LMFDB - Embedded newform 784.2.bb.b.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.4
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36747 - 1.71475i) q^{3} +(1.64860 - 1.31472i) q^{5} +(-1.20605 + 2.35488i) q^{7} +(-0.402843 + 1.76497i) q^{9} +O(q^{10})$	\(q+(-1.36747 - 1.71475i) q^{3} +(1.64860 - 1.31472i) q^{5} +(-1.20605 + 2.35488i) q^{7} +(-0.402843 + 1.76497i) q^{9} +(1.05178 - 0.240061i) q^{11} +(2.11117 - 0.481860i) q^{13} +(-4.50883 - 1.02911i) q^{15} +(3.50399 - 7.27611i) q^{17} +4.92145 q^{19} +(5.68727 - 1.15214i) q^{21} +(-3.41983 - 7.10135i) q^{23} +(-0.123196 + 0.539756i) q^{25} +(-2.35079 + 1.13208i) q^{27} +(-4.15434 - 2.00062i) q^{29} -3.18545 q^{31} +(-1.84992 - 1.47526i) q^{33} +(1.10769 + 5.46787i) q^{35} +(-0.399047 - 0.192171i) q^{37} +(-3.71323 - 2.96120i) q^{39} +(-6.95616 + 5.54735i) q^{41} +(3.49703 + 2.78878i) q^{43} +(1.65631 + 3.43936i) q^{45} +(-1.14186 - 5.00283i) q^{47} +(-4.09088 - 5.68020i) q^{49} +(-17.2683 + 3.94139i) q^{51} +(0.514057 - 0.247557i) q^{53} +(1.41835 - 1.77855i) q^{55} +(-6.72994 - 8.43907i) q^{57} +(6.38084 - 8.00132i) q^{59} +(-3.00244 + 6.23463i) q^{61} +(-3.67044 - 3.07729i) q^{63} +(2.84696 - 3.56998i) q^{65} -11.8184i q^{67} +(-7.50055 + 15.5751i) q^{69} +(-3.82590 - 7.94455i) q^{71} +(15.8020 + 3.60670i) q^{73} +(1.09401 - 0.526850i) q^{75} +(-0.703183 + 2.76633i) q^{77} -3.47997i q^{79} +(10.0491 + 4.83940i) q^{81} +(-1.33658 + 5.85592i) q^{83} +(-3.78933 - 16.6022i) q^{85} +(2.25036 + 9.85946i) q^{87} +(-3.30946 - 0.755363i) q^{89} +(-1.41146 + 5.55268i) q^{91} +(4.35602 + 5.46227i) q^{93} +(8.11351 - 6.47030i) q^{95} -10.5910i q^{97} +1.95306i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.36747	−	1.71475i	−0.789510	−	0.990014i	−0.999923	−	0.0124014i	$-0.996052\pi$
$3$	−1.36747	−	1.71475i	−0.789510	−	0.990014i	0.210413	−	0.977613i	$-0.432519\pi$
$4$		0			0
$5$	1.64860	−	1.31472i	0.737277	−	0.587959i	−0.181194	−	0.983447i	$-0.557996\pi$
$5$	1.64860	−	1.31472i	0.737277	−	0.587959i	0.918471	+	0.395489i	$0.129425\pi$
$6$		0			0
$7$	−1.20605	+	2.35488i	−0.455845	+	0.890059i
$7$	−1.20605	+	2.35488i	−0.455845	+	0.890059i
$8$		0			0
$9$	−0.402843	+	1.76497i	−0.134281	+	0.588323i
$10$		0			0
$11$	1.05178	−	0.240061i	0.317123	−	0.0723812i	−0.0609968	−	0.998138i	$-0.519428\pi$
$11$	1.05178	−	0.240061i	0.317123	−	0.0723812i	0.378120	+	0.925757i	$0.376571\pi$
$12$		0			0
$13$	2.11117	−	0.481860i	0.585532	−	0.133644i	0.0805153	−	0.996753i	$-0.474343\pi$
$13$	2.11117	−	0.481860i	0.585532	−	0.133644i	0.505017	+	0.863109i	$0.331486\pi$
$14$		0			0
$15$	−4.50883	−	1.02911i	−1.16417	−	0.265715i
$16$		0			0
$17$	3.50399	−	7.27611i	0.849842	−	1.76472i	0.242742	−	0.970091i	$-0.421953\pi$
$17$	3.50399	−	7.27611i	0.849842	−	1.76472i	0.607101	−	0.794625i	$-0.292332\pi$
$18$		0			0
$19$	4.92145			1.12906			0.564529	−	0.825413i	$-0.309058\pi$
$19$	4.92145			1.12906			0.564529	+	0.825413i	$0.309058\pi$
$20$		0			0
$21$	5.68727	−	1.15214i	1.24106	−	0.251418i
$22$		0			0
$23$	−3.41983	−	7.10135i	−0.713084	−	1.48073i	−0.869964	−	0.493116i	$-0.835858\pi$
$23$	−3.41983	−	7.10135i	−0.713084	−	1.48073i	0.156880	−	0.987618i	$-0.449856\pi$
$24$		0			0
$25$	−0.123196	+	0.539756i	−0.0246391	+	0.107951i
$26$		0			0
$27$	−2.35079	+	1.13208i	−0.452410	+	0.217869i
$28$		0			0
$29$	−4.15434	−	2.00062i	−0.771441	−	0.371506i	0.00639035	−	0.999980i	$-0.497966\pi$
$29$	−4.15434	−	2.00062i	−0.771441	−	0.371506i	−0.777831	+	0.628473i	$0.783680\pi$
$30$		0			0
$31$	−3.18545			−0.572124			−0.286062	−	0.958211i	$-0.592346\pi$
$31$	−3.18545			−0.572124			−0.286062	+	0.958211i	$0.592346\pi$
$32$		0			0
$33$	−1.84992	−	1.47526i	−0.322030	−	0.256810i
$34$		0			0
$35$	1.10769	+	5.46787i	0.187234	+	0.924238i
$36$		0			0
$37$	−0.399047	−	0.192171i	−0.0656029	−	0.0315927i	0.400795	−	0.916168i	$-0.368734\pi$
$37$	−0.399047	−	0.192171i	−0.0656029	−	0.0315927i	−0.466398	+	0.884575i	$0.654448\pi$
$38$		0			0
$39$	−3.71323	−	2.96120i	−0.594593	−	0.474172i
$40$		0			0
$41$	−6.95616	+	5.54735i	−1.08637	+	0.866351i	−0.991625	−	0.129151i	$-0.958775\pi$
$41$	−6.95616	+	5.54735i	−1.08637	+	0.866351i	−0.0947445	+	0.995502i	$0.530203\pi$
$42$		0			0
$43$	3.49703	+	2.78878i	0.533291	+	0.425286i	0.852754	−	0.522313i	$-0.174931\pi$
$43$	3.49703	+	2.78878i	0.533291	+	0.425286i	−0.319462	+	0.947599i	$0.603502\pi$
$44$		0			0
$45$	1.65631	+	3.43936i	0.246908	+	0.512709i
$46$		0			0
$47$	−1.14186	−	5.00283i	−0.166558	−	0.729737i	−0.987356	−	0.158519i	$-0.949328\pi$
$47$	−1.14186	−	5.00283i	−0.166558	−	0.729737i	0.820798	−	0.571218i	$-0.193529\pi$
$48$		0			0
$49$	−4.09088	−	5.68020i	−0.584411	−	0.811458i
$50$		0			0
$51$	−17.2683	+	3.94139i	−2.41805	+	0.551905i
$52$		0			0
$53$	0.514057	−	0.247557i	0.0706111	−	0.0340045i	−0.398245	−	0.917279i	$-0.630381\pi$
$53$	0.514057	−	0.247557i	0.0706111	−	0.0340045i	0.468856	+	0.883275i	$0.344666\pi$
$54$		0			0
$55$	1.41835	−	1.77855i	0.191250	−	0.239820i
$56$		0			0
$57$	−6.72994	−	8.43907i	−0.891402	−	1.11778i
$58$		0			0
$59$	6.38084	−	8.00132i	0.830715	−	1.04168i	−0.167724	−	0.985834i	$-0.553642\pi$
$59$	6.38084	−	8.00132i	0.830715	−	1.04168i	0.998439	−	0.0558495i	$-0.0177867\pi$
$60$		0			0
$61$	−3.00244	+	6.23463i	−0.384423	+	0.798263i	0.615526	+	0.788117i	$0.288944\pi$
$61$	−3.00244	+	6.23463i	−0.384423	+	0.798263i	−0.999949	+	0.0101456i	$0.996770\pi$
$62$		0			0
$63$	−3.67044	−	3.07729i	−0.462431	−	0.387702i
$64$		0			0
$65$	2.84696	−	3.56998i	0.353122	−	0.442801i
$66$		0			0
$67$		−	11.8184i		−	1.44384i	−0.691975	−	0.721921i	$-0.743259\pi$
$67$		−	11.8184i		−	1.44384i	0.691975	−	0.721921i	$-0.256741\pi$
$68$		0			0
$69$	−7.50055	+	15.5751i	−0.902960	+	1.87502i
$70$		0			0
$71$	−3.82590	−	7.94455i	−0.454050	−	0.942845i	−0.994818	−	0.101673i	$-0.967580\pi$
$71$	−3.82590	−	7.94455i	−0.454050	−	0.942845i	0.540768	−	0.841172i	$-0.318134\pi$
$72$		0			0
$73$	15.8020	+	3.60670i	1.84948	+	0.422132i	0.995216	−	0.0977039i	$-0.0311498\pi$
$73$	15.8020	+	3.60670i	1.84948	+	0.422132i	0.854266	+	0.519836i	$0.174007\pi$
$74$		0			0
$75$	1.09401	−	0.526850i	0.126326	−	0.0608354i
$76$		0			0
$77$	−0.703183	+	2.76633i	−0.0801352	+	0.315253i
$78$		0			0
$79$		−	3.47997i		−	0.391527i	−0.980651	−	0.195763i	$-0.937282\pi$
$79$		−	3.47997i		−	0.391527i	0.980651	−	0.195763i	$-0.0627185\pi$
$80$		0			0
$81$	10.0491	+	4.83940i	1.11657	+	0.537711i
$82$		0			0
$83$	−1.33658	+	5.85592i	−0.146708	+	0.642771i	0.847078	+	0.531468i	$0.178359\pi$
$83$	−1.33658	+	5.85592i	−0.146708	+	0.642771i	−0.993787	+	0.111303i	$0.964498\pi$
$84$		0			0
$85$	−3.78933	−	16.6022i	−0.411011	−	1.80076i
$86$		0			0
$87$	2.25036	+	9.85946i	0.241264	+	1.05705i
$88$		0			0
$89$	−3.30946	−	0.755363i	−0.350802	−	0.0800683i	0.0434889	−	0.999054i	$-0.486153\pi$
$89$	−3.30946	−	0.755363i	−0.350802	−	0.0800683i	−0.394291	+	0.918986i	$0.629010\pi$
$90$		0			0
$91$	−1.41146	+	5.55268i	−0.147961	+	0.582079i
$92$		0			0
$93$	4.35602	+	5.46227i	0.451698	+	0.566411i
$94$		0			0
$95$	8.11351	−	6.47030i	0.832428	−	0.663839i
$96$		0			0
$97$		−	10.5910i		−	1.07535i	−0.843153	−	0.537674i	$-0.819303\pi$
$97$		−	10.5910i		−	1.07535i	0.843153	−	0.537674i	$-0.180697\pi$
$98$		0			0
$99$			1.95306i			0.196290i
$100$		0			0
$101$	−5.15657	+	4.11223i	−0.513098	+	0.409182i	−0.845516	−	0.533950i	$-0.820707\pi$
$101$	−5.15657	+	4.11223i	−0.513098	+	0.409182i	0.332418	+	0.943132i	$0.392136\pi$
$102$		0			0
$103$	5.12362	+	6.42482i	0.504846	+	0.633056i	0.967315	−	0.253579i	$-0.0816078\pi$
$103$	5.12362	+	6.42482i	0.504846	+	0.633056i	−0.462469	+	0.886635i	$0.653036\pi$
$104$		0			0
$105$	7.86131	−	9.37657i	0.767185	−	0.915060i
$106$		0			0
$107$	3.43172	+	0.783268i	0.331757	+	0.0757213i	0.385155	−	0.922852i	$-0.374148\pi$
$107$	3.43172	+	0.783268i	0.331757	+	0.0757213i	−0.0533980	+	0.998573i	$0.517005\pi$
$108$		0			0
$109$	−1.85313	−	8.11908i	−0.177497	−	0.777667i	−0.982781	−	0.184777i	$-0.940844\pi$
$109$	−1.85313	−	8.11908i	−0.177497	−	0.777667i	0.805283	−	0.592891i	$-0.202013\pi$
$110$		0			0
$111$	0.216159	+	0.947056i	0.0205169	+	0.0898906i
$112$		0			0
$113$	0.868884	−	3.80683i	0.0817377	−	0.358116i	−0.917475	−	0.397794i	$-0.869776\pi$
$113$	0.868884	−	3.80683i	0.0817377	−	0.358116i	0.999213	+	0.0396775i	$0.0126331\pi$
$114$		0			0
$115$	−14.9742	−	7.21119i	−1.39635	−	0.672447i
$116$		0			0
$117$			3.92026i			0.362428i
$118$		0			0
$119$	12.9083	+	17.0268i	1.18331	+	1.56085i
$120$		0			0
$121$	−8.86205	+	4.26774i	−0.805641	+	0.387976i
$122$		0			0
$123$	19.0247	+	4.34226i	1.71540	+	0.391529i
$124$		0			0
$125$	5.08105	+	10.5509i	0.454463	+	0.943702i
$126$		0			0
$127$	−1.18729	+	2.46542i	−0.105355	+	0.218771i	−0.946981	−	0.321289i	$-0.895884\pi$
$127$	−1.18729	+	2.46542i	−0.105355	+	0.218771i	0.841627	+	0.540060i	$0.181598\pi$
$128$		0			0
$129$		−	9.81012i		−	0.863733i
$130$		0			0
$131$	8.39338	−	10.5250i	0.733333	−	0.919570i	−0.265677	−	0.964062i	$-0.585595\pi$
$131$	8.39338	−	10.5250i	0.733333	−	0.919570i	0.999010	+	0.0444918i	$0.0141669\pi$
$132$		0			0
$133$	−5.93552	+	11.5894i	−0.514675	+	1.00493i
$134$		0			0
$135$	−2.38715	+	4.95697i	−0.205453	+	0.426628i
$136$		0			0
$137$	8.34667	−	10.4664i	0.713104	−	0.894205i	−0.284821	−	0.958581i	$-0.591934\pi$
$137$	8.34667	−	10.4664i	0.713104	−	0.894205i	0.997926	+	0.0643760i	$0.0205057\pi$
$138$		0			0
$139$	11.7671	+	14.7555i	0.998073	+	1.25154i	0.967726	+	0.252005i	$0.0810899\pi$
$139$	11.7671	+	14.7555i	0.998073	+	1.25154i	0.0303473	+	0.999539i	$0.490339\pi$
$140$		0			0
$141$	−7.01716	+	8.79924i	−0.590951	+	0.741029i
$142$		0			0
$143$	2.10480	−	1.01362i	0.176012	−	0.0847631i
$144$		0			0
$145$	−9.47909	+	2.16354i	−0.787196	+	0.179672i
$146$		0			0
$147$	−4.14600	+	14.7824i	−0.341956	+	1.21923i
$148$		0			0
$149$	1.75875	+	7.70557i	0.144082	+	0.631265i	0.994462	+	0.105096i	$0.0335149\pi$
$149$	1.75875	+	7.70557i	0.144082	+	0.631265i	−0.850380	+	0.526169i	$0.823628\pi$
$150$		0			0
$151$	9.59780	+	19.9300i	0.781058	+	1.62188i	0.783108	+	0.621886i	$0.213633\pi$
$151$	9.59780	+	19.9300i	0.781058	+	1.62188i	−0.00204983	+	0.999998i	$0.500652\pi$
$152$		0			0
$153$	11.4306	+	9.11557i	0.924106	+	0.736950i
$154$		0			0
$155$	−5.25154	+	4.18797i	−0.421814	+	0.336386i
$156$		0			0
$157$	17.2620	+	13.7660i	1.37766	+	1.09865i	0.983759	+	0.179496i	$0.0574467\pi$
$157$	17.2620	+	13.7660i	1.37766	+	1.09865i	0.393903	+	0.919152i	$0.371125\pi$
$158$		0			0
$159$	−1.12746	−	0.542955i	−0.0894131	−	0.0430591i
$160$		0			0
$161$	20.8473	+	0.511320i	1.64300	+	0.0402977i
$162$		0			0
$163$	2.03784	+	1.62513i	0.159616	+	0.127290i	0.700041	−	0.714103i	$-0.253165\pi$
$163$	2.03784	+	1.62513i	0.159616	+	0.127290i	−0.540425	+	0.841392i	$0.681736\pi$
$164$		0			0
$165$	−4.98933			−0.388419
$166$		0			0
$167$	−1.69198	−	0.814816i	−0.130930	−	0.0630524i	0.367272	−	0.930114i	$-0.380292\pi$
$167$	−1.69198	−	0.814816i	−0.130930	−	0.0630524i	−0.498202	+	0.867061i	$0.666006\pi$
$168$		0			0
$169$	−7.48776	+	3.60592i	−0.575982	+	0.277378i
$170$		0			0
$171$	−1.98257	+	8.68621i	−0.151611	+	0.664251i
$172$		0			0
$173$	−1.37927	−	2.86409i	−0.104864	−	0.217753i	0.841934	−	0.539580i	$-0.181417\pi$
$173$	−1.37927	−	2.86409i	−0.104864	−	0.217753i	−0.946798	+	0.321828i	$0.895703\pi$
$174$		0			0
$175$	−1.12248	−	0.941084i	−0.0848513	−	0.0711392i
$176$		0			0
$177$	−22.4459			−1.68714
$178$		0			0
$179$	−1.70051	+	3.53114i	−0.127102	+	0.263930i	−0.954803	−	0.297239i	$-0.903934\pi$
$179$	−1.70051	+	3.53114i	−0.127102	+	0.263930i	0.827701	+	0.561169i	$0.189648\pi$
$180$		0			0
$181$	7.02485	+	1.60338i	0.522153	+	0.119178i	0.475470	−	0.879732i	$-0.342278\pi$
$181$	7.02485	+	1.60338i	0.522153	+	0.119178i	0.0466828	+	0.998910i	$0.485135\pi$
$182$		0			0
$183$	14.7966	−	3.37723i	1.09380	−	0.249652i
$184$		0			0
$185$	−0.910520	+	0.207820i	−0.0669427	+	0.0152792i
$186$		0			0
$187$	1.93870	−	8.49402i	0.141772	−	0.621144i
$188$		0			0
$189$	0.169265	−	6.90117i	0.0123122	−	0.501986i
$190$		0			0
$191$	3.42623	−	2.73232i	0.247913	−	0.197704i	−0.491647	−	0.870795i	$-0.663605\pi$
$191$	3.42623	−	2.73232i	0.247913	−	0.197704i	0.739560	+	0.673091i	$0.235034\pi$
$192$		0			0
$193$	−14.4718	−	18.1471i	−1.04170	−	1.30625i	−0.950602	−	0.310412i	$-0.899533\pi$
$193$	−14.4718	−	18.1471i	−1.04170	−	1.30625i	−0.0911009	−	0.995842i	$-0.529039\pi$
$194$		0			0
$195$	−10.0148			−0.717173
$196$		0			0
$197$	−1.16002			−0.0826481			−0.0413240	−	0.999146i	$-0.513158\pi$
$197$	−1.16002			−0.0826481			−0.0413240	+	0.999146i	$0.513158\pi$
$198$		0			0
$199$	−3.00209	−	3.76450i	−0.212812	−	0.266858i	0.663955	−	0.747772i	$-0.268876\pi$
$199$	−3.00209	−	3.76450i	−0.212812	−	0.266858i	−0.876768	+	0.480914i	$0.840305\pi$
$200$		0			0
$201$	−20.2656	+	16.1613i	−1.42942	+	1.13993i
$202$		0			0
$203$	9.72156	−	7.37009i	0.682320	−	0.517279i
$204$		0			0
$205$	−4.17474	+	18.2907i	−0.291577	+	1.27748i
$206$		0			0
$207$	13.9113	−	3.17517i	0.966904	−	0.220689i
$208$		0			0
$209$	5.17627	−	1.18145i	0.358050	−	0.0817225i
$210$		0			0
$211$	5.66616	+	1.29327i	0.390075	+	0.0890320i	0.413060	−	0.910704i	$-0.364460\pi$
$211$	5.66616	+	1.29327i	0.390075	+	0.0890320i	−0.0229852	+	0.999736i	$0.507317\pi$
$212$		0			0
$213$	−8.39116	+	17.4244i	−0.574953	+	1.19390i
$214$		0			0
$215$	9.43166			0.643234
$216$		0			0
$217$	3.84182	−	7.50135i	0.260800	−	0.509225i
$218$		0			0
$219$	−15.4241	−	32.0286i	−1.04227	−	2.16429i
$220$		0			0
$221$	3.89144	−	17.0495i	0.261767	−	1.14687i
$222$		0			0
$223$	−16.9804	+	8.17735i	−1.13709	+	0.547596i	−0.905133	−	0.425129i	$-0.860229\pi$
$223$	−16.9804	+	8.17735i	−1.13709	+	0.547596i	−0.231962	+	0.972725i	$0.574514\pi$
$224$		0			0
$225$	−0.903024	−	0.434873i	−0.0602016	−	0.0289916i
$226$		0			0
$227$	20.1491			1.33735			0.668673	−	0.743557i	$-0.266863\pi$
$227$	20.1491			1.33735			0.668673	+	0.743557i	$0.266863\pi$
$228$		0			0
$229$	−6.60026	−	5.26353i	−0.436158	−	0.347824i	0.380665	−	0.924713i	$-0.375695\pi$
$229$	−6.60026	−	5.26353i	−0.436158	−	0.347824i	−0.816823	+	0.576889i	$0.804267\pi$
$230$		0			0
$231$	5.70516	−	2.57709i	0.375372	−	0.169560i
$232$		0			0
$233$	9.25516	+	4.45705i	0.606326	+	0.291991i	0.711746	−	0.702437i	$-0.247905\pi$
$233$	9.25516	+	4.45705i	0.606326	+	0.291991i	−0.105420	+	0.994428i	$0.533619\pi$
$234$		0			0
$235$	−8.45977	−	6.74644i	−0.551855	−	0.440089i
$236$		0			0
$237$	−5.96729	+	4.75875i	−0.387617	+	0.309114i
$238$		0			0
$239$	9.18756	+	7.32684i	0.594294	+	0.473934i	0.873850	−	0.486196i	$-0.161616\pi$
$239$	9.18756	+	7.32684i	0.594294	+	0.473934i	−0.279556	+	0.960129i	$0.590187\pi$
$240$		0			0
$241$	−1.65636	−	3.43946i	−0.106695	−	0.221555i	0.840785	−	0.541369i	$-0.182094\pi$
$241$	−1.65636	−	3.43946i	−0.106695	−	0.221555i	−0.947480	+	0.319814i	$0.896380\pi$
$242$		0			0
$243$	−3.70170	−	16.2182i	−0.237464	−	1.04040i
$244$		0			0
$245$	−14.2121	−	3.98605i	−0.907977	−	0.254659i
$246$		0			0
$247$	10.3900	−	2.37145i	0.661100	−	0.150892i
$248$		0			0
$249$	11.8692	−	5.71590i	0.752180	−	0.362231i
$250$		0			0
$251$	5.81272	−	7.28892i	0.366895	−	0.460072i	−0.563776	−	0.825927i	$-0.690652\pi$
$251$	5.81272	−	7.28892i	0.366895	−	0.460072i	0.930672	+	0.365855i	$0.119223\pi$
$252$		0			0
$253$	−5.30166	−	6.64807i	−0.333312	−	0.417960i
$254$		0			0
$255$	−23.2868	+	29.2007i	−1.45828	+	1.82862i
$256$		0			0
$257$	−6.98226	+	14.4988i	−0.435541	+	0.904410i	0.561495	+	0.827480i	$0.310226\pi$
$257$	−6.98226	+	14.4988i	−0.435541	+	0.904410i	−0.997036	+	0.0769306i	$0.975488\pi$
$258$		0			0
$259$	0.933810	−	0.707938i	0.0580241	−	0.0439891i
$260$		0			0
$261$	5.20458	−	6.52634i	0.322156	−	0.403970i
$262$		0			0
$263$			5.03849i			0.310687i	0.987861	+	0.155343i	$0.0496484\pi$
$263$			5.03849i			0.310687i	−0.987861	+	0.155343i	$0.950352\pi$
$264$		0			0
$265$	0.522008	−	1.08396i	0.0320667	−	0.0665872i
$266$		0			0
$267$	3.23033	+	6.70785i	0.197693	+	0.410514i
$268$		0			0
$269$	28.1681	+	6.42917i	1.71744	+	0.391994i	0.964079	−	0.265617i	$-0.0855757\pi$
$269$	28.1681	+	6.42917i	1.71744	+	0.391994i	0.753358	+	0.657611i	$0.228433\pi$
$270$		0			0
$271$	−20.8120	+	10.0225i	−1.26424	+	0.608824i	−0.941292	−	0.337594i	$-0.890387\pi$
$271$	−20.8120	+	10.0225i	−1.26424	+	0.608824i	−0.322945	+	0.946418i	$0.604673\pi$
$272$		0			0
$273$	11.4516	−	5.17283i	0.693083	−	0.313074i
$274$		0			0
$275$			0.597277i			0.0360172i
$276$		0			0
$277$	−0.767788	−	0.369747i	−0.0461319	−	0.0222160i	0.410676	−	0.911782i	$-0.365293\pi$
$277$	−0.767788	−	0.369747i	−0.0461319	−	0.0222160i	−0.456807	+	0.889566i	$0.651007\pi$
$278$		0			0
$279$	1.28324	−	5.62223i	0.0768254	−	0.336594i
$280$		0			0
$281$	5.40816	+	23.6947i	0.322624	+	1.41351i	0.832865	+	0.553476i	$0.186699\pi$
$281$	5.40816	+	23.6947i	0.322624	+	1.41351i	−0.510242	+	0.860031i	$0.670444\pi$
$282$		0			0
$283$	2.39358	+	10.4870i	0.142284	+	0.623385i	0.994902	+	0.100851i	$0.0321564\pi$
$283$	2.39358	+	10.4870i	0.142284	+	0.623385i	−0.852618	+	0.522535i	$0.824986\pi$
$284$		0			0
$285$	−22.1900	−	5.06472i	−1.31442	−	0.300008i
$286$		0			0
$287$	−4.67384	−	23.0713i	−0.275888	−	1.36185i
$288$		0			0
$289$	−30.0645	−	37.6997i	−1.76850	−	2.21763i
$290$		0			0
$291$	−18.1609	+	14.4828i	−1.06461	+	0.848998i
$292$		0			0
$293$			19.8464i			1.15944i	0.814816	+	0.579719i	$0.196838\pi$
$293$			19.8464i			1.15944i	−0.814816	+	0.579719i	$0.803162\pi$
$294$		0			0
$295$		−	21.5800i		−	1.25644i
$296$		0			0
$297$	−2.20074	+	1.75503i	−0.127700	+	0.101837i
$298$		0			0
$299$	−10.6417	−	13.3442i	−0.615424	−	0.771718i
$300$		0			0
$301$	−10.7848	+	4.87164i	−0.621627	+	0.280797i
$302$		0			0
$303$	14.1029	+	3.21890i	0.810192	+	0.184921i
$304$		0			0
$305$	3.24694	+	14.2258i	0.185919	+	0.814565i
$306$		0			0
$307$	−1.05991	−	4.64375i	−0.0604920	−	0.265033i	0.935634	−	0.352972i	$-0.114829\pi$
$307$	−1.05991	−	4.64375i	−0.0604920	−	0.265033i	−0.996126	+	0.0879393i	$0.971972\pi$
$308$		0			0
$309$	4.01058	−	17.5715i	0.228154	−	0.999608i
$310$		0			0
$311$	8.07342	+	3.88795i	0.457801	+	0.220466i	0.648548	−	0.761174i	$-0.275377\pi$
$311$	8.07342	+	3.88795i	0.457801	+	0.220466i	−0.190747	+	0.981639i	$0.561091\pi$
$312$		0			0
$313$		−	16.0413i		−	0.906711i	−0.891330	−	0.453355i	$-0.850227\pi$
$313$		−	16.0413i		−	0.906711i	0.891330	−	0.453355i	$-0.149773\pi$
$314$		0			0
$315$	−10.0968	−	0.247645i	−0.568893	−	0.0139532i
$316$		0			0
$317$	−24.3009	+	11.7027i	−1.36487	+	0.657288i	−0.965718	−	0.259595i	$-0.916411\pi$
$317$	−24.3009	+	11.7027i	−1.36487	+	0.657288i	−0.399156	+	0.916883i	$0.630697\pi$
$318$		0			0
$319$	−4.84971	−	1.10691i	−0.271532	−	0.0619753i
$320$		0			0
$321$	−3.34967	−	6.95565i	−0.186960	−	0.388227i
$322$		0			0
$323$	17.2447	−	35.8090i	0.959521	−	1.99247i
$324$		0			0
$325$			1.19888i			0.0665017i
$326$		0			0
$327$	−11.3881	+	14.2803i	−0.629765	+	0.789701i
$328$		0			0
$329$	13.1582	+	3.34472i	0.725434	+	0.184401i
$330$		0			0
$331$	−10.8948	+	22.6233i	−0.598832	+	1.24349i	0.352643	+	0.935758i	$0.385283\pi$
$331$	−10.8948	+	22.6233i	−0.598832	+	1.24349i	−0.951474	+	0.307729i	$0.900431\pi$
$332$		0			0
$333$	0.499929	−	0.626891i	0.0273960	−	0.0343534i
$334$		0			0
$335$	−15.5378	−	19.4838i	−0.848920	−	1.06451i
$336$		0			0
$337$	11.9019	−	14.9245i	0.648339	−	0.812991i	−0.343679	−	0.939087i	$-0.611673\pi$
$337$	11.9019	−	14.9245i	0.648339	−	0.812991i	0.992018	+	0.126096i	$0.0402447\pi$
$338$		0			0
$339$	−7.71595	+	3.71581i	−0.419073	+	0.201815i
$340$		0			0
$341$	−3.35039	+	0.764704i	−0.181434	+	0.0414111i
$342$		0			0
$343$	18.3100	−	2.78289i	0.988646	−	0.150262i
$344$		0			0
$345$	8.11135	+	35.5381i	0.436700	+	1.91331i
$346$		0			0
$347$	6.90049	+	14.3290i	0.370438	+	0.769222i	0.999970	−	0.00775229i	$-0.00246765\pi$
$347$	6.90049	+	14.3290i	0.370438	+	0.769222i	−0.629532	+	0.776975i	$0.716753\pi$
$348$		0			0
$349$	26.5639	+	21.1840i	1.42193	+	1.13395i	0.970345	+	0.241726i	$0.0777134\pi$
$349$	26.5639	+	21.1840i	1.42193	+	1.13395i	0.451587	+	0.892227i	$0.350858\pi$
$350$		0			0
$351$	−4.41741	+	3.52277i	−0.235784	+	0.188031i
$352$		0			0
$353$	14.9652	+	11.9343i	0.796515	+	0.635199i	0.934793	−	0.355194i	$-0.115585\pi$
$353$	14.9652	+	11.9343i	0.796515	+	0.635199i	−0.138278	+	0.990393i	$0.544157\pi$
$354$		0			0
$355$	−16.7522	−	8.06744i	−0.889115	−	0.428175i
$356$		0			0
$357$	11.5450	−	45.4183i	0.611028	−	2.40379i
$358$		0			0
$359$	9.90359	+	7.89785i	0.522692	+	0.416833i	0.848970	−	0.528441i	$-0.177223\pi$
$359$	9.90359	+	7.89785i	0.522692	+	0.416833i	−0.326278	+	0.945274i	$0.605795\pi$
$360$		0			0
$361$	5.22065			0.274771
$362$		0			0
$363$	19.4367	+	9.36023i	1.02016	+	0.491285i
$364$		0			0
$365$	30.7929	−	14.8291i	1.61178	−	0.776191i
$366$		0			0
$367$	−5.40041	+	23.6608i	−0.281899	+	1.23508i	0.613456	+	0.789729i	$0.289779\pi$
$367$	−5.40041	+	23.6608i	−0.281899	+	1.23508i	−0.895355	+	0.445353i	$0.853078\pi$
$368$		0			0
$369$	−6.98867	−	14.5121i	−0.363816	−	0.755471i
$370$		0			0
$371$	−0.0370138	+	1.50911i	−0.00192166	+	0.0783489i
$372$		0			0
$373$	35.8324			1.85533			0.927665	−	0.373413i	$-0.121813\pi$
$373$	35.8324			1.85533			0.927665	+	0.373413i	$0.121813\pi$
$374$		0			0
$375$	11.1440	−	23.1408i	0.575475	−	1.19499i
$376$		0			0
$377$	−9.73451	−	2.22184i	−0.501353	−	0.114431i
$378$		0			0
$379$	−5.13342	+	1.17167i	−0.263686	+	0.0601847i	−0.352320	−	0.935880i	$-0.614607\pi$
$379$	−5.13342	+	1.17167i	−0.263686	+	0.0601847i	0.0886336	+	0.996064i	$0.471750\pi$
$380$		0			0
$381$	5.85117	−	1.33549i	0.299765	−	0.0684193i
$382$		0			0
$383$	−0.318441	+	1.39518i	−0.0162716	+	0.0712903i	−0.982412	−	0.186727i	$-0.940212\pi$
$383$	−0.318441	+	1.39518i	−0.0162716	+	0.0712903i	0.966140	+	0.258017i	$0.0830692\pi$
$384$		0			0
$385$	2.47767	+	5.48506i	0.126274	+	0.279545i
$386$		0			0
$387$	−6.33087	+	5.04870i	−0.321816	+	0.256640i
$388$		0			0
$389$	−22.3019	−	27.9658i	−1.13075	−	1.41792i	−0.894977	−	0.446113i	$-0.852808\pi$
$389$	−22.3019	−	27.9658i	−1.13075	−	1.41792i	−0.235777	−	0.971807i	$-0.575763\pi$
$390$		0			0
$391$	−63.6532			−3.21908
$392$		0			0
$393$	−29.5254			−1.48936
$394$		0			0
$395$	−4.57517	−	5.73708i	−0.230202	−	0.288664i
$396$		0			0
$397$	17.7990	−	14.1943i	0.893308	−	0.712389i	−0.0650732	−	0.997880i	$-0.520728\pi$
$397$	17.7990	−	14.1943i	0.893308	−	0.712389i	0.958381	+	0.285491i	$0.0921567\pi$
$398$		0			0
$399$	27.9896	−	5.67021i	1.40123	−	0.283865i
$400$		0			0
$401$	−7.15108	+	31.3309i	−0.357108	+	1.56459i	0.403251	+	0.915090i	$0.367880\pi$
$401$	−7.15108	+	31.3309i	−0.357108	+	1.56459i	−0.760359	+	0.649503i	$0.774977\pi$
$402$		0			0
$403$	−6.72502	+	1.53494i	−0.334997	+	0.0764609i
$404$		0			0
$405$	22.9294	−	5.23349i	1.13937	−	0.260054i
$406$		0			0
$407$	−0.465841	−	0.106325i	−0.0230909	−	0.00527035i
$408$		0			0
$409$	−2.93307	+	6.09058i	−0.145031	+	0.301160i	−0.960812	−	0.277201i	$-0.910593\pi$
$409$	−2.93307	+	6.09058i	−0.145031	+	0.301160i	0.815781	+	0.578361i	$0.196307\pi$
$410$		0			0
$411$	−29.3611			−1.44828
$412$		0			0
$413$	11.1465	+	24.6761i	0.548483	+	1.21423i
$414$		0			0
$415$	5.49539	+	11.4113i	0.269758	+	0.560158i
$416$		0			0
$417$	9.21086	−	40.3554i	0.451058	−	1.97621i
$418$		0			0
$419$	−15.8537	+	7.63473i	−0.774503	+	0.372981i	−0.779012	−	0.627009i	$-0.784279\pi$
$419$	−15.8537	+	7.63473i	−0.774503	+	0.372981i	0.00450911	+	0.999990i	$0.498565\pi$
$420$		0			0
$421$	−16.7598	−	8.07110i	−0.816823	−	0.393361i	−0.0216664	−	0.999765i	$-0.506897\pi$
$421$	−16.7598	−	8.07110i	−0.816823	−	0.393361i	−0.795157	+	0.606404i	$0.792611\pi$
$422$		0			0
$423$	9.28983			0.451687
$424$		0			0
$425$	3.49564	+	2.78768i	0.169564	+	0.135222i
$426$		0			0
$427$	−11.0607	−	14.5897i	−0.535264	−	0.706043i
$428$		0			0
$429$	−4.61636	−	2.22312i	−0.222880	−	0.107333i
$430$		0			0
$431$	−7.47212	−	5.95881i	−0.359919	−	0.287026i	0.426789	−	0.904351i	$-0.359645\pi$
$431$	−7.47212	−	5.95881i	−0.359919	−	0.287026i	−0.786708	+	0.617325i	$0.788216\pi$
$432$		0			0
$433$	5.94783	−	4.74323i	0.285834	−	0.227945i	−0.470067	−	0.882631i	$-0.655770\pi$
$433$	5.94783	−	4.74323i	0.285834	−	0.227945i	0.755901	+	0.654685i	$0.227199\pi$
$434$		0			0
$435$	16.6723	+	13.2957i	0.799377	+	0.637482i
$436$		0			0
$437$	−16.8305	−	34.9489i	−0.805112	−	1.67183i
$438$		0			0
$439$	−1.24310	−	5.44639i	−0.0593301	−	0.259942i	0.936561	−	0.350506i	$-0.113990\pi$
$439$	−1.24310	−	5.44639i	−0.0593301	−	0.259942i	−0.995891	+	0.0905636i	$0.971133\pi$
$440$		0			0
$441$	11.6734	−	4.93205i	0.555875	−	0.234860i
$442$		0			0
$443$	15.0378	−	3.43227i	0.714466	−	0.163072i	0.150188	−	0.988657i	$-0.452012\pi$
$443$	15.0378	−	3.43227i	0.714466	−	0.163072i	0.564278	+	0.825585i	$0.309155\pi$
$444$		0			0
$445$	−6.44907	+	3.10571i	−0.305715	+	0.147225i
$446$		0			0
$447$	10.8081	−	13.5530i	0.511207	−	0.641033i
$448$		0			0
$449$	4.84643	+	6.07723i	0.228717	+	0.286802i	0.882926	−	0.469511i	$-0.155570\pi$
$449$	4.84643	+	6.07723i	0.228717	+	0.286802i	−0.654209	+	0.756314i	$0.726998\pi$
$450$		0			0
$451$	−5.98463	+	7.50448i	−0.281805	+	0.353372i
$452$		0			0
$453$	21.0504	−	43.7116i	0.989035	−	2.05375i
$454$		0			0
$455$	4.97327	+	11.0098i	0.233151	+	0.516148i
$456$		0			0
$457$	−3.43855	+	4.31181i	−0.160849	+	0.201698i	−0.855724	−	0.517432i	$-0.826888\pi$
$457$	−3.43855	+	4.31181i	−0.160849	+	0.201698i	0.694876	+	0.719130i	$0.255459\pi$
$458$		0			0
$459$			21.0714i			0.983530i
$460$		0			0
$461$	5.16472	−	10.7247i	0.240545	−	0.499497i	−0.745389	−	0.666629i	$-0.767736\pi$
$461$	5.16472	−	10.7247i	0.240545	−	0.499497i	0.985934	+	0.167132i	$0.0534507\pi$
$462$		0			0
$463$	−13.6179	−	28.2778i	−0.632876	−	1.31418i	−0.932861	−	0.360236i	$-0.882696\pi$
$463$	−13.6179	−	28.2778i	−0.632876	−	1.31418i	0.299986	−	0.953944i	$-0.403018\pi$
$464$		0			0
$465$	14.3627	+	3.27819i	0.666053	+	0.152022i
$466$		0			0
$467$	25.7917	−	12.4206i	1.19350	−	0.574758i	0.271681	−	0.962387i	$-0.412420\pi$
$467$	25.7917	−	12.4206i	1.19350	−	0.574758i	0.921815	+	0.387630i	$0.126706\pi$
$468$		0			0
$469$	27.8308	+	14.2535i	1.28511	+	0.658168i
$470$		0			0
$471$		−	48.4248i		−	2.23130i
$472$		0			0
$473$	4.34757	+	2.09368i	0.199902	+	0.0962675i
$474$		0			0
$475$	−0.606301	+	2.65638i	−0.0278190	+	0.121883i
$476$		0			0
$477$	0.229846	+	1.00702i	0.0105239	+	0.0461083i
$478$		0			0
$479$	−6.31462	−	27.6661i	−0.288522	−	1.26410i	−0.886554	−	0.462626i	$-0.846907\pi$
$479$	−6.31462	−	27.6661i	−0.288522	−	1.26410i	0.598031	−	0.801473i	$-0.295950\pi$
$480$		0			0
$481$	−0.935054	−	0.213420i	−0.0426348	−	0.00973111i
$482$		0			0
$483$	−27.6313	−	36.4472i	−1.25727	−	1.65840i
$484$		0			0
$485$	−13.9241	−	17.4603i	−0.632261	−	0.792830i
$486$		0			0
$487$	−16.1790	+	12.9023i	−0.733141	+	0.584660i	−0.917281	−	0.398240i	$-0.869621\pi$
$487$	−16.1790	+	12.9023i	−0.733141	+	0.584660i	0.184141	+	0.982900i	$0.441050\pi$
$488$		0			0
$489$		−	5.71671i		−	0.258519i
$490$		0			0
$491$			13.7948i			0.622552i	0.950320	+	0.311276i	$0.100756\pi$
$491$			13.7948i			0.622552i	−0.950320	+	0.311276i	$0.899244\pi$
$492$		0			0
$493$	−29.1135	+	23.2172i	−1.31121	+	1.04565i
$494$		0			0
$495$	2.56772	+	3.21982i	0.115411	+	0.144720i
$496$		0			0
$497$	23.3227	+	0.572034i	1.04616	+	0.0256592i
$498$		0			0
$499$	−22.6204	−	5.16295i	−1.01263	−	0.231126i	−0.316154	−	0.948708i	$-0.602391\pi$
$499$	−22.6204	−	5.16295i	−1.01263	−	0.231126i	−0.696473	+	0.717583i	$0.745249\pi$
$500$		0			0
$501$	0.916528	+	4.01557i	0.0409475	+	0.179403i
$502$		0			0
$503$	−8.58905	−	37.6311i	−0.382967	−	1.67789i	−0.688130	−	0.725587i	$-0.741568\pi$
$503$	−8.58905	−	37.6311i	−0.382967	−	1.67789i	0.305164	−	0.952300i	$-0.401289\pi$
$504$		0			0
$505$	−3.09472	+	13.5589i	−0.137713	+	0.603361i
$506$		0			0
$507$	16.4226	+	7.90869i	0.729351	+	0.351237i
$508$		0			0
$509$			29.0616i			1.28813i	0.764970	+	0.644066i	$0.222754\pi$
$509$			29.0616i			1.28813i	−0.764970	+	0.644066i	$0.777246\pi$
$510$		0			0
$511$	−27.5513	+	32.8618i	−1.21880	+	1.45372i
$512$		0			0
$513$	−11.5693	+	5.57148i	−0.510797	+	0.245987i
$514$		0			0
$515$	16.8936	+	3.85586i	0.744422	+	0.169909i
$516$		0			0
$517$	−2.40197	−	4.98774i	−0.105639	−	0.219361i
$518$		0			0
$519$	−3.02510	+	6.28168i	−0.132787	+	0.275735i
$520$		0			0
$521$		−	26.4136i		−	1.15720i	−0.815612	−	0.578599i	$-0.803599\pi$
$521$		−	26.4136i		−	1.15720i	0.815612	−	0.578599i	$-0.196401\pi$
$522$		0			0
$523$	21.1259	−	26.4910i	0.923771	−	1.15837i	−0.0632845	−	0.997996i	$-0.520158\pi$
$523$	21.1259	−	26.4910i	0.923771	−	1.15837i	0.987056	−	0.160377i	$-0.0512710\pi$
$524$		0			0
$525$	−0.0787726	+	3.21168i	−0.00343792	+	0.140169i
$526$		0			0
$527$	−11.1618	+	23.1777i	−0.486216	+	1.00964i
$528$		0			0
$529$	−24.3936	+	30.5887i	−1.06059	+	1.32994i
$530$		0			0
$531$	11.5516	+	14.4853i	0.501298	+	0.628607i
$532$		0			0
$533$	−12.0126	+	15.0633i	−0.520322	+	0.652463i
$534$		0			0
$535$	6.68731	−	3.22044i	0.289118	−	0.139232i
$536$		0			0
$537$	8.38044	−	1.91278i	0.361643	−	0.0825426i
$538$		0			0
$539$	−5.66629	−	4.99225i	−0.244064	−	0.215031i
$540$		0			0
$541$	6.03887	+	26.4580i	0.259631	+	1.13752i	0.921647	+	0.388029i	$0.126844\pi$
$541$	6.03887	+	26.4580i	0.259631	+	1.13752i	−0.662016	+	0.749490i	$0.730299\pi$
$542$		0			0
$543$	−6.85688	−	14.2385i	−0.294257	−	0.611031i
$544$		0			0
$545$	−13.7294	−	10.9488i	−0.588101	−	0.468995i
$546$		0			0
$547$	29.3440	−	23.4011i	1.25466	−	1.00056i	0.255226	−	0.966882i	$-0.417850\pi$
$547$	29.3440	−	23.4011i	1.25466	−	1.00056i	0.999433	−	0.0336751i	$-0.0107211\pi$
$548$		0			0
$549$	−9.79442	−	7.81079i	−0.418016	−	0.333357i
$550$		0			0
$551$	−20.4453	−	9.84596i	−0.871001	−	0.419452i
$552$		0			0
$553$	8.19489	+	4.19702i	0.348482	+	0.178475i
$554$		0			0
$555$	1.60147	+	1.27713i	0.0679786	+	0.0542111i
$556$		0			0
$557$	−35.5640			−1.50690			−0.753448	−	0.657508i	$-0.771611\pi$
$557$	−35.5640			−1.50690			−0.753448	+	0.657508i	$0.771611\pi$
$558$		0			0
$559$	8.72661	+	4.20251i	0.369096	+	0.177747i
$560$		0			0
$561$	−17.2163	+	8.29092i	−0.726872	+	0.350043i
$562$		0			0
$563$	0.650256	−	2.84896i	0.0274050	−	0.120069i	−0.959375	−	0.282133i	$-0.908958\pi$
$563$	0.650256	−	2.84896i	0.0274050	−	0.120069i	0.986780	+	0.162064i	$0.0518151\pi$
$564$		0			0
$565$	−3.57245	−	7.41828i	−0.150294	−	0.312089i
$566$		0			0
$567$	−23.5159	+	17.8279i	−0.987576	+	0.748699i
$568$		0			0
$569$	25.0262			1.04915			0.524576	−	0.851364i	$-0.324224\pi$
$569$	25.0262			1.04915			0.524576	+	0.851364i	$0.324224\pi$
$570$		0			0
$571$	−11.7429	+	24.3843i	−0.491424	+	1.02045i	0.496860	+	0.867831i	$0.334486\pi$
$571$	−11.7429	+	24.3843i	−0.491424	+	1.02045i	−0.988285	+	0.152623i	$0.951228\pi$
$572$		0			0
$573$	−9.37053	−	2.13876i	−0.391459	−	0.0893481i
$574$		0			0
$575$	4.25430	−	0.971016i	0.177417	−	0.0404942i
$576$		0			0
$577$	−2.59179	+	0.591560i	−0.107898	+	0.0246269i	−0.276129	−	0.961121i	$-0.589052\pi$
$577$	−2.59179	+	0.591560i	−0.107898	+	0.0246269i	0.168231	+	0.985748i	$0.446195\pi$
$578$		0			0
$579$	−11.3280	+	49.6312i	−0.470775	+	2.06260i
$580$		0			0
$581$	−12.1780	−	10.2100i	−0.505228	−	0.423583i
$582$		0			0
$583$	0.481244	−	0.383780i	0.0199311	−	0.0158945i
$584$		0			0
$585$	5.15403	+	6.46295i	0.213093	+	0.267210i
$586$		0			0
$587$	−29.8629			−1.23257			−0.616286	−	0.787522i	$-0.711364\pi$
$587$	−29.8629			−1.23257			−0.616286	+	0.787522i	$0.711364\pi$
$588$		0			0
$589$	−15.6770			−0.645961
$590$		0			0
$591$	1.58630	+	1.98915i	0.0652515	+	0.0818228i
$592$		0			0
$593$	−30.6571	+	24.4483i	−1.25894	+	1.00397i	−0.259671	+	0.965697i	$0.583614\pi$
$593$	−30.6571	+	24.4483i	−1.25894	+	1.00397i	−0.999267	+	0.0382725i	$0.987814\pi$
$594$		0			0
$595$	43.6661	+	11.0996i	1.79014	+	0.455041i
$596$		0			0
$597$	−2.34992	+	10.2957i	−0.0961760	+	0.421375i
$598$		0			0
$599$	−7.89209	+	1.80132i	−0.322462	+	0.0735999i	−0.380688	−	0.924704i	$-0.624313\pi$
$599$	−7.89209	+	1.80132i	−0.322462	+	0.0735999i	0.0582258	+	0.998303i	$0.481456\pi$
$600$		0			0
$601$	−31.8023	+	7.25866i	−1.29724	+	0.296087i	−0.814750	−	0.579813i	$-0.803126\pi$
$601$	−31.8023	+	7.25866i	−1.29724	+	0.296087i	−0.482492	+	0.875900i	$0.660268\pi$
$602$		0			0
$603$	20.8590	+	4.76094i	0.849446	+	0.193881i
$604$		0			0
$605$	−8.99913	+	18.6869i	−0.365867	+	0.759730i
$606$		0			0
$607$	41.1532			1.67036			0.835178	−	0.549979i	$-0.185364\pi$
$607$	41.1532			1.67036			0.835178	+	0.549979i	$0.185364\pi$
$608$		0			0
$609$	−25.9319	−	6.59171i	−1.05081	−	0.267109i
$610$		0			0
$611$	−4.82132	−	10.0116i	−0.195050	−	0.405025i
$612$		0			0
$613$	2.34052	−	10.2545i	0.0945327	−	0.414175i	−0.905414	−	0.424530i	$-0.860439\pi$
$613$	2.34052	−	10.2545i	0.0945327	−	0.414175i	0.999946	+	0.0103557i	$0.00329638\pi$
$614$		0			0
$615$	37.0730	−	17.8534i	1.49493	−	0.719919i
$616$		0			0
$617$	22.7667	+	10.9639i	0.916552	+	0.441388i	0.831839	−	0.555017i	$-0.187288\pi$
$617$	22.7667	+	10.9639i	0.916552	+	0.441388i	0.0847134	+	0.996405i	$0.473003\pi$
$618$		0			0
$619$	24.3742			0.979680			0.489840	−	0.871812i	$-0.337055\pi$
$619$	24.3742			0.979680			0.489840	+	0.871812i	$0.337055\pi$
$620$		0			0
$621$	16.0786	+	12.8223i	0.645213	+	0.514540i
$622$		0			0
$623$	5.77017	−	6.88236i	0.231177	−	0.275736i
$624$		0			0
$625$	19.7540	+	9.51303i	0.790161	+	0.380521i
$626$		0			0
$627$	−9.10429	−	7.26043i	−0.363590	−	0.289954i
$628$		0			0
$629$	−2.79651	+	2.23015i	−0.111504	+	0.0889217i
$630$		0			0
$631$	−16.4077	−	13.0847i	−0.653181	−	0.520894i	0.239896	−	0.970799i	$-0.422887\pi$
$631$	−16.4077	−	13.0847i	−0.653181	−	0.520894i	−0.893077	+	0.449904i	$0.851458\pi$
$632$		0			0
$633$	−5.53068	−	11.4846i	−0.219825	−	0.456471i
$634$		0			0
$635$	1.28397	+	5.62544i	0.0509528	+	0.223239i
$636$		0			0
$637$	−11.3736	−	10.0206i	−0.450638	−	0.397032i
$638$		0			0
$639$	15.5631	−	3.55218i	0.615668	−	0.140522i
$640$		0			0
$641$	25.1987	−	12.1351i	0.995291	−	0.479307i	0.135953	−	0.990715i	$-0.456590\pi$
$641$	25.1987	−	12.1351i	0.995291	−	0.479307i	0.859338	+	0.511409i	$0.170876\pi$
$642$		0			0
$643$	11.0013	−	13.7952i	0.433848	−	0.544029i	−0.516062	−	0.856551i	$-0.672603\pi$
$643$	11.0013	−	13.7952i	0.433848	−	0.544029i	0.949910	+	0.312523i	$0.101174\pi$
$644$		0			0
$645$	−12.8975	−	16.1730i	−0.507839	−	0.636810i
$646$		0			0
$647$	−23.9765	+	30.0656i	−0.942613	+	1.18200i	0.0405336	+	0.999178i	$0.487094\pi$
$647$	−23.9765	+	30.0656i	−0.942613	+	1.18200i	−0.983146	+	0.182821i	$0.941477\pi$
$648$		0			0
$649$	4.79042	−	9.94740i	0.188040	−	0.390470i
$650$		0			0
$651$	−18.1166	+	3.67010i	−0.710044	+	0.143842i
$652$		0			0
$653$	13.7027	−	17.1826i	0.536226	−	0.672406i	−0.437740	−	0.899102i	$-0.644221\pi$
$653$	13.7027	−	17.1826i	0.536226	−	0.672406i	0.973966	+	0.226695i	$0.0727922\pi$
$654$		0			0
$655$		−	28.3864i		−	1.10915i
$656$		0			0
$657$	−12.7314	+	26.4371i	−0.496700	+	1.03141i
$658$		0			0
$659$	7.19798	+	14.9468i	0.280393	+	0.582243i	0.992836	−	0.119488i	$-0.0381253\pi$
$659$	7.19798	+	14.9468i	0.280393	+	0.582243i	−0.712442	+	0.701731i	$0.752411\pi$
$660$		0			0
$661$	−1.97120	−	0.449913i	−0.0766708	−	0.0174996i	0.184013	−	0.982924i	$-0.441091\pi$
$661$	−1.97120	−	0.449913i	−0.0766708	−	0.0174996i	−0.260684	+	0.965424i	$0.583948\pi$
$662$		0			0
$663$	−34.5572	+	16.6418i	−1.34209	+	0.646316i
$664$		0			0
$665$	5.45146	+	26.9098i	0.211398	+	1.04352i
$666$		0			0
$667$			36.3432i			1.40721i
$668$		0			0
$669$	37.2424	+	17.9350i	1.43987	+	0.693407i
$670$		0			0
$671$	−1.66120	+	7.27821i	−0.0641301	+	0.280972i
$672$		0			0
$673$	−4.17369	−	18.2861i	−0.160884	−	0.704878i	−0.989436	−	0.144967i	$-0.953692\pi$
$673$	−4.17369	−	18.2861i	−0.160884	−	0.704878i	0.828553	−	0.559911i	$-0.189165\pi$
$674$		0			0
$675$	−0.321440	−	1.40832i	−0.0123722	−	0.0542063i
$676$		0			0
$677$	−16.7181	−	3.81580i	−0.642529	−	0.146653i	−0.111172	−	0.993801i	$-0.535460\pi$
$677$	−16.7181	−	3.81580i	−0.642529	−	0.146653i	−0.531357	+	0.847148i	$0.678318\pi$
$678$		0			0
$679$	24.9404	+	12.7732i	0.957124	+	0.490192i
$680$		0			0
$681$	−27.5534	−	34.5508i	−1.05585	−	1.32399i
$682$		0			0
$683$	11.5778	−	9.23302i	0.443014	−	0.353292i	−0.376436	−	0.926443i	$-0.622851\pi$
$683$	11.5778	−	9.23302i	0.443014	−	0.353292i	0.819450	+	0.573151i	$0.194279\pi$
$684$		0			0
$685$		−	28.2284i		−	1.07855i
$686$		0			0
$687$			18.5156i			0.706413i
$688$		0			0
$689$	0.965972	−	0.770337i	0.0368006	−	0.0293475i
$690$		0			0
$691$	16.8462	+	21.1244i	0.640859	+	0.803611i	0.991110	−	0.133045i	$-0.0424753\pi$
$691$	16.8462	+	21.1244i	0.640859	+	0.803611i	−0.350252	+	0.936656i	$0.613904\pi$
$692$		0			0
$693$	−4.59922	−	2.35549i	−0.174710	−	0.0894778i
$694$		0			0
$695$	38.7985	+	8.85552i	1.47171	+	0.335909i
$696$		0			0
$697$	15.9888	+	70.0516i	0.605620	+	2.65340i
$698$		0			0
$699$	−5.01342	−	21.9652i	−0.189625	−	0.830801i
$700$		0			0
$701$	5.21768	−	22.8601i	0.197069	−	0.863416i	−0.775601	−	0.631224i	$-0.782553\pi$
$701$	5.21768	−	22.8601i	0.197069	−	0.863416i	0.972670	−	0.232192i	$-0.0745898\pi$
$702$		0			0
$703$	−1.96389	−	0.945759i	−0.0740695	−	0.0356700i
$704$		0			0
$705$			23.7320i			0.893799i
$706$		0			0
$707$	−3.46470	−	17.1026i	−0.130303	−	0.643211i
$708$		0			0
$709$	8.41708	−	4.05345i	0.316110	−	0.152231i	−0.269100	−	0.963112i	$-0.586726\pi$
$709$	8.41708	−	4.05345i	0.316110	−	0.152231i	0.585210	+	0.810882i	$0.301012\pi$
$710$		0			0
$711$	6.14204	+	1.40188i	0.230344	+	0.0525746i
$712$		0			0
$713$	10.8937	+	22.6210i	0.407973	+	0.847164i
$714$		0			0
$715$	2.13736	−	4.43827i	0.0799326	−	0.165982i
$716$		0			0
$717$		−	25.7736i		−	0.962535i
$718$		0			0
$719$	6.17417	−	7.74217i	0.230258	−	0.288734i	−0.653258	−	0.757135i	$-0.726598\pi$
$719$	6.17417	−	7.74217i	0.230258	−	0.288734i	0.883516	+	0.468401i	$0.155170\pi$
$720$		0			0
$721$	−21.3090	+	4.31683i	−0.793589	+	0.160767i
$722$		0			0
$723$	−3.63281	+	7.54361i	−0.135106	+	0.280550i
$724$		0			0
$725$	1.59164	−	1.99586i	0.0591122	−	0.0741243i
$726$		0			0
$727$	23.5521	+	29.5334i	0.873498	+	1.09533i	0.994712	+	0.102705i	$0.0327499\pi$
$727$	23.5521	+	29.5334i	0.873498	+	1.09533i	−0.121214	+	0.992626i	$0.538679\pi$
$728$		0			0
$729$	−1.88567	+	2.36455i	−0.0698395	+	0.0875760i
$730$		0			0
$731$	32.5450	−	15.6729i	1.20372	−	0.579682i
$732$		0			0
$733$	26.4021	−	6.02610i	0.975183	−	0.222579i	0.294899	−	0.955528i	$-0.404714\pi$
$733$	26.4021	−	6.02610i	0.975183	−	0.222579i	0.680283	+	0.732949i	$0.261857\pi$
$734$		0			0
$735$	12.5995	+	29.8210i	0.464740	+	1.09997i
$736$		0			0
$737$	−2.83713	−	12.4303i	−0.104507	−	0.457875i
$738$		0			0
$739$	12.6826	+	26.3356i	0.466535	+	0.968771i	0.992949	+	0.118542i	$0.0378221\pi$
$739$	12.6826	+	26.3356i	0.466535	+	0.968771i	−0.526414	+	0.850229i	$0.676464\pi$
$740$		0			0
$741$	−18.2745	−	14.5734i	−0.671329	−	0.535367i
$742$		0			0
$743$	−28.7765	+	22.9485i	−1.05571	+	0.841898i	−0.987790	−	0.155793i	$-0.950207\pi$
$743$	−28.7765	+	22.9485i	−1.05571	+	0.841898i	−0.0679174	+	0.997691i	$0.521635\pi$
$744$		0			0
$745$	13.0301	+	10.3912i	0.477386	+	0.380703i
$746$		0			0
$747$	−9.79709	−	4.71803i	−0.358457	−	0.172624i
$748$		0			0
$749$	−5.98333	+	7.13661i	−0.218626	+	0.260766i
$750$		0			0
$751$	15.9096	+	12.6875i	0.580549	+	0.462973i	0.869199	−	0.494462i	$-0.164635\pi$
$751$	15.9096	+	12.6875i	0.580549	+	0.462973i	−0.288650	+	0.957435i	$0.593206\pi$
$752$		0			0
$753$	−20.4474			−0.745146
$754$		0			0
$755$	42.0253	+	20.2383i	1.52946	+	0.736548i
$756$		0			0
$757$	−17.0146	+	8.19378i	−0.618404	+	0.297808i	−0.716735	−	0.697346i	$-0.754364\pi$
$757$	−17.0146	+	8.19378i	−0.618404	+	0.297808i	0.0983302	+	0.995154i	$0.468650\pi$
$758$		0			0
$759$	−4.14994	+	18.1821i	−0.150633	+	0.659968i
$760$		0			0
$761$	−3.21544	−	6.67693i	−0.116560	−	0.242038i	0.834524	−	0.550971i	$-0.185743\pi$
$761$	−3.21544	−	6.67693i	−0.116560	−	0.242038i	−0.951084	+	0.308933i	$0.900028\pi$
$762$		0			0
$763$	21.3544	+	5.42815i	0.773081	+	0.196512i
$764$		0			0
$765$	30.8288			1.11462
$766$		0			0
$767$	9.61550	−	19.9668i	0.347196	−	0.720959i
$768$		0			0
$769$	22.2032	+	5.06775i	0.800669	+	0.182748i	0.603230	−	0.797567i	$-0.293880\pi$
$769$	22.2032	+	5.06775i	0.800669	+	0.182748i	0.197440	+	0.980315i	$0.436737\pi$
$770$		0			0
$771$	34.4099	−	7.85384i	1.23924	−	0.282849i
$772$		0			0
$773$	45.4973	−	10.3845i	1.63642	−	0.373503i	0.697219	−	0.716859i	$-0.254421\pi$
$773$	45.4973	−	10.3845i	1.63642	−	0.373503i	0.939205	+	0.343356i	$0.111564\pi$
$774$		0			0
$775$	0.392434	−	1.71937i	0.0140967	−	0.0617615i
$776$		0			0
$777$	−2.49090	−	0.633170i	−0.0893605	−	0.0227148i
$778$		0			0
$779$	−34.2344	+	27.3010i	−1.22657	+	0.978160i
$780$		0			0
$781$	−5.93117	−	7.43745i	−0.212234	−	0.266133i
$782$		0			0
$783$	12.0308			0.429947
$784$		0			0
$785$	46.5566			1.66168
$786$		0			0
$787$	−30.1233	−	37.7734i	−1.07378	−	1.34648i	−0.934395	−	0.356239i	$-0.884059\pi$
$787$	−30.1233	−	37.7734i	−1.07378	−	1.34648i	−0.139385	−	0.990238i	$-0.544512\pi$
$788$		0			0
$789$	8.63978	−	6.88999i	0.307584	−	0.245290i
$790$		0			0
$791$	7.91669	+	6.63734i	0.281485	+	0.235997i
$792$		0			0
$793$	−3.33443	+	14.6091i	−0.118409	+	0.518784i
$794$		0			0
$795$	−2.57256	+	0.587169i	−0.0912392	+	0.0208248i
$796$		0			0
$797$	−22.7867	+	5.20091i	−0.807146	+	0.184226i	−0.606133	−	0.795363i	$-0.707280\pi$
$797$	−22.7867	+	5.20091i	−0.807146	+	0.184226i	−0.201012	+	0.979589i	$0.564423\pi$
$798$		0			0
$799$	−40.4022	−	9.22154i	−1.42933	−	0.326235i
$800$		0			0
$801$	2.66639	−	5.53681i	0.0942121	−	0.195633i
$802$		0			0
$803$	17.4860			0.617067
$804$		0			0
$805$	35.0411	−	26.5653i	1.23504	−	0.936303i
$806$		0			0
$807$	−27.4945	−	57.0930i	−0.967854	−	2.00977i
$808$		0			0
$809$	−10.3858	+	45.5032i	−0.365145	+	1.59981i	0.374778	+	0.927115i	$0.377719\pi$
$809$	−10.3858	+	45.5032i	−0.365145	+	1.59981i	−0.739923	+	0.672691i	$0.765138\pi$
$810$		0			0
$811$	13.8899	−	6.68901i	0.487739	−	0.234883i	−0.173818	−	0.984778i	$-0.555610\pi$
$811$	13.8899	−	6.68901i	0.487739	−	0.234883i	0.661557	+	0.749895i	$0.269896\pi$
$812$		0			0
$813$	45.6459	+	21.9819i	1.60087	+	0.770939i
$814$		0			0
$815$	5.49617			0.192522
$816$		0			0
$817$	17.2104	+	13.7249i	0.602117	+	0.480172i
$818$		0			0
$819$	−9.23172	−	4.72804i	−0.322583	−	0.165211i
$820$		0			0
$821$	4.17551	+	2.01082i	0.145726	+	0.0701780i	0.505326	−	0.862929i	$-0.331372\pi$
$821$	4.17551	+	2.01082i	0.145726	+	0.0701780i	−0.359599	+	0.933107i	$0.617087\pi$
$822$		0			0
$823$	9.05276	+	7.21933i	0.315559	+	0.251650i	0.768441	−	0.639920i	$-0.221033\pi$
$823$	9.05276	+	7.21933i	0.315559	+	0.251650i	−0.452882	+	0.891571i	$0.649604\pi$
$824$		0			0
$825$	1.02418	−	0.816759i	0.0356575	−	0.0284359i
$826$		0			0
$827$	−39.9798	−	31.8828i	−1.39023	−	1.10867i	−0.980511	−	0.196463i	$-0.937054\pi$
$827$	−39.9798	−	31.8828i	−1.39023	−	1.10867i	−0.409722	−	0.912210i	$-0.634374\pi$
$828$		0			0
$829$	3.94931	+	8.20083i	0.137165	+	0.284826i	0.958225	−	0.286016i	$-0.0923310\pi$
$829$	3.94931	+	8.20083i	0.137165	+	0.284826i	−0.821060	+	0.570842i	$0.806617\pi$
$830$		0			0
$831$	0.415902	+	1.82219i	0.0144275	+	0.0632110i
$832$		0			0
$833$	−55.6642	+	9.86231i	−1.92865	+	0.341709i
$834$		0			0
$835$	−3.86066	+	0.881170i	−0.133604	+	0.0304941i
$836$		0			0
$837$	7.48834	−	3.60619i	0.258835	−	0.124648i
$838$		0			0
$839$	−0.584067	+	0.732397i	−0.0201642	+	0.0252852i	−0.791811	−	0.610766i	$-0.790862\pi$
$839$	−0.584067	+	0.732397i	−0.0201642	+	0.0252852i	0.771647	+	0.636051i	$0.219433\pi$
$840$		0			0
$841$	−4.82519	−	6.05059i	−0.166386	−	0.208641i
$842$		0			0
$843$	33.2351	−	41.6755i	1.14468	−	1.43538i
$844$		0			0
$845$	−7.60358	+	15.7890i	−0.261571	+	0.543158i
$846$		0			0
$847$	0.638097	−	26.0161i	0.0219253	−	0.893925i
$848$		0			0
$849$	14.7094	−	18.4450i	0.504826	−	0.633032i
$850$		0			0
$851$			3.49096i			0.119669i
$852$		0			0
$853$	−7.81420	+	16.2264i	−0.267553	+	0.555580i	−0.990852	−	0.134956i	$-0.956911\pi$
$853$	−7.81420	+	16.2264i	−0.267553	+	0.555580i	0.723299	+	0.690535i	$0.242625\pi$
$854$		0			0
$855$	8.15143	+	16.9266i	0.278773	+	0.578878i
$856$		0			0
$857$	1.19222	+	0.272117i	0.0407256	+	0.00929534i	0.242835	−	0.970068i	$-0.421923\pi$
$857$	1.19222	+	0.272117i	0.0407256	+	0.00929534i	−0.202110	+	0.979363i	$0.564780\pi$
$858$		0			0
$859$	−4.43282	+	2.13473i	−0.151246	+	0.0728361i	−0.507976	−	0.861371i	$-0.669606\pi$
$859$	−4.43282	+	2.13473i	−0.151246	+	0.0728361i	0.356730	+	0.934208i	$0.383892\pi$
$860$		0			0
$861$	−33.1702	+	39.5638i	−1.13044	+	1.34833i
$862$		0			0
$863$			2.82246i			0.0960778i	0.998845	+	0.0480389i	$0.0152971\pi$
$863$			2.82246i			0.0960778i	−0.998845	+	0.0480389i	$0.984703\pi$
$864$		0			0
$865$	−6.03934	−	2.90839i	−0.205344	−	0.0988883i
$866$		0			0
$867$	−23.5334	+	103.106i	−0.799236	+	3.50168i
$868$		0			0
$869$	−0.835405	−	3.66015i	−0.0283392	−	0.124162i
$870$		0			0
$871$	−5.69479	−	24.9505i	−0.192961	−	0.845416i
$872$		0			0
$873$	18.6927	+	4.26649i	0.632653	+	0.144399i
$874$		0			0
$875$	−30.9741	−	0.759699i	−1.04711	−	0.0256825i
$876$		0			0
$877$	−34.0284	−	42.6703i	−1.14906	−	1.44087i	−0.878226	−	0.478245i	$-0.841273\pi$
$877$	−34.0284	−	42.6703i	−1.14906	−	1.44087i	−0.270831	−	0.962627i	$-0.587298\pi$
$878$		0			0
$879$	34.0317	−	27.1394i	1.14786	−	0.915388i
$880$		0			0
$881$		−	38.9542i		−	1.31240i	−0.754587	−	0.656200i	$-0.772163\pi$
$881$		−	38.9542i		−	1.31240i	0.754587	−	0.656200i	$-0.227837\pi$
$882$		0			0
$883$			39.7247i			1.33684i	0.743783	+	0.668422i	$0.233030\pi$
$883$			39.7247i			1.33684i	−0.743783	+	0.668422i	$0.766970\pi$
$884$		0			0
$885$	−37.0044	+	29.5100i	−1.24389	+	0.991968i
$886$		0			0
$887$	31.9258	+	40.0337i	1.07196	+	1.34420i	0.935409	+	0.353568i	$0.115032\pi$
$887$	31.9258	+	40.0337i	1.07196	+	1.34420i	0.136556	+	0.990632i	$0.456397\pi$
$888$		0			0
$889$	−4.37384	−	5.76934i	−0.146694	−	0.193497i
$890$		0			0
$891$	11.7312	+	2.67757i	0.393009	+	0.0897018i
$892$		0			0
$893$	−5.61962	−	24.6212i	−0.188053	−	0.823916i
$894$		0			0
$895$	1.83899	+	8.05713i	0.0614706	+	0.269320i
$896$		0			0
$897$	−8.32992	+	36.4957i	−0.278128	+	1.21856i
$898$		0			0
$899$	13.2334	+	6.37289i	0.441360	+	0.212548i
$900$		0			0
$901$		−	4.60777i		−	0.153507i
$902$		0			0
$903$	23.1016	+	11.8315i	0.768774	+	0.393728i
$904$		0			0
$905$	13.6892	−	6.59235i	0.455043	−	0.219137i
$906$		0			0
$907$	−44.0650	−	10.0576i	−1.46315	−	0.333956i	−0.584492	−	0.811399i	$-0.698706\pi$
$907$	−44.0650	−	10.0576i	−1.46315	−	0.333956i	−0.878662	+	0.477444i	$0.841563\pi$
$908$		0			0
$909$	−5.18067	−	10.7578i	−0.171832	−	0.356813i
$910$		0			0
$911$	−24.6395	+	51.1645i	−0.816344	+	1.69515i	−0.102627	+	0.994720i	$0.532725\pi$
$911$	−24.6395	+	51.1645i	−0.816344	+	1.69515i	−0.713716	+	0.700435i	$0.752989\pi$
$912$		0			0
$913$			6.47998i			0.214456i
$914$		0			0
$915$	19.9536	−	25.0210i	0.659646	−	0.827170i
$916$		0			0
$917$	14.6621	+	32.4590i	0.484186	+	1.07189i
$918$		0			0
$919$	−0.274879	+	0.570792i	−0.00906743	+	0.0188287i	−0.905453	−	0.424446i	$-0.860469\pi$
$919$	−0.274879	+	0.570792i	−0.00906743	+	0.0188287i	0.896386	+	0.443274i	$0.146183\pi$
$920$		0			0
$921$	−6.51350	+	8.16768i	−0.214627	+	0.269134i
$922$		0			0
$923$	−11.9053	−	14.9287i	−0.391867	−	0.491385i
$924$		0			0
$925$	0.152886	−	0.191713i	0.00502687	−	0.00630349i
$926$		0			0
$927$	−13.4036	+	6.45485i	−0.440233	+	0.212005i
$928$		0			0
$929$	30.8113	−	7.03248i	1.01089	−	0.230728i	0.315163	−	0.949038i	$-0.397941\pi$
$929$	30.8113	−	7.03248i	1.01089	−	0.230728i	0.695724	+	0.718309i	$0.255084\pi$
$930$		0			0
$931$	−20.1330	−	27.9548i	−0.659834	−	0.916182i
$932$		0			0
$933$	−4.37328	−	19.1606i	−0.143175	−	0.627290i
$934$		0			0
$935$	−7.97107	−	16.5521i	−0.260682	−	0.541311i
$936$		0			0
$937$	15.4935	+	12.3557i	0.506151	+	0.403642i	0.842997	−	0.537918i	$-0.180789\pi$
$937$	15.4935	+	12.3557i	0.506151	+	0.403642i	−0.336846	+	0.941560i	$0.609360\pi$
$938$		0			0
$939$	−27.5070	+	21.9361i	−0.897656	+	0.715857i
$940$		0			0
$941$	−18.9095	−	15.0799i	−0.616433	−	0.491589i	0.264779	−	0.964309i	$-0.414701\pi$
$941$	−18.9095	−	15.0799i	−0.616433	−	0.491589i	−0.881213	+	0.472720i	$0.843272\pi$
$942$		0			0
$943$	63.1825	+	30.4271i	2.05751	+	0.990843i
$944$		0			0
$945$	−8.79403	−	11.5998i	−0.286070	−	0.377342i
$946$		0			0
$947$	28.6910	+	22.8803i	0.932331	+	0.743509i	0.966703	−	0.255900i	$-0.0823717\pi$
$947$	28.6910	+	22.8803i	0.932331	+	0.743509i	−0.0343720	+	0.999409i	$0.510943\pi$
$948$		0			0
$949$	35.0985			1.13935
$950$		0			0
$951$	53.2980	+	25.6670i	1.72831	+	0.832308i
$952$		0			0
$953$	3.29129	−	1.58500i	0.106615	−	0.0513433i	−0.379816	−	0.925062i	$-0.624013\pi$
$953$	3.29129	−	1.58500i	0.106615	−	0.0513433i	0.486431	+	0.873719i	$0.338298\pi$
$954$		0			0
$955$	2.05625	−	9.00902i	0.0665387	−	0.291525i
$956$		0			0
$957$	4.73375	+	9.82973i	0.153020	+	0.317750i
$958$		0			0
$959$	14.5805	+	32.2784i	0.470830	+	1.04232i
$960$		0			0
$961$	−20.8529			−0.672674
$962$		0			0
$963$	−2.76489	+	5.74135i	−0.0890973	+	0.185012i
$964$		0			0
$965$	−47.7165	−	10.8910i	−1.53605	−	0.350593i
$966$		0			0
$967$	−46.7194	+	10.6634i	−1.50240	+	0.342912i	−0.893037	−	0.449983i	$-0.851430\pi$
$967$	−46.7194	+	10.6634i	−1.50240	+	0.342912i	−0.609358	+	0.792895i	$0.708573\pi$
$968$		0			0
$969$	−84.9853	+	19.3973i	−2.73012	+	0.623132i
$970$		0			0
$971$	6.53763	−	28.6432i	0.209803	−	0.919205i	−0.754895	−	0.655845i	$-0.772312\pi$
$971$	6.53763	−	28.6432i	0.209803	−	0.919205i	0.964698	−	0.263360i	$-0.0848306\pi$
$972$		0			0
$973$	−48.9391	+	9.91420i	−1.56892	+	0.317835i
$974$		0			0
$975$	2.05578	−	1.63943i	0.0658376	−	0.0525038i
$976$		0			0
$977$	−17.0022	−	21.3201i	−0.543948	−	0.682090i	0.431552	−	0.902088i	$-0.357966\pi$
$977$	−17.0022	−	21.3201i	−0.543948	−	0.682090i	−0.975500	+	0.219999i	$0.929395\pi$
$978$		0			0
$979$	−3.66215			−0.117043
$980$		0			0
$981$	15.0765			0.481354
$982$		0			0
$983$	−17.0281	−	21.3526i	−0.543113	−	0.681042i	0.432223	−	0.901767i	$-0.357729\pi$
$983$	−17.0281	−	21.3526i	−0.543113	−	0.681042i	−0.975336	+	0.220724i	$0.929158\pi$
$984$		0			0
$985$	−1.91241	+	1.52510i	−0.0609345	+	0.0485937i
$986$		0			0
$987$	−12.2581	−	27.1369i	−0.390178	−	0.863776i
$988$		0			0
$989$	7.84490	−	34.3708i	0.249453	−	1.09293i
$990$		0			0
$991$	7.09021	−	1.61829i	0.225228	−	0.0514068i	−0.108418	−	0.994105i	$-0.534578\pi$
$991$	7.09021	−	1.61829i	0.225228	−	0.0514068i	0.333645	+	0.942699i	$0.391721\pi$
$992$		0			0
$993$	53.6916	−	12.2548i	1.70385	−	0.388893i
$994$		0			0
$995$	−9.89850	−	2.25927i	−0.313803	−	0.0716236i
$996$		0			0
$997$	15.5389	−	32.2669i	0.492123	−	1.02190i	−0.496012	−	0.868316i	$-0.665203\pi$
$997$	15.5389	−	32.2669i	0.492123	−	1.02190i	0.988135	−	0.153588i	$-0.0490830\pi$
$998$		0			0
$999$	1.15563			0.0365625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.4	✓	120
4.3	odd	2	inner	784.2.bb.b.111.17	yes	120
49.34	odd	14	inner	784.2.bb.b.671.17	yes	120
196.83	even	14	inner	784.2.bb.b.671.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.4	✓	120	1.1	even	1	trivial
784.2.bb.b.111.17	yes	120	4.3	odd	2	inner
784.2.bb.b.671.4	yes	120	196.83	even	14	inner
784.2.bb.b.671.17	yes	120	49.34	odd	14	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36747 - 1.71475i) q^{3} +(1.64860 - 1.31472i) q^{5} +(-1.20605 + 2.35488i) q^{7} +(-0.402843 + 1.76497i) q^{9} +O(q^{10})\)	\(q+(-1.36747 - 1.71475i) q^{3} +(1.64860 - 1.31472i) q^{5} +(-1.20605 + 2.35488i) q^{7} +(-0.402843 + 1.76497i) q^{9} +(1.05178 - 0.240061i) q^{11} +(2.11117 - 0.481860i) q^{13} +(-4.50883 - 1.02911i) q^{15} +(3.50399 - 7.27611i) q^{17} +4.92145 q^{19} +(5.68727 - 1.15214i) q^{21} +(-3.41983 - 7.10135i) q^{23} +(-0.123196 + 0.539756i) q^{25} +(-2.35079 + 1.13208i) q^{27} +(-4.15434 - 2.00062i) q^{29} -3.18545 q^{31} +(-1.84992 - 1.47526i) q^{33} +(1.10769 + 5.46787i) q^{35} +(-0.399047 - 0.192171i) q^{37} +(-3.71323 - 2.96120i) q^{39} +(-6.95616 + 5.54735i) q^{41} +(3.49703 + 2.78878i) q^{43} +(1.65631 + 3.43936i) q^{45} +(-1.14186 - 5.00283i) q^{47} +(-4.09088 - 5.68020i) q^{49} +(-17.2683 + 3.94139i) q^{51} +(0.514057 - 0.247557i) q^{53} +(1.41835 - 1.77855i) q^{55} +(-6.72994 - 8.43907i) q^{57} +(6.38084 - 8.00132i) q^{59} +(-3.00244 + 6.23463i) q^{61} +(-3.67044 - 3.07729i) q^{63} +(2.84696 - 3.56998i) q^{65} -11.8184i q^{67} +(-7.50055 + 15.5751i) q^{69} +(-3.82590 - 7.94455i) q^{71} +(15.8020 + 3.60670i) q^{73} +(1.09401 - 0.526850i) q^{75} +(-0.703183 + 2.76633i) q^{77} -3.47997i q^{79} +(10.0491 + 4.83940i) q^{81} +(-1.33658 + 5.85592i) q^{83} +(-3.78933 - 16.6022i) q^{85} +(2.25036 + 9.85946i) q^{87} +(-3.30946 - 0.755363i) q^{89} +(-1.41146 + 5.55268i) q^{91} +(4.35602 + 5.46227i) q^{93} +(8.11351 - 6.47030i) q^{95} -10.5910i q^{97} +1.95306i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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