LMFDB - Embedded newform 1100.3.f.c.901.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,3,Mod(901,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.901"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1100.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$29.9728290796$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 83x^{6} + 1611x^{4} + 7105x^{2} + 400 $ x^8 + 83x^6 + 1611x^4 + 7105*x^2 + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.5
Root			$2.49129i$ of defining polynomial
Character	$\chi$	$=$	1100.901
Dual form			1100.3.f.c.901.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.638826 q^{3} -9.06537i q^{7} -8.59190 q^{9} +(10.0956 - 4.36788i) q^{11} +10.4302i q^{13} +3.39108i q^{17} -28.0187i q^{19} -5.79120i q^{21} -18.8226 q^{23} -11.2382 q^{27} +22.2253i q^{29} +0.00744511 q^{31} +(6.44935 - 2.79032i) q^{33} -8.96796 q^{37} +6.66311i q^{39} +16.5975i q^{41} -81.5368i q^{43} -59.1685 q^{47} -33.1809 q^{49} +2.16631i q^{51} -60.1508 q^{53} -17.8991i q^{57} -81.5361 q^{59} +114.695i q^{61} +77.8888i q^{63} -99.1084 q^{67} -12.0244 q^{69} +70.3598 q^{71} -16.4827i q^{73} +(-39.5965 - 91.5206i) q^{77} -118.929i q^{79} +70.1479 q^{81} -30.6387i q^{83} +14.1981i q^{87} -4.02316 q^{89} +94.5539 q^{91} +0.00475614 q^{93} -101.970 q^{97} +(-86.7406 + 37.5284i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 16 q^{9} + 3 q^{11} + 28 q^{23} - 10 q^{27} + 14 q^{31} - 31 q^{33} - 24 q^{37} - 32 q^{47} + 14 q^{49} + 98 q^{53} + 128 q^{59} - 42 q^{67} - 176 q^{69} - 34 q^{71} - 136 q^{77} - 128 q^{81}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 16 * q^9 + 3 * q^11 + 28 * q^23 - 10 * q^27 + 14 * q^31 - 31 * q^33 - 24 * q^37 - 32 * q^47 + 14 * q^49 + 98 * q^53 + 128 * q^59 - 42 * q^67 - 176 * q^69 - 34 * q^71 - 136 * q^77 - 128 * q^81 - 146 * q^89 + 114 * q^91 - 142 * q^93 + 296 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.638826			0.212942			0.106471	−	0.994316i	$-0.466045\pi$
$3$	0.638826			0.212942			0.106471	+	0.994316i	$0.466045\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	9.06537i		−	1.29505i	−0.762043	−	0.647526i	$-0.775804\pi$
$7$		−	9.06537i		−	1.29505i	0.762043	−	0.647526i	$-0.224196\pi$
$8$		0			0
$9$	−8.59190			−0.954656
$10$		0			0
$11$	10.0956	−	4.36788i	0.917784	−	0.397080i
$11$	10.0956	−	4.36788i	0.917784	−	0.397080i
$12$		0			0
$13$			10.4302i			0.802326i	0.916007	+	0.401163i	$0.131394\pi$
$13$			10.4302i			0.802326i	−0.916007	+	0.401163i	$0.868606\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			3.39108i			0.199475i	0.995014	+	0.0997376i	$0.0318003\pi$
$17$			3.39108i			0.199475i	−0.995014	+	0.0997376i	$0.968200\pi$
$18$		0			0
$19$		−	28.0187i		−	1.47467i	−0.675529	−	0.737333i	$-0.736085\pi$
$19$		−	28.0187i		−	1.47467i	0.675529	−	0.737333i	$-0.263915\pi$
$20$		0			0
$21$		−	5.79120i		−	0.275771i
$22$		0			0
$23$	−18.8226			−0.818375			−0.409188	−	0.912450i	$-0.634188\pi$
$23$	−18.8226			−0.818375			−0.409188	+	0.912450i	$0.634188\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−11.2382			−0.416229
$28$		0			0
$29$			22.2253i			0.766391i	0.923667	+	0.383195i	$0.125176\pi$
$29$			22.2253i			0.766391i	−0.923667	+	0.383195i	$0.874824\pi$
$30$		0			0
$31$	0.00744511			0.000240165			0.000120082	−	1.00000i	$-0.499962\pi$
$31$	0.00744511			0.000240165			0.000120082		1.00000i	$0.499962\pi$
$32$		0			0
$33$	6.44935	−	2.79032i	0.195435	−	0.0845551i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.96796			−0.242377			−0.121189	−	0.992629i	$-0.538671\pi$
$37$	−8.96796			−0.242377			−0.121189	+	0.992629i	$0.538671\pi$
$38$		0			0
$39$			6.66311i			0.170849i
$40$		0			0
$41$			16.5975i			0.404817i	0.979301	+	0.202408i	$0.0648768\pi$
$41$			16.5975i			0.404817i	−0.979301	+	0.202408i	$0.935123\pi$
$42$		0			0
$43$		−	81.5368i		−	1.89621i	−0.317964	−	0.948103i	$-0.602999\pi$
$43$		−	81.5368i		−	1.89621i	0.317964	−	0.948103i	$-0.397001\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−59.1685			−1.25890			−0.629452	−	0.777039i	$-0.716721\pi$
$47$	−59.1685			−1.25890			−0.629452	+	0.777039i	$0.716721\pi$
$48$		0			0
$49$	−33.1809			−0.677162
$50$		0			0
$51$			2.16631i			0.0424767i
$52$		0			0
$53$	−60.1508			−1.13492			−0.567460	−	0.823401i	$-0.692074\pi$
$53$	−60.1508			−1.13492			−0.567460	+	0.823401i	$0.692074\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	17.8991i		−	0.314019i
$58$		0			0
$59$	−81.5361			−1.38197			−0.690984	−	0.722870i	$-0.742823\pi$
$59$	−81.5361			−1.38197			−0.690984	+	0.722870i	$0.742823\pi$
$60$		0			0
$61$			114.695i			1.88024i	0.340843	+	0.940120i	$0.389288\pi$
$61$			114.695i			1.88024i	−0.340843	+	0.940120i	$0.610712\pi$
$62$		0			0
$63$			77.8888i			1.23633i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−99.1084			−1.47923			−0.739615	−	0.673030i	$-0.764992\pi$
$67$	−99.1084			−1.47923			−0.739615	+	0.673030i	$0.764992\pi$
$68$		0			0
$69$	−12.0244			−0.174267
$70$		0			0
$71$	70.3598			0.990983			0.495491	−	0.868613i	$-0.334988\pi$
$71$	70.3598			0.990983			0.495491	+	0.868613i	$0.334988\pi$
$72$		0			0
$73$		−	16.4827i		−	0.225791i	−0.993607	−	0.112895i	$-0.963988\pi$
$73$		−	16.4827i		−	0.225791i	0.993607	−	0.112895i	$-0.0360125\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−39.5965	−	91.5206i	−0.514240	−	1.18858i
$78$		0			0
$79$		−	118.929i		−	1.50543i	−0.658344	−	0.752717i	$-0.728743\pi$
$79$		−	118.929i		−	1.50543i	0.658344	−	0.752717i	$-0.271257\pi$
$80$		0			0
$81$	70.1479			0.866023
$82$		0			0
$83$		−	30.6387i		−	0.369141i	−0.982819	−	0.184570i	$-0.940911\pi$
$83$		−	30.6387i		−	0.369141i	0.982819	−	0.184570i	$-0.0590894\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			14.1981i			0.163197i
$88$		0			0
$89$	−4.02316			−0.0452041			−0.0226020	−	0.999745i	$-0.507195\pi$
$89$	−4.02316			−0.0452041			−0.0226020	+	0.999745i	$0.507195\pi$
$90$		0			0
$91$	94.5539			1.03905
$92$		0			0
$93$	0.00475614			5.11412e−5
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−101.970			−1.05124			−0.525619	−	0.850720i	$-0.676166\pi$
$97$	−101.970			−1.05124			−0.525619	+	0.850720i	$0.676166\pi$
$98$		0			0
$99$	−86.7406	+	37.5284i	−0.876168	+	0.379075i
$100$		0			0
$101$		−	149.468i		−	1.47988i	−0.672672	−	0.739940i	$-0.734854\pi$
$101$		−	149.468i		−	1.47988i	0.672672	−	0.739940i	$-0.265146\pi$
$102$		0			0
$103$	74.9240			0.727417			0.363709	−	0.931513i	$-0.381510\pi$
$103$	74.9240			0.727417			0.363709	+	0.931513i	$0.381510\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	94.4230i		−	0.882458i	−0.897395	−	0.441229i	$-0.854543\pi$
$107$		−	94.4230i		−	0.882458i	0.897395	−	0.441229i	$-0.145457\pi$
$108$		0			0
$109$		−	30.1807i		−	0.276887i	−0.990370	−	0.138444i	$-0.955790\pi$
$109$		−	30.1807i		−	0.276887i	0.990370	−	0.138444i	$-0.0442100\pi$
$110$		0			0
$111$	−5.72897			−0.0516124
$112$		0			0
$113$	−74.7503			−0.661507			−0.330753	−	0.943717i	$-0.607303\pi$
$113$	−74.7503			−0.661507			−0.330753	+	0.943717i	$0.607303\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	89.6155i		−	0.765945i
$118$		0			0
$119$	30.7414			0.258331
$120$		0			0
$121$	82.8432	−	88.1930i	0.684655	−	0.728868i
$122$		0			0
$123$			10.6029i			0.0862025i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			107.488i			0.846361i	0.906045	+	0.423181i	$0.139086\pi$
$127$			107.488i			0.846361i	−0.906045	+	0.423181i	$0.860914\pi$
$128$		0			0
$129$		−	52.0879i		−	0.403782i
$130$		0			0
$131$			201.887i			1.54112i	0.637367	+	0.770560i	$0.280024\pi$
$131$			201.887i			1.54112i	−0.637367	+	0.770560i	$0.719976\pi$
$132$		0			0
$133$	−254.000			−1.90977
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−136.064			−0.993166			−0.496583	−	0.867989i	$-0.665412\pi$
$137$	−136.064			−0.993166			−0.496583	+	0.867989i	$0.665412\pi$
$138$		0			0
$139$		−	6.92439i		−	0.0498157i	−0.999690	−	0.0249079i	$-0.992071\pi$
$139$		−	6.92439i		−	0.0498157i	0.999690	−	0.0249079i	$-0.00792924\pi$
$140$		0			0
$141$	−37.7984			−0.268074
$142$		0			0
$143$	45.5580	+	105.300i	0.318588	+	0.736362i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−21.1968			−0.144196
$148$		0			0
$149$			94.2807i			0.632756i	0.948633	+	0.316378i	$0.102467\pi$
$149$			94.2807i			0.632756i	−0.948633	+	0.316378i	$0.897533\pi$
$150$		0			0
$151$		−	152.478i		−	1.00979i	−0.863181	−	0.504894i	$-0.831532\pi$
$151$		−	152.478i		−	1.00979i	0.863181	−	0.504894i	$-0.168468\pi$
$152$		0			0
$153$		−	29.1358i		−	0.190430i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−168.579			−1.07375			−0.536876	−	0.843661i	$-0.680396\pi$
$157$	−168.579			−1.07375			−0.536876	+	0.843661i	$0.680396\pi$
$158$		0			0
$159$	−38.4259			−0.241672
$160$		0			0
$161$			170.634i			1.05984i
$162$		0			0
$163$	21.6126			0.132592			0.0662962	−	0.997800i	$-0.478882\pi$
$163$	21.6126			0.132592			0.0662962	+	0.997800i	$0.478882\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	247.745i		−	1.48350i	−0.670676	−	0.741750i	$-0.733996\pi$
$167$		−	247.745i		−	1.48350i	0.670676	−	0.741750i	$-0.266004\pi$
$168$		0			0
$169$	60.2103			0.356274
$170$		0			0
$171$			240.734i			1.40780i
$172$		0			0
$173$		−	208.255i		−	1.20379i	−0.798576	−	0.601894i	$-0.794413\pi$
$173$		−	208.255i		−	1.20379i	0.798576	−	0.601894i	$-0.205587\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−52.0874			−0.294279
$178$		0			0
$179$	−147.992			−0.826770			−0.413385	−	0.910556i	$-0.635654\pi$
$179$	−147.992			−0.826770			−0.413385	+	0.910556i	$0.635654\pi$
$180$		0			0
$181$	−11.0571			−0.0610887			−0.0305444	−	0.999533i	$-0.509724\pi$
$181$	−11.0571			−0.0610887			−0.0305444	+	0.999533i	$0.509724\pi$
$182$		0			0
$183$			73.2700i			0.400382i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	14.8118	+	34.2350i	0.0792076	+	0.183075i
$188$		0			0
$189$			101.878i			0.539038i
$190$		0			0
$191$	104.092			0.544985			0.272492	−	0.962158i	$-0.412152\pi$
$191$	104.092			0.544985			0.272492	+	0.962158i	$0.412152\pi$
$192$		0			0
$193$		−	267.361i		−	1.38529i	−0.721280	−	0.692644i	$-0.756446\pi$
$193$		−	267.361i		−	1.38529i	0.721280	−	0.692644i	$-0.243554\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			264.837i			1.34435i	0.740392	+	0.672175i	$0.234640\pi$
$197$			264.837i			1.34435i	−0.740392	+	0.672175i	$0.765360\pi$
$198$		0			0
$199$	−108.882			−0.547145			−0.273572	−	0.961851i	$-0.588205\pi$
$199$	−108.882			−0.547145			−0.273572	+	0.961851i	$0.588205\pi$
$200$		0			0
$201$	−63.3131			−0.314990
$202$		0			0
$203$	201.481			0.992516
$204$		0			0
$205$		0			0
$206$		0			0
$207$	161.722			0.781266
$208$		0			0
$209$	−122.382	−	282.866i	−0.585561	−	1.35343i
$210$		0			0
$211$		−	91.2096i		−	0.432273i	−0.976363	−	0.216136i	$-0.930654\pi$
$211$		−	91.2096i		−	0.432273i	0.976363	−	0.216136i	$-0.0693456\pi$
$212$		0			0
$213$	44.9477			0.211022
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	0.0674927i		−	0.000311026i
$218$		0			0
$219$		−	10.5296i		−	0.0480803i
$220$		0			0
$221$	−35.3697			−0.160044
$222$		0			0
$223$	2.12864			0.00954548			0.00477274	−	0.999989i	$-0.498481\pi$
$223$	2.12864			0.00954548			0.00477274	+	0.999989i	$0.498481\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			247.145i			1.08875i	0.838843	+	0.544373i	$0.183232\pi$
$227$			247.145i			1.08875i	−0.838843	+	0.544373i	$0.816768\pi$
$228$		0			0
$229$	307.707			1.34370			0.671849	−	0.740688i	$-0.265500\pi$
$229$	307.707			1.34370			0.671849	+	0.740688i	$0.265500\pi$
$230$		0			0
$231$	−25.2953	−	58.4658i	−0.109503	−	0.253098i
$232$		0			0
$233$			274.895i			1.17981i	0.807474	+	0.589903i	$0.200834\pi$
$233$			274.895i			1.17981i	−0.807474	+	0.589903i	$0.799166\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	75.9752i		−	0.320571i
$238$		0			0
$239$			191.500i			0.801253i	0.916241	+	0.400627i	$0.131208\pi$
$239$			191.500i			0.801253i	−0.916241	+	0.400627i	$0.868792\pi$
$240$		0			0
$241$			111.228i			0.461525i	0.973010	+	0.230763i	$0.0741221\pi$
$241$			111.228i			0.461525i	−0.973010	+	0.230763i	$0.925878\pi$
$242$		0			0
$243$	145.956			0.600641
$244$		0			0
$245$		0			0
$246$		0			0
$247$	292.241			1.18316
$248$		0			0
$249$		−	19.5728i		−	0.0786056i
$250$		0			0
$251$	−144.363			−0.575152			−0.287576	−	0.957758i	$-0.592849\pi$
$251$	−144.363			−0.575152			−0.287576	+	0.957758i	$0.592849\pi$
$252$		0			0
$253$	−190.026	+	82.2150i	−0.751092	+	0.324961i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	406.571			1.58199			0.790994	−	0.611823i	$-0.209564\pi$
$257$	406.571			1.58199			0.790994	+	0.611823i	$0.209564\pi$
$258$		0			0
$259$			81.2979i			0.313892i
$260$		0			0
$261$		−	190.958i		−	0.731639i
$262$		0			0
$263$			249.632i			0.949171i	0.880209	+	0.474585i	$0.157402\pi$
$263$			249.632i			0.949171i	−0.880209	+	0.474585i	$0.842598\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.57010			−0.00962585
$268$		0			0
$269$	183.714			0.682952			0.341476	−	0.939890i	$-0.389073\pi$
$269$	183.714			0.682952			0.341476	+	0.939890i	$0.389073\pi$
$270$		0			0
$271$		−	236.527i		−	0.872792i	−0.899755	−	0.436396i	$-0.856255\pi$
$271$		−	236.527i		−	0.872792i	0.899755	−	0.436396i	$-0.143745\pi$
$272$		0			0
$273$	60.4035			0.221258
$274$		0			0
$275$		0			0
$276$		0			0
$277$			22.7429i			0.0821043i	0.999157	+	0.0410522i	$0.0130710\pi$
$277$			22.7429i			0.0821043i	−0.999157	+	0.0410522i	$0.986929\pi$
$278$		0			0
$279$	−0.0639677			−0.000229275
$280$		0			0
$281$		−	316.963i		−	1.12798i	−0.825781	−	0.563991i	$-0.809265\pi$
$281$		−	316.963i		−	1.12798i	0.825781	−	0.563991i	$-0.190735\pi$
$282$		0			0
$283$			218.829i			0.773246i	0.922238	+	0.386623i	$0.126358\pi$
$283$			218.829i			0.773246i	−0.922238	+	0.386623i	$0.873642\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	150.462			0.524259
$288$		0			0
$289$	277.501			0.960210
$290$		0			0
$291$	−65.1412			−0.223853
$292$		0			0
$293$		−	205.688i		−	0.702005i	−0.936374	−	0.351003i	$-0.885841\pi$
$293$		−	205.688i		−	0.702005i	0.936374	−	0.351003i	$-0.114159\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−113.456	+	49.0870i	−0.382008	+	0.165276i
$298$		0			0
$299$		−	196.324i		−	0.656603i
$300$		0			0
$301$	−739.161			−2.45569
$302$		0			0
$303$		−	95.4841i		−	0.315129i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	351.513i		−	1.14499i	−0.819907	−	0.572497i	$-0.805975\pi$
$307$		−	351.513i		−	1.14499i	0.819907	−	0.572497i	$-0.194025\pi$
$308$		0			0
$309$	47.8634			0.154898
$310$		0			0
$311$	395.742			1.27248			0.636241	−	0.771490i	$-0.280488\pi$
$311$	395.742			1.27248			0.636241	+	0.771490i	$0.280488\pi$
$312$		0			0
$313$	−340.880			−1.08907			−0.544537	−	0.838736i	$-0.683295\pi$
$313$	−340.880			−1.08907			−0.544537	+	0.838736i	$0.683295\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	613.787			1.93624			0.968118	−	0.250493i	$-0.0805928\pi$
$317$	613.787			1.93624			0.968118	+	0.250493i	$0.0805928\pi$
$318$		0			0
$319$	97.0776	+	224.379i	0.304319	+	0.703381i
$320$		0			0
$321$		−	60.3199i		−	0.187912i
$322$		0			0
$323$	95.0134			0.294159
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	19.2802i		−	0.0589609i
$328$		0			0
$329$			536.385i			1.63035i
$330$		0			0
$331$	−2.96493			−0.00895750			−0.00447875	−	0.999990i	$-0.501426\pi$
$331$	−2.96493			−0.00895750			−0.00447875	+	0.999990i	$0.501426\pi$
$332$		0			0
$333$	77.0519			0.231387
$334$		0			0
$335$		0			0
$336$		0			0
$337$			44.4138i			0.131792i	0.997827	+	0.0658958i	$0.0209905\pi$
$337$			44.4138i			0.131792i	−0.997827	+	0.0658958i	$0.979009\pi$
$338$		0			0
$339$	−47.7525			−0.140863
$340$		0			0
$341$	0.0751631	−	0.0325194i	0.000220420	−	9.53647e-5i
$342$		0			0
$343$		−	143.406i		−	0.418093i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			481.360i			1.38720i	0.720358	+	0.693602i	$0.243977\pi$
$347$			481.360i			1.38720i	−0.720358	+	0.693602i	$0.756023\pi$
$348$		0			0
$349$		−	75.1868i		−	0.215435i	−0.994182	−	0.107717i	$-0.965646\pi$
$349$		−	75.1868i		−	0.215435i	0.994182	−	0.107717i	$-0.0343542\pi$
$350$		0			0
$351$		−	117.217i		−	0.333951i
$352$		0			0
$353$	187.670			0.531643			0.265822	−	0.964022i	$-0.414357\pi$
$353$	187.670			0.531643			0.265822	+	0.964022i	$0.414357\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	19.6384			0.0550095
$358$		0			0
$359$		−	402.781i		−	1.12195i	−0.827832	−	0.560976i	$-0.810426\pi$
$359$		−	402.781i		−	1.12195i	0.827832	−	0.560976i	$-0.189574\pi$
$360$		0			0
$361$	−424.046			−1.17464
$362$		0			0
$363$	52.9224	−	56.3400i	0.145792	−	0.155207i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	292.427			0.796805			0.398402	−	0.917211i	$-0.369565\pi$
$367$	292.427			0.796805			0.398402	+	0.917211i	$0.369565\pi$
$368$		0			0
$369$		−	142.604i		−	0.386460i
$370$		0			0
$371$			545.289i			1.46978i
$372$		0			0
$373$		−	232.155i		−	0.622398i	−0.950345	−	0.311199i	$-0.899269\pi$
$373$		−	232.155i		−	0.622398i	0.950345	−	0.311199i	$-0.100731\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−231.815			−0.614895
$378$		0			0
$379$	467.391			1.23322			0.616611	−	0.787268i	$-0.288505\pi$
$379$	467.391			1.23322			0.616611	+	0.787268i	$0.288505\pi$
$380$		0			0
$381$			68.6661i			0.180226i
$382$		0			0
$383$	721.494			1.88380			0.941898	−	0.335899i	$-0.109040\pi$
$383$	721.494			1.88380			0.941898	+	0.335899i	$0.109040\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			700.556i			1.81022i
$388$		0			0
$389$	643.293			1.65371			0.826854	−	0.562416i	$-0.190128\pi$
$389$	643.293			1.65371			0.826854	+	0.562416i	$0.190128\pi$
$390$		0			0
$391$		−	63.8290i		−	0.163245i
$392$		0			0
$393$			128.971i			0.328170i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	151.518			0.381658			0.190829	−	0.981623i	$-0.438882\pi$
$397$	151.518			0.381658			0.190829	+	0.981623i	$0.438882\pi$
$398$		0			0
$399$	−162.262			−0.406671
$400$		0			0
$401$	−314.057			−0.783184			−0.391592	−	0.920139i	$-0.628076\pi$
$401$	−314.057			−0.783184			−0.391592	+	0.920139i	$0.628076\pi$
$402$		0			0
$403$			0.0776543i			0.000192690i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−90.5372	+	39.1710i	−0.222450	+	0.0962433i
$408$		0			0
$409$			691.237i			1.69007i	0.534713	+	0.845034i	$0.320420\pi$
$409$			691.237i			1.69007i	−0.534713	+	0.845034i	$0.679580\pi$
$410$		0			0
$411$	−86.9211			−0.211487
$412$		0			0
$413$			739.155i			1.78972i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	4.42348i		−	0.0106079i
$418$		0			0
$419$	−439.877			−1.04983			−0.524913	−	0.851156i	$-0.675902\pi$
$419$	−439.877			−1.04983			−0.524913	+	0.851156i	$0.675902\pi$
$420$		0			0
$421$	−274.014			−0.650864			−0.325432	−	0.945565i	$-0.605510\pi$
$421$	−274.014			−0.650864			−0.325432	+	0.945565i	$0.605510\pi$
$422$		0			0
$423$	508.370			1.20182
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1039.75			2.43501
$428$		0			0
$429$	29.1037	+	67.2682i	0.0678407	+	0.156802i
$430$		0			0
$431$			419.940i			0.974340i	0.873307	+	0.487170i	$0.161971\pi$
$431$			419.940i			0.974340i	−0.873307	+	0.487170i	$0.838029\pi$
$432$		0			0
$433$	−396.492			−0.915686			−0.457843	−	0.889033i	$-0.651378\pi$
$433$	−396.492			−0.915686			−0.457843	+	0.889033i	$0.651378\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			527.385i			1.20683i
$438$		0			0
$439$		−	120.848i		−	0.275279i	−0.990482	−	0.137640i	$-0.956048\pi$
$439$		−	120.848i		−	0.275279i	0.990482	−	0.137640i	$-0.0439516\pi$
$440$		0			0
$441$	285.087			0.646456
$442$		0			0
$443$	374.096			0.844461			0.422231	−	0.906488i	$-0.361247\pi$
$443$	374.096			0.844461			0.422231	+	0.906488i	$0.361247\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			60.2290i			0.134741i
$448$		0			0
$449$	282.403			0.628959			0.314480	−	0.949264i	$-0.398170\pi$
$449$	282.403			0.628959			0.314480	+	0.949264i	$0.398170\pi$
$450$		0			0
$451$	72.4958	+	167.562i	0.160745	+	0.371534i
$452$		0			0
$453$		−	97.4069i		−	0.215026i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	513.069i		−	1.12269i	−0.827582	−	0.561345i	$-0.810284\pi$
$457$		−	513.069i		−	1.12269i	0.827582	−	0.561345i	$-0.189716\pi$
$458$		0			0
$459$		−	38.1095i		−	0.0830272i
$460$		0			0
$461$		−	712.598i		−	1.54577i	−0.634549	−	0.772883i	$-0.718814\pi$
$461$		−	712.598i		−	1.54577i	0.634549	−	0.772883i	$-0.281186\pi$
$462$		0			0
$463$	129.526			0.279754			0.139877	−	0.990169i	$-0.455329\pi$
$463$	129.526			0.279754			0.139877	+	0.990169i	$0.455329\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	397.672			0.851547			0.425773	−	0.904830i	$-0.360002\pi$
$467$	397.672			0.851547			0.425773	+	0.904830i	$0.360002\pi$
$468$		0			0
$469$			898.454i			1.91568i
$470$		0			0
$471$	−107.693			−0.228647
$472$		0			0
$473$	−356.143	−	823.165i	−0.752946	−	1.74031i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	516.809			1.08346
$478$		0			0
$479$		−	409.935i		−	0.855815i	−0.903823	−	0.427907i	$-0.859251\pi$
$479$		−	409.935i		−	0.855815i	0.903823	−	0.427907i	$-0.140749\pi$
$480$		0			0
$481$		−	93.5380i		−	0.194466i
$482$		0			0
$483$			109.006i			0.225684i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−847.021			−1.73926			−0.869631	−	0.493702i	$-0.835643\pi$
$487$	−847.021			−1.73926			−0.869631	+	0.493702i	$0.835643\pi$
$488$		0			0
$489$	13.8067			0.0282345
$490$		0			0
$491$		−	634.763i		−	1.29280i	−0.763000	−	0.646398i	$-0.776275\pi$
$491$		−	634.763i		−	1.29280i	0.763000	−	0.646398i	$-0.223725\pi$
$492$		0			0
$493$	−75.3678			−0.152876
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	637.837i		−	1.28337i
$498$		0			0
$499$	360.573			0.722591			0.361296	−	0.932451i	$-0.382335\pi$
$499$	360.573			0.722591			0.361296	+	0.932451i	$0.382335\pi$
$500$		0			0
$501$		−	158.266i		−	0.315900i
$502$		0			0
$503$			239.586i			0.476314i	0.971227	+	0.238157i	$0.0765433\pi$
$503$			239.586i			0.476314i	−0.971227	+	0.238157i	$0.923457\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	38.4639			0.0758657
$508$		0			0
$509$	−92.3407			−0.181416			−0.0907080	−	0.995878i	$-0.528913\pi$
$509$	−92.3407			−0.181416			−0.0907080	+	0.995878i	$0.528913\pi$
$510$		0			0
$511$	−149.422			−0.292411
$512$		0			0
$513$			314.879i			0.613798i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−597.343	+	258.441i	−1.15540	+	0.499886i
$518$		0			0
$519$		−	133.039i		−	0.256337i
$520$		0			0
$521$	−439.053			−0.842712			−0.421356	−	0.906895i	$-0.638446\pi$
$521$	−439.053			−0.842712			−0.421356	+	0.906895i	$0.638446\pi$
$522$		0			0
$523$			495.619i			0.947647i	0.880620	+	0.473823i	$0.157126\pi$
$523$			495.619i			0.947647i	−0.880620	+	0.473823i	$0.842874\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			0.0252470i			4.79069e-5i
$528$		0			0
$529$	−174.709			−0.330262
$530$		0			0
$531$	700.550			1.31930
$532$		0			0
$533$	−173.116			−0.324795
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−94.5410			−0.176054
$538$		0			0
$539$	−334.982	+	144.930i	−0.621488	+	0.268887i
$540$		0			0
$541$			572.642i			1.05849i	0.848470	+	0.529244i	$0.177524\pi$
$541$			572.642i			1.05849i	−0.848470	+	0.529244i	$0.822476\pi$
$542$		0			0
$543$	−7.06354			−0.0130084
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	131.117i		−	0.239702i	−0.992792	−	0.119851i	$-0.961758\pi$
$547$		−	131.117i		−	0.239702i	0.992792	−	0.119851i	$-0.0382417\pi$
$548$		0			0
$549$		−	985.445i		−	1.79498i
$550$		0			0
$551$	622.724			1.13017
$552$		0			0
$553$	−1078.14			−1.94962
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	433.908i		−	0.779008i	−0.921025	−	0.389504i	$-0.872646\pi$
$557$		−	433.908i		−	0.779008i	0.921025	−	0.389504i	$-0.127354\pi$
$558$		0			0
$559$	850.448			1.52137
$560$		0			0
$561$	9.46218	+	21.8702i	0.0168666	+	0.0389844i
$562$		0			0
$563$		−	405.058i		−	0.719464i	−0.933056	−	0.359732i	$-0.882868\pi$
$563$		−	405.058i		−	0.719464i	0.933056	−	0.359732i	$-0.117132\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	635.916i		−	1.12155i
$568$		0			0
$569$		−	422.003i		−	0.741657i	−0.928701	−	0.370829i	$-0.879074\pi$
$569$		−	422.003i		−	0.741657i	0.928701	−	0.370829i	$-0.120926\pi$
$570$		0			0
$571$		−	395.151i		−	0.692034i	−0.938228	−	0.346017i	$-0.887534\pi$
$571$		−	395.151i		−	0.692034i	0.938228	−	0.346017i	$-0.112466\pi$
$572$		0			0
$573$	66.4968			0.116050
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−728.545			−1.26264			−0.631322	−	0.775521i	$-0.717487\pi$
$577$	−728.545			−1.26264			−0.631322	+	0.775521i	$0.717487\pi$
$578$		0			0
$579$		−	170.797i		−	0.294986i
$580$		0			0
$581$	−277.751			−0.478057
$582$		0			0
$583$	−607.259	+	262.731i	−1.04161	+	0.450654i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	292.478			0.498259			0.249129	−	0.968470i	$-0.419856\pi$
$587$	292.478			0.498259			0.249129	+	0.968470i	$0.419856\pi$
$588$		0			0
$589$		−	0.208602i		−	0.000354163i
$590$		0			0
$591$			169.185i			0.286269i
$592$		0			0
$593$			189.061i			0.318821i	0.987212	+	0.159410i	$0.0509593\pi$
$593$			189.061i			0.318821i	−0.987212	+	0.159410i	$0.949041\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−69.5566			−0.116510
$598$		0			0
$599$	−333.334			−0.556485			−0.278242	−	0.960511i	$-0.589752\pi$
$599$	−333.334			−0.556485			−0.278242	+	0.960511i	$0.589752\pi$
$600$		0			0
$601$			473.020i			0.787055i	0.919313	+	0.393527i	$0.128745\pi$
$601$			473.020i			0.787055i	−0.919313	+	0.393527i	$0.871255\pi$
$602$		0			0
$603$	851.529			1.41215
$604$		0			0
$605$		0			0
$606$		0			0
$607$			1062.30i			1.75008i	0.484052	+	0.875039i	$0.339164\pi$
$607$			1062.30i			1.75008i	−0.484052	+	0.875039i	$0.660836\pi$
$608$		0			0
$609$	128.711			0.211349
$610$		0			0
$611$		−	617.141i		−	1.01005i
$612$		0			0
$613$		−	1093.66i		−	1.78411i	−0.451923	−	0.892057i	$-0.649262\pi$
$613$		−	1093.66i		−	1.78411i	0.451923	−	0.892057i	$-0.350738\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−793.012			−1.28527			−0.642636	−	0.766172i	$-0.722159\pi$
$617$	−793.012			−1.28527			−0.642636	+	0.766172i	$0.722159\pi$
$618$		0			0
$619$	−1156.20			−1.86786			−0.933928	−	0.357462i	$-0.883642\pi$
$619$	−1156.20			−1.86786			−0.933928	+	0.357462i	$0.883642\pi$
$620$		0			0
$621$	211.532			0.340631
$622$		0			0
$623$			36.4715i			0.0585417i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−78.1810	−	180.702i	−0.124691	−	0.288201i
$628$		0			0
$629$		−	30.4111i		−	0.0483483i
$630$		0			0
$631$	−184.009			−0.291614			−0.145807	−	0.989313i	$-0.546578\pi$
$631$	−184.009			−0.291614			−0.145807	+	0.989313i	$0.546578\pi$
$632$		0			0
$633$		−	58.2671i		−	0.0920491i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	346.085i		−	0.543304i
$638$		0			0
$639$	−604.524			−0.946047
$640$		0			0
$641$	1060.80			1.65492			0.827458	−	0.561528i	$-0.189786\pi$
$641$	1060.80			1.65492			0.827458	+	0.561528i	$0.189786\pi$
$642$		0			0
$643$	−345.954			−0.538031			−0.269015	−	0.963136i	$-0.586698\pi$
$643$	−345.954			−0.538031			−0.269015	+	0.963136i	$0.586698\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	582.248			0.899919			0.449959	−	0.893049i	$-0.351438\pi$
$647$	582.248			0.899919			0.449959	+	0.893049i	$0.351438\pi$
$648$		0			0
$649$	−823.158	+	356.140i	−1.26835	+	0.548752i
$650$		0			0
$651$		−	0.0431161i		−	6.62306e-5i
$652$		0			0
$653$	860.284			1.31743			0.658717	−	0.752391i	$-0.271100\pi$
$653$	860.284			1.31743			0.658717	+	0.752391i	$0.271100\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			141.618i			0.215552i
$658$		0			0
$659$			494.828i			0.750876i	0.926847	+	0.375438i	$0.122508\pi$
$659$			494.828i			0.750876i	−0.926847	+	0.375438i	$0.877492\pi$
$660$		0			0
$661$	−321.241			−0.485993			−0.242996	−	0.970027i	$-0.578130\pi$
$661$	−321.241			−0.485993			−0.242996	+	0.970027i	$0.578130\pi$
$662$		0			0
$663$	−22.5951			−0.0340801
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	418.339i		−	0.627195i
$668$		0			0
$669$	1.35983			0.00203264
$670$		0			0
$671$	500.973	+	1157.91i	0.746606	+	1.72565i
$672$		0			0
$673$		−	775.168i		−	1.15181i	−0.817517	−	0.575905i	$-0.804650\pi$
$673$		−	775.168i		−	1.15181i	0.817517	−	0.575905i	$-0.195350\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			273.752i			0.404360i	0.979348	+	0.202180i	$0.0648026\pi$
$677$			273.752i			0.404360i	−0.979348	+	0.202180i	$0.935197\pi$
$678$		0			0
$679$			924.397i			1.36141i
$680$		0			0
$681$			157.883i			0.231840i
$682$		0			0
$683$	−645.794			−0.945526			−0.472763	−	0.881190i	$-0.656743\pi$
$683$	−645.794			−0.945526			−0.472763	+	0.881190i	$0.656743\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	196.571			0.286130
$688$		0			0
$689$		−	627.386i		−	0.910575i
$690$		0			0
$691$	−519.100			−0.751231			−0.375615	−	0.926776i	$-0.622569\pi$
$691$	−519.100			−0.751231			−0.375615	+	0.926776i	$0.622569\pi$
$692$		0			0
$693$	340.209	+	786.335i	0.490922	+	1.13468i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−56.2833			−0.0807508
$698$		0			0
$699$			175.610i			0.251231i
$700$		0			0
$701$			450.375i			0.642475i	0.946999	+	0.321237i	$0.104099\pi$
$701$			450.375i			0.642475i	−0.946999	+	0.321237i	$0.895901\pi$
$702$		0			0
$703$			251.270i			0.357426i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1354.98			−1.91652
$708$		0			0
$709$	527.930			0.744612			0.372306	−	0.928110i	$-0.378567\pi$
$709$	527.930			0.744612			0.372306	+	0.928110i	$0.378567\pi$
$710$		0			0
$711$			1021.83i			1.43717i
$712$		0			0
$713$	−0.140137			−0.000196545
$714$		0			0
$715$		0			0
$716$		0			0
$717$			122.335i			0.170621i
$718$		0			0
$719$	−312.167			−0.434168			−0.217084	−	0.976153i	$-0.569655\pi$
$719$	−312.167			−0.434168			−0.217084	+	0.976153i	$0.569655\pi$
$720$		0			0
$721$		−	679.213i		−	0.942043i
$722$		0			0
$723$			71.0551i			0.0982782i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1414.10			−1.94512			−0.972558	−	0.232662i	$-0.925256\pi$
$727$	−1414.10			−1.94512			−0.972558	+	0.232662i	$0.925256\pi$
$728$		0			0
$729$	−538.090			−0.738121
$730$		0			0
$731$	276.498			0.378246
$732$		0			0
$733$			122.714i			0.167413i	0.996490	+	0.0837067i	$0.0266759\pi$
$733$			122.714i			0.167413i	−0.996490	+	0.0837067i	$0.973324\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1000.56	+	432.894i	−1.35761	+	0.587373i
$738$		0			0
$739$		−	1027.05i		−	1.38978i	−0.719115	−	0.694891i	$-0.755453\pi$
$739$		−	1027.05i		−	1.38978i	0.719115	−	0.694891i	$-0.244547\pi$
$740$		0			0
$741$	186.691			0.251945
$742$		0			0
$743$		−	609.811i		−	0.820742i	−0.911919	−	0.410371i	$-0.865399\pi$
$743$		−	609.811i		−	0.820742i	0.911919	−	0.410371i	$-0.134601\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			263.244i			0.352402i
$748$		0			0
$749$	−855.979			−1.14283
$750$		0			0
$751$	232.075			0.309021			0.154511	−	0.987991i	$-0.450620\pi$
$751$	232.075			0.309021			0.154511	+	0.987991i	$0.450620\pi$
$752$		0			0
$753$	−92.2229			−0.122474
$754$		0			0
$755$		0			0
$756$		0			0
$757$	929.780			1.22824			0.614122	−	0.789211i	$-0.289510\pi$
$757$	929.780			1.22824			0.614122	+	0.789211i	$0.289510\pi$
$758$		0			0
$759$	−121.394	+	52.5211i	−0.159939	+	0.0691978i
$760$		0			0
$761$			759.425i			0.997931i	0.866622	+	0.498965i	$0.166287\pi$
$761$			759.425i			0.997931i	−0.866622	+	0.498965i	$0.833713\pi$
$762$		0			0
$763$	−273.599			−0.358583
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	850.441i		−	1.10879i
$768$		0			0
$769$		−	1242.48i		−	1.61571i	−0.589384	−	0.807853i	$-0.700630\pi$
$769$		−	1242.48i		−	1.61571i	0.589384	−	0.807853i	$-0.299370\pi$
$770$		0			0
$771$	259.728			0.336872
$772$		0			0
$773$	−542.327			−0.701588			−0.350794	−	0.936453i	$-0.614088\pi$
$773$	−542.327			−0.701588			−0.350794	+	0.936453i	$0.614088\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			51.9353i			0.0668407i
$778$		0			0
$779$	465.039			0.596969
$780$		0			0
$781$	710.326	−	307.323i	0.909508	−	0.393500i
$782$		0			0
$783$		−	249.772i		−	0.318994i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	1265.30i		−	1.60775i	−0.594796	−	0.803877i	$-0.702767\pi$
$787$		−	1265.30i		−	1.60775i	0.594796	−	0.803877i	$-0.297233\pi$
$788$		0			0
$789$			159.471i			0.202118i
$790$		0			0
$791$			677.639i			0.856686i
$792$		0			0
$793$	−1196.29			−1.50857
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.70455			0.00464812			0.00232406	−	0.999997i	$-0.499260\pi$
$797$	3.70455			0.00464812			0.00232406	+	0.999997i	$0.499260\pi$
$798$		0			0
$799$		−	200.645i		−	0.251120i
$800$		0			0
$801$	34.5666			0.0431543
$802$		0			0
$803$	−71.9945	−	166.403i	−0.0896569	−	0.207227i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	117.361			0.145429
$808$		0			0
$809$			387.788i			0.479343i	0.970854	+	0.239671i	$0.0770397\pi$
$809$			387.788i			0.479343i	−0.970854	+	0.239671i	$0.922960\pi$
$810$		0			0
$811$		−	653.974i		−	0.806379i	−0.915116	−	0.403190i	$-0.867901\pi$
$811$		−	653.974i		−	0.806379i	0.915116	−	0.403190i	$-0.132099\pi$
$812$		0			0
$813$		−	151.100i		−	0.185854i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2284.55			−2.79627
$818$		0			0
$819$	−812.398			−0.991939
$820$		0			0
$821$		−	1276.47i		−	1.55477i	−0.629023	−	0.777387i	$-0.716545\pi$
$821$		−	1276.47i		−	1.55477i	0.629023	−	0.777387i	$-0.283455\pi$
$822$		0			0
$823$	−946.469			−1.15002			−0.575012	−	0.818145i	$-0.695003\pi$
$823$	−946.469			−1.15002			−0.575012	+	0.818145i	$0.695003\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	785.770i		−	0.950146i	−0.879946	−	0.475073i	$-0.842422\pi$
$827$		−	785.770i		−	0.950146i	0.879946	−	0.475073i	$-0.157578\pi$
$828$		0			0
$829$	711.369			0.858105			0.429052	−	0.903280i	$-0.358848\pi$
$829$	711.369			0.858105			0.429052	+	0.903280i	$0.358848\pi$
$830$		0			0
$831$			14.5288i			0.0174835i
$832$		0			0
$833$		−	112.519i		−	0.135077i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.0836695			−9.99635e−5
$838$		0			0
$839$	−1072.89			−1.27877			−0.639386	−	0.768886i	$-0.720811\pi$
$839$	−1072.89			−1.27877			−0.639386	+	0.768886i	$0.720811\pi$
$840$		0			0
$841$	347.035			0.412645
$842$		0			0
$843$		−	202.484i		−	0.240195i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−799.502	−	751.004i	−0.943922	−	0.886664i
$848$		0			0
$849$			139.793i			0.164657i
$850$		0			0
$851$	168.801			0.198356
$852$		0			0
$853$		−	678.071i		−	0.794925i	−0.917618	−	0.397462i	$-0.869891\pi$
$853$		−	678.071i		−	0.794925i	0.917618	−	0.397462i	$-0.130109\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	514.861i		−	0.600771i	−0.953818	−	0.300386i	$-0.902885\pi$
$857$		−	514.861i		−	0.600771i	0.953818	−	0.300386i	$-0.0971154\pi$
$858$		0			0
$859$	1048.57			1.22069			0.610346	−	0.792135i	$-0.291030\pi$
$859$	1048.57			1.22069			0.610346	+	0.792135i	$0.291030\pi$
$860$		0			0
$861$	96.1193			0.111637
$862$		0			0
$863$	962.788			1.11563			0.557814	−	0.829966i	$-0.311640\pi$
$863$	962.788			1.11563			0.557814	+	0.829966i	$0.311640\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	177.275			0.204469
$868$		0			0
$869$	−519.469	−	1200.67i	−0.597778	−	1.38166i
$870$		0			0
$871$		−	1033.72i		−	1.18682i
$872$		0			0
$873$	876.117			1.00357
$874$		0			0
$875$		0			0
$876$		0			0
$877$			297.443i			0.339160i	0.985516	+	0.169580i	$0.0542410\pi$
$877$			297.443i			0.339160i	−0.985516	+	0.169580i	$0.945759\pi$
$878$		0			0
$879$		−	131.399i		−	0.149487i
$880$		0			0
$881$	1259.46			1.42958			0.714789	−	0.699341i	$-0.246523\pi$
$881$	1259.46			1.42958			0.714789	+	0.699341i	$0.246523\pi$
$882$		0			0
$883$	−645.648			−0.731199			−0.365599	−	0.930772i	$-0.619136\pi$
$883$	−645.648			−0.731199			−0.365599	+	0.930772i	$0.619136\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			545.781i			0.615312i	0.951498	+	0.307656i	$0.0995445\pi$
$887$			545.781i			0.615312i	−0.951498	+	0.307656i	$0.900455\pi$
$888$		0			0
$889$	974.417			1.09608
$890$		0			0
$891$	708.186	−	306.398i	0.794822	−	0.343881i
$892$		0			0
$893$			1657.82i			1.85646i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	125.417i		−	0.139819i
$898$		0			0
$899$			0.165470i			0.000184060i
$900$		0			0
$901$		−	203.976i		−	0.226388i
$902$		0			0
$903$	−472.196			−0.522919
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−146.166			−0.161153			−0.0805766	−	0.996748i	$-0.525676\pi$
$907$	−146.166			−0.161153			−0.0805766	+	0.996748i	$0.525676\pi$
$908$		0			0
$909$			1284.21i			1.41278i
$910$		0			0
$911$	−1533.17			−1.68296			−0.841478	−	0.540292i	$-0.818314\pi$
$911$	−1533.17			−1.68296			−0.841478	+	0.540292i	$0.818314\pi$
$912$		0			0
$913$	−133.826	−	309.317i	−0.146578	−	0.338791i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1830.18			1.99583
$918$		0			0
$919$		−	402.371i		−	0.437836i	−0.975743	−	0.218918i	$-0.929747\pi$
$919$		−	402.371i		−	0.437836i	0.975743	−	0.218918i	$-0.0702527\pi$
$920$		0			0
$921$		−	224.556i		−	0.243817i
$922$		0			0
$923$			733.869i			0.795091i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−643.739			−0.694433
$928$		0			0
$929$	−602.857			−0.648932			−0.324466	−	0.945897i	$-0.605185\pi$
$929$	−602.857			−0.648932			−0.324466	+	0.945897i	$0.605185\pi$
$930$		0			0
$931$			929.685i			0.998587i
$932$		0			0
$933$	252.811			0.270965
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	847.671i		−	0.904665i	−0.891849	−	0.452333i	$-0.850592\pi$
$937$		−	847.671i		−	0.904665i	0.891849	−	0.452333i	$-0.149408\pi$
$938$		0			0
$939$	−217.763			−0.231910
$940$		0			0
$941$			1337.24i			1.42109i	0.703653	+	0.710544i	$0.251551\pi$
$941$			1337.24i			1.42109i	−0.703653	+	0.710544i	$0.748449\pi$
$942$		0			0
$943$		−	312.408i		−	0.331292i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1205.82			−1.27331			−0.636653	−	0.771151i	$-0.719682\pi$
$947$	−1205.82			−1.27331			−0.636653	+	0.771151i	$0.719682\pi$
$948$		0			0
$949$	171.918			0.181158
$950$		0			0
$951$	392.103			0.412306
$952$		0			0
$953$			647.299i			0.679223i	0.940566	+	0.339611i	$0.110296\pi$
$953$			647.299i			0.679223i	−0.940566	+	0.339611i	$0.889704\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	62.0157	+	143.339i	0.0648022	+	0.149779i
$958$		0			0
$959$			1233.47i			1.28620i
$960$		0			0
$961$	−961.000			−1.00000
$962$		0			0
$963$			811.273i			0.842443i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			887.321i			0.917602i	0.888539	+	0.458801i	$0.151721\pi$
$967$			887.321i			0.917602i	−0.888539	+	0.458801i	$0.848279\pi$
$968$		0			0
$969$	60.6971			0.0626389
$970$		0			0
$971$	1104.79			1.13778			0.568891	−	0.822413i	$-0.307373\pi$
$971$	1104.79			1.13778			0.568891	+	0.822413i	$0.307373\pi$
$972$		0			0
$973$	−62.7721			−0.0645140
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1577.70			1.61484			0.807420	−	0.589976i	$-0.200863\pi$
$977$	1577.70			1.61484			0.807420	+	0.589976i	$0.200863\pi$
$978$		0			0
$979$	−40.6163	+	17.5727i	−0.0414876	+	0.0179496i
$980$		0			0
$981$			259.310i			0.264332i
$982$		0			0
$983$	860.925			0.875814			0.437907	−	0.899020i	$-0.355720\pi$
$983$	860.925			0.875814			0.437907	+	0.899020i	$0.355720\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			342.657i			0.347170i
$988$		0			0
$989$			1534.74i			1.55181i
$990$		0			0
$991$	−620.455			−0.626090			−0.313045	−	0.949738i	$-0.601349\pi$
$991$	−620.455			−0.626090			−0.313045	+	0.949738i	$0.601349\pi$
$992$		0			0
$993$	−1.89408			−0.00190743
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	148.972i		−	0.149420i	−0.997205	−	0.0747100i	$-0.976197\pi$
$997$		−	148.972i		−	0.149420i	0.997205	−	0.0747100i	$-0.0238031\pi$
$998$		0			0
$999$	100.784			0.100884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.3.f.c.901.5	✓	8
5.2	odd	4		1100.3.e.c.549.8		16
5.3	odd	4		1100.3.e.c.549.9		16
5.4	even	2		1100.3.f.e.901.4	yes	8
11.10	odd	2	inner	1100.3.f.c.901.6	yes	8
55.32	even	4		1100.3.e.c.549.7		16
55.43	even	4		1100.3.e.c.549.10		16
55.54	odd	2		1100.3.f.e.901.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.3.e.c.549.7		16	55.32	even	4
1100.3.e.c.549.8		16	5.2	odd	4
1100.3.e.c.549.9		16	5.3	odd	4
1100.3.e.c.549.10		16	55.43	even	4
1100.3.f.c.901.5	✓	8	1.1	even	1	trivial
1100.3.f.c.901.6	yes	8	11.10	odd	2	inner
1100.3.f.e.901.3	yes	8	55.54	odd	2
1100.3.f.e.901.4	yes	8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1100.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.638826 q^{3} -9.06537i q^{7} -8.59190 q^{9} +(10.0956 - 4.36788i) q^{11} +10.4302i q^{13} +3.39108i q^{17} -28.0187i q^{19} -5.79120i q^{21} -18.8226 q^{23} -11.2382 q^{27} +22.2253i q^{29} +0.00744511 q^{31} +(6.44935 - 2.79032i) q^{33} -8.96796 q^{37} +6.66311i q^{39} +16.5975i q^{41} -81.5368i q^{43} -59.1685 q^{47} -33.1809 q^{49} +2.16631i q^{51} -60.1508 q^{53} -17.8991i q^{57} -81.5361 q^{59} +114.695i q^{61} +77.8888i q^{63} -99.1084 q^{67} -12.0244 q^{69} +70.3598 q^{71} -16.4827i q^{73} +(-39.5965 - 91.5206i) q^{77} -118.929i q^{79} +70.1479 q^{81} -30.6387i q^{83} +14.1981i q^{87} -4.02316 q^{89} +94.5539 q^{91} +0.00475614 q^{93} -101.970 q^{97} +(-86.7406 + 37.5284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 16 q^{9} + 3 q^{11} + 28 q^{23} - 10 q^{27} + 14 q^{31} - 31 q^{33} - 24 q^{37} - 32 q^{47} + 14 q^{49} + 98 q^{53} + 128 q^{59} - 42 q^{67} - 176 q^{69} - 34 q^{71} - 136 q^{77} - 128 q^{81}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 16 * q^9 + 3 * q^11 + 28 * q^23 - 10 * q^27 + 14 * q^31 - 31 * q^33 - 24 * q^37 - 32 * q^47 + 14 * q^49 + 98 * q^53 + 128 * q^59 - 42 * q^67 - 176 * q^69 - 34 * q^71 - 136 * q^77 - 128 * q^81 - 146 * q^89 + 114 * q^91 - 142 * q^93 + 296 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more