.8135	−	82.3812i	−0.217845	−	1.21149i
$69$	16.4296			0.238110
$70$		0			0
$71$			68.6944i			0.967527i	0.875199	+	0.483763i	$0.160730\pi$
$71$			68.6944i			0.967527i	−0.875199	+	0.483763i	$0.839270\pi$
$72$	−23.1504	+	6.32918i	−0.321533	+	0.0879053i
$73$			84.7825i			1.16140i	0.814116	+	0.580702i	$0.197222\pi$
$73$			84.7825i			1.16140i	−0.814116	+	0.580702i	$0.802778\pi$
$74$	8.91760	+	99.9811i	0.120508	+	1.35110i
$75$		0			0
$76$	19.7972	+	110.097i	0.260490	+	1.44864i
$77$			9.82388i			0.127583i
$78$	3.44261	+	38.5974i	0.0441361	+	0.494839i
$79$			23.2903i			0.294814i	0.989076	+	0.147407i	$0.0470928\pi$
$79$			23.2903i			0.294814i	−0.989076	+	0.147407i	$0.952907\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	146.690	−	13.0837i	1.78890	−	0.159557i
$83$	93.2595			1.12361			0.561804	−	0.827270i	$-0.310107\pi$
$83$	93.2595			1.12361			0.561804	+	0.827270i	$0.310107\pi$
$84$	8.14861	−	1.46525i	0.0970073	−	0.0174435i
$85$		0			0
$86$	38.0177	−	3.39091i	0.442067	−	0.0394292i
$87$	70.0104			0.804717
$88$	17.3435	+	63.4377i	0.197085	+	0.720883i
$89$	−62.9898			−0.707750			−0.353875	−	0.935293i	$-0.615136\pi$
$89$	−62.9898			−0.707750			−0.353875	+	0.935293i	$0.615136\pi$
$90$		0			0
$91$		−	13.3678i		−	0.146899i
$92$	−37.3436	+	6.71499i	−0.405909	+	0.0729890i
$93$			95.8049i			1.03016i
$94$	35.9767	−	3.20887i	0.382731	−	0.0341369i
$95$		0			0
$96$	50.0328	−	23.8478i	0.521175	−	0.248414i
$97$		−	91.3962i		−	0.942229i	−0.882072	−	0.471115i	$-0.843852\pi$
$97$		−	91.3962i		−	0.942229i	0.882072	−	0.471115i	$-0.156148\pi$
$98$	94.7677	−	8.45260i	0.967017	−	0.0862510i
$99$		−	24.6622i		−	0.249113i
$100$		0			0
$101$	−29.9780			−0.296811			−0.148406	−	0.988927i	$-0.547414\pi$
$101$	−29.9780			−0.296811			−0.148406	+	0.988927i	$0.547414\pi$
$102$	−6.43989	−	72.2019i	−0.0631362	−	0.707861i
$103$	−88.7485			−0.861636			−0.430818	−	0.902439i	$-0.641775\pi$
$103$	−88.7485			−0.861636			−0.430818	+	0.902439i	$0.641775\pi$
$104$	−23.6001	−	86.3228i	−0.226924	−	0.830027i
$105$		0			0
$106$	10.1671	+	113.990i	0.0959159	+	1.07538i
$107$	162.922			1.52263			0.761316	−	0.648381i	$-0.224553\pi$
$107$	162.922			1.52263			0.761316	+	0.648381i	$0.224553\pi$
$108$	−20.4565	+	3.67841i	−0.189412	+	0.0340594i
$109$	103.352			0.948182			0.474091	−	0.880476i	$-0.342777\pi$
$109$	103.352			0.948182			0.474091	+	0.880476i	$0.342777\pi$
$110$		0			0
$111$			86.9299i			0.783152i
$112$	−17.9225	+	6.66088i	−0.160022	+	0.0594722i
$113$		−	31.2691i		−	0.276717i	−0.990382	−	0.138359i	$-0.955817\pi$
$113$		−	31.2691i		−	0.276717i	0.990382	−	0.138359i	$-0.0441827\pi$
$114$	8.60647	+	96.4929i	0.0754954	+	0.846429i
$115$		0			0
$116$	−159.130	+	28.6141i	−1.37181	+	0.246673i
$117$			33.5590i			0.286829i
$118$	10.7789	+	120.849i	0.0913465	+	1.02415i
$119$			25.0064i			0.210138i
$120$		0			0
$121$	53.4198			0.441486
$122$	42.5348	−	3.79380i	0.348646	−	0.0310967i
$123$	127.541			1.03692
$124$	−39.1567	−	217.760i	−0.315780	−	1.75613i
$125$		0			0
$126$	7.14174	−	0.636992i	0.0566804	−	0.00505549i
$127$	−178.474			−1.40531			−0.702655	−	0.711531i	$-0.748002\pi$
$127$	−178.474			−1.40531			−0.702655	+	0.711531i	$0.748002\pi$
$128$	−103.975	+	74.6537i	−0.812305	+	0.583232i
$129$	33.0550			0.256240
$130$		0			0
$131$			153.743i			1.17361i	0.809727	+	0.586806i	$0.199615\pi$
$131$			153.743i			1.17361i	−0.809727	+	0.586806i	$0.800385\pi$
$132$	10.0797	+	56.0558i	0.0763617	+	0.424665i
$133$		−	33.4194i		−	0.251274i
$134$	19.2970	−	1.72115i	0.144007	−	0.0128444i
$135$		0			0
$136$	44.1473	+	161.479i	0.324613	+	1.18734i
$137$			52.9928i			0.386809i	0.981119	+	0.193405i	$0.0619530\pi$
$137$			52.9928i			0.386809i	−0.981119	+	0.193405i	$0.938047\pi$
$138$	−32.7293	+	2.91922i	−0.237169	+	0.0211537i
$139$		−	21.8420i		−	0.157137i	−0.996909	−	0.0785684i	$-0.974965\pi$
$139$		−	21.8420i		−	0.157137i	0.996909	−	0.0785684i	$-0.0250349\pi$
$140$		0			0
$141$	31.2804			0.221847
$142$	−12.2056	−	136.846i	−0.0859552	−	0.963701i
$143$	91.9598			0.643076
$144$	44.9932	−	16.7217i	0.312453	−	0.116123i
$145$		0			0
$146$	−15.0642	−	168.895i	−0.103179	−	1.15681i
$147$	82.3970			0.560524
$148$	−35.5294	−	197.587i	−0.240063	−	1.33505i
$149$	3.12940			0.0210027			0.0105013	−	0.999945i	$-0.496657\pi$
$149$	3.12940			0.0210027			0.0105013	+	0.999945i	$0.496657\pi$
$150$		0			0
$151$		−	296.461i		−	1.96332i	−0.190646	−	0.981659i	$-0.561058\pi$
$151$		−	296.461i		−	1.96332i	0.190646	−	0.981659i	$-0.438942\pi$
$152$	−58.9999	−	215.806i	−0.388157	−	1.41977i
$153$		−	62.7769i		−	0.410306i
$154$	−1.74551	−	19.5701i	−0.0113345	−	0.127078i
$155$		0			0
$156$	−13.7160	−	76.2779i	−0.0879231	−	0.488961i
$157$			265.686i			1.69227i	0.532972	+	0.846133i	$0.321075\pi$
$157$			265.686i			1.69227i	−0.532972	+	0.846133i	$0.678925\pi$
$158$	−4.13824	−	46.3965i	−0.0261914	−	0.293649i
$159$			99.1101i			0.623334i
$160$		0			0
$161$	11.3355			0.0704067
$162$	−17.9288	+	1.59912i	−0.110672	+	0.00987113i
$163$	−205.531			−1.26093			−0.630465	−	0.776218i	$-0.717136\pi$
$163$	−205.531			−1.26093			−0.630465	+	0.776218i	$0.717136\pi$
$164$	−289.895	+	52.1278i	−1.76765	+	0.317852i
$165$		0			0
$166$	−185.781	+	16.5704i	−1.11917	+	0.0998215i
$167$	−11.6359			−0.0696763			−0.0348381	−	0.999393i	$-0.511092\pi$
$167$	−11.6359			−0.0696763			−0.0348381	+	0.999393i	$0.511092\pi$
$168$	−15.9724	+	4.36677i	−0.0950740	+	0.0259927i
$169$	43.8657			0.259560
$170$		0			0
$171$			83.8970i			0.490626i
$172$	−75.1323	+	13.5100i	−0.436816	+	0.0785466i
$173$		−	106.062i		−	0.613077i	−0.951858	−	0.306538i	$-0.900829\pi$
$173$		−	106.062i		−	0.613077i	0.951858	−	0.306538i	$-0.0991708\pi$
$174$	−139.467	+	12.4395i	−0.801535	+	0.0714912i
$175$		0			0
$176$	−45.8214	−	123.292i	−0.260349	−	0.700523i
$177$			105.074i			0.593639i
$178$	125.481	−	11.1920i	0.704951	−	0.0628766i
$179$			43.3304i			0.242069i	0.992648	+	0.121035i	$0.0386212\pi$
$179$			43.3304i			0.242069i	−0.992648	+	0.121035i	$0.961379\pi$
$180$		0			0
$181$	203.614			1.12494			0.562469	−	0.826819i	$-0.309852\pi$
$181$	203.614			1.12494			0.562469	+	0.826819i	$0.309852\pi$
$182$	2.37520	+	26.6300i	0.0130506	+	0.146319i
$183$	36.9824			0.202090
$184$	73.1988	−	20.0121i	0.397819	−	0.108761i
$185$		0			0
$186$	−17.0227	−	190.852i	−0.0915197	−	1.02609i
$187$	−172.024			−0.919913
$188$	−71.0988	+	12.7847i	−0.378185	+	0.0680038i
$189$	6.20948			0.0328544
$190$		0			0
$191$		−	251.536i		−	1.31694i	−0.752606	−	0.658471i	$-0.771204\pi$
$191$		−	251.536i		−	1.31694i	0.752606	−	0.658471i	$-0.228796\pi$
$192$	−95.4327	+	56.3968i	−0.497045	+	0.293733i
$193$		−	281.811i		−	1.46016i	−0.683360	−	0.730081i	$-0.739482\pi$
$193$		−	281.811i		−	1.46016i	0.683360	−	0.730081i	$-0.260518\pi$
$194$	16.2393	+	182.070i	0.0837078	+	0.938503i
$195$		0			0
$196$	−187.284	+	33.6767i	−0.955531	+	0.171820i
$197$			243.485i			1.23596i	0.786193	+	0.617982i	$0.212049\pi$
$197$			243.485i			1.23596i	−0.786193	+	0.617982i	$0.787951\pi$
$198$	4.38198	+	49.1293i	0.0221312	+	0.248128i
$199$			121.958i			0.612853i	0.951894	+	0.306427i	$0.0991335\pi$
$199$			121.958i			0.612853i	−0.951894	+	0.306427i	$0.900867\pi$
$200$		0			0
$201$	16.7780			0.0834727
$202$	59.7188	−	5.32649i	0.295638	−	0.0263688i
$203$	48.3031			0.237946
$204$	25.6577	+	142.688i	0.125773	+	0.699453i
$205$		0			0
$206$	176.795	−	15.7689i	0.858229	−	0.0765479i
$207$	−28.4569			−0.137473
$208$	62.3515	+	167.770i	0.299767	+	0.806585i
$209$	229.898			1.09999
$210$		0			0
$211$		−	132.543i		−	0.628168i	−0.949395	−	0.314084i	$-0.898303\pi$
$211$		−	132.543i		−	0.628168i	0.949395	−	0.314084i	$-0.101697\pi$
$212$	−40.5076	−	225.272i	−0.191073	−	1.06260i
$213$		−	118.982i		−	0.558602i
$214$	−324.555	+	28.9480i	−1.51661	+	0.135271i
$215$		0			0
$216$	40.0977	−	10.9625i	0.185637	−	0.0507521i
$217$			66.0998i			0.304608i
$218$	−205.886	+	18.3636i	−0.944433	+	0.0842366i
$219$		−	146.848i		−	0.670537i
$220$		0			0
$221$	234.081			1.05919
$222$	−15.4457	−	173.172i	−0.0695754	−	0.780056i
$223$	−225.442			−1.01095			−0.505475	−	0.862841i	$-0.668683\pi$
$223$	−225.442			−1.01095			−0.505475	+	0.862841i	$0.668683\pi$
$224$	34.5198	−	16.4536i	0.154106	−	0.0734534i
$225$		0			0
$226$	5.55590	+	62.2908i	0.0245836	+	0.275623i
$227$	−108.080			−0.476124			−0.238062	−	0.971250i	$-0.576512\pi$
$227$	−108.080			−0.476124			−0.238062	+	0.971250i	$0.576512\pi$
$228$	−34.2898	−	190.693i	−0.150394	−	0.836375i
$229$	57.3495			0.250435			0.125217	−	0.992129i	$-0.460037\pi$
$229$	57.3495			0.250435			0.125217	+	0.992129i	$0.460037\pi$
$230$		0			0
$231$		−	17.0155i		−	0.0736600i
$232$	311.917	−	85.2762i	1.34447	−	0.367570i
$233$			285.320i			1.22455i	0.790646	+	0.612274i	$0.209745\pi$
$233$			285.320i			1.22455i	−0.790646	+	0.612274i	$0.790255\pi$
$234$	−5.96278	−	66.8527i	−0.0254820	−	0.285695i
$235$		0			0
$236$	−42.9451	−	238.828i	−0.181971	−	1.01198i
$237$		−	40.3400i		−	0.170211i
$238$	−4.44315	−	49.8151i	−0.0186687	−	0.209307i
$239$		−	77.2471i		−	0.323210i	−0.986856	−	0.161605i	$-0.948333\pi$
$239$		−	77.2471i		−	0.323210i	0.986856	−	0.161605i	$-0.0516670\pi$
$240$		0			0
$241$	−130.557			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$241$	−130.557			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$242$	−106.417	+	9.49164i	−0.439740	+	0.0392217i
$243$	−15.5885			−0.0641500
$244$	−84.0591	+	15.1152i	−0.344504	+	0.0619475i
$245$		0			0
$246$	−254.074	+	22.6616i	−1.03282	+	0.0921203i
$247$	−312.834			−1.26653
$248$	116.695	+	426.840i	0.470546	+	1.72113i
$249$	−161.530			−0.648715
$250$		0			0
$251$			437.197i			1.74182i	0.491441	+	0.870911i	$0.336470\pi$
$251$			437.197i			1.74182i	−0.491441	+	0.870911i	$0.663530\pi$
$252$	−14.1138	+	2.53789i	−0.0560072	+	0.0100710i
$253$			77.9788i			0.308216i
$254$	355.537	−	31.7114i	1.39975	−	0.124848i
$255$		0			0
$256$	193.863	−	167.191i	0.757279	−	0.653091i
$257$		−	74.3682i		−	0.289370i	−0.989478	−	0.144685i	$-0.953783\pi$
$257$		−	74.3682i		−	0.289370i	0.989478	−	0.144685i	$-0.0462169\pi$
$258$	−65.8486	+	5.87323i	−0.255227	+	0.0227644i
$259$			59.9766i			0.231570i
$260$		0			0
$261$	−121.261			−0.464603
$262$	−27.3172	−	306.271i	−0.104264	−	1.16897i
$263$	−458.790			−1.74445			−0.872225	−	0.489105i	$-0.837324\pi$
$263$	−458.790			−1.74445			−0.872225	+	0.489105i	$0.837324\pi$
$264$	−30.0398	−	109.877i	−0.113787	−	0.416202i
$265$		0			0
$266$	5.93797	+	66.5745i	0.0223232	+	0.250280i
$267$	109.101			0.408620
$268$	−38.1355	+	6.85739i	−0.142297	+	0.0255873i
$269$	320.405			1.19110			0.595549	−	0.803319i	$-0.296935\pi$
$269$	320.405			1.19110			0.595549	+	0.803319i	$0.296935\pi$
$270$		0			0
$271$		−	359.059i		−	1.32494i	−0.749088	−	0.662470i	$-0.769508\pi$
$271$		−	359.059i		−	1.32494i	0.749088	−	0.662470i	$-0.230492\pi$
$272$	−116.637	−	313.837i	−0.428813	−	1.15381i
$273$			23.1538i			0.0848124i
$274$	−9.41579	−	105.567i	−0.0343642	−	0.385280i
$275$		0			0
$276$	64.6810	−	11.6307i	0.234352	−	0.0421402i
$277$		−	138.027i		−	0.498293i	−0.968466	−	0.249147i	$-0.919850\pi$
$277$		−	138.027i		−	0.498293i	0.968466	−	0.249147i	$-0.0801501\pi$
$278$	3.88090	+	43.5113i	0.0139601	+	0.156516i
$279$		−	165.939i		−	0.594764i
$280$		0			0
$281$	462.504			1.64592			0.822960	−	0.568099i	$-0.192321\pi$
$281$	462.504			1.64592			0.822960	+	0.568099i	$0.192321\pi$
$282$	−62.3135	+	5.55792i	−0.220970	+	0.0197089i
$283$	323.973			1.14478			0.572391	−	0.819981i	$-0.306016\pi$
$283$	323.973			1.14478			0.572391	+	0.819981i	$0.306016\pi$
$284$	48.6295	+	270.440i	0.171231	+	0.952254i
$285$		0			0
$286$	−183.192	+	16.3394i	−0.640533	+	0.0571309i
$287$	87.9962			0.306607
$288$	−86.6594	+	41.3055i	−0.300901	+	0.143422i
$289$	−148.882			−0.515161
$290$		0			0
$291$			158.303i			0.543996i
$292$	60.0185	+	333.777i	0.205543	+	1.14307i
$293$			150.416i			0.513365i	0.966496	+	0.256683i	$0.0826295\pi$
$293$			150.416i			0.513365i	−0.966496	+	0.256683i	$0.917371\pi$
$294$	−164.142	+	14.6403i	−0.558308	+	0.0497970i
$295$		0			0
$296$	105.885	+	387.299i	0.357720	+	1.30844i
$297$			42.7161i			0.143825i
$298$	−6.23406	+	0.556033i	−0.0209196	+	0.00186588i
$299$		−	106.110i		−	0.354882i
$300$		0			0
$301$	22.8060			0.0757676
$302$	52.6753	+	590.577i	0.174421	+	1.95555i
$303$	51.9233			0.171364
$304$	155.878	+	419.421i	0.512755	+	1.37968i
$305$		0			0
$306$	11.1542	+	125.057i	0.0364517	+	0.408684i
$307$	563.915			1.83686			0.918428	−	0.395587i	$-0.129459\pi$
$307$	563.915			1.83686			0.918428	+	0.395587i	$0.129459\pi$
$308$	6.95443	+	38.6752i	0.0225793	+	0.125569i
$309$	153.717			0.497466
$310$		0			0
$311$			40.0214i			0.128686i	0.997928	+	0.0643431i	$0.0204952\pi$
$311$			40.0214i			0.128686i	−0.997928	+	0.0643431i	$0.979505\pi$
$312$	40.8766	+	149.515i	0.131015	+	0.479216i
$313$			1.82657i			0.00583568i	0.999996	+	0.00291784i	$0.000928778\pi$
$313$			1.82657i			0.00583568i	−0.999996	+	0.00291784i	$0.999071\pi$
$314$	−47.2071	−	529.270i	−0.150341	−	1.68557i
$315$		0			0
$316$	16.4875	+	91.6908i	0.0521756	+	0.290161i
$317$		−	246.416i		−	0.777338i	−0.921378	−	0.388669i	$-0.872935\pi$
$317$		−	246.416i		−	0.777338i	0.921378	−	0.388669i	$-0.127065\pi$
$318$	−17.6099	−	197.436i	−0.0553771	−	0.620869i
$319$			332.286i			1.04165i
$320$		0			0
$321$	−282.189			−0.879092
$322$	−22.5813	+	2.01409i	−0.0701283	+	0.00625494i
$323$	585.199			1.81176
$324$	35.4317	−	6.37120i	0.109357	−	0.0196642i
$325$		0			0
$326$	409.438	−	36.5189i	1.25594	−	0.112021i
$327$	−179.011			−0.547433
$328$	568.235	−	155.352i	1.73242	−	0.473634i
$329$	21.5817			0.0655978
$330$		0			0
$331$			417.672i			1.26185i	0.775844	+	0.630925i	$0.217325\pi$
$331$			417.672i			1.26185i	−0.775844	+	0.630925i	$0.782675\pi$
$332$	367.149	−	66.0194i	1.10587	−	0.198854i
$333$		−	150.567i		−	0.452153i
$334$	23.1798	−	2.06748i	0.0694007	−	0.00619005i
$335$		0			0
$336$	31.0427	−	11.5370i	0.0923889	−	0.0343363i
$337$			317.379i			0.941779i	0.882192	+	0.470889i	$0.156067\pi$
$337$			317.379i			0.941779i	−0.882192	+	0.470889i	$0.843933\pi$
$338$	−87.3845	+	7.79408i	−0.258534	+	0.0230594i
$339$			54.1596i			0.159763i
$340$		0			0
$341$	−454.713			−1.33347
$342$	−14.9068	−	167.131i	−0.0435873	−	0.488686i
$343$	115.405			0.336457
$344$	147.270	−	40.2627i	0.428110	−	0.117043i
$345$		0			0
$346$	18.8452	+	211.286i	0.0544659	+	0.610653i
$347$	222.581			0.641443			0.320721	−	0.947174i	$-0.396075\pi$
$347$	222.581			0.641443			0.320721	+	0.947174i	$0.396075\pi$
$348$	275.621	−	49.5611i	0.792014	−	0.142417i
$349$	−560.812			−1.60691			−0.803455	−	0.595366i	$-0.797007\pi$
$349$	−560.812			−1.60691			−0.803455	+	0.595366i	$0.797007\pi$
$350$		0			0
$351$		−	58.1259i		−	0.165601i
$352$	113.187	+	237.468i	0.321554	+	0.674624i
$353$			304.856i			0.863616i	0.901966	+	0.431808i	$0.142124\pi$
$353$			304.856i			0.863616i	−0.901966	+	0.431808i	$0.857876\pi$
$354$	−18.6696	−	209.317i	−0.0527390	−	0.591291i
$355$		0			0
$356$	−247.982	+	44.5911i	−0.696578	+	0.125256i
$357$		−	43.3124i		−	0.121323i
$358$	−7.69896	−	86.3181i	−0.0215055	−	0.241112i
$359$			105.860i			0.294874i	0.989071	+	0.147437i	$0.0471023\pi$
$359$			105.860i			0.294874i	−0.989071	+	0.147437i	$0.952898\pi$
$360$		0			0
$361$	−421.079			−1.16642
$362$	−405.617	+	36.1782i	−1.12049	+	0.0999396i
$363$	−92.5257			−0.254892
$364$	−9.46324	−	52.6273i	−0.0259979	−	0.144581i
$365$		0			0
$366$	−73.6724	+	6.57105i	−0.201291	+	0.0179537i
$367$	360.200			0.981470			0.490735	−	0.871309i	$-0.336728\pi$
$367$	360.200			0.981470			0.490735	+	0.871309i	$0.336728\pi$
$368$	−142.263	+	52.8719i	−0.386584	+	0.143674i
$369$	−220.908			−0.598667
$370$		0			0
$371$			68.3802i			0.184313i
$372$	67.8214	+	377.171i	0.182316	+	1.01390i
$373$		−	135.489i		−	0.363242i	−0.983369	−	0.181621i	$-0.941866\pi$
$373$		−	135.489i		−	0.363242i	0.983369	−	0.181621i	$-0.0581344\pi$
$374$	342.687	−	30.5652i	0.916275	−	0.0817252i
$375$		0			0
$376$	139.364	−	38.1012i	0.370648	−	0.101333i
$377$		−	452.158i		−	1.19936i
$378$	−12.3698	+	1.10330i	−0.0327245	+	0.00291879i
$379$		−	310.686i		−	0.819753i	−0.912141	−	0.409876i	$-0.865572\pi$
$379$		−	310.686i		−	0.819753i	0.912141	−	0.409876i	$-0.134428\pi$
$380$		0			0
$381$	309.126			0.811356
$382$	44.6930	+	501.083i	0.116997	+	1.31173i
$383$	−121.981			−0.318487			−0.159244	−	0.987239i	$-0.550906\pi$
$383$	−121.981			−0.318487			−0.159244	+	0.987239i	$0.550906\pi$
$384$	180.090	−	129.304i	0.468985	−	0.336729i
$385$		0			0
$386$	50.0723	+	561.394i	0.129721	+	1.45439i
$387$	−57.2530			−0.147941
$388$	−64.7004	−	359.814i	−0.166754	−	0.927356i
$389$	−544.266			−1.39914			−0.699570	−	0.714564i	$-0.746625\pi$
$389$	−544.266			−1.39914			−0.699570	+	0.714564i	$0.746625\pi$
$390$		0			0
$391$			198.493i			0.507654i
$392$	367.103	−	100.364i	0.936488	−	0.256030i
$393$		−	266.291i		−	0.677586i
$394$	−43.2625	−	485.044i	−0.109803	−	1.23108i
$395$		0			0
$396$	−17.4586	−	97.0915i	−0.0440874	−	0.245180i
$397$		−	504.528i		−	1.27085i	−0.772162	−	0.635425i	$-0.780825\pi$
$397$		−	504.528i		−	1.27085i	0.772162	−	0.635425i	$-0.219175\pi$
$398$	−21.6695	−	242.951i	−0.0544460	−	0.610430i
$399$			57.8841i			0.145073i
$400$		0			0
$401$	−278.018			−0.693312			−0.346656	−	0.937992i	$-0.612683\pi$
$401$	−278.018			−0.693312			−0.346656	+	0.937992i	$0.612683\pi$
$402$	−33.4233	+	2.98112i	−0.0831426	+	0.00741573i
$403$	618.750			1.53536
$404$	−118.019	+	21.2217i	−0.292126	+	0.0525290i
$405$		0			0
$406$	−96.2242	+	8.58251i	−0.237005	+	0.0211392i
$407$	−412.590			−1.01373
$408$	−76.4654	−	279.690i	−0.187415	−	0.685514i
$409$	296.549			0.725059			0.362530	−	0.931972i	$-0.381913\pi$
$409$	296.549			0.725059			0.362530	+	0.931972i	$0.381913\pi$
$410$		0			0
$411$		−	91.7863i		−	0.223324i
$412$	−349.390	+	62.8261i	−0.848035	+	0.152490i
$413$			72.4950i			0.175533i
$414$	56.6888	−	5.05623i	0.136929	−	0.0122131i
$415$		0			0
$416$	−154.019	−	323.134i	−0.370239	−	0.776764i
$417$			37.8315i			0.0907230i
$418$	−457.978	+	40.8483i	−1.09564	+	0.0977233i
$419$		−	315.615i		−	0.753258i	−0.926364	−	0.376629i	$-0.877083\pi$
$419$		−	315.615i		−	0.753258i	0.926364	−	0.376629i	$-0.122917\pi$
$420$		0			0
$421$	−360.355			−0.855951			−0.427975	−	0.903790i	$-0.640773\pi$
$421$	−360.355			−0.855951			−0.427975	+	0.903790i	$0.640773\pi$
$422$	23.5504	+	264.039i	0.0558066	+	0.625684i
$423$	−54.1793			−0.128084
$424$	120.721	+	441.565i	0.284720	+	1.04143i
$425$		0			0
$426$	21.1408	+	237.023i	0.0496263	+	0.556393i
$427$	25.5157			0.0597558
$428$	641.400	−	115.334i	1.49860	−	0.269472i
$429$	−159.279			−0.371280
$430$		0			0
$431$		−	523.617i		−	1.21489i	−0.794362	−	0.607445i	$-0.792195\pi$
$431$		−	523.617i		−	1.21489i	0.794362	−	0.607445i	$-0.207805\pi$
$432$	−77.9305	+	28.9628i	−0.180395	+	0.0670435i
$433$		−	21.5381i		−	0.0497415i	−0.999691	−	0.0248707i	$-0.992083\pi$
$433$		−	21.5381i		−	0.0497415i	0.999691	−	0.0248707i	$-0.00791742\pi$
$434$	−11.7446	−	131.677i	−0.0270614	−	0.303403i
$435$		0			0
$436$	406.882	−	73.1639i	0.933215	−	0.167807i
$437$		−	265.272i		−	0.607030i
$438$	26.0919	+	292.534i	0.0595706	+	0.667886i
$439$		−	247.777i		−	0.564412i	−0.959354	−	0.282206i	$-0.908934\pi$
$439$		−	247.777i		−	0.564412i	0.959354	−	0.282206i	$-0.0910662\pi$
$440$		0			0
$441$	−142.716			−0.323619
$442$	−466.311	+	41.5916i	−1.05500	+	0.0940987i
$443$	−584.775			−1.32003			−0.660017	−	0.751251i	$-0.729451\pi$
$443$	−584.775			−1.32003			−0.660017	+	0.751251i	$0.729451\pi$
$444$	61.5386	+	342.231i	0.138601	+	0.770790i
$445$		0			0
$446$	449.101	−	40.0566i	1.00695	−	0.0898130i
$447$	−5.42028			−0.0121259
$448$	−65.8430	+	38.9105i	−0.146971	+	0.0868538i
$449$	−152.093			−0.338738			−0.169369	−	0.985553i	$-0.554173\pi$
$449$	−152.093			−0.338738			−0.169369	+	0.985553i	$0.554173\pi$
$450$		0			0
$451$			605.342i			1.34222i
$452$	−22.1357	−	123.102i	−0.0489728	−	0.272349i
$453$			513.485i			1.13352i
$454$	215.306	−	19.2037i	0.474242	−	0.0422990i
$455$		0			0
$456$	102.191	+	373.786i	0.224103	+	0.819707i
$457$		−	602.441i		−	1.31825i	−0.752033	−	0.659126i	$-0.770926\pi$
$457$		−	602.441i		−	1.31825i	0.752033	−	0.659126i	$-0.229074\pi$
$458$	−114.246	+	10.1899i	−0.249444	+	0.0222487i
$459$			108.733i			0.236890i
$460$		0			0
$461$	−504.912			−1.09525			−0.547626	−	0.836723i	$-0.684468\pi$
$461$	−504.912			−1.09525			−0.547626	+	0.836723i	$0.684468\pi$
$462$	3.02331	+	33.8964i	0.00654397	+	0.0733687i
$463$	−504.560			−1.08976			−0.544881	−	0.838513i	$-0.683425\pi$
$463$	−504.560			−1.08976			−0.544881	+	0.838513i	$0.683425\pi$
$464$	−606.215	+	225.300i	−1.30650	+	0.485559i
$465$		0			0
$466$	−50.6957	−	568.383i	−0.108789	−	1.21971i
$467$	751.418			1.60903			0.804516	−	0.593931i	$-0.202425\pi$
$467$	751.418			1.60903			0.804516	+	0.593931i	$0.202425\pi$
$468$	23.7568	+	132.117i	0.0507624	+	0.282302i
$469$	11.5759			0.0246820
$470$		0			0
$471$		−	460.181i		−	0.977030i
$472$	127.986	+	468.136i	0.271156	+	0.991814i
$473$			156.887i			0.331685i
$474$	7.16763	+	80.3611i	0.0151216	+	0.169538i
$475$		0			0
$476$	17.7023	+	98.4468i	0.0371898	+	0.206821i
$477$		−	171.664i		−	0.359882i
$478$	13.7253	+	153.883i	0.0287140	+	0.321932i
$479$			581.401i			1.21378i	0.794786	+	0.606890i	$0.207583\pi$
$479$			581.401i			1.21378i	−0.794786	+	0.606890i	$0.792417\pi$
$480$		0			0
$481$	561.431			1.16722
$482$	260.082	−	23.1975i	0.539590	−	0.0481276i
$483$	−19.6336			−0.0406493
$484$	210.306	−	37.8164i	0.434517	−	0.0781331i
$485$		0			0
$486$	31.0536	−	2.76976i	0.0638964	−	0.00569910i
$487$	−557.489			−1.14474			−0.572371	−	0.819995i	$-0.693976\pi$
$487$	−557.489			−1.14474			−0.572371	+	0.819995i	$0.693976\pi$
$488$	164.768	−	45.0465i	0.337639	−	0.0923084i
$489$	355.991			0.727998
$490$		0			0
$491$			26.2032i			0.0533670i	0.999644	+	0.0266835i	$0.00849463\pi$
$491$			26.2032i			0.0533670i	−0.999644	+	0.0266835i	$0.991505\pi$
$492$	502.113	−	90.2880i	1.02055	−	0.183512i
$493$			845.824i			1.71567i
$494$	623.193	−	55.5844i	1.26152	−	0.112519i
$495$		0			0
$496$	−308.309	−	829.569i	−0.621590	−	1.67252i
$497$		−	82.0908i		−	0.165173i
$498$	321.783	−	28.7007i	0.646150	−	0.0576320i
$499$		−	444.615i		−	0.891011i	−0.895279	−	0.445506i	$-0.853024\pi$
$499$		−	444.615i		−	0.891011i	0.895279	−	0.445506i	$-0.146976\pi$
$500$		0			0
$501$	20.1540			0.0402276
$502$	−77.6814	−	870.937i	−0.154744	−	1.73493i
$503$	216.819			0.431052			0.215526	−	0.976498i	$-0.430853\pi$
$503$	216.819			0.431052			0.215526	+	0.976498i	$0.430853\pi$
$504$	27.6651	−	7.56346i	0.0548910	−	0.0150069i
$505$		0			0
$506$	−13.8553	−	155.341i	−0.0273820	−	0.306998i
$507$	−75.9777			−0.149857
$508$	−702.628	+	126.344i	−1.38313	+	0.248708i
$509$	−202.830			−0.398488			−0.199244	−	0.979950i	$-0.563849\pi$
$509$	−202.830			−0.398488			−0.199244	+	0.979950i	$0.563849\pi$
$510$		0			0
$511$		−	101.316i		−	0.198271i
$512$	−356.487	+	367.506i	−0.696264	+	0.717786i
$513$		−	145.314i		−	0.283263i
$514$	13.2138	+	148.148i	0.0257077	+	0.288226i
$515$		0			0
$516$	130.133	−	23.4000i	0.252196	−	0.0453489i
$517$			148.464i			0.287165i
$518$	−10.6567	−	119.479i	−0.0205727	−	0.230654i
$519$			183.705i			0.353960i
$520$		0			0
$521$	769.410			1.47679			0.738397	−	0.674366i	$-0.235583\pi$
$521$	769.410			1.47679			0.738397	+	0.674366i	$0.235583\pi$
$522$	241.564	−	21.5458i	0.462766	−	0.0412754i
$523$	38.9898			0.0745502			0.0372751	−	0.999305i	$-0.488132\pi$
$523$	38.9898			0.0745502			0.0372751	+	0.999305i	$0.488132\pi$
$524$	108.837	+	605.266i	0.207703	+	1.15509i
$525$		0			0
$526$	913.953	−	81.5180i	1.73755	−	0.154977i
$527$	−1157.46			−2.19632
$528$	79.3650	+	213.548i	0.150313	+	0.404447i
$529$	−439.023			−0.829911
$530$		0			0
$531$		−	181.994i		−	0.342737i
$532$	−23.6579	−	131.567i	−0.0444698	−	0.247307i
$533$		−	823.718i		−	1.54544i
$534$	−217.340	+	19.3852i	−0.407004	+	0.0363018i
$535$		0			0
$536$	74.7510	−	20.4365i	0.139461	−	0.0381277i
$537$		−	75.0504i		−	0.139759i
$538$	−638.277	+	56.9297i	−1.18639	+	0.105817i
$539$			391.076i			0.725558i
$540$		0			0
$541$	−32.0904			−0.0593168			−0.0296584	−	0.999560i	$-0.509442\pi$
$541$	−32.0904			−0.0593168			−0.0296584	+	0.999560i	$0.509442\pi$
$542$	63.7977	+	715.278i	0.117708	+	1.31970i
$543$	−352.669			−0.649483
$544$	288.115	+	604.467i	0.529622	+	1.11115i
$545$		0			0
$546$	−4.11397	−	46.1245i	−0.00753475	−	0.0844770i
$547$	254.839			0.465885			0.232942	−	0.972491i	$-0.425165\pi$
$547$	254.839			0.465885			0.232942	+	0.972491i	$0.425165\pi$
$548$	37.5142	+	208.625i	0.0684566	+	0.380703i
$549$	−64.0554			−0.116677
$550$		0			0
$551$		−	1130.39i		−	2.05152i
$552$	−126.784	+	34.6620i	−0.229681	+	0.0627934i
$553$		−	27.8323i		−	0.0503296i
$554$	24.5247	+	274.963i	0.0442685	+	0.496323i
$555$		0			0
$556$	−15.4622	−	85.9890i	−0.0278097	−	0.154656i
$557$			577.439i			1.03670i	0.855170	+	0.518348i	$0.173453\pi$
$557$			577.439i			1.03670i	−0.855170	+	0.518348i	$0.826547\pi$
$558$	29.4841	+	330.566i	0.0528389	+	0.592412i
$559$		−	213.484i		−	0.381903i
$560$		0			0
$561$	297.954			0.531112
$562$	−921.350	+	82.1778i	−1.63941	+	0.146224i
$563$	−367.058			−0.651967			−0.325984	−	0.945375i	$-0.605695\pi$
$563$	−367.058			−0.651967			−0.325984	+	0.945375i	$0.605695\pi$
$564$	123.147	−	22.1438i	0.218345	−	0.0392620i
$565$		0			0
$566$	−645.384	+	57.5636i	−1.14025	+	0.101703i
$567$	−10.7551			−0.0189685
$568$	−144.926	−	530.101i	−0.255152	−	0.933277i
$569$	522.006			0.917410			0.458705	−	0.888589i	$-0.348313\pi$
$569$	522.006			0.917410			0.458705	+	0.888589i	$0.348313\pi$
$570$		0			0
$571$			832.421i			1.45783i	0.684604	+	0.728915i	$0.259975\pi$
$571$			832.421i			1.45783i	−0.684604	+	0.728915i	$0.740025\pi$
$572$	362.033	−	65.0994i	0.632925	−	0.113810i
$573$			435.673i			0.760337i
$574$	−175.296	+	15.6352i	−0.305394	+	0.0272390i
$575$		0			0
$576$	165.294	−	97.6821i	0.286969	−	0.169587i
$577$			427.659i			0.741177i	0.928797	+	0.370588i	$0.120844\pi$
$577$			427.659i			0.741177i	−0.928797	+	0.370588i	$0.879156\pi$
$578$	296.586	−	26.4533i	0.513124	−	0.0457670i
$579$			488.112i			0.843025i
$580$		0			0
$581$	−111.446			−0.191818
$582$	−28.1273	−	315.354i	−0.0483287	−	0.541845i
$583$	−470.400			−0.806861
$584$	−178.868	−	654.250i	−0.306281	−	1.12029i
$585$		0			0
$586$	−26.7260	−	299.642i	−0.0456074	−	0.511335i
$587$	−586.262			−0.998743			−0.499372	−	0.866388i	$-0.666436\pi$
$587$	−586.262			−0.998743			−0.499372	+	0.866388i	$0.666436\pi$
$588$	324.385	−	58.3298i	0.551676	−	0.0992003i
$589$	1546.87			2.62626
$590$		0			0
$591$		−	421.728i		−	0.713584i
$592$	−279.748	−	752.721i	−0.472548	−	1.27149i
$593$		−	518.375i		−	0.874156i	−0.899424	−	0.437078i	$-0.856013\pi$
$593$		−	518.375i		−	0.874156i	0.899424	−	0.437078i	$-0.143987\pi$
$594$	−7.58981	−	85.0944i	−0.0127775	−	0.143257i
$595$		0			0
$596$	12.3200	−	2.21534i	0.0206712	−	0.00371701i
$597$		−	211.237i		−	0.353831i
$598$	18.8536	+	211.380i	0.0315277	+	0.353478i
$599$		−	405.480i		−	0.676928i	−0.940979	−	0.338464i	$-0.890093\pi$
$599$		−	405.480i		−	0.676928i	0.940979	−	0.338464i	$-0.109907\pi$
$600$		0			0
$601$	−350.551			−0.583279			−0.291640	−	0.956528i	$-0.594201\pi$
$601$	−350.551			−0.583279			−0.291640	+	0.956528i	$0.594201\pi$
$602$	−45.4317	+	4.05219i	−0.0754680	+	0.00673121i
$603$	−29.0604			−0.0481930
$604$	−209.868	−	1167.13i	−0.347464	−	1.93233i
$605$		0			0
$606$	−103.436	+	9.22576i	−0.170687	+	0.0152240i
$607$	737.786			1.21546			0.607731	−	0.794143i	$-0.292080\pi$
$607$	737.786			1.21546			0.607731	+	0.794143i	$0.292080\pi$
$608$	−385.046	−	807.829i	−0.633299	−	1.32867i
$609$	−83.6634			−0.137378
$610$		0			0
$611$		−	202.023i		−	0.330643i
$612$	−44.4404	−	247.144i	−0.0726151	−	0.403830i
$613$		−	345.495i		−	0.563614i	−0.959471	−	0.281807i	$-0.909066\pi$
$613$		−	345.495i		−	0.563614i	0.959471	−	0.281807i	$-0.0909338\pi$
$614$	−1123.37	+	100.197i	−1.82959	+	0.163187i
$615$		0			0
$616$	−20.7257	−	75.8090i	−0.0336456	−	0.123066i
$617$			862.171i			1.39736i	0.715434	+	0.698680i	$0.246229\pi$
$617$			862.171i			1.39736i	−0.715434	+	0.698680i	$0.753771\pi$
$618$	−306.218	+	27.3125i	−0.495499	+	0.0441950i
$619$		−	469.363i		−	0.758260i	−0.925343	−	0.379130i	$-0.876223\pi$
$619$		−	469.363i		−	0.758260i	0.925343	−	0.379130i	$-0.123777\pi$
$620$		0			0
$621$	49.2888			0.0793701
$622$	−7.11102	−	79.7264i	−0.0114325	−	0.128177i
$623$	75.2737			0.120824
$624$	−107.996	−	290.586i	−0.173070	−	0.465682i
$625$		0			0
$626$	−0.324545	−	3.63869i	−0.000518443	−	0.00581260i
$627$	−398.195			−0.635080
$628$	188.082	+	1045.97i	0.299494	+	1.66555i
$629$	−1050.24			−1.66969
$630$		0			0
$631$			323.243i			0.512271i	0.966641	+	0.256136i	$0.0824494\pi$
$631$			323.243i			0.512271i	−0.966641	+	0.256136i	$0.917551\pi$
$632$	−49.1362	−	179.727i	−0.0777472	−	0.284378i
$633$			229.572i			0.362673i
$634$	43.7833	+	490.883i	0.0690588	+	0.774264i
$635$		0			0
$636$	70.1611	+	390.183i	0.110316	+	0.613495i
$637$		−	532.156i		−	0.835410i
$638$	−59.0406	−	661.943i	−0.0925402	−	1.03753i
$639$			206.083i			0.322509i
$640$		0			0
$641$	−44.1100			−0.0688144			−0.0344072	−	0.999408i	$-0.510954\pi$
$641$	−44.1100			−0.0688144			−0.0344072	+	0.999408i	$0.510954\pi$
$642$	562.146	−	50.1394i	0.875616	−	0.0780987i
$643$	934.204			1.45288			0.726442	−	0.687228i	$-0.241173\pi$
$643$	934.204			1.45288			0.726442	+	0.687228i	$0.241173\pi$
$644$	44.6262	−	8.02451i	0.0692953	−	0.0124604i
$645$		0			0
$646$	−1165.77	+	103.978i	−1.80460	+	0.160957i
$647$	481.023			0.743467			0.371734	−	0.928339i	$-0.378763\pi$
$647$	481.023			0.743467			0.371734	+	0.928339i	$0.378763\pi$
$648$	−69.4512	+	18.9875i	−0.107178	+	0.0293018i
$649$	−498.706			−0.768422
$650$		0			0
$651$		−	114.488i		−	0.175865i
$652$	−809.148	+	145.498i	−1.24103	+	0.223156i
$653$		−	1131.38i		−	1.73259i	−0.499536	−	0.866293i	$-0.666496\pi$
$653$		−	1131.38i		−	1.73259i	0.499536	−	0.866293i	$-0.333504\pi$
$654$	356.606	−	31.8067i	0.545268	−	0.0486340i
$655$		0			0
$656$	−1104.37	+	410.440i	−1.68350	+	0.625670i
$657$			254.348i			0.387135i
$658$	−42.9927	+	3.83464i	−0.0653385	+	0.00582772i
$659$			154.348i			0.234215i	0.993119	+	0.117107i	$0.0373622\pi$
$659$			154.348i			0.234215i	−0.993119	+	0.117107i	$0.962638\pi$
$660$		0			0
$661$	795.115			1.20290			0.601448	−	0.798912i	$-0.294591\pi$
$661$	795.115			1.20290			0.601448	+	0.798912i	$0.294591\pi$
$662$	−74.2122	−	832.042i	−0.112103	−	1.25686i
$663$	−405.441			−0.611524
$664$	−719.665	+	196.752i	−1.08383	+	0.296313i
$665$		0			0
$666$	26.7528	+	299.943i	0.0401694	+	0.450365i
$667$	383.414			0.574834
$668$	−45.8090	+	8.23721i	−0.0685764	+	0.0123311i
$669$	390.477			0.583672
$670$		0			0
$671$			175.527i			0.261591i
$672$	−59.7900	+	28.4984i	−0.0889732	+	0.0424083i
$673$		−	197.215i		−	0.293039i	−0.989208	−	0.146520i	$-0.953193\pi$
$673$		−	197.215i		−	0.293039i	0.989208	−	0.146520i	$-0.0468071\pi$
$674$	−56.3921	−	632.249i	−0.0836678	−	0.938055i
$675$		0			0
$676$	172.693	−	31.0530i	0.255463	−	0.0459364i
$677$			530.367i			0.783408i	0.920091	+	0.391704i	$0.128114\pi$
$677$			530.367i			0.783408i	−0.920091	+	0.391704i	$0.871886\pi$
$678$	−9.62309	−	107.891i	−0.0141934	−	0.159131i
$679$			109.220i			0.160854i
$680$		0			0
$681$	187.200			0.274891
$682$	905.830	−	80.7935i	1.32820	−	0.118466i
$683$	797.231			1.16725			0.583625	−	0.812024i	$-0.301634\pi$
$683$	797.231			1.16725			0.583625	+	0.812024i	$0.301634\pi$
$684$	59.3916	+	330.291i	0.0868299	+	0.482881i
$685$		0			0
$686$	−229.897	+	20.5052i	−0.335127	+	0.0298909i
$687$	−99.3323			−0.144588
$688$	−286.221	+	106.374i	−0.416020	+	0.154613i
$689$	640.096			0.929022
$690$		0			0
$691$			498.569i			0.721518i	0.932659	+	0.360759i	$0.117482\pi$
$691$			498.569i			0.721518i	−0.932659	+	0.360759i	$0.882518\pi$
$692$	−75.0827	−	417.552i	−0.108501	−	0.603399i
$693$			29.4716i			0.0425276i
$694$	−443.401	+	39.5482i	−0.638906	+	0.0569859i
$695$		0			0
$696$	−540.256	+	147.703i	−0.776230	+	0.212217i
$697$			1540.88i			2.21073i
$698$	1117.19	−	99.6452i	1.60056	−	0.142758i
$699$		−	494.188i		−	0.706993i
$700$		0			0
$701$	−455.939			−0.650412			−0.325206	−	0.945643i	$-0.605434\pi$
$701$	−455.939			−0.650412			−0.325206	+	0.945643i	$0.605434\pi$
$702$	10.3278	+	115.792i	0.0147120	+	0.164946i
$703$	1403.57			1.99654
$704$	−267.672	−	452.946i	−0.380216	−	0.643389i
$705$		0			0
$706$	−54.1670	−	607.302i	−0.0767238	−	0.860201i
$707$	35.8241			0.0506706
$708$	74.3831	+	413.662i	0.105061	+	0.584268i
$709$	44.4190			0.0626502			0.0313251	−	0.999509i	$-0.490027\pi$
$709$	44.4190			0.0626502			0.0313251	+	0.999509i	$0.490027\pi$
$710$		0			0
$711$			69.8710i			0.0982715i
$712$	486.080	−	132.891i	0.682696	−	0.186645i
$713$			524.679i			0.735875i
$714$	7.69576	+	86.2823i	0.0107784	+	0.120843i
$715$		0			0
$716$	30.6741	+	170.586i	0.0428409	+	0.238248i
$717$			133.796i			0.186605i
$718$	−18.8092	−	210.882i	−0.0261966	−	0.293708i
$719$			1349.94i			1.87752i	0.344566	+	0.938762i	$0.388026\pi$
$719$			1349.94i			1.87752i	−0.344566	+	0.938762i	$0.611974\pi$
$720$		0			0
$721$	106.056			0.147095
$722$	838.827	−	74.8174i	1.16181	−	0.103625i
$723$	226.132			0.312769
$724$	801.599	−	144.140i	1.10718	−	0.199089i
$725$		0			0
$726$	184.320	−	16.4400i	0.253884	−	0.0226446i
$727$	191.470			0.263370			0.131685	−	0.991292i	$-0.457961\pi$
$727$	191.470			0.263370			0.131685	+	0.991292i	$0.457961\pi$
$728$	28.2025	+	103.157i	0.0387397	+	0.141699i
$729$	27.0000			0.0370370
$730$		0			0
$731$			399.351i			0.546308i
$732$	145.595	−	26.1803i	0.198900	−	0.0357654i
$733$			358.832i			0.489539i	0.969581	+	0.244769i	$0.0787122\pi$
$733$			358.832i			0.489539i	−0.969581	+	0.244769i	$0.921288\pi$
$734$	−717.551	+	64.0004i	−0.977589	+	0.0871940i
$735$		0			0
$736$	274.007	−	130.603i	0.372291	−	0.177450i
$737$			79.6324i			0.108049i
$738$	440.069	−	39.2510i	0.596300	−	0.0531857i
$739$			756.311i			1.02342i	0.859157	+	0.511712i	$0.170989\pi$
$739$			756.311i			1.02342i	−0.859157	+	0.511712i	$0.829011\pi$
$740$		0			0
$741$	541.844			0.731233
$742$	−12.1498	−	136.220i	−0.0163744	−	0.183584i
$743$	−1148.65			−1.54596			−0.772979	−	0.634432i	$-0.781234\pi$
$743$	−1148.65			−1.54596			−0.772979	+	0.634432i	$0.781234\pi$
$744$	−202.122	−	739.308i	−0.271670	−	0.993693i
$745$		0			0
$746$	24.0738	+	269.907i	0.0322705	+	0.361805i
$747$	279.778			0.374536
$748$	−677.233	+	121.777i	−0.905392	+	0.162804i
$749$	−194.694			−0.259938
$750$		0			0
$751$			431.186i			0.574149i	0.957908	+	0.287074i	$0.0926827\pi$
$751$			431.186i			0.574149i	−0.957908	+	0.287074i	$0.907317\pi$
$752$	−270.856	+	100.663i	−0.360180	+	0.133861i
$753$		−	757.248i		−	1.00564i
$754$	80.3395	+	900.739i	0.106551	+	1.19461i
$755$		0			0
$756$	24.4458	−	4.39576i	0.0323358	−	0.00581449i
$757$			645.657i			0.852916i	0.904507	+	0.426458i	$0.140239\pi$
$757$			645.657i			0.852916i	−0.904507	+	0.426458i	$0.859761\pi$
$758$	55.2029	+	618.916i	0.0728270	+	0.816511i
$759$		−	135.063i		−	0.177949i
$760$		0			0
$761$	−291.287			−0.382768			−0.191384	−	0.981515i	$-0.561298\pi$
$761$	−291.287			−0.382768			−0.191384	+	0.981515i	$0.561298\pi$
$762$	−615.808	+	54.9257i	−0.808147	+	0.0720810i
$763$	−123.507			−0.161870
$764$	−178.065	−	990.261i	−0.233069	−	1.29615i
$765$		0			0
$766$	242.997	−	21.6736i	0.317228	−	0.0282945i
$767$	678.614			0.884764
$768$	−335.781	+	289.584i	−0.437215	+	0.377063i
$769$	724.076			0.941582			0.470791	−	0.882245i	$-0.343969\pi$
$769$	724.076			0.941582			0.470791	+	0.882245i	$0.343969\pi$
$770$		0			0
$771$			128.809i			0.167068i
$772$	−199.497	−	1109.45i	−0.258416	−	1.43711i
$773$		−	399.686i		−	0.517058i	−0.966003	−	0.258529i	$-0.916762\pi$
$773$		−	399.686i		−	0.517058i	0.966003	−	0.258529i	$-0.0832378\pi$
$774$	114.053	−	10.1727i	0.147356	−	0.0131431i
$775$		0			0
$776$	192.821	+	705.287i	0.248481	+	0.908875i
$777$		−	103.882i		−	0.133697i
$778$	1084.23	−	96.7053i	1.39361	−	0.124300i
$779$		−	2059.28i		−	2.64349i
$780$		0			0
$781$	564.717			0.723070
$782$	−35.2683	−	395.416i	−0.0451001	−	0.505647i
$783$	210.031			0.268239
$784$	−713.471	+	265.161i	−0.910039	+	0.338215i
$785$		0			0
$786$	47.3147	+	530.476i	0.0601968	+	0.674906i
$787$	381.830			0.485172			0.242586	−	0.970130i	$-0.422004\pi$
$787$	381.830			0.485172			0.242586	+	0.970130i	$0.422004\pi$
$788$	172.366	+	958.565i	0.218738	+	1.21645i
$789$	794.648			1.00716
$790$		0			0
$791$			37.3670i			0.0472402i
$792$	52.0304	+	190.313i	0.0656950	+	0.240294i
$793$		−	238.849i		−	0.301196i
$794$	89.6446	+	1005.07i	0.112903	+	1.26583i
$795$		0			0
$796$	86.3353	+	480.131i	0.108461	+	0.603180i
$797$			18.3955i			0.0230810i	0.999933	+	0.0115405i	$0.00367353\pi$
$797$			18.3955i			0.0230810i	−0.999933	+	0.0115405i	$0.996326\pi$
$798$	−10.2849	−	115.310i	−0.0128883	−	0.144499i
$799$			377.912i			0.472981i
$800$		0			0
$801$	−188.969			−0.235917
$802$	553.837	−	49.3983i	0.690570	−	0.0615939i
$803$	696.974			0.867962
$804$	66.0527	−	11.8773i	0.0821551	−	0.0147728i
$805$		0			0
$806$	−1232.61	+	109.940i	−1.52929	+	0.136402i
$807$	−554.958			−0.687681
$808$	231.334	−	63.2453i	0.286304	−	0.0782739i
$809$	992.161			1.22640			0.613202	−	0.789926i	$-0.289881\pi$
$809$	992.161			1.22640			0.613202	+	0.789926i	$0.289881\pi$
$810$		0			0
$811$			482.957i			0.595509i	0.954643	+	0.297754i	$0.0962376\pi$
$811$			482.957i			0.595509i	−0.954643	+	0.297754i	$0.903762\pi$
$812$	190.162	−	34.1943i	0.234190	−	0.0421112i
$813$			621.908i			0.764955i
$814$	821.917	−	73.3091i	1.00973	−	0.0900603i
$815$		0			0
$816$	202.022	+	543.581i	0.247575	+	0.666153i
$817$		−	533.706i		−	0.653251i
$818$	−590.753	+	52.6910i	−0.722192	+	0.0644144i
$819$		−	40.1035i		−	0.0489665i
$820$		0			0
$821$	614.955			0.749031			0.374516	−	0.927221i	$-0.377809\pi$
$821$	614.955			0.749031			0.374516	+	0.927221i	$0.377809\pi$
$822$	16.3086	+	182.847i	0.0198402	+	0.222441i
$823$	11.2878			0.0137154			0.00685772	−	0.999976i	$-0.497817\pi$
$823$	11.2878			0.0137154			0.00685772	+	0.999976i	$0.497817\pi$
$824$	684.855	−	187.235i	0.831135	−	0.227227i
$825$		0			0
$826$	−12.8809	−	144.417i	−0.0155943	−	0.174839i
$827$	−449.125			−0.543078			−0.271539	−	0.962427i	$-0.587533\pi$
$827$	−449.125			−0.543078			−0.271539	+	0.962427i	$0.587533\pi$
$828$	−112.031	+	20.1450i	−0.135303	+	0.0243297i
$829$	−135.766			−0.163771			−0.0818855	−	0.996642i	$-0.526094\pi$
$829$	−135.766			−0.163771			−0.0818855	+	0.996642i	$0.526094\pi$
$830$		0			0
$831$			239.070i			0.287690i
$832$	364.235	+	616.346i	0.437782	+	0.740801i
$833$			995.472i			1.19504i
$834$	−6.72191	−	75.3638i	−0.00805985	−	0.0903643i
$835$		0			0
$836$	905.076	−	162.747i	1.08263	−	0.194674i
$837$			287.415i			0.343387i
$838$	56.0786	+	628.734i	0.0669196	+	0.750280i
$839$		−	1509.47i		−	1.79913i	−0.436789	−	0.899564i	$-0.643884\pi$
$839$		−	1509.47i		−	1.79913i	0.436789	−	0.899564i	$-0.356116\pi$
$840$		0			0
$841$	792.817			0.942707
$842$	717.861	−	64.0280i	0.852566	−	0.0760428i
$843$	−801.080			−0.950273
$844$	−93.8290	−	521.805i	−0.111172	−	0.618252i
$845$		0			0
$846$	107.930	−	9.62660i	0.127577	−	0.0113790i
$847$	−63.8374			−0.0753688
$848$	−318.945	−	858.188i	−0.376114	−	1.01201i
$849$	−561.138			−0.660940
$850$		0			0
$851$			476.075i			0.559430i
$852$	−84.2288	−	468.416i	−0.0988601	−	0.549784i
$853$			909.826i			1.06662i	0.845920	+	0.533310i	$0.179052\pi$
$853$			909.826i			1.06662i	−0.845920	+	0.533310i	$0.820948\pi$
$854$	−50.8297	+	4.53364i	−0.0595195	+	0.00530872i
$855$		0			0
$856$	−1257.23	+	343.720i	−1.46873	+	0.401542i
$857$		−	505.304i		−	0.589620i	−0.955556	−	0.294810i	$-0.904744\pi$
$857$		−	505.304i		−	0.589620i	0.955556	−	0.294810i	$-0.0952563\pi$
$858$	317.298	−	28.3008i	0.369812	−	0.0329846i
$859$			45.9728i			0.0535189i	0.999642	+	0.0267595i	$0.00851882\pi$
$859$			45.9728i			0.0535189i	−0.999642	+	0.0267595i	$0.991481\pi$
$860$		0			0
$861$	−152.414			−0.177020
$862$	93.0365	+	1043.09i	0.107931	+	1.21009i
$863$	−142.006			−0.164549			−0.0822746	−	0.996610i	$-0.526218\pi$
$863$	−142.006			−0.164549			−0.0822746	+	0.996610i	$0.526218\pi$
$864$	150.099	−	71.5433i	0.173725	−	0.0828047i
$865$		0			0
$866$	3.82689	+	42.9058i	0.00441904	+	0.0495448i
$867$	257.871			0.297429
$868$	46.7928	+	260.226i	0.0539088	+	0.299799i
$869$	191.463			0.220326
$870$		0			0
$871$		−	108.360i		−	0.124408i
$872$	−797.546	+	218.044i	−0.914617	+	0.250051i
$873$		−	274.189i		−	0.314076i
$874$	47.1336	+	528.446i	0.0539287	+	0.604630i
$875$		0			0
$876$	−103.955	−	578.119i	−0.118670	−	0.659953i
$877$			549.975i			0.627109i	0.949570	+	0.313555i	$0.101520\pi$
$877$			549.975i			0.627109i	−0.949570	+	0.313555i	$0.898480\pi$
$878$	44.0251	+	493.594i	0.0501425	+	0.562180i
$879$		−	260.528i		−	0.296391i
$880$		0			0
$881$	636.072			0.721989			0.360995	−	0.932568i	$-0.382437\pi$
$881$	636.072			0.721989			0.360995	+	0.932568i	$0.382437\pi$
$882$	284.303	−	25.3578i	0.322339	−	0.0287503i
$883$	−689.661			−0.781043			−0.390521	−	0.920594i	$-0.627705\pi$
$883$	−689.661			−0.781043			−0.390521	+	0.920594i	$0.627705\pi$
$884$	921.545	−	165.709i	1.04247	−	0.187453i
$885$		0			0
$886$	1164.93	−	103.903i	1.31481	−	0.117272i
$887$	−1053.94			−1.18821			−0.594103	−	0.804389i	$-0.702493\pi$
$887$	−1053.94			−1.18821			−0.594103	+	0.804389i	$0.702493\pi$
$888$	−183.398	−	670.821i	−0.206530	−	0.755429i
$889$	213.279			0.239909
$890$		0			0
$891$		−	73.9865i		−	0.0830376i
$892$	−887.533	+	159.593i	−0.994992	+	0.178916i
$893$		−	505.054i		−	0.565570i
$894$	10.7977	−	0.963078i	0.0120780	−	0.00107727i
$895$		0			0
$896$	124.252	−	89.2123i	0.138674	−	0.0995673i
$897$			183.787i			0.204891i
$898$	302.984	−	27.0240i	0.337399	−	0.0300936i
$899$			2235.78i			2.48696i
$900$		0			0
$901$	−1197.39			−1.32896
$902$	−107.557	−	1205.90i	−0.119243	−	1.33691i
$903$	−39.5012			−0.0437444
$904$	65.9691	+	241.297i	0.0729747	+	0.266922i
$905$		0			0
$906$	−91.2363	−	1022.91i	−0.100702	−	1.12904i
$907$	496.037			0.546899			0.273449	−	0.961886i	$-0.411835\pi$
$907$	496.037			0.546899			0.273449	+	0.961886i	$0.411835\pi$
$908$	−425.497	+	76.5112i	−0.468609	+	0.0842635i
$909$	−89.9339			−0.0989372
$910$		0			0
$911$			336.684i			0.369577i	0.982778	+	0.184788i	$0.0591599\pi$
$911$			336.684i			0.369577i	−0.982778	+	0.184788i	$0.940840\pi$
$912$	−269.988	−	726.459i	−0.296039	−	0.796556i
$913$		−	766.660i		−	0.839715i
$914$	107.042	+	1200.12i	0.117114	+	1.31304i
$915$		0			0
$916$	225.777	−	40.5984i	0.246481	−	0.0443214i
$917$		−	183.725i		−	0.200355i
$918$	−19.3197	−	216.606i	−0.0210454	−	0.235954i
$919$		−	937.464i		−	1.02009i	−0.860147	−	0.510046i	$-0.829629\pi$
$919$		−	937.464i		−	1.02009i	0.860147	−	0.510046i	$-0.170371\pi$
$920$		0			0
$921$	−976.729			−1.06051
$922$	1005.83	−	89.7129i	1.09092	−	0.0973025i
$923$	−768.439			−0.832545
$924$	−12.0454	−	66.9875i	−0.0130362	−	0.0724973i
$925$		0			0
$926$	1005.13	−	89.6504i	1.08545	−	0.0968147i
$927$	−266.246			−0.287212
$928$	1167.61	−	556.530i	1.25820	−	0.599709i
$929$	−858.647			−0.924270			−0.462135	−	0.886810i	$-0.652916\pi$
$929$	−858.647			−0.924270			−0.462135	+	0.886810i	$0.652916\pi$
$930$		0			0
$931$		−	1330.38i		−	1.42898i
$932$	201.981	+	1123.26i	0.216718	+	1.20522i
$933$		−	69.3191i		−	0.0742971i
$934$	−1496.89	+	133.512i	−1.60267	+	0.142947i
$935$		0			0
$936$	−70.8004	−	258.968i	−0.0756414	−	0.276676i
$937$		−	1276.09i		−	1.36189i	−0.732336	−	0.680943i	$-0.761570\pi$
$937$		−	1276.09i		−	1.36189i	0.732336	−	0.680943i	$-0.238430\pi$
$938$	−23.0602	+	2.05680i	−0.0245844	+	0.00219275i
$939$		−	3.16371i		−	0.00336923i
$940$		0			0
$941$	536.218			0.569838			0.284919	−	0.958552i	$-0.408033\pi$
$941$	536.218			0.569838			0.284919	+	0.958552i	$0.408033\pi$
$942$	81.7652	+	916.723i	0.0867995	+	0.973167i
$943$	698.485			0.740705
$944$	−338.138	−	909.830i	−0.358197	−	0.963803i
$945$		0			0
$946$	−27.8757	−	312.533i	−0.0294669	−	0.330373i
$947$	−48.1723			−0.0508683			−0.0254341	−	0.999677i	$-0.508097\pi$
$947$	−48.1723			−0.0508683			−0.0254341	+	0.999677i	$0.508097\pi$
$948$	−28.5572	−	158.813i	−0.0301236	−	0.167524i
$949$	−948.407			−0.999375
$950$		0			0
$951$			426.805i			0.448796i
$952$	−52.7567	−	192.970i	−0.0554167	−	0.202699i
$953$			1449.85i			1.52136i	0.649129	+	0.760679i	$0.275134\pi$
$953$			1449.85i			1.52136i	−0.649129	+	0.760679i	$0.724866\pi$
$954$	30.5013	+	341.970i	0.0319720	+	0.358459i
$955$		0			0
$956$	−54.6841	−	304.111i	−0.0572009	−	0.318108i
$957$		−	575.536i		−	0.601396i
$958$	−103.303	−	1158.20i	−0.107832	−	1.20898i
$959$		−	63.3272i		−	0.0660346i
$960$		0			0
$961$	−2098.53			−2.18369
$962$	−1118.42	+	99.7553i	−1.16260	+	0.103696i
$963$	488.765			0.507544
$964$	−513.986	+	92.4231i	−0.533181	+	0.0958746i
$965$		0			0
$966$	39.1120	−	3.48851i	0.0404886	−	0.00361129i
$967$	−1320.06			−1.36510			−0.682552	−	0.730837i	$-0.739130\pi$
$967$	−1320.06			−1.36510			−0.682552	+	0.730837i	$0.739130\pi$
$968$	−412.230	+	112.701i	−0.425857	+	0.116427i
$969$	−1013.59			−1.04602
$970$		0			0
$971$		−	1269.58i		−	1.30749i	−0.756713	−	0.653747i	$-0.773196\pi$
$971$		−	1269.58i		−	1.30749i	0.756713	−	0.653747i	$-0.226804\pi$
$972$	−61.3696	+	11.0352i	−0.0631374	+	0.0113531i
$973$			26.1015i			0.0268258i
$974$	1110.57	−	99.0548i	1.14021	−	0.101699i
$975$		0			0
$976$	−320.229	+	119.013i	−0.328103	+	0.121939i
$977$		−	1262.18i		−	1.29190i	−0.763382	−	0.645948i	$-0.776462\pi$
$977$		−	1262.18i		−	1.29190i	0.763382	−	0.645948i	$-0.223538\pi$
$978$	−709.167	+	63.2526i	−0.725119	+	0.0646755i
$979$			517.821i			0.528929i
$980$		0			0
$981$	310.055			0.316061
$982$	−4.65580	−	52.1992i	−0.00474114	−	0.0531560i
$983$	235.722			0.239798			0.119899	−	0.992786i	$-0.461743\pi$
$983$	235.722			0.239798			0.119899	+	0.992786i	$0.461743\pi$
$984$	−984.212	+	269.077i	−1.00022	+	0.273453i
$985$		0			0
$986$	−150.286	−	1684.96i	−0.152420	−	1.70888i
$987$	−37.3806			−0.0378729
$988$	−1231.58	+	221.458i	−1.24654	+	0.224148i
$989$	181.027			0.183040
$990$		0			0
$991$		−	1601.53i		−	1.61607i	−0.589135	−	0.808035i	$-0.700531\pi$
$991$		−	1601.53i		−	1.61607i	0.589135	−	0.808035i	$-0.299469\pi$
$992$	761.578	+	1597.80i	0.767719	+	1.61068i
$993$		−	723.430i		−	0.728530i
$994$	14.5859	+	163.532i	0.0146740	+	0.164520i
$995$		0			0
$996$	−635.921	+	114.349i	−0.638475	+	0.114808i
$997$		−	984.298i		−	0.987260i	−0.869672	−	0.493630i	$-0.835670\pi$
$997$		−	984.298i		−	0.987260i	0.869672	−	0.493630i	$-0.164330\pi$
$998$	78.9993	+	885.713i	0.0791576	+	0.887488i
$999$			260.790i			0.261051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.f.c.199.2		16
3.2	odd	2		900.3.f.h.199.15		16
4.3	odd	2	inner	300.3.f.c.199.16		16
5.2	odd	4		300.3.c.g.151.3	yes	8
5.3	odd	4		300.3.c.e.151.6	yes	8
5.4	even	2	inner	300.3.f.c.199.15		16
12.11	even	2		900.3.f.h.199.1		16
15.2	even	4		900.3.c.n.451.6		8
15.8	even	4		900.3.c.t.451.3		8
15.14	odd	2		900.3.f.h.199.2		16
20.3	even	4		300.3.c.e.151.5	✓	8
20.7	even	4		300.3.c.g.151.4	yes	8
20.19	odd	2	inner	300.3.f.c.199.1		16
60.23	odd	4		900.3.c.t.451.4		8
60.47	odd	4		900.3.c.n.451.5		8
60.59	even	2		900.3.f.h.199.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.5	✓	8	20.3	even	4
300.3.c.e.151.6	yes	8	5.3	odd	4
300.3.c.g.151.3	yes	8	5.2	odd	4
300.3.c.g.151.4	yes	8	20.7	even	4
300.3.f.c.199.1		16	20.19	odd	2	inner
300.3.f.c.199.2		16	1.1	even	1	trivial
300.3.f.c.199.15		16	5.4	even	2	inner
300.3.f.c.199.16		16	4.3	odd	2	inner
900.3.c.n.451.5		8	60.47	odd	4
900.3.c.n.451.6		8	15.2	even	4
900.3.c.t.451.3		8	15.8	even	4
900.3.c.t.451.4		8	60.23	odd	4
900.3.f.h.199.1		16	12.11	even	2
900.3.f.h.199.2		16	15.14	odd	2
900.3.f.h.199.15		16	3.2	odd	2
900.3.f.h.199.16		16	60.59	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99209 + 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 - 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.99209 + 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 - 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +3.00000 q^{9} -8.22072i q^{11} +(-6.81884 + 1.22614i) q^{12} +11.1863i q^{13} +(2.38058 - 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} -20.9256i q^{17} +(-5.97628 + 0.533041i) q^{18} +27.9657i q^{19} +2.06983 q^{21} +(1.46066 + 16.3764i) q^{22} -9.48564 q^{23} +(13.3659 - 3.65415i) q^{24} +(-1.98759 - 22.2842i) q^{26} -5.19615 q^{27} +(-4.70460 + 0.845964i) q^{28} -40.4205 q^{29} -55.3130i q^{31} +(-28.8865 + 13.7685i) q^{32} +14.2387i q^{33} +(3.71807 + 41.6858i) q^{34} +(11.8106 - 2.12373i) q^{36} -50.1890i q^{37} +(-4.96895 - 55.7102i) q^{38} -19.3753i q^{39} -73.6361 q^{41} +(-4.12328 + 0.367767i) q^{42} -19.0843 q^{43} +(-5.81954 - 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598 q^{47} +(-25.9768 + 9.65427i) q^{48} -47.5719 q^{49} +36.2442i q^{51} +(7.91894 + 44.0391i) q^{52} -57.2212i q^{53} +(10.3512 - 0.923254i) q^{54} +(9.22169 - 2.52115i) q^{56} -48.4380i q^{57} +(80.5213 - 7.18193i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(9.82804 + 110.189i) q^{62} -3.58504 q^{63} +(55.0981 - 32.5607i) q^{64} +(-2.52994 - 28.3648i) q^{66} -9.68679 q^{67} +(-14.8135 - 82.3812i) q^{68} +16.4296 q^{69} +68.6944i q^{71} +(-23.1504 + 6.32918i) q^{72} +84.7825i q^{73} +(8.91760 + 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} +9.82388i q^{77} +(3.44261 + 38.5974i) q^{78} +23.2903i q^{79} +9.00000 q^{81} +(146.690 - 13.0837i) q^{82} +93.2595 q^{83} +(8.14861 - 1.46525i) q^{84} +(38.0177 - 3.39091i) q^{86} +70.0104 q^{87} +(17.3435 + 63.4377i) q^{88} -62.9898 q^{89} -13.3678i q^{91} +(-37.3436 + 6.71499i) q^{92} +95.8049i q^{93} +(35.9767 - 3.20887i) q^{94} +(50.0328 - 23.8478i) q^{96} -91.3962i q^{97} +(94.7677 - 8.45260i) q^{98} -24.6622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * q^96

Introduction

L-functions

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