LMFDB - Embedded newform 696.2.y.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [696,2,Mod(25,696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(696, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("696.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 696 = 2^{3} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	696.y (of order $7$, degree $6$, 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:	$5.55758798068$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	696.49
Dual form			696.2.y.c.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 + 0.781831i) q^{3} +(-1.90319 + 0.916530i) q^{5} +(-1.94859 - 2.44345i) q^{7} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(0.623490 + 0.781831i) q^{3} +(-1.90319 + 0.916530i) q^{5} +(-1.94859 - 2.44345i) q^{7} +(-0.222521 + 0.974928i) q^{9} +(1.04250 + 4.56748i) q^{11} +(-0.403842 - 1.76935i) q^{13} +(-1.90319 - 0.916530i) q^{15} -4.02480 q^{17} +(-0.956536 + 1.19946i) q^{19} +(0.695444 - 3.04694i) q^{21} +(-5.37061 - 2.58635i) q^{23} +(-0.335331 + 0.420492i) q^{25} +(-0.900969 + 0.433884i) q^{27} +(-3.19812 + 4.33267i) q^{29} +(-9.89853 + 4.76688i) q^{31} +(-2.92101 + 3.66283i) q^{33} +(5.94804 + 2.86443i) q^{35} +(1.46519 - 6.41941i) q^{37} +(1.13154 - 1.41891i) q^{39} +5.17211 q^{41} +(-9.73495 - 4.68810i) q^{43} +(-0.470050 - 2.05942i) q^{45} +(-0.491841 - 2.15490i) q^{47} +(-0.615820 + 2.69808i) q^{49} +(-2.50942 - 3.14672i) q^{51} +(10.2361 - 4.92946i) q^{53} +(-6.17030 - 7.73731i) q^{55} -1.53416 q^{57} +6.67834 q^{59} +(3.02706 + 3.79581i) q^{61} +(2.81579 - 1.35601i) q^{63} +(2.39025 + 2.99727i) q^{65} +(0.154413 - 0.676527i) q^{67} +(-1.32643 - 5.81147i) q^{69} +(2.87494 + 12.5959i) q^{71} +(7.18973 + 3.46239i) q^{73} -0.537829 q^{75} +(9.12902 - 11.4474i) q^{77} +(0.230816 - 1.01127i) q^{79} +(-0.900969 - 0.433884i) q^{81} +(-11.2367 + 14.0903i) q^{83} +(7.65997 - 3.68885i) q^{85} +(-5.38141 + 0.200982i) q^{87} +(-7.63532 + 3.67698i) q^{89} +(-3.53639 + 4.43450i) q^{91} +(-9.89853 - 4.76688i) q^{93} +(0.721134 - 3.15949i) q^{95} +(2.92939 - 3.67334i) q^{97} -4.68494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9	$ 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9} - 12 q^{11} + 7 q^{13} + q^{15} - 38 q^{17} - 18 q^{19} + 4 q^{21} - 6 q^{23} - 19 q^{25} - 4 q^{27} + 5 q^{29} - 2 q^{31} + 2 q^{33} + 21 q^{35} - 18 q^{37} + 7 q^{39} - 70 q^{41} - q^{43} + q^{45} + 23 q^{47} + 8 q^{49} + 11 q^{51} + 26 q^{53} - 17 q^{55} + 10 q^{57} - 4 q^{59} + 10 q^{61} - 3 q^{63} + 43 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 8 q^{73} + 30 q^{75} - 36 q^{77} + 45 q^{79} - 4 q^{81} - 10 q^{83} - 53 q^{85} - 16 q^{87} + 10 q^{89} + 57 q^{91} - 2 q^{93} - 34 q^{95} + 96 q^{97} + 2 q^{99}+O(q^{100}) $ 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9 - 12 * q^11 + 7 * q^13 + q^15 - 38 * q^17 - 18 * q^19 + 4 * q^21 - 6 * q^23 - 19 * q^25 - 4 * q^27 + 5 * q^29 - 2 * q^31 + 2 * q^33 + 21 * q^35 - 18 * q^37 + 7 * q^39 - 70 * q^41 - q^43 + q^45 + 23 * q^47 + 8 * q^49 + 11 * q^51 + 26 * q^53 - 17 * q^55 + 10 * q^57 - 4 * q^59 + 10 * q^61 - 3 * q^63 + 43 * q^65 + 2 * q^67 + 8 * q^69 + 16 * q^71 + 8 * q^73 + 30 * q^75 - 36 * q^77 + 45 * q^79 - 4 * q^81 - 10 * q^83 - 53 * q^85 - 16 * q^87 + 10 * q^89 + 57 * q^91 - 2 * q^93 - 34 * q^95 + 96 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/696\mathbb{Z}\right)^\times$.

$n$	$175$	$233$	$349$	$553$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$4$		0			0
$5$	−1.90319	+	0.916530i	−0.851134	+	0.409884i	−0.807998	−	0.589185i	$-0.799449\pi$
$5$	−1.90319	+	0.916530i	−0.851134	+	0.409884i	−0.0431355	+	0.999069i	$0.513735\pi$
$6$		0			0
$7$	−1.94859	−	2.44345i	−0.736498	−	0.923539i	0.262647	−	0.964892i	$-0.415405\pi$
$7$	−1.94859	−	2.44345i	−0.736498	−	0.923539i	−0.999145	+	0.0413532i	$0.986833\pi$
$8$		0			0
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$		0			0
$11$	1.04250	+	4.56748i	0.314325	+	1.37715i	0.847345	+	0.531043i	$0.178200\pi$
$11$	1.04250	+	4.56748i	0.314325	+	1.37715i	−0.533020	+	0.846102i	$0.678943\pi$
$12$		0			0
$13$	−0.403842	−	1.76935i	−0.112006	−	0.490728i	−0.999550	−	0.0300057i	$-0.990447\pi$
$13$	−0.403842	−	1.76935i	−0.112006	−	0.490728i	0.887544	−	0.460723i	$-0.152410\pi$
$14$		0			0
$15$	−1.90319	−	0.916530i	−0.491402	−	0.236647i
$16$		0			0
$17$	−4.02480			−0.976158			−0.488079	−	0.872800i	$-0.662302\pi$
$17$	−4.02480			−0.976158			−0.488079	+	0.872800i	$0.662302\pi$
$18$		0			0
$19$	−0.956536	+	1.19946i	−0.219444	+	0.275174i	−0.879352	−	0.476172i	$-0.842024\pi$
$19$	−0.956536	+	1.19946i	−0.219444	+	0.275174i	0.659908	+	0.751347i	$0.270595\pi$
$20$		0			0
$21$	0.695444	−	3.04694i	0.151758	−	0.664896i
$22$		0			0
$23$	−5.37061	−	2.58635i	−1.11985	−	0.539291i	−0.220003	−	0.975499i	$-0.570607\pi$
$23$	−5.37061	−	2.58635i	−1.11985	−	0.539291i	−0.899846	+	0.436208i	$0.856321\pi$
$24$		0			0
$25$	−0.335331	+	0.420492i	−0.0670662	+	0.0840984i
$26$		0			0
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$		0			0
$29$	−3.19812	+	4.33267i	−0.593876	+	0.804556i
$29$	−3.19812	+	4.33267i	−0.593876	+	0.804556i
$30$		0			0
$31$	−9.89853	+	4.76688i	−1.77783	+	0.856157i	−0.818177	+	0.574966i	$0.805015\pi$
$31$	−9.89853	+	4.76688i	−1.77783	+	0.856157i	−0.959652	+	0.281191i	$0.909270\pi$
$32$		0			0
$33$	−2.92101	+	3.66283i	−0.508483	+	0.637617i
$34$		0			0
$35$	5.94804	+	2.86443i	1.00540	+	0.484176i
$36$		0			0
$37$	1.46519	−	6.41941i	0.240876	−	1.05534i	−0.699346	−	0.714783i	$-0.746526\pi$
$37$	1.46519	−	6.41941i	0.240876	−	1.05534i	0.940222	−	0.340562i	$-0.110617\pi$
$38$		0			0
$39$	1.13154	−	1.41891i	0.181191	−	0.227207i
$40$		0			0
$41$	5.17211			0.807748			0.403874	−	0.914815i	$-0.367663\pi$
$41$	5.17211			0.807748			0.403874	+	0.914815i	$0.367663\pi$
$42$		0			0
$43$	−9.73495	−	4.68810i	−1.48457	−	0.714929i	−0.496368	−	0.868112i	$-0.665333\pi$
$43$	−9.73495	−	4.68810i	−1.48457	−	0.714929i	−0.988198	+	0.153183i	$0.951048\pi$
$44$		0			0
$45$	−0.470050	−	2.05942i	−0.0700709	−	0.307001i
$46$		0			0
$47$	−0.491841	−	2.15490i	−0.0717424	−	0.314324i	0.926306	−	0.376773i	$-0.122966\pi$
$47$	−0.491841	−	2.15490i	−0.0717424	−	0.314324i	−0.998048	+	0.0624486i	$0.980109\pi$
$48$		0			0
$49$	−0.615820	+	2.69808i	−0.0879742	+	0.385440i
$50$		0			0
$51$	−2.50942	−	3.14672i	−0.351389	−	0.440628i
$52$		0			0
$53$	10.2361	−	4.92946i	1.40604	−	0.677113i	0.431663	−	0.902035i	$-0.357927\pi$
$53$	10.2361	−	4.92946i	1.40604	−	0.677113i	0.974377	+	0.224922i	$0.0722126\pi$
$54$		0			0
$55$	−6.17030	−	7.73731i	−0.832003	−	1.04330i
$56$		0			0
$57$	−1.53416			−0.203205
$58$		0			0
$59$	6.67834			0.869445			0.434723	−	0.900564i	$-0.356846\pi$
$59$	6.67834			0.869445			0.434723	+	0.900564i	$0.356846\pi$
$60$		0			0
$61$	3.02706	+	3.79581i	0.387575	+	0.486004i	0.936896	−	0.349607i	$-0.113685\pi$
$61$	3.02706	+	3.79581i	0.387575	+	0.486004i	−0.549321	+	0.835611i	$0.685114\pi$
$62$		0			0
$63$	2.81579	−	1.35601i	0.354757	−	0.170842i
$64$		0			0
$65$	2.39025	+	2.99727i	0.296474	+	0.371766i
$66$		0			0
$67$	0.154413	−	0.676527i	0.0188645	−	0.0826509i	−0.964619	−	0.263646i	$-0.915075\pi$
$67$	0.154413	−	0.676527i	0.0188645	−	0.0826509i	0.983484	+	0.180995i	$0.0579319\pi$
$68$		0			0
$69$	−1.32643	−	5.81147i	−0.159683	−	0.699619i
$70$		0			0
$71$	2.87494	+	12.5959i	0.341193	+	1.49486i	0.796561	+	0.604559i	$0.206651\pi$
$71$	2.87494	+	12.5959i	0.341193	+	1.49486i	−0.455368	+	0.890303i	$0.650492\pi$
$72$		0			0
$73$	7.18973	+	3.46239i	0.841494	+	0.405242i	0.804413	−	0.594070i	$-0.202480\pi$
$73$	7.18973	+	3.46239i	0.841494	+	0.405242i	0.0370807	+	0.999312i	$0.488194\pi$
$74$		0			0
$75$	−0.537829			−0.0621032
$76$		0			0
$77$	9.12902	−	11.4474i	1.04035	−	1.30456i
$78$		0			0
$79$	0.230816	−	1.01127i	0.0259688	−	0.113777i	−0.960282	−	0.279030i	$-0.909987\pi$
$79$	0.230816	−	1.01127i	0.0259688	−	0.113777i	0.986251	+	0.165253i	$0.0528442\pi$
$80$		0			0
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$		0			0
$83$	−11.2367	+	14.0903i	−1.23338	+	1.54661i	−0.501551	+	0.865128i	$0.667237\pi$
$83$	−11.2367	+	14.0903i	−1.23338	+	1.54661i	−0.731832	+	0.681485i	$0.761335\pi$
$84$		0			0
$85$	7.65997	−	3.68885i	0.830841	−	0.400112i
$86$		0			0
$87$	−5.38141	+	0.200982i	−0.576948	+	0.0215476i
$88$		0			0
$89$	−7.63532	+	3.67698i	−0.809343	+	0.389759i	−0.792327	−	0.610096i	$-0.791131\pi$
$89$	−7.63532	+	3.67698i	−0.809343	+	0.389759i	−0.0170153	+	0.999855i	$0.505416\pi$
$90$		0			0
$91$	−3.53639	+	4.43450i	−0.370715	+	0.464862i
$92$		0			0
$93$	−9.89853	−	4.76688i	−1.02643	−	0.494303i
$94$		0			0
$95$	0.721134	−	3.15949i	0.0739868	−	0.324157i
$96$		0			0
$97$	2.92939	−	3.67334i	0.297435	−	0.372972i	−0.610548	−	0.791980i	$-0.709051\pi$
$97$	2.92939	−	3.67334i	0.297435	−	0.372972i	0.907983	+	0.419008i	$0.137622\pi$
$98$		0			0
$99$	−4.68494			−0.470854
$100$		0			0
$101$	4.74320	+	2.28420i	0.471966	+	0.227287i	0.654719	−	0.755872i	$-0.272787\pi$
$101$	4.74320	+	2.28420i	0.471966	+	0.227287i	−0.182754	+	0.983159i	$0.558501\pi$
$102$		0			0
$103$	4.34612	+	19.0416i	0.428236	+	1.87622i	0.479505	+	0.877539i	$0.340816\pi$
$103$	4.34612	+	19.0416i	0.428236	+	1.87622i	−0.0512693	+	0.998685i	$0.516327\pi$
$104$		0			0
$105$	1.46904	+	6.43630i	0.143364	+	0.628119i
$106$		0			0
$107$	−1.36747	+	5.99130i	−0.132199	+	0.579201i	0.864823	+	0.502077i	$0.167431\pi$
$107$	−1.36747	+	5.99130i	−0.132199	+	0.579201i	−0.997022	+	0.0771235i	$0.975426\pi$
$108$		0			0
$109$	−0.455711	−	0.571444i	−0.0436492	−	0.0547344i	0.759528	−	0.650475i	$-0.225430\pi$
$109$	−0.455711	−	0.571444i	−0.0436492	−	0.0547344i	−0.803177	+	0.595741i	$0.796859\pi$
$110$		0			0
$111$	5.93243	−	2.85691i	0.563081	−	0.271166i
$112$		0			0
$113$	3.92981	+	4.92783i	0.369686	+	0.463571i	0.931526	−	0.363675i	$-0.118478\pi$
$113$	3.92981	+	4.92783i	0.369686	+	0.463571i	−0.561840	+	0.827246i	$0.689907\pi$
$114$		0			0
$115$	12.5918			1.17419
$116$		0			0
$117$	1.81485			0.167783
$118$		0			0
$119$	7.84269	+	9.83442i	0.718938	+	0.901520i
$120$		0			0
$121$	−9.86438	+	4.75043i	−0.896762	+	0.431858i
$122$		0			0
$123$	3.22476	+	4.04372i	0.290767	+	0.364610i
$124$		0			0
$125$	2.60306	−	11.4047i	0.232824	−	1.02007i
$126$		0			0
$127$	−4.43477	−	19.4300i	−0.393522	−	1.72413i	−0.652091	−	0.758141i	$-0.726108\pi$
$127$	−4.43477	−	19.4300i	−0.393522	−	1.72413i	0.258568	−	0.965993i	$-0.416749\pi$
$128$		0			0
$129$	−2.40433	−	10.5341i	−0.211690	−	0.927474i
$130$		0			0
$131$	−3.39514	−	1.63501i	−0.296634	−	0.142852i	0.279647	−	0.960103i	$-0.409783\pi$
$131$	−3.39514	−	1.63501i	−0.296634	−	0.142852i	−0.576282	+	0.817251i	$0.695497\pi$
$132$		0			0
$133$	4.79472			0.415755
$134$		0			0
$135$	1.31705	−	1.65153i	0.113354	−	0.142141i
$136$		0			0
$137$	1.08133	−	4.73764i	0.0923846	−	0.404764i	−0.907498	−	0.420055i	$-0.862011\pi$
$137$	1.08133	−	4.73764i	0.0923846	−	0.404764i	0.999883	+	0.0152919i	$0.00486776\pi$
$138$		0			0
$139$	−2.58238	−	1.24361i	−0.219034	−	0.105481i	0.321149	−	0.947029i	$-0.395931\pi$
$139$	−2.58238	−	1.24361i	−0.219034	−	0.105481i	−0.540183	+	0.841547i	$0.681645\pi$
$140$		0			0
$141$	1.37811	−	1.72809i	0.116058	−	0.145532i
$142$		0			0
$143$	7.66044	−	3.68907i	0.640598	−	0.308496i
$144$		0			0
$145$	2.11562	−	11.1771i	0.175693	−	0.928206i
$146$		0			0
$147$	−2.49340	+	1.20076i	−0.205652	+	0.0990370i
$148$		0			0
$149$	−4.11518	+	5.16027i	−0.337129	+	0.422746i	−0.921281	−	0.388898i	$-0.872856\pi$
$149$	−4.11518	+	5.16027i	−0.337129	+	0.422746i	0.584152	+	0.811644i	$0.301427\pi$
$150$		0			0
$151$	1.13778	+	0.547928i	0.0925916	+	0.0445898i	0.479606	−	0.877484i	$-0.340779\pi$
$151$	1.13778	+	0.547928i	0.0925916	+	0.0445898i	−0.387015	+	0.922074i	$0.626494\pi$
$152$		0			0
$153$	0.895603	−	3.92389i	0.0724052	−	0.317228i
$154$		0			0
$155$	14.4698	−	18.1446i	1.16224	−	1.45741i
$156$		0			0
$157$	−3.09312			−0.246858			−0.123429	−	0.992353i	$-0.539389\pi$
$157$	−3.09312			−0.246858			−0.123429	+	0.992353i	$0.539389\pi$
$158$		0			0
$159$	10.2361	+	4.92946i	0.811778	+	0.390931i
$160$		0			0
$161$	4.14549	+	18.1626i	0.326710	+	1.43141i
$162$		0			0
$163$	−0.965224	−	4.22892i	−0.0756022	−	0.331235i	0.922957	−	0.384904i	$-0.125765\pi$
$163$	−0.965224	−	4.22892i	−0.0756022	−	0.331235i	−0.998559	+	0.0536693i	$0.982908\pi$
$164$		0			0
$165$	2.20215	−	9.64827i	0.171437	−	0.751117i
$166$		0			0
$167$	3.19353	+	4.00456i	0.247123	+	0.309882i	0.889886	−	0.456183i	$-0.150784\pi$
$167$	3.19353	+	4.00456i	0.247123	+	0.309882i	−0.642764	+	0.766065i	$0.722212\pi$
$168$		0			0
$169$	8.74510	−	4.21142i	0.672700	−	0.323955i
$170$		0			0
$171$	−0.956536	−	1.19946i	−0.0731481	−	0.0917248i
$172$		0			0
$173$	−9.52263			−0.723992			−0.361996	−	0.932180i	$-0.617905\pi$
$173$	−9.52263			−0.723992			−0.361996	+	0.932180i	$0.617905\pi$
$174$		0			0
$175$	1.68088			0.127062
$176$		0			0
$177$	4.16388	+	5.22133i	0.312976	+	0.392460i
$178$		0			0
$179$	10.6886	−	5.14735i	0.798902	−	0.384731i	0.0105417	−	0.999944i	$-0.496644\pi$
$179$	10.6886	−	5.14735i	0.798902	−	0.384731i	0.788361	+	0.615213i	$0.210930\pi$
$180$		0			0
$181$	15.0510	+	18.8734i	1.11874	+	1.40285i	0.904713	+	0.426021i	$0.140085\pi$
$181$	15.0510	+	18.8734i	1.11874	+	1.40285i	0.214022	+	0.976829i	$0.431344\pi$
$182$		0			0
$183$	−1.08035	+	4.73330i	−0.0798614	+	0.349896i
$184$		0			0
$185$	3.09504	+	13.5603i	0.227552	+	0.996971i
$186$		0			0
$187$	−4.19584	−	18.3832i	−0.306830	−	1.34431i
$188$		0			0
$189$	2.81579	+	1.35601i	0.204819	+	0.0986356i
$190$		0			0
$191$	−17.1041			−1.23761			−0.618805	−	0.785545i	$-0.712383\pi$
$191$	−17.1041			−1.23761			−0.618805	+	0.785545i	$0.712383\pi$
$192$		0			0
$193$	−12.1366	+	15.2188i	−0.873610	+	1.09547i	0.121088	+	0.992642i	$0.461362\pi$
$193$	−12.1366	+	15.2188i	−0.873610	+	1.09547i	−0.994699	+	0.102831i	$0.967210\pi$
$194$		0			0
$195$	−0.853069	+	3.73754i	−0.0610895	+	0.267651i
$196$		0			0
$197$	2.11371	+	1.01791i	0.150596	+	0.0725232i	0.507664	−	0.861555i	$-0.330509\pi$
$197$	2.11371	+	1.01791i	0.150596	+	0.0725232i	−0.357068	+	0.934078i	$0.616224\pi$
$198$		0			0
$199$	−1.98967	+	2.49496i	−0.141044	+	0.176863i	−0.847336	−	0.531057i	$-0.821795\pi$
$199$	−1.98967	+	2.49496i	−0.141044	+	0.176863i	0.706292	+	0.707920i	$0.250366\pi$
$200$		0			0
$201$	0.625205	−	0.301083i	0.0440986	−	0.0212367i
$202$		0			0
$203$	16.8185	−	0.628129i	1.18043	−	0.0440860i
$204$		0			0
$205$	−9.84353	+	4.74039i	−0.687502	+	0.331083i
$206$		0			0
$207$	3.71658	−	4.66044i	0.258320	−	0.323923i
$208$		0			0
$209$	−6.47568	−	3.11852i	−0.447932	−	0.215713i
$210$		0			0
$211$	3.37950	−	14.8065i	0.232654	−	1.01932i	−0.714774	−	0.699356i	$-0.753470\pi$
$211$	3.37950	−	14.8065i	0.232654	−	1.01932i	0.947428	−	0.319969i	$-0.103673\pi$
$212$		0			0
$213$	−8.05540	+	10.1012i	−0.551947	+	0.692120i
$214$		0			0
$215$	22.8243			1.55660
$216$		0			0
$217$	30.9358	+	14.8979i	2.10006	+	1.01134i
$218$		0			0
$219$	1.77572	+	7.77992i	0.119992	+	0.525718i
$220$		0			0
$221$	1.62538	+	7.12126i	0.109335	+	0.479028i
$222$		0			0
$223$	−0.0365618	+	0.160188i	−0.00244836	+	0.0107270i	−0.976137	−	0.217154i	$-0.930323\pi$
$223$	−0.0365618	+	0.160188i	−0.00244836	+	0.0107270i	0.973689	+	0.227881i	$0.0731797\pi$
$224$		0			0
$225$	−0.335331	−	0.420492i	−0.0223554	−	0.0280328i
$226$		0			0
$227$	−2.13588	+	1.02858i	−0.141763	+	0.0682695i	−0.503420	−	0.864042i	$-0.667925\pi$
$227$	−2.13588	+	1.02858i	−0.141763	+	0.0682695i	0.361657	+	0.932311i	$0.382211\pi$
$228$		0			0
$229$	−15.8013	−	19.8143i	−1.04418	−	1.30936i	−0.949470	−	0.313859i	$-0.898378\pi$
$229$	−15.8013	−	19.8143i	−1.04418	−	1.30936i	−0.0947126	−	0.995505i	$-0.530193\pi$
$230$		0			0
$231$	14.6418			0.963360
$232$		0			0
$233$	9.18680			0.601847			0.300924	−	0.953648i	$-0.402705\pi$
$233$	9.18680			0.601847			0.300924	+	0.953648i	$0.402705\pi$
$234$		0			0
$235$	2.91110	+	3.65040i	0.189899	+	0.238126i
$236$		0			0
$237$	0.934554	−	0.450058i	0.0607058	−	0.0292344i
$238$		0			0
$239$	−13.3187	−	16.7011i	−0.861515	−	1.08031i	−0.995997	−	0.0893893i	$-0.971508\pi$
$239$	−13.3187	−	16.7011i	−0.861515	−	1.08031i	0.134482	−	0.990916i	$-0.457063\pi$
$240$		0			0
$241$	4.42700	−	19.3960i	0.285168	−	1.24940i	−0.605902	−	0.795539i	$-0.707188\pi$
$241$	4.42700	−	19.3960i	0.285168	−	1.24940i	0.891071	−	0.453865i	$-0.149955\pi$
$242$		0			0
$243$	−0.222521	−	0.974928i	−0.0142747	−	0.0625417i
$244$		0			0
$245$	−1.30085	−	5.69939i	−0.0831082	−	0.364121i
$246$		0			0
$247$	2.50854	+	1.20805i	0.159615	+	0.0768665i
$248$		0			0
$249$	−18.0222			−1.14211
$250$		0			0
$251$	−0.945206	+	1.18525i	−0.0596609	+	0.0748124i	−0.810767	−	0.585370i	$-0.800949\pi$
$251$	−0.945206	+	1.18525i	−0.0596609	+	0.0748124i	0.751106	+	0.660182i	$0.229521\pi$
$252$		0			0
$253$	6.21424	−	27.2264i	0.390686	−	1.71171i
$254$		0			0
$255$	7.65997	+	3.68885i	0.479686	+	0.231005i
$256$		0			0
$257$	−17.8076	+	22.3300i	−1.11081	+	1.39291i	−0.200139	+	0.979768i	$0.564139\pi$
$257$	−17.8076	+	22.3300i	−1.11081	+	1.39291i	−0.910668	+	0.413140i	$0.864432\pi$
$258$		0			0
$259$	−18.5406	+	8.92868i	−1.15206	+	0.554801i
$260$		0			0
$261$	−3.51239	−	4.08205i	−0.217412	−	0.252672i
$262$		0			0
$263$	−2.51537	+	1.21134i	−0.155104	+	0.0746942i	−0.509825	−	0.860278i	$-0.670290\pi$
$263$	−2.51537	+	1.21134i	−0.155104	+	0.0746942i	0.354721	+	0.934972i	$0.384576\pi$
$264$		0			0
$265$	−14.9633	+	18.7634i	−0.919190	+	1.15263i
$266$		0			0
$267$	−7.63532	−	3.67698i	−0.467274	−	0.225027i
$268$		0			0
$269$	−1.49724	+	6.55985i	−0.0912886	+	0.399961i	−0.999841	−	0.0178086i	$-0.994331\pi$
$269$	−1.49724	+	6.55985i	−0.0912886	+	0.399961i	0.908553	+	0.417770i	$0.137188\pi$
$270$		0			0
$271$	5.48976	−	6.88394i	0.333479	−	0.418169i	−0.586616	−	0.809865i	$-0.699540\pi$
$271$	5.48976	−	6.88394i	0.333479	−	0.418169i	0.920095	+	0.391696i	$0.128112\pi$
$272$		0			0
$273$	−5.67193			−0.343281
$274$		0			0
$275$	−2.27017	−	1.09326i	−0.136896	−	0.0659258i
$276$		0			0
$277$	−3.86776	−	16.9457i	−0.232391	−	1.01817i	−0.947650	−	0.319312i	$-0.896548\pi$
$277$	−3.86776	−	16.9457i	−0.232391	−	1.01817i	0.715259	−	0.698860i	$-0.246309\pi$
$278$		0			0
$279$	−2.44474	−	10.7111i	−0.146363	−	0.641256i
$280$		0			0
$281$	5.31145	−	23.2710i	0.316854	−	1.38823i	−0.526182	−	0.850372i	$-0.676377\pi$
$281$	5.31145	−	23.2710i	0.316854	−	1.38823i	0.843036	−	0.537857i	$-0.180766\pi$
$282$		0			0
$283$	9.99282	+	12.5306i	0.594012	+	0.744867i	0.984431	−	0.175770i	$-0.0562415\pi$
$283$	9.99282	+	12.5306i	0.594012	+	0.744867i	−0.390420	+	0.920637i	$0.627670\pi$
$284$		0			0
$285$	2.91981	−	1.40611i	0.172955	−	0.0832906i
$286$		0			0
$287$	−10.0783	−	12.6378i	−0.594904	−	0.745987i
$288$		0			0
$289$	−0.800975			−0.0471162
$290$		0			0
$291$	4.69838			0.275424
$292$		0			0
$293$	−6.99855	−	8.77590i	−0.408859	−	0.512693i	0.534182	−	0.845370i	$-0.320620\pi$
$293$	−6.99855	−	8.77590i	−0.408859	−	0.512693i	−0.943041	+	0.332676i	$0.892048\pi$
$294$		0			0
$295$	−12.7102	+	6.12089i	−0.740014	+	0.356372i
$296$		0			0
$297$	−2.92101	−	3.66283i	−0.169494	−	0.212539i
$298$		0			0
$299$	−2.40727	+	10.5469i	−0.139216	+	0.609945i
$300$		0			0
$301$	7.51425	+	32.9221i	0.433114	+	1.89760i
$302$		0			0
$303$	1.17147	+	5.13256i	0.0672994	+	0.294858i
$304$		0			0
$305$	−9.24006	−	4.44978i	−0.529084	−	0.254793i
$306$		0			0
$307$	14.0682			0.802914			0.401457	−	0.915878i	$-0.368504\pi$
$307$	14.0682			0.802914			0.401457	+	0.915878i	$0.368504\pi$
$308$		0			0
$309$	−12.1776	+	15.2702i	−0.692757	+	0.868690i
$310$		0			0
$311$	−1.24157	+	5.43966i	−0.0704028	+	0.308455i	−0.997853	−	0.0654915i	$-0.979138\pi$
$311$	−1.24157	+	5.43966i	−0.0704028	+	0.308455i	0.927450	+	0.373946i	$0.121996\pi$
$312$		0			0
$313$	1.92030	+	0.924768i	0.108542	+	0.0522710i	0.487367	−	0.873197i	$-0.337957\pi$
$313$	1.92030	+	0.924768i	0.108542	+	0.0522710i	−0.378825	+	0.925468i	$0.623672\pi$
$314$		0			0
$315$	−4.11617	+	5.16152i	−0.231920	+	0.290818i
$316$		0			0
$317$	6.02828	−	2.90306i	0.338582	−	0.163052i	−0.256865	−	0.966447i	$-0.582689\pi$
$317$	6.02828	−	2.90306i	0.338582	−	0.163052i	0.595446	+	0.803395i	$0.296975\pi$
$318$		0			0
$319$	−23.1234	−	10.0906i	−1.29466	−	0.564962i
$320$		0			0
$321$	−5.53679	+	2.66638i	−0.309034	+	0.148823i
$322$		0			0
$323$	3.84987	−	4.82758i	0.214212	−	0.268614i
$324$		0			0
$325$	0.879416	+	0.423505i	0.0487812	+	0.0234918i
$326$		0			0
$327$	0.162642	−	0.712579i	0.00899410	−	0.0394057i
$328$		0			0
$329$	−4.30700	+	5.40080i	−0.237452	+	0.297756i
$330$		0			0
$331$	−4.59771			−0.252713			−0.126357	−	0.991985i	$-0.540328\pi$
$331$	−4.59771			−0.252713			−0.126357	+	0.991985i	$0.540328\pi$
$332$		0			0
$333$	5.93243	+	2.85691i	0.325095	+	0.156558i
$334$		0			0
$335$	0.326179	+	1.42909i	0.0178211	+	0.0780793i
$336$		0			0
$337$	0.0277324	+	0.121504i	0.00151068	+	0.00661873i	0.975678	−	0.219210i	$-0.0703481\pi$
$337$	0.0277324	+	0.121504i	0.00151068	+	0.00661873i	−0.974167	+	0.225829i	$0.927491\pi$
$338$		0			0
$339$	−1.40253	+	6.14490i	−0.0761752	+	0.333745i
$340$		0			0
$341$	−32.0918	−	40.2418i	−1.73787	−	2.17922i
$342$		0			0
$343$	−11.9179	+	5.73937i	−0.643508	+	0.309897i
$344$		0			0
$345$	7.85084	+	9.84464i	0.422675	+	0.530018i
$346$		0			0
$347$	8.40968			0.451455			0.225728	−	0.974190i	$-0.427524\pi$
$347$	8.40968			0.451455			0.225728	+	0.974190i	$0.427524\pi$
$348$		0			0
$349$	3.31271			0.177325			0.0886626	−	0.996062i	$-0.471741\pi$
$349$	3.31271			0.177325			0.0886626	+	0.996062i	$0.471741\pi$
$350$		0			0
$351$	1.13154	+	1.41891i	0.0603971	+	0.0757355i
$352$		0			0
$353$	−21.6751	+	10.4382i	−1.15365	+	0.555569i	−0.910128	−	0.414327i	$-0.864017\pi$
$353$	−21.6751	+	10.4382i	−1.15365	+	0.555569i	−0.243522	+	0.969895i	$0.578303\pi$
$354$		0			0
$355$	−17.0161	−	21.3375i	−0.903121	−	1.13248i
$356$		0			0
$357$	−2.79902	+	12.2633i	−0.148140	+	0.649044i
$358$		0			0
$359$	−1.77272	−	7.76678i	−0.0935605	−	0.409915i	0.906360	−	0.422506i	$-0.138849\pi$
$359$	−1.77272	−	7.76678i	−0.0935605	−	0.409915i	−0.999921	+	0.0125905i	$0.995992\pi$
$360$		0			0
$361$	3.70416	+	16.2290i	0.194956	+	0.854157i
$362$		0			0
$363$	−9.86438	−	4.75043i	−0.517745	−	0.249333i
$364$		0			0
$365$	−16.8568			−0.882326
$366$		0			0
$367$	−23.0814	+	28.9431i	−1.20484	+	1.51082i	−0.400880	+	0.916131i	$0.631296\pi$
$367$	−23.0814	+	28.9431i	−1.20484	+	1.51082i	−0.803957	+	0.594687i	$0.797276\pi$
$368$		0			0
$369$	−1.15090	+	5.04243i	−0.0599136	+	0.262499i
$370$		0			0
$371$	−31.9909	−	15.4060i	−1.66089	−	0.799840i
$372$		0			0
$373$	−19.1504	+	24.0139i	−0.991571	+	1.24339i	−0.0217023	+	0.999764i	$0.506909\pi$
$373$	−19.1504	+	24.0139i	−0.991571	+	1.24339i	−0.969869	+	0.243627i	$0.921663\pi$
$374$		0			0
$375$	10.5396	−	5.07558i	0.544260	−	0.262102i
$376$		0			0
$377$	8.95752	+	3.90887i	0.461336	+	0.201317i
$378$		0			0
$379$	23.0908	−	11.1199i	1.18610	−	0.571193i	0.266414	−	0.963859i	$-0.414161\pi$
$379$	23.0908	−	11.1199i	1.18610	−	0.571193i	0.919681	+	0.392665i	$0.128447\pi$
$380$		0			0
$381$	12.4260	−	15.5817i	0.636601	−	0.798272i
$382$		0			0
$383$	17.2640	+	8.31393i	0.882152	+	0.424822i	0.819410	−	0.573208i	$-0.194301\pi$
$383$	17.2640	+	8.31393i	0.882152	+	0.424822i	0.0627418	+	0.998030i	$0.480016\pi$
$384$		0			0
$385$	−6.88238	+	30.1537i	−0.350759	+	1.53677i
$386$		0			0
$387$	6.73679	−	8.44767i	0.342451	−	0.429419i
$388$		0			0
$389$	−12.5166			−0.634618			−0.317309	−	0.948322i	$-0.602779\pi$
$389$	−12.5166			−0.634618			−0.317309	+	0.948322i	$0.602779\pi$
$390$		0			0
$391$	21.6156	+	10.4095i	1.09315	+	0.526433i
$392$		0			0
$393$	−0.838529	−	3.67384i	−0.0422982	−	0.185321i
$394$		0			0
$395$	0.487572	+	2.13619i	0.0245324	+	0.107483i
$396$		0			0
$397$	−1.08401	+	4.74934i	−0.0544047	+	0.238363i	−0.994818	−	0.101671i	$-0.967581\pi$
$397$	−1.08401	+	4.74934i	−0.0544047	+	0.238363i	0.940413	+	0.340033i	$0.110438\pi$
$398$		0			0
$399$	2.98946	+	3.74866i	0.149660	+	0.187668i
$400$		0			0
$401$	−31.2068	+	15.0284i	−1.55840	+	0.750484i	−0.997025	−	0.0770807i	$-0.975440\pi$
$401$	−31.2068	+	15.0284i	−1.55840	+	0.750484i	−0.561371	+	0.827564i	$0.689726\pi$
$402$		0			0
$403$	12.4317	+	15.5889i	0.619267	+	0.776536i
$404$		0			0
$405$	2.11239			0.104965
$406$		0			0
$407$	30.8480			1.52908
$408$		0			0
$409$	−8.95264	−	11.2263i	−0.442680	−	0.555103i	0.509568	−	0.860431i	$-0.329805\pi$
$409$	−8.95264	−	11.2263i	−0.442680	−	0.555103i	−0.952247	+	0.305328i	$0.901234\pi$
$410$		0			0
$411$	4.37823	−	2.10845i	0.215962	−	0.104002i
$412$		0			0
$413$	−13.0133	−	16.3182i	−0.640345	−	0.802967i
$414$		0			0
$415$	8.47133	−	37.1153i	0.415841	−	1.82192i
$416$		0			0
$417$	−0.637794	−	2.79436i	−0.0312329	−	0.136840i
$418$		0			0
$419$	−4.01286	−	17.5815i	−0.196041	−	0.858912i	−0.973264	−	0.229687i	$-0.926230\pi$
$419$	−4.01286	−	17.5815i	−0.196041	−	0.858912i	0.777223	−	0.629225i	$-0.216628\pi$
$420$		0			0
$421$	10.2869	+	4.95389i	0.501351	+	0.241438i	0.667427	−	0.744675i	$-0.267396\pi$
$421$	10.2869	+	4.95389i	0.501351	+	0.241438i	−0.166076	+	0.986113i	$0.553110\pi$
$422$		0			0
$423$	2.21031			0.107469
$424$		0			0
$425$	1.34964	−	1.69240i	0.0654672	−	0.0820933i
$426$		0			0
$427$	3.37640	−	14.7930i	0.163395	−	0.715882i
$428$		0			0
$429$	7.66044	+	3.68907i	0.369850	+	0.178110i
$430$		0			0
$431$	−9.18336	+	11.5156i	−0.442347	+	0.554685i	−0.952160	−	0.305600i	$-0.901143\pi$
$431$	−9.18336	+	11.5156i	−0.442347	+	0.554685i	0.509813	+	0.860285i	$0.329714\pi$
$432$		0			0
$433$	−8.75214	+	4.21481i	−0.420601	+	0.202551i	−0.632199	−	0.774806i	$-0.717848\pi$
$433$	−8.75214	+	4.21481i	−0.420601	+	0.202551i	0.211598	+	0.977357i	$0.432133\pi$
$434$		0			0
$435$	10.0577	−	5.31473i	0.482228	−	0.254822i
$436$		0			0
$437$	8.23939	−	3.96788i	0.394144	−	0.189810i
$438$		0			0
$439$	−22.8345	+	28.6335i	−1.08983	+	1.36660i	−0.164970	+	0.986299i	$0.552753\pi$
$439$	−22.8345	+	28.6335i	−1.08983	+	1.36660i	−0.924861	+	0.380306i	$0.875819\pi$
$440$		0			0
$441$	−2.49340	−	1.20076i	−0.118733	−	0.0571790i
$442$		0			0
$443$	−7.96875	+	34.9134i	−0.378607	+	1.65878i	0.323135	+	0.946353i	$0.395263\pi$
$443$	−7.96875	+	34.9134i	−0.378607	+	1.65878i	−0.701741	+	0.712432i	$0.747594\pi$
$444$		0			0
$445$	11.1614	−	13.9960i	0.529103	−	0.663474i
$446$		0			0
$447$	−6.60023			−0.312180
$448$		0			0
$449$	2.58773	+	1.24619i	0.122123	+	0.0588111i	0.493947	−	0.869492i	$-0.335554\pi$
$449$	2.58773	+	1.24619i	0.122123	+	0.0588111i	−0.371825	+	0.928303i	$0.621268\pi$
$450$		0			0
$451$	5.39191	+	23.6235i	0.253895	+	1.11239i
$452$		0			0
$453$	0.281010	+	1.23118i	0.0132030	+	0.0578460i
$454$		0			0
$455$	2.66609	−	11.6809i	0.124988	−	0.547610i
$456$		0			0
$457$	6.95759	+	8.72454i	0.325462	+	0.408117i	0.917463	−	0.397820i	$-0.130233\pi$
$457$	6.95759	+	8.72454i	0.325462	+	0.408117i	−0.592001	+	0.805937i	$0.701662\pi$
$458$		0			0
$459$	3.62622	−	1.74630i	0.169257	−	0.0815101i
$460$		0			0
$461$	−17.8107	−	22.3339i	−0.829528	−	1.04020i	−0.998510	−	0.0545760i	$-0.982619\pi$
$461$	−17.8107	−	22.3339i	−0.829528	−	1.04020i	0.168982	−	0.985619i	$-0.445952\pi$
$462$		0			0
$463$	−15.2268			−0.707648			−0.353824	−	0.935312i	$-0.615119\pi$
$463$	−15.2268			−0.707648			−0.353824	+	0.935312i	$0.615119\pi$
$464$		0			0
$465$	23.2078			1.07624
$466$		0			0
$467$	−2.77942	−	3.48529i	−0.128616	−	0.161280i	0.713353	−	0.700804i	$-0.247175\pi$
$467$	−2.77942	−	3.48529i	−0.128616	−	0.161280i	−0.841970	+	0.539525i	$0.818604\pi$
$468$		0			0
$469$	−1.95395	+	0.940973i	−0.0902250	+	0.0434501i
$470$		0			0
$471$	−1.92853	−	2.41830i	−0.0888620	−	0.111429i
$472$		0			0
$473$	11.2642	−	49.3515i	0.517926	−	2.26918i
$474$		0			0
$475$	−0.183606	−	0.804431i	−0.00842443	−	0.0369098i
$476$		0			0
$477$	2.52811	+	11.0764i	0.115754	+	0.507153i
$478$		0			0
$479$	−24.6315	−	11.8619i	−1.12544	−	0.541985i	−0.223874	−	0.974618i	$-0.571870\pi$
$479$	−24.6315	−	11.8619i	−1.12544	−	0.541985i	−0.901570	+	0.432633i	$0.857585\pi$
$480$		0			0
$481$	−11.9499			−0.544867
$482$		0			0
$483$	−11.6154	+	14.5652i	−0.528519	+	0.662742i
$484$		0			0
$485$	−2.20847	+	9.67596i	−0.100282	+	0.439363i
$486$		0			0
$487$	33.1363	+	15.9576i	1.50155	+	0.723109i	0.990637	−	0.136523i	$-0.0435927\pi$
$487$	33.1363	+	15.9576i	1.50155	+	0.723109i	0.510914	+	0.859632i	$0.329307\pi$
$488$		0			0
$489$	2.70450	−	3.39133i	0.122302	−	0.153361i
$490$		0			0
$491$	−34.6117	+	16.6681i	−1.56200	+	0.752222i	−0.997325	−	0.0730892i	$-0.976714\pi$
$491$	−34.6117	+	16.6681i	−1.56200	+	0.752222i	−0.564679	+	0.825311i	$0.691000\pi$
$492$		0			0
$493$	12.8718	−	17.4381i	0.579717	−	0.785374i
$494$		0			0
$495$	8.91634	−	4.29388i	0.400760	−	0.192996i
$496$		0			0
$497$	25.1755	−	31.5691i	1.12928	−	1.41607i
$498$		0			0
$499$	39.0189	+	18.7905i	1.74672	+	0.841178i	0.979945	+	0.199266i	$0.0638558\pi$
$499$	39.0189	+	18.7905i	1.74672	+	0.841178i	0.766778	+	0.641912i	$0.221859\pi$
$500$		0			0
$501$	−1.13976	+	4.99360i	−0.0509206	+	0.223098i
$502$		0			0
$503$	5.85084	−	7.33672i	0.260876	−	0.327128i	−0.634093	−	0.773257i	$-0.718626\pi$
$503$	5.85084	−	7.33672i	0.260876	−	0.327128i	0.894969	+	0.446129i	$0.147198\pi$
$504$		0			0
$505$	−11.1208			−0.494868
$506$		0			0
$507$	8.74510	+	4.21142i	0.388383	+	0.187036i
$508$		0			0
$509$	6.76130	+	29.6232i	0.299689	+	1.31302i	0.870591	+	0.492007i	$0.163736\pi$
$509$	6.76130	+	29.6232i	0.299689	+	1.31302i	−0.570902	+	0.821018i	$0.693406\pi$
$510$		0			0
$511$	−5.54964	−	24.3145i	−0.245501	−	1.07561i
$512$		0			0
$513$	0.341384	−	1.49570i	0.0150725	−	0.0660367i
$514$		0			0
$515$	−25.7237	−	32.2565i	−1.13352	−	1.42139i
$516$		0			0
$517$	9.32970	−	4.49295i	0.410320	−	0.197600i
$518$		0			0
$519$	−5.93727	−	7.44510i	−0.260617	−	0.326803i
$520$		0			0
$521$	−32.3293			−1.41637			−0.708186	−	0.706025i	$-0.750486\pi$
$521$	−32.3293			−1.41637			−0.708186	+	0.706025i	$0.750486\pi$
$522$		0			0
$523$	8.02151			0.350756			0.175378	−	0.984501i	$-0.443885\pi$
$523$	8.02151			0.350756			0.175378	+	0.984501i	$0.443885\pi$
$524$		0			0
$525$	1.04801	+	1.31416i	0.0457389	+	0.0573547i
$526$		0			0
$527$	39.8396	−	19.1858i	1.73544	−	0.835745i
$528$		0			0
$529$	7.81396	+	9.79840i	0.339737	+	0.426017i
$530$		0			0
$531$	−1.48607	+	6.51090i	−0.0644899	+	0.282549i
$532$		0			0
$533$	−2.08871	−	9.15125i	−0.0904722	−	0.396385i
$534$		0			0
$535$	−2.88863	−	12.6559i	−0.124887	−	0.547164i
$536$		0			0
$537$	10.6886	+	5.14735i	0.461247	+	0.222125i
$538$		0			0
$539$	−12.9654			−0.558460
$540$		0			0
$541$	23.2237	−	29.1216i	0.998464	−	1.25203i	0.0308700	−	0.999523i	$-0.490172\pi$
$541$	23.2237	−	29.1216i	0.998464	−	1.25203i	0.967594	−	0.252511i	$-0.0812564\pi$
$542$		0			0
$543$	−5.37166	+	23.5348i	−0.230520	+	1.00997i
$544$		0			0
$545$	1.39105	+	0.669896i	0.0595861	+	0.0286952i
$546$		0			0
$547$	26.2675	−	32.9384i	1.12312	−	1.40834i	0.221848	−	0.975081i	$-0.428791\pi$
$547$	26.2675	−	32.9384i	1.12312	−	1.40834i	0.901268	−	0.433262i	$-0.142637\pi$
$548$		0			0
$549$	−4.37423	+	2.10652i	−0.186688	+	0.0899040i
$550$		0			0
$551$	−2.13774	−	7.98036i	−0.0910706	−	0.339975i
$552$		0			0
$553$	−2.92076	+	1.40656i	−0.124203	+	0.0598131i
$554$		0			0
$555$	−8.67212	+	10.8745i	−0.368111	+	0.461597i
$556$		0			0
$557$	15.6837	+	7.55288i	0.664540	+	0.320026i	0.735570	−	0.677448i	$-0.236914\pi$
$557$	15.6837	+	7.55288i	0.664540	+	0.320026i	−0.0710299	+	0.997474i	$0.522629\pi$
$558$		0			0
$559$	−4.36350	+	19.1177i	−0.184556	+	0.808594i
$560$		0			0
$561$	11.7565	−	14.7422i	0.496359	−	0.622415i
$562$		0			0
$563$	−43.6163			−1.83821			−0.919105	−	0.394013i	$-0.871086\pi$
$563$	−43.6163			−1.83821			−0.919105	+	0.394013i	$0.871086\pi$
$564$		0			0
$565$	−11.9957	−	5.77682i	−0.504662	−	0.243033i
$566$		0			0
$567$	0.695444	+	3.04694i	0.0292059	+	0.127959i
$568$		0			0
$569$	10.2513	+	44.9141i	0.429759	+	1.88290i	0.468177	+	0.883635i	$0.344911\pi$
$569$	10.2513	+	44.9141i	0.429759	+	1.88290i	−0.0384181	+	0.999262i	$0.512232\pi$
$570$		0			0
$571$	5.20668	−	22.8120i	0.217893	−	0.954651i	−0.741139	−	0.671352i	$-0.765714\pi$
$571$	5.20668	−	22.8120i	0.217893	−	0.954651i	0.959032	−	0.283299i	$-0.0914289\pi$
$572$		0			0
$573$	−10.6642	−	13.3725i	−0.445505	−	0.558645i
$574$		0			0
$575$	2.88847	−	1.39101i	0.120458	−	0.0580093i
$576$		0			0
$577$	−20.5502	−	25.7691i	−0.855516	−	1.07278i	−0.996568	−	0.0827809i	$-0.973620\pi$
$577$	−20.5502	−	25.7691i	−0.855516	−	1.07278i	0.141052	−	0.990002i	$-0.454952\pi$
$578$		0			0
$579$	−19.4656			−0.808961
$580$		0			0
$581$	56.3247			2.33674
$582$		0			0
$583$	33.1863	+	41.6143i	1.37444	+	1.72349i
$584$		0			0
$585$	−3.45401	+	1.66336i	−0.142806	+	0.0687715i
$586$		0			0
$587$	6.51350	+	8.16767i	0.268841	+	0.337116i	0.897866	−	0.440269i	$-0.145117\pi$
$587$	6.51350	+	8.16767i	0.268841	+	0.337116i	−0.629025	+	0.777385i	$0.716546\pi$
$588$		0			0
$589$	3.75063	−	16.4326i	0.154542	−	0.677092i
$590$		0			0
$591$	0.522044	+	2.28723i	0.0214740	+	0.0940839i
$592$		0			0
$593$	0.997806	+	4.37167i	0.0409750	+	0.179523i	0.991274	−	0.131814i	$-0.0420802\pi$
$593$	0.997806	+	4.37167i	0.0409750	+	0.179523i	−0.950299	+	0.311337i	$0.899223\pi$
$594$		0			0
$595$	−23.9397	−	11.5287i	−0.981431	−	0.472632i
$596$		0			0
$597$	−3.19118			−0.130606
$598$		0			0
$599$	1.44077	−	1.80667i	0.0588682	−	0.0738184i	−0.751526	−	0.659704i	$-0.770682\pi$
$599$	1.44077	−	1.80667i	0.0588682	−	0.0738184i	0.810394	+	0.585885i	$0.199253\pi$
$600$		0			0
$601$	−3.05698	+	13.3935i	−0.124697	+	0.546333i	0.873528	+	0.486774i	$0.161827\pi$
$601$	−3.05698	+	13.3935i	−0.124697	+	0.546333i	−0.998225	+	0.0595589i	$0.981031\pi$
$602$		0			0
$603$	0.625205	+	0.301083i	0.0254603	+	0.0122610i
$604$		0			0
$605$	14.4199	−	18.0820i	0.586252	−	0.735137i
$606$		0			0
$607$	−34.6692	+	16.6958i	−1.40718	+	0.677662i	−0.974604	−	0.223935i	$-0.928110\pi$
$607$	−34.6692	+	16.6958i	−1.40718	+	0.677662i	−0.432576	+	0.901597i	$0.642395\pi$
$608$		0			0
$609$	10.9773	+	12.7576i	0.444821	+	0.516964i
$610$		0			0
$611$	−3.61413	+	1.74047i	−0.146212	+	0.0704121i
$612$		0			0
$613$	18.6812	−	23.4255i	0.754528	−	0.946149i	−0.245200	−	0.969473i	$-0.578853\pi$
$613$	18.6812	−	23.4255i	0.754528	−	0.946149i	0.999728	+	0.0233239i	$0.00742490\pi$
$614$		0			0
$615$	−9.84353	−	4.74039i	−0.396929	−	0.191151i
$616$		0			0
$617$	5.25108	−	23.0065i	0.211400	−	0.926205i	−0.752216	−	0.658916i	$-0.771015\pi$
$617$	5.25108	−	23.0065i	0.211400	−	0.926205i	0.963616	−	0.267289i	$-0.0861278\pi$
$618$		0			0
$619$	2.42675	−	3.04304i	0.0975392	−	0.122310i	−0.730666	−	0.682735i	$-0.760791\pi$
$619$	2.42675	−	3.04304i	0.0975392	−	0.122310i	0.828206	+	0.560424i	$0.189362\pi$
$620$		0			0
$621$	5.96092			0.239204
$622$		0			0
$623$	23.8626	+	11.4916i	0.956036	+	0.460403i
$624$		0			0
$625$	4.90027	+	21.4695i	0.196011	+	0.858779i
$626$		0			0
$627$	−1.59936	−	7.00726i	−0.0638723	−	0.279843i
$628$		0			0
$629$	−5.89709	+	25.8369i	−0.235133	+	1.03018i
$630$		0			0
$631$	−5.80192	−	7.27537i	−0.230971	−	0.289628i	0.652818	−	0.757515i	$-0.273587\pi$
$631$	−5.80192	−	7.27537i	−0.230971	−	0.289628i	−0.883788	+	0.467887i	$0.845015\pi$
$632$		0			0
$633$	13.6833	−	6.58953i	0.543863	−	0.261910i
$634$		0			0
$635$	26.2484	+	32.9144i	1.04164	+	1.30617i
$636$		0			0
$637$	5.02253			0.199000
$638$		0			0
$639$	−12.9199			−0.511102
$640$		0			0
$641$	15.9198	+	19.9628i	0.628793	+	0.788482i	0.989552	−	0.144178i	$-0.0460536\pi$
$641$	15.9198	+	19.9628i	0.628793	+	0.788482i	−0.360759	+	0.932659i	$0.617482\pi$
$642$		0			0
$643$	−27.7894	+	13.3826i	−1.09591	+	0.527760i	−0.892369	−	0.451307i	$-0.850958\pi$
$643$	−27.7894	+	13.3826i	−1.09591	+	0.527760i	−0.203537	+	0.979067i	$0.565244\pi$
$644$		0			0
$645$	14.2307	+	17.8447i	0.560333	+	0.702636i
$646$		0			0
$647$	−2.80884	+	12.3063i	−0.110427	+	0.483813i	0.889226	+	0.457468i	$0.151244\pi$
$647$	−2.80884	+	12.3063i	−0.110427	+	0.483813i	−0.999653	+	0.0263441i	$0.991613\pi$
$648$		0			0
$649$	6.96214	+	30.5031i	0.273288	+	1.19735i
$650$		0			0
$651$	7.64052	+	33.4753i	0.299456	+	1.31200i
$652$		0			0
$653$	14.2907	+	6.88204i	0.559238	+	0.269315i	0.692078	−	0.721823i	$-0.256695\pi$
$653$	14.2907	+	6.88204i	0.559238	+	0.269315i	−0.132840	+	0.991138i	$0.542410\pi$
$654$		0			0
$655$	7.96014			0.311028
$656$		0			0
$657$	−4.97545	+	6.23901i	−0.194111	+	0.243407i
$658$		0			0
$659$	4.32747	−	18.9599i	0.168574	−	0.738572i	−0.817994	−	0.575226i	$-0.804914\pi$
$659$	4.32747	−	18.9599i	0.168574	−	0.738572i	0.986569	−	0.163346i	$-0.0522288\pi$
$660$		0			0
$661$	−5.37568	−	2.58879i	−0.209090	−	0.100692i	0.326408	−	0.945229i	$-0.394162\pi$
$661$	−5.37568	−	2.58879i	−0.209090	−	0.100692i	−0.535498	+	0.844537i	$0.679876\pi$
$662$		0			0
$663$	−4.55422	+	5.71081i	−0.176871	+	0.221790i
$664$		0			0
$665$	−9.12527	+	4.39450i	−0.353863	+	0.170411i
$666$		0			0
$667$	28.3816	−	14.9976i	1.09894	−	0.580710i
$668$		0			0
$669$	−0.148036	+	0.0712903i	−0.00572340	+	0.00275624i
$670$		0			0
$671$	−14.1816	+	17.7831i	−0.547474	+	0.686511i
$672$		0			0
$673$	7.69346	+	3.70497i	0.296561	+	0.142816i	0.576248	−	0.817275i	$-0.304516\pi$
$673$	7.69346	+	3.70497i	0.296561	+	0.142816i	−0.279687	+	0.960091i	$0.590231\pi$
$674$		0			0
$675$	0.119678	−	0.524345i	0.00460642	−	0.0201820i
$676$		0			0
$677$	10.8859	−	13.6505i	0.418380	−	0.524632i	−0.527323	−	0.849665i	$-0.676804\pi$
$677$	10.8859	−	13.6505i	0.418380	−	0.524632i	0.945703	+	0.325033i	$0.105376\pi$
$678$		0			0
$679$	−14.6838			−0.563514
$680$		0			0
$681$	−2.13588	−	1.02858i	−0.0818469	−	0.0394154i
$682$		0			0
$683$	−5.32475	−	23.3293i	−0.203746	−	0.892670i	−0.968631	−	0.248503i	$-0.920061\pi$
$683$	−5.32475	−	23.3293i	−0.203746	−	0.892670i	0.764885	−	0.644167i	$-0.222796\pi$
$684$		0			0
$685$	2.28419	+	10.0077i	0.0872746	+	0.382375i
$686$		0			0
$687$	5.63943	−	24.7080i	0.215158	−	0.942668i
$688$		0			0
$689$	−12.8557	−	16.1205i	−0.489763	−	0.614143i
$690$		0			0
$691$	22.2559	−	10.7179i	0.846656	−	0.407728i	0.0403208	−	0.999187i	$-0.487162\pi$
$691$	22.2559	−	10.7179i	0.846656	−	0.407728i	0.806335	+	0.591459i	$0.201448\pi$
$692$		0			0
$693$	9.12902	+	11.4474i	0.346783	+	0.434852i
$694$		0			0
$695$	6.05456			0.229663
$696$		0			0
$697$	−20.8167			−0.788489
$698$		0			0
$699$	5.72787	+	7.18253i	0.216648	+	0.271668i
$700$		0			0
$701$	11.7127	−	5.64055i	0.442384	−	0.213041i	−0.199413	−	0.979916i	$-0.563904\pi$
$701$	11.7127	−	5.64055i	0.442384	−	0.213041i	0.641797	+	0.766875i	$0.278189\pi$
$702$		0			0
$703$	6.29831	+	7.89783i	0.237545	+	0.297872i
$704$		0			0
$705$	−1.03896	+	4.55197i	−0.0391294	+	0.171437i
$706$		0			0
$707$	−3.66120	−	16.0408i	−0.137694	−	0.603275i
$708$		0			0
$709$	3.59708	+	15.7598i	0.135091	+	0.591873i	0.996473	+	0.0839148i	$0.0267424\pi$
$709$	3.59708	+	15.7598i	0.135091	+	0.591873i	−0.861382	+	0.507958i	$0.830400\pi$
$710$		0			0
$711$	0.934554	+	0.450058i	0.0350485	+	0.0168785i
$712$		0			0
$713$	65.4900			2.45262
$714$		0			0
$715$	−11.1982	+	14.0420i	−0.418787	+	0.525142i
$716$		0			0
$717$	4.75339	−	20.8259i	0.177518	−	0.777759i
$718$		0			0
$719$	0.253381	+	0.122022i	0.00944953	+	0.00455065i	0.438603	−	0.898681i	$-0.355474\pi$
$719$	0.253381	+	0.122022i	0.00944953	+	0.00455065i	−0.429153	+	0.903232i	$0.641188\pi$
$720$		0			0
$721$	38.0585	−	47.7238i	1.41737	−	1.77733i
$722$		0			0
$723$	17.9246	−	8.63201i	0.666622	−	0.321028i
$724$		0			0
$725$	−0.749422	−	2.79766i	−0.0278329	−	0.103903i
$726$		0			0
$727$	−35.1272	+	16.9164i	−1.30280	+	0.627394i	−0.951147	−	0.308737i	$-0.900094\pi$
$727$	−35.1272	+	16.9164i	−1.30280	+	0.627394i	−0.351650	+	0.936131i	$0.614379\pi$
$728$		0			0
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$		0			0
$731$	39.1812	+	18.8687i	1.44917	+	0.697884i
$732$		0			0
$733$	−1.43801	+	6.30035i	−0.0531143	+	0.232709i	−0.994517	−	0.104576i	$-0.966651\pi$
$733$	−1.43801	+	6.30035i	−0.0531143	+	0.232709i	0.941403	+	0.337285i	$0.109509\pi$
$734$		0			0
$735$	3.64490	−	4.57056i	0.134444	−	0.168587i
$736$		0			0
$737$	3.25100			0.119752
$738$		0			0
$739$	33.2878	+	16.0306i	1.22451	+	0.589694i	0.930565	−	0.366128i	$-0.119317\pi$
$739$	33.2878	+	16.0306i	1.22451	+	0.589694i	0.293947	+	0.955822i	$0.405031\pi$
$740$		0			0
$741$	0.619559	+	2.71447i	0.0227601	+	0.0997184i
$742$		0			0
$743$	−5.26364	−	23.0615i	−0.193104	−	0.846044i	−0.974924	−	0.222540i	$-0.928565\pi$
$743$	−5.26364	−	23.0615i	−0.193104	−	0.846044i	0.781820	−	0.623505i	$-0.214292\pi$
$744$		0			0
$745$	3.10244	−	13.5927i	0.113665	−	0.497997i
$746$		0			0
$747$	−11.2367	−	14.0903i	−0.411128	−	0.515538i
$748$		0			0
$749$	17.3041	−	8.33322i	0.632278	−	0.304489i
$750$		0			0
$751$	−12.8351	−	16.0947i	−0.468358	−	0.587302i	0.490410	−	0.871492i	$-0.336847\pi$
$751$	−12.8351	−	16.0947i	−0.468358	−	0.587302i	−0.958768	+	0.284189i	$0.908276\pi$
$752$		0			0
$753$	−1.51599			−0.0552459
$754$		0			0
$755$	−2.66762			−0.0970845
$756$		0			0
$757$	−24.9611	−	31.3002i	−0.907226	−	1.13763i	−0.990001	−	0.141058i	$-0.954950\pi$
$757$	−24.9611	−	31.3002i	−0.907226	−	1.13763i	0.0827750	−	0.996568i	$-0.473622\pi$
$758$		0			0
$759$	25.1610	−	12.1169i	0.913285	−	0.439815i
$760$		0			0
$761$	−17.8158	−	22.3403i	−0.645822	−	0.809835i	0.345896	−	0.938273i	$-0.387575\pi$
$761$	−17.8158	−	22.3403i	−0.645822	−	0.809835i	−0.991718	+	0.128438i	$0.959004\pi$
$762$		0			0
$763$	−0.508303	+	2.22702i	−0.0184018	+	0.0806235i
$764$		0			0
$765$	1.89186	+	8.28877i	0.0684002	+	0.299681i
$766$		0			0
$767$	−2.69699	−	11.8163i	−0.0973827	−	0.426661i
$768$		0			0
$769$	30.8016	+	14.8333i	1.11074	+	0.534902i	0.897018	−	0.441994i	$-0.145729\pi$
$769$	30.8016	+	14.8333i	1.11074	+	0.534902i	0.213717	+	0.976896i	$0.431443\pi$
$770$		0			0
$771$	−28.5611			−1.02860
$772$		0			0
$773$	−30.7651	+	38.5783i	−1.10655	+	1.38756i	−0.192818	+	0.981234i	$0.561763\pi$
$773$	−30.7651	+	38.5783i	−1.10655	+	1.38756i	−0.913727	+	0.406329i	$0.866809\pi$
$774$		0			0
$775$	1.31485	−	5.76074i	0.0472308	−	0.206932i
$776$		0			0
$777$	−18.5406	−	8.92868i	−0.665140	−	0.320315i
$778$		0			0
$779$	−4.94731	+	6.20373i	−0.177256	+	0.222272i
$780$		0			0
$781$	−54.5345	+	26.2624i	−1.95140	+	0.939744i
$782$		0			0
$783$	1.00153	−	5.29121i	0.0357919	−	0.189093i
$784$		0			0
$785$	5.88681	−	2.83494i	0.210109	−	0.101183i
$786$		0			0
$787$	4.79647	−	6.01459i	0.170976	−	0.214397i	−0.688960	−	0.724800i	$-0.741932\pi$
$787$	4.79647	−	6.01459i	0.170976	−	0.214397i	0.859935	+	0.510403i	$0.170504\pi$
$788$		0			0
$789$	−2.51537	−	1.21134i	−0.0895494	−	0.0431247i
$790$		0			0
$791$	4.38333	−	19.2046i	0.155853	−	0.682838i
$792$		0			0
$793$	5.49365	−	6.88882i	0.195085	−	0.244629i
$794$		0			0
$795$	−23.9993			−0.851168
$796$		0			0
$797$	22.4033	+	10.7889i	0.793566	+	0.382161i	0.786325	−	0.617812i	$-0.211981\pi$
$797$	22.4033	+	10.7889i	0.793566	+	0.382161i	0.00724069	+	0.999974i	$0.497695\pi$
$798$		0			0
$799$	1.97956	+	8.67303i	0.0700319	+	0.306830i
$800$		0			0
$801$	−1.88577	−	8.26209i	−0.0666304	−	0.291927i
$802$		0			0
$803$	−8.31912	+	36.4484i	−0.293575	+	1.28624i
$804$		0			0
$805$	−24.5362	−	30.7674i	−0.864787	−	1.08441i
$806$		0			0
$807$	−6.06222	+	2.91941i	−0.213400	+	0.102768i
$808$		0			0
$809$	13.7769	+	17.2756i	0.484369	+	0.607379i	0.962624	−	0.270842i	$-0.0873021\pi$
$809$	13.7769	+	17.2756i	0.484369	+	0.607379i	−0.478255	+	0.878221i	$0.658731\pi$
$810$		0			0
$811$	54.8711			1.92679			0.963393	−	0.268094i	$-0.0863938\pi$
$811$	54.8711			1.92679			0.963393	+	0.268094i	$0.0863938\pi$
$812$		0			0
$813$	8.80489			0.308801
$814$		0			0
$815$	5.71294	+	7.16380i	0.200116	+	0.250937i
$816$		0			0
$817$	14.9350	−	7.19232i	0.522510	−	0.251627i
$818$		0			0
$819$	−3.53639	−	4.43450i	−0.123572	−	0.154954i
$820$		0			0
$821$	−7.85136	+	34.3990i	−0.274014	+	1.20054i	0.631214	+	0.775609i	$0.282557\pi$
$821$	−7.85136	+	34.3990i	−0.274014	+	1.20054i	−0.905228	+	0.424926i	$0.860300\pi$
$822$		0			0
$823$	5.25722	+	23.0334i	0.183255	+	0.802894i	0.980067	+	0.198666i	$0.0636610\pi$
$823$	5.25722	+	23.0334i	0.183255	+	0.802894i	−0.796812	+	0.604227i	$0.793482\pi$
$824$		0			0
$825$	−0.560685	−	2.45652i	−0.0195206	−	0.0855251i
$826$		0			0
$827$	−32.8478	−	15.8187i	−1.14223	−	0.550069i	−0.235539	−	0.971865i	$-0.575686\pi$
$827$	−32.8478	−	15.8187i	−1.14223	−	0.550069i	−0.906691	+	0.421796i	$0.861400\pi$
$828$		0			0
$829$	3.30966			0.114949			0.0574746	−	0.998347i	$-0.481695\pi$
$829$	3.30966			0.114949			0.0574746	+	0.998347i	$0.481695\pi$
$830$		0			0
$831$	10.8372	−	13.5894i	0.375939	−	0.471412i
$832$		0			0
$833$	2.47855	−	10.8592i	0.0858767	−	0.376251i
$834$		0			0
$835$	−9.74819	−	4.69448i	−0.337350	−	0.162459i
$836$		0			0
$837$	6.85000	−	8.58963i	0.236771	−	0.296901i
$838$		0			0
$839$	−22.2770	+	10.7280i	−0.769087	+	0.370373i	−0.776922	−	0.629597i	$-0.783220\pi$
$839$	−22.2770	+	10.7280i	−0.769087	+	0.370373i	0.00783528	+	0.999969i	$0.497506\pi$
$840$		0			0
$841$	−8.54403	−	27.7128i	−0.294622	−	0.955614i
$842$		0			0
$843$	21.5056	−	10.3566i	0.740692	−	0.356699i
$844$		0			0
$845$	−12.7837	+	16.0303i	−0.439773	+	0.551459i
$846$		0			0
$847$	30.8291	+	14.8465i	1.05930	+	0.510132i
$848$		0			0
$849$	−3.56640	+	15.6254i	−0.122398	+	0.536263i
$850$		0			0
$851$	−24.4718	+	30.6867i	−0.838882	+	1.05192i
$852$		0			0
$853$	−22.5898			−0.773461			−0.386730	−	0.922193i	$-0.626396\pi$
$853$	−22.5898			−0.773461			−0.386730	+	0.922193i	$0.626396\pi$
$854$		0			0
$855$	2.91981	+	1.40611i	0.0998554	+	0.0480878i
$856$		0			0
$857$	−7.22123	−	31.6383i	−0.246673	−	1.08074i	−0.934806	−	0.355159i	$-0.884427\pi$
$857$	−7.22123	−	31.6383i	−0.246673	−	1.08074i	0.688133	−	0.725584i	$-0.258430\pi$
$858$		0			0
$859$	0.940087	+	4.11879i	0.0320754	+	0.140531i	0.988430	−	0.151677i	$-0.0484672\pi$
$859$	0.940087	+	4.11879i	0.0320754	+	0.140531i	−0.956355	+	0.292208i	$0.905610\pi$
$860$		0			0
$861$	3.59691	−	15.7591i	0.122582	−	0.537069i
$862$		0			0
$863$	−22.8363	−	28.6359i	−0.777358	−	0.974776i	0.222642	−	0.974900i	$-0.428532\pi$
$863$	−22.8363	−	28.6359i	−0.777358	−	0.974776i	−1.00000		0.000123864i	$0.999961\pi$
$864$		0			0
$865$	18.1234	−	8.72778i	0.616214	−	0.296753i
$866$		0			0
$867$	−0.499400	−	0.626227i	−0.0169605	−	0.0212678i
$868$		0			0
$869$	4.85958			0.164850
$870$		0			0
$871$	−1.25937			−0.0426721
$872$		0			0
$873$	2.92939	+	3.67334i	0.0991450	+	0.124324i
$874$		0			0
$875$	−32.9392	+	15.8627i	−1.11355	+	0.536257i
$876$		0			0
$877$	33.6043	+	42.1385i	1.13474	+	1.42292i	0.891542	+	0.452938i	$0.149624\pi$
$877$	33.6043	+	42.1385i	1.13474	+	1.42292i	0.243196	+	0.969977i	$0.421804\pi$
$878$		0			0
$879$	2.49775	−	10.9434i	0.0842471	−	0.369111i
$880$		0			0
$881$	2.23579	+	9.79565i	0.0753258	+	0.330024i	0.998525	−	0.0542985i	$-0.0172922\pi$
$881$	2.23579	+	9.79565i	0.0753258	+	0.330024i	−0.923199	+	0.384322i	$0.874435\pi$
$882$		0			0
$883$	1.79926	+	7.88309i	0.0605501	+	0.265287i	0.996137	−	0.0878082i	$-0.0279863\pi$
$883$	1.79926	+	7.88309i	0.0605501	+	0.265287i	−0.935587	+	0.353095i	$0.885129\pi$
$884$		0			0
$885$	−12.7102	−	6.12089i	−0.427248	−	0.205752i
$886$		0			0
$887$	−23.0304			−0.773284			−0.386642	−	0.922230i	$-0.626365\pi$
$887$	−23.0304			−0.773284			−0.386642	+	0.922230i	$0.626365\pi$
$888$		0			0
$889$	−38.8348	+	48.6973i	−1.30248	+	1.63325i
$890$		0			0
$891$	1.04250	−	4.56748i	0.0349249	−	0.153016i
$892$		0			0
$893$	3.05517	+	1.47129i	0.102237	+	0.0492350i
$894$		0			0
$895$	−15.6247	+	19.5928i	−0.522278	+	0.654915i
$896$		0			0
$897$	−9.74683	+	4.69383i	−0.325437	+	0.156722i
$898$		0			0
$899$	11.0034	−	58.1321i	0.366984	−	1.93882i
$900$		0			0
$901$	−41.1984	+	19.8401i	−1.37252	+	0.660969i
$902$		0			0
$903$	−21.0545	+	26.4015i	−0.700649	+	0.878586i
$904$		0			0
$905$	−45.9431	−	22.1250i	−1.52720	−	0.735461i
$906$		0			0
$907$	−7.15893	+	31.3653i	−0.237708	+	1.04147i	0.705355	+	0.708854i	$0.250788\pi$
$907$	−7.15893	+	31.3653i	−0.237708	+	1.04147i	−0.943063	+	0.332614i	$0.892069\pi$
$908$		0			0
$909$	−3.28240	+	4.11599i	−0.108870	+	0.136519i
$910$		0			0
$911$	16.5489			0.548289			0.274145	−	0.961688i	$-0.411605\pi$
$911$	16.5489			0.548289			0.274145	+	0.961688i	$0.411605\pi$
$912$		0			0
$913$	−76.0713	−	36.6340i	−2.51759	−	1.21241i
$914$		0			0
$915$	−2.28211	−	9.99856i	−0.0754441	−	0.330542i
$916$		0			0
$917$	2.62065	+	11.4818i	0.0865415	+	0.379163i
$918$		0			0
$919$	2.41012	−	10.5594i	0.0795026	−	0.348323i	−0.919494	−	0.393103i	$-0.871401\pi$
$919$	2.41012	−	10.5594i	0.0795026	−	0.348323i	0.998997	+	0.0447798i	$0.0142586\pi$
$920$		0			0
$921$	8.77137	+	10.9990i	0.289027	+	0.362428i
$922$		0			0
$923$	21.1255	−	10.1735i	0.695356	−	0.334866i
$924$		0			0
$925$	2.20799	+	2.76873i	0.0725982	+	0.0910353i
$926$		0			0
$927$	−19.5313			−0.641492
$928$		0			0
$929$	55.1907			1.81075			0.905375	−	0.424614i	$-0.139590\pi$
$929$	55.1907			1.81075			0.905375	+	0.424614i	$0.139590\pi$
$930$		0			0
$931$	−2.64718	−	3.31946i	−0.0867579	−	0.108791i
$932$		0			0
$933$	−5.02700	+	2.42088i	−0.164577	+	0.0792560i
$934$		0			0
$935$	24.8342	+	31.1411i	0.812166	+	1.01842i
$936$		0			0
$937$	9.68655	−	42.4395i	0.316446	−	1.38644i	−0.527292	−	0.849684i	$-0.676793\pi$
$937$	9.68655	−	42.4395i	0.316446	−	1.38644i	0.843738	−	0.536756i	$-0.180350\pi$
$938$		0			0
$939$	0.474275	+	2.07794i	0.0154774	+	0.0678108i
$940$		0			0
$941$	9.66070	+	42.3263i	0.314930	+	1.37980i	0.846322	+	0.532671i	$0.178812\pi$
$941$	9.66070	+	42.3263i	0.314930	+	1.37980i	−0.531392	+	0.847126i	$0.678331\pi$
$942$		0			0
$943$	−27.7774	−	13.3769i	−0.904556	−	0.435611i
$944$		0			0
$945$	−6.60183			−0.214757
$946$		0			0
$947$	−25.8637	+	32.4321i	−0.840459	+	1.05390i	0.157337	+	0.987545i	$0.449709\pi$
$947$	−25.8637	+	32.4321i	−0.840459	+	1.05390i	−0.997796	+	0.0663569i	$0.978862\pi$
$948$		0			0
$949$	3.22265	−	14.1194i	0.104612	−	0.458334i
$950$		0			0
$951$	6.02828	+	2.90306i	0.195480	+	0.0941383i
$952$		0			0
$953$	−7.30846	+	9.16452i	−0.236744	+	0.296868i	−0.885984	−	0.463716i	$-0.846516\pi$
$953$	−7.30846	+	9.16452i	−0.236744	+	0.296868i	0.649240	+	0.760584i	$0.275087\pi$
$954$		0			0
$955$	32.5524	−	15.6764i	1.05337	−	0.507277i
$956$		0			0
$957$	−6.52809	−	24.3699i	−0.211023	−	0.787769i
$958$		0			0
$959$	−13.6833	+	6.58952i	−0.441856	+	0.212787i
$960$		0			0
$961$	55.9296	−	70.1335i	1.80418	−	2.26237i
$962$		0			0
$963$	−5.53679	−	2.66638i	−0.178421	−	0.0859229i
$964$		0			0
$965$	9.14979	−	40.0878i	0.294542	−	1.29047i
$966$		0			0
$967$	31.3221	−	39.2766i	1.00725	−	1.26305i	0.0427170	−	0.999087i	$-0.486399\pi$
$967$	31.3221	−	39.2766i	1.00725	−	1.26305i	0.964533	−	0.263964i	$-0.0850300\pi$
$968$		0			0
$969$	6.17471			0.198360
$970$		0			0
$971$	−16.5390	−	7.96475i	−0.530761	−	0.255601i	0.149254	−	0.988799i	$-0.452313\pi$
$971$	−16.5390	−	7.96475i	−0.530761	−	0.255601i	−0.680015	+	0.733198i	$0.738027\pi$
$972$		0			0
$973$	1.99329	+	8.73319i	0.0639021	+	0.279973i
$974$		0			0
$975$	0.217198	+	0.951606i	0.00695590	+	0.0304758i
$976$		0			0
$977$	7.72131	−	33.8293i	0.247027	−	1.08229i	−0.687439	−	0.726242i	$-0.741265\pi$
$977$	7.72131	−	33.8293i	0.247027	−	1.08229i	0.934466	−	0.356053i	$-0.115878\pi$
$978$		0			0
$979$	−24.7543	−	31.0409i	−0.791151	−	0.992072i
$980$		0			0
$981$	0.658522	−	0.317128i	0.0210250	−	0.0101251i
$982$		0			0
$983$	24.1672	+	30.3046i	0.770812	+	0.966568i	0.999977	−	0.00681953i	$-0.00217074\pi$
$983$	24.1672	+	30.3046i	0.770812	+	0.966568i	−0.229164	+	0.973388i	$0.573599\pi$
$984$		0			0
$985$	−4.95575			−0.157903
$986$		0			0
$987$	−6.90789			−0.219880
$988$		0			0
$989$	40.1575	+	50.3559i	1.27693	+	1.60123i
$990$		0			0
$991$	−36.7056	+	17.6765i	−1.16599	+	0.561512i	−0.913799	−	0.406166i	$-0.866866\pi$
$991$	−36.7056	+	17.6765i	−1.16599	+	0.561512i	−0.252191	+	0.967677i	$0.581151\pi$
$992$		0			0
$993$	−2.86663	−	3.59464i	−0.0909697	−	0.114072i
$994$		0			0
$995$	1.50001	−	6.57198i	0.0475536	−	0.208346i
$996$		0			0
$997$	−0.187625	−	0.822038i	−0.00594214	−	0.0260342i	0.971870	−	0.235518i	$-0.0756787\pi$
$997$	−0.187625	−	0.822038i	−0.00594214	−	0.0260342i	−0.977812	+	0.209484i	$0.932822\pi$
$998$		0			0
$999$	1.46519	+	6.41941i	0.0463565	+	0.203101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	696.2.y.c.49.1	✓	24
29.16	even	7	inner	696.2.y.c.625.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
696.2.y.c.49.1	✓	24	1.1	even	1	trivial
696.2.y.c.625.1	yes	24	29.16	even	7	inner

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:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.y (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 + 0.781831i) q^{3} +(-1.90319 + 0.916530i) q^{5} +(-1.94859 - 2.44345i) q^{7} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(0.623490 + 0.781831i) q^{3} +(-1.90319 + 0.916530i) q^{5} +(-1.94859 - 2.44345i) q^{7} +(-0.222521 + 0.974928i) q^{9} +(1.04250 + 4.56748i) q^{11} +(-0.403842 - 1.76935i) q^{13} +(-1.90319 - 0.916530i) q^{15} -4.02480 q^{17} +(-0.956536 + 1.19946i) q^{19} +(0.695444 - 3.04694i) q^{21} +(-5.37061 - 2.58635i) q^{23} +(-0.335331 + 0.420492i) q^{25} +(-0.900969 + 0.433884i) q^{27} +(-3.19812 + 4.33267i) q^{29} +(-9.89853 + 4.76688i) q^{31} +(-2.92101 + 3.66283i) q^{33} +(5.94804 + 2.86443i) q^{35} +(1.46519 - 6.41941i) q^{37} +(1.13154 - 1.41891i) q^{39} +5.17211 q^{41} +(-9.73495 - 4.68810i) q^{43} +(-0.470050 - 2.05942i) q^{45} +(-0.491841 - 2.15490i) q^{47} +(-0.615820 + 2.69808i) q^{49} +(-2.50942 - 3.14672i) q^{51} +(10.2361 - 4.92946i) q^{53} +(-6.17030 - 7.73731i) q^{55} -1.53416 q^{57} +6.67834 q^{59} +(3.02706 + 3.79581i) q^{61} +(2.81579 - 1.35601i) q^{63} +(2.39025 + 2.99727i) q^{65} +(0.154413 - 0.676527i) q^{67} +(-1.32643 - 5.81147i) q^{69} +(2.87494 + 12.5959i) q^{71} +(7.18973 + 3.46239i) q^{73} -0.537829 q^{75} +(9.12902 - 11.4474i) q^{77} +(0.230816 - 1.01127i) q^{79} +(-0.900969 - 0.433884i) q^{81} +(-11.2367 + 14.0903i) q^{83} +(7.65997 - 3.68885i) q^{85} +(-5.38141 + 0.200982i) q^{87} +(-7.63532 + 3.67698i) q^{89} +(-3.53639 + 4.43450i) q^{91} +(-9.89853 - 4.76688i) q^{93} +(0.721134 - 3.15949i) q^{95} +(2.92939 - 3.67334i) q^{97} -4.68494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9	\( 24 q - 4 q^{3} + q^{5} + 4 q^{7} - 4 q^{9} - 12 q^{11} + 7 q^{13} + q^{15} - 38 q^{17} - 18 q^{19} + 4 q^{21} - 6 q^{23} - 19 q^{25} - 4 q^{27} + 5 q^{29} - 2 q^{31} + 2 q^{33} + 21 q^{35} - 18 q^{37} + 7 q^{39} - 70 q^{41} - q^{43} + q^{45} + 23 q^{47} + 8 q^{49} + 11 q^{51} + 26 q^{53} - 17 q^{55} + 10 q^{57} - 4 q^{59} + 10 q^{61} - 3 q^{63} + 43 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 8 q^{73} + 30 q^{75} - 36 q^{77} + 45 q^{79} - 4 q^{81} - 10 q^{83} - 53 q^{85} - 16 q^{87} + 10 q^{89} + 57 q^{91} - 2 q^{93} - 34 q^{95} + 96 q^{97} + 2 q^{99}+O(q^{100}) \) 24 * q - 4 * q^3 + q^5 + 4 * q^7 - 4 * q^9 - 12 * q^11 + 7 * q^13 + q^15 - 38 * q^17 - 18 * q^19 + 4 * q^21 - 6 * q^23 - 19 * q^25 - 4 * q^27 + 5 * q^29 - 2 * q^31 + 2 * q^33 + 21 * q^35 - 18 * q^37 + 7 * q^39 - 70 * q^41 - q^43 + q^45 + 23 * q^47 + 8 * q^49 + 11 * q^51 + 26 * q^53 - 17 * q^55 + 10 * q^57 - 4 * q^59 + 10 * q^61 - 3 * q^63 + 43 * q^65 + 2 * q^67 + 8 * q^69 + 16 * q^71 + 8 * q^73 + 30 * q^75 - 36 * q^77 + 45 * q^79 - 4 * q^81 - 10 * q^83 - 53 * q^85 - 16 * q^87 + 10 * q^89 + 57 * q^91 - 2 * q^93 - 34 * q^95 + 96 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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