LMFDB - Embedded newform 76.3.j.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, 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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 $ x^18 + 93x^16 + 3429x^14 + 64261x^12 + 647217x^10 + 3386277x^8 + 8232133x^6 + 8319228x^4 + 2467872x^2 + 69312
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.2
Root			$0.176873i$ of defining polynomial
Character	$\chi$	$=$	76.29
Dual form			76.3.j.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37974 - 1.64431i) q^{3} +(3.12714 + 1.13819i) q^{5} +(5.96525 - 10.3321i) q^{7} +(0.762765 - 4.32585i) q^{9} +O(q^{10})$	\(q+(-1.37974 - 1.64431i) q^{3} +(3.12714 + 1.13819i) q^{5} +(5.96525 - 10.3321i) q^{7} +(0.762765 - 4.32585i) q^{9} +(-2.15570 - 3.73378i) q^{11} +(-4.95545 + 5.90568i) q^{13} +(-2.44311 - 6.71238i) q^{15} +(4.82095 + 27.3410i) q^{17} +(13.2467 + 13.6208i) q^{19} +(-25.2196 + 4.44690i) q^{21} +(3.33418 - 1.21354i) q^{23} +(-10.6676 - 8.95114i) q^{25} +(-24.8957 + 14.3735i) q^{27} +(14.6134 + 2.57674i) q^{29} +(-25.3991 - 14.6642i) q^{31} +(-3.16518 + 8.69625i) q^{33} +(30.4141 - 25.5204i) q^{35} +32.0207i q^{37} +16.5480 q^{39} +(11.1852 + 13.3300i) q^{41} +(1.29855 + 0.472634i) q^{43} +(7.30890 - 12.6594i) q^{45} +(0.165218 - 0.936998i) q^{47} +(-46.6684 - 80.8320i) q^{49} +(38.3053 - 45.6505i) q^{51} +(26.6762 + 73.2922i) q^{53} +(-2.49144 - 14.1296i) q^{55} +(4.11979 - 40.5747i) q^{57} +(95.8354 - 16.8984i) q^{59} +(36.0118 - 13.1072i) q^{61} +(-40.1451 - 33.6858i) q^{63} +(-22.2182 + 12.8277i) q^{65} +(-84.5455 - 14.9076i) q^{67} +(-6.59572 - 3.80804i) q^{69} +(-48.2730 + 132.629i) q^{71} +(81.3315 - 68.2453i) q^{73} +29.8909i q^{75} -51.4371 q^{77} +(-15.2189 - 18.1372i) q^{79} +(20.8348 + 7.58324i) q^{81} +(-64.1153 + 111.051i) q^{83} +(-16.0433 + 90.9863i) q^{85} +(-15.9257 - 27.5842i) q^{87} +(92.0067 - 109.649i) q^{89} +(31.4576 + 86.4291i) q^{91} +(10.9317 + 61.9965i) q^{93} +(25.9213 + 57.6713i) q^{95} +(-135.512 + 23.8943i) q^{97} +(-17.7961 + 6.47724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.37974	−	1.64431i	−0.459912	−	0.548102i	0.485390	−	0.874298i	$-0.338678\pi$
$3$	−1.37974	−	1.64431i	−0.459912	−	0.548102i	−0.945302	+	0.326196i	$0.894233\pi$
$4$		0			0
$5$	3.12714	+	1.13819i	0.625429	+	0.227637i	0.635240	−	0.772314i	$-0.280901\pi$
$5$	3.12714	+	1.13819i	0.625429	+	0.227637i	−0.00981176	+	0.999952i	$0.503123\pi$
$6$		0			0
$7$	5.96525	−	10.3321i	0.852178	−	1.47602i	−0.0270601	−	0.999634i	$-0.508615\pi$
$7$	5.96525	−	10.3321i	0.852178	−	1.47602i	0.879238	−	0.476382i	$-0.158052\pi$
$8$		0			0
$9$	0.762765	−	4.32585i	0.0847516	−	0.480650i
$10$		0			0
$11$	−2.15570	−	3.73378i	−0.195973	−	0.339434i	0.751246	−	0.660022i	$-0.229453\pi$
$11$	−2.15570	−	3.73378i	−0.195973	−	0.339434i	−0.947219	+	0.320588i	$0.896120\pi$
$12$		0			0
$13$	−4.95545	+	5.90568i	−0.381189	+	0.454283i	−0.922189	−	0.386739i	$-0.873601\pi$
$13$	−4.95545	+	5.90568i	−0.381189	+	0.454283i	0.541000	+	0.841022i	$0.318046\pi$
$14$		0			0
$15$	−2.44311	−	6.71238i	−0.162874	−	0.447492i
$16$		0			0
$17$	4.82095	+	27.3410i	0.283586	+	1.60829i	0.710295	+	0.703904i	$0.248562\pi$
$17$	4.82095	+	27.3410i	0.283586	+	1.60829i	−0.426709	+	0.904389i	$0.640327\pi$
$18$		0			0
$19$	13.2467	+	13.6208i	0.697194	+	0.716883i
$19$	13.2467	+	13.6208i	0.697194	+	0.716883i
$20$		0			0
$21$	−25.2196	+	4.44690i	−1.20093	+	0.211757i
$22$		0			0
$23$	3.33418	−	1.21354i	0.144964	−	0.0527627i	−0.268519	−	0.963274i	$-0.586534\pi$
$23$	3.33418	−	1.21354i	0.144964	−	0.0527627i	0.413483	+	0.910512i	$0.364312\pi$
$24$		0			0
$25$	−10.6676	−	8.95114i	−0.426702	−	0.358046i
$26$		0			0
$27$	−24.8957	+	14.3735i	−0.922062	+	0.532352i
$28$		0			0
$29$	14.6134	+	2.57674i	0.503912	+	0.0888532i	0.419825	−	0.907605i	$-0.362092\pi$
$29$	14.6134	+	2.57674i	0.503912	+	0.0888532i	0.0840869	+	0.996458i	$0.473203\pi$
$30$		0			0
$31$	−25.3991	−	14.6642i	−0.819325	−	0.473038i	0.0308585	−	0.999524i	$-0.490176\pi$
$31$	−25.3991	−	14.6642i	−0.819325	−	0.473038i	−0.850184	+	0.526486i	$0.823509\pi$
$32$		0			0
$33$	−3.16518	+	8.69625i	−0.0959145	+	0.263523i
$34$		0			0
$35$	30.4141	−	25.5204i	0.868973	−	0.729155i
$36$		0			0
$37$			32.0207i			0.865425i	0.901532	+	0.432713i	$0.142443\pi$
$37$			32.0207i			0.865425i	−0.901532	+	0.432713i	$0.857557\pi$
$38$		0			0
$39$	16.5480			0.424307
$40$		0			0
$41$	11.1852	+	13.3300i	0.272809	+	0.325121i	0.885002	−	0.465587i	$-0.154157\pi$
$41$	11.1852	+	13.3300i	0.272809	+	0.325121i	−0.612193	+	0.790708i	$0.709712\pi$
$42$		0			0
$43$	1.29855	+	0.472634i	0.0301989	+	0.0109915i	0.357075	−	0.934076i	$-0.383774\pi$
$43$	1.29855	+	0.472634i	0.0301989	+	0.0109915i	−0.326877	+	0.945067i	$0.605996\pi$
$44$		0			0
$45$	7.30890	−	12.6594i	0.162420	−	0.281320i
$46$		0			0
$47$	0.165218	−	0.936998i	0.00351528	−	0.0199361i	−0.983000	−	0.183607i	$-0.941223\pi$
$47$	0.165218	−	0.936998i	0.00351528	−	0.0199361i	0.986515	+	0.163671i	$0.0523336\pi$
$48$		0			0
$49$	−46.6684	−	80.8320i	−0.952415	−	1.64963i
$50$		0			0
$51$	38.3053	−	45.6505i	0.751084	−	0.895107i
$52$		0			0
$53$	26.6762	+	73.2922i	0.503324	+	1.38287i	0.888010	+	0.459824i	$0.152087\pi$
$53$	26.6762	+	73.2922i	0.503324	+	1.38287i	−0.384686	+	0.923047i	$0.625690\pi$
$54$		0			0
$55$	−2.49144	−	14.1296i	−0.0452989	−	0.256903i
$56$		0			0
$57$	4.11979	−	40.5747i	0.0722769	−	0.711836i
$58$		0			0
$59$	95.8354	−	16.8984i	1.62433	−	0.286413i	0.713952	−	0.700194i	$-0.246903\pi$
$59$	95.8354	−	16.8984i	1.62433	−	0.286413i	0.910376	+	0.413781i	$0.135792\pi$
$60$		0			0
$61$	36.0118	−	13.1072i	0.590357	−	0.214872i	−0.0295296	−	0.999564i	$-0.509401\pi$
$61$	36.0118	−	13.1072i	0.590357	−	0.214872i	0.619886	+	0.784692i	$0.287179\pi$
$62$		0			0
$63$	−40.1451	−	33.6858i	−0.637224	−	0.534695i
$64$		0			0
$65$	−22.2182	+	12.8277i	−0.341818	+	0.197349i
$66$		0			0
$67$	−84.5455	−	14.9076i	−1.26187	−	0.222502i	−0.497606	−	0.867403i	$-0.665788\pi$
$67$	−84.5455	−	14.9076i	−1.26187	−	0.222502i	−0.764266	+	0.644901i	$0.776899\pi$
$68$		0			0
$69$	−6.59572	−	3.80804i	−0.0955902	−	0.0551890i
$70$		0			0
$71$	−48.2730	+	132.629i	−0.679902	+	1.86802i	−0.236743	+	0.971572i	$0.576080\pi$
$71$	−48.2730	+	132.629i	−0.679902	+	1.86802i	−0.443159	+	0.896443i	$0.646142\pi$
$72$		0			0
$73$	81.3315	−	68.2453i	1.11413	−	0.934867i	0.115838	−	0.993268i	$-0.463045\pi$
$73$	81.3315	−	68.2453i	1.11413	−	0.934867i	0.998293	+	0.0584015i	$0.0186003\pi$
$74$		0			0
$75$			29.8909i			0.398546i
$76$		0			0
$77$	−51.4371			−0.668014
$78$		0			0
$79$	−15.2189	−	18.1372i	−0.192644	−	0.229584i	0.661073	−	0.750322i	$-0.270101\pi$
$79$	−15.2189	−	18.1372i	−0.192644	−	0.229584i	−0.853717	+	0.520738i	$0.825657\pi$
$80$		0			0
$81$	20.8348	+	7.58324i	0.257219	+	0.0936202i
$82$		0			0
$83$	−64.1153	+	111.051i	−0.772473	+	1.33796i	0.163730	+	0.986505i	$0.447647\pi$
$83$	−64.1153	+	111.051i	−0.772473	+	1.33796i	−0.936204	+	0.351458i	$0.885686\pi$
$84$		0			0
$85$	−16.0433	+	90.9863i	−0.188745	+	1.07043i
$86$		0			0
$87$	−15.9257	−	27.5842i	−0.183054	−	0.317060i
$88$		0			0
$89$	92.0067	−	109.649i	1.03378	−	1.23201i	0.0615240	−	0.998106i	$-0.480404\pi$
$89$	92.0067	−	109.649i	1.03378	−	1.23201i	0.972259	−	0.233909i	$-0.0751516\pi$
$90$		0			0
$91$	31.4576	+	86.4291i	0.345688	+	0.949771i
$92$		0			0
$93$	10.9317	+	61.9965i	0.117545	+	0.666629i
$94$		0			0
$95$	25.9213	+	57.6713i	0.272856	+	0.607066i
$96$		0			0
$97$	−135.512	+	23.8943i	−1.39703	+	0.246333i	−0.820921	−	0.571042i	$-0.806539\pi$
$97$	−135.512	+	23.8943i	−1.39703	+	0.246333i	−0.576105	+	0.817375i	$0.695428\pi$
$98$		0			0
$99$	−17.7961	+	6.47724i	−0.179758	+	0.0654266i
$100$		0			0
$101$	13.0272	+	10.9311i	0.128982	+	0.108229i	0.704997	−	0.709211i	$-0.250948\pi$
$101$	13.0272	+	10.9311i	0.128982	+	0.108229i	−0.576015	+	0.817439i	$0.695393\pi$
$102$		0			0
$103$	−11.9953	+	6.92548i	−0.116459	+	0.0672376i	−0.557098	−	0.830447i	$-0.688085\pi$
$103$	−11.9953	+	6.92548i	−0.116459	+	0.0672376i	0.440639	+	0.897684i	$0.354752\pi$
$104$		0			0
$105$	−83.9268	−	14.7986i	−0.799303	−	0.140939i
$106$		0			0
$107$	−120.222	−	69.4101i	−1.12357	−	0.648693i	−0.181259	−	0.983435i	$-0.558017\pi$
$107$	−120.222	−	69.4101i	−1.12357	−	0.648693i	−0.942310	+	0.334743i	$0.891351\pi$
$108$		0			0
$109$	−18.5843	+	51.0599i	−0.170498	+	0.468440i	−0.995284	−	0.0970058i	$-0.969073\pi$
$109$	−18.5843	+	51.0599i	−0.170498	+	0.468440i	0.824786	+	0.565445i	$0.191296\pi$
$110$		0			0
$111$	52.6519	−	44.1802i	0.474341	−	0.398019i
$112$		0			0
$113$		−	206.210i		−	1.82487i	−0.409220	−	0.912436i	$-0.634199\pi$
$113$		−	206.210i		−	1.82487i	0.409220	−	0.912436i	$-0.365801\pi$
$114$		0			0
$115$	11.8077			0.102676
$116$		0			0
$117$	21.7673	+	25.9412i	0.186045	+	0.221720i
$118$		0			0
$119$	311.248	+	113.285i	2.61553	+	0.951976i
$120$		0			0
$121$	51.2059	−	88.6913i	0.423190	−	0.732986i
$122$		0			0
$123$	6.48595	−	36.7837i	0.0527313	−	0.299054i
$124$		0			0
$125$	−64.7689	−	112.183i	−0.518151	−	0.897464i
$126$		0			0
$127$	−4.18560	+	4.98821i	−0.0329575	+	0.0392772i	−0.782271	−	0.622938i	$-0.785939\pi$
$127$	−4.18560	+	4.98821i	−0.0329575	+	0.0392772i	0.749314	+	0.662215i	$0.230383\pi$
$128$		0			0
$129$	−1.01450	−	2.78733i	−0.00786437	−	0.0216072i
$130$		0			0
$131$	1.31600	+	7.46342i	0.0100458	+	0.0569727i	0.989419	−	0.145089i	$-0.0463469\pi$
$131$	1.31600	+	7.46342i	0.0100458	+	0.0569727i	−0.979373	+	0.202062i	$0.935236\pi$
$132$		0			0
$133$	219.751	−	55.6149i	1.65226	−	0.418157i
$134$		0			0
$135$	−94.2121	+	16.6121i	−0.697867	+	0.123053i
$136$		0			0
$137$	−63.8611	+	23.2435i	−0.466140	+	0.169661i	−0.564403	−	0.825500i	$-0.690894\pi$
$137$	−63.8611	+	23.2435i	−0.466140	+	0.169661i	0.0982632	+	0.995160i	$0.468671\pi$
$138$		0			0
$139$	−97.0356	−	81.4225i	−0.698098	−	0.585773i	0.223134	−	0.974788i	$-0.428371\pi$
$139$	−97.0356	−	81.4225i	−0.698098	−	0.585773i	−0.921232	+	0.389014i	$0.872816\pi$
$140$		0			0
$141$	−1.76867	+	1.02114i	−0.0125437	+	0.00724214i
$142$		0			0
$143$	32.7329	+	5.77170i	0.228902	+	0.0403616i
$144$		0			0
$145$	42.7655	+	24.6907i	0.294934	+	0.170280i
$146$		0			0
$147$	−68.5224	+	188.264i	−0.466139	+	1.28071i
$148$		0			0
$149$	0.583952	−	0.489994i	0.00391914	−	0.00328855i	−0.640826	−	0.767686i	$-0.721408\pi$
$149$	0.583952	−	0.489994i	0.00391914	−	0.00328855i	0.644745	+	0.764398i	$0.276964\pi$
$150$		0			0
$151$		−	129.387i		−	0.856869i	−0.903573	−	0.428435i	$-0.859065\pi$
$151$		−	129.387i		−	0.856869i	0.903573	−	0.428435i	$-0.140935\pi$
$152$		0			0
$153$	121.950			0.797061
$154$		0			0
$155$	−62.7360	−	74.7659i	−0.404748	−	0.482360i
$156$		0			0
$157$	137.983	+	50.2215i	0.878869	+	0.319882i	0.741753	−	0.670673i	$-0.233994\pi$
$157$	137.983	+	50.2215i	0.878869	+	0.319882i	0.137116	+	0.990555i	$0.456217\pi$
$158$		0			0
$159$	83.7086	−	144.988i	0.526469	−	0.911872i
$160$		0			0
$161$	7.35075	−	41.6882i	0.0456569	−	0.258933i
$162$		0			0
$163$	0.0219995	+	0.0381043i	0.000134966	+	0.000233769i	0.866093	−	0.499883i	$-0.166624\pi$
$163$	0.0219995	+	0.0381043i	0.000134966	+	0.000233769i	−0.865958	+	0.500117i	$0.833290\pi$
$164$		0			0
$165$	−19.7959	+	23.5919i	−0.119975	+	0.142981i
$166$		0			0
$167$	33.4220	+	91.8262i	0.200132	+	0.549858i	0.998641	−	0.0521256i	$-0.0165996\pi$
$167$	33.4220	+	91.8262i	0.200132	+	0.549858i	−0.798509	+	0.601983i	$0.794377\pi$
$168$		0			0
$169$	19.0260	+	107.902i	0.112580	+	0.638473i
$170$		0			0
$171$	69.0256	−	46.9138i	0.403658	−	0.274349i
$172$		0			0
$173$	−251.801	+	44.3994i	−1.45550	+	0.256644i	−0.844742	−	0.535174i	$-0.820246\pi$
$173$	−251.801	+	44.3994i	−1.45550	+	0.256644i	−0.610758	+	0.791818i	$0.709135\pi$
$174$		0			0
$175$	−156.119	+	56.8226i	−0.892107	+	0.324701i
$176$		0			0
$177$	−160.014	−	134.267i	−0.904032	−	0.758573i
$178$		0			0
$179$	156.507	−	90.3591i	0.874339	−	0.504800i	0.00555105	−	0.999985i	$-0.498233\pi$
$179$	156.507	−	90.3591i	0.874339	−	0.504800i	0.868788	+	0.495185i	$0.164900\pi$
$180$		0			0
$181$	−231.073	−	40.7444i	−1.27665	−	0.225107i	−0.506092	−	0.862480i	$-0.668910\pi$
$181$	−231.073	−	40.7444i	−1.27665	−	0.225107i	−0.770556	+	0.637372i	$0.780021\pi$
$182$		0			0
$183$	−71.2390	−	41.1299i	−0.389284	−	0.224753i
$184$		0			0
$185$	−36.4456	+	100.133i	−0.197003	+	0.541262i
$186$		0			0
$187$	91.6927	−	76.9393i	0.490335	−	0.411440i
$188$		0			0
$189$			342.966i			1.81464i
$190$		0			0
$191$	−206.795			−1.08270			−0.541348	−	0.840799i	$-0.682086\pi$
$191$	−206.795			−1.08270			−0.541348	+	0.840799i	$0.682086\pi$
$192$		0			0
$193$	167.054	+	199.087i	0.865563	+	1.03154i	0.999179	+	0.0405043i	$0.0128965\pi$
$193$	167.054	+	199.087i	0.865563	+	1.03154i	−0.133617	+	0.991033i	$0.542659\pi$
$194$		0			0
$195$	51.7478	+	18.8347i	0.265374	+	0.0965881i
$196$		0			0
$197$	−145.219	+	251.527i	−0.737153	+	1.27679i	0.216619	+	0.976256i	$0.430497\pi$
$197$	−145.219	+	251.527i	−0.737153	+	1.27679i	−0.953772	+	0.300530i	$0.902836\pi$
$198$		0			0
$199$	−27.9206	+	158.345i	−0.140304	+	0.795705i	0.830714	+	0.556700i	$0.187933\pi$
$199$	−27.9206	+	158.345i	−0.140304	+	0.795705i	−0.971018	+	0.239006i	$0.923179\pi$
$200$		0			0
$201$	92.1377	+	159.587i	0.458397	+	0.793966i
$202$		0			0
$203$	113.796	−	135.617i	0.560571	−	0.668063i
$204$		0			0
$205$	19.8056	+	54.4155i	0.0966128	+	0.265441i
$206$		0			0
$207$	−2.70641	−	15.3488i	−0.0130744	−	0.0741489i
$208$		0			0
$209$	22.3011	−	78.8224i	0.106704	−	0.377141i
$210$		0			0
$211$	74.5924	−	13.1527i	0.353519	−	0.0623349i	0.00593109	−	0.999982i	$-0.498112\pi$
$211$	74.5924	−	13.1527i	0.353519	−	0.0623349i	0.347588	+	0.937648i	$0.387001\pi$
$212$		0			0
$213$	284.687	−	103.618i	1.33656	−	0.486467i
$214$		0			0
$215$	3.52281	+	2.95599i	0.0163852	+	0.0137488i
$216$		0			0
$217$	−303.024	+	174.951i	−1.39642	+	0.806225i
$218$		0			0
$219$	−224.432	−	39.5734i	−1.02480	−	0.180701i
$220$		0			0
$221$	−185.357	−	107.016i	−0.838720	−	0.484235i
$222$		0			0
$223$	49.7166	−	136.595i	0.222944	−	0.612534i	−0.776910	−	0.629612i	$-0.783214\pi$
$223$	49.7166	−	136.595i	0.222944	−	0.612534i	0.999854	+	0.0170775i	$0.00543620\pi$
$224$		0			0
$225$	−46.8582	+	39.3187i	−0.208258	+	0.174750i
$226$		0			0
$227$		−	215.945i		−	0.951300i	−0.879635	−	0.475650i	$-0.842213\pi$
$227$		−	215.945i		−	0.951300i	0.879635	−	0.475650i	$-0.157787\pi$
$228$		0			0
$229$	432.663			1.88936			0.944679	−	0.327997i	$-0.106374\pi$
$229$	432.663			1.88936			0.944679	+	0.327997i	$0.106374\pi$
$230$		0			0
$231$	70.9696	+	84.5783i	0.307228	+	0.366140i
$232$		0			0
$233$	−287.596	−	104.676i	−1.23432	−	0.449254i	−0.359243	−	0.933244i	$-0.616965\pi$
$233$	−287.596	−	104.676i	−1.23432	−	0.449254i	−0.875074	+	0.483990i	$0.839187\pi$
$234$		0			0
$235$	1.58314	−	2.74208i	0.00673676	−	0.0116684i
$236$		0			0
$237$	−8.82499	+	50.0490i	−0.0372362	+	0.211177i
$238$		0			0
$239$	−124.637	−	215.877i	−0.521492	−	0.903251i	−0.999688	−	0.0249977i	$-0.992042\pi$
$239$	−124.637	−	215.877i	−0.521492	−	0.903251i	0.478195	−	0.878254i	$-0.341291\pi$
$240$		0			0
$241$	190.006	−	226.440i	0.788406	−	0.939586i	−0.210875	−	0.977513i	$-0.567631\pi$
$241$	190.006	−	226.440i	0.788406	−	0.939586i	0.999280	+	0.0379275i	$0.0120756\pi$
$242$		0			0
$243$	72.2113	+	198.399i	0.297166	+	0.816456i
$244$		0			0
$245$	−53.9367	−	305.890i	−0.220150	−	1.24853i
$246$		0			0
$247$	−146.083	+	10.7335i	−0.591430	+	0.0434557i
$248$		0			0
$249$	271.064	−	47.7959i	1.08861	−	0.191951i
$250$		0			0
$251$	154.696	−	56.3047i	0.616318	−	0.224321i	−0.0149475	−	0.999888i	$-0.504758\pi$
$251$	154.696	−	56.3047i	0.616318	−	0.224321i	0.631265	+	0.775567i	$0.282536\pi$
$252$		0			0
$253$	−11.7186	−	9.83306i	−0.0463185	−	0.0388658i
$254$		0			0
$255$	171.745	−	99.1570i	0.673510	−	0.388851i
$256$		0			0
$257$	41.3027	+	7.28278i	0.160711	+	0.0283377i	0.253425	−	0.967355i	$-0.418443\pi$
$257$	41.3027	+	7.28278i	0.160711	+	0.0283377i	−0.0927138	+	0.995693i	$0.529554\pi$
$258$		0			0
$259$	330.842	+	191.012i	1.27738	+	0.737496i
$260$		0			0
$261$	22.2932	−	61.2501i	0.0854146	−	0.234675i
$262$		0			0
$263$	194.362	−	163.089i	0.739017	−	0.620109i	−0.193556	−	0.981089i	$-0.562002\pi$
$263$	194.362	−	163.089i	0.739017	−	0.620109i	0.932574	+	0.360980i	$0.117558\pi$
$264$		0			0
$265$			259.558i			0.979462i
$266$		0			0
$267$	−307.242			−1.15072
$268$		0			0
$269$	−121.621	−	144.942i	−0.452123	−	0.538819i	0.491046	−	0.871134i	$-0.336615\pi$
$269$	−121.621	−	144.942i	−0.452123	−	0.538819i	−0.943168	+	0.332315i	$0.892170\pi$
$270$		0			0
$271$	−156.279	−	56.8808i	−0.576674	−	0.209892i	0.0371840	−	0.999308i	$-0.488161\pi$
$271$	−156.279	−	56.8808i	−0.576674	−	0.209892i	−0.613858	+	0.789416i	$0.710383\pi$
$272$		0			0
$273$	98.7127	−	170.975i	0.361585	−	0.626283i
$274$		0			0
$275$	−10.4256	+	59.1262i	−0.0379111	+	0.215004i
$276$		0			0
$277$	−43.5944	−	75.5077i	−0.157381	−	0.272591i	0.776543	−	0.630065i	$-0.216972\pi$
$277$	−43.5944	−	75.5077i	−0.157381	−	0.272591i	−0.933923	+	0.357473i	$0.883638\pi$
$278$		0			0
$279$	−82.8086	+	98.6874i	−0.296805	+	0.353718i
$280$		0			0
$281$	−40.5710	−	111.468i	−0.144381	−	0.396683i	0.846332	−	0.532656i	$-0.178806\pi$
$281$	−40.5710	−	111.468i	−0.144381	−	0.396683i	−0.990712	+	0.135973i	$0.956584\pi$
$282$		0			0
$283$	16.0818	+	91.2045i	0.0568262	+	0.322277i	0.999948	−	0.0101691i	$-0.00323699\pi$
$283$	16.0818	+	91.2045i	0.0568262	+	0.322277i	−0.943122	+	0.332447i	$0.892126\pi$
$284$		0			0
$285$	59.0647	−	122.194i	0.207245	−	0.428750i
$286$		0			0
$287$	204.449	−	36.0499i	0.712365	−	0.125609i
$288$		0			0
$289$	−452.717	+	164.775i	−1.56649	+	0.570157i
$290$		0			0
$291$	226.260	+	189.855i	0.777525	+	0.652421i
$292$		0			0
$293$	−145.616	+	84.0713i	−0.496982	+	0.286933i	−0.727466	−	0.686143i	$-0.759302\pi$
$293$	−145.616	+	84.0713i	−0.496982	+	0.286933i	0.230484	+	0.973076i	$0.425969\pi$
$294$		0			0
$295$	318.925	+	56.2350i	1.08110	+	0.190627i
$296$		0			0
$297$	107.335	+	61.9699i	0.361397	+	0.208653i
$298$		0			0
$299$	−9.35558	+	25.7042i	−0.0312896	+	0.0859674i
$300$		0			0
$301$	12.6295	−	10.5974i	0.0419584	−	0.0352073i
$302$		0			0
$303$		−	36.5028i		−	0.120471i
$304$		0			0
$305$	127.532			0.418139
$306$		0			0
$307$	−182.360	−	217.328i	−0.594007	−	0.707910i	0.382364	−	0.924012i	$-0.375110\pi$
$307$	−182.360	−	217.328i	−0.594007	−	0.707910i	−0.976371	+	0.216102i	$0.930666\pi$
$308$		0			0
$309$	27.9379	+	10.1686i	0.0904140	+	0.0329080i
$310$		0			0
$311$	−183.318	+	317.516i	−0.589448	+	1.02095i	0.404857	+	0.914380i	$0.367321\pi$
$311$	−183.318	+	317.516i	−0.589448	+	1.02095i	−0.994305	+	0.106573i	$0.966012\pi$
$312$		0			0
$313$	31.9239	−	181.050i	0.101993	−	0.578433i	−0.890385	−	0.455208i	$-0.849565\pi$
$313$	31.9239	−	181.050i	0.101993	−	0.578433i	0.992379	−	0.123225i	$-0.0393238\pi$
$314$		0			0
$315$	−87.1989	−	151.033i	−0.276822	−	0.479469i
$316$		0			0
$317$	−257.834	+	307.275i	−0.813356	+	0.969320i	−0.999914	−	0.0131237i	$-0.995822\pi$
$317$	−257.834	+	307.275i	−0.813356	+	0.969320i	0.186558	+	0.982444i	$0.440267\pi$
$318$		0			0
$319$	−21.8812	−	60.1180i	−0.0685930	−	0.188458i
$320$		0			0
$321$	51.7430	+	293.449i	0.161193	+	0.914172i
$322$		0			0
$323$	−308.544	+	427.842i	−0.955244	+	1.32459i
$324$		0			0
$325$	105.725	−	18.6422i	0.325308	−	0.0573606i
$326$		0			0
$327$	109.600	−	39.8910i	0.335167	−	0.121991i
$328$		0			0
$329$	−8.69560	−	7.29648i	−0.0264304	−	0.0221777i
$330$		0			0
$331$	−48.3107	+	27.8922i	−0.145954	+	0.0842665i	−0.571199	−	0.820812i	$-0.693521\pi$
$331$	−48.3107	+	27.8922i	−0.145954	+	0.0842665i	0.425245	+	0.905078i	$0.360188\pi$
$332$		0			0
$333$	138.517	+	24.4243i	0.415967	+	0.0733462i
$334$		0			0
$335$	−247.418	−	142.847i	−0.738561	−	0.426409i
$336$		0			0
$337$	59.3567	−	163.081i	0.176133	−	0.483920i	−0.819941	−	0.572448i	$-0.805994\pi$
$337$	59.3567	−	163.081i	0.176133	−	0.483920i	0.996074	+	0.0885275i	$0.0282161\pi$
$338$		0			0
$339$	−339.073	+	284.516i	−1.00022	+	0.839280i
$340$		0			0
$341$			126.446i			0.370809i
$342$		0			0
$343$	−528.959			−1.54215
$344$		0			0
$345$	−16.2915	−	19.4155i	−0.0472218	−	0.0562767i
$346$		0			0
$347$	−20.5283	−	7.47171i	−0.0591595	−	0.0215323i	0.312271	−	0.949993i	$-0.398910\pi$
$347$	−20.5283	−	7.47171i	−0.0591595	−	0.0215323i	−0.371430	+	0.928461i	$0.621133\pi$
$348$		0			0
$349$	231.371	−	400.747i	0.662955	−	1.14827i	−0.316880	−	0.948466i	$-0.602635\pi$
$349$	231.371	−	400.747i	0.662955	−	1.14827i	0.979835	−	0.199807i	$-0.0640315\pi$
$350$		0			0
$351$	38.4839	−	218.253i	0.109641	−	0.621804i
$352$		0			0
$353$	266.754	+	462.031i	0.755676	+	1.30887i	0.945038	+	0.326962i	$0.106025\pi$
$353$	266.754	+	462.031i	0.755676	+	1.30887i	−0.189362	+	0.981907i	$0.560642\pi$
$354$		0			0
$355$	−301.913	+	359.806i	−0.850460	+	1.01354i
$356$		0			0
$357$	−243.165	−	668.091i	−0.681135	−	1.87140i
$358$		0			0
$359$	14.2166	+	80.6261i	0.0396004	+	0.224585i	0.998185	−	0.0602230i	$-0.0191812\pi$
$359$	14.2166	+	80.6261i	0.0396004	+	0.224585i	−0.958585	+	0.284808i	$0.908070\pi$
$360$		0			0
$361$	−10.0509	+	360.860i	−0.0278417	+	0.999612i
$362$		0			0
$363$	−216.486	+	38.1724i	−0.596381	+	0.105158i
$364$		0			0
$365$	332.011	−	120.842i	0.909620	−	0.331075i
$366$		0			0
$367$	366.063	+	307.164i	0.997448	+	0.836958i	0.986629	−	0.162984i	$-0.0521118\pi$
$367$	366.063	+	307.164i	0.997448	+	0.836958i	0.0108188	+	0.999941i	$0.496556\pi$
$368$		0			0
$369$	66.1951	−	38.2178i	0.179390	−	0.103571i
$370$		0			0
$371$	916.393	+	161.585i	2.47006	+	0.435538i
$372$		0			0
$373$	−148.146	−	85.5319i	−0.397173	−	0.229308i	0.288090	−	0.957603i	$-0.406980\pi$
$373$	−148.146	−	85.5319i	−0.397173	−	0.229308i	−0.685264	+	0.728295i	$0.740313\pi$
$374$		0			0
$375$	−95.0991	+	261.283i	−0.253598	+	0.696754i
$376$		0			0
$377$	−87.6336	+	73.5333i	−0.232450	+	0.195049i
$378$		0			0
$379$		−	520.729i		−	1.37395i	−0.726679	−	0.686977i	$-0.758937\pi$
$379$		−	520.729i		−	1.37395i	0.726679	−	0.686977i	$-0.241063\pi$
$380$		0			0
$381$	13.9772			0.0366855
$382$		0			0
$383$	176.408	+	210.235i	0.460595	+	0.548915i	0.945488	−	0.325658i	$-0.105586\pi$
$383$	176.408	+	210.235i	0.460595	+	0.548915i	−0.484893	+	0.874574i	$0.661141\pi$
$384$		0			0
$385$	−160.851	−	58.5450i	−0.417795	−	0.152065i
$386$		0			0
$387$	3.03503	−	5.25683i	0.00784247	−	0.0135835i
$388$		0			0
$389$	30.4119	−	172.475i	0.0781798	−	0.443380i	−0.920441	−	0.390881i	$-0.872170\pi$
$389$	30.4119	−	172.475i	0.0781798	−	0.443380i	0.998621	−	0.0524987i	$-0.0167185\pi$
$390$		0			0
$391$	49.2534	+	85.3093i	0.125968	+	0.218182i
$392$		0			0
$393$	10.4564	−	12.4615i	0.0266066	−	0.0317085i
$394$		0			0
$395$	−26.9482	−	74.0394i	−0.0682232	−	0.187442i
$396$		0			0
$397$	−9.49504	−	53.8490i	−0.0239170	−	0.135640i	0.970511	−	0.241056i	$-0.0774937\pi$
$397$	−9.49504	−	53.8490i	−0.0239170	−	0.135640i	−0.994428	+	0.105416i	$0.966383\pi$
$398$		0			0
$399$	−394.646	−	284.604i	−0.989089	−	0.713293i
$400$		0			0
$401$	−400.414	+	70.6039i	−0.998540	+	0.176070i	−0.648948	−	0.760833i	$-0.724791\pi$
$401$	−400.414	+	70.6039i	−0.998540	+	0.176070i	−0.349592	+	0.936902i	$0.613680\pi$
$402$		0			0
$403$	212.466	−	77.3312i	0.527210	−	0.191889i
$404$		0			0
$405$	56.5222	+	47.4277i	0.139561	+	0.117106i
$406$		0			0
$407$	119.558	−	69.0270i	0.293755	−	0.169600i
$408$		0			0
$409$	149.769	+	26.4083i	0.366182	+	0.0645679i	0.353712	−	0.935354i	$-0.384919\pi$
$409$	149.769	+	26.4083i	0.366182	+	0.0645679i	0.0124705	+	0.999922i	$0.496030\pi$
$410$		0			0
$411$	126.331	+	72.9372i	0.307375	+	0.177463i
$412$		0			0
$413$	397.086	−	1090.98i	0.961467	−	2.64161i
$414$		0			0
$415$	−326.894	+	274.297i	−0.787697	+	0.660957i
$416$		0			0
$417$			271.898i			0.652033i
$418$		0			0
$419$	212.218			0.506486			0.253243	−	0.967403i	$-0.418503\pi$
$419$	212.218			0.506486			0.253243	+	0.967403i	$0.418503\pi$
$420$		0			0
$421$	−244.289	−	291.133i	−0.580260	−	0.691527i	0.393443	−	0.919349i	$-0.371284\pi$
$421$	−244.289	−	291.133i	−0.580260	−	0.691527i	−0.973703	+	0.227822i	$0.926839\pi$
$422$		0			0
$423$	−3.92729	−	1.42942i	−0.00928438	−	0.00337924i
$424$		0			0
$425$	193.305	−	334.815i	0.454836	−	0.787799i
$426$		0			0
$427$	79.3939	−	450.265i	0.185934	−	1.05449i
$428$		0			0
$429$	−35.6724	−	61.7864i	−0.0831524	−	0.144024i
$430$		0			0
$431$	147.168	−	175.388i	0.341458	−	0.406933i	−0.567800	−	0.823166i	$-0.692205\pi$
$431$	147.168	−	175.388i	0.341458	−	0.406933i	0.909258	+	0.416233i	$0.136650\pi$
$432$		0			0
$433$	−58.0822	−	159.580i	−0.134139	−	0.368544i	0.854378	−	0.519652i	$-0.173938\pi$
$433$	−58.0822	−	159.580i	−0.134139	−	0.368544i	−0.988517	+	0.151107i	$0.951716\pi$
$434$		0			0
$435$	−18.4061	−	104.386i	−0.0423129	−	0.239968i
$436$		0			0
$437$	60.6962	+	29.3387i	0.138893	+	0.0671366i
$438$		0			0
$439$	764.306	−	134.768i	1.74102	−	0.306988i	0.789309	−	0.613996i	$-0.210439\pi$
$439$	764.306	−	134.768i	1.74102	−	0.306988i	0.951707	+	0.307008i	$0.0993279\pi$
$440$		0			0
$441$	−385.264	+	140.225i	−0.873615	+	0.317970i
$442$		0			0
$443$	86.2588	+	72.3797i	0.194715	+	0.163385i	0.734933	−	0.678140i	$-0.237214\pi$
$443$	86.2588	+	72.3797i	0.194715	+	0.163385i	−0.540218	+	0.841525i	$0.681658\pi$
$444$		0			0
$445$	412.519	−	238.168i	0.927010	−	0.535209i
$446$		0			0
$447$	−1.61140	−	0.284133i	−0.00360492	−	0.000635645i
$448$		0			0
$449$	536.347	+	309.660i	1.19454	+	0.689666i	0.959332	−	0.282280i	$-0.0910909\pi$
$449$	536.347	+	309.660i	1.19454	+	0.689666i	0.235204	+	0.971946i	$0.424424\pi$
$450$		0			0
$451$	25.6593	−	70.4983i	0.0568942	−	0.156315i
$452$		0			0
$453$	−212.752	+	178.520i	−0.469652	+	0.394085i
$454$		0			0
$455$			306.081i			0.672705i
$456$		0			0
$457$	409.681			0.896458			0.448229	−	0.893919i	$-0.352055\pi$
$457$	409.681			0.896458			0.448229	+	0.893919i	$0.352055\pi$
$458$		0			0
$459$	−513.007	−	611.378i	−1.11766	−	1.33198i
$460$		0			0
$461$	−739.047	−	268.991i	−1.60314	−	0.583495i	−0.623072	−	0.782164i	$-0.714116\pi$
$461$	−739.047	−	268.991i	−1.60314	−	0.583495i	−0.980067	+	0.198670i	$0.936338\pi$
$462$		0			0
$463$	−370.649	+	641.983i	−0.800538	+	1.38657i	0.118725	+	0.992927i	$0.462119\pi$
$463$	−370.649	+	641.983i	−0.800538	+	1.38657i	−0.919263	+	0.393645i	$0.871214\pi$
$464$		0			0
$465$	−36.3788	+	206.314i	−0.0782339	+	0.443687i
$466$		0			0
$467$	368.886	+	638.930i	0.789906	+	1.36816i	0.926024	+	0.377465i	$0.123204\pi$
$467$	368.886	+	638.930i	0.789906	+	1.36816i	−0.136117	+	0.990693i	$0.543462\pi$
$468$		0			0
$469$	−658.362	+	784.605i	−1.40376	+	1.67293i
$470$		0			0
$471$	−107.800	−	296.178i	−0.228875	−	0.628828i
$472$		0			0
$473$	−1.03457	−	5.86736i	−0.00218726	−	0.0124046i
$474$		0			0
$475$	−19.3882	−	263.873i	−0.0408174	−	0.555523i
$476$		0			0
$477$	337.399	−	59.4925i	0.707335	−	0.124722i
$478$		0			0
$479$	−326.465	+	118.823i	−0.681555	+	0.248066i	−0.659515	−	0.751692i	$-0.729238\pi$
$479$	−326.465	+	118.823i	−0.681555	+	0.248066i	−0.0220397	+	0.999757i	$0.507016\pi$
$480$		0			0
$481$	−189.104	−	158.677i	−0.393148	−	0.329890i
$482$		0			0
$483$	−78.6902	+	45.4318i	−0.162920	+	0.0940618i
$484$		0			0
$485$	−450.960	−	79.5165i	−0.929815	−	0.163951i
$486$		0			0
$487$	446.950	+	258.047i	0.917762	+	0.529870i	0.882920	−	0.469523i	$-0.155574\pi$
$487$	446.950	+	258.047i	0.917762	+	0.529870i	0.0348417	+	0.999393i	$0.488907\pi$
$488$		0			0
$489$	0.0323016	−	0.0887479i	6.60564e−5	−	0.000181488i
$490$		0			0
$491$	−223.421	+	187.473i	−0.455033	+	0.381818i	−0.841299	−	0.540569i	$-0.818209\pi$
$491$	−223.421	+	187.473i	−0.455033	+	0.381818i	0.386267	+	0.922387i	$0.373764\pi$
$492$		0			0
$493$			411.968i			0.835635i
$494$		0			0
$495$	−63.0232			−0.127319
$496$		0			0
$497$	1082.38	+	1289.93i	2.17782	+	2.59543i
$498$		0			0
$499$	−542.504	−	197.455i	−1.08718	−	0.395702i	−0.264606	−	0.964357i	$-0.585242\pi$
$499$	−542.504	−	197.455i	−1.08718	−	0.395702i	−0.822577	+	0.568654i	$0.807464\pi$
$500$		0			0
$501$	104.877	−	181.652i	0.209335	−	0.362579i
$502$		0			0
$503$	−91.3962	+	518.334i	−0.181702	+	1.03048i	0.748417	+	0.663228i	$0.230814\pi$
$503$	−91.3962	+	518.334i	−0.181702	+	1.03048i	−0.930120	+	0.367257i	$0.880297\pi$
$504$		0			0
$505$	28.2963	+	49.0106i	0.0560322	+	0.0970506i
$506$		0			0
$507$	151.173	−	180.161i	0.298171	−	0.355347i
$508$		0			0
$509$	126.119	+	346.509i	0.247778	+	0.680764i	0.999767	+	0.0215886i	$0.00687241\pi$
$509$	126.119	+	346.509i	0.247778	+	0.680764i	−0.751989	+	0.659176i	$0.770905\pi$
$510$		0			0
$511$	−219.955	−	1247.43i	−0.430440	−	2.44115i
$512$		0			0
$513$	−525.563	−	148.697i	−1.02449	−	0.289857i
$514$		0			0
$515$	−45.3934	+	8.00409i	−0.0881426	+	0.0155419i
$516$		0			0
$517$	−3.85470	+	1.40300i	−0.00745590	+	0.00271373i
$518$		0			0
$519$	420.426	+	352.779i	0.810069	+	0.679729i
$520$		0			0
$521$	−49.5400	+	28.6019i	−0.0950863	+	0.0548981i	−0.546789	−	0.837270i	$-0.684150\pi$
$521$	−49.5400	+	28.6019i	−0.0950863	+	0.0548981i	0.451703	+	0.892168i	$0.350817\pi$
$522$		0			0
$523$	−241.856	−	42.6458i	−0.462440	−	0.0815407i	−0.0624259	−	0.998050i	$-0.519884\pi$
$523$	−241.856	−	42.6458i	−0.462440	−	0.0815407i	−0.400014	+	0.916509i	$0.630995\pi$
$524$		0			0
$525$	308.837	+	178.307i	0.588260	+	0.339632i
$526$		0			0
$527$	278.485	−	765.131i	0.528435	−	1.45186i
$528$		0			0
$529$	−395.593	+	331.942i	−0.747814	+	0.627490i
$530$		0			0
$531$		−	427.459i		−	0.805008i
$532$		0			0
$533$	−134.150			−0.251689
$534$		0			0
$535$	−296.949	−	353.890i	−0.555045	−	0.661477i
$536$		0			0
$537$	−364.516	−	132.673i	−0.678801	−	0.247063i
$538$		0			0
$539$	−201.206	+	348.499i	−0.373294	+	0.646565i
$540$		0			0
$541$	−124.392	+	705.461i	−0.229929	+	1.30399i	0.623105	+	0.782138i	$0.285871\pi$
$541$	−124.392	+	705.461i	−0.229929	+	1.30399i	−0.853034	+	0.521855i	$0.825240\pi$
$542$		0			0
$543$	251.824	+	436.172i	0.463764	+	0.803263i
$544$		0			0
$545$	−116.231	+	138.519i	−0.213269	+	0.254164i
$546$		0			0
$547$	4.28047	+	11.7605i	0.00782536	+	0.0215000i	0.943544	−	0.331248i	$-0.107470\pi$
$547$	4.28047	+	11.7605i	0.00782536	+	0.0215000i	−0.935718	+	0.352748i	$0.885247\pi$
$548$		0			0
$549$	−29.2314	−	165.779i	−0.0532447	−	0.301966i
$550$		0			0
$551$	158.482	+	233.180i	0.287627	+	0.423193i
$552$		0			0
$553$	−278.180	+	49.0506i	−0.503037	+	0.0886990i
$554$		0			0
$555$	214.935	−	78.2300i	0.387271	−	0.140955i
$556$		0			0
$557$	−492.680	−	413.407i	−0.884524	−	0.742204i	0.0825802	−	0.996584i	$-0.473684\pi$
$557$	−492.680	−	413.407i	−0.884524	−	0.742204i	−0.967104	+	0.254381i	$0.918128\pi$
$558$		0			0
$559$	−9.22613	+	5.32671i	−0.0165047	+	0.00952900i
$560$		0			0
$561$	−253.023	−	44.6148i	−0.451022	−	0.0795274i
$562$		0			0
$563$	−278.970	−	161.063i	−0.495506	−	0.286080i	0.231350	−	0.972871i	$-0.425686\pi$
$563$	−278.970	−	161.063i	−0.495506	−	0.286080i	−0.726856	+	0.686790i	$0.759019\pi$
$564$		0			0
$565$	234.706	−	644.850i	0.415409	−	1.14133i
$566$		0			0
$567$	202.635	−	170.031i	0.357382	−	0.299879i
$568$		0			0
$569$			205.562i			0.361268i	0.983550	+	0.180634i	$0.0578150\pi$
$569$			205.562i			0.361268i	−0.983550	+	0.180634i	$0.942185\pi$
$570$		0			0
$571$	3.53858			0.00619716			0.00309858	−	0.999995i	$-0.499014\pi$
$571$	3.53858			0.00619716			0.00309858	+	0.999995i	$0.499014\pi$
$572$		0			0
$573$	285.323	+	340.034i	0.497945	+	0.593428i
$574$		0			0
$575$	−46.4301	−	16.8992i	−0.0807481	−	0.0293899i
$576$		0			0
$577$	63.4942	−	109.975i	0.110042	−	0.190598i	−0.805745	−	0.592263i	$-0.798235\pi$
$577$	63.4942	−	109.975i	0.110042	−	0.190598i	0.915787	+	0.401664i	$0.131568\pi$
$578$		0			0
$579$	96.8695	−	549.374i	0.167305	−	0.948833i
$580$		0			0
$581$	764.927	+	1324.89i	1.31657	+	2.28037i
$582$		0			0
$583$	216.151	−	257.599i	0.370756	−	0.441850i
$584$		0			0
$585$	38.5434	+	105.897i	0.0658861	+	0.181021i
$586$		0			0
$587$	−18.3661	−	104.159i	−0.0312881	−	0.177444i	0.965159	−	0.261664i	$-0.0842712\pi$
$587$	−18.3661	−	104.159i	−0.0312881	−	0.177444i	−0.996447	+	0.0842203i	$0.973160\pi$
$588$		0			0
$589$	−136.716	−	540.207i	−0.232116	−	0.917159i
$590$		0			0
$591$	613.951	−	108.256i	1.03883	−	0.183175i
$592$		0			0
$593$	421.609	−	153.453i	0.710977	−	0.258774i	0.0388864	−	0.999244i	$-0.487619\pi$
$593$	421.609	−	153.453i	0.710977	−	0.258774i	0.672090	+	0.740469i	$0.265397\pi$
$594$		0			0
$595$	844.378	+	708.518i	1.41912	+	1.19079i
$596$		0			0
$597$	298.891	−	172.565i	0.500655	−	0.289053i
$598$		0			0
$599$	−147.017	−	25.9230i	−0.245437	−	0.0432772i	0.0495762	−	0.998770i	$-0.484213\pi$
$599$	−147.017	−	25.9230i	−0.245437	−	0.0432772i	−0.295013	+	0.955493i	$0.595324\pi$
$600$		0			0
$601$	−116.563	−	67.2974i	−0.193948	−	0.111976i	0.399882	−	0.916567i	$-0.369051\pi$
$601$	−116.563	−	67.2974i	−0.193948	−	0.111976i	−0.593829	+	0.804591i	$0.702385\pi$
$602$		0			0
$603$	−128.977	+	354.360i	−0.213892	+	0.587662i
$604$		0			0
$605$	261.076	−	219.068i	0.431530	−	0.362097i
$606$		0			0
$607$		−	400.947i		−	0.660539i	−0.943887	−	0.330269i	$-0.892860\pi$
$607$		−	400.947i		−	0.660539i	0.943887	−	0.330269i	$-0.107140\pi$
$608$		0			0
$609$	−380.004			−0.623980
$610$		0			0
$611$	4.71488	+	5.61897i	0.00771666	+	0.00919636i
$612$		0			0
$613$	455.072	+	165.633i	0.742368	+	0.270200i	0.685391	−	0.728176i	$-0.259631\pi$
$613$	455.072	+	165.633i	0.742368	+	0.270200i	0.0569774	+	0.998375i	$0.481854\pi$
$614$		0			0
$615$	62.1492	−	107.646i	0.101056	−	0.175033i
$616$		0			0
$617$	115.386	−	654.384i	0.187011	−	1.06059i	−0.736334	−	0.676618i	$-0.763445\pi$
$617$	115.386	−	654.384i	0.187011	−	1.06059i	0.923345	−	0.383972i	$-0.125444\pi$
$618$		0			0
$619$	−297.354	−	515.032i	−0.480378	−	0.832039i	0.519369	−	0.854550i	$-0.326167\pi$
$619$	−297.354	−	515.032i	−0.480378	−	0.832039i	−0.999747	+	0.0225115i	$0.992834\pi$
$620$		0			0
$621$	−65.5637	+	78.1358i	−0.105578	+	0.125823i
$622$		0			0
$623$	−584.066	−	1604.71i	−0.937506	−	2.57578i
$624$		0			0
$625$	−14.4028	−	81.6826i	−0.0230446	−	0.130692i
$626$		0			0
$627$	−160.378	+	72.0843i	−0.255786	+	0.114967i
$628$		0			0
$629$	−875.478	+	154.370i	−1.39186	+	0.245422i
$630$		0			0
$631$	−643.868	+	234.349i	−1.02039	+	0.371393i	−0.797415	−	0.603431i	$-0.793800\pi$
$631$	−643.868	+	234.349i	−1.02039	+	0.371393i	−0.222978	+	0.974824i	$0.571578\pi$
$632$		0			0
$633$	−124.545	−	104.506i	−0.196753	−	0.165096i
$634$		0			0
$635$	−18.7665	+	10.8348i	−0.0295535	+	0.0170627i
$636$		0			0
$637$	708.630	+	124.951i	1.11245	+	0.196155i
$638$		0			0
$639$	536.913	+	309.987i	0.840239	+	0.485112i
$640$		0			0
$641$	231.631	−	636.401i	0.361359	−	0.992825i	−0.617191	−	0.786813i	$-0.711729\pi$
$641$	231.631	−	636.401i	0.361359	−	0.992825i	0.978550	−	0.206011i	$-0.0660483\pi$
$642$		0			0
$643$	−556.017	+	466.553i	−0.864723	+	0.725589i	−0.962980	−	0.269572i	$-0.913118\pi$
$643$	−556.017	+	466.553i	−0.864723	+	0.725589i	0.0982573	+	0.995161i	$0.468673\pi$
$644$		0			0
$645$		−	9.87106i		−	0.0153040i
$646$		0			0
$647$	759.149			1.17334			0.586668	−	0.809827i	$-0.300439\pi$
$647$	759.149			1.17334			0.586668	+	0.809827i	$0.300439\pi$
$648$		0			0
$649$	−269.687	−	321.400i	−0.415542	−	0.495224i
$650$		0			0
$651$	705.765	+	256.878i	1.08412	+	0.394589i
$652$		0			0
$653$	87.6230	−	151.767i	0.134185	−	0.232416i	−0.791101	−	0.611686i	$-0.790492\pi$
$653$	87.6230	−	151.767i	0.134185	−	0.232416i	0.925286	+	0.379270i	$0.123825\pi$
$654$		0			0
$655$	−4.37944	+	24.8370i	−0.00668617	+	0.0379191i
$656$		0			0
$657$	−233.182	−	403.883i	−0.354920	−	0.614739i
$658$		0			0
$659$	−140.799	+	167.798i	−0.213656	+	0.254625i	−0.862219	−	0.506536i	$-0.830926\pi$
$659$	−140.799	+	167.798i	−0.213656	+	0.254625i	0.648563	+	0.761161i	$0.275370\pi$
$660$		0			0
$661$	68.1467	+	187.231i	0.103096	+	0.283255i	0.980507	−	0.196486i	$-0.0629530\pi$
$661$	68.1467	+	187.231i	0.103096	+	0.283255i	−0.877410	+	0.479741i	$0.840731\pi$
$662$		0			0
$663$	79.7769	+	452.438i	0.120327	+	0.682410i
$664$		0			0
$665$	750.493	+	76.2020i	1.12856	+	0.114590i
$666$		0			0
$667$	51.8508	−	9.14270i	0.0777373	−	0.0137072i
$668$		0			0
$669$	−293.200	+	106.716i	−0.438266	+	0.159516i
$670$		0			0
$671$	−126.570	−	106.205i	−0.188629	−	0.158278i
$672$		0			0
$673$	1069.95	−	617.733i	1.58981	−	0.917880i	0.596478	−	0.802630i	$-0.296566\pi$
$673$	1069.95	−	617.733i	1.58981	−	0.917880i	0.993337	−	0.115250i	$-0.0367669\pi$
$674$		0			0
$675$	394.235	+	69.5143i	0.584052	+	0.102984i
$676$		0			0
$677$	−208.387	−	120.312i	−0.307809	−	0.177714i	0.338136	−	0.941097i	$-0.390203\pi$
$677$	−208.387	−	120.312i	−0.307809	−	0.177714i	−0.645946	+	0.763383i	$0.723537\pi$
$678$		0			0
$679$	−561.481	+	1542.66i	−0.826923	+	2.27195i
$680$		0			0
$681$	−355.080	+	297.947i	−0.521409	+	0.437514i
$682$		0			0
$683$		−	727.699i		−	1.06545i	−0.846290	−	0.532723i	$-0.821169\pi$
$683$		−	727.699i		−	1.06545i	0.846290	−	0.532723i	$-0.178831\pi$
$684$		0			0
$685$	−226.158			−0.330158
$686$		0			0
$687$	−596.961	−	711.430i	−0.868938	−	1.03556i
$688$		0			0
$689$	−565.032	−	205.655i	−0.820076	−	0.298483i
$690$		0			0
$691$	−64.0596	+	110.954i	−0.0927056	+	0.160571i	−0.908649	−	0.417561i	$-0.862885\pi$
$691$	−64.0596	+	110.954i	−0.0927056	+	0.160571i	0.815943	+	0.578132i	$0.196218\pi$
$692$		0			0
$693$	−39.2344	+	222.509i	−0.0566153	+	0.321081i
$694$		0			0
$695$	−210.770	−	365.064i	−0.303266	−	0.525273i
$696$		0			0
$697$	−310.531	+	370.077i	−0.445525	+	0.530956i
$698$		0			0
$699$	224.686	+	617.321i	0.321440	+	0.883149i
$700$		0			0
$701$	148.896	+	844.432i	0.212405	+	1.20461i	0.885353	+	0.464920i	$0.153917\pi$
$701$	148.896	+	844.432i	0.212405	+	1.20461i	−0.672947	+	0.739691i	$0.734972\pi$
$702$		0			0
$703$	−436.147	+	424.168i	−0.620408	+	0.603369i
$704$		0			0
$705$	−6.69313	+	1.18018i	−0.00949380	+	0.00167401i
$706$		0			0
$707$	190.652	−	69.3917i	0.269663	−	0.0981494i
$708$		0			0
$709$	−521.483	−	437.576i	−0.735519	−	0.617173i	0.196111	−	0.980582i	$-0.437169\pi$
$709$	−521.483	−	437.576i	−0.735519	−	0.617173i	−0.931630	+	0.363408i	$0.881613\pi$
$710$		0			0
$711$	−90.0671	+	52.0003i	−0.126677	+	0.0731368i
$712$		0			0
$713$	−102.481	−	18.0701i	−0.143732	−	0.0253438i
$714$		0			0
$715$	95.7913	+	55.3052i	0.133974	+	0.0773499i
$716$		0			0
$717$	−183.002	+	502.794i	−0.255233	+	0.701247i
$718$		0			0
$719$	−287.760	+	241.459i	−0.400222	+	0.335826i	−0.820580	−	0.571532i	$-0.806349\pi$
$719$	−287.760	+	241.459i	−0.400222	+	0.335826i	0.420357	+	0.907359i	$0.361905\pi$
$720$		0			0
$721$			165.249i			0.229194i
$722$		0			0
$723$	−634.495			−0.877586
$724$		0			0
$725$	−132.825	−	158.294i	−0.183207	−	0.218337i
$726$		0			0
$727$	1260.70	+	458.856i	1.73411	+	0.631164i	0.998910	−	0.0466872i	$-0.0148664\pi$
$727$	1260.70	+	458.856i	1.73411	+	0.631164i	0.735199	+	0.677851i	$0.237089\pi$
$728$		0			0
$729$	326.369	−	565.288i	0.447695	−	0.775430i
$730$		0			0
$731$	−6.66202	+	37.7822i	−0.00911358	+	0.0516857i
$732$		0			0
$733$	−167.328	−	289.820i	−0.228278	−	0.395389i	0.729020	−	0.684493i	$-0.239976\pi$
$733$	−167.328	−	289.820i	−0.228278	−	0.395389i	−0.957298	+	0.289103i	$0.906643\pi$
$734$		0			0
$735$	−428.559	+	510.737i	−0.583073	+	0.694880i
$736$		0			0
$737$	126.593	+	347.810i	0.171767	+	0.471927i
$738$		0			0
$739$	119.012	+	674.949i	0.161044	+	0.913327i	0.953050	+	0.302813i	$0.0979259\pi$
$739$	119.012	+	674.949i	0.161044	+	0.913327i	−0.792006	+	0.610514i	$0.790963\pi$
$740$		0			0
$741$	219.206	+	225.396i	0.295824	+	0.304178i
$742$		0			0
$743$	−925.061	+	163.113i	−1.24503	+	0.219533i	−0.757072	−	0.653331i	$-0.773371\pi$
$743$	−925.061	+	163.113i	−1.24503	+	0.219533i	−0.487963	+	0.872865i	$0.662260\pi$
$744$		0			0
$745$	2.38381	−	0.867634i	0.00319974	−	0.00116461i
$746$		0			0
$747$	431.485	+	362.059i	0.577624	+	0.484684i
$748$		0			0
$749$	−1434.31	+	828.097i	−1.91496	+	1.10560i
$750$		0			0
$751$	1139.15	+	200.863i	1.51685	+	0.267461i	0.869193	−	0.494473i	$-0.164639\pi$
$751$	1139.15	+	200.863i	1.51685	+	0.267461i	0.647654	+	0.761934i	$0.275750\pi$
$752$		0			0
$753$	−306.021	−	176.682i	−0.406403	−	0.234637i
$754$		0			0
$755$	147.267	−	404.612i	0.195056	−	0.535911i
$756$		0			0
$757$	277.077	−	232.495i	0.366019	−	0.307127i	−0.441165	−	0.897426i	$-0.645435\pi$
$757$	277.077	−	232.495i	0.366019	−	0.307127i	0.807184	+	0.590299i	$0.200990\pi$
$758$		0			0
$759$			32.8360i			0.0432621i
$760$		0			0
$761$	−5.16858			−0.00679183			−0.00339592	−	0.999994i	$-0.501081\pi$
$761$	−5.16858			−0.00679183			−0.00339592	+	0.999994i	$0.501081\pi$
$762$		0			0
$763$	416.697	+	496.600i	0.546130	+	0.650852i
$764$		0			0
$765$	381.356	+	138.802i	0.498505	+	0.181441i
$766$		0			0
$767$	−375.111	+	649.712i	−0.489063	+	0.847082i
$768$		0			0
$769$	171.070	−	970.187i	0.222458	−	1.26162i	−0.645028	−	0.764159i	$-0.723154\pi$
$769$	171.070	−	970.187i	0.222458	−	1.26162i	0.867486	−	0.497462i	$-0.165735\pi$
$770$		0			0
$771$	−45.0117	−	77.9625i	−0.0583809	−	0.101119i
$772$		0			0
$773$	482.128	−	574.578i	0.623710	−	0.743309i	−0.357993	−	0.933724i	$-0.616539\pi$
$773$	482.128	−	574.578i	0.623710	−	0.743309i	0.981704	+	0.190415i	$0.0609834\pi$
$774$		0			0
$775$	139.685	+	383.782i	0.180239	+	0.495202i
$776$		0			0
$777$	−142.393	−	807.551i	−0.183260	−	1.03932i
$778$		0			0
$779$	−33.3980	+	328.928i	−0.0428730	+	0.422244i
$780$		0			0
$781$	599.270	−	105.667i	0.767311	−	0.135298i
$782$		0			0
$783$	−400.848	+	145.897i	−0.511939	+	0.186330i
$784$		0			0
$785$	374.330	+	314.100i	0.476853	+	0.400127i
$786$		0			0
$787$	−122.515	+	70.7342i	−0.155674	+	0.0898783i	−0.575813	−	0.817581i	$-0.695314\pi$
$787$	−122.515	+	70.7342i	−0.155674	+	0.0898783i	0.420139	+	0.907460i	$0.361981\pi$
$788$		0			0
$789$	−536.335	−	94.5704i	−0.679766	−	0.119861i
$790$		0			0
$791$	−2130.59	−	1230.10i	−2.69354	−	1.55512i
$792$		0			0
$793$	−101.048	+	277.626i	−0.127424	+	0.350096i
$794$		0			0
$795$	426.792	−	358.121i	0.536845	−	0.450467i
$796$		0			0
$797$		−	400.697i		−	0.502757i	−0.967889	−	0.251378i	$-0.919116\pi$
$797$		−	400.697i		−	0.502757i	0.967889	−	0.251378i	$-0.0808838\pi$
$798$		0			0
$799$	26.4150			0.0330600
$800$		0			0
$801$	−404.147	−	481.644i	−0.504553	−	0.601303i
$802$		0			0
$803$	−430.139	−	156.558i	−0.535665	−	0.194966i
$804$		0			0
$805$	70.4358	−	121.998i	0.0874979	−	0.151551i
$806$		0			0
$807$	−70.5245	+	399.964i	−0.0873909	+	0.495619i
$808$		0			0
$809$	−37.1415	−	64.3309i	−0.0459103	−	0.0795190i	0.842157	−	0.539232i	$-0.181286\pi$
$809$	−37.1415	−	64.3309i	−0.0459103	−	0.0795190i	−0.888067	+	0.459713i	$0.847952\pi$
$810$		0			0
$811$	860.795	−	1025.86i	1.06140	−	1.26493i	0.0984801	−	0.995139i	$-0.468602\pi$
$811$	860.795	−	1025.86i	1.06140	−	1.26493i	0.962920	−	0.269788i	$-0.0869536\pi$
$812$		0			0
$813$	122.094	+	335.451i	0.150177	+	0.412608i
$814$		0			0
$815$	0.0254259	+	0.144197i	3.11974e−5	+	0.000176929i
$816$		0			0
$817$	10.7639	+	23.9481i	0.0131749	+	0.0293122i
$818$		0			0
$819$	397.874	−	70.1560i	0.485805	−	0.0856606i
$820$		0			0
$821$	970.080	−	353.080i	1.18158	−	0.430061i	0.324822	−	0.945775i	$-0.394695\pi$
$821$	970.080	−	353.080i	1.18158	−	0.430061i	0.856761	+	0.515714i	$0.172473\pi$
$822$		0			0
$823$	−669.625	−	561.882i	−0.813639	−	0.682724i	0.137835	−	0.990455i	$-0.455986\pi$
$823$	−669.625	−	561.882i	−0.813639	−	0.682724i	−0.951473	+	0.307731i	$0.900430\pi$
$824$		0			0
$825$	111.606	−	64.4358i	0.135280	−	0.0781040i
$826$		0			0
$827$	−683.431	−	120.507i	−0.826398	−	0.145716i	−0.255575	−	0.966789i	$-0.582265\pi$
$827$	−683.431	−	120.507i	−0.826398	−	0.145716i	−0.570823	+	0.821073i	$0.693376\pi$
$828$		0			0
$829$	768.640	+	443.774i	0.927189	+	0.535313i	0.885921	−	0.463835i	$-0.153527\pi$
$829$	768.640	+	443.774i	0.927189	+	0.535313i	0.0412674	+	0.999148i	$0.486860\pi$
$830$		0			0
$831$	−64.0090	+	175.863i	−0.0770265	+	0.211629i
$832$		0			0
$833$	1985.04	−	1665.65i	2.38300	−	1.99958i
$834$		0			0
$835$			325.194i			0.389454i
$836$		0			0
$837$	843.103			1.00729
$838$		0			0
$839$	622.420	+	741.772i	0.741860	+	0.884114i	0.996557	−	0.0829067i	$-0.0264204\pi$
$839$	622.420	+	741.772i	0.741860	+	0.884114i	−0.254698	+	0.967021i	$0.581976\pi$
$840$		0			0
$841$	−583.369	−	212.329i	−0.693661	−	0.252472i
$842$		0			0
$843$	−127.310	+	220.507i	−0.151020	+	0.261574i
$844$		0			0
$845$	−63.3155	+	359.080i	−0.0749295	+	0.424947i
$846$		0			0
$847$	−610.912	−	1058.13i	−0.721266	−	1.24927i
$848$		0			0
$849$	127.779	−	152.282i	0.150506	−	0.179366i
$850$		0			0
$851$	38.8585	+	106.763i	0.0456622	+	0.125456i
$852$		0			0
$853$	139.389	+	790.517i	0.163411	+	0.926749i	0.950688	+	0.310149i	$0.100379\pi$
$853$	139.389	+	790.517i	0.163411	+	0.926749i	−0.787277	+	0.616599i	$0.788510\pi$
$854$		0			0
$855$	269.249	−	68.1420i	0.314912	−	0.0796983i
$856$		0			0
$857$	55.7464	−	9.82959i	0.0650483	−	0.0114698i	−0.141029	−	0.990005i	$-0.545041\pi$
$857$	55.7464	−	9.82959i	0.0650483	−	0.0114698i	0.206078	+	0.978536i	$0.433930\pi$
$858$		0			0
$859$	647.054	−	235.509i	0.753265	−	0.274166i	0.0632858	−	0.997995i	$-0.479842\pi$
$859$	647.054	−	235.509i	0.753265	−	0.274166i	0.689979	+	0.723830i	$0.257620\pi$
$860$		0			0
$861$	−341.363	−	286.437i	−0.396472	−	0.332680i
$862$		0			0
$863$	732.793	−	423.078i	0.849123	−	0.490241i	−0.0112320	−	0.999937i	$-0.503575\pi$
$863$	732.793	−	423.078i	0.849123	−	0.490241i	0.860355	+	0.509696i	$0.170242\pi$
$864$		0			0
$865$	−837.954	−	147.754i	−0.968733	−	0.170814i
$866$		0			0
$867$	895.571	+	517.058i	1.03295	+	0.596376i
$868$		0			0
$869$	−34.9128	+	95.9222i	−0.0401759	+	0.110382i
$870$		0			0
$871$	507.001	−	425.424i	0.582090	−	0.488432i
$872$		0			0
$873$			604.429i			0.692358i
$874$		0			0
$875$	−1545.45			−1.76623
$876$		0			0
$877$	244.253	+	291.089i	0.278509	+	0.331914i	0.887106	−	0.461565i	$-0.152712\pi$
$877$	244.253	+	291.089i	0.278509	+	0.331914i	−0.608597	+	0.793479i	$0.708267\pi$
$878$		0			0
$879$	339.150	+	123.441i	0.385836	+	0.140433i
$880$		0			0
$881$	−70.3208	+	121.799i	−0.0798193	+	0.138251i	−0.903172	−	0.429279i	$-0.858768\pi$
$881$	−70.3208	+	121.799i	−0.0798193	+	0.138251i	0.823353	+	0.567530i	$0.192101\pi$
$882$		0			0
$883$	−140.301	+	795.685i	−0.158891	+	0.901116i	0.796251	+	0.604967i	$0.206814\pi$
$883$	−140.301	+	795.685i	−0.158891	+	0.901116i	−0.955142	+	0.296149i	$0.904298\pi$
$884$		0			0
$885$	−347.564	−	601.999i	−0.392728	−	0.680225i
$886$		0			0
$887$	857.318	−	1021.71i	0.966536	−	1.15187i	−0.0218269	−	0.999762i	$-0.506948\pi$
$887$	857.318	−	1021.71i	0.966536	−	1.15187i	0.988363	−	0.152112i	$-0.0486073\pi$
$888$		0			0
$889$	26.5706	+	73.0020i	0.0298882	+	0.0821170i
$890$		0			0
$891$	−16.5993	−	94.1396i	−0.0186300	−	0.105656i
$892$		0			0
$893$	14.9512	−	10.1617i	0.0167427	−	0.0113793i
$894$		0			0
$895$	592.264	−	104.432i	0.661748	−	0.116684i
$896$		0			0
$897$	55.1739	−	20.0816i	0.0615093	−	0.0223876i
$898$		0			0
$899$	−333.382	−	279.741i	−0.370837	−	0.311169i
$900$		0			0
$901$	−1875.28	+	1082.69i	−2.08133	+	1.20165i
$902$		0			0
$903$	−34.8507	−	6.14512i	−0.0385944	−	0.00680523i
$904$		0			0
$905$	−676.224	−	390.418i	−0.747209	−	0.431401i
$906$		0			0
$907$	−371.219	+	1019.92i	−0.409282	+	1.12449i	0.548287	+	0.836290i	$0.315280\pi$
$907$	−371.219	+	1019.92i	−0.409282	+	1.12449i	−0.957569	+	0.288203i	$0.906942\pi$
$908$		0			0
$909$	57.2231	−	48.0159i	0.0629517	−	0.0528228i
$910$		0			0
$911$			1064.07i			1.16802i	0.811745	+	0.584012i	$0.198518\pi$
$911$			1064.07i			1.16802i	−0.811745	+	0.584012i	$0.801482\pi$
$912$		0			0
$913$	552.853			0.605534
$914$		0			0
$915$	−175.961	−	209.702i	−0.192307	−	0.229183i
$916$		0			0
$917$	84.9632	+	30.9241i	0.0926534	+	0.0337231i
$918$		0			0
$919$	324.682	−	562.365i	0.353299	−	0.611932i	−0.633526	−	0.773721i	$-0.718393\pi$
$919$	324.682	−	562.365i	0.353299	−	0.611932i	0.986825	+	0.161789i	$0.0517265\pi$
$920$		0			0
$921$	−105.745	+	599.711i	−0.114816	+	0.651152i
$922$		0			0
$923$	−544.050	−	942.322i	−0.589437	−	1.02093i
$924$		0			0
$925$	286.622	−	341.583i	0.309862	−	0.369279i
$926$		0			0
$927$	20.8090	+	57.1723i	0.0224477	+	0.0616746i
$928$		0			0
$929$	−155.785	−	883.501i	−0.167691	−	0.951024i	−0.946246	−	0.323448i	$-0.895158\pi$
$929$	−155.785	−	883.501i	−0.167691	−	0.951024i	0.778555	−	0.627577i	$-0.215953\pi$
$930$		0			0
$931$	482.793	−	1706.41i	0.518575	−	1.83288i
$932$		0			0
$933$	775.025	−	136.658i	0.830681	−	0.146471i
$934$		0			0
$935$	374.307	−	136.237i	0.400329	−	0.145708i
$936$		0			0
$937$	−68.7858	−	57.7182i	−0.0734107	−	0.0615989i	0.605344	−	0.795964i	$-0.293036\pi$
$937$	−68.7858	−	57.7182i	−0.0734107	−	0.0615989i	−0.678755	+	0.734365i	$0.737480\pi$
$938$		0			0
$939$	−341.747	+	197.308i	−0.363948	+	0.210126i
$940$		0			0
$941$	−1079.12	−	190.278i	−1.14678	−	0.202209i	−0.432212	−	0.901772i	$-0.642267\pi$
$941$	−1079.12	−	190.278i	−1.14678	−	0.202209i	−0.714571	+	0.699563i	$0.753378\pi$
$942$		0			0
$943$	53.4698	+	30.8708i	0.0567018	+	0.0327368i
$944$		0			0
$945$	−390.360	+	1072.50i	−0.413079	+	1.13493i
$946$		0			0
$947$	811.240	−	680.711i	0.856642	−	0.718808i	−0.104600	−	0.994514i	$-0.533356\pi$
$947$	811.240	−	680.711i	0.856642	−	0.718808i	0.961242	+	0.275707i	$0.0889118\pi$
$948$		0			0
$949$			818.504i			0.862491i
$950$		0			0
$951$	860.996			0.905359
$952$		0			0
$953$	137.014	+	163.288i	0.143772	+	0.171341i	0.833125	−	0.553085i	$-0.186550\pi$
$953$	137.014	+	163.288i	0.143772	+	0.171341i	−0.689353	+	0.724426i	$0.742105\pi$
$954$		0			0
$955$	−646.678	−	235.371i	−0.677149	−	0.246462i
$956$		0			0
$957$	−68.6621	+	118.926i	−0.0717473	+	0.124270i
$958$		0			0
$959$	−140.792	+	798.474i	−0.146812	+	0.832611i
$960$		0			0
$961$	−50.4244	−	87.3377i	−0.0524708	−	0.0908821i
$962$		0			0
$963$	−391.959	+	467.118i	−0.407019	+	0.485066i
$964$		0			0
$965$	295.803	+	812.711i	0.306531	+	0.842188i
$966$		0			0
$967$	209.672	+	1189.11i	0.216827	+	1.22969i	0.877708	+	0.479196i	$0.159072\pi$
$967$	209.672	+	1189.11i	0.216827	+	1.22969i	−0.660881	+	0.750491i	$0.729817\pi$
$968$		0			0
$969$	1129.21	−	82.9696i	1.16534	−	0.0856239i
$970$		0			0
$971$	−608.774	+	107.343i	−0.626955	+	0.110549i	−0.478094	−	0.878309i	$-0.658672\pi$
$971$	−608.774	+	107.343i	−0.626955	+	0.110549i	−0.148862	+	0.988858i	$0.547561\pi$
$972$		0			0
$973$	−1420.11	+	516.877i	−1.45951	+	0.531220i
$974$		0			0
$975$	−176.526	−	148.123i	−0.181053	−	0.151921i
$976$		0			0
$977$	−706.559	+	407.932i	−0.723192	+	0.417535i	−0.815927	−	0.578156i	$-0.803773\pi$
$977$	−706.559	+	407.932i	−0.723192	+	0.417535i	0.0927341	+	0.995691i	$0.470439\pi$
$978$		0			0
$979$	−607.744	−	107.162i	−0.620781	−	0.109460i
$980$		0			0
$981$	206.702	+	119.340i	0.210706	+	0.121651i
$982$		0			0
$983$	112.189	−	308.237i	0.114129	−	0.313568i	−0.869456	−	0.494010i	$-0.835531\pi$
$983$	112.189	−	308.237i	0.114129	−	0.313568i	0.983586	+	0.180442i	$0.0577529\pi$
$984$		0			0
$985$	−740.406	+	621.274i	−0.751681	+	0.630735i
$986$		0			0
$987$			24.3654i			0.0246864i
$988$		0			0
$989$	4.90316			0.00495770
$990$		0			0
$991$	−355.583	−	423.767i	−0.358812	−	0.427616i	0.556196	−	0.831051i	$-0.312260\pi$
$991$	−355.583	−	423.767i	−0.358812	−	0.427616i	−0.915008	+	0.403435i	$0.867816\pi$
$992$		0			0
$993$	112.519	+	40.9537i	0.113313	+	0.0412424i
$994$		0			0
$995$	−267.538	+	463.390i	−0.268883	+	0.465718i
$996$		0			0
$997$	239.518	−	1358.37i	0.240239	−	1.36246i	−0.591057	−	0.806630i	$-0.701289\pi$
$997$	239.518	−	1358.37i	0.240239	−	1.36246i	0.831295	−	0.555831i	$-0.187600\pi$
$998$		0			0
$999$	−460.251	−	797.177i	−0.460711	−	0.797975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.29.2	yes	18
4.3	odd	2		304.3.z.b.257.2		18
19.2	odd	18	inner	76.3.j.a.21.2	✓	18
19.6	even	9		1444.3.c.c.721.6		18
19.13	odd	18		1444.3.c.c.721.13		18
76.59	even	18		304.3.z.b.97.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.21.2	✓	18	19.2	odd	18	inner
76.3.j.a.29.2	yes	18	1.1	even	1	trivial
304.3.z.b.97.2		18	76.59	even	18
304.3.z.b.257.2		18	4.3	odd	2
1444.3.c.c.721.6		18	19.6	even	9
1444.3.c.c.721.13		18	19.13	odd	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37974 - 1.64431i) q^{3} +(3.12714 + 1.13819i) q^{5} +(5.96525 - 10.3321i) q^{7} +(0.762765 - 4.32585i) q^{9} +O(q^{10})\)	\(q+(-1.37974 - 1.64431i) q^{3} +(3.12714 + 1.13819i) q^{5} +(5.96525 - 10.3321i) q^{7} +(0.762765 - 4.32585i) q^{9} +(-2.15570 - 3.73378i) q^{11} +(-4.95545 + 5.90568i) q^{13} +(-2.44311 - 6.71238i) q^{15} +(4.82095 + 27.3410i) q^{17} +(13.2467 + 13.6208i) q^{19} +(-25.2196 + 4.44690i) q^{21} +(3.33418 - 1.21354i) q^{23} +(-10.6676 - 8.95114i) q^{25} +(-24.8957 + 14.3735i) q^{27} +(14.6134 + 2.57674i) q^{29} +(-25.3991 - 14.6642i) q^{31} +(-3.16518 + 8.69625i) q^{33} +(30.4141 - 25.5204i) q^{35} +32.0207i q^{37} +16.5480 q^{39} +(11.1852 + 13.3300i) q^{41} +(1.29855 + 0.472634i) q^{43} +(7.30890 - 12.6594i) q^{45} +(0.165218 - 0.936998i) q^{47} +(-46.6684 - 80.8320i) q^{49} +(38.3053 - 45.6505i) q^{51} +(26.6762 + 73.2922i) q^{53} +(-2.49144 - 14.1296i) q^{55} +(4.11979 - 40.5747i) q^{57} +(95.8354 - 16.8984i) q^{59} +(36.0118 - 13.1072i) q^{61} +(-40.1451 - 33.6858i) q^{63} +(-22.2182 + 12.8277i) q^{65} +(-84.5455 - 14.9076i) q^{67} +(-6.59572 - 3.80804i) q^{69} +(-48.2730 + 132.629i) q^{71} +(81.3315 - 68.2453i) q^{73} +29.8909i q^{75} -51.4371 q^{77} +(-15.2189 - 18.1372i) q^{79} +(20.8348 + 7.58324i) q^{81} +(-64.1153 + 111.051i) q^{83} +(-16.0433 + 90.9863i) q^{85} +(-15.9257 - 27.5842i) q^{87} +(92.0067 - 109.649i) q^{89} +(31.4576 + 86.4291i) q^{91} +(10.9317 + 61.9965i) q^{93} +(25.9213 + 57.6713i) q^{95} +(-135.512 + 23.8943i) q^{97} +(-17.7961 + 6.47724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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