LMFDB - Embedded newform 1155.2.k.b.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.1
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66471 q^{2} +1.00000 q^{3} +5.10065 q^{4} +(-1.18527 - 1.89608i) q^{5} -2.66471 q^{6} +(2.09935 + 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.66471 q^{2} +1.00000 q^{3} +5.10065 q^{4} +(-1.18527 - 1.89608i) q^{5} -2.66471 q^{6} +(2.09935 + 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +(3.15840 + 5.05250i) q^{10} +(1.90151 + 2.71740i) q^{11} +5.10065 q^{12} -0.864827i q^{13} +(-5.59415 - 4.29069i) q^{14} +(-1.18527 - 1.89608i) q^{15} +11.8154 q^{16} -1.53725i q^{17} -2.66471 q^{18} +2.68287 q^{19} +(-6.04566 - 9.67127i) q^{20} +(2.09935 + 1.61019i) q^{21} +(-5.06697 - 7.24106i) q^{22} +7.32990i q^{23} -8.26233 q^{24} +(-2.19026 + 4.49475i) q^{25} +2.30451i q^{26} +1.00000 q^{27} +(10.7081 + 8.21304i) q^{28} +1.42095i q^{29} +(3.15840 + 5.05250i) q^{30} -0.551846i q^{31} -14.9598 q^{32} +(1.90151 + 2.71740i) q^{33} +4.09632i q^{34} +(0.564757 - 5.88906i) q^{35} +5.10065 q^{36} +5.97120i q^{37} -7.14906 q^{38} -0.864827i q^{39} +(9.79311 + 15.6661i) q^{40} -0.607303 q^{41} +(-5.59415 - 4.29069i) q^{42} -0.823316 q^{43} +(9.69896 + 13.8605i) q^{44} +(-1.18527 - 1.89608i) q^{45} -19.5320i q^{46} +8.37543 q^{47} +11.8154 q^{48} +(1.81456 + 6.76072i) q^{49} +(5.83640 - 11.9772i) q^{50} -1.53725i q^{51} -4.41118i q^{52} -8.21534i q^{53} -2.66471 q^{54} +(2.89860 - 6.82628i) q^{55} +(-17.3455 - 13.3039i) q^{56} +2.68287 q^{57} -3.78641i q^{58} +14.3900i q^{59} +(-6.04566 - 9.67127i) q^{60} -6.95852 q^{61} +1.47051i q^{62} +(2.09935 + 1.61019i) q^{63} +16.2328 q^{64} +(-1.63978 + 1.02505i) q^{65} +(-5.06697 - 7.24106i) q^{66} -7.78444i q^{67} -7.84099i q^{68} +7.32990i q^{69} +(-1.50491 + 15.6926i) q^{70} -4.38660 q^{71} -8.26233 q^{72} -3.89027i q^{73} -15.9115i q^{74} +(-2.19026 + 4.49475i) q^{75} +13.6844 q^{76} +(-0.383589 + 8.76658i) q^{77} +2.30451i q^{78} +8.94533i q^{79} +(-14.0044 - 22.4029i) q^{80} +1.00000 q^{81} +1.61828 q^{82} -13.1440i q^{83} +(10.7081 + 8.21304i) q^{84} +(-2.91476 + 1.82206i) q^{85} +2.19389 q^{86} +1.42095i q^{87} +(-15.7109 - 22.4520i) q^{88} -7.51433i q^{89} +(3.15840 + 5.05250i) q^{90} +(1.39254 - 1.81558i) q^{91} +37.3873i q^{92} -0.551846i q^{93} -22.3180 q^{94} +(-3.17993 - 5.08694i) q^{95} -14.9598 q^{96} -18.3921 q^{97} +(-4.83526 - 18.0153i) q^{98} +(1.90151 + 2.71740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.66471			−1.88423			−0.942116	−	0.335288i	$-0.891166\pi$
$2$	−2.66471			−1.88423			−0.942116	+	0.335288i	$0.891166\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	5.10065			2.55033
$5$	−1.18527	−	1.89608i	−0.530070	−	0.847954i
$5$	−1.18527	−	1.89608i	−0.530070	−	0.847954i
$6$	−2.66471			−1.08786
$7$	2.09935	+	1.61019i	0.793480	+	0.608596i
$7$	2.09935	+	1.61019i	0.793480	+	0.608596i
$8$	−8.26233			−2.92118
$9$	1.00000			0.333333
$10$	3.15840	+	5.05250i	0.998774	+	1.59774i
$11$	1.90151	+	2.71740i	0.573328	+	0.819326i
$11$	1.90151	+	2.71740i	0.573328	+	0.819326i
$12$	5.10065			1.47243
$13$		−	0.864827i		−	0.239860i	−0.992782	−	0.119930i	$-0.961733\pi$
$13$		−	0.864827i		−	0.239860i	0.992782	−	0.119930i	$-0.0382670\pi$
$14$	−5.59415	−	4.29069i	−1.49510	−	1.14673i
$15$	−1.18527	−	1.89608i	−0.306036	−	0.489567i
$16$	11.8154			2.95384
$17$		−	1.53725i		−	0.372838i	−0.982470	−	0.186419i	$-0.940312\pi$
$17$		−	1.53725i		−	0.372838i	0.982470	−	0.186419i	$-0.0596882\pi$
$18$	−2.66471			−0.628077
$19$	2.68287			0.615493			0.307746	−	0.951468i	$-0.400425\pi$
$19$	2.68287			0.615493			0.307746	+	0.951468i	$0.400425\pi$
$20$	−6.04566	−	9.67127i	−1.35185	−	2.16256i
$21$	2.09935	+	1.61019i	0.458116	+	0.351373i
$22$	−5.06697	−	7.24106i	−1.08028	−	1.54380i
$23$			7.32990i			1.52839i	0.644985	+	0.764195i	$0.276864\pi$
$23$			7.32990i			1.52839i	−0.644985	+	0.764195i	$0.723136\pi$
$24$	−8.26233			−1.68654
$25$	−2.19026	+	4.49475i	−0.438052	+	0.898949i
$26$			2.30451i			0.451951i
$27$	1.00000			0.192450
$28$	10.7081	+	8.21304i	2.02364	+	1.55212i
$29$			1.42095i			0.263864i	0.991259	+	0.131932i	$0.0421180\pi$
$29$			1.42095i			0.263864i	−0.991259	+	0.131932i	$0.957882\pi$
$30$	3.15840	+	5.05250i	0.576642	+	0.922457i
$31$		−	0.551846i		−	0.0991145i	−0.998771	−	0.0495573i	$-0.984219\pi$
$31$		−	0.551846i		−	0.0991145i	0.998771	−	0.0495573i	$-0.0157810\pi$
$32$	−14.9598			−2.64455
$33$	1.90151	+	2.71740i	0.331011	+	0.473038i
$34$			4.09632i			0.702513i
$35$	0.564757	−	5.88906i	0.0954614	−	0.995433i
$36$	5.10065			0.850109
$37$			5.97120i			0.981660i	0.871255	+	0.490830i	$0.163306\pi$
$37$			5.97120i			0.981660i	−0.871255	+	0.490830i	$0.836694\pi$
$38$	−7.14906			−1.15973
$39$		−	0.864827i		−	0.138483i
$40$	9.79311	+	15.6661i	1.54843	+	2.47702i
$41$	−0.607303			−0.0948447			−0.0474224	−	0.998875i	$-0.515101\pi$
$41$	−0.607303			−0.0948447			−0.0474224	+	0.998875i	$0.515101\pi$
$42$	−5.59415	−	4.29069i	−0.863197	−	0.662068i
$43$	−0.823316			−0.125554			−0.0627772	−	0.998028i	$-0.519996\pi$
$43$	−0.823316			−0.125554			−0.0627772	+	0.998028i	$0.519996\pi$
$44$	9.69896	+	13.8605i	1.46217	+	2.08955i
$45$	−1.18527	−	1.89608i	−0.176690	−	0.282651i
$46$		−	19.5320i		−	2.87984i
$47$	8.37543			1.22168			0.610841	−	0.791753i	$-0.290832\pi$
$47$	8.37543			1.22168			0.610841	+	0.791753i	$0.290832\pi$
$48$	11.8154			1.70540
$49$	1.81456	+	6.76072i	0.259223	+	0.965818i
$50$	5.83640	−	11.9772i	0.825392	−	1.69383i
$51$		−	1.53725i		−	0.215258i
$52$		−	4.41118i		−	0.611721i
$53$		−	8.21534i		−	1.12846i	−0.825616	−	0.564232i	$-0.809172\pi$
$53$		−	8.21534i		−	1.12846i	0.825616	−	0.564232i	$-0.190828\pi$
$54$	−2.66471			−0.362620
$55$	2.89860	−	6.82628i	0.390847	−	0.920455i
$56$	−17.3455	−	13.3039i	−2.31790	−	1.77781i
$57$	2.68287			0.355355
$58$		−	3.78641i		−	0.497180i
$59$			14.3900i			1.87341i	0.350114	+	0.936707i	$0.386143\pi$
$59$			14.3900i			1.87341i	−0.350114	+	0.936707i	$0.613857\pi$
$60$	−6.04566	−	9.67127i	−0.780492	−	1.24855i
$61$	−6.95852			−0.890947			−0.445473	−	0.895295i	$-0.646965\pi$
$61$	−6.95852			−0.890947			−0.445473	+	0.895295i	$0.646965\pi$
$62$			1.47051i			0.186755i
$63$	2.09935	+	1.61019i	0.264493	+	0.202865i
$64$	16.2328			2.02910
$65$	−1.63978	+	1.02505i	−0.203390	+	0.127142i
$66$	−5.06697	−	7.24106i	−0.623701	−	0.891313i
$67$		−	7.78444i		−	0.951021i	−0.879710	−	0.475510i	$-0.842263\pi$
$67$		−	7.78444i		−	0.951021i	0.879710	−	0.475510i	$-0.157737\pi$
$68$		−	7.84099i		−	0.950859i
$69$			7.32990i			0.882416i
$70$	−1.50491	+	15.6926i	−0.179871	+	1.87563i
$71$	−4.38660			−0.520594			−0.260297	−	0.965529i	$-0.583820\pi$
$71$	−4.38660			−0.520594			−0.260297	+	0.965529i	$0.583820\pi$
$72$	−8.26233			−0.973725
$73$		−	3.89027i		−	0.455322i	−0.973740	−	0.227661i	$-0.926892\pi$
$73$		−	3.89027i		−	0.455322i	0.973740	−	0.227661i	$-0.0731078\pi$
$74$		−	15.9115i		−	1.84967i
$75$	−2.19026	+	4.49475i	−0.252910	+	0.519009i
$76$	13.6844			1.56971
$77$	−0.383589	+	8.76658i	−0.0437140	+	0.999044i
$78$			2.30451i			0.260934i
$79$			8.94533i			1.00643i	0.864162	+	0.503214i	$0.167849\pi$
$79$			8.94533i			1.00643i	−0.864162	+	0.503214i	$0.832151\pi$
$80$	−14.0044	−	22.4029i	−1.56574	−	2.50472i
$81$	1.00000			0.111111
$82$	1.61828			0.178709
$83$		−	13.1440i		−	1.44274i	−0.692549	−	0.721371i	$-0.743512\pi$
$83$		−	13.1440i		−	1.44274i	0.692549	−	0.721371i	$-0.256488\pi$
$84$	10.7081	+	8.21304i	1.16835	+	0.896116i
$85$	−2.91476	+	1.82206i	−0.316150	+	0.197630i
$86$	2.19389			0.236574
$87$			1.42095i			0.152342i
$88$	−15.7109	−	22.4520i	−1.67479	−	2.39340i
$89$		−	7.51433i		−	0.796517i	−0.917273	−	0.398259i	$-0.869615\pi$
$89$		−	7.51433i		−	0.796517i	0.917273	−	0.398259i	$-0.130385\pi$
$90$	3.15840	+	5.05250i	0.332925	+	0.532581i
$91$	1.39254	−	1.81558i	0.145978	−	0.190324i
$92$			37.3873i			3.89790i
$93$		−	0.551846i		−	0.0572238i
$94$	−22.3180			−2.30193
$95$	−3.17993	−	5.08694i	−0.326254	−	0.521909i
$96$	−14.9598			−1.52683
$97$	−18.3921			−1.86744			−0.933719	−	0.358007i	$-0.883456\pi$
$97$	−18.3921			−1.86744			−0.933719	+	0.358007i	$0.883456\pi$
$98$	−4.83526	−	18.0153i	−0.488435	−	1.81982i
$99$	1.90151	+	2.71740i	0.191109	+	0.273109i
$100$	−11.1718	+	22.9262i	−1.11718	+	2.29262i
$101$	17.7370			1.76490			0.882451	−	0.470405i	$-0.155892\pi$
$101$	17.7370			1.76490			0.882451	+	0.470405i	$0.155892\pi$
$102$			4.09632i			0.405596i
$103$	15.5720			1.53436			0.767180	−	0.641432i	$-0.221659\pi$
$103$	15.5720			1.53436			0.767180	+	0.641432i	$0.221659\pi$
$104$			7.14549i			0.700673i
$105$	0.564757	−	5.88906i	0.0551146	−	0.574714i
$106$			21.8915i			2.12629i
$107$	16.4098			1.58639			0.793197	−	0.608965i	$-0.208415\pi$
$107$	16.4098			1.58639			0.793197	+	0.608965i	$0.208415\pi$
$108$	5.10065			0.490811
$109$			11.4582i			1.09749i	0.835988	+	0.548747i	$0.184895\pi$
$109$			11.4582i			1.09749i	−0.835988	+	0.548747i	$0.815105\pi$
$110$	−7.72392	+	18.1900i	−0.736447	+	1.73435i
$111$			5.97120i			0.566762i
$112$	24.8046	+	19.0250i	2.34382	+	1.79770i
$113$			3.87929i			0.364933i	0.983212	+	0.182466i	$0.0584081\pi$
$113$			3.87929i			0.364933i	−0.983212	+	0.182466i	$0.941592\pi$
$114$	−7.14906			−0.669571
$115$	13.8981	−	8.68792i	1.29600	−	0.810153i
$116$			7.24777i			0.672939i
$117$		−	0.864827i		−	0.0799533i
$118$		−	38.3450i		−	3.52995i
$119$	2.47527	−	3.22723i	0.226908	−	0.295840i
$120$	9.79311	+	15.6661i	0.893984	+	1.43011i
$121$	−3.76850	+	10.3343i	−0.342591	+	0.939485i
$122$	18.5424			1.67875
$123$	−0.607303			−0.0547586
$124$		−	2.81478i		−	0.252774i
$125$	11.1185	−	1.17458i	0.994466	−	0.105057i
$126$	−5.59415	−	4.29069i	−0.498367	−	0.382245i
$127$	16.1339			1.43165			0.715825	−	0.698279i	$-0.246051\pi$
$127$	16.1339			1.43165			0.715825	+	0.698279i	$0.246051\pi$
$128$	−13.3359			−1.17874
$129$	−0.823316			−0.0724889
$130$	4.36954	−	2.73147i	0.383234	−	0.239566i
$131$	7.98104			0.697307			0.348653	−	0.937252i	$-0.386639\pi$
$131$	7.98104			0.697307			0.348653	+	0.937252i	$0.386639\pi$
$132$	9.69896	+	13.8605i	0.844186	+	1.20640i
$133$	5.63229	+	4.31994i	0.488381	+	0.374586i
$134$			20.7432i			1.79194i
$135$	−1.18527	−	1.89608i	−0.102012	−	0.163189i
$136$			12.7013i			1.08913i
$137$			13.3208i			1.13807i	0.822312	+	0.569037i	$0.192684\pi$
$137$			13.3208i			1.13807i	−0.822312	+	0.569037i	$0.807316\pi$
$138$		−	19.5320i		−	1.66268i
$139$	5.61484			0.476245			0.238122	−	0.971235i	$-0.423468\pi$
$139$	5.61484			0.476245			0.238122	+	0.971235i	$0.423468\pi$
$140$	2.88063	−	30.0381i	0.243458	−	2.53868i
$141$	8.37543			0.705338
$142$	11.6890			0.980919
$143$	2.35008	−	1.64448i	0.196523	−	0.137518i
$144$	11.8154			0.984614
$145$	2.69424	−	1.68421i	0.223744	−	0.139866i
$146$			10.3664i			0.857932i
$147$	1.81456	+	6.76072i	0.149662	+	0.557615i
$148$			30.4571i			2.50355i
$149$			6.63536i			0.543590i	0.962355	+	0.271795i	$0.0876172\pi$
$149$			6.63536i			0.543590i	−0.962355	+	0.271795i	$0.912383\pi$
$150$	5.83640	−	11.9772i	0.476540	−	0.977932i
$151$		−	16.7964i		−	1.36687i	−0.730010	−	0.683436i	$-0.760485\pi$
$151$		−	16.7964i		−	1.36687i	0.730010	−	0.683436i	$-0.239515\pi$
$152$	−22.1668			−1.79796
$153$		−	1.53725i		−	0.124279i
$154$	1.02215	−	23.3603i	0.0823674	−	1.88243i
$155$	−1.04635	+	0.654088i	−0.0840446	+	0.0525376i
$156$		−	4.41118i		−	0.353177i
$157$	6.52197			0.520510			0.260255	−	0.965540i	$-0.416193\pi$
$157$	6.52197			0.520510			0.260255	+	0.965540i	$0.416193\pi$
$158$		−	23.8367i		−	1.89634i
$159$		−	8.21534i		−	0.651519i
$160$	17.7314	+	28.3651i	1.40179	+	2.24245i
$161$	−11.8026	+	15.3880i	−0.930172	+	1.21275i
$162$	−2.66471			−0.209359
$163$		−	3.51503i		−	0.275318i	−0.990480	−	0.137659i	$-0.956042\pi$
$163$		−	3.51503i		−	0.275318i	0.990480	−	0.137659i	$-0.0439578\pi$
$164$	−3.09764			−0.241885
$165$	2.89860	−	6.82628i	0.225656	−	0.531425i
$166$			35.0249i			2.71846i
$167$			16.2402i			1.25671i	0.777928	+	0.628354i	$0.216271\pi$
$167$			16.2402i			1.25671i	−0.777928	+	0.628354i	$0.783729\pi$
$168$	−17.3455	−	13.3039i	−1.33824	−	1.02642i
$169$	12.2521			0.942467
$170$	7.76697	−	4.85525i	0.595699	−	0.372381i
$171$	2.68287			0.205164
$172$	−4.19945			−0.320205
$173$			9.54156i			0.725432i	0.931900	+	0.362716i	$0.118150\pi$
$173$			9.54156i			0.725432i	−0.931900	+	0.362716i	$0.881850\pi$
$174$		−	3.78641i		−	0.287047i
$175$	−11.8355	+	5.90931i	−0.894683	+	0.446702i
$176$	22.4671	+	32.1071i	1.69352	+	2.42016i
$177$			14.3900i			1.08162i
$178$			20.0235i			1.50082i
$179$	−14.7615			−1.10333			−0.551664	−	0.834066i	$-0.686007\pi$
$179$	−14.7615			−1.10333			−0.551664	+	0.834066i	$0.686007\pi$
$180$	−6.04566	−	9.67127i	−0.450617	−	0.720854i
$181$		−	23.2469i		−	1.72793i	−0.503555	−	0.863963i	$-0.667975\pi$
$181$		−	23.2469i		−	1.72793i	0.503555	−	0.863963i	$-0.332025\pi$
$182$	−3.71070	+	4.83798i	−0.275056	+	0.358615i
$183$	−6.95852			−0.514388
$184$		−	60.5621i		−	4.46470i
$185$	11.3219	−	7.07750i	0.832403	−	0.520348i
$186$			1.47051i			0.107823i
$187$	4.17732	−	2.92310i	0.305476	−	0.213758i
$188$	42.7202			3.11569
$189$	2.09935	+	1.61019i	0.152705	+	0.117124i
$190$	8.47358	+	13.5552i	0.614738	+	0.983398i
$191$	15.8968			1.15025			0.575125	−	0.818066i	$-0.304953\pi$
$191$	15.8968			1.15025			0.575125	+	0.818066i	$0.304953\pi$
$192$	16.2328			1.17150
$193$	−8.32276			−0.599085			−0.299543	−	0.954083i	$-0.596834\pi$
$193$	−8.32276			−0.599085			−0.299543	+	0.954083i	$0.596834\pi$
$194$	49.0096			3.51868
$195$	−1.63978	+	1.02505i	−0.117427	+	0.0734057i
$196$	9.25543	+	34.4841i	0.661102	+	2.46315i
$197$	−13.2323			−0.942762			−0.471381	−	0.881930i	$-0.656244\pi$
$197$	−13.2323			−0.942762			−0.471381	+	0.881930i	$0.656244\pi$
$198$	−5.06697	−	7.24106i	−0.360094	−	0.514600i
$199$			3.83430i			0.271806i	0.990722	+	0.135903i	$0.0433936\pi$
$199$			3.83430i			0.271806i	−0.990722	+	0.135903i	$0.956606\pi$
$200$	18.0967	−	37.1371i	1.27963	−	2.62599i
$201$		−	7.78444i		−	0.549072i
$202$	−47.2640			−3.32548
$203$	−2.28800	+	2.98307i	−0.160586	+	0.209371i
$204$		−	7.84099i		−	0.548979i
$205$	0.719819	+	1.15150i	0.0502743	+	0.0804240i
$206$	−41.4949			−2.89109
$207$			7.32990i			0.509463i
$208$		−	10.2182i		−	0.708508i
$209$	5.10151	+	7.29042i	0.352879	+	0.504289i
$210$	−1.50491	+	15.6926i	−0.103849	+	1.08289i
$211$			17.3558i			1.19482i	0.801934	+	0.597412i	$0.203804\pi$
$211$			17.3558i			1.19482i	−0.801934	+	0.597412i	$0.796196\pi$
$212$		−	41.9036i		−	2.87795i
$213$	−4.38660			−0.300565
$214$	−43.7273			−2.98913
$215$	0.975853	+	1.56107i	0.0665526	+	0.106464i
$216$	−8.26233			−0.562180
$217$	0.888579	−	1.15852i	0.0603207	−	0.0786454i
$218$		−	30.5327i		−	2.06793i
$219$		−	3.89027i		−	0.262880i
$220$	14.7848	−	34.8185i	0.996789	−	2.34746i
$221$	−1.32946			−0.0894289
$222$		−	15.9115i		−	1.06791i
$223$	8.79032			0.588644			0.294322	−	0.955706i	$-0.404906\pi$
$223$	8.79032			0.588644			0.294322	+	0.955706i	$0.404906\pi$
$224$	−31.4059	−	24.0882i	−2.09840	−	1.60946i
$225$	−2.19026	+	4.49475i	−0.146017	+	0.299650i
$226$		−	10.3372i		−	0.687618i
$227$			16.2488i			1.07847i	0.842155	+	0.539236i	$0.181287\pi$
$227$			16.2488i			1.07847i	−0.842155	+	0.539236i	$0.818713\pi$
$228$	13.6844			0.906271
$229$		−	24.5602i		−	1.62299i	−0.584362	−	0.811493i	$-0.698655\pi$
$229$		−	24.5602i		−	1.62299i	0.584362	−	0.811493i	$-0.301345\pi$
$230$	−37.0343	+	23.1508i	−2.44197	+	1.52652i
$231$	−0.383589	+	8.76658i	−0.0252383	+	0.576798i
$232$		−	11.7404i		−	0.770792i
$233$	−17.2426			−1.12960			−0.564802	−	0.825227i	$-0.691047\pi$
$233$	−17.2426			−1.12960			−0.564802	+	0.825227i	$0.691047\pi$
$234$			2.30451i			0.150650i
$235$	−9.92716	−	15.8805i	−0.647576	−	1.03593i
$236$			73.3983i			4.77782i
$237$			8.94533i			0.581061i
$238$	−6.59587	+	8.59962i	−0.427547	+	0.557431i
$239$			2.60857i			0.168734i	0.996435	+	0.0843671i	$0.0268868\pi$
$239$			2.60857i			0.168734i	−0.996435	+	0.0843671i	$0.973113\pi$
$240$	−14.0044	−	22.4029i	−0.903982	−	1.44610i
$241$	−1.02093			−0.0657638			−0.0328819	−	0.999459i	$-0.510469\pi$
$241$	−1.02093			−0.0657638			−0.0328819	+	0.999459i	$0.510469\pi$
$242$	10.0419	−	27.5380i	0.645520	−	1.77021i
$243$	1.00000			0.0641500
$244$	−35.4930			−2.27221
$245$	10.6681	−	11.4538i	0.681563	−	0.731759i
$246$	1.61828			0.103178
$247$		−	2.32022i		−	0.147632i
$248$			4.55954i			0.289531i
$249$		−	13.1440i		−	0.832967i
$250$	−29.6274	+	3.12990i	−1.87380	+	0.197952i
$251$		−	15.9683i		−	1.00791i	−0.863730	−	0.503955i	$-0.831878\pi$
$251$		−	15.9683i		−	1.00791i	0.863730	−	0.503955i	$-0.168122\pi$
$252$	10.7081	+	8.21304i	0.674545	+	0.517373i
$253$	−19.9183	+	13.9379i	−1.25225	+	0.876268i
$254$	−42.9920			−2.69756
$255$	−2.91476	+	1.82206i	−0.182529	+	0.114102i
$256$	3.07071			0.191919
$257$	−24.0879			−1.50256			−0.751282	−	0.659981i	$-0.770564\pi$
$257$	−24.0879			−1.50256			−0.751282	+	0.659981i	$0.770564\pi$
$258$	2.19389			0.136586
$259$	−9.61479	+	12.5357i	−0.597434	+	0.778928i
$260$	−8.36397	+	5.22845i	−0.518711	+	0.324255i
$261$			1.42095i			0.0879546i
$262$	−21.2671			−1.31389
$263$	18.4313			1.13652			0.568260	−	0.822849i	$-0.307617\pi$
$263$	18.4313			1.13652			0.568260	+	0.822849i	$0.307617\pi$
$264$	−15.7109	−	22.4520i	−0.966941	−	1.38183i
$265$	−15.5770	+	9.73741i	−0.956885	+	0.598164i
$266$	−15.0084	−	11.5114i	−0.920223	−	0.705807i
$267$		−	7.51433i		−	0.459870i
$268$		−	39.7057i		−	2.42541i
$269$			10.2977i			0.627861i	0.949446	+	0.313931i	$0.101646\pi$
$269$			10.2977i			0.627861i	−0.949446	+	0.313931i	$0.898354\pi$
$270$	3.15840	+	5.05250i	0.192214	+	0.307486i
$271$	−23.6065			−1.43399			−0.716995	−	0.697078i	$-0.754483\pi$
$271$	−23.6065			−1.43399			−0.716995	+	0.697078i	$0.754483\pi$
$272$		−	18.1632i		−	1.10131i
$273$	1.39254	−	1.81558i	0.0842802	−	0.109884i
$274$		−	35.4960i		−	2.14439i
$275$	−16.3788	+	2.59501i	−0.987680	+	0.156485i
$276$			37.3873i			2.25045i
$277$	26.2554			1.57754			0.788768	−	0.614691i	$-0.210719\pi$
$277$	26.2554			1.57754			0.788768	+	0.614691i	$0.210719\pi$
$278$	−14.9619			−0.897356
$279$		−	0.551846i		−	0.0330382i
$280$	−4.66621	+	48.6574i	−0.278859	+	2.90783i
$281$		−	31.7030i		−	1.89124i	−0.325272	−	0.945620i	$-0.605456\pi$
$281$		−	31.7030i		−	1.89124i	0.325272	−	0.945620i	$-0.394544\pi$
$282$	−22.3180			−1.32902
$283$		−	7.26679i		−	0.431966i	−0.976397	−	0.215983i	$-0.930704\pi$
$283$		−	7.26679i		−	0.431966i	0.976397	−	0.215983i	$-0.0692955\pi$
$284$	−22.3745			−1.32768
$285$	−3.17993	−	5.08694i	−0.188363	−	0.301325i
$286$	−6.26227	+	4.38205i	−0.370296	+	0.259116i
$287$	−1.27494	−	0.977874i	−0.0752575	−	0.0577221i
$288$	−14.9598			−0.881516
$289$	14.6369			0.860992
$290$	−7.17935	+	4.48793i	−0.421586	+	0.263540i
$291$	−18.3921			−1.07817
$292$		−	19.8429i		−	1.16122i
$293$		−	31.4376i		−	1.83661i	−0.395877	−	0.918303i	$-0.629559\pi$
$293$		−	31.4376i		−	1.83661i	0.395877	−	0.918303i	$-0.370441\pi$
$294$	−4.83526	−	18.0153i	−0.281998	−	1.05068i
$295$	27.2846	−	17.0560i	1.58857	−	0.993040i
$296$		−	49.3361i		−	2.86760i
$297$	1.90151	+	2.71740i	0.110337	+	0.157679i
$298$		−	17.6813i		−	1.02425i
$299$	6.33910			0.366599
$300$	−11.1718	+	22.9262i	−0.645003	+	1.32364i
$301$	−1.72843	−	1.32570i	−0.0996250	−	0.0764119i
$302$			44.7575i			2.57550i
$303$	17.7370			1.01897
$304$	31.6991			1.81807
$305$	8.24773	+	13.1939i	0.472264	+	0.755482i
$306$			4.09632i			0.234171i
$307$		−	13.8197i		−	0.788733i	−0.918953	−	0.394366i	$-0.870964\pi$
$307$		−	13.8197i		−	0.788733i	0.918953	−	0.394366i	$-0.129036\pi$
$308$	−1.95656	+	44.7153i	−0.111485	+	2.54789i
$309$	15.5720			0.885863
$310$	2.78820	−	1.74295i	0.158359	−	0.0989930i
$311$		−	4.57177i		−	0.259241i	−0.991564	−	0.129621i	$-0.958624\pi$
$311$		−	4.57177i		−	0.259241i	0.991564	−	0.129621i	$-0.0413759\pi$
$312$			7.14549i			0.404533i
$313$	26.4180			1.49323			0.746616	−	0.665256i	$-0.231677\pi$
$313$	26.4180			1.49323			0.746616	+	0.665256i	$0.231677\pi$
$314$	−17.3791			−0.980762
$315$	0.564757	−	5.88906i	0.0318205	−	0.331811i
$316$			45.6270i			2.56672i
$317$			7.88446i			0.442835i	0.975179	+	0.221418i	$0.0710684\pi$
$317$			7.88446i			0.442835i	−0.975179	+	0.221418i	$0.928932\pi$
$318$			21.8915i			1.22761i
$319$	−3.86129	+	2.70195i	−0.216190	+	0.151280i
$320$	−19.2402	−	30.7787i	−1.07556	−	1.72058i
$321$	16.4098			0.915905
$322$	31.4503	−	41.0046i	1.75266	−	2.28510i
$323$		−	4.12424i		−	0.229479i
$324$	5.10065			0.283370
$325$	3.88718	+	1.89420i	0.215622	+	0.105071i
$326$			9.36651i			0.518763i
$327$			11.4582i			0.633639i
$328$	5.01774			0.277058
$329$	17.5830	+	13.4861i	0.969381	+	0.743510i
$330$	−7.72392	+	18.1900i	−0.425188	+	1.00133i
$331$	−5.20944			−0.286337			−0.143168	−	0.989698i	$-0.545729\pi$
$331$	−5.20944			−0.286337			−0.143168	+	0.989698i	$0.545729\pi$
$332$		−	67.0430i		−	3.67946i
$333$			5.97120i			0.327220i
$334$		−	43.2755i		−	2.36793i
$335$	−14.7599	+	9.22668i	−0.806422	+	0.504107i
$336$	24.8046	+	19.0250i	1.35320	+	1.03790i
$337$	0.820269			0.0446829			0.0223414	−	0.999750i	$-0.492888\pi$
$337$	0.820269			0.0446829			0.0223414	+	0.999750i	$0.492888\pi$
$338$	−32.6482			−1.77583
$339$			3.87929i			0.210694i
$340$	−14.8672	+	9.29370i	−0.806285	+	0.504022i
$341$	1.49959	−	1.04934i	0.0812071	−	0.0568251i
$342$	−7.14906			−0.386577
$343$	−7.07667	+	17.1149i	−0.382104	+	0.924119i
$344$	6.80251			0.366767
$345$	13.8981	−	8.68792i	0.748249	−	0.467742i
$346$		−	25.4255i		−	1.36688i
$347$	−9.64321			−0.517675			−0.258837	−	0.965921i	$-0.583339\pi$
$347$	−9.64321			−0.517675			−0.258837	+	0.965921i	$0.583339\pi$
$348$			7.24777i			0.388521i
$349$	7.03905			0.376792			0.188396	−	0.982093i	$-0.439671\pi$
$349$	7.03905			0.376792			0.188396	+	0.982093i	$0.439671\pi$
$350$	31.5382	−	15.7466i	1.68579	−	0.841690i
$351$		−	0.864827i		−	0.0461610i
$352$	−28.4463	−	40.6518i	−1.51619	−	2.16675i
$353$	−10.8364			−0.576766			−0.288383	−	0.957515i	$-0.593118\pi$
$353$	−10.8364			−0.576766			−0.288383	+	0.957515i	$0.593118\pi$
$354$		−	38.3450i		−	2.03802i
$355$	5.19931	+	8.31736i	0.275951	+	0.441440i
$356$		−	38.3280i		−	2.03138i
$357$	2.47527	−	3.22723i	0.131005	−	0.170803i
$358$	39.3351			2.07893
$359$		−	4.49768i		−	0.237378i	−0.992931	−	0.118689i	$-0.962131\pi$
$359$		−	4.49768i		−	0.237378i	0.992931	−	0.118689i	$-0.0378692\pi$
$360$	9.79311	+	15.6661i	0.516142	+	0.825674i
$361$	−11.8022			−0.621169
$362$			61.9460i			3.25581i
$363$	−3.76850	+	10.3343i	−0.197795	+	0.542412i
$364$	7.10286	−	9.26063i	0.372291	−	0.485389i
$365$	−7.37628	+	4.61103i	−0.386092	+	0.241352i
$366$	18.5424			0.969227
$367$	−1.71236			−0.0893847			−0.0446924	−	0.999001i	$-0.514231\pi$
$367$	−1.71236			−0.0893847			−0.0446924	+	0.999001i	$0.514231\pi$
$368$			86.6055i			4.51462i
$369$	−0.607303			−0.0316149
$370$	−30.1695	+	18.8594i	−1.56844	+	0.980456i
$371$	13.2283	−	17.2469i	0.686778	−	0.895414i
$372$		−	2.81478i		−	0.145939i
$373$	−27.0598			−1.40110			−0.700552	−	0.713601i	$-0.747063\pi$
$373$	−27.0598			−1.40110			−0.700552	+	0.713601i	$0.747063\pi$
$374$	−11.1313	+	7.78921i	−0.575588	+	0.402770i
$375$	11.1185	−	1.17458i	0.574155	−	0.0606549i
$376$	−69.2006			−3.56875
$377$	1.22888			0.0632903
$378$	−5.59415	−	4.29069i	−0.287732	−	0.220689i
$379$	−21.3719			−1.09780			−0.548899	−	0.835889i	$-0.684953\pi$
$379$	−21.3719			−1.09780			−0.548899	+	0.835889i	$0.684953\pi$
$380$	−16.2197	−	25.9467i	−0.832054	−	1.33104i
$381$	16.1339			0.826564
$382$	−42.3602			−2.16734
$383$	−28.3248			−1.44733			−0.723665	−	0.690152i	$-0.757544\pi$
$383$	−28.3248			−1.44733			−0.723665	+	0.690152i	$0.757544\pi$
$384$	−13.3359			−0.680545
$385$	17.0768	−	9.66346i	0.870315	−	0.492495i
$386$	22.1777			1.12881
$387$	−0.823316			−0.0418515
$388$	−93.8119			−4.76258
$389$	15.0506			0.763095			0.381547	−	0.924349i	$-0.375391\pi$
$389$	15.0506			0.763095			0.381547	+	0.924349i	$0.375391\pi$
$390$	4.36954	−	2.73147i	0.221260	−	0.138313i
$391$	11.2679			0.569842
$392$	−14.9925	−	55.8593i	−0.757235	−	2.82132i
$393$	7.98104			0.402590
$394$	35.2602			1.77638
$395$	16.9611	−	10.6026i	0.853405	−	0.533477i
$396$	9.69896	+	13.8605i	0.487391	+	0.696517i
$397$	1.61424			0.0810162			0.0405081	−	0.999179i	$-0.487102\pi$
$397$	1.61424			0.0810162			0.0405081	+	0.999179i	$0.487102\pi$
$398$		−	10.2173i		−	0.512146i
$399$	5.63229	+	4.31994i	0.281967	+	0.216267i
$400$	−25.8788	+	53.1071i	−1.29394	+	2.65535i
$401$	11.4134			0.569956			0.284978	−	0.958534i	$-0.408014\pi$
$401$	11.4134			0.569956			0.284978	+	0.958534i	$0.408014\pi$
$402$			20.7432i			1.03458i
$403$	−0.477251			−0.0237736
$404$	90.4705			4.50108
$405$	−1.18527	−	1.89608i	−0.0588966	−	0.0942171i
$406$	6.09685	−	7.94901i	0.302582	−	0.394503i
$407$	−16.2261	+	11.3543i	−0.804300	+	0.562813i
$408$			12.7013i			0.628807i
$409$	−39.2972			−1.94312			−0.971560	−	0.236794i	$-0.923903\pi$
$409$	−39.2972			−1.94312			−0.971560	+	0.236794i	$0.923903\pi$
$410$	−1.91810	−	3.06840i	−0.0947284	−	0.151537i
$411$			13.3208i			0.657067i
$412$	79.4276			3.91312
$413$	−23.1706	+	30.2096i	−1.14015	+	1.48652i
$414$		−	19.5320i		−	0.959947i
$415$	−24.9221	+	15.5792i	−1.22338	+	0.764754i
$416$			12.9376i			0.634320i
$417$	5.61484			0.274960
$418$	−13.5940	−	19.4268i	−0.664905	−	0.950197i
$419$			4.32026i			0.211059i	0.994416	+	0.105529i	$0.0336537\pi$
$419$			4.32026i			0.211059i	−0.994416	+	0.105529i	$0.966346\pi$
$420$	2.88063	−	30.0381i	0.140560	−	1.46571i
$421$	−5.64413			−0.275078			−0.137539	−	0.990496i	$-0.543919\pi$
$421$	−5.64413			−0.275078			−0.137539	+	0.990496i	$0.543919\pi$
$422$		−	46.2482i		−	2.25133i
$423$	8.37543			0.407227
$424$			67.8779i			3.29644i
$425$	6.90956	+	3.36698i	0.335163	+	0.163323i
$426$	11.6890			0.566334
$427$	−14.6084	−	11.2046i	−0.706949	−	0.542226i
$428$	83.7007			4.04582
$429$	2.35008	−	1.64448i	0.113463	−	0.0793962i
$430$	−2.60036	−	4.15980i	−0.125400	−	0.200604i
$431$		−	40.0098i		−	1.92720i	−0.267344	−	0.963601i	$-0.586146\pi$
$431$		−	40.0098i		−	1.92720i	0.267344	−	0.963601i	$-0.413854\pi$
$432$	11.8154			0.568467
$433$	8.18707			0.393445			0.196723	−	0.980459i	$-0.436970\pi$
$433$	8.18707			0.393445			0.196723	+	0.980459i	$0.436970\pi$
$434$	−2.36780	+	3.08711i	−0.113658	+	0.148186i
$435$	2.69424	−	1.68421i	0.129179	−	0.0807518i
$436$			58.4442i			2.79897i
$437$			19.6652i			0.940713i
$438$			10.3664i			0.495327i
$439$	−16.4327			−0.784289			−0.392144	−	0.919904i	$-0.628267\pi$
$439$	−16.4327			−0.784289			−0.392144	+	0.919904i	$0.628267\pi$
$440$	−23.9492	+	56.4010i	−1.14173	+	2.68881i
$441$	1.81456	+	6.76072i	0.0864075	+	0.321939i
$442$	3.54261			0.168505
$443$			14.4277i			0.685482i	0.939430	+	0.342741i	$0.111355\pi$
$443$			14.4277i			0.685482i	−0.939430	+	0.342741i	$0.888645\pi$
$444$			30.4571i			1.44543i
$445$	−14.2478	+	8.90652i	−0.675410	+	0.422210i
$446$	−23.4236			−1.10914
$447$			6.63536i			0.313842i
$448$	34.0783	+	26.1379i	1.61005	+	1.23490i
$449$	1.50128			0.0708500			0.0354250	−	0.999372i	$-0.488722\pi$
$449$	1.50128			0.0708500			0.0354250	+	0.999372i	$0.488722\pi$
$450$	5.83640	−	11.9772i	0.275131	−	0.564610i
$451$	−1.15479	−	1.65028i	−0.0543771	−	0.0777088i
$452$			19.7869i			0.930698i
$453$		−	16.7964i		−	0.789164i
$454$		−	43.2983i		−	2.03209i
$455$	−5.09302	−	0.488417i	−0.238764	−	0.0228973i
$456$	−22.1668			−1.03805
$457$	−19.1770			−0.897061			−0.448531	−	0.893767i	$-0.648053\pi$
$457$	−19.1770			−0.897061			−0.448531	+	0.893767i	$0.648053\pi$
$458$			65.4458i			3.05808i
$459$		−	1.53725i		−	0.0717527i
$460$	70.8894	−	44.3141i	3.30524	−	2.06616i
$461$	−17.1758			−0.799956			−0.399978	−	0.916525i	$-0.630982\pi$
$461$	−17.1758			−0.799956			−0.399978	+	0.916525i	$0.630982\pi$
$462$	1.02215	−	23.3603i	0.0475548	−	1.08682i
$463$		−	23.7081i		−	1.10181i	−0.834568	−	0.550905i	$-0.814283\pi$
$463$		−	23.7081i		−	1.10181i	0.834568	−	0.550905i	$-0.185717\pi$
$464$			16.7890i			0.779412i
$465$	−1.04635	+	0.654088i	−0.0485231	+	0.0303326i
$466$	45.9466			2.12843
$467$	−21.4893			−0.994408			−0.497204	−	0.867634i	$-0.665640\pi$
$467$	−21.4893			−0.994408			−0.497204	+	0.867634i	$0.665640\pi$
$468$		−	4.41118i		−	0.203907i
$469$	12.5344	−	16.3423i	0.578787	−	0.754616i
$470$	26.4529	+	42.3169i	1.22018	+	1.95193i
$471$	6.52197			0.300517
$472$		−	118.895i		−	5.47257i
$473$	−1.56555	−	2.23728i	−0.0719838	−	0.102870i
$474$		−	23.8367i		−	1.09485i
$475$	−5.87619	+	12.0588i	−0.269618	+	0.553297i
$476$	12.6255	−	16.4610i	0.578689	−	0.754488i
$477$		−	8.21534i		−	0.376155i
$478$		−	6.95106i		−	0.317934i
$479$	8.33633			0.380897			0.190448	−	0.981697i	$-0.439006\pi$
$479$	8.33633			0.380897			0.190448	+	0.981697i	$0.439006\pi$
$480$	17.7314	+	28.3651i	0.809326	+	1.29468i
$481$	5.16406			0.235461
$482$	2.72047			0.123914
$483$	−11.8026	+	15.3880i	−0.537035	+	0.700180i
$484$	−19.2218	+	52.7119i	−0.873719	+	2.39599i
$485$	21.7997	+	34.8730i	0.989872	+	1.58350i
$486$	−2.66471			−0.120873
$487$			6.05352i			0.274311i	0.990550	+	0.137156i	$0.0437961\pi$
$487$			6.05352i			0.274311i	−0.990550	+	0.137156i	$0.956204\pi$
$488$	57.4936			2.60261
$489$		−	3.51503i		−	0.158955i
$490$	−28.4275	+	30.5211i	−1.28422	+	1.37880i
$491$		−	25.3715i		−	1.14500i	−0.819905	−	0.572500i	$-0.805974\pi$
$491$		−	25.3715i		−	1.14500i	0.819905	−	0.572500i	$-0.194026\pi$
$492$	−3.09764			−0.139652
$493$	2.18436			0.0983785
$494$			6.18270i			0.278173i
$495$	2.89860	−	6.82628i	0.130282	−	0.306818i
$496$		−	6.52027i		−	0.292769i
$497$	−9.20902	−	7.06327i	−0.413081	−	0.316831i
$498$			35.0249i			1.56950i
$499$	31.5146			1.41079			0.705394	−	0.708815i	$-0.250770\pi$
$499$	31.5146			1.41079			0.705394	+	0.708815i	$0.250770\pi$
$500$	56.7115	−	5.99111i	2.53621	−	0.267931i
$501$			16.2402i			0.725560i
$502$			42.5508i			1.89913i
$503$			19.5773i			0.872907i	0.899727	+	0.436454i	$0.143766\pi$
$503$			19.5773i			0.872907i	−0.899727	+	0.436454i	$0.856234\pi$
$504$	−17.3455	−	13.3039i	−0.772632	−	0.592605i
$505$	−21.0232	−	33.6309i	−0.935520	−	1.49656i
$506$	53.0763	−	37.1404i	2.35953	−	1.65109i
$507$	12.2521			0.544134
$508$	82.2934			3.65118
$509$		−	24.6470i		−	1.09246i	−0.837635	−	0.546230i	$-0.816063\pi$
$509$		−	24.6470i		−	1.09246i	0.837635	−	0.546230i	$-0.183937\pi$
$510$	7.76697	−	4.85525i	0.343927	−	0.214994i
$511$	6.26409	−	8.16705i	0.277107	−	0.361289i
$512$	18.4893			0.817117
$513$	2.68287			0.118452
$514$	64.1873			2.83118
$515$	−18.4571	−	29.5259i	−0.813317	−	1.30107i
$516$	−4.19945			−0.184870
$517$	15.9260	+	22.7594i	0.700424	+	1.00096i
$518$	25.6206	−	33.4038i	1.12570	−	1.46768i
$519$			9.54156i			0.418828i
$520$	13.5484	−	8.46934i	0.594138	−	0.371405i
$521$		−	7.65022i		−	0.335162i	−0.985858	−	0.167581i	$-0.946404\pi$
$521$		−	7.65022i		−	0.335162i	0.985858	−	0.167581i	$-0.0535956\pi$
$522$		−	3.78641i		−	0.165727i
$523$		−	22.3884i		−	0.978978i	−0.872010	−	0.489489i	$-0.837183\pi$
$523$		−	22.3884i		−	0.978978i	0.872010	−	0.489489i	$-0.162817\pi$
$524$	40.7085			1.77836
$525$	−11.8355	+	5.90931i	−0.516545	+	0.257904i
$526$	−49.1139			−2.14147
$527$	−0.848326			−0.0369537
$528$	22.4671	+	32.1071i	0.977754	+	1.39728i
$529$	−30.7275			−1.33598
$530$	41.5080	−	25.9473i	1.80299	−	1.12708i
$531$			14.3900i			0.624471i
$532$	28.7284	+	22.0345i	1.24553	+	0.955317i
$533$			0.525212i			0.0227494i
$534$			20.0235i			0.866501i
$535$	−19.4501	−	31.1143i	−0.840899	−	1.34519i
$536$			64.3176i			2.77810i
$537$	−14.7615			−0.637007
$538$		−	27.4403i		−	1.18304i
$539$	−14.9212	+	17.7865i	−0.642700	+	0.766118i
$540$	−6.04566	−	9.67127i	−0.260164	−	0.416185i
$541$			18.5873i			0.799129i	0.916705	+	0.399565i	$0.130839\pi$
$541$			18.5873i			0.799129i	−0.916705	+	0.399565i	$0.869161\pi$
$542$	62.9042			2.70197
$543$		−	23.2469i		−	0.997618i
$544$			22.9970i			0.985988i
$545$	21.7257	−	13.5811i	0.930625	−	0.581748i
$546$	−3.71070	+	4.83798i	−0.158803	+	0.207046i
$547$	3.02733			0.129439			0.0647197	−	0.997903i	$-0.479385\pi$
$547$	3.02733			0.129439			0.0647197	+	0.997903i	$0.479385\pi$
$548$			67.9448i			2.90246i
$549$	−6.95852			−0.296982
$550$	43.6447	−	6.91493i	1.86102	−	0.294853i
$551$			3.81222i			0.162406i
$552$		−	60.5621i		−	2.57769i
$553$	−14.4037	+	18.7794i	−0.612508	+	0.798581i
$554$	−69.9630			−2.97244
$555$	11.3219	−	7.07750i	0.480588	−	0.300423i
$556$	28.6394			1.21458
$557$	37.3665			1.58327			0.791634	−	0.610996i	$-0.209231\pi$
$557$	37.3665			1.58327			0.791634	+	0.610996i	$0.209231\pi$
$558$			1.47051i			0.0622516i
$559$			0.712025i			0.0301155i
$560$	6.67281	−	69.5814i	0.281978	−	2.94035i
$561$	4.17732	−	2.92310i	0.176367	−	0.123414i
$562$			84.4791i			3.56354i
$563$		−	3.28145i		−	0.138297i	−0.997606	−	0.0691483i	$-0.977972\pi$
$563$		−	3.28145i		−	0.138297i	0.997606	−	0.0691483i	$-0.0220282\pi$
$564$	42.7202			1.79884
$565$	7.35545	−	4.59801i	0.309446	−	0.193440i
$566$			19.3639i			0.813923i
$567$	2.09935	+	1.61019i	0.0881645	+	0.0676217i
$568$	36.2436			1.52075
$569$			23.1895i			0.972154i	0.873916	+	0.486077i	$0.161573\pi$
$569$			23.1895i			0.972154i	−0.873916	+	0.486077i	$0.838427\pi$
$570$	8.47358	+	13.5552i	0.354919	+	0.567765i
$571$			18.0124i			0.753794i	0.926255	+	0.376897i	$0.123009\pi$
$571$			18.0124i			0.753794i	−0.926255	+	0.376897i	$0.876991\pi$
$572$	11.9869	−	8.38792i	0.501199	−	0.350717i
$573$	15.8968			0.664097
$574$	3.39735	+	2.60575i	0.141802	+	0.108762i
$575$	−32.9461	−	16.0544i	−1.37395	−	0.669515i
$576$	16.2328			0.676365
$577$	−26.7730			−1.11458			−0.557288	−	0.830319i	$-0.688158\pi$
$577$	−26.7730			−1.11458			−0.557288	+	0.830319i	$0.688158\pi$
$578$	−39.0029			−1.62231
$579$	−8.32276			−0.345882
$580$	13.7424	−	8.59058i	0.570621	−	0.356704i
$581$	21.1644	−	27.5939i	0.878047	−	1.14479i
$582$	49.0096			2.03151
$583$	22.3243	−	15.6216i	0.924580	−	0.646979i
$584$			32.1427i			1.33008i
$585$	−1.63978	+	1.02505i	−0.0677967	+	0.0423808i
$586$			83.7721i			3.46059i
$587$	−40.2952			−1.66316			−0.831581	−	0.555403i	$-0.812564\pi$
$587$	−40.2952			−1.66316			−0.831581	+	0.555403i	$0.812564\pi$
$588$	9.25543	+	34.4841i	0.381688	+	1.42210i
$589$		−	1.48053i		−	0.0610042i
$590$	−72.7054	+	45.4493i	−2.99323	+	1.87112i
$591$	−13.2323			−0.544304
$592$			70.5520i			2.89967i
$593$		−	29.8747i		−	1.22681i	−0.789769	−	0.613404i	$-0.789800\pi$
$593$		−	29.8747i		−	1.22681i	0.789769	−	0.613404i	$-0.210200\pi$
$594$	−5.06697	−	7.24106i	−0.207900	−	0.297104i
$595$	−9.05297	−	0.868173i	−0.371135	−	0.0355916i
$596$			33.8447i			1.38633i
$597$			3.83430i			0.156928i
$598$	−16.8918			−0.690758
$599$	5.01487			0.204902			0.102451	−	0.994738i	$-0.467332\pi$
$599$	5.01487			0.204902			0.102451	+	0.994738i	$0.467332\pi$
$600$	18.0967	−	37.1371i	0.738794	−	1.51612i
$601$	−8.64771			−0.352748			−0.176374	−	0.984323i	$-0.556437\pi$
$601$	−8.64771			−0.352748			−0.176374	+	0.984323i	$0.556437\pi$
$602$	4.60575	+	3.53259i	0.187717	+	0.143978i
$603$		−	7.78444i		−	0.317007i
$604$		−	85.6727i		−	3.48597i
$605$	24.0614	−	5.10360i	0.978237	−	0.207491i
$606$	−47.2640			−1.91997
$607$			48.8060i			1.98098i	0.137601	+	0.990488i	$0.456061\pi$
$607$			48.8060i			1.98098i	−0.137601	+	0.990488i	$0.543939\pi$
$608$	−40.1352			−1.62770
$609$	−2.28800	+	2.98307i	−0.0927146	+	0.120880i
$610$	−21.9778	−	35.1579i	−0.889854	−	1.42350i
$611$		−	7.24329i		−	0.293032i
$612$		−	7.84099i		−	0.316953i
$613$	18.4910			0.746846			0.373423	−	0.927661i	$-0.378184\pi$
$613$	18.4910			0.746846			0.373423	+	0.927661i	$0.378184\pi$
$614$			36.8255i			1.48616i
$615$	0.719819	+	1.15150i	0.0290259	+	0.0464328i
$616$	3.16934	−	72.4324i	0.127696	−	2.91838i
$617$		−	4.90065i		−	0.197293i	−0.995123	−	0.0986465i	$-0.968549\pi$
$617$		−	4.90065i		−	0.197293i	0.995123	−	0.0986465i	$-0.0314513\pi$
$618$	−41.4949			−1.66917
$619$			22.3396i			0.897902i	0.893556	+	0.448951i	$0.148202\pi$
$619$			22.3396i			0.897902i	−0.893556	+	0.448951i	$0.851798\pi$
$620$	−5.33705	+	3.33628i	−0.214341	+	0.133988i
$621$			7.32990i			0.294139i
$622$			12.1824i			0.488470i
$623$	12.0995	−	15.7752i	0.484757	−	0.632021i
$624$		−	10.2182i		−	0.409057i
$625$	−15.4055	−	19.6894i	−0.616220	−	0.787574i
$626$	−70.3961			−2.81359
$627$	5.10151	+	7.29042i	0.203735	+	0.291151i
$628$	33.2663			1.32747
$629$	9.17924			0.366000
$630$	−1.50491	+	15.6926i	−0.0599571	+	0.625209i
$631$	−14.9662			−0.595796			−0.297898	−	0.954598i	$-0.596286\pi$
$631$	−14.9662			−0.595796			−0.297898	+	0.954598i	$0.596286\pi$
$632$		−	73.9093i		−	2.93995i
$633$			17.3558i			0.689832i
$634$		−	21.0098i		−	0.834404i
$635$	−19.1230	−	30.5912i	−0.758874	−	1.21397i
$636$		−	41.9036i		−	1.66159i
$637$	5.84685	−	1.56928i	0.231661	−	0.0621771i
$638$	10.2892	−	7.19991i	0.407353	−	0.285047i
$639$	−4.38660			−0.173531
$640$	15.8067	+	25.2860i	0.624813	+	0.999516i
$641$	−13.6017			−0.537233			−0.268617	−	0.963247i	$-0.586566\pi$
$641$	−13.6017			−0.537233			−0.268617	+	0.963247i	$0.586566\pi$
$642$	−43.7273			−1.72578
$643$	−19.3513			−0.763140			−0.381570	−	0.924340i	$-0.624616\pi$
$643$	−19.3513			−0.763140			−0.381570	+	0.924340i	$0.624616\pi$
$644$	−60.2008	+	78.4891i	−2.37224	+	3.09290i
$645$	0.975853	+	1.56107i	0.0384242	+	0.0614673i
$646$			10.9899i			0.432392i
$647$	−36.1077			−1.41954			−0.709770	−	0.704434i	$-0.751201\pi$
$647$	−36.1077			−1.41954			−0.709770	+	0.704434i	$0.751201\pi$
$648$	−8.26233			−0.324575
$649$	−39.1033	+	27.3627i	−1.53494	+	1.07408i
$650$	−10.3582	−	5.04748i	−0.406281	−	0.197978i
$651$	0.888579	−	1.15852i	0.0348262	−	0.0454060i
$652$		−	17.9289i		−	0.702151i
$653$		−	33.8487i		−	1.32460i	−0.749238	−	0.662301i	$-0.769580\pi$
$653$		−	33.8487i		−	1.32460i	0.749238	−	0.662301i	$-0.230420\pi$
$654$		−	30.5327i		−	1.19392i
$655$	−9.45970	−	15.1327i	−0.369621	−	0.591284i
$656$	−7.17551			−0.280156
$657$		−	3.89027i		−	0.151774i
$658$	−46.8534	−	35.9364i	−1.82654	−	1.40095i
$659$		−	29.3891i		−	1.14484i	−0.819962	−	0.572418i	$-0.806005\pi$
$659$		−	29.3891i		−	1.14484i	0.819962	−	0.572418i	$-0.193995\pi$
$660$	14.7848	−	34.8185i	0.575496	−	1.35531i
$661$		−	16.7396i		−	0.651096i	−0.945526	−	0.325548i	$-0.894451\pi$
$661$		−	16.7396i		−	0.651096i	0.945526	−	0.325548i	$-0.105549\pi$
$662$	13.8816			0.539525
$663$	−1.32946			−0.0516318
$664$			108.600i			4.21450i
$665$	1.51517	−	15.7996i	0.0587558	−	0.612682i
$666$		−	15.9115i		−	0.616558i
$667$	−10.4154			−0.403287
$668$			82.8359i			3.20502i
$669$	8.79032			0.339854
$670$	39.3309	−	24.5864i	1.51949	−	0.949854i
$671$	−13.2317	−	18.9091i	−0.510805	−	0.729976i
$672$	−31.4059	−	24.0882i	−1.21151	−	0.929222i
$673$	−15.6776			−0.604327			−0.302163	−	0.953256i	$-0.597709\pi$
$673$	−15.6776			−0.604327			−0.302163	+	0.953256i	$0.597709\pi$
$674$	−2.18578			−0.0841929
$675$	−2.19026	+	4.49475i	−0.0843032	+	0.173003i
$676$	62.4936			2.40360
$677$			16.2016i			0.622679i	0.950299	+	0.311340i	$0.100778\pi$
$677$			16.2016i			0.622679i	−0.950299	+	0.311340i	$0.899222\pi$
$678$		−	10.3372i		−	0.396996i
$679$	−38.6116	−	29.6149i	−1.48178	−	1.13651i
$680$	24.0827	−	15.0545i	0.923529	−	0.577312i
$681$			16.2488i			0.622656i
$682$	−3.99595	+	2.79619i	−0.153013	+	0.107072i
$683$			40.3376i			1.54347i	0.635942	+	0.771737i	$0.280612\pi$
$683$			40.3376i			1.54347i	−0.635942	+	0.771737i	$0.719388\pi$
$684$	13.6844			0.523236
$685$	25.2574	−	15.7888i	0.965034	−	0.603258i
$686$	18.8572	−	45.6062i	0.719973	−	1.74125i
$687$		−	24.5602i		−	0.937032i
$688$	−9.72778			−0.370868
$689$	−7.10485			−0.270673
$690$	−37.0343	+	23.1508i	−1.40987	+	0.881334i
$691$			19.3016i			0.734268i	0.930168	+	0.367134i	$0.119661\pi$
$691$			19.3016i			0.734268i	−0.930168	+	0.367134i	$0.880339\pi$
$692$			48.6682i			1.85009i
$693$	−0.383589	+	8.76658i	−0.0145713	+	0.333015i
$694$	25.6963			0.975419
$695$	−6.65512	−	10.6462i	−0.252443	−	0.403834i
$696$		−	11.7404i		−	0.445017i
$697$			0.933577i			0.0353617i
$698$	−18.7570			−0.709963
$699$	−17.2426			−0.652177
$700$	−60.3690	+	30.1414i	−2.28173	+	1.13924i
$701$		−	15.8130i		−	0.597250i	−0.954370	−	0.298625i	$-0.903472\pi$
$701$		−	15.8130i		−	0.597250i	0.954370	−	0.298625i	$-0.0965280\pi$
$702$			2.30451i			0.0869781i
$703$			16.0200i			0.604204i
$704$	30.8668	+	44.1109i	1.16334	+	1.66249i
$705$	−9.92716	−	15.8805i	−0.373878	−	0.598094i
$706$	28.8759			1.08676
$707$	37.2363	+	28.5600i	1.40041	+	1.07411i
$708$			73.3983i			2.75848i
$709$	17.8940			0.672025			0.336012	−	0.941858i	$-0.390922\pi$
$709$	17.8940			0.672025			0.336012	+	0.941858i	$0.390922\pi$
$710$	−13.8546	−	22.1633i	−0.519955	−	0.831774i
$711$			8.94533i			0.335476i
$712$			62.0859i			2.32677i
$713$	4.04498			0.151486
$714$	−6.59587	+	8.59962i	−0.246844	+	0.321833i
$715$	−5.90355	−	2.50679i	−0.220780	−	0.0937486i
$716$	−75.2935			−2.81385
$717$			2.60857i			0.0974187i
$718$			11.9850i			0.447276i
$719$		−	4.73442i		−	0.176564i	−0.996096	−	0.0882821i	$-0.971862\pi$
$719$		−	4.73442i		−	0.176564i	0.996096	−	0.0882821i	$-0.0281377\pi$
$720$	−14.0044	−	22.4029i	−0.521914	−	0.834908i
$721$	32.6912	+	25.0740i	1.21748	+	0.933805i
$722$	31.4494			1.17043
$723$	−1.02093			−0.0379687
$724$		−	118.574i		−	4.40678i
$725$	−6.38681	−	3.11225i	−0.237200	−	0.115586i
$726$	10.0419	−	27.5380i	0.372691	−	1.02203i
$727$	−3.40475			−0.126275			−0.0631377	−	0.998005i	$-0.520111\pi$
$727$	−3.40475			−0.126275			−0.0631377	+	0.998005i	$0.520111\pi$
$728$	−11.5056	+	15.0009i	−0.426426	+	0.555970i
$729$	1.00000			0.0370370
$730$	19.6556	−	12.2870i	0.727487	−	0.454764i
$731$			1.26564i			0.0468115i
$732$	−35.4930			−1.31186
$733$			51.5861i			1.90537i	0.303953	+	0.952687i	$0.401694\pi$
$733$			51.5861i			1.90537i	−0.303953	+	0.952687i	$0.598306\pi$
$734$	4.56295			0.168421
$735$	10.6681	−	11.4538i	0.393501	−	0.422481i
$736$		−	109.654i		−	4.04190i
$737$	21.1534	−	14.8022i	0.779196	−	0.545246i
$738$	1.61828			0.0595698
$739$			2.40223i			0.0883674i	0.999023	+	0.0441837i	$0.0140687\pi$
$739$			2.40223i			0.0883674i	−0.999023	+	0.0441837i	$0.985931\pi$
$740$	57.7491	−	36.0999i	2.12290	−	1.32706i
$741$		−	2.32022i		−	0.0852353i
$742$	−35.2495	+	45.9579i	−1.29405	+	1.68717i
$743$	−20.2751			−0.743823			−0.371911	−	0.928268i	$-0.621297\pi$
$743$	−20.2751			−0.743823			−0.371911	+	0.928268i	$0.621297\pi$
$744$			4.55954i			0.167161i
$745$	12.5812	−	7.86470i	0.460939	−	0.288140i
$746$	72.1064			2.64000
$747$		−	13.1440i		−	0.480914i
$748$	21.3071	−	14.9097i	0.779064	−	0.545154i
$749$	34.4499	+	26.4229i	1.25877	+	0.965473i
$750$	−29.6274	+	3.12990i	−1.08184	+	0.114288i
$751$	−25.0938			−0.915685			−0.457843	−	0.889033i	$-0.651378\pi$
$751$	−25.0938			−0.915685			−0.457843	+	0.889033i	$0.651378\pi$
$752$	98.9588			3.60865
$753$		−	15.9683i		−	0.581917i
$754$	−3.27459			−0.119254
$755$	−31.8474	+	19.9083i	−1.15904	+	0.724537i
$756$	10.7081	+	8.21304i	0.389449	+	0.298705i
$757$		−	38.8462i		−	1.41189i	−0.708268	−	0.705944i	$-0.750523\pi$
$757$		−	38.8462i		−	1.41189i	0.708268	−	0.705944i	$-0.249477\pi$
$758$	56.9497			2.06851
$759$	−19.9183	+	13.9379i	−0.722987	+	0.505914i
$760$	26.2736	+	42.0300i	0.953045	+	1.52459i
$761$	−46.7951			−1.69632			−0.848161	−	0.529738i	$-0.822290\pi$
$761$	−46.7951			−1.69632			−0.848161	+	0.529738i	$0.822290\pi$
$762$	−42.9920			−1.55744
$763$	−18.4499	+	24.0548i	−0.667930	+	0.870841i
$764$	81.0839			2.93351
$765$	−2.91476	+	1.82206i	−0.105383	+	0.0658767i
$766$	75.4772			2.72710
$767$	12.4448			0.449357
$768$	3.07071			0.110805
$769$	1.96503			0.0708606			0.0354303	−	0.999372i	$-0.488720\pi$
$769$	1.96503			0.0708606			0.0354303	+	0.999372i	$0.488720\pi$
$770$	−45.5047	+	25.7503i	−1.63987	+	0.927975i
$771$	−24.0879			−0.867506
$772$	−42.4515			−1.52786
$773$	12.5159			0.450166			0.225083	−	0.974340i	$-0.427735\pi$
$773$	12.5159			0.450166			0.225083	+	0.974340i	$0.427735\pi$
$774$	2.19389			0.0788579
$775$	2.48041	+	1.20869i	0.0890989	+	0.0434174i
$776$	151.962			5.45511
$777$	−9.61479	+	12.5357i	−0.344929	+	0.449714i
$778$	−40.1054			−1.43785
$779$	−1.62931			−0.0583762
$780$	−8.36397	+	5.22845i	−0.299478	+	0.187209i
$781$	−8.34118	−	11.9201i	−0.298471	−	0.426536i
$782$	−30.0256			−1.07371
$783$			1.42095i			0.0507806i
$784$	21.4397	+	79.8804i	0.765703	+	2.85287i
$785$	−7.73031	−	12.3662i	−0.275907	−	0.441369i
$786$	−21.2671			−0.758573
$787$			22.0607i			0.786379i	0.919457	+	0.393190i	$0.128628\pi$
$787$			22.0607i			0.786379i	−0.919457	+	0.393190i	$0.871372\pi$
$788$	−67.4934			−2.40435
$789$	18.4313			0.656170
$790$	−45.1963	+	28.2529i	−1.60801	+	1.00519i
$791$	−6.24640	+	8.14399i	−0.222096	+	0.289567i
$792$	−15.7109	−	22.4520i	−0.558264	−	0.797798i
$793$			6.01791i			0.213702i
$794$	−4.30146			−0.152653
$795$	−15.5770	+	9.73741i	−0.552458	+	0.345350i
$796$			19.5575i			0.693195i
$797$	30.0551			1.06461			0.532303	−	0.846554i	$-0.321327\pi$
$797$	30.0551			1.06461			0.532303	+	0.846554i	$0.321327\pi$
$798$	−15.0084	−	11.5114i	−0.531291	−	0.407498i
$799$		−	12.8751i		−	0.455490i
$800$	32.7659	−	67.2406i	1.15845	−	2.37731i
$801$		−	7.51433i		−	0.265506i
$802$	−30.4132			−1.07393
$803$	10.5714	−	7.39740i	0.373057	−	0.261049i
$804$		−	39.7057i		−	1.40031i
$805$	43.1662	+	4.13961i	1.52141	+	0.145902i
$806$	1.27173			0.0447949
$807$			10.2977i			0.362496i
$808$	−146.549			−5.15559
$809$			33.2719i			1.16978i	0.811114	+	0.584888i	$0.198862\pi$
$809$			33.2719i			1.16978i	−0.811114	+	0.584888i	$0.801138\pi$
$810$	3.15840	+	5.05250i	0.110975	+	0.177527i
$811$	7.58505			0.266347			0.133174	−	0.991093i	$-0.457483\pi$
$811$	7.58505			0.266347			0.133174	+	0.991093i	$0.457483\pi$
$812$	−11.6703	+	15.2156i	−0.409548	+	0.533964i
$813$	−23.6065			−0.827915
$814$	43.2379	−	30.2559i	1.51549	−	1.06047i
$815$	−6.66478	+	4.16626i	−0.233457	+	0.145938i
$816$		−	18.1632i		−	0.635839i
$817$	−2.20885			−0.0772778
$818$	104.715			3.66129
$819$	1.39254	−	1.81558i	0.0486592	−	0.0634414i
$820$	3.67155	+	5.87339i	0.128216	+	0.205108i
$821$		−	9.21308i		−	0.321539i	−0.986992	−	0.160769i	$-0.948602\pi$
$821$		−	9.21308i		−	0.321539i	0.986992	−	0.160769i	$-0.0513976\pi$
$822$		−	35.4960i		−	1.23807i
$823$		−	31.0541i		−	1.08248i	−0.840869	−	0.541239i	$-0.817955\pi$
$823$		−	31.0541i		−	1.08248i	0.840869	−	0.541239i	$-0.182045\pi$
$824$	−128.661			−4.48213
$825$	−16.3788	+	2.59501i	−0.570238	+	0.0903465i
$826$	61.7429	−	80.4997i	2.14831	−	2.80094i
$827$	−25.0716			−0.871823			−0.435912	−	0.899989i	$-0.643574\pi$
$827$	−25.0716			−0.871823			−0.435912	+	0.899989i	$0.643574\pi$
$828$			37.3873i			1.29930i
$829$		−	20.3332i		−	0.706201i	−0.935585	−	0.353101i	$-0.885127\pi$
$829$		−	20.3332i		−	0.706201i	0.935585	−	0.353101i	$-0.114873\pi$
$830$	66.4101	−	41.5140i	2.30513	−	1.44097i
$831$	26.2554			0.910791
$832$		−	14.0385i		−	0.486698i
$833$	10.3929	−	2.78943i	0.360094	−	0.0966481i
$834$	−14.9619			−0.518088
$835$	30.7928	−	19.2491i	1.06563	−	0.666142i
$836$	26.0210	+	37.1859i	0.899957	+	1.28610i
$837$		−	0.551846i		−	0.0190746i
$838$		−	11.5122i		−	0.397683i
$839$			3.91149i			0.135040i	0.997718	+	0.0675198i	$0.0215086\pi$
$839$			3.91149i			0.135040i	−0.997718	+	0.0675198i	$0.978491\pi$
$840$	−4.66621	+	48.6574i	−0.161000	+	1.67884i
$841$	26.9809			0.930376
$842$	15.0400			0.518311
$843$		−	31.7030i		−	1.09191i
$844$			88.5261i			3.04719i
$845$	−14.5220	−	23.2310i	−0.499573	−	0.799169i
$846$	−22.3180			−0.767310
$847$	−24.5517	+	15.6274i	−0.843605	+	0.536964i
$848$		−	97.0673i		−	3.33330i
$849$		−	7.26679i		−	0.249396i
$850$	−18.4119	−	8.97202i	−0.631524	−	0.307738i
$851$	−43.7683			−1.50036
$852$	−22.3745			−0.766539
$853$		−	1.00626i		−	0.0344538i	−0.999852	−	0.0172269i	$-0.994516\pi$
$853$		−	1.00626i		−	0.0344538i	0.999852	−	0.0172269i	$-0.00548377\pi$
$854$	38.9270	+	29.8568i	1.33206	+	1.02168i
$855$	−3.17993	−	5.08694i	−0.108751	−	0.173970i
$856$	−135.583			−4.63414
$857$			33.8944i			1.15781i	0.815395	+	0.578905i	$0.196520\pi$
$857$			33.8944i			1.15781i	−0.815395	+	0.578905i	$0.803480\pi$
$858$	−6.26227	+	4.38205i	−0.213790	+	0.149601i
$859$			34.4495i			1.17540i	0.809078	+	0.587701i	$0.199967\pi$
$859$			34.4495i			1.17540i	−0.809078	+	0.587701i	$0.800033\pi$
$860$	4.97749	+	7.96250i	0.169731	+	0.271519i
$861$	−1.27494	−	0.977874i	−0.0434499	−	0.0333259i
$862$			106.614i			3.63129i
$863$		−	3.22432i		−	0.109757i	−0.998493	−	0.0548785i	$-0.982523\pi$
$863$		−	3.22432i		−	0.109757i	0.998493	−	0.0548785i	$-0.0174772\pi$
$864$	−14.9598			−0.508943
$865$	18.0916	−	11.3093i	0.615133	−	0.384529i
$866$	−21.8161			−0.741342
$867$	14.6369			0.497094
$868$	4.53233	−	5.90921i	0.153837	−	0.200572i
$869$	−24.3080	+	17.0097i	−0.824593	+	0.577013i
$870$	−7.17935	+	4.48793i	−0.243403	+	0.152155i
$871$	−6.73219			−0.228112
$872$		−	94.6713i		−	3.20597i
$873$	−18.3921			−0.622479
$874$		−	52.4019i		−	1.77252i
$875$	25.2329	+	15.4370i	0.853027	+	0.521867i
$876$		−	19.8429i		−	0.670431i
$877$	−7.74745			−0.261613			−0.130806	−	0.991408i	$-0.541757\pi$
$877$	−7.74745			−0.261613			−0.130806	+	0.991408i	$0.541757\pi$
$878$	43.7882			1.47778
$879$		−	31.4376i		−	1.06037i
$880$	34.2481	−	80.6550i	1.15450	−	2.71888i
$881$			22.6712i			0.763813i	0.924201	+	0.381907i	$0.124732\pi$
$881$			22.6712i			0.763813i	−0.924201	+	0.381907i	$0.875268\pi$
$882$	−4.83526	−	18.0153i	−0.162812	−	0.606608i
$883$			8.85959i			0.298149i	0.988826	+	0.149074i	$0.0476294\pi$
$883$			8.85959i			0.298149i	−0.988826	+	0.149074i	$0.952371\pi$
$884$	−6.78110			−0.228073
$885$	27.2846	−	17.0560i	0.917161	−	0.573332i
$886$		−	38.4456i		−	1.29161i
$887$		−	50.8004i		−	1.70571i	−0.522147	−	0.852856i	$-0.674869\pi$
$887$		−	50.8004i		−	1.70571i	0.522147	−	0.852856i	$-0.325131\pi$
$888$		−	49.3361i		−	1.65561i
$889$	33.8707	+	25.9787i	1.13599	+	0.871296i
$890$	37.9662	−	23.7333i	1.27263	−	0.795541i
$891$	1.90151	+	2.71740i	0.0637031	+	0.0910362i
$892$	44.8364			1.50123
$893$	22.4702			0.751936
$894$		−	17.6813i		−	0.591350i
$895$	17.4964	+	27.9891i	0.584841	+	0.935572i
$896$	−27.9967	−	21.4734i	−0.935305	−	0.717375i
$897$	6.33910			0.211656
$898$	−4.00048			−0.133498
$899$	0.784146			0.0261527
$900$	−11.1718	+	22.9262i	−0.372392	+	0.764205i
$901$	−12.6290			−0.420734
$902$	3.07719	+	4.39752i	0.102459	+	0.146421i
$903$	−1.72843	−	1.32570i	−0.0575185	−	0.0441164i
$904$		−	32.0520i		−	1.06603i
$905$	−44.0780	+	27.5538i	−1.46520	+	0.915921i
$906$			44.7575i			1.48697i
$907$		−	34.0993i		−	1.13225i	−0.824320	−	0.566125i	$-0.808442\pi$
$907$		−	34.0993i		−	1.13225i	0.824320	−	0.566125i	$-0.191558\pi$
$908$			82.8796i			2.75046i
$909$	17.7370			0.588300
$910$	13.5714	+	1.30149i	0.449887	+	0.0431439i
$911$	13.9029			0.460622			0.230311	−	0.973117i	$-0.426026\pi$
$911$	13.9029			0.460622			0.230311	+	0.973117i	$0.426026\pi$
$912$	31.6991			1.04966
$913$	35.7175	−	24.9935i	1.18208	−	0.827164i
$914$	51.1010			1.69027
$915$	8.24773	+	13.1939i	0.272662	+	0.436178i
$916$		−	125.273i		−	4.13915i
$917$	16.7550	+	12.8510i	0.553299	+	0.424378i
$918$			4.09632i			0.135199i
$919$			31.1901i			1.02887i	0.857531	+	0.514433i	$0.171997\pi$
$919$			31.1901i			1.02887i	−0.857531	+	0.514433i	$0.828003\pi$
$920$	−114.831	+	71.7825i	−3.78586	+	2.36660i
$921$		−	13.8197i		−	0.455375i
$922$	45.7684			1.50730
$923$			3.79365i			0.124870i
$924$	−1.95656	+	44.7153i	−0.0643660	+	1.47102i
$925$	−26.8391	−	13.0785i	−0.882463	−	0.430019i
$926$			63.1752i			2.07607i
$927$	15.5720			0.511453
$928$		−	21.2571i		−	0.697800i
$929$			30.5461i			1.00218i	0.865394	+	0.501092i	$0.167068\pi$
$929$			30.5461i			1.00218i	−0.865394	+	0.501092i	$0.832932\pi$
$930$	2.78820	−	1.74295i	0.0914288	−	0.0571536i
$931$	4.86822	+	18.1381i	0.159550	+	0.594454i
$932$	−87.9488			−2.88086
$933$		−	4.57177i		−	0.149673i
$934$	57.2628			1.87370
$935$	−10.4937	−	4.45588i	−0.343181	−	0.145723i
$936$			7.14549i			0.233558i
$937$			2.87984i			0.0940802i	0.998893	+	0.0470401i	$0.0149789\pi$
$937$			2.87984i			0.0940802i	−0.998893	+	0.0470401i	$0.985021\pi$
$938$	−33.4006	+	43.5474i	−1.09057	+	1.42187i
$939$	26.4180			0.862117
$940$	−50.6350	−	81.0010i	−1.65153	−	2.64196i
$941$	26.5254			0.864702			0.432351	−	0.901705i	$-0.357684\pi$
$941$	26.5254			0.864702			0.432351	+	0.901705i	$0.357684\pi$
$942$	−17.3791			−0.566243
$943$		−	4.45147i		−	0.144960i
$944$			170.023i			5.53377i
$945$	0.564757	−	5.88906i	0.0183715	−	0.191571i
$946$	4.17172	+	5.96168i	0.135634	+	0.193831i
$947$		−	6.15057i		−	0.199867i	−0.994994	−	0.0999333i	$-0.968137\pi$
$947$		−	6.15057i		−	0.199867i	0.994994	−	0.0999333i	$-0.0318630\pi$
$948$			45.6270i			1.48190i
$949$	−3.36441			−0.109213
$950$	15.6583	−	32.1332i	0.508023	−	1.04254i
$951$			7.88446i			0.255671i
$952$	−20.4515	+	26.6645i	−0.662837	+	0.864200i
$953$	−11.6177			−0.376333			−0.188166	−	0.982137i	$-0.560254\pi$
$953$	−11.6177			−0.376333			−0.188166	+	0.982137i	$0.560254\pi$
$954$			21.8915i			0.708762i
$955$	−18.8420	−	30.1416i	−0.609712	−	0.975359i
$956$			13.3054i			0.430327i
$957$	−3.86129	+	2.70195i	−0.124818	+	0.0873418i
$958$	−22.2139			−0.717697
$959$	−21.4491	+	27.9651i	−0.692627	+	0.903039i
$960$	−19.2402	−	30.7787i	−0.620976	−	0.993377i
$961$	30.6955			0.990176
$962$	−13.7607			−0.443663
$963$	16.4098			0.528798
$964$	−5.20740			−0.167719
$965$	9.86473	+	15.7806i	0.317557	+	0.507997i
$966$	31.4503	−	41.0046i	1.01190	−	1.31930i
$967$	36.8220			1.18412			0.592058	−	0.805895i	$-0.298316\pi$
$967$	36.8220			1.18412			0.592058	+	0.805895i	$0.298316\pi$
$968$	31.1366	−	85.3857i	1.00077	−	2.74440i
$969$		−	4.12424i		−	0.132490i
$970$	−58.0897	−	92.9263i	−1.86515	−	2.98368i
$971$		−	19.0710i		−	0.612019i	−0.952029	−	0.306009i	$-0.901006\pi$
$971$		−	19.0710i		−	0.612019i	0.952029	−	0.306009i	$-0.0989939\pi$
$972$	5.10065			0.163604
$973$	11.7875	+	9.04098i	0.377891	+	0.289841i
$974$		−	16.1309i		−	0.516866i
$975$	3.88718	+	1.89420i	0.124489	+	0.0606629i
$976$	−82.2175			−2.63172
$977$		−	23.1779i		−	0.741527i	−0.928727	−	0.370764i	$-0.879096\pi$
$977$		−	23.1779i		−	0.741527i	0.928727	−	0.370764i	$-0.120904\pi$
$978$			9.36651i			0.299508i
$979$	20.4194	−	14.2886i	0.652608	−	0.456666i
$980$	54.4145	−	58.4221i	1.73821	−	1.86623i
$981$			11.4582i			0.365832i
$982$			67.6076i			2.15744i
$983$	−11.1133			−0.354459			−0.177230	−	0.984170i	$-0.556714\pi$
$983$	−11.1133			−0.354459			−0.177230	+	0.984170i	$0.556714\pi$
$984$	5.01774			0.159960
$985$	15.6839	+	25.0895i	0.499730	+	0.799419i
$986$	−5.82067			−0.185368
$987$	17.5830	+	13.4861i	0.559672	+	0.429266i
$988$		−	11.8346i		−	0.376510i
$989$		−	6.03482i		−	0.191896i
$990$	−7.72392	+	18.1900i	−0.245482	+	0.578117i
$991$	−21.0898			−0.669939			−0.334969	−	0.942229i	$-0.608726\pi$
$991$	−21.0898			−0.669939			−0.334969	+	0.942229i	$0.608726\pi$
$992$			8.25552i			0.262113i
$993$	−5.20944			−0.165317
$994$	24.5393	+	18.8215i	0.778340	+	0.596983i
$995$	7.27016	−	4.54469i	0.230479	−	0.144076i
$996$		−	67.0430i		−	2.12434i
$997$		−	32.2736i		−	1.02212i	−0.859546	−	0.511058i	$-0.829254\pi$
$997$		−	32.2736i		−	1.02212i	0.859546	−	0.511058i	$-0.170746\pi$
$998$	−83.9772			−2.65825
$999$			5.97120i			0.188921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.1	yes	48
5.4	even	2		1155.2.k.a.769.48	yes	48
7.6	odd	2		1155.2.k.a.769.2	yes	48
11.10	odd	2	inner	1155.2.k.b.769.48	yes	48
35.34	odd	2	inner	1155.2.k.b.769.47	yes	48
55.54	odd	2		1155.2.k.a.769.1	✓	48
77.76	even	2		1155.2.k.a.769.47	yes	48
385.384	even	2	inner	1155.2.k.b.769.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.1	✓	48	55.54	odd	2
1155.2.k.a.769.2	yes	48	7.6	odd	2
1155.2.k.a.769.47	yes	48	77.76	even	2
1155.2.k.a.769.48	yes	48	5.4	even	2
1155.2.k.b.769.1	yes	48	1.1	even	1	trivial
1155.2.k.b.769.2	yes	48	385.384	even	2	inner
1155.2.k.b.769.47	yes	48	35.34	odd	2	inner
1155.2.k.b.769.48	yes	48	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.66471 q^{2} +1.00000 q^{3} +5.10065 q^{4} +(-1.18527 - 1.89608i) q^{5} -2.66471 q^{6} +(2.09935 + 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.66471 q^{2} +1.00000 q^{3} +5.10065 q^{4} +(-1.18527 - 1.89608i) q^{5} -2.66471 q^{6} +(2.09935 + 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +(3.15840 + 5.05250i) q^{10} +(1.90151 + 2.71740i) q^{11} +5.10065 q^{12} -0.864827i q^{13} +(-5.59415 - 4.29069i) q^{14} +(-1.18527 - 1.89608i) q^{15} +11.8154 q^{16} -1.53725i q^{17} -2.66471 q^{18} +2.68287 q^{19} +(-6.04566 - 9.67127i) q^{20} +(2.09935 + 1.61019i) q^{21} +(-5.06697 - 7.24106i) q^{22} +7.32990i q^{23} -8.26233 q^{24} +(-2.19026 + 4.49475i) q^{25} +2.30451i q^{26} +1.00000 q^{27} +(10.7081 + 8.21304i) q^{28} +1.42095i q^{29} +(3.15840 + 5.05250i) q^{30} -0.551846i q^{31} -14.9598 q^{32} +(1.90151 + 2.71740i) q^{33} +4.09632i q^{34} +(0.564757 - 5.88906i) q^{35} +5.10065 q^{36} +5.97120i q^{37} -7.14906 q^{38} -0.864827i q^{39} +(9.79311 + 15.6661i) q^{40} -0.607303 q^{41} +(-5.59415 - 4.29069i) q^{42} -0.823316 q^{43} +(9.69896 + 13.8605i) q^{44} +(-1.18527 - 1.89608i) q^{45} -19.5320i q^{46} +8.37543 q^{47} +11.8154 q^{48} +(1.81456 + 6.76072i) q^{49} +(5.83640 - 11.9772i) q^{50} -1.53725i q^{51} -4.41118i q^{52} -8.21534i q^{53} -2.66471 q^{54} +(2.89860 - 6.82628i) q^{55} +(-17.3455 - 13.3039i) q^{56} +2.68287 q^{57} -3.78641i q^{58} +14.3900i q^{59} +(-6.04566 - 9.67127i) q^{60} -6.95852 q^{61} +1.47051i q^{62} +(2.09935 + 1.61019i) q^{63} +16.2328 q^{64} +(-1.63978 + 1.02505i) q^{65} +(-5.06697 - 7.24106i) q^{66} -7.78444i q^{67} -7.84099i q^{68} +7.32990i q^{69} +(-1.50491 + 15.6926i) q^{70} -4.38660 q^{71} -8.26233 q^{72} -3.89027i q^{73} -15.9115i q^{74} +(-2.19026 + 4.49475i) q^{75} +13.6844 q^{76} +(-0.383589 + 8.76658i) q^{77} +2.30451i q^{78} +8.94533i q^{79} +(-14.0044 - 22.4029i) q^{80} +1.00000 q^{81} +1.61828 q^{82} -13.1440i q^{83} +(10.7081 + 8.21304i) q^{84} +(-2.91476 + 1.82206i) q^{85} +2.19389 q^{86} +1.42095i q^{87} +(-15.7109 - 22.4520i) q^{88} -7.51433i q^{89} +(3.15840 + 5.05250i) q^{90} +(1.39254 - 1.81558i) q^{91} +37.3873i q^{92} -0.551846i q^{93} -22.3180 q^{94} +(-3.17993 - 5.08694i) q^{95} -14.9598 q^{96} -18.3921 q^{97} +(-4.83526 - 18.0153i) q^{98} +(1.90151 + 2.71740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more