LMFDB - Embedded newform 675.3.g.k.568.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,3,Mod(82,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("675.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.g (of order $4$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 217x^{12} + 9264x^{8} + 59497x^{4} + 28561 $ x^16 + 217x^12 + 9264x^8 + 59497*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			568.7
Root			$1.85358 - 1.85358i$ of defining polynomial
Character	$\chi$	$=$	675.568
Dual form			675.3.g.k.82.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85358 - 1.85358i) q^{2} -2.87153i q^{4} +(-1.80972 + 1.80972i) q^{7} +(2.09171 + 2.09171i) q^{8} +O(q^{10})$	\(q+(1.85358 - 1.85358i) q^{2} -2.87153i q^{4} +(-1.80972 + 1.80972i) q^{7} +(2.09171 + 2.09171i) q^{8} +2.05878 q^{11} +(16.3641 + 16.3641i) q^{13} +6.70894i q^{14} +19.2404 q^{16} +(-14.0526 + 14.0526i) q^{17} +7.13001i q^{19} +(3.81612 - 3.81612i) q^{22} +(12.5675 + 12.5675i) q^{23} +60.6642 q^{26} +(5.19667 + 5.19667i) q^{28} -36.5390i q^{29} -22.1056 q^{31} +(27.2969 - 27.2969i) q^{32} +52.0955i q^{34} +(39.3412 - 39.3412i) q^{37} +(13.2161 + 13.2161i) q^{38} -14.6864 q^{41} +(46.9899 + 46.9899i) q^{43} -5.91185i q^{44} +46.5899 q^{46} +(56.2870 - 56.2870i) q^{47} +42.4498i q^{49} +(46.9899 - 46.9899i) q^{52} +(21.4083 + 21.4083i) q^{53} -7.57082 q^{56} +(-67.7281 - 67.7281i) q^{58} -36.9457i q^{59} -46.3359 q^{61} +(-40.9745 + 40.9745i) q^{62} -24.2323i q^{64} +(-76.9734 + 76.9734i) q^{67} +(40.3526 + 40.3526i) q^{68} +102.118 q^{71} +(10.4292 + 10.4292i) q^{73} -145.844i q^{74} +20.4741 q^{76} +(-3.72582 + 3.72582i) q^{77} -73.5321i q^{79} +(-27.2224 + 27.2224i) q^{82} +(-56.6893 - 56.6893i) q^{83} +174.199 q^{86} +(4.30637 + 4.30637i) q^{88} +73.0044i q^{89} -59.2288 q^{91} +(36.0881 - 36.0881i) q^{92} -208.665i q^{94} +(-78.3975 + 78.3975i) q^{97} +(78.6842 + 78.6842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 28 q^{13} - 20 q^{16} - 176 q^{22} - 80 q^{28} - 208 q^{31} + 176 q^{37} + 188 q^{43} + 188 q^{46} + 188 q^{52} - 504 q^{58} + 296 q^{61} - 304 q^{67} + 56 q^{73} - 732 q^{76} + 76 q^{82} + 1128 q^{88} + 200 q^{91} + 284 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 28 * q^13 - 20 * q^16 - 176 * q^22 - 80 * q^28 - 208 * q^31 + 176 * q^37 + 188 * q^43 + 188 * q^46 + 188 * q^52 - 504 * q^58 + 296 * q^61 - 304 * q^67 + 56 * q^73 - 732 * q^76 + 76 * q^82 + 1128 * q^88 + 200 * q^91 + 284 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.85358	−	1.85358i	0.926791	−	0.926791i	−0.0707062	−	0.997497i	$-0.522525\pi$
$2$	1.85358	−	1.85358i	0.926791	−	0.926791i	0.997497	+	0.0707062i	$0.0225253\pi$
$3$		0			0
$3$		0			0
$4$		−	2.87153i		−	0.717883i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.80972	+	1.80972i	−0.258532	+	0.258532i	−0.824457	−	0.565925i	$-0.808519\pi$
$7$	−1.80972	+	1.80972i	−0.258532	+	0.258532i	0.565925	+	0.824457i	$0.308519\pi$
$8$	2.09171	+	2.09171i	0.261464	+	0.261464i
$9$		0			0
$10$		0			0
$11$	2.05878			0.187162			0.0935809	−	0.995612i	$-0.470169\pi$
$11$	2.05878			0.187162			0.0935809	+	0.995612i	$0.470169\pi$
$12$		0			0
$13$	16.3641	+	16.3641i	1.25877	+	1.25877i	0.951679	+	0.307094i	$0.0993566\pi$
$13$	16.3641	+	16.3641i	1.25877	+	1.25877i	0.307094	+	0.951679i	$0.400643\pi$
$14$			6.70894i			0.479210i
$15$		0			0
$16$	19.2404			1.20253
$17$	−14.0526	+	14.0526i	−0.826626	+	0.826626i	−0.987048	−	0.160422i	$-0.948714\pi$
$17$	−14.0526	+	14.0526i	−0.826626	+	0.826626i	0.160422	+	0.987048i	$0.448714\pi$
$18$		0			0
$19$			7.13001i			0.375264i	0.982239	+	0.187632i	$0.0600812\pi$
$19$			7.13001i			0.375264i	−0.982239	+	0.187632i	$0.939919\pi$
$20$		0			0
$21$		0			0
$22$	3.81612	−	3.81612i	0.173460	−	0.173460i
$23$	12.5675	+	12.5675i	0.546415	+	0.546415i	0.925402	−	0.378987i	$-0.123728\pi$
$23$	12.5675	+	12.5675i	0.546415	+	0.546415i	−0.378987	+	0.925402i	$0.623728\pi$
$24$		0			0
$25$		0			0
$26$	60.6642			2.33324
$27$		0			0
$28$	5.19667	+	5.19667i	0.185595	+	0.185595i
$29$		−	36.5390i		−	1.25997i	−0.776609	−	0.629983i	$-0.783062\pi$
$29$		−	36.5390i		−	1.25997i	0.776609	−	0.629983i	$-0.216938\pi$
$30$		0			0
$31$	−22.1056			−0.713083			−0.356541	−	0.934280i	$-0.616044\pi$
$31$	−22.1056			−0.713083			−0.356541	+	0.934280i	$0.616044\pi$
$32$	27.2969	−	27.2969i	0.853028	−	0.853028i
$33$		0			0
$34$			52.0955i			1.53222i
$35$		0			0
$36$		0			0
$37$	39.3412	−	39.3412i	1.06327	−	1.06327i	0.0654164	−	0.997858i	$-0.479162\pi$
$37$	39.3412	−	39.3412i	1.06327	−	1.06327i	0.997858	−	0.0654164i	$-0.0208376\pi$
$38$	13.2161	+	13.2161i	0.347791	+	0.347791i
$39$		0			0
$40$		0			0
$41$	−14.6864			−0.358204			−0.179102	−	0.983831i	$-0.557319\pi$
$41$	−14.6864			−0.358204			−0.179102	+	0.983831i	$0.557319\pi$
$42$		0			0
$43$	46.9899	+	46.9899i	1.09279	+	1.09279i	0.995230	+	0.0975584i	$0.0311033\pi$
$43$	46.9899	+	46.9899i	1.09279	+	1.09279i	0.0975584	+	0.995230i	$0.468897\pi$
$44$		−	5.91185i		−	0.134360i
$45$		0			0
$46$	46.5899			1.01282
$47$	56.2870	−	56.2870i	1.19760	−	1.19760i	0.222712	−	0.974884i	$-0.428509\pi$
$47$	56.2870	−	56.2870i	1.19760	−	1.19760i	0.974884	−	0.222712i	$-0.0714909\pi$
$48$		0			0
$49$			42.4498i			0.866323i
$50$		0			0
$51$		0			0
$52$	46.9899	−	46.9899i	0.903652	−	0.903652i
$53$	21.4083	+	21.4083i	0.403930	+	0.403930i	0.879615	−	0.475685i	$-0.157800\pi$
$53$	21.4083	+	21.4083i	0.403930	+	0.403930i	−0.475685	+	0.879615i	$0.657800\pi$
$54$		0			0
$55$		0			0
$56$	−7.57082			−0.135193
$57$		0			0
$58$	−67.7281	−	67.7281i	−1.16773	−	1.16773i
$59$		−	36.9457i		−	0.626197i	−0.949721	−	0.313099i	$-0.898633\pi$
$59$		−	36.9457i		−	0.626197i	0.949721	−	0.313099i	$-0.101367\pi$
$60$		0			0
$61$	−46.3359			−0.759605			−0.379802	−	0.925068i	$-0.624008\pi$
$61$	−46.3359			−0.759605			−0.379802	+	0.925068i	$0.624008\pi$
$62$	−40.9745	+	40.9745i	−0.660879	+	0.660879i
$63$		0			0
$64$		−	24.2323i		−	0.378629i
$65$		0			0
$66$		0			0
$67$	−76.9734	+	76.9734i	−1.14886	+	1.14886i	−0.162079	+	0.986778i	$0.551820\pi$
$67$	−76.9734	+	76.9734i	−1.14886	+	1.14886i	−0.986778	+	0.162079i	$0.948180\pi$
$68$	40.3526	+	40.3526i	0.593421	+	0.593421i
$69$		0			0
$70$		0			0
$71$	102.118			1.43828			0.719140	−	0.694865i	$-0.244536\pi$
$71$	102.118			1.43828			0.719140	+	0.694865i	$0.244536\pi$
$72$		0			0
$73$	10.4292	+	10.4292i	0.142865	+	0.142865i	0.774922	−	0.632057i	$-0.217789\pi$
$73$	10.4292	+	10.4292i	0.142865	+	0.142865i	−0.632057	+	0.774922i	$0.717789\pi$
$74$		−	145.844i		−	1.97087i
$75$		0			0
$76$	20.4741			0.269396
$77$	−3.72582	+	3.72582i	−0.0483873	+	0.0483873i
$78$		0			0
$79$		−	73.5321i		−	0.930786i	−0.885104	−	0.465393i	$-0.845913\pi$
$79$		−	73.5321i		−	0.930786i	0.885104	−	0.465393i	$-0.154087\pi$
$80$		0			0
$81$		0			0
$82$	−27.2224	+	27.2224i	−0.331980	+	0.331980i
$83$	−56.6893	−	56.6893i	−0.683003	−	0.683003i	0.277673	−	0.960676i	$-0.410437\pi$
$83$	−56.6893	−	56.6893i	−0.683003	−	0.683003i	−0.960676	+	0.277673i	$0.910437\pi$
$84$		0			0
$85$		0			0
$86$	174.199			2.02557
$87$		0			0
$88$	4.30637	+	4.30637i	0.0489360	+	0.0489360i
$89$			73.0044i			0.820274i	0.912024	+	0.410137i	$0.134519\pi$
$89$			73.0044i			0.820274i	−0.912024	+	0.410137i	$0.865481\pi$
$90$		0			0
$91$	−59.2288			−0.650866
$92$	36.0881	−	36.0881i	0.392262	−	0.392262i
$93$		0			0
$94$		−	208.665i		−	2.21984i
$95$		0			0
$96$		0			0
$97$	−78.3975	+	78.3975i	−0.808222	+	0.808222i	−0.984365	−	0.176143i	$-0.943638\pi$
$97$	−78.3975	+	78.3975i	−0.808222	+	0.808222i	0.176143	+	0.984365i	$0.443638\pi$
$98$	78.6842	+	78.6842i	0.802900	+	0.802900i
$99$		0			0
$100$		0			0
$101$	−60.3120			−0.597148			−0.298574	−	0.954386i	$-0.596511\pi$
$101$	−60.3120			−0.597148			−0.298574	+	0.954386i	$0.596511\pi$
$102$		0			0
$103$	−66.9105	−	66.9105i	−0.649617	−	0.649617i	0.303284	−	0.952900i	$-0.401917\pi$
$103$	−66.9105	−	66.9105i	−0.649617	−	0.649617i	−0.952900	+	0.303284i	$0.901917\pi$
$104$			68.4577i			0.658247i
$105$		0			0
$106$	79.3641			0.748717
$107$	49.2226	−	49.2226i	0.460024	−	0.460024i	−0.438639	−	0.898663i	$-0.644539\pi$
$107$	49.2226	−	49.2226i	0.460024	−	0.460024i	0.898663	+	0.438639i	$0.144539\pi$
$108$		0			0
$109$			33.0939i			0.303614i	0.988410	+	0.151807i	$0.0485092\pi$
$109$			33.0939i			0.303614i	−0.988410	+	0.151807i	$0.951491\pi$
$110$		0			0
$111$		0			0
$112$	−34.8198	+	34.8198i	−0.310891	+	0.310891i
$113$	−6.79790	−	6.79790i	−0.0601584	−	0.0601584i	0.676388	−	0.736546i	$-0.263544\pi$
$113$	−6.79790	−	6.79790i	−0.0601584	−	0.0601584i	−0.736546	+	0.676388i	$0.763544\pi$
$114$		0			0
$115$		0			0
$116$	−104.923			−0.904509
$117$		0			0
$118$	−68.4818	−	68.4818i	−0.580354	−	0.580354i
$119$		−	50.8628i		−	0.427418i
$120$		0			0
$121$	−116.761			−0.964970
$122$	−85.8874	+	85.8874i	−0.703995	+	0.703995i
$123$		0			0
$124$			63.4768i			0.511910i
$125$		0			0
$126$		0			0
$127$	−111.358	+	111.358i	−0.876835	+	0.876835i	−0.993206	−	0.116371i	$-0.962874\pi$
$127$	−111.358	+	111.358i	−0.876835	+	0.876835i	0.116371	+	0.993206i	$0.462874\pi$
$128$	64.2710	+	64.2710i	0.502117	+	0.502117i
$129$		0			0
$130$		0			0
$131$	−53.1896			−0.406028			−0.203014	−	0.979176i	$-0.565074\pi$
$131$	−53.1896			−0.406028			−0.203014	+	0.979176i	$0.565074\pi$
$132$		0			0
$133$	−12.9033	−	12.9033i	−0.0970176	−	0.0970176i
$134$			285.353i			2.12950i
$135$		0			0
$136$	−58.7881			−0.432265
$137$	20.0488	−	20.0488i	0.146341	−	0.146341i	−0.630140	−	0.776482i	$-0.717003\pi$
$137$	20.0488	−	20.0488i	0.146341	−	0.146341i	0.776482	+	0.630140i	$0.217003\pi$
$138$		0			0
$139$		−	130.488i		−	0.938762i	−0.882996	−	0.469381i	$-0.844477\pi$
$139$		−	130.488i		−	0.938762i	0.882996	−	0.469381i	$-0.155523\pi$
$140$		0			0
$141$		0			0
$142$	189.284	−	189.284i	1.33299	−	1.33299i
$143$	33.6900	+	33.6900i	0.235594	+	0.235594i
$144$		0			0
$145$		0			0
$146$	38.6626			0.264812
$147$		0			0
$148$	−112.969	−	112.969i	−0.763306	−	0.763306i
$149$		−	165.939i		−	1.11369i	−0.830617	−	0.556844i	$-0.812012\pi$
$149$		−	165.939i		−	1.11369i	0.830617	−	0.556844i	$-0.187988\pi$
$150$		0			0
$151$	89.5470			0.593027			0.296513	−	0.955029i	$-0.404176\pi$
$151$	89.5470			0.593027			0.296513	+	0.955029i	$0.404176\pi$
$152$	−14.9139	+	14.9139i	−0.0981179	+	0.0981179i
$153$		0			0
$154$			13.8122i			0.0896897i
$155$		0			0
$156$		0			0
$157$	58.5049	−	58.5049i	0.372643	−	0.372643i	−0.495796	−	0.868439i	$-0.665124\pi$
$157$	58.5049	−	58.5049i	0.372643	−	0.372643i	0.868439	+	0.495796i	$0.165124\pi$
$158$	−136.298	−	136.298i	−0.862644	−	0.862644i
$159$		0			0
$160$		0			0
$161$	−45.4875			−0.282531
$162$		0			0
$163$	32.4956	+	32.4956i	0.199360	+	0.199360i	0.799725	−	0.600366i	$-0.204978\pi$
$163$	32.4956	+	32.4956i	0.199360	+	0.199360i	−0.600366	+	0.799725i	$0.704978\pi$
$164$			42.1724i			0.257149i
$165$		0			0
$166$	−210.156			−1.26600
$167$	−78.6216	+	78.6216i	−0.470788	+	0.470788i	−0.902170	−	0.431382i	$-0.858026\pi$
$167$	−78.6216	+	78.6216i	−0.470788	+	0.470788i	0.431382	+	0.902170i	$0.358026\pi$
$168$		0			0
$169$			366.564i			2.16902i
$170$		0			0
$171$		0			0
$172$	134.933	−	134.933i	0.784494	−	0.784494i
$173$	−197.965	−	197.965i	−1.14431	−	1.14431i	−0.987654	−	0.156654i	$-0.949929\pi$
$173$	−197.965	−	197.965i	−1.14431	−	1.14431i	−0.156654	−	0.987654i	$-0.550071\pi$
$174$		0			0
$175$		0			0
$176$	39.6118			0.225067
$177$		0			0
$178$	135.320	+	135.320i	0.760222	+	0.760222i
$179$		−	264.555i		−	1.47796i	−0.673727	−	0.738981i	$-0.735308\pi$
$179$		−	264.555i		−	1.47796i	0.673727	−	0.738981i	$-0.264692\pi$
$180$		0			0
$181$	114.827			0.634403			0.317201	−	0.948358i	$-0.397257\pi$
$181$	114.827			0.634403			0.317201	+	0.948358i	$0.397257\pi$
$182$	−109.785	+	109.785i	−0.603216	+	0.603216i
$183$		0			0
$184$			52.5753i			0.285735i
$185$		0			0
$186$		0			0
$187$	−28.9313	+	28.9313i	−0.154713	+	0.154713i
$188$	−161.630	−	161.630i	−0.859734	−	0.859734i
$189$		0			0
$190$		0			0
$191$	−194.636			−1.01904			−0.509518	−	0.860460i	$-0.670176\pi$
$191$	−194.636			−1.01904			−0.509518	+	0.860460i	$0.670176\pi$
$192$		0			0
$193$	−141.848	−	141.848i	−0.734966	−	0.734966i	0.236633	−	0.971599i	$-0.423956\pi$
$193$	−141.848	−	141.848i	−0.734966	−	0.734966i	−0.971599	+	0.236633i	$0.923956\pi$
$194$			290.632i			1.49810i
$195$		0			0
$196$	121.896			0.621918
$197$	66.5728	−	66.5728i	0.337933	−	0.337933i	−0.517656	−	0.855589i	$-0.673195\pi$
$197$	66.5728	−	66.5728i	0.337933	−	0.337933i	0.855589	+	0.517656i	$0.173195\pi$
$198$		0			0
$199$			50.9462i			0.256011i	0.991773	+	0.128006i	$0.0408575\pi$
$199$			50.9462i			0.256011i	−0.991773	+	0.128006i	$0.959142\pi$
$200$		0			0
$201$		0			0
$202$	−111.793	+	111.793i	−0.553432	+	0.553432i
$203$	66.1255	+	66.1255i	0.325741	+	0.325741i
$204$		0			0
$205$		0			0
$206$	−248.048			−1.20412
$207$		0			0
$208$	314.851	+	314.851i	1.51371	+	1.51371i
$209$			14.6791i			0.0702351i
$210$		0			0
$211$	182.712			0.865932			0.432966	−	0.901410i	$-0.357467\pi$
$211$	182.712			0.865932			0.432966	+	0.901410i	$0.357467\pi$
$212$	61.4746	−	61.4746i	0.289974	−	0.289974i
$213$		0			0
$214$		−	182.476i		−	0.852692i
$215$		0			0
$216$		0			0
$217$	40.0049	−	40.0049i	0.184355	−	0.184355i
$218$	61.3423	+	61.3423i	0.281387	+	0.281387i
$219$		0			0
$220$		0			0
$221$	−459.916			−2.08107
$222$		0			0
$223$	271.161	+	271.161i	1.21597	+	1.21597i	0.969031	+	0.246940i	$0.0794249\pi$
$223$	271.161	+	271.161i	1.21597	+	1.21597i	0.246940	+	0.969031i	$0.420575\pi$
$224$			98.7995i			0.441069i
$225$		0			0
$226$	−25.2009			−0.111508
$227$	118.724	−	118.724i	0.523012	−	0.523012i	−0.395468	−	0.918480i	$-0.629418\pi$
$227$	118.724	−	118.724i	0.523012	−	0.523012i	0.918480	+	0.395468i	$0.129418\pi$
$228$		0			0
$229$		−	96.1274i		−	0.419771i	−0.977726	−	0.209885i	$-0.932691\pi$
$229$		−	96.1274i		−	0.419771i	0.977726	−	0.209885i	$-0.0673090\pi$
$230$		0			0
$231$		0			0
$232$	76.4290	−	76.4290i	0.329435	−	0.329435i
$233$	−20.3322	−	20.3322i	−0.0872627	−	0.0872627i	0.662128	−	0.749391i	$-0.269653\pi$
$233$	−20.3322	−	20.3322i	−0.0872627	−	0.0872627i	−0.749391	+	0.662128i	$0.769653\pi$
$234$		0			0
$235$		0			0
$236$	−106.091			−0.449536
$237$		0			0
$238$	−94.2783	−	94.2783i	−0.396127	−	0.396127i
$239$			88.5788i			0.370622i	0.982680	+	0.185311i	$0.0593293\pi$
$239$			88.5788i			0.370622i	−0.982680	+	0.185311i	$0.940671\pi$
$240$		0			0
$241$	−141.038			−0.585220			−0.292610	−	0.956232i	$-0.594524\pi$
$241$	−141.038			−0.585220			−0.292610	+	0.956232i	$0.594524\pi$
$242$	−216.427	+	216.427i	−0.894326	+	0.894326i
$243$		0			0
$244$			133.055i			0.545307i
$245$		0			0
$246$		0			0
$247$	−116.676	+	116.676i	−0.472372	+	0.472372i
$248$	−46.2384	−	46.2384i	−0.186445	−	0.186445i
$249$		0			0
$250$		0			0
$251$	77.6528			0.309374			0.154687	−	0.987964i	$-0.450563\pi$
$251$	77.6528			0.309374			0.154687	+	0.987964i	$0.450563\pi$
$252$		0			0
$253$	25.8738	+	25.8738i	0.102268	+	0.102268i
$254$			412.823i			1.62529i
$255$		0			0
$256$	335.192			1.30934
$257$	98.4646	−	98.4646i	0.383131	−	0.383131i	−0.489098	−	0.872229i	$-0.662674\pi$
$257$	98.4646	−	98.4646i	0.383131	−	0.383131i	0.872229	+	0.489098i	$0.162674\pi$
$258$		0			0
$259$			142.393i			0.549780i
$260$		0			0
$261$		0			0
$262$	−98.5914	+	98.5914i	−0.376303	+	0.376303i
$263$	126.086	+	126.086i	0.479416	+	0.479416i	0.904945	−	0.425529i	$-0.139912\pi$
$263$	126.086	+	126.086i	0.479416	+	0.479416i	−0.425529	+	0.904945i	$0.639912\pi$
$264$		0			0
$265$		0			0
$266$	−47.8348			−0.179830
$267$		0			0
$268$	221.032	+	221.032i	0.824744	+	0.824744i
$269$		−	175.683i		−	0.653096i	−0.945181	−	0.326548i	$-0.894115\pi$
$269$		−	175.683i		−	0.653096i	0.945181	−	0.326548i	$-0.105885\pi$
$270$		0			0
$271$	79.8046			0.294482			0.147241	−	0.989101i	$-0.452961\pi$
$271$	79.8046			0.294482			0.147241	+	0.989101i	$0.452961\pi$
$272$	−270.379	+	270.379i	−0.994040	+	0.994040i
$273$		0			0
$274$		−	74.3241i		−	0.271256i
$275$		0			0
$276$		0			0
$277$	204.250	−	204.250i	0.737364	−	0.737364i	−0.234703	−	0.972067i	$-0.575412\pi$
$277$	204.250	−	204.250i	0.737364	−	0.737364i	0.972067	+	0.234703i	$0.0754118\pi$
$278$	−241.870	−	241.870i	−0.870036	−	0.870036i
$279$		0			0
$280$		0			0
$281$	291.935			1.03891			0.519457	−	0.854497i	$-0.326134\pi$
$281$	291.935			1.03891			0.519457	+	0.854497i	$0.326134\pi$
$282$		0			0
$283$	98.4389	+	98.4389i	0.347841	+	0.347841i	0.859305	−	0.511464i	$-0.170897\pi$
$283$	98.4389	+	98.4389i	0.347841	+	0.347841i	−0.511464	+	0.859305i	$0.670897\pi$
$284$		−	293.235i		−	1.03252i
$285$		0			0
$286$	124.894			0.436693
$287$	26.5782	−	26.5782i	0.0926071	−	0.0926071i
$288$		0			0
$289$		−	105.954i		−	0.366622i
$290$		0			0
$291$		0			0
$292$	29.9477	−	29.9477i	0.102561	−	0.102561i
$293$	−253.598	−	253.598i	−0.865522	−	0.865522i	0.126451	−	0.991973i	$-0.459641\pi$
$293$	−253.598	−	253.598i	−0.865522	−	0.865522i	−0.991973	+	0.126451i	$0.959641\pi$
$294$		0			0
$295$		0			0
$296$	164.580			0.556015
$297$		0			0
$298$	−307.582	−	307.582i	−1.03216	−	1.03216i
$299$			411.312i			1.37562i
$300$		0			0
$301$	−170.077			−0.565041
$302$	165.983	−	165.983i	0.549612	−	0.549612i
$303$		0			0
$304$			137.185i			0.451265i
$305$		0			0
$306$		0			0
$307$	135.946	−	135.946i	0.442822	−	0.442822i	−0.450137	−	0.892959i	$-0.648625\pi$
$307$	135.946	−	135.946i	0.442822	−	0.442822i	0.892959	+	0.450137i	$0.148625\pi$
$308$	10.6988	+	10.6988i	0.0347364	+	0.0347364i
$309$		0			0
$310$		0			0
$311$	−104.078			−0.334657			−0.167329	−	0.985901i	$-0.553514\pi$
$311$	−104.078			−0.334657			−0.167329	+	0.985901i	$0.553514\pi$
$312$		0			0
$313$	−40.9560	−	40.9560i	−0.130850	−	0.130850i	0.638649	−	0.769498i	$-0.279494\pi$
$313$	−40.9560	−	40.9560i	−0.130850	−	0.130850i	−0.769498	+	0.638649i	$0.779494\pi$
$314$		−	216.887i		−	0.690724i
$315$		0			0
$316$	−211.150			−0.668195
$317$	−347.406	+	347.406i	−1.09592	+	1.09592i	−0.101037	+	0.994883i	$0.532216\pi$
$317$	−347.406	+	347.406i	−1.09592	+	1.09592i	−0.994883	+	0.101037i	$0.967784\pi$
$318$		0			0
$319$		−	75.2258i		−	0.235818i
$320$		0			0
$321$		0			0
$322$	−84.3148	+	84.3148i	−0.261847	+	0.261847i
$323$	−100.196	−	100.196i	−0.310203	−	0.310203i
$324$		0			0
$325$		0			0
$326$	120.467			0.369529
$327$		0			0
$328$	−30.7196	−	30.7196i	−0.0936573	−	0.0936573i
$329$			203.728i			0.619233i
$330$		0			0
$331$	25.0983			0.0758256			0.0379128	−	0.999281i	$-0.487929\pi$
$331$	25.0983			0.0758256			0.0379128	+	0.999281i	$0.487929\pi$
$332$	−162.785	+	162.785i	−0.490316	+	0.490316i
$333$		0			0
$334$			291.463i			0.872644i
$335$		0			0
$336$		0			0
$337$	73.3287	−	73.3287i	0.217593	−	0.217593i	−0.589891	−	0.807483i	$-0.700829\pi$
$337$	73.3287	−	73.3287i	0.217593	−	0.217593i	0.807483	+	0.589891i	$0.200829\pi$
$338$	679.457	+	679.457i	2.01023	+	2.01023i
$339$		0			0
$340$		0			0
$341$	−45.5105			−0.133462
$342$		0			0
$343$	−165.499	−	165.499i	−0.482504	−	0.482504i
$344$			196.578i			0.571449i
$345$		0			0
$346$	−733.889			−2.12107
$347$	25.1989	−	25.1989i	0.0726192	−	0.0726192i	−0.669864	−	0.742484i	$-0.733648\pi$
$347$	25.1989	−	25.1989i	0.0726192	−	0.0726192i	0.742484	+	0.669864i	$0.233648\pi$
$348$		0			0
$349$			112.522i			0.322412i	0.986921	+	0.161206i	$0.0515384\pi$
$349$			112.522i			0.322412i	−0.986921	+	0.161206i	$0.948462\pi$
$350$		0			0
$351$		0			0
$352$	56.1983	−	56.1983i	0.159654	−	0.159654i
$353$	6.07002	+	6.07002i	0.0171955	+	0.0171955i	0.715652	−	0.698457i	$-0.246130\pi$
$353$	6.07002	+	6.07002i	0.0171955	+	0.0171955i	−0.698457	+	0.715652i	$0.746130\pi$
$354$		0			0
$355$		0			0
$356$	209.634			0.588861
$357$		0			0
$358$	−490.374	−	490.374i	−1.36976	−	1.36976i
$359$		−	576.227i		−	1.60509i	−0.596592	−	0.802544i	$-0.703479\pi$
$359$		−	576.227i		−	1.60509i	0.596592	−	0.802544i	$-0.296521\pi$
$360$		0			0
$361$	310.163			0.859177
$362$	212.841	−	212.841i	0.587958	−	0.587958i
$363$		0			0
$364$			170.077i			0.467245i
$365$		0			0
$366$		0			0
$367$	−110.722	+	110.722i	−0.301695	+	0.301695i	−0.841677	−	0.539982i	$-0.818431\pi$
$367$	−110.722	+	110.722i	−0.301695	+	0.301695i	0.539982	+	0.841677i	$0.318431\pi$
$368$	241.805	+	241.805i	0.657079	+	0.657079i
$369$		0			0
$370$		0			0
$371$	−77.4861			−0.208857
$372$		0			0
$373$	70.1819	+	70.1819i	0.188155	+	0.188155i	0.794898	−	0.606743i	$-0.207524\pi$
$373$	70.1819	+	70.1819i	0.188155	+	0.188155i	−0.606743	+	0.794898i	$0.707524\pi$
$374$			107.253i			0.286773i
$375$		0			0
$376$	235.472			0.626256
$377$	597.927	−	597.927i	1.58601	−	1.58601i
$378$		0			0
$379$		−	648.160i		−	1.71018i	−0.518476	−	0.855092i	$-0.673500\pi$
$379$		−	648.160i		−	1.71018i	0.518476	−	0.855092i	$-0.326500\pi$
$380$		0			0
$381$		0			0
$382$	−360.774	+	360.774i	−0.944434	+	0.944434i
$383$	−377.891	−	377.891i	−0.986659	−	0.986659i	0.0132527	−	0.999912i	$-0.495781\pi$
$383$	−377.891	−	377.891i	−0.986659	−	0.986659i	−0.999912	+	0.0132527i	$0.995781\pi$
$384$		0			0
$385$		0			0
$386$	−525.855			−1.36232
$387$		0			0
$388$	225.121	+	225.121i	0.580208	+	0.580208i
$389$		−	139.022i		−	0.357382i	−0.983905	−	0.178691i	$-0.942814\pi$
$389$		−	139.022i		−	0.357382i	0.983905	−	0.178691i	$-0.0571863\pi$
$390$		0			0
$391$	−353.214			−0.903362
$392$	−88.7927	+	88.7927i	−0.226512	+	0.226512i
$393$		0			0
$394$		−	246.796i		−	0.626386i
$395$		0			0
$396$		0			0
$397$	291.864	−	291.864i	0.735175	−	0.735175i	−0.236465	−	0.971640i	$-0.575989\pi$
$397$	291.864	−	291.864i	0.735175	−	0.735175i	0.971640	+	0.236465i	$0.0759889\pi$
$398$	94.4330	+	94.4330i	0.237269	+	0.237269i
$399$		0			0
$400$		0			0
$401$	−231.602			−0.577562			−0.288781	−	0.957395i	$-0.593250\pi$
$401$	−231.602			−0.577562			−0.288781	+	0.957395i	$0.593250\pi$
$402$		0			0
$403$	−361.737	−	361.737i	−0.897610	−	0.897610i
$404$			173.188i			0.428683i
$405$		0			0
$406$	245.138			0.603788
$407$	80.9948	−	80.9948i	0.199004	−	0.199004i
$408$		0			0
$409$			5.56023i			0.0135947i	0.999977	+	0.00679735i	$0.00216368\pi$
$409$			5.56023i			0.0135947i	−0.999977	+	0.00679735i	$0.997836\pi$
$410$		0			0
$411$		0			0
$412$	−192.136	+	192.136i	−0.466349	+	0.466349i
$413$	66.8614	+	66.8614i	0.161892	+	0.161892i
$414$		0			0
$415$		0			0
$416$	893.375			2.14754
$417$		0			0
$418$	27.2090	+	27.2090i	0.0650932	+	0.0650932i
$419$		−	556.456i		−	1.32806i	−0.747707	−	0.664028i	$-0.768845\pi$
$419$		−	556.456i		−	1.32806i	0.747707	−	0.664028i	$-0.231155\pi$
$420$		0			0
$421$	−593.997			−1.41092			−0.705459	−	0.708751i	$-0.749259\pi$
$421$	−593.997			−1.41092			−0.705459	+	0.708751i	$0.749259\pi$
$422$	338.671	−	338.671i	0.802537	−	0.802537i
$423$		0			0
$424$			89.5598i			0.211226i
$425$		0			0
$426$		0			0
$427$	83.8551	−	83.8551i	0.196382	−	0.196382i
$428$	−141.344	−	141.344i	−0.330243	−	0.330243i
$429$		0			0
$430$		0			0
$431$	566.825			1.31514			0.657569	−	0.753394i	$-0.271585\pi$
$431$	566.825			1.31514			0.657569	+	0.753394i	$0.271585\pi$
$432$		0			0
$433$	−347.506	−	347.506i	−0.802555	−	0.802555i	0.180940	−	0.983494i	$-0.442086\pi$
$433$	−347.506	−	347.506i	−0.802555	−	0.802555i	−0.983494	+	0.180940i	$0.942086\pi$
$434$		−	148.305i		−	0.341716i
$435$		0			0
$436$	95.0302			0.217959
$437$	−89.6068	+	89.6068i	−0.205050	+	0.205050i
$438$		0			0
$439$		−	805.424i		−	1.83468i	−0.398106	−	0.917340i	$-0.630332\pi$
$439$		−	805.424i		−	1.83468i	0.398106	−	0.917340i	$-0.369668\pi$
$440$		0			0
$441$		0			0
$442$	−852.493	+	852.493i	−1.92872	+	1.92872i
$443$	524.532	+	524.532i	1.18405	+	1.18405i	0.978687	+	0.205359i	$0.0658361\pi$
$443$	524.532	+	524.532i	1.18405	+	1.18405i	0.205359	+	0.978687i	$0.434164\pi$
$444$		0			0
$445$		0			0
$446$	1005.24			2.25390
$447$		0			0
$448$	43.8537	+	43.8537i	0.0978877	+	0.0978877i
$449$		−	345.404i		−	0.769273i	−0.923068	−	0.384637i	$-0.874327\pi$
$449$		−	345.404i		−	0.769273i	0.923068	−	0.384637i	$-0.125673\pi$
$450$		0			0
$451$	−30.2360			−0.0670421
$452$	−19.5204	+	19.5204i	−0.0431867	+	0.0431867i
$453$		0			0
$454$		−	440.128i		−	0.969445i
$455$		0			0
$456$		0			0
$457$	−331.219	+	331.219i	−0.724769	+	0.724769i	−0.969573	−	0.244804i	$-0.921276\pi$
$457$	−331.219	+	331.219i	−0.724769	+	0.724769i	0.244804	+	0.969573i	$0.421276\pi$
$458$	−178.180	−	178.180i	−0.389040	−	0.389040i
$459$		0			0
$460$		0			0
$461$	−69.3667			−0.150470			−0.0752351	−	0.997166i	$-0.523971\pi$
$461$	−69.3667			−0.150470			−0.0752351	+	0.997166i	$0.523971\pi$
$462$		0			0
$463$	−162.327	−	162.327i	−0.350598	−	0.350598i	0.509734	−	0.860332i	$-0.329744\pi$
$463$	−162.327	−	162.327i	−0.350598	−	0.350598i	−0.860332	+	0.509734i	$0.829744\pi$
$464$		−	703.027i		−	1.51514i
$465$		0			0
$466$	−75.3748			−0.161749
$467$	−104.749	+	104.749i	−0.224303	+	0.224303i	−0.810308	−	0.586005i	$-0.800700\pi$
$467$	−104.749	+	104.749i	−0.224303	+	0.224303i	0.586005	+	0.810308i	$0.300700\pi$
$468$		0			0
$469$		−	278.601i		−	0.594032i
$470$		0			0
$471$		0			0
$472$	77.2795	−	77.2795i	0.163728	−	0.163728i
$473$	96.7418	+	96.7418i	0.204528	+	0.204528i
$474$		0			0
$475$		0			0
$476$	−146.054			−0.306836
$477$		0			0
$478$	164.188	+	164.188i	0.343489	+	0.343489i
$479$		−	504.447i		−	1.05313i	−0.850136	−	0.526563i	$-0.823481\pi$
$479$		−	504.447i		−	1.05313i	0.850136	−	0.526563i	$-0.176519\pi$
$480$		0			0
$481$	1287.56			2.67684
$482$	−261.425	+	261.425i	−0.542376	+	0.542376i
$483$		0			0
$484$			335.284i			0.692736i
$485$		0			0
$486$		0			0
$487$	435.576	−	435.576i	0.894407	−	0.894407i	−0.100527	−	0.994934i	$-0.532053\pi$
$487$	435.576	−	435.576i	0.894407	−	0.894407i	0.994934	+	0.100527i	$0.0320529\pi$
$488$	−96.9212	−	96.9212i	−0.198609	−	0.198609i
$489$		0			0
$490$		0			0
$491$	488.734			0.995386			0.497693	−	0.867353i	$-0.334181\pi$
$491$	488.734			0.995386			0.497693	+	0.867353i	$0.334181\pi$
$492$		0			0
$493$	513.470	+	513.470i	1.04152	+	1.04152i
$494$			432.537i			0.875580i
$495$		0			0
$496$	−425.321			−0.857501
$497$	−184.805	+	184.805i	−0.371841	+	0.371841i
$498$		0			0
$499$			521.418i			1.04493i	0.852662	+	0.522463i	$0.174987\pi$
$499$			521.418i			1.04493i	−0.852662	+	0.522463i	$0.825013\pi$
$500$		0			0
$501$		0			0
$502$	143.936	−	143.936i	0.286725	−	0.286725i
$503$	638.392	+	638.392i	1.26917	+	1.26917i	0.946518	+	0.322650i	$0.104574\pi$
$503$	638.392	+	638.392i	1.26917	+	1.26917i	0.322650	+	0.946518i	$0.395426\pi$
$504$		0			0
$505$		0			0
$506$	95.9184			0.189562
$507$		0			0
$508$	319.768	+	319.768i	0.629465	+	0.629465i
$509$			862.426i			1.69435i	0.531311	+	0.847177i	$0.321700\pi$
$509$			862.426i			1.69435i	−0.531311	+	0.847177i	$0.678300\pi$
$510$		0			0
$511$	−37.7478			−0.0738704
$512$	364.222	−	364.222i	0.711372	−	0.711372i
$513$		0			0
$514$		−	365.024i		−	0.710164i
$515$		0			0
$516$		0			0
$517$	115.883	−	115.883i	0.224144	−	0.224144i
$518$	263.937	+	263.937i	0.509531	+	0.509531i
$519$		0			0
$520$		0			0
$521$	−810.812			−1.55626			−0.778130	−	0.628103i	$-0.783832\pi$
$521$	−810.812			−1.55626			−0.778130	+	0.628103i	$0.783832\pi$
$522$		0			0
$523$	−81.0491	−	81.0491i	−0.154970	−	0.154970i	0.625364	−	0.780333i	$-0.284951\pi$
$523$	−81.0491	−	81.0491i	−0.154970	−	0.154970i	−0.780333	+	0.625364i	$0.784951\pi$
$524$			152.736i			0.291480i
$525$		0			0
$526$	467.423			0.888637
$527$	310.642	−	310.642i	0.589453	−	0.589453i
$528$		0			0
$529$		−	213.114i		−	0.402862i
$530$		0			0
$531$		0			0
$532$	−37.0524	+	37.0524i	−0.0696473	+	0.0696473i
$533$	−240.328	−	240.328i	−0.450898	−	0.450898i
$534$		0			0
$535$		0			0
$536$	−322.012			−0.600768
$537$		0			0
$538$	−325.642	−	325.642i	−0.605283	−	0.605283i
$539$			87.3948i			0.162143i
$540$		0			0
$541$	−473.428			−0.875098			−0.437549	−	0.899195i	$-0.644153\pi$
$541$	−473.428			−0.875098			−0.437549	+	0.899195i	$0.644153\pi$
$542$	147.924	−	147.924i	0.272923	−	0.272923i
$543$		0			0
$544$			767.187i			1.41027i
$545$		0			0
$546$		0			0
$547$	−44.8918	+	44.8918i	−0.0820691	+	0.0820691i	−0.746950	−	0.664881i	$-0.768482\pi$
$547$	−44.8918	+	44.8918i	−0.0820691	+	0.0820691i	0.664881	+	0.746950i	$0.268482\pi$
$548$	−57.5707	−	57.5707i	−0.105056	−	0.105056i
$549$		0			0
$550$		0			0
$551$	260.524			0.472820
$552$		0			0
$553$	133.073	+	133.073i	0.240638	+	0.240638i
$554$		−	757.188i		−	1.36676i
$555$		0			0
$556$	−374.700			−0.673921
$557$	−245.069	+	245.069i	−0.439981	+	0.439981i	−0.892005	−	0.452025i	$-0.850702\pi$
$557$	−245.069	+	245.069i	−0.439981	+	0.439981i	0.452025	+	0.892005i	$0.350702\pi$
$558$		0			0
$559$			1537.89i			2.75114i
$560$		0			0
$561$		0			0
$562$	541.125	−	541.125i	0.962856	−	0.962856i
$563$	−92.1197	−	92.1197i	−0.163623	−	0.163623i	0.620547	−	0.784170i	$-0.286911\pi$
$563$	−92.1197	−	92.1197i	−0.163623	−	0.163623i	−0.784170	+	0.620547i	$0.786911\pi$
$564$		0			0
$565$		0			0
$566$	364.929			0.644751
$567$		0			0
$568$	213.601	+	213.601i	0.376058	+	0.376058i
$569$			52.7798i			0.0927589i	0.998924	+	0.0463794i	$0.0147683\pi$
$569$			52.7798i			0.0927589i	−0.998924	+	0.0463794i	$0.985232\pi$
$570$		0			0
$571$	187.813			0.328919			0.164459	−	0.986384i	$-0.447412\pi$
$571$	187.813			0.328919			0.164459	+	0.986384i	$0.447412\pi$
$572$	96.7418	−	96.7418i	0.169129	−	0.169129i
$573$		0			0
$574$		−	98.5299i		−	0.171655i
$575$		0			0
$576$		0			0
$577$	−115.526	+	115.526i	−0.200218	+	0.200218i	−0.800093	−	0.599875i	$-0.795217\pi$
$577$	−115.526	+	115.526i	−0.200218	+	0.200218i	0.599875	+	0.800093i	$0.295217\pi$
$578$	−196.394	−	196.394i	−0.339782	−	0.339782i
$579$		0			0
$580$		0			0
$581$	205.184			0.353156
$582$		0			0
$583$	44.0750	+	44.0750i	0.0756003	+	0.0756003i
$584$			43.6296i			0.0747081i
$585$		0			0
$586$	−940.129			−1.60432
$587$	572.894	−	572.894i	0.975969	−	0.975969i	−0.0237494	−	0.999718i	$-0.507560\pi$
$587$	572.894	−	572.894i	0.975969	−	0.975969i	0.999718	+	0.0237494i	$0.00756038\pi$
$588$		0			0
$589$		−	157.613i		−	0.267594i
$590$		0			0
$591$		0			0
$592$	756.941	−	756.941i	1.27862	−	1.27862i
$593$	374.017	+	374.017i	0.630721	+	0.630721i	0.948249	−	0.317528i	$-0.102853\pi$
$593$	374.017	+	374.017i	0.630721	+	0.630721i	−0.317528	+	0.948249i	$0.602853\pi$
$594$		0			0
$595$		0			0
$596$	−476.500			−0.799497
$597$		0			0
$598$	762.400	+	762.400i	1.27492	+	1.27492i
$599$			541.163i			0.903443i	0.892159	+	0.451722i	$0.149190\pi$
$599$			541.163i			0.903443i	−0.892159	+	0.451722i	$0.850810\pi$
$600$		0			0
$601$	915.778			1.52376			0.761878	−	0.647720i	$-0.224277\pi$
$601$	915.778			1.52376			0.761878	+	0.647720i	$0.224277\pi$
$602$	−315.252	+	315.252i	−0.523675	+	0.523675i
$603$		0			0
$604$		−	257.137i		−	0.425724i
$605$		0			0
$606$		0			0
$607$	789.819	−	789.819i	1.30118	−	1.30118i	0.373591	−	0.927594i	$-0.378127\pi$
$607$	789.819	−	789.819i	1.30118	−	1.30118i	0.927594	−	0.373591i	$-0.121873\pi$
$608$	194.627	+	194.627i	0.320110	+	0.320110i
$609$		0			0
$610$		0			0
$611$	1842.17			3.01500
$612$		0			0
$613$	−54.2959	−	54.2959i	−0.0885741	−	0.0885741i	0.661432	−	0.750006i	$-0.269949\pi$
$613$	−54.2959	−	54.2959i	−0.0885741	−	0.0885741i	−0.750006	+	0.661432i	$0.769949\pi$
$614$		−	503.976i		−	0.820807i
$615$		0			0
$616$	−15.5867			−0.0253030
$617$	−546.520	+	546.520i	−0.885770	+	0.885770i	−0.994114	−	0.108343i	$-0.965445\pi$
$617$	−546.520	+	546.520i	−0.885770	+	0.885770i	0.108343	+	0.994114i	$0.465445\pi$
$618$		0			0
$619$			770.649i			1.24499i	0.782623	+	0.622495i	$0.213881\pi$
$619$			770.649i			1.24499i	−0.782623	+	0.622495i	$0.786119\pi$
$620$		0			0
$621$		0			0
$622$	−192.918	+	192.918i	−0.310157	+	0.310157i
$623$	−132.118	−	132.118i	−0.212067	−	0.212067i
$624$		0			0
$625$		0			0
$626$	−151.830			−0.242541
$627$		0			0
$628$	−167.999	−	167.999i	−0.267514	−	0.267514i
$629$			1105.69i			1.75786i
$630$		0			0
$631$	1187.77			1.88236			0.941181	−	0.337903i	$-0.109718\pi$
$631$	1187.77			1.88236			0.941181	+	0.337903i	$0.109718\pi$
$632$	153.808	−	153.808i	0.243367	−	0.243367i
$633$		0			0
$634$			1287.89i			2.03138i
$635$		0			0
$636$		0			0
$637$	−694.651	+	694.651i	−1.09050	+	1.09050i
$638$	−139.437	−	139.437i	−0.218554	−	0.218554i
$639$		0			0
$640$		0			0
$641$	−684.175			−1.06736			−0.533678	−	0.845688i	$-0.679190\pi$
$641$	−684.175			−1.06736			−0.533678	+	0.845688i	$0.679190\pi$
$642$		0			0
$643$	−5.98402	−	5.98402i	−0.00930640	−	0.00930640i	0.702438	−	0.711745i	$-0.252095\pi$
$643$	−5.98402	−	5.98402i	−0.00930640	−	0.00930640i	−0.711745	+	0.702438i	$0.752095\pi$
$644$			130.619i			0.202824i
$645$		0			0
$646$	−371.441			−0.574987
$647$	−425.885	+	425.885i	−0.658246	+	0.658246i	−0.954965	−	0.296719i	$-0.904107\pi$
$647$	−425.885	+	425.885i	−0.658246	+	0.658246i	0.296719	+	0.954965i	$0.404107\pi$
$648$		0			0
$649$		−	76.0630i		−	0.117200i
$650$		0			0
$651$		0			0
$652$	93.3122	−	93.3122i	0.143117	−	0.143117i
$653$	−285.832	−	285.832i	−0.437721	−	0.437721i	0.453523	−	0.891245i	$-0.350167\pi$
$653$	−285.832	−	285.832i	−0.437721	−	0.437721i	−0.891245	+	0.453523i	$0.850167\pi$
$654$		0			0
$655$		0			0
$656$	−282.572			−0.430750
$657$		0			0
$658$	377.626	+	377.626i	0.573900	+	0.573900i
$659$		−	968.254i		−	1.46928i	−0.678458	−	0.734639i	$-0.737352\pi$
$659$		−	968.254i		−	1.46928i	0.678458	−	0.734639i	$-0.262648\pi$
$660$		0			0
$661$	−552.045			−0.835166			−0.417583	−	0.908639i	$-0.637123\pi$
$661$	−552.045			−0.835166			−0.417583	+	0.908639i	$0.637123\pi$
$662$	46.5217	−	46.5217i	0.0702745	−	0.0702745i
$663$		0			0
$664$		−	237.155i		−	0.357161i
$665$		0			0
$666$		0			0
$667$	459.206	−	459.206i	0.688465	−	0.688465i
$668$	225.764	+	225.764i	0.337971	+	0.337971i
$669$		0			0
$670$		0			0
$671$	−95.3954			−0.142169
$672$		0			0
$673$	−480.638	−	480.638i	−0.714172	−	0.714172i	0.253233	−	0.967405i	$-0.418506\pi$
$673$	−480.638	−	480.638i	−0.714172	−	0.714172i	−0.967405	+	0.253233i	$0.918506\pi$
$674$		−	271.841i		−	0.403326i
$675$		0			0
$676$	1052.60			1.55710
$677$	−480.020	+	480.020i	−0.709040	+	0.709040i	−0.966333	−	0.257294i	$-0.917169\pi$
$677$	−480.020	+	480.020i	−0.709040	+	0.709040i	0.257294	+	0.966333i	$0.417169\pi$
$678$		0			0
$679$		−	283.755i		−	0.417902i
$680$		0			0
$681$		0			0
$682$	−84.3574	+	84.3574i	−0.123691	+	0.123691i
$683$	−641.686	−	641.686i	−0.939511	−	0.939511i	0.0587612	−	0.998272i	$-0.481285\pi$
$683$	−641.686	−	641.686i	−0.939511	−	0.939511i	−0.998272	+	0.0587612i	$0.981285\pi$
$684$		0			0
$685$		0			0
$686$	−613.531			−0.894360
$687$		0			0
$688$	904.106	+	904.106i	1.31411	+	1.31411i
$689$			700.653i			1.01691i
$690$		0			0
$691$	−849.132			−1.22885			−0.614423	−	0.788977i	$-0.710611\pi$
$691$	−849.132			−1.22885			−0.614423	+	0.788977i	$0.710611\pi$
$692$	−568.463	+	568.463i	−0.821479	+	0.821479i
$693$		0			0
$694$		−	93.4164i		−	0.134606i
$695$		0			0
$696$		0			0
$697$	206.382	−	206.382i	0.296101	−	0.296101i
$698$	208.568	+	208.568i	0.298809	+	0.298809i
$699$		0			0
$700$		0			0
$701$	−295.917			−0.422136			−0.211068	−	0.977471i	$-0.567694\pi$
$701$	−295.917			−0.422136			−0.211068	+	0.977471i	$0.567694\pi$
$702$		0			0
$703$	280.503	+	280.503i	0.399009	+	0.399009i
$704$		−	49.8889i		−	0.0708650i
$705$		0			0
$706$	22.5026			0.0318733
$707$	109.148	−	109.148i	0.154382	−	0.154382i
$708$		0			0
$709$		−	634.567i		−	0.895018i	−0.894280	−	0.447509i	$-0.852311\pi$
$709$		−	634.567i		−	0.895018i	0.894280	−	0.447509i	$-0.147689\pi$
$710$		0			0
$711$		0			0
$712$	−152.704	+	152.704i	−0.214472	+	0.214472i
$713$	−277.813	−	277.813i	−0.389639	−	0.389639i
$714$		0			0
$715$		0			0
$716$	−759.678			−1.06100
$717$		0			0
$718$	−1068.08	−	1068.08i	−1.48758	−	1.48758i
$719$			200.698i			0.279135i	0.990213	+	0.139568i	$0.0445712\pi$
$719$			200.698i			0.279135i	−0.990213	+	0.139568i	$0.955429\pi$
$720$		0			0
$721$	242.179			0.335893
$722$	574.912	−	574.912i	0.796277	−	0.796277i
$723$		0			0
$724$		−	329.729i		−	0.455427i
$725$		0			0
$726$		0			0
$727$	−566.268	+	566.268i	−0.778910	+	0.778910i	−0.979646	−	0.200735i	$-0.935667\pi$
$727$	−566.268	+	566.268i	−0.778910	+	0.778910i	0.200735	+	0.979646i	$0.435667\pi$
$728$	−123.889	−	123.889i	−0.170178	−	0.170178i
$729$		0			0
$730$		0			0
$731$	−1320.66			−1.80665
$732$		0			0
$733$	452.422	+	452.422i	0.617219	+	0.617219i	0.944817	−	0.327598i	$-0.106239\pi$
$733$	452.422	+	452.422i	0.617219	+	0.617219i	−0.327598	+	0.944817i	$0.606239\pi$
$734$			410.465i			0.559216i
$735$		0			0
$736$	686.109			0.932214
$737$	−158.471	+	158.471i	−0.215022	+	0.215022i
$738$		0			0
$739$		−	831.653i		−	1.12538i	−0.826669	−	0.562688i	$-0.809767\pi$
$739$		−	831.653i		−	1.12538i	0.826669	−	0.562688i	$-0.190233\pi$
$740$		0			0
$741$		0			0
$742$	−143.627	+	143.627i	−0.193567	+	0.193567i
$743$	314.358	+	314.358i	0.423093	+	0.423093i	0.886267	−	0.463174i	$-0.153290\pi$
$743$	314.358	+	314.358i	0.423093	+	0.423093i	−0.463174	+	0.886267i	$0.653290\pi$
$744$		0			0
$745$		0			0
$746$	260.176			0.348761
$747$		0			0
$748$	83.0771	+	83.0771i	0.111066	+	0.111066i
$749$			178.158i			0.237862i
$750$		0			0
$751$	227.368			0.302754			0.151377	−	0.988476i	$-0.451629\pi$
$751$	227.368			0.302754			0.151377	+	0.988476i	$0.451629\pi$
$752$	1082.99	−	1082.99i	1.44014	−	1.44014i
$753$		0			0
$754$		−	2216.61i		−	2.93980i
$755$		0			0
$756$		0			0
$757$	−453.799	+	453.799i	−0.599470	+	0.599470i	−0.940171	−	0.340702i	$-0.889335\pi$
$757$	−453.799	+	453.799i	−0.599470	+	0.599470i	0.340702	+	0.940171i	$0.389335\pi$
$758$	−1201.42	−	1201.42i	−1.58498	−	1.58498i
$759$		0			0
$760$		0			0
$761$	−819.267			−1.07657			−0.538283	−	0.842764i	$-0.680927\pi$
$761$	−819.267			−1.07657			−0.538283	+	0.842764i	$0.680927\pi$
$762$		0			0
$763$	−59.8908	−	59.8908i	−0.0784938	−	0.0784938i
$764$			558.903i			0.731549i
$765$		0			0
$766$	−1400.90			−1.82885
$767$	604.581	−	604.581i	0.788241	−	0.788241i
$768$		0			0
$769$			194.732i			0.253227i	0.991952	+	0.126614i	$0.0404108\pi$
$769$			194.732i			0.253227i	−0.991952	+	0.126614i	$0.959589\pi$
$770$		0			0
$771$		0			0
$772$	−407.322	+	407.322i	−0.527619	+	0.527619i
$773$	−57.3776	−	57.3776i	−0.0742271	−	0.0742271i	0.669019	−	0.743246i	$-0.266715\pi$
$773$	−57.3776	−	57.3776i	−0.0742271	−	0.0742271i	−0.743246	+	0.669019i	$0.766715\pi$
$774$		0			0
$775$		0			0
$776$	−327.969			−0.422641
$777$		0			0
$778$	−257.688	−	257.688i	−0.331219	−	0.331219i
$779$		−	104.714i		−	0.134421i
$780$		0			0
$781$	210.238			0.269191
$782$	−654.712	+	654.712i	−0.837228	+	0.837228i
$783$		0			0
$784$			816.753i			1.04178i
$785$		0			0
$786$		0			0
$787$	−650.541	+	650.541i	−0.826609	+	0.826609i	−0.987046	−	0.160437i	$-0.948710\pi$
$787$	−650.541	+	650.541i	−0.826609	+	0.826609i	0.160437	+	0.987046i	$0.448710\pi$
$788$	−191.166	−	191.166i	−0.242596	−	0.242596i
$789$		0			0
$790$		0			0
$791$	24.6046			0.0311057
$792$		0			0
$793$	−758.243	−	758.243i	−0.956170	−	0.956170i
$794$		−	1081.99i		−	1.36271i
$795$		0			0
$796$	146.294			0.183786
$797$	304.474	−	304.474i	0.382025	−	0.382025i	−0.489806	−	0.871831i	$-0.662932\pi$
$797$	304.474	−	304.474i	0.382025	−	0.382025i	0.871831	+	0.489806i	$0.162932\pi$
$798$		0			0
$799$			1581.96i			1.97993i
$800$		0			0
$801$		0			0
$802$	−429.294	+	429.294i	−0.535279	+	0.535279i
$803$	21.4714	+	21.4714i	0.0267389	+	0.0267389i
$804$		0			0
$805$		0			0
$806$	−1341.02			−1.66379
$807$		0			0
$808$	−126.155	−	126.155i	−0.156133	−	0.156133i
$809$			324.798i			0.401480i	0.979645	+	0.200740i	$0.0643347\pi$
$809$			324.798i			0.401480i	−0.979645	+	0.200740i	$0.935665\pi$
$810$		0			0
$811$	−341.672			−0.421297			−0.210649	−	0.977562i	$-0.567558\pi$
$811$	−341.672			−0.421297			−0.210649	+	0.977562i	$0.567558\pi$
$812$	189.881	−	189.881i	0.233844	−	0.233844i
$813$		0			0
$814$		−	300.261i		−	0.368871i
$815$		0			0
$816$		0			0
$817$	−335.039	+	335.039i	−0.410084	+	0.410084i
$818$	10.3063	+	10.3063i	0.0125994	+	0.0125994i
$819$		0			0
$820$		0			0
$821$	1063.72			1.29564			0.647821	−	0.761793i	$-0.275681\pi$
$821$	1063.72			1.29564			0.647821	+	0.761793i	$0.275681\pi$
$822$		0			0
$823$	−384.927	−	384.927i	−0.467712	−	0.467712i	0.433461	−	0.901173i	$-0.357292\pi$
$823$	−384.927	−	384.927i	−0.467712	−	0.467712i	−0.901173	+	0.433461i	$0.857292\pi$
$824$		−	279.915i		−	0.339702i
$825$		0			0
$826$	247.866			0.300080
$827$	−464.647	+	464.647i	−0.561846	+	0.561846i	−0.929832	−	0.367985i	$-0.880048\pi$
$827$	−464.647	+	464.647i	−0.561846	+	0.561846i	0.367985	+	0.929832i	$0.380048\pi$
$828$		0			0
$829$		−	1169.96i		−	1.41130i	−0.708563	−	0.705648i	$-0.750656\pi$
$829$		−	1169.96i		−	1.41130i	0.708563	−	0.705648i	$-0.249344\pi$
$830$		0			0
$831$		0			0
$832$	396.538	−	396.538i	0.476609	−	0.476609i
$833$	−596.532	−	596.532i	−0.716125	−	0.716125i
$834$		0			0
$835$		0			0
$836$	42.1516			0.0504205
$837$		0			0
$838$	−1031.44	−	1031.44i	−1.23083	−	1.23083i
$839$			1023.15i			1.21949i	0.792598	+	0.609745i	$0.208728\pi$
$839$			1023.15i			1.21949i	−0.792598	+	0.609745i	$0.791272\pi$
$840$		0			0
$841$	−494.102			−0.587517
$842$	−1101.02	+	1101.02i	−1.30763	+	1.30763i
$843$		0			0
$844$		−	524.662i		−	0.621637i
$845$		0			0
$846$		0			0
$847$	211.306	−	211.306i	0.249475	−	0.249475i
$848$	411.905	+	411.905i	0.485737	+	0.485737i
$849$		0			0
$850$		0			0
$851$	988.843			1.16198
$852$		0			0
$853$	1074.01	+	1074.01i	1.25909	+	1.25909i	0.951527	+	0.307565i	$0.0995143\pi$
$853$	1074.01	+	1074.01i	1.25909	+	1.25909i	0.307565	+	0.951527i	$0.400486\pi$
$854$		−	310.864i		−	0.364010i
$855$		0			0
$856$	205.919			0.240559
$857$	−969.340	+	969.340i	−1.13109	+	1.13109i	−0.141088	+	0.989997i	$0.545060\pi$
$857$	−969.340	+	969.340i	−1.13109	+	1.13109i	−0.989997	+	0.141088i	$0.954940\pi$
$858$		0			0
$859$			615.624i			0.716675i	0.933592	+	0.358338i	$0.116656\pi$
$859$			615.624i			0.716675i	−0.933592	+	0.358338i	$0.883344\pi$
$860$		0			0
$861$		0			0
$862$	1050.66	−	1050.66i	1.21886	−	1.21886i
$863$	691.930	+	691.930i	0.801773	+	0.801773i	0.983373	−	0.181600i	$-0.0581275\pi$
$863$	691.930	+	691.930i	0.801773	+	0.801773i	−0.181600	+	0.983373i	$0.558128\pi$
$864$		0			0
$865$		0			0
$866$	−1288.26			−1.48760
$867$		0			0
$868$	−114.875	−	114.875i	−0.132345	−	0.132345i
$869$		−	151.386i		−	0.174208i
$870$		0			0
$871$	−2519.19			−2.89230
$872$	−69.2228	+	69.2228i	−0.0793840	+	0.0793840i
$873$		0			0
$874$			332.187i			0.380077i
$875$		0			0
$876$		0			0
$877$	−332.120	+	332.120i	−0.378700	+	0.378700i	−0.870633	−	0.491933i	$-0.836291\pi$
$877$	−332.120	+	332.120i	−0.378700	+	0.378700i	0.491933	+	0.870633i	$0.336291\pi$
$878$	−1492.92	−	1492.92i	−1.70036	−	1.70036i
$879$		0			0
$880$		0			0
$881$	−239.224			−0.271537			−0.135768	−	0.990741i	$-0.543350\pi$
$881$	−239.224			−0.271537			−0.135768	+	0.990741i	$0.543350\pi$
$882$		0			0
$883$	−2.33713	−	2.33713i	−0.00264681	−	0.00264681i	0.705782	−	0.708429i	$-0.250596\pi$
$883$	−2.33713	−	2.33713i	−0.00264681	−	0.00264681i	−0.708429	+	0.705782i	$0.750596\pi$
$884$			1320.66i			1.49396i
$885$		0			0
$886$	1944.53			2.19473
$887$	−980.906	+	980.906i	−1.10587	+	1.10587i	−0.112182	+	0.993688i	$0.535784\pi$
$887$	−980.906	+	980.906i	−1.10587	+	1.10587i	−0.993688	+	0.112182i	$0.964216\pi$
$888$		0			0
$889$		−	403.054i		−	0.453379i
$890$		0			0
$891$		0			0
$892$	778.648	−	778.648i	0.872924	−	0.872924i
$893$	401.327	+	401.327i	0.449415	+	0.449415i
$894$		0			0
$895$		0			0
$896$	−232.625			−0.259626
$897$		0			0
$898$	−640.234	−	640.234i	−0.712955	−	0.712955i
$899$			807.716i			0.898461i
$900$		0			0
$901$	−601.686			−0.667798
$902$	−56.0449	+	56.0449i	−0.0621340	+	0.0621340i
$903$		0			0
$904$		−	28.4384i		−	0.0314585i
$905$		0			0
$906$		0			0
$907$	−167.419	+	167.419i	−0.184586	+	0.184586i	−0.793351	−	0.608765i	$-0.791665\pi$
$907$	−167.419	+	167.419i	−0.184586	+	0.184586i	0.608765	+	0.793351i	$0.291665\pi$
$908$	−340.919	−	340.919i	−0.375461	−	0.375461i
$909$		0			0
$910$		0			0
$911$	954.706			1.04798			0.523988	−	0.851726i	$-0.324444\pi$
$911$	954.706			1.04798			0.523988	+	0.851726i	$0.324444\pi$
$912$		0			0
$913$	−116.711	−	116.711i	−0.127832	−	0.127832i
$914$			1227.88i			1.34342i
$915$		0			0
$916$	−276.033			−0.301346
$917$	96.2585	−	96.2585i	0.104971	−	0.104971i
$918$		0			0
$919$		−	549.663i		−	0.598110i	−0.954236	−	0.299055i	$-0.903329\pi$
$919$		−	549.663i		−	0.598110i	0.954236	−	0.299055i	$-0.0966714\pi$
$920$		0			0
$921$		0			0
$922$	−128.577	+	128.577i	−0.139454	+	0.139454i
$923$	1671.06	+	1671.06i	1.81047	+	1.81047i
$924$		0			0
$925$		0			0
$926$	−601.772			−0.649861
$927$		0			0
$928$	−997.402	−	997.402i	−1.07479	−	1.07479i
$929$		−	338.546i		−	0.364419i	−0.983260	−	0.182210i	$-0.941675\pi$
$929$		−	338.546i		−	0.364419i	0.983260	−	0.182210i	$-0.0583250\pi$
$930$		0			0
$931$	−302.668			−0.325100
$932$	−58.3846	+	58.3846i	−0.0626444	+	0.0626444i
$933$		0			0
$934$			388.323i			0.415763i
$935$		0			0
$936$		0			0
$937$	−721.149	+	721.149i	−0.769636	+	0.769636i	−0.978042	−	0.208406i	$-0.933172\pi$
$937$	−721.149	+	721.149i	−0.769636	+	0.769636i	0.208406	+	0.978042i	$0.433172\pi$
$938$	−516.409	−	516.409i	−0.550543	−	0.550543i
$939$		0			0
$940$		0			0
$941$	18.0797			0.0192133			0.00960663	−	0.999954i	$-0.496942\pi$
$941$	18.0797			0.0192133			0.00960663	+	0.999954i	$0.496942\pi$
$942$		0			0
$943$	−184.572	−	184.572i	−0.195728	−	0.195728i
$944$		−	710.850i		−	0.753019i
$945$		0			0
$946$	358.638			0.379110
$947$	126.473	−	126.473i	0.133551	−	0.133551i	−0.637171	−	0.770722i	$-0.719896\pi$
$947$	126.473	−	126.473i	0.133551	−	0.133551i	0.770722	+	0.637171i	$0.219896\pi$
$948$		0			0
$949$			341.327i			0.359670i
$950$		0			0
$951$		0			0
$952$	106.390	−	106.390i	0.111754	−	0.111754i
$953$	−1120.28	−	1120.28i	−1.17553	−	1.17553i	−0.980872	−	0.194656i	$-0.937641\pi$
$953$	−1120.28	−	1120.28i	−1.17553	−	1.17553i	−0.194656	−	0.980872i	$-0.562359\pi$
$954$		0			0
$955$		0			0
$956$	254.357			0.266063
$957$		0			0
$958$	−935.034	−	935.034i	−0.976027	−	0.976027i
$959$			72.5654i			0.0756678i
$960$		0			0
$961$	−472.344			−0.491513
$962$	2386.60	−	2386.60i	2.48087	−	2.48087i
$963$		0			0
$964$			404.995i			0.420119i
$965$		0			0
$966$		0			0
$967$	−265.571	+	265.571i	−0.274634	+	0.274634i	−0.830962	−	0.556329i	$-0.812210\pi$
$967$	−265.571	+	265.571i	−0.274634	+	0.274634i	0.556329	+	0.830962i	$0.312210\pi$
$968$	−244.231	−	244.231i	−0.252305	−	0.252305i
$969$		0			0
$970$		0			0
$971$	−416.272			−0.428704			−0.214352	−	0.976756i	$-0.568764\pi$
$971$	−416.272			−0.428704			−0.214352	+	0.976756i	$0.568764\pi$
$972$		0			0
$973$	236.147	+	236.147i	0.242700	+	0.242700i
$974$		−	1614.75i		−	1.65786i
$975$		0			0
$976$	−891.523			−0.913445
$977$	446.115	−	446.115i	0.456617	−	0.456617i	−0.440926	−	0.897543i	$-0.645350\pi$
$977$	446.115	−	446.115i	0.456617	−	0.456617i	0.897543	+	0.440926i	$0.145350\pi$
$978$		0			0
$979$			150.300i			0.153524i
$980$		0			0
$981$		0			0
$982$	905.909	−	905.909i	0.922515	−	0.922515i
$983$	783.072	+	783.072i	0.796615	+	0.796615i	0.982560	−	0.185945i	$-0.0595347\pi$
$983$	783.072	+	783.072i	0.796615	+	0.796615i	−0.185945	+	0.982560i	$0.559535\pi$
$984$		0			0
$985$		0			0
$986$	1903.52			1.93055
$987$		0			0
$988$	335.039	+	335.039i	0.339108	+	0.339108i
$989$			1181.09i			1.19423i
$990$		0			0
$991$	416.020			0.419798			0.209899	−	0.977723i	$-0.432686\pi$
$991$	416.020			0.419798			0.209899	+	0.977723i	$0.432686\pi$
$992$	−603.413	+	603.413i	−0.608279	+	0.608279i
$993$		0			0
$994$			685.102i			0.689238i
$995$		0			0
$996$		0			0
$997$	268.813	−	268.813i	0.269621	−	0.269621i	−0.559326	−	0.828948i	$-0.688940\pi$
$997$	268.813	−	268.813i	0.269621	−	0.269621i	0.828948	+	0.559326i	$0.188940\pi$
$998$	966.491	+	966.491i	0.968427	+	0.968427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.g.k.568.7		16
3.2	odd	2	inner	675.3.g.k.568.2		16
5.2	odd	4	inner	675.3.g.k.82.7		16
5.3	odd	4		135.3.g.a.82.2	yes	16
5.4	even	2		135.3.g.a.28.2	✓	16
15.2	even	4	inner	675.3.g.k.82.2		16
15.8	even	4		135.3.g.a.82.7	yes	16
15.14	odd	2		135.3.g.a.28.7	yes	16
45.4	even	6		405.3.l.o.298.2		32
45.13	odd	12		405.3.l.o.217.7		32
45.14	odd	6		405.3.l.o.298.7		32
45.23	even	12		405.3.l.o.217.2		32
45.29	odd	6		405.3.l.o.28.2		32
45.34	even	6		405.3.l.o.28.7		32
45.38	even	12		405.3.l.o.352.7		32
45.43	odd	12		405.3.l.o.352.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.2	✓	16	5.4	even	2
135.3.g.a.28.7	yes	16	15.14	odd	2
135.3.g.a.82.2	yes	16	5.3	odd	4
135.3.g.a.82.7	yes	16	15.8	even	4
405.3.l.o.28.2		32	45.29	odd	6
405.3.l.o.28.7		32	45.34	even	6
405.3.l.o.217.2		32	45.23	even	12
405.3.l.o.217.7		32	45.13	odd	12
405.3.l.o.298.2		32	45.4	even	6
405.3.l.o.298.7		32	45.14	odd	6
405.3.l.o.352.2		32	45.43	odd	12
405.3.l.o.352.7		32	45.38	even	12
675.3.g.k.82.2		16	15.2	even	4	inner
675.3.g.k.82.7		16	5.2	odd	4	inner
675.3.g.k.568.2		16	3.2	odd	2	inner
675.3.g.k.568.7		16	1.1	even	1	trivial

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.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85358 - 1.85358i) q^{2} -2.87153i q^{4} +(-1.80972 + 1.80972i) q^{7} +(2.09171 + 2.09171i) q^{8} +O(q^{10})\)	\(q+(1.85358 - 1.85358i) q^{2} -2.87153i q^{4} +(-1.80972 + 1.80972i) q^{7} +(2.09171 + 2.09171i) q^{8} +2.05878 q^{11} +(16.3641 + 16.3641i) q^{13} +6.70894i q^{14} +19.2404 q^{16} +(-14.0526 + 14.0526i) q^{17} +7.13001i q^{19} +(3.81612 - 3.81612i) q^{22} +(12.5675 + 12.5675i) q^{23} +60.6642 q^{26} +(5.19667 + 5.19667i) q^{28} -36.5390i q^{29} -22.1056 q^{31} +(27.2969 - 27.2969i) q^{32} +52.0955i q^{34} +(39.3412 - 39.3412i) q^{37} +(13.2161 + 13.2161i) q^{38} -14.6864 q^{41} +(46.9899 + 46.9899i) q^{43} -5.91185i q^{44} +46.5899 q^{46} +(56.2870 - 56.2870i) q^{47} +42.4498i q^{49} +(46.9899 - 46.9899i) q^{52} +(21.4083 + 21.4083i) q^{53} -7.57082 q^{56} +(-67.7281 - 67.7281i) q^{58} -36.9457i q^{59} -46.3359 q^{61} +(-40.9745 + 40.9745i) q^{62} -24.2323i q^{64} +(-76.9734 + 76.9734i) q^{67} +(40.3526 + 40.3526i) q^{68} +102.118 q^{71} +(10.4292 + 10.4292i) q^{73} -145.844i q^{74} +20.4741 q^{76} +(-3.72582 + 3.72582i) q^{77} -73.5321i q^{79} +(-27.2224 + 27.2224i) q^{82} +(-56.6893 - 56.6893i) q^{83} +174.199 q^{86} +(4.30637 + 4.30637i) q^{88} +73.0044i q^{89} -59.2288 q^{91} +(36.0881 - 36.0881i) q^{92} -208.665i q^{94} +(-78.3975 + 78.3975i) q^{97} +(78.6842 + 78.6842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 28 q^{13} - 20 q^{16} - 176 q^{22} - 80 q^{28} - 208 q^{31} + 176 q^{37} + 188 q^{43} + 188 q^{46} + 188 q^{52} - 504 q^{58} + 296 q^{61} - 304 q^{67} + 56 q^{73} - 732 q^{76} + 76 q^{82} + 1128 q^{88} + 200 q^{91} + 284 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 28 * q^13 - 20 * q^16 - 176 * q^22 - 80 * q^28 - 208 * q^31 + 176 * q^37 + 188 * q^43 + 188 * q^46 + 188 * q^52 - 504 * q^58 + 296 * q^61 - 304 * q^67 + 56 * q^73 - 732 * q^76 + 76 * q^82 + 1128 * q^88 + 200 * q^91 + 284 * q^97

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