LMFDB - Embedded newform 675.3.i.a.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,3,Mod(224,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("675.224");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.i (of order $6$, degree $2$, 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:	$18.3924178443$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	675.449
Dual form			675.3.i.a.224.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.73205 + 1.00000i) q^{7} -8.66025 q^{8} +O(q^{10})$	\(q+(-0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.73205 + 1.00000i) q^{7} -8.66025 q^{8} +(1.50000 - 0.866025i) q^{11} +(3.46410 + 2.00000i) q^{13} +(3.00000 + 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} -15.5885 q^{17} -11.0000 q^{19} +(-2.59808 - 1.50000i) q^{22} +(-13.8564 + 24.0000i) q^{23} -6.92820i q^{26} +2.00000i q^{28} +(39.0000 - 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(-7.79423 + 13.5000i) q^{32} +(13.5000 + 23.3827i) q^{34} +34.0000i q^{37} +(9.52628 + 16.5000i) q^{38} +(10.5000 + 6.06218i) q^{41} +(-52.8275 + 30.5000i) q^{43} -1.73205i q^{44} +48.0000 q^{46} +(-24.2487 - 42.0000i) q^{47} +(-22.5000 + 38.9711i) q^{49} +(3.46410 - 2.00000i) q^{52} +(15.0000 - 8.66025i) q^{56} +(-67.5500 - 39.0000i) q^{58} +(43.5000 + 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} +55.4256 q^{62} +71.0000 q^{64} +(-26.8468 - 15.5000i) q^{67} +(-7.79423 + 13.5000i) q^{68} +31.1769i q^{71} +65.0000i q^{73} +(51.0000 - 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(-1.73205 + 3.00000i) q^{77} +(19.0000 + 32.9090i) q^{79} -21.0000i q^{82} +(24.2487 + 42.0000i) q^{83} +(91.5000 + 52.8275i) q^{86} +(-12.9904 + 7.50000i) q^{88} +124.708i q^{89} -8.00000 q^{91} +(13.8564 + 24.0000i) q^{92} +(-42.0000 + 72.7461i) q^{94} +(99.5929 - 57.5000i) q^{97} +77.9423 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} + 6 q^{11} + 12 q^{14} + 22 q^{16} - 44 q^{19} + 156 q^{29} - 64 q^{31} + 54 q^{34} + 42 q^{41} + 192 q^{46} - 90 q^{49} + 60 q^{56} + 174 q^{59} - 112 q^{61} + 284 q^{64} + 204 q^{74} - 22 q^{76} + 76 q^{79} + 366 q^{86} - 32 q^{91} - 168 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^11 + 12 * q^14 + 22 * q^16 - 44 * q^19 + 156 * q^29 - 64 * q^31 + 54 * q^34 + 42 * q^41 + 192 * q^46 - 90 * q^49 + 60 * q^56 + 174 * q^59 - 112 * q^61 + 284 * q^64 + 204 * q^74 - 22 * q^76 + 76 * q^79 + 366 * q^86 - 32 * q^91 - 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	1.50000i	−0.433013	−	0.750000i	0.564118	−	0.825694i	$-0.309216\pi$
$2$	−0.866025	−	1.50000i	−0.433013	−	0.750000i	−0.997131	+	0.0756939i	$0.975883\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.125000	−	0.216506i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	+	1.00000i	−0.247436	+	0.142857i	−0.618590	−	0.785714i	$-0.712296\pi$
$7$	−1.73205	+	1.00000i	−0.247436	+	0.142857i	0.371154	+	0.928571i	$0.378962\pi$
$8$	−8.66025			−1.08253
$9$		0			0
$10$		0			0
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	−0.430266	−	0.902702i	$-0.641580\pi$
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	0.566630	+	0.823972i	$0.308247\pi$
$12$		0			0
$13$	3.46410	+	2.00000i	0.266469	+	0.153846i	0.627282	−	0.778792i	$-0.284167\pi$
$13$	3.46410	+	2.00000i	0.266469	+	0.153846i	−0.360813	+	0.932638i	$0.617501\pi$
$14$	3.00000	+	1.73205i	0.214286	+	0.123718i
$15$		0			0
$16$	5.50000	+	9.52628i	0.343750	+	0.595392i
$17$	−15.5885			−0.916968			−0.458484	−	0.888703i	$-0.651607\pi$
$17$	−15.5885			−0.916968			−0.458484	+	0.888703i	$0.651607\pi$
$18$		0			0
$19$	−11.0000			−0.578947			−0.289474	−	0.957186i	$-0.593480\pi$
$19$	−11.0000			−0.578947			−0.289474	+	0.957186i	$0.593480\pi$
$20$		0			0
$21$		0			0
$22$	−2.59808	−	1.50000i	−0.118094	−	0.0681818i
$23$	−13.8564	+	24.0000i	−0.602452	+	1.04348i	0.389996	+	0.920817i	$0.372476\pi$
$23$	−13.8564	+	24.0000i	−0.602452	+	1.04348i	−0.992449	+	0.122662i	$0.960857\pi$
$24$		0			0
$25$		0			0
$26$		−	6.92820i		−	0.266469i
$27$		0			0
$28$			2.00000i			0.0714286i
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.357316	−	0.933984i	$-0.383692\pi$
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.987511	+	0.157547i	$0.0503586\pi$
$30$		0			0
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	0.483696	+	0.875236i	$0.339294\pi$
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	−0.999825	+	0.0187254i	$0.994039\pi$
$32$	−7.79423	+	13.5000i	−0.243570	+	0.421875i
$33$		0			0
$34$	13.5000	+	23.3827i	0.397059	+	0.687726i
$35$		0			0
$36$		0			0
$37$			34.0000i			0.918919i	0.888199	+	0.459459i	$0.151957\pi$
$37$			34.0000i			0.918919i	−0.888199	+	0.459459i	$0.848043\pi$
$38$	9.52628	+	16.5000i	0.250692	+	0.434211i
$39$		0			0
$40$		0			0
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	0.622553	−	0.782578i	$-0.286095\pi$
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	−0.366456	+	0.930436i	$0.619429\pi$
$42$		0			0
$43$	−52.8275	+	30.5000i	−1.22855	+	0.709302i	−0.966726	−	0.255814i	$-0.917657\pi$
$43$	−52.8275	+	30.5000i	−1.22855	+	0.709302i	−0.261822	+	0.965116i	$0.584323\pi$
$44$		−	1.73205i		−	0.0393648i
$45$		0			0
$46$	48.0000			1.04348
$47$	−24.2487	−	42.0000i	−0.515930	−	0.893617i	−0.999829	−	0.0184931i	$-0.994113\pi$
$47$	−24.2487	−	42.0000i	−0.515930	−	0.893617i	0.483899	−	0.875124i	$-0.339220\pi$
$48$		0			0
$49$	−22.5000	+	38.9711i	−0.459184	+	0.795329i
$50$		0			0
$51$		0			0
$52$	3.46410	−	2.00000i	0.0666173	−	0.0384615i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$	15.0000	−	8.66025i	0.267857	−	0.154647i
$57$		0			0
$58$	−67.5500	−	39.0000i	−1.16465	−	0.672414i
$59$	43.5000	+	25.1147i	0.737288	+	0.425674i	0.821082	−	0.570810i	$-0.193371\pi$
$59$	43.5000	+	25.1147i	0.737288	+	0.425674i	−0.0837943	+	0.996483i	$0.526704\pi$
$60$		0			0
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	0.539893	−	0.841734i	$-0.318465\pi$
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	−0.998909	+	0.0466940i	$0.985131\pi$
$62$	55.4256			0.893962
$63$		0			0
$64$	71.0000			1.10938
$65$		0			0
$66$		0			0
$67$	−26.8468	−	15.5000i	−0.400698	−	0.231343i	0.286087	−	0.958204i	$-0.407645\pi$
$67$	−26.8468	−	15.5000i	−0.400698	−	0.231343i	−0.686785	+	0.726860i	$0.740979\pi$
$68$	−7.79423	+	13.5000i	−0.114621	+	0.198529i
$69$		0			0
$70$		0			0
$71$			31.1769i			0.439111i	0.975600	+	0.219556i	$0.0704608\pi$
$71$			31.1769i			0.439111i	−0.975600	+	0.219556i	$0.929539\pi$
$72$		0			0
$73$			65.0000i			0.890411i	0.895428	+	0.445205i	$0.146869\pi$
$73$			65.0000i			0.890411i	−0.895428	+	0.445205i	$0.853131\pi$
$74$	51.0000	−	29.4449i	0.689189	−	0.397904i
$75$		0			0
$76$	−5.50000	+	9.52628i	−0.0723684	+	0.125346i
$77$	−1.73205	+	3.00000i	−0.0224942	+	0.0389610i
$78$		0			0
$79$	19.0000	+	32.9090i	0.240506	+	0.416569i	0.960859	−	0.277039i	$-0.0893532\pi$
$79$	19.0000	+	32.9090i	0.240506	+	0.416569i	−0.720352	+	0.693608i	$0.756020\pi$
$80$		0			0
$81$		0			0
$82$		−	21.0000i		−	0.256098i
$83$	24.2487	+	42.0000i	0.292153	+	0.506024i	0.974319	−	0.225174i	$-0.0722950\pi$
$83$	24.2487	+	42.0000i	0.292153	+	0.506024i	−0.682165	+	0.731198i	$0.738962\pi$
$84$		0			0
$85$		0			0
$86$	91.5000	+	52.8275i	1.06395	+	0.614274i
$87$		0			0
$88$	−12.9904	+	7.50000i	−0.147618	+	0.0852273i
$89$			124.708i			1.40121i	0.713549	+	0.700605i	$0.247086\pi$
$89$			124.708i			1.40121i	−0.713549	+	0.700605i	$0.752914\pi$
$90$		0			0
$91$	−8.00000			−0.0879121
$92$	13.8564	+	24.0000i	0.150613	+	0.260870i
$93$		0			0
$94$	−42.0000	+	72.7461i	−0.446809	+	0.773895i
$95$		0			0
$96$		0			0
$97$	99.5929	−	57.5000i	1.02673	−	0.592784i	0.110685	−	0.993856i	$-0.464696\pi$
$97$	99.5929	−	57.5000i	1.02673	−	0.592784i	0.916047	+	0.401072i	$0.131362\pi$
$98$	77.9423			0.795329
$99$		0			0
$100$		0			0
$101$	−39.0000	+	22.5167i	−0.386139	+	0.222937i	−0.680486	−	0.732761i	$-0.738231\pi$
$101$	−39.0000	+	22.5167i	−0.386139	+	0.222937i	0.294347	+	0.955699i	$0.404898\pi$
$102$		0			0
$103$	34.6410	+	20.0000i	0.336321	+	0.194175i	0.658644	−	0.752455i	$-0.271130\pi$
$103$	34.6410	+	20.0000i	0.336321	+	0.194175i	−0.322323	+	0.946630i	$0.604464\pi$
$104$	−30.0000	−	17.3205i	−0.288462	−	0.166543i
$105$		0			0
$106$		0			0
$107$	140.296			1.31118			0.655589	−	0.755118i	$-0.272420\pi$
$107$	140.296			1.31118			0.655589	+	0.755118i	$0.272420\pi$
$108$		0			0
$109$	52.0000			0.477064			0.238532	−	0.971135i	$-0.423334\pi$
$109$	52.0000			0.477064			0.238532	+	0.971135i	$0.423334\pi$
$110$		0			0
$111$		0			0
$112$	−19.0526	−	11.0000i	−0.170112	−	0.0982143i
$113$	−45.0333	+	78.0000i	−0.398525	+	0.690265i	−0.993544	−	0.113446i	$-0.963811\pi$
$113$	−45.0333	+	78.0000i	−0.398525	+	0.690265i	0.595019	+	0.803711i	$0.297144\pi$
$114$		0			0
$115$		0			0
$116$		−	45.0333i		−	0.388218i
$117$		0			0
$118$		−	87.0000i		−	0.737288i
$119$	27.0000	−	15.5885i	0.226891	−	0.130995i
$120$		0			0
$121$	−59.0000	+	102.191i	−0.487603	+	0.844554i
$122$	−48.4974	+	84.0000i	−0.397520	+	0.688525i
$123$		0			0
$124$	16.0000	+	27.7128i	0.129032	+	0.223490i
$125$		0			0
$126$		0			0
$127$			16.0000i			0.125984i	0.998014	+	0.0629921i	$0.0200643\pi$
$127$			16.0000i			0.125984i	−0.998014	+	0.0629921i	$0.979936\pi$
$128$	−30.3109	−	52.5000i	−0.236804	−	0.410156i
$129$		0			0
$130$		0			0
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.129826	−	0.991537i	$-0.541442\pi$
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.923609	+	0.383336i	$0.874775\pi$
$132$		0			0
$133$	19.0526	−	11.0000i	0.143252	−	0.0827068i
$134$			53.6936i			0.400698i
$135$		0			0
$136$	135.000			0.992647
$137$	−94.3968	−	163.500i	−0.689028	−	1.19343i	−0.972153	−	0.234348i	$-0.924705\pi$
$137$	−94.3968	−	163.500i	−0.689028	−	1.19343i	0.283125	−	0.959083i	$-0.408629\pi$
$138$		0			0
$139$	2.50000	−	4.33013i	0.0179856	−	0.0311520i	−0.856893	−	0.515495i	$-0.827608\pi$
$139$	2.50000	−	4.33013i	0.0179856	−	0.0311520i	0.874878	+	0.484343i	$0.160941\pi$
$140$		0			0
$141$		0			0
$142$	46.7654	−	27.0000i	0.329334	−	0.190141i
$143$	6.92820			0.0484490
$144$		0			0
$145$		0			0
$146$	97.5000	−	56.2917i	0.667808	−	0.385559i
$147$		0			0
$148$	29.4449	+	17.0000i	0.198952	+	0.114865i
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.0133049	−	0.999911i	$-0.504235\pi$
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.872601	+	0.488433i	$0.837569\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	0.831012	−	0.556255i	$-0.187762\pi$
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	−0.897237	+	0.441550i	$0.854429\pi$
$152$	95.2628			0.626729
$153$		0			0
$154$	6.00000			0.0389610
$155$		0			0
$156$		0			0
$157$	−34.6410	−	20.0000i	−0.220643	−	0.127389i	0.385605	−	0.922664i	$-0.373993\pi$
$157$	−34.6410	−	20.0000i	−0.220643	−	0.127389i	−0.606248	+	0.795276i	$0.707326\pi$
$158$	32.9090	−	57.0000i	0.208285	−	0.360759i
$159$		0			0
$160$		0			0
$161$		−	55.4256i		−	0.344259i
$162$		0			0
$163$		−	106.000i		−	0.650307i	−0.945661	−	0.325153i	$-0.894584\pi$
$163$		−	106.000i		−	0.650307i	0.945661	−	0.325153i	$-0.105416\pi$
$164$	10.5000	−	6.06218i	0.0640244	−	0.0369645i
$165$		0			0
$166$	42.0000	−	72.7461i	0.253012	−	0.438230i
$167$	−95.2628	+	165.000i	−0.570436	+	0.988024i	0.426085	+	0.904683i	$0.359892\pi$
$167$	−95.2628	+	165.000i	−0.570436	+	0.988024i	−0.996521	+	0.0833409i	$0.973441\pi$
$168$		0			0
$169$	−76.5000	−	132.502i	−0.452663	−	0.784035i
$170$		0			0
$171$		0			0
$172$			61.0000i			0.354651i
$173$	−116.047	−	201.000i	−0.670794	−	1.16185i	−0.977679	−	0.210103i	$-0.932620\pi$
$173$	−116.047	−	201.000i	−0.670794	−	1.16185i	0.306885	−	0.951747i	$-0.400713\pi$
$174$		0			0
$175$		0			0
$176$	16.5000	+	9.52628i	0.0937500	+	0.0541266i
$177$		0			0
$178$	187.061	−	108.000i	1.05091	−	0.606742i
$179$			62.3538i			0.348345i	0.984715	+	0.174173i	$0.0557251\pi$
$179$			62.3538i			0.348345i	−0.984715	+	0.174173i	$0.944275\pi$
$180$		0			0
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$	6.92820	+	12.0000i	0.0380671	+	0.0659341i
$183$		0			0
$184$	120.000	−	207.846i	0.652174	−	1.12960i
$185$		0			0
$186$		0			0
$187$	−23.3827	+	13.5000i	−0.125041	+	0.0721925i
$188$	−48.4974			−0.257965
$189$		0			0
$190$		0			0
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.923308	−	0.384060i	$-0.874525\pi$
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.129048	+	0.991638i	$0.541192\pi$
$192$		0			0
$193$	229.497	+	132.500i	1.18910	+	0.686528i	0.958103	−	0.286425i	$-0.0924670\pi$
$193$	229.497	+	132.500i	1.18910	+	0.686528i	0.231000	+	0.972954i	$0.425800\pi$
$194$	−172.500	−	99.5929i	−0.889175	−	0.513366i
$195$		0			0
$196$	22.5000	+	38.9711i	0.114796	+	0.198832i
$197$	−124.708			−0.633034			−0.316517	−	0.948587i	$-0.602513\pi$
$197$	−124.708			−0.633034			−0.316517	+	0.948587i	$0.602513\pi$
$198$		0			0
$199$	−290.000			−1.45729			−0.728643	−	0.684893i	$-0.759849\pi$
$199$	−290.000			−1.45729			−0.728643	+	0.684893i	$0.759849\pi$
$200$		0			0
$201$		0			0
$202$	67.5500	+	39.0000i	0.334406	+	0.193069i
$203$	−45.0333	+	78.0000i	−0.221839	+	0.384236i
$204$		0			0
$205$		0			0
$206$		−	69.2820i		−	0.336321i
$207$		0			0
$208$			44.0000i			0.211538i
$209$	−16.5000	+	9.52628i	−0.0789474	+	0.0455803i
$210$		0			0
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$		0			0
$214$	−121.500	−	210.444i	−0.567757	−	0.983384i
$215$		0			0
$216$		0			0
$217$		−	64.0000i		−	0.294931i
$218$	−45.0333	−	78.0000i	−0.206575	−	0.357798i
$219$		0			0
$220$		0			0
$221$	−54.0000	−	31.1769i	−0.244344	−	0.141072i
$222$		0			0
$223$	−45.0333	+	26.0000i	−0.201943	+	0.116592i	−0.597562	−	0.801823i	$-0.703864\pi$
$223$	−45.0333	+	26.0000i	−0.201943	+	0.116592i	0.395618	+	0.918415i	$0.370530\pi$
$224$		−	31.1769i		−	0.139183i
$225$		0			0
$226$	156.000			0.690265
$227$	−94.3968	−	163.500i	−0.415845	−	0.720264i	0.579672	−	0.814850i	$-0.303181\pi$
$227$	−94.3968	−	163.500i	−0.415845	−	0.720264i	−0.995517	+	0.0945856i	$0.969847\pi$
$228$		0			0
$229$	133.000	−	230.363i	0.580786	−	1.00595i	−0.414600	−	0.910004i	$-0.636079\pi$
$229$	133.000	−	230.363i	0.580786	−	1.00595i	0.995386	−	0.0959473i	$-0.0305880\pi$
$230$		0			0
$231$		0			0
$232$	−337.750	+	195.000i	−1.45582	+	0.840517i
$233$	202.650			0.869742			0.434871	−	0.900493i	$-0.356794\pi$
$233$	202.650			0.869742			0.434871	+	0.900493i	$0.356794\pi$
$234$		0			0
$235$		0			0
$236$	43.5000	−	25.1147i	0.184322	−	0.106418i
$237$		0			0
$238$	−46.7654	−	27.0000i	−0.196493	−	0.113445i
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.457252	−	0.889337i	$-0.651166\pi$
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.998815	+	0.0486764i	$0.984500\pi$
$240$		0			0
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	0.715773	−	0.698333i	$-0.246075\pi$
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	−0.962661	+	0.270711i	$0.912741\pi$
$242$	204.382			0.844554
$243$		0			0
$244$	−56.0000			−0.229508
$245$		0			0
$246$		0			0
$247$	−38.1051	−	22.0000i	−0.154272	−	0.0890688i
$248$	138.564	−	240.000i	0.558726	−	0.967742i
$249$		0			0
$250$		0			0
$251$			389.711i			1.55264i	0.630342	+	0.776318i	$0.282915\pi$
$251$			389.711i			1.55264i	−0.630342	+	0.776318i	$0.717085\pi$
$252$		0			0
$253$			48.0000i			0.189723i
$254$	24.0000	−	13.8564i	0.0944882	−	0.0545528i
$255$		0			0
$256$	89.5000	−	155.019i	0.349609	−	0.605541i
$257$	−87.4686	+	151.500i	−0.340345	+	0.589494i	−0.984497	−	0.175403i	$-0.943877\pi$
$257$	−87.4686	+	151.500i	−0.340345	+	0.589494i	0.644152	+	0.764897i	$0.277210\pi$
$258$		0			0
$259$	−34.0000	−	58.8897i	−0.131274	−	0.227373i
$260$		0			0
$261$		0			0
$262$			276.000i			1.05344i
$263$	−22.5167	−	39.0000i	−0.0856147	−	0.148289i	0.820038	−	0.572309i	$-0.193952\pi$
$263$	−22.5167	−	39.0000i	−0.0856147	−	0.148289i	−0.905653	+	0.424020i	$0.860619\pi$
$264$		0			0
$265$		0			0
$266$	−33.0000	−	19.0526i	−0.124060	−	0.0716262i
$267$		0			0
$268$	−26.8468	+	15.5000i	−0.100175	+	0.0578358i
$269$		−	187.061i		−	0.695396i	−0.937607	−	0.347698i	$-0.886963\pi$
$269$		−	187.061i		−	0.695396i	0.937607	−	0.347698i	$-0.113037\pi$
$270$		0			0
$271$	−268.000			−0.988930			−0.494465	−	0.869198i	$-0.664636\pi$
$271$	−268.000			−0.988930			−0.494465	+	0.869198i	$0.664636\pi$
$272$	−85.7365	−	148.500i	−0.315208	−	0.545956i
$273$		0			0
$274$	−163.500	+	283.190i	−0.596715	+	1.03354i
$275$		0			0
$276$		0			0
$277$	−48.4974	+	28.0000i	−0.175081	+	0.101083i	−0.584979	−	0.811048i	$-0.698897\pi$
$277$	−48.4974	+	28.0000i	−0.175081	+	0.101083i	0.409899	+	0.912131i	$0.365564\pi$
$278$	−8.66025			−0.0311520
$279$		0			0
$280$		0			0
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	−0.423402	−	0.905942i	$-0.639164\pi$
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	0.572868	+	0.819648i	$0.305831\pi$
$282$		0			0
$283$	−323.894	−	187.000i	−1.14450	−	0.660777i	−0.196959	−	0.980412i	$-0.563107\pi$
$283$	−323.894	−	187.000i	−1.14450	−	0.660777i	−0.947541	+	0.319634i	$0.896440\pi$
$284$	27.0000	+	15.5885i	0.0950704	+	0.0548889i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.0209790	−	0.0363367i
$287$	−24.2487			−0.0844903
$288$		0			0
$289$	−46.0000			−0.159170
$290$		0			0
$291$		0			0
$292$	56.2917	+	32.5000i	0.192780	+	0.111301i
$293$	126.440	−	219.000i	0.431535	−	0.747440i	−0.565471	−	0.824768i	$-0.691306\pi$
$293$	126.440	−	219.000i	0.431535	−	0.747440i	0.997006	+	0.0773280i	$0.0246389\pi$
$294$		0			0
$295$		0			0
$296$		−	294.449i		−	0.994759i
$297$		0			0
$298$			264.000i			0.885906i
$299$	−96.0000	+	55.4256i	−0.321070	+	0.185370i
$300$		0			0
$301$	61.0000	−	105.655i	0.202658	−	0.351014i
$302$	−17.3205	+	30.0000i	−0.0573527	+	0.0993377i
$303$		0			0
$304$	−60.5000	−	104.789i	−0.199013	−	0.344701i
$305$		0			0
$306$		0			0
$307$		−	533.000i		−	1.73616i	−0.496428	−	0.868078i	$-0.665355\pi$
$307$		−	533.000i		−	1.73616i	0.496428	−	0.868078i	$-0.334645\pi$
$308$	1.73205	+	3.00000i	0.00562354	+	0.00974026i
$309$		0			0
$310$		0			0
$311$	213.000	+	122.976i	0.684887	+	0.395420i	0.801694	−	0.597735i	$-0.203932\pi$
$311$	213.000	+	122.976i	0.684887	+	0.395420i	−0.116806	+	0.993155i	$0.537266\pi$
$312$		0			0
$313$	134.234	−	77.5000i	0.428862	−	0.247604i	−0.269999	−	0.962860i	$-0.587024\pi$
$313$	134.234	−	77.5000i	0.428862	−	0.247604i	0.698862	+	0.715257i	$0.253690\pi$
$314$			69.2820i			0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$	−24.2487	−	42.0000i	−0.0764944	−	0.132492i	0.825241	−	0.564781i	$-0.191039\pi$
$317$	−24.2487	−	42.0000i	−0.0764944	−	0.132492i	−0.901735	+	0.432289i	$0.857706\pi$
$318$		0			0
$319$	39.0000	−	67.5500i	0.122257	−	0.211755i
$320$		0			0
$321$		0			0
$322$	−83.1384	+	48.0000i	−0.258194	+	0.149068i
$323$	171.473			0.530876
$324$		0			0
$325$		0			0
$326$	−159.000	+	91.7987i	−0.487730	+	0.281591i
$327$		0			0
$328$	−90.9327	−	52.5000i	−0.277234	−	0.160061i
$329$	84.0000	+	48.4974i	0.255319	+	0.147409i
$330$		0			0
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	0.864511	−	0.502614i	$-0.167628\pi$
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	−0.867532	+	0.497381i	$0.834295\pi$
$332$	48.4974			0.146077
$333$		0			0
$334$	330.000			0.988024
$335$		0			0
$336$		0			0
$337$	66.6840	+	38.5000i	0.197875	+	0.114243i	0.595664	−	0.803234i	$-0.296889\pi$
$337$	66.6840	+	38.5000i	0.197875	+	0.114243i	−0.397789	+	0.917477i	$0.630222\pi$
$338$	−132.502	+	229.500i	−0.392017	+	0.678994i
$339$		0			0
$340$		0			0
$341$			55.4256i			0.162538i
$342$		0			0
$343$		−	188.000i		−	0.548105i
$344$	457.500	−	264.138i	1.32994	−	0.767842i
$345$		0			0
$346$	−201.000	+	348.142i	−0.580925	+	1.00619i
$347$	−56.2917	+	97.5000i	−0.162224	+	0.280980i	−0.935666	−	0.352887i	$-0.885200\pi$
$347$	−56.2917	+	97.5000i	−0.162224	+	0.280980i	0.773442	+	0.633867i	$0.218533\pi$
$348$		0			0
$349$	208.000	+	360.267i	0.595989	+	1.03228i	0.993407	+	0.114645i	$0.0365730\pi$
$349$	208.000	+	360.267i	0.595989	+	1.03228i	−0.397418	+	0.917638i	$0.630094\pi$
$350$		0			0
$351$		0			0
$352$			27.0000i			0.0767045i
$353$	0.866025	+	1.50000i	0.00245333	+	0.00424929i	0.867249	−	0.497874i	$-0.165886\pi$
$353$	0.866025	+	1.50000i	0.00245333	+	0.00424929i	−0.864796	+	0.502123i	$0.832552\pi$
$354$		0			0
$355$		0			0
$356$	108.000	+	62.3538i	0.303371	+	0.175151i
$357$		0			0
$358$	93.5307	−	54.0000i	0.261259	−	0.150838i
$359$			592.361i			1.65003i	0.565110	+	0.825016i	$0.308834\pi$
$359$			592.361i			1.65003i	−0.565110	+	0.825016i	$0.691166\pi$
$360$		0			0
$361$	−240.000			−0.664820
$362$	200.918	+	348.000i	0.555022	+	0.961326i
$363$		0			0
$364$	−4.00000	+	6.92820i	−0.0109890	+	0.0190335i
$365$		0			0
$366$		0			0
$367$	310.037	−	179.000i	0.844788	−	0.487738i	−0.0141011	−	0.999901i	$-0.504489\pi$
$367$	310.037	−	179.000i	0.844788	−	0.487738i	0.858889	+	0.512162i	$0.171155\pi$
$368$	−304.841			−0.828372
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	502.295	+	290.000i	1.34663	+	0.777480i	0.987771	−	0.155910i	$-0.0498310\pi$
$373$	502.295	+	290.000i	1.34663	+	0.777480i	0.358863	+	0.933390i	$0.383164\pi$
$374$	40.5000	+	23.3827i	0.108289	+	0.0625206i
$375$		0			0
$376$	210.000	+	363.731i	0.558511	+	0.967369i
$377$	180.133			0.477807
$378$		0			0
$379$	−83.0000			−0.218997			−0.109499	−	0.993987i	$-0.534925\pi$
$379$	−83.0000			−0.218997			−0.109499	+	0.993987i	$0.534925\pi$
$380$		0			0
$381$		0			0
$382$	348.142	+	201.000i	0.911367	+	0.526178i
$383$	−278.860	+	483.000i	−0.728094	+	1.26110i	0.229593	+	0.973287i	$0.426260\pi$
$383$	−278.860	+	483.000i	−0.728094	+	1.26110i	−0.957688	+	0.287810i	$0.907073\pi$
$384$		0			0
$385$		0			0
$386$		−	458.993i		−	1.18910i
$387$		0			0
$388$		−	115.000i		−	0.296392i
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.948668	−	0.316274i	$-0.897568\pi$
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.200432	+	0.979708i	$0.564235\pi$
$390$		0			0
$391$	216.000	−	374.123i	0.552430	−	0.956836i
$392$	194.856	−	337.500i	0.497081	−	0.860969i
$393$		0			0
$394$	108.000	+	187.061i	0.274112	+	0.474775i
$395$		0			0
$396$		0			0
$397$		−	362.000i		−	0.911839i	−0.890021	−	0.455919i	$-0.849311\pi$
$397$		−	362.000i		−	0.911839i	0.890021	−	0.455919i	$-0.150689\pi$
$398$	251.147	+	435.000i	0.631024	+	1.09296i
$399$		0			0
$400$		0			0
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	0.0112291	−	0.999937i	$-0.496426\pi$
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	−0.860356	+	0.509693i	$0.829759\pi$
$402$		0			0
$403$	−110.851	+	64.0000i	−0.275065	+	0.158809i
$404$			45.0333i			0.111469i
$405$		0			0
$406$	156.000			0.384236
$407$	29.4449	+	51.0000i	0.0723461	+	0.125307i
$408$		0			0
$409$	110.500	−	191.392i	0.270171	−	0.467950i	−0.698734	−	0.715381i	$-0.746253\pi$
$409$	110.500	−	191.392i	0.270171	−	0.467950i	0.968905	+	0.247431i	$0.0795864\pi$
$410$		0			0
$411$		0			0
$412$	34.6410	−	20.0000i	0.0840801	−	0.0485437i
$413$	−100.459			−0.243242
$414$		0			0
$415$		0			0
$416$	−54.0000	+	31.1769i	−0.129808	+	0.0749445i
$417$		0			0
$418$	28.5788	+	16.5000i	0.0683704	+	0.0394737i
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.987401	+	0.158236i	$0.0505807\pi$
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.630737	+	0.775997i	$0.282753\pi$
$420$		0			0
$421$	341.000	+	590.629i	0.809976	+	1.40292i	0.912880	+	0.408229i	$0.133853\pi$
$421$	341.000	+	590.629i	0.809976	+	1.40292i	−0.102903	+	0.994691i	$0.532813\pi$
$422$	−162.813			−0.385812
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	96.9948	+	56.0000i	0.227154	+	0.131148i
$428$	70.1481	−	121.500i	0.163897	−	0.283879i
$429$		0			0
$430$		0			0
$431$			280.592i			0.651026i	0.945538	+	0.325513i	$0.105537\pi$
$431$			280.592i			0.651026i	−0.945538	+	0.325513i	$0.894463\pi$
$432$		0			0
$433$		−	295.000i		−	0.681293i	−0.940191	−	0.340647i	$-0.889354\pi$
$433$		−	295.000i		−	0.681293i	0.940191	−	0.340647i	$-0.110646\pi$
$434$	−96.0000	+	55.4256i	−0.221198	+	0.127709i
$435$		0			0
$436$	26.0000	−	45.0333i	0.0596330	−	0.103287i
$437$	152.420	−	264.000i	0.348788	−	0.604119i
$438$		0			0
$439$	406.000	+	703.213i	0.924829	+	1.60185i	0.791836	+	0.610734i	$0.209126\pi$
$439$	406.000	+	703.213i	0.924829	+	1.60185i	0.132993	+	0.991117i	$0.457541\pi$
$440$		0			0
$441$		0			0
$442$			108.000i			0.244344i
$443$	−45.8993	−	79.5000i	−0.103610	−	0.179458i	0.809559	−	0.587038i	$-0.199706\pi$
$443$	−45.8993	−	79.5000i	−0.103610	−	0.179458i	−0.913170	+	0.407580i	$0.866373\pi$
$444$		0			0
$445$		0			0
$446$	78.0000	+	45.0333i	0.174888	+	0.100972i
$447$		0			0
$448$	−122.976	+	71.0000i	−0.274499	+	0.158482i
$449$		−	639.127i		−	1.42344i	−0.702461	−	0.711722i	$-0.747915\pi$
$449$		−	639.127i		−	1.42344i	0.702461	−	0.711722i	$-0.252085\pi$
$450$		0			0
$451$	21.0000			0.0465632
$452$	45.0333	+	78.0000i	0.0996312	+	0.172566i
$453$		0			0
$454$	−163.500	+	283.190i	−0.360132	+	0.623767i
$455$		0			0
$456$		0			0
$457$	−56.2917	+	32.5000i	−0.123176	+	0.0711160i	−0.560322	−	0.828275i	$-0.689323\pi$
$457$	−56.2917	+	32.5000i	−0.123176	+	0.0711160i	0.437146	+	0.899391i	$0.355989\pi$
$458$	−460.726			−1.00595
$459$		0			0
$460$		0			0
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.496753	−	0.867892i	$-0.334525\pi$
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.999993	+	0.00374501i	$0.00119208\pi$
$462$		0			0
$463$	−635.663	−	367.000i	−1.37292	−	0.792657i	−0.381627	−	0.924317i	$-0.624636\pi$
$463$	−635.663	−	367.000i	−1.37292	−	0.792657i	−0.991295	+	0.131660i	$0.957969\pi$
$464$	429.000	+	247.683i	0.924569	+	0.533800i
$465$		0			0
$466$	−175.500	−	303.975i	−0.376609	−	0.652307i
$467$	202.650			0.433940			0.216970	−	0.976178i	$-0.430383\pi$
$467$	202.650			0.433940			0.216970	+	0.976178i	$0.430383\pi$
$468$		0			0
$469$	62.0000			0.132196
$470$		0			0
$471$		0			0
$472$	−376.721	−	217.500i	−0.798138	−	0.460805i
$473$	−52.8275	+	91.5000i	−0.111686	+	0.193446i
$474$		0			0
$475$		0			0
$476$		−	31.1769i		−	0.0654977i
$477$		0			0
$478$			696.000i			1.45607i
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.160857	−	0.986978i	$-0.448574\pi$
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.935176	+	0.354183i	$0.115241\pi$
$480$		0			0
$481$	−68.0000	+	117.779i	−0.141372	+	0.244864i
$482$	−103.057	+	178.500i	−0.213811	+	0.370332i
$483$		0			0
$484$	59.0000	+	102.191i	0.121901	+	0.211138i
$485$		0			0
$486$		0			0
$487$			106.000i			0.217659i	0.994060	+	0.108830i	$0.0347103\pi$
$487$			106.000i			0.217659i	−0.994060	+	0.108830i	$0.965290\pi$
$488$	242.487	+	420.000i	0.496900	+	0.860656i
$489$		0			0
$490$		0			0
$491$	199.500	+	115.181i	0.406314	+	0.234585i	0.689205	−	0.724567i	$-0.257960\pi$
$491$	199.500	+	115.181i	0.406314	+	0.234585i	−0.282891	+	0.959152i	$0.591293\pi$
$492$		0			0
$493$	−607.950	+	351.000i	−1.23316	+	0.711968i
$494$			76.2102i			0.154272i
$495$		0			0
$496$	−352.000			−0.709677
$497$	−31.1769	−	54.0000i	−0.0627302	−	0.108652i
$498$		0			0
$499$	−393.500	+	681.562i	−0.788577	+	1.36586i	0.138261	+	0.990396i	$0.455849\pi$
$499$	−393.500	+	681.562i	−0.788577	+	1.36586i	−0.926839	+	0.375460i	$0.877485\pi$
$500$		0			0
$501$		0			0
$502$	584.567	−	337.500i	1.16448	−	0.672311i
$503$	623.538			1.23964			0.619819	−	0.784745i	$-0.287206\pi$
$503$	623.538			1.23964			0.619819	+	0.784745i	$0.287206\pi$
$504$		0			0
$505$		0			0
$506$	72.0000	−	41.5692i	0.142292	−	0.0821526i
$507$		0			0
$508$	13.8564	+	8.00000i	0.0272764	+	0.0157480i
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	0.306034	−	0.952020i	$-0.400998\pi$
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	−0.671457	+	0.741044i	$0.734331\pi$
$510$		0			0
$511$	−65.0000	−	112.583i	−0.127202	−	0.220320i
$512$	−552.524			−1.07915
$513$		0			0
$514$	303.000			0.589494
$515$		0			0
$516$		0			0
$517$	−72.7461	−	42.0000i	−0.140708	−	0.0812379i
$518$	−58.8897	+	102.000i	−0.113687	+	0.196911i
$519$		0			0
$520$		0			0
$521$			202.650i			0.388963i	0.980906	+	0.194482i	$0.0623025\pi$
$521$			202.650i			0.388963i	−0.980906	+	0.194482i	$0.937698\pi$
$522$		0			0
$523$		−	250.000i		−	0.478011i	−0.971018	−	0.239006i	$-0.923179\pi$
$523$		−	250.000i		−	0.478011i	0.971018	−	0.239006i	$-0.0768215\pi$
$524$	−138.000	+	79.6743i	−0.263359	+	0.152050i
$525$		0			0
$526$	−39.0000	+	67.5500i	−0.0741445	+	0.128422i
$527$	249.415	−	432.000i	0.473274	−	0.819734i
$528$		0			0
$529$	−119.500	−	206.980i	−0.225898	−	0.391267i
$530$		0			0
$531$		0			0
$532$		−	22.0000i		−	0.0413534i
$533$	24.2487	+	42.0000i	0.0454948	+	0.0787992i
$534$		0			0
$535$		0			0
$536$	232.500	+	134.234i	0.433769	+	0.250436i
$537$		0			0
$538$	−280.592	+	162.000i	−0.521547	+	0.301115i
$539$			77.9423i			0.144605i
$540$		0			0
$541$	650.000			1.20148			0.600739	−	0.799445i	$-0.294873\pi$
$541$	650.000			1.20148			0.600739	+	0.799445i	$0.294873\pi$
$542$	232.095	+	402.000i	0.428219	+	0.741697i
$543$		0			0
$544$	121.500	−	210.444i	0.223346	−	0.386846i
$545$		0			0
$546$		0			0
$547$	−539.534	+	311.500i	−0.986351	+	0.569470i	−0.904181	−	0.427149i	$-0.859518\pi$
$547$	−539.534	+	311.500i	−0.986351	+	0.569470i	−0.0821692	+	0.996618i	$0.526185\pi$
$548$	−188.794			−0.344514
$549$		0			0
$550$		0			0
$551$	−429.000	+	247.683i	−0.778584	+	0.449516i
$552$		0			0
$553$	−65.8179	−	38.0000i	−0.119020	−	0.0687161i
$554$	84.0000	+	48.4974i	0.151625	+	0.0875405i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.00449640	−	0.00778800i
$557$	−530.008			−0.951540			−0.475770	−	0.879570i	$-0.657830\pi$
$557$	−530.008			−0.951540			−0.475770	+	0.879570i	$0.657830\pi$
$558$		0			0
$559$	−244.000			−0.436494
$560$		0			0
$561$		0			0
$562$	−72.7461	−	42.0000i	−0.129442	−	0.0747331i
$563$	56.2917	−	97.5000i	0.0999852	−	0.173179i	−0.811693	−	0.584084i	$-0.801454\pi$
$563$	56.2917	−	97.5000i	0.0999852	−	0.173179i	0.911678	+	0.410905i	$0.134787\pi$
$564$		0			0
$565$		0			0
$566$			647.787i			1.14450i
$567$		0			0
$568$		−	270.000i		−	0.475352i
$569$	565.500	−	326.492i	0.993849	−	0.573799i	0.0874263	−	0.996171i	$-0.472136\pi$
$569$	565.500	−	326.492i	0.993849	−	0.573799i	0.906423	+	0.422372i	$0.138802\pi$
$570$		0			0
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	−0.999660	−	0.0260926i	$-0.991694\pi$
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	0.522427	+	0.852684i	$0.325027\pi$
$572$	3.46410	−	6.00000i	0.00605612	−	0.0104895i
$573$		0			0
$574$	21.0000	+	36.3731i	0.0365854	+	0.0633677i
$575$		0			0
$576$		0			0
$577$			871.000i			1.50953i	0.655994	+	0.754766i	$0.272250\pi$
$577$			871.000i			1.50953i	−0.655994	+	0.754766i	$0.727750\pi$
$578$	39.8372	+	69.0000i	0.0689224	+	0.119377i
$579$		0			0
$580$		0			0
$581$	−84.0000	−	48.4974i	−0.144578	−	0.0834723i
$582$		0			0
$583$		0			0
$584$		−	562.917i		−	0.963898i
$585$		0			0
$586$	−438.000			−0.747440
$587$	−0.866025	−	1.50000i	−0.00147534	−	0.00255537i	0.865287	−	0.501277i	$-0.167136\pi$
$587$	−0.866025	−	1.50000i	−0.00147534	−	0.00255537i	−0.866762	+	0.498722i	$0.833803\pi$
$588$		0			0
$589$	176.000	−	304.841i	0.298812	−	0.517557i
$590$		0			0
$591$		0			0
$592$	−323.894	+	187.000i	−0.547117	+	0.315878i
$593$	187.061			0.315449			0.157725	−	0.987483i	$-0.449584\pi$
$593$	187.061			0.315449			0.157725	+	0.987483i	$0.449584\pi$
$594$		0			0
$595$		0			0
$596$	−132.000	+	76.2102i	−0.221477	+	0.127870i
$597$		0			0
$598$	166.277	+	96.0000i	0.278055	+	0.160535i
$599$	489.000	+	282.324i	0.816361	+	0.471326i	0.849160	−	0.528136i	$-0.177109\pi$
$599$	489.000	+	282.324i	0.816361	+	0.471326i	−0.0327992	+	0.999462i	$0.510442\pi$
$600$		0			0
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	0.608036	−	0.793909i	$-0.291958\pi$
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	−0.991564	+	0.129620i	$0.958624\pi$
$602$	−211.310			−0.351014
$603$		0			0
$604$	−20.0000			−0.0331126
$605$		0			0
$606$		0			0
$607$	−96.9948	−	56.0000i	−0.159794	−	0.0922570i	0.417971	−	0.908461i	$-0.362741\pi$
$607$	−96.9948	−	56.0000i	−0.159794	−	0.0922570i	−0.577765	+	0.816204i	$0.696075\pi$
$608$	85.7365	−	148.500i	0.141014	−	0.244243i
$609$		0			0
$610$		0			0
$611$		−	193.990i		−	0.317495i
$612$		0			0
$613$			902.000i			1.47145i	0.677279	+	0.735726i	$0.263159\pi$
$613$			902.000i			1.47145i	−0.677279	+	0.735726i	$0.736841\pi$
$614$	−799.500	+	461.592i	−1.30212	+	0.751778i
$615$		0			0
$616$	15.0000	−	25.9808i	0.0243506	−	0.0421766i
$617$	177.535	−	307.500i	0.287739	−	0.498379i	−0.685530	−	0.728044i	$-0.740430\pi$
$617$	177.535	−	307.500i	0.287739	−	0.498379i	0.973270	+	0.229665i	$0.0737630\pi$
$618$		0			0
$619$	−399.500	−	691.954i	−0.645396	−	1.11786i	−0.984210	−	0.177005i	$-0.943359\pi$
$619$	−399.500	−	691.954i	−0.645396	−	1.11786i	0.338814	−	0.940853i	$-0.389974\pi$
$620$		0			0
$621$		0			0
$622$		−	426.000i		−	0.684887i
$623$	−124.708	−	216.000i	−0.200173	−	0.346709i
$624$		0			0
$625$		0			0
$626$	−232.500	−	134.234i	−0.371406	−	0.214431i
$627$		0			0
$628$	−34.6410	+	20.0000i	−0.0551609	+	0.0318471i
$629$		−	530.008i		−	0.842619i
$630$		0			0
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$	−164.545	−	285.000i	−0.260356	−	0.450949i
$633$		0			0
$634$	−42.0000	+	72.7461i	−0.0662461	+	0.114742i
$635$		0			0
$636$		0			0
$637$	−155.885	+	90.0000i	−0.244717	+	0.141287i
$638$	−135.100			−0.211755
$639$		0			0
$640$		0			0
$641$	325.500	−	187.928i	0.507800	−	0.293179i	−0.224129	−	0.974560i	$-0.571954\pi$
$641$	325.500	−	187.928i	0.507800	−	0.293179i	0.731929	+	0.681381i	$0.238620\pi$
$642$		0			0
$643$	11.2583	+	6.50000i	0.0175091	+	0.0101089i	0.508729	−	0.860927i	$-0.330116\pi$
$643$	11.2583	+	6.50000i	0.0175091	+	0.0101089i	−0.491220	+	0.871036i	$0.663449\pi$
$644$	−48.0000	−	27.7128i	−0.0745342	−	0.0430323i
$645$		0			0
$646$	−148.500	−	257.210i	−0.229876	−	0.398157i
$647$	−467.654			−0.722803			−0.361402	−	0.932410i	$-0.617702\pi$
$647$	−467.654			−0.722803			−0.361402	+	0.932410i	$0.617702\pi$
$648$		0			0
$649$	87.0000			0.134052
$650$		0			0
$651$		0			0
$652$	−91.7987	−	53.0000i	−0.140796	−	0.0812883i
$653$	188.794	−	327.000i	0.289117	−	0.500766i	−0.684482	−	0.729030i	$-0.739972\pi$
$653$	188.794	−	327.000i	0.289117	−	0.500766i	0.973599	+	0.228264i	$0.0733049\pi$
$654$		0			0
$655$		0			0
$656$			133.368i			0.203305i
$657$		0			0
$658$		−	168.000i		−	0.255319i
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.979162	−	0.203082i	$-0.934904\pi$
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.313706	+	0.949520i	$0.601571\pi$
$660$		0			0
$661$	191.000	−	330.822i	0.288956	−	0.500487i	−0.684605	−	0.728915i	$-0.740025\pi$
$661$	191.000	−	330.822i	0.288956	−	0.500487i	0.973561	+	0.228428i	$0.0733585\pi$
$662$	−1.73205	+	3.00000i	−0.00261639	+	0.00453172i
$663$		0			0
$664$	−210.000	−	363.731i	−0.316265	−	0.547787i
$665$		0			0
$666$		0			0
$667$			1248.00i			1.87106i
$668$	95.2628	+	165.000i	0.142609	+	0.247006i
$669$		0			0
$670$		0			0
$671$	−84.0000	−	48.4974i	−0.125186	−	0.0722763i
$672$		0			0
$673$	500.563	−	289.000i	0.743778	−	0.429421i	−0.0796633	−	0.996822i	$-0.525385\pi$
$673$	500.563	−	289.000i	0.743778	−	0.429421i	0.823441	+	0.567401i	$0.192051\pi$
$674$		−	133.368i		−	0.197875i
$675$		0			0
$676$	−153.000			−0.226331
$677$	349.874	+	606.000i	0.516801	+	0.895126i	0.999810	+	0.0195100i	$0.00621062\pi$
$677$	349.874	+	606.000i	0.516801	+	0.895126i	−0.483009	+	0.875616i	$0.660456\pi$
$678$		0			0
$679$	−115.000	+	199.186i	−0.169367	+	0.293352i
$680$		0			0
$681$		0			0
$682$	83.1384	−	48.0000i	0.121904	−	0.0703812i
$683$	−1044.43			−1.52918			−0.764588	−	0.644520i	$-0.777057\pi$
$683$	−1044.43			−1.52918			−0.764588	+	0.644520i	$0.777057\pi$
$684$		0			0
$685$		0			0
$686$	−282.000	+	162.813i	−0.411079	+	0.237336i
$687$		0			0
$688$	−581.103	−	335.500i	−0.844627	−	0.487645i
$689$		0			0
$690$		0			0
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	0.792636	−	0.609695i	$-0.208708\pi$
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	−0.924329	+	0.381596i	$0.875375\pi$
$692$	−232.095			−0.335397
$693$		0			0
$694$	195.000			0.280980
$695$		0			0
$696$		0			0
$697$	−163.679	−	94.5000i	−0.234833	−	0.135581i
$698$	360.267	−	624.000i	0.516141	−	0.893983i
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		−	374.000i		−	0.532006i
$704$	106.500	−	61.4878i	0.151278	−	0.0873406i
$705$		0			0
$706$	1.50000	−	2.59808i	0.00212465	−	0.00367999i
$707$	45.0333	−	78.0000i	0.0636964	−	0.110325i
$708$		0			0
$709$	−350.000	−	606.218i	−0.493653	−	0.855032i	0.506320	−	0.862346i	$-0.331005\pi$
$709$	−350.000	−	606.218i	−0.493653	−	0.855032i	−0.999973	+	0.00731341i	$0.997672\pi$
$710$		0			0
$711$		0			0
$712$		−	1080.00i		−	1.51685i
$713$	−443.405	−	768.000i	−0.621886	−	1.07714i
$714$		0			0
$715$		0			0
$716$	54.0000	+	31.1769i	0.0754190	+	0.0435432i
$717$		0			0
$718$	888.542	−	513.000i	1.23752	−	0.714485i
$719$		−	592.361i		−	0.823868i	−0.911214	−	0.411934i	$-0.864853\pi$
$719$		−	592.361i		−	0.823868i	0.911214	−	0.411934i	$-0.135147\pi$
$720$		0			0
$721$	−80.0000			−0.110957
$722$	207.846	+	360.000i	0.287875	+	0.498615i
$723$		0			0
$724$	−116.000	+	200.918i	−0.160221	+	0.277511i
$725$		0			0
$726$		0			0
$727$	575.041	−	332.000i	0.790978	−	0.456671i	−0.0493289	−	0.998783i	$-0.515708\pi$
$727$	575.041	−	332.000i	0.790978	−	0.456671i	0.840307	+	0.542111i	$0.182375\pi$
$728$	69.2820			0.0951676
$729$		0			0
$730$		0			0
$731$	823.500	−	475.448i	1.12654	−	0.650408i
$732$		0			0
$733$	580.237	+	335.000i	0.791592	+	0.457026i	0.840523	−	0.541776i	$-0.182248\pi$
$733$	580.237	+	335.000i	0.791592	+	0.457026i	−0.0489306	+	0.998802i	$0.515581\pi$
$734$	−537.000	−	310.037i	−0.731608	−	0.422394i
$735$		0			0
$736$	−216.000	−	374.123i	−0.293478	−	0.508319i
$737$	−53.6936			−0.0728542
$738$		0			0
$739$	−317.000			−0.428958			−0.214479	−	0.976729i	$-0.568805\pi$
$739$	−317.000			−0.428958			−0.214479	+	0.976729i	$0.568805\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−310.037	+	537.000i	−0.417277	+	0.722746i	−0.995665	−	0.0930168i	$-0.970349\pi$
$743$	−310.037	+	537.000i	−0.417277	+	0.722746i	0.578387	+	0.815762i	$0.303682\pi$
$744$		0			0
$745$		0			0
$746$		−	1004.59i		−	1.34663i
$747$		0			0
$748$			27.0000i			0.0360963i
$749$	−243.000	+	140.296i	−0.324433	+	0.187311i
$750$		0			0
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.0124237	+	0.999923i	$0.503955\pi$
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.859747	+	0.510721i	$0.829379\pi$
$752$	266.736	−	462.000i	0.354702	−	0.614362i
$753$		0			0
$754$	−156.000	−	270.200i	−0.206897	−	0.358355i
$755$		0			0
$756$		0			0
$757$		−	218.000i		−	0.287979i	−0.989579	−	0.143989i	$-0.954007\pi$
$757$		−	218.000i		−	0.287979i	0.989579	−	0.143989i	$-0.0459931\pi$
$758$	71.8801	+	124.500i	0.0948286	+	0.164248i
$759$		0			0
$760$		0			0
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	0.0763232	−	0.997083i	$-0.475682\pi$
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	−0.825338	+	0.564639i	$0.809015\pi$
$762$		0			0
$763$	−90.0666	+	52.0000i	−0.118043	+	0.0681520i
$764$			232.095i			0.303789i
$765$		0			0
$766$	966.000			1.26110
$767$	100.459	+	174.000i	0.130976	+	0.226858i
$768$		0			0
$769$	511.000	−	885.078i	0.664499	−	1.15095i	−0.314921	−	0.949118i	$-0.601978\pi$
$769$	511.000	−	885.078i	0.664499	−	1.15095i	0.979421	−	0.201829i	$-0.0646885\pi$
$770$		0			0
$771$		0			0
$772$	229.497	−	132.500i	0.297276	−	0.171632i
$773$	1184.72			1.53263			0.766315	−	0.642465i	$-0.222088\pi$
$773$	1184.72			1.53263			0.766315	+	0.642465i	$0.222088\pi$
$774$		0			0
$775$		0			0
$776$	−862.500	+	497.965i	−1.11147	+	0.641707i
$777$		0			0
$778$	774.227	+	447.000i	0.995150	+	0.574550i
$779$	−115.500	−	66.6840i	−0.148267	−	0.0856020i
$780$		0			0
$781$	27.0000	+	46.7654i	0.0345711	+	0.0598788i
$782$	−748.246			−0.956836
$783$		0			0
$784$	−495.000			−0.631378
$785$		0			0
$786$		0			0
$787$	−112.583	−	65.0000i	−0.143054	−	0.0825921i	0.426765	−	0.904363i	$-0.359653\pi$
$787$	−112.583	−	65.0000i	−0.143054	−	0.0825921i	−0.569819	+	0.821771i	$0.692987\pi$
$788$	−62.3538	+	108.000i	−0.0791292	+	0.137056i
$789$		0			0
$790$		0			0
$791$		−	180.133i		−	0.227729i
$792$		0			0
$793$		−	224.000i		−	0.282472i
$794$	−543.000	+	313.501i	−0.683879	+	0.394838i
$795$		0			0
$796$	−145.000	+	251.147i	−0.182161	+	0.315512i
$797$	−157.617	+	273.000i	−0.197762	+	0.342535i	−0.947803	−	0.318858i	$-0.896701\pi$
$797$	−157.617	+	273.000i	−0.197762	+	0.342535i	0.750040	+	0.661392i	$0.230034\pi$
$798$		0			0
$799$	378.000	+	654.715i	0.473091	+	0.819418i
$800$		0			0
$801$		0			0
$802$			681.000i			0.849127i
$803$	56.2917	+	97.5000i	0.0701017	+	0.121420i
$804$		0			0
$805$		0			0
$806$	192.000	+	110.851i	0.238213	+	0.137533i
$807$		0			0
$808$	337.750	−	195.000i	0.418007	−	0.241337i
$809$		−	140.296i		−	0.173419i	−0.996234	−	0.0867096i	$-0.972365\pi$
$809$		−	140.296i		−	0.173419i	0.996234	−	0.0867096i	$-0.0276352\pi$
$810$		0			0
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$	45.0333	+	78.0000i	0.0554598	+	0.0960591i
$813$		0			0
$814$	51.0000	−	88.3346i	0.0626536	−	0.108519i
$815$		0			0
$816$		0			0
$817$	581.103	−	335.500i	0.711264	−	0.410649i
$818$	−382.783			−0.467950
$819$		0			0
$820$		0			0
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	−0.784408	−	0.620245i	$-0.787033\pi$
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	0.144944	+	0.989440i	$0.453700\pi$
$822$		0			0
$823$	704.945	+	407.000i	0.856555	+	0.494532i	0.862857	−	0.505448i	$-0.168673\pi$
$823$	704.945	+	407.000i	0.856555	+	0.494532i	−0.00630221	+	0.999980i	$0.502006\pi$
$824$	−300.000	−	173.205i	−0.364078	−	0.210200i
$825$		0			0
$826$	87.0000	+	150.688i	0.105327	+	0.182432i
$827$	1434.14			1.73415			0.867073	−	0.498182i	$-0.165999\pi$
$827$	1434.14			1.73415			0.867073	+	0.498182i	$0.165999\pi$
$828$		0			0
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$		0			0
$832$	245.951	+	142.000i	0.295614	+	0.170673i
$833$	350.740	−	607.500i	0.421057	−	0.729292i
$834$		0			0
$835$		0			0
$836$			19.0526i			0.0227901i
$837$		0			0
$838$		−	1356.00i		−	1.61814i
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	−0.851246	−	0.524767i	$-0.824153\pi$
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	0.0288384	+	0.999584i	$0.490819\pi$
$840$		0			0
$841$	593.500	−	1027.97i	0.705707	−	1.22232i
$842$	590.629	−	1023.00i	0.701460	−	1.21496i
$843$		0			0
$844$	−47.0000	−	81.4064i	−0.0556872	−	0.0964531i
$845$		0			0
$846$		0			0
$847$		−	236.000i		−	0.278630i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−816.000	−	471.118i	−0.958872	−	0.553605i
$852$		0			0
$853$	1233.22	−	712.000i	1.44574	−	0.834701i	0.447521	−	0.894274i	$-0.352307\pi$
$853$	1233.22	−	712.000i	1.44574	−	0.834701i	0.998224	+	0.0595725i	$0.0189738\pi$
$854$		−	193.990i		−	0.227154i
$855$		0			0
$856$	−1215.00			−1.41939
$857$	349.874	+	606.000i	0.408255	+	0.707118i	0.994694	−	0.102875i	$-0.0328042\pi$
$857$	349.874	+	606.000i	0.408255	+	0.707118i	−0.586440	+	0.809993i	$0.699471\pi$
$858$		0			0
$859$	155.500	−	269.334i	0.181024	−	0.313544i	−0.761205	−	0.648511i	$-0.775392\pi$
$859$	155.500	−	269.334i	0.181024	−	0.313544i	0.942230	+	0.334968i	$0.108725\pi$
$860$		0			0
$861$		0			0
$862$	420.888	−	243.000i	0.488270	−	0.281903i
$863$	−1028.84			−1.19216			−0.596082	−	0.802923i	$-0.703277\pi$
$863$	−1028.84			−1.19216			−0.596082	+	0.802923i	$0.703277\pi$
$864$		0			0
$865$		0			0
$866$	−442.500	+	255.477i	−0.510970	+	0.295009i
$867$		0			0
$868$	−55.4256	−	32.0000i	−0.0638544	−	0.0368664i
$869$	57.0000	+	32.9090i	0.0655926	+	0.0378699i
$870$		0			0
$871$	−62.0000	−	107.387i	−0.0711825	−	0.123292i
$872$	−450.333			−0.516437
$873$		0			0
$874$	−528.000			−0.604119
$875$		0			0
$876$		0			0
$877$	90.0666	+	52.0000i	0.102699	+	0.0592930i	0.550470	−	0.834855i	$-0.314449\pi$
$877$	90.0666	+	52.0000i	0.102699	+	0.0592930i	−0.447771	+	0.894148i	$0.647782\pi$
$878$	703.213	−	1218.00i	0.800926	−	1.38724i
$879$		0			0
$880$		0			0
$881$		−	62.3538i		−	0.0707762i	−0.999374	−	0.0353881i	$-0.988733\pi$
$881$		−	62.3538i		−	0.0707762i	0.999374	−	0.0353881i	$-0.0112667\pi$
$882$		0			0
$883$			119.000i			0.134768i	0.997727	+	0.0673839i	$0.0214652\pi$
$883$			119.000i			0.134768i	−0.997727	+	0.0673839i	$0.978535\pi$
$884$	−54.0000	+	31.1769i	−0.0610860	+	0.0352680i
$885$		0			0
$886$	−79.5000	+	137.698i	−0.0897291	+	0.155415i
$887$	−594.093	+	1029.00i	−0.669778	+	1.16009i	0.308188	+	0.951326i	$0.400278\pi$
$887$	−594.093	+	1029.00i	−0.669778	+	1.16009i	−0.977966	+	0.208765i	$0.933056\pi$
$888$		0			0
$889$	−16.0000	−	27.7128i	−0.0179978	−	0.0311730i
$890$		0			0
$891$		0			0
$892$			52.0000i			0.0582960i
$893$	266.736	+	462.000i	0.298696	+	0.517357i
$894$		0			0
$895$		0			0
$896$	105.000	+	60.6218i	0.117188	+	0.0676582i
$897$		0			0
$898$	−958.690	+	553.500i	−1.06758	+	0.616370i
$899$			1441.07i			1.60297i
$900$		0			0
$901$		0			0
$902$	−18.1865	−	31.5000i	−0.0201625	−	0.0349224i
$903$		0			0
$904$	390.000	−	675.500i	0.431416	−	0.747234i
$905$		0			0
$906$		0			0
$907$	−601.888	+	347.500i	−0.663603	+	0.383131i	−0.793648	−	0.608377i	$-0.791821\pi$
$907$	−601.888	+	347.500i	−0.663603	+	0.383131i	0.130046	+	0.991508i	$0.458488\pi$
$908$	−188.794			−0.207922
$909$		0			0
$910$		0			0
$911$	1500.00	−	866.025i	1.64654	−	0.950632i	0.668110	−	0.744062i	$-0.267103\pi$
$911$	1500.00	−	866.025i	1.64654	−	0.950632i	0.978432	−	0.206569i	$-0.0662299\pi$
$912$		0			0
$913$	72.7461	+	42.0000i	0.0796781	+	0.0460022i
$914$	97.5000	+	56.2917i	0.106674	+	0.0615882i
$915$		0			0
$916$	−133.000	−	230.363i	−0.145197	−	0.251488i
$917$	318.697			0.347543
$918$		0			0
$919$	−56.0000			−0.0609358			−0.0304679	−	0.999536i	$-0.509700\pi$
$919$	−56.0000			−0.0609358			−0.0304679	+	0.999536i	$0.509700\pi$
$920$		0			0
$921$		0			0
$922$	−1195.12	−	690.000i	−1.29622	−	0.748373i
$923$	−62.3538	+	108.000i	−0.0675556	+	0.117010i
$924$		0			0
$925$		0			0
$926$			1271.33i			1.37292i
$927$		0			0
$928$			702.000i			0.756466i
$929$	−690.000	+	398.372i	−0.742734	+	0.428818i	−0.823063	−	0.567951i	$-0.807736\pi$
$929$	−690.000	+	398.372i	−0.742734	+	0.428818i	0.0803285	+	0.996768i	$0.474403\pi$
$930$		0			0
$931$	247.500	−	428.683i	0.265843	−	0.460454i
$932$	101.325	−	175.500i	0.108718	−	0.188305i
$933$		0			0
$934$	−175.500	−	303.975i	−0.187901	−	0.325455i
$935$		0			0
$936$		0			0
$937$		−	470.000i		−	0.501601i	−0.968039	−	0.250800i	$-0.919306\pi$
$937$		−	470.000i		−	0.501601i	0.968039	−	0.250800i	$-0.0806938\pi$
$938$	−53.6936	−	93.0000i	−0.0572426	−	0.0991471i
$939$		0			0
$940$		0			0
$941$	348.000	+	200.918i	0.369819	+	0.213515i	0.673380	−	0.739297i	$-0.264842\pi$
$941$	348.000	+	200.918i	0.369819	+	0.213515i	−0.303560	+	0.952812i	$0.598175\pi$
$942$		0			0
$943$	−290.985	+	168.000i	−0.308573	+	0.178155i
$944$			552.524i			0.585301i
$945$		0			0
$946$	183.000			0.193446
$947$	−0.866025	−	1.50000i	−0.000914494	−	0.00158395i	0.865568	−	0.500792i	$-0.166958\pi$
$947$	−0.866025	−	1.50000i	−0.000914494	−	0.00158395i	−0.866482	+	0.499208i	$0.833624\pi$
$948$		0			0
$949$	−130.000	+	225.167i	−0.136986	+	0.237267i
$950$		0			0
$951$		0			0
$952$	−233.827	+	135.000i	−0.245616	+	0.141807i
$953$	826.188			0.866934			0.433467	−	0.901169i	$-0.357290\pi$
$953$	826.188			0.866934			0.433467	+	0.901169i	$0.357290\pi$
$954$		0			0
$955$		0			0
$956$	−348.000	+	200.918i	−0.364017	+	0.210165i
$957$		0			0
$958$	−909.327	−	525.000i	−0.949193	−	0.548017i
$959$	327.000	+	188.794i	0.340980	+	0.196865i
$960$		0			0
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$	235.559			0.244864
$963$		0			0
$964$	−119.000			−0.123444
$965$		0			0
$966$		0			0
$967$	1040.96	+	601.000i	1.07649	+	0.621510i	0.929946	−	0.367695i	$-0.119853\pi$
$967$	1040.96	+	601.000i	1.07649	+	0.621510i	0.146540	+	0.989205i	$0.453186\pi$
$968$	510.955	−	885.000i	0.527846	−	0.914256i
$969$		0			0
$970$		0			0
$971$			187.061i			0.192648i	0.995350	+	0.0963241i	$0.0307085\pi$
$971$			187.061i			0.192648i	−0.995350	+	0.0963241i	$0.969291\pi$
$972$		0			0
$973$			10.0000i			0.0102775i
$974$	159.000	−	91.7987i	0.163244	−	0.0942492i
$975$		0			0
$976$	308.000	−	533.472i	0.315574	−	0.546590i
$977$	208.712	−	361.500i	0.213626	−	0.370010i	−0.739221	−	0.673463i	$-0.764806\pi$
$977$	208.712	−	361.500i	0.213626	−	0.370010i	0.952847	+	0.303453i	$0.0981394\pi$
$978$		0			0
$979$	108.000	+	187.061i	0.110317	+	0.191074i
$980$		0			0
$981$		0			0
$982$		−	399.000i		−	0.406314i
$983$	−583.701	−	1011.00i	−0.593796	−	1.02848i	−0.993716	−	0.111934i	$-0.964295\pi$
$983$	−583.701	−	1011.00i	−0.593796	−	1.02848i	0.399920	−	0.916550i	$-0.369038\pi$
$984$		0			0
$985$		0			0
$986$	1053.00	+	607.950i	1.06795	+	0.616582i
$987$		0			0
$988$	−38.1051	+	22.0000i	−0.0385679	+	0.0222672i
$989$		−	1690.48i		−	1.70928i
$990$		0			0
$991$	−1420.00			−1.43290			−0.716448	−	0.697640i	$-0.754233\pi$
$991$	−1420.00			−1.43290			−0.716448	+	0.697640i	$0.754233\pi$
$992$	−249.415	−	432.000i	−0.251427	−	0.435484i
$993$		0			0
$994$	−54.0000	+	93.5307i	−0.0543260	+	0.0940953i
$995$		0			0
$996$		0			0
$997$	−453.797	+	262.000i	−0.455163	+	0.262788i	−0.710008	−	0.704193i	$-0.751309\pi$
$997$	−453.797	+	262.000i	−0.455163	+	0.262788i	0.254845	+	0.966982i	$0.417975\pi$
$998$	1363.12			1.36586
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.i.a.449.1		4
3.2	odd	2		225.3.i.a.149.2		4
5.2	odd	4		27.3.d.a.17.1		2
5.3	odd	4		675.3.j.a.476.1		2
5.4	even	2	inner	675.3.i.a.449.2		4
9.2	odd	6	inner	675.3.i.a.224.2		4
9.7	even	3		225.3.i.a.74.1		4
15.2	even	4		9.3.d.a.5.1	yes	2
15.8	even	4		225.3.j.a.176.1		2
15.14	odd	2		225.3.i.a.149.1		4
20.7	even	4		432.3.q.a.17.1		2
40.27	even	4		1728.3.q.b.449.1		2
40.37	odd	4		1728.3.q.a.449.1		2
45.2	even	12		27.3.d.a.8.1		2
45.7	odd	12		9.3.d.a.2.1	✓	2
45.22	odd	12		81.3.b.a.80.2		2
45.29	odd	6	inner	675.3.i.a.224.1		4
45.32	even	12		81.3.b.a.80.1		2
45.34	even	6		225.3.i.a.74.2		4
45.38	even	12		675.3.j.a.251.1		2
45.43	odd	12		225.3.j.a.101.1		2
60.47	odd	4		144.3.q.a.113.1		2
105.2	even	12		441.3.n.b.410.1		2
105.17	odd	12		441.3.j.b.275.1		2
105.32	even	12		441.3.j.a.275.1		2
105.47	odd	12		441.3.n.a.410.1		2
105.62	odd	4		441.3.r.a.50.1		2
120.77	even	4		576.3.q.b.257.1		2
120.107	odd	4		576.3.q.a.257.1		2
180.7	even	12		144.3.q.a.65.1		2
180.47	odd	12		432.3.q.a.305.1		2
180.67	even	12		1296.3.e.a.161.2		2
180.167	odd	12		1296.3.e.a.161.1		2
315.52	even	12		441.3.n.a.128.1		2
315.97	even	12		441.3.r.a.344.1		2
315.142	odd	12		441.3.j.a.263.1		2
315.187	even	12		441.3.j.b.263.1		2
315.277	odd	12		441.3.n.b.128.1		2
360.187	even	12		576.3.q.a.65.1		2
360.227	odd	12		1728.3.q.b.1601.1		2
360.277	odd	12		576.3.q.b.65.1		2
360.317	even	12		1728.3.q.a.1601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	45.7	odd	12
9.3.d.a.5.1	yes	2	15.2	even	4
27.3.d.a.8.1		2	45.2	even	12
27.3.d.a.17.1		2	5.2	odd	4
81.3.b.a.80.1		2	45.32	even	12
81.3.b.a.80.2		2	45.22	odd	12
144.3.q.a.65.1		2	180.7	even	12
144.3.q.a.113.1		2	60.47	odd	4
225.3.i.a.74.1		4	9.7	even	3
225.3.i.a.74.2		4	45.34	even	6
225.3.i.a.149.1		4	15.14	odd	2
225.3.i.a.149.2		4	3.2	odd	2
225.3.j.a.101.1		2	45.43	odd	12
225.3.j.a.176.1		2	15.8	even	4
432.3.q.a.17.1		2	20.7	even	4
432.3.q.a.305.1		2	180.47	odd	12
441.3.j.a.263.1		2	315.142	odd	12
441.3.j.a.275.1		2	105.32	even	12
441.3.j.b.263.1		2	315.187	even	12
441.3.j.b.275.1		2	105.17	odd	12
441.3.n.a.128.1		2	315.52	even	12
441.3.n.a.410.1		2	105.47	odd	12
441.3.n.b.128.1		2	315.277	odd	12
441.3.n.b.410.1		2	105.2	even	12
441.3.r.a.50.1		2	105.62	odd	4
441.3.r.a.344.1		2	315.97	even	12
576.3.q.a.65.1		2	360.187	even	12
576.3.q.a.257.1		2	120.107	odd	4
576.3.q.b.65.1		2	360.277	odd	12
576.3.q.b.257.1		2	120.77	even	4
675.3.i.a.224.1		4	45.29	odd	6	inner
675.3.i.a.224.2		4	9.2	odd	6	inner
675.3.i.a.449.1		4	1.1	even	1	trivial
675.3.i.a.449.2		4	5.4	even	2	inner
675.3.j.a.251.1		2	45.38	even	12
675.3.j.a.476.1		2	5.3	odd	4
1296.3.e.a.161.1		2	180.167	odd	12
1296.3.e.a.161.2		2	180.67	even	12
1728.3.q.a.449.1		2	40.37	odd	4
1728.3.q.a.1601.1		2	360.317	even	12
1728.3.q.b.449.1		2	40.27	even	4
1728.3.q.b.1601.1		2	360.227	odd	12

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.73205 + 1.00000i) q^{7} -8.66025 q^{8} +O(q^{10})\)	\(q+(-0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.73205 + 1.00000i) q^{7} -8.66025 q^{8} +(1.50000 - 0.866025i) q^{11} +(3.46410 + 2.00000i) q^{13} +(3.00000 + 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} -15.5885 q^{17} -11.0000 q^{19} +(-2.59808 - 1.50000i) q^{22} +(-13.8564 + 24.0000i) q^{23} -6.92820i q^{26} +2.00000i q^{28} +(39.0000 - 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(-7.79423 + 13.5000i) q^{32} +(13.5000 + 23.3827i) q^{34} +34.0000i q^{37} +(9.52628 + 16.5000i) q^{38} +(10.5000 + 6.06218i) q^{41} +(-52.8275 + 30.5000i) q^{43} -1.73205i q^{44} +48.0000 q^{46} +(-24.2487 - 42.0000i) q^{47} +(-22.5000 + 38.9711i) q^{49} +(3.46410 - 2.00000i) q^{52} +(15.0000 - 8.66025i) q^{56} +(-67.5500 - 39.0000i) q^{58} +(43.5000 + 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} +55.4256 q^{62} +71.0000 q^{64} +(-26.8468 - 15.5000i) q^{67} +(-7.79423 + 13.5000i) q^{68} +31.1769i q^{71} +65.0000i q^{73} +(51.0000 - 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(-1.73205 + 3.00000i) q^{77} +(19.0000 + 32.9090i) q^{79} -21.0000i q^{82} +(24.2487 + 42.0000i) q^{83} +(91.5000 + 52.8275i) q^{86} +(-12.9904 + 7.50000i) q^{88} +124.708i q^{89} -8.00000 q^{91} +(13.8564 + 24.0000i) q^{92} +(-42.0000 + 72.7461i) q^{94} +(99.5929 - 57.5000i) q^{97} +77.9423 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} + 6 q^{11} + 12 q^{14} + 22 q^{16} - 44 q^{19} + 156 q^{29} - 64 q^{31} + 54 q^{34} + 42 q^{41} + 192 q^{46} - 90 q^{49} + 60 q^{56} + 174 q^{59} - 112 q^{61} + 284 q^{64} + 204 q^{74} - 22 q^{76} + 76 q^{79} + 366 q^{86} - 32 q^{91} - 168 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^11 + 12 * q^14 + 22 * q^16 - 44 * q^19 + 156 * q^29 - 64 * q^31 + 54 * q^34 + 42 * q^41 + 192 * q^46 - 90 * q^49 + 60 * q^56 + 174 * q^59 - 112 * q^61 + 284 * q^64 + 204 * q^74 - 22 * q^76 + 76 * q^79 + 366 * q^86 - 32 * q^91 - 168 * q^94

Introduction

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