LMFDB - Embedded newform 1050.3.q.c.649.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.8
Root			$-0.159959 - 0.596975i$ of defining polynomial
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.c.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(4.79227 + 5.10237i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(4.79227 + 5.10237i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(9.03504 + 15.6491i) q^{11} +(-1.73205 + 3.00000i) q^{12} -18.6604 q^{13} +(2.26139 + 9.63774i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-0.770543 - 1.33462i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(-29.4836 - 17.0224i) q^{19} +(-3.50333 + 11.6072i) q^{21} +25.5549i q^{22} +(23.3720 + 13.4938i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-22.8542 - 13.1949i) q^{26} -5.19615 q^{27} +(-4.04529 + 13.4028i) q^{28} +16.4662 q^{29} +(-24.1988 + 13.9712i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-15.6491 + 27.1051i) q^{33} -2.17942i q^{34} -6.00000 q^{36} +(44.7480 + 25.8353i) q^{37} +(-24.0733 - 41.6961i) q^{38} +(-16.1604 - 27.9906i) q^{39} -37.4818i q^{41} +(-12.4982 + 11.7386i) q^{42} -63.6947i q^{43} +(-18.0701 + 31.2983i) q^{44} +(19.0831 + 33.0529i) q^{46} +(-14.1204 + 24.4572i) q^{47} -6.92820 q^{48} +(-3.06832 + 48.9038i) q^{49} +(1.33462 - 2.31163i) q^{51} +(-18.6604 - 32.3208i) q^{52} +(0.384239 - 0.221841i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-14.4317 + 13.5546i) q^{56} -58.9672i q^{57} +(20.1669 + 11.6434i) q^{58} +(-64.2260 + 37.0809i) q^{59} +(91.0443 + 52.5645i) q^{61} -39.5164 q^{62} +(-20.4447 + 4.79713i) q^{63} -8.00000 q^{64} +(-38.3324 + 22.1312i) q^{66} +(11.0062 - 6.35442i) q^{67} +(1.54109 - 2.66924i) q^{68} +46.7439i q^{69} -45.7647 q^{71} +(-7.34847 - 4.24264i) q^{72} +(18.2133 + 31.5463i) q^{73} +(36.5366 + 63.2833i) q^{74} -68.0895i q^{76} +(-36.5494 + 121.095i) q^{77} -45.7085i q^{78} +(-66.5990 + 115.353i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(26.5037 - 45.9057i) q^{82} -49.9265 q^{83} +(-23.6076 + 5.53924i) q^{84} +(45.0389 - 78.0097i) q^{86} +(14.2602 + 24.6994i) q^{87} +(-44.2625 + 25.5549i) q^{88} +(-85.9133 - 49.6020i) q^{89} +(-89.4257 - 95.2123i) q^{91} +53.9752i q^{92} +(-41.9135 - 24.1988i) q^{93} +(-34.5878 + 19.9693i) q^{94} +(-8.48528 - 4.89898i) q^{96} +150.376 q^{97} +(-38.3381 + 57.7251i) q^{98} -54.2102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	4.79227	+	5.10237i	0.684610	+	0.728910i
$7$	4.79227	+	5.10237i	0.684610	+	0.728910i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	9.03504	+	15.6491i	0.821367	+	1.42265i	0.904664	+	0.426125i	$0.140122\pi$
$11$	9.03504	+	15.6491i	0.821367	+	1.42265i	−0.0832974	+	0.996525i	$0.526545\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	−18.6604			−1.43542			−0.717708	−	0.696344i	$-0.754809\pi$
$13$	−18.6604			−1.43542			−0.717708	+	0.696344i	$0.754809\pi$
$14$	2.26139	+	9.63774i	0.161528	+	0.688410i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−0.770543	−	1.33462i	−0.0453261	−	0.0785070i	0.842472	−	0.538740i	$-0.181099\pi$
$17$	−0.770543	−	1.33462i	−0.0453261	−	0.0785070i	−0.887798	+	0.460233i	$0.847766\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	−29.4836	−	17.0224i	−1.55177	−	0.895914i	−0.997998	−	0.0632454i	$-0.979855\pi$
$19$	−29.4836	−	17.0224i	−1.55177	−	0.895914i	−0.553771	−	0.832669i	$-0.686812\pi$
$20$		0			0
$21$	−3.50333	+	11.6072i	−0.166825	+	0.552723i
$22$			25.5549i			1.16159i
$23$	23.3720	+	13.4938i	1.01617	+	0.586687i	0.912993	−	0.407975i	$-0.133765\pi$
$23$	23.3720	+	13.4938i	1.01617	+	0.586687i	0.103179	+	0.994663i	$0.467098\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$		0			0
$26$	−22.8542	−	13.1949i	−0.879009	−	0.507496i
$27$	−5.19615			−0.192450
$28$	−4.04529	+	13.4028i	−0.144475	+	0.478672i
$29$	16.4662			0.567802			0.283901	−	0.958854i	$-0.408371\pi$
$29$	16.4662			0.567802			0.283901	+	0.958854i	$0.408371\pi$
$30$		0			0
$31$	−24.1988	+	13.9712i	−0.780605	+	0.450683i	−0.836645	−	0.547746i	$-0.815486\pi$
$31$	−24.1988	+	13.9712i	−0.780605	+	0.450683i	0.0560395	+	0.998429i	$0.482153\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	−15.6491	+	27.1051i	−0.474216	+	0.821367i
$34$		−	2.17942i		−	0.0641007i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	44.7480	+	25.8353i	1.20941	+	0.698251i	0.962630	−	0.270821i	$-0.0872953\pi$
$37$	44.7480	+	25.8353i	1.20941	+	0.698251i	0.246777	+	0.969072i	$0.420629\pi$
$38$	−24.0733	−	41.6961i	−0.633507	−	1.09727i
$39$	−16.1604	−	27.9906i	−0.414369	−	0.717708i
$40$		0			0
$41$		−	37.4818i		−	0.914191i	−0.889418	−	0.457095i	$-0.848890\pi$
$41$		−	37.4818i		−	0.914191i	0.889418	−	0.457095i	$-0.151110\pi$
$42$	−12.4982	+	11.7386i	−0.297576	+	0.279491i
$43$		−	63.6947i		−	1.48127i	−0.671907	−	0.740636i	$-0.734524\pi$
$43$		−	63.6947i		−	1.48127i	0.671907	−	0.740636i	$-0.265476\pi$
$44$	−18.0701	+	31.2983i	−0.410684	+	0.711325i
$45$		0			0
$46$	19.0831	+	33.0529i	0.414851	+	0.718542i
$47$	−14.1204	+	24.4572i	−0.300434	+	0.520367i	−0.976234	−	0.216718i	$-0.930465\pi$
$47$	−14.1204	+	24.4572i	−0.300434	+	0.520367i	0.675800	+	0.737085i	$0.263798\pi$
$48$	−6.92820			−0.144338
$49$	−3.06832	+	48.9038i	−0.0626188	+	0.998038i
$50$		0			0
$51$	1.33462	−	2.31163i	0.0261690	−	0.0453261i
$52$	−18.6604	−	32.3208i	−0.358854	−	0.621553i
$53$	0.384239	−	0.221841i	0.00724980	−	0.00418567i	−0.496371	−	0.868111i	$-0.665334\pi$
$53$	0.384239	−	0.221841i	0.00724980	−	0.00418567i	0.503621	+	0.863925i	$0.332001\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−14.4317	+	13.5546i	−0.257709	+	0.242046i
$57$		−	58.9672i		−	1.03451i
$58$	20.1669	+	11.6434i	0.347706	+	0.200748i
$59$	−64.2260	+	37.0809i	−1.08858	+	0.628490i	−0.933197	−	0.359365i	$-0.882993\pi$
$59$	−64.2260	+	37.0809i	−1.08858	+	0.628490i	−0.155379	+	0.987855i	$0.549660\pi$
$60$		0			0
$61$	91.0443	+	52.5645i	1.49253	+	0.861712i	0.999963	−	0.00856246i	$-0.00272555\pi$
$61$	91.0443	+	52.5645i	1.49253	+	0.861712i	0.492566	+	0.870275i	$0.336059\pi$
$62$	−39.5164			−0.637361
$63$	−20.4447	+	4.79713i	−0.324520	+	0.0761449i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−38.3324	+	22.1312i	−0.580794	+	0.335322i
$67$	11.0062	−	6.35442i	0.164271	−	0.0948420i	−0.415611	−	0.909543i	$-0.636432\pi$
$67$	11.0062	−	6.35442i	0.164271	−	0.0948420i	0.579882	+	0.814701i	$0.303099\pi$
$68$	1.54109	−	2.66924i	0.0226630	−	0.0392535i
$69$			46.7439i			0.677448i
$70$		0			0
$71$	−45.7647			−0.644573			−0.322286	−	0.946642i	$-0.604451\pi$
$71$	−45.7647			−0.644573			−0.322286	+	0.946642i	$0.604451\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	18.2133	+	31.5463i	0.249497	+	0.432141i	0.963386	−	0.268117i	$-0.0864015\pi$
$73$	18.2133	+	31.5463i	0.249497	+	0.432141i	−0.713889	+	0.700258i	$0.753068\pi$
$74$	36.5366	+	63.2833i	0.493738	+	0.855179i
$75$		0			0
$76$		−	68.0895i		−	0.895914i
$77$	−36.5494	+	121.095i	−0.474667	+	1.57266i
$78$		−	45.7085i		−	0.586006i
$79$	−66.5990	+	115.353i	−0.843025	+	1.46016i	0.0442994	+	0.999018i	$0.485894\pi$
$79$	−66.5990	+	115.353i	−0.843025	+	1.46016i	−0.887325	+	0.461145i	$0.847439\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	26.5037	−	45.9057i	0.323215	−	0.559825i
$83$	−49.9265			−0.601524			−0.300762	−	0.953699i	$-0.597241\pi$
$83$	−49.9265			−0.601524			−0.300762	+	0.953699i	$0.597241\pi$
$84$	−23.6076	+	5.53924i	−0.281042	+	0.0659434i
$85$		0			0
$86$	45.0389	−	78.0097i	0.523709	−	0.907090i
$87$	14.2602	+	24.6994i	0.163910	+	0.283901i
$88$	−44.2625	+	25.5549i	−0.502983	+	0.290397i
$89$	−85.9133	−	49.6020i	−0.965318	−	0.557326i	−0.0675121	−	0.997718i	$-0.521506\pi$
$89$	−85.9133	−	49.6020i	−0.965318	−	0.557326i	−0.897806	+	0.440392i	$0.854839\pi$
$90$		0			0
$91$	−89.4257	−	95.2123i	−0.982700	−	1.04629i
$92$			53.9752i			0.586687i
$93$	−41.9135	−	24.1988i	−0.450683	−	0.260202i
$94$	−34.5878	+	19.9693i	−0.367955	+	0.212439i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$	150.376			1.55027			0.775134	−	0.631796i	$-0.217682\pi$
$97$	150.376			1.55027			0.775134	+	0.631796i	$0.217682\pi$
$98$	−38.3381	+	57.7251i	−0.391206	+	0.589032i
$99$	−54.2102			−0.547578
$100$		0			0
$101$	40.7726	−	23.5401i	0.403689	−	0.233070i	−0.284386	−	0.958710i	$-0.591790\pi$
$101$	40.7726	−	23.5401i	0.403689	−	0.233070i	0.688074	+	0.725640i	$0.258456\pi$
$102$	3.26914	−	1.88744i	0.0320504	−	0.0185043i
$103$	37.9728	−	65.7708i	0.368668	−	0.638552i	−0.620690	−	0.784056i	$-0.713147\pi$
$103$	37.9728	−	65.7708i	0.368668	−	0.638552i	0.989358	+	0.145505i	$0.0464806\pi$
$104$		−	52.7796i		−	0.507496i
$105$		0			0
$106$	0.627460			0.00591944
$107$	−92.8597	−	53.6125i	−0.867847	−	0.501052i	−0.00121497	−	0.999999i	$-0.500387\pi$
$107$	−92.8597	−	53.6125i	−0.867847	−	0.501052i	−0.866632	+	0.498947i	$0.833720\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	40.4452	+	70.0532i	0.371057	+	0.642690i	0.989728	−	0.142960i	$-0.0456621\pi$
$109$	40.4452	+	70.0532i	0.371057	+	0.642690i	−0.618671	+	0.785650i	$0.712329\pi$
$110$		0			0
$111$			89.4961i			0.806271i
$112$	−27.2597	+	6.39617i	−0.243390	+	0.0571087i
$113$		−	79.9061i		−	0.707134i	−0.935409	−	0.353567i	$-0.884969\pi$
$113$		−	79.9061i		−	0.707134i	0.935409	−	0.353567i	$-0.115031\pi$
$114$	41.6961	−	72.2198i	0.365755	−	0.633507i
$115$		0			0
$116$	16.4662	+	28.5204i	0.141950	+	0.245865i
$117$	27.9906	−	48.4812i	0.239236	−	0.414369i
$118$	−104.881			−0.888819
$119$	3.11707	−	10.3275i	0.0261939	−	0.0867853i
$120$		0			0
$121$	−102.764	+	177.992i	−0.849288	+	1.47101i
$122$	74.3374	+	128.756i	0.609323	+	1.05538i
$123$	56.2227	−	32.4602i	0.457095	−	0.263904i
$124$	−48.3975	−	27.9423i	−0.390303	−	0.225341i
$125$		0			0
$126$	−28.4317	−	8.58136i	−0.225648	−	0.0681060i
$127$		−	99.1937i		−	0.781053i	−0.920592	−	0.390526i	$-0.872293\pi$
$127$		−	99.1937i		−	0.781053i	0.920592	−	0.390526i	$-0.127707\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	95.5420	−	55.1612i	0.740636	−	0.427606i
$130$		0			0
$131$	144.309	+	83.3170i	1.10160	+	0.636008i	0.936640	−	0.350293i	$-0.113918\pi$
$131$	144.309	+	83.3170i	1.10160	+	0.636008i	0.164958	+	0.986301i	$0.447251\pi$
$132$	−62.5966			−0.474216
$133$	−54.4390	−	232.012i	−0.409316	−	1.74445i
$134$	17.9730			0.134127
$135$		0			0
$136$	3.77487	−	2.17942i	0.0277564	−	0.0160252i
$137$	131.218	−	75.7587i	0.957795	−	0.552983i	0.0623012	−	0.998057i	$-0.480156\pi$
$137$	131.218	−	75.7587i	0.957795	−	0.552983i	0.895494	+	0.445074i	$0.146823\pi$
$138$	−33.0529	+	57.2494i	−0.239514	+	0.414851i
$139$			151.816i			1.09220i	0.837719	+	0.546101i	$0.183889\pi$
$139$			151.816i			1.09220i	−0.837719	+	0.546101i	$0.816111\pi$
$140$		0			0
$141$	−48.9145			−0.346911
$142$	−56.0500	−	32.3605i	−0.394719	−	0.227891i
$143$	−168.597	−	292.019i	−1.17900	−	2.04209i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$			51.5149i			0.352842i
$147$	−76.0130	+	37.7495i	−0.517095	+	0.256799i
$148$			103.341i			0.698251i
$149$	16.5970	−	28.7468i	0.111389	−	0.192931i	−0.804941	−	0.593354i	$-0.797803\pi$
$149$	16.5970	−	28.7468i	0.111389	−	0.192931i	0.916331	+	0.400423i	$0.131137\pi$
$150$		0			0
$151$	4.65158	+	8.05678i	0.0308052	+	0.0533562i	0.881017	−	0.473085i	$-0.156860\pi$
$151$	4.65158	+	8.05678i	0.0308052	+	0.0533562i	−0.850212	+	0.526441i	$0.823526\pi$
$152$	48.1465	−	83.3923i	0.316754	−	0.548633i
$153$	4.62326			0.0302174
$154$	−130.391	+	122.466i	−0.846693	+	0.795235i
$155$		0			0
$156$	32.3208	−	55.9812i	0.207184	−	0.358854i
$157$	11.9942	+	20.7746i	0.0763963	+	0.132322i	0.901693	−	0.432378i	$-0.142325\pi$
$157$	11.9942	+	20.7746i	0.0763963	+	0.132322i	−0.825296	+	0.564700i	$0.808992\pi$
$158$	−163.134	+	94.1852i	−1.03249	+	0.596109i
$159$	0.665522	+	0.384239i	0.00418567	+	0.00241660i
$160$		0			0
$161$	43.1543	+	183.918i	0.268039	+	1.14235i
$162$		−	12.7279i		−	0.0785674i
$163$	219.215	+	126.564i	1.34488	+	0.776464i	0.987518	−	0.157504i	$-0.0503446\pi$
$163$	219.215	+	126.564i	1.34488	+	0.776464i	0.357357	+	0.933968i	$0.383678\pi$
$164$	64.9204	−	37.4818i	0.395856	−	0.228548i
$165$		0			0
$166$	−61.1472	−	35.3033i	−0.368357	−	0.212671i
$167$	85.7259			0.513329			0.256664	−	0.966501i	$-0.417376\pi$
$167$	85.7259			0.513329			0.256664	+	0.966501i	$0.417376\pi$
$168$	−32.8301	−	9.90890i	−0.195417	−	0.0589816i
$169$	179.211			1.06042
$170$		0			0
$171$	88.4508	−	51.0671i	0.517256	−	0.298638i
$172$	110.322	−	63.6947i	0.641409	−	0.370318i
$173$	9.73826	−	16.8672i	0.0562905	−	0.0974980i	−0.836507	−	0.547956i	$-0.815406\pi$
$173$	9.73826	−	16.8672i	0.0562905	−	0.0974980i	0.892798	+	0.450458i	$0.148739\pi$
$174$			40.3339i			0.231804i
$175$		0			0
$176$	−72.2803			−0.410684
$177$	−111.243	−	64.2260i	−0.628490	−	0.362859i
$178$	−70.1479	−	121.500i	−0.394089	−	0.682583i
$179$	126.417	+	218.961i	0.706241	+	1.22324i	0.966242	+	0.257637i	$0.0829437\pi$
$179$	126.417	+	218.961i	0.706241	+	1.22324i	−0.260001	+	0.965608i	$0.583723\pi$
$180$		0			0
$181$			144.224i			0.796820i	0.917207	+	0.398410i	$0.130438\pi$
$181$			144.224i			0.796820i	−0.917207	+	0.398410i	$0.869562\pi$
$182$	−42.1984	−	179.844i	−0.231859	−	0.988155i
$183$			182.089i			0.995020i
$184$	−38.1663	+	66.1059i	−0.207425	+	0.359271i
$185$		0			0
$186$	−34.2222	−	59.2746i	−0.183990	−	0.318681i
$187$	13.9238	−	24.1167i	0.0744587	−	0.128966i
$188$	−56.4816			−0.300434
$189$	−24.9014	−	26.5127i	−0.131753	−	0.140279i
$190$		0			0
$191$	157.049	−	272.017i	0.822246	−	1.42417i	−0.0817601	−	0.996652i	$-0.526054\pi$
$191$	157.049	−	272.017i	0.822246	−	1.42417i	0.904006	−	0.427520i	$-0.140613\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	45.7507	−	26.4142i	0.237050	−	0.136861i	−0.376770	−	0.926307i	$-0.622965\pi$
$193$	45.7507	−	26.4142i	0.237050	−	0.136861i	0.613820	+	0.789446i	$0.289632\pi$
$194$	184.172	+	106.332i	0.949342	+	0.548103i
$195$		0			0
$196$	−87.7723	+	43.5893i	−0.447818	+	0.222395i
$197$		−	54.2005i		−	0.275129i	−0.990493	−	0.137565i	$-0.956073\pi$
$197$		−	54.2005i		−	0.275129i	0.990493	−	0.137565i	$-0.0439275\pi$
$198$	−66.3937	−	38.3324i	−0.335322	−	0.193598i
$199$	−19.8934	+	11.4855i	−0.0999670	+	0.0577160i	−0.549150	−	0.835724i	$-0.685048\pi$
$199$	−19.8934	+	11.4855i	−0.0999670	+	0.0577160i	0.449183	+	0.893440i	$0.351715\pi$
$200$		0			0
$201$	19.0632	+	11.0062i	0.0948420	+	0.0547571i
$202$	66.5813			0.329611
$203$	78.9107	+	84.0168i	0.388722	+	0.413876i
$204$	5.33848			0.0261690
$205$		0			0
$206$	93.0140	−	53.7017i	0.451524	−	0.260688i
$207$	−70.1159	+	40.4814i	−0.338724	+	0.195562i
$208$	37.3208	−	64.6415i	0.179427	−	0.310777i
$209$		−	615.191i		−	2.94350i
$210$		0			0
$211$	−292.203			−1.38485			−0.692425	−	0.721490i	$-0.743457\pi$
$211$	−292.203			−1.38485			−0.692425	+	0.721490i	$0.743457\pi$
$212$	0.768479	+	0.443681i	0.00362490	+	0.00209284i
$213$	−39.6334	−	68.6470i	−0.186072	−	0.322286i
$214$	−75.8196	−	131.323i	−0.354297	−	0.613661i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−187.253	−	56.5174i	−0.862917	−	0.260449i
$218$			114.396i			0.524754i
$219$	−31.5463	+	54.6398i	−0.144047	+	0.249497i
$220$		0			0
$221$	14.3786	+	24.9045i	0.0650617	+	0.112690i
$222$	−63.2833	+	109.610i	−0.285060	+	0.493738i
$223$	271.305			1.21661			0.608306	−	0.793702i	$-0.291849\pi$
$223$	271.305			1.21661			0.608306	+	0.793702i	$0.291849\pi$
$224$	−37.9089	−	11.4418i	−0.169236	−	0.0510795i
$225$		0			0
$226$	56.5021	−	97.8646i	0.250009	−	0.433029i
$227$	−74.3044	−	128.699i	−0.327332	−	0.566956i	0.654649	−	0.755933i	$-0.272816\pi$
$227$	−74.3044	−	128.699i	−0.327332	−	0.566956i	−0.981982	+	0.188977i	$0.939483\pi$
$228$	102.134	−	58.9672i	0.447957	−	0.258628i
$229$	−21.9394	−	12.6667i	−0.0958053	−	0.0553132i	0.451332	−	0.892356i	$-0.350949\pi$
$229$	−21.9394	−	12.6667i	−0.0958053	−	0.0553132i	−0.547137	+	0.837043i	$0.684282\pi$
$230$		0			0
$231$	−213.295	+	50.0473i	−0.923356	+	0.216655i
$232$			46.5736i			0.200748i
$233$	354.106	+	204.443i	1.51977	+	0.877438i	0.999729	+	0.0232943i	$0.00741547\pi$
$233$	354.106	+	204.443i	1.51977	+	0.877438i	0.520038	+	0.854143i	$0.325918\pi$
$234$	68.5627	−	39.5847i	0.293003	−	0.169165i
$235$		0			0
$236$	−128.452	−	74.1618i	−0.544288	−	0.314245i
$237$	−230.706			−0.973442
$238$	11.1202	−	10.4444i	0.0467236	−	0.0438840i
$239$	−67.0352			−0.280482			−0.140241	−	0.990117i	$-0.544788\pi$
$239$	−67.0352			−0.280482			−0.140241	+	0.990117i	$0.544788\pi$
$240$		0			0
$241$	205.143	−	118.440i	0.851217	−	0.491451i	−0.00984406	−	0.999952i	$-0.503134\pi$
$241$	205.143	−	118.440i	0.851217	−	0.491451i	0.861061	+	0.508501i	$0.169800\pi$
$242$	−251.719	+	145.330i	−1.04016	+	0.600537i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			210.258i			0.861712i
$245$		0			0
$246$	91.8113			0.373217
$247$	550.176	+	317.644i	2.22743	+	1.28601i
$248$	−39.5164	−	68.4444i	−0.159340	−	0.275986i
$249$	−43.2376	−	74.8897i	−0.173645	−	0.300762i
$250$		0			0
$251$			483.382i			1.92582i	0.269815	+	0.962912i	$0.413037\pi$
$251$			483.382i			1.92582i	−0.269815	+	0.962912i	$0.586963\pi$
$252$	−28.7536	−	30.6142i	−0.114102	−	0.121485i
$253$			487.668i			1.92754i
$254$	70.1406	−	121.487i	0.276144	−	0.478295i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−162.291	+	281.097i	−0.631484	+	1.09376i	0.355764	+	0.934576i	$0.384221\pi$
$257$	−162.291	+	281.097i	−0.631484	+	1.09376i	−0.987248	+	0.159187i	$0.949113\pi$
$258$	156.019			0.604727
$259$	82.6234	+	352.131i	0.319009	+	1.35958i
$260$		0			0
$261$	−24.6994	+	42.7806i	−0.0946336	+	0.163910i
$262$	117.828	+	204.084i	0.449726	+	0.778948i
$263$	266.192	−	153.686i	1.01214	−	0.584358i	0.100320	−	0.994955i	$-0.468013\pi$
$263$	266.192	−	153.686i	1.01214	−	0.584358i	0.911817	+	0.410598i	$0.134680\pi$
$264$	−76.6648	−	44.2625i	−0.290397	−	0.167661i
$265$		0			0
$266$	97.3834	−	322.650i	0.366103	−	1.21297i
$267$		−	171.827i		−	0.643545i
$268$	22.0123	+	12.7088i	0.0821356	+	0.0474210i
$269$	65.6866	−	37.9242i	0.244188	−	0.140982i	−0.372912	−	0.927867i	$-0.621641\pi$
$269$	65.6866	−	37.9242i	0.244188	−	0.140982i	0.617100	+	0.786885i	$0.288307\pi$
$270$		0			0
$271$	−18.8151	−	10.8629i	−0.0694283	−	0.0400844i	0.464884	−	0.885372i	$-0.346096\pi$
$271$	−18.8151	−	10.8629i	−0.0694283	−	0.0400844i	−0.534312	+	0.845287i	$0.679429\pi$
$272$	6.16434			0.0226630
$273$	65.3735	−	216.595i	0.239463	−	0.793387i
$274$	214.278			0.782036
$275$		0			0
$276$	−80.9628	+	46.7439i	−0.293344	+	0.169362i
$277$	96.7627	−	55.8659i	0.349324	−	0.201682i	−0.315064	−	0.949071i	$-0.602026\pi$
$277$	96.7627	−	55.8659i	0.349324	−	0.201682i	0.664387	+	0.747388i	$0.268693\pi$
$278$	−107.350	+	185.936i	−0.386152	+	0.668835i
$279$		−	83.8270i		−	0.300455i
$280$		0			0
$281$	−188.298			−0.670101			−0.335051	−	0.942200i	$-0.608753\pi$
$281$	−188.298			−0.670101			−0.335051	+	0.942200i	$0.608753\pi$
$282$	−59.9078	−	34.5878i	−0.212439	−	0.122652i
$283$	108.408	+	187.769i	0.383069	+	0.663495i	0.991499	−	0.130113i	$-0.0415339\pi$
$283$	108.408	+	187.769i	0.383069	+	0.663495i	−0.608430	+	0.793607i	$0.708201\pi$
$284$	−45.7647	−	79.2667i	−0.161143	−	0.279108i
$285$		0			0
$286$		−	476.866i		−	1.66736i
$287$	191.246	−	179.623i	0.666363	−	0.625864i
$288$		−	16.9706i		−	0.0589256i
$289$	143.313	−	248.225i	0.495891	−	0.858909i
$290$		0			0
$291$	130.230	+	225.564i	0.447524	+	0.775134i
$292$	−36.4265	+	63.0926i	−0.124748	+	0.216071i
$293$	−57.3776			−0.195828			−0.0979140	−	0.995195i	$-0.531217\pi$
$293$	−57.3776			−0.195828			−0.0979140	+	0.995195i	$0.531217\pi$
$294$	−119.789	−	7.51583i	−0.407447	−	0.0255640i
$295$		0			0
$296$	−73.0732	+	126.567i	−0.246869	+	0.427590i
$297$	−46.9474	−	81.3153i	−0.158072	−	0.273789i
$298$	40.6541	−	23.4717i	0.136423	−	0.0787640i
$299$	−436.130	−	251.800i	−1.45863	−	0.842140i
$300$		0			0
$301$	324.994	−	305.242i	1.07971	−	1.01409i
$302$			13.1567i			0.0435651i
$303$	70.6202	+	40.7726i	0.233070	+	0.134563i
$304$	117.934	−	68.0895i	0.387942	−	0.223979i
$305$		0			0
$306$	5.66231	+	3.26914i	0.0185043	+	0.0106835i
$307$	291.273			0.948773			0.474386	−	0.880317i	$-0.342670\pi$
$307$	291.273			0.948773			0.474386	+	0.880317i	$0.342670\pi$
$308$	−246.292	+	57.7896i	−0.799650	+	0.187629i
$309$	131.542			0.425701
$310$		0			0
$311$	216.368	−	124.920i	0.695717	−	0.401673i	−0.110033	−	0.993928i	$-0.535096\pi$
$311$	216.368	−	124.920i	0.695717	−	0.401673i	0.805750	+	0.592255i	$0.201762\pi$
$312$	79.1694	−	45.7085i	0.253748	−	0.146502i
$313$	1.89274	−	3.27832i	0.00604709	−	0.0104739i	−0.862986	−	0.505228i	$-0.831408\pi$
$313$	1.89274	−	3.27832i	0.00604709	−	0.0104739i	0.869033	+	0.494754i	$0.164742\pi$
$314$			33.9248i			0.108041i
$315$		0			0
$316$	−266.396			−0.843025
$317$	−61.8004	−	35.6805i	−0.194954	−	0.112557i	0.399346	−	0.916800i	$-0.369237\pi$
$317$	−61.8004	−	35.6805i	−0.194954	−	0.112557i	−0.594300	+	0.804244i	$0.702571\pi$
$318$	0.543397	+	0.941190i	0.00170879	+	0.00295972i
$319$	148.773	+	257.683i	0.466373	+	0.807783i
$320$		0			0
$321$		−	185.719i		−	0.578565i
$322$	−77.1968	+	255.768i	−0.239742	+	0.794310i
$323$			52.4659i			0.162433i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	178.988	+	310.016i	0.549043	+	0.950970i
$327$	−70.0532	+	121.336i	−0.214230	+	0.371057i
$328$	106.015			0.323215
$329$	−192.459	+	45.1582i	−0.584981	+	0.137259i
$330$		0			0
$331$	170.983	−	296.152i	0.516566	−	0.894718i	−0.483249	−	0.875483i	$-0.660544\pi$
$331$	170.983	−	296.152i	0.516566	−	0.894718i	0.999815	−	0.0192351i	$-0.00612311\pi$
$332$	−49.9265	−	86.4752i	−0.150381	−	0.260467i
$333$	−134.244	+	77.5059i	−0.403135	+	0.232750i
$334$	104.992	+	60.6174i	0.314349	+	0.181489i
$335$		0			0
$336$	−33.2018	−	35.3502i	−0.0988149	−	0.105209i
$337$		−	246.396i		−	0.731145i	−0.930783	−	0.365573i	$-0.880873\pi$
$337$		−	246.396i		−	0.731145i	0.930783	−	0.365573i	$-0.119127\pi$
$338$	219.487	+	126.721i	0.649371	+	0.374915i
$339$	119.859	−	69.2007i	0.353567	−	0.204132i
$340$		0			0
$341$	−437.273	−	252.460i	−1.28233	−	0.740352i
$342$	144.440			0.422338
$343$	−264.230	+	218.705i	−0.770349	+	0.637623i
$344$	180.156			0.523709
$345$		0			0
$346$	23.8538	−	13.7720i	0.0689415	−	0.0398034i
$347$	−119.816	+	69.1758i	−0.345291	+	0.199354i	−0.662609	−	0.748965i	$-0.730551\pi$
$347$	−119.816	+	69.1758i	−0.345291	+	0.199354i	0.317318	+	0.948319i	$0.397218\pi$
$348$	−28.5204	+	49.3987i	−0.0819551	+	0.141950i
$349$		−	115.858i		−	0.331971i	−0.986128	−	0.165986i	$-0.946919\pi$
$349$		−	115.858i		−	0.331971i	0.986128	−	0.165986i	$-0.0530805\pi$
$350$		0			0
$351$	96.9623			0.276246
$352$	−88.5249	−	51.1099i	−0.251491	−	0.145199i
$353$	93.6093	+	162.136i	0.265182	+	0.459309i	0.967611	−	0.252445i	$-0.0812346\pi$
$353$	93.6093	+	162.136i	0.265182	+	0.459309i	−0.702429	+	0.711754i	$0.747901\pi$
$354$	−90.8293	−	157.321i	−0.256580	−	0.444409i
$355$		0			0
$356$		−	198.408i		−	0.557326i
$357$	18.1906	−	4.26823i	0.0509542	−	0.0119558i
$358$			357.562i			0.998775i
$359$	318.748	−	552.087i	0.887876	−	1.53785i	0.0454957	−	0.998965i	$-0.485513\pi$
$359$	318.748	−	552.087i	0.887876	−	1.53785i	0.842381	−	0.538883i	$-0.181153\pi$
$360$		0			0
$361$	399.022	+	691.127i	1.10532	+	1.91448i
$362$	−101.982	+	176.638i	−0.281718	+	0.487951i
$363$	−355.984			−0.980673
$364$	75.4868	−	250.102i	0.207381	−	0.687094i
$365$		0			0
$366$	−128.756	+	223.012i	−0.351793	+	0.609323i
$367$	−27.5252	−	47.6750i	−0.0750005	−	0.129905i	0.826086	−	0.563544i	$-0.190563\pi$
$367$	−27.5252	−	47.6750i	−0.0750005	−	0.129905i	−0.901087	+	0.433639i	$0.857229\pi$
$368$	−93.4878	+	53.9752i	−0.254043	+	0.146672i
$369$	97.3806	+	56.2227i	0.263904	+	0.152365i
$370$		0			0
$371$	2.97329	+	0.897411i	0.00801426	+	0.00241890i
$372$		−	96.7950i		−	0.260202i
$373$	−233.097	−	134.578i	−0.624924	−	0.360800i	0.153859	−	0.988093i	$-0.450830\pi$
$373$	−233.097	−	134.578i	−0.624924	−	0.360800i	−0.778784	+	0.627293i	$0.784163\pi$
$374$	34.1061	−	19.6912i	0.0911929	−	0.0526502i
$375$		0			0
$376$	−69.1755	−	39.9385i	−0.183978	−	0.106219i
$377$	−307.267			−0.815031
$378$	−11.7505	−	50.0792i	−0.0310860	−	0.132485i
$379$	−469.785			−1.23954			−0.619769	−	0.784784i	$-0.712774\pi$
$379$	−469.785			−1.23954			−0.619769	+	0.784784i	$0.712774\pi$
$380$		0			0
$381$	148.791	−	85.9043i	0.390526	−	0.225471i
$382$	384.690	−	222.101i	1.00704	−	0.581416i
$383$	201.105	−	348.324i	0.525078	−	0.909462i	−0.474495	−	0.880258i	$-0.657369\pi$
$383$	201.105	−	348.324i	0.525078	−	0.909462i	0.999573	−	0.0292039i	$-0.00929723\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	74.7107			0.193551
$387$	165.484	+	95.5420i	0.427606	+	0.246879i
$388$	150.376	+	260.459i	0.387567	+	0.671286i
$389$	−55.3803	−	95.9215i	−0.142366	−	0.246585i	0.786021	−	0.618200i	$-0.212138\pi$
$389$	−55.3803	−	95.9215i	−0.142366	−	0.246585i	−0.928387	+	0.371615i	$0.878804\pi$
$390$		0			0
$391$		−	41.5902i		−	0.106369i
$392$	−138.321	−	8.67853i	−0.352860	−	0.0221391i
$393$			288.619i			0.734399i
$394$	38.3255	−	66.3817i	0.0972729	−	0.168482i
$395$		0			0
$396$	−54.2102	−	93.8949i	−0.136895	−	0.237108i
$397$	209.907	−	363.569i	0.528733	−	0.915792i	−0.470706	−	0.882290i	$-0.656001\pi$
$397$	209.907	−	363.569i	0.528733	−	0.915792i	0.999439	−	0.0335018i	$-0.0106659\pi$
$398$	−32.4858			−0.0816227
$399$	300.873	−	282.587i	0.754066	−	0.708238i
$400$		0			0
$401$	−157.034	+	271.990i	−0.391605	+	0.678280i	−0.992661	−	0.120927i	$-0.961413\pi$
$401$	−157.034	+	271.990i	−0.391605	+	0.678280i	0.601056	+	0.799207i	$0.294747\pi$
$402$	15.5651	+	26.9595i	0.0387191	+	0.0670634i
$403$	451.559	−	260.708i	1.12049	−	0.646917i
$404$	81.5451	+	47.0801i	0.201844	+	0.116535i
$405$		0			0
$406$	37.2366	+	158.697i	0.0917156	+	0.390880i
$407$			933.691i			2.29408i
$408$	6.53827	+	3.77487i	0.0160252	+	0.00925214i
$409$	−105.506	+	60.9140i	−0.257961	+	0.148934i	−0.623404	−	0.781900i	$-0.714251\pi$
$409$	−105.506	+	60.9140i	−0.257961	+	0.148934i	0.365443	+	0.930834i	$0.380918\pi$
$410$		0			0
$411$	227.276	+	131.218i	0.552983	+	0.319265i
$412$	151.891			0.368668
$413$	−496.989	−	150.003i	−1.20336	−	0.363203i
$414$	−114.499			−0.276567
$415$		0			0
$416$	91.4169	−	52.7796i	0.219752	−	0.126874i
$417$	−227.724	+	131.477i	−0.546101	+	0.315292i
$418$	435.006	−	753.452i	1.04068	−	1.80252i
$419$		−	43.0872i		−	0.102833i	−0.998677	−	0.0514167i	$-0.983626\pi$
$419$		−	43.0872i		−	0.102833i	0.998677	−	0.0514167i	$-0.0163737\pi$
$420$		0			0
$421$	135.571			0.322022			0.161011	−	0.986953i	$-0.448525\pi$
$421$	135.571			0.322022			0.161011	+	0.986953i	$0.448525\pi$
$422$	−357.874	−	206.619i	−0.848043	−	0.489618i
$423$	−42.3612	−	73.3717i	−0.100145	−	0.173456i
$424$	0.627460	+	1.08679i	0.00147986	+	0.00256319i
$425$		0			0
$426$		−	112.100i		−	0.263146i
$427$	168.106	+	716.445i	0.393690	+	1.67786i
$428$		−	214.450i		−	0.501052i
$429$	292.019	−	505.792i	0.680698	−	1.17900i
$430$		0			0
$431$	−95.6132	−	165.607i	−0.221840	−	0.384239i	0.733527	−	0.679661i	$-0.237873\pi$
$431$	−95.6132	−	165.607i	−0.221840	−	0.384239i	−0.955367	+	0.295422i	$0.904540\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	339.825			0.784815			0.392408	−	0.919791i	$-0.371642\pi$
$433$	339.825			0.784815			0.392408	+	0.919791i	$0.371642\pi$
$434$	−189.373	−	201.627i	−0.436344	−	0.464579i
$435$		0			0
$436$	−80.8905	+	140.106i	−0.185529	+	0.321345i
$437$	−459.393	−	795.692i	−1.05124	−	1.82081i
$438$	−77.2723	+	44.6132i	−0.176421	+	0.101857i
$439$	−286.015	−	165.131i	−0.651515	−	0.376153i	0.137521	−	0.990499i	$-0.456086\pi$
$439$	−286.015	−	165.131i	−0.651515	−	0.376153i	−0.789037	+	0.614346i	$0.789420\pi$
$440$		0			0
$441$	−122.453	−	81.3275i	−0.277672	−	0.184416i
$442$			40.6690i			0.0920112i
$443$	486.414	+	280.831i	1.09800	+	0.633931i	0.935695	−	0.352810i	$-0.114774\pi$
$443$	486.414	+	280.831i	1.09800	+	0.633931i	0.162305	+	0.986741i	$0.448107\pi$
$444$	−155.012	+	89.4961i	−0.349125	+	0.201568i
$445$		0			0
$446$	332.279	+	191.841i	0.745020	+	0.430138i
$447$	57.4936			0.128621
$448$	−38.3381	−	40.8189i	−0.0855762	−	0.0911137i
$449$	386.250			0.860244			0.430122	−	0.902771i	$-0.358471\pi$
$449$	386.250			0.860244			0.430122	+	0.902771i	$0.358471\pi$
$450$		0			0
$451$	586.558	−	338.650i	1.30057	−	0.750886i
$452$	138.401	−	79.9061i	0.306198	−	0.176783i
$453$	−8.05678	+	13.9548i	−0.0177854	+	0.0308052i
$454$		−	210.165i		−	0.462918i
$455$		0			0
$456$	166.785			0.365755
$457$	432.203	+	249.533i	0.945741	+	0.546024i	0.891755	−	0.452518i	$-0.149474\pi$
$457$	432.203	+	249.533i	0.945741	+	0.546024i	0.0539854	+	0.998542i	$0.482808\pi$
$458$	−17.9135	−	31.0270i	−0.0391124	−	0.0677446i
$459$	4.00386	+	6.93489i	0.00872300	+	0.0151087i
$460$		0			0
$461$		−	618.290i		−	1.34119i	−0.741823	−	0.670596i	$-0.766038\pi$
$461$		−	618.290i		−	1.34119i	0.741823	−	0.670596i	$-0.233962\pi$
$462$	−296.621	−	89.5273i	−0.642037	−	0.193782i
$463$		−	194.433i		−	0.419941i	−0.977708	−	0.209971i	$-0.932663\pi$
$463$		−	194.433i		−	0.419941i	0.977708	−	0.209971i	$-0.0673368\pi$
$464$	−32.9325	+	57.0407i	−0.0709752	+	0.122933i
$465$		0			0
$466$	289.126	+	500.781i	0.620442	+	1.07464i
$467$	75.8923	−	131.449i	0.162510	−	0.281476i	−0.773258	−	0.634091i	$-0.781374\pi$
$467$	75.8923	−	131.449i	0.162510	−	0.281476i	0.935768	+	0.352615i	$0.114708\pi$
$468$	111.962			0.239236
$469$	85.1671	+	25.7055i	0.181593	+	0.0548091i
$470$		0			0
$471$	−20.7746	+	35.9827i	−0.0441074	+	0.0763963i
$472$	−104.881	−	181.659i	−0.222205	−	0.384870i
$473$	996.767	−	575.484i	2.10733	−	1.21667i
$474$	−282.556	−	163.134i	−0.596109	−	0.344164i
$475$		0			0
$476$	21.0047	−	4.92852i	0.0441276	−	0.0103540i
$477$			1.33104i			0.00279045i
$478$	−82.1010	−	47.4010i	−0.171759	−	0.0991653i
$479$	−194.656	+	112.385i	−0.406381	+	0.234624i	−0.689233	−	0.724539i	$-0.742053\pi$
$479$	−194.656	+	112.385i	−0.406381	+	0.234624i	0.282853	+	0.959163i	$0.408719\pi$
$480$		0			0
$481$	−835.016	−	482.097i	−1.73600	−	1.00228i
$482$	334.998			0.695016
$483$	−238.505	+	224.009i	−0.493799	+	0.463788i
$484$	−411.055			−0.849288
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−60.2432	+	34.7814i	−0.123703	+	0.0714198i	−0.560575	−	0.828104i	$-0.689420\pi$
$487$	−60.2432	+	34.7814i	−0.123703	+	0.0714198i	0.436872	+	0.899524i	$0.356086\pi$
$488$	−148.675	+	257.512i	−0.304661	+	0.527689i
$489$			438.429i			0.896584i
$490$		0			0
$491$	−750.454			−1.52842			−0.764210	−	0.644967i	$-0.776871\pi$
$491$	−750.454			−1.52842			−0.764210	+	0.644967i	$0.776871\pi$
$492$	112.445	+	64.9204i	0.228548	+	0.131952i
$493$	−12.6880	−	21.9762i	−0.0257362	−	0.0445764i
$494$	449.217	+	778.067i	0.909346	+	1.57503i
$495$		0			0
$496$		−	111.769i		−	0.225341i
$497$	−219.317	−	233.508i	−0.441281	−	0.469835i
$498$		−	122.294i		−	0.245571i
$499$	80.0848	−	138.711i	0.160491	−	0.277978i	−0.774554	−	0.632508i	$-0.782026\pi$
$499$	80.0848	−	138.711i	0.160491	−	0.277978i	0.935045	+	0.354530i	$0.115359\pi$
$500$		0			0
$501$	74.2408	+	128.589i	0.148185	+	0.256664i
$502$	−341.803	+	592.019i	−0.680882	+	1.17932i
$503$	−724.412			−1.44018			−0.720092	−	0.693879i	$-0.755900\pi$
$503$	−724.412			−1.44018			−0.720092	+	0.693879i	$0.755900\pi$
$504$	−13.5683	−	57.8265i	−0.0269213	−	0.114735i
$505$		0			0
$506$	−344.834	+	597.269i	−0.681489	+	1.18037i
$507$	155.201	+	268.816i	0.306117	+	0.530209i
$508$	171.809	−	99.1937i	0.338206	−	0.195263i
$509$	711.944	+	411.041i	1.39871	+	0.807547i	0.994258	−	0.107012i	$-0.0341283\pi$
$509$	711.944	+	411.041i	1.39871	+	0.807547i	0.404454	+	0.914558i	$0.367462\pi$
$510$		0			0
$511$	−73.6780	+	244.109i	−0.144184	+	0.477709i
$512$		−	22.6274i		−	0.0441942i
$513$	153.201	+	88.4508i	0.298638	+	0.172419i
$514$	−397.531	+	229.515i	−0.773407	+	0.446527i
$515$		0			0
$516$	191.084	+	110.322i	0.370318	+	0.213803i
$517$	−510.313			−0.987066
$518$	−147.801	+	489.694i	−0.285331	+	0.945355i
$519$	33.7343			0.0649987
$520$		0			0
$521$	392.147	−	226.406i	0.752681	−	0.434561i	−0.0739805	−	0.997260i	$-0.523570\pi$
$521$	392.147	−	226.406i	0.752681	−	0.434561i	0.826662	+	0.562699i	$0.190237\pi$
$522$	−60.5008	+	34.9302i	−0.115902	+	0.0669161i
$523$	−487.051	+	843.597i	−0.931264	+	1.61300i	−0.150100	+	0.988671i	$0.547960\pi$
$523$	−487.051	+	843.597i	−0.931264	+	1.61300i	−0.781164	+	0.624326i	$0.785374\pi$
$524$			333.268i			0.636008i
$525$		0			0
$526$	434.690			0.826406
$527$	37.2924	+	21.5308i	0.0707635	+	0.0408553i
$528$	−62.5966	−	108.420i	−0.118554	−	0.205342i
$529$	99.6657	+	172.626i	0.188404	+	0.326325i
$530$		0			0
$531$		−	222.485i		−	0.418993i
$532$	347.418	−	326.303i	0.653041	−	0.613352i
$533$			699.426i			1.31224i
$534$	121.500	−	210.444i	0.227528	−	0.394089i
$535$		0			0
$536$	17.9730	+	31.1302i	0.0335317	+	0.0580786i
$537$	−218.961	+	379.251i	−0.407748	+	0.706241i
$538$	107.266			0.199379
$539$	−793.026	+	393.831i	−1.47129	+	0.730670i
$540$		0			0
$541$	−138.078	+	239.158i	−0.255228	+	0.442067i	−0.964957	−	0.262407i	$-0.915484\pi$
$541$	−138.078	+	239.158i	−0.255228	+	0.442067i	0.709730	+	0.704474i	$0.248817\pi$
$542$	−15.3624	−	26.6085i	−0.0283440	−	0.0490932i
$543$	−216.337	+	124.902i	−0.398410	+	0.230022i
$544$	7.54975	+	4.35885i	0.0138782	+	0.00801259i
$545$		0			0
$546$	233.221	−	219.047i	0.427146	−	0.401186i
$547$		−	426.436i		−	0.779591i	−0.920901	−	0.389795i	$-0.872546\pi$
$547$		−	426.436i		−	0.779591i	0.920901	−	0.389795i	$-0.127454\pi$
$548$	262.436	+	151.517i	0.478897	+	0.276492i
$549$	−273.133	+	157.693i	−0.497510	+	0.287237i
$550$		0			0
$551$	−485.484	−	280.295i	−0.881097	−	0.508702i
$552$	−132.212			−0.239514
$553$	−907.733	+	212.989i	−1.64147	+	0.385152i
$554$	158.013			0.285222
$555$		0			0
$556$	−262.953	+	151.816i	−0.472938	+	0.273051i
$557$	105.617	−	60.9782i	0.189618	−	0.109476i	−0.402186	−	0.915558i	$-0.631749\pi$
$557$	105.617	−	60.9782i	0.189618	−	0.109476i	0.591804	+	0.806082i	$0.298416\pi$
$558$	59.2746	−	102.667i	0.106227	−	0.183990i
$559$			1188.57i			2.12624i
$560$		0			0
$561$	48.2334			0.0859775
$562$	−230.618	−	133.147i	−0.410351	−	0.236917i
$563$	−217.391	−	376.532i	−0.386130	−	0.668796i	0.605796	−	0.795620i	$-0.292855\pi$
$563$	−217.391	−	376.532i	−0.386130	−	0.668796i	−0.991925	+	0.126824i	$0.959522\pi$
$564$	−48.9145	−	84.7224i	−0.0867278	−	0.150217i
$565$		0			0
$566$			306.625i			0.541741i
$567$	18.2038	−	60.3127i	0.0321055	−	0.106372i
$568$		−	129.442i		−	0.227891i
$569$	−148.138	+	256.583i	−0.260349	+	0.450937i	−0.966335	−	0.257289i	$-0.917171\pi$
$569$	−148.138	+	256.583i	−0.260349	+	0.450937i	0.705986	+	0.708226i	$0.250504\pi$
$570$		0			0
$571$	−29.9578	−	51.8885i	−0.0524655	−	0.0908730i	0.838600	−	0.544748i	$-0.183375\pi$
$571$	−29.9578	−	51.8885i	−0.0524655	−	0.0908730i	−0.891065	+	0.453875i	$0.850041\pi$
$572$	337.195	−	584.039i	0.589502	−	1.02105i
$573$	544.034			0.949448
$574$	361.240	−	84.7609i	0.629338	−	0.147667i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−166.351	−	288.128i	−0.288303	−	0.499355i	0.685102	−	0.728447i	$-0.259758\pi$
$577$	−166.351	−	288.128i	−0.288303	−	0.499355i	−0.973405	+	0.229092i	$0.926424\pi$
$578$	351.043	−	202.675i	0.607340	−	0.350648i
$579$	79.2426	+	45.7507i	0.136861	+	0.0790168i
$580$		0			0
$581$	−239.261	−	254.743i	−0.411809	−	0.438456i
$582$			368.345i			0.632895i
$583$	6.94323	+	4.00868i	0.0119095	+	0.00687595i
$584$	−89.2264	+	51.5149i	−0.152785	+	0.0882104i
$585$		0			0
$586$	−70.2729	−	40.5721i	−0.119920	−	0.0692356i
$587$	−656.221			−1.11792			−0.558961	−	0.829194i	$-0.688800\pi$
$587$	−656.221			−1.11792			−0.558961	+	0.829194i	$0.688800\pi$
$588$	−141.397	−	93.9089i	−0.240471	−	0.159709i
$589$	951.289			1.61509
$590$		0			0
$591$	81.3007	−	46.9390i	0.137565	−	0.0794230i
$592$	−178.992	+	103.341i	−0.302352	+	0.174563i
$593$	204.271	−	353.808i	0.344471	−	0.596640i	−0.640787	−	0.767719i	$-0.721392\pi$
$593$	204.271	−	353.808i	0.344471	−	0.596640i	0.985257	+	0.171078i	$0.0547251\pi$
$594$		−	132.787i		−	0.223548i
$595$		0			0
$596$	66.3879			0.111389
$597$	−34.4564	−	19.8934i	−0.0577160	−	0.0333223i
$598$	−356.099	−	616.781i	−0.595483	−	1.03141i
$599$	−588.643	−	1019.56i	−0.982709	−	1.70210i	−0.651705	−	0.758472i	$-0.725946\pi$
$599$	−588.643	−	1019.56i	−0.982709	−	1.70210i	−0.331003	−	0.943630i	$-0.607387\pi$
$600$		0			0
$601$			162.592i			0.270536i	0.990809	+	0.135268i	$0.0431896\pi$
$601$			162.592i			0.270536i	−0.990809	+	0.135268i	$0.956810\pi$
$602$	613.873	−	144.038i	1.01972	−	0.239266i
$603$			38.1265i			0.0632280i
$604$	−9.30317	+	16.1136i	−0.0154026	+	0.0266781i
$605$		0			0
$606$	57.6611	+	99.8720i	0.0951504	+	0.164805i
$607$	−183.664	+	318.116i	−0.302577	+	0.524079i	−0.976719	−	0.214523i	$-0.931180\pi$
$607$	−183.664	+	318.116i	−0.302577	+	0.524079i	0.674142	+	0.738602i	$0.264514\pi$
$608$	192.586			0.316754
$609$	−57.6866	+	191.127i	−0.0947235	+	0.313837i
$610$		0			0
$611$	263.492	−	456.382i	0.431248	−	0.746943i
$612$	4.62326	+	8.00772i	0.00755434	+	0.0130845i
$613$	316.335	−	182.636i	0.516044	−	0.297938i	−0.219270	−	0.975664i	$-0.570368\pi$
$613$	316.335	−	182.636i	0.516044	−	0.297938i	0.735315	+	0.677726i	$0.237034\pi$
$614$	356.735	+	205.961i	0.581002	+	0.335442i
$615$		0			0
$616$	−342.508	−	103.377i	−0.556020	−	0.167820i
$617$			64.2245i			0.104092i	0.998645	+	0.0520458i	$0.0165742\pi$
$617$			64.2245i			0.104092i	−0.998645	+	0.0520458i	$0.983426\pi$
$618$	161.105	+	93.0140i	0.260688	+	0.150508i
$619$	990.646	−	571.949i	1.60040	−	0.923989i	0.608989	−	0.793178i	$-0.291575\pi$
$619$	990.646	−	571.949i	1.60040	−	0.923989i	0.991407	−	0.130811i	$-0.0417581\pi$
$620$		0			0
$621$	−121.444	−	70.1159i	−0.195562	−	0.112908i
$622$	353.328			0.568051
$623$	−158.632	−	676.067i	−0.254625	−	1.08518i
$624$	129.283			0.207184
$625$		0			0
$626$	4.63624	−	2.67674i	0.00740614	−	0.00427594i
$627$	922.787	−	532.771i	1.47175	−	0.849715i
$628$	−23.9884	+	41.5492i	−0.0381982	+	0.0661611i
$629$		−	79.6288i		−	0.126596i
$630$		0			0
$631$	257.367			0.407872			0.203936	−	0.978984i	$-0.434627\pi$
$631$	257.367			0.407872			0.203936	+	0.978984i	$0.434627\pi$
$632$	−326.267	−	188.370i	−0.516246	−	0.298055i
$633$	−253.055	−	438.305i	−0.399771	−	0.692425i
$634$	−50.4598	−	87.3990i	−0.0795897	−	0.137853i
$635$		0			0
$636$			1.53696i			0.00241660i
$637$	57.2562	−	912.565i	0.0898841	−	1.43260i
$638$			420.794i			0.659552i
$639$	68.6470	−	118.900i	0.107429	−	0.186072i
$640$		0			0
$641$	−99.4860	−	172.315i	−0.155204	−	0.268822i	0.777929	−	0.628352i	$-0.216270\pi$
$641$	−99.4860	−	172.315i	−0.155204	−	0.268822i	−0.933133	+	0.359530i	$0.882937\pi$
$642$	131.323	−	227.459i	0.204554	−	0.354297i
$643$	708.223			1.10144			0.550718	−	0.834692i	$-0.314354\pi$
$643$	708.223			1.10144			0.550718	+	0.834692i	$0.314354\pi$
$644$	−275.401	+	258.664i	−0.427642	+	0.401652i
$645$		0			0
$646$	−37.0990	+	64.2573i	−0.0574288	+	0.0994695i
$647$	81.2876	+	140.794i	0.125638	+	0.217611i	0.921982	−	0.387233i	$-0.126569\pi$
$647$	81.2876	+	140.794i	0.125638	+	0.217611i	−0.796344	+	0.604844i	$0.793236\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	−1160.57	−	670.054i	−1.78824	−	1.03244i
$650$		0			0
$651$	−77.3897	−	329.825i	−0.118878	−	0.506644i
$652$			506.255i			0.776464i
$653$	−862.354	−	497.880i	−1.32060	−	0.762450i	−0.336778	−	0.941584i	$-0.609337\pi$
$653$	−862.354	−	497.880i	−1.32060	−	0.762450i	−0.983825	+	0.179134i	$0.942671\pi$
$654$	−171.595	+	99.0702i	−0.262377	+	0.151483i
$655$		0			0
$656$	129.841	+	74.9636i	0.197928	+	0.114274i
$657$	−109.280			−0.166331
$658$	−267.644	−	80.7815i	−0.406754	−	0.122768i
$659$	−897.542			−1.36198			−0.680988	−	0.732295i	$-0.738449\pi$
$659$	−897.542			−1.36198			−0.680988	+	0.732295i	$0.738449\pi$
$660$		0			0
$661$	−74.7048	+	43.1308i	−0.113018	+	0.0652508i	−0.555443	−	0.831554i	$-0.687451\pi$
$661$	−74.7048	+	43.1308i	−0.113018	+	0.0652508i	0.442426	+	0.896805i	$0.354118\pi$
$662$	418.822	−	241.807i	0.632661	−	0.365267i
$663$	−24.9045	+	43.1359i	−0.0375634	+	0.0650617i
$664$		−	141.213i		−	0.212671i
$665$		0			0
$666$	−219.220			−0.329159
$667$	384.848	+	222.192i	0.576984	+	0.333122i
$668$	85.7259	+	148.482i	0.128332	+	0.222278i
$669$	234.957	+	406.957i	0.351206	+	0.608306i
$670$		0			0
$671$			1899.69i			2.83113i
$672$	−15.6674	−	66.7723i	−0.0233145	−	0.0993635i
$673$			486.598i			0.723028i	0.932367	+	0.361514i	$0.117740\pi$
$673$			486.598i			0.723028i	−0.932367	+	0.361514i	$0.882260\pi$
$674$	174.228	−	301.772i	0.258499	−	0.447733i
$675$		0			0
$676$	179.211	+	310.402i	0.265105	+	0.459175i
$677$	27.4627	−	47.5668i	0.0405653	−	0.0702612i	−0.845030	−	0.534719i	$-0.820417\pi$
$677$	27.4627	−	47.5668i	0.0405653	−	0.0702612i	0.885595	+	0.464458i	$0.153751\pi$
$678$	195.729			0.288686
$679$	720.643	+	767.274i	1.06133	+	1.13001i
$680$		0			0
$681$	128.699	−	222.913i	0.188985	−	0.327332i
$682$	−357.032	−	618.398i	−0.523508	−	0.906742i
$683$	−826.509	+	477.185i	−1.21012	+	0.698661i	−0.962784	−	0.270270i	$-0.912887\pi$
$683$	−826.509	+	477.185i	−1.21012	+	0.698661i	−0.247331	+	0.968931i	$0.579554\pi$
$684$	176.902	+	102.134i	0.258628	+	0.149319i
$685$		0			0
$686$	−478.261	+	81.0188i	−0.697174	+	0.118103i
$687$		−	43.8788i		−	0.0638702i
$688$	220.645	+	127.389i	0.320705	+	0.185159i
$689$	−7.17006	+	4.13964i	−0.0104065	+	0.00600818i
$690$		0			0
$691$	−22.3860	−	12.9246i	−0.0323966	−	0.0187042i	0.483714	−	0.875226i	$-0.339287\pi$
$691$	−22.3860	−	12.9246i	−0.0323966	−	0.0187042i	−0.516111	+	0.856522i	$0.672621\pi$
$692$	38.9530			0.0562905
$693$	−259.790	−	276.601i	−0.374877	−	0.399135i
$694$	−195.659			−0.281929
$695$		0			0
$696$	−69.8604	+	40.3339i	−0.100374	+	0.0579510i
$697$	−50.0240	+	28.8814i	−0.0717704	+	0.0414367i
$698$	81.9239	−	141.896i	0.117370	−	0.203290i
$699$			708.211i			1.01318i
$700$		0			0
$701$	−942.060			−1.34388			−0.671940	−	0.740606i	$-0.734539\pi$
$701$	−942.060			−1.34388			−0.671940	+	0.740606i	$0.734539\pi$
$702$	118.754	+	68.5627i	0.169165	+	0.0976677i
$703$	−879.556	−	1523.44i	−1.25115	−	2.16705i
$704$	−72.2803	−	125.193i	−0.102671	−	0.177831i
$705$		0			0
$706$			264.767i			0.375024i
$707$	315.503	+	95.2264i	0.446256	+	0.134691i
$708$		−	256.904i		−	0.362859i
$709$	−168.282	+	291.473i	−0.237351	+	0.411105i	−0.959953	−	0.280160i	$-0.909613\pi$
$709$	−168.282	+	291.473i	−0.237351	+	0.411105i	0.722602	+	0.691264i	$0.242946\pi$
$710$		0			0
$711$	−199.797	−	346.059i	−0.281008	−	0.486721i
$712$	140.296	−	242.999i	0.197045	−	0.341291i
$713$	−754.097			−1.05764
$714$	25.2970	+	7.63524i	0.0354300	+	0.0106936i
$715$		0			0
$716$	−252.834	+	437.922i	−0.353120	+	0.611622i
$717$	−58.0542	−	100.553i	−0.0809681	−	0.140241i
$718$	780.769	−	450.777i	1.08742	−	0.627823i
$719$	111.447	+	64.3438i	0.155002	+	0.0894907i	0.575495	−	0.817805i	$-0.304809\pi$
$719$	111.447	+	64.3438i	0.155002	+	0.0894907i	−0.420493	+	0.907296i	$0.638143\pi$
$720$		0			0
$721$	517.563	−	121.440i	0.717840	−	0.168433i
$722$			1128.61i			1.56317i
$723$	355.319	+	205.143i	0.491451	+	0.283739i
$724$	−249.804	+	144.224i	−0.345033	+	0.199205i
$725$		0			0
$726$	−435.990	−	251.719i	−0.600537	−	0.346720i
$727$	684.683			0.941792			0.470896	−	0.882189i	$-0.343931\pi$
$727$	684.683			0.941792			0.470896	+	0.882189i	$0.343931\pi$
$728$	269.301	−	252.934i	0.369919	−	0.347437i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−85.0082	+	49.0795i	−0.116290	+	0.0671402i
$732$	−315.387	+	182.089i	−0.430856	+	0.248755i
$733$	−295.911	+	512.533i	−0.403699	+	0.699227i	−0.994169	−	0.107832i	$-0.965609\pi$
$733$	−295.911	+	512.533i	−0.403699	+	0.699227i	0.590470	+	0.807059i	$0.298942\pi$
$734$		−	77.8530i		−	0.106067i
$735$		0			0
$736$	−152.665			−0.207425
$737$	198.882	+	114.825i	0.269854	+	0.155800i
$738$	79.5110	+	137.717i	0.107738	+	0.186608i
$739$	252.105	+	436.659i	0.341144	+	0.590878i	0.984645	−	0.174567i	$-0.0558525\pi$
$739$	252.105	+	436.659i	0.341144	+	0.590878i	−0.643502	+	0.765445i	$0.722519\pi$
$740$		0			0
$741$			1100.35i			1.48496i
$742$	3.00696	+	3.20153i	0.00405250	+	0.00431473i
$743$			983.540i			1.32374i	0.749618	+	0.661871i	$0.230237\pi$
$743$			983.540i			1.32374i	−0.749618	+	0.661871i	$0.769763\pi$
$744$	68.4444	−	118.549i	0.0919952	−	0.159340i
$745$		0			0
$746$	−190.323	−	329.649i	−0.255124	−	0.441888i
$747$	74.8897	−	129.713i	0.100254	−	0.173645i
$748$	55.6951			0.0744587
$749$	−171.457	−	730.730i	−0.228915	−	0.975607i
$750$		0			0
$751$	−458.462	+	794.080i	−0.610469	+	1.05736i	0.380692	+	0.924702i	$0.375686\pi$
$751$	−458.462	+	794.080i	−0.610469	+	1.05736i	−0.991161	+	0.132662i	$0.957648\pi$
$752$	−56.4816	−	97.8290i	−0.0751085	−	0.130092i
$753$	−725.073	+	418.621i	−0.962912	+	0.555938i
$754$	−376.323	−	217.270i	−0.499103	−	0.288157i
$755$		0			0
$756$	21.0200	−	69.6431i	0.0278042	−	0.0921205i
$757$		−	82.2419i		−	0.108642i	−0.998524	−	0.0543209i	$-0.982701\pi$
$757$		−	82.2419i		−	0.108642i	0.998524	−	0.0543209i	$-0.0172994\pi$
$758$	−575.367	−	332.188i	−0.759059	−	0.438243i
$759$	−731.502	+	422.333i	−0.963771	+	0.556434i
$760$		0			0
$761$	303.297	+	175.108i	0.398550	+	0.230103i	0.685858	−	0.727735i	$-0.259427\pi$
$761$	303.297	+	175.108i	0.398550	+	0.230103i	−0.287308	+	0.957838i	$0.592760\pi$
$762$	242.974			0.318864
$763$	−163.613	+	542.080i	−0.214434	+	0.710459i
$764$	628.196			0.822246
$765$		0			0
$766$	492.604	−	284.405i	0.643087	−	0.371286i
$767$	1198.48	−	691.944i	1.56256	−	0.902144i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$		−	319.560i		−	0.415553i	−0.978176	−	0.207777i	$-0.933377\pi$
$769$		−	319.560i		−	0.415553i	0.978176	−	0.207777i	$-0.0666227\pi$
$770$		0			0
$771$	−562.194			−0.729175
$772$	91.5015	+	52.8284i	0.118525	+	0.0684306i
$773$	−500.507	−	866.904i	−0.647487	−	1.12148i	−0.983721	−	0.179702i	$-0.942487\pi$
$773$	−500.507	−	866.904i	−0.647487	−	1.12148i	0.336235	−	0.941778i	$-0.390847\pi$
$774$	135.117	+	234.029i	0.174570	+	0.302363i
$775$		0			0
$776$			425.328i			0.548103i
$777$	−456.642	+	428.889i	−0.587699	+	0.551981i
$778$		−	156.639i		−	0.201336i
$779$	−638.030	+	1105.10i	−0.819037	+	1.41861i
$780$		0			0
$781$	−413.485	−	716.178i	−0.529431	−	0.917001i
$782$	29.4087	−	50.9374i	0.0376071	−	0.0651374i
$783$	−85.5611			−0.109273
$784$	−163.271	−	108.437i	−0.208254	−	0.138312i
$785$		0			0
$786$	−204.084	+	353.484i	−0.259649	+	0.449726i
$787$	−64.8506	−	112.324i	−0.0824022	−	0.142725i	0.821879	−	0.569662i	$-0.192926\pi$
$787$	−64.8506	−	112.324i	−0.0824022	−	0.142725i	−0.904281	+	0.426937i	$0.859593\pi$
$788$	93.8780	−	54.2005i	0.119134	−	0.0687823i
$789$	461.058	+	266.192i	0.584358	+	0.337379i
$790$		0			0
$791$	407.710	−	382.931i	0.515437	−	0.484111i
$792$		−	153.330i		−	0.193598i
$793$	−1698.92	−	980.874i	−2.14240	−	1.23692i
$794$	514.165	−	296.853i	0.647563	−	0.373870i
$795$		0			0
$796$	−39.7869	−	22.9710i	−0.0499835	−	0.0288580i
$797$	−420.926			−0.528138			−0.264069	−	0.964504i	$-0.585065\pi$
$797$	−420.926			−0.528138			−0.264069	+	0.964504i	$0.585065\pi$
$798$	568.311	−	133.348i	0.712169	−	0.167102i
$799$	43.5215			0.0544700
$800$		0			0
$801$	257.740	−	148.806i	0.321773	−	0.185775i
$802$	−384.652	+	222.079i	−0.479616	+	0.276907i
$803$	−329.115	+	570.044i	−0.409857	+	0.709893i
$804$			44.0247i			0.0547571i
$805$		0			0
$806$	737.392			0.914879
$807$	113.773	+	65.6866i	0.140982	+	0.0813961i
$808$	66.5813	+	115.322i	0.0824026	+	0.142726i
$809$	−582.166	−	1008.34i	−0.719612	−	1.24640i	−0.961154	−	0.276014i	$-0.910987\pi$
$809$	−582.166	−	1008.34i	−0.719612	−	1.24640i	0.241542	−	0.970390i	$-0.422347\pi$
$810$		0			0
$811$		−	753.691i		−	0.929335i	−0.885485	−	0.464668i	$-0.846174\pi$
$811$		−	753.691i		−	0.929335i	0.885485	−	0.464668i	$-0.153826\pi$
$812$	−66.6108	+	220.694i	−0.0820330	+	0.271791i
$813$		−	37.6301i		−	0.0462855i
$814$	−660.219	+	1143.53i	−0.811080	+	1.40483i
$815$		0			0
$816$	5.33848	+	9.24652i	0.00654225	+	0.0113315i
$817$	−1084.23	+	1877.95i	−1.32709	+	2.29859i
$818$	−172.291			−0.210625
$819$	381.507	−	89.5163i	0.465821	−	0.109300i
$820$		0			0
$821$	184.398	−	319.387i	0.224602	−	0.389022i	−0.731598	−	0.681736i	$-0.761225\pi$
$821$	184.398	−	319.387i	0.224602	−	0.389022i	0.956200	+	0.292714i	$0.0945584\pi$
$822$	185.570	+	321.417i	0.225754	+	0.391018i
$823$	−447.082	+	258.123i	−0.543234	+	0.313636i	−0.746389	−	0.665510i	$-0.768214\pi$
$823$	−447.082	+	258.123i	−0.543234	+	0.313636i	0.203155	+	0.979147i	$0.434881\pi$
$824$	186.028	+	107.403i	0.225762	+	0.130344i
$825$		0			0
$826$	−502.616	−	535.139i	−0.608494	−	0.647869i
$827$			534.206i			0.645957i	0.946406	+	0.322978i	$0.104684\pi$
$827$			534.206i			0.645957i	−0.946406	+	0.322978i	$0.895316\pi$
$828$	−140.232	−	80.9628i	−0.169362	−	0.0977812i
$829$	−692.720	+	399.942i	−0.835610	+	0.482439i	−0.855769	−	0.517357i	$-0.826916\pi$
$829$	−692.720	+	399.942i	−0.835610	+	0.482439i	0.0201599	+	0.999797i	$0.493582\pi$
$830$		0			0
$831$	167.598	+	96.7627i	0.201682	+	0.116441i
$832$	149.283			0.179427
$833$	67.6323	−	33.5875i	0.0811912	−	0.0403211i
$834$	−371.872			−0.445890
$835$		0			0
$836$	1065.54	−	615.191i	1.27457	−	0.735874i
$837$	125.740	−	72.5963i	0.150228	−	0.0867339i
$838$	30.4673	−	52.7708i	0.0363571	−	0.0629724i
$839$			1250.09i			1.48998i	0.667078	+	0.744988i	$0.267545\pi$
$839$			1250.09i			1.48998i	−0.667078	+	0.744988i	$0.732455\pi$
$840$		0			0
$841$	−569.863			−0.677601
$842$	166.040	+	95.8634i	0.197198	+	0.113852i
$843$	−163.071	−	282.448i	−0.193442	−	0.335051i
$844$	−292.203	−	506.111i	−0.346212	−	0.599657i
$845$		0			0
$846$		−	119.816i		−	0.141626i
$847$	−1400.65	+	328.647i	−1.65366	+	0.388013i
$848$			1.77473i			0.00209284i
$849$	−187.769	+	325.225i	−0.221165	+	0.383069i
$850$		0			0
$851$	697.233	+	1207.64i	0.819310	+	1.41909i
$852$	79.2667	−	137.294i	0.0930361	−	0.161143i
$853$	427.261			0.500893			0.250446	−	0.968130i	$-0.419423\pi$
$853$	427.261			0.500893			0.250446	+	0.968130i	$0.419423\pi$
$854$	−300.716	+	996.330i	−0.352127	+	1.16666i
$855$		0			0
$856$	151.639	−	262.647i	0.177149	−	0.306830i
$857$	−210.603	−	364.774i	−0.245744	−	0.425641i	0.716597	−	0.697488i	$-0.245699\pi$
$857$	−210.603	−	364.774i	−0.245744	−	0.425641i	−0.962341	+	0.271847i	$0.912366\pi$
$858$	715.298	−	412.978i	0.833681	−	0.481326i
$859$	−666.524	−	384.818i	−0.775930	−	0.447983i	0.0590558	−	0.998255i	$-0.481191\pi$
$859$	−666.524	−	384.818i	−0.775930	−	0.447983i	−0.834986	+	0.550271i	$0.814524\pi$
$860$		0			0
$861$	435.058	+	131.311i	0.505294	+	0.152510i
$862$		−	270.435i		−	0.313730i
$863$	1314.98	+	759.204i	1.52373	+	0.879726i	0.999606	+	0.0280846i	$0.00894079\pi$
$863$	1314.98	+	759.204i	1.52373	+	0.879726i	0.524125	+	0.851641i	$0.324393\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$		0			0
$866$	416.199	+	240.293i	0.480599	+	0.277474i
$867$	496.449			0.572606
$868$	−89.3619	−	380.849i	−0.102952	−	0.438766i
$869$	−2406.90			−2.76973
$870$		0			0
$871$	−205.380	+	118.576i	−0.235798	+	0.136138i
$872$	−198.140	+	114.396i	−0.227225	+	0.131189i
$873$	−225.564	+	390.689i	−0.258378	+	0.447524i
$874$		−	1299.36i		−	1.48668i
$875$		0			0
$876$	−126.185			−0.144047
$877$	−1390.69	−	802.916i	−1.58574	−	0.915525i	−0.993998	−	0.109395i	$-0.965109\pi$
$877$	−1390.69	−	802.916i	−1.58574	−	0.915525i	−0.591738	−	0.806131i	$-0.701558\pi$
$878$	−233.530	−	404.487i	−0.265980	−	0.460691i
$879$	−49.6905	−	86.0664i	−0.0565307	−	0.0979140i
$880$		0			0
$881$			538.120i			0.610806i	0.952223	+	0.305403i	$0.0987912\pi$
$881$			538.120i			0.610806i	−0.952223	+	0.305403i	$0.901209\pi$
$882$	−92.4670	−	186.193i	−0.104838	−	0.211103i
$883$			880.262i			0.996899i	0.866919	+	0.498450i	$0.166097\pi$
$883$			880.262i			0.996899i	−0.866919	+	0.498450i	$0.833903\pi$
$884$	−28.7573	+	49.8091i	−0.0325309	+	0.0563451i
$885$		0			0
$886$	397.155	+	687.893i	0.448257	+	0.776403i
$887$	402.406	−	696.988i	0.453671	−	0.785781i	−0.544940	−	0.838475i	$-0.683448\pi$
$887$	402.406	−	696.988i	0.453671	−	0.785781i	0.998611	+	0.0526943i	$0.0167809\pi$
$888$	−253.133			−0.285060
$889$	506.123	−	475.363i	0.569317	−	0.534717i
$890$		0			0
$891$	81.3153	−	140.842i	0.0912630	−	0.158072i
$892$	271.305	+	469.913i	0.304153	+	0.526809i
$893$	832.641	−	480.725i	0.932408	−	0.538326i
$894$	70.4150	+	40.6541i	0.0787640	+	0.0454744i
$895$		0			0
$896$	−18.0911	−	77.1020i	−0.0201910	−	0.0860513i
$897$		−	872.261i		−	0.972420i
$898$	473.057	+	273.120i	0.526790	+	0.304142i
$899$	−398.463	+	230.053i	−0.443229	+	0.255898i
$900$		0			0
$901$	−0.592146	−	0.341876i	−0.000657210	−	0.000379440i
$902$	957.846			1.06191
$903$	739.316	+	223.143i	0.818733	+	0.247113i
$904$	226.009			0.250009
$905$		0			0
$906$	−19.7350	+	11.3940i	−0.0217826	+	0.0125762i
$907$	−923.473	+	533.167i	−1.01816	+	0.587836i	−0.913571	−	0.406679i	$-0.866687\pi$
$907$	−923.473	+	533.167i	−1.01816	+	0.587836i	−0.104591	+	0.994515i	$0.533353\pi$
$908$	148.609	−	257.398i	0.163666	−	0.283478i
$909$			141.240i			0.155380i
$910$		0			0
$911$	−1052.95			−1.15582			−0.577911	−	0.816100i	$-0.696132\pi$
$911$	−1052.95			−1.15582			−0.577911	+	0.816100i	$0.696132\pi$
$912$	204.268	+	117.934i	0.223979	+	0.129314i
$913$	−451.087	−	781.306i	−0.494072	−	0.855757i
$914$	352.893	+	611.228i	0.386097	+	0.668740i
$915$		0			0
$916$		−	50.6669i		−	0.0553132i
$917$	266.455	+	1135.60i	0.290572	+	1.23838i
$918$			11.3246i			0.0123362i
$919$	−714.350	+	1237.29i	−0.777312	+	1.34634i	0.156174	+	0.987730i	$0.450084\pi$
$919$	−714.350	+	1237.29i	−0.777312	+	1.34634i	−0.933486	+	0.358614i	$0.883249\pi$
$920$		0			0
$921$	252.250	+	436.910i	0.273887	+	0.474386i
$922$	437.197	−	757.247i	0.474183	−	0.821309i
$923$	853.987			0.925230
$924$	−299.980	−	319.391i	−0.324653	−	0.345661i
$925$		0			0
$926$	137.485	−	238.131i	0.148472	−	0.257160i
$927$	113.918	+	197.313i	0.122889	+	0.212851i
$928$	−80.6678	+	46.5736i	−0.0869265	+	0.0501870i
$929$	1523.62	+	879.664i	1.64007	+	0.946893i	0.980808	+	0.194978i	$0.0624635\pi$
$929$	1523.62	+	879.664i	1.64007	+	0.946893i	0.659260	+	0.751915i	$0.270870\pi$
$930$		0			0
$931$	922.925	−	1389.63i	0.991326	−	1.49262i
$932$			817.772i			0.877438i
$933$	374.761	+	216.368i	0.401673	+	0.231906i
$934$	185.897	−	107.328i	0.199034	−	0.114912i
$935$		0			0
$936$	137.125	+	79.1694i	0.146502	+	0.0845827i
$937$	−1264.00			−1.34898			−0.674490	−	0.738284i	$-0.735637\pi$
$937$	−1264.00			−1.34898			−0.674490	+	0.738284i	$0.735637\pi$
$938$	86.1315	+	91.7049i	0.0918246	+	0.0977664i
$939$	6.55664			0.00698258
$940$		0			0
$941$	228.636	−	132.003i	0.242971	−	0.140280i	−0.373570	−	0.927602i	$-0.621867\pi$
$941$	228.636	−	132.003i	0.242971	−	0.140280i	0.616542	+	0.787322i	$0.288533\pi$
$942$	−50.8872	+	29.3797i	−0.0540203	+	0.0311887i
$943$	505.773	−	876.024i	0.536344	−	0.928975i
$944$		−	296.647i		−	0.314245i
$945$		0			0
$946$	1627.71			1.72063
$947$	−60.6086	−	34.9924i	−0.0640006	−	0.0369508i	0.467658	−	0.883909i	$-0.345098\pi$
$947$	−60.6086	−	34.9924i	−0.0640006	−	0.0369508i	−0.531659	+	0.846959i	$0.678431\pi$
$948$	−230.706	−	399.594i	−0.243360	−	0.421513i
$949$	−339.867	−	588.667i	−0.358132	−	0.620302i
$950$		0			0
$951$		−	123.601i		−	0.129969i
$952$	29.2104	+	8.81641i	0.0306832	+	0.00926094i
$953$		−	1410.53i		−	1.48009i	−0.672555	−	0.740047i	$-0.734803\pi$
$953$		−	1410.53i		−	1.48009i	0.672555	−	0.740047i	$-0.265197\pi$
$954$	−0.941190	+	1.63019i	−0.000986573	+	0.00170879i
$955$		0			0
$956$	−67.0352	−	116.108i	−0.0701205	−	0.121452i
$957$	−257.683	+	446.319i	−0.269261	+	0.466373i
$958$	−317.872			−0.331808
$959$	1015.38	+	306.466i	1.05879	+	0.319568i
$960$		0			0
$961$	−90.1133	+	156.081i	−0.0937704	+	0.162415i
$962$	−681.788	−	1180.89i	−0.708719	−	1.22754i
$963$	278.579	−	160.838i	0.289282	−	0.167017i
$964$	410.287	+	236.879i	0.425609	+	0.245725i
$965$		0			0
$966$	−450.506	+	105.706i	−0.466362	+	0.109427i
$967$			1581.56i			1.63554i	0.575548	+	0.817768i	$0.304789\pi$
$967$			1581.56i			1.63554i	−0.575548	+	0.817768i	$0.695211\pi$
$968$	−503.438	−	290.660i	−0.520080	−	0.300269i
$969$	−78.6988	+	45.4368i	−0.0812165	+	0.0468904i
$970$		0			0
$971$	−518.308	−	299.245i	−0.533788	−	0.308182i	0.208770	−	0.977965i	$-0.433054\pi$
$971$	−518.308	−	299.245i	−0.533788	−	0.308182i	−0.742557	+	0.669782i	$0.766387\pi$
$972$	31.1769			0.0320750
$973$	−774.622	+	727.544i	−0.796117	+	0.747732i
$974$	−98.3767			−0.101003
$975$		0			0
$976$	−364.177	+	210.258i	−0.373132	+	0.215428i
$977$	149.631	−	86.3897i	0.153154	−	0.0884235i	−0.421465	−	0.906845i	$-0.638484\pi$
$977$	149.631	−	86.3897i	0.153154	−	0.0884235i	0.574618	+	0.818421i	$0.305150\pi$
$978$	−310.016	+	536.964i	−0.316990	+	0.549043i
$979$		−	1792.63i		−	1.83108i
$980$		0			0
$981$	−242.671			−0.247371
$982$	−919.115	−	530.651i	−0.935962	−	0.540378i
$983$	−108.206	−	187.419i	−0.110078	−	0.190660i	0.805724	−	0.592292i	$-0.201777\pi$
$983$	−108.206	−	187.419i	−0.110078	−	0.190660i	−0.915801	+	0.401631i	$0.868443\pi$
$984$	91.8113	+	159.022i	0.0933042	+	0.161608i
$985$		0			0
$986$		−	35.8869i		−	0.0363965i
$987$	−234.411	−	249.580i	−0.237499	−	0.252867i
$988$			1270.58i			1.28601i
$989$	859.484	−	1488.67i	0.869043	−	1.50523i
$990$		0			0
$991$	160.993	+	278.849i	0.162455	+	0.281381i	0.935749	−	0.352667i	$-0.114725\pi$
$991$	160.993	+	278.849i	0.162455	+	0.281381i	−0.773293	+	0.634048i	$0.781392\pi$
$992$	79.0328	−	136.889i	0.0796702	−	0.137993i
$993$	592.303			0.596479
$994$	−103.492	−	441.068i	−0.104116	−	0.443731i
$995$		0			0
$996$	86.4752	−	149.779i	0.0868225	−	0.150381i
$997$	23.4063	+	40.5409i	0.0234767	+	0.0406629i	0.877525	−	0.479531i	$-0.159193\pi$
$997$	23.4063	+	40.5409i	0.0234767	+	0.0406629i	−0.854048	+	0.520194i	$0.825860\pi$
$998$	196.167	−	113.257i	0.196560	−	0.113484i
$999$	−232.518	−	134.244i	−0.232750	−	0.134378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.c.649.8		16
5.2	odd	4		210.3.o.a.61.1	yes	8
5.3	odd	4		1050.3.p.b.901.4		8
5.4	even	2	inner	1050.3.q.c.649.1		16
7.3	odd	6	inner	1050.3.q.c.199.1		16
15.2	even	4		630.3.v.b.271.4		8
35.2	odd	12		1470.3.f.a.391.8		8
35.3	even	12		1050.3.p.b.451.4		8
35.12	even	12		1470.3.f.a.391.5		8
35.17	even	12		210.3.o.a.31.1	✓	8
35.24	odd	6	inner	1050.3.q.c.199.8		16
105.17	odd	12		630.3.v.b.451.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.1	✓	8	35.17	even	12
210.3.o.a.61.1	yes	8	5.2	odd	4
630.3.v.b.271.4		8	15.2	even	4
630.3.v.b.451.4		8	105.17	odd	12
1050.3.p.b.451.4		8	35.3	even	12
1050.3.p.b.901.4		8	5.3	odd	4
1050.3.q.c.199.1		16	7.3	odd	6	inner
1050.3.q.c.199.8		16	35.24	odd	6	inner
1050.3.q.c.649.1		16	5.4	even	2	inner
1050.3.q.c.649.8		16	1.1	even	1	trivial
1470.3.f.a.391.5		8	35.12	even	12
1470.3.f.a.391.8		8	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(4.79227 + 5.10237i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(4.79227 + 5.10237i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(9.03504 + 15.6491i) q^{11} +(-1.73205 + 3.00000i) q^{12} -18.6604 q^{13} +(2.26139 + 9.63774i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-0.770543 - 1.33462i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(-29.4836 - 17.0224i) q^{19} +(-3.50333 + 11.6072i) q^{21} +25.5549i q^{22} +(23.3720 + 13.4938i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-22.8542 - 13.1949i) q^{26} -5.19615 q^{27} +(-4.04529 + 13.4028i) q^{28} +16.4662 q^{29} +(-24.1988 + 13.9712i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-15.6491 + 27.1051i) q^{33} -2.17942i q^{34} -6.00000 q^{36} +(44.7480 + 25.8353i) q^{37} +(-24.0733 - 41.6961i) q^{38} +(-16.1604 - 27.9906i) q^{39} -37.4818i q^{41} +(-12.4982 + 11.7386i) q^{42} -63.6947i q^{43} +(-18.0701 + 31.2983i) q^{44} +(19.0831 + 33.0529i) q^{46} +(-14.1204 + 24.4572i) q^{47} -6.92820 q^{48} +(-3.06832 + 48.9038i) q^{49} +(1.33462 - 2.31163i) q^{51} +(-18.6604 - 32.3208i) q^{52} +(0.384239 - 0.221841i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-14.4317 + 13.5546i) q^{56} -58.9672i q^{57} +(20.1669 + 11.6434i) q^{58} +(-64.2260 + 37.0809i) q^{59} +(91.0443 + 52.5645i) q^{61} -39.5164 q^{62} +(-20.4447 + 4.79713i) q^{63} -8.00000 q^{64} +(-38.3324 + 22.1312i) q^{66} +(11.0062 - 6.35442i) q^{67} +(1.54109 - 2.66924i) q^{68} +46.7439i q^{69} -45.7647 q^{71} +(-7.34847 - 4.24264i) q^{72} +(18.2133 + 31.5463i) q^{73} +(36.5366 + 63.2833i) q^{74} -68.0895i q^{76} +(-36.5494 + 121.095i) q^{77} -45.7085i q^{78} +(-66.5990 + 115.353i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(26.5037 - 45.9057i) q^{82} -49.9265 q^{83} +(-23.6076 + 5.53924i) q^{84} +(45.0389 - 78.0097i) q^{86} +(14.2602 + 24.6994i) q^{87} +(-44.2625 + 25.5549i) q^{88} +(-85.9133 - 49.6020i) q^{89} +(-89.4257 - 95.2123i) q^{91} +53.9752i q^{92} +(-41.9135 - 24.1988i) q^{93} +(-34.5878 + 19.9693i) q^{94} +(-8.48528 - 4.89898i) q^{96} +150.376 q^{97} +(-38.3381 + 57.7251i) q^{98} -54.2102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more