LMFDB - Embedded newform 1050.3.f.b.601.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(601,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1050.601");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.b.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +1.00806 q^{11} +3.46410i q^{12} +7.05322i q^{13} +(-1.47723 - 9.78866i) q^{14} +4.00000 q^{16} +7.09185i q^{17} +4.24264 q^{18} +4.04257i q^{19} +(-11.9886 + 1.80922i) q^{21} -1.42561 q^{22} -25.4766 q^{23} -4.89898i q^{24} -9.97476i q^{26} -5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} +17.2909 q^{29} +23.6516i q^{31} -5.65685 q^{32} +1.74600i q^{33} -10.0294i q^{34} -6.00000 q^{36} +29.2171 q^{37} -5.71705i q^{38} -12.2165 q^{39} +5.16217i q^{41} +(16.9545 - 2.55863i) q^{42} -45.6529 q^{43} +2.01611 q^{44} +36.0294 q^{46} -61.0391i q^{47} +6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} -12.2834 q^{51} +14.1064i q^{52} -74.8237 q^{53} +7.34847i q^{54} +(-2.95445 - 19.5773i) q^{56} -7.00193 q^{57} -24.4531 q^{58} +50.5639i q^{59} +58.0943i q^{61} -33.4485i q^{62} +(-3.13367 - 20.7649i) q^{63} +8.00000 q^{64} -2.46922i q^{66} +73.5827 q^{67} +14.1837i q^{68} -44.1268i q^{69} +99.8513 q^{71} +8.48528 q^{72} +1.15350i q^{73} -41.3192 q^{74} +8.08514i q^{76} +(1.05297 + 6.97738i) q^{77} +17.2768 q^{78} -102.445 q^{79} +9.00000 q^{81} -7.30042i q^{82} -83.4227i q^{83} +(-23.9772 + 3.61845i) q^{84} +64.5629 q^{86} +29.9488i q^{87} -2.85121 q^{88} -69.0342i q^{89} +(-48.8198 + 7.36749i) q^{91} -50.9533 q^{92} -40.9658 q^{93} +86.3223i q^{94} -9.79796i q^{96} +152.172i q^{97} +(66.2104 - 20.4496i) q^{98} -3.02417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 24 * q^9	$ 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	1.04456	+	6.92163i	0.149222	+	0.988804i
$7$	1.04456	+	6.92163i	0.149222	+	0.988804i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	1.00806			0.0916414			0.0458207	−	0.998950i	$-0.485410\pi$
$11$	1.00806			0.0916414			0.0458207	+	0.998950i	$0.485410\pi$
$12$			3.46410i			0.288675i
$13$			7.05322i			0.542556i	0.962501	+	0.271278i	$0.0874462\pi$
$13$			7.05322i			0.542556i	−0.962501	+	0.271278i	$0.912554\pi$
$14$	−1.47723	−	9.78866i	−0.105516	−	0.699190i
$15$		0			0
$16$	4.00000			0.250000
$17$			7.09185i			0.417168i	0.978004	+	0.208584i	$0.0668854\pi$
$17$			7.09185i			0.417168i	−0.978004	+	0.208584i	$0.933115\pi$
$18$	4.24264			0.235702
$19$			4.04257i			0.212767i	0.994325	+	0.106383i	$0.0339271\pi$
$19$			4.04257i			0.212767i	−0.994325	+	0.106383i	$0.966073\pi$
$20$		0			0
$21$	−11.9886	+	1.80922i	−0.570886	+	0.0861535i
$22$	−1.42561			−0.0648003
$23$	−25.4766			−1.10768			−0.553840	−	0.832623i	$-0.686838\pi$
$23$	−25.4766			−1.10768			−0.553840	+	0.832623i	$0.686838\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$		−	9.97476i		−	0.383645i
$27$		−	5.19615i		−	0.192450i
$28$	2.08911	+	13.8433i	0.0746112	+	0.494402i
$29$	17.2909			0.596239			0.298119	−	0.954529i	$-0.403641\pi$
$29$	17.2909			0.596239			0.298119	+	0.954529i	$0.403641\pi$
$30$		0			0
$31$			23.6516i			0.762956i	0.924378	+	0.381478i	$0.124585\pi$
$31$			23.6516i			0.762956i	−0.924378	+	0.381478i	$0.875415\pi$
$32$	−5.65685			−0.176777
$33$			1.74600i			0.0529092i
$34$		−	10.0294i		−	0.294982i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	29.2171			0.789651			0.394826	−	0.918756i	$-0.370805\pi$
$37$	29.2171			0.789651			0.394826	+	0.918756i	$0.370805\pi$
$38$		−	5.71705i		−	0.150449i
$39$	−12.2165			−0.313245
$40$		0			0
$41$			5.16217i			0.125907i	0.998016	+	0.0629533i	$0.0200519\pi$
$41$			5.16217i			0.125907i	−0.998016	+	0.0629533i	$0.979948\pi$
$42$	16.9545	−	2.55863i	0.403677	−	0.0609198i
$43$	−45.6529			−1.06169			−0.530847	−	0.847467i	$-0.678126\pi$
$43$	−45.6529			−1.06169			−0.530847	+	0.847467i	$0.678126\pi$
$44$	2.01611			0.0458207
$45$		0			0
$46$	36.0294			0.783248
$47$		−	61.0391i		−	1.29870i	−0.760488	−	0.649352i	$-0.775040\pi$
$47$		−	61.0391i		−	1.29870i	0.760488	−	0.649352i	$-0.224960\pi$
$48$			6.92820i			0.144338i
$49$	−46.8178	+	14.4601i	−0.955465	+	0.295103i
$50$		0			0
$51$	−12.2834			−0.240852
$52$			14.1064i			0.271278i
$53$	−74.8237			−1.41177			−0.705884	−	0.708328i	$-0.749450\pi$
$53$	−74.8237			−1.41177			−0.705884	+	0.708328i	$0.749450\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	−2.95445	−	19.5773i	−0.0527581	−	0.349595i
$57$	−7.00193			−0.122841
$58$	−24.4531			−0.421604
$59$			50.5639i			0.857014i	0.903538	+	0.428507i	$0.140960\pi$
$59$			50.5639i			0.857014i	−0.903538	+	0.428507i	$0.859040\pi$
$60$		0			0
$61$			58.0943i			0.952365i	0.879346	+	0.476183i	$0.157980\pi$
$61$			58.0943i			0.952365i	−0.879346	+	0.476183i	$0.842020\pi$
$62$		−	33.4485i		−	0.539491i
$63$	−3.13367	−	20.7649i	−0.0497408	−	0.329601i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	2.46922i		−	0.0374125i
$67$	73.5827			1.09825			0.549125	−	0.835741i	$-0.314961\pi$
$67$	73.5827			1.09825			0.549125	+	0.835741i	$0.314961\pi$
$68$			14.1837i			0.208584i
$69$		−	44.1268i		−	0.639519i
$70$		0			0
$71$	99.8513			1.40636			0.703178	−	0.711013i	$-0.251764\pi$
$71$	99.8513			1.40636			0.703178	+	0.711013i	$0.251764\pi$
$72$	8.48528			0.117851
$73$			1.15350i			0.0158014i	0.999969	+	0.00790069i	$0.00251489\pi$
$73$			1.15350i			0.0158014i	−0.999969	+	0.00790069i	$0.997485\pi$
$74$	−41.3192			−0.558368
$75$		0			0
$76$			8.08514i			0.106383i
$77$	1.05297	+	6.97738i	0.0136749	+	0.0906154i
$78$	17.2768			0.221497
$79$	−102.445			−1.29677			−0.648387	−	0.761311i	$-0.724556\pi$
$79$	−102.445			−1.29677			−0.648387	+	0.761311i	$0.724556\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	7.30042i		−	0.0890295i
$83$		−	83.4227i		−	1.00509i	−0.864550	−	0.502546i	$-0.832397\pi$
$83$		−	83.4227i		−	1.00509i	0.864550	−	0.502546i	$-0.167603\pi$
$84$	−23.9772	+	3.61845i	−0.285443	+	0.0430768i
$85$		0			0
$86$	64.5629			0.750732
$87$			29.9488i			0.344239i
$88$	−2.85121			−0.0324001
$89$		−	69.0342i		−	0.775666i	−0.921730	−	0.387833i	$-0.873224\pi$
$89$		−	69.0342i		−	0.775666i	0.921730	−	0.387833i	$-0.126776\pi$
$90$		0			0
$91$	−48.8198	+	7.36749i	−0.536481	+	0.0809614i
$92$	−50.9533			−0.553840
$93$	−40.9658			−0.440493
$94$			86.3223i			0.918323i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$			152.172i			1.56878i	0.620268	+	0.784390i	$0.287024\pi$
$97$			152.172i			1.56878i	−0.620268	+	0.784390i	$0.712976\pi$
$98$	66.2104	−	20.4496i	0.675616	−	0.208669i
$99$	−3.02417			−0.0305471
$100$		0			0
$101$		−	66.8354i		−	0.661737i	−0.943677	−	0.330869i	$-0.892658\pi$
$101$		−	66.8354i		−	0.661737i	0.943677	−	0.330869i	$-0.107342\pi$
$102$	17.3714			0.170308
$103$		−	65.0648i		−	0.631697i	−0.948810	−	0.315848i	$-0.897711\pi$
$103$		−	65.0648i		−	0.631697i	0.948810	−	0.315848i	$-0.102289\pi$
$104$		−	19.9495i		−	0.191822i
$105$		0			0
$106$	105.817			0.998270
$107$	−10.8093			−0.101021			−0.0505106	−	0.998724i	$-0.516085\pi$
$107$	−10.8093			−0.101021			−0.0505106	+	0.998724i	$0.516085\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−152.035			−1.39482			−0.697410	−	0.716673i	$-0.745664\pi$
$109$	−152.035			−1.39482			−0.697410	+	0.716673i	$0.745664\pi$
$110$		0			0
$111$			50.6055i			0.455905i
$112$	4.17822	+	27.6865i	0.0373056	+	0.247201i
$113$	−223.980			−1.98212			−0.991060	−	0.133419i	$-0.957404\pi$
$113$	−223.980			−1.98212			−0.991060	+	0.133419i	$0.957404\pi$
$114$	9.90223			0.0868617
$115$		0			0
$116$	34.5818			0.298119
$117$		−	21.1597i		−	0.180852i
$118$		−	71.5081i		−	0.606001i
$119$	−49.0871	+	7.40784i	−0.412497	+	0.0622507i
$120$		0			0
$121$	−119.984			−0.991602
$122$		−	82.1577i		−	0.673424i
$123$	−8.94115			−0.0726923
$124$			47.3033i			0.381478i
$125$		0			0
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	−178.242			−1.40348			−0.701739	−	0.712434i	$-0.747593\pi$
$127$	−178.242			−1.40348			−0.701739	+	0.712434i	$0.747593\pi$
$128$	−11.3137			−0.0883883
$129$		−	79.0731i		−	0.612970i
$130$		0			0
$131$		−	124.116i		−	0.947453i	−0.880672	−	0.473726i	$-0.842909\pi$
$131$		−	124.116i		−	0.947453i	0.880672	−	0.473726i	$-0.157091\pi$
$132$			3.49201i			0.0264546i
$133$	−27.9811	+	4.22269i	−0.210385	+	0.0317495i
$134$	−104.062			−0.776579
$135$		0			0
$136$		−	20.0588i		−	0.147491i
$137$	82.7435			0.603967			0.301984	−	0.953313i	$-0.402351\pi$
$137$	82.7435			0.603967			0.301984	+	0.953313i	$0.402351\pi$
$138$			62.4048i			0.452209i
$139$		−	112.631i		−	0.810298i	−0.914251	−	0.405149i	$-0.867220\pi$
$139$		−	112.631i		−	0.810298i	0.914251	−	0.405149i	$-0.132780\pi$
$140$		0			0
$141$	105.723			0.749807
$142$	−141.211			−0.994444
$143$			7.11004i			0.0497206i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	1.63130i		−	0.0111733i
$147$	−25.0455	−	81.0908i	−0.170378	−	0.551638i
$148$	58.4342			0.394826
$149$	−32.3830			−0.217336			−0.108668	−	0.994078i	$-0.534658\pi$
$149$	−32.3830			−0.217336			−0.108668	+	0.994078i	$0.534658\pi$
$150$		0			0
$151$	−45.7944			−0.303274			−0.151637	−	0.988436i	$-0.548455\pi$
$151$	−45.7944			−0.303274			−0.151637	+	0.988436i	$0.548455\pi$
$152$		−	11.4341i		−	0.0752244i
$153$		−	21.2756i		−	0.139056i
$154$	−1.48913	−	9.86751i	−0.00966965	−	0.0640748i
$155$		0			0
$156$	−24.4331			−0.156622
$157$			251.015i			1.59882i	0.600784	+	0.799411i	$0.294855\pi$
$157$			251.015i			1.59882i	−0.600784	+	0.799411i	$0.705145\pi$
$158$	144.879			0.916958
$159$		−	129.598i		−	0.815084i
$160$		0			0
$161$	−26.6118	−	176.340i	−0.165291	−	1.09528i
$162$	−12.7279			−0.0785674
$163$	−138.555			−0.850032			−0.425016	−	0.905186i	$-0.639732\pi$
$163$	−138.555			−0.850032			−0.425016	+	0.905186i	$0.639732\pi$
$164$			10.3243i			0.0629533i
$165$		0			0
$166$			117.977i			0.710708i
$167$		−	180.489i		−	1.08077i	−0.841417	−	0.540386i	$-0.818278\pi$
$167$		−	180.489i		−	1.08077i	0.841417	−	0.540386i	$-0.181722\pi$
$168$	33.9089	−	5.11726i	0.201839	−	0.0304599i
$169$	119.252			0.705633
$170$		0			0
$171$		−	12.1277i		−	0.0709222i
$172$	−91.3058			−0.530847
$173$			292.353i			1.68990i	0.534846	+	0.844950i	$0.320370\pi$
$173$			292.353i			1.68990i	−0.534846	+	0.844950i	$0.679630\pi$
$174$		−	42.3539i		−	0.243413i
$175$		0			0
$176$	4.03222			0.0229104
$177$	−87.5792			−0.494798
$178$			97.6292i			0.548478i
$179$	−273.253			−1.52655			−0.763277	−	0.646071i	$-0.776411\pi$
$179$	−273.253			−1.52655			−0.763277	+	0.646071i	$0.776411\pi$
$180$		0			0
$181$		−	156.148i		−	0.862698i	−0.902185	−	0.431349i	$-0.858038\pi$
$181$		−	156.148i		−	0.862698i	0.902185	−	0.431349i	$-0.141962\pi$
$182$	69.0416	−	10.4192i	0.379349	−	0.0572484i
$183$	−100.622			−0.549848
$184$	72.0588			0.391624
$185$		0			0
$186$	57.9345			0.311476
$187$			7.14898i			0.0382299i
$188$		−	122.078i		−	0.649352i
$189$	35.9658	−	5.42767i	0.190295	−	0.0287178i
$190$		0			0
$191$	−275.462			−1.44221			−0.721104	−	0.692827i	$-0.756365\pi$
$191$	−275.462			−1.44221			−0.721104	+	0.692827i	$0.756365\pi$
$192$			13.8564i			0.0721688i
$193$	9.69062			0.0502105			0.0251052	−	0.999685i	$-0.492008\pi$
$193$	9.69062			0.0502105			0.0251052	+	0.999685i	$0.492008\pi$
$194$		−	215.203i		−	1.10929i
$195$		0			0
$196$	−93.6356	+	28.9201i	−0.477733	+	0.147552i
$197$	65.1041			0.330478			0.165239	−	0.986254i	$-0.447161\pi$
$197$	65.1041			0.330478			0.165239	+	0.986254i	$0.447161\pi$
$198$	4.27682			0.0216001
$199$			220.166i			1.10636i	0.833062	+	0.553180i	$0.186586\pi$
$199$			220.166i			1.10636i	−0.833062	+	0.553180i	$0.813414\pi$
$200$		0			0
$201$			127.449i			0.634074i
$202$			94.5196i			0.467919i
$203$	18.0613	+	119.681i	0.0889721	+	0.589563i
$204$	−24.5669			−0.120426
$205$		0			0
$206$			92.0155i			0.446677i
$207$	76.4299			0.369227
$208$			28.2129i			0.135639i
$209$			4.07513i			0.0194982i
$210$		0			0
$211$	9.08550			0.0430593			0.0215296	−	0.999768i	$-0.493146\pi$
$211$	9.08550			0.0430593			0.0215296	+	0.999768i	$0.493146\pi$
$212$	−149.647			−0.705884
$213$			172.948i			0.811960i
$214$	15.2866			0.0714328
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−163.708	+	24.7055i	−0.754414	+	0.113850i
$218$	215.010			0.986286
$219$	−1.99792			−0.00912293
$220$		0			0
$221$	−50.0204			−0.226337
$222$		−	71.5670i		−	0.322374i
$223$		−	438.428i		−	1.96604i	−0.183489	−	0.983022i	$-0.558739\pi$
$223$		−	438.428i		−	1.96604i	0.183489	−	0.983022i	$-0.441261\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$		0			0
$226$	316.755			1.40157
$227$		−	235.641i		−	1.03807i	−0.854754	−	0.519033i	$-0.826292\pi$
$227$		−	235.641i		−	1.03807i	0.854754	−	0.519033i	$-0.173708\pi$
$228$	−14.0039			−0.0614205
$229$			301.350i			1.31594i	0.753044	+	0.657970i	$0.228584\pi$
$229$			301.350i			1.31594i	−0.753044	+	0.657970i	$0.771416\pi$
$230$		0			0
$231$	−12.0852	+	1.82380i	−0.0523168	+	0.00789523i
$232$	−48.9061			−0.210802
$233$	−48.9562			−0.210113			−0.105056	−	0.994466i	$-0.533502\pi$
$233$	−48.9562			−0.210113			−0.105056	+	0.994466i	$0.533502\pi$
$234$			29.9243i			0.127882i
$235$		0			0
$236$			101.128i			0.428507i
$237$		−	177.440i		−	0.748693i
$238$	69.4197	−	10.4763i	0.291679	−	0.0440179i
$239$	39.0966			0.163584			0.0817921	−	0.996649i	$-0.473936\pi$
$239$	39.0966			0.163584			0.0817921	+	0.996649i	$0.473936\pi$
$240$		0			0
$241$			163.337i			0.677745i	0.940832	+	0.338873i	$0.110046\pi$
$241$			163.337i			0.677745i	−0.940832	+	0.338873i	$0.889954\pi$
$242$	169.683			0.701168
$243$			15.5885i			0.0641500i
$244$			116.189i			0.476183i
$245$		0			0
$246$	12.6447			0.0514012
$247$	−28.5131			−0.115438
$248$		−	66.8969i		−	0.269746i
$249$	144.492			0.580290
$250$		0			0
$251$		−	2.50618i		−	0.00998480i	−0.999988	−	0.00499240i	$-0.998411\pi$
$251$		−	2.50618i		−	0.00998480i	0.999988	−	0.00499240i	$-0.00158914\pi$
$252$	−6.26734	−	41.5298i	−0.0248704	−	0.164801i
$253$	−25.6819			−0.101509
$254$	252.072			0.992409
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	205.951i		−	0.801365i	−0.916217	−	0.400682i	$-0.868773\pi$
$257$		−	205.951i		−	0.801365i	0.916217	−	0.400682i	$-0.131227\pi$
$258$			111.826i			0.433435i
$259$	30.5189	+	202.230i	0.117834	+	0.780810i
$260$		0			0
$261$	−51.8728			−0.198746
$262$			175.527i			0.669950i
$263$	431.680			1.64137			0.820685	−	0.571381i	$-0.193592\pi$
$263$	431.680			1.64137			0.820685	+	0.571381i	$0.193592\pi$
$264$		−	4.93844i		−	0.0187062i
$265$		0			0
$266$	39.5713	−	5.97178i	0.148764	−	0.0224503i
$267$	119.571			0.447831
$268$	147.165			0.549125
$269$			401.016i			1.49077i	0.666636	+	0.745384i	$0.267734\pi$
$269$			401.016i			1.49077i	−0.666636	+	0.745384i	$0.732266\pi$
$270$		0			0
$271$			409.154i			1.50979i	0.655844	+	0.754897i	$0.272313\pi$
$271$			409.154i			1.50979i	−0.655844	+	0.754897i	$0.727687\pi$
$272$			28.3674i			0.104292i
$273$	−12.7609	−	84.5583i	−0.0467431	−	0.309737i
$274$	−117.017			−0.427070
$275$		0			0
$276$		−	88.2537i		−	0.319760i
$277$	311.824			1.12572			0.562859	−	0.826553i	$-0.309701\pi$
$277$	311.824			1.12572			0.562859	+	0.826553i	$0.309701\pi$
$278$			159.285i			0.572968i
$279$		−	70.9549i		−	0.254319i
$280$		0			0
$281$	−131.505			−0.467990			−0.233995	−	0.972238i	$-0.575180\pi$
$281$	−131.505			−0.467990			−0.233995	+	0.972238i	$0.575180\pi$
$282$	−149.515			−0.530194
$283$			50.6362i			0.178926i	0.995990	+	0.0894632i	$0.0285151\pi$
$283$			50.6362i			0.178926i	−0.995990	+	0.0894632i	$0.971485\pi$
$284$	199.703			0.703178
$285$		0			0
$286$		−	10.0551i		−	0.0351578i
$287$	−35.7306	+	5.39218i	−0.124497	+	0.0187881i
$288$	16.9706			0.0589256
$289$	238.706			0.825971
$290$		0			0
$291$	−263.569			−0.905735
$292$			2.30700i			0.00790069i
$293$		−	176.891i		−	0.603725i	−0.953351	−	0.301863i	$-0.902392\pi$
$293$		−	176.891i		−	0.603725i	0.953351	−	0.301863i	$-0.0976084\pi$
$294$	35.4198	+	114.680i	0.120475	+	0.390067i
$295$		0			0
$296$	−82.6384			−0.279184
$297$		−	5.23801i		−	0.0176364i
$298$	45.7965			0.153680
$299$		−	179.692i		−	0.600978i
$300$		0			0
$301$	−47.6870	−	315.992i	−0.158429	−	1.04981i
$302$	64.7631			0.214447
$303$	115.762			0.382054
$304$			16.1703i			0.0531917i
$305$		0			0
$306$			30.0882i			0.0983274i
$307$			569.023i			1.85349i	0.375686	+	0.926747i	$0.377407\pi$
$307$			569.023i			1.85349i	−0.375686	+	0.926747i	$0.622593\pi$
$308$	2.10594	+	13.9548i	0.00683747	+	0.0453077i
$309$	112.696			0.364710
$310$		0			0
$311$			322.176i			1.03593i	0.855401	+	0.517967i	$0.173311\pi$
$311$			322.176i			1.03593i	−0.855401	+	0.517967i	$0.826689\pi$
$312$	34.5536			0.110749
$313$		−	21.5138i		−	0.0687340i	−0.999409	−	0.0343670i	$-0.989058\pi$
$313$		−	21.5138i		−	0.0687340i	0.999409	−	0.0343670i	$-0.0109415\pi$
$314$		−	354.989i		−	1.13054i
$315$		0			0
$316$	−204.890			−0.648387
$317$	384.271			1.21221			0.606106	−	0.795384i	$-0.292731\pi$
$317$	384.271			1.21221			0.606106	+	0.795384i	$0.292731\pi$
$318$			183.280i			0.576352i
$319$	17.4302			0.0546402
$320$		0			0
$321$		−	18.7222i		−	0.0583246i
$322$	37.6348	+	249.382i	0.116878	+	0.774479i
$323$	−28.6693			−0.0887594
$324$	18.0000			0.0555556
$325$		0			0
$326$	195.947			0.601063
$327$		−	263.333i		−	0.805299i
$328$		−	14.6008i		−	0.0445147i
$329$	422.490	−	63.7588i	1.28416	−	0.193796i
$330$		0			0
$331$	28.0523			0.0847503			0.0423751	−	0.999102i	$-0.486508\pi$
$331$	28.0523			0.0847503			0.0423751	+	0.999102i	$0.486508\pi$
$332$		−	166.845i		−	0.502546i
$333$	−87.6513			−0.263217
$334$			255.250i			0.764221i
$335$		0			0
$336$	−47.9544	+	7.23690i	−0.142722	+	0.0215384i
$337$	481.854			1.42983			0.714917	−	0.699210i	$-0.246465\pi$
$337$	481.854			1.42983			0.714917	+	0.699210i	$0.246465\pi$
$338$	−168.648			−0.498958
$339$		−	387.944i		−	1.14438i
$340$		0			0
$341$			23.8422i			0.0699184i
$342$			17.1512i			0.0501496i
$343$	−148.991	−	308.951i	−0.434376	−	0.900732i
$344$	129.126			0.375366
$345$		0			0
$346$		−	413.449i		−	1.19494i
$347$	−376.261			−1.08432			−0.542162	−	0.840274i	$-0.682394\pi$
$347$	−376.261			−1.08432			−0.542162	+	0.840274i	$0.682394\pi$
$348$			59.8975i			0.172119i
$349$		−	260.936i		−	0.747668i	−0.927496	−	0.373834i	$-0.878043\pi$
$349$		−	260.936i		−	0.747668i	0.927496	−	0.373834i	$-0.121957\pi$
$350$		0			0
$351$	36.6496			0.104415
$352$	−5.70242			−0.0162001
$353$			142.203i			0.402841i	0.979505	+	0.201421i	$0.0645558\pi$
$353$			142.203i			0.402841i	−0.979505	+	0.201421i	$0.935444\pi$
$354$	123.856			0.349875
$355$		0			0
$356$		−	138.068i		−	0.387833i
$357$	−12.8308	−	85.0214i	−0.0359405	−	0.238155i
$358$	386.438			1.07944
$359$	214.757			0.598209			0.299104	−	0.954220i	$-0.403312\pi$
$359$	214.757			0.598209			0.299104	+	0.954220i	$0.403312\pi$
$360$		0			0
$361$	344.658			0.954730
$362$			220.827i			0.610019i
$363$		−	207.818i		−	0.572502i
$364$	−97.6395	+	14.7350i	−0.268240	+	0.0404807i
$365$		0			0
$366$	142.301			0.388801
$367$			291.094i			0.793172i	0.917997	+	0.396586i	$0.129805\pi$
$367$			291.094i			0.793172i	−0.917997	+	0.396586i	$0.870195\pi$
$368$	−101.907			−0.276920
$369$		−	15.4865i		−	0.0419689i
$370$		0			0
$371$	−78.1575	−	517.901i	−0.210667	−	1.39596i
$372$	−81.9317			−0.220246
$373$	677.342			1.81593			0.907966	−	0.419044i	$-0.137635\pi$
$373$	677.342			1.81593			0.907966	+	0.419044i	$0.137635\pi$
$374$		−	10.1102i		−	0.0270326i
$375$		0			0
$376$			172.645i			0.459161i
$377$			121.957i			0.323493i
$378$	−50.8634	+	7.67589i	−0.134559	+	0.0203066i
$379$	679.912			1.79396			0.896981	−	0.442069i	$-0.145755\pi$
$379$	679.912			1.79396			0.896981	+	0.442069i	$0.145755\pi$
$380$		0			0
$381$		−	308.724i		−	0.810299i
$382$	389.562			1.01979
$383$			742.938i			1.93979i	0.243530	+	0.969893i	$0.421695\pi$
$383$			742.938i			1.93979i	−0.243530	+	0.969893i	$0.578305\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−13.7046			−0.0355042
$387$	136.959			0.353898
$388$			304.343i			0.784390i
$389$	497.964			1.28011			0.640056	−	0.768328i	$-0.278911\pi$
$389$	497.964			1.28011			0.640056	+	0.768328i	$0.278911\pi$
$390$		0			0
$391$		−	180.677i		−	0.462088i
$392$	132.421	−	40.8992i	0.337808	−	0.104335i
$393$	214.976			0.547012
$394$	−92.0711			−0.233683
$395$		0			0
$396$	−6.04833			−0.0152736
$397$		−	79.8232i		−	0.201066i	−0.994934	−	0.100533i	$-0.967945\pi$
$397$		−	79.8232i		−	0.201066i	0.994934	−	0.100533i	$-0.0320548\pi$
$398$		−	311.361i		−	0.782315i
$399$	−7.31391	−	48.4648i	−0.0183306	−	0.121466i
$400$		0			0
$401$	30.9575			0.0772008			0.0386004	−	0.999255i	$-0.487710\pi$
$401$	30.9575			0.0772008			0.0386004	+	0.999255i	$0.487710\pi$
$402$		−	180.240i		−	0.448358i
$403$	−166.820			−0.413946
$404$		−	133.671i		−	0.330869i
$405$		0			0
$406$	−25.5426	−	169.255i	−0.0629128	−	0.416884i
$407$	29.4525			0.0723648
$408$	34.7428			0.0851540
$409$			179.566i			0.439036i	0.975608	+	0.219518i	$0.0704484\pi$
$409$			179.566i			0.439036i	−0.975608	+	0.219518i	$0.929552\pi$
$410$		0			0
$411$			143.316i			0.348701i
$412$		−	130.130i		−	0.315848i
$413$	−349.984	+	52.8168i	−0.847419	+	0.127886i
$414$	−108.088			−0.261083
$415$		0			0
$416$		−	39.8991i		−	0.0959112i
$417$	195.083			0.467826
$418$		−	5.76311i		−	0.0137873i
$419$		−	283.259i		−	0.676035i	−0.941140	−	0.338017i	$-0.890244\pi$
$419$		−	283.259i		−	0.676035i	0.941140	−	0.338017i	$-0.109756\pi$
$420$		0			0
$421$	−600.315			−1.42593			−0.712963	−	0.701202i	$-0.752647\pi$
$421$	−600.315			−1.42593			−0.712963	+	0.701202i	$0.752647\pi$
$422$	−12.8488			−0.0304475
$423$			183.117i			0.432901i
$424$	211.633			0.499135
$425$		0			0
$426$		−	244.585i		−	0.574143i
$427$	−402.107	+	60.6827i	−0.941702	+	0.142114i
$428$	−21.6185			−0.0505106
$429$	−12.3150			−0.0287062
$430$		0			0
$431$	267.667			0.621036			0.310518	−	0.950567i	$-0.399497\pi$
$431$	267.667			0.621036			0.310518	+	0.950567i	$0.399497\pi$
$432$		−	20.7846i		−	0.0481125i
$433$		−	312.397i		−	0.721471i	−0.932668	−	0.360736i	$-0.882526\pi$
$433$		−	312.397i		−	0.721471i	0.932668	−	0.360736i	$-0.117474\pi$
$434$	231.518	−	34.9388i	0.533451	−	0.0805042i
$435$		0			0
$436$	−304.071			−0.697410
$437$		−	102.991i		−	0.235677i
$438$	2.82549			0.00645089
$439$		−	72.4481i		−	0.165030i	−0.996590	−	0.0825150i	$-0.973705\pi$
$439$		−	72.4481i		−	0.165030i	0.996590	−	0.0825150i	$-0.0262952\pi$
$440$		0			0
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	70.7396			0.160044
$443$	279.795			0.631591			0.315795	−	0.948827i	$-0.397729\pi$
$443$	279.795			0.631591			0.315795	+	0.948827i	$0.397729\pi$
$444$			101.211i			0.227953i
$445$		0			0
$446$			620.030i			1.39020i
$447$		−	56.0890i		−	0.125479i
$448$	8.35645	+	55.3730i	0.0186528	+	0.123600i
$449$	−165.129			−0.367770			−0.183885	−	0.982948i	$-0.558867\pi$
$449$	−165.129			−0.367770			−0.183885	+	0.982948i	$0.558867\pi$
$450$		0			0
$451$			5.20376i			0.0115383i
$452$	−447.959			−0.991060
$453$		−	79.3183i		−	0.175096i
$454$			333.246i			0.734023i
$455$		0			0
$456$	19.8045			0.0434308
$457$	387.165			0.847189			0.423594	−	0.905852i	$-0.360768\pi$
$457$	387.165			0.847189			0.423594	+	0.905852i	$0.360768\pi$
$458$		−	426.173i		−	0.930510i
$459$	36.8503			0.0802840
$460$		0			0
$461$		−	74.1988i		−	0.160952i	−0.996757	−	0.0804759i	$-0.974356\pi$
$461$		−	74.1988i		−	0.160952i	0.996757	−	0.0804759i	$-0.0256440\pi$
$462$	17.0910	−	2.57924i	0.0369936	−	0.00558277i
$463$	423.801			0.915336			0.457668	−	0.889123i	$-0.348685\pi$
$463$	423.801			0.915336			0.457668	+	0.889123i	$0.348685\pi$
$464$	69.1637			0.149060
$465$		0			0
$466$	69.2345			0.148572
$467$			327.240i			0.700727i	0.936614	+	0.350364i	$0.113942\pi$
$467$			327.240i			0.700727i	−0.936614	+	0.350364i	$0.886058\pi$
$468$		−	42.3193i		−	0.0904259i
$469$	76.8613	+	509.312i	0.163883	+	1.08595i
$470$		0			0
$471$	−434.771			−0.923080
$472$		−	143.016i		−	0.303000i
$473$	−46.0207			−0.0972953
$474$			250.939i			0.529406i
$475$		0			0
$476$	−98.1743	+	14.8157i	−0.206249	+	0.0311254i
$477$	224.471			0.470589
$478$	−55.2910			−0.115671
$479$			427.880i			0.893277i	0.894715	+	0.446638i	$0.147379\pi$
$479$			427.880i			0.893277i	−0.894715	+	0.446638i	$0.852621\pi$
$480$		0			0
$481$			206.075i			0.428430i
$482$		−	230.993i		−	0.479238i
$483$	305.429	−	46.0930i	0.632359	−	0.0954306i
$484$	−239.968			−0.495801
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$	−815.490			−1.67452			−0.837259	−	0.546807i	$-0.815843\pi$
$487$	−815.490			−1.67452			−0.837259	+	0.546807i	$0.815843\pi$
$488$		−	164.315i		−	0.336712i
$489$		−	239.985i		−	0.490766i
$490$		0			0
$491$	6.57128			0.0133835			0.00669173	−	0.999978i	$-0.497870\pi$
$491$	6.57128			0.0133835			0.00669173	+	0.999978i	$0.497870\pi$
$492$	−17.8823			−0.0363461
$493$			122.625i			0.248732i
$494$	40.3237			0.0816268
$495$		0			0
$496$			94.6066i			0.190739i
$497$	104.300	+	691.134i	0.209860	+	1.39061i
$498$	−204.343			−0.410327
$499$	−468.850			−0.939579			−0.469790	−	0.882778i	$-0.655670\pi$
$499$	−468.850			−0.939579			−0.469790	+	0.882778i	$0.655670\pi$
$500$		0			0
$501$	312.616			0.623984
$502$			3.54428i			0.00706032i
$503$		−	567.093i		−	1.12742i	−0.825972	−	0.563711i	$-0.809373\pi$
$503$		−	567.093i		−	1.12742i	0.825972	−	0.563711i	$-0.190627\pi$
$504$	8.86335	+	58.7319i	0.0175860	+	0.116532i
$505$		0			0
$506$	36.3197			0.0717780
$507$			206.551i			0.407398i
$508$	−356.483			−0.701739
$509$			464.735i			0.913036i	0.889714	+	0.456518i	$0.150904\pi$
$509$			464.735i			0.913036i	−0.889714	+	0.456518i	$0.849096\pi$
$510$		0			0
$511$	−7.98410	+	1.20490i	−0.0156245	+	0.00235792i
$512$	−22.6274			−0.0441942
$513$	21.0058			0.0409470
$514$			291.258i			0.566651i
$515$		0			0
$516$		−	158.146i		−	0.306485i
$517$		−	61.5308i		−	0.119015i
$518$	−43.1602	−	285.996i	−0.0833209	−	0.552116i
$519$	−506.370			−0.975664
$520$		0			0
$521$			925.284i			1.77598i	0.459866	+	0.887988i	$0.347897\pi$
$521$			925.284i			1.77598i	−0.459866	+	0.887988i	$0.652103\pi$
$522$	73.3592			0.140535
$523$			743.118i			1.42088i	0.703760	+	0.710438i	$0.251503\pi$
$523$			743.118i			1.42088i	−0.703760	+	0.710438i	$0.748497\pi$
$524$		−	248.233i		−	0.473726i
$525$		0			0
$526$	−610.488			−1.16062
$527$	−167.734			−0.318281
$528$			6.98402i			0.0132273i
$529$	120.059			0.226955
$530$		0			0
$531$		−	151.692i		−	0.285671i
$532$	−55.9623	+	8.44538i	−0.105192	+	0.0158748i
$533$	−36.4100			−0.0683114
$534$	−169.099			−0.316664
$535$		0			0
$536$	−208.123			−0.388290
$537$		−	473.288i		−	0.881357i
$538$		−	567.123i		−	1.05413i
$539$	−47.1950	+	14.5765i	−0.0875602	+	0.0270437i
$540$		0			0
$541$	224.274			0.414555			0.207277	−	0.978282i	$-0.433540\pi$
$541$	224.274			0.414555			0.207277	+	0.978282i	$0.433540\pi$
$542$		−	578.631i		−	1.06759i
$543$	270.457			0.498079
$544$		−	40.1176i		−	0.0737455i
$545$		0			0
$546$	18.0466	+	119.584i	0.0330524	+	0.219017i
$547$	−636.899			−1.16435			−0.582175	−	0.813064i	$-0.697798\pi$
$547$	−636.899			−1.16435			−0.582175	+	0.813064i	$0.697798\pi$
$548$	165.487			0.301984
$549$		−	174.283i		−	0.317455i
$550$		0			0
$551$			69.8997i			0.126860i
$552$			124.810i			0.226104i
$553$	−107.010	−	709.087i	−0.193508	−	1.28226i
$554$	−440.986			−0.796003
$555$		0			0
$556$		−	225.263i		−	0.405149i
$557$	−715.978			−1.28542			−0.642709	−	0.766111i	$-0.722189\pi$
$557$	−715.978			−1.28542			−0.642709	+	0.766111i	$0.722189\pi$
$558$			100.345i			0.179830i
$559$		−	322.000i		−	0.576029i
$560$		0			0
$561$	−12.3824			−0.0220720
$562$	185.976			0.330919
$563$			911.747i			1.61944i	0.586813	+	0.809722i	$0.300382\pi$
$563$			911.747i			1.61944i	−0.586813	+	0.809722i	$0.699618\pi$
$564$	211.446			0.374904
$565$		0			0
$566$		−	71.6103i		−	0.126520i
$567$	9.40101	+	62.2946i	0.0165803	+	0.109867i
$568$	−282.422			−0.497222
$569$	83.3213			0.146435			0.0732173	−	0.997316i	$-0.476673\pi$
$569$	83.3213			0.146435			0.0732173	+	0.997316i	$0.476673\pi$
$570$		0			0
$571$	112.867			0.197666			0.0988328	−	0.995104i	$-0.468489\pi$
$571$	112.867			0.197666			0.0988328	+	0.995104i	$0.468489\pi$
$572$			14.2201i			0.0248603i
$573$		−	477.114i		−	0.832659i
$574$	50.5307	−	7.62570i	0.0880327	−	0.0132852i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	187.954i		−	0.325743i	−0.986647	−	0.162872i	$-0.947924\pi$
$577$		−	187.954i		−	0.325743i	0.986647	−	0.162872i	$-0.0520757\pi$
$578$	−337.581			−0.584050
$579$			16.7846i			0.0289890i
$580$		0			0
$581$	577.420	−	87.1397i	0.993839	−	0.149982i
$582$	372.743			0.640452
$583$	−75.4264			−0.129376
$584$		−	3.26259i		−	0.00558663i
$585$		0			0
$586$			250.162i			0.426898i
$587$			137.244i			0.233806i	0.993143	+	0.116903i	$0.0372967\pi$
$587$			137.244i			0.233806i	−0.993143	+	0.116903i	$0.962703\pi$
$588$	−50.0911	−	162.182i	−0.0851889	−	0.275819i
$589$	−95.6134			−0.162332
$590$		0			0
$591$			112.764i			0.190801i
$592$	116.868			0.197413
$593$			691.207i			1.16561i	0.812612	+	0.582805i	$0.198045\pi$
$593$			691.207i			1.16561i	−0.812612	+	0.582805i	$0.801955\pi$
$594$			7.40767i			0.0124708i
$595$		0			0
$596$	−64.7660			−0.108668
$597$	−381.338			−0.638758
$598$			254.123i			0.424956i
$599$	−915.774			−1.52884			−0.764419	−	0.644720i	$-0.776974\pi$
$599$	−915.774			−1.52884			−0.764419	+	0.644720i	$0.776974\pi$
$600$		0			0
$601$		−	178.510i		−	0.297022i	−0.988911	−	0.148511i	$-0.952552\pi$
$601$		−	178.510i		−	0.297022i	0.988911	−	0.148511i	$-0.0474480\pi$
$602$	67.4396	+	446.880i	0.112026	+	0.742326i
$603$	−220.748			−0.366083
$604$	−91.5889			−0.151637
$605$		0			0
$606$	−163.713			−0.270153
$607$		−	673.634i		−	1.10978i	−0.831925	−	0.554888i	$-0.812761\pi$
$607$		−	673.634i		−	1.10978i	0.831925	−	0.554888i	$-0.187239\pi$
$608$		−	22.8682i		−	0.0376122i
$609$	−207.294	+	31.2832i	−0.340384	+	0.0513681i
$610$		0			0
$611$	430.522			0.704619
$612$		−	42.5511i		−	0.0695280i
$613$	−859.658			−1.40238			−0.701189	−	0.712976i	$-0.747347\pi$
$613$	−859.658			−1.40238			−0.701189	+	0.712976i	$0.747347\pi$
$614$		−	804.720i		−	1.31062i
$615$		0			0
$616$	−2.97825	−	19.7350i	−0.00483482	−	0.0320374i
$617$	695.263			1.12684			0.563422	−	0.826169i	$-0.309484\pi$
$617$	695.263			1.12684			0.563422	+	0.826169i	$0.309484\pi$
$618$	−159.376			−0.257889
$619$		−	1036.53i		−	1.67452i	−0.546808	−	0.837258i	$-0.684157\pi$
$619$		−	1036.53i		−	1.67452i	0.546808	−	0.837258i	$-0.315843\pi$
$620$		0			0
$621$			132.381i			0.213173i
$622$		−	455.625i		−	0.732516i
$623$	477.829	−	72.1102i	0.766981	−	0.115747i
$624$	−48.8662			−0.0783112
$625$		0			0
$626$			30.4250i			0.0486023i
$627$	−7.05834			−0.0112573
$628$			502.030i			0.799411i
$629$			207.203i			0.329417i
$630$		0			0
$631$	702.851			1.11387			0.556934	−	0.830557i	$-0.311978\pi$
$631$	702.851			1.11387			0.556934	+	0.830557i	$0.311978\pi$
$632$	289.759			0.458479
$633$			15.7366i			0.0248603i
$634$	−543.442			−0.857164
$635$		0			0
$636$		−	259.197i		−	0.407542i
$637$	−101.990	−	330.216i	−0.160110	−	0.518393i
$638$	−24.6500			−0.0386364
$639$	−299.554			−0.468786
$640$		0			0
$641$	−421.315			−0.657277			−0.328639	−	0.944456i	$-0.606590\pi$
$641$	−421.315			−0.657277			−0.328639	+	0.944456i	$0.606590\pi$
$642$			26.4772i			0.0412417i
$643$			414.352i			0.644404i	0.946671	+	0.322202i	$0.104423\pi$
$643$			414.352i			0.644404i	−0.946671	+	0.322202i	$0.895577\pi$
$644$	−53.2236	−	352.680i	−0.0826453	−	0.547639i
$645$		0			0
$646$	40.5445			0.0627624
$647$			116.692i			0.180358i	0.995926	+	0.0901790i	$0.0287439\pi$
$647$			116.692i			0.180358i	−0.995926	+	0.0901790i	$0.971256\pi$
$648$	−25.4558			−0.0392837
$649$			50.9712i			0.0785380i
$650$		0			0
$651$	−42.7911	−	283.550i	−0.0657314	−	0.435561i
$652$	−277.110			−0.425016
$653$	−168.591			−0.258178			−0.129089	−	0.991633i	$-0.541205\pi$
$653$	−168.591			−0.258178			−0.129089	+	0.991633i	$0.541205\pi$
$654$			372.409i			0.569433i
$655$		0			0
$656$			20.6487i			0.0314767i
$657$		−	3.46050i		−	0.00526713i
$658$	−597.491	+	90.1685i	−0.908041	+	0.137034i
$659$	−1009.52			−1.53189			−0.765946	−	0.642904i	$-0.777729\pi$
$659$	−1009.52			−1.53189			−0.765946	+	0.642904i	$0.777729\pi$
$660$		0			0
$661$			646.529i			0.978107i	0.872254	+	0.489054i	$0.162658\pi$
$661$			646.529i			0.978107i	−0.872254	+	0.489054i	$0.837342\pi$
$662$	−39.6720			−0.0599275
$663$		−	86.6379i		−	0.130676i
$664$			235.955i			0.355354i
$665$		0			0
$666$	123.958			0.186123
$667$	−440.515			−0.660442
$668$		−	360.978i		−	0.540386i
$669$	759.379			1.13510
$670$		0			0
$671$			58.5623i			0.0872761i
$672$	67.8178	−	10.2345i	0.100919	−	0.0152299i
$673$	840.576			1.24900			0.624500	−	0.781025i	$-0.285303\pi$
$673$	840.576			1.24900			0.624500	+	0.781025i	$0.285303\pi$
$674$	−681.444			−1.01104
$675$		0			0
$676$	238.504			0.352817
$677$		−	379.146i		−	0.560038i	−0.959994	−	0.280019i	$-0.909659\pi$
$677$		−	379.146i		−	0.560038i	0.959994	−	0.280019i	$-0.0903408\pi$
$678$			548.635i			0.809197i
$679$	−1053.27	+	158.952i	−1.55121	+	0.234097i
$680$		0			0
$681$	408.142			0.599327
$682$		−	33.7179i		−	0.0494398i
$683$	115.942			0.169754			0.0848770	−	0.996391i	$-0.472950\pi$
$683$	115.942			0.169754			0.0848770	+	0.996391i	$0.472950\pi$
$684$		−	24.2554i		−	0.0354611i
$685$		0			0
$686$	210.705	+	436.923i	0.307150	+	0.636914i
$687$	−521.954			−0.759758
$688$	−182.612			−0.265424
$689$		−	527.748i		−	0.765962i
$690$		0			0
$691$			112.794i			0.163233i	0.996664	+	0.0816167i	$0.0260083\pi$
$691$			112.794i			0.163233i	−0.996664	+	0.0816167i	$0.973992\pi$
$692$			584.705i			0.844950i
$693$	−3.15891	−	20.9322i	−0.00455832	−	0.0302051i
$694$	532.113			0.766733
$695$		0			0
$696$		−	84.7079i		−	0.121707i
$697$	−36.6094			−0.0525242
$698$			369.020i			0.528681i
$699$		−	84.7947i		−	0.121309i
$700$		0			0
$701$	192.764			0.274985			0.137492	−	0.990503i	$-0.456096\pi$
$701$	192.764			0.274985			0.137492	+	0.990503i	$0.456096\pi$
$702$	−51.8304			−0.0738325
$703$			118.112i			0.168012i
$704$	8.06445			0.0114552
$705$		0			0
$706$		−	201.105i		−	0.284852i
$707$	462.610	−	69.8134i	0.654328	−	0.0987459i
$708$	−175.158			−0.247399
$709$	−317.352			−0.447604			−0.223802	−	0.974635i	$-0.571847\pi$
$709$	−317.352			−0.447604			−0.223802	+	0.974635i	$0.571847\pi$
$710$		0			0
$711$	307.336			0.432258
$712$			195.258i			0.274239i
$713$		−	602.564i		−	0.845111i
$714$	18.1454	+	120.238i	0.0254138	+	0.168401i
$715$		0			0
$716$	−546.506			−0.763277
$717$			67.7173i			0.0944454i
$718$	−303.712			−0.422998
$719$			668.666i			0.929995i	0.885312	+	0.464997i	$0.153945\pi$
$719$			668.666i			0.929995i	−0.885312	+	0.464997i	$0.846055\pi$
$720$		0			0
$721$	450.354	−	67.9638i	0.624624	−	0.0942633i
$722$	−487.420			−0.675096
$723$	−282.907			−0.391296
$724$		−	312.297i		−	0.431349i
$725$		0			0
$726$			293.899i			0.404820i
$727$		−	164.229i		−	0.225900i	−0.993601	−	0.112950i	$-0.963970\pi$
$727$		−	164.229i		−	0.225900i	0.993601	−	0.112950i	$-0.0360300\pi$
$728$	138.083	−	20.8384i	0.189675	−	0.0286242i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	323.764i		−	0.442905i
$732$	−201.244			−0.274924
$733$			986.499i			1.34584i	0.739717	+	0.672919i	$0.234960\pi$
$733$			986.499i			1.34584i	−0.739717	+	0.672919i	$0.765040\pi$
$734$		−	411.669i		−	0.560858i
$735$		0			0
$736$	144.118			0.195812
$737$	74.1755			0.100645
$738$			21.9012i			0.0296765i
$739$	−645.708			−0.873759			−0.436880	−	0.899520i	$-0.643916\pi$
$739$	−645.708			−0.873759			−0.436880	+	0.899520i	$0.643916\pi$
$740$		0			0
$741$		−	49.3862i		−	0.0666480i
$742$	110.531	+	732.423i	0.148964	+	0.987093i
$743$	−45.9927			−0.0619013			−0.0309507	−	0.999521i	$-0.509853\pi$
$743$	−45.9927			−0.0619013			−0.0309507	+	0.999521i	$0.509853\pi$
$744$	115.869			0.155738
$745$		0			0
$746$	−957.907			−1.28406
$747$			250.268i			0.335031i
$748$			14.2980i			0.0191149i
$749$	−11.2909	−	74.8177i	−0.0150746	−	0.0998902i
$750$		0			0
$751$	638.813			0.850616			0.425308	−	0.905049i	$-0.360166\pi$
$751$	638.813			0.850616			0.425308	+	0.905049i	$0.360166\pi$
$752$		−	244.156i		−	0.324676i
$753$	4.34084			0.00576472
$754$		−	172.473i		−	0.228744i
$755$		0			0
$756$	71.9316	−	10.8553i	0.0951477	−	0.0143589i
$757$	1133.23			1.49700			0.748502	−	0.663133i	$-0.230774\pi$
$757$	1133.23			1.49700			0.748502	+	0.663133i	$0.230774\pi$
$758$	−961.540			−1.26852
$759$		−	44.4823i		−	0.0586065i
$760$		0			0
$761$			846.462i			1.11230i	0.831081	+	0.556151i	$0.187722\pi$
$761$			846.462i			1.11230i	−0.831081	+	0.556151i	$0.812278\pi$
$762$			436.601i			0.572968i
$763$	−158.809	−	1052.33i	−0.208138	−	1.37920i
$764$	−550.923			−0.721104
$765$		0			0
$766$		−	1050.67i		−	1.37164i
$767$	−356.638			−0.464978
$768$			27.7128i			0.0360844i
$769$		−	894.921i		−	1.16375i	−0.813280	−	0.581873i	$-0.802320\pi$
$769$		−	894.921i		−	1.16375i	0.813280	−	0.581873i	$-0.197680\pi$
$770$		0			0
$771$	356.717			0.462668
$772$	19.3812			0.0251052
$773$		−	104.513i		−	0.135204i	−0.997712	−	0.0676019i	$-0.978465\pi$
$773$		−	104.513i		−	0.135204i	0.997712	−	0.0676019i	$-0.0215348\pi$
$774$	−193.689			−0.250244
$775$		0			0
$776$		−	430.406i		−	0.554647i
$777$	−350.272	+	52.8603i	−0.450801	+	0.0680313i
$778$	−704.227			−0.905176
$779$	−20.8684			−0.0267888
$780$		0			0
$781$	100.656			0.128881
$782$			255.515i			0.326746i
$783$		−	89.8463i		−	0.114746i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$		0			0
$786$	−304.022			−0.386796
$787$		−	349.479i		−	0.444065i	−0.975039	−	0.222032i	$-0.928731\pi$
$787$		−	349.479i		−	0.444065i	0.975039	−	0.222032i	$-0.0712691\pi$
$788$	130.208			0.165239
$789$			747.692i			0.947645i
$790$		0			0
$791$	−233.959	−	1550.30i	−0.295776	−	1.95993i
$792$	8.55364			0.0108000
$793$	−409.752			−0.516711
$794$			112.887i			0.142175i
$795$		0			0
$796$			440.332i			0.553180i
$797$			606.585i			0.761085i	0.924763	+	0.380543i	$0.124263\pi$
$797$			606.585i			0.761085i	−0.924763	+	0.380543i	$0.875737\pi$
$798$	10.3434	+	68.5395i	0.0129617	+	0.0858891i
$799$	432.880			0.541778
$800$		0			0
$801$			207.103i			0.258555i
$802$	−43.7805			−0.0545892
$803$			1.16279i			0.00144806i
$804$			254.898i			0.317037i
$805$		0			0
$806$	235.920			0.292704
$807$	−694.581			−0.860695
$808$			189.039i			0.233959i
$809$	−157.390			−0.194548			−0.0972742	−	0.995258i	$-0.531012\pi$
$809$	−157.390			−0.194548			−0.0972742	+	0.995258i	$0.531012\pi$
$810$		0			0
$811$		−	443.035i		−	0.546283i	−0.961974	−	0.273141i	$-0.911937\pi$
$811$		−	443.035i		−	0.546283i	0.961974	−	0.273141i	$-0.0880626\pi$
$812$	36.1227	+	239.363i	0.0444861	+	0.294782i
$813$	−708.676			−0.871680
$814$	−41.6521			−0.0511696
$815$		0			0
$816$	−49.1338			−0.0602130
$817$		−	184.555i		−	0.225893i
$818$		−	253.944i		−	0.310445i
$819$	146.459	−	22.1025i	0.178827	−	0.0269871i
$820$		0			0
$821$	768.304			0.935815			0.467907	−	0.883777i	$-0.345008\pi$
$821$	768.304			0.935815			0.467907	+	0.883777i	$0.345008\pi$
$822$		−	202.679i		−	0.246569i
$823$	1094.49			1.32988			0.664938	−	0.746899i	$-0.268458\pi$
$823$	1094.49			1.32988			0.664938	+	0.746899i	$0.268458\pi$
$824$			184.031i			0.223339i
$825$		0			0
$826$	494.952	−	74.6942i	0.599216	−	0.0904288i
$827$	−1258.41			−1.52165			−0.760826	−	0.648956i	$-0.775206\pi$
$827$	−1258.41			−1.52165			−0.760826	+	0.648956i	$0.775206\pi$
$828$	152.860			0.184613
$829$			182.499i			0.220143i	0.993924	+	0.110072i	$0.0351081\pi$
$829$			182.499i			0.220143i	−0.993924	+	0.110072i	$0.964892\pi$
$830$		0			0
$831$			540.095i			0.649934i
$832$			56.4258i			0.0678195i
$833$	−102.549	−	332.025i	−0.123108	−	0.398589i
$834$	−275.890			−0.330803
$835$		0			0
$836$			8.15027i			0.00974912i
$837$	122.898			0.146831
$838$			400.588i			0.478029i
$839$			1157.55i			1.37968i	0.723963	+	0.689839i	$0.242319\pi$
$839$			1157.55i			1.37968i	−0.723963	+	0.689839i	$0.757681\pi$
$840$		0			0
$841$	−542.024			−0.644499
$842$	848.973			1.00828
$843$		−	227.774i		−	0.270194i
$844$	18.1710			0.0215296
$845$		0			0
$846$		−	258.967i		−	0.306108i
$847$	−125.330	−	830.483i	−0.147969	−	0.980500i
$848$	−299.295			−0.352942
$849$	−87.7044			−0.103303
$850$		0			0
$851$	−744.354			−0.874681
$852$			345.895i			0.405980i
$853$		−	1038.69i		−	1.21769i	−0.793290	−	0.608844i	$-0.791634\pi$
$853$		−	1038.69i		−	1.21769i	0.793290	−	0.608844i	$-0.208366\pi$
$854$	568.665	−	85.8184i	0.665884	−	0.100490i
$855$		0			0
$856$	30.5732			0.0357164
$857$			1206.41i			1.40771i	0.710344	+	0.703854i	$0.248539\pi$
$857$			1206.41i			1.40771i	−0.710344	+	0.703854i	$0.751461\pi$
$858$	17.4160			0.0202983
$859$		−	333.020i		−	0.387683i	−0.981033	−	0.193841i	$-0.937905\pi$
$859$		−	333.020i		−	0.387683i	0.981033	−	0.193841i	$-0.0620947\pi$
$860$		0			0
$861$	−9.33953	−	61.8873i	−0.0108473	−	0.0718784i
$862$	−378.538			−0.439139
$863$	−683.072			−0.791508			−0.395754	−	0.918357i	$-0.629517\pi$
$863$	−683.072			−0.791508			−0.395754	+	0.918357i	$0.629517\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$			441.796i			0.510157i
$867$			413.450i			0.476875i
$868$	−327.416	+	49.4109i	−0.377207	+	0.0569250i
$869$	−103.270			−0.118838
$870$		0			0
$871$			518.995i			0.595861i
$872$	430.021			0.493143
$873$		−	456.515i		−	0.522926i
$874$			145.651i			0.166649i
$875$		0			0
$876$	−3.99584			−0.00456146
$877$	792.582			0.903743			0.451871	−	0.892083i	$-0.350757\pi$
$877$	792.582			0.903743			0.451871	+	0.892083i	$0.350757\pi$
$878$			102.457i			0.116694i
$879$	306.385			0.348561
$880$		0			0
$881$		−	260.584i		−	0.295782i	−0.989004	−	0.147891i	$-0.952752\pi$
$881$		−	260.584i		−	0.295782i	0.989004	−	0.147891i	$-0.0472485\pi$
$882$	−198.631	+	61.3488i	−0.225205	+	0.0695565i
$883$	−25.2235			−0.0285657			−0.0142828	−	0.999898i	$-0.504547\pi$
$883$	−25.2235			−0.0285657			−0.0142828	+	0.999898i	$0.504547\pi$
$884$	−100.041			−0.113168
$885$		0			0
$886$	−395.690			−0.446602
$887$		−	1430.63i		−	1.61289i	−0.591308	−	0.806446i	$-0.701388\pi$
$887$		−	1430.63i		−	1.61289i	0.591308	−	0.806446i	$-0.298612\pi$
$888$		−	143.134i		−	0.161187i
$889$	−186.184	−	1233.72i	−0.209430	−	1.38776i
$890$		0			0
$891$	9.07250			0.0101824
$892$		−	876.855i		−	0.983022i
$893$	246.755			0.276321
$894$			79.3219i			0.0887269i
$895$		0			0
$896$	−11.8178	−	78.3093i	−0.0131895	−	0.0873987i
$897$	311.236			0.346975
$898$	233.528			0.260053
$899$			408.959i			0.454904i
$900$		0			0
$901$		−	530.638i		−	0.588944i
$902$		−	7.35923i		−	0.00815879i
$903$	547.314	−	82.5963i	0.606107	−	0.0914688i
$904$	633.510			0.700785
$905$		0			0
$906$			112.173i			0.123811i
$907$	1208.91			1.33287			0.666436	−	0.745563i	$-0.267819\pi$
$907$	1208.91			1.33287			0.666436	+	0.745563i	$0.267819\pi$
$908$		−	471.282i		−	0.519033i
$909$			200.506i			0.220579i
$910$		0			0
$911$	604.287			0.663323			0.331661	−	0.943398i	$-0.392391\pi$
$911$	604.287			0.663323			0.331661	+	0.943398i	$0.392391\pi$
$912$	−28.0077			−0.0307102
$913$		−	84.0947i		−	0.0921081i
$914$	−547.534			−0.599053
$915$		0			0
$916$			602.700i			0.657970i
$917$	859.087	−	129.646i	0.936845	−	0.141381i
$918$	−52.1143			−0.0567693
$919$	264.211			0.287498			0.143749	−	0.989614i	$-0.454084\pi$
$919$	264.211			0.287498			0.143749	+	0.989614i	$0.454084\pi$
$920$		0			0
$921$	−985.576			−1.07012
$922$			104.933i			0.113810i
$923$			704.274i			0.763027i
$924$	−24.1704	+	3.64760i	−0.0261584	+	0.00394762i
$925$		0			0
$926$	−599.345			−0.647240
$927$			195.194i			0.210566i
$928$	−97.8122			−0.105401
$929$			828.146i			0.891439i	0.895173	+	0.445719i	$0.147052\pi$
$929$			828.146i			0.891439i	−0.895173	+	0.445719i	$0.852948\pi$
$930$		0			0
$931$	−58.4558	−	189.264i	−0.0627881	−	0.203291i
$932$	−97.9124			−0.105056
$933$	−558.024			−0.598097
$934$		−	462.787i		−	0.495489i
$935$		0			0
$936$			59.8486i			0.0639408i
$937$			396.006i			0.422632i	0.977418	+	0.211316i	$0.0677749\pi$
$937$			396.006i			0.422632i	−0.977418	+	0.211316i	$0.932225\pi$
$938$	−108.698	−	720.276i	−0.115883	−	0.767885i
$939$	37.2629			0.0396836
$940$		0			0
$941$			457.424i			0.486105i	0.970013	+	0.243052i	$0.0781487\pi$
$941$			457.424i			0.486105i	−0.970013	+	0.243052i	$0.921851\pi$
$942$	614.859			0.652716
$943$		−	131.515i		−	0.139464i
$944$			202.255i			0.214254i
$945$		0			0
$946$	65.0830			0.0687981
$947$	−203.596			−0.214991			−0.107495	−	0.994206i	$-0.534283\pi$
$947$	−203.596			−0.214991			−0.107495	+	0.994206i	$0.534283\pi$
$948$		−	354.881i		−	0.374347i
$949$	−8.13590			−0.00857313
$950$		0			0
$951$			665.578i			0.699871i
$952$	138.839	−	20.9525i	0.145840	−	0.0220090i
$953$	−119.616			−0.125516			−0.0627578	−	0.998029i	$-0.519990\pi$
$953$	−119.616			−0.125516			−0.0627578	+	0.998029i	$0.519990\pi$
$954$	−317.450			−0.332757
$955$		0			0
$956$	78.1932			0.0817921
$957$			30.1900i			0.0315465i
$958$		−	605.113i		−	0.631642i
$959$	86.4303	+	572.720i	0.0901254	+	0.597205i
$960$		0			0
$961$	401.600			0.417898
$962$		−	291.434i		−	0.302946i
$963$	32.4278			0.0336737
$964$			326.673i			0.338873i
$965$		0			0
$966$	−431.943	+	65.1853i	−0.447145	+	0.0674796i
$967$	−427.535			−0.442126			−0.221063	−	0.975260i	$-0.570953\pi$
$967$	−427.535			−0.442126			−0.221063	+	0.975260i	$0.570953\pi$
$968$	339.366			0.350584
$969$		−	49.6567i		−	0.0512453i
$970$		0			0
$971$		−	6.82181i		−	0.00702555i	−0.999994	−	0.00351278i	$-0.998882\pi$
$971$		−	6.82181i		−	0.00702555i	0.999994	−	0.00351278i	$-0.00111815\pi$
$972$			31.1769i			0.0320750i
$973$	779.593	−	117.650i	0.801226	−	0.120915i
$974$	1153.28			1.18406
$975$		0			0
$976$			232.377i			0.238091i
$977$	−251.640			−0.257564			−0.128782	−	0.991673i	$-0.541107\pi$
$977$	−251.640			−0.257564			−0.128782	+	0.991673i	$0.541107\pi$
$978$			339.390i			0.347024i
$979$		−	69.5904i		−	0.0710831i
$980$		0			0
$981$	456.106			0.464940
$982$	−9.29320			−0.00946354
$983$		−	743.441i		−	0.756298i	−0.925745	−	0.378149i	$-0.876561\pi$
$983$		−	743.441i		−	0.756298i	0.925745	−	0.378149i	$-0.123439\pi$
$984$	25.2894			0.0257006
$985$		0			0
$986$		−	173.417i		−	0.175880i
$987$	110.433	+	731.774i	0.111888	+	0.741412i
$988$	−57.0263			−0.0577189
$989$	1163.08			1.17602
$990$		0			0
$991$	−579.815			−0.585080			−0.292540	−	0.956253i	$-0.594501\pi$
$991$	−579.815			−0.585080			−0.292540	+	0.956253i	$0.594501\pi$
$992$		−	133.794i		−	0.134873i
$993$			48.5881i			0.0489306i
$994$	−147.503	−	977.410i	−0.148393	−	0.983310i
$995$		0			0
$996$	288.985			0.290145
$997$		−	723.701i		−	0.725878i	−0.931813	−	0.362939i	$-0.881773\pi$
$997$		−	723.701i		−	0.725878i	0.931813	−	0.362939i	$-0.118227\pi$
$998$	663.054			0.664383
$999$		−	151.817i		−	0.151968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.b.601.4		8
5.2	odd	4		1050.3.h.b.349.5		16
5.3	odd	4		1050.3.h.b.349.12		16
5.4	even	2		210.3.f.a.181.5	✓	8
7.6	odd	2	inner	1050.3.f.b.601.2		8
15.14	odd	2		630.3.f.c.181.3		8
20.19	odd	2		1680.3.s.a.1441.5		8
35.13	even	4		1050.3.h.b.349.13		16
35.27	even	4		1050.3.h.b.349.4		16
35.34	odd	2		210.3.f.a.181.8	yes	8
105.104	even	2		630.3.f.c.181.1		8
140.139	even	2		1680.3.s.a.1441.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.5	✓	8	5.4	even	2
210.3.f.a.181.8	yes	8	35.34	odd	2
630.3.f.c.181.1		8	105.104	even	2
630.3.f.c.181.3		8	15.14	odd	2
1050.3.f.b.601.2		8	7.6	odd	2	inner
1050.3.f.b.601.4		8	1.1	even	1	trivial
1050.3.h.b.349.4		16	35.27	even	4
1050.3.h.b.349.5		16	5.2	odd	4
1050.3.h.b.349.12		16	5.3	odd	4
1050.3.h.b.349.13		16	35.13	even	4
1680.3.s.a.1441.3		8	140.139	even	2
1680.3.s.a.1441.5		8	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +1.00806 q^{11} +3.46410i q^{12} +7.05322i q^{13} +(-1.47723 - 9.78866i) q^{14} +4.00000 q^{16} +7.09185i q^{17} +4.24264 q^{18} +4.04257i q^{19} +(-11.9886 + 1.80922i) q^{21} -1.42561 q^{22} -25.4766 q^{23} -4.89898i q^{24} -9.97476i q^{26} -5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} +17.2909 q^{29} +23.6516i q^{31} -5.65685 q^{32} +1.74600i q^{33} -10.0294i q^{34} -6.00000 q^{36} +29.2171 q^{37} -5.71705i q^{38} -12.2165 q^{39} +5.16217i q^{41} +(16.9545 - 2.55863i) q^{42} -45.6529 q^{43} +2.01611 q^{44} +36.0294 q^{46} -61.0391i q^{47} +6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} -12.2834 q^{51} +14.1064i q^{52} -74.8237 q^{53} +7.34847i q^{54} +(-2.95445 - 19.5773i) q^{56} -7.00193 q^{57} -24.4531 q^{58} +50.5639i q^{59} +58.0943i q^{61} -33.4485i q^{62} +(-3.13367 - 20.7649i) q^{63} +8.00000 q^{64} -2.46922i q^{66} +73.5827 q^{67} +14.1837i q^{68} -44.1268i q^{69} +99.8513 q^{71} +8.48528 q^{72} +1.15350i q^{73} -41.3192 q^{74} +8.08514i q^{76} +(1.05297 + 6.97738i) q^{77} +17.2768 q^{78} -102.445 q^{79} +9.00000 q^{81} -7.30042i q^{82} -83.4227i q^{83} +(-23.9772 + 3.61845i) q^{84} +64.5629 q^{86} +29.9488i q^{87} -2.85121 q^{88} -69.0342i q^{89} +(-48.8198 + 7.36749i) q^{91} -50.9533 q^{92} -40.9658 q^{93} +86.3223i q^{94} -9.79796i q^{96} +152.172i q^{97} +(66.2104 - 20.4496i) q^{98} -3.02417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 24 * q^9	\( 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * q^99

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