LMFDB - Embedded newform 784.2.bp.b.495.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(47,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 5]))

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

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

chi := DirichletCharacter("784.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bp (of order $42$, degree $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			495.3
Character	$\chi$	$=$	784.495
Dual form			784.2.bp.b.255.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997747 - 0.680253i) q^{3} +(-0.577971 - 0.0433130i) q^{5} +(-1.06691 + 2.42109i) q^{7} +(-0.563267 - 1.43518i) q^{9} +O(q^{10})$	\(q+(-0.997747 - 0.680253i) q^{3} +(-0.577971 - 0.0433130i) q^{5} +(-1.06691 + 2.42109i) q^{7} +(-0.563267 - 1.43518i) q^{9} +(0.867361 + 0.340414i) q^{11} +(2.03975 - 1.62664i) q^{13} +(0.547206 + 0.436382i) q^{15} +(0.990564 + 1.06757i) q^{17} +(-1.33941 + 2.31993i) q^{19} +(2.71147 - 1.68987i) q^{21} +(-4.12561 + 4.44635i) q^{23} +(-4.61198 - 0.695144i) q^{25} +(-1.22042 + 5.34701i) q^{27} +(1.21760 + 5.33464i) q^{29} +(4.61662 + 7.99622i) q^{31} +(-0.633840 - 0.929672i) q^{33} +(0.721510 - 1.35311i) q^{35} +(5.63426 + 1.73794i) q^{37} +(-3.14168 + 0.235436i) q^{39} +(4.20149 + 8.72449i) q^{41} +(2.46495 - 5.11851i) q^{43} +(0.263390 + 0.853890i) q^{45} +(-4.68237 + 0.705753i) q^{47} +(-4.72339 - 5.16619i) q^{49} +(-0.262113 - 1.73900i) q^{51} +(10.8238 - 3.33869i) q^{53} +(-0.486566 - 0.234318i) q^{55} +(2.91454 - 1.40357i) q^{57} +(0.514227 + 6.86188i) q^{59} +(-2.12285 + 6.88211i) q^{61} +(4.07566 + 0.167490i) q^{63} +(-1.24937 + 0.851806i) q^{65} +(2.56661 - 1.48183i) q^{67} +(7.14096 - 1.62988i) q^{69} +(-3.73940 - 0.853493i) q^{71} +(-0.598711 + 3.97219i) q^{73} +(4.12872 + 3.83089i) q^{75} +(-1.74957 + 1.73677i) q^{77} +(-2.43768 - 1.40740i) q^{79} +(1.46443 - 1.35879i) q^{81} +(3.55127 - 4.45316i) q^{83} +(-0.526278 - 0.659932i) q^{85} +(2.41405 - 6.15089i) q^{87} +(-14.0189 + 5.50202i) q^{89} +(1.76203 + 6.67390i) q^{91} +(0.833229 - 11.1187i) q^{93} +(0.874626 - 1.28284i) q^{95} -4.45067i q^{97} -1.43656i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9	$ 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9} + 18 q^{11} + 16 q^{17} + 7 q^{19} + 5 q^{21} + 54 q^{23} - 4 q^{25} - 53 q^{27} - 16 q^{29} + 5 q^{31} - 3 q^{33} - 9 q^{35} + 2 q^{37} - 43 q^{39} - 28 q^{41} - 111 q^{45} - 60 q^{47} - 58 q^{49} - 3 q^{51} - 70 q^{53} + 69 q^{55} + 31 q^{57} + 9 q^{59} - 8 q^{61} + 93 q^{63} - 8 q^{65} - 21 q^{67} - 56 q^{69} - 63 q^{71} - 24 q^{73} + 2 q^{75} - 18 q^{77} + 21 q^{79} + 45 q^{81} + 60 q^{83} + 6 q^{85} - 6 q^{87} + 7 q^{89} + 66 q^{93} + 15 q^{95}+O(q^{100}) $ 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9 + 18 * q^11 + 16 * q^17 + 7 * q^19 + 5 * q^21 + 54 * q^23 - 4 * q^25 - 53 * q^27 - 16 * q^29 + 5 * q^31 - 3 * q^33 - 9 * q^35 + 2 * q^37 - 43 * q^39 - 28 * q^41 - 111 * q^45 - 60 * q^47 - 58 * q^49 - 3 * q^51 - 70 * q^53 + 69 * q^55 + 31 * q^57 + 9 * q^59 - 8 * q^61 + 93 * q^63 - 8 * q^65 - 21 * q^67 - 56 * q^69 - 63 * q^71 - 24 * q^73 + 2 * q^75 - 18 * q^77 + 21 * q^79 + 45 * q^81 + 60 * q^83 + 6 * q^85 - 6 * q^87 + 7 * q^89 + 66 * q^93 + 15 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{29}{42}\right)$

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
$3$	−0.997747	−	0.680253i	−0.576050	−	0.392744i	0.239959	−	0.970783i	$-0.422866\pi$
$3$	−0.997747	−	0.680253i	−0.576050	−	0.392744i	−0.816009	+	0.578039i	$0.803818\pi$
$4$		0			0
$5$	−0.577971	−	0.0433130i	−0.258477	−	0.0193701i	−0.0551385	−	0.998479i	$-0.517560\pi$
$5$	−0.577971	−	0.0433130i	−0.258477	−	0.0193701i	−0.203338	+	0.979109i	$0.565179\pi$
$6$		0			0
$7$	−1.06691	+	2.42109i	−0.403255	+	0.915088i
$7$	−1.06691	+	2.42109i	−0.403255	+	0.915088i
$8$		0			0
$9$	−0.563267	−	1.43518i	−0.187756	−	0.478393i
$10$		0			0
$11$	0.867361	+	0.340414i	0.261519	+	0.102639i	0.492478	−	0.870325i	$-0.336091\pi$
$11$	0.867361	+	0.340414i	0.261519	+	0.102639i	−0.230959	+	0.972963i	$0.574186\pi$
$12$		0			0
$13$	2.03975	−	1.62664i	0.565724	−	0.451150i	−0.298392	−	0.954444i	$-0.596450\pi$
$13$	2.03975	−	1.62664i	0.565724	−	0.451150i	0.864115	+	0.503294i	$0.167879\pi$
$14$		0			0
$15$	0.547206	+	0.436382i	0.141288	+	0.112673i
$16$		0			0
$17$	0.990564	+	1.06757i	0.240247	+	0.258925i	0.841653	−	0.540019i	$-0.181583\pi$
$17$	0.990564	+	1.06757i	0.240247	+	0.258925i	−0.601406	+	0.798944i	$0.705392\pi$
$18$		0			0
$19$	−1.33941	+	2.31993i	−0.307282	+	0.532229i	−0.977767	−	0.209695i	$-0.932753\pi$
$19$	−1.33941	+	2.31993i	−0.307282	+	0.532229i	0.670484	+	0.741924i	$0.266086\pi$
$20$		0			0
$21$	2.71147	−	1.68987i	0.591690	−	0.368760i
$22$		0			0
$23$	−4.12561	+	4.44635i	−0.860249	+	0.927128i	−0.997992	−	0.0633403i	$-0.979825\pi$
$23$	−4.12561	+	4.44635i	−0.860249	+	0.927128i	0.137743	+	0.990468i	$0.456015\pi$
$24$		0			0
$25$	−4.61198	−	0.695144i	−0.922396	−	0.139029i
$26$		0			0
$27$	−1.22042	+	5.34701i	−0.234870	+	1.02903i
$28$		0			0
$29$	1.21760	+	5.33464i	0.226102	+	0.990617i	0.952785	+	0.303645i	$0.0982036\pi$
$29$	1.21760	+	5.33464i	0.226102	+	0.990617i	−0.726683	+	0.686973i	$0.758939\pi$
$30$		0			0
$31$	4.61662	+	7.99622i	0.829169	+	1.43616i	0.898691	+	0.438583i	$0.144519\pi$
$31$	4.61662	+	7.99622i	0.829169	+	1.43616i	−0.0695218	+	0.997580i	$0.522147\pi$
$32$		0			0
$33$	−0.633840	−	0.929672i	−0.110337	−	0.161835i
$34$		0			0
$35$	0.721510	−	1.35311i	0.121957	−	0.228718i
$36$		0			0
$37$	5.63426	+	1.73794i	0.926267	+	0.285715i	0.720956	−	0.692981i	$-0.243703\pi$
$37$	5.63426	+	1.73794i	0.926267	+	0.285715i	0.205311	+	0.978697i	$0.434179\pi$
$38$		0			0
$39$	−3.14168	+	0.235436i	−0.503071	+	0.0377000i
$40$		0			0
$41$	4.20149	+	8.72449i	0.656163	+	1.36254i	0.917674	+	0.397335i	$0.130065\pi$
$41$	4.20149	+	8.72449i	0.656163	+	1.36254i	−0.261511	+	0.965201i	$0.584221\pi$
$42$		0			0
$43$	2.46495	−	5.11851i	0.375901	−	0.780566i	−0.624099	−	0.781345i	$-0.714534\pi$
$43$	2.46495	−	5.11851i	0.375901	−	0.780566i	1.00000		0.000779214i	$0.000248031\pi$
$44$		0			0
$45$	0.263390	+	0.853890i	0.0392639	+	0.127290i
$46$		0			0
$47$	−4.68237	+	0.705753i	−0.682993	+	0.102945i	−0.481369	−	0.876518i	$-0.659860\pi$
$47$	−4.68237	+	0.705753i	−0.682993	+	0.102945i	−0.201625	+	0.979463i	$0.564622\pi$
$48$		0			0
$49$	−4.72339	−	5.16619i	−0.674771	−	0.738028i
$50$		0			0
$51$	−0.262113	−	1.73900i	−0.0367031	−	0.243509i
$52$		0			0
$53$	10.8238	−	3.33869i	1.48676	−	0.458605i	0.558175	−	0.829724i	$-0.311502\pi$
$53$	10.8238	−	3.33869i	1.48676	−	0.458605i	0.928585	+	0.371119i	$0.121026\pi$
$54$		0			0
$55$	−0.486566	−	0.234318i	−0.0656085	−	0.0315954i
$56$		0			0
$57$	2.91454	−	1.40357i	0.386040	−	0.185907i
$58$		0			0
$59$	0.514227	+	6.86188i	0.0669466	+	0.893340i	0.925046	+	0.379856i	$0.124026\pi$
$59$	0.514227	+	6.86188i	0.0669466	+	0.893340i	−0.858099	+	0.513484i	$0.828354\pi$
$60$		0			0
$61$	−2.12285	+	6.88211i	−0.271803	+	0.881164i	0.712041	+	0.702138i	$0.247771\pi$
$61$	−2.12285	+	6.88211i	−0.271803	+	0.881164i	−0.983844	+	0.179027i	$0.942705\pi$
$62$		0			0
$63$	4.07566	+	0.167490i	0.513485	+	0.0211018i
$64$		0			0
$65$	−1.24937	+	0.851806i	−0.154965	+	0.105654i
$66$		0			0
$67$	2.56661	−	1.48183i	0.313561	−	0.181035i	−0.334958	−	0.942233i	$-0.608722\pi$
$67$	2.56661	−	1.48183i	0.313561	−	0.181035i	0.648519	+	0.761198i	$0.275389\pi$
$68$		0			0
$69$	7.14096	−	1.62988i	0.859670	−	0.196214i
$70$		0			0
$71$	−3.73940	−	0.853493i	−0.443785	−	0.101291i	−0.00521166	−	0.999986i	$-0.501659\pi$
$71$	−3.73940	−	0.853493i	−0.443785	−	0.101291i	−0.438573	+	0.898695i	$0.644516\pi$
$72$		0			0
$73$	−0.598711	+	3.97219i	−0.0700738	+	0.464909i	0.926083	+	0.377320i	$0.123154\pi$
$73$	−0.598711	+	3.97219i	−0.0700738	+	0.464909i	−0.996157	+	0.0875893i	$0.972084\pi$
$74$		0			0
$75$	4.12872	+	3.83089i	0.476743	+	0.442353i
$76$		0			0
$77$	−1.74957	+	1.73677i	−0.199382	+	0.197923i
$78$		0			0
$79$	−2.43768	−	1.40740i	−0.274261	−	0.158345i	0.356562	−	0.934272i	$-0.383949\pi$
$79$	−2.43768	−	1.40740i	−0.274261	−	0.158345i	−0.630822	+	0.775927i	$0.717282\pi$
$80$		0			0
$81$	1.46443	−	1.35879i	0.162715	−	0.150977i
$82$		0			0
$83$	3.55127	−	4.45316i	0.389803	−	0.488797i	−0.547749	−	0.836643i	$-0.684515\pi$
$83$	3.55127	−	4.45316i	0.389803	−	0.488797i	0.937552	+	0.347845i	$0.113087\pi$
$84$		0			0
$85$	−0.526278	−	0.659932i	−0.0570828	−	0.0715796i
$86$		0			0
$87$	2.41405	−	6.15089i	0.258813	−	0.659445i
$88$		0			0
$89$	−14.0189	+	5.50202i	−1.48600	+	0.583213i	−0.963091	−	0.269174i	$-0.913249\pi$
$89$	−14.0189	+	5.50202i	−1.48600	+	0.583213i	−0.522911	+	0.852387i	$0.675154\pi$
$90$		0			0
$91$	1.76203	+	6.67390i	0.184710	+	0.699615i
$92$		0			0
$93$	0.833229	−	11.1187i	0.0864019	−	1.15295i
$94$		0			0
$95$	0.874626	−	1.28284i	0.0897347	−	0.131617i
$96$		0			0
$97$		−	4.45067i		−	0.451897i	−0.974139	−	0.225948i	$-0.927452\pi$
$97$		−	4.45067i		−	0.451897i	0.974139	−	0.225948i	$-0.0725481\pi$
$98$		0			0
$99$		−	1.43656i		−	0.144380i
$100$		0			0
$101$	−1.74860	+	2.56473i	−0.173992	+	0.255200i	−0.903323	−	0.428962i	$-0.858879\pi$
$101$	−1.74860	+	2.56473i	−0.173992	+	0.255200i	0.729330	+	0.684162i	$0.239832\pi$
$102$		0			0
$103$	−0.0973914	+	1.29960i	−0.00959626	+	0.128053i	−0.999944	−	0.0105493i	$-0.996642\pi$
$103$	−0.0973914	+	1.29960i	−0.00959626	+	0.128053i	0.990348	+	0.138603i	$0.0442610\pi$
$104$		0			0
$105$	−1.64034	+	0.859255i	−0.160081	+	0.0838547i
$106$		0			0
$107$	−14.9983	+	5.88639i	−1.44994	+	0.569058i	−0.954135	−	0.299377i	$-0.903221\pi$
$107$	−14.9983	+	5.88639i	−1.44994	+	0.569058i	−0.495802	+	0.868436i	$0.665126\pi$
$108$		0			0
$109$	2.27642	−	5.80023i	0.218042	−	0.555561i	−0.779441	−	0.626476i	$-0.784497\pi$
$109$	2.27642	−	5.80023i	0.218042	−	0.555561i	0.997482	+	0.0709150i	$0.0225919\pi$
$110$		0			0
$111$	−4.43933	−	5.56675i	−0.421363	−	0.528372i
$112$		0			0
$113$	−9.34266	+	11.7153i	−0.878883	+	1.10208i	0.115187	+	0.993344i	$0.463253\pi$
$113$	−9.34266	+	11.7153i	−0.878883	+	1.10208i	−0.994070	+	0.108741i	$0.965318\pi$
$114$		0			0
$115$	2.57707	−	2.39117i	0.240313	−	0.222978i
$116$		0			0
$117$	−3.48345	−	2.01117i	−0.322045	−	0.185933i
$118$		0			0
$119$	−3.64154	+	1.25924i	−0.333820	+	0.115434i
$120$		0			0
$121$	−7.42714	−	6.89138i	−0.675194	−	0.626489i
$122$		0			0
$123$	1.74283	−	11.5629i	0.157146	−	1.04259i
$124$		0			0
$125$	5.46079	+	1.24639i	0.488428	+	0.111480i
$126$		0			0
$127$	10.9163	−	2.49158i	0.968666	−	0.221092i	0.291213	−	0.956658i	$-0.405941\pi$
$127$	10.9163	−	2.49158i	0.968666	−	0.221092i	0.677452	+	0.735567i	$0.263084\pi$
$128$		0			0
$129$	−5.94128	+	3.43020i	−0.523100	+	0.302012i
$130$		0			0
$131$	5.49641	−	3.74739i	0.480224	−	0.327411i	−0.298896	−	0.954286i	$-0.596619\pi$
$131$	5.49641	−	3.74739i	0.480224	−	0.327411i	0.779120	+	0.626875i	$0.215666\pi$
$132$		0			0
$133$	−4.18774	−	5.71801i	−0.363123	−	0.495814i
$134$		0			0
$135$	0.936964	−	3.03756i	0.0806410	−	0.261432i
$136$		0			0
$137$	−1.04020	−	13.8804i	−0.0888699	−	1.18589i	−0.846204	−	0.532859i	$-0.821118\pi$
$137$	−1.04020	−	13.8804i	−0.0888699	−	1.18589i	0.757334	−	0.653027i	$-0.226501\pi$
$138$		0			0
$139$	3.82910	−	1.84400i	0.324780	−	0.156406i	−0.264388	−	0.964416i	$-0.585170\pi$
$139$	3.82910	−	1.84400i	0.324780	−	0.156406i	0.589168	+	0.808011i	$0.299456\pi$
$140$		0			0
$141$	5.15191	+	2.48103i	0.433869	+	0.208940i
$142$		0			0
$143$	2.32293	−	0.716529i	0.194253	−	0.0599191i
$144$		0			0
$145$	−0.472677	−	3.13601i	−0.0392537	−	0.260431i
$146$		0			0
$147$	1.19844	+	8.36766i	0.0988455	+	0.690153i
$148$		0			0
$149$	3.10332	−	0.467751i	0.254234	−	0.0383196i	−0.0206886	−	0.999786i	$-0.506586\pi$
$149$	3.10332	−	0.467751i	0.254234	−	0.0383196i	0.274923	+	0.961466i	$0.411348\pi$
$150$		0			0
$151$	−4.20020	−	13.6167i	−0.341807	−	1.10811i	−0.949454	−	0.313905i	$-0.898363\pi$
$151$	−4.20020	−	13.6167i	−0.341807	−	1.10811i	0.607647	−	0.794207i	$-0.292113\pi$
$152$		0			0
$153$	0.974209	−	2.02297i	0.0787602	−	0.163547i
$154$		0			0
$155$	−2.32193	−	4.82154i	−0.186502	−	0.387276i
$156$		0			0
$157$	−5.23605	+	0.392388i	−0.417882	+	0.0313160i	−0.282013	−	0.959411i	$-0.591002\pi$
$157$	−5.23605	+	0.392388i	−0.417882	+	0.0313160i	−0.135870	+	0.990727i	$0.543383\pi$
$158$		0			0
$159$	−13.0706	−	4.03173i	−1.03656	−	0.319737i
$160$		0			0
$161$	−6.36336	−	14.7324i	−0.501503	−	1.16107i
$162$		0			0
$163$	−7.43834	−	10.9100i	−0.582616	−	0.854540i	0.415877	−	0.909421i	$-0.363475\pi$
$163$	−7.43834	−	10.9100i	−0.582616	−	0.854540i	−0.998493	+	0.0548805i	$0.982522\pi$
$164$		0			0
$165$	0.326074	+	0.564777i	0.0253849	+	0.0439679i
$166$		0			0
$167$	0.953785	+	4.17880i	0.0738061	+	0.323366i	0.998331	−	0.0577568i	$-0.0183948\pi$
$167$	0.953785	+	4.17880i	0.0738061	+	0.323366i	−0.924525	+	0.381122i	$0.875538\pi$
$168$		0			0
$169$	−1.37818	+	6.03818i	−0.106014	+	0.464476i
$170$		0			0
$171$	4.08397	+	0.615559i	0.312309	+	0.0470730i
$172$		0			0
$173$	−6.89410	+	7.43007i	−0.524148	+	0.564898i	−0.938527	−	0.345207i	$-0.887809\pi$
$173$	−6.89410	+	7.43007i	−0.524148	+	0.564898i	0.414378	+	0.910105i	$0.363999\pi$
$174$		0			0
$175$	6.60359	−	10.4244i	0.499184	−	0.788009i
$176$		0			0
$177$	4.15474	−	7.19622i	0.312290	−	0.540901i
$178$		0			0
$179$	−7.18123	−	7.73953i	−0.536751	−	0.578480i	0.405201	−	0.914228i	$-0.367201\pi$
$179$	−7.18123	−	7.73953i	−0.536751	−	0.578480i	−0.941952	+	0.335748i	$0.891011\pi$
$180$		0			0
$181$	16.0230	+	12.7779i	1.19098	+	0.949774i	0.999497	−	0.0317220i	$-0.0100991\pi$
$181$	16.0230	+	12.7779i	1.19098	+	0.949774i	0.191482	+	0.981496i	$0.438671\pi$
$182$		0			0
$183$	6.79965	−	5.42254i	0.502644	−	0.400845i
$184$		0			0
$185$	−3.18117	−	1.24852i	−0.233884	−	0.0917927i
$186$		0			0
$187$	0.495759	+	1.26317i	0.0362535	+	0.0923725i
$188$		0			0
$189$	−11.6435	−	8.65955i	−0.846943	−	0.629890i
$190$		0			0
$191$	4.75682	+	0.356475i	0.344192	+	0.0257936i	0.245705	−	0.969345i	$-0.420981\pi$
$191$	4.75682	+	0.356475i	0.344192	+	0.0257936i	0.0984870	+	0.995138i	$0.468600\pi$
$192$		0			0
$193$	12.0543	+	8.21851i	0.867690	+	0.591581i	0.913259	−	0.407380i	$-0.133558\pi$
$193$	12.0543	+	8.21851i	0.867690	+	0.591581i	−0.0455684	+	0.998961i	$0.514510\pi$
$194$		0			0
$195$	1.82600			0.130762
$196$		0			0
$197$	6.87832			0.490060			0.245030	−	0.969515i	$-0.421202\pi$
$197$	6.87832			0.490060			0.245030	+	0.969515i	$0.421202\pi$
$198$		0			0
$199$	18.8128	+	12.8263i	1.33360	+	0.909234i	0.999446	−	0.0332840i	$-0.0105966\pi$
$199$	18.8128	+	12.8263i	1.33360	+	0.909234i	0.334155	+	0.942518i	$0.391549\pi$
$200$		0			0
$201$	−3.56885	−	0.267448i	−0.251727	−	0.0188644i
$202$		0			0
$203$	−14.2147	−	2.74368i	−0.997678	−	0.192568i
$204$		0			0
$205$	−2.05046	−	5.22448i	−0.143210	−	0.364894i
$206$		0			0
$207$	8.70513	+	3.41651i	0.605048	+	0.237464i
$208$		0			0
$209$	−1.95149	+	1.55626i	−0.134988	+	0.107649i
$210$		0			0
$211$	2.30923	+	1.84155i	0.158974	+	0.126778i	0.699746	−	0.714392i	$-0.253296\pi$
$211$	2.30923	+	1.84155i	0.158974	+	0.126778i	−0.540772	+	0.841169i	$0.681868\pi$
$212$		0			0
$213$	3.15038	+	3.39531i	0.215861	+	0.232643i
$214$		0			0
$215$	−1.64637	+	2.85159i	−0.112281	+	0.194477i
$216$		0			0
$217$	−24.2851	+	2.64600i	−1.64858	+	0.179622i
$218$		0			0
$219$	3.29945	−	3.55597i	0.222956	−	0.240290i
$220$		0			0
$221$	3.75706	+	0.566286i	0.252727	+	0.0380925i
$222$		0			0
$223$	5.56415	−	24.3781i	0.372603	−	1.63248i	−0.346836	−	0.937926i	$-0.612744\pi$
$223$	5.56415	−	24.3781i	0.372603	−	1.63248i	0.719439	−	0.694555i	$-0.244399\pi$
$224$		0			0
$225$	1.60012	+	7.01057i	0.106675	+	0.467372i
$226$		0			0
$227$	−7.57664	−	13.1231i	−0.502879	−	0.871012i	−0.999994	−	0.00332750i	$-0.998941\pi$
$227$	−7.57664	−	13.1231i	−0.502879	−	0.871012i	0.497116	−	0.867684i	$-0.334393\pi$
$228$		0			0
$229$	−6.87033	−	10.0769i	−0.454004	−	0.665902i	0.529182	−	0.848508i	$-0.322499\pi$
$229$	−6.87033	−	10.0769i	−0.454004	−	0.665902i	−0.983186	+	0.182607i	$0.941547\pi$
$230$		0			0
$231$	2.92708	−	0.542707i	0.192587	−	0.0357075i
$232$		0			0
$233$	−18.7305	−	5.77758i	−1.22707	−	0.378502i	−0.387562	−	0.921844i	$-0.626683\pi$
$233$	−18.7305	−	5.77758i	−1.22707	−	0.378502i	−0.839512	+	0.543342i	$0.817159\pi$
$234$		0			0
$235$	2.73684	−	0.205098i	0.178532	−	0.0133791i
$236$		0			0
$237$	1.47481	+	3.06247i	0.0957990	+	0.198929i
$238$		0			0
$239$	3.87202	−	8.04033i	0.250460	−	0.520086i	−0.737395	−	0.675461i	$-0.763945\pi$
$239$	3.87202	−	8.04033i	0.250460	−	0.520086i	0.987855	+	0.155376i	$0.0496588\pi$
$240$		0			0
$241$	3.97546	+	12.8881i	0.256082	+	0.830196i	0.988746	+	0.149606i	$0.0478005\pi$
$241$	3.97546	+	12.8881i	0.256082	+	0.830196i	−0.732664	+	0.680590i	$0.761723\pi$
$242$		0			0
$243$	13.8843	−	2.09273i	0.890681	−	0.134249i
$244$		0			0
$245$	2.50622	+	3.19050i	0.160117	+	0.203833i
$246$		0			0
$247$	1.04164	+	6.91082i	0.0662779	+	0.439725i
$248$		0			0
$249$	−6.57255	+	2.02736i	−0.416518	+	0.128479i
$250$		0			0
$251$	−8.77820	−	4.22736i	−0.554075	−	0.266829i	0.135825	−	0.990733i	$-0.456631\pi$
$251$	−8.77820	−	4.22736i	−0.554075	−	0.266829i	−0.689901	+	0.723904i	$0.742346\pi$
$252$		0			0
$253$	−5.09199	+	2.45217i	−0.320131	+	0.154167i
$254$		0			0
$255$	0.0761722	+	1.01645i	0.00477009	+	0.0636524i
$256$		0			0
$257$	−1.02602	+	3.32629i	−0.0640016	+	0.207488i	−0.981925	−	0.189269i	$-0.939388\pi$
$257$	−1.02602	+	3.32629i	−0.0640016	+	0.207488i	0.917924	+	0.396757i	$0.129864\pi$
$258$		0			0
$259$	−10.2190	+	11.7868i	−0.634976	+	0.732399i
$260$		0			0
$261$	6.97034	−	4.75229i	0.431453	−	0.294160i
$262$		0			0
$263$	−20.6816	+	11.9405i	−1.27528	+	0.736285i	−0.975977	−	0.217873i	$-0.930088\pi$
$263$	−20.6816	+	11.9405i	−1.27528	+	0.736285i	−0.299305	+	0.954157i	$0.596755\pi$
$264$		0			0
$265$	−6.40044	+	1.46086i	−0.393176	+	0.0897399i
$266$		0			0
$267$	17.7301	+	4.04678i	1.08506	+	0.247659i
$268$		0			0
$269$	−4.63524	+	30.7528i	−0.282615	+	1.87503i	0.173100	+	0.984904i	$0.444622\pi$
$269$	−4.63524	+	30.7528i	−0.282615	+	1.87503i	−0.455715	+	0.890126i	$0.650616\pi$
$270$		0			0
$271$	14.3774	+	13.3403i	0.873366	+	0.810365i	0.983000	−	0.183607i	$-0.0587773\pi$
$271$	14.3774	+	13.3403i	0.873366	+	0.810365i	−0.109634	+	0.993972i	$0.534968\pi$
$272$		0			0
$273$	2.78188	−	7.85749i	0.168367	−	0.475557i
$274$		0			0
$275$	−3.76362	−	2.17292i	−0.226955	−	0.131032i
$276$		0			0
$277$	20.8430	−	19.3395i	1.25234	−	1.16200i	0.272510	−	0.962153i	$-0.412146\pi$
$277$	20.8430	−	19.3395i	1.25234	−	1.16200i	0.979827	−	0.199846i	$-0.0640443\pi$
$278$		0			0
$279$	8.87563	−	11.1297i	0.531370	−	0.666317i
$280$		0			0
$281$	15.5695	+	19.5235i	0.928797	+	1.16467i	0.986073	+	0.166316i	$0.0531872\pi$
$281$	15.5695	+	19.5235i	0.928797	+	1.16467i	−0.0572757	+	0.998358i	$0.518241\pi$
$282$		0			0
$283$	2.13280	−	5.43427i	0.126782	−	0.323034i	−0.853363	−	0.521317i	$-0.825441\pi$
$283$	2.13280	−	5.43427i	0.126782	−	0.323034i	0.980145	+	0.198282i	$0.0635363\pi$
$284$		0			0
$285$	−1.74531	+	0.684984i	−0.103383	+	0.0405750i
$286$		0			0
$287$	−25.6054	+	0.863940i	−1.51144	+	0.0509967i
$288$		0			0
$289$	1.11191	−	14.8375i	0.0654067	−	0.872792i
$290$		0			0
$291$	−3.02758	+	4.44064i	−0.177480	+	0.260315i
$292$		0			0
$293$		−	11.0172i		−	0.643633i	−0.946802	−	0.321817i	$-0.895707\pi$
$293$		−	11.0172i		−	0.643633i	0.946802	−	0.321817i	$-0.104293\pi$
$294$		0			0
$295$		−	3.98824i		−	0.232204i
$296$		0			0
$297$	−2.87875	+	4.22234i	−0.167042	+	0.245005i
$298$		0			0
$299$	−1.18257	+	15.7803i	−0.0683898	+	0.912599i
$300$		0			0
$301$	9.76252	+	11.4289i	0.562702	+	0.658750i
$302$		0			0
$303$	3.48932	−	1.36946i	0.200456	−	0.0786733i
$304$		0			0
$305$	1.52503	−	3.88572i	0.0873231	−	0.222496i
$306$		0			0
$307$	0.694807	+	0.871261i	0.0396547	+	0.0497255i	0.801263	−	0.598312i	$-0.204162\pi$
$307$	0.694807	+	0.871261i	0.0396547	+	0.0497255i	−0.761609	+	0.648037i	$0.775590\pi$
$308$		0			0
$309$	0.981227	−	1.23042i	0.0558201	−	0.0699962i
$310$		0			0
$311$	−12.2836	+	11.3975i	−0.696540	+	0.646294i	−0.946777	−	0.321890i	$-0.895682\pi$
$311$	−12.2836	+	11.3975i	−0.696540	+	0.646294i	0.250237	+	0.968184i	$0.419491\pi$
$312$		0			0
$313$	−11.9237	−	6.88416i	−0.673968	−	0.389116i	0.123610	−	0.992331i	$-0.460553\pi$
$313$	−11.9237	−	6.88416i	−0.673968	−	0.389116i	−0.797578	+	0.603215i	$0.793886\pi$
$314$		0			0
$315$	−2.34836	−	0.273334i	−0.132315	−	0.0154006i
$316$		0			0
$317$	8.64217	+	8.01876i	0.485392	+	0.450378i	0.884510	−	0.466521i	$-0.154493\pi$
$317$	8.64217	+	8.01876i	0.485392	+	0.450378i	−0.399117	+	0.916900i	$0.630683\pi$
$318$		0			0
$319$	−0.759891	+	5.04154i	−0.0425457	+	0.282272i
$320$		0			0
$321$	18.9687	+	4.32948i	1.05873	+	0.241648i
$322$		0			0
$323$	−3.80347	+	0.868118i	−0.211631	+	0.0483034i
$324$		0			0
$325$	−10.5380	+	6.08413i	−0.584544	+	0.337487i
$326$		0			0
$327$	−6.21691	+	4.23862i	−0.343796	+	0.234396i
$328$		0			0
$329$	3.28698	−	12.0894i	0.181217	−	0.666512i
$330$		0			0
$331$	−4.04270	+	13.1061i	−0.222207	+	0.720378i	0.773986	+	0.633203i	$0.218260\pi$
$331$	−4.04270	+	13.1061i	−0.222207	+	0.720378i	−0.996193	+	0.0871750i	$0.972216\pi$
$332$		0			0
$333$	−0.679336	−	9.06510i	−0.0372274	−	0.496765i
$334$		0			0
$335$	−1.54761	+	0.745290i	−0.0845550	+	0.0407195i
$336$		0			0
$337$	13.9433	+	6.71476i	0.759542	+	0.365776i	0.773226	−	0.634130i	$-0.218642\pi$
$337$	13.9433	+	6.71476i	0.759542	+	0.365776i	−0.0136843	+	0.999906i	$0.504356\pi$
$338$		0			0
$339$	17.2910	−	5.33356i	0.939118	−	0.289679i
$340$		0			0
$341$	1.28225	+	8.50717i	0.0694377	+	0.460689i
$342$		0			0
$343$	17.5473	−	5.92390i	0.947465	−	0.319861i
$344$		0			0
$345$	−4.19786	+	0.632726i	−0.226005	+	0.0340648i
$346$		0			0
$347$	−4.83828	−	15.6853i	−0.259732	−	0.842031i	−0.987692	−	0.156412i	$-0.950007\pi$
$347$	−4.83828	−	15.6853i	−0.259732	−	0.842031i	0.727960	−	0.685620i	$-0.240469\pi$
$348$		0			0
$349$	14.2429	−	29.5758i	0.762407	−	1.58315i	−0.0490871	−	0.998795i	$-0.515631\pi$
$349$	14.2429	−	29.5758i	0.762407	−	1.58315i	0.811494	−	0.584360i	$-0.198655\pi$
$350$		0			0
$351$	6.20834	+	12.8917i	0.331376	+	0.688110i
$352$		0			0
$353$	2.59415	−	0.194405i	0.138073	−	0.0103471i	−0.00551433	−	0.999985i	$-0.501755\pi$
$353$	2.59415	−	0.194405i	0.138073	−	0.0103471i	0.143587	+	0.989638i	$0.454136\pi$
$354$		0			0
$355$	2.12430	+	0.655259i	0.112746	+	0.0347776i
$356$		0			0
$357$	4.48994	+	1.22077i	0.237633	+	0.0646098i
$358$		0			0
$359$	4.46466	+	6.54845i	0.235636	+	0.345614i	0.925783	−	0.378055i	$-0.123407\pi$
$359$	4.46466	+	6.54845i	0.235636	+	0.345614i	−0.690148	+	0.723668i	$0.742454\pi$
$360$		0			0
$361$	5.91194	+	10.2398i	0.311155	+	0.538936i
$362$		0			0
$363$	2.72253	+	11.9282i	0.142896	+	0.626067i
$364$		0			0
$365$	0.518085	−	2.26988i	0.0271178	−	0.118811i
$366$		0			0
$367$	−14.0751	−	2.12148i	−0.734713	−	0.110740i	−0.228981	−	0.973431i	$-0.573539\pi$
$367$	−14.0751	−	2.12148i	−0.734713	−	0.110740i	−0.505732	+	0.862691i	$0.668778\pi$
$368$		0			0
$369$	10.1547	−	10.9441i	0.528630	−	0.569728i
$370$		0			0
$371$	−3.46474	+	29.7675i	−0.179880	+	1.54545i
$372$		0			0
$373$	6.88663	−	11.9280i	0.356576	−	0.617608i	−0.630810	−	0.775937i	$-0.717277\pi$
$373$	6.88663	−	11.9280i	0.356576	−	0.617608i	0.987386	+	0.158329i	$0.0506107\pi$
$374$		0			0
$375$	−4.60063	−	4.95830i	−0.237575	−	0.256045i
$376$		0			0
$377$	11.1611	+	8.90071i	0.574828	+	0.458410i
$378$		0			0
$379$	−28.0264	+	22.3503i	−1.43962	+	1.14806i	−0.476435	+	0.879210i	$0.658071\pi$
$379$	−28.0264	+	22.3503i	−1.43962	+	1.14806i	−0.963183	+	0.268848i	$0.913357\pi$
$380$		0			0
$381$	−12.5866	−	4.93988i	−0.644832	−	0.253078i
$382$		0			0
$383$	2.16645	+	5.52002i	0.110700	+	0.282060i	0.975479	−	0.220094i	$-0.0706364\pi$
$383$	2.16645	+	5.52002i	0.110700	+	0.282060i	−0.864778	+	0.502154i	$0.832541\pi$
$384$		0			0
$385$	1.08643	−	0.928025i	0.0553695	−	0.0472965i
$386$		0			0
$387$	−8.73441	−	0.654554i	−0.443995	−	0.0332728i
$388$		0			0
$389$	17.1224	+	11.6738i	0.868139	+	0.591887i	0.913389	−	0.407089i	$-0.133456\pi$
$389$	17.1224	+	11.6738i	0.868139	+	0.591887i	−0.0452499	+	0.998976i	$0.514408\pi$
$390$		0			0
$391$	−8.83348			−0.446728
$392$		0			0
$393$	−8.03320			−0.405222
$394$		0			0
$395$	1.34795	+	0.919018i	0.0678229	+	0.0462408i
$396$		0			0
$397$	−29.6992	−	2.22565i	−1.49056	−	0.111702i	−0.695629	−	0.718401i	$-0.744874\pi$
$397$	−29.6992	−	2.22565i	−1.49056	−	0.111702i	−0.794932	+	0.606699i	$0.792493\pi$
$398$		0			0
$399$	0.288611	+	8.55385i	0.0144486	+	0.428228i
$400$		0			0
$401$	0.677107	+	1.72524i	0.0338131	+	0.0861544i	0.946783	−	0.321872i	$-0.104312\pi$
$401$	0.677107	+	1.72524i	0.0338131	+	0.0861544i	−0.912970	+	0.408027i	$0.866217\pi$
$402$		0			0
$403$	22.4237	+	8.80066i	1.11701	+	0.438392i
$404$		0			0
$405$	−0.905253	+	0.721915i	−0.0449824	+	0.0358723i
$406$		0			0
$407$	4.29532	+	3.42540i	0.212911	+	0.169791i
$408$		0			0
$409$	0.566129	+	0.610142i	0.0279933	+	0.0301696i	0.746893	−	0.664944i	$-0.231545\pi$
$409$	0.566129	+	0.610142i	0.0279933	+	0.0301696i	−0.718900	+	0.695113i	$0.755354\pi$
$410$		0			0
$411$	−8.40436	+	14.5568i	−0.414556	+	0.718033i
$412$		0			0
$413$	−17.1619	−	6.07603i	−0.844481	−	0.298982i
$414$		0			0
$415$	−2.24541	+	2.41998i	−0.110223	+	0.118792i
$416$		0			0
$417$	−5.07486	−	0.764912i	−0.248517	−	0.0374579i
$418$		0			0
$419$	−0.476597	+	2.08811i	−0.0232833	+	0.102011i	−0.985234	−	0.171211i	$-0.945232\pi$
$419$	−0.476597	+	2.08811i	−0.0232833	+	0.102011i	0.961951	+	0.273222i	$0.0880892\pi$
$420$		0			0
$421$	3.26924	+	14.3235i	0.159333	+	0.698083i	0.989971	+	0.141270i	$0.0451187\pi$
$421$	3.26924	+	14.3235i	0.159333	+	0.698083i	−0.830638	+	0.556813i	$0.812024\pi$
$422$		0			0
$423$	3.65031	+	6.32251i	0.177484	+	0.307411i
$424$		0			0
$425$	−3.82634	−	5.61221i	−0.185605	−	0.272232i
$426$		0			0
$427$	−14.3973	−	12.4822i	−0.696737	−	0.604058i
$428$		0			0
$429$	−2.80512	−	0.865264i	−0.135432	−	0.0417753i
$430$		0			0
$431$	−23.8875	+	1.79012i	−1.15062	+	0.0862272i	−0.636350	−	0.771400i	$-0.719557\pi$
$431$	−23.8875	+	1.79012i	−1.15062	+	0.0862272i	−0.514271	+	0.857628i	$0.671938\pi$
$432$		0			0
$433$	5.42770	+	11.2707i	0.260838	+	0.541637i	0.989723	−	0.143000i	$-0.0456750\pi$
$433$	5.42770	+	11.2707i	0.260838	+	0.541637i	−0.728884	+	0.684637i	$0.759961\pi$
$434$		0			0
$435$	−1.66166	+	3.45048i	−0.0796707	+	0.165438i
$436$		0			0
$437$	−4.78933	−	15.5266i	−0.229105	−	0.742739i
$438$		0			0
$439$	−7.26877	+	1.09559i	−0.346919	+	0.0522897i	−0.320191	−	0.947353i	$-0.603747\pi$
$439$	−7.26877	+	1.09559i	−0.346919	+	0.0522897i	−0.0267284	+	0.999643i	$0.508509\pi$
$440$		0			0
$441$	−4.75389	+	9.68887i	−0.226376	+	0.461375i
$442$		0			0
$443$	−4.31742	−	28.6442i	−0.205127	−	1.36093i	−0.820029	−	0.572323i	$-0.806043\pi$
$443$	−4.31742	−	28.6442i	−0.205127	−	1.36093i	0.614902	−	0.788604i	$-0.289196\pi$
$444$		0			0
$445$	8.34084	−	2.57281i	0.395394	−	0.121963i
$446$		0			0
$447$	−3.41452	−	1.64435i	−0.161501	−	0.0777749i
$448$		0			0
$449$	25.5750	−	12.3163i	1.20696	−	0.581240i	0.281306	−	0.959618i	$-0.409232\pi$
$449$	25.5750	−	12.3163i	1.20696	−	0.581240i	0.925651	+	0.378378i	$0.123518\pi$
$450$		0			0
$451$	0.674272	+	8.99753i	0.0317502	+	0.423677i
$452$		0			0
$453$	−5.07206	+	16.4432i	−0.238306	+	0.772570i
$454$		0			0
$455$	−0.729334	−	3.93364i	−0.0341917	−	0.184412i
$456$		0			0
$457$	22.5960	−	15.4057i	1.05700	−	0.720648i	0.0954901	−	0.995430i	$-0.469558\pi$
$457$	22.5960	−	15.4057i	1.05700	−	0.720648i	0.961506	+	0.274782i	$0.0886058\pi$
$458$		0			0
$459$	−6.91724	+	3.99367i	−0.322869	+	0.186409i
$460$		0			0
$461$	−25.8157	+	5.89227i	−1.20236	+	0.274430i	−0.776358	−	0.630293i	$-0.782935\pi$
$461$	−25.8157	+	5.89227i	−1.20236	+	0.274430i	−0.426000	+	0.904723i	$0.640078\pi$
$462$		0			0
$463$	14.5376	+	3.31812i	0.675620	+	0.154206i	0.546546	−	0.837429i	$-0.315942\pi$
$463$	14.5376	+	3.31812i	0.675620	+	0.154206i	0.129074	+	0.991635i	$0.458799\pi$
$464$		0			0
$465$	−0.963165	+	6.39019i	−0.0446657	+	0.296338i
$466$		0			0
$467$	18.5051	+	17.1702i	0.856313	+	0.794542i	0.980253	−	0.197748i	$-0.0633627\pi$
$467$	18.5051	+	17.1702i	0.856313	+	0.794542i	−0.123940	+	0.992290i	$0.539553\pi$
$468$		0			0
$469$	0.849308	+	7.79499i	0.0392174	+	0.359939i
$470$		0			0
$471$	5.49118	+	3.17033i	0.253020	+	0.146081i
$472$		0			0
$473$	3.88041	−	3.60050i	0.178422	−	0.165551i
$474$		0			0
$475$	7.79003	−	9.76839i	0.357431	−	0.448205i
$476$		0			0
$477$	−10.8883	−	13.6535i	−0.498541	−	0.625151i
$478$		0			0
$479$	−3.22879	+	8.22681i	−0.147527	+	0.375893i	−0.985466	−	0.169871i	$-0.945665\pi$
$479$	−3.22879	+	8.22681i	−0.147527	+	0.375893i	0.837939	+	0.545763i	$0.183760\pi$
$480$		0			0
$481$	14.3195	−	5.61998i	0.652912	−	0.256249i
$482$		0			0
$483$	−3.67269	+	19.0279i	−0.167113	+	0.865798i
$484$		0			0
$485$	−0.192772	+	2.57236i	−0.00875331	+	0.116805i
$486$		0			0
$487$	−20.6434	+	30.2784i	−0.935444	+	1.37204i	−0.00723937	+	0.999974i	$0.502304\pi$
$487$	−20.6434	+	30.2784i	−0.935444	+	1.37204i	−0.928205	+	0.372070i	$0.878648\pi$
$488$		0			0
$489$			15.9454i			0.721077i
$490$		0			0
$491$			18.1475i			0.818985i	0.912313	+	0.409492i	$0.134294\pi$
$491$			18.1475i			0.818985i	−0.912313	+	0.409492i	$0.865706\pi$
$492$		0			0
$493$	−4.48901	+	6.58417i	−0.202175	+	0.296536i
$494$		0			0
$495$	−0.0622218	+	0.830293i	−0.00279666	+	0.0373189i
$496$		0			0
$497$	6.05600	−	8.14283i	0.271649	−	0.365256i
$498$		0			0
$499$	16.0971	−	6.31766i	0.720606	−	0.282817i	0.0234387	−	0.999725i	$-0.492539\pi$
$499$	16.0971	−	6.31766i	0.720606	−	0.282817i	0.697168	+	0.716908i	$0.254443\pi$
$500$		0			0
$501$	1.89101	−	4.81821i	0.0844839	−	0.215262i
$502$		0			0
$503$	−8.35635	−	10.4785i	−0.372591	−	0.467214i	0.559820	−	0.828614i	$-0.310870\pi$
$503$	−8.35635	−	10.4785i	−0.372591	−	0.467214i	−0.932411	+	0.361400i	$0.882299\pi$
$504$		0			0
$505$	1.12173	−	1.40660i	0.0499162	−	0.0625929i
$506$		0			0
$507$	5.48256	−	5.08708i	0.243489	−	0.225925i
$508$		0			0
$509$	33.3655	+	19.2636i	1.47890	+	0.853842i	0.999715	−	0.0238733i	$-0.00759982\pi$
$509$	33.3655	+	19.2636i	1.47890	+	0.853842i	0.479183	+	0.877715i	$0.340933\pi$
$510$		0			0
$511$	−8.97827	−	5.68751i	−0.397175	−	0.251601i
$512$		0			0
$513$	−10.7701	−	9.99316i	−0.475510	−	0.441209i
$514$		0			0
$515$	0.112579	−	0.746912i	0.00496082	−	0.0329129i
$516$		0			0
$517$	−4.30155	−	0.981801i	−0.189182	−	0.0431796i
$518$		0			0
$519$	11.9329	−	2.72360i	0.523796	−	0.119553i
$520$		0			0
$521$	−8.38985	+	4.84388i	−0.367566	+	0.212214i	−0.672394	−	0.740193i	$-0.734734\pi$
$521$	−8.38985	+	4.84388i	−0.367566	+	0.212214i	0.304829	+	0.952407i	$0.401401\pi$
$522$		0			0
$523$	35.1666	−	23.9762i	1.53773	−	1.04840i	0.562608	−	0.826724i	$-0.309798\pi$
$523$	35.1666	−	23.9762i	1.53773	−	1.04840i	0.975119	−	0.221681i	$-0.0711545\pi$
$524$		0			0
$525$	−13.6799	+	5.90879i	−0.597041	+	0.257881i
$526$		0			0
$527$	−3.96350	+	12.8493i	−0.172653	+	0.559726i
$528$		0			0
$529$	−1.03058	−	13.7521i	−0.0448077	−	0.597917i
$530$		0			0
$531$	9.55839	−	4.60308i	0.414799	−	0.199756i
$532$		0			0
$533$	22.7616	+	10.9614i	0.985914	+	0.474791i
$534$		0			0
$535$	8.92353	−	2.75254i	0.385798	−	0.119003i
$536$		0			0
$537$	1.90022	+	12.6072i	0.0820006	+	0.544039i
$538$		0			0
$539$	−2.33824	−	6.08887i	−0.100715	−	0.262266i
$540$		0			0
$541$	−11.6359	+	1.75383i	−0.500265	+	0.0754029i	−0.394328	−	0.918970i	$-0.629022\pi$
$541$	−11.6359	+	1.75383i	−0.500265	+	0.0754029i	−0.105938	+	0.994373i	$0.533784\pi$
$542$		0			0
$543$	−7.29469	−	23.6488i	−0.313045	−	1.01487i
$544$		0			0
$545$	−1.56693	+	3.25377i	−0.0671200	+	0.139376i
$546$		0			0
$547$	−6.27119	−	13.0223i	−0.268137	−	0.556791i	0.722810	−	0.691047i	$-0.242850\pi$
$547$	−6.27119	−	13.0223i	−0.268137	−	0.556791i	−0.990947	+	0.134255i	$0.957136\pi$
$548$		0			0
$549$	11.0728	−	0.829792i	0.472576	−	0.0354147i
$550$		0			0
$551$	−14.0069	−	4.32054i	−0.596712	−	0.184061i
$552$		0			0
$553$	6.00824	−	4.40029i	0.255496	−	0.187119i
$554$		0			0
$555$	2.32469	+	3.40970i	0.0986778	+	0.144734i
$556$		0			0
$557$	14.3098	+	24.7853i	0.606325	+	1.05019i	0.991841	+	0.127485i	$0.0406905\pi$
$557$	14.3098	+	24.7853i	0.606325	+	1.05019i	−0.385515	+	0.922702i	$0.625976\pi$
$558$		0			0
$559$	−3.29813	−	14.4501i	−0.139496	−	0.611172i
$560$		0			0
$561$	0.364635	−	1.59757i	0.0153949	−	0.0674495i
$562$		0			0
$563$	−10.4346	−	1.57277i	−0.439767	−	0.0662842i	−0.0745726	−	0.997216i	$-0.523759\pi$
$563$	−10.4346	−	1.57277i	−0.439767	−	0.0662842i	−0.365194	+	0.930931i	$0.618997\pi$
$564$		0			0
$565$	5.90721	−	6.36646i	0.248518	−	0.267839i
$566$		0			0
$567$	1.72735	+	4.99524i	0.0725418	+	0.209780i
$568$		0			0
$569$	−0.291088	+	0.504179i	−0.0122030	+	0.0211363i	−0.872062	−	0.489395i	$-0.837218\pi$
$569$	−0.291088	+	0.504179i	−0.0122030	+	0.0211363i	0.859859	+	0.510531i	$0.170551\pi$
$570$		0			0
$571$	17.6086	+	18.9775i	0.736895	+	0.794184i	0.984632	−	0.174643i	$-0.0558773\pi$
$571$	17.6086	+	18.9775i	0.736895	+	0.794184i	−0.247737	+	0.968827i	$0.579687\pi$
$572$		0			0
$573$	−4.50362	−	3.59151i	−0.188141	−	0.150038i
$574$		0			0
$575$	22.1181	−	17.6386i	0.922387	−	0.735579i
$576$		0			0
$577$	18.7920	+	7.37533i	0.782322	+	0.307039i	0.722682	−	0.691181i	$-0.242909\pi$
$577$	18.7920	+	7.37533i	0.782322	+	0.307039i	0.0596406	+	0.998220i	$0.481005\pi$
$578$		0			0
$579$	−6.43652	−	16.4000i	−0.267493	−	0.681561i
$580$		0			0
$581$	6.99261	+	13.3491i	0.290102	+	0.553814i
$582$		0			0
$583$	10.5247	+	0.788714i	0.435887	+	0.0326652i
$584$		0			0
$585$	1.92622	+	1.31328i	0.0796395	+	0.0542973i
$586$		0			0
$587$	14.5757			0.601602			0.300801	−	0.953687i	$-0.402746\pi$
$587$	14.5757			0.601602			0.300801	+	0.953687i	$0.402746\pi$
$588$		0			0
$589$	−24.7342			−1.01916
$590$		0			0
$591$	−6.86283	−	4.67900i	−0.282299	−	0.192468i
$592$		0			0
$593$	5.38392	+	0.403469i	0.221091	+	0.0165685i	0.184815	−	0.982773i	$-0.440831\pi$
$593$	5.38392	+	0.403469i	0.221091	+	0.0165685i	0.0362761	+	0.999342i	$0.488450\pi$
$594$		0			0
$595$	2.15925	−	0.570079i	0.0885206	−	0.0233710i
$596$		0			0
$597$	−10.0452	−	25.5949i	−0.411124	−	1.04753i
$598$		0			0
$599$	21.6093	+	8.48104i	0.882934	+	0.346526i	0.763110	−	0.646269i	$-0.223672\pi$
$599$	21.6093	+	8.48104i	0.882934	+	0.346526i	0.119824	+	0.992795i	$0.461767\pi$
$600$		0			0
$601$	13.2105	−	10.5351i	0.538870	−	0.429734i	−0.315861	−	0.948805i	$-0.602293\pi$
$601$	13.2105	−	10.5351i	0.538870	−	0.429734i	0.854731	+	0.519071i	$0.173722\pi$
$602$		0			0
$603$	−3.57238	−	2.84888i	−0.145479	−	0.116015i
$604$		0			0
$605$	3.99419	+	4.30471i	0.162387	+	0.175011i
$606$		0			0
$607$	−19.1012	+	33.0843i	−0.775296	+	1.34285i	0.159332	+	0.987225i	$0.449066\pi$
$607$	−19.1012	+	33.0843i	−0.775296	+	1.34285i	−0.934628	+	0.355627i	$0.884267\pi$
$608$		0			0
$609$	12.3163	+	12.4071i	0.499082	+	0.502761i
$610$		0			0
$611$	−8.40283	+	9.05610i	−0.339942	+	0.366371i
$612$		0			0
$613$	−48.8866	−	7.36847i	−1.97451	−	0.297610i	−0.995666	−	0.0930027i	$-0.970353\pi$
$613$	−48.8866	−	7.36847i	−1.97451	−	0.297610i	−0.978844	−	0.204607i	$-0.934408\pi$
$614$		0			0
$615$	−1.50813	+	6.60754i	−0.0608136	+	0.266442i
$616$		0			0
$617$	3.41240	+	14.9507i	0.137378	+	0.601892i	0.996005	+	0.0892921i	$0.0284605\pi$
$617$	3.41240	+	14.9507i	0.137378	+	0.601892i	−0.858628	+	0.512600i	$0.828682\pi$
$618$		0			0
$619$	−23.1671	−	40.1266i	−0.931164	−	1.61282i	−0.781336	−	0.624110i	$-0.785462\pi$
$619$	−23.1671	−	40.1266i	−0.931164	−	1.61282i	−0.149827	−	0.988712i	$-0.547872\pi$
$620$		0			0
$621$	−18.7397	−	27.4861i	−0.751999	−	1.10298i
$622$		0			0
$623$	1.63605	−	39.8113i	0.0655471	−	1.59501i
$624$		0			0
$625$	19.1821	+	5.91690i	0.767285	+	0.236676i
$626$		0			0
$627$	3.00575	−	0.225250i	0.120038	−	0.00899561i
$628$		0			0
$629$	3.72572	+	7.73653i	0.148554	+	0.308476i
$630$		0			0
$631$	4.33025	−	8.99186i	0.172384	−	0.357960i	−0.796820	−	0.604216i	$-0.793486\pi$
$631$	4.33025	−	8.99186i	0.172384	−	0.357960i	0.969205	+	0.246256i	$0.0792005\pi$
$632$		0			0
$633$	−1.05131	−	3.40826i	−0.0417858	−	0.135466i
$634$		0			0
$635$	−6.41723	+	0.967242i	−0.254660	+	0.0383838i
$636$		0			0
$637$	−18.0381	−	2.85444i	−0.714695	−	0.113097i
$638$		0			0
$639$	0.881362	+	5.84746i	0.0348662	+	0.231322i
$640$		0			0
$641$	18.8887	−	5.82640i	0.746060	−	0.230129i	0.101662	−	0.994819i	$-0.467584\pi$
$641$	18.8887	−	5.82640i	0.746060	−	0.230129i	0.644398	+	0.764690i	$0.277108\pi$
$642$		0			0
$643$	11.3224	+	5.45260i	0.446513	+	0.215029i	0.643608	−	0.765355i	$-0.277437\pi$
$643$	11.3224	+	5.45260i	0.446513	+	0.215029i	−0.197095	+	0.980384i	$0.563151\pi$
$644$		0			0
$645$	3.58246	−	1.72522i	0.141059	−	0.0679306i
$646$		0			0
$647$	1.91278	+	25.5243i	0.0751993	+	1.00346i	0.899389	+	0.437150i	$0.144012\pi$
$647$	1.91278	+	25.5243i	0.0751993	+	1.00346i	−0.824189	+	0.566314i	$0.808369\pi$
$648$		0			0
$649$	−1.88986	+	6.12678i	−0.0741835	+	0.240497i
$650$		0			0
$651$	26.0304	+	13.8800i	1.02021	+	0.543999i
$652$		0			0
$653$	−30.8690	+	21.0461i	−1.20800	+	0.823597i	−0.988382	−	0.151990i	$-0.951432\pi$
$653$	−30.8690	+	21.0461i	−1.20800	+	0.823597i	−0.219613	+	0.975587i	$0.570480\pi$
$654$		0			0
$655$	−3.33908	+	1.92782i	−0.130469	+	0.0753261i
$656$		0			0
$657$	6.03804	−	1.37814i	0.235566	−	0.0537665i
$658$		0			0
$659$	−44.8617	−	10.2394i	−1.74756	−	0.398870i	−0.775084	−	0.631858i	$-0.782292\pi$
$659$	−44.8617	−	10.2394i	−1.74756	−	0.398870i	−0.972480	+	0.232988i	$0.925150\pi$
$660$		0			0
$661$	5.09446	−	33.7996i	0.198152	−	1.31465i	−0.639646	−	0.768670i	$-0.720919\pi$
$661$	5.09446	−	33.7996i	0.198152	−	1.31465i	0.837798	−	0.545981i	$-0.183843\pi$
$662$		0			0
$663$	−3.36338	−	3.12076i	−0.130623	−	0.121200i
$664$		0			0
$665$	2.17273	+	3.48623i	0.0842548	+	0.135190i
$666$		0			0
$667$	−28.7430	−	16.5948i	−1.11293	−	0.642552i
$668$		0			0
$669$	−22.1349	+	20.5382i	−0.855785	+	0.794053i
$670$		0			0
$671$	−4.18405	+	5.24663i	−0.161523	+	0.202544i
$672$		0			0
$673$	−16.6735	−	20.9079i	−0.642716	−	0.805941i	0.348623	−	0.937263i	$-0.386649\pi$
$673$	−16.6735	−	20.9079i	−0.642716	−	0.805941i	−0.991340	+	0.131322i	$0.958078\pi$
$674$		0			0
$675$	9.34550	−	23.8120i	0.359709	−	0.916522i
$676$		0			0
$677$	−31.8545	+	12.5020i	−1.22427	+	0.480490i	−0.887373	−	0.461052i	$-0.847472\pi$
$677$	−31.8545	+	12.5020i	−1.22427	+	0.480490i	−0.336896	+	0.941542i	$0.609377\pi$
$678$		0			0
$679$	10.7755	+	4.74848i	0.413525	+	0.182230i
$680$		0			0
$681$	−1.36747	+	18.2476i	−0.0524015	+	0.699249i
$682$		0			0
$683$	28.6134	−	41.9681i	1.09486	−	1.60586i	0.352569	−	0.935786i	$-0.385308\pi$
$683$	28.6134	−	41.9681i	1.09486	−	1.60586i	0.742291	−	0.670078i	$-0.233739\pi$
$684$		0			0
$685$			8.06755i			0.308245i
$686$		0			0
$687$			14.7278i			0.561900i
$688$		0			0
$689$	16.6469	−	24.4165i	0.634196	−	0.930195i
$690$		0			0
$691$	1.16250	−	15.5124i	0.0442235	−	0.590121i	−0.930440	−	0.366444i	$-0.880575\pi$
$691$	1.16250	−	15.5124i	0.0442235	−	0.590121i	0.974663	−	0.223677i	$-0.0718059\pi$
$692$		0			0
$693$	3.47806	+	1.53269i	0.132120	+	0.0582220i
$694$		0			0
$695$	−2.29298	+	0.899929i	−0.0869777	+	0.0341362i
$696$		0			0
$697$	−5.15219	+	13.1276i	−0.195153	+	0.497242i
$698$		0			0
$699$	14.7581	+	18.5060i	0.558201	+	0.699962i
$700$		0			0
$701$	−20.6986	+	25.9553i	−0.781777	+	0.980317i	0.218214	+	0.975901i	$0.429977\pi$
$701$	−20.6986	+	25.9553i	−0.781777	+	0.980317i	−0.999990	+	0.00441592i	$0.998594\pi$
$702$		0			0
$703$	−11.5785	+	10.7433i	−0.436691	+	0.405190i
$704$		0			0
$705$	−2.87020	−	1.65711i	−0.108098	−	0.0624103i
$706$		0			0
$707$	−4.34384	−	6.96986i	−0.163367	−	0.262129i
$708$		0			0
$709$	4.24714	+	3.94077i	0.159505	+	0.147999i	0.755888	−	0.654701i	$-0.227206\pi$
$709$	4.24714	+	3.94077i	0.159505	+	0.147999i	−0.596383	+	0.802700i	$0.703396\pi$
$710$		0			0
$711$	−0.646803	+	4.29125i	−0.0242570	+	0.160935i
$712$		0			0
$713$	−54.6003	−	12.4622i	−2.04480	−	0.466712i
$714$		0			0
$715$	−1.37362	+	0.313520i	−0.0513705	+	0.0117250i
$716$		0			0
$717$	−9.33275	+	5.38827i	−0.348538	+	0.201228i
$718$		0			0
$719$	43.4348	−	29.6134i	1.61985	−	1.10439i	0.698527	−	0.715583i	$-0.253839\pi$
$719$	43.4348	−	29.6134i	1.61985	−	1.10439i	0.921318	−	0.388809i	$-0.127113\pi$
$720$		0			0
$721$	−3.04254	−	1.62235i	−0.113310	−	0.0604195i
$722$		0			0
$723$	4.80067	−	15.5634i	0.178539	−	0.578809i
$724$		0			0
$725$	−1.90719	−	25.4496i	−0.0708311	−	0.945176i
$726$		0			0
$727$	15.3008	−	7.36847i	0.567475	−	0.273281i	−0.128069	−	0.991765i	$-0.540878\pi$
$727$	15.3008	−	7.36847i	0.567475	−	0.273281i	0.695544	+	0.718484i	$0.255164\pi$
$728$		0			0
$729$	−20.6763	−	9.95718i	−0.765789	−	0.368784i
$730$		0			0
$731$	7.90608	−	2.43870i	0.292417	−	0.0901987i
$732$		0			0
$733$	−2.39005	−	15.8570i	−0.0882786	−	0.585691i	−0.988612	−	0.150489i	$-0.951915\pi$
$733$	−2.39005	−	15.8570i	−0.0882786	−	0.585691i	0.900333	−	0.435202i	$-0.143323\pi$
$734$		0			0
$735$	−0.330235	−	4.88817i	−0.0121809	−	0.180303i
$736$		0			0
$737$	2.73062	−	0.411574i	0.100584	−	0.0151605i
$738$		0			0
$739$	−13.7529	−	44.5857i	−0.505908	−	1.64011i	−0.743491	−	0.668745i	$-0.766832\pi$
$739$	−13.7529	−	44.5857i	−0.505908	−	1.64011i	0.237584	−	0.971367i	$-0.423645\pi$
$740$		0			0
$741$	3.66181	−	7.60383i	0.134520	−	0.279334i
$742$		0			0
$743$	−5.86208	−	12.1727i	−0.215059	−	0.446574i	0.765332	−	0.643635i	$-0.222575\pi$
$743$	−5.86208	−	12.1727i	−0.215059	−	0.446574i	−0.980391	+	0.197061i	$0.936860\pi$
$744$		0			0
$745$	−1.81389	+	0.135932i	−0.0664558	+	0.00498018i
$746$		0			0
$747$	−8.39140	−	2.58840i	−0.307025	−	0.0947047i
$748$		0			0
$749$	1.75035	−	42.5925i	0.0639563	−	1.55630i
$750$		0			0
$751$	10.7179	+	15.7203i	0.391102	+	0.573641i	0.970409	−	0.241468i	$-0.0776290\pi$
$751$	10.7179	+	15.7203i	0.391102	+	0.573641i	−0.579307	+	0.815110i	$0.696677\pi$
$752$		0			0
$753$	5.88276	+	10.1892i	0.214380	+	0.371316i
$754$		0			0
$755$	1.83781	+	8.05199i	0.0668849	+	0.293042i
$756$		0			0
$757$	8.72491	−	38.2263i	0.317112	−	1.38936i	−0.525479	−	0.850807i	$-0.676114\pi$
$757$	8.72491	−	38.2263i	0.317112	−	1.38936i	0.842591	−	0.538553i	$-0.181029\pi$
$758$		0			0
$759$	6.74862	+	1.01719i	0.244959	+	0.0369217i
$760$		0			0
$761$	21.2009	−	22.8491i	0.768532	−	0.828280i	−0.220592	−	0.975366i	$-0.570799\pi$
$761$	21.2009	−	22.8491i	0.768532	−	0.828280i	0.989124	+	0.147086i	$0.0469894\pi$
$762$		0			0
$763$	11.6142	+	11.6998i	0.420461	+	0.423560i
$764$		0			0
$765$	−0.650686	+	1.12702i	−0.0235256	+	0.0407475i
$766$		0			0
$767$	12.2107	+	13.1600i	0.440903	+	0.475181i
$768$		0			0
$769$	10.9375	+	8.72234i	0.394415	+	0.314536i	0.800537	−	0.599283i	$-0.204548\pi$
$769$	10.9375	+	8.72234i	0.394415	+	0.314536i	−0.406122	+	0.913819i	$0.633119\pi$
$770$		0			0
$771$	3.28643	−	2.62084i	0.118358	−	0.0943872i
$772$		0			0
$773$	−29.7564	−	11.6785i	−1.07026	−	0.420048i	−0.236194	−	0.971706i	$-0.575900\pi$
$773$	−29.7564	−	11.6785i	−1.07026	−	0.420048i	−0.834070	+	0.551658i	$0.813995\pi$
$774$		0			0
$775$	−15.7332	−	40.0876i	−0.565154	−	1.43999i
$776$		0			0
$777$	18.2140	−	4.80881i	0.653423	−	0.172515i
$778$		0			0
$779$	−25.8677	−	1.93852i	−0.926808	−	0.0694547i
$780$		0			0
$781$	−2.95287	−	2.01323i	−0.105662	−	0.0720391i
$782$		0			0
$783$	−30.0104			−1.07248
$784$		0			0
$785$	3.04328			0.108619
$786$		0			0
$787$	15.5686	+	10.6145i	0.554961	+	0.378366i	0.808083	−	0.589068i	$-0.200505\pi$
$787$	15.5686	+	10.6145i	0.554961	+	0.378366i	−0.253122	+	0.967434i	$0.581458\pi$
$788$		0			0
$789$	28.7576	+	2.15508i	1.02380	+	0.0767230i
$790$		0			0
$791$	−18.3961	−	35.1187i	−0.654090	−	1.24868i
$792$		0			0
$793$	6.86467	+	17.4909i	0.243771	+	0.621120i
$794$		0			0
$795$	7.37978	+	2.89635i	0.261734	+	0.102723i
$796$		0			0
$797$	−19.5565	+	15.5958i	−0.692728	+	0.552432i	−0.905331	−	0.424706i	$-0.860377\pi$
$797$	−19.5565	+	15.5958i	−0.692728	+	0.552432i	0.212603	+	0.977139i	$0.431806\pi$
$798$		0			0
$799$	−5.39163	−	4.29968i	−0.190742	−	0.152112i
$800$		0			0
$801$	15.7928	+	17.0206i	0.558011	+	0.601392i
$802$		0			0
$803$	−1.87149	+	3.24151i	−0.0660434	+	0.114390i
$804$		0			0
$805$	3.03974	+	8.79049i	0.107137	+	0.309824i
$806$		0			0
$807$	25.5445	−	27.5304i	0.899207	−	0.969115i
$808$		0			0
$809$	−27.5680	−	4.15521i	−0.969240	−	0.146089i	−0.354704	−	0.934978i	$-0.615418\pi$
$809$	−27.5680	−	4.15521i	−0.969240	−	0.146089i	−0.614536	+	0.788889i	$0.710657\pi$
$810$		0			0
$811$	−6.49765	+	28.4681i	−0.228163	+	0.999649i	0.722973	+	0.690877i	$0.242775\pi$
$811$	−6.49765	+	28.4681i	−0.228163	+	0.999649i	−0.951136	+	0.308772i	$0.900082\pi$
$812$		0			0
$813$	−5.27026	−	23.0905i	−0.184836	−	0.809820i
$814$		0			0
$815$	3.82660	+	6.62787i	0.134040	+	0.232164i
$816$		0			0
$817$	8.57302	+	12.5743i	0.299932	+	0.439920i
$818$		0			0
$819$	8.58577	−	6.28801i	0.300011	−	0.219721i
$820$		0			0
$821$	13.5101	+	4.16732i	0.471506	+	0.145440i	0.521397	−	0.853314i	$-0.325411\pi$
$821$	13.5101	+	4.16732i	0.471506	+	0.145440i	−0.0498906	+	0.998755i	$0.515887\pi$
$822$		0			0
$823$	3.01052	−	0.225608i	0.104940	−	0.00786418i	−0.0221565	−	0.999755i	$-0.507053\pi$
$823$	3.01052	−	0.225608i	0.104940	−	0.00786418i	0.127097	+	0.991890i	$0.459434\pi$
$824$		0			0
$825$	2.27700	+	4.72824i	0.0792750	+	0.164616i
$826$		0			0
$827$	5.07661	−	10.5417i	0.176531	−	0.366571i	−0.793863	−	0.608096i	$-0.791933\pi$
$827$	5.07661	−	10.5417i	0.176531	−	0.366571i	0.970394	+	0.241526i	$0.0776478\pi$
$828$		0			0
$829$	−2.48587	−	8.05899i	−0.0863378	−	0.279900i	0.902100	−	0.431527i	$-0.142025\pi$
$829$	−2.48587	−	8.05899i	−0.0863378	−	0.279900i	−0.988438	+	0.151627i	$0.951549\pi$
$830$		0			0
$831$	−33.9519	+	5.11742i	−1.17778	+	0.177521i
$832$		0			0
$833$	0.836469	−	10.1600i	0.0289819	−	0.352024i
$834$		0			0
$835$	−0.370264	−	2.45654i	−0.0128135	−	0.0850121i
$836$		0			0
$837$	−48.3901	+	14.9264i	−1.67261	+	0.515931i
$838$		0			0
$839$	−28.2482	−	13.6036i	−0.975236	−	0.469649i	−0.122772	−	0.992435i	$-0.539178\pi$
$839$	−28.2482	−	13.6036i	−0.975236	−	0.469649i	−0.852464	+	0.522786i	$0.824893\pi$
$840$		0			0
$841$	−0.847719	+	0.408240i	−0.0292317	+	0.0140772i
$842$		0			0
$843$	−2.25349	−	30.0707i	−0.0776142	−	1.03569i
$844$		0			0
$845$	1.05808	−	3.43021i	0.0363990	−	0.118003i
$846$		0			0
$847$	24.6088	−	10.6293i	0.845568	−	0.365227i
$848$		0			0
$849$	−5.82467	+	3.97119i	−0.199902	+	0.136291i
$850$		0			0
$851$	−30.9722	+	17.8818i	−1.06171	+	0.612981i
$852$		0			0
$853$	−10.1946	+	2.32684i	−0.349055	+	0.0796696i	−0.393454	−	0.919344i	$-0.628720\pi$
$853$	−10.1946	+	2.32684i	−0.349055	+	0.0796696i	0.0443987	+	0.999014i	$0.485863\pi$
$854$		0			0
$855$	−2.33375	−	0.532664i	−0.0798127	−	0.0182167i
$856$		0			0
$857$	4.33706	−	28.7745i	0.148151	−	0.982918i	−0.783977	−	0.620790i	$-0.786812\pi$
$857$	4.33706	−	28.7745i	0.148151	−	0.982918i	0.932128	−	0.362128i	$-0.117950\pi$
$858$		0			0
$859$	35.9157	+	33.3249i	1.22543	+	1.13703i	0.986111	+	0.166089i	$0.0531139\pi$
$859$	35.9157	+	33.3249i	1.22543	+	1.13703i	0.239317	+	0.970942i	$0.423077\pi$
$860$		0			0
$861$	26.1354	+	16.5562i	0.890694	+	0.564233i
$862$		0			0
$863$	36.1781	+	20.8874i	1.23152	+	0.711016i	0.967346	−	0.253461i	$-0.0815688\pi$
$863$	36.1781	+	20.8874i	1.23152	+	0.711016i	0.264170	+	0.964476i	$0.414902\pi$
$864$		0			0
$865$	4.30641	−	3.99576i	0.146422	−	0.135860i
$866$		0			0
$867$	−11.2026	+	14.0477i	−0.380461	+	0.477084i
$868$		0			0
$869$	−1.63525	−	2.05054i	−0.0554722	−	0.0695599i
$870$		0			0
$871$	2.82482	−	7.19752i	0.0957154	−	0.243879i
$872$		0			0
$873$	−6.38751	+	2.50691i	−0.216185	+	0.0848462i
$874$		0			0
$875$	−8.84381	+	11.8913i	−0.298975	+	0.401999i
$876$		0			0
$877$	−1.91001	+	25.4874i	−0.0644966	+	0.860647i	0.867328	+	0.497737i	$0.165836\pi$
$877$	−1.91001	+	25.4874i	−0.0644966	+	0.860647i	−0.931824	+	0.362910i	$0.881783\pi$
$878$		0			0
$879$	−7.49450	+	10.9924i	−0.252783	+	0.370765i
$880$		0			0
$881$		−	58.8889i		−	1.98402i	−0.126174	−	0.992008i	$-0.540270\pi$
$881$		−	58.8889i		−	1.98402i	0.126174	−	0.992008i	$-0.459730\pi$
$882$		0			0
$883$		−	9.62123i		−	0.323780i	−0.986809	−	0.161890i	$-0.948241\pi$
$883$		−	9.62123i		−	0.323780i	0.986809	−	0.161890i	$-0.0517590\pi$
$884$		0			0
$885$	−2.71301	+	3.97926i	−0.0911969	+	0.133761i
$886$		0			0
$887$	4.18310	−	55.8196i	0.140455	−	1.87424i	−0.270689	−	0.962667i	$-0.587252\pi$
$887$	4.18310	−	55.8196i	0.140455	−	1.87424i	0.411144	−	0.911570i	$-0.365129\pi$
$888$		0			0
$889$	−5.61441	+	29.0877i	−0.188301	+	0.975570i
$890$		0			0
$891$	1.73274	−	0.680052i	0.0580491	−	0.0227826i
$892$		0			0
$893$	4.63433	−	11.8081i	0.155082	−	0.395142i
$894$		0			0
$895$	3.81533	+	4.78427i	0.127532	+	0.159920i
$896$		0			0
$897$	11.9145	−	14.9403i	0.397814	−	0.498843i
$898$		0			0
$899$	−37.0357	+	34.3641i	−1.23521	+	1.14611i
$900$		0			0
$901$	14.2859	+	8.24799i	0.475934	+	0.274780i
$902$		0			0
$903$	−1.96601	−	18.0441i	−0.0654247	−	0.600471i
$904$		0			0
$905$	−8.70738	−	8.07927i	−0.289443	−	0.268564i
$906$		0			0
$907$	2.13896	−	14.1911i	0.0710229	−	0.471206i	−0.924841	−	0.380353i	$-0.875803\pi$
$907$	2.13896	−	14.1911i	0.0710229	−	0.471206i	0.995864	−	0.0908532i	$-0.0289594\pi$
$908$		0			0
$909$	4.66577	+	1.06493i	0.154754	+	0.0353216i
$910$		0			0
$911$	14.4667	−	3.30194i	0.479304	−	0.109398i	0.0239590	−	0.999713i	$-0.492373\pi$
$911$	14.4667	−	3.30194i	0.479304	−	0.109398i	0.455345	+	0.890315i	$0.349516\pi$
$912$		0			0
$913$	4.59616	−	2.65359i	0.152111	−	0.0878211i
$914$		0			0
$915$	−4.16487	+	2.83956i	−0.137686	+	0.0938729i
$916$		0			0
$917$	3.20859	+	17.3055i	0.105957	+	0.571477i
$918$		0			0
$919$	9.44684	−	30.6259i	0.311623	−	1.01026i	−0.655339	−	0.755335i	$-0.727474\pi$
$919$	9.44684	−	30.6259i	0.311623	−	1.01026i	0.966962	−	0.254921i	$-0.0820495\pi$
$920$		0			0
$921$	−0.100565	−	1.34194i	−0.00331372	−	0.0442185i
$922$		0			0
$923$	−9.01575	+	4.34176i	−0.296757	+	0.142911i
$924$		0			0
$925$	−24.7770	−	11.9320i	−0.814662	−	0.392320i
$926$		0			0
$927$	1.92002	−	0.592246i	0.0630616	−	0.0194519i
$928$		0			0
$929$	1.21121	+	8.03588i	0.0397387	+	0.263649i	0.999874	−	0.0158875i	$-0.00505736\pi$
$929$	1.21121	+	8.03588i	0.0397387	+	0.263649i	−0.960135	+	0.279536i	$0.909819\pi$
$930$		0			0
$931$	18.3118	−	4.03828i	0.600145	−	0.132349i
$932$		0			0
$933$	20.0091	−	3.01589i	0.655070	−	0.0987359i
$934$		0			0
$935$	−0.231823	−	0.751551i	−0.00758142	−	0.0245784i
$936$		0			0
$937$	−2.38845	+	4.95968i	−0.0780274	+	0.162026i	−0.936333	−	0.351113i	$-0.885803\pi$
$937$	−2.38845	+	4.95968i	−0.0780274	+	0.162026i	0.858306	+	0.513139i	$0.171517\pi$
$938$		0			0
$939$	7.21389	+	14.9798i	0.235416	+	0.488847i
$940$		0			0
$941$	6.56400	−	0.491904i	0.213980	−	0.0160356i	0.0326915	−	0.999465i	$-0.489592\pi$
$941$	6.56400	−	0.491904i	0.213980	−	0.0160356i	0.181289	+	0.983430i	$0.441973\pi$
$942$		0			0
$943$	−56.1258	−	17.3125i	−1.82771	−	0.563773i
$944$		0			0
$945$	6.35456	+	5.50929i	0.206714	+	0.179217i
$946$		0			0
$947$	7.25727	+	10.6445i	0.235829	+	0.345898i	0.925850	−	0.377892i	$-0.123351\pi$
$947$	7.25727	+	10.6445i	0.235829	+	0.345898i	−0.690020	+	0.723790i	$0.742398\pi$
$948$		0			0
$949$	5.24011	+	9.07615i	0.170101	+	0.294624i
$950$		0			0
$951$	−3.16792	−	13.8796i	−0.102727	−	0.450075i
$952$		0			0
$953$	−0.601923	+	2.63720i	−0.0194982	+	0.0854272i	−0.983741	−	0.179594i	$-0.942522\pi$
$953$	−0.601923	+	2.63720i	−0.0194982	+	0.0854272i	0.964243	+	0.265021i	$0.0853789\pi$
$954$		0			0
$955$	−2.73387	−	0.412064i	−0.0884659	−	0.0133341i
$956$		0			0
$957$	4.18770	−	4.51327i	0.135369	−	0.145893i
$958$		0			0
$959$	34.7157	+	12.2908i	1.12103	+	0.396891i
$960$		0			0
$961$	−27.1263	+	46.9842i	−0.875043	+	1.51562i
$962$		0			0
$963$	16.8960	+	18.2096i	0.544468	+	0.586796i
$964$		0			0
$965$	−6.61110	−	5.27217i	−0.212819	−	0.169717i
$966$		0			0
$967$	−17.9033	+	14.2774i	−0.575731	+	0.459130i	−0.867554	−	0.497342i	$-0.834309\pi$
$967$	−17.9033	+	14.2774i	−0.575731	+	0.459130i	0.291824	+	0.956472i	$0.405738\pi$
$968$		0			0
$969$	4.38544	+	1.72116i	0.140881	+	0.0552916i
$970$		0			0
$971$	1.03630	+	2.64045i	0.0332565	+	0.0847361i	0.946537	−	0.322594i	$-0.104555\pi$
$971$	1.03630	+	2.64045i	0.0332565	+	0.0847361i	−0.913281	+	0.407330i	$0.866460\pi$
$972$		0			0
$973$	0.379176	+	11.2380i	0.0121558	+	0.360274i
$974$		0			0
$975$	14.6530	+	1.09809i	0.469272	+	0.0351671i
$976$		0			0
$977$	23.2226	+	15.8329i	0.742957	+	0.506540i	0.874652	−	0.484751i	$-0.161090\pi$
$977$	23.2226	+	15.8329i	0.742957	+	0.506540i	−0.131695	+	0.991290i	$0.542042\pi$
$978$		0			0
$979$	−14.0324			−0.448478
$980$		0			0
$981$	−9.60660			−0.306715
$982$		0			0
$983$	22.4656	+	15.3168i	0.716543	+	0.488531i	0.865877	−	0.500256i	$-0.166761\pi$
$983$	22.4656	+	15.3168i	0.716543	+	0.488531i	−0.149335	+	0.988787i	$0.547713\pi$
$984$		0			0
$985$	−3.97547	−	0.297921i	−0.126669	−	0.00949254i
$986$		0			0
$987$	−11.5034	+	9.82622i	−0.366159	+	0.312772i
$988$		0			0
$989$	12.5893	+	32.0770i	0.400316	+	1.01999i
$990$		0			0
$991$	54.7661	+	21.4941i	1.73970	+	0.682783i	0.999951	+	0.00990153i	$0.00315181\pi$
$991$	54.7661	+	21.4941i	1.73970	+	0.682783i	0.739751	+	0.672881i	$0.234943\pi$
$992$		0			0
$993$	12.9491	−	10.3265i	0.410927	−	0.327703i
$994$		0			0
$995$	−10.3177	−	8.22809i	−0.327093	−	0.260848i
$996$		0			0
$997$	23.3454	+	25.1604i	0.739358	+	0.796838i	0.985006	−	0.172521i	$-0.0551913\pi$
$997$	23.3454	+	25.1604i	0.739358	+	0.796838i	−0.245648	+	0.969359i	$0.579001\pi$
$998$		0			0
$999$	−16.1690	+	28.0055i	−0.511563	+	0.886053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bp.b.495.3	yes	108
4.3	odd	2		784.2.bp.a.495.7	yes	108
49.10	odd	42		784.2.bp.a.255.7	✓	108
196.59	even	42	inner	784.2.bp.b.255.3	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bp.a.255.7	✓	108	49.10	odd	42
784.2.bp.a.495.7	yes	108	4.3	odd	2
784.2.bp.b.255.3	yes	108	196.59	even	42	inner
784.2.bp.b.495.3	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bp (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997747 - 0.680253i) q^{3} +(-0.577971 - 0.0433130i) q^{5} +(-1.06691 + 2.42109i) q^{7} +(-0.563267 - 1.43518i) q^{9} +O(q^{10})\)	\(q+(-0.997747 - 0.680253i) q^{3} +(-0.577971 - 0.0433130i) q^{5} +(-1.06691 + 2.42109i) q^{7} +(-0.563267 - 1.43518i) q^{9} +(0.867361 + 0.340414i) q^{11} +(2.03975 - 1.62664i) q^{13} +(0.547206 + 0.436382i) q^{15} +(0.990564 + 1.06757i) q^{17} +(-1.33941 + 2.31993i) q^{19} +(2.71147 - 1.68987i) q^{21} +(-4.12561 + 4.44635i) q^{23} +(-4.61198 - 0.695144i) q^{25} +(-1.22042 + 5.34701i) q^{27} +(1.21760 + 5.33464i) q^{29} +(4.61662 + 7.99622i) q^{31} +(-0.633840 - 0.929672i) q^{33} +(0.721510 - 1.35311i) q^{35} +(5.63426 + 1.73794i) q^{37} +(-3.14168 + 0.235436i) q^{39} +(4.20149 + 8.72449i) q^{41} +(2.46495 - 5.11851i) q^{43} +(0.263390 + 0.853890i) q^{45} +(-4.68237 + 0.705753i) q^{47} +(-4.72339 - 5.16619i) q^{49} +(-0.262113 - 1.73900i) q^{51} +(10.8238 - 3.33869i) q^{53} +(-0.486566 - 0.234318i) q^{55} +(2.91454 - 1.40357i) q^{57} +(0.514227 + 6.86188i) q^{59} +(-2.12285 + 6.88211i) q^{61} +(4.07566 + 0.167490i) q^{63} +(-1.24937 + 0.851806i) q^{65} +(2.56661 - 1.48183i) q^{67} +(7.14096 - 1.62988i) q^{69} +(-3.73940 - 0.853493i) q^{71} +(-0.598711 + 3.97219i) q^{73} +(4.12872 + 3.83089i) q^{75} +(-1.74957 + 1.73677i) q^{77} +(-2.43768 - 1.40740i) q^{79} +(1.46443 - 1.35879i) q^{81} +(3.55127 - 4.45316i) q^{83} +(-0.526278 - 0.659932i) q^{85} +(2.41405 - 6.15089i) q^{87} +(-14.0189 + 5.50202i) q^{89} +(1.76203 + 6.67390i) q^{91} +(0.833229 - 11.1187i) q^{93} +(0.874626 - 1.28284i) q^{95} -4.45067i q^{97} -1.43656i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9	\( 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9} + 18 q^{11} + 16 q^{17} + 7 q^{19} + 5 q^{21} + 54 q^{23} - 4 q^{25} - 53 q^{27} - 16 q^{29} + 5 q^{31} - 3 q^{33} - 9 q^{35} + 2 q^{37} - 43 q^{39} - 28 q^{41} - 111 q^{45} - 60 q^{47} - 58 q^{49} - 3 q^{51} - 70 q^{53} + 69 q^{55} + 31 q^{57} + 9 q^{59} - 8 q^{61} + 93 q^{63} - 8 q^{65} - 21 q^{67} - 56 q^{69} - 63 q^{71} - 24 q^{73} + 2 q^{75} - 18 q^{77} + 21 q^{79} + 45 q^{81} + 60 q^{83} + 6 q^{85} - 6 q^{87} + 7 q^{89} + 66 q^{93} + 15 q^{95}+O(q^{100}) \) 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9 + 18 * q^11 + 16 * q^17 + 7 * q^19 + 5 * q^21 + 54 * q^23 - 4 * q^25 - 53 * q^27 - 16 * q^29 + 5 * q^31 - 3 * q^33 - 9 * q^35 + 2 * q^37 - 43 * q^39 - 28 * q^41 - 111 * q^45 - 60 * q^47 - 58 * q^49 - 3 * q^51 - 70 * q^53 + 69 * q^55 + 31 * q^57 + 9 * q^59 - 8 * q^61 + 93 * q^63 - 8 * q^65 - 21 * q^67 - 56 * q^69 - 63 * q^71 - 24 * q^73 + 2 * q^75 - 18 * q^77 + 21 * q^79 + 45 * q^81 + 60 * q^83 + 6 * q^85 - 6 * q^87 + 7 * q^89 + 66 * q^93 + 15 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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