LMFDB - Embedded newform 920.2.bv.a.217.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.28
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10676 - 0.458297i) q^{3} +(-2.23427 - 0.0896231i) q^{5} +(1.66374 - 0.908469i) q^{7} +(1.49949 - 0.684792i) q^{9} +O(q^{10})$	\(q+(2.10676 - 0.458297i) q^{3} +(-2.23427 - 0.0896231i) q^{5} +(1.66374 - 0.908469i) q^{7} +(1.49949 - 0.684792i) q^{9} +(-0.566289 - 0.490692i) q^{11} +(1.53215 - 2.80592i) q^{13} +(-4.74814 + 0.835145i) q^{15} +(5.94880 + 4.45322i) q^{17} +(0.974717 - 6.77931i) q^{19} +(3.08874 - 2.67641i) q^{21} +(0.956275 - 4.69953i) q^{23} +(4.98394 + 0.400485i) q^{25} +(-2.33275 + 1.74628i) q^{27} +(-4.82631 + 0.693919i) q^{29} +(7.40286 - 4.75753i) q^{31} +(-1.41792 - 0.774240i) q^{33} +(-3.79866 + 1.88066i) q^{35} +(0.138920 + 0.0518146i) q^{37} +(1.94192 - 6.61356i) q^{39} +(1.76209 - 3.85844i) q^{41} +(0.921583 + 4.23645i) q^{43} +(-3.41163 + 1.39562i) q^{45} +(-2.27667 - 2.27667i) q^{47} +(-1.84178 + 2.86587i) q^{49} +(14.5736 + 6.65552i) q^{51} +(-1.41464 - 2.59073i) q^{53} +(1.22127 + 1.14709i) q^{55} +(-1.05344 - 14.7290i) q^{57} +(1.51072 + 5.14504i) q^{59} +(-5.46498 - 8.50368i) q^{61} +(1.87264 - 2.50155i) q^{63} +(-3.67471 + 6.13187i) q^{65} +(-0.820801 - 0.0587048i) q^{67} +(-0.139140 - 10.3390i) q^{69} +(9.72617 + 11.2246i) q^{71} +(7.62740 + 10.1890i) q^{73} +(10.6835 - 1.44040i) q^{75} +(-1.38793 - 0.301927i) q^{77} +(-10.0146 + 2.94056i) q^{79} +(-7.35275 + 8.48553i) q^{81} +(-2.56650 + 6.88105i) q^{83} +(-12.8921 - 10.4828i) q^{85} +(-9.84984 + 3.67380i) q^{87} +(-11.9004 - 7.64792i) q^{89} -6.06021i q^{91} +(13.4156 - 13.4156i) q^{93} +(-2.78537 + 15.0595i) q^{95} +(-2.23229 - 5.98501i) q^{97} +(-1.18517 - 0.347996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.10676	−	0.458297i	1.21634	−	0.264598i	0.441792	−	0.897118i	$-0.354343\pi$
$3$	2.10676	−	0.458297i	1.21634	−	0.264598i	0.774544	+	0.632520i	$0.217979\pi$
$4$		0			0
$5$	−2.23427	−	0.0896231i	−0.999196	−	0.0400807i
$5$	−2.23427	−	0.0896231i	−0.999196	−	0.0400807i
$6$		0			0
$7$	1.66374	−	0.908469i	0.628833	−	0.343369i	−0.133025	−	0.991113i	$-0.542469\pi$
$7$	1.66374	−	0.908469i	0.628833	−	0.343369i	0.761858	+	0.647744i	$0.224287\pi$
$8$		0			0
$9$	1.49949	−	0.684792i	0.499829	−	0.228264i
$10$		0			0
$11$	−0.566289	−	0.490692i	−0.170743	−	0.147949i	0.565298	−	0.824887i	$-0.308761\pi$
$11$	−0.566289	−	0.490692i	−0.170743	−	0.147949i	−0.736040	+	0.676938i	$0.763307\pi$
$12$		0			0
$13$	1.53215	−	2.80592i	0.424941	−	0.778222i	−0.574240	−	0.818687i	$-0.694702\pi$
$13$	1.53215	−	2.80592i	0.424941	−	0.778222i	0.999181	+	0.0404655i	$0.0128841\pi$
$14$		0			0
$15$	−4.74814	+	0.835145i	−1.22596	+	0.215633i
$16$		0			0
$17$	5.94880	+	4.45322i	1.44280	+	1.08006i	0.981204	+	0.192972i	$0.0618126\pi$
$17$	5.94880	+	4.45322i	1.44280	+	1.08006i	0.461592	+	0.887092i	$0.347278\pi$
$18$		0			0
$19$	0.974717	−	6.77931i	0.223615	−	1.55528i	−0.500583	−	0.865688i	$-0.666881\pi$
$19$	0.974717	−	6.77931i	0.223615	−	1.55528i	0.724199	−	0.689591i	$-0.242210\pi$
$20$		0			0
$21$	3.08874	−	2.67641i	0.674018	−	0.584040i
$22$		0			0
$23$	0.956275	−	4.69953i	0.199397	−	0.979919i
$23$	0.956275	−	4.69953i	0.199397	−	0.979919i
$24$		0			0
$25$	4.98394	+	0.400485i	0.996787	+	0.0800969i
$26$		0			0
$27$	−2.33275	+	1.74628i	−0.448939	+	0.336071i
$28$		0			0
$29$	−4.82631	+	0.693919i	−0.896224	+	0.128858i	−0.575007	−	0.818148i	$-0.695001\pi$
$29$	−4.82631	+	0.693919i	−0.896224	+	0.128858i	−0.321216	+	0.947006i	$0.604092\pi$
$30$		0			0
$31$	7.40286	−	4.75753i	1.32959	−	0.854477i	0.333496	−	0.942751i	$-0.391772\pi$
$31$	7.40286	−	4.75753i	1.32959	−	0.854477i	0.996096	+	0.0882744i	$0.0281352\pi$
$32$		0			0
$33$	−1.41792	−	0.774240i	−0.246827	−	0.134778i
$34$		0			0
$35$	−3.79866	+	1.88066i	−0.642090	+	0.317889i
$36$		0			0
$37$	0.138920	+	0.0518146i	0.0228384	+	0.00851827i	0.360857	−	0.932621i	$-0.382484\pi$
$37$	0.138920	+	0.0518146i	0.0228384	+	0.00851827i	−0.338019	+	0.941139i	$0.609757\pi$
$38$		0			0
$39$	1.94192	−	6.61356i	0.310956	−	1.05902i
$40$		0			0
$41$	1.76209	−	3.85844i	0.275192	−	0.602587i	−0.720689	−	0.693259i	$-0.756174\pi$
$41$	1.76209	−	3.85844i	0.275192	−	0.602587i	0.995881	+	0.0906721i	$0.0289015\pi$
$42$		0			0
$43$	0.921583	+	4.23645i	0.140540	+	0.646053i	0.992479	+	0.122412i	$0.0390629\pi$
$43$	0.921583	+	4.23645i	0.140540	+	0.646053i	−0.851939	+	0.523641i	$0.824573\pi$
$44$		0			0
$45$	−3.41163	+	1.39562i	−0.508576	+	0.208047i
$46$		0			0
$47$	−2.27667	−	2.27667i	−0.332087	−	0.332087i	0.521292	−	0.853378i	$-0.325450\pi$
$47$	−2.27667	−	2.27667i	−0.332087	−	0.332087i	−0.853378	+	0.521292i	$0.825450\pi$
$48$		0			0
$49$	−1.84178	+	2.86587i	−0.263112	+	0.409410i
$50$		0			0
$51$	14.5736	+	6.65552i	2.04071	+	0.931960i
$52$		0			0
$53$	−1.41464	−	2.59073i	−0.194316	−	0.355864i	0.762295	−	0.647229i	$-0.224072\pi$
$53$	−1.41464	−	2.59073i	−0.194316	−	0.355864i	−0.956612	+	0.291365i	$0.905890\pi$
$54$		0			0
$55$	1.22127	+	1.14709i	0.164676	+	0.154674i
$56$		0			0
$57$	−1.05344	−	14.7290i	−0.139532	−	1.95091i
$58$		0			0
$59$	1.51072	+	5.14504i	0.196679	+	0.669828i	0.997483	+	0.0709015i	$0.0225876\pi$
$59$	1.51072	+	5.14504i	0.196679	+	0.669828i	−0.800804	+	0.598926i	$0.795594\pi$
$60$		0			0
$61$	−5.46498	−	8.50368i	−0.699719	−	1.08878i	−0.991221	−	0.132214i	$-0.957791\pi$
$61$	−5.46498	−	8.50368i	−0.699719	−	1.08878i	0.291502	−	0.956570i	$-0.405845\pi$
$62$		0			0
$63$	1.87264	−	2.50155i	0.235930	−	0.315166i
$64$		0			0
$65$	−3.67471	+	6.13187i	−0.455791	+	0.760564i
$66$		0			0
$67$	−0.820801	−	0.0587048i	−0.100277	−	0.00717194i	0.0211106	−	0.999777i	$-0.493280\pi$
$67$	−0.820801	−	0.0587048i	−0.100277	−	0.00717194i	−0.121387	+	0.992605i	$0.538734\pi$
$68$		0			0
$69$	−0.139140	−	10.3390i	−0.0167504	−	1.24467i
$70$		0			0
$71$	9.72617	+	11.2246i	1.15428	+	1.33211i	0.934249	+	0.356622i	$0.116072\pi$
$71$	9.72617	+	11.2246i	1.15428	+	1.33211i	0.220035	+	0.975492i	$0.429383\pi$
$72$		0			0
$73$	7.62740	+	10.1890i	0.892720	+	1.19253i	0.980525	+	0.196396i	$0.0629238\pi$
$73$	7.62740	+	10.1890i	0.892720	+	1.19253i	−0.0878050	+	0.996138i	$0.527985\pi$
$74$		0			0
$75$	10.6835	−	1.44040i	1.23362	−	0.166323i
$76$		0			0
$77$	−1.38793	−	0.301927i	−0.158170	−	0.0344077i
$78$		0			0
$79$	−10.0146	+	2.94056i	−1.12673	+	0.330839i	−0.791423	−	0.611269i	$-0.790659\pi$
$79$	−10.0146	+	2.94056i	−1.12673	+	0.330839i	−0.335310	+	0.942108i	$0.608841\pi$
$80$		0			0
$81$	−7.35275	+	8.48553i	−0.816972	+	0.942836i
$82$		0			0
$83$	−2.56650	+	6.88105i	−0.281710	+	0.755293i	0.716617	+	0.697467i	$0.245690\pi$
$83$	−2.56650	+	6.88105i	−0.281710	+	0.755293i	−0.998327	+	0.0578261i	$0.981583\pi$
$84$		0			0
$85$	−12.8921	−	10.4828i	−1.39835	−	1.13702i
$86$		0			0
$87$	−9.84984	+	3.67380i	−1.05601	+	0.393873i
$88$		0			0
$89$	−11.9004	−	7.64792i	−1.26144	−	0.810677i	−0.272958	−	0.962026i	$-0.588002\pi$
$89$	−11.9004	−	7.64792i	−1.26144	−	0.810677i	−0.988480	+	0.151348i	$0.951638\pi$
$90$		0			0
$91$		−	6.06021i		−	0.635283i
$92$		0			0
$93$	13.4156	−	13.4156i	1.39114	−	1.39114i
$94$		0			0
$95$	−2.78537	+	15.0595i	−0.285772	+	1.54507i
$96$		0			0
$97$	−2.23229	−	5.98501i	−0.226655	−	0.607686i	0.772987	−	0.634421i	$-0.218762\pi$
$97$	−2.23229	−	5.98501i	−0.226655	−	0.607686i	−0.999643	+	0.0267354i	$0.991489\pi$
$98$		0			0
$99$	−1.18517	−	0.347996i	−0.119114	−	0.0349749i
$100$		0			0
$101$	4.03207	+	8.82900i	0.401206	+	0.878518i	0.997147	+	0.0754900i	$0.0240521\pi$
$101$	4.03207	+	8.82900i	0.401206	+	0.878518i	−0.595941	+	0.803029i	$0.703221\pi$
$102$		0			0
$103$	−9.71910	+	0.695123i	−0.957651	+	0.0684925i	−0.541407	−	0.840761i	$-0.682108\pi$
$103$	−9.71910	+	0.695123i	−0.957651	+	0.0684925i	−0.416244	+	0.909253i	$0.636654\pi$
$104$		0			0
$105$	−7.14094	+	5.70299i	−0.696885	+	0.556555i
$106$		0			0
$107$	−1.02448	+	4.70946i	−0.0990403	+	0.455281i	0.900741	+	0.434357i	$0.143024\pi$
$107$	−1.02448	+	4.70946i	−0.0990403	+	0.455281i	−0.999781	+	0.0209238i	$0.993339\pi$
$108$		0			0
$109$	1.43383	+	9.97252i	0.137336	+	0.955194i	0.935644	+	0.352945i	$0.114820\pi$
$109$	1.43383	+	9.97252i	0.137336	+	0.955194i	−0.798308	+	0.602249i	$0.794271\pi$
$110$		0			0
$111$	0.316418	+	0.0454940i	0.0300330	+	0.00431810i
$112$		0			0
$113$	−1.11690	+	15.6163i	−0.105069	+	1.46906i	0.622284	+	0.782792i	$0.286205\pi$
$113$	−1.11690	+	15.6163i	−0.105069	+	1.46906i	−0.727353	+	0.686264i	$0.759250\pi$
$114$		0			0
$115$	−2.55776	+	10.4143i	−0.238513	+	0.971139i
$116$		0			0
$117$	0.375962	−	5.25664i	0.0347577	−	0.485976i
$118$		0			0
$119$	13.9428	+	2.00468i	1.27814	+	0.183769i
$120$		0			0
$121$	−1.48556	−	10.3323i	−0.135051	−	0.939299i
$122$		0			0
$123$	1.94398	−	8.93634i	0.175283	−	0.805763i
$124$		0			0
$125$	−11.0996	−	1.34147i	−0.992776	−	0.119984i
$126$		0			0
$127$	13.6994	−	0.979799i	1.21562	−	0.0869431i	0.551248	−	0.834342i	$-0.314152\pi$
$127$	13.6994	−	0.979799i	1.21562	−	0.0869431i	0.664376	+	0.747399i	$0.268697\pi$
$128$		0			0
$129$	3.88310	+	8.50280i	0.341888	+	0.748630i
$130$		0			0
$131$	18.8634	+	5.53878i	1.64810	+	0.483926i	0.968366	−	0.249533i	$-0.0802771\pi$
$131$	18.8634	+	5.53878i	1.64810	+	0.483926i	0.679734	+	0.733459i	$0.262095\pi$
$132$		0			0
$133$	−4.53711	−	12.1645i	−0.393418	−	1.05479i
$134$		0			0
$135$	5.36851	−	3.69259i	0.462048	−	0.317807i
$136$		0			0
$137$	2.55681	−	2.55681i	0.218443	−	0.218443i	−0.589399	−	0.807842i	$-0.700635\pi$
$137$	2.55681	−	2.55681i	0.218443	−	0.218443i	0.807842	+	0.589399i	$0.200635\pi$
$138$		0			0
$139$		−	12.0908i		−	1.02552i	−0.858531	−	0.512762i	$-0.828622\pi$
$139$		−	12.0908i		−	1.02552i	0.858531	−	0.512762i	$-0.171378\pi$
$140$		0			0
$141$	−5.83978	−	3.75300i	−0.491798	−	0.316059i
$142$		0			0
$143$	−2.24448	+	0.837148i	−0.187693	+	0.0700058i
$144$		0			0
$145$	10.8455	−	1.11785i	0.900668	−	0.0928327i
$146$		0			0
$147$	−2.56677	+	6.88177i	−0.211703	+	0.567599i
$148$		0			0
$149$	−10.4038	+	12.0067i	−0.852314	+	0.983623i	−0.999985	−	0.00541328i	$-0.998277\pi$
$149$	−10.4038	+	12.0067i	−0.852314	+	0.983623i	0.147671	+	0.989037i	$0.452822\pi$
$150$		0			0
$151$	−3.27746	+	0.962349i	−0.266716	+	0.0783149i	−0.412356	−	0.911023i	$-0.635294\pi$
$151$	−3.27746	+	0.962349i	−0.266716	+	0.0783149i	0.145640	+	0.989338i	$0.453476\pi$
$152$		0			0
$153$	11.9697	+	2.60384i	0.967691	+	0.210508i
$154$		0			0
$155$	−16.9664	+	9.96614i	−1.36277	+	0.800499i
$156$		0			0
$157$	−6.91546	−	9.23797i	−0.551914	−	0.737270i	0.434659	−	0.900595i	$-0.356869\pi$
$157$	−6.91546	−	9.23797i	−0.551914	−	0.737270i	−0.986572	+	0.163325i	$0.947778\pi$
$158$		0			0
$159$	−4.16763	−	4.80970i	−0.330515	−	0.381434i
$160$		0			0
$161$	−2.67838	−	8.68751i	−0.211086	−	0.684672i
$162$		0			0
$163$	7.76130	+	0.555099i	0.607912	+	0.0434787i	0.371902	−	0.928272i	$-0.378706\pi$
$163$	7.76130	+	0.555099i	0.607912	+	0.0434787i	0.236010	+	0.971751i	$0.424160\pi$
$164$		0			0
$165$	3.09862	+	1.85694i	0.241227	+	0.144563i
$166$		0			0
$167$	8.14748	−	10.8838i	0.630471	−	0.842211i	−0.365600	−	0.930772i	$-0.619136\pi$
$167$	8.14748	−	10.8838i	0.630471	−	0.842211i	0.996071	+	0.0885614i	$0.0282269\pi$
$168$		0			0
$169$	1.50263	+	2.33814i	0.115587	+	0.179857i
$170$		0			0
$171$	−3.18084	−	10.8330i	−0.243245	−	0.828417i
$172$		0			0
$173$	−0.848202	−	11.8594i	−0.0644876	−	0.901655i	−0.922000	−	0.387191i	$-0.873445\pi$
$173$	−0.848202	−	11.8594i	−0.0644876	−	0.901655i	0.857512	−	0.514464i	$-0.172009\pi$
$174$		0			0
$175$	8.65578	−	3.86145i	0.654315	−	0.291898i
$176$		0			0
$177$	5.54068	+	10.1470i	0.416463	+	0.762695i
$178$		0			0
$179$	9.98299	+	4.55908i	0.746163	+	0.340761i	0.751948	−	0.659222i	$-0.229114\pi$
$179$	9.98299	+	4.55908i	0.746163	+	0.340761i	−0.00578510	+	0.999983i	$0.501841\pi$
$180$		0			0
$181$	−0.892761	+	1.38916i	−0.0663584	+	0.103256i	−0.872847	−	0.487994i	$-0.837729\pi$
$181$	−0.892761	+	1.38916i	−0.0663584	+	0.103256i	0.806489	+	0.591250i	$0.201365\pi$
$182$		0			0
$183$	−15.4106	−	15.4106i	−1.13918	−	1.13918i
$184$		0			0
$185$	−0.305742	−	0.128218i	−0.0224786	−	0.00942680i
$186$		0			0
$187$	−1.18358	−	5.44084i	−0.0865521	−	0.397874i
$188$		0			0
$189$	−2.29465	+	5.02458i	−0.166911	+	0.365484i
$190$		0			0
$191$	−2.78615	+	9.48874i	−0.201598	+	0.686581i	0.795180	+	0.606374i	$0.207376\pi$
$191$	−2.78615	+	9.48874i	−0.201598	+	0.686581i	−0.996778	+	0.0802074i	$0.974442\pi$
$192$		0			0
$193$	7.74668	+	2.88936i	0.557618	+	0.207981i	0.612443	−	0.790515i	$-0.290187\pi$
$193$	7.74668	+	2.88936i	0.557618	+	0.207981i	−0.0548242	+	0.998496i	$0.517460\pi$
$194$		0			0
$195$	−4.93150	+	14.6024i	−0.353152	+	1.04570i
$196$		0			0
$197$	−9.40268	−	5.13425i	−0.669913	−	0.365800i	0.108019	−	0.994149i	$-0.465549\pi$
$197$	−9.40268	−	5.13425i	−0.669913	−	0.365800i	−0.777932	+	0.628349i	$0.783731\pi$
$198$		0			0
$199$	−5.38049	+	3.45783i	−0.381413	+	0.245119i	−0.717272	−	0.696793i	$-0.754610\pi$
$199$	−5.38049	+	3.45783i	−0.381413	+	0.245119i	0.335859	+	0.941912i	$0.390973\pi$
$200$		0			0
$201$	−1.75613	+	0.252493i	−0.123868	+	0.0178095i
$202$		0			0
$203$	−7.39931	+	5.53905i	−0.519329	+	0.388765i
$204$		0			0
$205$	−4.28279	+	8.46287i	−0.299123	+	0.591073i
$206$		0			0
$207$	−1.78428	−	7.70172i	−0.124016	−	0.535307i
$208$		0			0
$209$	−3.87853	+	3.36076i	−0.268283	+	0.232469i
$210$		0			0
$211$	−3.59701	+	25.0178i	−0.247628	+	1.72229i	0.364215	+	0.931315i	$0.381337\pi$
$211$	−3.59701	+	25.0178i	−0.247628	+	1.72229i	−0.611844	+	0.790979i	$0.709572\pi$
$212$		0			0
$213$	25.6348	+	19.1900i	1.75647	+	1.31488i
$214$		0			0
$215$	−1.67938	−	9.54797i	−0.114533	−	0.651166i
$216$		0			0
$217$	7.99433	−	14.6405i	0.542691	−	0.993864i
$218$		0			0
$219$	20.7387	+	17.9701i	1.40139	+	1.21431i
$220$		0			0
$221$	21.6098	−	9.86887i	1.45363	−	0.663852i
$222$		0			0
$223$	−10.2766	+	5.61147i	−0.688174	+	0.375772i	−0.784971	−	0.619533i	$-0.787322\pi$
$223$	−10.2766	+	5.61147i	−0.688174	+	0.375772i	0.0967966	+	0.995304i	$0.469140\pi$
$224$		0			0
$225$	7.74759	−	2.81244i	0.516506	−	0.187496i
$226$		0			0
$227$	−4.63451	+	1.00818i	−0.307603	+	0.0669150i	−0.363717	−	0.931509i	$-0.618493\pi$
$227$	−4.63451	+	1.00818i	−0.307603	+	0.0669150i	0.0561140	+	0.998424i	$0.482129\pi$
$228$		0			0
$229$	−9.12639			−0.603089			−0.301544	−	0.953452i	$-0.597502\pi$
$229$	−9.12639			−0.603089			−0.301544	+	0.953452i	$0.597502\pi$
$230$		0			0
$231$	−3.06241			−0.201492
$232$		0			0
$233$	−25.6434	+	5.57838i	−1.67996	+	0.365452i	−0.948584	−	0.316527i	$-0.897483\pi$
$233$	−25.6434	+	5.57838i	−1.67996	+	0.365452i	−0.731372	+	0.681979i	$0.761120\pi$
$234$		0			0
$235$	4.88266	+	5.29074i	0.318509	+	0.345130i
$236$		0			0
$237$	−19.7507	+	10.7847i	−1.28295	+	0.700542i
$238$		0			0
$239$	12.4364	−	5.67951i	0.804443	−	0.367377i	0.0296252	−	0.999561i	$-0.490569\pi$
$239$	12.4364	−	5.67951i	0.804443	−	0.367377i	0.774818	+	0.632184i	$0.217841\pi$
$240$		0			0
$241$	15.8527	+	13.7364i	1.02116	+	0.884842i	0.993392	−	0.114773i	$-0.0366140\pi$
$241$	15.8527	+	13.7364i	1.02116	+	0.884842i	0.0277698	+	0.999614i	$0.491159\pi$
$242$		0			0
$243$	−7.41201	+	13.5741i	−0.475480	+	0.870777i
$244$		0			0
$245$	4.37189	−	6.23807i	0.279310	−	0.398535i
$246$		0			0
$247$	−17.5288	−	13.1219i	−1.11533	−	0.834925i
$248$		0			0
$249$	−2.25342	+	15.6729i	−0.142805	+	0.993230i
$250$		0			0
$251$	−4.83197	+	4.18693i	−0.304991	+	0.264277i	−0.793886	−	0.608066i	$-0.791946\pi$
$251$	−4.83197	+	4.18693i	−0.304991	+	0.264277i	0.488895	+	0.872343i	$0.337400\pi$
$252$		0			0
$253$	−2.84755	+	2.19205i	−0.179024	+	0.137813i
$254$		0			0
$255$	−31.9648	−	16.1764i	−2.00171	−	1.01300i
$256$		0			0
$257$	−1.08038	+	0.808765i	−0.0673925	+	0.0504494i	−0.632443	−	0.774607i	$-0.717948\pi$
$257$	−1.08038	+	0.808765i	−0.0673925	+	0.0504494i	0.565050	+	0.825056i	$0.308857\pi$
$258$		0			0
$259$	0.278199	−	0.0399989i	0.0172864	−	0.00248541i
$260$		0			0
$261$	−6.76180	+	4.34554i	−0.418545	+	0.268982i
$262$		0			0
$263$	3.19522	+	1.74472i	0.197026	+	0.107584i	0.574733	−	0.818341i	$-0.305106\pi$
$263$	3.19522	+	1.74472i	0.197026	+	0.107584i	−0.377708	+	0.925925i	$0.623288\pi$
$264$		0			0
$265$	2.92851	+	5.91517i	0.179897	+	0.363366i
$266$		0			0
$267$	−28.5762	−	10.6584i	−1.74884	−	0.652282i
$268$		0			0
$269$	−3.26793	+	11.1295i	−0.199249	+	0.678579i	0.797877	+	0.602820i	$0.205956\pi$
$269$	−3.26793	+	11.1295i	−0.199249	+	0.678579i	−0.997126	+	0.0757595i	$0.975862\pi$
$270$		0			0
$271$	−8.79006	+	19.2475i	−0.533958	+	1.16920i	0.429922	+	0.902866i	$0.358541\pi$
$271$	−8.79006	+	19.2475i	−0.533958	+	1.16920i	−0.963880	+	0.266338i	$0.914186\pi$
$272$		0			0
$273$	−2.77738	−	12.7674i	−0.168094	−	0.772718i
$274$		0			0
$275$	−2.62583	−	2.67237i	−0.158344	−	0.161150i
$276$		0			0
$277$	−18.9531	−	18.9531i	−1.13878	−	1.13878i	−0.988669	−	0.150115i	$-0.952036\pi$
$277$	−18.9531	−	18.9531i	−1.13878	−	1.13878i	−0.150115	−	0.988669i	$-0.547964\pi$
$278$		0			0
$279$	7.84256	−	12.2033i	0.469522	−	0.730590i
$280$		0			0
$281$	−14.2734	−	6.51843i	−0.851477	−	0.388857i	−0.0586321	−	0.998280i	$-0.518674\pi$
$281$	−14.2734	−	6.51843i	−0.851477	−	0.388857i	−0.792845	+	0.609423i	$0.791401\pi$
$282$		0			0
$283$	2.69756	+	4.94022i	0.160354	+	0.293666i	0.945486	−	0.325662i	$-0.105587\pi$
$283$	2.69756	+	4.94022i	0.160354	+	0.293666i	−0.785133	+	0.619328i	$0.787405\pi$
$284$		0			0
$285$	1.03361	+	33.0031i	0.0612259	+	1.95494i
$286$		0			0
$287$	−0.573618	−	8.02022i	−0.0338596	−	0.473419i
$288$		0			0
$289$	10.7677	+	36.6713i	0.633391	+	2.15713i
$290$		0			0
$291$	−7.44581	−	11.5859i	−0.436481	−	0.679178i
$292$		0			0
$293$	−8.64378	+	11.5467i	−0.504975	+	0.674567i	−0.978508	−	0.206209i	$-0.933887\pi$
$293$	−8.64378	+	11.5467i	−0.504975	+	0.674567i	0.473533	+	0.880776i	$0.342978\pi$
$294$		0			0
$295$	−2.91425	−	11.6308i	−0.169674	−	0.677173i
$296$		0			0
$297$	2.17790	+	0.155766i	0.126374	+	0.00903848i
$298$		0			0
$299$	−11.7213	−	9.88359i	−0.677862	−	0.571583i
$300$		0			0
$301$	5.38195	+	6.21110i	0.310211	+	0.358002i
$302$		0			0
$303$	12.5409	+	16.7527i	0.720455	+	0.962415i
$304$		0			0
$305$	11.4481	+	19.4893i	0.655518	+	1.11596i
$306$		0			0
$307$	−15.6687	−	3.40852i	−0.894262	−	0.194535i	−0.258125	−	0.966111i	$-0.583105\pi$
$307$	−15.6687	−	3.40852i	−0.894262	−	0.194535i	−0.636136	+	0.771577i	$0.719468\pi$
$308$		0			0
$309$	−20.1572	+	5.91868i	−1.14670	+	0.336702i
$310$		0			0
$311$	−4.71781	+	5.44464i	−0.267522	+	0.308737i	−0.873577	−	0.486686i	$-0.838206\pi$
$311$	−4.71781	+	5.44464i	−0.267522	+	0.308737i	0.606055	+	0.795423i	$0.292751\pi$
$312$		0			0
$313$	9.93238	−	26.6297i	0.561411	−	1.50520i	−0.277386	−	0.960759i	$-0.589468\pi$
$313$	9.93238	−	26.6297i	0.561411	−	1.50520i	0.838797	−	0.544444i	$-0.183259\pi$
$314$		0			0
$315$	−4.40817	+	5.42131i	−0.248373	+	0.305456i
$316$		0			0
$317$	−2.67319	+	0.997050i	−0.150141	+	0.0559999i	−0.423411	−	0.905938i	$-0.639168\pi$
$317$	−2.67319	+	0.997050i	−0.150141	+	0.0559999i	0.273270	+	0.961937i	$0.411895\pi$
$318$		0			0
$319$	3.07359	+	1.97528i	0.172088	+	0.110594i
$320$		0			0
$321$			10.3912i			0.579980i
$322$		0			0
$323$	35.9881	−	35.9881i	2.00243	−	2.00243i
$324$		0			0
$325$	8.75985	−	13.3709i	0.485909	−	0.741685i
$326$		0			0
$327$	7.59110	+	20.3525i	0.419789	+	1.12550i
$328$		0			0
$329$	−5.85606	−	1.71950i	−0.322855	−	0.0947988i
$330$		0			0
$331$	−7.55242	−	16.5375i	−0.415119	−	0.908983i	−0.995511	−	0.0946459i	$-0.969828\pi$
$331$	−7.55242	−	16.5375i	−0.415119	−	0.908983i	0.580393	−	0.814337i	$-0.302899\pi$
$332$		0			0
$333$	0.243791	−	0.0174363i	0.0133597	−	0.000955504i
$334$		0			0
$335$	1.82863	+	0.204725i	0.0999087	+	0.0111853i
$336$		0			0
$337$	−1.75745	+	8.07886i	−0.0957343	+	0.440084i	0.904182	+	0.427147i	$0.140481\pi$
$337$	−1.75745	+	8.07886i	−0.0957343	+	0.440084i	−0.999916	+	0.0129362i	$0.995882\pi$
$338$		0			0
$339$	4.80385	+	33.4115i	0.260909	+	1.81467i
$340$		0			0
$341$	−6.52664	−	0.938389i	−0.353437	−	0.0508166i
$342$		0			0
$343$	−1.40731	+	19.6767i	−0.0759874	+	1.06244i
$344$		0			0
$345$	−0.615739	+	23.1126i	−0.0331503	+	1.24434i
$346$		0			0
$347$	0.127796	−	1.78682i	0.00686046	−	0.0959218i	−0.992868	−	0.119218i	$-0.961961\pi$
$347$	0.127796	−	1.78682i	0.00686046	−	0.0959218i	0.999729	+	0.0232958i	$0.00741595\pi$
$348$		0			0
$349$	35.5001	+	5.10415i	1.90028	+	0.273219i	0.990031	−	0.140847i	$-0.0449827\pi$
$349$	35.5001	+	5.10415i	1.90028	+	0.273219i	0.910247	+	0.414066i	$0.135892\pi$
$350$		0			0
$351$	1.32579	+	9.22107i	0.0707654	+	0.492184i
$352$		0			0
$353$	5.45701	−	25.0855i	0.290447	−	1.33516i	−0.568324	−	0.822805i	$-0.692408\pi$
$353$	5.45701	−	25.0855i	0.290447	−	1.33516i	0.858771	−	0.512360i	$-0.171228\pi$
$354$		0			0
$355$	−20.7249	−	25.9505i	−1.09996	−	1.37731i
$356$		0			0
$357$	30.2929	−	2.16659i	1.60327	−	0.114668i
$358$		0			0
$359$	10.1171	+	22.1533i	0.533958	+	1.16921i	0.963879	+	0.266339i	$0.0858142\pi$
$359$	10.1171	+	22.1533i	0.533958	+	1.16921i	−0.429921	+	0.902867i	$0.641459\pi$
$360$		0			0
$361$	−26.7786	−	7.86289i	−1.40940	−	0.413837i
$362$		0			0
$363$	−7.86496	−	21.0868i	−0.412803	−	1.10677i
$364$		0			0
$365$	−16.1285	−	23.4486i	−0.844205	−	1.22736i
$366$		0			0
$367$	17.9853	−	17.9853i	0.938825	−	0.938825i	−0.0594083	−	0.998234i	$-0.518921\pi$
$367$	17.9853	−	17.9853i	0.938825	−	0.938825i	0.998234	+	0.0594083i	$0.0189214\pi$
$368$		0			0
$369$		−	6.99234i		−	0.364007i
$370$		0			0
$371$	−4.70719	−	3.02513i	−0.244385	−	0.157057i
$372$		0			0
$373$	10.5414	−	3.93175i	0.545814	−	0.203578i	−0.0614045	−	0.998113i	$-0.519558\pi$
$373$	10.5414	−	3.93175i	0.545814	−	0.203578i	0.607219	+	0.794535i	$0.292285\pi$
$374$		0			0
$375$	−23.9989	+	2.26075i	−1.23930	+	0.116745i
$376$		0			0
$377$	−5.44754	+	14.6054i	−0.280563	+	0.752218i
$378$		0			0
$379$	16.4011	−	18.9279i	0.842470	−	0.972262i	−0.157414	−	0.987533i	$-0.550316\pi$
$379$	16.4011	−	18.9279i	0.842470	−	0.972262i	0.999883	+	0.0152709i	$0.00486106\pi$
$380$		0			0
$381$	28.4122	−	8.34257i	1.45560	−	0.427403i
$382$		0			0
$383$	8.31958	+	1.80981i	0.425111	+	0.0924772i	0.420031	−	0.907510i	$-0.362019\pi$
$383$	8.31958	+	1.80981i	0.425111	+	0.0924772i	0.00508006	+	0.999987i	$0.498383\pi$
$384$		0			0
$385$	3.07396	+	0.798977i	0.156664	+	0.0407196i
$386$		0			0
$387$	4.28299	+	5.72140i	0.217717	+	0.290835i
$388$		0			0
$389$	−12.9697	−	14.9679i	−0.657591	−	0.758900i	0.324791	−	0.945786i	$-0.394706\pi$
$389$	−12.9697	−	14.9679i	−0.657591	−	0.758900i	−0.982382	+	0.186886i	$0.940161\pi$
$390$		0			0
$391$	26.6167	−	23.6981i	1.34606	−	1.19846i
$392$		0			0
$393$	42.2789	+	3.02385i	2.13269	+	0.152533i
$394$		0			0
$395$	22.6389	−	5.67246i	1.13909	−	0.285413i
$396$		0			0
$397$	1.69071	−	2.25852i	0.0848542	−	0.113352i	−0.756105	−	0.654450i	$-0.772900\pi$
$397$	1.69071	−	2.25852i	0.0848542	−	0.113352i	0.840960	+	0.541098i	$0.181991\pi$
$398$		0			0
$399$	−15.1335	−	23.5482i	−0.757624	−	1.17889i
$400$		0			0
$401$	0.364714	+	1.24210i	0.0182130	+	0.0620277i	0.968098	−	0.250572i	$-0.0806185\pi$
$401$	0.364714	+	1.24210i	0.0182130	+	0.0620277i	−0.949885	+	0.312599i	$0.898800\pi$
$402$		0			0
$403$	−2.00697	−	28.0610i	−0.0999741	−	1.39782i
$404$		0			0
$405$	17.1885	−	18.3000i	0.854105	−	0.909334i
$406$		0			0
$407$	−0.0532441	−	0.0975092i	−0.00263921	−	0.00483335i
$408$		0			0
$409$	5.58794	+	2.55193i	0.276306	+	0.126185i	0.548749	−	0.835987i	$-0.315104\pi$
$409$	5.58794	+	2.55193i	0.276306	+	0.126185i	−0.272443	+	0.962172i	$0.587832\pi$
$410$		0			0
$411$	4.21480	−	6.55836i	0.207901	−	0.323500i
$412$		0			0
$413$	7.18755	+	7.18755i	0.353676	+	0.353676i
$414$		0			0
$415$	6.35095	−	15.1441i	0.311756	−	0.743395i
$416$		0			0
$417$	−5.54115	−	25.4723i	−0.271351	−	1.24738i
$418$		0			0
$419$	−1.49224	+	3.26755i	−0.0729007	+	0.159630i	−0.942574	−	0.333998i	$-0.891602\pi$
$419$	−1.49224	+	3.26755i	−0.0729007	+	0.159630i	0.869673	+	0.493628i	$0.164330\pi$
$420$		0			0
$421$	3.89022	−	13.2489i	0.189598	−	0.645710i	−0.808745	−	0.588159i	$-0.799853\pi$
$421$	3.89022	−	13.2489i	0.189598	−	0.645710i	0.998343	−	0.0575505i	$-0.0183290\pi$
$422$		0			0
$423$	−4.97288	−	1.85479i	−0.241790	−	0.0901829i
$424$		0			0
$425$	27.8650	+	24.5770i	1.35165	+	1.19216i
$426$		0			0
$427$	−16.8176	−	9.18311i	−0.813862	−	0.444402i
$428$		0			0
$429$	−4.34491	+	2.79230i	−0.209774	+	0.134814i
$430$		0			0
$431$	−9.30427	+	1.33775i	−0.448171	+	0.0644373i	−0.362705	−	0.931904i	$-0.618147\pi$
$431$	−9.30427	+	1.33775i	−0.448171	+	0.0644373i	−0.0854656	+	0.996341i	$0.527238\pi$
$432$		0			0
$433$	19.9123	−	14.9062i	0.956924	−	0.716344i	−0.00200304	−	0.999998i	$-0.500638\pi$
$433$	19.9123	−	14.9062i	0.956924	−	0.716344i	0.958927	+	0.283654i	$0.0915467\pi$
$434$		0			0
$435$	22.3365	−	7.32549i	1.07095	−	0.351230i
$436$		0			0
$437$	−30.9274	−	11.0636i	−1.47946	−	0.529243i
$438$		0			0
$439$	−3.24223	+	2.80941i	−0.154743	+	0.134086i	−0.728791	−	0.684736i	$-0.759918\pi$
$439$	−3.24223	+	2.80941i	−0.154743	+	0.134086i	0.574048	+	0.818821i	$0.305372\pi$
$440$		0			0
$441$	−0.799202	+	5.55857i	−0.0380572	+	0.264694i
$442$		0			0
$443$	−16.0653	−	12.0263i	−0.763285	−	0.571388i	0.145152	−	0.989409i	$-0.453633\pi$
$443$	−16.0653	−	12.0263i	−0.763285	−	0.571388i	−0.908437	+	0.418021i	$0.862724\pi$
$444$		0			0
$445$	25.9033	+	18.1541i	1.22793	+	0.860585i
$446$		0			0
$447$	−16.4157	+	30.0631i	−0.776436	+	1.42194i
$448$		0			0
$449$	6.77526	+	5.87080i	0.319744	+	0.277060i	0.799913	−	0.600116i	$-0.204879\pi$
$449$	6.77526	+	5.87080i	0.319744	+	0.277060i	−0.480168	+	0.877176i	$0.659424\pi$
$450$		0			0
$451$	−2.89116	+	1.32035i	−0.136139	+	0.0621727i
$452$		0			0
$453$	−6.46377	+	3.52948i	−0.303694	+	0.165830i
$454$		0			0
$455$	−0.543135	+	13.5402i	−0.0254626	+	0.634773i
$456$		0			0
$457$	5.84372	−	1.27122i	0.273358	−	0.0594653i	−0.0737967	−	0.997273i	$-0.523512\pi$
$457$	5.84372	−	1.27122i	0.273358	−	0.0594653i	0.347154	+	0.937808i	$0.387148\pi$
$458$		0			0
$459$	−21.6536			−1.01071
$460$		0			0
$461$	38.5251			1.79429			0.897147	−	0.441733i	$-0.145636\pi$
$461$	38.5251			1.79429			0.897147	+	0.441733i	$0.145636\pi$
$462$		0			0
$463$	10.9069	−	2.37265i	0.506887	−	0.110267i	0.0481526	−	0.998840i	$-0.484667\pi$
$463$	10.9069	−	2.37265i	0.506887	−	0.110267i	0.458734	+	0.888573i	$0.348303\pi$
$464$		0			0
$465$	−31.1765	+	28.7718i	−1.44578	+	1.33426i
$466$		0			0
$467$	−7.66254	+	4.18406i	−0.354580	+	0.193615i	−0.646660	−	0.762779i	$-0.723835\pi$
$467$	−7.66254	+	4.18406i	−0.354580	+	0.193615i	0.292080	+	0.956394i	$0.405653\pi$
$468$		0			0
$469$	−1.41893	+	0.648002i	−0.0655200	+	0.0299220i
$470$		0			0
$471$	−18.8029	−	16.2928i	−0.866392	−	0.750733i
$472$		0			0
$473$	1.55691	−	2.85127i	0.0715868	−	0.131102i
$474$		0			0
$475$	7.57294	−	33.3973i	0.347470	−	1.53237i
$476$		0			0
$477$	−3.89535	−	2.91602i	−0.178356	−	0.133516i
$478$		0			0
$479$	2.55241	−	17.7524i	0.116623	−	0.811128i	−0.844609	−	0.535384i	$-0.820167\pi$
$479$	2.55241	−	17.7524i	0.116623	−	0.811128i	0.961231	−	0.275744i	$-0.0889241\pi$
$480$		0			0
$481$	0.358234	−	0.310412i	0.0163341	−	0.0141535i
$482$		0			0
$483$	−9.62415	−	17.0750i	−0.437914	−	0.776938i
$484$		0			0
$485$	4.45116	+	13.5722i	0.202117	+	0.616282i
$486$		0			0
$487$	5.67398	−	4.24749i	0.257112	−	0.192472i	−0.462944	−	0.886388i	$-0.653207\pi$
$487$	5.67398	−	4.24749i	0.257112	−	0.192472i	0.720056	+	0.693916i	$0.244116\pi$
$488$		0			0
$489$	16.6056	−	2.38752i	0.750930	−	0.107967i
$490$		0			0
$491$	30.4968	−	19.5991i	1.37630	−	0.884494i	0.377168	−	0.926145i	$-0.376898\pi$
$491$	30.4968	−	19.5991i	1.37630	−	0.884494i	0.999132	+	0.0416508i	$0.0132617\pi$
$492$		0			0
$493$	−31.8010	−	17.3646i	−1.43224	−	0.782064i
$494$		0			0
$495$	2.61679	+	0.883735i	0.117616	+	0.0397210i
$496$		0			0
$497$	26.3790	+	9.83885i	1.18326	+	0.441333i
$498$		0			0
$499$	−0.181122	+	0.616846i	−0.00810814	+	0.0276138i	−0.963448	−	0.267896i	$-0.913671\pi$
$499$	−0.181122	+	0.616846i	−0.00810814	+	0.0276138i	0.955340	+	0.295510i	$0.0954897\pi$
$500$		0			0
$501$	12.1768	−	26.6634i	0.544018	−	1.19123i
$502$		0			0
$503$	7.67149	+	35.2653i	0.342055	+	1.57240i	0.751290	+	0.659972i	$0.229432\pi$
$503$	7.67149	+	35.2653i	0.342055	+	1.57240i	−0.409236	+	0.912429i	$0.634205\pi$
$504$		0			0
$505$	−8.21745	−	20.0878i	−0.365672	−	0.893893i
$506$		0			0
$507$	4.23723	+	4.23723i	0.188182	+	0.188182i
$508$		0			0
$509$	−3.67982	+	5.72591i	−0.163105	+	0.253796i	−0.913180	−	0.407556i	$-0.866381\pi$
$509$	−3.67982	+	5.72591i	−0.163105	+	0.253796i	0.750075	+	0.661353i	$0.230017\pi$
$510$		0			0
$511$	21.9464	+	10.0226i	0.970851	+	0.443373i
$512$		0			0
$513$	9.56478	+	17.5166i	0.422295	+	0.773376i
$514$		0			0
$515$	21.7774	−	0.682038i	0.959627	−	0.0300542i
$516$		0			0
$517$	0.172109	+	2.40640i	0.00756935	+	0.105833i
$518$		0			0
$519$	−7.22208	−	24.5962i	−0.317014	−	1.07965i
$520$		0			0
$521$	11.5736	+	18.0088i	0.507047	+	0.788981i	0.996548	−	0.0830223i	$-0.0264573\pi$
$521$	11.5736	+	18.0088i	0.507047	+	0.788981i	−0.489501	+	0.872003i	$0.662821\pi$
$522$		0			0
$523$	0.460984	−	0.615802i	0.0201574	−	0.0269271i	−0.790349	−	0.612656i	$-0.790101\pi$
$523$	0.460984	−	0.615802i	0.0201574	−	0.0269271i	0.810507	+	0.585729i	$0.199192\pi$
$524$		0			0
$525$	16.4659	−	12.1020i	0.718632	−	0.528176i
$526$		0			0
$527$	65.2244	+	4.66494i	2.84122	+	0.203208i
$528$		0			0
$529$	−21.1711	−	8.98807i	−0.920482	−	0.390786i
$530$		0			0
$531$	5.78859	+	6.68039i	0.251204	+	0.289904i
$532$		0			0
$533$	−8.12668	−	10.8560i	−0.352006	−	0.470224i
$534$		0			0
$535$	2.71104	−	10.4304i	0.117209	−	0.450945i
$536$		0			0
$537$	23.1211	+	5.02969i	0.997750	+	0.217047i
$538$		0			0
$539$	2.44924	−	0.719163i	0.105496	−	0.0309765i
$540$		0			0
$541$	−22.7229	+	26.2236i	−0.976935	+	1.12744i	0.0148970	+	0.999889i	$0.495258\pi$
$541$	−22.7229	+	26.2236i	−0.976935	+	1.12744i	−0.991832	+	0.127554i	$0.959287\pi$
$542$		0			0
$543$	−1.24418	+	3.33578i	−0.0533929	+	0.143152i
$544$		0			0
$545$	−2.30980	−	22.4098i	−0.0989410	−	0.959931i
$546$		0			0
$547$	−10.9260	+	4.07518i	−0.467161	+	0.174242i	−0.572011	−	0.820246i	$-0.693837\pi$
$547$	−10.9260	+	4.07518i	−0.467161	+	0.174242i	0.104850	+	0.994488i	$0.466564\pi$
$548$		0			0
$549$	−14.0179	−	9.00877i	−0.598270	−	0.384485i
$550$		0			0
$551$			33.3954i			1.42269i
$552$		0			0
$553$	−13.9903	+	13.9903i	−0.594927	+	0.594927i
$554$		0			0
$555$	−0.702886	−	0.130004i	−0.0298358	−	0.00551837i
$556$		0			0
$557$	−4.43812	−	11.8991i	−0.188049	−	0.504180i	0.808375	−	0.588668i	$-0.200347\pi$
$557$	−4.43812	−	11.8991i	−0.188049	−	0.504180i	−0.996425	+	0.0844879i	$0.973075\pi$
$558$		0			0
$559$	13.2991	+	3.90498i	0.562493	+	0.165163i
$560$		0			0
$561$	−4.98704	−	10.9201i	−0.210553	−	0.461047i
$562$		0			0
$563$	−45.6979	+	3.26838i	−1.92594	+	0.137746i	−0.981564	−	0.191132i	$-0.938784\pi$
$563$	−45.6979	+	3.26838i	−1.92594	+	0.137746i	−0.944373	+	0.328877i	$0.893330\pi$
$564$		0			0
$565$	3.89503	−	34.7909i	0.163865	−	1.46366i
$566$		0			0
$567$	−4.52420	+	20.7974i	−0.189999	+	0.873410i
$568$		0			0
$569$	−5.69381	−	39.6013i	−0.238697	−	1.66017i	−0.658516	−	0.752567i	$-0.728815\pi$
$569$	−5.69381	−	39.6013i	−0.238697	−	1.66017i	0.419819	−	0.907608i	$-0.362094\pi$
$570$		0			0
$571$	−1.42013	−	0.204184i	−0.0594305	−	0.00854481i	0.112535	−	0.993648i	$-0.464103\pi$
$571$	−1.42013	−	0.204184i	−0.0594305	−	0.00854481i	−0.171966	+	0.985103i	$0.555012\pi$
$572$		0			0
$573$	−1.52107	+	21.2673i	−0.0635436	+	0.888456i
$574$		0			0
$575$	6.64810	−	23.0392i	0.277245	−	0.960799i
$576$		0			0
$577$	−0.457350	+	6.39459i	−0.0190397	+	0.266210i	0.979011	+	0.203806i	$0.0653313\pi$
$577$	−0.457350	+	6.39459i	−0.0190397	+	0.266210i	−0.998051	+	0.0624041i	$0.980123\pi$
$578$		0			0
$579$	17.6445	+	2.53690i	0.733282	+	0.105430i
$580$		0			0
$581$	1.98124	+	13.7798i	0.0821957	+	0.571684i
$582$		0			0
$583$	−0.470153	+	2.16126i	−0.0194717	+	0.0895101i
$584$		0			0
$585$	−1.31112	+	11.7111i	−0.0542081	+	0.484193i
$586$		0			0
$587$	−21.4358	+	1.53312i	−0.884751	+	0.0632786i	−0.506315	−	0.862349i	$-0.668993\pi$
$587$	−21.4358	+	1.53312i	−0.884751	+	0.0632786i	−0.378436	+	0.925627i	$0.623538\pi$
$588$		0			0
$589$	−25.0370	−	54.8235i	−1.03163	−	2.25896i
$590$		0			0
$591$	−22.1622	−	6.50739i	−0.911629	−	0.267678i
$592$		0			0
$593$	−5.31275	−	14.2440i	−0.218168	−	0.584932i	0.781050	−	0.624469i	$-0.214685\pi$
$593$	−5.31275	−	14.2440i	−0.218168	−	0.584932i	−0.999218	+	0.0395366i	$0.987412\pi$
$594$		0			0
$595$	−30.9724	−	5.72860i	−1.26975	−	0.234850i
$596$		0			0
$597$	−9.75067	+	9.75067i	−0.399068	+	0.399068i
$598$		0			0
$599$			18.0152i			0.736080i	0.929810	+	0.368040i	$0.119971\pi$
$599$			18.0152i			0.736080i	−0.929810	+	0.368040i	$0.880029\pi$
$600$		0			0
$601$	−7.23122	−	4.64722i	−0.294968	−	0.189564i	0.384784	−	0.923007i	$-0.374276\pi$
$601$	−7.23122	−	4.64722i	−0.294968	−	0.189564i	−0.679751	+	0.733443i	$0.737912\pi$
$602$		0			0
$603$	−1.27098	+	0.474051i	−0.0517583	+	0.0193049i
$604$		0			0
$605$	2.39313	+	23.2183i	0.0972945	+	0.943957i
$606$		0			0
$607$	1.47552	−	3.95601i	0.0598894	−	0.160570i	−0.903559	−	0.428464i	$-0.859055\pi$
$607$	1.47552	−	3.95601i	0.0598894	−	0.160570i	0.963448	+	0.267894i	$0.0863277\pi$
$608$		0			0
$609$	−13.0500	+	15.0605i	−0.528813	+	0.610282i
$610$		0			0
$611$	−9.87635	+	2.89996i	−0.399554	+	0.117320i
$612$		0			0
$613$	23.5358	+	5.11990i	0.950601	+	0.206791i	0.661025	−	0.750364i	$-0.270122\pi$
$613$	23.5358	+	5.11990i	0.950601	+	0.206791i	0.289577	+	0.957155i	$0.406486\pi$
$614$		0			0
$615$	−5.14429	+	19.7920i	−0.207438	+	0.798090i
$616$		0			0
$617$	−25.3169	−	33.8194i	−1.01922	−	1.36152i	−0.930838	−	0.365432i	$-0.880921\pi$
$617$	−25.3169	−	33.8194i	−1.01922	−	1.36152i	−0.0883821	−	0.996087i	$-0.528170\pi$
$618$		0			0
$619$	24.3699	+	28.1244i	0.979510	+	1.13042i	0.991450	+	0.130487i	$0.0416539\pi$
$619$	24.3699	+	28.1244i	0.979510	+	1.13042i	−0.0119396	+	0.999929i	$0.503801\pi$
$620$		0			0
$621$	5.97592	+	12.6328i	0.239806	+	0.506935i
$622$		0			0
$623$	−26.7470	−	1.91298i	−1.07160	−	0.0766420i
$624$		0			0
$625$	24.6792	+	3.99198i	0.987169	+	0.159679i
$626$		0			0
$627$	−6.63088	+	8.85782i	−0.264812	+	0.353747i
$628$		0			0
$629$	0.595668	+	0.926878i	0.0237508	+	0.0369570i
$630$		0			0
$631$	12.6939	+	43.2316i	0.505338	+	1.72102i	0.677107	+	0.735885i	$0.263234\pi$
$631$	12.6939	+	43.2316i	0.505338	+	1.72102i	−0.171769	+	0.985137i	$0.554948\pi$
$632$		0			0
$633$	3.88753	+	54.3548i	0.154515	+	2.16041i
$634$		0			0
$635$	−30.6959	+	0.961355i	−1.21813	+	0.0381502i
$636$		0			0
$637$	5.21952	+	9.55883i	0.206805	+	0.378735i
$638$		0			0
$639$	22.2708	+	10.1707i	0.881018	+	0.402347i
$640$		0			0
$641$	1.02456	−	1.59425i	0.0404677	−	0.0629689i	−0.820430	−	0.571747i	$-0.806266\pi$
$641$	1.02456	−	1.59425i	0.0404677	−	0.0629689i	0.860898	+	0.508778i	$0.169902\pi$
$642$		0			0
$643$	1.70332	+	1.70332i	0.0671722	+	0.0671722i	0.739895	−	0.672723i	$-0.234875\pi$
$643$	1.70332	+	1.70332i	0.0671722	+	0.0671722i	−0.672723	+	0.739895i	$0.734875\pi$
$644$		0			0
$645$	−7.91385	−	19.3456i	−0.311608	−	0.761732i
$646$		0			0
$647$	2.60418	+	11.9712i	0.102381	+	0.470638i	0.999579	+	0.0290095i	$0.00923531\pi$
$647$	2.60418	+	11.9712i	0.102381	+	0.470638i	−0.897198	+	0.441628i	$0.854401\pi$
$648$		0			0
$649$	1.66913	−	3.65488i	0.0655190	−	0.143467i
$650$		0			0
$651$	10.1324	−	34.5078i	0.397120	−	1.35247i
$652$		0			0
$653$	−41.5228	−	15.4872i	−1.62491	−	0.606061i	−0.638395	−	0.769709i	$-0.720401\pi$
$653$	−41.5228	−	15.4872i	−1.62491	−	0.606061i	−0.986519	+	0.163648i	$0.947674\pi$
$654$		0			0
$655$	−41.6495	−	14.0657i	−1.62738	−	0.549594i
$656$		0			0
$657$	18.4145	+	10.0551i	0.718420	+	0.392287i
$658$		0			0
$659$	38.8612	−	24.9746i	1.51382	−	0.972872i	0.520959	−	0.853582i	$-0.325575\pi$
$659$	38.8612	−	24.9746i	1.51382	−	0.972872i	0.992859	−	0.119290i	$-0.0380618\pi$
$660$		0			0
$661$	16.0848	−	2.31265i	0.625627	−	0.0899515i	0.177792	−	0.984068i	$-0.443104\pi$
$661$	16.0848	−	2.31265i	0.625627	−	0.0899515i	0.447834	+	0.894116i	$0.352195\pi$
$662$		0			0
$663$	41.0037	−	30.6950i	1.59245	−	1.19209i
$664$		0			0
$665$	9.04693	+	27.5854i	0.350825	+	1.06971i
$666$		0			0
$667$	−1.35419	+	23.3450i	−0.0524345	+	0.903920i
$668$		0			0
$669$	−19.0786	+	16.5317i	−0.737623	+	0.639154i
$670$		0			0
$671$	−1.07793	+	7.49717i	−0.0416130	+	0.289425i
$672$		0			0
$673$	10.8947	+	8.15568i	0.419960	+	0.314378i	0.788275	−	0.615323i	$-0.210974\pi$
$673$	10.8947	+	8.15568i	0.419960	+	0.314378i	−0.368315	+	0.929701i	$0.620065\pi$
$674$		0			0
$675$	−12.3257	+	7.76910i	−0.474415	+	0.299033i
$676$		0			0
$677$	9.08842	−	16.6442i	0.349296	−	0.639689i	−0.642677	−	0.766138i	$-0.722176\pi$
$677$	9.08842	−	16.6442i	0.349296	−	0.639689i	0.991973	+	0.126449i	$0.0403579\pi$
$678$		0			0
$679$	−9.15115	−	7.92951i	−0.351189	−	0.304307i
$680$		0			0
$681$	−9.30174	+	4.24796i	−0.356443	+	0.162782i
$682$		0			0
$683$	−1.99131	+	1.08734i	−0.0761954	+	0.0416058i	−0.516895	−	0.856049i	$-0.672912\pi$
$683$	−1.99131	+	1.08734i	−0.0761954	+	0.0416058i	0.440700	+	0.897655i	$0.354730\pi$
$684$		0			0
$685$	−5.94177	+	5.48347i	−0.227023	+	0.209512i
$686$		0			0
$687$	−19.2271	+	4.18259i	−0.733559	+	0.159576i
$688$		0			0
$689$	−9.43681			−0.359514
$690$		0			0
$691$	25.7036			0.977813			0.488906	−	0.872336i	$-0.337396\pi$
$691$	25.7036			0.977813			0.488906	+	0.872336i	$0.337396\pi$
$692$		0			0
$693$	−2.28795	+	0.497712i	−0.0869119	+	0.0189065i
$694$		0			0
$695$	−1.08361	+	27.0140i	−0.0411037	+	1.02470i
$696$		0			0
$697$	27.6648	−	15.1061i	1.04788	−	0.572185i
$698$		0			0
$699$	−51.4678	+	23.5046i	−1.94669	+	0.889025i
$700$		0			0
$701$	−18.3741	−	15.9212i	−0.693980	−	0.601337i	0.234767	−	0.972052i	$-0.424567\pi$
$701$	−18.3741	−	15.9212i	−0.693980	−	0.601337i	−0.928747	+	0.370714i	$0.879113\pi$
$702$		0			0
$703$	0.486675	−	0.891279i	0.0183553	−	0.0336152i
$704$		0			0
$705$	12.7113	+	8.90859i	0.478735	+	0.335517i
$706$		0			0
$707$	14.7292	+	11.0261i	0.553947	+	0.414680i
$708$		0			0
$709$	3.46164	−	24.0763i	0.130005	−	0.904203i	−0.815538	−	0.578704i	$-0.803559\pi$
$709$	3.46164	−	24.0763i	0.130005	−	0.904203i	0.945542	−	0.325499i	$-0.105532\pi$
$710$		0			0
$711$	−13.0031	+	11.2673i	−0.487655	+	0.422555i
$712$		0			0
$713$	−15.2790	−	39.3394i	−0.572201	−	1.47327i
$714$		0			0
$715$	5.08981	−	1.66926i	0.190348	−	0.0624267i
$716$		0			0
$717$	23.5975	−	17.6649i	0.881266	−	0.659708i
$718$		0			0
$719$	−9.01077	+	1.29555i	−0.336045	+	0.0483160i	−0.308272	−	0.951298i	$-0.599751\pi$
$719$	−9.01077	+	1.29555i	−0.336045	+	0.0483160i	−0.0277731	+	0.999614i	$0.508842\pi$
$720$		0			0
$721$	−15.5385	+	9.98599i	−0.578684	+	0.371898i
$722$		0			0
$723$	39.6931	+	21.6741i	1.47620	+	0.806067i
$724$		0			0
$725$	−24.3319	+	1.52558i	−0.903665	+	0.0566587i
$726$		0			0
$727$	25.4373	+	9.48763i	0.943418	+	0.351877i	0.773654	−	0.633608i	$-0.218427\pi$
$727$	25.4373	+	9.48763i	0.943418	+	0.351877i	0.169764	+	0.985485i	$0.445700\pi$
$728$		0			0
$729$	0.0955153	−	0.325295i	0.00353761	−	0.0120480i
$730$		0			0
$731$	−13.3835	+	29.3058i	−0.495007	+	1.08391i
$732$		0			0
$733$	8.14418	+	37.4382i	0.300812	+	1.38281i	0.840895	+	0.541199i	$0.182029\pi$
$733$	8.14418	+	37.4382i	0.300812	+	1.38281i	−0.540083	+	0.841612i	$0.681607\pi$
$734$		0			0
$735$	6.35162	−	15.1457i	0.234283	−	0.558658i
$736$		0			0
$737$	0.436005	+	0.436005i	0.0160604	+	0.0160604i
$738$		0			0
$739$	13.3940	−	20.8415i	0.492708	−	0.766668i	−0.502487	−	0.864585i	$-0.667582\pi$
$739$	13.3940	−	20.8415i	0.492708	−	0.766668i	0.995195	+	0.0979168i	$0.0312179\pi$
$740$		0			0
$741$	−42.9425	−	19.6112i	−1.57753	−	0.720435i
$742$		0			0
$743$	−16.4922	−	30.2032i	−0.605040	−	1.10805i	−0.983239	−	0.182323i	$-0.941638\pi$
$743$	−16.4922	−	30.2032i	−0.605040	−	1.10805i	0.378199	−	0.925724i	$-0.376544\pi$
$744$		0			0
$745$	24.3210	−	25.8937i	0.891054	−	0.948672i
$746$		0			0
$747$	0.863661	+	12.0756i	0.0315997	+	0.441821i
$748$		0			0
$749$	2.57393	+	8.76601i	0.0940495	+	0.320303i
$750$		0			0
$751$	−22.6244	−	35.2042i	−0.825576	−	1.28462i	−0.956060	−	0.293171i	$-0.905290\pi$
$751$	−22.6244	−	35.2042i	−0.825576	−	1.28462i	0.130484	−	0.991450i	$-0.458347\pi$
$752$		0			0
$753$	−8.26093	+	11.0353i	−0.301045	+	0.402149i
$754$		0			0
$755$	7.40899	−	1.85641i	0.269641	−	0.0675618i
$756$		0			0
$757$	−2.03754	−	0.145728i	−0.0740555	−	0.00529656i	0.0342622	−	0.999413i	$-0.489092\pi$
$757$	−2.03754	−	0.145728i	−0.0740555	−	0.00529656i	−0.108318	+	0.994116i	$0.534546\pi$
$758$		0			0
$759$	−4.99448	+	5.92314i	−0.181288	+	0.214996i
$760$		0			0
$761$	−1.00170	−	1.15602i	−0.0363115	−	0.0419057i	0.737303	−	0.675562i	$-0.236099\pi$
$761$	−1.00170	−	1.15602i	−0.0363115	−	0.0419057i	−0.773615	+	0.633656i	$0.781553\pi$
$762$		0			0
$763$	11.4452	+	15.2890i	0.414345	+	0.553501i
$764$		0			0
$765$	−26.5101	−	6.89045i	−0.958476	−	0.249125i
$766$		0			0
$767$	16.7512	+	3.64401i	0.604852	+	0.131577i
$768$		0			0
$769$	−20.6493	+	6.06318i	−0.744633	+	0.218644i	−0.631974	−	0.774990i	$-0.717755\pi$
$769$	−20.6493	+	6.06318i	−0.744633	+	0.218644i	−0.112659	+	0.993634i	$0.535937\pi$
$770$		0			0
$771$	−1.90545	+	2.19901i	−0.0686231	+	0.0791952i
$772$		0			0
$773$	−1.01389	+	2.71834i	−0.0364670	+	0.0977717i	−0.953907	−	0.300102i	$-0.902979\pi$
$773$	−1.01389	+	2.71834i	−0.0364670	+	0.0977717i	0.917440	+	0.397874i	$0.130252\pi$
$774$		0			0
$775$	38.8007	−	20.7465i	1.39376	−	0.745235i
$776$		0			0
$777$	0.567765	−	0.211766i	0.0203685	−	0.00759705i
$778$		0			0
$779$	−24.4400	−	15.7066i	−0.875654	−	0.562748i
$780$		0			0
$781$		−	11.1289i		−	0.398224i
$782$		0			0
$783$	10.0468	−	10.0468i	0.359044	−	0.359044i
$784$		0			0
$785$	14.6231	+	21.2599i	0.521920	+	0.758799i
$786$		0			0
$787$	1.04815	+	2.81020i	0.0373625	+	0.100173i	0.954291	−	0.298878i	$-0.0966124\pi$
$787$	1.04815	+	2.81020i	0.0373625	+	0.100173i	−0.916929	+	0.399051i	$0.869340\pi$
$788$		0			0
$789$	7.53114	+	2.21134i	0.268116	+	0.0787259i
$790$		0			0
$791$	12.3287	+	26.9960i	0.438357	+	0.959868i
$792$		0			0
$793$	−32.2338	+	2.30541i	−1.14466	+	0.0818674i
$794$		0			0
$795$	8.88056	+	11.1197i	0.314961	+	0.394375i
$796$		0			0
$797$	−3.11505	+	14.3197i	−0.110341	+	0.507228i	0.888491	+	0.458895i	$0.151755\pi$
$797$	−3.11505	+	14.3197i	−0.110341	+	0.507228i	−0.998831	+	0.0483333i	$0.984609\pi$
$798$		0			0
$799$	−3.40495	−	23.6820i	−0.120459	−	0.837808i
$800$		0			0
$801$	−23.0817	−	3.31865i	−0.815552	−	0.117259i
$802$		0			0
$803$	0.680357	−	9.51264i	0.0240093	−	0.335694i
$804$		0			0
$805$	5.20563	+	19.6503i	0.183474	+	0.692582i
$806$		0			0
$807$	−1.78409	+	24.9449i	−0.0628030	+	0.878101i
$808$		0			0
$809$	24.2444	+	3.48582i	0.852387	+	0.122555i	0.554640	−	0.832090i	$-0.312856\pi$
$809$	24.2444	+	3.48582i	0.852387	+	0.122555i	0.297747	+	0.954645i	$0.403765\pi$
$810$		0			0
$811$	−6.89585	−	47.9617i	−0.242146	−	1.68416i	−0.641308	−	0.767283i	$-0.721608\pi$
$811$	−6.89585	−	47.9617i	−0.242146	−	1.68416i	0.399162	−	0.916880i	$-0.369301\pi$
$812$		0			0
$813$	−9.69742	+	44.5783i	−0.340103	+	1.56343i
$814$		0			0
$815$	−17.2911	−	1.93583i	−0.605681	−	0.0678093i
$816$		0			0
$817$	29.6185	−	2.11836i	1.03622	−	0.0741119i
$818$		0			0
$819$	−4.14999	−	9.08721i	−0.145012	−	0.317533i
$820$		0			0
$821$	−7.61029	−	2.23458i	−0.265601	−	0.0779875i	0.146220	−	0.989252i	$-0.453289\pi$
$821$	−7.61029	−	2.23458i	−0.265601	−	0.0779875i	−0.411822	+	0.911265i	$0.635107\pi$
$822$		0			0
$823$	16.2065	+	43.4514i	0.564924	+	1.51462i	0.834147	+	0.551542i	$0.185960\pi$
$823$	16.2065	+	43.4514i	0.564924	+	1.51462i	−0.269223	+	0.963078i	$0.586767\pi$
$824$		0			0
$825$	−6.75673	−	4.42662i	−0.235239	−	0.154115i
$826$		0			0
$827$	39.4200	−	39.4200i	1.37077	−	1.37077i	0.511458	−	0.859308i	$-0.329105\pi$
$827$	39.4200	−	39.4200i	1.37077	−	1.37077i	0.859308	−	0.511458i	$-0.170895\pi$
$828$		0			0
$829$		−	10.1902i		−	0.353921i	−0.984218	−	0.176960i	$-0.943374\pi$
$829$		−	10.1902i		−	0.353921i	0.984218	−	0.176960i	$-0.0566264\pi$
$830$		0			0
$831$	−48.6158	−	31.2435i	−1.68646	−	1.08382i
$832$		0			0
$833$	−23.7188	+	8.84664i	−0.821806	+	0.306518i
$834$		0			0
$835$	−19.1791	+	23.5871i	−0.663721	+	0.816264i
$836$		0			0
$837$	−8.96108	+	24.0256i	−0.309740	+	0.830446i
$838$		0			0
$839$	9.95942	−	11.4938i	0.343837	−	0.396810i	−0.557323	−	0.830296i	$-0.688171\pi$
$839$	9.95942	−	11.4938i	0.343837	−	0.396810i	0.901160	+	0.433486i	$0.142717\pi$
$840$		0			0
$841$	−5.01353	+	1.47211i	−0.172880	+	0.0507622i
$842$		0			0
$843$	−33.0579	−	7.19130i	−1.13857	−	0.247681i
$844$		0			0
$845$	−3.14773	−	5.35870i	−0.108285	−	0.184345i
$846$		0			0
$847$	−11.8581	−	15.8406i	−0.407450	−	0.544290i
$848$		0			0
$849$	7.94719	+	9.17155i	0.272747	+	0.314767i
$850$		0			0
$851$	0.376350	−	0.603311i	0.0129011	−	0.0206812i
$852$		0			0
$853$	−32.8883	−	2.35222i	−1.12607	−	0.0805384i	−0.504150	−	0.863616i	$-0.668194\pi$
$853$	−32.8883	−	2.35222i	−1.12607	−	0.0805384i	−0.621924	+	0.783078i	$0.713649\pi$
$854$		0			0
$855$	6.13598	+	24.4888i	0.209846	+	0.837501i
$856$		0			0
$857$	−10.0745	+	13.4579i	−0.344138	+	0.459714i	−0.938901	−	0.344187i	$-0.888155\pi$
$857$	−10.0745	+	13.4579i	−0.344138	+	0.459714i	0.594764	+	0.803901i	$0.297246\pi$
$858$		0			0
$859$	2.66647	+	4.14911i	0.0909788	+	0.141566i	0.883760	−	0.467941i	$-0.155004\pi$
$859$	2.66647	+	4.14911i	0.0909788	+	0.141566i	−0.792781	+	0.609507i	$0.791368\pi$
$860$		0			0
$861$	−4.88411	−	16.6338i	−0.166450	−	0.566877i
$862$		0			0
$863$	3.60100	+	50.3486i	0.122579	+	1.71389i	0.571741	+	0.820434i	$0.306268\pi$
$863$	3.60100	+	50.3486i	0.122579	+	1.71389i	−0.449161	+	0.893451i	$0.648277\pi$
$864$		0			0
$865$	0.832236	+	26.5732i	0.0282969	+	0.903515i
$866$		0			0
$867$	39.4911	+	72.3226i	1.34119	+	2.45620i
$868$		0			0
$869$	7.11408	+	3.24889i	0.241329	+	0.110211i
$870$		0			0
$871$	−1.42231	+	2.21316i	−0.0481931	+	0.0749899i
$872$		0			0
$873$	−7.44579	−	7.44579i	−0.252002	−	0.252002i
$874$		0			0
$875$	−19.6854	+	7.85176i	−0.665489	+	0.265438i
$876$		0			0
$877$	11.1542	+	51.2752i	0.376652	+	1.73144i	0.641475	+	0.767144i	$0.278323\pi$
$877$	11.1542	+	51.2752i	0.376652	+	1.73144i	−0.264823	+	0.964297i	$0.585314\pi$
$878$		0			0
$879$	−12.9185	+	28.2876i	−0.435730	+	0.954115i
$880$		0			0
$881$	−11.6245	+	39.5893i	−0.391638	+	1.33380i	0.494016	+	0.869453i	$0.335528\pi$
$881$	−11.6245	+	39.5893i	−0.391638	+	1.33380i	−0.885654	+	0.464345i	$0.846290\pi$
$882$		0			0
$883$	−18.1912	−	6.78498i	−0.612184	−	0.228333i	0.0241976	−	0.999707i	$-0.492297\pi$
$883$	−18.1912	−	6.78498i	−0.612184	−	0.228333i	−0.636382	+	0.771374i	$0.719570\pi$
$884$		0			0
$885$	−11.4700	−	23.1677i	−0.385559	−	0.778774i
$886$		0			0
$887$	12.3704	+	6.75474i	0.415357	+	0.226802i	0.673318	−	0.739353i	$-0.264869\pi$
$887$	12.3704	+	6.75474i	0.415357	+	0.226802i	−0.257961	+	0.966155i	$0.583050\pi$
$888$		0			0
$889$	21.9020	−	14.0756i	0.734571	−	0.472080i
$890$		0			0
$891$	8.32757	−	1.19732i	0.278984	−	0.0401118i
$892$		0			0
$893$	−17.6534	+	13.2151i	−0.590747	+	0.442228i
$894$		0			0
$895$	−21.8961	−	11.0809i	−0.731906	−	0.370394i
$896$		0			0
$897$	−29.2236	−	15.4505i	−0.975747	−	0.515876i
$898$		0			0
$899$	−32.4272	+	28.0983i	−1.08151	+	0.937131i
$900$		0			0
$901$	3.12164	−	21.7115i	0.103997	−	0.723313i
$902$		0			0
$903$	14.1850	+	10.6187i	0.472047	+	0.353370i
$904$		0			0
$905$	2.11917	−	3.02376i	0.0704436	−	0.100513i
$906$		0			0
$907$	−5.87071	+	10.7514i	−0.194934	+	0.356995i	−0.956803	−	0.290736i	$-0.906100\pi$
$907$	−5.87071	+	10.7514i	−0.194934	+	0.356995i	0.761870	+	0.647730i	$0.224282\pi$
$908$		0			0
$909$	12.0921	+	10.4778i	0.401069	+	0.347528i
$910$		0			0
$911$	−2.92909	+	1.33767i	−0.0970451	+	0.0443190i	−0.463346	−	0.886177i	$-0.653351\pi$
$911$	−2.92909	+	1.33767i	−0.0970451	+	0.0443190i	0.366301	+	0.930496i	$0.380624\pi$
$912$		0			0
$913$	4.82986	−	2.63730i	0.159845	−	0.0872819i
$914$		0			0
$915$	33.0503	+	35.8126i	1.09261	+	1.18393i
$916$		0			0
$917$	36.4155	−	7.92170i	1.20254	−	0.261598i
$918$		0			0
$919$	−3.09934			−0.102238			−0.0511189	−	0.998693i	$-0.516279\pi$
$919$	−3.09934			−0.102238			−0.0511189	+	0.998693i	$0.516279\pi$
$920$		0			0
$921$	−34.5723			−1.13920
$922$		0			0
$923$	46.3972	−	10.0931i	1.52718	−	0.332218i
$924$		0			0
$925$	0.671619	+	0.313876i	0.0220827	+	0.0103202i
$926$		0			0
$927$	−14.0976	+	7.69789i	−0.463027	+	0.252832i
$928$		0			0
$929$	−13.5231	+	6.17577i	−0.443677	+	0.202621i	−0.624711	−	0.780856i	$-0.714783\pi$
$929$	−13.5231	+	6.17577i	−0.443677	+	0.202621i	0.181033	+	0.983477i	$0.442056\pi$
$930$		0			0
$931$	17.6334	+	15.2794i	0.577911	+	0.500763i
$932$		0			0
$933$	−7.44401	+	13.6327i	−0.243706	+	0.446314i
$934$		0			0
$935$	2.15682	+	12.2624i	0.0705355	+	0.401023i
$936$		0			0
$937$	−31.1578	−	23.3244i	−1.01788	−	0.761975i	−0.0463576	−	0.998925i	$-0.514761\pi$
$937$	−31.1578	−	23.3244i	−1.01788	−	0.761975i	−0.971522	+	0.236950i	$0.923852\pi$
$938$		0			0
$939$	8.72078	−	60.6543i	0.284592	−	1.97938i
$940$		0			0
$941$	33.9879	−	29.4507i	1.10797	−	0.960065i	0.108553	−	0.994091i	$-0.465378\pi$
$941$	33.9879	−	29.4507i	1.10797	−	0.960065i	0.999421	+	0.0340253i	$0.0108327\pi$
$942$		0			0
$943$	−16.4478	−	11.9707i	−0.535614	−	0.389820i
$944$		0			0
$945$	5.57718	−	11.0206i	0.181426	−	0.358501i
$946$		0			0
$947$	18.6839	−	13.9866i	0.607146	−	0.454503i	−0.250945	−	0.968001i	$-0.580741\pi$
$947$	18.6839	−	13.9866i	0.607146	−	0.454503i	0.858091	+	0.513498i	$0.171651\pi$
$948$		0			0
$949$	40.2758	−	5.79079i	1.30741	−	0.187977i
$950$		0			0
$951$	−5.17482	+	3.32565i	−0.167805	+	0.107842i
$952$		0			0
$953$	−24.6953	−	13.4846i	−0.799958	−	0.436810i	0.0266107	−	0.999646i	$-0.491529\pi$
$953$	−24.6953	−	13.4846i	−0.799958	−	0.436810i	−0.826569	+	0.562836i	$0.809710\pi$
$954$		0			0
$955$	7.07542	−	20.9507i	0.228955	−	0.677949i
$956$		0			0
$957$	7.38056	+	2.75281i	0.238580	+	0.0889856i
$958$		0			0
$959$	1.93108	−	6.57665i	0.0623578	−	0.212371i
$960$		0			0
$961$	19.2904	−	42.2400i	0.622270	−	1.36258i
$962$		0			0
$963$	1.68881	+	7.76333i	0.0544211	+	0.250170i
$964$		0			0
$965$	−17.0492	−	7.14990i	−0.548834	−	0.230163i
$966$		0			0
$967$	−34.5145	−	34.5145i	−1.10991	−	1.10991i	−0.993161	−	0.116750i	$-0.962752\pi$
$967$	−34.5145	−	34.5145i	−1.10991	−	1.10991i	−0.116750	−	0.993161i	$-0.537248\pi$
$968$		0			0
$969$	59.3249	−	92.3114i	1.90579	−	2.96547i
$970$		0			0
$971$	−12.5229	−	5.71900i	−0.401878	−	0.183531i	0.204214	−	0.978926i	$-0.434536\pi$
$971$	−12.5229	−	5.71900i	−0.401878	−	0.183531i	−0.606091	+	0.795395i	$0.707263\pi$
$972$		0			0
$973$	−10.9841	−	20.1158i	−0.352133	−	0.644883i
$974$		0			0
$975$	12.3270	−	32.1839i	0.394781	−	1.03071i
$976$		0			0
$977$	4.17950	+	58.4370i	0.133714	+	1.86957i	0.414840	+	0.909895i	$0.363838\pi$
$977$	4.17950	+	58.4370i	0.133714	+	1.86957i	−0.281126	+	0.959671i	$0.590708\pi$
$978$		0			0
$979$	2.98629	+	10.1704i	0.0954422	+	0.325046i
$980$		0			0
$981$	8.97911	+	13.9718i	0.286681	+	0.446084i
$982$		0			0
$983$	−3.67620	+	4.91083i	−0.117253	+	0.156631i	−0.855328	−	0.518088i	$-0.826644\pi$
$983$	−3.67620	+	4.91083i	−0.117253	+	0.156631i	0.738075	+	0.674719i	$0.235735\pi$
$984$		0			0
$985$	20.5480	+	12.3140i	0.654713	+	0.392357i
$986$		0			0
$987$	−13.1253	−	0.938742i	−0.417784	−	0.0298805i
$988$		0			0
$989$	20.7906	−	0.279794i	0.661102	−	0.00889694i
$990$		0			0
$991$	5.07759	+	5.85985i	0.161295	+	0.186144i	0.830644	−	0.556804i	$-0.187972\pi$
$991$	5.07759	+	5.85985i	0.161295	+	0.186144i	−0.669349	+	0.742948i	$0.733427\pi$
$992$		0			0
$993$	−23.4902	−	31.3792i	−0.745438	−	0.995789i
$994$		0			0
$995$	12.3314	−	7.24352i	0.390931	−	0.229635i
$996$		0			0
$997$	19.7108	+	4.28781i	0.624246	+	0.135796i	0.513552	−	0.858058i	$-0.328329\pi$
$997$	19.7108	+	4.28781i	0.624246	+	0.135796i	0.110693	+	0.993855i	$0.464693\pi$
$998$		0			0
$999$	−0.414550	+	0.121723i	−0.0131158	+	0.00385114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.28	yes	720
5.3	odd	4	inner	920.2.bv.a.33.28	✓	720
23.7	odd	22	inner	920.2.bv.a.697.28	yes	720
115.53	even	44	inner	920.2.bv.a.513.28	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.28	✓	720	5.3	odd	4	inner
920.2.bv.a.217.28	yes	720	1.1	even	1	trivial
920.2.bv.a.513.28	yes	720	115.53	even	44	inner
920.2.bv.a.697.28	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10676 - 0.458297i) q^{3} +(-2.23427 - 0.0896231i) q^{5} +(1.66374 - 0.908469i) q^{7} +(1.49949 - 0.684792i) q^{9} +O(q^{10})\)	\(q+(2.10676 - 0.458297i) q^{3} +(-2.23427 - 0.0896231i) q^{5} +(1.66374 - 0.908469i) q^{7} +(1.49949 - 0.684792i) q^{9} +(-0.566289 - 0.490692i) q^{11} +(1.53215 - 2.80592i) q^{13} +(-4.74814 + 0.835145i) q^{15} +(5.94880 + 4.45322i) q^{17} +(0.974717 - 6.77931i) q^{19} +(3.08874 - 2.67641i) q^{21} +(0.956275 - 4.69953i) q^{23} +(4.98394 + 0.400485i) q^{25} +(-2.33275 + 1.74628i) q^{27} +(-4.82631 + 0.693919i) q^{29} +(7.40286 - 4.75753i) q^{31} +(-1.41792 - 0.774240i) q^{33} +(-3.79866 + 1.88066i) q^{35} +(0.138920 + 0.0518146i) q^{37} +(1.94192 - 6.61356i) q^{39} +(1.76209 - 3.85844i) q^{41} +(0.921583 + 4.23645i) q^{43} +(-3.41163 + 1.39562i) q^{45} +(-2.27667 - 2.27667i) q^{47} +(-1.84178 + 2.86587i) q^{49} +(14.5736 + 6.65552i) q^{51} +(-1.41464 - 2.59073i) q^{53} +(1.22127 + 1.14709i) q^{55} +(-1.05344 - 14.7290i) q^{57} +(1.51072 + 5.14504i) q^{59} +(-5.46498 - 8.50368i) q^{61} +(1.87264 - 2.50155i) q^{63} +(-3.67471 + 6.13187i) q^{65} +(-0.820801 - 0.0587048i) q^{67} +(-0.139140 - 10.3390i) q^{69} +(9.72617 + 11.2246i) q^{71} +(7.62740 + 10.1890i) q^{73} +(10.6835 - 1.44040i) q^{75} +(-1.38793 - 0.301927i) q^{77} +(-10.0146 + 2.94056i) q^{79} +(-7.35275 + 8.48553i) q^{81} +(-2.56650 + 6.88105i) q^{83} +(-12.8921 - 10.4828i) q^{85} +(-9.84984 + 3.67380i) q^{87} +(-11.9004 - 7.64792i) q^{89} -6.06021i q^{91} +(13.4156 - 13.4156i) q^{93} +(-2.78537 + 15.0595i) q^{95} +(-2.23229 - 5.98501i) q^{97} +(-1.18517 - 0.347996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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