LMFDB - Embedded newform 1071.2.n.a.820.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(64,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1071.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.n (of order $4$, degree $2$, 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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.125772815663104.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 27x^{8} + 107x^{4} + 1 $ x^12 + 27x^8 + 107x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			820.6
Root			$0.219986 + 0.219986i$ of defining polynomial
Character	$\chi$	$=$	1071.820
Dual form			1071.2.n.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05288i q^{2} -2.21432 q^{4} +(-1.82126 + 1.82126i) q^{5} +(-0.707107 - 0.707107i) q^{7} -0.439973i q^{8} +O(q^{10})$	\(q+2.05288i q^{2} -2.21432 q^{4} +(-1.82126 + 1.82126i) q^{5} +(-0.707107 - 0.707107i) q^{7} -0.439973i q^{8} +(-3.73883 - 3.73883i) q^{10} +(-3.22264 - 3.22264i) q^{11} +0.539223 q^{13} +(1.45161 - 1.45161i) q^{14} -3.52543 q^{16} +(1.23735 - 3.93306i) q^{17} -2.26088i q^{19} +(4.03285 - 4.03285i) q^{20} +(6.61570 - 6.61570i) q^{22} +(0.756132 + 0.756132i) q^{23} -1.63399i q^{25} +1.10696i q^{26} +(1.56576 + 1.56576i) q^{28} +(1.56310 - 1.56310i) q^{29} +(-3.92989 + 3.92989i) q^{31} -8.11723i q^{32} +(8.07410 + 2.54014i) q^{34} +2.57565 q^{35} +(1.70814 - 1.70814i) q^{37} +4.64132 q^{38} +(0.801306 + 0.801306i) q^{40} +(-3.78725 - 3.78725i) q^{41} -3.43635i q^{43} +(7.13596 + 7.13596i) q^{44} +(-1.55225 + 1.55225i) q^{46} -6.05205 q^{47} +1.00000i q^{49} +3.35438 q^{50} -1.19401 q^{52} -9.01579i q^{53} +11.7385 q^{55} +(-0.311108 + 0.311108i) q^{56} +(3.20887 + 3.20887i) q^{58} +10.0778i q^{59} +(2.48862 + 2.48862i) q^{61} +(-8.06759 - 8.06759i) q^{62} +9.61285 q^{64} +(-0.982066 + 0.982066i) q^{65} -2.85449 q^{67} +(-2.73989 + 8.70905i) q^{68} +5.28751i q^{70} +(6.24920 - 6.24920i) q^{71} +(11.2613 - 11.2613i) q^{73} +(3.50660 + 3.50660i) q^{74} +5.00632i q^{76} +4.55750i q^{77} +(-3.24490 - 3.24490i) q^{79} +(6.42072 - 6.42072i) q^{80} +(7.77476 - 7.77476i) q^{82} +13.0277i q^{83} +(4.90959 + 9.41667i) q^{85} +7.05442 q^{86} +(-1.41788 + 1.41788i) q^{88} -14.6325 q^{89} +(-0.381288 - 0.381288i) q^{91} +(-1.67432 - 1.67432i) q^{92} -12.4241i q^{94} +(4.11766 + 4.11766i) q^{95} +(5.81211 - 5.81211i) q^{97} -2.05288 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{5}+O(q^{10}) $ 12 * q - 8 * q^5	$ 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) $ 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$			2.05288i			1.45161i	0.687903	+	0.725803i	$0.258532\pi$
$2$			2.05288i			1.45161i	−0.687903	+	0.725803i	$0.741468\pi$
$3$		0			0
$3$		0			0
$4$	−2.21432			−1.10716
$5$	−1.82126	+	1.82126i	−0.814493	+	0.814493i	−0.985304	−	0.170811i	$-0.945361\pi$
$5$	−1.82126	+	1.82126i	−0.814493	+	0.814493i	0.170811	+	0.985304i	$0.445361\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		−	0.439973i		−	0.155554i
$9$		0			0
$10$	−3.73883	−	3.73883i	−1.18232	−	1.18232i
$11$	−3.22264	−	3.22264i	−0.971663	−	0.971663i	0.0279462	−	0.999609i	$-0.491103\pi$
$11$	−3.22264	−	3.22264i	−0.971663	−	0.971663i	−0.999609	+	0.0279462i	$0.991103\pi$
$12$		0			0
$13$	0.539223			0.149554			0.0747768	−	0.997200i	$-0.476176\pi$
$13$	0.539223			0.149554			0.0747768	+	0.997200i	$0.476176\pi$
$14$	1.45161	−	1.45161i	0.387958	−	0.387958i
$15$		0			0
$16$	−3.52543			−0.881357
$17$	1.23735	−	3.93306i	0.300102	−	0.953907i
$17$	1.23735	−	3.93306i	0.300102	−	0.953907i
$18$		0			0
$19$		−	2.26088i		−	0.518682i	−0.965786	−	0.259341i	$-0.916495\pi$
$19$		−	2.26088i		−	0.518682i	0.965786	−	0.259341i	$-0.0835054\pi$
$20$	4.03285	−	4.03285i	0.901774	−	0.901774i
$21$		0			0
$22$	6.61570	−	6.61570i	1.41047	−	1.41047i
$23$	0.756132	+	0.756132i	0.157664	+	0.157664i	0.781531	−	0.623866i	$-0.214439\pi$
$23$	0.756132	+	0.756132i	0.157664	+	0.157664i	−0.623866	+	0.781531i	$0.714439\pi$
$24$		0			0
$25$		−	1.63399i		−	0.326797i
$26$			1.10696i			0.217093i
$27$		0			0
$28$	1.56576	+	1.56576i	0.295901	+	0.295901i
$29$	1.56310	−	1.56310i	0.290261	−	0.290261i	−0.546922	−	0.837183i	$-0.684201\pi$
$29$	1.56310	−	1.56310i	0.290261	−	0.290261i	0.837183	+	0.546922i	$0.184201\pi$
$30$		0			0
$31$	−3.92989	+	3.92989i	−0.705828	+	0.705828i	−0.965655	−	0.259827i	$-0.916335\pi$
$31$	−3.92989	+	3.92989i	−0.705828	+	0.705828i	0.259827	+	0.965655i	$0.416335\pi$
$32$		−	8.11723i		−	1.43494i
$33$		0			0
$34$	8.07410	+	2.54014i	1.38470	+	0.435630i
$35$	2.57565			0.435365
$36$		0			0
$37$	1.70814	−	1.70814i	0.280816	−	0.280816i	−0.552618	−	0.833434i	$-0.686371\pi$
$37$	1.70814	−	1.70814i	0.280816	−	0.280816i	0.833434	+	0.552618i	$0.186371\pi$
$38$	4.64132			0.752922
$39$		0			0
$40$	0.801306	+	0.801306i	0.126698	+	0.126698i
$41$	−3.78725	−	3.78725i	−0.591468	−	0.591468i	0.346560	−	0.938028i	$-0.387350\pi$
$41$	−3.78725	−	3.78725i	−0.591468	−	0.591468i	−0.938028	+	0.346560i	$0.887350\pi$
$42$		0			0
$43$		−	3.43635i		−	0.524038i	−0.965063	−	0.262019i	$-0.915612\pi$
$43$		−	3.43635i		−	0.524038i	0.965063	−	0.262019i	$-0.0843884\pi$
$44$	7.13596	+	7.13596i	1.07579	+	1.07579i
$45$		0			0
$46$	−1.55225	+	1.55225i	−0.228867	+	0.228867i
$47$	−6.05205			−0.882783			−0.441391	−	0.897315i	$-0.645515\pi$
$47$	−6.05205			−0.882783			−0.441391	+	0.897315i	$0.645515\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	3.35438			0.474381
$51$		0			0
$52$	−1.19401			−0.165580
$53$		−	9.01579i		−	1.23841i	−0.785228	−	0.619207i	$-0.787454\pi$
$53$		−	9.01579i		−	1.23841i	0.785228	−	0.619207i	$-0.212546\pi$
$54$		0			0
$55$	11.7385			1.58283
$56$	−0.311108	+	0.311108i	−0.0415735	+	0.0415735i
$57$		0			0
$58$	3.20887	+	3.20887i	0.421345	+	0.421345i
$59$			10.0778i			1.31202i	0.754753	+	0.656010i	$0.227757\pi$
$59$			10.0778i			1.31202i	−0.754753	+	0.656010i	$0.772243\pi$
$60$		0			0
$61$	2.48862	+	2.48862i	0.318635	+	0.318635i	0.848243	−	0.529608i	$-0.177661\pi$
$61$	2.48862	+	2.48862i	0.318635	+	0.318635i	−0.529608	+	0.848243i	$0.677661\pi$
$62$	−8.06759	−	8.06759i	−1.02458	−	1.02458i
$63$		0			0
$64$	9.61285			1.20161
$65$	−0.982066	+	0.982066i	−0.121810	+	0.121810i
$66$		0			0
$67$	−2.85449			−0.348731			−0.174366	−	0.984681i	$-0.555787\pi$
$67$	−2.85449			−0.348731			−0.174366	+	0.984681i	$0.555787\pi$
$68$	−2.73989	+	8.70905i	−0.332261	+	1.05613i
$69$		0			0
$70$			5.28751i			0.631978i
$71$	6.24920	−	6.24920i	0.741644	−	0.741644i	−0.231251	−	0.972894i	$-0.574282\pi$
$71$	6.24920	−	6.24920i	0.741644	−	0.741644i	0.972894	+	0.231251i	$0.0742817\pi$
$72$		0			0
$73$	11.2613	−	11.2613i	1.31803	−	1.31803i	0.402696	−	0.915334i	$-0.368073\pi$
$73$	11.2613	−	11.2613i	1.31803	−	1.31803i	0.915334	−	0.402696i	$-0.131927\pi$
$74$	3.50660	+	3.50660i	0.407634	+	0.407634i
$75$		0			0
$76$			5.00632i			0.574264i
$77$			4.55750i			0.519376i
$78$		0			0
$79$	−3.24490	−	3.24490i	−0.365080	−	0.365080i	0.500599	−	0.865679i	$-0.333113\pi$
$79$	−3.24490	−	3.24490i	−0.365080	−	0.365080i	−0.865679	+	0.500599i	$0.833113\pi$
$80$	6.42072	−	6.42072i	0.717859	−	0.717859i
$81$		0			0
$82$	7.77476	−	7.77476i	0.858579	−	0.858579i
$83$			13.0277i			1.42998i	0.699136	+	0.714989i	$0.253568\pi$
$83$			13.0277i			1.42998i	−0.699136	+	0.714989i	$0.746432\pi$
$84$		0			0
$85$	4.90959	+	9.41667i	0.532519	+	1.02138i
$86$	7.05442			0.760697
$87$		0			0
$88$	−1.41788	+	1.41788i	−0.151146	+	0.151146i
$89$	−14.6325			−1.55104			−0.775518	−	0.631325i	$-0.782511\pi$
$89$	−14.6325			−1.55104			−0.775518	+	0.631325i	$0.782511\pi$
$90$		0			0
$91$	−0.381288	−	0.381288i	−0.0399699	−	0.0399699i
$92$	−1.67432	−	1.67432i	−0.174560	−	0.174560i
$93$		0			0
$94$		−	12.4241i		−	1.28145i
$95$	4.11766	+	4.11766i	0.422463	+	0.422463i
$96$		0			0
$97$	5.81211	−	5.81211i	0.590130	−	0.590130i	−0.347536	−	0.937667i	$-0.612982\pi$
$97$	5.81211	−	5.81211i	0.590130	−	0.590130i	0.937667	+	0.347536i	$0.112982\pi$
$98$	−2.05288			−0.207372
$99$		0			0
$100$			3.61817i			0.361817i
$101$	2.58708			0.257424			0.128712	−	0.991682i	$-0.458916\pi$
$101$	2.58708			0.257424			0.128712	+	0.991682i	$0.458916\pi$
$102$		0			0
$103$	−16.7011			−1.64560			−0.822802	−	0.568328i	$-0.807590\pi$
$103$	−16.7011			−1.64560			−0.822802	+	0.568328i	$0.807590\pi$
$104$		−	0.237244i		−	0.0232637i
$105$		0			0
$106$	18.5083			1.79769
$107$	−1.92395	+	1.92395i	−0.185995	+	0.185995i	−0.793962	−	0.607967i	$-0.791985\pi$
$107$	−1.92395	+	1.92395i	−0.185995	+	0.185995i	0.607967	+	0.793962i	$0.291985\pi$
$108$		0			0
$109$	−12.0022	−	12.0022i	−1.14960	−	1.14960i	−0.986632	−	0.162966i	$-0.947894\pi$
$109$	−12.0022	−	12.0022i	−1.14960	−	1.14960i	−0.162966	−	0.986632i	$-0.552106\pi$
$110$			24.0978i			2.29764i
$111$		0			0
$112$	2.49285	+	2.49285i	0.235553	+	0.235553i
$113$	−13.0638	−	13.0638i	−1.22894	−	1.22894i	−0.964366	−	0.264573i	$-0.914769\pi$
$113$	−13.0638	−	13.0638i	−1.22894	−	1.22894i	−0.264573	−	0.964366i	$-0.585231\pi$
$114$		0			0
$115$	−2.75423			−0.256833
$116$	−3.46121	+	3.46121i	−0.321366	+	0.321366i
$117$		0			0
$118$	−20.6885			−1.90453
$119$	−3.65603	+	1.90615i	−0.335148	+	0.174737i
$120$		0			0
$121$			9.77085i			0.888259i
$122$	−5.10884	+	5.10884i	−0.462533	+	0.462533i
$123$		0			0
$124$	8.70202	−	8.70202i	0.781465	−	0.781465i
$125$	−6.13039	−	6.13039i	−0.548319	−	0.548319i
$126$		0			0
$127$			15.9466i			1.41503i	0.706697	+	0.707517i	$0.250185\pi$
$127$			15.9466i			1.41503i	−0.706697	+	0.707517i	$0.749815\pi$
$128$			3.49957i			0.309322i
$129$		0			0
$130$	−2.01607	−	2.01607i	−0.176821	−	0.176821i
$131$	11.7753	−	11.7753i	1.02882	−	1.02882i	0.0292429	−	0.999572i	$-0.490690\pi$
$131$	11.7753	−	11.7753i	1.02882	−	1.02882i	0.999572	−	0.0292429i	$-0.00930963\pi$
$132$		0			0
$133$	−1.59869	+	1.59869i	−0.138624	+	0.138624i
$134$		−	5.85993i		−	0.506221i
$135$		0			0
$136$	−1.73044	−	0.544402i	−0.148384	−	0.0466821i
$137$	−10.3796			−0.886793			−0.443397	−	0.896326i	$-0.646227\pi$
$137$	−10.3796			−0.886793			−0.443397	+	0.896326i	$0.646227\pi$
$138$		0			0
$139$	−7.39360	+	7.39360i	−0.627117	+	0.627117i	−0.947342	−	0.320224i	$-0.896242\pi$
$139$	−7.39360	+	7.39360i	−0.627117	+	0.627117i	0.320224	+	0.947342i	$0.396242\pi$
$140$	−5.70332			−0.482018
$141$		0			0
$142$	12.8289	+	12.8289i	1.07657	+	1.07657i
$143$	−1.73772	−	1.73772i	−0.145316	−	0.145316i
$144$		0			0
$145$			5.69364i			0.472831i
$146$	23.1180	+	23.1180i	1.91326	+	1.91326i
$147$		0			0
$148$	−3.78236	+	3.78236i	−0.310908	+	0.310908i
$149$	20.1878			1.65385			0.826925	−	0.562312i	$-0.190088\pi$
$149$	20.1878			1.65385			0.826925	+	0.562312i	$0.190088\pi$
$150$		0			0
$151$			17.8477i			1.45243i	0.687470	+	0.726213i	$0.258721\pi$
$151$			17.8477i			1.45243i	−0.687470	+	0.726213i	$0.741279\pi$
$152$	−0.994727			−0.0806830
$153$		0			0
$154$	−9.35601			−0.753929
$155$		−	14.3147i		−	1.14978i
$156$		0			0
$157$	−10.2137			−0.815141			−0.407570	−	0.913174i	$-0.633624\pi$
$157$	−10.2137			−0.815141			−0.407570	+	0.913174i	$0.633624\pi$
$158$	6.66139	−	6.66139i	0.529952	−	0.529952i
$159$		0			0
$160$	14.7836	+	14.7836i	1.16875	+	1.16875i
$161$		−	1.06933i		−	0.0842752i
$162$		0			0
$163$	1.28230	+	1.28230i	0.100438	+	0.100438i	0.755540	−	0.655102i	$-0.227375\pi$
$163$	1.28230	+	1.28230i	0.100438	+	0.100438i	−0.655102	+	0.755540i	$0.727375\pi$
$164$	8.38617	+	8.38617i	0.654850	+	0.654850i
$165$		0			0
$166$	−26.7444			−2.07577
$167$	−16.5152	+	16.5152i	−1.27799	+	1.27799i	−0.336193	+	0.941793i	$0.609140\pi$
$167$	−16.5152	+	16.5152i	−1.27799	+	1.27799i	−0.941793	+	0.336193i	$0.890860\pi$
$168$		0			0
$169$	−12.7092			−0.977634
$170$	−19.3313	+	10.0788i	−1.48264	+	0.773008i
$171$		0			0
$172$			7.60918i			0.580194i
$173$	−6.24574	+	6.24574i	−0.474855	+	0.474855i	−0.903482	−	0.428627i	$-0.858998\pi$
$173$	−6.24574	+	6.24574i	−0.474855	+	0.474855i	0.428627	+	0.903482i	$0.358998\pi$
$174$		0			0
$175$	−1.15540	+	1.15540i	−0.0873402	+	0.0873402i
$176$	11.3612	+	11.3612i	0.856382	+	0.856382i
$177$		0			0
$178$		−	30.0387i		−	2.25149i
$179$		−	21.0211i		−	1.57119i	−0.618739	−	0.785597i	$-0.712356\pi$
$179$		−	21.0211i		−	1.57119i	0.618739	−	0.785597i	$-0.287644\pi$
$180$		0			0
$181$	−3.54410	−	3.54410i	−0.263431	−	0.263431i	0.563016	−	0.826446i	$-0.309641\pi$
$181$	−3.54410	−	3.54410i	−0.263431	−	0.263431i	−0.826446	+	0.563016i	$0.809641\pi$
$182$	0.782740	−	0.782740i	0.0580205	−	0.0580205i
$183$		0			0
$184$	0.332678	−	0.332678i	0.0245253	−	0.0245253i
$185$			6.22193i			0.457445i
$186$		0			0
$187$	−16.6624	+	8.68730i	−1.21847	+	0.635278i
$188$	13.4012			0.977382
$189$		0			0
$190$	−8.45306	+	8.45306i	−0.613250	+	0.613250i
$191$	16.7581			1.21258			0.606288	−	0.795245i	$-0.292658\pi$
$191$	16.7581			1.21258			0.606288	+	0.795245i	$0.292658\pi$
$192$		0			0
$193$	−10.7687	−	10.7687i	−0.775148	−	0.775148i	0.203854	−	0.979001i	$-0.434653\pi$
$193$	−10.7687	−	10.7687i	−0.775148	−	0.775148i	−0.979001	+	0.203854i	$0.934653\pi$
$194$	11.9316	+	11.9316i	0.856637	+	0.856637i
$195$		0			0
$196$		−	2.21432i		−	0.158166i
$197$	−7.10404	−	7.10404i	−0.506142	−	0.506142i	0.407198	−	0.913340i	$-0.366506\pi$
$197$	−7.10404	−	7.10404i	−0.506142	−	0.506142i	−0.913340	+	0.407198i	$0.866506\pi$
$198$		0			0
$199$	0.270684	−	0.270684i	0.0191883	−	0.0191883i	−0.697448	−	0.716636i	$-0.745681\pi$
$199$	0.270684	−	0.270684i	0.0191883	−	0.0191883i	0.716636	+	0.697448i	$0.245681\pi$
$200$	−0.718909			−0.0508346
$201$		0			0
$202$			5.31097i			0.373678i
$203$	−2.21056			−0.155151
$204$		0			0
$205$	13.7951			0.963494
$206$		−	34.2853i		−	2.38877i
$207$		0			0
$208$	−1.90099			−0.131810
$209$	−7.28602	+	7.28602i	−0.503984	+	0.503984i
$210$		0			0
$211$	−17.2365	−	17.2365i	−1.18661	−	1.18661i	−0.977999	−	0.208608i	$-0.933107\pi$
$211$	−17.2365	−	17.2365i	−1.18661	−	1.18661i	−0.208608	−	0.977999i	$-0.566893\pi$
$212$			19.9638i			1.37112i
$213$		0			0
$214$	−3.94964	−	3.94964i	−0.269992	−	0.269992i
$215$	6.25849	+	6.25849i	0.426826	+	0.426826i
$216$		0			0
$217$	5.55770			0.377281
$218$	24.6390	−	24.6390i	1.66876	−	1.66876i
$219$		0			0
$220$	−25.9929			−1.75244
$221$	0.667209	−	2.12080i	0.0448814	−	0.142660i
$222$		0			0
$223$			6.40836i			0.429135i	0.976709	+	0.214568i	$0.0688343\pi$
$223$			6.40836i			0.429135i	−0.976709	+	0.214568i	$0.931166\pi$
$224$	−5.73975	+	5.73975i	−0.383503	+	0.383503i
$225$		0			0
$226$	26.8184	−	26.8184i	1.78393	−	1.78393i
$227$	4.39397	+	4.39397i	0.291638	+	0.291638i	0.837727	−	0.546089i	$-0.183884\pi$
$227$	4.39397	+	4.39397i	0.291638	+	0.291638i	−0.546089	+	0.837727i	$0.683884\pi$
$228$		0			0
$229$			14.9779i			0.989769i	0.868959	+	0.494884i	$0.164790\pi$
$229$			14.9779i			0.989769i	−0.868959	+	0.494884i	$0.835210\pi$
$230$		−	5.65410i		−	0.372821i
$231$		0			0
$232$	−0.687724	−	0.687724i	−0.0451513	−	0.0451513i
$233$	3.74165	−	3.74165i	0.245124	−	0.245124i	−0.573842	−	0.818966i	$-0.694548\pi$
$233$	3.74165	−	3.74165i	0.245124	−	0.245124i	0.818966	+	0.573842i	$0.194548\pi$
$234$		0			0
$235$	11.0224	−	11.0224i	0.719020	−	0.719020i
$236$		−	22.3155i		−	1.45261i
$237$		0			0
$238$	−3.91310	−	7.50540i	−0.253649	−	0.486503i
$239$	22.9361			1.48361			0.741806	−	0.670615i	$-0.233970\pi$
$239$	22.9361			1.48361			0.741806	+	0.670615i	$0.233970\pi$
$240$		0			0
$241$	−6.68903	+	6.68903i	−0.430878	+	0.430878i	−0.888927	−	0.458049i	$-0.848548\pi$
$241$	−6.68903	+	6.68903i	−0.430878	+	0.430878i	0.458049	+	0.888927i	$0.348548\pi$
$242$	−20.0584			−1.28940
$243$		0			0
$244$	−5.51060	−	5.51060i	−0.352780	−	0.352780i
$245$	−1.82126	−	1.82126i	−0.116356	−	0.116356i
$246$		0			0
$247$		−	1.21912i		−	0.0775708i
$248$	1.72904	+	1.72904i	0.109794	+	0.109794i
$249$		0			0
$250$	12.5850	−	12.5850i	0.795943	−	0.795943i
$251$	−19.2612			−1.21576			−0.607879	−	0.794030i	$-0.707980\pi$
$251$	−19.2612			−1.21576			−0.607879	+	0.794030i	$0.707980\pi$
$252$		0			0
$253$		−	4.87349i		−	0.306394i
$254$	−32.7365			−2.05407
$255$		0			0
$256$	12.0415			0.752593
$257$		−	4.69415i		−	0.292813i	−0.989225	−	0.146407i	$-0.953229\pi$
$257$		−	4.69415i		−	0.292813i	0.989225	−	0.146407i	$-0.0467708\pi$
$258$		0			0
$259$	−2.41567			−0.150102
$260$	2.17461	−	2.17461i	0.134864	−	0.134864i
$261$		0			0
$262$	24.1733	+	24.1733i	1.49343	+	1.49343i
$263$		−	3.18952i		−	0.196674i	−0.995153	−	0.0983371i	$-0.968648\pi$
$263$		−	3.18952i		−	0.196674i	0.995153	−	0.0983371i	$-0.0313523\pi$
$264$		0			0
$265$	16.4201	+	16.4201i	1.00868	+	1.00868i
$266$	−3.28191	−	3.28191i	−0.201227	−	0.201227i
$267$		0			0
$268$	6.32075			0.386101
$269$	−18.5439	+	18.5439i	−1.13064	+	1.13064i	−0.140569	+	0.990071i	$0.544893\pi$
$269$	−18.5439	+	18.5439i	−1.13064	+	1.13064i	−0.990071	+	0.140569i	$0.955107\pi$
$270$		0			0
$271$	−2.97043			−0.180441			−0.0902203	−	0.995922i	$-0.528757\pi$
$271$	−2.97043			−0.180441			−0.0902203	+	0.995922i	$0.528757\pi$
$272$	−4.36220	+	13.8657i	−0.264497	+	0.840733i
$273$		0			0
$274$		−	21.3082i		−	1.28727i
$275$	−5.26575	+	5.26575i	−0.317537	+	0.317537i
$276$		0			0
$277$	19.7005	−	19.7005i	1.18369	−	1.18369i	0.204908	−	0.978781i	$-0.434310\pi$
$277$	19.7005	−	19.7005i	1.18369	−	1.18369i	0.978781	−	0.204908i	$-0.0656897\pi$
$278$	−15.1782	−	15.1782i	−0.910327	−	0.910327i
$279$		0			0
$280$		−	1.13322i		−	0.0677227i
$281$		−	26.5597i		−	1.58442i	−0.610248	−	0.792210i	$-0.708930\pi$
$281$		−	26.5597i		−	1.58442i	0.610248	−	0.792210i	$-0.291070\pi$
$282$		0			0
$283$	−8.95508	−	8.95508i	−0.532324	−	0.532324i	0.388939	−	0.921263i	$-0.372842\pi$
$283$	−8.95508	−	8.95508i	−0.532324	−	0.532324i	−0.921263	+	0.388939i	$0.872842\pi$
$284$	−13.8377	+	13.8377i	−0.821118	+	0.821118i
$285$		0			0
$286$	3.56734	−	3.56734i	0.210941	−	0.210941i
$287$			5.35597i			0.316153i
$288$		0			0
$289$	−13.9379	−	9.73317i	−0.819877	−	0.572539i
$290$	−11.6884			−0.686365
$291$		0			0
$292$	−24.9360	+	24.9360i	−1.45927	+	1.45927i
$293$	17.6451			1.03084			0.515420	−	0.856938i	$-0.327636\pi$
$293$	17.6451			1.03084			0.515420	+	0.856938i	$0.327636\pi$
$294$		0			0
$295$	−18.3543	−	18.3543i	−1.06863	−	1.06863i
$296$	−0.751534	−	0.751534i	−0.0436820	−	0.0436820i
$297$		0			0
$298$			41.4432i			2.40074i
$299$	0.407724	+	0.407724i	0.0235793	+	0.0235793i
$300$		0			0
$301$	−2.42987	+	2.42987i	−0.140055	+	0.140055i
$302$	−36.6392			−2.10835
$303$		0			0
$304$			7.97058i			0.457144i
$305$	−9.06485			−0.519052
$306$		0			0
$307$	−6.55463			−0.374093			−0.187046	−	0.982351i	$-0.559891\pi$
$307$	−6.55463			−0.374093			−0.187046	+	0.982351i	$0.559891\pi$
$308$		−	10.0918i		−	0.575032i
$309$		0			0
$310$	29.3864			1.66903
$311$	−5.46506	+	5.46506i	−0.309895	+	0.309895i	−0.844869	−	0.534974i	$-0.820321\pi$
$311$	−5.46506	+	5.46506i	−0.309895	+	0.309895i	0.534974	+	0.844869i	$0.320321\pi$
$312$		0			0
$313$	−2.69576	−	2.69576i	−0.152373	−	0.152373i	0.626804	−	0.779177i	$-0.284363\pi$
$313$	−2.69576	−	2.69576i	−0.152373	−	0.152373i	−0.779177	+	0.626804i	$0.784363\pi$
$314$		−	20.9675i		−	1.18326i
$315$		0			0
$316$	7.18524	+	7.18524i	0.404201	+	0.404201i
$317$	−1.27004	−	1.27004i	−0.0713323	−	0.0713323i	0.670541	−	0.741873i	$-0.266062\pi$
$317$	−1.27004	−	1.27004i	−0.0713323	−	0.0713323i	−0.741873	+	0.670541i	$0.766062\pi$
$318$		0			0
$319$	−10.0747			−0.564072
$320$	−17.5075	+	17.5075i	−0.978699	+	0.978699i
$321$		0			0
$322$	2.19521			0.122334
$323$	−8.89219	−	2.79751i	−0.494775	−	0.155658i
$324$		0			0
$325$		−	0.881083i		−	0.0488737i
$326$	−2.63241	+	2.63241i	−0.145796	+	0.145796i
$327$		0			0
$328$	−1.66629	+	1.66629i	−0.0920052	+	0.0920052i
$329$	4.27945	+	4.27945i	0.235934	+	0.235934i
$330$		0			0
$331$			9.11987i			0.501274i	0.968081	+	0.250637i	$0.0806400\pi$
$331$			9.11987i			0.501274i	−0.968081	+	0.250637i	$0.919360\pi$
$332$		−	28.8475i		−	1.58321i
$333$		0			0
$334$	−33.9038	−	33.9038i	−1.85513	−	1.85513i
$335$	5.19877	−	5.19877i	0.284039	−	0.284039i
$336$		0			0
$337$	−15.9634	+	15.9634i	−0.869583	+	0.869583i	−0.992426	−	0.122844i	$-0.960799\pi$
$337$	−15.9634	+	15.9634i	−0.869583	+	0.869583i	0.122844	+	0.992426i	$0.460799\pi$
$338$		−	26.0906i		−	1.41914i
$339$		0			0
$340$	−10.8714	−	20.8515i	−0.589584	−	1.13083i
$341$	25.3292			1.37165
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−1.51190			−0.0815162
$345$		0			0
$346$	−12.8218	−	12.8218i	−0.689302	−	0.689302i
$347$	16.4962	+	16.4962i	0.885560	+	0.885560i	0.994093	−	0.108533i	$-0.0346153\pi$
$347$	16.4962	+	16.4962i	0.885560	+	0.885560i	−0.108533	+	0.994093i	$0.534615\pi$
$348$		0			0
$349$		−	5.31582i		−	0.284549i	−0.989827	−	0.142275i	$-0.954558\pi$
$349$		−	5.31582i		−	0.284549i	0.989827	−	0.142275i	$-0.0454416\pi$
$350$	−2.37190	−	2.37190i	−0.126784	−	0.126784i
$351$		0			0
$352$	−26.1589	+	26.1589i	−1.39428	+	1.39428i
$353$	−20.6211			−1.09755			−0.548774	−	0.835971i	$-0.684905\pi$
$353$	−20.6211			−1.09755			−0.548774	+	0.835971i	$0.684905\pi$
$354$		0			0
$355$			22.7629i			1.20813i
$356$	32.4009			1.71725
$357$		0			0
$358$	43.1539			2.28075
$359$			35.8317i			1.89113i	0.325439	+	0.945563i	$0.394488\pi$
$359$			35.8317i			1.89113i	−0.325439	+	0.945563i	$0.605512\pi$
$360$		0			0
$361$	13.8884			0.730969
$362$	7.27561	−	7.27561i	0.382398	−	0.382398i
$363$		0			0
$364$	0.844294	+	0.844294i	0.0442531	+	0.0442531i
$365$			41.0194i			2.14705i
$366$		0			0
$367$	−9.14781	−	9.14781i	−0.477512	−	0.477512i	0.426823	−	0.904335i	$-0.359633\pi$
$367$	−9.14781	−	9.14781i	−0.477512	−	0.477512i	−0.904335	+	0.426823i	$0.859633\pi$
$368$	−2.66569	−	2.66569i	−0.138959	−	0.138959i
$369$		0			0
$370$	−12.7729			−0.664030
$371$	−6.37512	+	6.37512i	−0.330980	+	0.330980i
$372$		0			0
$373$	8.38663			0.434243			0.217122	−	0.976145i	$-0.430333\pi$
$373$	8.38663			0.434243			0.217122	+	0.976145i	$0.430333\pi$
$374$	−17.8340	−	34.2059i	−0.922174	−	1.76875i
$375$		0			0
$376$			2.66274i			0.137320i
$377$	0.842862	−	0.842862i	0.0434096	−	0.0434096i
$378$		0			0
$379$	23.0850	−	23.0850i	1.18580	−	1.18580i	0.207576	−	0.978219i	$-0.433443\pi$
$379$	23.0850	−	23.0850i	1.18580	−	1.18580i	0.978219	−	0.207576i	$-0.0665575\pi$
$380$	−9.11781	−	9.11781i	−0.467734	−	0.467734i
$381$		0			0
$382$			34.4024i			1.76018i
$383$		−	23.0029i		−	1.17539i	−0.809082	−	0.587696i	$-0.800035\pi$
$383$		−	23.0029i		−	1.17539i	0.809082	−	0.587696i	$-0.199965\pi$
$384$		0			0
$385$	−8.30041	−	8.30041i	−0.423028	−	0.423028i
$386$	22.1069	−	22.1069i	1.12521	−	1.12521i
$387$		0			0
$388$	−12.8699	+	12.8699i	−0.653369	+	0.653369i
$389$		−	0.283025i		−	0.0143499i	−0.999974	−	0.00717496i	$-0.997716\pi$
$389$		−	0.283025i		−	0.0143499i	0.999974	−	0.00717496i	$-0.00228388\pi$
$390$		0			0
$391$	3.90952	−	2.03831i	0.197713	−	0.103082i
$392$	0.439973			0.0222220
$393$		0			0
$394$	14.5838	−	14.5838i	0.734719	−	0.734719i
$395$	11.8196			0.594709
$396$		0			0
$397$	21.5366	+	21.5366i	1.08089	+	1.08089i	0.996427	+	0.0844626i	$0.0269174\pi$
$397$	21.5366	+	21.5366i	1.08089	+	1.08089i	0.0844626	+	0.996427i	$0.473083\pi$
$398$	0.555682	+	0.555682i	0.0278538	+	0.0278538i
$399$		0			0
$400$			5.76050i			0.288025i
$401$	−10.1299	−	10.1299i	−0.505865	−	0.505865i	0.407390	−	0.913254i	$-0.366439\pi$
$401$	−10.1299	−	10.1299i	−0.505865	−	0.505865i	−0.913254	+	0.407390i	$0.866439\pi$
$402$		0			0
$403$	−2.11909	+	2.11909i	−0.105559	+	0.105559i
$404$	−5.72862			−0.285010
$405$		0			0
$406$		−	4.53802i		−	0.225218i
$407$	−11.0094			−0.545717
$408$		0			0
$409$	9.48809			0.469156			0.234578	−	0.972097i	$-0.424629\pi$
$409$	9.48809			0.469156			0.234578	+	0.972097i	$0.424629\pi$
$410$			28.3198i			1.39861i
$411$		0			0
$412$	36.9815			1.82195
$413$	7.12609	−	7.12609i	0.350652	−	0.350652i
$414$		0			0
$415$	−23.7269	−	23.7269i	−1.16471	−	1.16471i
$416$		−	4.37700i		−	0.214600i
$417$		0			0
$418$	−14.9573	−	14.9573i	−0.731587	−	0.731587i
$419$	−0.551638	−	0.551638i	−0.0269493	−	0.0269493i	0.693504	−	0.720453i	$-0.256066\pi$
$419$	−0.551638	−	0.551638i	−0.0269493	−	0.0269493i	−0.720453	+	0.693504i	$0.756066\pi$
$420$		0			0
$421$	13.9668			0.680699			0.340349	−	0.940299i	$-0.389455\pi$
$421$	13.9668			0.680699			0.340349	+	0.940299i	$0.389455\pi$
$422$	35.3844	−	35.3844i	1.72249	−	1.72249i
$423$		0			0
$424$	−3.96670			−0.192640
$425$	−6.42656	−	2.02182i	−0.311734	−	0.0980725i
$426$		0			0
$427$		−	3.51944i		−	0.170318i
$428$	4.26024	−	4.26024i	0.205926	−	0.205926i
$429$		0			0
$430$	−12.8479	+	12.8479i	−0.619583	+	0.619583i
$431$	4.52293	+	4.52293i	0.217862	+	0.217862i	0.807597	−	0.589735i	$-0.200768\pi$
$431$	4.52293	+	4.52293i	0.217862	+	0.217862i	−0.589735	+	0.807597i	$0.700768\pi$
$432$		0			0
$433$			12.9303i			0.621391i	0.950509	+	0.310696i	$0.100562\pi$
$433$			12.9303i			0.621391i	−0.950509	+	0.310696i	$0.899438\pi$
$434$			11.4093i			0.547664i
$435$		0			0
$436$	26.5766	+	26.5766i	1.27279	+	1.27279i
$437$	1.70953	−	1.70953i	0.0817777	−	0.0817777i
$438$		0			0
$439$	−1.87405	+	1.87405i	−0.0894433	+	0.0894433i	−0.750413	−	0.660969i	$-0.770145\pi$
$439$	−1.87405	+	1.87405i	−0.0894433	+	0.0894433i	0.660969	+	0.750413i	$0.270145\pi$
$440$		−	5.16464i		−	0.246215i
$441$		0			0
$442$	4.35374	+	1.36970i	0.207086	+	0.0651501i
$443$	20.2018			0.959816			0.479908	−	0.877319i	$-0.340670\pi$
$443$	20.2018			0.959816			0.479908	+	0.877319i	$0.340670\pi$
$444$		0			0
$445$	26.6495	−	26.6495i	1.26331	−	1.26331i
$446$	−13.1556			−0.622936
$447$		0			0
$448$	−6.79731	−	6.79731i	−0.321143	−	0.321143i
$449$	9.43365	+	9.43365i	0.445201	+	0.445201i	0.893756	−	0.448554i	$-0.148061\pi$
$449$	9.43365	+	9.43365i	0.445201	+	0.445201i	−0.448554	+	0.893756i	$0.648061\pi$
$450$		0			0
$451$			24.4099i			1.14942i
$452$	28.9274	+	28.9274i	1.36063	+	1.36063i
$453$		0			0
$454$	−9.02030	+	9.02030i	−0.423343	+	0.423343i
$455$	1.38885			0.0651104
$456$		0			0
$457$			22.9549i			1.07379i	0.843650	+	0.536893i	$0.180402\pi$
$457$			22.9549i			1.07379i	−0.843650	+	0.536893i	$0.819598\pi$
$458$	−30.7479			−1.43675
$459$		0			0
$460$	6.09874			0.284355
$461$			35.5073i			1.65374i	0.562393	+	0.826870i	$0.309881\pi$
$461$			35.5073i			1.65374i	−0.562393	+	0.826870i	$0.690119\pi$
$462$		0			0
$463$	−30.0184			−1.39507			−0.697537	−	0.716549i	$-0.745721\pi$
$463$	−30.0184			−1.39507			−0.697537	+	0.716549i	$0.745721\pi$
$464$	−5.51061	+	5.51061i	−0.255824	+	0.255824i
$465$		0			0
$466$	7.68116	+	7.68116i	0.355823	+	0.355823i
$467$		−	4.26657i		−	0.197433i	−0.995116	−	0.0987166i	$-0.968526\pi$
$467$		−	4.26657i		−	0.197433i	0.995116	−	0.0987166i	$-0.0314737\pi$
$468$		0			0
$469$	2.01843	+	2.01843i	0.0932024	+	0.0932024i
$470$	22.6276	+	22.6276i	1.04373	+	1.04373i
$471$		0			0
$472$	4.43396			0.204090
$473$	−11.0741	+	11.0741i	−0.509189	+	0.509189i
$474$		0			0
$475$	−3.69425			−0.169504
$476$	8.09563	−	4.22083i	0.371062	−	0.193461i
$477$		0			0
$478$			47.0850i			2.15362i
$479$	−0.296251	+	0.296251i	−0.0135361	+	0.0135361i	−0.713842	−	0.700306i	$-0.753047\pi$
$479$	−0.296251	+	0.296251i	−0.0135361	+	0.0135361i	0.700306	+	0.713842i	$0.253047\pi$
$480$		0			0
$481$	0.921067	−	0.921067i	0.0419970	−	0.0419970i
$482$	−13.7318	−	13.7318i	−0.625465	−	0.625465i
$483$		0			0
$484$		−	21.6358i		−	0.983445i
$485$			21.1707i			0.961314i
$486$		0			0
$487$	−0.629731	−	0.629731i	−0.0285358	−	0.0285358i	0.692695	−	0.721231i	$-0.256423\pi$
$487$	−0.629731	−	0.629731i	−0.0285358	−	0.0285358i	−0.721231	+	0.692695i	$0.756423\pi$
$488$	1.09493	−	1.09493i	0.0495649	−	0.0495649i
$489$		0			0
$490$	3.73883	−	3.73883i	0.168903	−	0.168903i
$491$			23.1490i			1.04470i	0.852732	+	0.522349i	$0.174944\pi$
$491$			23.1490i			1.04470i	−0.852732	+	0.522349i	$0.825056\pi$
$492$		0			0
$493$	−4.21367	−	8.08190i	−0.189774	−	0.363990i
$494$	2.50271			0.112602
$495$		0			0
$496$	13.8545	−	13.8545i	0.622087	−	0.622087i
$497$	−8.83770			−0.396425
$498$		0			0
$499$	20.2633	+	20.2633i	0.907112	+	0.907112i	0.996038	−	0.0889262i	$-0.0283435\pi$
$499$	20.2633	+	20.2633i	0.907112	+	0.907112i	−0.0889262	+	0.996038i	$0.528344\pi$
$500$	13.5746	+	13.5746i	0.607077	+	0.607077i
$501$		0			0
$502$		−	39.5410i		−	1.76480i
$503$	3.25021	+	3.25021i	0.144920	+	0.144920i	0.775844	−	0.630925i	$-0.217324\pi$
$503$	3.25021	+	3.25021i	0.144920	+	0.144920i	−0.630925	+	0.775844i	$0.717324\pi$
$504$		0			0
$505$	−4.71175	+	4.71175i	−0.209670	+	0.209670i
$506$	10.0047			0.444763
$507$		0			0
$508$		−	35.3109i		−	1.56667i
$509$	26.6430			1.18093			0.590465	−	0.807064i	$-0.298945\pi$
$509$	26.6430			1.18093			0.590465	+	0.807064i	$0.298945\pi$
$510$		0			0
$511$	−15.9258			−0.704517
$512$			31.7189i			1.40179i
$513$		0			0
$514$	9.63653			0.425049
$515$	30.4170	−	30.4170i	1.34033	−	1.34033i
$516$		0			0
$517$	19.5036	+	19.5036i	0.857768	+	0.857768i
$518$		−	4.95908i		−	0.217890i
$519$		0			0
$520$	0.432083	+	0.432083i	0.0189481	+	0.0189481i
$521$	24.4774	+	24.4774i	1.07237	+	1.07237i	0.997168	+	0.0752065i	$0.0239616\pi$
$521$	24.4774	+	24.4774i	1.07237	+	1.07237i	0.0752065	+	0.997168i	$0.476038\pi$
$522$		0			0
$523$	32.1612			1.40631			0.703156	−	0.711035i	$-0.251773\pi$
$523$	32.1612			1.40631			0.703156	+	0.711035i	$0.251773\pi$
$524$	−26.0743	+	26.0743i	−1.13906	+	1.13906i
$525$		0			0
$526$	6.54770			0.285493
$527$	10.5938	+	20.3191i	0.461474	+	0.885115i
$528$		0			0
$529$		−	21.8565i		−	0.950284i
$530$	−33.7085	+	33.7085i	−1.46420	+	1.46420i
$531$		0			0
$532$	3.54000	−	3.54000i	0.153479	−	0.153479i
$533$	−2.04217	−	2.04217i	−0.0884563	−	0.0884563i
$534$		0			0
$535$		−	7.00803i		−	0.302983i
$536$			1.25590i			0.0542465i
$537$		0			0
$538$	−38.0684	−	38.0684i	−1.64124	−	1.64124i
$539$	3.22264	−	3.22264i	0.138809	−	0.138809i
$540$		0			0
$541$	5.29064	−	5.29064i	0.227462	−	0.227462i	−0.584169	−	0.811632i	$-0.698580\pi$
$541$	5.29064	−	5.29064i	0.227462	−	0.227462i	0.811632	+	0.584169i	$0.198580\pi$
$542$		−	6.09793i		−	0.261929i
$543$		0			0
$544$	−31.9255	−	10.0439i	−1.36880	−	0.430628i
$545$	43.7181			1.87268
$546$		0			0
$547$	−12.1811	+	12.1811i	−0.520824	+	0.520824i	−0.917820	−	0.396996i	$-0.870053\pi$
$547$	−12.1811	+	12.1811i	−0.520824	+	0.520824i	0.396996	+	0.917820i	$0.370053\pi$
$548$	22.9839			0.981822
$549$		0			0
$550$	−10.8100	−	10.8100i	−0.460938	−	0.460938i
$551$	−3.53400	−	3.53400i	−0.150553	−	0.150553i
$552$		0			0
$553$			4.58898i			0.195143i
$554$	40.4428	+	40.4428i	1.71825	+	1.71825i
$555$		0			0
$556$	16.3718	−	16.3718i	0.694319	−	0.694319i
$557$	29.4028			1.24584			0.622918	−	0.782287i	$-0.285947\pi$
$557$	29.4028			1.24584			0.622918	+	0.782287i	$0.285947\pi$
$558$		0			0
$559$		−	1.85296i		−	0.0783719i
$560$	−9.08028			−0.383712
$561$		0			0
$562$	54.5240			2.29995
$563$			24.3440i			1.02598i	0.858395	+	0.512989i	$0.171462\pi$
$563$			24.3440i			1.02598i	−0.858395	+	0.512989i	$0.828538\pi$
$564$		0			0
$565$	47.5852			2.00192
$566$	18.3837	−	18.3837i	0.772725	−	0.772725i
$567$		0			0
$568$	−2.74948	−	2.74948i	−0.115366	−	0.115366i
$569$		−	41.0990i		−	1.72296i	−0.507791	−	0.861480i	$-0.669538\pi$
$569$		−	41.0990i		−	1.72296i	0.507791	−	0.861480i	$-0.330462\pi$
$570$		0			0
$571$	−10.1458	−	10.1458i	−0.424587	−	0.424587i	0.462193	−	0.886779i	$-0.347063\pi$
$571$	−10.1458	−	10.1458i	−0.424587	−	0.424587i	−0.886779	+	0.462193i	$0.847063\pi$
$572$	3.84788	+	3.84788i	0.160888	+	0.160888i
$573$		0			0
$574$	−10.9952			−0.458930
$575$	1.23551	−	1.23551i	0.0515243	−	0.0515243i
$576$		0			0
$577$	−21.7259			−0.904463			−0.452231	−	0.891901i	$-0.649372\pi$
$577$	−21.7259			−0.904463			−0.452231	+	0.891901i	$0.649372\pi$
$578$	19.9810	−	28.6129i	0.831101	−	1.19014i
$579$		0			0
$580$		−	12.6075i		−	0.523500i
$581$	9.21199	−	9.21199i	0.382178	−	0.382178i
$582$		0			0
$583$	−29.0547	+	29.0547i	−1.20332	+	1.20332i
$584$	−4.95465	−	4.95465i	−0.205025	−	0.205025i
$585$		0			0
$586$			36.2234i			1.49637i
$587$			28.7001i			1.18458i	0.805725	+	0.592290i	$0.201776\pi$
$587$			28.7001i			1.18458i	−0.805725	+	0.592290i	$0.798224\pi$
$588$		0			0
$589$	8.88501	+	8.88501i	0.366101	+	0.366101i
$590$	37.6792	−	37.6792i	1.55123	−	1.55123i
$591$		0			0
$592$	−6.02191	+	6.02191i	−0.247499	+	0.247499i
$593$		−	2.82738i		−	0.116106i	−0.998313	−	0.0580532i	$-0.981511\pi$
$593$		−	2.82738i		−	0.116106i	0.998313	−	0.0580532i	$-0.0184893\pi$
$594$		0			0
$595$	3.18699	−	10.1302i	0.130654	−	0.415297i
$596$	−44.7023			−1.83108
$597$		0			0
$598$	−0.837009	+	0.837009i	−0.0342278	+	0.0342278i
$599$	−9.17083			−0.374710			−0.187355	−	0.982292i	$-0.559991\pi$
$599$	−9.17083			−0.374710			−0.187355	+	0.982292i	$0.559991\pi$
$600$		0			0
$601$	−1.59740	−	1.59740i	−0.0651594	−	0.0651594i	0.673776	−	0.738936i	$-0.264671\pi$
$601$	−1.59740	−	1.59740i	−0.0651594	−	0.0651594i	−0.738936	+	0.673776i	$0.764671\pi$
$602$	−4.98823	−	4.98823i	−0.203305	−	0.203305i
$603$		0			0
$604$		−	39.5205i		−	1.60807i
$605$	−17.7953	−	17.7953i	−0.723480	−	0.723480i
$606$		0			0
$607$	22.9865	−	22.9865i	0.932993	−	0.932993i	−0.0648988	−	0.997892i	$-0.520672\pi$
$607$	22.9865	−	22.9865i	0.932993	−	0.932993i	0.997892	+	0.0648988i	$0.0206725\pi$
$608$	−18.3521			−0.744276
$609$		0			0
$610$		−	18.6091i		−	0.753459i
$611$	−3.26341			−0.132023
$612$		0			0
$613$	−9.89012			−0.399458			−0.199729	−	0.979851i	$-0.564006\pi$
$613$	−9.89012			−0.399458			−0.199729	+	0.979851i	$0.564006\pi$
$614$		−	13.4559i		−	0.543035i
$615$		0			0
$616$	2.00518			0.0807909
$617$	−31.8166	+	31.8166i	−1.28089	+	1.28089i	−0.340724	+	0.940163i	$0.610672\pi$
$617$	−31.8166	+	31.8166i	−1.28089	+	1.28089i	−0.940163	+	0.340724i	$0.889328\pi$
$618$		0			0
$619$	7.95464	+	7.95464i	0.319724	+	0.319724i	0.848661	−	0.528937i	$-0.177409\pi$
$619$	7.95464	+	7.95464i	0.319724	+	0.319724i	−0.528937	+	0.848661i	$0.677409\pi$
$620$			31.6973i			1.27300i
$621$		0			0
$622$	−11.2191	−	11.2191i	−0.449845	−	0.449845i
$623$	10.3467	+	10.3467i	0.414532	+	0.414532i
$624$		0			0
$625$	30.5000			1.22000
$626$	5.53407	−	5.53407i	0.221186	−	0.221186i
$627$		0			0
$628$	22.6164			0.902491
$629$	−4.60464	−	8.83177i	−0.183599	−	0.352146i
$630$		0			0
$631$		−	9.50420i		−	0.378356i	−0.981943	−	0.189178i	$-0.939418\pi$
$631$		−	9.50420i		−	0.378356i	0.981943	−	0.189178i	$-0.0605824\pi$
$632$	−1.42767	+	1.42767i	−0.0567895	+	0.0567895i
$633$		0			0
$634$	2.60723	−	2.60723i	0.103546	−	0.103546i
$635$	−29.0430	−	29.0430i	−1.15253	−	1.15253i
$636$		0			0
$637$			0.539223i			0.0213648i
$638$		−	20.6821i		−	0.818811i
$639$		0			0
$640$	−6.37364	−	6.37364i	−0.251940	−	0.251940i
$641$	15.5408	−	15.5408i	0.613823	−	0.613823i	−0.330117	−	0.943940i	$-0.607088\pi$
$641$	15.5408	−	15.5408i	0.613823	−	0.613823i	0.943940	+	0.330117i	$0.107088\pi$
$642$		0			0
$643$	10.0223	−	10.0223i	0.395239	−	0.395239i	−0.481311	−	0.876550i	$-0.659839\pi$
$643$	10.0223	−	10.0223i	0.395239	−	0.395239i	0.876550	+	0.481311i	$0.159839\pi$
$644$			2.36784i			0.0933061i
$645$		0			0
$646$	5.74295	−	18.2546i	0.225954	−	0.718218i
$647$	5.70580			0.224318			0.112159	−	0.993690i	$-0.464223\pi$
$647$	5.70580			0.224318			0.112159	+	0.993690i	$0.464223\pi$
$648$		0			0
$649$	32.4772	−	32.4772i	1.27484	−	1.27484i
$650$	1.80876			0.0709453
$651$		0			0
$652$	−2.83943	−	2.83943i	−0.111201	−	0.111201i
$653$	−21.3215	−	21.3215i	−0.834377	−	0.834377i	0.153735	−	0.988112i	$-0.450870\pi$
$653$	−21.3215	−	21.3215i	−0.834377	−	0.834377i	−0.988112	+	0.153735i	$0.950870\pi$
$654$		0			0
$655$			42.8919i			1.67593i
$656$	13.3517	+	13.3517i	0.521295	+	0.521295i
$657$		0			0
$658$	−8.78520	+	8.78520i	−0.342483	+	0.342483i
$659$	−35.6173			−1.38745			−0.693726	−	0.720239i	$-0.744032\pi$
$659$	−35.6173			−1.38745			−0.693726	+	0.720239i	$0.744032\pi$
$660$		0			0
$661$			8.04663i			0.312977i	0.987680	+	0.156489i	$0.0500175\pi$
$661$			8.04663i			0.312977i	−0.987680	+	0.156489i	$0.949983\pi$
$662$	−18.7220			−0.727652
$663$		0			0
$664$	5.73184			0.222439
$665$		−	5.82325i		−	0.225816i
$666$		0			0
$667$	2.36383			0.0915278
$668$	36.5700	−	36.5700i	1.41494	−	1.41494i
$669$		0			0
$670$	10.6725	+	10.6725i	0.412313	+	0.412313i
$671$		−	16.0399i		−	0.619212i
$672$		0			0
$673$	27.3152	+	27.3152i	1.05292	+	1.05292i	0.998519	+	0.0544031i	$0.0173256\pi$
$673$	27.3152	+	27.3152i	1.05292	+	1.05292i	0.0544031	+	0.998519i	$0.482674\pi$
$674$	−32.7710	−	32.7710i	−1.26229	−	1.26229i
$675$		0			0
$676$	28.1423			1.08240
$677$	24.7420	−	24.7420i	0.950912	−	0.950912i	−0.0479382	−	0.998850i	$-0.515265\pi$
$677$	24.7420	−	24.7420i	0.950912	−	0.950912i	0.998850	+	0.0479382i	$0.0152650\pi$
$678$		0			0
$679$	−8.21956			−0.315438
$680$	4.14308	−	2.16008i	0.158880	−	0.0828355i
$681$		0			0
$682$			51.9979i			1.99110i
$683$	−15.1928	+	15.1928i	−0.581337	+	0.581337i	−0.935270	−	0.353934i	$-0.884844\pi$
$683$	−15.1928	+	15.1928i	−0.581337	+	0.581337i	0.353934	+	0.935270i	$0.384844\pi$
$684$		0			0
$685$	18.9041	−	18.9041i	0.722287	−	0.722287i
$686$	1.45161	+	1.45161i	0.0554226	+	0.0554226i
$687$		0			0
$688$			12.1146i			0.461865i
$689$		−	4.86152i		−	0.185209i
$690$		0			0
$691$	11.3932	+	11.3932i	0.433417	+	0.433417i	0.889789	−	0.456372i	$-0.150851\pi$
$691$	11.3932	+	11.3932i	0.433417	+	0.433417i	−0.456372	+	0.889789i	$0.650851\pi$
$692$	13.8301	−	13.8301i	0.525740	−	0.525740i
$693$		0			0
$694$	−33.8646	+	33.8646i	−1.28548	+	1.28548i
$695$		−	26.9314i		−	1.02157i
$696$		0			0
$697$	−19.5816	+	10.2093i	−0.741707	+	0.386705i
$698$	10.9127			0.413054
$699$		0			0
$700$	2.55843	−	2.55843i	0.0966996	−	0.0966996i
$701$	7.04558			0.266108			0.133054	−	0.991109i	$-0.457522\pi$
$701$	7.04558			0.266108			0.133054	+	0.991109i	$0.457522\pi$
$702$		0			0
$703$	−3.86190	−	3.86190i	−0.145654	−	0.145654i
$704$	−30.9788	−	30.9788i	−1.16756	−	1.16756i
$705$		0			0
$706$		−	42.3326i		−	1.59321i
$707$	−1.82934	−	1.82934i	−0.0687995	−	0.0687995i
$708$		0			0
$709$	7.08914	−	7.08914i	0.266238	−	0.266238i	−0.561344	−	0.827582i	$-0.689716\pi$
$709$	7.08914	−	7.08914i	0.266238	−	0.266238i	0.827582	+	0.561344i	$0.189716\pi$
$710$	−46.7294			−1.75372
$711$		0			0
$712$			6.43788i			0.241270i
$713$	−5.94303			−0.222568
$714$		0			0
$715$	6.32970			0.236717
$716$			46.5475i			1.73956i
$717$		0			0
$718$	−73.5583			−2.74517
$719$	6.79480	−	6.79480i	0.253403	−	0.253403i	−0.568961	−	0.822364i	$-0.692654\pi$
$719$	6.79480	−	6.79480i	0.253403	−	0.253403i	0.822364	+	0.568961i	$0.192654\pi$
$720$		0			0
$721$	11.8094	+	11.8094i	0.439806	+	0.439806i
$722$			28.5112i			1.06108i
$723$		0			0
$724$	7.84777	+	7.84777i	0.291660	+	0.291660i
$725$	−2.55409	−	2.55409i	−0.0948565	−	0.0948565i
$726$		0			0
$727$	−45.5477			−1.68927			−0.844636	−	0.535342i	$-0.820183\pi$
$727$	−45.5477			−1.68927			−0.844636	+	0.535342i	$0.820183\pi$
$728$	−0.167757	+	0.167757i	−0.00621747	+	0.00621747i
$729$		0			0
$730$	−84.2079			−3.11667
$731$	−13.5154	−	4.25198i	−0.499884	−	0.157265i
$732$		0			0
$733$		−	11.0025i		−	0.406387i	−0.979139	−	0.203193i	$-0.934868\pi$
$733$		−	11.0025i		−	0.406387i	0.979139	−	0.203193i	$-0.0651320\pi$
$734$	18.7794	−	18.7794i	0.693159	−	0.693159i
$735$		0			0
$736$	6.13770	−	6.13770i	0.226239	−	0.226239i
$737$	9.19900	+	9.19900i	0.338849	+	0.338849i
$738$		0			0
$739$			22.4175i			0.824640i	0.911039	+	0.412320i	$0.135281\pi$
$739$			22.4175i			0.824640i	−0.911039	+	0.412320i	$0.864719\pi$
$740$		−	13.7773i		−	0.506465i
$741$		0			0
$742$	−13.0874	−	13.0874i	−0.480453	−	0.480453i
$743$	−20.0607	+	20.0607i	−0.735954	+	0.735954i	−0.971792	−	0.235838i	$-0.924216\pi$
$743$	−20.0607	+	20.0607i	−0.735954	+	0.735954i	0.235838	+	0.971792i	$0.424216\pi$
$744$		0			0
$745$	−36.7673	+	36.7673i	−1.34705	+	1.34705i
$746$			17.2167i			0.630350i
$747$		0			0
$748$	36.8959	−	19.2365i	1.34905	−	0.703355i
$749$	2.72087			0.0994186
$750$		0			0
$751$	29.1114	−	29.1114i	1.06229	−	1.06229i	0.0643642	−	0.997926i	$-0.479498\pi$
$751$	29.1114	−	29.1114i	1.06229	−	1.06229i	0.997926	−	0.0643642i	$-0.0205019\pi$
$752$	21.3361			0.778047
$753$		0			0
$754$	1.73030	+	1.73030i	0.0630137	+	0.0630137i
$755$	−32.5053	−	32.5053i	−1.18299	−	1.18299i
$756$		0			0
$757$			4.36243i			0.158555i	0.996853	+	0.0792776i	$0.0252613\pi$
$757$			4.36243i			0.158555i	−0.996853	+	0.0792776i	$0.974739\pi$
$758$	47.3907	+	47.3907i	1.72131	+	1.72131i
$759$		0			0
$760$	1.81166	−	1.81166i	0.0657157	−	0.0657157i
$761$	−10.0672			−0.364937			−0.182469	−	0.983212i	$-0.558409\pi$
$761$	−10.0672			−0.364937			−0.182469	+	0.983212i	$0.558409\pi$
$762$		0			0
$763$			16.9736i			0.614486i
$764$	−37.1079			−1.34252
$765$		0			0
$766$	47.2222			1.70621
$767$			5.43419i			0.196217i
$768$		0			0
$769$	−16.8712			−0.608390			−0.304195	−	0.952610i	$-0.598387\pi$
$769$	−16.8712			−0.608390			−0.304195	+	0.952610i	$0.598387\pi$
$770$	17.0397	−	17.0397i	0.614070	−	0.614070i
$771$		0			0
$772$	23.8453	+	23.8453i	0.858213	+	0.858213i
$773$		−	41.1629i		−	1.48053i	−0.672316	−	0.740264i	$-0.734701\pi$
$773$		−	41.1629i		−	1.48053i	0.672316	−	0.740264i	$-0.265299\pi$
$774$		0			0
$775$	6.42138	+	6.42138i	0.230663	+	0.230663i
$776$	−2.55717	−	2.55717i	−0.0917971	−	0.0917971i
$777$		0			0
$778$	0.581016			0.0208304
$779$	−8.56252	+	8.56252i	−0.306784	+	0.306784i
$780$		0			0
$781$	−40.2779			−1.44126
$782$	4.18441	+	8.02577i	0.149634	+	0.287001i
$783$		0			0
$784$		−	3.52543i		−	0.125908i
$785$	18.6018	−	18.6018i	0.663926	−	0.663926i
$786$		0			0
$787$	−14.0002	+	14.0002i	−0.499055	+	0.499055i	−0.911144	−	0.412089i	$-0.864799\pi$
$787$	−14.0002	+	14.0002i	−0.499055	+	0.499055i	0.412089	+	0.911144i	$0.364799\pi$
$788$	15.7306	+	15.7306i	0.560380	+	0.560380i
$789$		0			0
$790$			24.2643i			0.863284i
$791$			18.4750i			0.656895i
$792$		0			0
$793$	1.34192	+	1.34192i	0.0476530	+	0.0476530i
$794$	−44.2120	+	44.2120i	−1.56903	+	1.56903i
$795$		0			0
$796$	−0.599381	+	0.599381i	−0.0212445	+	0.0212445i
$797$		−	11.4587i		−	0.405889i	−0.979190	−	0.202944i	$-0.934949\pi$
$797$		−	11.4587i		−	0.405889i	0.979190	−	0.202944i	$-0.0650511\pi$
$798$		0			0
$799$	−7.48853	+	23.8031i	−0.264925	+	0.842093i
$800$	−13.2634			−0.468933
$801$		0			0
$802$	20.7956	−	20.7956i	0.734317	−	0.734317i
$803$	−72.5820			−2.56136
$804$		0			0
$805$	1.94753	+	1.94753i	0.0686416	+	0.0686416i
$806$	−4.35023	−	4.35023i	−0.153230	−	0.153230i
$807$		0			0
$808$		−	1.13825i		−	0.0400433i
$809$	−27.9243	−	27.9243i	−0.981767	−	0.981767i	0.0180693	−	0.999837i	$-0.494248\pi$
$809$	−27.9243	−	27.9243i	−0.981767	−	0.981767i	−0.999837	+	0.0180693i	$0.994248\pi$
$810$		0			0
$811$	−21.2950	+	21.2950i	−0.747767	+	0.747767i	−0.974059	−	0.226292i	$-0.927339\pi$
$811$	−21.2950	+	21.2950i	−0.747767	+	0.747767i	0.226292	+	0.974059i	$0.427339\pi$
$812$	4.89489			0.171777
$813$		0			0
$814$		−	22.6010i		−	0.792166i
$815$	−4.67082			−0.163612
$816$		0			0
$817$	−7.76919			−0.271809
$818$			19.4779i			0.681029i
$819$		0			0
$820$	−30.5468			−1.06674
$821$	17.2136	−	17.2136i	0.600758	−	0.600758i	−0.339756	−	0.940514i	$-0.610344\pi$
$821$	17.2136	−	17.2136i	0.600758	−	0.600758i	0.940514	+	0.339756i	$0.110344\pi$
$822$		0			0
$823$	−35.7278	−	35.7278i	−1.24539	−	1.24539i	−0.957733	−	0.287658i	$-0.907123\pi$
$823$	−35.7278	−	35.7278i	−1.24539	−	1.24539i	−0.287658	−	0.957733i	$-0.592877\pi$
$824$			7.34801i			0.255980i
$825$		0			0
$826$	14.6290	+	14.6290i	0.509008	+	0.509008i
$827$	−29.1826	−	29.1826i	−1.01478	−	1.01478i	−0.999889	−	0.0148883i	$-0.995261\pi$
$827$	−29.1826	−	29.1826i	−1.01478	−	1.01478i	−0.0148883	−	0.999889i	$-0.504739\pi$
$828$		0			0
$829$	46.5593			1.61707			0.808535	−	0.588448i	$-0.200261\pi$
$829$	46.5593			1.61707			0.808535	+	0.588448i	$0.200261\pi$
$830$	48.7085	−	48.7085i	1.69070	−	1.69070i
$831$		0			0
$832$	5.18347			0.179705
$833$	3.93306	+	1.23735i	0.136272	+	0.0428717i
$834$		0			0
$835$		−	60.1571i		−	2.08182i
$836$	16.1336	−	16.1336i	0.557991	−	0.557991i
$837$		0			0
$838$	1.13245	−	1.13245i	0.0391197	−	0.0391197i
$839$	−36.9879	−	36.9879i	−1.27696	−	1.27696i	−0.942358	−	0.334606i	$-0.891397\pi$
$839$	−36.9879	−	36.9879i	−1.27696	−	1.27696i	−0.334606	−	0.942358i	$-0.608603\pi$
$840$		0			0
$841$			24.1134i			0.831497i
$842$			28.6721i			0.988106i
$843$		0			0
$844$	38.1671	+	38.1671i	1.31376	+	1.31376i
$845$	23.1468	−	23.1468i	0.796276	−	0.796276i
$846$		0			0
$847$	6.90903	−	6.90903i	0.237397	−	0.237397i
$848$			31.7845i			1.09148i
$849$		0			0
$850$	4.15055	−	13.1930i	0.142363	−	0.452515i
$851$	2.58315			0.0885494
$852$		0			0
$853$	30.4541	−	30.4541i	1.04273	−	1.04273i	0.0436823	−	0.999045i	$-0.486091\pi$
$853$	30.4541	−	30.4541i	1.04273	−	1.04273i	0.999045	−	0.0436823i	$-0.0139089\pi$
$854$	7.22499			0.247234
$855$		0			0
$856$	0.846485	+	0.846485i	0.0289323	+	0.0289323i
$857$	22.1665	+	22.1665i	0.757193	+	0.757193i	0.975811	−	0.218617i	$-0.0701546\pi$
$857$	22.1665	+	22.1665i	0.757193	+	0.757193i	−0.218617	+	0.975811i	$0.570155\pi$
$858$		0			0
$859$		−	43.9565i		−	1.49978i	−0.661565	−	0.749888i	$-0.730107\pi$
$859$		−	43.9565i		−	1.49978i	0.661565	−	0.749888i	$-0.269893\pi$
$860$	−13.8583	−	13.8583i	−0.472564	−	0.472564i
$861$		0			0
$862$	−9.28505	+	9.28505i	−0.316250	+	0.316250i
$863$	−13.9004			−0.473175			−0.236587	−	0.971610i	$-0.576029\pi$
$863$	−13.9004			−0.473175			−0.236587	+	0.971610i	$0.576029\pi$
$864$		0			0
$865$		−	22.7503i		−	0.773532i
$866$	−26.5444			−0.902015
$867$		0			0
$868$	−12.3065			−0.417711
$869$			20.9143i			0.709469i
$870$		0			0
$871$	−1.53921			−0.0521540
$872$	−5.28062	+	5.28062i	−0.178824	+	0.178824i
$873$		0			0
$874$	3.50945	+	3.50945i	0.118709	+	0.118709i
$875$			8.66968i			0.293089i
$876$		0			0
$877$	−8.00995	−	8.00995i	−0.270477	−	0.270477i	0.558815	−	0.829292i	$-0.311256\pi$
$877$	−8.00995	−	8.00995i	−0.270477	−	0.270477i	−0.829292	+	0.558815i	$0.811256\pi$
$878$	−3.84719	−	3.84719i	−0.129836	−	0.129836i
$879$		0			0
$880$	−41.3834			−1.39503
$881$	8.65624	−	8.65624i	0.291636	−	0.291636i	−0.546090	−	0.837726i	$-0.683884\pi$
$881$	8.65624	−	8.65624i	0.291636	−	0.291636i	0.837726	+	0.546090i	$0.183884\pi$
$882$		0			0
$883$	32.2293			1.08460			0.542300	−	0.840185i	$-0.317553\pi$
$883$	32.2293			1.08460			0.542300	+	0.840185i	$0.317553\pi$
$884$	−1.47742	+	4.69612i	−0.0496908	+	0.157948i
$885$		0			0
$886$			41.4719i			1.39327i
$887$	9.48296	−	9.48296i	0.318407	−	0.318407i	−0.529748	−	0.848155i	$-0.677714\pi$
$887$	9.48296	−	9.48296i	0.318407	−	0.318407i	0.848155	+	0.529748i	$0.177714\pi$
$888$		0			0
$889$	11.2760	−	11.2760i	0.378184	−	0.378184i
$890$	54.7083	+	54.7083i	1.83383	+	1.83383i
$891$		0			0
$892$		−	14.1902i		−	0.475122i
$893$			13.6830i			0.457884i
$894$		0			0
$895$	38.2850	+	38.2850i	1.27973	+	1.27973i
$896$	2.47457	−	2.47457i	0.0826697	−	0.0826697i
$897$		0			0
$898$	−19.3662	+	19.3662i	−0.646257	+	0.646257i
$899$			12.2856i			0.409749i
$900$		0			0
$901$	−35.4596	−	11.1557i	−1.18133	−	0.371651i
$902$	−50.1106			−1.66850
$903$		0			0
$904$	−5.74772	+	5.74772i	−0.191166	+	0.191166i
$905$	12.9095			0.429125
$906$		0			0
$907$	3.44192	+	3.44192i	0.114287	+	0.114287i	0.761938	−	0.647650i	$-0.224248\pi$
$907$	3.44192	+	3.44192i	0.114287	+	0.114287i	−0.647650	+	0.761938i	$0.724248\pi$
$908$	−9.72965	−	9.72965i	−0.322890	−	0.322890i
$909$		0			0
$910$			2.85115i			0.0945146i
$911$	37.7949	+	37.7949i	1.25220	+	1.25220i	0.954731	+	0.297469i	$0.0961426\pi$
$911$	37.7949	+	37.7949i	1.25220	+	1.25220i	0.297469	+	0.954731i	$0.403857\pi$
$912$		0			0
$913$	41.9837	−	41.9837i	1.38946	−	1.38946i
$914$	−47.1237			−1.55871
$915$		0			0
$916$		−	33.1659i		−	1.09583i
$917$	−16.6528			−0.549925
$918$		0			0
$919$	−6.36472			−0.209953			−0.104976	−	0.994475i	$-0.533477\pi$
$919$	−6.36472			−0.209953			−0.104976	+	0.994475i	$0.533477\pi$
$920$			1.21179i			0.0399514i
$921$		0			0
$922$	−72.8922			−2.40058
$923$	3.36971	−	3.36971i	0.110915	−	0.110915i
$924$		0			0
$925$	−2.79107	−	2.79107i	−0.0917698	−	0.0917698i
$926$		−	61.6242i		−	2.02510i
$927$		0			0
$928$	−12.6881	−	12.6881i	−0.416507	−	0.416507i
$929$	25.5211	+	25.5211i	0.837319	+	0.837319i	0.988505	−	0.151187i	$-0.0483094\pi$
$929$	25.5211	+	25.5211i	0.837319	+	0.837319i	−0.151187	+	0.988505i	$0.548309\pi$
$930$		0			0
$931$	2.26088			0.0740974
$932$	−8.28521	+	8.28521i	−0.271391	+	0.271391i
$933$		0			0
$934$	8.75875			0.286595
$935$	14.5247	−	46.1684i	0.475009	−	1.50987i
$936$		0			0
$937$		−	22.3783i		−	0.731068i	−0.930798	−	0.365534i	$-0.880886\pi$
$937$		−	22.3783i		−	0.731068i	0.930798	−	0.365534i	$-0.119114\pi$
$938$	−4.14359	+	4.14359i	−0.135293	+	0.135293i
$939$		0			0
$940$	−24.4071	+	24.4071i	−0.796070	+	0.796070i
$941$	15.2514	+	15.2514i	0.497182	+	0.497182i	0.910560	−	0.413378i	$-0.135651\pi$
$941$	15.2514	+	15.2514i	0.497182	+	0.497182i	−0.413378	+	0.910560i	$0.635651\pi$
$942$		0			0
$943$		−	5.72732i		−	0.186507i
$944$		−	35.5286i		−	1.15636i
$945$		0			0
$946$	−22.7339	−	22.7339i	−0.739142	−	0.739142i
$947$	−31.9742	+	31.9742i	−1.03902	+	1.03902i	−0.0398149	+	0.999207i	$0.512677\pi$
$947$	−31.9742	+	31.9742i	−1.03902	+	1.03902i	−0.999207	+	0.0398149i	$0.987323\pi$
$948$		0			0
$949$	6.07233	−	6.07233i	0.197116	−	0.197116i
$950$		−	7.58386i		−	0.246053i
$951$		0			0
$952$	0.838655	+	1.60856i	0.0271810	+	0.0521336i
$953$	−49.5095			−1.60377			−0.801885	−	0.597479i	$-0.796169\pi$
$953$	−49.5095			−1.60377			−0.801885	+	0.597479i	$0.796169\pi$
$954$		0			0
$955$	−30.5209	+	30.5209i	−0.987634	+	0.987634i
$956$	−50.7878			−1.64259
$957$		0			0
$958$	−0.608169	−	0.608169i	−0.0196490	−	0.0196490i
$959$	7.33952	+	7.33952i	0.237005	+	0.237005i
$960$		0			0
$961$			0.111991i			0.00361260i
$962$	1.89084	+	1.89084i	0.0609632	+	0.0609632i
$963$		0			0
$964$	14.8116	−	14.8116i	0.477051	−	0.477051i
$965$	39.2252			1.26270
$966$		0			0
$967$		−	18.6762i		−	0.600586i	−0.953847	−	0.300293i	$-0.902916\pi$
$967$		−	18.6762i		−	0.600586i	0.953847	−	0.300293i	$-0.0970844\pi$
$968$	4.29891			0.138172
$969$		0			0
$970$	−43.4610			−1.39545
$971$		−	46.4734i		−	1.49140i	−0.666280	−	0.745701i	$-0.732115\pi$
$971$		−	46.4734i		−	1.49140i	0.666280	−	0.745701i	$-0.267885\pi$
$972$		0			0
$973$	10.4561			0.335208
$974$	1.29276	−	1.29276i	0.0414228	−	0.0414228i
$975$		0			0
$976$	−8.77345	−	8.77345i	−0.280831	−	0.280831i
$977$			50.2595i			1.60794i	0.594668	+	0.803972i	$0.297284\pi$
$977$			50.2595i			1.60794i	−0.594668	+	0.803972i	$0.702716\pi$
$978$		0			0
$979$	47.1552	+	47.1552i	1.50709	+	1.50709i
$980$	4.03285	+	4.03285i	0.128825	+	0.128825i
$981$		0			0
$982$	−47.5221			−1.51649
$983$	3.47345	−	3.47345i	0.110786	−	0.110786i	−0.649541	−	0.760327i	$-0.725039\pi$
$983$	3.47345	−	3.47345i	0.110786	−	0.110786i	0.760327	+	0.649541i	$0.225039\pi$
$984$		0			0
$985$	25.8766			0.824498
$986$	16.5912	−	8.65017i	0.528370	−	0.275477i
$987$		0			0
$988$			2.69952i			0.0858833i
$989$	2.59834	−	2.59834i	0.0826223	−	0.0826223i
$990$		0			0
$991$	35.9159	−	35.9159i	1.14091	−	1.14091i	0.152621	−	0.988285i	$-0.451229\pi$
$991$	35.9159	−	35.9159i	1.14091	−	1.14091i	0.988285	−	0.152621i	$-0.0487712\pi$
$992$	31.8998	+	31.8998i	1.01282	+	1.01282i
$993$		0			0
$994$		−	18.1428i		−	0.575453i
$995$			0.985973i			0.0312574i
$996$		0			0
$997$	−21.2614	−	21.2614i	−0.673356	−	0.673356i	0.285132	−	0.958488i	$-0.407963\pi$
$997$	−21.2614	−	21.2614i	−0.673356	−	0.673356i	−0.958488	+	0.285132i	$0.907963\pi$
$998$	−41.5982	+	41.5982i	−1.31677	+	1.31677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.n.a.820.6		12
3.2	odd	2		357.2.k.a.106.1	yes	12
17.13	even	4	inner	1071.2.n.a.64.1		12
51.8	odd	8		6069.2.a.x.1.1		6
51.26	odd	8		6069.2.a.y.1.1		6
51.47	odd	4		357.2.k.a.64.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.a.64.6	✓	12	51.47	odd	4
357.2.k.a.106.1	yes	12	3.2	odd	2
1071.2.n.a.64.1		12	17.13	even	4	inner
1071.2.n.a.820.6		12	1.1	even	1	trivial
6069.2.a.x.1.1		6	51.8	odd	8
6069.2.a.y.1.1		6	51.26	odd	8

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.05288i q^{2} -2.21432 q^{4} +(-1.82126 + 1.82126i) q^{5} +(-0.707107 - 0.707107i) q^{7} -0.439973i q^{8} +O(q^{10})\)	\(q+2.05288i q^{2} -2.21432 q^{4} +(-1.82126 + 1.82126i) q^{5} +(-0.707107 - 0.707107i) q^{7} -0.439973i q^{8} +(-3.73883 - 3.73883i) q^{10} +(-3.22264 - 3.22264i) q^{11} +0.539223 q^{13} +(1.45161 - 1.45161i) q^{14} -3.52543 q^{16} +(1.23735 - 3.93306i) q^{17} -2.26088i q^{19} +(4.03285 - 4.03285i) q^{20} +(6.61570 - 6.61570i) q^{22} +(0.756132 + 0.756132i) q^{23} -1.63399i q^{25} +1.10696i q^{26} +(1.56576 + 1.56576i) q^{28} +(1.56310 - 1.56310i) q^{29} +(-3.92989 + 3.92989i) q^{31} -8.11723i q^{32} +(8.07410 + 2.54014i) q^{34} +2.57565 q^{35} +(1.70814 - 1.70814i) q^{37} +4.64132 q^{38} +(0.801306 + 0.801306i) q^{40} +(-3.78725 - 3.78725i) q^{41} -3.43635i q^{43} +(7.13596 + 7.13596i) q^{44} +(-1.55225 + 1.55225i) q^{46} -6.05205 q^{47} +1.00000i q^{49} +3.35438 q^{50} -1.19401 q^{52} -9.01579i q^{53} +11.7385 q^{55} +(-0.311108 + 0.311108i) q^{56} +(3.20887 + 3.20887i) q^{58} +10.0778i q^{59} +(2.48862 + 2.48862i) q^{61} +(-8.06759 - 8.06759i) q^{62} +9.61285 q^{64} +(-0.982066 + 0.982066i) q^{65} -2.85449 q^{67} +(-2.73989 + 8.70905i) q^{68} +5.28751i q^{70} +(6.24920 - 6.24920i) q^{71} +(11.2613 - 11.2613i) q^{73} +(3.50660 + 3.50660i) q^{74} +5.00632i q^{76} +4.55750i q^{77} +(-3.24490 - 3.24490i) q^{79} +(6.42072 - 6.42072i) q^{80} +(7.77476 - 7.77476i) q^{82} +13.0277i q^{83} +(4.90959 + 9.41667i) q^{85} +7.05442 q^{86} +(-1.41788 + 1.41788i) q^{88} -14.6325 q^{89} +(-0.381288 - 0.381288i) q^{91} +(-1.67432 - 1.67432i) q^{92} -12.4241i q^{94} +(4.11766 + 4.11766i) q^{95} +(5.81211 - 5.81211i) q^{97} -2.05288 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{5}+O(q^{10}) \) 12 * q - 8 * q^5	\( 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) \) 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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