LMFDB - Embedded newform 700.5.o.b.549.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.11
Character	$\chi$	$=$	700.549
Dual form			700.5.o.b.649.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.252864 - 0.437973i) q^{3} +(48.2934 + 8.29155i) q^{7} +(40.3721 + 69.9266i) q^{9} +(-106.173 + 183.897i) q^{11} -45.2171 q^{13} +(125.724 - 217.760i) q^{17} +(-405.974 + 234.389i) q^{19} +(15.8431 - 19.0546i) q^{21} +(-809.163 + 467.170i) q^{23} +81.7986 q^{27} +816.585 q^{29} +(-853.479 - 492.757i) q^{31} +(53.6948 + 93.0021i) q^{33} +(-474.487 + 273.945i) q^{37} +(-11.4338 + 19.8039i) q^{39} -2483.32i q^{41} -1880.19i q^{43} +(-289.936 - 502.185i) q^{47} +(2263.50 + 800.854i) q^{49} +(-63.5821 - 110.127i) q^{51} +(312.644 + 180.505i) q^{53} +237.075i q^{57} +(-5282.61 - 3049.91i) q^{59} +(-1532.63 + 884.865i) q^{61} +(1369.91 + 3711.74i) q^{63} +(5176.10 + 2988.43i) q^{67} +472.523i q^{69} +1012.99 q^{71} +(1541.84 - 2670.55i) q^{73} +(-6652.26 + 8000.69i) q^{77} +(-361.636 - 626.371i) q^{79} +(-3249.46 + 5628.23i) q^{81} +8101.85 q^{83} +(206.485 - 357.643i) q^{87} +(-2390.20 + 1379.98i) q^{89} +(-2183.69 - 374.920i) q^{91} +(-431.629 + 249.201i) q^{93} -16667.1 q^{97} -17145.8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 468 q^{9} - 300 q^{11} - 1956 q^{19} - 5152 q^{21} + 624 q^{29} + 10392 q^{31} + 13440 q^{39} + 16384 q^{49} + 4264 q^{51} - 20016 q^{59} + 4416 q^{61} - 59664 q^{71} - 18664 q^{79} + 14132 q^{81}+ \cdots - 6120 q^{99}+O(q^{100}) $ 40 * q - 468 * q^9 - 300 * q^11 - 1956 * q^19 - 5152 * q^21 + 624 * q^29 + 10392 * q^31 + 13440 * q^39 + 16384 * q^49 + 4264 * q^51 - 20016 * q^59 + 4416 * q^61 - 59664 * q^71 - 18664 * q^79 + 14132 * q^81 + 32112 * q^89 + 14512 * q^91 - 6120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$	0.252864	−	0.437973i	0.0280960	−	0.0486637i	−0.851636	−	0.524134i	$-0.824389\pi$
$3$	0.252864	−	0.437973i	0.0280960	−	0.0486637i	0.879732	+	0.475471i	$0.157722\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	48.2934	+	8.29155i	0.985579	+	0.169215i
$7$	48.2934	+	8.29155i	0.985579	+	0.169215i
$8$		0			0
$9$	40.3721	+	69.9266i	0.498421	+	0.863291i
$10$		0			0
$11$	−106.173	+	183.897i	−0.877465	+	1.51981i	−0.0233507	+	0.999727i	$0.507433\pi$
$11$	−106.173	+	183.897i	−0.877465	+	1.51981i	−0.854114	+	0.520086i	$0.825900\pi$
$12$		0			0
$13$	−45.2171			−0.267557			−0.133778	−	0.991011i	$-0.542711\pi$
$13$	−45.2171			−0.267557			−0.133778	+	0.991011i	$0.542711\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	125.724	−	217.760i	0.435031	−	0.753495i	−0.562268	−	0.826955i	$-0.690071\pi$
$17$	125.724	−	217.760i	0.435031	−	0.753495i	0.997298	+	0.0734603i	$0.0234042\pi$
$18$		0			0
$19$	−405.974	+	234.389i	−1.12458	+	0.649278i	−0.942567	−	0.334018i	$-0.891595\pi$
$19$	−405.974	+	234.389i	−1.12458	+	0.649278i	−0.182015	+	0.983296i	$0.558262\pi$
$20$		0			0
$21$	15.8431	−	19.0546i	0.0359255	−	0.0432077i
$22$		0			0
$23$	−809.163	+	467.170i	−1.52961	+	0.883120i	−0.530231	+	0.847853i	$0.677895\pi$
$23$	−809.163	+	467.170i	−1.52961	+	0.883120i	−0.999378	+	0.0352667i	$0.988772\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	81.7986			0.112207
$28$		0			0
$29$	816.585			0.970969			0.485484	−	0.874245i	$-0.338643\pi$
$29$	816.585			0.970969			0.485484	+	0.874245i	$0.338643\pi$
$30$		0			0
$31$	−853.479	−	492.757i	−0.888116	−	0.512754i	−0.0147902	−	0.999891i	$-0.504708\pi$
$31$	−853.479	−	492.757i	−0.888116	−	0.512754i	−0.873326	+	0.487137i	$0.838041\pi$
$32$		0			0
$33$	53.6948	+	93.0021i	0.0493065	+	0.0854014i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−474.487	+	273.945i	−0.346594	+	0.200106i	−0.663184	−	0.748456i	$-0.730795\pi$
$37$	−474.487	+	273.945i	−0.346594	+	0.200106i	0.316590	+	0.948562i	$0.397462\pi$
$38$		0			0
$39$	−11.4338	+	19.8039i	−0.00751728	+	0.0130203i
$40$		0			0
$41$		−	2483.32i		−	1.47729i	−0.674094	−	0.738645i	$-0.735466\pi$
$41$		−	2483.32i		−	1.47729i	0.674094	−	0.738645i	$-0.264534\pi$
$42$		0			0
$43$		−	1880.19i		−	1.01687i	−0.861101	−	0.508433i	$-0.830225\pi$
$43$		−	1880.19i		−	1.01687i	0.861101	−	0.508433i	$-0.169775\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−289.936	−	502.185i	−0.131252	−	0.227336i	0.792907	−	0.609342i	$-0.208566\pi$
$47$	−289.936	−	502.185i	−0.131252	−	0.227336i	−0.924160	+	0.382007i	$0.875233\pi$
$48$		0			0
$49$	2263.50	+	800.854i	0.942732	+	0.333550i
$50$		0			0
$51$	−63.5821	−	110.127i	−0.0244453	−	0.0423404i
$52$		0			0
$53$	312.644	+	180.505i	0.111301	+	0.0642595i	0.554617	−	0.832106i	$-0.312865\pi$
$53$	312.644	+	180.505i	0.111301	+	0.0642595i	−0.443316	+	0.896365i	$0.646198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			237.075i			0.0729685i
$58$		0			0
$59$	−5282.61	−	3049.91i	−1.51755	−	0.876160i	−0.999787	−	0.0206388i	$-0.993430\pi$
$59$	−5282.61	−	3049.91i	−1.51755	−	0.876160i	−0.517767	−	0.855522i	$-0.673237\pi$
$60$		0			0
$61$	−1532.63	+	884.865i	−0.411887	+	0.237803i	−0.691600	−	0.722281i	$-0.743094\pi$
$61$	−1532.63	+	884.865i	−0.411887	+	0.237803i	0.279713	+	0.960084i	$0.409761\pi$
$62$		0			0
$63$	1369.91	+	3711.74i	0.345152	+	0.935182i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5176.10	+	2988.43i	1.15306	+	0.665722i	0.949632	−	0.313367i	$-0.101457\pi$
$67$	5176.10	+	2988.43i	1.15306	+	0.665722i	0.203432	+	0.979089i	$0.434790\pi$
$68$		0			0
$69$			472.523i			0.0992486i
$70$		0			0
$71$	1012.99			0.200949			0.100475	−	0.994940i	$-0.467964\pi$
$71$	1012.99			0.200949			0.100475	+	0.994940i	$0.467964\pi$
$72$		0			0
$73$	1541.84	−	2670.55i	0.289331	−	0.501135i	−0.684319	−	0.729182i	$-0.739901\pi$
$73$	1541.84	−	2670.55i	0.289331	−	0.501135i	0.973650	+	0.228047i	$0.0732339\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6652.26	+	8000.69i	−1.12199	+	1.34942i
$78$		0			0
$79$	−361.636	−	626.371i	−0.0579451	−	0.100364i	0.835598	−	0.549342i	$-0.185122\pi$
$79$	−361.636	−	626.371i	−0.0579451	−	0.100364i	−0.893543	+	0.448978i	$0.851788\pi$
$80$		0			0
$81$	−3249.46	+	5628.23i	−0.495269	+	0.857830i
$82$		0			0
$83$	8101.85			1.17606			0.588028	−	0.808840i	$-0.299904\pi$
$83$	8101.85			1.17606			0.588028	+	0.808840i	$0.299904\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	206.485	−	357.643i	0.0272804	−	0.0472510i
$88$		0			0
$89$	−2390.20	+	1379.98i	−0.301755	+	0.174218i	−0.643231	−	0.765672i	$-0.722406\pi$
$89$	−2390.20	+	1379.98i	−0.301755	+	0.174218i	0.341476	+	0.939890i	$0.389073\pi$
$90$		0			0
$91$	−2183.69	−	374.920i	−0.263698	−	0.0452747i
$92$		0			0
$93$	−431.629	+	249.201i	−0.0499050	+	0.0288127i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−16667.1			−1.77140			−0.885702	−	0.464254i	$-0.846323\pi$
$97$	−16667.1			−1.77140			−0.885702	+	0.464254i	$0.846323\pi$
$98$		0			0
$99$	−17145.8			−1.74939
$100$		0			0
$101$	−12363.0	−	7137.76i	−1.21194	−	0.699711i	−0.248755	−	0.968566i	$-0.580021\pi$
$101$	−12363.0	−	7137.76i	−1.21194	−	0.699711i	−0.963181	+	0.268855i	$0.913355\pi$
$102$		0			0
$103$	−9402.08	−	16284.9i	−0.886236	−	1.53501i	−0.844290	−	0.535887i	$-0.819977\pi$
$103$	−9402.08	−	16284.9i	−0.886236	−	1.53501i	−0.0419464	−	0.999120i	$-0.513356\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7830.70	+	4521.05i	−0.683963	+	0.394886i	−0.801347	−	0.598200i	$-0.795883\pi$
$107$	−7830.70	+	4521.05i	−0.683963	+	0.394886i	0.117383	+	0.993087i	$0.462549\pi$
$108$		0			0
$109$	6679.42	−	11569.1i	0.562194	−	0.973748i	−0.435111	−	0.900377i	$-0.643291\pi$
$109$	6679.42	−	11569.1i	0.562194	−	0.973748i	0.997305	−	0.0733712i	$-0.0233758\pi$
$110$		0			0
$111$			277.084i			0.0224887i
$112$		0			0
$113$			9056.23i			0.709236i	0.935011	+	0.354618i	$0.115389\pi$
$113$			9056.23i			0.709236i	−0.935011	+	0.354618i	$0.884611\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1825.51	−	3161.87i	−0.133356	−	0.230979i
$118$		0			0
$119$	7877.20	−	9473.92i	0.556260	−	0.669015i
$120$		0			0
$121$	−15225.0	−	26370.5i	−1.03989	−	1.80114i
$122$		0			0
$123$	−1087.63	−	627.944i	−0.0718904	−	0.0415060i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			30092.6i			1.86575i	0.360203	+	0.932874i	$0.382707\pi$
$127$			30092.6i			1.86575i	−0.360203	+	0.932874i	$0.617293\pi$
$128$		0			0
$129$	−823.472	−	475.432i	−0.0494845	−	0.0285699i
$130$		0			0
$131$	−15708.5	+	9069.32i	−0.915362	+	0.528485i	−0.882153	−	0.470964i	$-0.843906\pi$
$131$	−15708.5	+	9069.32i	−0.915362	+	0.528485i	−0.0332096	+	0.999448i	$0.510573\pi$
$132$		0			0
$133$	−21549.3	+	7953.30i	−1.21823	+	0.449618i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	22287.3	+	12867.6i	1.18745	+	0.685576i	0.957727	−	0.287680i	$-0.0928839\pi$
$137$	22287.3	+	12867.6i	1.18745	+	0.685576i	0.229725	+	0.973256i	$0.426217\pi$
$138$		0			0
$139$			7509.03i			0.388646i	0.980938	+	0.194323i	$0.0622510\pi$
$139$			7509.03i			0.388646i	−0.980938	+	0.194323i	$0.937749\pi$
$140$		0			0
$141$	−293.258			−0.0147507
$142$		0			0
$143$	4800.84	−	8315.30i	0.234772	−	0.406636i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	923.111	−	788.846i	0.0427188	−	0.0365054i
$148$		0			0
$149$	9159.85	+	15865.3i	0.412587	+	0.714622i	0.995172	−	0.0981478i	$-0.0312918\pi$
$149$	9159.85	+	15865.3i	0.412587	+	0.714622i	−0.582584	+	0.812770i	$0.697958\pi$
$150$		0			0
$151$	14118.8	−	24454.4i	0.619216	−	1.07251i	−0.370413	−	0.928867i	$-0.620784\pi$
$151$	14118.8	−	24454.4i	0.619216	−	1.07251i	0.989629	−	0.143647i	$-0.0458829\pi$
$152$		0			0
$153$	20303.0			0.867314
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8441.07	−	14620.4i	0.342451	−	0.593142i	−0.642436	−	0.766339i	$-0.722076\pi$
$157$	8441.07	−	14620.4i	0.342451	−	0.593142i	0.984887	+	0.173197i	$0.0554096\pi$
$158$		0			0
$159$	158.113	−	91.2864i	0.00625421	−	0.00361087i
$160$		0			0
$161$	−42950.8	+	15852.0i	−1.65699	+	0.611552i
$162$		0			0
$163$	−3352.33	+	1935.47i	−0.126175	+	0.0728469i	−0.561759	−	0.827301i	$-0.689875\pi$
$163$	−3352.33	+	1935.47i	−0.126175	+	0.0728469i	0.435584	+	0.900148i	$0.356542\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−23763.4			−0.852072			−0.426036	−	0.904706i	$-0.640090\pi$
$167$	−23763.4			−0.852072			−0.426036	+	0.904706i	$0.640090\pi$
$168$		0			0
$169$	−26516.4			−0.928413
$170$		0			0
$171$	−32780.1	−	18925.6i	−1.12103	−	0.647228i
$172$		0			0
$173$	7185.09	+	12444.9i	0.240071	+	0.415816i	0.960734	−	0.277470i	$-0.0894958\pi$
$173$	7185.09	+	12444.9i	0.240071	+	0.415816i	−0.720663	+	0.693285i	$0.756163\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2671.56	+	1542.43i	−0.0852744	+	0.0492332i
$178$		0			0
$179$	−18366.3	+	31811.4i	−0.573212	+	0.992833i	0.423021	+	0.906120i	$0.360970\pi$
$179$	−18366.3	+	31811.4i	−0.573212	+	0.992833i	−0.996233	+	0.0867131i	$0.972364\pi$
$180$		0			0
$181$		−	10730.7i		−	0.327544i	−0.986498	−	0.163772i	$-0.947634\pi$
$181$		−	10730.7i		−	0.327544i	0.986498	−	0.163772i	$-0.0523661\pi$
$182$		0			0
$183$			895.002i			0.0267253i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	26697.0	+	46240.6i	0.763448	+	1.32233i
$188$		0			0
$189$	3950.33	+	678.237i	0.110589	+	0.0189871i
$190$		0			0
$191$	−28115.3	−	48697.2i	−0.770684	−	1.33486i	−0.937189	−	0.348823i	$-0.886581\pi$
$191$	−28115.3	−	48697.2i	−0.770684	−	1.33486i	0.166505	−	0.986041i	$-0.446752\pi$
$192$		0			0
$193$	−12786.7	−	7382.43i	−0.343278	−	0.198191i	0.318443	−	0.947942i	$-0.396840\pi$
$193$	−12786.7	−	7382.43i	−0.343278	−	0.198191i	−0.661720	+	0.749751i	$0.730173\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			57662.6i			1.48580i	0.669400	+	0.742902i	$0.266551\pi$
$197$			57662.6i			1.48580i	−0.669400	+	0.742902i	$0.733449\pi$
$198$		0			0
$199$	−20182.3	−	11652.2i	−0.509641	−	0.294241i	0.223045	−	0.974808i	$-0.428400\pi$
$199$	−20182.3	−	11652.2i	−0.509641	−	0.294241i	−0.732686	+	0.680567i	$0.761734\pi$
$200$		0			0
$201$	2617.70	−	1511.33i	0.0647930	−	0.0374083i
$202$		0			0
$203$	39435.6	+	6770.75i	0.956967	+	0.164303i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−65335.3	−	37721.3i	−1.52478	−	0.880332i
$208$		0			0
$209$		−	99543.5i		−	2.27887i
$210$		0			0
$211$	643.371			0.0144510			0.00722548	−	0.999974i	$-0.497700\pi$
$211$	643.371			0.0144510			0.00722548	+	0.999974i	$0.497700\pi$
$212$		0			0
$213$	256.148	−	443.661i	0.00564587	−	0.00977894i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−37131.7	−	30873.5i	−0.788543	−	0.655642i
$218$		0			0
$219$	−779.754	−	1350.57i	−0.0162581	−	0.0281598i
$220$		0			0
$221$	−5684.86	+	9846.47i	−0.116395	+	0.201603i
$222$		0			0
$223$	14109.4			0.283726			0.141863	−	0.989886i	$-0.454691\pi$
$223$	14109.4			0.283726			0.141863	+	0.989886i	$0.454691\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−42055.0	+	72841.4i	−0.816142	+	1.41360i	0.0923628	+	0.995725i	$0.470558\pi$
$227$	−42055.0	+	72841.4i	−0.816142	+	1.41360i	−0.908505	+	0.417874i	$0.862775\pi$
$228$		0			0
$229$	−23336.1	+	13473.1i	−0.444997	+	0.256919i	−0.705715	−	0.708496i	$-0.749374\pi$
$229$	−23336.1	+	13473.1i	−0.444997	+	0.256919i	0.260718	+	0.965415i	$0.416041\pi$
$230$		0			0
$231$	1821.97	+	4936.60i	0.0341443	+	0.0925132i
$232$		0			0
$233$	−33977.2	+	19616.7i	−0.625858	+	0.361339i	−0.779146	−	0.626842i	$-0.784347\pi$
$233$	−33977.2	+	19616.7i	−0.625858	+	0.361339i	0.153288	+	0.988182i	$0.451014\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−365.779			−0.00651211
$238$		0			0
$239$	938.827			0.0164358			0.00821788	−	0.999966i	$-0.497384\pi$
$239$	938.827			0.0164358			0.00821788	+	0.999966i	$0.497384\pi$
$240$		0			0
$241$	1811.67	+	1045.97i	0.0311921	+	0.0180088i	0.515515	−	0.856881i	$-0.327601\pi$
$241$	1811.67	+	1045.97i	0.0311921	+	0.0180088i	−0.484323	+	0.874889i	$0.660934\pi$
$242$		0			0
$243$	4956.19	+	8584.37i	0.0839335	+	0.145377i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	18357.0	−	10598.4i	0.300889	−	0.173719i
$248$		0			0
$249$	2048.67	−	3548.40i	0.0330425	−	0.0572313i
$250$		0			0
$251$			77587.0i			1.23152i	0.787934	+	0.615760i	$0.211151\pi$
$251$			77587.0i			1.23152i	−0.787934	+	0.615760i	$0.788849\pi$
$252$		0			0
$253$		−	198404.i		−	3.09963i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5964.17	+	10330.2i	0.0902991	+	0.156403i	0.907637	−	0.419756i	$-0.137884\pi$
$257$	5964.17	+	10330.2i	0.0902991	+	0.156403i	−0.817338	+	0.576159i	$0.804551\pi$
$258$		0			0
$259$	−25186.0	+	9295.51i	−0.375457	+	0.138571i
$260$		0			0
$261$	32967.3	+	57101.0i	0.483952	+	0.838229i
$262$		0			0
$263$	−16408.9	−	9473.71i	−0.237230	−	0.136965i	0.376673	−	0.926346i	$-0.377068\pi$
$263$	−16408.9	−	9473.71i	−0.237230	−	0.136965i	−0.613903	+	0.789382i	$0.710401\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			1395.79i			0.0195793i
$268$		0			0
$269$	73508.3	+	42440.0i	1.01585	+	0.586504i	0.912901	−	0.408182i	$-0.133837\pi$
$269$	73508.3	+	42440.0i	1.01585	+	0.586504i	0.102954	+	0.994686i	$0.467171\pi$
$270$		0			0
$271$	−34775.7	+	20077.8i	−0.473519	+	0.273387i	−0.717712	−	0.696340i	$-0.754810\pi$
$271$	−34775.7	+	20077.8i	−0.473519	+	0.273387i	0.244192	+	0.969727i	$0.421477\pi$
$272$		0			0
$273$	−716.380	+	861.593i	−0.00961210	+	0.0115605i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	55993.3	+	32327.7i	0.729754	+	0.421323i	0.818332	−	0.574746i	$-0.194899\pi$
$277$	55993.3	+	32327.7i	0.729754	+	0.421323i	−0.0885784	+	0.996069i	$0.528232\pi$
$278$		0			0
$279$		−	79574.5i		−	1.02227i
$280$		0			0
$281$	31445.7			0.398244			0.199122	−	0.979975i	$-0.436191\pi$
$281$	31445.7			0.398244			0.199122	+	0.979975i	$0.436191\pi$
$282$		0			0
$283$	−72527.4	+	125621.i	−0.905586	+	1.56852i	−0.0854562	+	0.996342i	$0.527235\pi$
$283$	−72527.4	+	125621.i	−0.905586	+	1.56852i	−0.820129	+	0.572178i	$0.806099\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	20590.6	−	119928.i	0.249980	−	1.45599i
$288$		0			0
$289$	10147.5	+	17576.0i	0.121497	+	0.210439i
$290$		0			0
$291$	−4214.52	+	7299.77i	−0.0497694	+	0.0862031i
$292$		0			0
$293$	65860.7			0.767169			0.383585	−	0.923506i	$-0.374689\pi$
$293$	65860.7			0.767169			0.383585	+	0.923506i	$0.374689\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8684.82	+	15042.6i	−0.0984573	+	0.170533i
$298$		0			0
$299$	36588.0	−	21124.1i	0.409257	−	0.236285i
$300$		0			0
$301$	15589.7	−	90800.5i	0.172069	−	1.00220i
$302$		0			0
$303$	−6252.30	+	3609.77i	−0.0681011	+	0.0393182i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	75636.9			0.802523			0.401261	−	0.915964i	$-0.368572\pi$
$307$	75636.9			0.802523			0.401261	+	0.915964i	$0.368572\pi$
$308$		0			0
$309$	−9509.80			−0.0995988
$310$		0			0
$311$	24176.3	+	13958.2i	0.249959	+	0.144314i	0.619745	−	0.784803i	$-0.287236\pi$
$311$	24176.3	+	13958.2i	0.249959	+	0.144314i	−0.369787	+	0.929117i	$0.620569\pi$
$312$		0			0
$313$	24198.6	+	41913.1i	0.247002	+	0.427820i	0.962693	−	0.270597i	$-0.0872212\pi$
$313$	24198.6	+	41913.1i	0.247002	+	0.427820i	−0.715690	+	0.698418i	$0.753888\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4441.67	+	2564.40i	−0.0442005	+	0.0255192i	−0.521937	−	0.852984i	$-0.674791\pi$
$317$	−4441.67	+	2564.40i	−0.0442005	+	0.0255192i	0.477737	+	0.878503i	$0.341457\pi$
$318$		0			0
$319$	−86699.4	+	150168.i	−0.851991	+	1.47569i
$320$		0			0
$321$			4572.85i			0.0443789i
$322$		0			0
$323$			117873.i			1.12982i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3377.97	−	5850.82i	−0.0315908	−	0.0547169i
$328$		0			0
$329$	−9838.12	−	26656.2i	−0.0908909	−	0.246267i
$330$		0			0
$331$	−38682.4	−	66999.8i	−0.353067	−	0.611530i	0.633718	−	0.773564i	$-0.281528\pi$
$331$	−38682.4	−	66999.8i	−0.353067	−	0.611530i	−0.986785	+	0.162034i	$0.948195\pi$
$332$		0			0
$333$	−38312.1	−	22119.5i	−0.345500	−	0.199474i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	149619.i		−	1.31743i	−0.752392	−	0.658716i	$-0.771100\pi$
$337$		−	149619.i		−	1.31743i	0.752392	−	0.658716i	$-0.228900\pi$
$338$		0			0
$339$	3966.39	+	2290.00i	0.0345141	+	0.0199267i
$340$		0			0
$341$	181233.	−	104635.i	1.55858	−	0.899847i
$342$		0			0
$343$	102672.	+	57443.8i	0.872696	+	0.488265i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8421.59	−	4862.21i	−0.0699415	−	0.0403808i	0.464621	−	0.885509i	$-0.346190\pi$
$347$	−8421.59	−	4862.21i	−0.0699415	−	0.0403808i	−0.534563	+	0.845129i	$0.679524\pi$
$348$		0			0
$349$			120587.i			0.990031i	0.868884	+	0.495016i	$0.164838\pi$
$349$			120587.i			0.990031i	−0.868884	+	0.495016i	$0.835162\pi$
$350$		0			0
$351$	−3698.69			−0.0300216
$352$		0			0
$353$	50375.8	−	87253.5i	0.404271	−	0.700218i	−0.589965	−	0.807429i	$-0.700859\pi$
$353$	50375.8	−	87253.5i	0.404271	−	0.700218i	0.994236	+	0.107210i	$0.0341919\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2157.47	−	5845.62i	−0.0169281	−	0.0458663i
$358$		0			0
$359$	95046.0	+	164624.i	0.737471	+	1.27734i	0.953631	+	0.300979i	$0.0973133\pi$
$359$	95046.0	+	164624.i	0.737471	+	1.27734i	−0.216160	+	0.976358i	$0.569353\pi$
$360$		0			0
$361$	44716.2	−	77450.7i	0.343123	−	0.594307i
$362$		0			0
$363$	−15399.4			−0.116867
$364$		0			0
$365$		0			0
$366$		0			0
$367$	96415.0	−	166996.i	0.715835	−	1.23986i	−0.246802	−	0.969066i	$-0.579380\pi$
$367$	96415.0	−	166996.i	0.715835	−	1.23986i	0.962637	−	0.270796i	$-0.0872869\pi$
$368$		0			0
$369$	173650.	−	100257.i	1.27533	−	0.736313i
$370$		0			0
$371$	13601.9	+	11309.5i	0.0988219	+	0.0821666i
$372$		0			0
$373$	−134506.	+	77656.9i	−0.966770	+	0.558165i	−0.898250	−	0.439485i	$-0.855161\pi$
$373$	−134506.	+	77656.9i	−0.966770	+	0.558165i	−0.0685200	+	0.997650i	$0.521828\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−36923.6			−0.259789
$378$		0			0
$379$	−11340.1			−0.0789472			−0.0394736	−	0.999221i	$-0.512568\pi$
$379$	−11340.1			−0.0789472			−0.0394736	+	0.999221i	$0.512568\pi$
$380$		0			0
$381$	13179.8	+	7609.35i	0.0907942	+	0.0524201i
$382$		0			0
$383$	9003.33	+	15594.2i	0.0613770	+	0.106308i	0.895081	−	0.445903i	$-0.147117\pi$
$383$	9003.33	+	15594.2i	0.0613770	+	0.106308i	−0.833704	+	0.552211i	$0.813784\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	131475.	−	75907.1i	0.877852	−	0.506828i
$388$		0			0
$389$	104843.	−	181594.i	0.692854	−	1.20006i	−0.278045	−	0.960568i	$-0.589687\pi$
$389$	104843.	−	181594.i	0.692854	−	1.20006i	0.970899	−	0.239490i	$-0.0769801\pi$
$390$		0			0
$391$			234938.i			1.53674i
$392$		0			0
$393$			9173.23i			0.0593932i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	101932.	+	176552.i	0.646740	+	1.12019i	0.983897	+	0.178738i	$0.0572016\pi$
$397$	101932.	+	176552.i	0.646740	+	1.12019i	−0.337156	+	0.941449i	$0.609465\pi$
$398$		0			0
$399$	−1965.71	+	11449.1i	−0.0123474	+	0.0719162i
$400$		0			0
$401$	150116.	+	260008.i	0.933549	+	1.61695i	0.777202	+	0.629251i	$0.216638\pi$
$401$	150116.	+	260008.i	0.933549	+	1.61695i	0.156347	+	0.987702i	$0.450028\pi$
$402$		0			0
$403$	38591.8	+	22281.0i	0.237621	+	0.137191i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	116343.i		−	0.702344i
$408$		0			0
$409$	−94863.0	−	54769.2i	−0.567088	−	0.327408i	0.188898	−	0.981997i	$-0.439509\pi$
$409$	−94863.0	−	54769.2i	−0.567088	−	0.327408i	−0.755985	+	0.654589i	$0.772842\pi$
$410$		0			0
$411$	11271.3	−	6507.49i	0.0667253	−	0.0385239i
$412$		0			0
$413$	−229826.	−	191092.i	−1.34741	−	1.12032i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3288.75	+	1898.76i	0.0189130	+	0.0109194i
$418$		0			0
$419$			85384.2i			0.486350i	0.969982	+	0.243175i	$0.0781890\pi$
$419$			85384.2i			0.486350i	−0.969982	+	0.243175i	$0.921811\pi$
$420$		0			0
$421$	133199.			0.751513			0.375757	−	0.926718i	$-0.377383\pi$
$421$	133199.			0.751513			0.375757	+	0.926718i	$0.377383\pi$
$422$		0			0
$423$	23410.7	−	40548.5i	0.130838	−	0.226618i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−81352.8	+	30025.2i	−0.446187	+	0.164676i
$428$		0			0
$429$	−2427.92	−	4205.28i	−0.0131923	−	0.0228497i
$430$		0			0
$431$	−47243.2	+	81827.6i	−0.254322	+	0.440499i	−0.964711	−	0.263310i	$-0.915186\pi$
$431$	−47243.2	+	81827.6i	−0.254322	+	0.440499i	0.710389	+	0.703809i	$0.248519\pi$
$432$		0			0
$433$	−268999.			−1.43474			−0.717372	−	0.696691i	$-0.754655\pi$
$433$	−268999.			−1.43474			−0.717372	+	0.696691i	$0.754655\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	218999.	−	379318.i	1.14678	−	1.98628i
$438$		0			0
$439$	27940.5	−	16131.5i	0.144979	−	0.0837036i	−0.425756	−	0.904838i	$-0.639992\pi$
$439$	27940.5	−	16131.5i	0.144979	−	0.0837036i	0.570735	+	0.821134i	$0.306658\pi$
$440$		0			0
$441$	35381.4	+	190611.i	0.181927	+	0.980101i
$442$		0			0
$443$	182039.	−	105100.i	0.927591	−	0.535545i	0.0415419	−	0.999137i	$-0.486773\pi$
$443$	182039.	−	105100.i	0.927591	−	0.535545i	0.886049	+	0.463592i	$0.153440\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9264.79			0.0463682
$448$		0			0
$449$	72203.4			0.358150			0.179075	−	0.983835i	$-0.442690\pi$
$449$	72203.4			0.358150			0.179075	+	0.983835i	$0.442690\pi$
$450$		0			0
$451$	456677.	+	263663.i	2.24521	+	1.29627i
$452$		0			0
$453$	−7140.25	−	12367.3i	−0.0347950	−	0.0602667i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−346877.	+	200269.i	−1.66090	+	0.958919i	−0.688609	+	0.725133i	$0.741778\pi$
$457$	−346877.	+	200269.i	−1.66090	+	0.958919i	−0.972288	+	0.233786i	$0.924888\pi$
$458$		0			0
$459$	10284.0	−	17812.5i	0.0488133	−	0.0845471i
$460$		0			0
$461$		−	49928.5i		−	0.234934i	−0.993077	−	0.117467i	$-0.962523\pi$
$461$		−	49928.5i		−	0.234934i	0.993077	−	0.117467i	$-0.0374775\pi$
$462$		0			0
$463$			17248.5i			0.0804617i	0.999190	+	0.0402309i	$0.0128093\pi$
$463$			17248.5i			0.0804617i	−0.999190	+	0.0402309i	$0.987191\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−140847.	−	243954.i	−0.645822	−	1.11860i	−0.984111	−	0.177555i	$-0.943181\pi$
$467$	−140847.	−	243954.i	−0.645822	−	1.11860i	0.338288	−	0.941042i	$-0.390152\pi$
$468$		0			0
$469$	225193.	+	187239.i	1.02379	+	0.851238i
$470$		0			0
$471$	−4268.89	−	7393.93i	−0.0192430	−	0.0333299i
$472$		0			0
$473$	345761.	+	199625.i	1.54545	+	0.892264i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			29149.5i			0.128113i
$478$		0			0
$479$	−210162.	−	121337.i	−0.915974	−	0.528838i	−0.0336257	−	0.999434i	$-0.510705\pi$
$479$	−210162.	−	121337.i	−0.915974	−	0.528838i	−0.882349	+	0.470597i	$0.844039\pi$
$480$		0			0
$481$	21454.9	−	12387.0i	0.0927335	−	0.0535397i
$482$		0			0
$483$	−3917.94	+	22819.7i	−0.0167944	+	0.0978174i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	183874.	+	106160.i	0.775289	+	0.447613i	0.834758	−	0.550617i	$-0.185608\pi$
$487$	183874.	+	106160.i	0.775289	+	0.447613i	−0.0594694	+	0.998230i	$0.518941\pi$
$488$		0			0
$489$			1957.64i			0.00818683i
$490$		0			0
$491$	113473.			0.470685			0.235342	−	0.971913i	$-0.424379\pi$
$491$	113473.			0.470685			0.235342	+	0.971913i	$0.424379\pi$
$492$		0			0
$493$	102664.	−	177820.i	0.422401	−	0.731620i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	48920.5	+	8399.22i	0.198051	+	0.0340037i
$498$		0			0
$499$	−62483.6	−	108225.i	−0.250937	−	0.434636i	0.712847	−	0.701320i	$-0.247405\pi$
$499$	−62483.6	−	108225.i	−0.250937	−	0.434636i	−0.963784	+	0.266684i	$0.914072\pi$
$500$		0			0
$501$	−6008.92	+	10407.8i	−0.0239398	+	0.0414650i
$502$		0			0
$503$	19956.1			0.0788752			0.0394376	−	0.999222i	$-0.487443\pi$
$503$	19956.1			0.0788752			0.0394376	+	0.999222i	$0.487443\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6705.05	+	11613.5i	−0.0260847	+	0.0451801i
$508$		0			0
$509$	−139552.	+	80570.2i	−0.538641	+	0.310985i	−0.744528	−	0.667591i	$-0.767325\pi$
$509$	−139552.	+	80570.2i	−0.538641	+	0.310985i	0.205887	+	0.978576i	$0.433992\pi$
$510$		0			0
$511$	96603.8	−	116186.i	0.369958	−	0.444949i
$512$		0			0
$513$	−33208.1	+	19172.7i	−0.126186	+	0.0728533i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	123134.			0.460677
$518$		0			0
$519$	7267.41			0.0269802
$520$		0			0
$521$	−164098.	−	94742.2i	−0.604545	−	0.349034i	0.166282	−	0.986078i	$-0.446824\pi$
$521$	−164098.	−	94742.2i	−0.604545	−	0.349034i	−0.770828	+	0.637044i	$0.780157\pi$
$522$		0			0
$523$	141732.	+	245488.i	0.518162	+	0.897483i	0.999777	+	0.0211003i	$0.00671694\pi$
$523$	141732.	+	245488.i	0.518162	+	0.897483i	−0.481615	+	0.876383i	$0.659950\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−214605.	+	123903.i	−0.772715	+	0.446127i
$528$		0			0
$529$	296576.	−	513685.i	1.05980	−	1.83563i
$530$		0			0
$531$		−	492526.i		−	1.74679i
$532$		0			0
$533$			112289.i			0.395259i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	9288.36	+	16087.9i	0.0322100	+	0.0557893i
$538$		0			0
$539$	−387598.	+	331223.i	−1.33415	+	1.14010i
$540$		0			0
$541$	−38150.1	−	66077.9i	−0.130347	−	0.225768i	0.793463	−	0.608618i	$-0.208276\pi$
$541$	−38150.1	−	66077.9i	−0.130347	−	0.225768i	−0.923810	+	0.382850i	$0.874942\pi$
$542$		0			0
$543$	−4699.74	−	2713.40i	−0.0159395	−	0.00920267i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	441553.i		−	1.47573i	−0.674946	−	0.737867i	$-0.735833\pi$
$547$		−	441553.i		−	1.47573i	0.674946	−	0.737867i	$-0.264167\pi$
$548$		0			0
$549$	−123751.	−	71447.7i	−0.410586	−	0.237052i
$550$		0			0
$551$	−331512.	+	191399.i	−1.09193	+	0.630429i
$552$		0			0
$553$	−12271.0	−	33248.1i	−0.0401264	−	0.108722i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	28144.5	+	16249.3i	0.0907159	+	0.0523749i	0.544672	−	0.838649i	$-0.316654\pi$
$557$	28144.5	+	16249.3i	0.0907159	+	0.0523749i	−0.453956	+	0.891024i	$0.649988\pi$
$558$		0			0
$559$			85016.5i			0.272069i
$560$		0			0
$561$	27002.9			0.0857994
$562$		0			0
$563$	11647.2	−	20173.6i	0.0367456	−	0.0636452i	−0.847068	−	0.531485i	$-0.821634\pi$
$563$	11647.2	−	20173.6i	0.0367456	−	0.0636452i	0.883813	+	0.467840i	$0.154968\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−203594.	+	244863.i	−0.633284	+	0.761653i
$568$		0			0
$569$	265132.	+	459222.i	0.818913	+	1.41840i	0.906484	+	0.422241i	$0.138756\pi$
$569$	265132.	+	459222.i	0.818913	+	1.41840i	−0.0875701	+	0.996158i	$0.527910\pi$
$570$		0			0
$571$	−40585.1	+	70295.4i	−0.124478	+	0.215603i	−0.921529	−	0.388310i	$-0.873059\pi$
$571$	−40585.1	+	70295.4i	−0.124478	+	0.215603i	0.797051	+	0.603913i	$0.206392\pi$
$572$		0			0
$573$	−28437.4			−0.0866126
$574$		0			0
$575$		0			0
$576$		0			0
$577$	261245.	−	452490.i	0.784688	−	1.35912i	−0.144498	−	0.989505i	$-0.546157\pi$
$577$	261245.	−	452490.i	0.784688	−	1.35912i	0.929185	−	0.369614i	$-0.120510\pi$
$578$		0			0
$579$	−6466.62	+	3733.50i	−0.0192895	+	0.0111368i
$580$		0			0
$581$	391266.	+	67176.9i	1.15910	+	0.199007i
$582$		0			0
$583$	−66388.8	+	38329.6i	−0.195325	+	0.112771i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	534587.			1.55147			0.775733	−	0.631061i	$-0.217380\pi$
$587$	534587.			1.55147			0.775733	+	0.631061i	$0.217380\pi$
$588$		0			0
$589$	461987.			1.33168
$590$		0			0
$591$	25254.7	+	14580.8i	0.0723048	+	0.0417452i
$592$		0			0
$593$	−200296.	−	346922.i	−0.569590	−	0.986559i	−0.996606	−	0.0823148i	$-0.973769\pi$
$593$	−200296.	−	346922.i	−0.569590	−	0.986559i	0.427016	−	0.904244i	$-0.359565\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10206.8	+	5892.87i	−0.0286378	+	0.0165340i
$598$		0			0
$599$	−208037.	+	360331.i	−0.579812	+	1.00426i	0.415689	+	0.909507i	$0.363541\pi$
$599$	−208037.	+	360331.i	−0.579812	+	1.00426i	−0.995500	+	0.0947564i	$0.969793\pi$
$600$		0			0
$601$		−	208179.i		−	0.576351i	−0.957578	−	0.288175i	$-0.906951\pi$
$601$		−	208179.i		−	0.576351i	0.957578	−	0.288175i	$-0.0930486\pi$
$602$		0			0
$603$			482596.i			1.32724i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	242055.	+	419251.i	0.656956	+	1.13788i	0.981400	+	0.191976i	$0.0614895\pi$
$607$	242055.	+	419251.i	0.656956	+	1.13788i	−0.324444	+	0.945905i	$0.605177\pi$
$608$		0			0
$609$	12937.3	−	15559.7i	0.0348825	−	0.0419533i
$610$		0			0
$611$	13110.1	+	22707.3i	0.0351174	+	0.0608252i
$612$		0			0
$613$	−362093.	−	209055.i	−0.963607	−	0.556339i	−0.0663254	−	0.997798i	$-0.521128\pi$
$613$	−362093.	−	209055.i	−0.963607	−	0.556339i	−0.897281	+	0.441460i	$0.854461\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	84089.6i		−	0.220888i	−0.993882	−	0.110444i	$-0.964773\pi$
$617$		−	84089.6i		−	0.220888i	0.993882	−	0.110444i	$-0.0352273\pi$
$618$		0			0
$619$	−268098.	−	154786.i	−0.699701	−	0.403972i	0.107535	−	0.994201i	$-0.465704\pi$
$619$	−268098.	−	154786.i	−0.699701	−	0.403972i	−0.807236	+	0.590229i	$0.799037\pi$
$620$		0			0
$621$	−66188.4	+	38213.9i	−0.171632	+	0.0990919i
$622$		0			0
$623$	−126873.	+	46825.5i	−0.326884	+	0.120644i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−43597.4	−	25171.0i	−0.110898	−	0.0640272i
$628$		0			0
$629$			137766.i			0.348209i
$630$		0			0
$631$	−698410.			−1.75409			−0.877045	−	0.480408i	$-0.840489\pi$
$631$	−698410.			−1.75409			−0.877045	+	0.480408i	$0.840489\pi$
$632$		0			0
$633$	162.685	−	281.780i	0.000406014	−	0.000703237i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−102349.	−	36212.3i	−0.252234	−	0.0892435i
$638$		0			0
$639$	40896.4	+	70834.6i	0.100157	+	0.173478i
$640$		0			0
$641$	−134751.	+	233396.i	−0.327956	+	0.568037i	−0.982106	−	0.188328i	$-0.939693\pi$
$641$	−134751.	+	233396.i	−0.327956	+	0.568037i	0.654150	+	0.756365i	$0.273027\pi$
$642$		0			0
$643$	67730.3			0.163818			0.0819089	−	0.996640i	$-0.473898\pi$
$643$	67730.3			0.163818			0.0819089	+	0.996640i	$0.473898\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−270817.	+	469068.i	−0.646944	+	1.12054i	0.336904	+	0.941539i	$0.390620\pi$
$647$	−270817.	+	469068.i	−0.646944	+	1.12054i	−0.983849	+	0.179002i	$0.942713\pi$
$648$		0			0
$649$	1.12174e6	−	647638.i	2.66320	−	1.53760i
$650$		0			0
$651$	−22911.1	+	8455.88i	−0.0540609	+	0.0199525i
$652$		0			0
$653$	18149.6	−	10478.7i	0.0425637	−	0.0245742i	−0.478567	−	0.878051i	$-0.658844\pi$
$653$	18149.6	−	10478.7i	0.0425637	−	0.0245742i	0.521131	+	0.853477i	$0.325510\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	248990.			0.576834
$658$		0			0
$659$	−352991.			−0.812817			−0.406409	−	0.913691i	$-0.633219\pi$
$659$	−352991.			−0.812817			−0.406409	+	0.913691i	$0.633219\pi$
$660$		0			0
$661$	−331273.	−	191260.i	−0.758199	−	0.437746i	0.0704500	−	0.997515i	$-0.477556\pi$
$661$	−331273.	−	191260.i	−0.758199	−	0.437746i	−0.828649	+	0.559769i	$0.810890\pi$
$662$		0			0
$663$	2875.00	+	4979.64i	0.00654049	+	0.0113285i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−660750.	+	381484.i	−1.48520	+	0.857482i
$668$		0			0
$669$	3567.76	−	6179.54i	0.00797156	−	0.0138071i
$670$		0			0
$671$		−	375796.i		−	0.834655i
$672$		0			0
$673$		−	436693.i		−	0.964153i	−0.876129	−	0.482077i	$-0.839883\pi$
$673$		−	436693.i		−	0.964153i	0.876129	−	0.482077i	$-0.160117\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	217479.	+	376685.i	0.474504	+	0.821865i	0.999574	−	0.0291939i	$-0.00929402\pi$
$677$	217479.	+	376685.i	0.474504	+	0.821865i	−0.525070	+	0.851059i	$0.675961\pi$
$678$		0			0
$679$	−804913.	−	138196.i	−1.74586	−	0.299749i
$680$		0			0
$681$	21268.4	+	36837.9i	0.0458607	+	0.0794330i
$682$		0			0
$683$	−89862.6	−	51882.2i	−0.192636	−	0.111218i	0.400580	−	0.916262i	$-0.368809\pi$
$683$	−89862.6	−	51882.2i	−0.192636	−	0.111218i	−0.593216	+	0.805043i	$0.702142\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			13627.4i			0.0288736i
$688$		0			0
$689$	−14136.8	−	8161.90i	−0.0297792	−	0.0171930i
$690$		0			0
$691$	−268293.	+	154899.i	−0.561893	+	0.324409i	−0.753905	−	0.656984i	$-0.771832\pi$
$691$	−268293.	+	154899.i	−0.561893	+	0.324409i	0.192012	+	0.981393i	$0.438499\pi$
$692$		0			0
$693$	−828026.	−	142165.i	−1.72416	−	0.296023i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−540769.	−	312213.i	−1.11313	−	0.642666i
$698$		0			0
$699$			19841.5i			0.0406088i
$700$		0			0
$701$	−201098.			−0.409234			−0.204617	−	0.978842i	$-0.565595\pi$
$701$	−201098.			−0.409234			−0.204617	+	0.978842i	$0.565595\pi$
$702$		0			0
$703$	128420.	−	222429.i	0.259849	−	0.450071i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−537866.	−	447214.i	−1.07606	−	0.894699i
$708$		0			0
$709$	−380972.	−	659864.i	−0.757881	−	1.31269i	−0.943929	−	0.330148i	$-0.892901\pi$
$709$	−380972.	−	659864.i	−0.757881	−	1.31269i	0.186048	−	0.982541i	$-0.440432\pi$
$710$		0			0
$711$	29200.0	−	50575.9i	0.0577622	−	0.100047i
$712$		0			0
$713$	920805.			1.81129
$714$		0			0
$715$		0			0
$716$		0			0
$717$	237.396	−	411.181i	0.000461779	−	0.000799825i
$718$		0			0
$719$	−116578.	+	67306.3i	−0.225506	+	0.130196i	−0.608497	−	0.793556i	$-0.708227\pi$
$719$	−116578.	+	67306.3i	−0.225506	+	0.130196i	0.382991	+	0.923752i	$0.374894\pi$
$720$		0			0
$721$	−319031.	−	864410.i	−0.613710	−	1.66284i
$722$		0			0
$723$	916.212	−	528.975i	0.00175275	−	0.00101195i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	13108.8			0.0248024			0.0124012	−	0.999923i	$-0.496052\pi$
$727$	13108.8			0.0248024			0.0124012	+	0.999923i	$0.496052\pi$
$728$		0			0
$729$	−521399.			−0.981105
$730$		0			0
$731$	−409430.	−	236384.i	−0.766204	−	0.442368i
$732$		0			0
$733$	362547.	+	627950.i	0.674771	+	1.16874i	0.976536	+	0.215355i	$0.0690908\pi$
$733$	362547.	+	627950.i	0.674771	+	1.16874i	−0.301765	+	0.953382i	$0.597576\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.09913e6	+	634581.i	−2.02355	+	1.16829i
$738$		0			0
$739$	−89456.6	+	154943.i	−0.163804	+	0.283716i	−0.936230	−	0.351388i	$-0.885710\pi$
$739$	−89456.6	+	154943.i	−0.163804	+	0.283716i	0.772426	+	0.635105i	$0.219043\pi$
$740$		0			0
$741$		−	10719.8i		−	0.0195232i
$742$		0			0
$743$			503755.i			0.912518i	0.889847	+	0.456259i	$0.150811\pi$
$743$			503755.i			0.912518i	−0.889847	+	0.456259i	$0.849189\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	327089.	+	566535.i	0.586172	+	1.01528i
$748$		0			0
$749$	−415657.	+	153408.i	−0.740921	+	0.273455i
$750$		0			0
$751$	110955.	+	192179.i	0.196728	+	0.340742i	0.947465	−	0.319858i	$-0.103635\pi$
$751$	110955.	+	192179.i	0.196728	+	0.340742i	−0.750738	+	0.660600i	$0.770302\pi$
$752$		0			0
$753$	33981.0	+	19619.0i	0.0599303	+	0.0346008i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			609454.i			1.06353i	0.846892	+	0.531764i	$0.178471\pi$
$757$			609454.i			1.06353i	−0.846892	+	0.531764i	$0.821529\pi$
$758$		0			0
$759$	−86895.7	−	50169.2i	−0.150839	−	0.0870871i
$760$		0			0
$761$	25738.1	−	14859.9i	0.0444434	−	0.0256594i	−0.477614	−	0.878570i	$-0.658498\pi$
$761$	25738.1	−	14859.9i	0.0444434	−	0.0256594i	0.522057	+	0.852911i	$0.325165\pi$
$762$		0			0
$763$	418498.	−	503328.i	0.718859	−	0.864574i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	238864.	+	137908.i	0.406032	+	0.234423i
$768$		0			0
$769$		−	917153.i		−	1.55092i	−0.631397	−	0.775460i	$-0.717518\pi$
$769$		−	917153.i		−	1.55092i	0.631397	−	0.775460i	$-0.282482\pi$
$770$		0			0
$771$	6032.50			0.0101482
$772$		0			0
$773$	322053.	−	557812.i	0.538975	−	0.933531i	−0.459985	−	0.887927i	$-0.652145\pi$
$773$	322053.	−	557812.i	0.538975	−	0.933531i	0.998960	−	0.0456046i	$-0.0145214\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2297.45	+	13381.3i	−0.00380544	+	0.0221644i
$778$		0			0
$779$	582065.	+	1.00817e6i	0.959172	+	1.66133i
$780$		0			0
$781$	−107552.	+	186285.i	−0.176326	+	0.305405i
$782$		0			0
$783$	66795.5			0.108949
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−432899.	+	749803.i	−0.698935	+	1.21059i	0.269901	+	0.962888i	$0.413009\pi$
$787$	−432899.	+	749803.i	−0.698935	+	1.21059i	−0.968836	+	0.247703i	$0.920324\pi$
$788$		0			0
$789$	−8298.46	+	4791.12i	−0.0133304	+	0.00769632i
$790$		0			0
$791$	−75090.2	+	437356.i	−0.120014	+	0.699008i
$792$		0			0
$793$	69301.1	−	40011.0i	0.110203	−	0.0636258i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	679441.			1.06963			0.534817	−	0.844968i	$-0.320381\pi$
$797$	679441.			1.06963			0.534817	+	0.844968i	$0.320381\pi$
$798$		0			0
$799$	−145808.			−0.228395
$800$		0			0
$801$	−192995.	−	111426.i	−0.300802	−	0.173668i
$802$		0			0
$803$	327405.	+	567082.i	0.507755	+	0.879457i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	37175.2	−	21463.1i	0.0570829	−	0.0329568i
$808$		0			0
$809$	62901.2	−	108948.i	0.0961085	−	0.166465i	−0.813962	−	0.580918i	$-0.802694\pi$
$809$	62901.2	−	108948.i	0.0961085	−	0.166465i	0.910071	+	0.414453i	$0.136027\pi$
$810$		0			0
$811$			977721.i			1.48653i	0.668998	+	0.743265i	$0.266724\pi$
$811$			977721.i			1.48653i	−0.668998	+	0.743265i	$0.733276\pi$
$812$		0			0
$813$			20307.8i			0.0307243i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	440695.	+	763307.i	0.660229	+	1.14355i
$818$		0			0
$819$	−61943.2	−	167834.i	−0.0923476	−	0.250214i
$820$		0			0
$821$	−526935.	−	912679.i	−0.781756	−	1.35404i	−0.930918	−	0.365228i	$-0.880991\pi$
$821$	−526935.	−	912679.i	−0.781756	−	1.35404i	0.149162	−	0.988813i	$-0.452342\pi$
$822$		0			0
$823$	477455.	+	275659.i	0.704909	+	0.406979i	0.809173	−	0.587570i	$-0.199915\pi$
$823$	477455.	+	275659.i	0.704909	+	0.406979i	−0.104264	+	0.994550i	$0.533249\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	172431.i		−	0.252119i	−0.992023	−	0.126059i	$-0.959767\pi$
$827$		−	172431.i		−	0.252119i	0.992023	−	0.126059i	$-0.0402330\pi$
$828$		0			0
$829$	−200582.	−	115806.i	−0.291865	−	0.168508i	0.346918	−	0.937896i	$-0.387228\pi$
$829$	−200582.	−	115806.i	−0.291865	−	0.168508i	−0.638783	+	0.769387i	$0.720562\pi$
$830$		0			0
$831$	28317.4	−	16349.0i	0.0410063	−	0.0236750i
$832$		0			0
$833$	458970.	−	392214.i	0.661446	−	0.565240i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−69813.4	−	40306.8i	−0.0996525	−	0.0575344i
$838$		0			0
$839$		−	250894.i		−	0.356424i	−0.983992	−	0.178212i	$-0.942969\pi$
$839$		−	250894.i		−	0.356424i	0.983992	−	0.178212i	$-0.0570312\pi$
$840$		0			0
$841$	−40470.2			−0.0572194
$842$		0			0
$843$	7951.49	−	13772.4i	0.0111891	−	0.0193800i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−516615.	−	1.39976e6i	−0.720112	−	1.95113i
$848$		0			0
$849$	36679.2	+	63530.2i	0.0508867	+	0.0881383i
$850$		0			0
$851$	255958.	−	443333.i	0.353435	−	0.612168i
$852$		0			0
$853$	−1.44175e6			−1.98150			−0.990748	−	0.135711i	$-0.956668\pi$
$853$	−1.44175e6			−1.98150			−0.990748	+	0.135711i	$0.956668\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	69114.7	−	119710.i	0.0941041	−	0.162993i	−0.815130	−	0.579278i	$-0.803335\pi$
$857$	69114.7	−	119710.i	0.0941041	−	0.162993i	0.909234	+	0.416285i	$0.136668\pi$
$858$		0			0
$859$	405697.	−	234229.i	0.549813	−	0.317435i	−0.199234	−	0.979952i	$-0.563845\pi$
$859$	405697.	−	234229.i	0.549813	−	0.317435i	0.749047	+	0.662517i	$0.230512\pi$
$860$		0			0
$861$	−47318.7	−	39343.7i	−0.0638303	−	0.0530724i
$862$		0			0
$863$	−595253.	+	343669.i	−0.799245	+	0.461444i	−0.843207	−	0.537589i	$-0.819335\pi$
$863$	−595253.	+	343669.i	−0.799245	+	0.461444i	0.0439621	+	0.999033i	$0.486002\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	10263.8			0.0136543
$868$		0			0
$869$	153584.			0.203379
$870$		0			0
$871$	−234048.	−	135128.i	−0.308510	−	0.178118i
$872$		0			0
$873$	−672888.	−	1.16548e6i	−0.882906	−	1.52924i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−182571.	+	105408.i	−0.237374	+	0.137048i	−0.613969	−	0.789330i	$-0.710428\pi$
$877$	−182571.	+	105408.i	−0.237374	+	0.137048i	0.376595	+	0.926378i	$0.377095\pi$
$878$		0			0
$879$	16653.8	−	28845.3i	0.0215544	−	0.0373333i
$880$		0			0
$881$		−	367667.i		−	0.473699i	−0.971546	−	0.236850i	$-0.923885\pi$
$881$		−	367667.i		−	0.473699i	0.971546	−	0.236850i	$-0.0761149\pi$
$882$		0			0
$883$		−	1.11838e6i		−	1.43439i	−0.696872	−	0.717196i	$-0.745425\pi$
$883$		−	1.11838e6i		−	1.43439i	0.696872	−	0.717196i	$-0.254575\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	642118.	+	1.11218e6i	0.816145	+	1.41360i	0.908503	+	0.417879i	$0.137226\pi$
$887$	642118.	+	1.11218e6i	0.816145	+	1.41360i	−0.0923576	+	0.995726i	$0.529440\pi$
$888$		0			0
$889$	−249515.	+	1.45328e6i	−0.315713	+	1.83884i
$890$		0			0
$891$	−690011.	−	1.19513e6i	−0.869161	−	1.50543i
$892$		0			0
$893$	235413.	+	135916.i	0.295208	+	0.170438i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	21366.1i		−	0.0265546i
$898$		0			0
$899$	−696938.	−	402378.i	−0.862333	−	0.497868i
$900$		0			0
$901$	78613.5	−	45387.5i	0.0968384	−	0.0559097i
$902$		0			0
$903$	−35826.2	−	29788.1i	−0.0439364	−	0.0365314i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	340115.	+	196365.i	0.413439	+	0.238699i	0.692266	−	0.721642i	$-0.256612\pi$
$907$	340115.	+	196365.i	0.413439	+	0.238699i	−0.278827	+	0.960341i	$0.589946\pi$
$908$		0			0
$909$		−	1.15267e6i		−	1.39500i
$910$		0			0
$911$	−582974.			−0.702445			−0.351223	−	0.936292i	$-0.614234\pi$
$911$	−582974.			−0.702445			−0.351223	+	0.936292i	$0.614234\pi$
$912$		0			0
$913$	−860200.	+	1.48991e6i	−1.03195	+	1.78739i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−833817.	+	307740.i	−0.991589	+	0.365970i
$918$		0			0
$919$	268690.	+	465385.i	0.318142	+	0.551038i	0.980100	−	0.198503i	$-0.0636078\pi$
$919$	268690.	+	465385.i	0.318142	+	0.551038i	−0.661958	+	0.749541i	$0.730274\pi$
$920$		0			0
$921$	19125.9	−	33127.0i	0.0225477	−	0.0390537i
$922$		0			0
$923$	−45804.2			−0.0537653
$924$		0			0
$925$		0			0
$926$		0			0
$927$	759164.	−	1.31491e6i	0.883438	−	1.53016i
$928$		0			0
$929$	742125.	−	428466.i	0.859896	−	0.496461i	−0.00408163	−	0.999992i	$-0.501299\pi$
$929$	742125.	−	428466.i	0.859896	−	0.496461i	0.863977	+	0.503531i	$0.167966\pi$
$930$		0			0
$931$	−1.10663e6	+	205414.i	−1.27675	+	0.236991i
$932$		0			0
$933$	12226.6	−	7059.04i	0.0140457	−	0.00810929i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.10816e6			−1.26218			−0.631092	−	0.775708i	$-0.717393\pi$
$937$	−1.10816e6			−1.26218			−0.631092	+	0.775708i	$0.717393\pi$
$938$		0			0
$939$	24475.8			0.0277591
$940$		0			0
$941$	1.03129e6	+	595418.i	1.16467	+	0.672424i	0.952419	−	0.304791i	$-0.0985866\pi$
$941$	1.03129e6	+	595418.i	1.16467	+	0.672424i	0.212253	+	0.977215i	$0.431920\pi$
$942$		0			0
$943$	1.16014e6	+	2.00941e6i	1.30462	+	2.25968i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−407696.	+	235384.i	−0.454608	+	0.262468i	−0.709774	−	0.704429i	$-0.751203\pi$
$947$	−407696.	+	235384.i	−0.454608	+	0.262468i	0.255166	+	0.966897i	$0.417870\pi$
$948$		0			0
$949$	−69717.6	+	120754.i	−0.0774124	+	0.134082i
$950$		0			0
$951$			2593.78i			0.00286795i
$952$		0			0
$953$		−	987964.i		−	1.08782i	−0.839145	−	0.543908i	$-0.816944\pi$
$953$		−	987964.i		−	1.08782i	0.839145	−	0.543908i	$-0.183056\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	43846.4	+	75944.1i	0.0478751	+	0.0829221i
$958$		0			0
$959$	969636.	+	806214.i	1.05432	+	0.876624i
$960$		0			0
$961$	23857.6	+	41322.6i	0.0258333	+	0.0447447i
$962$		0			0
$963$	−632284.	−	365049.i	−0.681804	−	0.393640i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	498312.i		−	0.532903i	−0.963848	−	0.266451i	$-0.914149\pi$
$967$		−	498312.i		−	0.532903i	0.963848	−	0.266451i	$-0.0858512\pi$
$968$		0			0
$969$	51625.4	+	29805.9i	0.0549814	+	0.0317435i
$970$		0			0
$971$	−575246.	+	332118.i	−0.610119	+	0.352253i	−0.773012	−	0.634391i	$-0.781251\pi$
$971$	−575246.	+	332118.i	−0.610119	+	0.352253i	0.162893	+	0.986644i	$0.447918\pi$
$972$		0			0
$973$	−62261.4	+	362636.i	−0.0657648	+	0.383041i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	625763.	+	361284.i	0.655572	+	0.378495i	0.790588	−	0.612349i	$-0.209775\pi$
$977$	625763.	+	361284.i	0.655572	+	0.378495i	−0.135016	+	0.990843i	$0.543108\pi$
$978$		0			0
$979$		−	586069.i		−	0.611481i
$980$		0			0
$981$	1.07865e6			1.12084
$982$		0			0
$983$	533658.	−	924322.i	0.552276	−	0.956569i	−0.445834	−	0.895115i	$-0.647093\pi$
$983$	533658.	−	924322.i	0.552276	−	0.956569i	0.998110	−	0.0614538i	$-0.0195737\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−14162.4	−	2431.56i	−0.0145380	−	0.00249604i
$988$		0			0
$989$	878368.	+	1.52138e6i	0.898015	+	1.55541i
$990$		0			0
$991$	775245.	−	1.34276e6i	0.789391	−	1.36726i	−0.136950	−	0.990578i	$-0.543730\pi$
$991$	775245.	−	1.34276e6i	0.789391	−	1.36726i	0.926341	−	0.376687i	$-0.122937\pi$
$992$		0			0
$993$	−39125.5			−0.0396791
$994$		0			0
$995$		0			0
$996$		0			0
$997$	802368.	−	1.38974e6i	0.807204	−	1.39812i	−0.107589	−	0.994195i	$-0.534313\pi$
$997$	802368.	−	1.38974e6i	0.807204	−	1.39812i	0.914793	−	0.403923i	$-0.132354\pi$
$998$		0			0
$999$	−38812.4	+	22408.3i	−0.0388901	+	0.0224532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.b.549.11		40
5.2	odd	4		700.5.s.b.101.6		20
5.3	odd	4		140.5.r.a.101.5	yes	20
5.4	even	2	inner	700.5.o.b.549.10		40
7.5	odd	6	inner	700.5.o.b.649.10		40
35.3	even	12		980.5.d.a.881.11		20
35.12	even	12		700.5.s.b.201.6		20
35.18	odd	12		980.5.d.a.881.10		20
35.19	odd	6	inner	700.5.o.b.649.11		40
35.33	even	12		140.5.r.a.61.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.5.r.a.61.5	✓	20	35.33	even	12
140.5.r.a.101.5	yes	20	5.3	odd	4
700.5.o.b.549.10		40	5.4	even	2	inner
700.5.o.b.549.11		40	1.1	even	1	trivial
700.5.o.b.649.10		40	7.5	odd	6	inner
700.5.o.b.649.11		40	35.19	odd	6	inner
700.5.s.b.101.6		20	5.2	odd	4
700.5.s.b.201.6		20	35.12	even	12
980.5.d.a.881.10		20	35.18	odd	12
980.5.d.a.881.11		20	35.3	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.252864 - 0.437973i) q^{3} +(48.2934 + 8.29155i) q^{7} +(40.3721 + 69.9266i) q^{9} +(-106.173 + 183.897i) q^{11} -45.2171 q^{13} +(125.724 - 217.760i) q^{17} +(-405.974 + 234.389i) q^{19} +(15.8431 - 19.0546i) q^{21} +(-809.163 + 467.170i) q^{23} +81.7986 q^{27} +816.585 q^{29} +(-853.479 - 492.757i) q^{31} +(53.6948 + 93.0021i) q^{33} +(-474.487 + 273.945i) q^{37} +(-11.4338 + 19.8039i) q^{39} -2483.32i q^{41} -1880.19i q^{43} +(-289.936 - 502.185i) q^{47} +(2263.50 + 800.854i) q^{49} +(-63.5821 - 110.127i) q^{51} +(312.644 + 180.505i) q^{53} +237.075i q^{57} +(-5282.61 - 3049.91i) q^{59} +(-1532.63 + 884.865i) q^{61} +(1369.91 + 3711.74i) q^{63} +(5176.10 + 2988.43i) q^{67} +472.523i q^{69} +1012.99 q^{71} +(1541.84 - 2670.55i) q^{73} +(-6652.26 + 8000.69i) q^{77} +(-361.636 - 626.371i) q^{79} +(-3249.46 + 5628.23i) q^{81} +8101.85 q^{83} +(206.485 - 357.643i) q^{87} +(-2390.20 + 1379.98i) q^{89} +(-2183.69 - 374.920i) q^{91} +(-431.629 + 249.201i) q^{93} -16667.1 q^{97} -17145.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 468 q^{9} - 300 q^{11} - 1956 q^{19} - 5152 q^{21} + 624 q^{29} + 10392 q^{31} + 13440 q^{39} + 16384 q^{49} + 4264 q^{51} - 20016 q^{59} + 4416 q^{61} - 59664 q^{71} - 18664 q^{79} + 14132 q^{81}+ \cdots - 6120 q^{99}+O(q^{100}) \) 40 * q - 468 * q^9 - 300 * q^11 - 1956 * q^19 - 5152 * q^21 + 624 * q^29 + 10392 * q^31 + 13440 * q^39 + 16384 * q^49 + 4264 * q^51 - 20016 * q^59 + 4416 * q^61 - 59664 * q^71 - 18664 * q^79 + 14132 * q^81 + 32112 * q^89 + 14512 * q^91 - 6120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more