LMFDB - Embedded newform 300.3.f.c.199.14

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			199.14
Root			$0.717516 + 1.21868i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92737 + 0.534079i) q^{2} -1.73205 q^{3} +(3.42952 + 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716 q^{7} +(5.51043 + 5.79958i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.92737 + 0.534079i) q^{2} -1.73205 q^{3} +(3.42952 + 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716 q^{7} +(5.51043 + 5.79958i) q^{8} +3.00000 q^{9} +14.5382i q^{11} +(-5.94010 - 3.56583i) q^{12} +22.4802i q^{13} +(-23.0738 - 6.39379i) q^{14} +(7.52322 + 14.1209i) q^{16} -12.6890i q^{17} +(5.78211 + 1.60224i) q^{18} +8.76336i q^{19} +20.7355 q^{21} +(-7.76455 + 28.0205i) q^{22} -4.99653 q^{23} +(-9.54435 - 10.0452i) q^{24} +(-12.0062 + 43.3278i) q^{26} -5.19615 q^{27} +(-41.0570 - 24.6464i) q^{28} -2.74712 q^{29} -16.3466i q^{31} +(6.95833 + 31.2343i) q^{32} -25.1809i q^{33} +(6.77695 - 24.4565i) q^{34} +(10.2886 + 6.17621i) q^{36} -32.4872i q^{37} +(-4.68032 + 16.8902i) q^{38} -38.9369i q^{39} +42.7586 q^{41} +(39.9650 + 11.0744i) q^{42} -16.5435 q^{43} +(-29.9303 + 49.8591i) q^{44} +(-9.63018 - 2.66854i) q^{46} -48.5912 q^{47} +(-13.0306 - 24.4582i) q^{48} +94.3200 q^{49} +21.9781i q^{51} +(-46.2809 + 77.0964i) q^{52} +94.1066i q^{53} +(-10.0149 - 2.77515i) q^{54} +(-65.9689 - 69.4305i) q^{56} -15.1786i q^{57} +(-5.29471 - 1.46718i) q^{58} -43.2650i q^{59} +56.7678 q^{61} +(8.73038 - 31.5060i) q^{62} -35.9149 q^{63} +(-3.27028 + 63.9164i) q^{64} +(13.4486 - 48.5330i) q^{66} +61.1106 q^{67} +(26.1234 - 43.5173i) q^{68} +8.65425 q^{69} +39.6643i q^{71} +(16.5313 + 17.3987i) q^{72} -99.5452i q^{73} +(17.3507 - 62.6149i) q^{74} +(-18.0414 + 30.0541i) q^{76} -174.046i q^{77} +(20.7954 - 75.0459i) q^{78} +10.7780i q^{79} +9.00000 q^{81} +(82.4118 + 22.8365i) q^{82} +140.263 q^{83} +(71.1127 + 42.6889i) q^{84} +(-31.8855 - 8.83554i) q^{86} +4.75815 q^{87} +(-84.3156 + 80.1118i) q^{88} -54.8723 q^{89} -269.125i q^{91} +(-17.1357 - 10.2865i) q^{92} +28.3132i q^{93} +(-93.6533 - 25.9515i) q^{94} +(-12.0522 - 54.0994i) q^{96} -14.1601i q^{97} +(181.790 + 50.3743i) q^{98} +43.6146i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.92737	+	0.534079i	0.963686	+	0.267039i
$2$	1.92737	+	0.534079i	0.963686	+	0.267039i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	3.42952	+	2.05874i	0.857380	+	0.514684i
$5$		0			0
$5$		0			0
$6$	−3.33830	−	0.925051i	−0.556384	−	0.154175i
$7$	−11.9716			−1.71023			−0.855117	−	0.518436i	$-0.826515\pi$
$7$	−11.9716			−1.71023			−0.855117	+	0.518436i	$0.826515\pi$
$8$	5.51043	+	5.79958i	0.688804	+	0.724948i
$9$	3.00000			0.333333
$10$		0			0
$11$			14.5382i			1.32166i	0.750537	+	0.660828i	$0.229795\pi$
$11$			14.5382i			1.32166i	−0.750537	+	0.660828i	$0.770205\pi$
$12$	−5.94010	−	3.56583i	−0.495009	−	0.297153i
$13$			22.4802i			1.72925i	0.502418	+	0.864625i	$0.332444\pi$
$13$			22.4802i			1.72925i	−0.502418	+	0.864625i	$0.667556\pi$
$14$	−23.0738	−	6.39379i	−1.64813	−	0.456699i
$15$		0			0
$16$	7.52322	+	14.1209i	0.470201	+	0.882559i
$17$		−	12.6890i		−	0.746414i	−0.927748	−	0.373207i	$-0.878258\pi$
$17$		−	12.6890i		−	0.746414i	0.927748	−	0.373207i	$-0.121742\pi$
$18$	5.78211	+	1.60224i	0.321229	+	0.0890131i
$19$			8.76336i			0.461229i	0.973045	+	0.230615i	$0.0740737\pi$
$19$			8.76336i			0.461229i	−0.973045	+	0.230615i	$0.925926\pi$
$20$		0			0
$21$	20.7355			0.987404
$22$	−7.76455	+	28.0205i	−0.352934	+	1.27366i
$23$	−4.99653			−0.217241			−0.108620	−	0.994083i	$-0.534643\pi$
$23$	−4.99653			−0.217241			−0.108620	+	0.994083i	$0.534643\pi$
$24$	−9.54435	−	10.0452i	−0.397681	−	0.418549i
$25$		0			0
$26$	−12.0062	+	43.3278i	−0.461778	+	1.66645i
$27$	−5.19615			−0.192450
$28$	−41.0570	−	24.6464i	−1.46632	−	0.880229i
$29$	−2.74712			−0.0947282			−0.0473641	−	0.998878i	$-0.515082\pi$
$29$	−2.74712			−0.0947282			−0.0473641	+	0.998878i	$0.515082\pi$
$30$		0			0
$31$		−	16.3466i		−	0.527310i	−0.964617	−	0.263655i	$-0.915072\pi$
$31$		−	16.3466i		−	0.527310i	0.964617	−	0.263655i	$-0.0849281\pi$
$32$	6.95833	+	31.2343i	0.217448	+	0.976072i
$33$		−	25.1809i		−	0.763058i
$34$	6.77695	−	24.4565i	0.199322	−	0.719309i
$35$		0			0
$36$	10.2886	+	6.17621i	0.285793	+	0.171561i
$37$		−	32.4872i		−	0.878032i	−0.898479	−	0.439016i	$-0.855327\pi$
$37$		−	32.4872i		−	0.878032i	0.898479	−	0.439016i	$-0.144673\pi$
$38$	−4.68032	+	16.8902i	−0.123166	+	0.444480i
$39$		−	38.9369i		−	0.998383i
$40$		0			0
$41$	42.7586			1.04289			0.521447	−	0.853284i	$-0.325393\pi$
$41$	42.7586			1.04289			0.521447	+	0.853284i	$0.325393\pi$
$42$	39.9650	+	11.0744i	0.951547	+	0.263676i
$43$	−16.5435			−0.384733			−0.192367	−	0.981323i	$-0.561616\pi$
$43$	−16.5435			−0.384733			−0.192367	+	0.981323i	$0.561616\pi$
$44$	−29.9303	+	49.8591i	−0.680235	+	1.13316i
$45$		0			0
$46$	−9.63018	−	2.66854i	−0.209352	−	0.0580118i
$47$	−48.5912			−1.03386			−0.516928	−	0.856029i	$-0.672924\pi$
$47$	−48.5912			−1.03386			−0.516928	+	0.856029i	$0.672924\pi$
$48$	−13.0306	−	24.4582i	−0.271471	−	0.509546i
$49$	94.3200			1.92490
$50$		0			0
$51$			21.9781i			0.430943i
$52$	−46.2809	+	77.0964i	−0.890017	+	1.48262i
$53$			94.1066i			1.77560i	0.460233	+	0.887798i	$0.347766\pi$
$53$			94.1066i			1.77560i	−0.460233	+	0.887798i	$0.652234\pi$
$54$	−10.0149	−	2.77515i	−0.185461	−	0.0513917i
$55$		0			0
$56$	−65.9689	−	69.4305i	−1.17802	−	1.23983i
$57$		−	15.1786i		−	0.266291i
$58$	−5.29471	−	1.46718i	−0.0912882	−	0.0252961i
$59$		−	43.2650i		−	0.733305i	−0.930358	−	0.366653i	$-0.880504\pi$
$59$		−	43.2650i		−	0.733305i	0.930358	−	0.366653i	$-0.119496\pi$
$60$		0			0
$61$	56.7678			0.930620			0.465310	−	0.885148i	$-0.345943\pi$
$61$	56.7678			0.930620			0.465310	+	0.885148i	$0.345943\pi$
$62$	8.73038	−	31.5060i	0.140813	−	0.508161i
$63$	−35.9149			−0.570078
$64$	−3.27028	+	63.9164i	−0.0510981	+	0.998694i
$65$		0			0
$66$	13.4486	−	48.5330i	0.203767	−	0.735348i
$67$	61.1106			0.912098			0.456049	−	0.889955i	$-0.349264\pi$
$67$	61.1106			0.912098			0.456049	+	0.889955i	$0.349264\pi$
$68$	26.1234	−	43.5173i	0.384167	−	0.639961i
$69$	8.65425			0.125424
$70$		0			0
$71$			39.6643i			0.558652i	0.960196	+	0.279326i	$0.0901110\pi$
$71$			39.6643i			0.558652i	−0.960196	+	0.279326i	$0.909889\pi$
$72$	16.5313	+	17.3987i	0.229601	+	0.241649i
$73$		−	99.5452i		−	1.36363i	−0.731523	−	0.681817i	$-0.761190\pi$
$73$		−	99.5452i		−	1.36363i	0.731523	−	0.681817i	$-0.238810\pi$
$74$	17.3507	−	62.6149i	0.234469	−	0.846147i
$75$		0			0
$76$	−18.0414	+	30.0541i	−0.237387	+	0.395449i
$77$		−	174.046i		−	2.26034i
$78$	20.7954	−	75.0459i	0.266607	−	0.962127i
$79$			10.7780i			0.136430i	0.997671	+	0.0682151i	$0.0217304\pi$
$79$			10.7780i			0.136430i	−0.997671	+	0.0682151i	$0.978270\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	82.4118	+	22.8365i	1.00502	+	0.278494i
$83$	140.263			1.68991			0.844955	−	0.534837i	$-0.179627\pi$
$83$	140.263			1.68991			0.844955	+	0.534837i	$0.179627\pi$
$84$	71.1127	+	42.6889i	0.846580	+	0.508201i
$85$		0			0
$86$	−31.8855	−	8.83554i	−0.370762	−	0.102739i
$87$	4.75815			0.0546913
$88$	−84.3156	+	80.1118i	−0.958131	+	0.910362i
$89$	−54.8723			−0.616543			−0.308271	−	0.951298i	$-0.599751\pi$
$89$	−54.8723			−0.616543			−0.308271	+	0.951298i	$0.599751\pi$
$90$		0			0
$91$		−	269.125i		−	2.95742i
$92$	−17.1357	−	10.2865i	−0.186258	−	0.111810i
$93$			28.3132i			0.304443i
$94$	−93.6533	−	25.9515i	−0.996312	−	0.276080i
$95$		0			0
$96$	−12.0522	−	54.0994i	−0.125544	−	0.563535i
$97$		−	14.1601i		−	0.145980i	−0.997333	−	0.0729902i	$-0.976746\pi$
$97$		−	14.1601i		−	0.145980i	0.997333	−	0.0729902i	$-0.0232542\pi$
$98$	181.790	+	50.3743i	1.85500	+	0.514023i
$99$			43.6146i			0.440552i
$100$		0			0
$101$	−163.410			−1.61792			−0.808962	−	0.587861i	$-0.799970\pi$
$101$	−163.410			−1.61792			−0.808962	+	0.587861i	$0.799970\pi$
$102$	−11.7380	+	42.3599i	−0.115079	+	0.415293i
$103$	169.591			1.64651			0.823255	−	0.567672i	$-0.192156\pi$
$103$	169.591			1.64651			0.823255	+	0.567672i	$0.192156\pi$
$104$	−130.376	+	123.876i	−1.25362	+	1.19111i
$105$		0			0
$106$	−50.2603	+	181.378i	−0.474154	+	1.71112i
$107$	−8.14840			−0.0761532			−0.0380766	−	0.999275i	$-0.512123\pi$
$107$	−8.14840			−0.0761532			−0.0380766	+	0.999275i	$0.512123\pi$
$108$	−17.8203	−	10.6975i	−0.165003	−	0.0990510i
$109$	25.2322			0.231488			0.115744	−	0.993279i	$-0.463075\pi$
$109$	25.2322			0.231488			0.115744	+	0.993279i	$0.463075\pi$
$110$		0			0
$111$			56.2695i			0.506932i
$112$	−90.0652	−	169.051i	−0.804153	−	1.50938i
$113$			97.8142i			0.865613i	0.901487	+	0.432806i	$0.142477\pi$
$113$			97.8142i			0.865613i	−0.901487	+	0.432806i	$0.857523\pi$
$114$	8.10655	−	29.2548i	0.0711101	−	0.256621i
$115$		0			0
$116$	−9.42129	−	5.65559i	−0.0812180	−	0.0487551i
$117$			67.4407i			0.576417i
$118$	23.1069	−	83.3877i	0.195821	−	0.706676i
$119$			151.909i			1.27654i
$120$		0			0
$121$	−90.3597			−0.746774
$122$	109.413	+	30.3185i	0.896825	+	0.248512i
$123$	−74.0601			−0.602115
$124$	33.6534	−	56.0611i	0.271398	−	0.452105i
$125$		0			0
$126$	−69.2213	−	19.1814i	−0.549376	−	0.152233i
$127$	167.563			1.31939			0.659695	−	0.751533i	$-0.270685\pi$
$127$	167.563			1.31939			0.659695	+	0.751533i	$0.270685\pi$
$128$	−40.4394	+	121.444i	−0.315933	+	0.948782i
$129$	28.6542			0.222126
$130$		0			0
$131$			82.0465i			0.626309i	0.949702	+	0.313155i	$0.101386\pi$
$131$			82.0465i			0.626309i	−0.949702	+	0.313155i	$0.898614\pi$
$132$	51.8409	−	86.3585i	0.392734	−	0.654231i
$133$		−	104.912i		−	0.788810i
$134$	117.783	+	32.6378i	0.878976	+	0.243566i
$135$		0			0
$136$	73.5911	−	69.9221i	0.541111	−	0.514133i
$137$			254.459i			1.85737i	0.370874	+	0.928683i	$0.379058\pi$
$137$			254.459i			1.85737i	−0.370874	+	0.928683i	$0.620942\pi$
$138$	16.6800	+	4.62205i	0.120869	+	0.0334931i
$139$			78.9483i			0.567974i	0.958828	+	0.283987i	$0.0916572\pi$
$139$			78.9483i			0.567974i	−0.958828	+	0.283987i	$0.908343\pi$
$140$		0			0
$141$	84.1624			0.596897
$142$	−21.1838	+	76.4478i	−0.149182	+	0.538365i
$143$	−326.823			−2.28547
$144$	22.5696	+	42.3628i	0.156734	+	0.294186i
$145$		0			0
$146$	53.1650	−	191.861i	0.364144	−	1.31411i
$147$	−163.367			−1.11134
$148$	66.8825	−	111.415i	0.451909	−	0.752807i
$149$	32.3433			0.217069			0.108534	−	0.994093i	$-0.465384\pi$
$149$	32.3433			0.217069			0.108534	+	0.994093i	$0.465384\pi$
$150$		0			0
$151$			38.7953i			0.256922i	0.991715	+	0.128461i	$0.0410038\pi$
$151$			38.7953i			0.256922i	−0.991715	+	0.128461i	$0.958996\pi$
$152$	−50.8238	+	48.2899i	−0.334367	+	0.317697i
$153$		−	38.0671i		−	0.248805i
$154$	92.9543	−	335.452i	0.603600	−	2.17826i
$155$		0			0
$156$	80.1608	−	133.535i	0.513851	−	0.855993i
$157$		−	44.2021i		−	0.281542i	−0.990042	−	0.140771i	$-0.955042\pi$
$157$		−	44.2021i		−	0.281542i	0.990042	−	0.140771i	$-0.0449581\pi$
$158$	−5.75629	+	20.7732i	−0.0364322	+	0.131476i
$159$		−	162.997i		−	1.02514i
$160$		0			0
$161$	59.8167			0.371532
$162$	17.3463	+	4.80671i	0.107076	+	0.0296710i
$163$	52.9366			0.324764			0.162382	−	0.986728i	$-0.448082\pi$
$163$	52.9366			0.324764			0.162382	+	0.986728i	$0.448082\pi$
$164$	146.642	+	88.0287i	0.894156	+	0.536760i
$165$		0			0
$166$	270.338	+	74.9112i	1.62854	+	0.451272i
$167$	−179.273			−1.07349			−0.536745	−	0.843744i	$-0.680346\pi$
$167$	−179.273			−1.07349			−0.536745	+	0.843744i	$0.680346\pi$
$168$	114.261	+	120.257i	0.680128	+	0.715816i
$169$	−336.361			−1.99030
$170$		0			0
$171$			26.2901i			0.153743i
$172$	−56.7364	−	34.0587i	−0.329863	−	0.198016i
$173$		−	177.276i		−	1.02471i	−0.858772	−	0.512357i	$-0.828772\pi$
$173$		−	177.276i		−	1.02471i	0.858772	−	0.512357i	$-0.171228\pi$
$174$	9.17071	+	2.54122i	0.0527053	+	0.0146047i
$175$		0			0
$176$	−205.293	+	109.374i	−1.16644	+	0.621444i
$177$			74.9372i			0.423374i
$178$	−105.759	−	29.3061i	−0.594154	−	0.164641i
$179$		−	102.849i		−	0.574573i	−0.957845	−	0.287286i	$-0.907247\pi$
$179$		−	102.849i		−	0.574573i	0.957845	−	0.287286i	$-0.0927532\pi$
$180$		0			0
$181$	−115.413			−0.637640			−0.318820	−	0.947815i	$-0.603286\pi$
$181$	−115.413			−0.637640			−0.318820	+	0.947815i	$0.603286\pi$
$182$	143.734	−	518.704i	0.789747	−	2.85002i
$183$	−98.3247			−0.537294
$184$	−27.5331	−	28.9778i	−0.149636	−	0.157488i
$185$		0			0
$186$	−15.1215	+	54.5700i	−0.0812982	+	0.293387i
$187$	184.476			0.986503
$188$	−166.645	−	100.036i	−0.886407	−	0.532109i
$189$	62.2064			0.329135
$190$		0			0
$191$			191.305i			1.00160i	0.865563	+	0.500799i	$0.166960\pi$
$191$			191.305i			1.00160i	−0.865563	+	0.500799i	$0.833040\pi$
$192$	5.66429	−	110.706i	0.0295015	−	0.576596i
$193$			160.332i			0.830734i	0.909654	+	0.415367i	$0.136347\pi$
$193$			160.332i			0.830734i	−0.909654	+	0.415367i	$0.863653\pi$
$194$	7.56261	−	27.2918i	0.0389825	−	0.140679i
$195$		0			0
$196$	323.472	+	194.180i	1.65037	+	0.990714i
$197$			355.081i			1.80244i	0.433362	+	0.901220i	$0.357327\pi$
$197$			355.081i			1.80244i	−0.433362	+	0.901220i	$0.642673\pi$
$198$	−23.2936	+	84.0616i	−0.117645	+	0.424554i
$199$		−	88.2032i		−	0.443232i	−0.975134	−	0.221616i	$-0.928867\pi$
$199$		−	88.2032i		−	0.443232i	0.975134	−	0.221616i	$-0.0711332\pi$
$200$		0			0
$201$	−105.847			−0.526600
$202$	−314.952	−	87.2740i	−1.55917	−	0.432049i
$203$	32.8875			0.162007
$204$	−45.2470	+	75.3742i	−0.221799	+	0.369482i
$205$		0			0
$206$	326.864	+	90.5747i	1.58672	+	0.439683i
$207$	−14.9896			−0.0724135
$208$	−317.442	+	169.124i	−1.52617	+	0.813095i
$209$	−127.404			−0.609586
$210$		0			0
$211$		−	190.584i		−	0.903243i	−0.892210	−	0.451622i	$-0.850846\pi$
$211$		−	190.584i		−	0.903243i	0.892210	−	0.451622i	$-0.149154\pi$
$212$	−193.741	+	322.741i	−0.913871	+	1.52236i
$213$		−	68.7006i		−	0.322538i
$214$	−15.7050	−	4.35188i	−0.0733878	−	0.0203359i
$215$		0			0
$216$	−28.6330	−	30.1355i	−0.132560	−	0.139516i
$217$			195.696i			0.901824i
$218$	48.6318	+	13.4760i	0.223082	+	0.0618164i
$219$			172.417i			0.787294i
$220$		0			0
$221$	285.253			1.29074
$222$	−30.0523	+	108.452i	−0.135371	+	0.488523i
$223$	79.2869			0.355547			0.177773	−	0.984071i	$-0.443111\pi$
$223$	79.2869			0.355547			0.177773	+	0.984071i	$0.443111\pi$
$224$	−83.3026	−	373.926i	−0.371887	−	1.66931i
$225$		0			0
$226$	−52.2405	+	188.524i	−0.231153	+	0.834178i
$227$	353.645			1.55791			0.778953	−	0.627082i	$-0.215751\pi$
$227$	353.645			1.55791			0.778953	+	0.627082i	$0.215751\pi$
$228$	31.2487	−	52.0552i	0.137056	−	0.228312i
$229$	22.7911			0.0995244			0.0497622	−	0.998761i	$-0.484154\pi$
$229$	22.7911			0.0995244			0.0497622	+	0.998761i	$0.484154\pi$
$230$		0			0
$231$			301.457i			1.30501i
$232$	−15.1378	−	15.9321i	−0.0652491	−	0.0686730i
$233$		−	189.710i		−	0.814205i	−0.913382	−	0.407103i	$-0.866539\pi$
$233$		−	189.710i		−	0.814205i	0.913382	−	0.407103i	$-0.133461\pi$
$234$	−36.0187	+	129.983i	−0.153926	+	0.555484i
$235$		0			0
$236$	89.0712	−	148.378i	0.377420	−	0.628721i
$237$		−	18.6680i		−	0.0787680i
$238$	−81.1311	+	292.784i	−0.340887	+	1.23019i
$239$		−	267.778i		−	1.12041i	−0.828355	−	0.560204i	$-0.810723\pi$
$239$		−	267.778i		−	1.12041i	0.828355	−	0.560204i	$-0.189277\pi$
$240$		0			0
$241$	−301.663			−1.25171			−0.625857	−	0.779938i	$-0.715251\pi$
$241$	−301.663			−1.25171			−0.625857	+	0.779938i	$0.715251\pi$
$242$	−174.157	−	48.2592i	−0.719656	−	0.199418i
$243$	−15.5885			−0.0641500
$244$	194.686	+	116.870i	0.797895	+	0.478975i
$245$		0			0
$246$	−142.741	−	39.5539i	−0.580249	−	0.160788i
$247$	−197.002			−0.797580
$248$	94.8035	−	90.0769i	0.382272	−	0.363213i
$249$	−242.942			−0.975670
$250$		0			0
$251$			63.1891i			0.251749i	0.992046	+	0.125875i	$0.0401737\pi$
$251$			63.1891i			0.251749i	−0.992046	+	0.125875i	$0.959826\pi$
$252$	−123.171	−	73.9393i	−0.488773	−	0.293410i
$253$		−	72.6407i		−	0.287117i
$254$	322.955	+	89.4916i	1.27148	+	0.352329i
$255$		0			0
$256$	−142.802	+	212.470i	−0.557822	+	0.829961i
$257$		−	150.719i		−	0.586456i	−0.956043	−	0.293228i	$-0.905271\pi$
$257$		−	150.719i		−	0.586456i	0.956043	−	0.293228i	$-0.0947295\pi$
$258$	55.2273	+	15.3036i	0.214059	+	0.0593163i
$259$			388.925i			1.50164i
$260$		0			0
$261$	−8.24135			−0.0315761
$262$	−43.8193	+	158.134i	−0.167249	+	0.603565i
$263$	−203.755			−0.774735			−0.387368	−	0.921925i	$-0.626616\pi$
$263$	−203.755			−0.774735			−0.387368	+	0.921925i	$0.626616\pi$
$264$	146.039	−	138.758i	0.553177	−	0.525598i
$265$		0			0
$266$	56.0311	−	202.204i	0.210643	−	0.760165i
$267$	95.0416			0.355961
$268$	209.580	+	125.810i	0.782014	+	0.469442i
$269$	−76.3986			−0.284010			−0.142005	−	0.989866i	$-0.545355\pi$
$269$	−76.3986			−0.284010			−0.142005	+	0.989866i	$0.545355\pi$
$270$		0			0
$271$			169.216i			0.624414i	0.950014	+	0.312207i	$0.101068\pi$
$271$			169.216i			0.624414i	−0.950014	+	0.312207i	$0.898932\pi$
$272$	179.181	−	95.4624i	0.658755	−	0.350965i
$273$			466.139i			1.70747i
$274$	−135.901	+	490.437i	−0.495990	+	1.78992i
$275$		0			0
$276$	29.6799	+	17.8168i	0.107536	+	0.0645537i
$277$			273.891i			0.988774i	0.869242	+	0.494387i	$0.164607\pi$
$277$			273.891i			0.988774i	−0.869242	+	0.494387i	$0.835393\pi$
$278$	−42.1646	+	152.163i	−0.151671	+	0.547348i
$279$		−	49.0399i		−	0.175770i
$280$		0			0
$281$	−311.672			−1.10915			−0.554577	−	0.832133i	$-0.687120\pi$
$281$	−311.672			−1.10915			−0.554577	+	0.832133i	$0.687120\pi$
$282$	162.212	+	44.9494i	0.575221	+	0.159395i
$283$	264.566			0.934861			0.467431	−	0.884030i	$-0.345180\pi$
$283$	264.566			0.934861			0.467431	+	0.884030i	$0.345180\pi$
$284$	−81.6583	+	136.029i	−0.287529	+	0.478977i
$285$		0			0
$286$	−629.909	−	174.549i	−2.20248	−	0.610311i
$287$	−511.891			−1.78359
$288$	20.8750	+	93.7029i	0.0724826	+	0.325357i
$289$	127.988			0.442866
$290$		0			0
$291$			24.5260i			0.0842818i
$292$	204.937	−	341.392i	0.701840	−	1.16915i
$293$			121.281i			0.413927i	0.978349	+	0.206964i	$0.0663582\pi$
$293$			121.281i			0.413927i	−0.978349	+	0.206964i	$0.933642\pi$
$294$	−314.869	−	87.2508i	−1.07098	−	0.296772i
$295$		0			0
$296$	188.412	−	179.018i	0.636527	−	0.604792i
$297$		−	75.5428i		−	0.254353i
$298$	62.3375	+	17.2739i	0.209186	+	0.0579659i
$299$		−	112.323i		−	0.375663i
$300$		0			0
$301$	198.053			0.657984
$302$	−20.7197	+	74.7729i	−0.0686083	+	0.247592i
$303$	283.035			0.934109
$304$	−123.747	+	65.9286i	−0.407062	+	0.216870i
$305$		0			0
$306$	20.3308	−	73.3695i	0.0664407	−	0.239770i
$307$	161.768			0.526932			0.263466	−	0.964669i	$-0.415134\pi$
$307$	161.768			0.526932			0.263466	+	0.964669i	$0.415134\pi$
$308$	358.315	−	596.895i	1.16336	−	1.93797i
$309$	−293.739			−0.950613
$310$		0			0
$311$		−	26.3813i		−	0.0848273i	−0.999100	−	0.0424137i	$-0.986495\pi$
$311$		−	26.3813i		−	0.0848273i	0.999100	−	0.0424137i	$-0.0135047\pi$
$312$	225.818	−	214.559i	0.723775	−	0.687690i
$313$			5.39902i			0.0172493i	0.999963	+	0.00862463i	$0.00274534\pi$
$313$			5.39902i			0.0172493i	−0.999963	+	0.00862463i	$0.997255\pi$
$314$	23.6074	−	85.1938i	0.0751827	−	0.271318i
$315$		0			0
$316$	−22.1890	+	36.9633i	−0.0702184	+	0.116972i
$317$		−	270.157i		−	0.852231i	−0.904669	−	0.426116i	$-0.859882\pi$
$317$		−	270.157i		−	0.852231i	0.904669	−	0.426116i	$-0.140118\pi$
$318$	87.0535	−	314.157i	0.273753	−	0.987914i
$319$		−	39.9382i		−	0.125198i
$320$		0			0
$321$	14.1134			0.0439671
$322$	115.289	+	31.9468i	0.358040	+	0.0992137i
$323$	111.199			0.344268
$324$	30.8657	+	18.5286i	0.0952644	+	0.0571871i
$325$		0			0
$326$	102.028	+	28.2723i	0.312971	+	0.0867248i
$327$	−43.7034			−0.133650
$328$	235.619	+	247.982i	0.718349	+	0.756043i
$329$	581.716			1.76813
$330$		0			0
$331$		−	480.728i		−	1.45235i	−0.687510	−	0.726174i	$-0.741296\pi$
$331$		−	480.728i		−	1.45235i	0.687510	−	0.726174i	$-0.258704\pi$
$332$	481.033	+	288.763i	1.44890	+	0.869770i
$333$		−	97.4616i		−	0.292677i
$334$	−345.526	−	95.7459i	−1.03451	−	0.286664i
$335$		0			0
$336$	155.997	+	292.805i	0.464278	+	0.871442i
$337$		−	568.382i		−	1.68659i	−0.537448	−	0.843297i	$-0.680612\pi$
$337$		−	568.382i		−	1.68659i	0.537448	−	0.843297i	$-0.319388\pi$
$338$	−648.293	−	179.643i	−1.91803	−	0.531489i
$339$		−	169.419i		−	0.499762i
$340$		0			0
$341$	237.651			0.696923
$342$	−14.0410	+	50.6707i	−0.0410554	+	0.148160i
$343$	−542.554			−1.58179
$344$	−91.1620	−	95.9455i	−0.265006	−	0.278911i
$345$		0			0
$346$	94.6791	−	341.676i	0.273639	−	0.987503i
$347$	370.184			1.06681			0.533406	−	0.845859i	$-0.320912\pi$
$347$	370.184			1.06681			0.533406	+	0.845859i	$0.320912\pi$
$348$	16.3182	+	9.79576i	0.0468913	+	0.0281487i
$349$	488.570			1.39991			0.699957	−	0.714185i	$-0.253203\pi$
$349$	488.570			1.39991			0.699957	+	0.714185i	$0.253203\pi$
$350$		0			0
$351$		−	116.811i		−	0.332794i
$352$	−454.091	+	101.162i	−1.29003	+	0.287391i
$353$		−	649.728i		−	1.84059i	−0.391226	−	0.920295i	$-0.627949\pi$
$353$		−	649.728i		−	1.84059i	0.391226	−	0.920295i	$-0.372051\pi$
$354$	−40.0224	+	144.432i	−0.113058	+	0.407999i
$355$		0			0
$356$	−188.186	−	112.968i	−0.528612	−	0.317325i
$357$		−	263.113i		−	0.737012i
$358$	54.9292	−	198.227i	0.153434	−	0.553708i
$359$			405.910i			1.13067i	0.824862	+	0.565334i	$0.191253\pi$
$359$			405.910i			1.13067i	−0.824862	+	0.565334i	$0.808747\pi$
$360$		0			0
$361$	284.204			0.787268
$362$	−222.443	−	61.6395i	−0.614484	−	0.170275i
$363$	156.508			0.431150
$364$	554.058	−	922.970i	1.52214	−	2.53563i
$365$		0			0
$366$	−189.508	−	52.5131i	−0.517782	−	0.143479i
$367$	46.2347			0.125980			0.0629900	−	0.998014i	$-0.479936\pi$
$367$	46.2347			0.125980			0.0629900	+	0.998014i	$0.479936\pi$
$368$	−37.5900	−	70.5558i	−0.102147	−	0.191728i
$369$	128.276			0.347631
$370$		0			0
$371$		−	1126.61i		−	3.03668i
$372$	−58.2893	+	97.1006i	−0.156692	+	0.261023i
$373$			138.262i			0.370676i	0.982675	+	0.185338i	$0.0593380\pi$
$373$			138.262i			0.370676i	−0.982675	+	0.185338i	$0.940662\pi$
$374$	355.554	+	98.5247i	0.950679	+	0.263435i
$375$		0			0
$376$	−267.759	−	281.809i	−0.712124	−	0.749491i
$377$		−	61.7559i		−	0.163809i
$378$	119.895	+	33.2231i	0.317182	+	0.0878919i
$379$			254.516i			0.671546i	0.941943	+	0.335773i	$0.108998\pi$
$379$			254.516i			0.671546i	−0.941943	+	0.335773i	$0.891002\pi$
$380$		0			0
$381$	−290.227			−0.761750
$382$	−102.172	+	368.716i	−0.267466	+	0.965226i
$383$	62.7205			0.163761			0.0818805	−	0.996642i	$-0.473907\pi$
$383$	62.7205			0.163761			0.0818805	+	0.996642i	$0.473907\pi$
$384$	70.0431	−	210.347i	0.182404	−	0.547779i
$385$		0			0
$386$	−85.6298	+	309.019i	−0.221839	+	0.800567i
$387$	−49.6306			−0.128244
$388$	29.1519	−	48.5623i	0.0751338	−	0.125161i
$389$	−110.130			−0.283112			−0.141556	−	0.989930i	$-0.545210\pi$
$389$	−110.130			−0.283112			−0.141556	+	0.989930i	$0.545210\pi$
$390$		0			0
$391$			63.4012i			0.162152i
$392$	519.744	+	547.016i	1.32588	+	1.39545i
$393$		−	142.109i		−	0.361600i
$394$	−189.641	+	684.372i	−0.481322	+	1.73698i
$395$		0			0
$396$	−89.7910	+	149.577i	−0.226745	+	0.377720i
$397$		−	292.953i		−	0.737916i	−0.929446	−	0.368958i	$-0.879715\pi$
$397$		−	292.953i		−	0.737916i	0.929446	−	0.368958i	$-0.120285\pi$
$398$	47.1074	−	170.000i	0.118360	−	0.427136i
$399$			181.712i			0.455419i
$400$		0			0
$401$	518.103			1.29203			0.646014	−	0.763325i	$-0.276435\pi$
$401$	518.103			1.29203			0.646014	+	0.763325i	$0.276435\pi$
$402$	−204.006	−	56.5304i	−0.507477	−	0.140623i
$403$	367.476			0.911851
$404$	−560.419	−	336.419i	−1.38718	−	0.832720i
$405$		0			0
$406$	63.3864	+	17.5645i	0.156124	+	0.0432623i
$407$	472.306			1.16046
$408$	−127.464	+	121.109i	−0.312411	+	0.296835i
$409$	181.984			0.444948			0.222474	−	0.974939i	$-0.428587\pi$
$409$	181.984			0.444948			0.222474	+	0.974939i	$0.428587\pi$
$410$		0			0
$411$		−	440.736i		−	1.07235i
$412$	581.614	+	349.142i	1.41168	+	0.847432i
$413$			517.953i			1.25412i
$414$	−28.8905	−	8.00563i	−0.0697839	−	0.0193373i
$415$		0			0
$416$	−702.155	+	156.425i	−1.68787	+	0.376022i
$417$		−	136.743i		−	0.327920i
$418$	−245.554	−	68.0435i	−0.587450	−	0.162784i
$419$		−	163.347i		−	0.389849i	−0.980818	−	0.194925i	$-0.937554\pi$
$419$		−	163.347i		−	0.389849i	0.980818	−	0.194925i	$-0.0624462\pi$
$420$		0			0
$421$	−467.206			−1.10975			−0.554876	−	0.831933i	$-0.687234\pi$
$421$	−467.206			−1.10975			−0.554876	+	0.831933i	$0.687234\pi$
$422$	101.787	−	367.327i	0.241201	−	0.870442i
$423$	−145.774			−0.344619
$424$	−545.779	+	518.568i	−1.28721	+	1.22304i
$425$		0			0
$426$	36.6915	−	132.411i	0.0861303	−	0.310825i
$427$	−679.603			−1.59158
$428$	−27.9451	−	16.7754i	−0.0652923	−	0.0391948i
$429$	566.073			1.31952
$430$		0			0
$431$			685.527i			1.59055i	0.606248	+	0.795275i	$0.292674\pi$
$431$			685.527i			1.59055i	−0.606248	+	0.795275i	$0.707326\pi$
$432$	−39.0918	−	73.3746i	−0.0904902	−	0.169849i
$433$			592.777i			1.36900i	0.729013	+	0.684500i	$0.239979\pi$
$433$			592.777i			1.36900i	−0.729013	+	0.684500i	$0.760021\pi$
$434$	−104.517	+	377.178i	−0.240822	+	0.869074i
$435$		0			0
$436$	86.5343	+	51.9464i	0.198473	+	0.119143i
$437$		−	43.7864i		−	0.100198i
$438$	−92.0844	+	332.312i	−0.210238	+	0.758704i
$439$		−	464.439i		−	1.05795i	−0.848638	−	0.528974i	$-0.822577\pi$
$439$		−	464.439i		−	1.05795i	0.848638	−	0.528974i	$-0.177423\pi$
$440$		0			0
$441$	282.960			0.641633
$442$	549.788	+	152.347i	1.24386	+	0.344677i
$443$	54.2868			0.122544			0.0612718	−	0.998121i	$-0.480484\pi$
$443$	54.2868			0.122544			0.0612718	+	0.998121i	$0.480484\pi$
$444$	−115.844	+	192.977i	−0.260910	+	0.434633i
$445$		0			0
$446$	152.815	+	42.3454i	0.342635	+	0.0949449i
$447$	−56.0202			−0.125325
$448$	39.1506	−	765.184i	0.0873897	−	1.70800i
$449$	428.051			0.953343			0.476671	−	0.879082i	$-0.341843\pi$
$449$	428.051			0.953343			0.476671	+	0.879082i	$0.341843\pi$
$450$		0			0
$451$			621.634i			1.37835i
$452$	−201.374	+	335.456i	−0.445517	+	0.742159i
$453$		−	67.1954i		−	0.148334i
$454$	681.605	+	188.874i	1.50133	+	0.416022i
$455$		0			0
$456$	88.0294	−	83.6405i	0.193047	−	0.183422i
$457$			66.5848i			0.145700i	0.997343	+	0.0728498i	$0.0232094\pi$
$457$			66.5848i			0.145700i	−0.997343	+	0.0728498i	$0.976791\pi$
$458$	43.9269	+	12.1722i	0.0959103	+	0.0265769i
$459$			65.9342i			0.143648i
$460$		0			0
$461$	−238.626			−0.517627			−0.258814	−	0.965927i	$-0.583332\pi$
$461$	−238.626			−0.517627			−0.258814	+	0.965927i	$0.583332\pi$
$462$	−161.002	+	581.019i	−0.348488	+	1.25762i
$463$	−386.958			−0.835762			−0.417881	−	0.908502i	$-0.637227\pi$
$463$	−386.958			−0.835762			−0.417881	+	0.908502i	$0.637227\pi$
$464$	−20.6672	−	38.7919i	−0.0445413	−	0.0836032i
$465$		0			0
$466$	101.320	−	365.641i	0.217425	−	0.784638i
$467$	−235.964			−0.505276			−0.252638	−	0.967561i	$-0.581298\pi$
$467$	−235.964			−0.505276			−0.252638	+	0.967561i	$0.581298\pi$
$468$	−138.843	+	231.289i	−0.296672	+	0.494208i
$469$	−731.593			−1.55990
$470$		0			0
$471$			76.5602i			0.162548i
$472$	250.919	−	238.409i	0.531608	−	0.505104i
$473$		−	240.513i		−	0.508485i
$474$	9.97018	−	35.9802i	0.0210341	−	0.0759076i
$475$		0			0
$476$	−312.740	+	520.974i	−0.657016	+	1.09448i
$477$			282.320i			0.591866i
$478$	143.014	−	516.107i	0.299193	−	1.07972i
$479$		−	529.496i		−	1.10542i	−0.833374	−	0.552710i	$-0.813594\pi$
$479$		−	529.496i		−	1.10542i	0.833374	−	0.552710i	$-0.186406\pi$
$480$		0			0
$481$	730.320			1.51834
$482$	−581.417	−	161.112i	−1.20626	−	0.334257i
$483$	−103.606			−0.214504
$484$	−309.890	−	186.027i	−0.640270	−	0.384353i
$485$		0			0
$486$	−30.0447	−	8.32546i	−0.0618205	−	0.0171306i
$487$	−880.801			−1.80863			−0.904314	−	0.426869i	$-0.859617\pi$
$487$	−880.801			−1.80863			−0.904314	+	0.426869i	$0.859617\pi$
$488$	312.815	+	329.230i	0.641015	+	0.674651i
$489$	−91.6888			−0.187503
$490$		0			0
$491$			86.4466i			0.176062i	0.996118	+	0.0880312i	$0.0280575\pi$
$491$			86.4466i			0.176062i	−0.996118	+	0.0880312i	$0.971942\pi$
$492$	−253.991	−	152.470i	−0.516241	−	0.309899i
$493$			34.8583i			0.0707065i
$494$	−379.697	−	105.215i	−0.768617	−	0.212985i
$495$		0			0
$496$	230.830	−	122.979i	0.465383	−	0.247942i
$497$		−	474.846i		−	0.955425i
$498$	−468.239	−	129.750i	−0.940239	−	0.260542i
$499$		−	874.536i		−	1.75258i	−0.481786	−	0.876289i	$-0.660012\pi$
$499$		−	874.536i		−	1.75258i	0.481786	−	0.876289i	$-0.339988\pi$
$500$		0			0
$501$	310.510			0.619780
$502$	−33.7479	+	121.789i	−0.0672269	+	0.242607i
$503$	−17.5479			−0.0348865			−0.0174433	−	0.999848i	$-0.505553\pi$
$503$	−17.5479			−0.0348865			−0.0174433	+	0.999848i	$0.505553\pi$
$504$	−197.907	−	208.291i	−0.392672	−	0.413277i
$505$		0			0
$506$	38.7958	−	140.006i	0.0766716	−	0.276691i
$507$	582.595			1.14910
$508$	574.659	+	344.967i	1.13122	+	0.679069i
$509$	−609.132			−1.19672			−0.598362	−	0.801226i	$-0.704181\pi$
$509$	−609.132			−1.19672			−0.598362	+	0.801226i	$0.704181\pi$
$510$		0			0
$511$			1191.72i			2.33213i
$512$	−388.709	+	333.241i	−0.759197	+	0.650861i
$513$		−	45.5357i		−	0.0887636i
$514$	80.4959	−	290.492i	0.156607	−	0.565159i
$515$		0			0
$516$	98.2703	+	58.9915i	0.190446	+	0.114325i
$517$		−	706.430i		−	1.36640i
$518$	−207.716	+	749.602i	−0.400997	+	1.44711i
$519$			307.050i			0.591619i
$520$		0			0
$521$	433.724			0.832484			0.416242	−	0.909254i	$-0.363347\pi$
$521$	433.724			0.832484			0.416242	+	0.909254i	$0.363347\pi$
$522$	−15.8841	−	4.40153i	−0.0304294	−	0.00843205i
$523$	473.223			0.904823			0.452412	−	0.891809i	$-0.350564\pi$
$523$	473.223			0.904823			0.452412	+	0.891809i	$0.350564\pi$
$524$	−168.912	+	281.380i	−0.322351	+	0.536985i
$525$		0			0
$526$	−392.712	−	108.821i	−0.746601	−	0.206885i
$527$	−207.423			−0.393592
$528$	355.579	−	189.442i	0.673444	−	0.358791i
$529$	−504.035			−0.952807
$530$		0			0
$531$		−	129.795i		−	0.244435i
$532$	215.985	−	359.797i	0.405988	−	0.676310i
$533$			961.224i			1.80342i
$534$	183.181	+	50.7597i	0.343035	+	0.0950556i
$535$		0			0
$536$	336.746	+	354.416i	0.628257	+	0.661223i
$537$			178.139i			0.331730i
$538$	−147.249	−	40.8029i	−0.273696	−	0.0758418i
$539$			1371.24i			2.54405i
$540$		0			0
$541$	294.889			0.545081			0.272540	−	0.962144i	$-0.412136\pi$
$541$	294.889			0.545081			0.272540	+	0.962144i	$0.412136\pi$
$542$	−90.3747	+	326.142i	−0.166743	+	0.601739i
$543$	199.901			0.368141
$544$	396.333	−	88.2946i	0.728554	−	0.162306i
$545$		0			0
$546$	−248.955	+	898.422i	−0.455961	+	1.64546i
$547$	966.695			1.76727			0.883634	−	0.468179i	$-0.155090\pi$
$547$	966.695			1.76727			0.883634	+	0.468179i	$0.155090\pi$
$548$	−523.864	+	872.673i	−0.955956	+	1.59247i
$549$	170.303			0.310207
$550$		0			0
$551$		−	24.0740i		−	0.0436914i
$552$	47.6887	+	50.1910i	0.0863925	+	0.0909258i
$553$		−	129.030i		−	0.233327i
$554$	−146.279	+	527.889i	−0.264042	+	0.952868i
$555$		0			0
$556$	−162.534	+	270.755i	−0.292327	+	0.486969i
$557$		−	74.2603i		−	0.133322i	−0.997776	−	0.0666609i	$-0.978765\pi$
$557$		−	74.2603i		−	0.133322i	0.997776	−	0.0666609i	$-0.0212346\pi$
$558$	26.1911	−	94.5180i	0.0469375	−	0.169387i
$559$		−	371.903i		−	0.665300i
$560$		0			0
$561$	−319.522			−0.569558
$562$	−600.708	−	166.457i	−1.06887	−	0.296187i
$563$	663.688			1.17884			0.589421	−	0.807826i	$-0.299356\pi$
$563$	663.688			1.17884			0.589421	+	0.807826i	$0.299356\pi$
$564$	288.637	+	173.268i	0.511767	+	0.307213i
$565$		0			0
$566$	509.916	+	141.299i	0.900912	+	0.249645i
$567$	−107.745			−0.190026
$568$	−230.036	+	218.567i	−0.404993	+	0.384802i
$569$	667.450			1.17302			0.586511	−	0.809941i	$-0.300501\pi$
$569$	667.450			1.17302			0.586511	+	0.809941i	$0.300501\pi$
$570$		0			0
$571$			185.898i			0.325565i	0.986662	+	0.162782i	$0.0520469\pi$
$571$			185.898i			0.325565i	−0.986662	+	0.162782i	$0.947953\pi$
$572$	−1120.84	−	672.841i	−1.95952	−	1.17630i
$573$		−	331.350i		−	0.578273i
$574$	−986.603	−	273.390i	−1.71882	−	0.476289i
$575$		0			0
$576$	−9.81084	+	191.749i	−0.0170327	+	0.332898i
$577$			664.331i			1.15135i	0.817678	+	0.575676i	$0.195261\pi$
$577$			664.331i			1.15135i	−0.817678	+	0.575676i	$0.804739\pi$
$578$	246.681	+	68.3557i	0.426783	+	0.118263i
$579$		−	277.703i		−	0.479625i
$580$		0			0
$581$	−1679.17			−2.89014
$582$	−13.0988	+	47.2707i	−0.0225066	+	0.0812212i
$583$	−1368.14			−2.34673
$584$	577.321	−	548.537i	0.988563	−	0.939276i
$585$		0			0
$586$	−64.7734	+	233.753i	−0.110535	+	0.398896i
$587$	−763.083			−1.29997			−0.649986	−	0.759946i	$-0.725225\pi$
$587$	−763.083			−1.29997			−0.649986	+	0.759946i	$0.725225\pi$
$588$	−560.270	−	336.329i	−0.952841	−	0.571989i
$589$	143.251			0.243211
$590$		0			0
$591$		−	615.018i		−	1.04064i
$592$	458.750	−	244.408i	0.774915	−	0.412852i
$593$			286.193i			0.482618i	0.970448	+	0.241309i	$0.0775768\pi$
$593$			286.193i			0.482618i	−0.970448	+	0.241309i	$0.922423\pi$
$594$	40.3458	−	145.599i	0.0679222	−	0.245116i
$595$		0			0
$596$	110.922	+	66.5862i	0.186111	+	0.111722i
$597$			152.772i			0.255900i
$598$	59.9895	−	216.489i	0.100317	−	0.362021i
$599$		−	604.151i		−	1.00860i	−0.863529	−	0.504300i	$-0.831751\pi$
$599$		−	604.151i		−	1.00860i	0.863529	−	0.504300i	$-0.168249\pi$
$600$		0			0
$601$	275.562			0.458505			0.229253	−	0.973367i	$-0.426372\pi$
$601$	275.562			0.458505			0.229253	+	0.973367i	$0.426372\pi$
$602$	381.722	+	105.776i	0.634089	+	0.175707i
$603$	183.332			0.304033
$604$	−79.8692	+	133.049i	−0.132234	+	0.220280i
$605$		0			0
$606$	545.514	+	151.163i	0.900188	+	0.249444i
$607$	−52.1487			−0.0859121			−0.0429561	−	0.999077i	$-0.513678\pi$
$607$	−52.1487			−0.0859121			−0.0429561	+	0.999077i	$0.513678\pi$
$608$	−273.717	+	60.9784i	−0.450193	+	0.100293i
$609$	−56.9628			−0.0935349
$610$		0			0
$611$		−	1092.34i		−	1.78779i
$612$	78.3702	−	130.552i	0.128056	−	0.213320i
$613$		−	898.128i		−	1.46513i	−0.680695	−	0.732567i	$-0.738322\pi$
$613$		−	898.128i		−	1.46513i	0.680695	−	0.732567i	$-0.261678\pi$
$614$	311.787	+	86.3968i	0.507796	+	0.140711i
$615$		0			0
$616$	1009.39	−	959.070i	1.63863	−	1.55693i
$617$			636.868i			1.03220i	0.856528	+	0.516101i	$0.172617\pi$
$617$			636.868i			1.03220i	−0.856528	+	0.516101i	$0.827383\pi$
$618$	−566.145	−	156.880i	−0.916092	−	0.253851i
$619$			190.559i			0.307849i	0.988083	+	0.153925i	$0.0491913\pi$
$619$			190.559i			0.307849i	−0.988083	+	0.153925i	$0.950809\pi$
$620$		0			0
$621$	25.9628			0.0418080
$622$	14.0897	−	50.8466i	0.0226522	−	0.0817469i
$623$	656.911			1.05443
$624$	549.826	−	292.931i	0.881132	−	0.469441i
$625$		0			0
$626$	−2.88350	+	10.4059i	−0.00460623	+	0.0166229i
$627$	220.669			0.351945
$628$	91.0004	−	151.592i	0.144905	−	0.241388i
$629$	−412.231			−0.655376
$630$		0			0
$631$			578.160i			0.916261i	0.888885	+	0.458130i	$0.151481\pi$
$631$			578.160i			0.916261i	−0.888885	+	0.458130i	$0.848519\pi$
$632$	−62.5078	+	59.3913i	−0.0989047	+	0.0939736i
$633$			330.102i			0.521488i
$634$	144.285	−	520.693i	0.227579	−	0.821283i
$635$		0			0
$636$	335.569	−	559.003i	0.527624	−	0.878936i
$637$			2120.34i			3.32863i
$638$	21.3301	−	76.9757i	0.0334328	−	0.120652i
$639$			118.993i			0.186217i
$640$		0			0
$641$	−35.3085			−0.0550834			−0.0275417	−	0.999621i	$-0.508768\pi$
$641$	−35.3085			−0.0550834			−0.0275417	+	0.999621i	$0.508768\pi$
$642$	27.2018	+	7.53768i	0.0423704	+	0.0117409i
$643$	−1045.67			−1.62623			−0.813117	−	0.582100i	$-0.802231\pi$
$643$	−1045.67			−1.62623			−0.813117	+	0.582100i	$0.802231\pi$
$644$	205.143	+	123.147i	0.318544	+	0.191222i
$645$		0			0
$646$	214.321	+	59.3888i	0.331766	+	0.0919331i
$647$	2.71164			0.00419110			0.00209555	−	0.999998i	$-0.499333\pi$
$647$	2.71164			0.00419110			0.00209555	+	0.999998i	$0.499333\pi$
$648$	49.5939	+	52.1962i	0.0765338	+	0.0805497i
$649$	628.996			0.969177
$650$		0			0
$651$		−	338.955i		−	0.520668i
$652$	181.547	+	108.982i	0.278446	+	0.167151i
$653$		−	206.765i		−	0.316639i	−0.987388	−	0.158319i	$-0.949392\pi$
$653$		−	206.765i		−	0.316639i	0.987388	−	0.158319i	$-0.0506076\pi$
$654$	−84.2327	−	23.3411i	−0.128796	−	0.0356897i
$655$		0			0
$656$	321.682	+	603.792i	0.490370	+	0.920415i
$657$		−	298.636i		−	0.454544i
$658$	1121.18	+	310.682i	1.70393	+	0.472161i
$659$			708.330i			1.07486i	0.843309	+	0.537428i	$0.180604\pi$
$659$			708.330i			1.07486i	−0.843309	+	0.537428i	$0.819396\pi$
$660$		0			0
$661$	1229.66			1.86031			0.930155	−	0.367167i	$-0.119672\pi$
$661$	1229.66			1.86031			0.930155	+	0.367167i	$0.119672\pi$
$662$	256.746	−	926.540i	0.387834	−	1.39961i
$663$	−494.072			−0.745207
$664$	772.907	+	813.464i	1.16402	+	1.22510i
$665$		0			0
$666$	52.0521	−	187.845i	0.0781564	−	0.282049i
$667$	13.7261			0.0205788
$668$	−614.820	−	369.076i	−0.920390	−	0.552508i
$669$	−137.329			−0.205275
$670$		0			0
$671$			825.303i			1.22996i
$672$	144.284	+	647.658i	0.214709	+	0.963777i
$673$		−	753.492i		−	1.11960i	−0.828627	−	0.559801i	$-0.810878\pi$
$673$		−	753.492i		−	1.11960i	0.828627	−	0.559801i	$-0.189122\pi$
$674$	303.561	−	1095.48i	0.450387	−	1.62535i
$675$		0			0
$676$	−1153.56	−	692.479i	−1.70645	−	1.02438i
$677$		−	332.246i		−	0.490762i	−0.969427	−	0.245381i	$-0.921087\pi$
$677$		−	332.246i		−	0.490762i	0.969427	−	0.245381i	$-0.0789131\pi$
$678$	90.4832	−	326.534i	0.133456	−	0.481613i
$679$			169.520i			0.249661i
$680$		0			0
$681$	−612.531			−0.899458
$682$	458.041	+	126.924i	0.671615	+	0.186106i
$683$	−1120.62			−1.64074			−0.820368	−	0.571835i	$-0.806232\pi$
$683$	−1120.62			−1.64074			−0.820368	+	0.571835i	$0.806232\pi$
$684$	−54.1243	+	90.1623i	−0.0791291	+	0.131816i
$685$		0			0
$686$	−1045.70	−	289.767i	−1.52435	−	0.422400i
$687$	−39.4753			−0.0574605
$688$	−124.461	−	233.610i	−0.180902	−	0.339550i
$689$	−2115.54			−3.07045
$690$		0			0
$691$			331.115i			0.479182i	0.970874	+	0.239591i	$0.0770134\pi$
$691$			331.115i			0.479182i	−0.970874	+	0.239591i	$0.922987\pi$
$692$	364.964	−	607.970i	0.527404	−	0.878570i
$693$		−	522.139i		−	0.753447i
$694$	713.482	+	197.707i	1.02807	+	0.284881i
$695$		0			0
$696$	26.2194	+	27.5953i	0.0376716	+	0.0396484i
$697$		−	542.566i		−	0.778431i
$698$	941.655	+	260.935i	1.34908	+	0.373832i
$699$			328.587i			0.470081i
$700$		0			0
$701$	−564.971			−0.805949			−0.402975	−	0.915211i	$-0.632024\pi$
$701$	−564.971			−0.805949			−0.402975	+	0.915211i	$0.632024\pi$
$702$	62.3861	−	225.138i	0.0888691	−	0.320709i
$703$	284.697			0.404974
$704$	−929.230	−	47.5440i	−1.31993	−	0.0675341i
$705$		0			0
$706$	347.006	−	1252.27i	0.491510	−	1.77375i
$707$	1956.29			2.76703
$708$	−154.276	+	256.999i	−0.217904	+	0.362992i
$709$	−1.56083			−0.00220146			−0.00110073	−	0.999999i	$-0.500350\pi$
$709$	−1.56083			−0.00220146			−0.00110073	+	0.999999i	$0.500350\pi$
$710$		0			0
$711$			32.3339i			0.0454767i
$712$	−302.370	−	318.236i	−0.424677	−	0.446961i
$713$			81.6765i			0.114553i
$714$	140.523	−	507.117i	0.196811	−	0.710248i
$715$		0			0
$716$	211.738	−	352.721i	0.295723	−	0.492627i
$717$			463.804i			0.646868i
$718$	−216.788	+	782.339i	−0.301933	+	1.08961i
$719$		−	75.0325i		−	0.104357i	−0.998638	−	0.0521784i	$-0.983384\pi$
$719$		−	75.0325i		−	0.104357i	0.998638	−	0.0521784i	$-0.0166164\pi$
$720$		0			0
$721$	−2030.28			−2.81592
$722$	547.766	+	151.787i	0.758678	+	0.210231i
$723$	522.496			0.722678
$724$	−395.810	−	237.604i	−0.546699	−	0.328183i
$725$		0			0
$726$	301.648	+	83.5874i	0.415493	+	0.115134i
$727$	−1229.26			−1.69087			−0.845433	−	0.534082i	$-0.820657\pi$
$727$	−1229.26			−1.69087			−0.845433	+	0.534082i	$0.820657\pi$
$728$	1560.81	−	1483.00i	2.14397	−	2.03708i
$729$	27.0000			0.0370370
$730$		0			0
$731$			209.922i			0.287170i
$732$	−337.207	−	202.425i	−0.460665	−	0.276536i
$733$		−	691.736i		−	0.943705i	−0.881678	−	0.471852i	$-0.843586\pi$
$733$		−	691.736i		−	0.943705i	0.881678	−	0.471852i	$-0.156414\pi$
$734$	89.1114	+	24.6930i	0.121405	+	0.0336416i
$735$		0			0
$736$	−34.7676	−	156.063i	−0.0472385	−	0.212042i
$737$			888.438i			1.20548i
$738$	247.235	+	68.5094i	0.335007	+	0.0928312i
$739$		−	71.4311i		−	0.0966591i	−0.998831	−	0.0483296i	$-0.984610\pi$
$739$		−	71.4311i		−	0.0966591i	0.998831	−	0.0483296i	$-0.0153898\pi$
$740$		0			0
$741$	341.218			0.460483
$742$	601.698	−	2171.40i	0.810914	−	2.92641i
$743$	1006.92			1.35521			0.677605	−	0.735426i	$-0.263018\pi$
$743$	1006.92			1.35521			0.677605	+	0.735426i	$0.263018\pi$
$744$	−164.205	+	156.018i	−0.220705	+	0.209701i
$745$		0			0
$746$	−73.8428	+	266.482i	−0.0989850	+	0.357215i
$747$	420.788			0.563303
$748$	632.664	+	379.787i	0.845808	+	0.507737i
$749$	97.5496			0.130240
$750$		0			0
$751$		−	1110.14i		−	1.47822i	−0.673587	−	0.739108i	$-0.735247\pi$
$751$		−	1110.14i		−	1.47822i	0.673587	−	0.739108i	$-0.264753\pi$
$752$	−365.562	−	686.154i	−0.486120	−	0.912439i
$753$		−	109.447i		−	0.145347i
$754$	32.9825	−	119.026i	0.0437433	−	0.157860i
$755$		0			0
$756$	213.338	+	128.067i	0.282193	+	0.169400i
$757$			326.752i			0.431641i	0.976433	+	0.215821i	$0.0692426\pi$
$757$			326.752i			0.431641i	−0.976433	+	0.215821i	$0.930757\pi$
$758$	−135.932	+	490.547i	−0.179329	+	0.647160i
$759$			125.817i			0.165767i
$760$		0			0
$761$	162.162			0.213091			0.106546	−	0.994308i	$-0.466021\pi$
$761$	162.162			0.213091			0.106546	+	0.994308i	$0.466021\pi$
$762$	−559.375	−	155.004i	−0.734088	−	0.203417i
$763$	−302.070			−0.395898
$764$	−393.847	+	656.085i	−0.515507	+	0.858750i
$765$		0			0
$766$	120.886	+	33.4977i	0.157814	+	0.0437306i
$767$	972.608			1.26807
$768$	247.341	−	368.009i	0.322059	−	0.479178i
$769$	154.694			0.201162			0.100581	−	0.994929i	$-0.467930\pi$
$769$	154.694			0.201162			0.100581	+	0.994929i	$0.467930\pi$
$770$		0			0
$771$			261.053i			0.338590i
$772$	−330.081	+	549.861i	−0.427566	+	0.712255i
$773$			208.302i			0.269472i	0.990882	+	0.134736i	$0.0430187\pi$
$773$			208.302i			0.269472i	−0.990882	+	0.134736i	$0.956981\pi$
$774$	−95.6566	−	26.5066i	−0.123587	−	0.0342463i
$775$		0			0
$776$	82.1226	−	78.0283i	0.105828	−	0.100552i
$777$		−	673.637i		−	0.866972i
$778$	−212.262	−	58.8183i	−0.272831	−	0.0756019i
$779$			374.709i			0.481013i
$780$		0			0
$781$	−576.648			−0.738346
$782$	−33.8612	+	122.198i	−0.0433008	+	0.156263i
$783$	14.2744			0.0182304
$784$	709.590	+	1331.89i	0.905089	+	1.69884i
$785$		0			0
$786$	75.8972	−	273.896i	0.0965613	−	0.348468i
$787$	−377.158			−0.479235			−0.239617	−	0.970867i	$-0.577022\pi$
$787$	−377.158			−0.479235			−0.239617	+	0.970867i	$0.577022\pi$
$788$	−731.017	+	1217.76i	−0.927687	+	1.54538i
$789$	352.915			0.447294
$790$		0			0
$791$		−	1171.00i		−	1.48040i
$792$	−252.947	+	240.336i	−0.319377	+	0.303454i
$793$			1276.15i			1.60927i
$794$	156.460	−	564.629i	0.197053	−	0.711119i
$795$		0			0
$796$	181.587	−	302.495i	0.228124	−	0.380018i
$797$			321.141i			0.402937i	0.979495	+	0.201468i	$0.0645713\pi$
$797$			321.141i			0.402937i	−0.979495	+	0.201468i	$0.935429\pi$
$798$	−97.0487	+	350.227i	−0.121615	+	0.438881i
$799$			616.576i			0.771685i
$800$		0			0
$801$	−164.617			−0.205514
$802$	998.577	+	276.708i	1.24511	+	0.345022i
$803$	1447.21			1.80225
$804$	−363.003	−	217.910i	−0.451496	−	0.271032i
$805$		0			0
$806$	708.263	+	196.261i	0.878738	+	0.243500i
$807$	132.326			0.163973
$808$	−900.462	−	947.712i	−1.11443	−	1.17291i
$809$	861.938			1.06544			0.532718	−	0.846293i	$-0.321171\pi$
$809$	861.938			1.06544			0.532718	+	0.846293i	$0.321171\pi$
$810$		0			0
$811$		−	1011.44i		−	1.24715i	−0.781765	−	0.623574i	$-0.785680\pi$
$811$		−	1011.44i		−	1.24715i	0.781765	−	0.623574i	$-0.214320\pi$
$812$	112.788	+	67.7066i	0.138902	+	0.0833825i
$813$		−	293.091i		−	0.360506i
$814$	910.308	+	252.248i	1.11832	+	0.309887i
$815$		0			0
$816$	−310.351	+	165.346i	−0.380332	+	0.202630i
$817$		−	144.977i		−	0.177450i
$818$	350.750	+	97.1935i	0.428790	+	0.118818i
$819$		−	807.376i		−	0.985807i
$820$		0			0
$821$	68.0368			0.0828707			0.0414353	−	0.999141i	$-0.486807\pi$
$821$	68.0368			0.0828707			0.0414353	+	0.999141i	$0.486807\pi$
$822$	235.388	−	849.462i	0.286360	−	1.03341i
$823$	980.340			1.19118			0.595589	−	0.803289i	$-0.296919\pi$
$823$	980.340			1.19118			0.595589	+	0.803289i	$0.296919\pi$
$824$	934.517	+	983.554i	1.13412	+	1.19363i
$825$		0			0
$826$	−276.628	+	998.288i	−0.334900	+	1.20858i
$827$	−1183.88			−1.43153			−0.715766	−	0.698341i	$-0.753922\pi$
$827$	−1183.88			−1.43153			−0.715766	+	0.698341i	$0.753922\pi$
$828$	−51.4071	−	30.8596i	−0.0620859	−	0.0372701i
$829$	−98.7892			−0.119167			−0.0595833	−	0.998223i	$-0.518977\pi$
$829$	−98.7892			−0.119167			−0.0595833	+	0.998223i	$0.518977\pi$
$830$		0			0
$831$		−	474.392i		−	0.570869i
$832$	−1436.86	−	73.5167i	−1.72699	−	0.0883614i
$833$		−	1196.83i		−	1.43677i
$834$	73.0313	−	263.554i	0.0875675	−	0.316012i
$835$		0			0
$836$	−436.933	−	262.290i	−0.522647	−	0.313744i
$837$			84.9395i			0.101481i
$838$	87.2401	−	314.830i	0.104105	−	0.375692i
$839$			407.965i			0.486251i	0.969995	+	0.243125i	$0.0781727\pi$
$839$			407.965i			0.486251i	−0.969995	+	0.243125i	$0.921827\pi$
$840$		0			0
$841$	−833.453			−0.991027
$842$	−900.479	−	249.525i	−1.06945	−	0.296347i
$843$	539.832			0.640370
$844$	392.363	−	653.613i	0.464885	−	0.774423i
$845$		0			0
$846$	−280.960	−	77.8546i	−0.332104	−	0.0920267i
$847$	1081.75			1.27716
$848$	−1328.87	+	707.984i	−1.56707	+	0.834887i
$849$	−458.241			−0.539742
$850$		0			0
$851$			162.323i			0.190744i
$852$	141.436	−	235.610i	0.166005	−	0.276537i
$853$			907.020i			1.06333i	0.846955	+	0.531665i	$0.178433\pi$
$853$			907.020i			1.06333i	−0.846955	+	0.531665i	$0.821567\pi$
$854$	−1309.85	−	362.962i	−1.53378	−	0.425014i
$855$		0			0
$856$	−44.9012	−	47.2573i	−0.0524546	−	0.0552071i
$857$		−	693.549i		−	0.809275i	−0.914477	−	0.404638i	$-0.867398\pi$
$857$		−	693.549i		−	0.809275i	0.914477	−	0.404638i	$-0.132602\pi$
$858$	1091.03	+	302.328i	1.27160	+	0.352363i
$859$		−	397.401i		−	0.462632i	−0.972879	−	0.231316i	$-0.925697\pi$
$859$		−	397.401i		−	0.462632i	0.972879	−	0.231316i	$-0.0743031\pi$
$860$		0			0
$861$	886.621			1.02976
$862$	−366.126	+	1321.27i	−0.424740	+	1.53279i
$863$	−1193.06			−1.38246			−0.691229	−	0.722636i	$-0.742930\pi$
$863$	−1193.06			−1.38246			−0.691229	+	0.722636i	$0.742930\pi$
$864$	−36.1566	−	162.298i	−0.0418479	−	0.187845i
$865$		0			0
$866$	−316.590	+	1142.50i	−0.365577	+	1.31929i
$867$	−221.682			−0.255689
$868$	−402.886	+	671.142i	−0.464154	+	0.773206i
$869$	−156.693			−0.180314
$870$		0			0
$871$			1373.78i			1.57724i
$872$	139.040	+	146.336i	0.159450	+	0.167817i
$873$		−	42.4803i		−	0.0486601i
$874$	23.3854	−	84.3927i	0.0267567	−	0.0965591i
$875$		0			0
$876$	−354.962	+	591.309i	−0.405208	+	0.675010i
$877$		−	136.545i		−	0.155695i	−0.996965	−	0.0778477i	$-0.975195\pi$
$877$		−	136.545i		−	0.155695i	0.996965	−	0.0778477i	$-0.0248048\pi$
$878$	248.047	−	895.146i	0.282514	−	1.01953i
$879$		−	210.064i		−	0.238981i
$880$		0			0
$881$	−836.578			−0.949578			−0.474789	−	0.880100i	$-0.657476\pi$
$881$	−836.578			−0.949578			−0.474789	+	0.880100i	$0.657476\pi$
$882$	545.369	+	151.123i	0.618332	+	0.171341i
$883$	632.625			0.716450			0.358225	−	0.933635i	$-0.383382\pi$
$883$	632.625			0.716450			0.358225	+	0.933635i	$0.383382\pi$
$884$	978.280	+	587.260i	1.10665	+	0.664321i
$885$		0			0
$886$	104.631	+	28.9934i	0.118093	+	0.0327239i
$887$	290.957			0.328024			0.164012	−	0.986458i	$-0.447556\pi$
$887$	290.957			0.328024			0.164012	+	0.986458i	$0.447556\pi$
$888$	−326.339	+	310.069i	−0.367499	+	0.349177i
$889$	−2006.00			−2.25646
$890$		0			0
$891$			130.844i			0.146851i
$892$	271.916	+	163.231i	0.304838	+	0.182994i
$893$		−	425.822i		−	0.476844i
$894$	−107.972	−	29.9192i	−0.120774	−	0.0334667i
$895$		0			0
$896$	484.126	−	1453.88i	0.540319	−	1.62264i
$897$			194.550i			0.216889i
$898$	825.013	+	228.613i	0.918723	+	0.254580i
$899$			44.9061i			0.0499511i
$900$		0			0
$901$	1194.12			1.32533
$902$	−332.001	+	1198.12i	−0.368073	+	1.32829i
$903$	−343.038			−0.379887
$904$	−567.282	+	538.999i	−0.627524	+	0.596237i
$905$		0			0
$906$	35.8876	−	129.510i	0.0396110	−	0.142947i
$907$	473.341			0.521875			0.260938	−	0.965356i	$-0.415968\pi$
$907$	473.341			0.521875			0.260938	+	0.965356i	$0.415968\pi$
$908$	1212.83	+	728.061i	1.33572	+	0.801830i
$909$	−490.231			−0.539308
$910$		0			0
$911$			1176.67i			1.29163i	0.763495	+	0.645813i	$0.223482\pi$
$911$			1176.67i			1.29163i	−0.763495	+	0.645813i	$0.776518\pi$
$912$	214.336	−	114.192i	0.235017	−	0.125210i
$913$			2039.17i			2.23348i
$914$	−35.5615	+	128.334i	−0.0389075	+	0.140409i
$915$		0			0
$916$	78.1625	+	46.9208i	0.0853303	+	0.0512236i
$917$		−	982.230i		−	1.07113i
$918$	−35.2140	+	127.080i	−0.0383595	+	0.138431i
$919$			1491.24i			1.62267i	0.584580	+	0.811336i	$0.301259\pi$
$919$			1491.24i			1.62267i	−0.584580	+	0.811336i	$0.698741\pi$
$920$		0			0
$921$	−280.190			−0.304224
$922$	−459.921	−	127.445i	−0.498830	−	0.138227i
$923$	−891.663			−0.966048
$924$	−620.620	+	1033.85i	−0.671667	+	1.11889i
$925$		0			0
$926$	−745.812	−	206.666i	−0.805412	−	0.223181i
$927$	508.772			0.548837
$928$	−19.1154	−	85.8043i	−0.0205984	−	0.0924615i
$929$	1217.24			1.31027			0.655134	−	0.755513i	$-0.272612\pi$
$929$	1217.24			1.31027			0.655134	+	0.755513i	$0.272612\pi$
$930$		0			0
$931$			826.560i			0.887819i
$932$	390.562	−	650.613i	0.419058	−	0.698083i
$933$			45.6938i			0.0489751i
$934$	−454.790	−	126.023i	−0.486927	−	0.134928i
$935$		0			0
$936$	−391.128	+	371.628i	−0.417872	+	0.397038i
$937$		−	468.840i		−	0.500363i	−0.968199	−	0.250182i	$-0.919510\pi$
$937$		−	468.840i		−	0.500363i	0.968199	−	0.250182i	$-0.0804903\pi$
$938$	−1410.05	−	390.728i	−1.50325	−	0.416555i
$939$		−	9.35138i		−	0.00995887i
$940$		0			0
$941$	358.033			0.380481			0.190241	−	0.981737i	$-0.439073\pi$
$941$	358.033			0.380481			0.190241	+	0.981737i	$0.439073\pi$
$942$	−40.8892	+	147.560i	−0.0434068	+	0.156645i
$943$	−213.645			−0.226559
$944$	610.943	−	325.492i	0.647185	−	0.344801i
$945$		0			0
$946$	128.453	−	463.559i	0.135785	−	0.490020i
$947$	−1148.77			−1.21306			−0.606532	−	0.795059i	$-0.707440\pi$
$947$	−1148.77			−1.21306			−0.606532	+	0.795059i	$0.707440\pi$
$948$	38.4325	−	64.0223i	0.0405406	−	0.0675341i
$949$	2237.80			2.35806
$950$		0			0
$951$			467.926i			0.492036i
$952$	−881.006	+	837.082i	−0.925427	+	0.879288i
$953$		−	911.785i		−	0.956753i	−0.878155	−	0.478376i	$-0.841226\pi$
$953$		−	911.785i		−	0.956753i	0.878155	−	0.478376i	$-0.158774\pi$
$954$	−150.781	+	544.135i	−0.158051	+	0.570372i
$955$		0			0
$956$	551.283	−	918.348i	0.576656	−	0.960615i
$957$			69.1750i			0.0722831i
$958$	282.792	−	1020.54i	0.295190	−	1.06528i
$959$		−	3046.29i		−	3.17653i
$960$		0			0
$961$	693.788			0.721944
$962$	1407.60	+	390.048i	1.46320	+	0.405455i
$963$	−24.4452			−0.0253844
$964$	−1034.56	−	621.045i	−1.07320	−	0.644237i
$965$		0			0
$966$	−199.686	−	55.3335i	−0.206715	−	0.0572811i
$967$	−311.565			−0.322197			−0.161099	−	0.986938i	$-0.551504\pi$
$967$	−311.565			−0.322197			−0.161099	+	0.986938i	$0.551504\pi$
$968$	−497.921	−	524.048i	−0.514381	−	0.541372i
$969$	−192.602			−0.198763
$970$		0			0
$971$		−	370.530i		−	0.381596i	−0.981629	−	0.190798i	$-0.938892\pi$
$971$		−	370.530i		−	0.381596i	0.981629	−	0.190798i	$-0.0611075\pi$
$972$	−53.4609	−	32.0925i	−0.0550010	−	0.0330170i
$973$		−	945.141i		−	0.971368i
$974$	−1697.63	−	470.417i	−1.74295	−	0.482974i
$975$		0			0
$976$	427.077	+	801.615i	0.437578	+	0.821327i
$977$			1402.53i			1.43555i	0.696278	+	0.717773i	$0.254838\pi$
$977$			1402.53i			1.43555i	−0.696278	+	0.717773i	$0.745162\pi$
$978$	−176.718	−	48.9690i	−0.180694	−	0.0500706i
$979$		−	797.746i		−	0.814858i
$980$		0			0
$981$	75.6966			0.0771626
$982$	−46.1693	+	166.615i	−0.0470156	+	0.169669i
$983$	−988.944			−1.00605			−0.503023	−	0.864273i	$-0.667779\pi$
$983$	−988.944			−1.00605			−0.503023	+	0.864273i	$0.667779\pi$
$984$	−408.103	−	429.518i	−0.414739	−	0.436502i
$985$		0			0
$986$	−18.6171	+	67.1849i	−0.0188814	+	0.0681388i
$987$	−1007.56			−1.02083
$988$	−675.624	−	405.576i	−0.683830	−	0.410502i
$989$	82.6603			0.0835797
$990$		0			0
$991$			90.1483i			0.0909670i	0.998965	+	0.0454835i	$0.0144828\pi$
$991$			90.1483i			0.0909670i	−0.998965	+	0.0454835i	$0.985517\pi$
$992$	510.575	−	113.745i	0.514693	−	0.114663i
$993$			832.644i			0.838514i
$994$	253.605	−	915.205i	0.255136	−	0.920729i
$995$		0			0
$996$	−833.174	−	500.153i	−0.836520	−	0.502162i
$997$		−	655.605i		−	0.657578i	−0.944403	−	0.328789i	$-0.893360\pi$
$997$		−	655.605i		−	0.657578i	0.944403	−	0.328789i	$-0.106640\pi$
$998$	467.071	−	1685.56i	0.468007	−	1.68893i
$999$			168.808i			0.168977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.f.c.199.14		16
3.2	odd	2		900.3.f.h.199.3		16
4.3	odd	2	inner	300.3.f.c.199.4		16
5.2	odd	4		300.3.c.e.151.4	yes	8
5.3	odd	4		300.3.c.g.151.5	yes	8
5.4	even	2	inner	300.3.f.c.199.3		16
12.11	even	2		900.3.f.h.199.13		16
15.2	even	4		900.3.c.t.451.5		8
15.8	even	4		900.3.c.n.451.4		8
15.14	odd	2		900.3.f.h.199.14		16
20.3	even	4		300.3.c.g.151.6	yes	8
20.7	even	4		300.3.c.e.151.3	✓	8
20.19	odd	2	inner	300.3.f.c.199.13		16
60.23	odd	4		900.3.c.n.451.3		8
60.47	odd	4		900.3.c.t.451.6		8
60.59	even	2		900.3.f.h.199.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.3	✓	8	20.7	even	4
300.3.c.e.151.4	yes	8	5.2	odd	4
300.3.c.g.151.5	yes	8	5.3	odd	4
300.3.c.g.151.6	yes	8	20.3	even	4
300.3.f.c.199.3		16	5.4	even	2	inner
300.3.f.c.199.4		16	4.3	odd	2	inner
300.3.f.c.199.13		16	20.19	odd	2	inner
300.3.f.c.199.14		16	1.1	even	1	trivial
900.3.c.n.451.3		8	60.23	odd	4
900.3.c.n.451.4		8	15.8	even	4
900.3.c.t.451.5		8	15.2	even	4
900.3.c.t.451.6		8	60.47	odd	4
900.3.f.h.199.3		16	3.2	odd	2
900.3.f.h.199.4		16	60.59	even	2
900.3.f.h.199.13		16	12.11	even	2
900.3.f.h.199.14		16	15.14	odd	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)

\(f(q)\)	\(=\)	\(q+(1.92737 + 0.534079i) q^{2} -1.73205 q^{3} +(3.42952 + 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716 q^{7} +(5.51043 + 5.79958i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.92737 + 0.534079i) q^{2} -1.73205 q^{3} +(3.42952 + 2.05874i) q^{4} +(-3.33830 - 0.925051i) q^{6} -11.9716 q^{7} +(5.51043 + 5.79958i) q^{8} +3.00000 q^{9} +14.5382i q^{11} +(-5.94010 - 3.56583i) q^{12} +22.4802i q^{13} +(-23.0738 - 6.39379i) q^{14} +(7.52322 + 14.1209i) q^{16} -12.6890i q^{17} +(5.78211 + 1.60224i) q^{18} +8.76336i q^{19} +20.7355 q^{21} +(-7.76455 + 28.0205i) q^{22} -4.99653 q^{23} +(-9.54435 - 10.0452i) q^{24} +(-12.0062 + 43.3278i) q^{26} -5.19615 q^{27} +(-41.0570 - 24.6464i) q^{28} -2.74712 q^{29} -16.3466i q^{31} +(6.95833 + 31.2343i) q^{32} -25.1809i q^{33} +(6.77695 - 24.4565i) q^{34} +(10.2886 + 6.17621i) q^{36} -32.4872i q^{37} +(-4.68032 + 16.8902i) q^{38} -38.9369i q^{39} +42.7586 q^{41} +(39.9650 + 11.0744i) q^{42} -16.5435 q^{43} +(-29.9303 + 49.8591i) q^{44} +(-9.63018 - 2.66854i) q^{46} -48.5912 q^{47} +(-13.0306 - 24.4582i) q^{48} +94.3200 q^{49} +21.9781i q^{51} +(-46.2809 + 77.0964i) q^{52} +94.1066i q^{53} +(-10.0149 - 2.77515i) q^{54} +(-65.9689 - 69.4305i) q^{56} -15.1786i q^{57} +(-5.29471 - 1.46718i) q^{58} -43.2650i q^{59} +56.7678 q^{61} +(8.73038 - 31.5060i) q^{62} -35.9149 q^{63} +(-3.27028 + 63.9164i) q^{64} +(13.4486 - 48.5330i) q^{66} +61.1106 q^{67} +(26.1234 - 43.5173i) q^{68} +8.65425 q^{69} +39.6643i q^{71} +(16.5313 + 17.3987i) q^{72} -99.5452i q^{73} +(17.3507 - 62.6149i) q^{74} +(-18.0414 + 30.0541i) q^{76} -174.046i q^{77} +(20.7954 - 75.0459i) q^{78} +10.7780i q^{79} +9.00000 q^{81} +(82.4118 + 22.8365i) q^{82} +140.263 q^{83} +(71.1127 + 42.6889i) q^{84} +(-31.8855 - 8.83554i) q^{86} +4.75815 q^{87} +(-84.3156 + 80.1118i) q^{88} -54.8723 q^{89} -269.125i q^{91} +(-17.1357 - 10.2865i) q^{92} +28.3132i q^{93} +(-93.6533 - 25.9515i) q^{94} +(-12.0522 - 54.0994i) q^{96} -14.1601i q^{97} +(181.790 + 50.3743i) q^{98} +43.6146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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