LMFDB - Embedded newform 592.2.be.e.415.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			415.4
Root			$2.13532i$ of defining polynomial
Character	$\chi$	$=$	592.415
Dual form			592.2.be.e.495.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06766 - 1.84924i) q^{3} +(1.91328 - 0.512663i) q^{5} +(1.95018 + 1.12593i) q^{7} +(-0.779794 - 1.35064i) q^{9} +O(q^{10})$	\(q+(1.06766 - 1.84924i) q^{3} +(1.91328 - 0.512663i) q^{5} +(1.95018 + 1.12593i) q^{7} +(-0.779794 - 1.35064i) q^{9} +5.67508 q^{11} +(-3.75917 + 1.00727i) q^{13} +(1.09470 - 4.08547i) q^{15} +(-0.686886 + 2.56349i) q^{17} +(0.0131756 + 0.0491721i) q^{19} +(4.16425 - 2.40423i) q^{21} +(-1.92745 + 1.92745i) q^{23} +(-0.932291 + 0.538259i) q^{25} +3.07574 q^{27} +(-3.06381 + 3.06381i) q^{29} +(-4.81995 - 4.81995i) q^{31} +(6.05905 - 10.4946i) q^{33} +(4.30847 + 1.15445i) q^{35} +(-3.26622 - 5.13145i) q^{37} +(-2.15084 + 8.02703i) q^{39} +(-7.86172 - 4.53897i) q^{41} +(2.99745 - 2.99745i) q^{43} +(-2.18439 - 2.18439i) q^{45} +0.988615i q^{47} +(-0.964544 - 1.67064i) q^{49} +(4.00716 + 4.00716i) q^{51} +(-1.98567 - 3.43928i) q^{53} +(10.8580 - 2.90940i) q^{55} +(0.104998 + 0.0281342i) q^{57} +(-7.88178 - 2.11192i) q^{59} +(2.60679 + 9.72868i) q^{61} -3.51199i q^{63} +(-6.67598 + 3.85438i) q^{65} +(-1.22176 + 2.11615i) q^{67} +(1.50646 + 5.62217i) q^{69} +(-10.1023 - 5.83257i) q^{71} -10.5606i q^{73} +2.29871i q^{75} +(11.0674 + 6.38976i) q^{77} +(2.08068 + 7.76521i) q^{79} +(5.62322 - 9.73971i) q^{81} +(8.83505 - 5.10092i) q^{83} +5.25683i q^{85} +(2.39462 + 8.93683i) q^{87} +(7.54755 + 2.02236i) q^{89} +(-8.46516 - 2.26823i) q^{91} +(-14.0593 + 3.76718i) q^{93} +(0.0504175 + 0.0873257i) q^{95} +(12.3336 + 12.3336i) q^{97} +(-4.42539 - 7.66500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.06766	−	1.84924i	0.616414	−	1.06766i	−0.373721	−	0.927541i	$-0.621918\pi$
$3$	1.06766	−	1.84924i	0.616414	−	1.06766i	0.990135	−	0.140119i	$-0.0447484\pi$
$4$		0			0
$5$	1.91328	−	0.512663i	0.855647	−	0.229270i	0.195776	−	0.980649i	$-0.437277\pi$
$5$	1.91328	−	0.512663i	0.855647	−	0.229270i	0.659871	+	0.751379i	$0.270611\pi$
$6$		0			0
$7$	1.95018	+	1.12593i	0.737097	+	0.425563i	0.821013	−	0.570910i	$-0.193409\pi$
$7$	1.95018	+	1.12593i	0.737097	+	0.425563i	−0.0839158	+	0.996473i	$0.526743\pi$
$8$		0			0
$9$	−0.779794	−	1.35064i	−0.259931	−	0.450214i
$10$		0			0
$11$	5.67508			1.71110			0.855550	−	0.517720i	$-0.173219\pi$
$11$	5.67508			1.71110			0.855550	+	0.517720i	$0.173219\pi$
$12$		0			0
$13$	−3.75917	+	1.00727i	−1.04261	+	0.279366i	−0.739193	−	0.673493i	$-0.764793\pi$
$13$	−3.75917	+	1.00727i	−1.04261	+	0.279366i	−0.303414	+	0.952859i	$0.598126\pi$
$14$		0			0
$15$	1.09470	−	4.08547i	0.282650	−	1.05486i
$16$		0			0
$17$	−0.686886	+	2.56349i	−0.166594	+	0.621738i	0.831237	+	0.555918i	$0.187633\pi$
$17$	−0.686886	+	2.56349i	−0.166594	+	0.621738i	−0.997831	+	0.0658205i	$0.979034\pi$
$18$		0			0
$19$	0.0131756	+	0.0491721i	0.00302270	+	0.0112809i	0.967421	−	0.253174i	$-0.0814746\pi$
$19$	0.0131756	+	0.0491721i	0.00302270	+	0.0112809i	−0.964398	+	0.264455i	$0.914808\pi$
$20$		0			0
$21$	4.16425	−	2.40423i	0.908713	−	0.524646i
$22$		0			0
$23$	−1.92745	+	1.92745i	−0.401900	+	0.401900i	−0.878902	−	0.477002i	$-0.841723\pi$
$23$	−1.92745	+	1.92745i	−0.401900	+	0.401900i	0.477002	+	0.878902i	$0.341723\pi$
$24$		0			0
$25$	−0.932291	+	0.538259i	−0.186458	+	0.107652i
$26$		0			0
$27$	3.07574			0.591926
$28$		0			0
$29$	−3.06381	+	3.06381i	−0.568936	+	0.568936i	−0.931830	−	0.362895i	$-0.881788\pi$
$29$	−3.06381	+	3.06381i	−0.568936	+	0.568936i	0.362895	+	0.931830i	$0.381788\pi$
$30$		0			0
$31$	−4.81995	−	4.81995i	−0.865689	−	0.865689i	0.126303	−	0.991992i	$-0.459689\pi$
$31$	−4.81995	−	4.81995i	−0.865689	−	0.865689i	−0.991992	+	0.126303i	$0.959689\pi$
$32$		0			0
$33$	6.05905	−	10.4946i	1.05475	−	1.82687i
$34$		0			0
$35$	4.30847	+	1.15445i	0.728264	+	0.195138i
$36$		0			0
$37$	−3.26622	−	5.13145i	−0.536963	−	0.843606i
$37$	−3.26622	−	5.13145i	−0.536963	−	0.843606i
$38$		0			0
$39$	−2.15084	+	8.02703i	−0.344410	+	1.28535i
$40$		0			0
$41$	−7.86172	−	4.53897i	−1.22779	−	0.708867i	−0.261226	−	0.965278i	$-0.584127\pi$
$41$	−7.86172	−	4.53897i	−1.22779	−	0.708867i	−0.966568	+	0.256410i	$0.917460\pi$
$42$		0			0
$43$	2.99745	−	2.99745i	0.457107	−	0.457107i	−0.440597	−	0.897705i	$-0.645233\pi$
$43$	2.99745	−	2.99745i	0.457107	−	0.457107i	0.897705	+	0.440597i	$0.145233\pi$
$44$		0			0
$45$	−2.18439	−	2.18439i	−0.325630	−	0.325630i
$46$		0			0
$47$			0.988615i			0.144204i	0.997397	+	0.0721022i	$0.0229708\pi$
$47$			0.988615i			0.144204i	−0.997397	+	0.0721022i	$0.977029\pi$
$48$		0			0
$49$	−0.964544	−	1.67064i	−0.137792	−	0.238663i
$50$		0			0
$51$	4.00716	+	4.00716i	0.561114	+	0.561114i
$52$		0			0
$53$	−1.98567	−	3.43928i	−0.272753	−	0.472422i	0.696813	−	0.717253i	$-0.254601\pi$
$53$	−1.98567	−	3.43928i	−0.272753	−	0.472422i	−0.969566	+	0.244831i	$0.921267\pi$
$54$		0			0
$55$	10.8580	−	2.90940i	1.46410	−	0.392304i
$56$		0			0
$57$	0.104998	+	0.0281342i	0.0139074	+	0.00372646i
$58$		0			0
$59$	−7.88178	−	2.11192i	−1.02612	−	0.274948i	−0.293770	−	0.955876i	$-0.594910\pi$
$59$	−7.88178	−	2.11192i	−1.02612	−	0.274948i	−0.732350	+	0.680928i	$0.761577\pi$
$60$		0			0
$61$	2.60679	+	9.72868i	0.333765	+	1.24563i	0.905201	+	0.424983i	$0.139720\pi$
$61$	2.60679	+	9.72868i	0.333765	+	1.24563i	−0.571436	+	0.820647i	$0.693613\pi$
$62$		0			0
$63$		−	3.51199i		−	0.442469i
$64$		0			0
$65$	−6.67598	+	3.85438i	−0.828053	+	0.478077i
$66$		0			0
$67$	−1.22176	+	2.11615i	−0.149262	+	0.258529i	−0.930955	−	0.365134i	$-0.881023\pi$
$67$	−1.22176	+	2.11615i	−0.149262	+	0.258529i	0.781693	+	0.623664i	$0.214356\pi$
$68$		0			0
$69$	1.50646	+	5.62217i	0.181356	+	0.676829i
$70$		0			0
$71$	−10.1023	−	5.83257i	−1.19892	−	0.692199i	−0.238609	−	0.971116i	$-0.576691\pi$
$71$	−10.1023	−	5.83257i	−1.19892	−	0.692199i	−0.960315	+	0.278917i	$0.910025\pi$
$72$		0			0
$73$		−	10.5606i		−	1.23602i	−0.786169	−	0.618011i	$-0.787939\pi$
$73$		−	10.5606i		−	1.23602i	0.786169	−	0.618011i	$-0.212061\pi$
$74$		0			0
$75$			2.29871i			0.265432i
$76$		0			0
$77$	11.0674	+	6.38976i	1.26125	+	0.728181i
$78$		0			0
$79$	2.08068	+	7.76521i	0.234095	+	0.873654i	0.978555	+	0.205987i	$0.0660404\pi$
$79$	2.08068	+	7.76521i	0.234095	+	0.873654i	−0.744460	+	0.667667i	$0.767293\pi$
$80$		0			0
$81$	5.62322	−	9.73971i	0.624803	−	1.08219i
$82$		0			0
$83$	8.83505	−	5.10092i	0.969773	−	0.559898i	0.0706056	−	0.997504i	$-0.477507\pi$
$83$	8.83505	−	5.10092i	0.969773	−	0.559898i	0.899167	+	0.437606i	$0.144173\pi$
$84$		0			0
$85$			5.25683i			0.570184i
$86$		0			0
$87$	2.39462	+	8.93683i	0.256730	+	0.958129i
$88$		0			0
$89$	7.54755	+	2.02236i	0.800038	+	0.214370i	0.635601	−	0.772018i	$-0.280752\pi$
$89$	7.54755	+	2.02236i	0.800038	+	0.214370i	0.164438	+	0.986387i	$0.447419\pi$
$90$		0			0
$91$	−8.46516	−	2.26823i	−0.887390	−	0.237775i
$92$		0			0
$93$	−14.0593	+	3.76718i	−1.45788	+	0.390639i
$94$		0			0
$95$	0.0504175	+	0.0873257i	0.00517273	+	0.00895942i
$96$		0			0
$97$	12.3336	+	12.3336i	1.25229	+	1.25229i	0.954692	+	0.297595i	$0.0961846\pi$
$97$	12.3336	+	12.3336i	1.25229	+	1.25229i	0.297595	+	0.954692i	$0.403815\pi$
$98$		0			0
$99$	−4.42539	−	7.66500i	−0.444769	−	0.770362i
$100$		0			0
$101$			15.2272i			1.51516i	0.652743	+	0.757579i	$0.273618\pi$
$101$			15.2272i			1.51516i	−0.652743	+	0.757579i	$0.726382\pi$
$102$		0			0
$103$	2.73559	+	2.73559i	0.269546	+	0.269546i	0.828917	−	0.559371i	$-0.188957\pi$
$103$	2.73559	+	2.73559i	0.269546	+	0.269546i	−0.559371	+	0.828917i	$0.688957\pi$
$104$		0			0
$105$	6.73483	−	6.73483i	0.657252	−	0.657252i
$106$		0			0
$107$	−11.9114	−	6.87705i	−1.15152	−	0.664829i	−0.202262	−	0.979332i	$-0.564829\pi$
$107$	−11.9114	−	6.87705i	−1.15152	−	0.664829i	−0.949257	+	0.314502i	$0.898162\pi$
$108$		0			0
$109$	−4.07703	+	15.2157i	−0.390509	+	1.45740i	0.438788	+	0.898590i	$0.355408\pi$
$109$	−4.07703	+	15.2157i	−0.390509	+	1.45740i	−0.829297	+	0.558808i	$0.811259\pi$
$110$		0			0
$111$	−12.9765	+	0.561379i	−1.23168	+	0.0532838i
$112$		0			0
$113$	−8.15643	−	2.18551i	−0.767293	−	0.205595i	−0.146118	−	0.989267i	$-0.546678\pi$
$113$	−8.15643	−	2.18551i	−0.767293	−	0.205595i	−0.621175	+	0.783672i	$0.713344\pi$
$114$		0			0
$115$	−2.69962	+	4.67588i	−0.251741	+	0.436028i
$116$		0			0
$117$	4.29184	+	4.29184i	0.396781	+	0.396781i
$118$		0			0
$119$	−4.22587	+	4.22587i	−0.387385	+	0.387385i
$120$		0			0
$121$	21.2065			1.92786
$122$		0			0
$123$	−16.7873	+	9.69214i	−1.51366	+	0.873911i
$124$		0			0
$125$	−8.51090	+	8.51090i	−0.761238	+	0.761238i
$126$		0			0
$127$	9.25682	−	5.34443i	0.821410	−	0.474241i	−0.0294923	−	0.999565i	$-0.509389\pi$
$127$	9.25682	−	5.34443i	0.821410	−	0.474241i	0.850903	+	0.525324i	$0.176056\pi$
$128$		0			0
$129$	−2.34275	−	8.74327i	−0.206268	−	0.769802i
$130$		0			0
$131$	2.32982	−	8.69500i	0.203557	−	0.759685i	−0.786327	−	0.617810i	$-0.788020\pi$
$131$	2.32982	−	8.69500i	0.203557	−	0.759685i	0.989885	−	0.141875i	$-0.0453132\pi$
$132$		0			0
$133$	−0.0296698	+	0.110729i	−0.00257270	+	0.00960144i
$134$		0			0
$135$	5.88476	−	1.57682i	0.506480	−	0.135711i
$136$		0			0
$137$	−4.60431			−0.393372			−0.196686	−	0.980466i	$-0.563018\pi$
$137$	−4.60431			−0.393372			−0.196686	+	0.980466i	$0.563018\pi$
$138$		0			0
$139$	7.40299	+	12.8223i	0.627913	+	1.08758i	0.987970	+	0.154647i	$0.0494240\pi$
$139$	7.40299	+	12.8223i	0.627913	+	1.08758i	−0.360057	+	0.932930i	$0.617243\pi$
$140$		0			0
$141$	1.82819	+	1.05550i	0.153961	+	0.0888895i
$142$		0			0
$143$	−21.3336	+	5.71632i	−1.78400	+	0.478023i
$144$		0			0
$145$	−4.29124	+	7.43265i	−0.356368	+	0.617248i
$146$		0			0
$147$	−4.11922			−0.339747
$148$		0			0
$149$	10.8267			0.886956			0.443478	−	0.896285i	$-0.353744\pi$
$149$	10.8267			0.886956			0.443478	+	0.896285i	$0.353744\pi$
$150$		0			0
$151$	4.01462	−	6.95352i	0.326705	−	0.565869i	−0.655151	−	0.755498i	$-0.727395\pi$
$151$	4.01462	−	6.95352i	0.326705	−	0.565869i	0.981856	+	0.189629i	$0.0607284\pi$
$152$		0			0
$153$	3.99799	−	1.07126i	0.323219	−	0.0866062i
$154$		0			0
$155$	−11.6930	−	6.75093i	−0.939200	−	0.542248i
$156$		0			0
$157$	−7.36145	−	12.7504i	−0.587508	−	1.01759i	−0.994558	−	0.104188i	$-0.966776\pi$
$157$	−7.36145	−	12.7504i	−0.587508	−	1.01759i	0.407050	−	0.913406i	$-0.366558\pi$
$158$		0			0
$159$	−8.48008			−0.672514
$160$		0			0
$161$	−5.92903	+	1.58868i	−0.467273	+	0.125206i
$162$		0			0
$163$	−1.12523	+	4.19941i	−0.0881347	+	0.328923i	−0.995889	−	0.0905783i	$-0.971128\pi$
$163$	−1.12523	+	4.19941i	−0.0881347	+	0.328923i	0.907755	+	0.419502i	$0.137795\pi$
$164$		0			0
$165$	6.21250	−	23.1854i	0.483643	−	1.80498i
$166$		0			0
$167$	−2.64528	−	9.87232i	−0.204698	−	0.763943i	−0.989541	−	0.144249i	$-0.953923\pi$
$167$	−2.64528	−	9.87232i	−0.204698	−	0.763943i	0.784843	−	0.619694i	$-0.212743\pi$
$168$		0			0
$169$	1.85846	−	1.07298i	0.142958	−	0.0825371i
$170$		0			0
$171$	0.0561397	−	0.0561397i	0.00429311	−	0.00429311i
$172$		0			0
$173$	−3.90504	+	2.25457i	−0.296895	+	0.171412i	−0.641047	−	0.767502i	$-0.721500\pi$
$173$	−3.90504	+	2.25457i	−0.296895	+	0.171412i	0.344152	+	0.938914i	$0.388166\pi$
$174$		0			0
$175$	−2.42417			−0.183250
$176$		0			0
$177$	−12.3205	+	12.3205i	−0.926065	+	0.926065i
$178$		0			0
$179$	14.1173	+	14.1173i	1.05517	+	1.05517i	0.998386	+	0.0567887i	$0.0180861\pi$
$179$	14.1173	+	14.1173i	1.05517	+	1.05517i	0.0567887	+	0.998386i	$0.481914\pi$
$180$		0			0
$181$	0.553271	−	0.958294i	0.0411243	−	0.0712295i	−0.844731	−	0.535192i	$-0.820239\pi$
$181$	0.553271	−	0.958294i	0.0411243	−	0.0712295i	0.885855	+	0.463962i	$0.153573\pi$
$182$		0			0
$183$	20.7738	+	5.56633i	1.53565	+	0.411475i
$184$		0			0
$185$	−8.87991	−	8.14346i	−0.652864	−	0.598719i
$186$		0			0
$187$	−3.89813	+	14.5480i	−0.285060	+	1.06386i
$188$		0			0
$189$	5.99823	+	3.46308i	0.436307	+	0.251902i
$190$		0			0
$191$	12.6721	−	12.6721i	0.916924	−	0.916924i	−0.0798803	−	0.996804i	$-0.525454\pi$
$191$	12.6721	−	12.6721i	0.916924	−	0.916924i	0.996804	+	0.0798803i	$0.0254538\pi$
$192$		0			0
$193$	−11.5009	−	11.5009i	−0.827851	−	0.827851i	0.159368	−	0.987219i	$-0.449054\pi$
$193$	−11.5009	−	11.5009i	−0.827851	−	0.827851i	−0.987219	+	0.159368i	$0.949054\pi$
$194$		0			0
$195$			16.4607i			1.17877i
$196$		0			0
$197$	7.17912	+	12.4346i	0.511491	+	0.885928i	0.999911	+	0.0133197i	$0.00423993\pi$
$197$	7.17912	+	12.4346i	0.511491	+	0.885928i	−0.488420	+	0.872608i	$0.662427\pi$
$198$		0			0
$199$	−3.25947	−	3.25947i	−0.231058	−	0.231058i	0.582076	−	0.813134i	$-0.302240\pi$
$199$	−3.25947	−	3.25947i	−0.231058	−	0.231058i	−0.813134	+	0.582076i	$0.802240\pi$
$200$		0			0
$201$	2.60885	+	4.51867i	0.184014	+	0.318722i
$202$		0			0
$203$	−9.42462	+	2.52532i	−0.661479	+	0.177243i
$204$		0			0
$205$	−17.3687	−	4.65392i	−1.21308	−	0.325044i
$206$		0			0
$207$	4.10630	+	1.10028i	0.285408	+	0.0764748i
$208$		0			0
$209$	0.0747728	+	0.279056i	0.00517214	+	0.0193027i
$210$		0			0
$211$			19.8439i			1.36611i	0.730367	+	0.683055i	$0.239349\pi$
$211$			19.8439i			1.36611i	−0.730367	+	0.683055i	$0.760651\pi$
$212$		0			0
$213$	−21.5717	+	12.4544i	−1.47807	+	0.853362i
$214$		0			0
$215$	4.19830	−	7.27167i	0.286322	−	0.495924i
$216$		0			0
$217$	−3.97280	−	14.8267i	−0.269691	−	1.00650i
$218$		0			0
$219$	−19.5291	−	11.2751i	−1.31965	−	0.761901i
$220$		0			0
$221$		−	10.3285i		−	0.694769i
$222$		0			0
$223$			20.1307i			1.34805i	0.738708	+	0.674026i	$0.235436\pi$
$223$			20.1307i			1.34805i	−0.738708	+	0.674026i	$0.764564\pi$
$224$		0			0
$225$	1.45399	+	0.839462i	0.0969327	+	0.0559641i
$226$		0			0
$227$	−4.56138	−	17.0233i	−0.302750	−	1.12988i	−0.934865	−	0.355003i	$-0.884480\pi$
$227$	−4.56138	−	17.0233i	−0.302750	−	1.12988i	0.632116	−	0.774874i	$-0.282187\pi$
$228$		0			0
$229$	8.63995	−	14.9648i	0.570944	−	0.988904i	−0.425526	−	0.904946i	$-0.639911\pi$
$229$	8.63995	−	14.9648i	0.570944	−	0.988904i	0.996469	−	0.0839572i	$-0.0267559\pi$
$230$		0			0
$231$	23.6324	−	13.6442i	1.55490	−	0.897721i
$232$		0			0
$233$			21.1216i			1.38372i	0.722032	+	0.691860i	$0.243208\pi$
$233$			21.1216i			1.38372i	−0.722032	+	0.691860i	$0.756792\pi$
$234$		0			0
$235$	0.506827	+	1.89150i	0.0330617	+	0.123388i
$236$		0			0
$237$	16.5812	+	4.44292i	1.07706	+	0.288598i
$238$		0			0
$239$	−16.6674	−	4.46602i	−1.07813	−	0.288883i	−0.324298	−	0.945955i	$-0.605128\pi$
$239$	−16.6674	−	4.46602i	−1.07813	−	0.288883i	−0.753828	+	0.657072i	$0.771795\pi$
$240$		0			0
$241$	24.3368	−	6.52102i	1.56767	−	0.420056i	0.632588	−	0.774488i	$-0.281993\pi$
$241$	24.3368	−	6.52102i	1.56767	−	0.420056i	0.935082	+	0.354433i	$0.115326\pi$
$242$		0			0
$243$	−7.39377	−	12.8064i	−0.474311	−	0.821530i
$244$		0			0
$245$	−2.70192	−	2.70192i	−0.172619	−	0.172619i
$246$		0			0
$247$	−0.0990590	−	0.171575i	−0.00630297	−	0.0109171i
$248$		0			0
$249$		−	21.7842i		−	1.38052i
$250$		0			0
$251$	2.12209	+	2.12209i	0.133945	+	0.133945i	0.770901	−	0.636955i	$-0.219806\pi$
$251$	2.12209	+	2.12209i	0.133945	+	0.133945i	−0.636955	+	0.770901i	$0.719806\pi$
$252$		0			0
$253$	−10.9384	+	10.9384i	−0.687691	+	0.687691i
$254$		0			0
$255$	9.72115	+	5.61251i	0.608762	+	0.351469i
$256$		0			0
$257$	1.17447	−	4.38318i	0.0732614	−	0.273415i	−0.919572	−	0.392921i	$-0.871464\pi$
$257$	1.17447	−	4.38318i	0.0732614	−	0.273415i	0.992833	+	0.119506i	$0.0381311\pi$
$258$		0			0
$259$	−0.592020	−	13.6848i	−0.0367864	−	0.850331i
$260$		0			0
$261$	6.52726	+	1.74897i	0.404027	+	0.108259i
$262$		0			0
$263$	4.57169	−	7.91840i	0.281902	−	0.488269i	−0.689951	−	0.723856i	$-0.742368\pi$
$263$	4.57169	−	7.91840i	0.281902	−	0.488269i	0.971853	+	0.235587i	$0.0757012\pi$
$264$		0			0
$265$	−5.56234	−	5.56234i	−0.341692	−	0.341692i
$266$		0			0
$267$	11.7980	−	11.7980i	0.722028	−	0.722028i
$268$		0			0
$269$	19.3403			1.17920			0.589600	−	0.807696i	$-0.299286\pi$
$269$	19.3403			1.17920			0.589600	+	0.807696i	$0.299286\pi$
$270$		0			0
$271$	11.0097	−	6.35645i	0.668791	−	0.386127i	−0.126828	−	0.991925i	$-0.540479\pi$
$271$	11.0097	−	6.35645i	0.668791	−	0.386127i	0.795618	+	0.605798i	$0.207146\pi$
$272$		0			0
$273$	−13.2324	+	13.2324i	−0.800863	+	0.800863i
$274$		0			0
$275$	−5.29082	+	3.05466i	−0.319049	+	0.184203i
$276$		0			0
$277$	−1.72198	−	6.42650i	−0.103463	−	0.386131i	0.894703	−	0.446662i	$-0.147387\pi$
$277$	−1.72198	−	6.42650i	−0.103463	−	0.386131i	−0.998166	+	0.0605309i	$0.980721\pi$
$278$		0			0
$279$	−2.75146	+	10.2686i	−0.164726	+	0.614765i
$280$		0			0
$281$	−3.90982	+	14.5917i	−0.233241	+	0.870466i	0.745693	+	0.666289i	$0.232118\pi$
$281$	−3.90982	+	14.5917i	−0.233241	+	0.870466i	−0.978934	+	0.204177i	$0.934548\pi$
$282$		0			0
$283$	21.0193	−	5.63210i	1.24947	−	0.334793i	0.427336	−	0.904093i	$-0.359452\pi$
$283$	21.0193	−	5.63210i	1.24947	−	0.334793i	0.822130	+	0.569300i	$0.192786\pi$
$284$		0			0
$285$	0.215315			0.0127542
$286$		0			0
$287$	−10.2212	−	17.7036i	−0.603336	−	1.04501i
$288$		0			0
$289$	8.62275	+	4.97834i	0.507220	+	0.292844i
$290$		0			0
$291$	35.9759	−	9.63971i	2.10894	−	0.565090i
$292$		0			0
$293$	13.5862	−	23.5321i	0.793717	−	1.37476i	−0.129934	−	0.991523i	$-0.541476\pi$
$293$	13.5862	−	23.5321i	0.793717	−	1.37476i	0.923651	−	0.383236i	$-0.125190\pi$
$294$		0			0
$295$	−16.1628			−0.941034
$296$		0			0
$297$	17.4551			1.01284
$298$		0			0
$299$	5.30415	−	9.18705i	0.306747	−	0.531301i
$300$		0			0
$301$	9.22049	−	2.47062i	0.531460	−	0.142404i
$302$		0			0
$303$	28.1587	+	16.2574i	1.61767	+	0.933964i
$304$		0			0
$305$	9.97507	+	17.2773i	0.571171	+	0.989297i
$306$		0			0
$307$	27.6388			1.57743			0.788714	−	0.614760i	$-0.210747\pi$
$307$	27.6388			1.57743			0.788714	+	0.614760i	$0.210747\pi$
$308$		0			0
$309$	7.97944	−	2.13809i	0.453935	−	0.121631i
$310$		0			0
$311$	1.40177	−	5.23147i	0.0794870	−	0.296649i	−0.914726	−	0.404074i	$-0.867594\pi$
$311$	1.40177	−	5.23147i	0.0794870	−	0.296649i	0.994213	+	0.107425i	$0.0342605\pi$
$312$		0			0
$313$	3.29391	−	12.2930i	0.186183	−	0.694843i	−0.808192	−	0.588920i	$-0.799553\pi$
$313$	3.29391	−	12.2930i	0.186183	−	0.694843i	0.994374	−	0.105923i	$-0.0337799\pi$
$314$		0			0
$315$	−1.80047	−	6.71943i	−0.101445	−	0.378597i
$316$		0			0
$317$	−22.3927	+	12.9284i	−1.25770	+	0.726133i	−0.972627	−	0.232373i	$-0.925351\pi$
$317$	−22.3927	+	12.9284i	−1.25770	+	0.726133i	−0.285072	+	0.958506i	$0.592018\pi$
$318$		0			0
$319$	−17.3874	+	17.3874i	−0.973506	+	0.973506i
$320$		0			0
$321$	−25.4346	+	14.6847i	−1.41962	+	0.819620i
$322$		0			0
$323$	−0.135103			−0.00751731
$324$		0			0
$325$	2.96247	−	2.96247i	0.164328	−	0.164328i
$326$		0			0
$327$	23.7846	+	23.7846i	1.31529	+	1.31529i
$328$		0			0
$329$	−1.11312	+	1.92797i	−0.0613680	+	0.106293i
$330$		0			0
$331$	31.2513	+	8.37376i	1.71773	+	0.460264i	0.977298	−	0.211870i	$-0.0679555\pi$
$331$	31.2513	+	8.37376i	1.71773	+	0.460264i	0.740429	+	0.672134i	$0.234622\pi$
$332$		0			0
$333$	−4.38378	+	8.41297i	−0.240230	+	0.461028i
$334$		0			0
$335$	−1.25271	+	4.67516i	−0.0684426	+	0.255431i
$336$		0			0
$337$	−18.3851	−	10.6146i	−1.00150	−	0.578215i	−0.0928069	−	0.995684i	$-0.529584\pi$
$337$	−18.3851	−	10.6146i	−1.00150	−	0.578215i	−0.908691	+	0.417469i	$0.862917\pi$
$338$		0			0
$339$	−12.7498	+	12.7498i	−0.692476	+	0.692476i
$340$		0			0
$341$	−27.3536	−	27.3536i	−1.48128	−	1.48128i
$342$		0			0
$343$		−	20.1071i		−	1.08568i
$344$		0			0
$345$	5.76456	+	9.98450i	0.310353	+	0.537548i
$346$		0			0
$347$	−5.27864	−	5.27864i	−0.283372	−	0.283372i	0.551080	−	0.834452i	$-0.314216\pi$
$347$	−5.27864	−	5.27864i	−0.283372	−	0.283372i	−0.834452	+	0.551080i	$0.814216\pi$
$348$		0			0
$349$	6.51785	+	11.2892i	0.348892	+	0.604299i	0.986053	−	0.166432i	$-0.0532245\pi$
$349$	6.51785	+	11.2892i	0.348892	+	0.604299i	−0.637161	+	0.770731i	$0.719891\pi$
$350$		0			0
$351$	−11.5622	+	3.09809i	−0.617146	+	0.165364i
$352$		0			0
$353$	−27.4807	−	7.36343i	−1.46265	−	0.391916i	−0.562246	−	0.826970i	$-0.690063\pi$
$353$	−27.4807	−	7.36343i	−1.46265	−	0.391916i	−0.900404	+	0.435054i	$0.856729\pi$
$354$		0			0
$355$	−22.3187	−	5.98029i	−1.18456	−	0.317401i
$356$		0			0
$357$	3.30286	+	12.3265i	0.174806	+	0.652385i
$358$		0			0
$359$			17.6841i			0.933332i	0.884434	+	0.466666i	$0.154545\pi$
$359$			17.6841i			0.933332i	−0.884434	+	0.466666i	$0.845455\pi$
$360$		0			0
$361$	16.4522	−	9.49870i	0.865907	−	0.499932i
$362$		0			0
$363$	22.6413	−	39.2159i	1.18836	−	2.05830i
$364$		0			0
$365$	−5.41402	−	20.2054i	−0.283383	−	1.05760i
$366$		0			0
$367$	0.618590	+	0.357143i	0.0322902	+	0.0186427i	0.516058	−	0.856554i	$-0.327399\pi$
$367$	0.618590	+	0.357143i	0.0322902	+	0.0186427i	−0.483768	+	0.875196i	$0.660732\pi$
$368$		0			0
$369$			14.1578i			0.737028i
$370$		0			0
$371$		−	8.94294i		−	0.464294i
$372$		0			0
$373$	0.791678	+	0.457076i	0.0409916	+	0.0236665i	0.520356	−	0.853950i	$-0.325799\pi$
$373$	0.791678	+	0.457076i	0.0409916	+	0.0236665i	−0.479364	+	0.877616i	$0.659133\pi$
$374$		0			0
$375$	6.65196	+	24.8255i	0.343506	+	1.28198i
$376$		0			0
$377$	8.43132	−	14.6035i	0.434235	−	0.752117i
$378$		0			0
$379$	19.9632	−	11.5257i	1.02544	−	0.592037i	0.109764	−	0.993958i	$-0.464991\pi$
$379$	19.9632	−	11.5257i	1.02544	−	0.592037i	0.915674	+	0.401921i	$0.131657\pi$
$380$		0			0
$381$		−	22.8241i		−	1.16932i
$382$		0			0
$383$	−2.67353	−	9.97776i	−0.136611	−	0.509840i	−0.999986	−	0.00527685i	$-0.998320\pi$
$383$	−2.67353	−	9.97776i	−0.136611	−	0.509840i	0.863375	−	0.504563i	$-0.168346\pi$
$384$		0			0
$385$	24.4509	+	6.55159i	1.24613	+	0.333900i
$386$		0			0
$387$	−6.38589	−	1.71109i	−0.324613	−	0.0869797i
$388$		0			0
$389$	13.8749	−	3.71777i	0.703485	−	0.188498i	0.110694	−	0.993855i	$-0.464693\pi$
$389$	13.8749	−	3.71777i	0.703485	−	0.188498i	0.592791	+	0.805356i	$0.298026\pi$
$390$		0			0
$391$	−3.61706	−	6.26493i	−0.182923	−	0.316831i
$392$		0			0
$393$	−13.5917	−	13.5917i	−0.685610	−	0.685610i
$394$		0			0
$395$	7.96187	+	13.7904i	0.400605	+	0.693868i
$396$		0			0
$397$		−	33.4451i		−	1.67856i	−0.543698	−	0.839281i	$-0.682976\pi$
$397$		−	33.4451i		−	1.67856i	0.543698	−	0.839281i	$-0.317024\pi$
$398$		0			0
$399$	0.173088	+	0.173088i	0.00866522	+	0.00866522i
$400$		0			0
$401$	−16.7318	+	16.7318i	−0.835547	+	0.835547i	−0.988269	−	0.152722i	$-0.951196\pi$
$401$	−16.7318	+	16.7318i	−0.835547	+	0.835547i	0.152722	+	0.988269i	$0.451196\pi$
$402$		0			0
$403$	22.9740	+	13.2640i	1.14442	+	0.660729i
$404$		0			0
$405$	5.76564	−	21.5177i	0.286497	−	1.06922i
$406$		0			0
$407$	−18.5360	−	29.1214i	−0.918798	−	1.44349i
$408$		0			0
$409$	18.2095	+	4.87921i	0.900400	+	0.241262i	0.679188	−	0.733964i	$-0.262332\pi$
$409$	18.2095	+	4.87921i	0.900400	+	0.241262i	0.221212	+	0.975226i	$0.428999\pi$
$410$		0			0
$411$	−4.91583	+	8.51447i	−0.242480	+	0.419988i
$412$		0			0
$413$	−12.9930	−	12.9930i	−0.639342	−	0.639342i
$414$		0			0
$415$	14.2889	−	14.2889i	0.701415	−	0.701415i
$416$		0			0
$417$	31.6155			1.54822
$418$		0			0
$419$	−11.8842	+	6.86137i	−0.580583	+	0.335200i	−0.761365	−	0.648324i	$-0.775470\pi$
$419$	−11.8842	+	6.86137i	−0.580583	+	0.335200i	0.180782	+	0.983523i	$0.442137\pi$
$420$		0			0
$421$	1.01688	−	1.01688i	0.0495599	−	0.0495599i	−0.681893	−	0.731452i	$-0.738843\pi$
$421$	1.01688	−	1.01688i	0.0495599	−	0.0495599i	0.731452	+	0.681893i	$0.238843\pi$
$422$		0			0
$423$	1.33527	−	0.770916i	0.0649229	−	0.0374832i
$424$		0			0
$425$	−0.739444	−	2.75964i	−0.0358683	−	0.133862i
$426$		0			0
$427$	−5.87015	+	21.9077i	−0.284077	+	1.06019i
$428$		0			0
$429$	−12.2062	+	45.5540i	−0.589319	+	2.19937i
$430$		0			0
$431$	−22.9450	+	6.14809i	−1.10522	+	0.296143i	−0.764889	−	0.644162i	$-0.777206\pi$
$431$	−22.9450	+	6.14809i	−1.10522	+	0.296143i	−0.340332	+	0.940305i	$0.610540\pi$
$432$		0			0
$433$	−25.2499			−1.21343			−0.606717	−	0.794918i	$-0.707514\pi$
$433$	−25.2499			−1.21343			−0.606717	+	0.794918i	$0.707514\pi$
$434$		0			0
$435$	9.16317	+	15.8711i	0.439340	+	0.760960i
$436$		0			0
$437$	−0.120172	−	0.0693813i	−0.00574861	−	0.00331896i
$438$		0			0
$439$	−35.1016	+	9.40545i	−1.67531	+	0.448898i	−0.966534	−	0.256537i	$-0.917418\pi$
$439$	−35.1016	+	9.40545i	−1.67531	+	0.448898i	−0.708775	+	0.705435i	$0.750752\pi$
$440$		0			0
$441$	−1.50429	+	2.60551i	−0.0716329	+	0.124072i
$442$		0			0
$443$	−10.9810			−0.521721			−0.260861	−	0.965377i	$-0.584006\pi$
$443$	−10.9810			−0.521721			−0.260861	+	0.965377i	$0.584006\pi$
$444$		0			0
$445$	15.4774			0.733699
$446$		0			0
$447$	11.5592	−	20.0211i	0.546732	−	0.946967i
$448$		0			0
$449$	−24.6596	+	6.60753i	−1.16376	+	0.311829i	−0.788467	−	0.615077i	$-0.789125\pi$
$449$	−24.6596	+	6.60753i	−1.16376	+	0.311829i	−0.375293	+	0.926906i	$0.622458\pi$
$450$		0			0
$451$	−44.6159	−	25.7590i	−2.10088	−	1.21294i
$452$		0			0
$453$	−8.57249	−	14.8480i	−0.402771	−	0.697619i
$454$		0			0
$455$	−17.3591			−0.813808
$456$		0			0
$457$	−26.4357	+	7.08341i	−1.23661	+	0.331348i	−0.817149	−	0.576426i	$-0.804447\pi$
$457$	−26.4357	+	7.08341i	−1.23661	+	0.331348i	−0.419459	+	0.907774i	$0.637780\pi$
$458$		0			0
$459$	−2.11268	+	7.88464i	−0.0986115	+	0.368023i
$460$		0			0
$461$	0.650510	−	2.42774i	0.0302973	−	0.113071i	−0.949121	−	0.314911i	$-0.898025\pi$
$461$	0.650510	−	2.42774i	0.0302973	−	0.113071i	0.979419	+	0.201840i	$0.0646921\pi$
$462$		0			0
$463$	3.77583	+	14.0916i	0.175478	+	0.654891i	0.996470	+	0.0839518i	$0.0267542\pi$
$463$	3.77583	+	14.0916i	0.175478	+	0.654891i	−0.820992	+	0.570939i	$0.806579\pi$
$464$		0			0
$465$	−24.9682	+	14.4154i	−1.15787	+	0.668498i
$466$		0			0
$467$	−16.2065	+	16.2065i	−0.749948	+	0.749948i	−0.974469	−	0.224521i	$-0.927918\pi$
$467$	−16.2065	+	16.2065i	−0.749948	+	0.749948i	0.224521	+	0.974469i	$0.427918\pi$
$468$		0			0
$469$	−4.76530	+	2.75125i	−0.220041	+	0.127041i
$470$		0			0
$471$	−31.4381			−1.44859
$472$		0			0
$473$	17.0108	−	17.0108i	0.782156	−	0.782156i
$474$		0			0
$475$	−0.0387509	−	0.0387509i	−0.00177801	−	0.00177801i
$476$		0			0
$477$	−3.09683	+	5.36386i	−0.141794	+	0.245594i
$478$		0			0
$479$	10.3294	+	2.76775i	0.471961	+	0.126462i	0.486957	−	0.873426i	$-0.338107\pi$
$479$	10.3294	+	2.76775i	0.471961	+	0.126462i	−0.0149958	+	0.999888i	$0.504773\pi$
$480$		0			0
$481$	17.4470	+	16.0001i	0.795516	+	0.729540i
$482$		0			0
$483$	−3.39234	+	12.6604i	−0.154357	+	0.576067i
$484$		0			0
$485$	29.9207	+	17.2747i	1.35863	+	0.784404i
$486$		0			0
$487$	−22.7820	+	22.7820i	−1.03235	+	1.03235i	−0.0328917	+	0.999459i	$0.510472\pi$
$487$	−22.7820	+	22.7820i	−1.03235	+	1.03235i	−0.999459	+	0.0328917i	$0.989528\pi$
$488$		0			0
$489$	6.56436	+	6.56436i	0.296851	+	0.296851i
$490$		0			0
$491$			38.1666i			1.72243i	0.508237	+	0.861217i	$0.330297\pi$
$491$			38.1666i			1.72243i	−0.508237	+	0.861217i	$0.669703\pi$
$492$		0			0
$493$	−5.74957	−	9.95855i	−0.258948	−	0.448511i
$494$		0			0
$495$	−12.3966	−	12.3966i	−0.557186	−	0.557186i
$496$		0			0
$497$	−13.1342	−	22.7491i	−0.589149	−	1.02044i
$498$		0			0
$499$	10.5484	−	2.82644i	0.472213	−	0.126529i	−0.0148615	−	0.999890i	$-0.504731\pi$
$499$	10.5484	−	2.82644i	0.472213	−	0.126529i	0.487074	+	0.873361i	$0.338064\pi$
$500$		0			0
$501$	−21.0806	−	5.64852i	−0.941810	−	0.252357i
$502$		0			0
$503$	21.9016	+	5.86852i	0.976544	+	0.261664i	0.711589	−	0.702596i	$-0.247976\pi$
$503$	21.9016	+	5.86852i	0.976544	+	0.261664i	0.264956	+	0.964261i	$0.414643\pi$
$504$		0			0
$505$	7.80640	+	29.1339i	0.347380	+	1.29644i
$506$		0			0
$507$		−	4.58232i		−	0.203508i
$508$		0			0
$509$	−32.7328	+	18.8983i	−1.45086	+	0.837652i	−0.998530	−	0.0542004i	$-0.982739\pi$
$509$	−32.7328	+	18.8983i	−1.45086	+	0.837652i	−0.452326	+	0.891853i	$0.649406\pi$
$510$		0			0
$511$	11.8905	−	20.5950i	0.526006	−	0.911068i
$512$		0			0
$513$	0.0405248	+	0.151241i	0.00178921	+	0.00667744i
$514$		0			0
$515$	6.63640	+	3.83153i	0.292435	+	0.168837i
$516$		0			0
$517$			5.61047i			0.246748i
$518$		0			0
$519$			9.62847i			0.422643i
$520$		0			0
$521$	−0.727458	−	0.419998i	−0.0318705	−	0.0184004i	0.483980	−	0.875079i	$-0.339191\pi$
$521$	−0.727458	−	0.419998i	−0.0318705	−	0.0184004i	−0.515851	+	0.856679i	$0.672524\pi$
$522$		0			0
$523$	−2.70747	−	10.1044i	−0.118389	−	0.441835i	0.881129	−	0.472876i	$-0.156784\pi$
$523$	−2.70747	−	10.1044i	−0.118389	−	0.441835i	−0.999518	+	0.0310414i	$0.990118\pi$
$524$		0			0
$525$	−2.58819	+	4.48288i	−0.112958	+	0.195649i
$526$		0			0
$527$	15.6667	−	9.04516i	0.682451	−	0.394013i
$528$		0			0
$529$			15.5699i			0.676952i
$530$		0			0
$531$	3.29372	+	12.2923i	0.142935	+	0.533441i
$532$		0			0
$533$	34.1255	+	9.14390i	1.47814	+	0.396066i
$534$		0			0
$535$	−26.3155	−	7.05122i	−1.13772	−	0.304851i
$536$		0			0
$537$	41.1787	−	11.0338i	1.77699	−	0.476144i
$538$		0			0
$539$	−5.47386	−	9.48100i	−0.235776	−	0.408376i
$540$		0			0
$541$	25.7834	+	25.7834i	1.10851	+	1.10851i	0.993346	+	0.115168i	$0.0367405\pi$
$541$	25.7834	+	25.7834i	1.10851	+	1.10851i	0.115168	+	0.993346i	$0.463259\pi$
$542$		0			0
$543$	−1.18141	−	2.04626i	−0.0506992	−	0.0878136i
$544$		0			0
$545$			31.2021i			1.33655i
$546$		0			0
$547$	−7.31894	−	7.31894i	−0.312935	−	0.312935i	0.533110	−	0.846046i	$-0.321023\pi$
$547$	−7.31894	−	7.31894i	−0.312935	−	0.312935i	−0.846046	+	0.533110i	$0.821023\pi$
$548$		0			0
$549$	11.1072	−	11.1072i	0.474044	−	0.474044i
$550$		0			0
$551$	−0.191022	−	0.110287i	−0.00813781	−	0.00469836i
$552$		0			0
$553$	−4.68542	+	17.4862i	−0.199244	+	0.743590i
$554$		0			0
$555$	−24.5399	+	7.72665i	−1.04166	+	0.327978i
$556$		0			0
$557$	3.53484	+	0.947158i	0.149776	+	0.0401324i	0.332928	−	0.942952i	$-0.391963\pi$
$557$	3.53484	+	0.947158i	0.149776	+	0.0401324i	−0.183152	+	0.983085i	$0.558630\pi$
$558$		0			0
$559$	−8.24871	+	14.2872i	−0.348883	+	0.604283i
$560$		0			0
$561$	22.7409	+	22.7409i	0.960122	+	0.960122i
$562$		0			0
$563$	25.9958	−	25.9958i	1.09559	−	1.09559i	0.100674	−	0.994920i	$-0.467900\pi$
$563$	25.9958	−	25.9958i	1.09559	−	1.09559i	0.994920	−	0.100674i	$-0.0320998\pi$
$564$		0			0
$565$	−16.7260			−0.703669
$566$		0			0
$567$	21.9325	−	12.6628i	0.921080	−	0.531786i
$568$		0			0
$569$	5.78067	−	5.78067i	0.242338	−	0.242338i	−0.575479	−	0.817817i	$-0.695184\pi$
$569$	5.78067	−	5.78067i	0.242338	−	0.242338i	0.817817	+	0.575479i	$0.195184\pi$
$570$		0			0
$571$	35.3140	−	20.3885i	1.47785	−	0.853234i	0.478159	−	0.878274i	$-0.341304\pi$
$571$	35.3140	−	20.3885i	1.47785	−	0.853234i	0.999686	+	0.0250393i	$0.00797108\pi$
$572$		0			0
$573$	−9.90431	−	36.9634i	−0.413758	−	1.54417i
$574$		0			0
$575$	0.759476	−	2.83440i	0.0316724	−	0.118203i
$576$		0			0
$577$	7.53300	−	28.1136i	0.313603	−	1.17038i	−0.611680	−	0.791105i	$-0.709506\pi$
$577$	7.53300	−	28.1136i	0.313603	−	1.17038i	0.925283	−	0.379277i	$-0.123827\pi$
$578$		0			0
$579$	−33.5469	+	8.98886i	−1.39416	+	0.373564i
$580$		0			0
$581$	22.9732			0.953089
$582$		0			0
$583$	−11.2688	−	19.5182i	−0.466707	−	0.808361i
$584$		0			0
$585$	10.4118	+	6.01124i	0.430474	+	0.248534i
$586$		0			0
$587$	−13.7899	+	3.69500i	−0.569172	+	0.152509i	−0.531917	−	0.846797i	$-0.678528\pi$
$587$	−13.7899	+	3.69500i	−0.569172	+	0.152509i	−0.0372550	+	0.999306i	$0.511861\pi$
$588$		0			0
$589$	0.173501	−	0.300513i	0.00714900	−	0.0123824i
$590$		0			0
$591$	30.6594			1.26116
$592$		0			0
$593$	−9.47781			−0.389207			−0.194604	−	0.980882i	$-0.562342\pi$
$593$	−9.47781			−0.389207			−0.194604	+	0.980882i	$0.562342\pi$
$594$		0			0
$595$	−5.91885	+	10.2517i	−0.242649	+	0.420281i
$596$		0			0
$597$	−9.50756	+	2.54754i	−0.389118	+	0.104264i
$598$		0			0
$599$	−18.3073	−	10.5697i	−0.748017	−	0.431868i	0.0769603	−	0.997034i	$-0.475479\pi$
$599$	−18.3073	−	10.5697i	−0.748017	−	0.431868i	−0.824977	+	0.565167i	$0.808812\pi$
$600$		0			0
$601$	−3.90941	−	6.77129i	−0.159468	−	0.276207i	0.775209	−	0.631705i	$-0.217645\pi$
$601$	−3.90941	−	6.77129i	−0.159468	−	0.276207i	−0.934677	+	0.355498i	$0.884311\pi$
$602$		0			0
$603$	3.81089			0.155192
$604$		0			0
$605$	40.5741	−	10.8718i	1.64957	−	0.442001i
$606$		0			0
$607$	−5.19164	+	19.3755i	−0.210722	+	0.786426i	0.776907	+	0.629616i	$0.216788\pi$
$607$	−5.19164	+	19.3755i	−0.210722	+	0.786426i	−0.987629	+	0.156810i	$0.949879\pi$
$608$		0			0
$609$	−5.39236	+	20.1246i	−0.218510	+	0.815489i
$610$		0			0
$611$	−0.995799	−	3.71637i	−0.0402857	−	0.150348i
$612$		0			0
$613$	−6.53079	+	3.77055i	−0.263776	+	0.152291i	−0.626056	−	0.779778i	$-0.715332\pi$
$613$	−6.53079	+	3.77055i	−0.263776	+	0.152291i	0.362280	+	0.932069i	$0.381998\pi$
$614$		0			0
$615$	−27.1501	+	27.1501i	−1.09480	+	1.09480i
$616$		0			0
$617$	−22.2729	+	12.8593i	−0.896674	+	0.517695i	−0.876120	−	0.482094i	$-0.839876\pi$
$617$	−22.2729	+	12.8593i	−0.896674	+	0.517695i	−0.0205541	+	0.999789i	$0.506543\pi$
$618$		0			0
$619$	23.3558			0.938750			0.469375	−	0.882999i	$-0.344479\pi$
$619$	23.3558			0.938750			0.469375	+	0.882999i	$0.344479\pi$
$620$		0			0
$621$	−5.92832	+	5.92832i	−0.237895	+	0.237895i
$622$		0			0
$623$	12.4420	+	12.4420i	0.498478	+	0.498478i
$624$		0			0
$625$	−9.22926	+	15.9856i	−0.369171	+	0.639422i
$626$		0			0
$627$	0.595873	+	0.159664i	0.0237969	+	0.00637635i
$628$		0			0
$629$	15.3980	−	4.84821i	0.613957	−	0.193311i
$630$		0			0
$631$	6.36974	−	23.7722i	0.253575	−	0.946356i	−0.715302	−	0.698816i	$-0.753711\pi$
$631$	6.36974	−	23.7722i	0.253575	−	0.946356i	0.968877	−	0.247541i	$-0.0796225\pi$
$632$		0			0
$633$	36.6962	+	21.1865i	1.45854	+	0.842089i
$634$		0			0
$635$	14.9710	−	14.9710i	0.594108	−	0.594108i
$636$		0			0
$637$	5.30867	+	5.30867i	0.210337	+	0.210337i
$638$		0			0
$639$			18.1928i			0.719697i
$640$		0			0
$641$	1.11113	+	1.92453i	0.0438869	+	0.0760144i	0.887134	−	0.461511i	$-0.152693\pi$
$641$	1.11113	+	1.92453i	0.0438869	+	0.0760144i	−0.843248	+	0.537525i	$0.819359\pi$
$642$		0			0
$643$	−28.1467	−	28.1467i	−1.11000	−	1.11000i	−0.993150	−	0.116850i	$-0.962720\pi$
$643$	−28.1467	−	28.1467i	−1.11000	−	1.11000i	−0.116850	−	0.993150i	$-0.537280\pi$
$644$		0			0
$645$	−8.96471	−	15.5273i	−0.352985	−	0.611388i
$646$		0			0
$647$	−16.4045	+	4.39558i	−0.644928	+	0.172808i	−0.566435	−	0.824107i	$-0.691678\pi$
$647$	−16.4045	+	4.39558i	−0.644928	+	0.172808i	−0.0784934	+	0.996915i	$0.525011\pi$
$648$		0			0
$649$	−44.7297	−	11.9853i	−1.75579	−	0.470463i
$650$		0			0
$651$	−31.6597	−	8.48320i	−1.24084	−	0.332483i
$652$		0			0
$653$	8.89129	+	33.1828i	0.347943	+	1.29854i	0.889136	+	0.457643i	$0.151306\pi$
$653$	8.89129	+	33.1828i	0.347943	+	1.29854i	−0.541193	+	0.840899i	$0.682027\pi$
$654$		0			0
$655$		−	17.8304i		−	0.696692i
$656$		0			0
$657$	−14.2636	+	8.23508i	−0.556475	+	0.321281i
$658$		0			0
$659$	−13.9451	+	24.1537i	−0.543226	+	0.940894i	0.455491	+	0.890241i	$0.349464\pi$
$659$	−13.9451	+	24.1537i	−0.543226	+	0.940894i	−0.998716	+	0.0506539i	$0.983869\pi$
$660$		0			0
$661$	−11.4500	−	42.7320i	−0.445354	−	1.66208i	−0.715001	−	0.699124i	$-0.753574\pi$
$661$	−11.4500	−	42.7320i	−0.445354	−	1.66208i	0.269647	−	0.962959i	$-0.413093\pi$
$662$		0			0
$663$	−19.0999	−	11.0273i	−0.741777	−	0.428265i
$664$		0			0
$665$			0.227067i			0.00880529i
$666$		0			0
$667$		−	11.8107i		−	0.457311i
$668$		0			0
$669$	37.2265	+	21.4927i	1.43926	+	0.830957i
$670$		0			0
$671$	14.7937	+	55.2110i	0.571106	+	2.13140i
$672$		0			0
$673$	−15.0859	+	26.1295i	−0.581518	+	1.00722i	0.413782	+	0.910376i	$0.364208\pi$
$673$	−15.0859	+	26.1295i	−0.581518	+	1.00722i	−0.995300	+	0.0968422i	$0.969126\pi$
$674$		0			0
$675$	−2.86748	+	1.65554i	−0.110370	+	0.0637219i
$676$		0			0
$677$		−	14.7571i		−	0.567162i	−0.958948	−	0.283581i	$-0.908477\pi$
$677$		−	14.7571i		−	0.567162i	0.958948	−	0.283581i	$-0.0915225\pi$
$678$		0			0
$679$	10.1659	+	37.9395i	0.390130	+	1.45598i
$680$		0			0
$681$	−36.3502	−	9.74001i	−1.39294	−	0.373238i
$682$		0			0
$683$	−1.78383	−	0.477975i	−0.0682562	−	0.0182892i	0.224529	−	0.974467i	$-0.427916\pi$
$683$	−1.78383	−	0.477975i	−0.0682562	−	0.0182892i	−0.292786	+	0.956178i	$0.594582\pi$
$684$		0			0
$685$	−8.80935	+	2.36046i	−0.336588	+	0.0901885i
$686$		0			0
$687$	−18.4490	−	31.9547i	−0.703875	−	1.21915i
$688$		0			0
$689$	10.9287	+	10.9287i	0.416352	+	0.416352i
$690$		0			0
$691$	−5.53148	−	9.58080i	−0.210427	−	0.364471i	0.741421	−	0.671040i	$-0.234152\pi$
$691$	−5.53148	−	9.58080i	−0.210427	−	0.364471i	−0.951848	+	0.306569i	$0.900819\pi$
$692$		0			0
$693$		−	19.9308i		−	0.757109i
$694$		0			0
$695$	20.7376	+	20.7376i	0.786621	+	0.786621i
$696$		0			0
$697$	17.0357	−	17.0357i	0.645274	−	0.645274i
$698$		0			0
$699$	39.0588	+	22.5506i	1.47734	+	0.852943i
$700$		0			0
$701$	8.97424	−	33.4923i	0.338952	−	1.26499i	−0.560568	−	0.828109i	$-0.689417\pi$
$701$	8.97424	−	33.4923i	0.338952	−	1.26499i	0.899520	−	0.436879i	$-0.143916\pi$
$702$		0			0
$703$	0.209290	−	0.228217i	0.00789352	−	0.00860737i
$704$		0			0
$705$	4.03896	+	1.08224i	0.152116	+	0.0407594i
$706$		0			0
$707$	−17.1448	+	29.6956i	−0.644796	+	1.11682i
$708$		0			0
$709$	4.68625	+	4.68625i	0.175996	+	0.175996i	0.789608	−	0.613612i	$-0.210284\pi$
$709$	4.68625	+	4.68625i	0.175996	+	0.175996i	−0.613612	+	0.789608i	$0.710284\pi$
$710$		0			0
$711$	8.86552	−	8.86552i	0.332483	−	0.332483i
$712$		0			0
$713$	18.5804			0.695841
$714$		0			0
$715$	−37.8867	+	21.8739i	−1.41688	+	0.818037i
$716$		0			0
$717$	−26.0539	+	26.0539i	−0.973001	+	0.973001i
$718$		0			0
$719$	26.6281	−	15.3737i	0.993061	−	0.573344i	0.0868728	−	0.996219i	$-0.472313\pi$
$719$	26.6281	−	15.3737i	0.993061	−	0.573344i	0.906188	+	0.422876i	$0.138979\pi$
$720$		0			0
$721$	2.25479	+	8.41498i	0.0839726	+	0.313390i
$722$		0			0
$723$	13.9245	−	51.9668i	0.517856	−	1.93267i
$724$		0			0
$725$	1.20724	−	4.50549i	0.0448358	−	0.167330i
$726$		0			0
$727$	21.6467	−	5.80021i	0.802831	−	0.215118i	0.166004	−	0.986125i	$-0.446913\pi$
$727$	21.6467	−	5.80021i	0.802831	−	0.215118i	0.636827	+	0.771007i	$0.280247\pi$
$728$		0			0
$729$	2.16322			0.0801193
$730$		0			0
$731$	5.62504	+	9.74286i	0.208050	+	0.360353i
$732$		0			0
$733$	−12.8600	−	7.42475i	−0.474997	−	0.274239i	0.243332	−	0.969943i	$-0.421759\pi$
$733$	−12.8600	−	7.42475i	−0.474997	−	0.274239i	−0.718329	+	0.695704i	$0.755093\pi$
$734$		0			0
$735$	−7.88124	+	2.11177i	−0.290704	+	0.0778939i
$736$		0			0
$737$	−6.93359	+	12.0093i	−0.255402	+	0.442370i
$738$		0			0
$739$	−23.3413			−0.858622			−0.429311	−	0.903157i	$-0.641244\pi$
$739$	−23.3413			−0.858622			−0.429311	+	0.903157i	$0.641244\pi$
$740$		0			0
$741$	−0.423045			−0.0155410
$742$		0			0
$743$	20.0523	−	34.7317i	0.735649	−	1.27418i	−0.218789	−	0.975772i	$-0.570211\pi$
$743$	20.0523	−	34.7317i	0.735649	−	1.27418i	0.954438	−	0.298410i	$-0.0964561\pi$
$744$		0			0
$745$	20.7145	−	5.55044i	0.758921	−	0.203352i
$746$		0			0
$747$	−13.7790	−	7.95533i	−0.504149	−	0.291070i
$748$		0			0
$749$	−15.4862	−	26.8229i	−0.565854	−	0.980088i
$750$		0			0
$751$	−13.6589			−0.498419			−0.249210	−	0.968450i	$-0.580171\pi$
$751$	−13.6589			−0.498419			−0.249210	+	0.968450i	$0.580171\pi$
$752$		0			0
$753$	6.18993	−	1.65859i	0.225574	−	0.0604423i
$754$		0			0
$755$	4.11629	−	15.3622i	0.149807	−	0.559088i
$756$		0			0
$757$	−7.43899	+	27.7627i	−0.270375	+	1.00905i	0.688503	+	0.725233i	$0.258268\pi$
$757$	−7.43899	+	27.7627i	−0.270375	+	1.00905i	−0.958878	+	0.283819i	$0.908399\pi$
$758$		0			0
$759$	8.54925	+	31.9062i	0.310318	+	1.15812i
$760$		0			0
$761$	−20.9998	+	12.1243i	−0.761244	+	0.439504i	−0.829742	−	0.558147i	$-0.811513\pi$
$761$	−20.9998	+	12.1243i	−0.761244	+	0.439504i	0.0684983	+	0.997651i	$0.478179\pi$
$762$		0			0
$763$	−25.0828	+	25.0828i	−0.908058	+	0.908058i
$764$		0			0
$765$	7.10011	−	4.09925i	0.256705	−	0.148209i
$766$		0			0
$767$	31.7562			1.14665
$768$		0			0
$769$	1.71561	−	1.71561i	0.0618664	−	0.0618664i	−0.675497	−	0.737363i	$-0.736071\pi$
$769$	1.71561	−	1.71561i	0.0618664	−	0.0618664i	0.737363	+	0.675497i	$0.236071\pi$
$770$		0			0
$771$	−6.85162	−	6.85162i	−0.246755	−	0.246755i
$772$		0			0
$773$	17.0308	−	29.4983i	0.612556	−	1.06098i	−0.378252	−	0.925703i	$-0.623475\pi$
$773$	17.0308	−	29.4983i	0.612556	−	1.06098i	0.990808	−	0.135276i	$-0.0431920\pi$
$774$		0			0
$775$	7.08798	+	1.89922i	0.254608	+	0.0682219i
$776$		0			0
$777$	−25.9385	−	13.5159i	−0.930540	−	0.484880i
$778$		0			0
$779$	0.119608	−	0.446381i	0.00428539	−	0.0159933i
$780$		0			0
$781$	−57.3314	−	33.1003i	−2.05148	−	1.18442i
$782$		0			0
$783$	−9.42349	+	9.42349i	−0.336768	+	0.336768i
$784$		0			0
$785$	−20.6212	−	20.6212i	−0.736003	−	0.736003i
$786$		0			0
$787$			22.9532i			0.818192i	0.912491	+	0.409096i	$0.134156\pi$
$787$			22.9532i			0.818192i	−0.912491	+	0.409096i	$0.865844\pi$
$788$		0			0
$789$	−9.76202	−	16.9083i	−0.347537	−	0.601952i
$790$		0			0
$791$	−13.4457	−	13.4457i	−0.478075	−	0.478075i
$792$		0			0
$793$	−19.5988	−	33.9460i	−0.695972	−	1.20546i
$794$		0			0
$795$	−16.2248	+	4.34742i	−0.575435	+	0.154187i
$796$		0			0
$797$	42.7655	+	11.4590i	1.51483	+	0.405898i	0.918037	−	0.396495i	$-0.129773\pi$
$797$	42.7655	+	11.4590i	1.51483	+	0.405898i	0.596796	+	0.802393i	$0.296440\pi$
$798$		0			0
$799$	−2.53431	−	0.679066i	−0.0896574	−	0.0240236i
$800$		0			0
$801$	−3.15405	−	11.7711i	−0.111443	−	0.415910i
$802$		0			0
$803$		−	59.9321i		−	2.11496i
$804$		0			0
$805$	−10.5295	+	6.07920i	−0.371115	+	0.214263i
$806$		0			0
$807$	20.6489	−	35.7649i	0.726874	−	1.25898i
$808$		0			0
$809$	9.98302	+	37.2572i	0.350984	+	1.30989i	0.885463	+	0.464710i	$0.153841\pi$
$809$	9.98302	+	37.2572i	0.350984	+	1.30989i	−0.534479	+	0.845182i	$0.679492\pi$
$810$		0			0
$811$	19.2356	+	11.1057i	0.675453	+	0.389973i	0.798140	−	0.602473i	$-0.205818\pi$
$811$	19.2356	+	11.1057i	0.675453	+	0.389973i	−0.122687	+	0.992445i	$0.539151\pi$
$812$		0			0
$813$		−	27.1461i		−	0.952055i
$814$		0			0
$815$			8.61153i			0.301649i
$816$		0			0
$817$	0.186885	+	0.107898i	0.00653826	+	0.00377487i
$818$		0			0
$819$	3.53751	+	13.2022i	0.123611	+	0.461321i
$820$		0			0
$821$	0.540585	−	0.936320i	0.0188665	−	0.0326778i	−0.856438	−	0.516250i	$-0.827328\pi$
$821$	0.540585	−	0.936320i	0.0188665	−	0.0326778i	0.875305	+	0.483572i	$0.160661\pi$
$822$		0			0
$823$	38.2411	−	22.0785i	1.33300	−	0.769609i	0.347243	−	0.937775i	$-0.387118\pi$
$823$	38.2411	−	22.0785i	1.33300	−	0.769609i	0.985759	+	0.168166i	$0.0537845\pi$
$824$		0			0
$825$			13.0453i			0.454181i
$826$		0			0
$827$	11.2796	+	42.0959i	0.392228	+	1.46382i	0.826450	+	0.563010i	$0.190357\pi$
$827$	11.2796	+	42.0959i	0.392228	+	1.46382i	−0.434222	+	0.900806i	$0.642976\pi$
$828$		0			0
$829$	−44.0396	−	11.8004i	−1.52956	−	0.409844i	−0.606683	−	0.794944i	$-0.707500\pi$
$829$	−44.0396	−	11.8004i	−1.52956	−	0.409844i	−0.922875	+	0.385100i	$0.874167\pi$
$830$		0			0
$831$	−13.7226	−	3.67697i	−0.476033	−	0.127553i
$832$		0			0
$833$	4.94520	−	1.32506i	0.171341	−	0.0459107i
$834$		0			0
$835$	−10.1224	−	17.5324i	−0.350298	−	0.606735i
$836$		0			0
$837$	−14.8249	−	14.8249i	−0.512424	−	0.512424i
$838$		0			0
$839$	11.9206	+	20.6471i	0.411545	+	0.712817i	0.995059	−	0.0992863i	$-0.0316560\pi$
$839$	11.9206	+	20.6471i	0.411545	+	0.712817i	−0.583514	+	0.812103i	$0.698323\pi$
$840$		0			0
$841$			10.2261i			0.352625i
$842$		0			0
$843$	22.8091	+	22.8091i	0.785588	+	0.785588i
$844$		0			0
$845$	3.00568	−	3.00568i	0.103399	−	0.103399i
$846$		0			0
$847$	41.3564	+	23.8771i	1.42102	+	0.820428i
$848$		0			0
$849$	12.0263	−	44.8828i	0.412742	−	1.54038i
$850$		0			0
$851$	16.1861	+	3.59514i	0.554851	+	0.123240i
$852$		0			0
$853$	47.7130	+	12.7847i	1.63366	+	0.437739i	0.954974	−	0.296688i	$-0.0958822\pi$
$853$	47.7130	+	12.7847i	1.63366	+	0.437739i	0.678688	+	0.734427i	$0.262549\pi$
$854$		0			0
$855$	0.0786305	−	0.136192i	0.00268911	−	0.00465767i
$856$		0			0
$857$	0.772015	+	0.772015i	0.0263715	+	0.0263715i	0.720170	−	0.693798i	$-0.244064\pi$
$857$	0.772015	+	0.772015i	0.0263715	+	0.0263715i	−0.693798	+	0.720170i	$0.744064\pi$
$858$		0			0
$859$	−38.4311	+	38.4311i	−1.31125	+	1.31125i	−0.390758	+	0.920493i	$0.627787\pi$
$859$	−38.4311	+	38.4311i	−1.31125	+	1.31125i	−0.920493	+	0.390758i	$0.872213\pi$
$860$		0			0
$861$	−43.6509			−1.48762
$862$		0			0
$863$	23.1050	−	13.3397i	0.786503	−	0.454088i	−0.0522272	−	0.998635i	$-0.516632\pi$
$863$	23.1050	−	13.3397i	0.786503	−	0.454088i	0.838730	+	0.544548i	$0.183299\pi$
$864$		0			0
$865$	−6.31561	+	6.31561i	−0.214737	+	0.214737i
$866$		0			0
$867$	18.4123	−	10.6304i	0.625315	−	0.361026i
$868$		0			0
$869$	11.8080	+	44.0681i	0.400560	+	1.49491i
$870$		0			0
$871$	2.46128	−	9.18563i	0.0833974	−	0.311243i
$872$		0			0
$873$	7.04062	−	26.2760i	0.238289	−	0.889307i
$874$		0			0
$875$	−26.1805	+	7.01504i	−0.885061	+	0.237151i
$876$		0			0
$877$	6.94063			0.234369			0.117184	−	0.993110i	$-0.462613\pi$
$877$	6.94063			0.234369			0.117184	+	0.993110i	$0.462613\pi$
$878$		0			0
$879$	−29.0110	−	50.2485i	−0.978516	−	1.69484i
$880$		0			0
$881$	−27.6087	−	15.9399i	−0.930160	−	0.537028i	−0.0432977	−	0.999062i	$-0.513786\pi$
$881$	−27.6087	−	15.9399i	−0.930160	−	0.537028i	−0.886862	+	0.462034i	$0.847120\pi$
$882$		0			0
$883$	30.5105	−	8.17527i	1.02676	−	0.275120i	0.294144	−	0.955761i	$-0.404966\pi$
$883$	30.5105	−	8.17527i	1.02676	−	0.275120i	0.732617	+	0.680642i	$0.238299\pi$
$884$		0			0
$885$	−17.2564	+	29.8889i	−0.580066	+	1.00470i
$886$		0			0
$887$	−0.203076			−0.00681861			−0.00340931	−	0.999994i	$-0.501085\pi$
$887$	−0.203076			−0.00681861			−0.00340931	+	0.999994i	$0.501085\pi$
$888$		0			0
$889$	24.0699			0.807279
$890$		0			0
$891$	31.9122	−	55.2736i	1.06910	−	1.85174i
$892$		0			0
$893$	−0.0486123	+	0.0130256i	−0.00162675	+	0.000435886i
$894$		0			0
$895$	34.2478	+	19.7730i	1.14478	+	0.660937i
$896$		0			0
$897$	−11.3260	−	19.6173i	−0.378166	−	0.655002i
$898$		0			0
$899$	29.5348			0.985042
$900$		0			0
$901$	10.1805	−	2.72786i	0.339162	−	0.0908781i
$902$		0			0
$903$	5.27557	−	19.6887i	0.175560	−	0.655199i
$904$		0			0
$905$	0.567284	−	2.11713i	0.0188572	−	0.0703758i
$906$		0			0
$907$	7.97836	+	29.7756i	0.264917	+	0.988684i	0.962301	+	0.271986i	$0.0876806\pi$
$907$	7.97836	+	29.7756i	0.264917	+	0.988684i	−0.697384	+	0.716698i	$0.745653\pi$
$908$		0			0
$909$	20.5665	−	11.8740i	0.682146	−	0.393837i
$910$		0			0
$911$	28.5040	−	28.5040i	0.944380	−	0.944380i	−0.0541524	−	0.998533i	$-0.517246\pi$
$911$	28.5040	−	28.5040i	0.944380	−	0.944380i	0.998533	+	0.0541524i	$0.0172457\pi$
$912$		0			0
$913$	50.1396	−	28.9481i	1.65938	−	0.958042i
$914$		0			0
$915$	42.5999			1.40831
$916$		0			0
$917$	14.3335	−	14.3335i	0.473335	−	0.473335i
$918$		0			0
$919$	−21.5496	−	21.5496i	−0.710857	−	0.710857i	0.255858	−	0.966714i	$-0.417642\pi$
$919$	−21.5496	−	21.5496i	−0.710857	−	0.710857i	−0.966714	+	0.255858i	$0.917642\pi$
$920$		0			0
$921$	29.5088	−	51.1107i	0.972348	−	1.68416i
$922$		0			0
$923$	43.8513	+	11.7499i	1.44338	+	0.386753i
$924$		0			0
$925$	5.80712	+	3.02594i	0.190937	+	0.0994922i
$926$		0			0
$927$	1.56161	−	5.82800i	0.0512900	−	0.191417i
$928$		0			0
$929$	2.35127	+	1.35750i	0.0771426	+	0.0445383i	0.538075	−	0.842897i	$-0.319152\pi$
$929$	2.35127	+	1.35750i	0.0771426	+	0.0445383i	−0.460933	+	0.887435i	$0.652485\pi$
$930$		0			0
$931$	0.0694404	−	0.0694404i	0.00227582	−	0.00227582i
$932$		0			0
$933$	−8.17763	−	8.17763i	−0.267724	−	0.267724i
$934$		0			0
$935$			29.8329i			0.975641i
$936$		0			0
$937$	−6.76680	−	11.7204i	−0.221062	−	0.382890i	0.734069	−	0.679075i	$-0.237619\pi$
$937$	−6.76680	−	11.7204i	−0.221062	−	0.382890i	−0.955131	+	0.296185i	$0.904286\pi$
$938$		0			0
$939$	−19.2160	−	19.2160i	−0.627090	−	0.627090i
$940$		0			0
$941$	5.78286	+	10.0162i	0.188516	+	0.326519i	0.944756	−	0.327775i	$-0.106299\pi$
$941$	5.78286	+	10.0162i	0.188516	+	0.326519i	−0.756240	+	0.654295i	$0.772966\pi$
$942$		0			0
$943$	23.9017	−	6.40443i	0.778345	−	0.208557i
$944$		0			0
$945$	13.2517	+	3.55079i	0.431078	+	0.115507i
$946$		0			0
$947$	−42.7659	−	11.4591i	−1.38970	−	0.372370i	−0.515067	−	0.857150i	$-0.672233\pi$
$947$	−42.7659	−	11.4591i	−1.38970	−	0.372370i	−0.874636	+	0.484780i	$0.838900\pi$
$948$		0			0
$949$	10.6373	+	39.6990i	0.345302	+	1.28869i
$950$		0			0
$951$			55.2126i			1.79039i
$952$		0			0
$953$	4.32610	−	2.49767i	0.140136	−	0.0809076i	−0.428293	−	0.903640i	$-0.640885\pi$
$953$	4.32610	−	2.49767i	0.140136	−	0.0809076i	0.568429	+	0.822732i	$0.307551\pi$
$954$		0			0
$955$	17.7489	−	30.7420i	0.574340	−	0.994787i
$956$		0			0
$957$	13.5896	+	50.7172i	0.439291	+	1.63945i
$958$		0			0
$959$	−8.97921	−	5.18415i	−0.289954	−	0.167405i
$960$		0			0
$961$			15.4639i			0.498834i
$962$		0			0
$963$			21.4507i			0.691240i
$964$		0			0
$965$	−27.9005	−	16.1084i	−0.898149	−	0.518547i
$966$		0			0
$967$	−9.78297	−	36.5105i	−0.314599	−	1.17410i	−0.924362	−	0.381516i	$-0.875402\pi$
$967$	−9.78297	−	36.5105i	−0.314599	−	1.17410i	0.609763	−	0.792584i	$-0.291265\pi$
$968$		0			0
$969$	−0.144244	+	0.249837i	−0.00463377	+	0.00802593i
$970$		0			0
$971$	2.23153	−	1.28838i	0.0716133	−	0.0413459i	−0.463766	−	0.885958i	$-0.653502\pi$
$971$	2.23153	−	1.28838i	0.0716133	−	0.0413459i	0.535379	+	0.844612i	$0.320169\pi$
$972$		0			0
$973$			33.3411i			1.06887i
$974$		0			0
$975$	−2.31541	−	8.64124i	−0.0741526	−	0.276741i
$976$		0			0
$977$	−37.0383	−	9.92439i	−1.18496	−	0.317509i	−0.388068	−	0.921631i	$-0.626858\pi$
$977$	−37.0383	−	9.92439i	−1.18496	−	0.317509i	−0.796892	+	0.604121i	$0.793524\pi$
$978$		0			0
$979$	42.8329	+	11.4770i	1.36895	+	0.366808i
$980$		0			0
$981$	23.7302	−	6.35849i	0.757647	−	0.203011i
$982$		0			0
$983$	−14.9770	−	25.9410i	−0.477693	−	0.827389i	0.521980	−	0.852958i	$-0.325194\pi$
$983$	−14.9770	−	25.9410i	−0.477693	−	0.827389i	−0.999673	+	0.0255691i	$0.991860\pi$
$984$		0			0
$985$	20.1105	+	20.1105i	0.640772	+	0.640772i
$986$		0			0
$987$	2.37686	+	4.11684i	0.0756562	+	0.131040i
$988$		0			0
$989$			11.5549i			0.367423i
$990$		0			0
$991$	3.16899	+	3.16899i	0.100666	+	0.100666i	0.755646	−	0.654980i	$-0.227323\pi$
$991$	3.16899	+	3.16899i	0.100666	+	0.100666i	−0.654980	+	0.755646i	$0.727323\pi$
$992$		0			0
$993$	48.8509	−	48.8509i	1.55024	−	1.55024i
$994$		0			0
$995$	−7.90731	−	4.56529i	−0.250679	−	0.144729i
$996$		0			0
$997$	−1.46739	+	5.47638i	−0.0464728	+	0.173439i	−0.985262	−	0.171055i	$-0.945283\pi$
$997$	−1.46739	+	5.47638i	−0.0464728	+	0.173439i	0.938789	+	0.344493i	$0.111949\pi$
$998$		0			0
$999$	−10.0460	−	15.7830i	−0.317843	−	0.499352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.415.4	✓	20
4.3	odd	2		592.2.be.f.415.2	yes	20
37.14	odd	12		592.2.be.f.495.2	yes	20
148.51	even	12	inner	592.2.be.e.495.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.415.4	✓	20	1.1	even	1	trivial
592.2.be.e.495.4	yes	20	148.51	even	12	inner
592.2.be.f.415.2	yes	20	4.3	odd	2
592.2.be.f.495.2	yes	20	37.14	odd	12

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06766 - 1.84924i) q^{3} +(1.91328 - 0.512663i) q^{5} +(1.95018 + 1.12593i) q^{7} +(-0.779794 - 1.35064i) q^{9} +O(q^{10})\)	\(q+(1.06766 - 1.84924i) q^{3} +(1.91328 - 0.512663i) q^{5} +(1.95018 + 1.12593i) q^{7} +(-0.779794 - 1.35064i) q^{9} +5.67508 q^{11} +(-3.75917 + 1.00727i) q^{13} +(1.09470 - 4.08547i) q^{15} +(-0.686886 + 2.56349i) q^{17} +(0.0131756 + 0.0491721i) q^{19} +(4.16425 - 2.40423i) q^{21} +(-1.92745 + 1.92745i) q^{23} +(-0.932291 + 0.538259i) q^{25} +3.07574 q^{27} +(-3.06381 + 3.06381i) q^{29} +(-4.81995 - 4.81995i) q^{31} +(6.05905 - 10.4946i) q^{33} +(4.30847 + 1.15445i) q^{35} +(-3.26622 - 5.13145i) q^{37} +(-2.15084 + 8.02703i) q^{39} +(-7.86172 - 4.53897i) q^{41} +(2.99745 - 2.99745i) q^{43} +(-2.18439 - 2.18439i) q^{45} +0.988615i q^{47} +(-0.964544 - 1.67064i) q^{49} +(4.00716 + 4.00716i) q^{51} +(-1.98567 - 3.43928i) q^{53} +(10.8580 - 2.90940i) q^{55} +(0.104998 + 0.0281342i) q^{57} +(-7.88178 - 2.11192i) q^{59} +(2.60679 + 9.72868i) q^{61} -3.51199i q^{63} +(-6.67598 + 3.85438i) q^{65} +(-1.22176 + 2.11615i) q^{67} +(1.50646 + 5.62217i) q^{69} +(-10.1023 - 5.83257i) q^{71} -10.5606i q^{73} +2.29871i q^{75} +(11.0674 + 6.38976i) q^{77} +(2.08068 + 7.76521i) q^{79} +(5.62322 - 9.73971i) q^{81} +(8.83505 - 5.10092i) q^{83} +5.25683i q^{85} +(2.39462 + 8.93683i) q^{87} +(7.54755 + 2.02236i) q^{89} +(-8.46516 - 2.26823i) q^{91} +(-14.0593 + 3.76718i) q^{93} +(0.0504175 + 0.0873257i) q^{95} +(12.3336 + 12.3336i) q^{97} +(-4.42539 - 7.66500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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