LMFDB - Embedded newform 300.3.f.c.199.4

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			199.4
Root			$1.21868 + 0.717516i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.3

$q$-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	$-0.173485\pi$
$7$	11.9716			1.71023			0.855117	+	0.518436i	$0.173485\pi$
$8$	−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	$-0.770205\pi$
$11$		−	14.5382i		−	1.32166i	0.750537	−	0.660828i	$-0.229795\pi$
$12$	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	$-0.925926\pi$
$19$		−	8.76336i		−	0.461229i	0.973045	−	0.230615i	$-0.0740737\pi$
$20$		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	$-0.465357\pi$
$23$	4.99653			0.217241			0.108620	+	0.994083i	$0.465357\pi$
$24$	−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	$0.0849281\pi$
$31$			16.3466i			0.527310i	−0.964617	+	0.263655i	$0.915072\pi$
$32$	−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	$-0.438384\pi$
$43$	16.5435			0.384733			0.192367	+	0.981323i	$0.438384\pi$
$44$	−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	$-0.327076\pi$
$47$	48.5912			1.03386			0.516928	+	0.856029i	$0.327076\pi$
$48$	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	$0.119496\pi$
$59$			43.2650i			0.733305i	−0.930358	+	0.366653i	$0.880504\pi$
$60$		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	$-0.650736\pi$
$67$	−61.1106			−0.912098			−0.456049	+	0.889955i	$0.650736\pi$
$68$	−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	$-0.909889\pi$
$71$		−	39.6643i		−	0.558652i	0.960196	−	0.279326i	$-0.0901110\pi$
$72$	−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	$-0.978270\pi$
$79$		−	10.7780i		−	0.136430i	0.997671	−	0.0682151i	$-0.0217304\pi$
$80$		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	$-0.820373\pi$
$83$	−140.263			−1.68991			−0.844955	+	0.534837i	$0.820373\pi$
$84$	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	$-0.807844\pi$
$103$	−169.591			−1.64651			−0.823255	+	0.567672i	$0.807844\pi$
$104$	−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	$-0.487877\pi$
$107$	8.14840			0.0761532			0.0380766	+	0.999275i	$0.487877\pi$
$108$	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	$-0.729315\pi$
$127$	−167.563			−1.31939			−0.659695	+	0.751533i	$0.729315\pi$
$128$	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	$-0.898614\pi$
$131$		−	82.0465i		−	0.626309i	0.949702	−	0.313155i	$-0.101386\pi$
$132$	−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	$-0.908343\pi$
$139$		−	78.9483i		−	0.567974i	0.958828	−	0.283987i	$-0.0916572\pi$
$140$		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	$-0.958996\pi$
$151$		−	38.7953i		−	0.256922i	0.991715	−	0.128461i	$-0.0410038\pi$
$152$	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	$-0.551918\pi$
$163$	−52.9366			−0.324764			−0.162382	+	0.986728i	$0.551918\pi$
$164$	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	$-0.319654\pi$
$167$	179.273			1.07349			0.536745	+	0.843744i	$0.319654\pi$
$168$	−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	$0.0927532\pi$
$179$			102.849i			0.574573i	−0.957845	+	0.287286i	$0.907247\pi$
$180$		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	$-0.833040\pi$
$191$		−	191.305i		−	1.00160i	0.865563	−	0.500799i	$-0.166960\pi$
$192$	−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	$0.0711332\pi$
$199$			88.2032i			0.443232i	−0.975134	+	0.221616i	$0.928867\pi$
$200$		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	$0.149154\pi$
$211$			190.584i			0.903243i	−0.892210	+	0.451622i	$0.850846\pi$
$212$	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	$-0.556889\pi$
$223$	−79.2869			−0.355547			−0.177773	+	0.984071i	$0.556889\pi$
$224$	−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	$-0.784249\pi$
$227$	−353.645			−1.55791			−0.778953	+	0.627082i	$0.784249\pi$
$228$	−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	$0.189277\pi$
$239$			267.778i			1.12041i	−0.828355	+	0.560204i	$0.810723\pi$
$240$		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	$-0.959826\pi$
$251$		−	63.1891i		−	0.251749i	0.992046	−	0.125875i	$-0.0401737\pi$
$252$	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	$-0.373384\pi$
$263$	203.755			0.774735			0.387368	+	0.921925i	$0.373384\pi$
$264$	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	$-0.898932\pi$
$271$		−	169.216i		−	0.624414i	0.950014	−	0.312207i	$-0.101068\pi$
$272$	−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	$-0.654820\pi$
$283$	−264.566			−0.934861			−0.467431	+	0.884030i	$0.654820\pi$
$284$	−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	$-0.584866\pi$
$307$	−161.768			−0.526932			−0.263466	+	0.964669i	$0.584866\pi$
$308$	−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	$0.0135047\pi$
$311$			26.3813i			0.0848273i	−0.999100	+	0.0424137i	$0.986495\pi$
$312$	−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	$0.258704\pi$
$331$			480.728i			1.45235i	−0.687510	+	0.726174i	$0.741296\pi$
$332$	−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	$-0.679088\pi$
$347$	−370.184			−1.06681			−0.533406	+	0.845859i	$0.679088\pi$
$348$	−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	$-0.808747\pi$
$359$		−	405.910i		−	1.13067i	0.824862	−	0.565334i	$-0.191253\pi$
$360$		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	$-0.520064\pi$
$367$	−46.2347			−0.125980			−0.0629900	+	0.998014i	$0.520064\pi$
$368$	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	$-0.891002\pi$
$379$		−	254.516i		−	0.671546i	0.941943	−	0.335773i	$-0.108998\pi$
$380$		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	$-0.526093\pi$
$383$	−62.7205			−0.163761			−0.0818805	+	0.996642i	$0.526093\pi$
$384$	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	$0.0624462\pi$
$419$			163.347i			0.389849i	−0.980818	+	0.194925i	$0.937554\pi$
$420$		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	$-0.707326\pi$
$431$		−	685.527i		−	1.59055i	0.606248	−	0.795275i	$-0.292674\pi$
$432$	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	$0.177423\pi$
$439$			464.439i			1.05795i	−0.848638	+	0.528974i	$0.822577\pi$
$440$		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	$-0.519516\pi$
$443$	−54.2868			−0.122544			−0.0612718	+	0.998121i	$0.519516\pi$
$444$	−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	$-0.362773\pi$
$463$	386.958			0.835762			0.417881	+	0.908502i	$0.362773\pi$
$464$	−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	$-0.418702\pi$
$467$	235.964			0.505276			0.252638	+	0.967561i	$0.418702\pi$
$468$	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	$0.186406\pi$
$479$			529.496i			1.10542i	−0.833374	+	0.552710i	$0.813594\pi$
$480$		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	$-0.140383\pi$
$487$	880.801			1.80863			0.904314	+	0.426869i	$0.140383\pi$
$488$	−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	$-0.971942\pi$
$491$		−	86.4466i		−	0.176062i	0.996118	−	0.0880312i	$-0.0280575\pi$
$492$	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	$0.339988\pi$
$499$			874.536i			1.75258i	−0.481786	+	0.876289i	$0.660012\pi$
$500$		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	$-0.494447\pi$
$503$	17.5479			0.0348865			0.0174433	+	0.999848i	$0.494447\pi$
$504$	−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	$-0.649436\pi$
$523$	−473.223			−0.904823			−0.452412	+	0.891809i	$0.649436\pi$
$524$	−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	$-0.844910\pi$
$547$	−966.695			−1.76727			−0.883634	+	0.468179i	$0.844910\pi$
$548$	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	$-0.700644\pi$
$563$	−663.688			−1.17884			−0.589421	+	0.807826i	$0.700644\pi$
$564$	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	$-0.947953\pi$
$571$		−	185.898i		−	0.325565i	0.986662	−	0.162782i	$-0.0520469\pi$
$572$	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	$-0.274775\pi$
$587$	763.083			1.29997			0.649986	+	0.759946i	$0.274775\pi$
$588$	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	$0.168249\pi$
$599$			604.151i			1.00860i	−0.863529	+	0.504300i	$0.831751\pi$
$600$		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	$-0.486322\pi$
$607$	52.1487			0.0859121			0.0429561	+	0.999077i	$0.486322\pi$
$608$	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	$-0.950809\pi$
$619$		−	190.559i		−	0.307849i	0.988083	−	0.153925i	$-0.0491913\pi$
$620$		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	$-0.848519\pi$
$631$		−	578.160i		−	0.916261i	0.888885	−	0.458130i	$-0.151481\pi$
$632$	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	$-0.197769\pi$
$643$	1045.67			1.62623			0.813117	+	0.582100i	$0.197769\pi$
$644$	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	$-0.500667\pi$
$647$	−2.71164			−0.00419110			−0.00209555	+	0.999998i	$0.500667\pi$
$648$	−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	$-0.819396\pi$
$659$		−	708.330i		−	1.07486i	0.843309	−	0.537428i	$-0.180604\pi$
$660$		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	$-0.193768\pi$
$683$	1120.62			1.64074			0.820368	+	0.571835i	$0.193768\pi$
$684$	−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	$-0.922987\pi$
$691$		−	331.115i		−	0.479182i	0.970874	−	0.239591i	$-0.0770134\pi$
$692$	−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	$0.0166164\pi$
$719$			75.0325i			0.104357i	−0.998638	+	0.0521784i	$0.983384\pi$
$720$		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	$-0.179343\pi$
$727$	1229.26			1.69087			0.845433	+	0.534082i	$0.179343\pi$
$728$	−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	$0.0153898\pi$
$739$			71.4311i			0.0966591i	−0.998831	+	0.0483296i	$0.984610\pi$
$740$		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	$-0.736982\pi$
$743$	−1006.92			−1.35521			−0.677605	+	0.735426i	$0.736982\pi$
$744$	−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	$0.264753\pi$
$751$			1110.14i			1.47822i	−0.673587	+	0.739108i	$0.735247\pi$
$752$	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	$-0.422978\pi$
$787$	377.158			0.479235			0.239617	+	0.970867i	$0.422978\pi$
$788$	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	$0.214320\pi$
$811$			1011.44i			1.24715i	−0.781765	+	0.623574i	$0.785680\pi$
$812$	−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	$-0.703081\pi$
$823$	−980.340			−1.19118			−0.595589	+	0.803289i	$0.703081\pi$
$824$	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	$-0.246078\pi$
$827$	1183.88			1.43153			0.715766	+	0.698341i	$0.246078\pi$
$828$	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	$-0.921827\pi$
$839$		−	407.965i		−	0.486251i	0.969995	−	0.243125i	$-0.0781727\pi$
$840$		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	$0.0743031\pi$
$859$			397.401i			0.462632i	−0.972879	+	0.231316i	$0.925697\pi$
$860$		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	$-0.257070\pi$
$863$	1193.06			1.38246			0.691229	+	0.722636i	$0.257070\pi$
$864$	−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	$-0.616618\pi$
$883$	−632.625			−0.716450			−0.358225	+	0.933635i	$0.616618\pi$
$884$	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	$-0.552444\pi$
$887$	−290.957			−0.328024			−0.164012	+	0.986458i	$0.552444\pi$
$888$	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	$-0.584032\pi$
$907$	−473.341			−0.521875			−0.260938	+	0.965356i	$0.584032\pi$
$908$	−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	$-0.776518\pi$
$911$		−	1176.67i		−	1.29163i	0.763495	−	0.645813i	$-0.223482\pi$
$912$	−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	$-0.698741\pi$
$919$		−	1491.24i		−	1.62267i	0.584580	−	0.811336i	$-0.301259\pi$
$920$		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	$-0.292560\pi$
$947$	1148.77			1.21306			0.606532	+	0.795059i	$0.292560\pi$
$948$	−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	$-0.448496\pi$
$967$	311.565			0.322197			0.161099	+	0.986938i	$0.448496\pi$
$968$	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	$0.0611075\pi$
$971$			370.530i			0.381596i	−0.981629	+	0.190798i	$0.938892\pi$
$972$	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	$-0.332221\pi$
$983$	988.944			1.00605			0.503023	+	0.864273i	$0.332221\pi$
$984$	−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	$-0.985517\pi$
$991$		−	90.1483i		−	0.0909670i	0.998965	−	0.0454835i	$-0.0144828\pi$
$992$	−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.199.4		16
3.2	odd	2		900.3.f.h.199.13		16
4.3	odd	2	inner	300.3.f.c.199.14		16
5.2	odd	4		300.3.c.e.151.3	✓	8
5.3	odd	4		300.3.c.g.151.6	yes	8
5.4	even	2	inner	300.3.f.c.199.13		16
12.11	even	2		900.3.f.h.199.3		16
15.2	even	4		900.3.c.t.451.6		8
15.8	even	4		900.3.c.n.451.3		8
15.14	odd	2		900.3.f.h.199.4		16
20.3	even	4		300.3.c.g.151.5	yes	8
20.7	even	4		300.3.c.e.151.4	yes	8
20.19	odd	2	inner	300.3.f.c.199.3		16
60.23	odd	4		900.3.c.n.451.4		8
60.47	odd	4		900.3.c.t.451.5		8
60.59	even	2		900.3.f.h.199.14		16

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

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