LMFDB - Embedded newform 300.3.c.e.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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, 0]))

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.4069419264.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 $ x^8 - 7x^6 + 50x^4 - 84x^3 + 55x^2 - 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.5
Root			$0.845613 + 0.488215i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.e.151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.177680 - 1.99209i) q^{2} +1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501i q^{7} +(-2.10973 + 7.71680i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.177680 - 1.99209i) q^{2} +1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501i q^{7} +(-2.10973 + 7.71680i) q^{8} -3.00000 q^{9} +8.22072i q^{11} +(1.22614 - 6.81884i) q^{12} -11.1863 q^{13} +(-2.38058 - 0.212331i) q^{14} +(14.9977 + 5.57389i) q^{16} -20.9256 q^{17} +(-0.533041 + 5.97628i) q^{18} +27.9657i q^{19} +2.06983 q^{21} +(16.3764 + 1.46066i) q^{22} +9.48564i q^{23} +(-13.3659 - 3.65415i) q^{24} +(-1.98759 + 22.2842i) q^{26} -5.19615i q^{27} +(-0.845964 + 4.70460i) q^{28} +40.4205 q^{29} +55.3130i q^{31} +(13.7685 - 28.8865i) q^{32} -14.2387 q^{33} +(-3.71807 + 41.6858i) q^{34} +(11.8106 + 2.12373i) q^{36} -50.1890 q^{37} +(55.7102 + 4.96895i) q^{38} -19.3753i q^{39} -73.6361 q^{41} +(0.367767 - 4.12328i) q^{42} +19.0843i q^{43} +(5.81954 - 32.3638i) q^{44} +(18.8963 + 1.68541i) q^{46} -18.0598i q^{47} +(-9.65427 + 25.9768i) q^{48} +47.5719 q^{49} -36.2442i q^{51} +(44.0391 + 7.91894i) q^{52} +57.2212 q^{53} +(-10.3512 - 0.923254i) q^{54} +(9.22169 + 2.52115i) q^{56} -48.4380 q^{57} +(7.18193 - 80.5213i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(110.189 + 9.82804i) q^{62} +3.58504i q^{63} +(-55.0981 - 32.5607i) q^{64} +(-2.52994 + 28.3648i) q^{66} -9.68679i q^{67} +(82.3812 + 14.8135i) q^{68} -16.4296 q^{69} -68.6944i q^{71} +(6.32918 - 23.1504i) q^{72} -84.7825 q^{73} +(-8.91760 + 99.9811i) q^{74} +(19.7972 - 110.097i) q^{76} +9.82388 q^{77} +(-38.5974 - 3.44261i) q^{78} +23.2903i q^{79} +9.00000 q^{81} +(-13.0837 + 146.690i) q^{82} -93.2595i q^{83} +(-8.14861 - 1.46525i) q^{84} +(38.0177 + 3.39091i) q^{86} +70.0104i q^{87} +(-63.4377 - 17.3435i) q^{88} +62.9898 q^{89} +13.3678i q^{91} +(6.71499 - 37.3436i) q^{92} -95.8049 q^{93} +(-35.9767 - 3.20887i) q^{94} +(50.0328 + 23.8478i) q^{96} -91.3962 q^{97} +(8.45260 - 94.7677i) q^{98} -24.6622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	$ 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} - 8 q^{13} + 22 q^{14} + 40 q^{16} + 6 q^{18} + 24 q^{21} - 4 q^{22} - 36 q^{24} - 66 q^{26} - 104 q^{28} - 32 q^{29} - 112 q^{32} + 124 q^{34} + 24 q^{36} + 176 q^{37} + 170 q^{38} - 16 q^{41} - 54 q^{42} + 40 q^{44} - 76 q^{46} - 24 q^{48} + 16 q^{49} - 56 q^{52} + 304 q^{53} + 18 q^{54} - 172 q^{56} - 72 q^{57} + 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 108 q^{66} - 88 q^{68} - 96 q^{69} + 60 q^{72} - 240 q^{73} - 108 q^{74} + 120 q^{76} + 384 q^{77} - 150 q^{78} + 72 q^{81} - 320 q^{82} - 144 q^{84} + 214 q^{86} + 200 q^{88} + 128 q^{89} - 312 q^{92} - 72 q^{93} + 12 q^{94} + 96 q^{96} - 216 q^{97} - 60 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 - 8 * q^13 + 22 * q^14 + 40 * q^16 + 6 * q^18 + 24 * q^21 - 4 * q^22 - 36 * q^24 - 66 * q^26 - 104 * q^28 - 32 * q^29 - 112 * q^32 + 124 * q^34 + 24 * q^36 + 176 * q^37 + 170 * q^38 - 16 * q^41 - 54 * q^42 + 40 * q^44 - 76 * q^46 - 24 * q^48 + 16 * q^49 - 56 * q^52 + 304 * q^53 + 18 * q^54 - 172 * q^56 - 72 * q^57 + 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 108 * q^66 - 88 * q^68 - 96 * q^69 + 60 * q^72 - 240 * q^73 - 108 * q^74 + 120 * q^76 + 384 * q^77 - 150 * q^78 + 72 * q^81 - 320 * q^82 - 144 * q^84 + 214 * q^86 + 200 * q^88 + 128 * q^89 - 312 * q^92 - 72 * q^93 + 12 * q^94 + 96 * q^96 - 216 * q^97 - 60 * q^98

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 $

$2$	0.177680	−	1.99209i	0.0888402	−	0.996046i
$2$	0.177680	−	1.99209i	0.0888402	−	0.996046i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.93686	−	0.707911i	−0.984215	−	0.176978i
$5$		0			0
$5$		0			0
$6$	3.45040	+	0.307751i	0.575067	+	0.0512919i
$7$		−	1.19501i		−	0.170716i	−0.996350	−	0.0853582i	$-0.972797\pi$
$7$		−	1.19501i		−	0.170716i	0.996350	−	0.0853582i	$-0.0272035\pi$
$8$	−2.10973	+	7.71680i	−0.263716	+	0.964600i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			8.22072i			0.747338i	0.927562	+	0.373669i	$0.121900\pi$
$11$			8.22072i			0.747338i	−0.927562	+	0.373669i	$0.878100\pi$
$12$	1.22614	−	6.81884i	0.102178	−	0.568237i
$13$	−11.1863			−0.860488			−0.430244	−	0.902713i	$-0.641572\pi$
$13$	−11.1863			−0.860488			−0.430244	+	0.902713i	$0.641572\pi$
$14$	−2.38058	−	0.212331i	−0.170041	−	0.0151665i
$15$		0			0
$16$	14.9977	+	5.57389i	0.937358	+	0.348368i
$17$	−20.9256			−1.23092			−0.615459	−	0.788169i	$-0.711030\pi$
$17$	−20.9256			−1.23092			−0.615459	+	0.788169i	$0.711030\pi$
$18$	−0.533041	+	5.97628i	−0.0296134	+	0.332015i
$19$			27.9657i			1.47188i	0.677048	+	0.735939i	$0.263259\pi$
$19$			27.9657i			1.47188i	−0.677048	+	0.735939i	$0.736741\pi$
$20$		0			0
$21$	2.06983			0.0985631
$22$	16.3764	+	1.46066i	0.744383	+	0.0663937i
$23$			9.48564i			0.412419i	0.978508	+	0.206209i	$0.0661128\pi$
$23$			9.48564i			0.412419i	−0.978508	+	0.206209i	$0.933887\pi$
$24$	−13.3659	−	3.65415i	−0.556912	−	0.152256i
$25$		0			0
$26$	−1.98759	+	22.2842i	−0.0764459	+	0.857085i
$27$		−	5.19615i		−	0.192450i
$28$	−0.845964	+	4.70460i	−0.0302130	+	0.168022i
$29$	40.4205			1.39381			0.696905	−	0.717163i	$-0.254560\pi$
$29$	40.4205			1.39381			0.696905	+	0.717163i	$0.254560\pi$
$30$		0			0
$31$			55.3130i			1.78429i	0.451748	+	0.892145i	$0.350800\pi$
$31$			55.3130i			1.78429i	−0.451748	+	0.892145i	$0.649200\pi$
$32$	13.7685	−	28.8865i	0.430266	−	0.902702i
$33$	−14.2387			−0.431476
$34$	−3.71807	+	41.6858i	−0.109355	+	1.22605i
$35$		0			0
$36$	11.8106	+	2.12373i	0.328072	+	0.0589926i
$37$	−50.1890			−1.35646			−0.678230	−	0.734850i	$-0.737253\pi$
$37$	−50.1890			−1.35646			−0.678230	+	0.734850i	$0.737253\pi$
$38$	55.7102	+	4.96895i	1.46606	+	0.130762i
$39$		−	19.3753i		−	0.496803i
$40$		0			0
$41$	−73.6361			−1.79600			−0.898001	−	0.439994i	$-0.854981\pi$
$41$	−73.6361			−1.79600			−0.898001	+	0.439994i	$0.854981\pi$
$42$	0.367767	−	4.12328i	0.00875637	−	0.0981734i
$43$			19.0843i			0.443822i	0.975067	+	0.221911i	$0.0712294\pi$
$43$			19.0843i			0.443822i	−0.975067	+	0.221911i	$0.928771\pi$
$44$	5.81954	−	32.3638i	0.132262	−	0.735541i
$45$		0			0
$46$	18.8963	+	1.68541i	0.410788	+	0.0366394i
$47$		−	18.0598i		−	0.384251i	−0.981370	−	0.192125i	$-0.938462\pi$
$47$		−	18.0598i		−	0.384251i	0.981370	−	0.192125i	$-0.0615380\pi$
$48$	−9.65427	+	25.9768i	−0.201131	+	0.541184i
$49$	47.5719			0.970856
$50$		0			0
$51$		−	36.2442i		−	0.710671i
$52$	44.0391	+	7.91894i	0.846905	+	0.152287i
$53$	57.2212			1.07965			0.539823	−	0.841779i	$-0.318491\pi$
$53$	57.2212			1.07965			0.539823	+	0.841779i	$0.318491\pi$
$54$	−10.3512	−	0.923254i	−0.191689	−	0.0170973i
$55$		0			0
$56$	9.22169	+	2.52115i	0.164673	+	0.0450206i
$57$	−48.4380			−0.849789
$58$	7.18193	−	80.5213i	0.123826	−	1.38830i
$59$		−	60.6645i		−	1.02821i	−0.857727	−	0.514106i	$-0.828124\pi$
$59$		−	60.6645i		−	1.02821i	0.857727	−	0.514106i	$-0.171876\pi$
$60$		0			0
$61$	−21.3518			−0.350030			−0.175015	−	0.984566i	$-0.555997\pi$
$61$	−21.3518			−0.350030			−0.175015	+	0.984566i	$0.555997\pi$
$62$	110.189	+	9.82804i	1.77724	+	0.158517i
$63$			3.58504i			0.0569054i
$64$	−55.0981	−	32.5607i	−0.860908	−	0.508761i
$65$		0			0
$66$	−2.52994	+	28.3648i	−0.0383324	+	0.429770i
$67$		−	9.68679i		−	0.144579i	−0.997384	−	0.0722895i	$-0.976969\pi$
$67$		−	9.68679i		−	0.144579i	0.997384	−	0.0722895i	$-0.0230305\pi$
$68$	82.3812	+	14.8135i	1.21149	+	0.217845i
$69$	−16.4296			−0.238110
$70$		0			0
$71$		−	68.6944i		−	0.967527i	−0.875199	−	0.483763i	$-0.839270\pi$
$71$		−	68.6944i		−	0.967527i	0.875199	−	0.483763i	$-0.160730\pi$
$72$	6.32918	−	23.1504i	0.0879053	−	0.321533i
$73$	−84.7825			−1.16140			−0.580702	−	0.814116i	$-0.697222\pi$
$73$	−84.7825			−1.16140			−0.580702	+	0.814116i	$0.697222\pi$
$74$	−8.91760	+	99.9811i	−0.120508	+	1.35110i
$75$		0			0
$76$	19.7972	−	110.097i	0.260490	−	1.44864i
$77$	9.82388			0.127583
$78$	−38.5974	−	3.44261i	−0.494839	−	0.0441361i
$79$			23.2903i			0.294814i	0.989076	+	0.147407i	$0.0470928\pi$
$79$			23.2903i			0.294814i	−0.989076	+	0.147407i	$0.952907\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−13.0837	+	146.690i	−0.159557	+	1.78890i
$83$		−	93.2595i		−	1.12361i	−0.827270	−	0.561804i	$-0.810107\pi$
$83$		−	93.2595i		−	1.12361i	0.827270	−	0.561804i	$-0.189893\pi$
$84$	−8.14861	−	1.46525i	−0.0970073	−	0.0174435i
$85$		0			0
$86$	38.0177	+	3.39091i	0.442067	+	0.0394292i
$87$			70.0104i			0.804717i
$88$	−63.4377	−	17.3435i	−0.720883	−	0.197085i
$89$	62.9898			0.707750			0.353875	−	0.935293i	$-0.384864\pi$
$89$	62.9898			0.707750			0.353875	+	0.935293i	$0.384864\pi$
$90$		0			0
$91$			13.3678i			0.146899i
$92$	6.71499	−	37.3436i	0.0729890	−	0.405909i
$93$	−95.8049			−1.03016
$94$	−35.9767	−	3.20887i	−0.382731	−	0.0341369i
$95$		0			0
$96$	50.0328	+	23.8478i	0.521175	+	0.248414i
$97$	−91.3962			−0.942229			−0.471115	−	0.882072i	$-0.656148\pi$
$97$	−91.3962			−0.942229			−0.471115	+	0.882072i	$0.656148\pi$
$98$	8.45260	−	94.7677i	0.0862510	−	0.967017i
$99$		−	24.6622i		−	0.249113i
$100$		0			0
$101$	−29.9780			−0.296811			−0.148406	−	0.988927i	$-0.547414\pi$
$101$	−29.9780			−0.296811			−0.148406	+	0.988927i	$0.547414\pi$
$102$	−72.2019	−	6.43989i	−0.707861	−	0.0631362i
$103$			88.7485i			0.861636i	0.902439	+	0.430818i	$0.141775\pi$
$103$			88.7485i			0.861636i	−0.902439	+	0.430818i	$0.858225\pi$
$104$	23.6001	−	86.3228i	0.226924	−	0.830027i
$105$		0			0
$106$	10.1671	−	113.990i	0.0959159	−	1.07538i
$107$			162.922i			1.52263i	0.648381	+	0.761316i	$0.275447\pi$
$107$			162.922i			1.52263i	−0.648381	+	0.761316i	$0.724553\pi$
$108$	−3.67841	+	20.4565i	−0.0340594	+	0.189412i
$109$	−103.352			−0.948182			−0.474091	−	0.880476i	$-0.657223\pi$
$109$	−103.352			−0.948182			−0.474091	+	0.880476i	$0.657223\pi$
$110$		0			0
$111$		−	86.9299i		−	0.783152i
$112$	6.66088	−	17.9225i	0.0594722	−	0.160022i
$113$	31.2691			0.276717			0.138359	−	0.990382i	$-0.455817\pi$
$113$	31.2691			0.276717			0.138359	+	0.990382i	$0.455817\pi$
$114$	−8.60647	+	96.4929i	−0.0754954	+	0.846429i
$115$		0			0
$116$	−159.130	−	28.6141i	−1.37181	−	0.246673i
$117$	33.5590			0.286829
$118$	−120.849	−	10.7789i	−1.02415	−	0.0913465i
$119$			25.0064i			0.210138i
$120$		0			0
$121$	53.4198			0.441486
$122$	−3.79380	+	42.5348i	−0.0310967	+	0.348646i
$123$		−	127.541i		−	1.03692i
$124$	39.1567	−	217.760i	0.315780	−	1.75613i
$125$		0			0
$126$	7.14174	+	0.636992i	0.0566804	+	0.00505549i
$127$		−	178.474i		−	1.40531i	−0.711531	−	0.702655i	$-0.751998\pi$
$127$		−	178.474i		−	1.40531i	0.711531	−	0.702655i	$-0.248002\pi$
$128$	−74.6537	+	103.975i	−0.583232	+	0.812305i
$129$	−33.0550			−0.256240
$130$		0			0
$131$		−	153.743i		−	1.17361i	−0.809727	−	0.586806i	$-0.800385\pi$
$131$		−	153.743i		−	1.17361i	0.809727	−	0.586806i	$-0.199615\pi$
$132$	56.0558	+	10.0797i	0.424665	+	0.0763617i
$133$	33.4194			0.251274
$134$	−19.2970	−	1.72115i	−0.144007	−	0.0128444i
$135$		0			0
$136$	44.1473	−	161.479i	0.324613	−	1.18734i
$137$	52.9928			0.386809			0.193405	−	0.981119i	$-0.438047\pi$
$137$	52.9928			0.386809			0.193405	+	0.981119i	$0.438047\pi$
$138$	−2.91922	+	32.7293i	−0.0211537	+	0.237169i
$139$		−	21.8420i		−	0.157137i	−0.996909	−	0.0785684i	$-0.974965\pi$
$139$		−	21.8420i		−	0.157137i	0.996909	−	0.0785684i	$-0.0250349\pi$
$140$		0			0
$141$	31.2804			0.221847
$142$	−136.846	−	12.2056i	−0.963701	−	0.0859552i
$143$		−	91.9598i		−	0.643076i
$144$	−44.9932	−	16.7217i	−0.312453	−	0.116123i
$145$		0			0
$146$	−15.0642	+	168.895i	−0.103179	+	1.15681i
$147$			82.3970i			0.560524i
$148$	197.587	+	35.5294i	1.33505	+	0.240063i
$149$	−3.12940			−0.0210027			−0.0105013	−	0.999945i	$-0.503343\pi$
$149$	−3.12940			−0.0210027			−0.0105013	+	0.999945i	$0.503343\pi$
$150$		0			0
$151$			296.461i			1.96332i	0.190646	+	0.981659i	$0.438942\pi$
$151$			296.461i			1.96332i	−0.190646	+	0.981659i	$0.561058\pi$
$152$	−215.806	−	58.9999i	−1.41977	−	0.388157i
$153$	62.7769			0.410306
$154$	1.74551	−	19.5701i	0.0113345	−	0.127078i
$155$		0			0
$156$	−13.7160	+	76.2779i	−0.0879231	+	0.488961i
$157$	265.686			1.69227			0.846133	−	0.532972i	$-0.178925\pi$
$157$	265.686			1.69227			0.846133	+	0.532972i	$0.178925\pi$
$158$	46.3965	+	4.13824i	0.293649	+	0.0261914i
$159$			99.1101i			0.623334i
$160$		0			0
$161$	11.3355			0.0704067
$162$	1.59912	−	17.9288i	0.00987113	−	0.110672i
$163$			205.531i			1.26093i	0.776218	+	0.630465i	$0.217136\pi$
$163$			205.531i			1.26093i	−0.776218	+	0.630465i	$0.782864\pi$
$164$	289.895	+	52.1278i	1.76765	+	0.317852i
$165$		0			0
$166$	−185.781	−	16.5704i	−1.11917	−	0.0998215i
$167$		−	11.6359i		−	0.0696763i	−0.999393	−	0.0348381i	$-0.988908\pi$
$167$		−	11.6359i		−	0.0696763i	0.999393	−	0.0348381i	$-0.0110916\pi$
$168$	−4.36677	+	15.9724i	−0.0259927	+	0.0950740i
$169$	−43.8657			−0.259560
$170$		0			0
$171$		−	83.8970i		−	0.490626i
$172$	13.5100	−	75.1323i	0.0785466	−	0.436816i
$173$	106.062			0.613077			0.306538	−	0.951858i	$-0.400829\pi$
$173$	106.062			0.613077			0.306538	+	0.951858i	$0.400829\pi$
$174$	139.467	+	12.4395i	0.801535	+	0.0714912i
$175$		0			0
$176$	−45.8214	+	123.292i	−0.260349	+	0.700523i
$177$	105.074			0.593639
$178$	11.1920	−	125.481i	0.0628766	−	0.704951i
$179$			43.3304i			0.242069i	0.992648	+	0.121035i	$0.0386212\pi$
$179$			43.3304i			0.242069i	−0.992648	+	0.121035i	$0.961379\pi$
$180$		0			0
$181$	203.614			1.12494			0.562469	−	0.826819i	$-0.309852\pi$
$181$	203.614			1.12494			0.562469	+	0.826819i	$0.309852\pi$
$182$	26.6300	+	2.37520i	0.146319	+	0.0130506i
$183$		−	36.9824i		−	0.202090i
$184$	−73.1988	−	20.0121i	−0.397819	−	0.108761i
$185$		0			0
$186$	−17.0227	+	190.852i	−0.0915197	+	1.02609i
$187$		−	172.024i		−	0.919913i
$188$	−12.7847	+	71.0988i	−0.0680038	+	0.378185i
$189$	−6.20948			−0.0328544
$190$		0			0
$191$			251.536i			1.31694i	0.752606	+	0.658471i	$0.228796\pi$
$191$			251.536i			1.31694i	−0.752606	+	0.658471i	$0.771204\pi$
$192$	56.3968	−	95.4327i	0.293733	−	0.497045i
$193$	281.811			1.46016			0.730081	−	0.683360i	$-0.239482\pi$
$193$	281.811			1.46016			0.730081	+	0.683360i	$0.239482\pi$
$194$	−16.2393	+	182.070i	−0.0837078	+	0.938503i
$195$		0			0
$196$	−187.284	−	33.6767i	−0.955531	−	0.171820i
$197$	243.485			1.23596			0.617982	−	0.786193i	$-0.287951\pi$
$197$	243.485			1.23596			0.617982	+	0.786193i	$0.287951\pi$
$198$	−49.1293	−	4.38198i	−0.248128	−	0.0221312i
$199$			121.958i			0.612853i	0.951894	+	0.306427i	$0.0991335\pi$
$199$			121.958i			0.612853i	−0.951894	+	0.306427i	$0.900867\pi$
$200$		0			0
$201$	16.7780			0.0834727
$202$	−5.32649	+	59.7188i	−0.0263688	+	0.295638i
$203$		−	48.3031i		−	0.237946i
$204$	−25.6577	+	142.688i	−0.125773	+	0.699453i
$205$		0			0
$206$	176.795	+	15.7689i	0.858229	+	0.0765479i
$207$		−	28.4569i		−	0.137473i
$208$	−167.770	−	62.3515i	−0.806585	−	0.299767i
$209$	−229.898			−1.09999
$210$		0			0
$211$			132.543i			0.628168i	0.949395	+	0.314084i	$0.101697\pi$
$211$			132.543i			0.628168i	−0.949395	+	0.314084i	$0.898303\pi$
$212$	−225.272	−	40.5076i	−1.06260	−	0.191073i
$213$	118.982			0.558602
$214$	324.555	+	28.9480i	1.51661	+	0.135271i
$215$		0			0
$216$	40.0977	+	10.9625i	0.185637	+	0.0507521i
$217$	66.0998			0.304608
$218$	−18.3636	+	205.886i	−0.0842366	+	0.944433i
$219$		−	146.848i		−	0.670537i
$220$		0			0
$221$	234.081			1.05919
$222$	−173.172	−	15.4457i	−0.780056	−	0.0695754i
$223$			225.442i			1.01095i	0.862841	+	0.505475i	$0.168683\pi$
$223$			225.442i			1.01095i	−0.862841	+	0.505475i	$0.831317\pi$
$224$	−34.5198	−	16.4536i	−0.154106	−	0.0734534i
$225$		0			0
$226$	5.55590	−	62.2908i	0.0245836	−	0.275623i
$227$		−	108.080i		−	0.476124i	−0.971250	−	0.238062i	$-0.923488\pi$
$227$		−	108.080i		−	0.476124i	0.971250	−	0.238062i	$-0.0765122\pi$
$228$	190.693	+	34.2898i	0.836375	+	0.150394i
$229$	−57.3495			−0.250435			−0.125217	−	0.992129i	$-0.539963\pi$
$229$	−57.3495			−0.250435			−0.125217	+	0.992129i	$0.539963\pi$
$230$		0			0
$231$			17.0155i			0.0736600i
$232$	−85.2762	+	311.917i	−0.367570	+	1.34447i
$233$	−285.320			−1.22455			−0.612274	−	0.790646i	$-0.709745\pi$
$233$	−285.320			−1.22455			−0.612274	+	0.790646i	$0.709745\pi$
$234$	5.96278	−	66.8527i	0.0254820	−	0.285695i
$235$		0			0
$236$	−42.9451	+	238.828i	−0.181971	+	1.01198i
$237$	−40.3400			−0.170211
$238$	49.8151	+	4.44315i	0.209307	+	0.0186687i
$239$		−	77.2471i		−	0.323210i	−0.986856	−	0.161605i	$-0.948333\pi$
$239$		−	77.2471i		−	0.323210i	0.986856	−	0.161605i	$-0.0516670\pi$
$240$		0			0
$241$	−130.557			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$241$	−130.557			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$242$	9.49164	−	106.417i	0.0392217	−	0.439740i
$243$			15.5885i			0.0641500i
$244$	84.0591	+	15.1152i	0.344504	+	0.0619475i
$245$		0			0
$246$	−254.074	−	22.6616i	−1.03282	−	0.0921203i
$247$		−	312.834i		−	1.26653i
$248$	−426.840	−	116.695i	−1.72113	−	0.470546i
$249$	161.530			0.648715
$250$		0			0
$251$		−	437.197i		−	1.74182i	−0.491441	−	0.870911i	$-0.663530\pi$
$251$		−	437.197i		−	1.74182i	0.491441	−	0.870911i	$-0.336470\pi$
$252$	2.53789	−	14.1138i	0.0100710	−	0.0560072i
$253$	−77.9788			−0.308216
$254$	−355.537	−	31.7114i	−1.39975	−	0.124848i
$255$		0			0
$256$	193.863	+	167.191i	0.757279	+	0.653091i
$257$	−74.3682			−0.289370			−0.144685	−	0.989478i	$-0.546217\pi$
$257$	−74.3682			−0.289370			−0.144685	+	0.989478i	$0.546217\pi$
$258$	−5.87323	+	65.8486i	−0.0227644	+	0.255227i
$259$			59.9766i			0.231570i
$260$		0			0
$261$	−121.261			−0.464603
$262$	−306.271	−	27.3172i	−1.16897	−	0.104264i
$263$			458.790i			1.74445i	0.489105	+	0.872225i	$0.337324\pi$
$263$			458.790i			1.74445i	−0.489105	+	0.872225i	$0.662676\pi$
$264$	30.0398	−	109.877i	0.113787	−	0.416202i
$265$		0			0
$266$	5.93797	−	66.5745i	0.0223232	−	0.250280i
$267$			109.101i			0.408620i
$268$	−6.85739	+	38.1355i	−0.0255873	+	0.142297i
$269$	−320.405			−1.19110			−0.595549	−	0.803319i	$-0.703065\pi$
$269$	−320.405			−1.19110			−0.595549	+	0.803319i	$0.703065\pi$
$270$		0			0
$271$			359.059i			1.32494i	0.749088	+	0.662470i	$0.230492\pi$
$271$			359.059i			1.32494i	−0.749088	+	0.662470i	$0.769508\pi$
$272$	−313.837	−	116.637i	−1.15381	−	0.428813i
$273$	−23.1538			−0.0848124
$274$	9.41579	−	105.567i	0.0343642	−	0.385280i
$275$		0			0
$276$	64.6810	+	11.6307i	0.234352	+	0.0421402i
$277$	−138.027			−0.498293			−0.249147	−	0.968466i	$-0.580150\pi$
$277$	−138.027			−0.498293			−0.249147	+	0.968466i	$0.580150\pi$
$278$	−43.5113	−	3.88090i	−0.156516	−	0.0139601i
$279$		−	165.939i		−	0.594764i
$280$		0			0
$281$	462.504			1.64592			0.822960	−	0.568099i	$-0.192321\pi$
$281$	462.504			1.64592			0.822960	+	0.568099i	$0.192321\pi$
$282$	5.55792	−	62.3135i	0.0197089	−	0.220970i
$283$		−	323.973i		−	1.14478i	−0.819981	−	0.572391i	$-0.806016\pi$
$283$		−	323.973i		−	1.14478i	0.819981	−	0.572391i	$-0.193984\pi$
$284$	−48.6295	+	270.440i	−0.171231	+	0.952254i
$285$		0			0
$286$	−183.192	−	16.3394i	−0.640533	−	0.0571309i
$287$			87.9962i			0.306607i
$288$	−41.3055	+	86.6594i	−0.143422	+	0.300901i
$289$	148.882			0.515161
$290$		0			0
$291$		−	158.303i		−	0.543996i
$292$	333.777	+	60.0185i	1.14307	+	0.205543i
$293$	−150.416			−0.513365			−0.256683	−	0.966496i	$-0.582629\pi$
$293$	−150.416			−0.513365			−0.256683	+	0.966496i	$0.582629\pi$
$294$	164.142	+	14.6403i	0.558308	+	0.0497970i
$295$		0			0
$296$	105.885	−	387.299i	0.357720	−	1.30844i
$297$	42.7161			0.143825
$298$	−0.556033	+	6.23406i	−0.00186588	+	0.0209196i
$299$		−	106.110i		−	0.354882i
$300$		0			0
$301$	22.8060			0.0757676
$302$	590.577	+	52.6753i	1.95555	+	0.174421i
$303$		−	51.9233i		−	0.171364i
$304$	−155.878	+	419.421i	−0.512755	+	1.37968i
$305$		0			0
$306$	11.1542	−	125.057i	0.0364517	−	0.408684i
$307$			563.915i			1.83686i	0.395587	+	0.918428i	$0.370541\pi$
$307$			563.915i			1.83686i	−0.395587	+	0.918428i	$0.629459\pi$
$308$	−38.6752	−	6.95443i	−0.125569	−	0.0225793i
$309$	−153.717			−0.497466
$310$		0			0
$311$		−	40.0214i		−	0.128686i	−0.997928	−	0.0643431i	$-0.979505\pi$
$311$		−	40.0214i		−	0.128686i	0.997928	−	0.0643431i	$-0.0204952\pi$
$312$	149.515	+	40.8766i	0.479216	+	0.131015i
$313$	−1.82657			−0.00583568			−0.00291784	−	0.999996i	$-0.500929\pi$
$313$	−1.82657			−0.00583568			−0.00291784	+	0.999996i	$0.500929\pi$
$314$	47.2071	−	529.270i	0.150341	−	1.68557i
$315$		0			0
$316$	16.4875	−	91.6908i	0.0521756	−	0.290161i
$317$	−246.416			−0.777338			−0.388669	−	0.921378i	$-0.627065\pi$
$317$	−246.416			−0.777338			−0.388669	+	0.921378i	$0.627065\pi$
$318$	197.436	+	17.6099i	0.620869	+	0.0553771i
$319$			332.286i			1.04165i
$320$		0			0
$321$	−282.189			−0.879092
$322$	2.01409	−	22.5813i	0.00625494	−	0.0701283i
$323$		−	585.199i		−	1.81176i
$324$	−35.4317	−	6.37120i	−0.109357	−	0.0196642i
$325$		0			0
$326$	409.438	+	36.5189i	1.25594	+	0.112021i
$327$		−	179.011i		−	0.547433i
$328$	155.352	−	568.235i	0.473634	−	1.73242i
$329$	−21.5817			−0.0655978
$330$		0			0
$331$		−	417.672i		−	1.26185i	−0.775844	−	0.630925i	$-0.782675\pi$
$331$		−	417.672i		−	1.26185i	0.775844	−	0.630925i	$-0.217325\pi$
$332$	−66.0194	+	367.149i	−0.198854	+	1.10587i
$333$	150.567			0.452153
$334$	−23.1798	−	2.06748i	−0.0694007	−	0.00619005i
$335$		0			0
$336$	31.0427	+	11.5370i	0.0923889	+	0.0343363i
$337$	317.379			0.941779			0.470889	−	0.882192i	$-0.343933\pi$
$337$	317.379			0.941779			0.470889	+	0.882192i	$0.343933\pi$
$338$	−7.79408	+	87.3845i	−0.0230594	+	0.258534i
$339$			54.1596i			0.159763i
$340$		0			0
$341$	−454.713			−1.33347
$342$	−167.131	−	14.9068i	−0.488686	−	0.0435873i
$343$		−	115.405i		−	0.336457i
$344$	−147.270	−	40.2627i	−0.428110	−	0.117043i
$345$		0			0
$346$	18.8452	−	211.286i	0.0544659	−	0.610653i
$347$			222.581i			0.641443i	0.947174	+	0.320721i	$0.103925\pi$
$347$			222.581i			0.641443i	−0.947174	+	0.320721i	$0.896075\pi$
$348$	49.5611	−	275.621i	0.142417	−	0.792014i
$349$	560.812			1.60691			0.803455	−	0.595366i	$-0.202993\pi$
$349$	560.812			1.60691			0.803455	+	0.595366i	$0.202993\pi$
$350$		0			0
$351$			58.1259i			0.165601i
$352$	237.468	+	113.187i	0.674624	+	0.321554i
$353$	−304.856			−0.863616			−0.431808	−	0.901966i	$-0.642124\pi$
$353$	−304.856			−0.863616			−0.431808	+	0.901966i	$0.642124\pi$
$354$	18.6696	−	209.317i	0.0527390	−	0.591291i
$355$		0			0
$356$	−247.982	−	44.5911i	−0.696578	−	0.125256i
$357$	−43.3124			−0.121323
$358$	86.3181	+	7.69896i	0.241112	+	0.0215055i
$359$			105.860i			0.294874i	0.989071	+	0.147437i	$0.0471023\pi$
$359$			105.860i			0.294874i	−0.989071	+	0.147437i	$0.952898\pi$
$360$		0			0
$361$	−421.079			−1.16642
$362$	36.1782	−	405.617i	0.0999396	−	1.12049i
$363$			92.5257i			0.254892i
$364$	9.46324	−	52.6273i	0.0259979	−	0.144581i
$365$		0			0
$366$	−73.6724	−	6.57105i	−0.201291	−	0.0179537i
$367$			360.200i			0.981470i	0.871309	+	0.490735i	$0.163272\pi$
$367$			360.200i			0.981470i	−0.871309	+	0.490735i	$0.836728\pi$
$368$	−52.8719	+	142.263i	−0.143674	+	0.386584i
$369$	220.908			0.598667
$370$		0			0
$371$		−	68.3802i		−	0.184313i
$372$	377.171	+	67.8214i	1.01390	+	0.182316i
$373$	135.489			0.363242			0.181621	−	0.983369i	$-0.441866\pi$
$373$	135.489			0.363242			0.181621	+	0.983369i	$0.441866\pi$
$374$	−342.687	−	30.5652i	−0.916275	−	0.0817252i
$375$		0			0
$376$	139.364	+	38.1012i	0.370648	+	0.101333i
$377$	−452.158			−1.19936
$378$	−1.10330	+	12.3698i	−0.00291879	+	0.0327245i
$379$		−	310.686i		−	0.819753i	−0.912141	−	0.409876i	$-0.865572\pi$
$379$		−	310.686i		−	0.819753i	0.912141	−	0.409876i	$-0.134428\pi$
$380$		0			0
$381$	309.126			0.811356
$382$	501.083	+	44.6930i	1.31173	+	0.116997i
$383$			121.981i			0.318487i	0.987239	+	0.159244i	$0.0509056\pi$
$383$			121.981i			0.318487i	−0.987239	+	0.159244i	$0.949094\pi$
$384$	−180.090	−	129.304i	−0.468985	−	0.336729i
$385$		0			0
$386$	50.0723	−	561.394i	0.129721	−	1.45439i
$387$		−	57.2530i		−	0.147941i
$388$	359.814	+	64.7004i	0.927356	+	0.166754i
$389$	544.266			1.39914			0.699570	−	0.714564i	$-0.253375\pi$
$389$	544.266			1.39914			0.699570	+	0.714564i	$0.253375\pi$
$390$		0			0
$391$		−	198.493i		−	0.507654i
$392$	−100.364	+	367.103i	−0.256030	+	0.936488i
$393$	266.291			0.677586
$394$	43.2625	−	485.044i	0.109803	−	1.23108i
$395$		0			0
$396$	−17.4586	+	97.0915i	−0.0440874	+	0.245180i
$397$	−504.528			−1.27085			−0.635425	−	0.772162i	$-0.719175\pi$
$397$	−504.528			−1.27085			−0.635425	+	0.772162i	$0.719175\pi$
$398$	242.951	+	21.6695i	0.610430	+	0.0544460i
$399$			57.8841i			0.145073i
$400$		0			0
$401$	−278.018			−0.693312			−0.346656	−	0.937992i	$-0.612683\pi$
$401$	−278.018			−0.693312			−0.346656	+	0.937992i	$0.612683\pi$
$402$	2.98112	−	33.4233i	0.00741573	−	0.0831426i
$403$		−	618.750i		−	1.53536i
$404$	118.019	+	21.2217i	0.292126	+	0.0525290i
$405$		0			0
$406$	−96.2242	−	8.58251i	−0.237005	−	0.0211392i
$407$		−	412.590i		−	1.01373i
$408$	279.690	+	76.4654i	0.685514	+	0.187415i
$409$	−296.549			−0.725059			−0.362530	−	0.931972i	$-0.618087\pi$
$409$	−296.549			−0.725059			−0.362530	+	0.931972i	$0.618087\pi$
$410$		0			0
$411$			91.7863i			0.223324i
$412$	62.8261	−	349.390i	0.152490	−	0.848035i
$413$	−72.4950			−0.175533
$414$	−56.6888	−	5.05623i	−0.136929	−	0.0122131i
$415$		0			0
$416$	−154.019	+	323.134i	−0.370239	+	0.776764i
$417$	37.8315			0.0907230
$418$	−40.8483	+	457.978i	−0.0977233	+	1.09564i
$419$		−	315.615i		−	0.753258i	−0.926364	−	0.376629i	$-0.877083\pi$
$419$		−	315.615i		−	0.753258i	0.926364	−	0.376629i	$-0.122917\pi$
$420$		0			0
$421$	−360.355			−0.855951			−0.427975	−	0.903790i	$-0.640773\pi$
$421$	−360.355			−0.855951			−0.427975	+	0.903790i	$0.640773\pi$
$422$	264.039	+	23.5504i	0.625684	+	0.0558066i
$423$			54.1793i			0.128084i
$424$	−120.721	+	441.565i	−0.284720	+	1.04143i
$425$		0			0
$426$	21.1408	−	237.023i	0.0496263	−	0.556393i
$427$			25.5157i			0.0597558i
$428$	115.334	−	641.400i	0.269472	−	1.49860i
$429$	159.279			0.371280
$430$		0			0
$431$			523.617i			1.21489i	0.794362	+	0.607445i	$0.207805\pi$
$431$			523.617i			1.21489i	−0.794362	+	0.607445i	$0.792195\pi$
$432$	28.9628	−	77.9305i	0.0670435	−	0.180395i
$433$	21.5381			0.0497415			0.0248707	−	0.999691i	$-0.492083\pi$
$433$	21.5381			0.0497415			0.0248707	+	0.999691i	$0.492083\pi$
$434$	11.7446	−	131.677i	0.0270614	−	0.303403i
$435$		0			0
$436$	406.882	+	73.1639i	0.933215	+	0.167807i
$437$	−265.272			−0.607030
$438$	−292.534	−	26.0919i	−0.667886	−	0.0595706i
$439$		−	247.777i		−	0.564412i	−0.959354	−	0.282206i	$-0.908934\pi$
$439$		−	247.777i		−	0.564412i	0.959354	−	0.282206i	$-0.0910662\pi$
$440$		0			0
$441$	−142.716			−0.323619
$442$	41.5916	−	466.311i	0.0940987	−	1.05500i
$443$			584.775i			1.32003i	0.751251	+	0.660017i	$0.229451\pi$
$443$			584.775i			1.32003i	−0.751251	+	0.660017i	$0.770549\pi$
$444$	−61.5386	+	342.231i	−0.138601	+	0.770790i
$445$		0			0
$446$	449.101	+	40.0566i	1.00695	+	0.0898130i
$447$		−	5.42028i		−	0.0121259i
$448$	−38.9105	+	65.8430i	−0.0868538	+	0.146971i
$449$	152.093			0.338738			0.169369	−	0.985553i	$-0.445827\pi$
$449$	152.093			0.338738			0.169369	+	0.985553i	$0.445827\pi$
$450$		0			0
$451$		−	605.342i		−	1.34222i
$452$	−123.102	−	22.1357i	−0.272349	−	0.0489728i
$453$	−513.485			−1.13352
$454$	−215.306	−	19.2037i	−0.474242	−	0.0422990i
$455$		0			0
$456$	102.191	−	373.786i	0.224103	−	0.819707i
$457$	−602.441			−1.31825			−0.659126	−	0.752033i	$-0.729074\pi$
$457$	−602.441			−1.31825			−0.659126	+	0.752033i	$0.729074\pi$
$458$	−10.1899	+	114.246i	−0.0222487	+	0.249444i
$459$			108.733i			0.236890i
$460$		0			0
$461$	−504.912			−1.09525			−0.547626	−	0.836723i	$-0.684468\pi$
$461$	−504.912			−1.09525			−0.547626	+	0.836723i	$0.684468\pi$
$462$	33.8964	+	3.02331i	0.0733687	+	0.00654397i
$463$			504.560i			1.08976i	0.838513	+	0.544881i	$0.183425\pi$
$463$			504.560i			1.08976i	−0.838513	+	0.544881i	$0.816575\pi$
$464$	606.215	+	225.300i	1.30650	+	0.485559i
$465$		0			0
$466$	−50.6957	+	568.383i	−0.108789	+	1.21971i
$467$			751.418i			1.60903i	0.593931	+	0.804516i	$0.297575\pi$
$467$			751.418i			1.60903i	−0.593931	+	0.804516i	$0.702425\pi$
$468$	−132.117	−	23.7568i	−0.282302	−	0.0507624i
$469$	−11.5759			−0.0246820
$470$		0			0
$471$			460.181i			0.977030i
$472$	468.136	+	127.986i	0.991814	+	0.271156i
$473$	−156.887			−0.331685
$474$	−7.16763	+	80.3611i	−0.0151216	+	0.169538i
$475$		0			0
$476$	17.7023	−	98.4468i	0.0371898	−	0.206821i
$477$	−171.664			−0.359882
$478$	−153.883	−	13.7253i	−0.321932	−	0.0287140i
$479$			581.401i			1.21378i	0.794786	+	0.606890i	$0.207583\pi$
$479$			581.401i			1.21378i	−0.794786	+	0.606890i	$0.792417\pi$
$480$		0			0
$481$	561.431			1.16722
$482$	−23.1975	+	260.082i	−0.0481276	+	0.539590i
$483$			19.6336i			0.0406493i
$484$	−210.306	−	37.8164i	−0.434517	−	0.0781331i
$485$		0			0
$486$	31.0536	+	2.76976i	0.0638964	+	0.00569910i
$487$		−	557.489i		−	1.14474i	−0.819995	−	0.572371i	$-0.806024\pi$
$487$		−	557.489i		−	1.14474i	0.819995	−	0.572371i	$-0.193976\pi$
$488$	45.0465	−	164.768i	0.0923084	−	0.337639i
$489$	−355.991			−0.727998
$490$		0			0
$491$		−	26.2032i		−	0.0533670i	−0.999644	−	0.0266835i	$-0.991505\pi$
$491$		−	26.2032i		−	0.0533670i	0.999644	−	0.0266835i	$-0.00849463\pi$
$492$	−90.2880	+	502.113i	−0.183512	+	1.02055i
$493$	−845.824			−1.71567
$494$	−623.193	−	55.5844i	−1.26152	−	0.112519i
$495$		0			0
$496$	−308.309	+	829.569i	−0.621590	+	1.67252i
$497$	−82.0908			−0.165173
$498$	28.7007	−	321.783i	0.0576320	−	0.646150i
$499$		−	444.615i		−	0.891011i	−0.895279	−	0.445506i	$-0.853024\pi$
$499$		−	444.615i		−	0.891011i	0.895279	−	0.445506i	$-0.146976\pi$
$500$		0			0
$501$	20.1540			0.0402276
$502$	−870.937	−	77.6814i	−1.73493	−	0.154744i
$503$		−	216.819i		−	0.431052i	−0.976498	−	0.215526i	$-0.930853\pi$
$503$		−	216.819i		−	0.431052i	0.976498	−	0.215526i	$-0.0691466\pi$
$504$	−27.6651	−	7.56346i	−0.0548910	−	0.0150069i
$505$		0			0
$506$	−13.8553	+	155.341i	−0.0273820	+	0.306998i
$507$		−	75.9777i		−	0.149857i
$508$	−126.344	+	702.628i	−0.248708	+	1.38313i
$509$	202.830			0.398488			0.199244	−	0.979950i	$-0.436151\pi$
$509$	202.830			0.398488			0.199244	+	0.979950i	$0.436151\pi$
$510$		0			0
$511$			101.316i			0.198271i
$512$	367.506	−	356.487i	0.717786	−	0.696264i
$513$	145.314			0.283263
$514$	−13.2138	+	148.148i	−0.0257077	+	0.288226i
$515$		0			0
$516$	130.133	+	23.4000i	0.252196	+	0.0453489i
$517$	148.464			0.287165
$518$	119.479	+	10.6567i	0.230654	+	0.0205727i
$519$			183.705i			0.353960i
$520$		0			0
$521$	769.410			1.47679			0.738397	−	0.674366i	$-0.235583\pi$
$521$	769.410			1.47679			0.738397	+	0.674366i	$0.235583\pi$
$522$	−21.5458	+	241.564i	−0.0412754	+	0.462766i
$523$		−	38.9898i		−	0.0745502i	−0.999305	−	0.0372751i	$-0.988132\pi$
$523$		−	38.9898i		−	0.0745502i	0.999305	−	0.0372751i	$-0.0118678\pi$
$524$	−108.837	+	605.266i	−0.207703	+	1.15509i
$525$		0			0
$526$	913.953	+	81.5180i	1.73755	+	0.154977i
$527$		−	1157.46i		−	2.19632i
$528$	−213.548	−	79.3650i	−0.404447	−	0.150313i
$529$	439.023			0.829911
$530$		0			0
$531$			181.994i			0.342737i
$532$	−131.567	−	23.6579i	−0.247307	−	0.0444698i
$533$	823.718			1.54544
$534$	217.340	+	19.3852i	0.407004	+	0.0363018i
$535$		0			0
$536$	74.7510	+	20.4365i	0.139461	+	0.0381277i
$537$	−75.0504			−0.139759
$538$	−56.9297	+	638.277i	−0.105817	+	1.18639i
$539$			391.076i			0.725558i
$540$		0			0
$541$	−32.0904			−0.0593168			−0.0296584	−	0.999560i	$-0.509442\pi$
$541$	−32.0904			−0.0593168			−0.0296584	+	0.999560i	$0.509442\pi$
$542$	715.278	+	63.7977i	1.31970	+	0.117708i
$543$			352.669i			0.649483i
$544$	−288.115	+	604.467i	−0.529622	+	1.11115i
$545$		0			0
$546$	−4.11397	+	46.1245i	−0.00753475	+	0.0844770i
$547$			254.839i			0.465885i	0.972491	+	0.232942i	$0.0748354\pi$
$547$			254.839i			0.465885i	−0.972491	+	0.232942i	$0.925165\pi$
$548$	−208.625	−	37.5142i	−0.380703	−	0.0684566i
$549$	64.0554			0.116677
$550$		0			0
$551$			1130.39i			2.05152i
$552$	34.6620	−	126.784i	0.0627934	−	0.229681i
$553$	27.8323			0.0503296
$554$	−24.5247	+	274.963i	−0.0442685	+	0.496323i
$555$		0			0
$556$	−15.4622	+	85.9890i	−0.0278097	+	0.154656i
$557$	577.439			1.03670			0.518348	−	0.855170i	$-0.326547\pi$
$557$	577.439			1.03670			0.518348	+	0.855170i	$0.326547\pi$
$558$	−330.566	−	29.4841i	−0.592412	−	0.0528389i
$559$		−	213.484i		−	0.381903i
$560$		0			0
$561$	297.954			0.531112
$562$	82.1778	−	921.350i	0.146224	−	1.63941i
$563$			367.058i			0.651967i	0.945375	+	0.325984i	$0.105695\pi$
$563$			367.058i			0.651967i	−0.945375	+	0.325984i	$0.894305\pi$
$564$	−123.147	−	22.1438i	−0.218345	−	0.0392620i
$565$		0			0
$566$	−645.384	−	57.5636i	−1.14025	−	0.101703i
$567$		−	10.7551i		−	0.0189685i
$568$	530.101	+	144.926i	0.933277	+	0.255152i
$569$	−522.006			−0.917410			−0.458705	−	0.888589i	$-0.651687\pi$
$569$	−522.006			−0.917410			−0.458705	+	0.888589i	$0.651687\pi$
$570$		0			0
$571$		−	832.421i		−	1.45783i	−0.684604	−	0.728915i	$-0.740025\pi$
$571$		−	832.421i		−	1.45783i	0.684604	−	0.728915i	$-0.259975\pi$
$572$	−65.0994	+	362.033i	−0.113810	+	0.632925i
$573$	−435.673			−0.760337
$574$	175.296	+	15.6352i	0.305394	+	0.0272390i
$575$		0			0
$576$	165.294	+	97.6821i	0.286969	+	0.169587i
$577$	427.659			0.741177			0.370588	−	0.928797i	$-0.379156\pi$
$577$	427.659			0.741177			0.370588	+	0.928797i	$0.379156\pi$
$578$	26.4533	−	296.586i	0.0457670	−	0.513124i
$579$			488.112i			0.843025i
$580$		0			0
$581$	−111.446			−0.191818
$582$	−315.354	−	28.1273i	−0.541845	−	0.0483287i
$583$			470.400i			0.806861i
$584$	178.868	−	654.250i	0.306281	−	1.12029i
$585$		0			0
$586$	−26.7260	+	299.642i	−0.0456074	+	0.511335i
$587$		−	586.262i		−	0.998743i	−0.866388	−	0.499372i	$-0.833564\pi$
$587$		−	586.262i		−	0.998743i	0.866388	−	0.499372i	$-0.166436\pi$
$588$	58.3298	−	324.385i	0.0992003	−	0.551676i
$589$	−1546.87			−2.62626
$590$		0			0
$591$			421.728i			0.713584i
$592$	−752.721	−	279.748i	−1.27149	−	0.472548i
$593$	518.375			0.874156			0.437078	−	0.899424i	$-0.356013\pi$
$593$	518.375			0.874156			0.437078	+	0.899424i	$0.356013\pi$
$594$	7.58981	−	85.0944i	0.0127775	−	0.143257i
$595$		0			0
$596$	12.3200	+	2.21534i	0.0206712	+	0.00371701i
$597$	−211.237			−0.353831
$598$	−211.380	−	18.8536i	−0.353478	−	0.0315277i
$599$		−	405.480i		−	0.676928i	−0.940979	−	0.338464i	$-0.890093\pi$
$599$		−	405.480i		−	0.676928i	0.940979	−	0.338464i	$-0.109907\pi$
$600$		0			0
$601$	−350.551			−0.583279			−0.291640	−	0.956528i	$-0.594201\pi$
$601$	−350.551			−0.583279			−0.291640	+	0.956528i	$0.594201\pi$
$602$	4.05219	−	45.4317i	0.00673121	−	0.0754680i
$603$			29.0604i			0.0481930i
$604$	209.868	−	1167.13i	0.347464	−	1.93233i
$605$		0			0
$606$	−103.436	−	9.22576i	−0.170687	−	0.0152240i
$607$			737.786i			1.21546i	0.794143	+	0.607731i	$0.207920\pi$
$607$			737.786i			1.21546i	−0.794143	+	0.607731i	$0.792080\pi$
$608$	807.829	+	385.046i	1.32867	+	0.633299i
$609$	83.6634			0.137378
$610$		0			0
$611$			202.023i			0.330643i
$612$	−247.144	−	44.4404i	−0.403830	−	0.0726151i
$613$	345.495			0.563614			0.281807	−	0.959471i	$-0.409066\pi$
$613$	345.495			0.563614			0.281807	+	0.959471i	$0.409066\pi$
$614$	1123.37	+	100.197i	1.82959	+	0.163187i
$615$		0			0
$616$	−20.7257	+	75.8090i	−0.0336456	+	0.123066i
$617$	862.171			1.39736			0.698680	−	0.715434i	$-0.253771\pi$
$617$	862.171			1.39736			0.698680	+	0.715434i	$0.253771\pi$
$618$	−27.3125	+	306.218i	−0.0441950	+	0.495499i
$619$		−	469.363i		−	0.758260i	−0.925343	−	0.379130i	$-0.876223\pi$
$619$		−	469.363i		−	0.758260i	0.925343	−	0.379130i	$-0.123777\pi$
$620$		0			0
$621$	49.2888			0.0793701
$622$	−79.7264	−	7.11102i	−0.128177	−	0.0114325i
$623$		−	75.2737i		−	0.120824i
$624$	107.996	−	290.586i	0.173070	−	0.465682i
$625$		0			0
$626$	−0.324545	+	3.63869i	−0.000518443	+	0.00581260i
$627$		−	398.195i		−	0.635080i
$628$	−1045.97	−	188.082i	−1.66555	−	0.299494i
$629$	1050.24			1.66969
$630$		0			0
$631$		−	323.243i		−	0.512271i	−0.966641	−	0.256136i	$-0.917551\pi$
$631$		−	323.243i		−	0.512271i	0.966641	−	0.256136i	$-0.0824494\pi$
$632$	−179.727	−	49.1362i	−0.284378	−	0.0777472i
$633$	−229.572			−0.362673
$634$	−43.7833	+	490.883i	−0.0690588	+	0.774264i
$635$		0			0
$636$	70.1611	−	390.183i	0.110316	−	0.613495i
$637$	−532.156			−0.835410
$638$	661.943	+	59.0406i	1.03753	+	0.0925402i
$639$			206.083i			0.322509i
$640$		0			0
$641$	−44.1100			−0.0688144			−0.0344072	−	0.999408i	$-0.510954\pi$
$641$	−44.1100			−0.0688144			−0.0344072	+	0.999408i	$0.510954\pi$
$642$	−50.1394	+	562.146i	−0.0780987	+	0.875616i
$643$		−	934.204i		−	1.45288i	−0.687228	−	0.726442i	$-0.741173\pi$
$643$		−	934.204i		−	1.45288i	0.687228	−	0.726442i	$-0.258827\pi$
$644$	−44.6262	−	8.02451i	−0.0692953	−	0.0124604i
$645$		0			0
$646$	−1165.77	−	103.978i	−1.80460	−	0.160957i
$647$			481.023i			0.743467i	0.928339	+	0.371734i	$0.121237\pi$
$647$			481.023i			0.743467i	−0.928339	+	0.371734i	$0.878763\pi$
$648$	−18.9875	+	69.4512i	−0.0293018	+	0.107178i
$649$	498.706			0.768422
$650$		0			0
$651$			114.488i			0.175865i
$652$	145.498	−	809.148i	0.223156	−	1.24103i
$653$	1131.38			1.73259			0.866293	−	0.499536i	$-0.166496\pi$
$653$	1131.38			1.73259			0.866293	+	0.499536i	$0.166496\pi$
$654$	−356.606	−	31.8067i	−0.545268	−	0.0486340i
$655$		0			0
$656$	−1104.37	−	410.440i	−1.68350	−	0.625670i
$657$	254.348			0.387135
$658$	−3.83464	+	42.9927i	−0.00582772	+	0.0653385i
$659$			154.348i			0.234215i	0.993119	+	0.117107i	$0.0373622\pi$
$659$			154.348i			0.234215i	−0.993119	+	0.117107i	$0.962638\pi$
$660$		0			0
$661$	795.115			1.20290			0.601448	−	0.798912i	$-0.294591\pi$
$661$	795.115			1.20290			0.601448	+	0.798912i	$0.294591\pi$
$662$	−832.042	−	74.2122i	−1.25686	−	0.112103i
$663$			405.441i			0.611524i
$664$	719.665	+	196.752i	1.08383	+	0.296313i
$665$		0			0
$666$	26.7528	−	299.943i	0.0401694	−	0.450365i
$667$			383.414i			0.574834i
$668$	−8.23721	+	45.8090i	−0.0123311	+	0.0685764i
$669$	−390.477			−0.583672
$670$		0			0
$671$		−	175.527i		−	0.261591i
$672$	28.4984	−	59.7900i	0.0424083	−	0.0889732i
$673$	197.215			0.293039			0.146520	−	0.989208i	$-0.453193\pi$
$673$	197.215			0.293039			0.146520	+	0.989208i	$0.453193\pi$
$674$	56.3921	−	632.249i	0.0836678	−	0.938055i
$675$		0			0
$676$	172.693	+	31.0530i	0.255463	+	0.0459364i
$677$	530.367			0.783408			0.391704	−	0.920091i	$-0.371886\pi$
$677$	530.367			0.783408			0.391704	+	0.920091i	$0.371886\pi$
$678$	107.891	+	9.62309i	0.159131	+	0.0141934i
$679$			109.220i			0.160854i
$680$		0			0
$681$	187.200			0.274891
$682$	−80.7935	+	905.830i	−0.118466	+	1.32820i
$683$		−	797.231i		−	1.16725i	−0.812024	−	0.583625i	$-0.801634\pi$
$683$		−	797.231i		−	1.16725i	0.812024	−	0.583625i	$-0.198366\pi$
$684$	−59.3916	+	330.291i	−0.0868299	+	0.482881i
$685$		0			0
$686$	−229.897	−	20.5052i	−0.335127	−	0.0298909i
$687$		−	99.3323i		−	0.144588i
$688$	−106.374	+	286.221i	−0.154613	+	0.416020i
$689$	−640.096			−0.929022
$690$		0			0
$691$		−	498.569i		−	0.721518i	−0.932659	−	0.360759i	$-0.882518\pi$
$691$		−	498.569i		−	0.721518i	0.932659	−	0.360759i	$-0.117482\pi$
$692$	−417.552	−	75.0827i	−0.603399	−	0.108501i
$693$	−29.4716			−0.0425276
$694$	443.401	+	39.5482i	0.638906	+	0.0569859i
$695$		0			0
$696$	−540.256	−	147.703i	−0.776230	−	0.212217i
$697$	1540.88			2.21073
$698$	99.6452	−	1117.19i	0.142758	−	1.60056i
$699$		−	494.188i		−	0.706993i
$700$		0			0
$701$	−455.939			−0.650412			−0.325206	−	0.945643i	$-0.605434\pi$
$701$	−455.939			−0.650412			−0.325206	+	0.945643i	$0.605434\pi$
$702$	115.792	+	10.3278i	0.164946	+	0.0147120i
$703$		−	1403.57i		−	1.99654i
$704$	267.672	−	452.946i	0.380216	−	0.643389i
$705$		0			0
$706$	−54.1670	+	607.302i	−0.0767238	+	0.860201i
$707$			35.8241i			0.0506706i
$708$	−413.662	−	74.3831i	−0.584268	−	0.105061i
$709$	−44.4190			−0.0626502			−0.0313251	−	0.999509i	$-0.509973\pi$
$709$	−44.4190			−0.0626502			−0.0313251	+	0.999509i	$0.509973\pi$
$710$		0			0
$711$		−	69.8710i		−	0.0982715i
$712$	−132.891	+	486.080i	−0.186645	+	0.682696i
$713$	−524.679			−0.735875
$714$	−7.69576	+	86.2823i	−0.0107784	+	0.120843i
$715$		0			0
$716$	30.6741	−	170.586i	0.0428409	−	0.238248i
$717$	133.796			0.186605
$718$	210.882	+	18.8092i	0.293708	+	0.0261966i
$719$			1349.94i			1.87752i	0.344566	+	0.938762i	$0.388026\pi$
$719$			1349.94i			1.87752i	−0.344566	+	0.938762i	$0.611974\pi$
$720$		0			0
$721$	106.056			0.147095
$722$	−74.8174	+	838.827i	−0.103625	+	1.16181i
$723$		−	226.132i		−	0.312769i
$724$	−801.599	−	144.140i	−1.10718	−	0.199089i
$725$		0			0
$726$	184.320	+	16.4400i	0.253884	+	0.0226446i
$727$			191.470i			0.263370i	0.991292	+	0.131685i	$0.0420387\pi$
$727$			191.470i			0.263370i	−0.991292	+	0.131685i	$0.957961\pi$
$728$	−103.157	−	28.2025i	−0.141699	−	0.0387397i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	399.351i		−	0.546308i
$732$	−26.1803	+	145.595i	−0.0357654	+	0.198900i
$733$	−358.832			−0.489539			−0.244769	−	0.969581i	$-0.578712\pi$
$733$	−358.832			−0.489539			−0.244769	+	0.969581i	$0.578712\pi$
$734$	717.551	+	64.0004i	0.977589	+	0.0871940i
$735$		0			0
$736$	274.007	+	130.603i	0.372291	+	0.177450i
$737$	79.6324			0.108049
$738$	39.2510	−	440.069i	0.0531857	−	0.596300i
$739$			756.311i			1.02342i	0.859157	+	0.511712i	$0.170989\pi$
$739$			756.311i			1.02342i	−0.859157	+	0.511712i	$0.829011\pi$
$740$		0			0
$741$	541.844			0.731233
$742$	−136.220	−	12.1498i	−0.183584	−	0.0163744i
$743$			1148.65i			1.54596i	0.634432	+	0.772979i	$0.281234\pi$
$743$			1148.65i			1.54596i	−0.634432	+	0.772979i	$0.718766\pi$
$744$	202.122	−	739.308i	0.271670	−	0.993693i
$745$		0			0
$746$	24.0738	−	269.907i	0.0322705	−	0.361805i
$747$			279.778i			0.374536i
$748$	−121.777	+	677.233i	−0.162804	+	0.905392i
$749$	194.694			0.259938
$750$		0			0
$751$		−	431.186i		−	0.574149i	−0.957908	−	0.287074i	$-0.907317\pi$
$751$		−	431.186i		−	0.574149i	0.957908	−	0.287074i	$-0.0926827\pi$
$752$	100.663	−	270.856i	0.133861	−	0.360180i
$753$	757.248			1.00564
$754$	−80.3395	+	900.739i	−0.106551	+	1.19461i
$755$		0			0
$756$	24.4458	+	4.39576i	0.0323358	+	0.00581449i
$757$	645.657			0.852916			0.426458	−	0.904507i	$-0.359761\pi$
$757$	645.657			0.852916			0.426458	+	0.904507i	$0.359761\pi$
$758$	−618.916	−	55.2029i	−0.816511	−	0.0728270i
$759$		−	135.063i		−	0.177949i
$760$		0			0
$761$	−291.287			−0.382768			−0.191384	−	0.981515i	$-0.561298\pi$
$761$	−291.287			−0.382768			−0.191384	+	0.981515i	$0.561298\pi$
$762$	54.9257	−	615.808i	0.0720810	−	0.808147i
$763$			123.507i			0.161870i
$764$	178.065	−	990.261i	0.233069	−	1.29615i
$765$		0			0
$766$	242.997	+	21.6736i	0.317228	+	0.0282945i
$767$			678.614i			0.884764i
$768$	−289.584	+	335.781i	−0.377063	+	0.437215i
$769$	−724.076			−0.941582			−0.470791	−	0.882245i	$-0.656031\pi$
$769$	−724.076			−0.941582			−0.470791	+	0.882245i	$0.656031\pi$
$770$		0			0
$771$		−	128.809i		−	0.167068i
$772$	−1109.45	−	199.497i	−1.43711	−	0.258416i
$773$	399.686			0.517058			0.258529	−	0.966003i	$-0.416762\pi$
$773$	399.686			0.517058			0.258529	+	0.966003i	$0.416762\pi$
$774$	−114.053	−	10.1727i	−0.147356	−	0.0131431i
$775$		0			0
$776$	192.821	−	705.287i	0.248481	−	0.908875i
$777$	−103.882			−0.133697
$778$	96.7053	−	1084.23i	0.124300	−	1.39361i
$779$		−	2059.28i		−	2.64349i
$780$		0			0
$781$	564.717			0.723070
$782$	−395.416	−	35.2683i	−0.505647	−	0.0451001i
$783$		−	210.031i		−	0.268239i
$784$	713.471	+	265.161i	0.910039	+	0.338215i
$785$		0			0
$786$	47.3147	−	530.476i	0.0601968	−	0.674906i
$787$			381.830i			0.485172i	0.970130	+	0.242586i	$0.0779957\pi$
$787$			381.830i			0.485172i	−0.970130	+	0.242586i	$0.922004\pi$
$788$	−958.565	−	172.366i	−1.21645	−	0.218738i
$789$	−794.648			−1.00716
$790$		0			0
$791$		−	37.3670i		−	0.0472402i
$792$	190.313	+	52.0304i	0.240294	+	0.0656950i
$793$	238.849			0.301196
$794$	−89.6446	+	1005.07i	−0.112903	+	1.26583i
$795$		0			0
$796$	86.3353	−	480.131i	0.108461	−	0.603180i
$797$	18.3955			0.0230810			0.0115405	−	0.999933i	$-0.496326\pi$
$797$	18.3955			0.0230810			0.0115405	+	0.999933i	$0.496326\pi$
$798$	115.310	+	10.2849i	0.144499	+	0.0128883i
$799$			377.912i			0.472981i
$800$		0			0
$801$	−188.969			−0.235917
$802$	−49.3983	+	553.837i	−0.0615939	+	0.690570i
$803$		−	696.974i		−	0.867962i
$804$	−66.0527	−	11.8773i	−0.0821551	−	0.0147728i
$805$		0			0
$806$	−1232.61	−	109.940i	−1.52929	−	0.136402i
$807$		−	554.958i		−	0.687681i
$808$	63.2453	−	231.334i	0.0782739	−	0.286304i
$809$	−992.161			−1.22640			−0.613202	−	0.789926i	$-0.710119\pi$
$809$	−992.161			−1.22640			−0.613202	+	0.789926i	$0.710119\pi$
$810$		0			0
$811$		−	482.957i		−	0.595509i	−0.954643	−	0.297754i	$-0.903762\pi$
$811$		−	482.957i		−	0.595509i	0.954643	−	0.297754i	$-0.0962376\pi$
$812$	−34.1943	+	190.162i	−0.0421112	+	0.234190i
$813$	−621.908			−0.764955
$814$	−821.917	−	73.3091i	−1.00973	−	0.0900603i
$815$		0			0
$816$	202.022	−	543.581i	0.247575	−	0.666153i
$817$	−533.706			−0.653251
$818$	−52.6910	+	590.753i	−0.0644144	+	0.722192i
$819$		−	40.1035i		−	0.0489665i
$820$		0			0
$821$	614.955			0.749031			0.374516	−	0.927221i	$-0.377809\pi$
$821$	614.955			0.749031			0.374516	+	0.927221i	$0.377809\pi$
$822$	182.847	+	16.3086i	0.222441	+	0.0198402i
$823$		−	11.2878i		−	0.0137154i	−0.999976	−	0.00685772i	$-0.997817\pi$
$823$		−	11.2878i		−	0.0137154i	0.999976	−	0.00685772i	$-0.00218290\pi$
$824$	−684.855	−	187.235i	−0.831135	−	0.227227i
$825$		0			0
$826$	−12.8809	+	144.417i	−0.0155943	+	0.174839i
$827$		−	449.125i		−	0.543078i	−0.962427	−	0.271539i	$-0.912467\pi$
$827$		−	449.125i		−	0.543078i	0.962427	−	0.271539i	$-0.0875325\pi$
$828$	−20.1450	+	112.031i	−0.0243297	+	0.135303i
$829$	135.766			0.163771			0.0818855	−	0.996642i	$-0.473906\pi$
$829$	135.766			0.163771			0.0818855	+	0.996642i	$0.473906\pi$
$830$		0			0
$831$		−	239.070i		−	0.287690i
$832$	616.346	+	364.235i	0.740801	+	0.437782i
$833$	−995.472			−1.19504
$834$	6.72191	−	75.3638i	0.00805985	−	0.0903643i
$835$		0			0
$836$	905.076	+	162.747i	1.08263	+	0.194674i
$837$	287.415			0.343387
$838$	−628.734	−	56.0786i	−0.750280	−	0.0669196i
$839$		−	1509.47i		−	1.79913i	−0.436789	−	0.899564i	$-0.643884\pi$
$839$		−	1509.47i		−	1.79913i	0.436789	−	0.899564i	$-0.356116\pi$
$840$		0			0
$841$	792.817			0.942707
$842$	−64.0280	+	717.861i	−0.0760428	+	0.852566i
$843$			801.080i			0.950273i
$844$	93.8290	−	521.805i	0.111172	−	0.618252i
$845$		0			0
$846$	107.930	+	9.62660i	0.127577	+	0.0113790i
$847$		−	63.8374i		−	0.0753688i
$848$	858.188	+	318.945i	1.01201	+	0.376114i
$849$	561.138			0.660940
$850$		0			0
$851$		−	476.075i		−	0.559430i
$852$	−468.416	−	84.2288i	−0.549784	−	0.0988601i
$853$	−909.826			−1.06662			−0.533310	−	0.845920i	$-0.679052\pi$
$853$	−909.826			−1.06662			−0.533310	+	0.845920i	$0.679052\pi$
$854$	50.8297	+	4.53364i	0.0595195	+	0.00530872i
$855$		0			0
$856$	−1257.23	−	343.720i	−1.46873	−	0.401542i
$857$	−505.304			−0.589620			−0.294810	−	0.955556i	$-0.595256\pi$
$857$	−505.304			−0.589620			−0.294810	+	0.955556i	$0.595256\pi$
$858$	28.3008	−	317.298i	0.0329846	−	0.369812i
$859$			45.9728i			0.0535189i	0.999642	+	0.0267595i	$0.00851882\pi$
$859$			45.9728i			0.0535189i	−0.999642	+	0.0267595i	$0.991481\pi$
$860$		0			0
$861$	−152.414			−0.177020
$862$	1043.09	+	93.0365i	1.21009	+	0.107931i
$863$			142.006i			0.164549i	0.996610	+	0.0822746i	$0.0262185\pi$
$863$			142.006i			0.164549i	−0.996610	+	0.0822746i	$0.973782\pi$
$864$	−150.099	−	71.5433i	−0.173725	−	0.0828047i
$865$		0			0
$866$	3.82689	−	42.9058i	0.00441904	−	0.0495448i
$867$			257.871i			0.297429i
$868$	−260.226	−	46.7928i	−0.299799	−	0.0539088i
$869$	−191.463			−0.220326
$870$		0			0
$871$			108.360i			0.124408i
$872$	218.044	−	797.546i	0.250051	−	0.914617i
$873$	274.189			0.314076
$874$	−47.1336	+	528.446i	−0.0539287	+	0.604630i
$875$		0			0
$876$	−103.955	+	578.119i	−0.118670	+	0.659953i
$877$	549.975			0.627109			0.313555	−	0.949570i	$-0.398480\pi$
$877$	549.975			0.627109			0.313555	+	0.949570i	$0.398480\pi$
$878$	−493.594	−	44.0251i	−0.562180	−	0.0501425i
$879$		−	260.528i		−	0.296391i
$880$		0			0
$881$	636.072			0.721989			0.360995	−	0.932568i	$-0.382437\pi$
$881$	636.072			0.721989			0.360995	+	0.932568i	$0.382437\pi$
$882$	−25.3578	+	284.303i	−0.0287503	+	0.322339i
$883$			689.661i			0.781043i	0.920594	+	0.390521i	$0.127705\pi$
$883$			689.661i			0.781043i	−0.920594	+	0.390521i	$0.872295\pi$
$884$	−921.545	−	165.709i	−1.04247	−	0.187453i
$885$		0			0
$886$	1164.93	+	103.903i	1.31481	+	0.117272i
$887$		−	1053.94i		−	1.18821i	−0.804389	−	0.594103i	$-0.797507\pi$
$887$		−	1053.94i		−	1.18821i	0.804389	−	0.594103i	$-0.202493\pi$
$888$	670.821	+	183.398i	0.755429	+	0.206530i
$889$	−213.279			−0.239909
$890$		0			0
$891$			73.9865i			0.0830376i
$892$	159.593	−	887.533i	0.178916	−	0.994992i
$893$	505.054			0.565570
$894$	−10.7977	−	0.963078i	−0.0120780	−	0.00107727i
$895$		0			0
$896$	124.252	+	89.2123i	0.138674	+	0.0995673i
$897$	183.787			0.204891
$898$	27.0240	−	302.984i	0.0300936	−	0.337399i
$899$			2235.78i			2.48696i
$900$		0			0
$901$	−1197.39			−1.32896
$902$	−1205.90	−	107.557i	−1.33691	−	0.119243i
$903$			39.5012i			0.0437444i
$904$	−65.9691	+	241.297i	−0.0729747	+	0.266922i
$905$		0			0
$906$	−91.2363	+	1022.91i	−0.100702	+	1.12904i
$907$			496.037i			0.546899i	0.961886	+	0.273449i	$0.0881646\pi$
$907$			496.037i			0.546899i	−0.961886	+	0.273449i	$0.911835\pi$
$908$	−76.5112	+	425.497i	−0.0842635	+	0.468609i
$909$	89.9339			0.0989372
$910$		0			0
$911$		−	336.684i		−	0.369577i	−0.982778	−	0.184788i	$-0.940840\pi$
$911$		−	336.684i		−	0.369577i	0.982778	−	0.184788i	$-0.0591599\pi$
$912$	−726.459	−	269.988i	−0.796556	−	0.296039i
$913$	766.660			0.839715
$914$	−107.042	+	1200.12i	−0.117114	+	1.31304i
$915$		0			0
$916$	225.777	+	40.5984i	0.246481	+	0.0443214i
$917$	−183.725			−0.200355
$918$	216.606	+	19.3197i	0.235954	+	0.0210454i
$919$		−	937.464i		−	1.02009i	−0.860147	−	0.510046i	$-0.829629\pi$
$919$		−	937.464i		−	1.02009i	0.860147	−	0.510046i	$-0.170371\pi$
$920$		0			0
$921$	−976.729			−1.06051
$922$	−89.7129	+	1005.83i	−0.0973025	+	1.09092i
$923$			768.439i			0.832545i
$924$	12.0454	−	66.9875i	0.0130362	−	0.0724973i
$925$		0			0
$926$	1005.13	+	89.6504i	1.08545	+	0.0968147i
$927$		−	266.246i		−	0.287212i
$928$	556.530	−	1167.61i	0.599709	−	1.25820i
$929$	858.647			0.924270			0.462135	−	0.886810i	$-0.347084\pi$
$929$	858.647			0.924270			0.462135	+	0.886810i	$0.347084\pi$
$930$		0			0
$931$			1330.38i			1.42898i
$932$	1123.26	+	201.981i	1.20522	+	0.216718i
$933$	69.3191			0.0742971
$934$	1496.89	+	133.512i	1.60267	+	0.142947i
$935$		0			0
$936$	−70.8004	+	258.968i	−0.0756414	+	0.276676i
$937$	−1276.09			−1.36189			−0.680943	−	0.732336i	$-0.738430\pi$
$937$	−1276.09			−1.36189			−0.680943	+	0.732336i	$0.738430\pi$
$938$	−2.05680	+	23.0602i	−0.00219275	+	0.0245844i
$939$		−	3.16371i		−	0.00336923i
$940$		0			0
$941$	536.218			0.569838			0.284919	−	0.958552i	$-0.408033\pi$
$941$	536.218			0.569838			0.284919	+	0.958552i	$0.408033\pi$
$942$	916.723	+	81.7652i	0.973167	+	0.0867995i
$943$		−	698.485i		−	0.740705i
$944$	338.138	−	909.830i	0.358197	−	0.963803i
$945$		0			0
$946$	−27.8757	+	312.533i	−0.0294669	+	0.330373i
$947$		−	48.1723i		−	0.0508683i	−0.999677	−	0.0254341i	$-0.991903\pi$
$947$		−	48.1723i		−	0.0508683i	0.999677	−	0.0254341i	$-0.00809681\pi$
$948$	158.813	+	28.5572i	0.167524	+	0.0301236i
$949$	948.407			0.999375
$950$		0			0
$951$		−	426.805i		−	0.448796i
$952$	−192.970	−	52.7567i	−0.202699	−	0.0554167i
$953$	−1449.85			−1.52136			−0.760679	−	0.649129i	$-0.775134\pi$
$953$	−1449.85			−1.52136			−0.760679	+	0.649129i	$0.775134\pi$
$954$	−30.5013	+	341.970i	−0.0319720	+	0.358459i
$955$		0			0
$956$	−54.6841	+	304.111i	−0.0572009	+	0.318108i
$957$	−575.536			−0.601396
$958$	1158.20	+	103.303i	1.20898	+	0.107832i
$959$		−	63.3272i		−	0.0660346i
$960$		0			0
$961$	−2098.53			−2.18369
$962$	99.7553	−	1118.42i	0.103696	−	1.16260i
$963$		−	488.765i		−	0.507544i
$964$	513.986	+	92.4231i	0.533181	+	0.0958746i
$965$		0			0
$966$	39.1120	+	3.48851i	0.0404886	+	0.00361129i
$967$		−	1320.06i		−	1.36510i	−0.730837	−	0.682552i	$-0.760870\pi$
$967$		−	1320.06i		−	1.36510i	0.730837	−	0.682552i	$-0.239130\pi$
$968$	−112.701	+	412.230i	−0.116427	+	0.425857i
$969$	1013.59			1.04602
$970$		0			0
$971$			1269.58i			1.30749i	0.756713	+	0.653747i	$0.226804\pi$
$971$			1269.58i			1.30749i	−0.756713	+	0.653747i	$0.773196\pi$
$972$	11.0352	−	61.3696i	0.0113531	−	0.0631374i
$973$	−26.1015			−0.0268258
$974$	−1110.57	−	99.0548i	−1.14021	−	0.101699i
$975$		0			0
$976$	−320.229	−	119.013i	−0.328103	−	0.121939i
$977$	−1262.18			−1.29190			−0.645948	−	0.763382i	$-0.723538\pi$
$977$	−1262.18			−1.29190			−0.645948	+	0.763382i	$0.723538\pi$
$978$	−63.2526	+	709.167i	−0.0646755	+	0.725119i
$979$			517.821i			0.528929i
$980$		0			0
$981$	310.055			0.316061
$982$	−52.1992	−	4.65580i	−0.0531560	−	0.00474114i
$983$		−	235.722i		−	0.239798i	−0.992786	−	0.119899i	$-0.961743\pi$
$983$		−	235.722i		−	0.239798i	0.992786	−	0.119899i	$-0.0382571\pi$
$984$	984.212	+	269.077i	1.00022	+	0.273453i
$985$		0			0
$986$	−150.286	+	1684.96i	−0.152420	+	1.70888i
$987$		−	37.3806i		−	0.0378729i
$988$	−221.458	+	1231.58i	−0.224148	+	1.24654i
$989$	−181.027			−0.183040
$990$		0			0
$991$			1601.53i			1.61607i	0.589135	+	0.808035i	$0.299469\pi$
$991$			1601.53i			1.61607i	−0.589135	+	0.808035i	$0.700531\pi$
$992$	1597.80	+	761.578i	1.61068	+	0.767719i
$993$	723.430			0.728530
$994$	−14.5859	+	163.532i	−0.0146740	+	0.164520i
$995$		0			0
$996$	−635.921	−	114.349i	−0.638475	−	0.114808i
$997$	−984.298			−0.987260			−0.493630	−	0.869672i	$-0.664330\pi$
$997$	−984.298			−0.987260			−0.493630	+	0.869672i	$0.664330\pi$
$998$	−885.713	−	78.9993i	−0.887488	−	0.0791576i
$999$			260.790i			0.261051i

Twists

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

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

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.177680 - 1.99209i) q^{2} +1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501i q^{7} +(-2.10973 + 7.71680i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.177680 - 1.99209i) q^{2} +1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501i q^{7} +(-2.10973 + 7.71680i) q^{8} -3.00000 q^{9} +8.22072i q^{11} +(1.22614 - 6.81884i) q^{12} -11.1863 q^{13} +(-2.38058 - 0.212331i) q^{14} +(14.9977 + 5.57389i) q^{16} -20.9256 q^{17} +(-0.533041 + 5.97628i) q^{18} +27.9657i q^{19} +2.06983 q^{21} +(16.3764 + 1.46066i) q^{22} +9.48564i q^{23} +(-13.3659 - 3.65415i) q^{24} +(-1.98759 + 22.2842i) q^{26} -5.19615i q^{27} +(-0.845964 + 4.70460i) q^{28} +40.4205 q^{29} +55.3130i q^{31} +(13.7685 - 28.8865i) q^{32} -14.2387 q^{33} +(-3.71807 + 41.6858i) q^{34} +(11.8106 + 2.12373i) q^{36} -50.1890 q^{37} +(55.7102 + 4.96895i) q^{38} -19.3753i q^{39} -73.6361 q^{41} +(0.367767 - 4.12328i) q^{42} +19.0843i q^{43} +(5.81954 - 32.3638i) q^{44} +(18.8963 + 1.68541i) q^{46} -18.0598i q^{47} +(-9.65427 + 25.9768i) q^{48} +47.5719 q^{49} -36.2442i q^{51} +(44.0391 + 7.91894i) q^{52} +57.2212 q^{53} +(-10.3512 - 0.923254i) q^{54} +(9.22169 + 2.52115i) q^{56} -48.4380 q^{57} +(7.18193 - 80.5213i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(110.189 + 9.82804i) q^{62} +3.58504i q^{63} +(-55.0981 - 32.5607i) q^{64} +(-2.52994 + 28.3648i) q^{66} -9.68679i q^{67} +(82.3812 + 14.8135i) q^{68} -16.4296 q^{69} -68.6944i q^{71} +(6.32918 - 23.1504i) q^{72} -84.7825 q^{73} +(-8.91760 + 99.9811i) q^{74} +(19.7972 - 110.097i) q^{76} +9.82388 q^{77} +(-38.5974 - 3.44261i) q^{78} +23.2903i q^{79} +9.00000 q^{81} +(-13.0837 + 146.690i) q^{82} -93.2595i q^{83} +(-8.14861 - 1.46525i) q^{84} +(38.0177 + 3.39091i) q^{86} +70.0104i q^{87} +(-63.4377 - 17.3435i) q^{88} +62.9898 q^{89} +13.3678i q^{91} +(6.71499 - 37.3436i) q^{92} -95.8049 q^{93} +(-35.9767 - 3.20887i) q^{94} +(50.0328 + 23.8478i) q^{96} -91.3962 q^{97} +(8.45260 - 94.7677i) q^{98} -24.6622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	\( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} - 8 q^{13} + 22 q^{14} + 40 q^{16} + 6 q^{18} + 24 q^{21} - 4 q^{22} - 36 q^{24} - 66 q^{26} - 104 q^{28} - 32 q^{29} - 112 q^{32} + 124 q^{34} + 24 q^{36} + 176 q^{37} + 170 q^{38} - 16 q^{41} - 54 q^{42} + 40 q^{44} - 76 q^{46} - 24 q^{48} + 16 q^{49} - 56 q^{52} + 304 q^{53} + 18 q^{54} - 172 q^{56} - 72 q^{57} + 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 108 q^{66} - 88 q^{68} - 96 q^{69} + 60 q^{72} - 240 q^{73} - 108 q^{74} + 120 q^{76} + 384 q^{77} - 150 q^{78} + 72 q^{81} - 320 q^{82} - 144 q^{84} + 214 q^{86} + 200 q^{88} + 128 q^{89} - 312 q^{92} - 72 q^{93} + 12 q^{94} + 96 q^{96} - 216 q^{97} - 60 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 - 8 * q^13 + 22 * q^14 + 40 * q^16 + 6 * q^18 + 24 * q^21 - 4 * q^22 - 36 * q^24 - 66 * q^26 - 104 * q^28 - 32 * q^29 - 112 * q^32 + 124 * q^34 + 24 * q^36 + 176 * q^37 + 170 * q^38 - 16 * q^41 - 54 * q^42 + 40 * q^44 - 76 * q^46 - 24 * q^48 + 16 * q^49 - 56 * q^52 + 304 * q^53 + 18 * q^54 - 172 * q^56 - 72 * q^57 + 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 108 * q^66 - 88 * q^68 - 96 * q^69 + 60 * q^72 - 240 * q^73 - 108 * q^74 + 120 * q^76 + 384 * q^77 - 150 * q^78 + 72 * q^81 - 320 * q^82 - 144 * q^84 + 214 * q^86 + 200 * q^88 + 128 * q^89 - 312 * q^92 - 72 * q^93 + 12 * q^94 + 96 * q^96 - 216 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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