LMFDB - Embedded newform 693.2.bu.f.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(118,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("693.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.4
Character	$\chi$	$=$	693.118
Dual form			693.2.bu.f.370.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29930 - 1.78834i) q^{2} +(-0.891932 + 2.74508i) q^{4} +(2.07229 - 2.85226i) q^{5} +(-1.48601 - 2.18901i) q^{7} +(1.86340 - 0.605454i) q^{8} +O(q^{10})$	\(q+(-1.29930 - 1.78834i) q^{2} +(-0.891932 + 2.74508i) q^{4} +(2.07229 - 2.85226i) q^{5} +(-1.48601 - 2.18901i) q^{7} +(1.86340 - 0.605454i) q^{8} -7.79336 q^{10} +(0.691907 - 3.24365i) q^{11} +(2.25356 - 1.63731i) q^{13} +(-1.98392 + 5.50168i) q^{14} +(1.16634 + 0.847394i) q^{16} +(-3.22730 - 2.34477i) q^{17} +(1.49400 + 4.59807i) q^{19} +(5.98136 + 8.23264i) q^{20} +(-6.69975 + 2.97713i) q^{22} +6.74587 q^{23} +(-2.29594 - 7.06616i) q^{25} +(-5.85612 - 1.90277i) q^{26} +(7.33445 - 2.12677i) q^{28} +(-7.53228 - 2.44739i) q^{29} +(0.0789450 + 0.108659i) q^{31} -7.10541i q^{32} +8.81808i q^{34} +(-9.32309 - 0.297783i) q^{35} +(2.17150 - 6.68319i) q^{37} +(6.28175 - 8.64608i) q^{38} +(2.13459 - 6.56958i) q^{40} +(2.16426 + 6.66091i) q^{41} +0.541053i q^{43} +(8.28696 + 4.79246i) q^{44} +(-8.76494 - 12.0639i) q^{46} +(-9.57909 + 3.11244i) q^{47} +(-2.58356 + 6.50578i) q^{49} +(-9.65358 + 13.2870i) q^{50} +(2.48452 + 7.64658i) q^{52} +(-5.89006 + 4.27938i) q^{53} +(-7.81791 - 8.69529i) q^{55} +(-4.09437 - 3.17929i) q^{56} +(5.40997 + 16.6502i) q^{58} +(5.55659 + 1.80544i) q^{59} +(-2.17611 - 1.58103i) q^{61} +(0.0917447 - 0.282361i) q^{62} +(-10.3742 + 7.53731i) q^{64} -9.82072i q^{65} +7.96771 q^{67} +(9.31512 - 6.76783i) q^{68} +(11.5810 + 17.0598i) q^{70} +(3.12305 + 2.26903i) q^{71} +(-0.723874 + 2.22786i) q^{73} +(-14.7733 + 4.80012i) q^{74} -13.9546 q^{76} +(-8.12857 + 3.30550i) q^{77} +(-0.279518 - 0.384724i) q^{79} +(4.83398 - 1.57066i) q^{80} +(9.09994 - 12.5250i) q^{82} +(4.06746 + 2.95518i) q^{83} +(-13.3758 + 4.34606i) q^{85} +(0.967586 - 0.702992i) q^{86} +(-0.674586 - 6.46313i) q^{88} -6.44482i q^{89} +(-6.93289 - 2.50002i) q^{91} +(-6.01686 + 18.5180i) q^{92} +(18.0123 + 13.0867i) q^{94} +(16.2109 + 5.26725i) q^{95} +(3.22443 + 4.43805i) q^{97} +(14.9914 - 3.83272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} + 20 q^{8}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 + 20 * q^8	$ 64 q + 12 q^{4} + 10 q^{7} + 20 q^{8} + 16 q^{11} - 12 q^{14} - 16 q^{16} - 40 q^{22} + 24 q^{23} + 44 q^{25} - 30 q^{28} + 40 q^{29} + 40 q^{35} + 32 q^{37} - 22 q^{44} - 70 q^{46} - 50 q^{49} + 64 q^{53} - 80 q^{56} + 2 q^{58} + 72 q^{64} - 8 q^{67} - 26 q^{70} - 68 q^{71} - 80 q^{74} - 90 q^{77} + 40 q^{79} - 40 q^{85} + 62 q^{86} + 140 q^{88} + 54 q^{91} - 18 q^{92} - 20 q^{95}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 + 20 * q^8 + 16 * q^11 - 12 * q^14 - 16 * q^16 - 40 * q^22 + 24 * q^23 + 44 * q^25 - 30 * q^28 + 40 * q^29 + 40 * q^35 + 32 * q^37 - 22 * q^44 - 70 * q^46 - 50 * q^49 + 64 * q^53 - 80 * q^56 + 2 * q^58 + 72 * q^64 - 8 * q^67 - 26 * q^70 - 68 * q^71 - 80 * q^74 - 90 * q^77 + 40 * q^79 - 40 * q^85 + 62 * q^86 + 140 * q^88 + 54 * q^91 - 18 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.29930	−	1.78834i	−0.918747	−	1.26455i	−0.964090	−	0.265576i	$-0.914438\pi$
$2$	−1.29930	−	1.78834i	−0.918747	−	1.26455i	0.0453426	−	0.998971i	$-0.485562\pi$
$3$		0			0
$3$		0			0
$4$	−0.891932	+	2.74508i	−0.445966	+	1.37254i
$5$	2.07229	−	2.85226i	0.926757	−	1.27557i	−0.0343544	−	0.999410i	$-0.510937\pi$
$5$	2.07229	−	2.85226i	0.926757	−	1.27557i	0.961111	−	0.276162i	$-0.0890625\pi$
$6$		0			0
$7$	−1.48601	−	2.18901i	−0.561658	−	0.827369i
$7$	−1.48601	−	2.18901i	−0.561658	−	0.827369i
$8$	1.86340	−	0.605454i	0.658810	−	0.214060i
$9$		0			0
$10$	−7.79336			−2.46448
$11$	0.691907	−	3.24365i	0.208618	−	0.977997i
$11$	0.691907	−	3.24365i	0.208618	−	0.977997i
$12$		0			0
$13$	2.25356	−	1.63731i	0.625025	−	0.454107i	−0.229648	−	0.973274i	$-0.573758\pi$
$13$	2.25356	−	1.63731i	0.625025	−	0.454107i	0.854673	+	0.519167i	$0.173758\pi$
$14$	−1.98392	+	5.50168i	−0.530225	+	1.47039i
$15$		0			0
$16$	1.16634	+	0.847394i	0.291584	+	0.211848i
$17$	−3.22730	−	2.34477i	−0.782735	−	0.568690i	0.123064	−	0.992399i	$-0.460728\pi$
$17$	−3.22730	−	2.34477i	−0.782735	−	0.568690i	−0.905799	+	0.423708i	$0.860728\pi$
$18$		0			0
$19$	1.49400	+	4.59807i	0.342748	+	1.05487i	0.962778	+	0.270292i	$0.0871202\pi$
$19$	1.49400	+	4.59807i	0.342748	+	1.05487i	−0.620030	+	0.784578i	$0.712880\pi$
$20$	5.98136	+	8.23264i	1.33747	+	1.84087i
$21$		0			0
$22$	−6.69975	+	2.97713i	−1.42839	+	0.634725i
$23$	6.74587			1.40661			0.703305	−	0.710888i	$-0.251707\pi$
$23$	6.74587			1.40661			0.703305	+	0.710888i	$0.251707\pi$
$24$		0			0
$25$	−2.29594	−	7.06616i	−0.459187	−	1.41323i
$26$	−5.85612	−	1.90277i	−1.14848	−	0.373164i
$27$		0			0
$28$	7.33445	−	2.12677i	1.38608	−	0.401922i
$29$	−7.53228	−	2.44739i	−1.39871	−	0.454468i	−0.489936	−	0.871758i	$-0.662980\pi$
$29$	−7.53228	−	2.44739i	−1.39871	−	0.454468i	−0.908773	+	0.417290i	$0.862980\pi$
$30$		0			0
$31$	0.0789450	+	0.108659i	0.0141789	+	0.0195156i	0.816048	−	0.577985i	$-0.196161\pi$
$31$	0.0789450	+	0.108659i	0.0141789	+	0.0195156i	−0.801869	+	0.597500i	$0.796161\pi$
$32$		−	7.10541i		−	1.25607i
$33$		0			0
$34$			8.81808i			1.51229i
$35$	−9.32309	−	0.297783i	−1.57589	−	0.0503345i
$36$		0			0
$37$	2.17150	−	6.68319i	0.356992	−	1.09871i	−0.597853	−	0.801606i	$-0.703979\pi$
$37$	2.17150	−	6.68319i	0.356992	−	1.09871i	0.954845	−	0.297104i	$-0.0960207\pi$
$38$	6.28175	−	8.64608i	1.01903	−	1.40258i
$39$		0			0
$40$	2.13459	−	6.56958i	0.337508	−	1.03874i
$41$	2.16426	+	6.66091i	0.338001	+	1.04026i	0.965225	+	0.261421i	$0.0841910\pi$
$41$	2.16426	+	6.66091i	0.338001	+	1.04026i	−0.627224	+	0.778839i	$0.715809\pi$
$42$		0			0
$43$			0.541053i			0.0825097i	0.999149	+	0.0412549i	$0.0131356\pi$
$43$			0.541053i			0.0825097i	−0.999149	+	0.0412549i	$0.986864\pi$
$44$	8.28696	+	4.79246i	1.24931	+	0.722490i
$45$		0			0
$46$	−8.76494	−	12.0639i	−1.29232	−	1.77873i
$47$	−9.57909	+	3.11244i	−1.39725	+	0.453995i	−0.908302	−	0.418315i	$-0.862621\pi$
$47$	−9.57909	+	3.11244i	−1.39725	+	0.453995i	−0.488952	+	0.872311i	$0.662621\pi$
$48$		0			0
$49$	−2.58356	+	6.50578i	−0.369079	+	0.929398i
$50$	−9.65358	+	13.2870i	−1.36522	+	1.87907i
$51$		0			0
$52$	2.48452	+	7.64658i	0.344541	+	1.06039i
$53$	−5.89006	+	4.27938i	−0.809062	+	0.587818i	−0.913558	−	0.406707i	$-0.866677\pi$
$53$	−5.89006	+	4.27938i	−0.809062	+	0.587818i	0.104497	+	0.994525i	$0.466677\pi$
$54$		0			0
$55$	−7.81791	−	8.69529i	−1.05417	−	1.17247i
$56$	−4.09437	−	3.17929i	−0.547133	−	0.424851i
$57$		0			0
$58$	5.40997	+	16.6502i	0.710364	+	2.18628i
$59$	5.55659	+	1.80544i	0.723406	+	0.235049i	0.647499	−	0.762066i	$-0.275815\pi$
$59$	5.55659	+	1.80544i	0.723406	+	0.235049i	0.0759067	+	0.997115i	$0.475815\pi$
$60$		0			0
$61$	−2.17611	−	1.58103i	−0.278622	−	0.202431i	0.439694	−	0.898148i	$-0.355087\pi$
$61$	−2.17611	−	1.58103i	−0.278622	−	0.202431i	−0.718316	+	0.695717i	$0.755087\pi$
$62$	0.0917447	−	0.282361i	0.0116516	−	0.0358599i
$63$		0			0
$64$	−10.3742	+	7.53731i	−1.29678	+	0.942164i
$65$		−	9.82072i		−	1.21811i
$66$		0			0
$67$	7.96771			0.973411			0.486705	−	0.873566i	$-0.338198\pi$
$67$	7.96771			0.973411			0.486705	+	0.873566i	$0.338198\pi$
$68$	9.31512	−	6.76783i	1.12962	−	0.820720i
$69$		0			0
$70$	11.5810	+	17.0598i	1.38419	+	2.03903i
$71$	3.12305	+	2.26903i	0.370638	+	0.269284i	0.757475	−	0.652864i	$-0.226433\pi$
$71$	3.12305	+	2.26903i	0.370638	+	0.269284i	−0.386838	+	0.922148i	$0.626433\pi$
$72$		0			0
$73$	−0.723874	+	2.22786i	−0.0847230	+	0.260751i	−0.984439	−	0.175724i	$-0.943773\pi$
$73$	−0.723874	+	2.22786i	−0.0847230	+	0.260751i	0.899716	+	0.436475i	$0.143773\pi$
$74$	−14.7733	+	4.80012i	−1.71736	+	0.558003i
$75$		0			0
$76$	−13.9546			−1.60071
$77$	−8.12857	+	3.30550i	−0.926337	+	0.376697i
$78$		0			0
$79$	−0.279518	−	0.384724i	−0.0314483	−	0.0432848i	0.793003	−	0.609217i	$-0.208516\pi$
$79$	−0.279518	−	0.384724i	−0.0314483	−	0.0432848i	−0.824452	+	0.565932i	$0.808516\pi$
$80$	4.83398	−	1.57066i	0.540456	−	0.175605i
$81$		0			0
$82$	9.09994	−	12.5250i	1.00492	−	1.38315i
$83$	4.06746	+	2.95518i	0.446461	+	0.324373i	0.788197	−	0.615423i	$-0.211015\pi$
$83$	4.06746	+	2.95518i	0.446461	+	0.324373i	−0.341736	+	0.939796i	$0.611015\pi$
$84$		0			0
$85$	−13.3758	+	4.34606i	−1.45081	+	0.471397i
$86$	0.967586	−	0.702992i	0.104337	−	0.0758056i
$87$		0			0
$88$	−0.674586	−	6.46313i	−0.0719111	−	0.688972i
$89$		−	6.44482i		−	0.683150i	−0.939855	−	0.341575i	$-0.889040\pi$
$89$		−	6.44482i		−	0.683150i	0.939855	−	0.341575i	$-0.110960\pi$
$90$		0			0
$91$	−6.93289	−	2.50002i	−0.726765	−	0.262073i
$92$	−6.01686	+	18.5180i	−0.627301	+	1.93063i
$93$		0			0
$94$	18.0123	+	13.0867i	1.85782	+	1.34979i
$95$	16.2109	+	5.26725i	1.66321	+	0.540408i
$96$		0			0
$97$	3.22443	+	4.43805i	0.327391	+	0.450616i	0.940706	−	0.339223i	$-0.110164\pi$
$97$	3.22443	+	4.43805i	0.327391	+	0.450616i	−0.613314	+	0.789839i	$0.710164\pi$
$98$	14.9914	−	3.83272i	1.51436	−	0.387163i
$99$		0			0
$100$	21.4450			2.14450
$101$	−15.5504	+	11.2981i	−1.54733	+	1.12420i	−0.601802	+	0.798645i	$0.705550\pi$
$101$	−15.5504	+	11.2981i	−1.54733	+	1.12420i	−0.945524	+	0.325553i	$0.894450\pi$
$102$		0			0
$103$	−5.90906	−	1.91997i	−0.582237	−	0.189180i	0.00306532	−	0.999995i	$-0.499024\pi$
$103$	−5.90906	−	1.91997i	−0.582237	−	0.189180i	−0.585303	+	0.810815i	$0.699024\pi$
$104$	3.20796	−	4.41538i	0.314566	−	0.432964i
$105$		0			0
$106$	15.3060	+	4.97321i	1.48665	+	0.483041i
$107$	6.71684	−	2.18243i	0.649341	−	0.210984i	0.0342176	−	0.999414i	$-0.489106\pi$
$107$	6.71684	−	2.18243i	0.649341	−	0.210984i	0.615124	+	0.788431i	$0.289106\pi$
$108$		0			0
$109$		−	1.00106i		−	0.0958846i	−0.998850	−	0.0479423i	$-0.984734\pi$
$109$		−	1.00106i		−	0.0958846i	0.998850	−	0.0479423i	$-0.0152664\pi$
$110$	−5.39227	+	25.2789i	−0.514133	+	2.41025i
$111$		0			0
$112$	0.121768	−	3.81236i	0.0115060	−	0.360234i
$113$	−1.91205	−	5.88470i	−0.179871	−	0.553586i	0.819951	−	0.572433i	$-0.194000\pi$
$113$	−1.91205	−	5.88470i	−0.179871	−	0.553586i	−0.999822	+	0.0188474i	$0.994000\pi$
$114$		0			0
$115$	13.9794	−	19.2410i	1.30359	−	1.79423i
$116$	13.4366	−	18.4938i	1.24755	−	1.71711i
$117$		0			0
$118$	−3.99095	−	12.2829i	−0.367397	−	1.13073i
$119$	−0.336938	+	10.5489i	−0.0308870	+	0.967021i
$120$		0			0
$121$	−10.0425	−	4.48861i	−0.912957	−	0.408055i
$122$			5.94587i			0.538313i
$123$		0			0
$124$	−0.368690	+	0.119795i	−0.0331094	+	0.0107579i
$125$	−8.14722	−	2.64719i	−0.728709	−	0.236772i
$126$		0			0
$127$	1.92576	−	2.65059i	0.170884	−	0.235202i	−0.714982	−	0.699143i	$-0.753565\pi$
$127$	1.92576	−	2.65059i	0.170884	−	0.235202i	0.885866	+	0.463941i	$0.153565\pi$
$128$	13.4433	+	4.36798i	1.18823	+	0.386078i
$129$		0			0
$130$	−17.5628	+	12.7601i	−1.54036	+	1.11914i
$131$	20.7430			1.81232			0.906161	−	0.422934i	$-0.139000\pi$
$131$	20.7430			1.81232			0.906161	+	0.422934i	$0.139000\pi$
$132$		0			0
$133$	7.84513	−	10.1032i	0.680259	−	0.876056i
$134$	−10.3525	−	14.2490i	−0.894319	−	1.23092i
$135$		0			0
$136$	−7.43339	−	2.41526i	−0.637408	−	0.207106i
$137$	2.13273	+	1.54952i	0.182211	+	0.132384i	0.675152	−	0.737679i	$-0.264078\pi$
$137$	2.13273	+	1.54952i	0.182211	+	0.132384i	−0.492941	+	0.870063i	$0.664078\pi$
$138$		0			0
$139$	3.30962	−	10.1860i	0.280719	−	0.863963i	−0.706931	−	0.707283i	$-0.749921\pi$
$139$	3.30962	−	10.1860i	0.280719	−	0.863963i	0.987649	−	0.156680i	$-0.0500793\pi$
$140$	9.13300	−	25.3271i	0.771879	−	2.14053i
$141$		0			0
$142$		−	8.53323i		−	0.716093i
$143$	−3.75160	−	8.44262i	−0.313724	−	0.706007i
$144$		0			0
$145$	−22.5897	+	16.4124i	−1.87597	+	1.36297i
$146$	4.92470	−	1.60013i	0.407571	−	0.132428i
$147$		0			0
$148$	16.4091	+	11.9219i	1.34882	+	0.979974i
$149$	6.90041	−	9.49760i	0.565303	−	0.778073i	−0.426685	−	0.904400i	$-0.640319\pi$
$149$	6.90041	−	9.49760i	0.565303	−	0.778073i	0.991989	+	0.126327i	$0.0403188\pi$
$150$		0			0
$151$	−0.914205	+	0.297043i	−0.0743970	+	0.0241730i	−0.345979	−	0.938242i	$-0.612453\pi$
$151$	−0.914205	+	0.297043i	−0.0743970	+	0.0241730i	0.271582	+	0.962415i	$0.412453\pi$
$152$	5.56784	+	7.66348i	0.451612	+	0.621590i
$153$		0			0
$154$	16.4728	+	10.2418i	1.32742	+	0.825307i
$155$	0.473520			0.0380340
$156$		0			0
$157$	0.909917	−	0.295650i	0.0726193	−	0.0235954i	−0.272482	−	0.962161i	$-0.587845\pi$
$157$	0.909917	−	0.295650i	0.0726193	−	0.0235954i	0.345101	+	0.938565i	$0.387845\pi$
$158$	−0.324838	+	0.999747i	−0.0258427	+	0.0795356i
$159$		0			0
$160$	−20.2665	−	14.7245i	−1.60221	−	1.16407i
$161$	−10.0244	−	14.7668i	−0.790035	−	1.16379i
$162$		0			0
$163$	17.4752	−	12.6965i	1.36876	−	0.994464i	0.370929	−	0.928661i	$-0.379039\pi$
$163$	17.4752	−	12.6965i	1.36876	−	0.994464i	0.997833	−	0.0658025i	$-0.0209607\pi$
$164$	−20.2151			−1.57854
$165$		0			0
$166$		−	11.1137i		−	0.862589i
$167$	−6.70719	+	4.87306i	−0.519018	+	0.377089i	−0.816234	−	0.577722i	$-0.803942\pi$
$167$	−6.70719	+	4.87306i	−0.519018	+	0.377089i	0.297216	+	0.954810i	$0.403942\pi$
$168$		0			0
$169$	−1.61946	+	4.98420i	−0.124574	+	0.383400i
$170$	25.1515	+	18.2736i	1.92903	+	1.40152i
$171$		0			0
$172$	−1.48524	−	0.482582i	−0.113248	−	0.0367965i
$173$	−6.28942	−	19.3568i	−0.478176	−	1.47167i	−0.841626	−	0.540060i	$-0.818402\pi$
$173$	−6.28942	−	19.3568i	−0.478176	−	1.47167i	0.363451	−	0.931613i	$-0.381598\pi$
$174$		0			0
$175$	−12.0561	+	15.5262i	−0.911359	+	1.17367i
$176$	3.55565	−	3.19687i	0.268017	−	0.240973i
$177$		0			0
$178$	−11.5255	+	8.37379i	−0.863875	+	0.627642i
$179$	−4.14231	−	12.7487i	−0.309611	−	0.952883i	−0.977916	−	0.208997i	$-0.932980\pi$
$179$	−4.14231	−	12.7487i	−0.309611	−	0.952883i	0.668306	−	0.743887i	$-0.267020\pi$
$180$		0			0
$181$	1.13769	−	1.56589i	0.0845635	−	0.116392i	−0.764639	−	0.644458i	$-0.777083\pi$
$181$	1.13769	−	1.56589i	0.0845635	−	0.116392i	0.849203	+	0.528067i	$0.177083\pi$
$182$	4.53706	+	15.6467i	0.336309	+	1.15981i
$183$		0			0
$184$	12.5702	−	4.08432i	0.926690	−	0.301100i
$185$	−14.5622	−	20.0432i	−1.07064	−	1.47361i
$186$		0			0
$187$	−9.83860	+	8.84587i	−0.719470	+	0.646874i
$188$		−	29.0715i		−	2.12026i
$189$		0			0
$190$	−11.6433	−	35.8344i	−0.844694	−	2.59970i
$191$	1.87384	−	5.76709i	0.135586	−	0.417292i	−0.860094	−	0.510135i	$-0.829595\pi$
$191$	1.87384	−	5.76709i	0.135586	−	0.417292i	0.995681	+	0.0928428i	$0.0295954\pi$
$192$		0			0
$193$	13.4003	−	18.4439i	0.964571	−	1.32762i	0.0198296	−	0.999803i	$-0.493688\pi$
$193$	13.4003	−	18.4439i	0.964571	−	1.32762i	0.944742	−	0.327815i	$-0.106312\pi$
$194$	3.74722	−	11.5328i	0.269035	−	0.828004i
$195$		0			0
$196$	−15.5546	−	12.8948i	−1.11104	−	0.921057i
$197$		−	16.0353i		−	1.14247i	−0.820788	−	0.571234i	$-0.806465\pi$
$197$		−	16.0353i		−	1.14247i	0.820788	−	0.571234i	$-0.193535\pi$
$198$		0			0
$199$			2.01928i			0.143143i	0.997435	+	0.0715716i	$0.0228015\pi$
$199$			2.01928i			0.143143i	−0.997435	+	0.0715716i	$0.977199\pi$
$200$	−8.55648	−	11.7770i	−0.605034	−	0.832758i
$201$		0			0
$202$	40.4095	+	13.1298i	2.84320	+	0.923813i
$203$	5.83568	+	20.1251i	0.409584	+	1.41251i
$204$		0			0
$205$	23.4837	+	7.63030i	1.64017	+	0.532924i
$206$	4.24411	+	13.0620i	0.295701	+	0.910076i
$207$		0			0
$208$	4.01585			0.278449
$209$	15.9482	−	1.66459i	1.10316	−	0.115142i
$210$		0			0
$211$	−7.66670	−	10.5523i	−0.527797	−	0.726451i	0.458995	−	0.888439i	$-0.348209\pi$
$211$	−7.66670	−	10.5523i	−0.527797	−	0.726451i	−0.986793	+	0.161988i	$0.948209\pi$
$212$	−6.49372	−	19.9856i	−0.445991	−	1.37262i
$213$		0			0
$214$	−12.6302	−	9.17634i	−0.863380	−	0.627282i
$215$	1.54322	+	1.12122i	0.105247	+	0.0764665i
$216$		0			0
$217$	0.120542	−	0.334279i	0.00818292	−	0.0226924i
$218$	−1.79024	+	1.30069i	−0.121251	+	0.0880937i
$219$		0			0
$220$	30.8424	−	13.7052i	2.07939	−	0.924007i
$221$	−11.1120			−0.747475
$222$		0			0
$223$	20.4866	−	6.65651i	1.37189	−	0.445753i	0.471893	−	0.881656i	$-0.343571\pi$
$223$	20.4866	−	6.65651i	1.37189	−	0.445753i	0.899994	+	0.435902i	$0.143571\pi$
$224$	−15.5538	+	10.5587i	−1.03924	+	0.705483i
$225$		0			0
$226$	−8.03950	+	11.0654i	−0.534779	+	0.736061i
$227$	1.88230	−	5.79314i	0.124933	−	0.384504i	−0.868956	−	0.494890i	$-0.835209\pi$
$227$	1.88230	−	5.79314i	0.124933	−	0.384504i	0.993889	+	0.110385i	$0.0352085\pi$
$228$		0			0
$229$	13.2498	+	18.2367i	0.875569	+	1.20512i	0.977629	+	0.210339i	$0.0674567\pi$
$229$	13.2498	+	18.2367i	0.875569	+	1.20512i	−0.102060	+	0.994778i	$0.532543\pi$
$230$	−52.5730			−3.46656
$231$		0			0
$232$	−15.5174			−1.01877
$233$	8.70071	+	11.9755i	0.570002	+	0.784541i	0.992555	−	0.121797i	$-0.0388658\pi$
$233$	8.70071	+	11.9755i	0.570002	+	0.784541i	−0.422553	+	0.906338i	$0.638866\pi$
$234$		0			0
$235$	−10.9732	+	33.7720i	−0.715811	+	2.20304i
$236$	−9.91220	+	13.6430i	−0.645229	+	0.888082i
$237$		0			0
$238$	19.3029	−	13.1037i	1.25122	−	0.849390i
$239$	−12.8328	+	4.16962i	−0.830083	+	0.269710i	−0.693081	−	0.720860i	$-0.743747\pi$
$239$	−12.8328	+	4.16962i	−0.830083	+	0.269710i	−0.137003	+	0.990571i	$0.543747\pi$
$240$		0			0
$241$	0.252855			0.0162878			0.00814391	−	0.999967i	$-0.497408\pi$
$241$	0.252855			0.0162878			0.00814391	+	0.999967i	$0.497408\pi$
$242$	5.02116	+	23.7915i	0.322772	+	1.52938i
$243$		0			0
$244$	6.28102	−	4.56342i	0.402101	−	0.292143i
$245$	13.2023	+	20.8509i	0.843466	+	1.33211i
$246$		0			0
$247$	10.8953	+	7.91588i	0.693250	+	0.503675i
$248$	0.212894	+	0.154676i	0.0135188	+	0.00982196i
$249$		0			0
$250$	5.85164	+	18.0095i	0.370090	+	1.13902i
$251$	14.5027	+	19.9613i	0.915404	+	1.25994i	0.965287	+	0.261190i	$0.0841149\pi$
$251$	14.5027	+	19.9613i	0.915404	+	1.25994i	−0.0498839	+	0.998755i	$0.515885\pi$
$252$		0			0
$253$	4.66751	−	21.8812i	0.293444	−	1.37566i
$254$	−7.24231			−0.454423
$255$		0			0
$256$	−1.73026	−	5.32518i	−0.108141	−	0.332824i
$257$	24.1792	+	7.85630i	1.50826	+	0.490062i	0.942413	−	0.334451i	$-0.108551\pi$
$257$	24.1792	+	7.85630i	1.50826	+	0.490062i	0.565843	+	0.824513i	$0.308551\pi$
$258$		0			0
$259$	−17.8565	+	5.17784i	−1.10955	+	0.321735i
$260$	26.9587	+	8.75942i	1.67191	+	0.543236i
$261$		0			0
$262$	−26.9514	−	37.0955i	−1.66507	−	2.29177i
$263$			20.9489i			1.29176i	0.763437	+	0.645882i	$0.223510\pi$
$263$			20.9489i			1.29176i	−0.763437	+	0.645882i	$0.776490\pi$
$264$		0			0
$265$			25.6681i			1.57678i
$266$	−28.2611	−	0.902671i	−1.73280	−	0.0553463i
$267$		0			0
$268$	−7.10666	+	21.8720i	−0.434108	+	1.33605i
$269$	0.647881	−	0.891732i	0.0395020	−	0.0543699i	−0.788809	−	0.614638i	$-0.789302\pi$
$269$	0.647881	−	0.891732i	0.0395020	−	0.0543699i	0.828311	+	0.560268i	$0.189302\pi$
$270$		0			0
$271$	−3.79212	+	11.6710i	−0.230355	+	0.708960i	0.767349	+	0.641230i	$0.221576\pi$
$271$	−3.79212	+	11.6710i	−0.230355	+	0.708960i	−0.997704	+	0.0677300i	$0.978424\pi$
$272$	−1.77718	−	5.46959i	−0.107757	−	0.331642i
$273$		0			0
$274$		−	5.82733i		−	0.352042i
$275$	−24.5087	+	2.55809i	−1.47793	+	0.154258i
$276$		0			0
$277$	−0.672399	−	0.925478i	−0.0404006	−	0.0556066i	0.788339	−	0.615241i	$-0.210941\pi$
$277$	−0.672399	−	0.925478i	−0.0404006	−	0.0556066i	−0.828739	+	0.559635i	$0.810941\pi$
$278$	−22.5162	+	7.31596i	−1.35043	+	0.438782i
$279$		0			0
$280$	−17.5529	+	5.08982i	−1.04899	+	0.304175i
$281$	4.89460	−	6.73684i	0.291987	−	0.401886i	−0.637671	−	0.770309i	$-0.720102\pi$
$281$	4.89460	−	6.73684i	0.291987	−	0.401886i	0.929658	+	0.368423i	$0.120102\pi$
$282$		0			0
$283$	4.95289	+	15.2434i	0.294419	+	0.906128i	0.983416	+	0.181364i	$0.0580512\pi$
$283$	4.95289	+	15.2434i	0.294419	+	0.906128i	−0.688997	+	0.724764i	$0.741949\pi$
$284$	−9.01422	+	6.54921i	−0.534895	+	0.388624i
$285$		0			0
$286$	−10.2238	+	17.6787i	−0.604546	+	1.04536i
$287$	11.3647	−	14.6358i	0.670838	−	0.863922i
$288$		0			0
$289$	−0.335775	−	1.03341i	−0.0197515	−	0.0607888i
$290$	58.7018	+	19.0734i	3.44709	+	1.12003i
$291$		0			0
$292$	−5.47000	−	3.97419i	−0.320108	−	0.232572i
$293$	1.90121	−	5.85134i	0.111070	−	0.341839i	−0.880037	−	0.474905i	$-0.842482\pi$
$293$	1.90121	−	5.85134i	0.111070	−	0.341839i	0.991107	+	0.133066i	$0.0424824\pi$
$294$		0			0
$295$	16.6645	−	12.1074i	0.970243	−	0.704923i
$296$		−	13.7682i		−	0.800259i
$297$		0			0
$298$	−25.9507			−1.50328
$299$	15.2022	−	11.0451i	0.879167	−	0.638752i
$300$		0			0
$301$	1.18437	−	0.804009i	0.0682660	−	0.0463423i
$302$	1.71905	+	1.24896i	0.0989200	+	0.0718696i
$303$		0			0
$304$	−2.15386	+	6.62891i	−0.123533	+	0.380194i
$305$	−9.01906	+	2.93047i	−0.516430	+	0.167798i
$306$		0			0
$307$	12.1473			0.693281			0.346641	−	0.937998i	$-0.387322\pi$
$307$	12.1473			0.693281			0.346641	+	0.937998i	$0.387322\pi$
$308$	−1.82374	−	25.2619i	−0.103917	−	1.43943i
$309$		0			0
$310$	−0.615247	−	0.846814i	−0.0349437	−	0.0480958i
$311$	−9.47712	+	3.07930i	−0.537398	+	0.174611i	−0.565127	−	0.825004i	$-0.691173\pi$
$311$	−9.47712	+	3.07930i	−0.537398	+	0.174611i	0.0277282	+	0.999615i	$0.491173\pi$
$312$		0			0
$313$	17.3454	−	23.8739i	0.980419	−	1.34943i	0.0438162	−	0.999040i	$-0.486048\pi$
$313$	17.3454	−	23.8739i	0.980419	−	1.34943i	0.936603	−	0.350392i	$-0.113952\pi$
$314$	−1.71098	−	1.24310i	−0.0965563	−	0.0701523i
$315$		0			0
$316$	1.30541	−	0.424154i	0.0734351	−	0.0238605i
$317$	−0.109226	+	0.0793571i	−0.00613472	+	0.00445714i	−0.590848	−	0.806783i	$-0.701207\pi$
$317$	−0.109226	+	0.0793571i	−0.00613472	+	0.00445714i	0.584714	+	0.811240i	$0.301207\pi$
$318$		0			0
$319$	−13.1501	+	22.7387i	−0.736264	+	1.27312i
$320$			45.2095i			2.52729i
$321$		0			0
$322$	−13.3833	+	37.1136i	−0.745820	+	2.06826i
$323$	5.95982	−	18.3424i	0.331613	−	1.02060i
$324$		0			0
$325$	−16.7435	−	12.1649i	−0.928762	−	0.674785i
$326$	−45.4112	−	14.7550i	−2.51509	−	0.817203i
$327$		0			0
$328$	8.06576	+	11.1016i	0.445357	+	0.612981i
$329$	21.0478	+	16.3437i	1.16040	+	0.901055i
$330$		0			0
$331$	−12.3359			−0.678040			−0.339020	−	0.940779i	$-0.610095\pi$
$331$	−12.3359			−0.678040			−0.339020	+	0.940779i	$0.610095\pi$
$332$	−11.7401	+	8.52969i	−0.644323	+	0.468128i
$333$		0			0
$334$	17.4294	+	5.66315i	0.953693	+	0.309874i
$335$	16.5114	−	22.7260i	0.902115	−	1.24166i
$336$		0			0
$337$	−15.2935	−	4.96918i	−0.833093	−	0.270688i	−0.138745	−	0.990328i	$-0.544307\pi$
$337$	−15.2935	−	4.96918i	−0.833093	−	0.270688i	−0.694348	+	0.719640i	$0.744307\pi$
$338$	11.0176	−	3.57984i	0.599280	−	0.194718i
$339$		0			0
$340$		−	40.5941i		−	2.20153i
$341$	0.407073	−	0.180889i	0.0220442	−	0.00979566i
$342$		0			0
$343$	18.0804	−	4.01221i	0.976252	−	0.216639i
$344$	0.327583	+	1.00820i	0.0176621	+	0.0543583i
$345$		0			0
$346$	−26.4447	+	36.3981i	−1.42168	+	1.95677i
$347$	9.49707	−	13.0716i	0.509829	−	0.701720i	−0.474061	−	0.880492i	$-0.657212\pi$
$347$	9.49707	−	13.0716i	0.509829	−	0.701720i	0.983891	+	0.178772i	$0.0572125\pi$
$348$		0			0
$349$	0.861095	+	2.65018i	0.0460933	+	0.141861i	0.971454	−	0.237226i	$-0.0762382\pi$
$349$	0.861095	+	2.65018i	0.0460933	+	0.141861i	−0.925361	+	0.379087i	$0.876238\pi$
$350$	43.4307	+	1.38720i	2.32147	+	0.0741487i
$351$		0			0
$352$	−23.0475	−	4.91628i	−1.22843	−	0.262039i
$353$			34.0678i			1.81324i	0.421944	+	0.906622i	$0.361348\pi$
$353$			34.0678i			1.81324i	−0.421944	+	0.906622i	$0.638652\pi$
$354$		0			0
$355$	12.9437	−	4.20567i	0.686982	−	0.223214i
$356$	17.6916	+	5.74834i	0.937652	+	0.304662i
$357$		0			0
$358$	−17.4169	+	23.9723i	−0.920512	+	1.26698i
$359$	1.67352	+	0.543761i	0.0883252	+	0.0286986i	0.352846	−	0.935681i	$-0.385214\pi$
$359$	1.67352	+	0.543761i	0.0883252	+	0.0286986i	−0.264521	+	0.964380i	$0.585214\pi$
$360$		0			0
$361$	−3.53888	+	2.57115i	−0.186257	+	0.135324i
$362$	−4.27854			−0.224875
$363$		0			0
$364$	13.0464	−	16.8015i	0.683819	−	0.880640i
$365$	4.85435	+	6.68144i	0.254088	+	0.349723i
$366$		0			0
$367$	−12.8164	−	4.16430i	−0.669010	−	0.217375i	−0.0452325	−	0.998976i	$-0.514403\pi$
$367$	−12.8164	−	4.16430i	−0.669010	−	0.217375i	−0.623777	+	0.781602i	$0.714403\pi$
$368$	7.86796	+	5.71641i	0.410146	+	0.297988i
$369$		0			0
$370$	−16.9233	+	52.0845i	−0.879799	+	2.70774i
$371$	18.1203	+	6.53422i	0.940759	+	0.339240i
$372$		0			0
$373$		−	17.5264i		−	0.907483i	−0.891133	−	0.453741i	$-0.850089\pi$
$373$		−	17.5264i		−	0.907483i	0.891133	−	0.453741i	$-0.149911\pi$
$374$	28.6028	+	6.10129i	1.47901	+	0.315490i
$375$		0			0
$376$	−15.9652	+	11.5994i	−0.823343	+	0.598194i
$377$	−20.9816	+	6.81732i	−1.08061	+	0.351110i
$378$		0			0
$379$	18.7536	+	13.6253i	0.963308	+	0.699884i	0.953917	−	0.300072i	$-0.0970106\pi$
$379$	18.7536	+	13.6253i	0.963308	+	0.699884i	0.00939149	+	0.999956i	$0.497011\pi$
$380$	−28.9181	+	39.8023i	−1.48347	+	2.04182i
$381$		0			0
$382$	−12.7482	+	4.14215i	−0.652256	+	0.211931i
$383$	−11.8248	−	16.2755i	−0.604221	−	0.831639i	0.391866	−	0.920022i	$-0.371830\pi$
$383$	−11.8248	−	16.2755i	−0.604221	−	0.831639i	−0.996086	+	0.0883839i	$0.971830\pi$
$384$		0			0
$385$	−7.41661	+	30.0348i	−0.377985	+	1.53071i
$386$	−50.3949			−2.56503
$387$		0			0
$388$	−15.0588	+	4.89290i	−0.764495	+	0.248399i
$389$	−5.21714	+	16.0567i	−0.264520	+	0.814108i	0.727284	+	0.686337i	$0.240782\pi$
$389$	−5.21714	+	16.0567i	−0.264520	+	0.814108i	−0.991804	+	0.127771i	$0.959218\pi$
$390$		0			0
$391$	−21.7709	−	15.8175i	−1.10100	−	0.799926i
$392$	−0.875235	+	13.6871i	−0.0442060	+	0.691302i
$393$		0			0
$394$	−28.6765	+	20.8347i	−1.44470	+	1.04964i
$395$	−1.67658			−0.0843578
$396$		0			0
$397$		−	33.9923i		−	1.70602i	−0.521891	−	0.853012i	$-0.674773\pi$
$397$		−	33.9923i		−	1.70602i	0.521891	−	0.853012i	$-0.325227\pi$
$398$	3.61117	−	2.62367i	0.181011	−	0.131512i
$399$		0			0
$400$	3.30999	−	10.1871i	0.165499	−	0.509355i
$401$	−24.4089	−	17.7341i	−1.21892	−	0.885599i	−0.222912	−	0.974839i	$-0.571556\pi$
$401$	−24.4089	−	17.7341i	−1.21892	−	0.885599i	−0.996010	+	0.0892397i	$0.971556\pi$
$402$		0			0
$403$	0.355815	+	0.115611i	0.0177244	+	0.00575900i
$404$	−17.1442	−	52.7644i	−0.852955	−	2.62512i
$405$		0			0
$406$	28.4082	−	36.5848i	1.40988	−	1.81567i
$407$	−20.1755	−	11.6677i	−1.00006	−	0.578348i
$408$		0			0
$409$	−13.1555	+	9.55802i	−0.650497	+	0.472613i	−0.863440	−	0.504451i	$-0.831695\pi$
$409$	−13.1555	+	9.55802i	−0.650497	+	0.472613i	0.212944	+	0.977064i	$0.431695\pi$
$410$	−16.8669	−	51.9109i	−0.832995	−	2.56369i
$411$		0			0
$412$	10.5410	−	14.5084i	0.519316	−	0.714777i
$413$	−4.30499	−	14.8463i	−0.211835	−	0.730541i
$414$		0			0
$415$	16.8579	−	5.47747i	0.827522	−	0.268878i
$416$	−11.6337	−	16.0125i	−0.570391	−	0.785076i
$417$		0			0
$418$	−23.6985	−	26.3581i	−1.15913	−	1.28922i
$419$		−	9.34075i		−	0.456326i	−0.973623	−	0.228163i	$-0.926728\pi$
$419$		−	9.34075i		−	0.456326i	0.973623	−	0.228163i	$-0.0732718\pi$
$420$		0			0
$421$	−7.39554	−	22.7611i	−0.360436	−	1.10931i	−0.952790	−	0.303631i	$-0.901801\pi$
$421$	−7.39554	−	22.7611i	−0.360436	−	1.10931i	0.592353	−	0.805678i	$-0.298199\pi$
$422$	−8.90973	+	27.4213i	−0.433719	+	1.33485i
$423$		0			0
$424$	−8.38455	+	11.5403i	−0.407190	+	0.560449i
$425$	−9.15886	+	28.1881i	−0.444270	+	1.36732i
$426$		0			0
$427$	−0.227191	+	7.11296i	−0.0109945	+	0.344220i
$428$			20.3849i			0.985340i
$429$		0			0
$430$		−	4.21662i		−	0.203343i
$431$	18.1758	+	25.0168i	0.875496	+	1.20502i	0.977648	+	0.210248i	$0.0674271\pi$
$431$	18.1758	+	25.0168i	0.875496	+	1.20502i	−0.102152	+	0.994769i	$0.532573\pi$
$432$		0			0
$433$	−24.2698	−	7.88575i	−1.16633	−	0.378965i	−0.339061	−	0.940764i	$-0.610109\pi$
$433$	−24.2698	−	7.88575i	−1.16633	−	0.378965i	−0.827274	+	0.561799i	$0.810109\pi$
$434$	−0.754426	+	0.218761i	−0.0362136	+	0.0105009i
$435$		0			0
$436$	2.74801	+	0.892882i	0.131606	+	0.0427613i
$437$	10.0784	+	31.0180i	0.482113	+	1.48379i
$438$		0			0
$439$	−6.26322			−0.298927			−0.149464	−	0.988767i	$-0.547755\pi$
$439$	−6.26322			−0.298927			−0.149464	+	0.988767i	$0.547755\pi$
$440$	−19.8325	−	11.4694i	−0.945476	−	0.546781i
$441$		0			0
$442$	14.4379	+	19.8721i	0.686741	+	0.945218i
$443$	7.55146	+	23.2410i	0.358781	+	1.10421i	0.953785	+	0.300491i	$0.0971505\pi$
$443$	7.55146	+	23.2410i	0.358781	+	1.10421i	−0.595004	+	0.803723i	$0.702849\pi$
$444$		0			0
$445$	−18.3823	−	13.3555i	−0.871406	−	0.633114i
$446$	−38.5225	−	27.9882i	−1.82409	−	1.32528i
$447$		0			0
$448$	31.9155	+	11.5088i	1.50786	+	0.543739i
$449$	0.793587	−	0.576575i	0.0374517	−	0.0272102i	−0.568902	−	0.822405i	$-0.692632\pi$
$449$	0.793587	−	0.576575i	0.0374517	−	0.0272102i	0.606354	+	0.795195i	$0.292632\pi$
$450$		0			0
$451$	23.1031	−	2.41138i	1.08788	−	0.113547i
$452$	17.8594			0.840036
$453$		0			0
$454$	−12.8058	+	4.16085i	−0.601005	+	0.195279i
$455$	−21.4977	+	14.5937i	−1.00783	+	0.684162i
$456$		0			0
$457$	−12.4420	+	17.1250i	−0.582014	+	0.801073i	−0.993914	−	0.110156i	$-0.964865\pi$
$457$	−12.4420	+	17.1250i	−0.582014	+	0.801073i	0.411901	+	0.911229i	$0.364865\pi$
$458$	15.3980	−	47.3902i	0.719501	−	2.21440i
$459$		0			0
$460$	40.3495	+	55.5363i	1.88130	+	2.58939i
$461$	−1.41877			−0.0660786			−0.0330393	−	0.999454i	$-0.510519\pi$
$461$	−1.41877			−0.0660786			−0.0330393	+	0.999454i	$0.510519\pi$
$462$		0			0
$463$	−39.4892			−1.83522			−0.917609	−	0.397485i	$-0.869883\pi$
$463$	−39.4892			−1.83522			−0.917609	+	0.397485i	$0.869883\pi$
$464$	−6.71128	−	9.23729i	−0.311564	−	0.428830i
$465$		0			0
$466$	10.1114	−	31.1197i	0.468401	−	1.44159i
$467$	−16.7285	+	23.0248i	−0.774101	+	1.06546i	0.221807	+	0.975091i	$0.428804\pi$
$467$	−16.7285	+	23.0248i	−0.774101	+	1.06546i	−0.995908	+	0.0903684i	$0.971196\pi$
$468$		0			0
$469$	−11.8401	−	17.4414i	−0.546725	−	0.805370i
$470$	74.6533	−	24.2563i	3.44350	−	1.11886i
$471$		0			0
$472$	11.4472			0.526902
$473$	1.75499	+	0.374358i	0.0806943	+	0.0172130i
$474$		0			0
$475$	29.0606	−	21.1137i	1.33339	−	0.968765i
$476$	−28.6572	−	10.3339i	−1.31350	−	0.473652i
$477$		0			0
$478$	24.1304	+	17.5318i	1.10370	+	0.801884i
$479$	−7.96798	−	5.78908i	−0.364066	−	0.264510i	0.390680	−	0.920527i	$-0.372240\pi$
$479$	−7.96798	−	5.78908i	−0.364066	−	0.264510i	−0.754746	+	0.656017i	$0.772240\pi$
$480$		0			0
$481$	−6.04883	−	18.6164i	−0.275803	−	0.848834i
$482$	−0.328536	−	0.452190i	−0.0149644	−	0.0205967i
$483$		0			0
$484$	21.2789	−	23.5641i	0.967221	−	1.07109i
$485$	19.3405			0.878205
$486$		0			0
$487$	0.130607	+	0.401967i	0.00591836	+	0.0182148i	0.953972	−	0.299895i	$-0.0969518\pi$
$487$	0.130607	+	0.401967i	0.00591836	+	0.0182148i	−0.948054	+	0.318110i	$0.896952\pi$
$488$	−5.01220	−	1.62856i	−0.226892	−	0.0737215i
$489$		0			0
$490$	20.1346	−	50.7019i	0.909587	−	2.29048i
$491$	26.8810	+	8.73416i	1.21312	+	0.394167i	0.844572	−	0.535441i	$-0.179855\pi$
$491$	26.8810	+	8.73416i	1.21312	+	0.394167i	0.368549	+	0.929608i	$0.379855\pi$
$492$		0			0
$493$	18.5704	+	25.5599i	0.836367	+	1.15116i
$494$		−	29.7696i		−	1.33940i
$495$		0			0
$496$			0.193630i			0.00869425i
$497$	0.326054	−	10.2082i	0.0146255	−	0.457900i
$498$		0			0
$499$	6.16638	−	18.9782i	0.276045	−	0.849580i	−0.712896	−	0.701270i	$-0.752617\pi$
$499$	6.16638	−	18.9782i	0.276045	−	0.849580i	0.988941	−	0.148310i	$-0.0473833\pi$
$500$	14.5335	−	20.0037i	0.649959	−	0.894592i
$501$		0			0
$502$	16.8541	−	51.8716i	0.752235	−	2.31514i
$503$	1.17263	+	3.60899i	0.0522851	+	0.160917i	0.973790	−	0.227451i	$-0.0730391\pi$
$503$	1.17263	+	3.60899i	0.0522851	+	0.160917i	−0.921504	+	0.388368i	$0.873039\pi$
$504$		0			0
$505$			67.7668i			3.01558i
$506$	−45.1956	+	20.0833i	−2.00919	+	0.892812i
$507$		0			0
$508$	5.55844	+	7.65053i	0.246616	+	0.339437i
$509$	−15.4210	+	5.01059i	−0.683525	+	0.222091i	−0.630138	−	0.776483i	$-0.717002\pi$
$509$	−15.4210	+	5.01059i	−0.683525	+	0.222091i	−0.0533868	+	0.998574i	$0.517002\pi$
$510$		0			0
$511$	5.95249	−	1.72604i	0.263323	−	0.0763556i
$512$	9.34167	−	12.8577i	0.412847	−	0.568236i
$513$		0			0
$514$	−17.3664	−	53.4483i	−0.766000	−	2.35750i
$515$	−17.7216	+	12.8755i	−0.780905	+	0.567361i
$516$		0			0
$517$	3.46781	+	33.2247i	0.152514	+	1.46122i
$518$	32.4607	+	25.2058i	1.42624	+	1.10748i
$519$		0			0
$520$	−5.94600	−	18.2999i	−0.260749	−	0.802504i
$521$	5.57596	+	1.81174i	0.244287	+	0.0793737i	0.428601	−	0.903494i	$-0.359006\pi$
$521$	5.57596	+	1.81174i	0.244287	+	0.0793737i	−0.184314	+	0.982867i	$0.559006\pi$
$522$		0			0
$523$	31.6555	+	22.9990i	1.38420	+	1.00568i	0.996474	+	0.0839014i	$0.0267381\pi$
$523$	31.6555	+	22.9990i	1.38420	+	1.00568i	0.387722	+	0.921776i	$0.373262\pi$
$524$	−18.5013	+	56.9412i	−0.808234	+	2.48749i
$525$		0			0
$526$	37.4637	−	27.2190i	1.63350	−	1.18680i
$527$		−	0.535781i		−	0.0233390i
$528$		0			0
$529$	22.5067			0.978554
$530$	45.9033	−	33.3507i	1.99391	−	1.44866i
$531$		0			0
$532$	20.7367	+	30.5469i	0.899051	+	1.32438i
$533$	15.7832	+	11.4672i	0.683648	+	0.496700i
$534$		0			0
$535$	7.69437	−	23.6808i	0.332657	−	1.02381i
$536$	14.8470	−	4.82409i	0.641293	−	0.208369i
$537$		0			0
$538$	−2.43652			−0.105046
$539$	19.3149	+	12.8815i	0.831952	+	0.554848i
$540$		0			0
$541$	−8.32708	−	11.4612i	−0.358009	−	0.492757i	0.591584	−	0.806244i	$-0.298503\pi$
$541$	−8.32708	−	11.4612i	−0.358009	−	0.492757i	−0.949593	+	0.313487i	$0.898503\pi$
$542$	25.7988	−	8.38253i	1.10815	−	0.360060i
$543$		0			0
$544$	−16.6606	+	22.9313i	−0.714316	+	0.983171i
$545$	−2.85530	−	2.07450i	−0.122308	−	0.0888617i
$546$		0			0
$547$	11.6764	−	3.79388i	0.499246	−	0.162215i	−0.0485601	−	0.998820i	$-0.515463\pi$
$547$	11.6764	−	3.79388i	0.499246	−	0.162215i	0.547806	+	0.836605i	$0.315463\pi$
$548$	−6.15580	+	4.47245i	−0.262963	+	0.191054i
$549$		0			0
$550$	36.4190	+	40.5062i	1.55291	+	1.72719i
$551$		−	38.2904i		−	1.63122i
$552$		0			0
$553$	−0.426799	+	1.18357i	−0.0181493	+	0.0503306i
$554$	−0.781418	+	2.40496i	−0.0331993	+	0.102177i
$555$		0			0
$556$	25.0094	+	18.1704i	1.06064	+	0.770597i
$557$	27.6012	+	8.96816i	1.16950	+	0.379993i	0.828456	−	0.560054i	$-0.189220\pi$
$557$	27.6012	+	8.96816i	1.16950	+	0.379993i	0.341043	+	0.940048i	$0.389220\pi$
$558$		0			0
$559$	0.885869	+	1.21929i	0.0374683	+	0.0515706i
$560$	−10.6215	−	8.24764i	−0.448841	−	0.348526i
$561$		0			0
$562$	−18.4073			−0.776467
$563$	32.0527	−	23.2877i	1.35086	−	0.981458i	0.351893	−	0.936040i	$-0.385538\pi$
$563$	32.0527	−	23.2877i	1.35086	−	0.981458i	0.998968	−	0.0454175i	$-0.0144618\pi$
$564$		0			0
$565$	−20.7470	−	6.74112i	−0.872835	−	0.283601i
$566$	20.8251	−	28.6633i	0.875345	−	1.20481i
$567$		0			0
$568$	7.19327	+	2.33724i	0.301823	+	0.0980682i
$569$	24.1141	−	7.83513i	1.01091	−	0.328466i	0.243696	−	0.969852i	$-0.421640\pi$
$569$	24.1141	−	7.83513i	1.01091	−	0.328466i	0.767218	+	0.641386i	$0.221640\pi$
$570$		0			0
$571$			9.22801i			0.386180i	0.981181	+	0.193090i	$0.0618510\pi$
$571$			9.22801i			0.386180i	−0.981181	+	0.193090i	$0.938149\pi$
$572$	26.5219	−	2.76821i	1.10894	−	0.115745i
$573$		0			0
$574$	−40.9400	−	1.30764i	−1.70880	−	0.0545798i
$575$	−15.4881	−	47.6674i	−0.645897	−	1.98787i
$576$		0			0
$577$	−4.00282	+	5.50942i	−0.166640	+	0.229360i	−0.884168	−	0.467170i	$-0.845274\pi$
$577$	−4.00282	+	5.50942i	−0.166640	+	0.229360i	0.717528	+	0.696530i	$0.245274\pi$
$578$	−1.41181	+	1.94319i	−0.0587237	+	0.0808262i
$579$		0			0
$580$	−24.9049	−	76.6493i	−1.03412	−	3.18269i
$581$	0.424652	−	13.2951i	0.0176175	−	0.551575i
$582$		0			0
$583$	9.80543	+	22.0662i	0.406100	+	0.913889i
$584$			4.58965i			0.189921i
$585$		0			0
$586$	−12.9344	+	4.20265i	−0.534317	+	0.173610i
$587$	−37.9944	−	12.3451i	−1.56820	−	0.509537i	−0.609214	−	0.793006i	$-0.708515\pi$
$587$	−37.9944	−	12.3451i	−1.56820	−	0.509537i	−0.958982	+	0.283469i	$0.908515\pi$
$588$		0			0
$589$	−0.381675	+	0.525331i	−0.0157267	+	0.0216459i
$590$	−43.3045	−	14.0705i	−1.78282	−	0.579272i
$591$		0			0
$592$	8.19600	−	5.95474i	0.336853	−	0.244738i
$593$	5.39895			0.221708			0.110854	−	0.993837i	$-0.464641\pi$
$593$	5.39895			0.221708			0.110854	+	0.993837i	$0.464641\pi$
$594$		0			0
$595$	29.3902	+	22.8215i	1.20488	+	0.935592i
$596$	19.9170	+	27.4134i	0.815833	+	1.12290i
$597$		0			0
$598$	−39.5046	−	12.8358i	−1.61546	−	0.524896i
$599$	−4.87697	−	3.54332i	−0.199267	−	0.144776i	0.483677	−	0.875247i	$-0.339301\pi$
$599$	−4.87697	−	3.54332i	−0.199267	−	0.144776i	−0.682944	+	0.730470i	$0.739301\pi$
$600$		0			0
$601$	−7.54914	+	23.2339i	−0.307936	+	0.947729i	0.670629	+	0.741792i	$0.266024\pi$
$601$	−7.54914	+	23.2339i	−0.307936	+	0.947729i	−0.978565	+	0.205937i	$0.933976\pi$
$602$	−2.97670	−	1.07341i	−0.121321	−	0.0437487i
$603$		0			0
$604$		−	2.77451i		−	0.112893i
$605$	−33.6137	+	19.3423i	−1.36659	+	0.786374i
$606$		0			0
$607$	−1.34519	+	0.977334i	−0.0545994	+	0.0396688i	−0.614750	−	0.788722i	$-0.710743\pi$
$607$	−1.34519	+	0.977334i	−0.0545994	+	0.0396688i	0.560151	+	0.828391i	$0.310743\pi$
$608$	32.6712	−	10.6155i	1.32499	−	0.430516i
$609$		0			0
$610$	16.9592	+	12.3216i	0.686657	+	0.498886i
$611$	−16.4910	+	22.6980i	−0.667156	+	0.918261i
$612$		0			0
$613$	−23.5680	+	7.65771i	−0.951903	+	0.309292i	−0.743489	−	0.668749i	$-0.766830\pi$
$613$	−23.5680	+	7.65771i	−0.951903	+	0.309292i	−0.208414	+	0.978041i	$0.566830\pi$
$614$	−15.7830	−	21.7235i	−0.636950	−	0.876687i
$615$		0			0
$616$	−13.1454	+	11.0809i	−0.529644	+	0.446464i
$617$	−22.3563			−0.900030			−0.450015	−	0.893021i	$-0.648581\pi$
$617$	−22.3563			−0.900030			−0.450015	+	0.893021i	$0.648581\pi$
$618$		0			0
$619$	−20.6550	+	6.71121i	−0.830193	+	0.269746i	−0.693127	−	0.720816i	$-0.743767\pi$
$619$	−20.6550	+	6.71121i	−0.830193	+	0.269746i	−0.137067	+	0.990562i	$0.543767\pi$
$620$	−0.422348	+	1.29985i	−0.0169619	+	0.0522033i
$621$		0			0
$622$	17.8205	+	12.9474i	0.714538	+	0.519142i
$623$	−14.1078	+	9.57706i	−0.565217	+	0.383697i
$624$		0			0
$625$	5.62028	−	4.08337i	0.224811	−	0.163335i
$626$	−65.2316			−2.60718
$627$		0			0
$628$			2.76150i			0.110196i
$629$	−22.6786	+	16.4770i	−0.904256	+	0.656980i
$630$		0			0
$631$	−0.827036	+	2.54535i	−0.0329238	+	0.101329i	−0.966168	−	0.257914i	$-0.916965\pi$
$631$	−0.827036	+	2.54535i	−0.0329238	+	0.101329i	0.933244	+	0.359243i	$0.116965\pi$
$632$	−0.753786	−	0.547658i	−0.0299840	−	0.0217847i
$633$		0			0
$634$	0.283835	+	0.0922235i	0.0112725	+	0.00366266i
$635$	−3.56943	−	10.9856i	−0.141649	−	0.435949i
$636$		0			0
$637$	4.82977	+	18.8912i	0.191362	+	0.748498i
$638$	57.7506	−	6.02769i	2.28637	−	0.238638i
$639$		0			0
$640$	40.3170	−	29.2920i	1.59367	−	1.15787i
$641$	−6.63655	−	20.4252i	−0.262128	−	0.806747i	−0.992341	−	0.123528i	$-0.960579\pi$
$641$	−6.63655	−	20.4252i	−0.262128	−	0.806747i	0.730213	−	0.683219i	$-0.239421\pi$
$642$		0			0
$643$	−17.4500	+	24.0179i	−0.688162	+	0.947174i	−0.999996	−	0.00296277i	$-0.999057\pi$
$643$	−17.4500	+	24.0179i	−0.688162	+	0.947174i	0.311833	+	0.950137i	$0.399057\pi$
$644$	49.4772	−	14.3469i	1.94967	−	0.565347i
$645$		0			0
$646$	−40.5461	+	13.1742i	−1.59527	+	0.518334i
$647$	4.80509	+	6.61364i	0.188907	+	0.260009i	0.892957	−	0.450142i	$-0.148627\pi$
$647$	4.80509	+	6.61364i	0.188907	+	0.260009i	−0.704049	+	0.710151i	$0.748627\pi$
$648$		0			0
$649$	9.70087	−	16.7744i	0.380792	−	0.658454i
$650$			45.7489i			1.79442i
$651$		0			0
$652$	19.2662	+	59.2952i	0.754522	+	2.32218i
$653$	3.89436	−	11.9856i	0.152398	−	0.469034i	−0.845490	−	0.533992i	$-0.820691\pi$
$653$	3.89436	−	11.9856i	0.152398	−	0.469034i	0.997888	+	0.0649580i	$0.0206914\pi$
$654$		0			0
$655$	42.9855	−	59.1644i	1.67958	−	2.31175i
$656$	−3.12016	+	9.60285i	−0.121822	+	0.374928i
$657$		0			0
$658$	1.88052	−	58.8760i	0.0733104	−	2.29522i
$659$			5.74307i			0.223718i	0.993724	+	0.111859i	$0.0356805\pi$
$659$			5.74307i			0.223718i	−0.993724	+	0.111859i	$0.964319\pi$
$660$		0			0
$661$			23.4602i			0.912495i	0.889853	+	0.456247i	$0.150807\pi$
$661$			23.4602i			0.912495i	−0.889853	+	0.456247i	$0.849193\pi$
$662$	16.0280	+	22.0607i	0.622947	+	0.857413i
$663$		0			0
$664$	9.36852	+	3.04402i	0.363569	+	0.118131i
$665$	−12.5595	−	43.3131i	−0.487036	−	1.67961i
$666$		0			0
$667$	−50.8118	−	16.5097i	−1.96744	−	0.639260i
$668$	−7.39460	−	22.7583i	−0.286106	−	0.880543i
$669$		0			0
$670$	−62.0952			−2.39895
$671$	−6.63399	+	5.96460i	−0.256102	+	0.230261i
$672$		0			0
$673$	6.36107	+	8.75526i	0.245201	+	0.337490i	0.913823	−	0.406112i	$-0.133116\pi$
$673$	6.36107	+	8.75526i	0.245201	+	0.337490i	−0.668622	+	0.743602i	$0.733116\pi$
$674$	10.9844	+	33.8065i	0.423104	+	1.30218i
$675$		0			0
$676$	−12.2376	−	8.89114i	−0.470677	−	0.341967i
$677$	35.0406	+	25.4585i	1.34672	+	0.978449i	0.999168	+	0.0407889i	$0.0129871\pi$
$677$	35.0406	+	25.4585i	1.34672	+	0.978449i	0.347552	+	0.937661i	$0.387013\pi$
$678$		0			0
$679$	4.92341	−	13.6533i	0.188943	−	0.523966i
$680$	−22.2931	+	16.1969i	−0.854901	+	0.621122i
$681$		0			0
$682$	−0.852402	−	0.492955i	−0.0326402	−	0.0188762i
$683$	−43.4846			−1.66389			−0.831945	−	0.554858i	$-0.812773\pi$
$683$	−43.4846			−1.66389			−0.831945	+	0.554858i	$0.812773\pi$
$684$		0			0
$685$	8.83926	−	2.87205i	0.337731	−	0.109735i
$686$	−30.6672	−	27.1209i	−1.17088	−	1.03548i
$687$		0			0
$688$	−0.458485	+	0.631050i	−0.0174796	+	0.0240586i
$689$	−6.26694	+	19.2877i	−0.238751	+	0.734801i
$690$		0			0
$691$	−12.1427	−	16.7130i	−0.461931	−	0.635793i	0.512977	−	0.858402i	$-0.328543\pi$
$691$	−12.1427	−	16.7130i	−0.461931	−	0.635793i	−0.974908	+	0.222609i	$0.928543\pi$
$692$	58.7459			2.23318
$693$		0			0
$694$	−35.7160			−1.35576
$695$	−22.1946	−	30.5482i	−0.841889	−	1.15876i
$696$		0			0
$697$	8.63359	−	26.5715i	0.327020	−	1.00647i
$698$	3.62059	−	4.98332i	0.137041	−	0.188621i
$699$		0			0
$700$	−31.8675	−	46.9435i	−1.20448	−	1.77430i
$701$	−15.3472	+	4.98660i	−0.579655	+	0.188341i	−0.584146	−	0.811649i	$-0.698570\pi$
$701$	−15.3472	+	4.98660i	−0.579655	+	0.188341i	0.00449096	+	0.999990i	$0.498570\pi$
$702$		0			0
$703$	33.9740			1.28135
$704$	17.2704	+	38.8655i	0.650903	+	1.46480i
$705$		0			0
$706$	60.9247	−	44.2644i	2.29293	−	1.66591i
$707$	47.8397	+	17.2511i	1.79920	+	0.648794i
$708$		0			0
$709$	7.64021	+	5.55094i	0.286934	+	0.208470i	0.721936	−	0.691960i	$-0.243252\pi$
$709$	7.64021	+	5.55094i	0.286934	+	0.208470i	−0.435002	+	0.900429i	$0.643252\pi$
$710$	−24.3390	−	17.6833i	−0.913427	−	0.663644i
$711$		0			0
$712$	−3.90205	−	12.0093i	−0.146235	−	0.450066i
$713$	0.532553	+	0.732996i	0.0199443	+	0.0274509i
$714$		0			0
$715$	−31.8550	−	6.79502i	−1.19131	−	0.254119i
$716$	38.6909			1.44595
$717$		0			0
$718$	−1.20199	−	3.69934i	−0.0448578	−	0.138058i
$719$	19.3401	+	6.28399i	0.721265	+	0.234353i	0.646572	−	0.762853i	$-0.276202\pi$
$719$	19.3401	+	6.28399i	0.721265	+	0.234353i	0.0746934	+	0.997207i	$0.476202\pi$
$720$		0			0
$721$	4.57808	+	15.7881i	0.170497	+	0.587980i
$722$	9.19617	+	2.98802i	0.342246	+	0.111202i
$723$		0			0
$724$	3.28376	+	4.51971i	0.122040	+	0.167974i
$725$			58.8434i			2.18539i
$726$		0			0
$727$		−	23.7796i		−	0.881935i	−0.897523	−	0.440968i	$-0.854635\pi$
$727$		−	23.7796i		−	0.881935i	0.897523	−	0.440968i	$-0.145365\pi$
$728$	−14.4324	−	0.460976i	−0.534900	−	0.0170849i
$729$		0			0
$730$	5.64141	−	17.3625i	0.208798	−	0.642614i
$731$	1.26864	−	1.74614i	0.0469225	−	0.0645833i
$732$		0			0
$733$	−6.07169	+	18.6868i	−0.224263	+	0.690211i	0.774102	+	0.633060i	$0.218202\pi$
$733$	−6.07169	+	18.6868i	−0.224263	+	0.690211i	−0.998366	+	0.0571506i	$0.981798\pi$
$734$	9.20522	+	28.3307i	0.339771	+	1.04571i
$735$		0			0
$736$		−	47.9322i		−	1.76680i
$737$	5.51291	−	25.8445i	0.203071	−	0.951993i
$738$		0			0
$739$	26.2260	+	36.0970i	0.964740	+	1.32785i	0.944660	+	0.328052i	$0.106392\pi$
$739$	26.2260	+	36.0970i	0.964740	+	1.32785i	0.0200801	+	0.999798i	$0.493608\pi$
$740$	68.0088	−	22.0974i	2.50005	−	0.812317i
$741$		0			0
$742$	−11.8584	−	40.8952i	−0.435335	−	1.50131i
$743$	−12.3111	+	16.9448i	−0.451651	+	0.621644i	−0.972751	−	0.231852i	$-0.925522\pi$
$743$	−12.3111	+	16.9448i	−0.451651	+	0.621644i	0.521101	+	0.853495i	$0.325522\pi$
$744$		0			0
$745$	−12.7900	−	39.3636i	−0.468589	−	1.44217i
$746$	−31.3432	+	22.7721i	−1.14755	+	0.833747i
$747$		0			0
$748$	−15.5073	−	34.8977i	−0.567003	−	1.27599i
$749$	−14.7587	−	11.4601i	−0.539270	−	0.418744i
$750$		0			0
$751$	−0.413842	−	1.27367i	−0.0151013	−	0.0464770i	0.943222	−	0.332163i	$-0.107778\pi$
$751$	−0.413842	−	1.27367i	−0.0151013	−	0.0464770i	−0.958323	+	0.285686i	$0.907778\pi$
$752$	−13.8099	−	4.48711i	−0.503596	−	0.163628i
$753$		0			0
$754$	39.4531	+	28.6644i	1.43680	+	1.04390i
$755$	−1.04725	+	3.22312i	−0.0381135	+	0.117301i
$756$		0			0
$757$	−7.25984	+	5.27458i	−0.263863	+	0.191708i	−0.711849	−	0.702333i	$-0.752142\pi$
$757$	−7.25984	+	5.27458i	−0.263863	+	0.191708i	0.447985	+	0.894041i	$0.352142\pi$
$758$		−	51.2412i		−	1.86117i
$759$		0			0
$760$	33.3965			1.21142
$761$	−23.0606	+	16.7545i	−0.835946	+	0.607350i	−0.921235	−	0.389006i	$-0.872819\pi$
$761$	−23.0606	+	16.7545i	−0.835946	+	0.607350i	0.0852891	+	0.996356i	$0.472819\pi$
$762$		0			0
$763$	−2.19134	+	1.48759i	−0.0793320	+	0.0538544i
$764$	14.1598	+	10.2877i	0.512284	+	0.372196i
$765$		0			0
$766$	−13.7420	+	42.2936i	−0.496520	+	1.52813i
$767$	15.4782	−	5.02916i	0.558884	−	0.181592i
$768$		0			0
$769$	1.15096			0.0415047			0.0207524	−	0.999785i	$-0.493394\pi$
$769$	1.15096			0.0415047			0.0207524	+	0.999785i	$0.493394\pi$
$770$	63.3489	−	25.7609i	2.28293	−	0.928360i
$771$		0			0
$772$	38.6779	+	53.2355i	1.39205	+	1.91599i
$773$	−41.4573	+	13.4703i	−1.49111	+	0.484493i	−0.937412	−	0.348222i	$-0.886786\pi$
$773$	−41.4573	+	13.4703i	−1.49111	+	0.484493i	−0.553703	+	0.832714i	$0.686786\pi$
$774$		0			0
$775$	0.586546	−	0.807311i	0.0210694	−	0.0289995i
$776$	8.69543	+	6.31760i	0.312148	+	0.226789i
$777$		0			0
$778$	35.4935	−	11.5325i	1.27250	−	0.413462i
$779$	−27.3939	+	19.9029i	−0.981489	+	0.713094i
$780$		0			0
$781$	9.52079	−	8.56012i	0.340680	−	0.306305i
$782$			59.4856i			2.12720i
$783$		0			0
$784$	−8.52626	+	5.39865i	−0.304509	+	0.192809i
$785$	1.04234	−	3.20800i	0.0372027	−	0.114498i
$786$		0			0
$787$	14.1271	+	10.2640i	0.503578	+	0.365870i	0.810382	−	0.585902i	$-0.199260\pi$
$787$	14.1271	+	10.2640i	0.503578	+	0.365870i	−0.306804	+	0.951773i	$0.599260\pi$
$788$	44.0182	+	14.3024i	1.56808	+	0.509502i
$789$		0			0
$790$	2.17839	+	2.99829i	0.0775035	+	0.106674i
$791$	−10.0403	+	12.9302i	−0.356994	+	0.459746i
$792$		0			0
$793$	−7.49263			−0.266071
$794$	−60.7898	+	44.1663i	−2.15735	+	1.56741i
$795$		0			0
$796$	−5.54311	−	1.80106i	−0.196470	−	0.0638370i
$797$	17.2907	−	23.7987i	0.612470	−	0.842992i	−0.384308	−	0.923205i	$-0.625560\pi$
$797$	17.2907	−	23.7987i	0.612470	−	0.842992i	0.996778	+	0.0802128i	$0.0255600\pi$
$798$		0			0
$799$	38.2125	+	12.4160i	1.35186	+	0.439247i
$800$	−50.2080	+	16.3136i	−1.77512	+	0.576772i
$801$		0			0
$802$			66.6934i			2.35503i
$803$	6.72553	+	3.88946i	0.237339	+	0.137256i
$804$		0			0
$805$	−62.8923	−	2.00881i	−2.21666	−	0.0708011i
$806$	−0.255560	−	0.786532i	−0.00900170	−	0.0277044i
$807$		0			0
$808$	−22.1362	+	30.4678i	−0.778748	+	1.07185i
$809$	30.5509	−	42.0497i	1.07411	−	1.47839i	0.208269	−	0.978072i	$-0.433217\pi$
$809$	30.5509	−	42.0497i	1.07411	−	1.47839i	0.865843	−	0.500316i	$-0.166783\pi$
$810$		0			0
$811$	14.9314	+	45.9543i	0.524314	+	1.61367i	0.765669	+	0.643235i	$0.222408\pi$
$811$	14.9314	+	45.9543i	0.524314	+	1.61367i	−0.241355	+	0.970437i	$0.577592\pi$
$812$	−60.4501	−	1.93080i	−2.12138	−	0.0677579i
$813$		0			0
$814$	5.34820	+	51.2405i	0.187454	+	1.79598i
$815$		−	76.1546i		−	2.66758i
$816$		0			0
$817$	−2.48780	+	0.808335i	−0.0870370	+	0.0282800i
$818$	34.1860	+	11.1077i	1.19528	+	0.388371i
$819$		0			0
$820$	−41.8917	+	57.6589i	−1.46292	+	2.01354i
$821$	−26.2988	−	8.54501i	−0.917836	−	0.298223i	−0.188257	−	0.982120i	$-0.560284\pi$
$821$	−26.2988	−	8.54501i	−0.917836	−	0.298223i	−0.729579	+	0.683897i	$0.760284\pi$
$822$		0			0
$823$	−37.3858	+	27.1623i	−1.30319	+	0.946820i	−0.999981	−	0.00610551i	$-0.998057\pi$
$823$	−37.3858	+	27.1623i	−1.30319	+	0.946820i	−0.303205	+	0.952925i	$0.598057\pi$
$824$	−12.1734			−0.424080
$825$		0			0
$826$	−20.9568	+	26.9887i	−0.729181	+	0.939058i
$827$	−15.5930	−	21.4619i	−0.542220	−	0.746302i	0.446711	−	0.894678i	$-0.352595\pi$
$827$	−15.5930	−	21.4619i	−0.542220	−	0.746302i	−0.988931	+	0.148376i	$0.952595\pi$
$828$		0			0
$829$	22.8514	+	7.42486i	0.793661	+	0.257876i	0.677662	−	0.735373i	$-0.262993\pi$
$829$	22.8514	+	7.42486i	0.793661	+	0.257876i	0.115998	+	0.993249i	$0.462993\pi$
$830$	−31.6991	−	23.0308i	−1.10029	−	0.799410i
$831$		0			0
$832$	−11.0380	+	33.9716i	−0.382675	+	1.17775i
$833$	23.5925	−	14.9383i	0.817431	−	0.517580i
$834$		0			0
$835$			29.2291i			1.01151i
$836$	−9.65531	+	45.2640i	−0.333936	+	1.56549i
$837$		0			0
$838$	−16.7044	+	12.1365i	−0.577045	+	0.419248i
$839$	31.8386	−	10.3450i	1.09919	−	0.357148i	0.297399	−	0.954753i	$-0.403881\pi$
$839$	31.8386	−	10.3450i	1.09919	−	0.357148i	0.801791	+	0.597605i	$0.203881\pi$
$840$		0			0
$841$	27.2841	+	19.8230i	0.940830	+	0.683553i
$842$	−31.0956	+	42.7994i	−1.07162	+	1.47496i
$843$		0			0
$844$	35.8051	−	11.6338i	1.23246	−	0.400452i
$845$	10.8603	+	14.9479i	0.373604	+	0.514222i
$846$		0			0
$847$	5.09767	+	28.6533i	0.175158	+	0.984540i
$848$	−10.4961			−0.360438
$849$		0			0
$850$	62.3100	−	20.2457i	2.13721	−	0.694423i
$851$	14.6487	−	45.0839i	0.502149	−	1.54546i
$852$		0			0
$853$	0.605211	+	0.439712i	0.0207220	+	0.0150554i	0.598098	−	0.801423i	$-0.295923\pi$
$853$	0.605211	+	0.439712i	0.0207220	+	0.0150554i	−0.577376	+	0.816478i	$0.695923\pi$
$854$	13.0156	−	8.83561i	0.445384	−	0.302348i
$855$		0			0
$856$	11.1948	−	8.13348i	0.382630	−	0.277997i
$857$	47.6127			1.62642			0.813210	−	0.581971i	$-0.197718\pi$
$857$	47.6127			1.62642			0.813210	+	0.581971i	$0.197718\pi$
$858$		0			0
$859$		−	20.2115i		−	0.689606i	−0.938675	−	0.344803i	$-0.887946\pi$
$859$		−	20.2115i		−	0.689606i	0.938675	−	0.344803i	$-0.112054\pi$
$860$	−4.45429	+	3.23623i	−0.151890	+	0.110355i
$861$		0			0
$862$	21.1227	−	65.0089i	0.719441	−	2.21421i
$863$	18.3682	+	13.3453i	0.625260	+	0.454278i	0.854755	−	0.519032i	$-0.173707\pi$
$863$	18.3682	+	13.3453i	0.625260	+	0.454278i	−0.229495	+	0.973310i	$0.573707\pi$
$864$		0			0
$865$	−68.2443	−	22.1739i	−2.32038	−	0.753936i
$866$	17.4315	+	53.6487i	0.592348	+	1.82306i
$867$		0			0
$868$	0.810110	+	0.629052i	0.0274969	+	0.0213514i
$869$	−1.44131	+	0.640466i	−0.0488931	+	0.0217263i
$870$		0			0
$871$	17.9557	−	13.0456i	0.608406	−	0.442033i
$872$	−0.606099	−	1.86538i	−0.0205251	−	0.0631698i
$873$		0			0
$874$	42.3758	−	58.3253i	1.43338	−	1.97288i
$875$	6.31210	+	21.7681i	0.213388	+	0.735897i
$876$		0			0
$877$	6.08956	−	1.97862i	0.205630	−	0.0668132i	−0.204391	−	0.978889i	$-0.565521\pi$
$877$	6.08956	−	1.97862i	0.205630	−	0.0668132i	0.410021	+	0.912076i	$0.365521\pi$
$878$	8.13784	+	11.2008i	0.274639	+	0.378008i
$879$		0			0
$880$	−1.74999	−	16.7665i	−0.0589923	−	0.565198i
$881$			26.5347i			0.893976i	0.894540	+	0.446988i	$0.147503\pi$
$881$			26.5347i			0.893976i	−0.894540	+	0.446988i	$0.852497\pi$
$882$		0			0
$883$	0.182661	+	0.562172i	0.00614702	+	0.0189186i	0.954083	−	0.299542i	$-0.0968340\pi$
$883$	0.182661	+	0.562172i	0.00614702	+	0.0189186i	−0.947936	+	0.318461i	$0.896834\pi$
$884$	9.91117	−	30.5034i	0.333349	−	1.02594i
$885$		0			0
$886$	31.7512	−	43.7017i	1.06670	−	1.46819i
$887$	−14.2057	+	43.7206i	−0.476980	+	1.46799i	0.366289	+	0.930501i	$0.380628\pi$
$887$	−14.2057	+	43.7206i	−0.476980	+	1.46799i	−0.843269	+	0.537492i	$0.819372\pi$
$888$		0			0
$889$	−8.66387	−	0.276728i	−0.290577	−	0.00928115i
$890$			50.2268i			1.68361i
$891$		0			0
$892$			62.1747i			2.08176i
$893$	−28.6224	−	39.3953i	−0.957812	−	1.31831i
$894$		0			0
$895$	−44.9467	−	14.6041i	−1.50240	−	0.488161i
$896$	−10.4152	−	35.9183i	−0.347948	−	1.19995i
$897$		0			0
$898$	−2.06222	−	0.670057i	−0.0688173	−	0.0223601i
$899$	−0.328707	−	1.01166i	−0.0109630	−	0.0337406i
$900$		0			0
$901$	29.0431			0.967567
$902$	−34.3304	−	38.1831i	−1.14308	−	1.27136i
$903$		0			0
$904$	−7.12583	−	9.80786i	−0.237002	−	0.326205i
$905$	−2.10872	−	6.48996i	−0.0700961	−	0.215734i
$906$		0			0
$907$	21.4785	+	15.6051i	0.713183	+	0.518158i	0.884199	−	0.467110i	$-0.154705\pi$
$907$	21.4785	+	15.6051i	0.713183	+	0.518158i	−0.171016	+	0.985268i	$0.554705\pi$
$908$	14.2238	+	10.3342i	0.472032	+	0.342952i
$909$		0			0
$910$	54.0305	+	19.4835i	1.79109	+	0.645873i
$911$	17.9072	−	13.0104i	0.593293	−	0.431053i	−0.250199	−	0.968194i	$-0.580496\pi$
$911$	17.9072	−	13.0104i	0.593293	−	0.431053i	0.843492	+	0.537142i	$0.180496\pi$
$912$		0			0
$913$	12.3999	−	11.1487i	0.410376	−	0.368968i
$914$	46.7913			1.54772
$915$		0			0
$916$	−61.8793	+	20.1058i	−2.04455	+	0.664314i
$917$	−30.8242	−	45.4066i	−1.01791	−	1.49946i
$918$		0			0
$919$	22.8773	−	31.4879i	0.754652	−	1.03869i	−0.242988	−	0.970029i	$-0.578127\pi$
$919$	22.8773	−	31.4879i	0.754652	−	1.03869i	0.997640	−	0.0686605i	$-0.0218725\pi$
$920$	14.3996	−	44.3175i	0.474742	−	1.46111i
$921$		0			0
$922$	1.84341	+	2.53724i	0.0607095	+	0.0835595i
$923$	10.7531			0.353941
$924$		0			0
$925$	−52.2101			−1.71666
$926$	51.3085	+	70.6201i	1.68610	+	2.32072i
$927$		0			0
$928$	−17.3897	+	53.5200i	−0.570845	+	1.75688i
$929$	17.2422	−	23.7319i	0.565698	−	0.778617i	−0.426339	−	0.904564i	$-0.640197\pi$
$929$	17.2422	−	23.7319i	0.565698	−	0.778617i	0.992037	+	0.125947i	$0.0401969\pi$
$930$		0			0
$931$	−33.7739	−	2.15971i	−1.10689	−	0.0707815i
$932$	−40.6342	+	13.2029i	−1.33102	+	0.432474i
$933$		0			0
$934$	62.9115			2.05853
$935$	4.84230	+	46.3935i	0.158360	+	1.51723i
$936$		0			0
$937$	−8.46634	+	6.15116i	−0.276583	+	0.200950i	−0.717426	−	0.696635i	$-0.754680\pi$
$937$	−8.46634	+	6.15116i	−0.276583	+	0.200950i	0.440842	+	0.897585i	$0.354680\pi$
$938$	−15.8073	+	43.8358i	−0.516127	+	1.43129i
$939$		0			0
$940$	−82.9196	−	60.2446i	−2.70454	−	1.96496i
$941$	35.6430	+	25.8961i	1.16193	+	0.844190i	0.990021	−	0.140923i	$-0.0450071\pi$
$941$	35.6430	+	25.8961i	1.16193	+	0.844190i	0.171907	+	0.985113i	$0.445007\pi$
$942$		0			0
$943$	14.5998	+	44.9336i	0.475436	+	1.46324i
$944$	4.95093	+	6.81438i	0.161139	+	0.221789i
$945$		0			0
$946$	−1.61078	−	3.62492i	−0.0523710	−	0.117856i
$947$	35.0592			1.13927			0.569635	−	0.821898i	$-0.307085\pi$
$947$	35.0592			1.13927			0.569635	+	0.821898i	$0.307085\pi$
$948$		0			0
$949$	2.01639	+	6.20581i	0.0654548	+	0.201449i
$950$	−75.5171	−	24.5370i	−2.45010	−	0.796085i
$951$		0			0
$952$	5.75906	+	19.8609i	0.186652	+	0.643695i
$953$	−14.5051	−	4.71300i	−0.469867	−	0.152669i	0.0645068	−	0.997917i	$-0.479453\pi$
$953$	−14.5051	−	4.71300i	−0.469867	−	0.152669i	−0.534374	+	0.845248i	$0.679453\pi$
$954$		0			0
$955$	−12.5661	−	17.2958i	−0.406630	−	0.559679i
$956$		−	38.9461i		−	1.25961i
$957$		0			0
$958$			21.7712i			0.703397i
$959$	0.222662	−	6.97116i	0.00719012	−	0.225110i
$960$		0			0
$961$	9.57395	−	29.4656i	0.308837	−	0.950503i
$962$	−25.4331	+	35.0057i	−0.819997	+	1.12863i
$963$		0			0
$964$	−0.225529	+	0.694108i	−0.00726381	+	0.0223557i
$965$	−24.8376	−	76.4421i	−0.799549	−	2.46076i
$966$		0			0
$967$		−	35.2028i		−	1.13204i	−0.824390	−	0.566022i	$-0.808482\pi$
$967$		−	35.2028i		−	1.13204i	0.824390	−	0.566022i	$-0.191518\pi$
$968$	−21.4309	−	2.28376i	−0.688814	−	0.0734028i
$969$		0			0
$970$	−25.1291	−	34.5873i	−0.806848	−	1.11053i
$971$	−45.1439	+	14.6681i	−1.44874	+	0.470723i	−0.924609	−	0.380918i	$-0.875608\pi$
$971$	−45.1439	+	14.6681i	−1.44874	+	0.470723i	−0.524126	+	0.851640i	$0.675608\pi$
$972$		0			0
$973$	−27.2154	+	7.89164i	−0.872485	+	0.252994i
$974$	0.549155	−	0.755847i	0.0175961	−	0.0242189i
$975$		0			0
$976$	−1.19832	−	3.68804i	−0.0383572	−	0.118051i
$977$	12.3533	−	8.97523i	0.395219	−	0.287143i	−0.372372	−	0.928084i	$-0.621455\pi$
$977$	12.3533	−	8.97523i	0.395219	−	0.287143i	0.767591	+	0.640940i	$0.221455\pi$
$978$		0			0
$979$	−20.9047	−	4.45921i	−0.668119	−	0.142517i
$980$	−69.0130	+	17.6440i	−2.20454	+	0.563616i
$981$		0			0
$982$	−19.3069	−	59.4206i	−0.616109	−	1.89619i
$983$	−3.13931	−	1.02002i	−0.100129	−	0.0325337i	0.258524	−	0.966005i	$-0.416764\pi$
$983$	−3.13931	−	1.02002i	−0.100129	−	0.0325337i	−0.358653	+	0.933471i	$0.616764\pi$
$984$		0			0
$985$	−45.7369	−	33.2298i	−1.45730	−	1.05879i
$986$	21.5813	−	66.4203i	0.687287	−	2.11525i
$987$		0			0
$988$	−31.4476	+	22.8480i	−1.00048	+	0.726893i
$989$			3.64987i			0.116059i
$990$		0			0
$991$	53.1350			1.68789			0.843944	−	0.536432i	$-0.180228\pi$
$991$	53.1350			1.68789			0.843944	+	0.536432i	$0.180228\pi$
$992$	0.772064	−	0.560937i	0.0245130	−	0.0178098i
$993$		0			0
$994$	−18.6793	+	12.6805i	−0.592473	+	0.402199i
$995$	5.75953	+	4.18454i	0.182589	+	0.132659i
$996$		0			0
$997$	3.10555	−	9.55789i	0.0983536	−	0.302701i	−0.889760	−	0.456430i	$-0.849128\pi$
$997$	3.10555	−	9.55789i	0.0983536	−	0.302701i	0.988113	+	0.153728i	$0.0491280\pi$
$998$	−41.9514	+	13.6309i	−1.32795	+	0.431477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.bu.f.118.4		64
3.2	odd	2		231.2.w.a.118.13	✓	64
7.6	odd	2	inner	693.2.bu.f.118.3		64
11.7	odd	10	inner	693.2.bu.f.370.3		64
21.20	even	2		231.2.w.a.118.14	yes	64
33.29	even	10		231.2.w.a.139.14	yes	64
77.62	even	10	inner	693.2.bu.f.370.4		64
231.62	odd	10		231.2.w.a.139.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.118.13	✓	64	3.2	odd	2
231.2.w.a.118.14	yes	64	21.20	even	2
231.2.w.a.139.13	yes	64	231.62	odd	10
231.2.w.a.139.14	yes	64	33.29	even	10
693.2.bu.f.118.3		64	7.6	odd	2	inner
693.2.bu.f.118.4		64	1.1	even	1	trivial
693.2.bu.f.370.3		64	11.7	odd	10	inner
693.2.bu.f.370.4		64	77.62	even	10	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29930 - 1.78834i) q^{2} +(-0.891932 + 2.74508i) q^{4} +(2.07229 - 2.85226i) q^{5} +(-1.48601 - 2.18901i) q^{7} +(1.86340 - 0.605454i) q^{8} +O(q^{10})\)	\(q+(-1.29930 - 1.78834i) q^{2} +(-0.891932 + 2.74508i) q^{4} +(2.07229 - 2.85226i) q^{5} +(-1.48601 - 2.18901i) q^{7} +(1.86340 - 0.605454i) q^{8} -7.79336 q^{10} +(0.691907 - 3.24365i) q^{11} +(2.25356 - 1.63731i) q^{13} +(-1.98392 + 5.50168i) q^{14} +(1.16634 + 0.847394i) q^{16} +(-3.22730 - 2.34477i) q^{17} +(1.49400 + 4.59807i) q^{19} +(5.98136 + 8.23264i) q^{20} +(-6.69975 + 2.97713i) q^{22} +6.74587 q^{23} +(-2.29594 - 7.06616i) q^{25} +(-5.85612 - 1.90277i) q^{26} +(7.33445 - 2.12677i) q^{28} +(-7.53228 - 2.44739i) q^{29} +(0.0789450 + 0.108659i) q^{31} -7.10541i q^{32} +8.81808i q^{34} +(-9.32309 - 0.297783i) q^{35} +(2.17150 - 6.68319i) q^{37} +(6.28175 - 8.64608i) q^{38} +(2.13459 - 6.56958i) q^{40} +(2.16426 + 6.66091i) q^{41} +0.541053i q^{43} +(8.28696 + 4.79246i) q^{44} +(-8.76494 - 12.0639i) q^{46} +(-9.57909 + 3.11244i) q^{47} +(-2.58356 + 6.50578i) q^{49} +(-9.65358 + 13.2870i) q^{50} +(2.48452 + 7.64658i) q^{52} +(-5.89006 + 4.27938i) q^{53} +(-7.81791 - 8.69529i) q^{55} +(-4.09437 - 3.17929i) q^{56} +(5.40997 + 16.6502i) q^{58} +(5.55659 + 1.80544i) q^{59} +(-2.17611 - 1.58103i) q^{61} +(0.0917447 - 0.282361i) q^{62} +(-10.3742 + 7.53731i) q^{64} -9.82072i q^{65} +7.96771 q^{67} +(9.31512 - 6.76783i) q^{68} +(11.5810 + 17.0598i) q^{70} +(3.12305 + 2.26903i) q^{71} +(-0.723874 + 2.22786i) q^{73} +(-14.7733 + 4.80012i) q^{74} -13.9546 q^{76} +(-8.12857 + 3.30550i) q^{77} +(-0.279518 - 0.384724i) q^{79} +(4.83398 - 1.57066i) q^{80} +(9.09994 - 12.5250i) q^{82} +(4.06746 + 2.95518i) q^{83} +(-13.3758 + 4.34606i) q^{85} +(0.967586 - 0.702992i) q^{86} +(-0.674586 - 6.46313i) q^{88} -6.44482i q^{89} +(-6.93289 - 2.50002i) q^{91} +(-6.01686 + 18.5180i) q^{92} +(18.0123 + 13.0867i) q^{94} +(16.2109 + 5.26725i) q^{95} +(3.22443 + 4.43805i) q^{97} +(14.9914 - 3.83272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} + 20 q^{8}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 + 20 * q^8	\( 64 q + 12 q^{4} + 10 q^{7} + 20 q^{8} + 16 q^{11} - 12 q^{14} - 16 q^{16} - 40 q^{22} + 24 q^{23} + 44 q^{25} - 30 q^{28} + 40 q^{29} + 40 q^{35} + 32 q^{37} - 22 q^{44} - 70 q^{46} - 50 q^{49} + 64 q^{53} - 80 q^{56} + 2 q^{58} + 72 q^{64} - 8 q^{67} - 26 q^{70} - 68 q^{71} - 80 q^{74} - 90 q^{77} + 40 q^{79} - 40 q^{85} + 62 q^{86} + 140 q^{88} + 54 q^{91} - 18 q^{92} - 20 q^{95}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 + 20 * q^8 + 16 * q^11 - 12 * q^14 - 16 * q^16 - 40 * q^22 + 24 * q^23 + 44 * q^25 - 30 * q^28 + 40 * q^29 + 40 * q^35 + 32 * q^37 - 22 * q^44 - 70 * q^46 - 50 * q^49 + 64 * q^53 - 80 * q^56 + 2 * q^58 + 72 * q^64 - 8 * q^67 - 26 * q^70 - 68 * q^71 - 80 * q^74 - 90 * q^77 + 40 * q^79 - 40 * q^85 + 62 * q^86 + 140 * q^88 + 54 * q^91 - 18 * q^92 - 20 * q^95

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