LMFDB - Embedded newform 315.2.j.e.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.2.j.e.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 - 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +O(q^{10})$	\(q+(1.20711 - 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(-1.20711 - 2.09077i) q^{10} +(-0.414214 - 0.717439i) q^{11} -4.82843 q^{13} +(2.41421 - 5.91359i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(2.41421 + 4.18154i) q^{17} +(-1.41421 + 2.44949i) q^{19} -3.82843 q^{20} -2.00000 q^{22} +(0.207107 - 0.358719i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} +(-6.20711 - 8.00436i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-0.792893 - 1.37333i) q^{32} +11.6569 q^{34} +(1.00000 - 2.44949i) q^{35} +(3.41421 + 5.91359i) q^{38} +(-2.20711 + 3.82282i) q^{40} +7.82843 q^{41} +3.58579 q^{43} +(-1.58579 + 2.74666i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +(6.74264 - 1.88064i) q^{49} -2.41421 q^{50} +(9.24264 + 16.0087i) q^{52} +(-0.585786 - 1.01461i) q^{53} -0.828427 q^{55} +(-11.5711 + 1.58346i) q^{56} +(1.20711 - 2.09077i) q^{58} +(2.24264 + 3.88437i) q^{59} +(-2.74264 + 4.75039i) q^{61} +14.4853 q^{62} -9.82843 q^{64} +(-2.41421 + 4.18154i) q^{65} +(-4.79289 - 8.30153i) q^{67} +(9.24264 - 16.0087i) q^{68} +(-3.91421 - 5.04757i) q^{70} -4.48528 q^{71} +(0.414214 + 0.717439i) q^{73} +10.8284 q^{76} +(-1.34315 - 1.73205i) q^{77} +(-7.41421 + 12.8418i) q^{79} +(1.50000 + 2.59808i) q^{80} +(9.44975 - 16.3674i) q^{82} -13.7279 q^{83} +4.82843 q^{85} +(4.32843 - 7.49706i) q^{86} +(1.82843 + 3.16693i) q^{88} +(-4.32843 + 7.49706i) q^{89} +(-12.6569 + 1.73205i) q^{91} -1.58579 q^{92} +(-2.41421 - 4.18154i) q^{94} +(1.41421 + 2.44949i) q^{95} +11.6569 q^{97} +(4.20711 - 16.3674i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 2 q^{10} + 4 q^{11} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{20} - 8 q^{22} - 2 q^{23} - 2 q^{25} - 12 q^{26} - 22 q^{28} + 4 q^{29} + 12 q^{31} - 6 q^{32} + 24 q^{34} + 4 q^{35} + 8 q^{38} - 6 q^{40} + 20 q^{41} + 20 q^{43} - 12 q^{44} - 2 q^{46} + 4 q^{47} + 10 q^{49} - 4 q^{50} + 20 q^{52} - 8 q^{53} + 8 q^{55} - 18 q^{56} + 2 q^{58} - 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} - 4 q^{65} - 22 q^{67} + 20 q^{68} - 10 q^{70} + 16 q^{71} - 4 q^{73} + 32 q^{76} - 28 q^{77} - 24 q^{79} + 6 q^{80} + 18 q^{82} - 4 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 12 q^{92} - 4 q^{94} + 24 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 2 * q^10 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^20 - 8 * q^22 - 2 * q^23 - 2 * q^25 - 12 * q^26 - 22 * q^28 + 4 * q^29 + 12 * q^31 - 6 * q^32 + 24 * q^34 + 4 * q^35 + 8 * q^38 - 6 * q^40 + 20 * q^41 + 20 * q^43 - 12 * q^44 - 2 * q^46 + 4 * q^47 + 10 * q^49 - 4 * q^50 + 20 * q^52 - 8 * q^53 + 8 * q^55 - 18 * q^56 + 2 * q^58 - 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 - 4 * q^65 - 22 * q^67 + 20 * q^68 - 10 * q^70 + 16 * q^71 - 4 * q^73 + 32 * q^76 - 28 * q^77 - 24 * q^79 + 6 * q^80 + 18 * q^82 - 4 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 12 * q^92 - 4 * q^94 + 24 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	−0.0244272	−	0.999702i	$-0.507776\pi$
$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	0.877981	−	0.478696i	$-0.158890\pi$
$3$		0			0
$3$		0			0
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$	−4.41421			−1.56066
$9$		0			0
$10$	−1.20711	−	2.09077i	−0.381721	−	0.661160i
$11$	−0.414214	−	0.717439i	−0.124890	−	0.216316i	0.796800	−	0.604243i	$-0.206524\pi$
$11$	−0.414214	−	0.717439i	−0.124890	−	0.216316i	−0.921690	+	0.387927i	$0.873191\pi$
$12$		0			0
$13$	−4.82843			−1.33916			−0.669582	−	0.742738i	$-0.733527\pi$
$13$	−4.82843			−1.33916			−0.669582	+	0.742738i	$0.733527\pi$
$14$	2.41421	−	5.91359i	0.645226	−	1.58047i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	2.41421	+	4.18154i	0.585533	+	1.01417i	0.994809	+	0.101762i	$0.0324480\pi$
$17$	2.41421	+	4.18154i	0.585533	+	1.01417i	−0.409276	+	0.912411i	$0.634219\pi$
$18$		0			0
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	−3.82843			−0.856062
$21$		0			0
$22$	−2.00000			−0.426401
$23$	0.207107	−	0.358719i	0.0431847	−	0.0747982i	−0.843625	−	0.536933i	$-0.819583\pi$
$23$	0.207107	−	0.358719i	0.0431847	−	0.0747982i	0.886810	+	0.462134i	$0.152916\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.82843	+	10.0951i	−1.14305	+	1.97982i
$27$		0			0
$28$	−6.20711	−	8.00436i	−1.17303	−	1.51268i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−0.792893	−	1.37333i	−0.140165	−	0.242773i
$33$		0			0
$34$	11.6569			1.99913
$35$	1.00000	−	2.44949i	0.169031	−	0.414039i
$36$		0			0
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	3.41421	+	5.91359i	0.553859	+	0.959311i
$39$		0			0
$40$	−2.20711	+	3.82282i	−0.348974	+	0.604441i
$41$	7.82843			1.22259			0.611297	−	0.791401i	$-0.290648\pi$
$41$	7.82843			1.22259			0.611297	+	0.791401i	$0.290648\pi$
$42$		0			0
$43$	3.58579			0.546827			0.273414	−	0.961897i	$-0.411847\pi$
$43$	3.58579			0.546827			0.273414	+	0.961897i	$0.411847\pi$
$44$	−1.58579	+	2.74666i	−0.239066	+	0.414075i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−2.41421			−0.341421
$51$		0			0
$52$	9.24264	+	16.0087i	1.28172	+	2.22001i
$53$	−0.585786	−	1.01461i	−0.0804640	−	0.139368i	0.822985	−	0.568063i	$-0.192307\pi$
$53$	−0.585786	−	1.01461i	−0.0804640	−	0.139368i	−0.903449	+	0.428695i	$0.858974\pi$
$54$		0			0
$55$	−0.828427			−0.111705
$56$	−11.5711	+	1.58346i	−1.54625	+	0.211599i
$57$		0			0
$58$	1.20711	−	2.09077i	0.158501	−	0.274532i
$59$	2.24264	+	3.88437i	0.291967	+	0.505702i	0.974275	−	0.225363i	$-0.0723569\pi$
$59$	2.24264	+	3.88437i	0.291967	+	0.505702i	−0.682308	+	0.731065i	$0.739024\pi$
$60$		0			0
$61$	−2.74264	+	4.75039i	−0.351159	+	0.608226i	−0.986453	−	0.164045i	$-0.947546\pi$
$61$	−2.74264	+	4.75039i	−0.351159	+	0.608226i	0.635294	+	0.772271i	$0.280879\pi$
$62$	14.4853			1.83963
$63$		0			0
$64$	−9.82843			−1.22855
$65$	−2.41421	+	4.18154i	−0.299446	+	0.518656i
$66$		0			0
$67$	−4.79289	−	8.30153i	−0.585545	−	1.01419i	−0.994807	−	0.101777i	$-0.967547\pi$
$67$	−4.79289	−	8.30153i	−0.585545	−	1.01419i	0.409262	−	0.912417i	$-0.365786\pi$
$68$	9.24264	−	16.0087i	1.12083	−	1.94134i
$69$		0			0
$70$	−3.91421	−	5.04757i	−0.467838	−	0.603300i
$71$	−4.48528			−0.532305			−0.266152	−	0.963931i	$-0.585752\pi$
$71$	−4.48528			−0.532305			−0.266152	+	0.963931i	$0.585752\pi$
$72$		0			0
$73$	0.414214	+	0.717439i	0.0484800	+	0.0839699i	0.889247	−	0.457427i	$-0.151229\pi$
$73$	0.414214	+	0.717439i	0.0484800	+	0.0839699i	−0.840767	+	0.541397i	$0.817896\pi$
$74$		0			0
$75$		0			0
$76$	10.8284			1.24211
$77$	−1.34315	−	1.73205i	−0.153066	−	0.197386i
$78$		0			0
$79$	−7.41421	+	12.8418i	−0.834164	+	1.44481i	0.0605449	+	0.998165i	$0.480716\pi$
$79$	−7.41421	+	12.8418i	−0.834164	+	1.44481i	−0.894709	+	0.446649i	$0.852617\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	9.44975	−	16.3674i	1.04355	−	1.80748i
$83$	−13.7279			−1.50684			−0.753418	−	0.657542i	$-0.771596\pi$
$83$	−13.7279			−1.50684			−0.753418	+	0.657542i	$0.771596\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$	4.32843	−	7.49706i	0.466746	−	0.808428i
$87$		0			0
$88$	1.82843	+	3.16693i	0.194911	+	0.337596i
$89$	−4.32843	+	7.49706i	−0.458812	+	0.794686i	−0.998898	−	0.0469234i	$-0.985058\pi$
$89$	−4.32843	+	7.49706i	−0.458812	+	0.794686i	0.540086	+	0.841610i	$0.318392\pi$
$90$		0			0
$91$	−12.6569	+	1.73205i	−1.32680	+	0.181568i
$92$	−1.58579			−0.165330
$93$		0			0
$94$	−2.41421	−	4.18154i	−0.249007	−	0.431293i
$95$	1.41421	+	2.44949i	0.145095	+	0.251312i
$96$		0			0
$97$	11.6569			1.18357			0.591787	−	0.806094i	$-0.298423\pi$
$97$	11.6569			1.18357			0.591787	+	0.806094i	$0.298423\pi$
$98$	4.20711	−	16.3674i	0.424982	−	1.65336i
$99$		0			0
$100$	−1.91421	+	3.31552i	−0.191421	+	0.331552i
$101$	−5.15685	−	8.93193i	−0.513126	−	0.888761i	−0.999884	−	0.0152237i	$-0.995154\pi$
$101$	−5.15685	−	8.93193i	−0.513126	−	0.888761i	0.486758	−	0.873537i	$-0.338179\pi$
$102$		0			0
$103$	1.20711	−	2.09077i	0.118940	−	0.206010i	−0.800408	−	0.599456i	$-0.795384\pi$
$103$	1.20711	−	2.09077i	0.118940	−	0.206010i	0.919348	+	0.393446i	$0.128717\pi$
$104$	21.3137			2.08998
$105$		0			0
$106$	−2.82843			−0.274721
$107$	5.62132	−	9.73641i	0.543434	−	0.941255i	−0.455270	−	0.890353i	$-0.650457\pi$
$107$	5.62132	−	9.73641i	0.543434	−	0.941255i	0.998704	−	0.0509012i	$-0.0162093\pi$
$108$		0			0
$109$	6.74264	+	11.6786i	0.645828	+	1.11861i	0.984110	+	0.177562i	$0.0568210\pi$
$109$	6.74264	+	11.6786i	0.645828	+	1.11861i	−0.338282	+	0.941045i	$0.609846\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	−3.00000	+	7.34847i	−0.283473	+	0.694365i
$113$	4.48528			0.421940			0.210970	−	0.977493i	$-0.432338\pi$
$113$	4.48528			0.421940			0.210970	+	0.977493i	$0.432338\pi$
$114$		0			0
$115$	−0.207107	−	0.358719i	−0.0193128	−	0.0334508i
$116$	−1.91421	−	3.31552i	−0.177730	−	0.307838i
$117$		0			0
$118$	10.8284			0.996838
$119$	7.82843	+	10.0951i	0.717631	+	0.925419i
$120$		0			0
$121$	5.15685	−	8.93193i	0.468805	−	0.811994i
$122$	6.62132	+	11.4685i	0.599466	+	1.03831i
$123$		0			0
$124$	11.4853	−	19.8931i	1.03141	−	1.78645i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.31371			−0.826458			−0.413229	−	0.910627i	$-0.635599\pi$
$127$	−9.31371			−0.826458			−0.413229	+	0.910627i	$0.635599\pi$
$128$	−10.2782	+	17.8023i	−0.908471	+	1.57352i
$129$		0			0
$130$	5.82843	+	10.0951i	0.511187	+	0.885402i
$131$	−9.65685	+	16.7262i	−0.843723	+	1.46137i	0.0430021	+	0.999075i	$0.486308\pi$
$131$	−9.65685	+	16.7262i	−0.843723	+	1.46137i	−0.886725	+	0.462297i	$0.847026\pi$
$132$		0			0
$133$	−2.82843	+	6.92820i	−0.245256	+	0.600751i
$134$	−23.1421			−1.99918
$135$		0			0
$136$	−10.6569	−	18.4582i	−0.913818	−	1.58278i
$137$	−4.82843	−	8.36308i	−0.412520	−	0.714506i	0.582644	−	0.812727i	$-0.302018\pi$
$137$	−4.82843	−	8.36308i	−0.412520	−	0.714506i	−0.995165	+	0.0982211i	$0.968685\pi$
$138$		0			0
$139$	−16.1421			−1.36916			−0.684579	−	0.728939i	$-0.740014\pi$
$139$	−16.1421			−1.36916			−0.684579	+	0.728939i	$0.740014\pi$
$140$	−10.0355	+	1.37333i	−0.848157	+	0.116068i
$141$		0			0
$142$	−5.41421	+	9.37769i	−0.454351	+	0.786959i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$	2.00000			0.165521
$147$		0			0
$148$		0			0
$149$	−1.08579	+	1.88064i	−0.0889511	+	0.154068i	−0.907068	−	0.420984i	$-0.861685\pi$
$149$	−1.08579	+	1.88064i	−0.0889511	+	0.154068i	0.818117	+	0.575052i	$0.195018\pi$
$150$		0			0
$151$	−5.82843	−	10.0951i	−0.474311	−	0.821530i	0.525257	−	0.850944i	$-0.323969\pi$
$151$	−5.82843	−	10.0951i	−0.474311	−	0.821530i	−0.999567	+	0.0294137i	$0.990636\pi$
$152$	6.24264	−	10.8126i	0.506345	−	0.877015i
$153$		0			0
$154$	−5.24264	+	0.717439i	−0.422464	+	0.0578129i
$155$	6.00000			0.481932
$156$		0			0
$157$	−8.65685	−	14.9941i	−0.690892	−	1.19666i	−0.971546	−	0.236851i	$-0.923885\pi$
$157$	−8.65685	−	14.9941i	−0.690892	−	1.19666i	0.280654	−	0.959809i	$-0.409449\pi$
$158$	17.8995	+	31.0028i	1.42401	+	2.46645i
$159$		0			0
$160$	−1.58579			−0.125367
$161$	0.414214	−	1.01461i	0.0326446	−	0.0799626i
$162$		0			0
$163$	−6.17157	+	10.6895i	−0.483395	+	0.837265i	−0.999818	−	0.0190689i	$-0.993930\pi$
$163$	−6.17157	+	10.6895i	−0.483395	+	0.837265i	0.516423	+	0.856333i	$0.327263\pi$
$164$	−14.9853	−	25.9553i	−1.17015	−	2.02677i
$165$		0			0
$166$	−16.5711	+	28.7019i	−1.28616	+	2.22770i
$167$	−22.4142			−1.73446			−0.867232	−	0.497904i	$-0.834103\pi$
$167$	−22.4142			−1.73446			−0.867232	+	0.497904i	$0.834103\pi$
$168$		0			0
$169$	10.3137			0.793362
$170$	5.82843	−	10.0951i	0.447020	−	0.774261i
$171$		0			0
$172$	−6.86396	−	11.8887i	−0.523372	−	0.906507i
$173$	1.65685	−	2.86976i	0.125968	−	0.218183i	−0.796143	−	0.605109i	$-0.793130\pi$
$173$	1.65685	−	2.86976i	0.125968	−	0.218183i	0.922111	+	0.386925i	$0.126463\pi$
$174$		0			0
$175$	−1.62132	−	2.09077i	−0.122560	−	0.158047i
$176$	2.48528			0.187335
$177$		0			0
$178$	10.4497	+	18.0995i	0.783242	+	1.35661i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	2.65685			0.197482			0.0987412	−	0.995113i	$-0.468518\pi$
$181$	2.65685			0.197482			0.0987412	+	0.995113i	$0.468518\pi$
$182$	−11.6569	+	28.5533i	−0.864064	+	2.11651i
$183$		0			0
$184$	−0.914214	+	1.58346i	−0.0673967	+	0.116735i
$185$		0			0
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	−7.65685			−0.558433
$189$		0			0
$190$	6.82843			0.495386
$191$	−6.41421	+	11.1097i	−0.464116	+	0.803873i	−0.999161	−	0.0409507i	$-0.986961\pi$
$191$	−6.41421	+	11.1097i	−0.464116	+	0.803873i	0.535045	+	0.844824i	$0.320295\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	14.0711	−	24.3718i	1.01024	−	1.74979i
$195$		0			0
$196$	−19.1421	−	18.7554i	−1.36730	−	1.33967i
$197$	12.3431			0.879413			0.439706	−	0.898142i	$-0.355083\pi$
$197$	12.3431			0.879413			0.439706	+	0.898142i	$0.355083\pi$
$198$		0			0
$199$	4.82843	+	8.36308i	0.342278	+	0.592843i	0.984855	−	0.173378i	$-0.0554682\pi$
$199$	4.82843	+	8.36308i	0.342278	+	0.592843i	−0.642577	+	0.766221i	$0.722135\pi$
$200$	2.20711	+	3.82282i	0.156066	+	0.270314i
$201$		0			0
$202$	−24.8995			−1.75192
$203$	2.62132	−	0.358719i	0.183981	−	0.0251772i
$204$		0			0
$205$	3.91421	−	6.77962i	0.273381	−	0.473509i
$206$	−2.91421	−	5.04757i	−0.203043	−	0.351681i
$207$		0			0
$208$	7.24264	−	12.5446i	0.502187	−	0.869813i
$209$	2.34315			0.162079
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$	−2.24264	+	3.88437i	−0.154025	+	0.266779i
$213$		0			0
$214$	−13.5711	−	23.5058i	−0.927699	−	1.60682i
$215$	1.79289	−	3.10538i	0.122274	−	0.211785i
$216$		0			0
$217$	9.72792	+	12.5446i	0.660374	+	0.851584i
$218$	32.5563			2.20499
$219$		0			0
$220$	1.58579	+	2.74666i	0.106914	+	0.185180i
$221$	−11.6569	−	20.1903i	−0.784125	−	1.35814i
$222$		0			0
$223$	0.343146			0.0229787			0.0114894	−	0.999934i	$-0.496343\pi$
$223$	0.343146			0.0229787			0.0114894	+	0.999934i	$0.496343\pi$
$224$	−2.57107	−	3.31552i	−0.171787	−	0.221527i
$225$		0			0
$226$	5.41421	−	9.37769i	0.360148	−	0.623795i
$227$	−3.48528	−	6.03668i	−0.231326	−	0.400669i	0.726872	−	0.686773i	$-0.240973\pi$
$227$	−3.48528	−	6.03668i	−0.231326	−	0.400669i	−0.958199	+	0.286104i	$0.907640\pi$
$228$		0			0
$229$	5.82843	−	10.0951i	0.385153	−	0.667105i	−0.606637	−	0.794979i	$-0.707482\pi$
$229$	5.82843	−	10.0951i	0.385153	−	0.667105i	0.991790	+	0.127874i	$0.0408152\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$	−4.41421			−0.289807
$233$	−8.41421	+	14.5738i	−0.551233	+	0.954764i	0.446952	+	0.894558i	$0.352509\pi$
$233$	−8.41421	+	14.5738i	−0.551233	+	0.954764i	−0.998186	+	0.0602067i	$0.980824\pi$
$234$		0			0
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	8.58579	−	14.8710i	0.558887	−	0.968021i
$237$		0			0
$238$	30.5563	−	4.18154i	1.98067	−	0.271049i
$239$	21.3137			1.37867			0.689335	−	0.724443i	$-0.257903\pi$
$239$	21.3137			1.37867			0.689335	+	0.724443i	$0.257903\pi$
$240$		0			0
$241$	−13.8284	−	23.9515i	−0.890767	−	1.54285i	−0.838957	−	0.544197i	$-0.816834\pi$
$241$	−13.8284	−	23.9515i	−0.890767	−	1.54285i	−0.0518100	−	0.998657i	$-0.516499\pi$
$242$	−12.4497	−	21.5636i	−0.800300	−	1.38616i
$243$		0			0
$244$	21.0000			1.34439
$245$	1.74264	−	6.77962i	0.111333	−	0.433134i
$246$		0			0
$247$	6.82843	−	11.8272i	0.434482	−	0.752546i
$248$	−13.2426	−	22.9369i	−0.840909	−	1.45650i
$249$		0			0
$250$	−1.20711	+	2.09077i	−0.0763441	+	0.132232i
$251$	9.31371			0.587876			0.293938	−	0.955824i	$-0.405034\pi$
$251$	9.31371			0.587876			0.293938	+	0.955824i	$0.405034\pi$
$252$		0			0
$253$	−0.343146			−0.0215734
$254$	−11.2426	+	19.4728i	−0.705426	+	1.22183i
$255$		0			0
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	3.17157	−	5.49333i	0.197837	−	0.342664i	−0.749990	−	0.661450i	$-0.769942\pi$
$257$	3.17157	−	5.49333i	0.197837	−	0.342664i	0.947827	+	0.318785i	$0.103275\pi$
$258$		0			0
$259$		0			0
$260$	18.4853			1.14641
$261$		0			0
$262$	23.3137	+	40.3805i	1.44033	+	2.49472i
$263$	−14.5208	−	25.1508i	−0.895392	−	1.55086i	−0.833319	−	0.552793i	$-0.813562\pi$
$263$	−14.5208	−	25.1508i	−0.895392	−	1.55086i	−0.0620729	−	0.998072i	$-0.519771\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$	11.0711	+	14.2767i	0.678811	+	0.875359i
$267$		0			0
$268$	−18.3492	+	31.7818i	−1.12086	+	1.94138i
$269$	10.2279	+	17.7153i	0.623607	+	1.08012i	0.988808	+	0.149191i	$0.0476669\pi$
$269$	10.2279	+	17.7153i	0.623607	+	1.08012i	−0.365201	+	0.930929i	$0.619000\pi$
$270$		0			0
$271$	−8.24264	+	14.2767i	−0.500705	+	0.867246i	0.499295	+	0.866432i	$0.333592\pi$
$271$	−8.24264	+	14.2767i	−0.500705	+	0.867246i	−1.00000		0.000813982i	$0.999741\pi$
$272$	−14.4853			−0.878299
$273$		0			0
$274$	−23.3137			−1.40843
$275$	−0.414214	+	0.717439i	−0.0249780	+	0.0432632i
$276$		0			0
$277$	−8.07107	−	13.9795i	−0.484943	−	0.839947i	0.514907	−	0.857246i	$-0.327826\pi$
$277$	−8.07107	−	13.9795i	−0.484943	−	0.839947i	−0.999850	+	0.0172994i	$0.994493\pi$
$278$	−19.4853	+	33.7495i	−1.16865	+	2.02416i
$279$		0			0
$280$	−4.41421	+	10.8126i	−0.263800	+	0.646175i
$281$	30.2843			1.80661			0.903304	−	0.429001i	$-0.141134\pi$
$281$	30.2843			1.80661			0.903304	+	0.429001i	$0.141134\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	8.58579	+	14.8710i	0.509473	+	0.882433i
$285$		0			0
$286$	9.65685			0.571022
$287$	20.5208	−	2.80821i	1.21131	−	0.165763i
$288$		0			0
$289$	−3.15685	+	5.46783i	−0.185697	+	0.321637i
$290$	−1.20711	−	2.09077i	−0.0708838	−	0.122774i
$291$		0			0
$292$	1.58579	−	2.74666i	0.0928011	−	0.160736i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$		0			0
$295$	4.48528			0.261143
$296$		0			0
$297$		0			0
$298$	2.62132	+	4.54026i	0.151849	+	0.263010i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	9.39949	−	1.28629i	0.541778	−	0.0741406i
$302$	−28.1421			−1.61940
$303$		0			0
$304$	−4.24264	−	7.34847i	−0.243332	−	0.421464i
$305$	2.74264	+	4.75039i	0.157043	+	0.272007i
$306$		0			0
$307$	−4.75736			−0.271517			−0.135758	−	0.990742i	$-0.543347\pi$
$307$	−4.75736			−0.271517			−0.135758	+	0.990742i	$0.543347\pi$
$308$	−3.17157	+	7.76874i	−0.180717	+	0.442665i
$309$		0			0
$310$	7.24264	−	12.5446i	0.411354	−	0.712487i
$311$	−6.58579	−	11.4069i	−0.373446	−	0.646827i	0.616647	−	0.787239i	$-0.288490\pi$
$311$	−6.58579	−	11.4069i	−0.373446	−	0.646827i	−0.990093	+	0.140413i	$0.955157\pi$
$312$		0			0
$313$	3.17157	−	5.49333i	0.179268	−	0.310501i	−0.762362	−	0.647151i	$-0.775960\pi$
$313$	3.17157	−	5.49333i	0.179268	−	0.310501i	0.941630	+	0.336650i	$0.109294\pi$
$314$	−41.7990			−2.35885
$315$		0			0
$316$	56.7696			3.19354
$317$	−6.89949	+	11.9503i	−0.387514	+	0.671194i	−0.992115	−	0.125335i	$-0.960000\pi$
$317$	−6.89949	+	11.9503i	−0.387514	+	0.671194i	0.604600	+	0.796529i	$0.293333\pi$
$318$		0			0
$319$	−0.414214	−	0.717439i	−0.0231915	−	0.0401689i
$320$	−4.91421	+	8.51167i	−0.274713	+	0.475817i
$321$		0			0
$322$	−1.62132	−	2.09077i	−0.0903527	−	0.116514i
$323$	−13.6569			−0.759888
$324$		0			0
$325$	2.41421	+	4.18154i	0.133916	+	0.231950i
$326$	14.8995	+	25.8067i	0.825207	+	1.42930i
$327$		0			0
$328$	−34.5563			−1.90806
$329$	2.00000	−	4.89898i	0.110264	−	0.270089i
$330$		0			0
$331$	−11.4853	+	19.8931i	−0.631288	+	1.09342i	0.356001	+	0.934486i	$0.384140\pi$
$331$	−11.4853	+	19.8931i	−0.631288	+	1.09342i	−0.987289	+	0.158937i	$0.949193\pi$
$332$	26.2782	+	45.5151i	1.44220	+	2.49797i
$333$		0			0
$334$	−27.0563	+	46.8630i	−1.48046	+	2.56423i
$335$	−9.58579			−0.523727
$336$		0			0
$337$	9.17157			0.499607			0.249804	−	0.968296i	$-0.419634\pi$
$337$	9.17157			0.499607			0.249804	+	0.968296i	$0.419634\pi$
$338$	12.4497	−	21.5636i	0.677177	−	1.17290i
$339$		0			0
$340$	−9.24264	−	16.0087i	−0.501253	−	0.868195i
$341$	2.48528	−	4.30463i	0.134586	−	0.233109i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	−15.8284			−0.853412
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	3.96447	+	6.86666i	0.212824	+	0.368621i	0.952597	−	0.304235i	$-0.0984007\pi$
$347$	3.96447	+	6.86666i	0.212824	+	0.368621i	−0.739773	+	0.672856i	$0.765067\pi$
$348$		0			0
$349$	−15.3431			−0.821300			−0.410650	−	0.911793i	$-0.634698\pi$
$349$	−15.3431			−0.821300			−0.410650	+	0.911793i	$0.634698\pi$
$350$	−6.32843	+	0.866025i	−0.338269	+	0.0462910i
$351$		0			0
$352$	−0.656854	+	1.13770i	−0.0350104	+	0.0606399i
$353$	−13.4142	−	23.2341i	−0.713967	−	1.23663i	−0.963357	−	0.268223i	$-0.913564\pi$
$353$	−13.4142	−	23.2341i	−0.713967	−	1.23663i	0.249390	−	0.968403i	$-0.419770\pi$
$354$		0			0
$355$	−2.24264	+	3.88437i	−0.119027	+	0.206161i
$356$	33.1421			1.75653
$357$		0			0
$358$	−24.1421			−1.27595
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	3.20711	−	5.55487i	0.168562	−	0.291958i
$363$		0			0
$364$	29.9706	+	38.6485i	1.57088	+	2.02573i
$365$	0.828427			0.0433619
$366$		0			0
$367$	1.37868	+	2.38794i	0.0719665	+	0.124650i	0.899763	−	0.436379i	$-0.143739\pi$
$367$	1.37868	+	2.38794i	0.0719665	+	0.124650i	−0.827797	+	0.561028i	$0.810406\pi$
$368$	0.621320	+	1.07616i	0.0323886	+	0.0560986i
$369$		0			0
$370$		0			0
$371$	−1.89949	−	2.44949i	−0.0986169	−	0.127171i
$372$		0			0
$373$	10.4853	−	18.1610i	0.542907	−	0.940343i	−0.455828	−	0.890068i	$-0.650657\pi$
$373$	10.4853	−	18.1610i	0.542907	−	0.940343i	0.998735	−	0.0502752i	$-0.0160098\pi$
$374$	−4.82843	−	8.36308i	−0.249672	−	0.432445i
$375$		0			0
$376$	−4.41421	+	7.64564i	−0.227646	+	0.394294i
$377$	−4.82843			−0.248677
$378$		0			0
$379$	26.8284			1.37808			0.689042	−	0.724722i	$-0.258032\pi$
$379$	26.8284			1.37808			0.689042	+	0.724722i	$0.258032\pi$
$380$	5.41421	−	9.37769i	0.277743	−	0.481065i
$381$		0			0
$382$	15.4853	+	26.8213i	0.792296	+	1.37230i
$383$	−1.44975	+	2.51104i	−0.0740786	+	0.128308i	−0.900685	−	0.434472i	$-0.856935\pi$
$383$	−1.44975	+	2.51104i	−0.0740786	+	0.128308i	0.826607	+	0.562780i	$0.190268\pi$
$384$		0			0
$385$	−2.17157	+	0.297173i	−0.110674	+	0.0151453i
$386$	4.82843			0.245760
$387$		0			0
$388$	−22.3137	−	38.6485i	−1.13281	−	1.96208i
$389$	11.8284	+	20.4874i	0.599725	+	1.03875i	0.992861	+	0.119274i	$0.0380567\pi$
$389$	11.8284	+	20.4874i	0.599725	+	1.03875i	−0.393136	+	0.919480i	$0.628610\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−29.7635	+	8.30153i	−1.50328	+	0.419291i
$393$		0			0
$394$	14.8995	−	25.8067i	0.750626	−	1.30012i
$395$	7.41421	+	12.8418i	0.373050	+	0.646141i
$396$		0			0
$397$	8.31371	−	14.3998i	0.417253	−	0.722704i	−0.578409	−	0.815747i	$-0.696326\pi$
$397$	8.31371	−	14.3998i	0.417253	−	0.722704i	0.995662	+	0.0930434i	$0.0296595\pi$
$398$	23.3137			1.16861
$399$		0			0
$400$	3.00000			0.150000
$401$	15.1569	−	26.2524i	0.756897	−	1.31098i	−0.187528	−	0.982259i	$-0.560048\pi$
$401$	15.1569	−	26.2524i	0.756897	−	1.31098i	0.944426	−	0.328725i	$-0.106619\pi$
$402$		0			0
$403$	−14.4853	−	25.0892i	−0.721563	−	1.24978i
$404$	−19.7426	+	34.1953i	−0.982233	+	1.70128i
$405$		0			0
$406$	2.41421	−	5.91359i	0.119815	−	0.293487i
$407$		0			0
$408$		0			0
$409$	7.39949	+	12.8163i	0.365881	+	0.633725i	0.988917	−	0.148468i	$-0.0474342\pi$
$409$	7.39949	+	12.8163i	0.365881	+	0.633725i	−0.623036	+	0.782193i	$0.714101\pi$
$410$	−9.44975	−	16.3674i	−0.466690	−	0.808330i
$411$		0			0
$412$	−9.24264			−0.455352
$413$	7.27208	+	9.37769i	0.357836	+	0.461446i
$414$		0			0
$415$	−6.86396	+	11.8887i	−0.336939	+	0.583595i
$416$	3.82843	+	6.63103i	0.187704	+	0.325113i
$417$		0			0
$418$	2.82843	−	4.89898i	0.138343	−	0.239617i
$419$	0.686292			0.0335275			0.0167638	−	0.999859i	$-0.494664\pi$
$419$	0.686292			0.0335275			0.0167638	+	0.999859i	$0.494664\pi$
$420$		0			0
$421$	13.4853			0.657232			0.328616	−	0.944464i	$-0.393418\pi$
$421$	13.4853			0.657232			0.328616	+	0.944464i	$0.393418\pi$
$422$	24.7279	−	42.8300i	1.20374	−	2.08493i
$423$		0			0
$424$	2.58579	+	4.47871i	0.125577	+	0.217506i
$425$	2.41421	−	4.18154i	0.117107	−	0.202835i
$426$		0			0
$427$	−5.48528	+	13.4361i	−0.265451	+	0.650220i
$428$	−43.0416			−2.08050
$429$		0			0
$430$	−4.32843	−	7.49706i	−0.208735	−	0.361540i
$431$	8.89949	+	15.4144i	0.428674	+	0.742484i	0.996756	−	0.0804875i	$-0.0256477\pi$
$431$	8.89949	+	15.4144i	0.428674	+	0.742484i	−0.568082	+	0.822972i	$0.692314\pi$
$432$		0			0
$433$	7.79899			0.374796			0.187398	−	0.982284i	$-0.439995\pi$
$433$	7.79899			0.374796			0.187398	+	0.982284i	$0.439995\pi$
$434$	37.9706	−	5.19615i	1.82265	−	0.249423i
$435$		0			0
$436$	25.8137	−	44.7107i	1.23625	−	2.14125i
$437$	0.585786	+	1.01461i	0.0280220	+	0.0485355i
$438$		0			0
$439$	16.9706	−	29.3939i	0.809961	−	1.40289i	−0.102930	−	0.994689i	$-0.532822\pi$
$439$	16.9706	−	29.3939i	0.809961	−	1.40289i	0.912890	−	0.408205i	$-0.133845\pi$
$440$	3.65685			0.174334
$441$		0			0
$442$	−56.2843			−2.67717
$443$	15.1066	−	26.1654i	0.717736	−	1.24316i	−0.244158	−	0.969735i	$-0.578512\pi$
$443$	15.1066	−	26.1654i	0.717736	−	1.24316i	0.961895	−	0.273420i	$-0.0881550\pi$
$444$		0			0
$445$	4.32843	+	7.49706i	0.205187	+	0.355395i
$446$	0.414214	−	0.717439i	0.0196136	−	0.0339717i
$447$		0			0
$448$	−25.7635	+	3.52565i	−1.21721	+	0.166571i
$449$	−3.82843			−0.180675			−0.0903373	−	0.995911i	$-0.528795\pi$
$449$	−3.82843			−0.180675			−0.0903373	+	0.995911i	$0.528795\pi$
$450$		0			0
$451$	−3.24264	−	5.61642i	−0.152690	−	0.264467i
$452$	−8.58579	−	14.8710i	−0.403841	−	0.699474i
$453$		0			0
$454$	−16.8284			−0.789797
$455$	−4.82843	+	11.8272i	−0.226360	+	0.554467i
$456$		0			0
$457$	−12.1421	+	21.0308i	−0.567985	+	0.983779i	0.428780	+	0.903409i	$0.358944\pi$
$457$	−12.1421	+	21.0308i	−0.567985	+	0.983779i	−0.996765	+	0.0803702i	$0.974390\pi$
$458$	−14.0711	−	24.3718i	−0.657498	−	1.13882i
$459$		0			0
$460$	−0.792893	+	1.37333i	−0.0369688	+	0.0640319i
$461$	−41.3137			−1.92417			−0.962086	−	0.272748i	$-0.912068\pi$
$461$	−41.3137			−1.92417			−0.962086	+	0.272748i	$0.912068\pi$
$462$		0			0
$463$	−37.0416			−1.72147			−0.860735	−	0.509053i	$-0.829996\pi$
$463$	−37.0416			−1.72147			−0.860735	+	0.509053i	$0.829996\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	20.3137	+	35.1844i	0.941014	+	1.62988i
$467$	−1.55025	+	2.68512i	−0.0717371	+	0.124252i	−0.899663	−	0.436586i	$-0.856188\pi$
$467$	−1.55025	+	2.68512i	−0.0717371	+	0.124252i	0.827926	+	0.560838i	$0.189521\pi$
$468$		0			0
$469$	−15.5416	−	20.0417i	−0.717646	−	0.925439i
$470$	−4.82843			−0.222719
$471$		0			0
$472$	−9.89949	−	17.1464i	−0.455661	−	0.789228i
$473$	−1.48528	−	2.57258i	−0.0682933	−	0.118287i
$474$		0			0
$475$	2.82843			0.129777
$476$	18.4853	−	45.2795i	0.847271	−	2.07538i
$477$		0			0
$478$	25.7279	−	44.5621i	1.17677	−	2.03822i
$479$	−17.8284	−	30.8797i	−0.814602	−	1.41093i	−0.909614	−	0.415455i	$-0.863622\pi$
$479$	−17.8284	−	30.8797i	−0.814602	−	1.41093i	0.0950120	−	0.995476i	$-0.469711\pi$
$480$		0			0
$481$		0			0
$482$	−66.7696			−3.04127
$483$		0			0
$484$	−39.4853			−1.79479
$485$	5.82843	−	10.0951i	0.264655	−	0.458396i
$486$		0			0
$487$	−2.17157	−	3.76127i	−0.0984034	−	0.170440i	0.812621	−	0.582793i	$-0.198040\pi$
$487$	−2.17157	−	3.76127i	−0.0984034	−	0.170440i	−0.911024	+	0.412353i	$0.864707\pi$
$488$	12.1066	−	20.9692i	0.548040	−	0.949233i
$489$		0			0
$490$	−12.0711	−	11.8272i	−0.545315	−	0.534298i
$491$	−9.31371			−0.420322			−0.210161	−	0.977667i	$-0.567399\pi$
$491$	−9.31371			−0.420322			−0.210161	+	0.977667i	$0.567399\pi$
$492$		0			0
$493$	2.41421	+	4.18154i	0.108731	+	0.188327i
$494$	−16.4853	−	28.5533i	−0.741708	−	1.28468i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	−11.7574	+	1.60896i	−0.527390	+	0.0721716i
$498$		0			0
$499$	0.414214	−	0.717439i	0.0185427	−	0.0321170i	−0.856605	−	0.515973i	$-0.827431\pi$
$499$	0.414214	−	0.717439i	0.0185427	−	0.0321170i	0.875148	+	0.483856i	$0.160764\pi$
$500$	1.91421	+	3.31552i	0.0856062	+	0.148274i
$501$		0			0
$502$	11.2426	−	19.4728i	0.501784	−	0.869115i
$503$	15.8701			0.707611			0.353805	−	0.935319i	$-0.384887\pi$
$503$	15.8701			0.707611			0.353805	+	0.935319i	$0.384887\pi$
$504$		0			0
$505$	−10.3137			−0.458954
$506$	−0.414214	+	0.717439i	−0.0184140	+	0.0318941i
$507$		0			0
$508$	17.8284	+	30.8797i	0.791009	+	1.37007i
$509$	6.67157	−	11.5555i	0.295712	−	0.512189i	−0.679438	−	0.733733i	$-0.737776\pi$
$509$	6.67157	−	11.5555i	0.295712	−	0.512189i	0.975150	+	0.221544i	$0.0711097\pi$
$510$		0			0
$511$	1.34315	+	1.73205i	0.0594173	+	0.0766214i
$512$	31.2426			1.38074
$513$		0			0
$514$	−7.65685	−	13.2621i	−0.337729	−	0.584964i
$515$	−1.20711	−	2.09077i	−0.0531915	−	0.0921303i
$516$		0			0
$517$	−1.65685			−0.0728684
$518$		0			0
$519$		0			0
$520$	10.6569	−	18.4582i	0.467334	−	0.809446i
$521$	7.48528	+	12.9649i	0.327936	+	0.568002i	0.982102	−	0.188349i	$-0.0603136\pi$
$521$	7.48528	+	12.9649i	0.327936	+	0.568002i	−0.654166	+	0.756351i	$0.726980\pi$
$522$		0			0
$523$	−17.8284	+	30.8797i	−0.779583	+	1.35028i	0.152600	+	0.988288i	$0.451235\pi$
$523$	−17.8284	+	30.8797i	−0.779583	+	1.35028i	−0.932182	+	0.361989i	$0.882098\pi$
$524$	73.9411			3.23013
$525$		0			0
$526$	−70.1127			−3.05706
$527$	−14.4853	+	25.0892i	−0.630989	+	1.09290i
$528$		0			0
$529$	11.4142	+	19.7700i	0.496270	+	0.859565i
$530$	−1.41421	+	2.44949i	−0.0614295	+	0.106399i
$531$		0			0
$532$	28.3848	−	3.88437i	1.23064	−	0.168409i
$533$	−37.7990			−1.63726
$534$		0			0
$535$	−5.62132	−	9.73641i	−0.243031	−	0.420942i
$536$	21.1569	+	36.6447i	0.913837	+	1.58281i
$537$		0			0
$538$	49.3848			2.12913
$539$	−4.14214	−	4.05845i	−0.178414	−	0.174810i
$540$		0			0
$541$	−3.67157	+	6.35935i	−0.157853	+	0.273410i	−0.934094	−	0.357026i	$-0.883791\pi$
$541$	−3.67157	+	6.35935i	−0.157853	+	0.273410i	0.776241	+	0.630436i	$0.217124\pi$
$542$	19.8995	+	34.4669i	0.854756	+	1.48048i
$543$		0			0
$544$	3.82843	−	6.63103i	0.164142	−	0.284303i
$545$	13.4853			0.577646
$546$		0			0
$547$	24.8995			1.06463			0.532313	−	0.846548i	$-0.321323\pi$
$547$	24.8995			1.06463			0.532313	+	0.846548i	$0.321323\pi$
$548$	−18.4853	+	32.0174i	−0.789652	+	1.36772i
$549$		0			0
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−1.41421	+	2.44949i	−0.0602475	+	0.104352i
$552$		0			0
$553$	−14.8284	+	36.3221i	−0.630569	+	1.54457i
$554$	−38.9706			−1.65570
$555$		0			0
$556$	30.8995	+	53.5195i	1.31043	+	2.26973i
$557$	11.1421	+	19.2987i	0.472107	+	0.817714i	0.999491	−	0.0319135i	$-0.0101601\pi$
$557$	11.1421	+	19.2987i	0.472107	+	0.817714i	−0.527383	+	0.849628i	$0.676827\pi$
$558$		0			0
$559$	−17.3137			−0.732292
$560$	4.86396	+	6.27231i	0.205540	+	0.265054i
$561$		0			0
$562$	36.5563	−	63.3175i	1.54204	−	2.67089i
$563$	20.8640	+	36.1374i	0.879311	+	1.52301i	0.852098	+	0.523382i	$0.175330\pi$
$563$	20.8640	+	36.1374i	0.879311	+	1.52301i	0.0272129	+	0.999630i	$0.491337\pi$
$564$		0			0
$565$	2.24264	−	3.88437i	0.0943486	−	0.163417i
$566$	−33.7990			−1.42068
$567$		0			0
$568$	19.7990			0.830747
$569$	3.82843	−	6.63103i	0.160496	−	0.277987i	−0.774551	−	0.632512i	$-0.782024\pi$
$569$	3.82843	−	6.63103i	0.160496	−	0.277987i	0.935047	+	0.354525i	$0.115357\pi$
$570$		0			0
$571$	−4.58579	−	7.94282i	−0.191909	−	0.332396i	0.753974	−	0.656905i	$-0.228135\pi$
$571$	−4.58579	−	7.94282i	−0.191909	−	0.332396i	−0.945883	+	0.324508i	$0.894801\pi$
$572$	7.65685	−	13.2621i	0.320149	−	0.554515i
$573$		0			0
$574$	18.8995	−	46.2941i	0.788850	−	1.93228i
$575$	−0.414214			−0.0172739
$576$		0			0
$577$	21.9706	+	38.0541i	0.914646	+	1.58421i	0.807418	+	0.589980i	$0.200864\pi$
$577$	21.9706	+	38.0541i	0.914646	+	1.58421i	0.107228	+	0.994234i	$0.465802\pi$
$578$	7.62132	+	13.2005i	0.317005	+	0.549069i
$579$		0			0
$580$	−3.82843			−0.158967
$581$	−35.9853	+	4.92447i	−1.49292	+	0.204302i
$582$		0			0
$583$	−0.485281	+	0.840532i	−0.0200983	+	0.0348113i
$584$	−1.82843	−	3.16693i	−0.0756609	−	0.131048i
$585$		0			0
$586$	19.3137	−	33.4523i	0.797842	−	1.38190i
$587$	34.2843			1.41506			0.707532	−	0.706682i	$-0.249809\pi$
$587$	34.2843			1.41506			0.707532	+	0.706682i	$0.249809\pi$
$588$		0			0
$589$	−16.9706			−0.699260
$590$	5.41421	−	9.37769i	0.222900	−	0.386074i
$591$		0			0
$592$		0			0
$593$	2.10051	−	3.63818i	0.0862574	−	0.149402i	−0.819669	−	0.572838i	$-0.805843\pi$
$593$	2.10051	−	3.63818i	0.0862574	−	0.149402i	0.905926	+	0.423435i	$0.139176\pi$
$594$		0			0
$595$	12.6569	−	1.73205i	0.518880	−	0.0710072i
$596$	8.31371			0.340543
$597$		0			0
$598$	2.41421	+	4.18154i	0.0987245	+	0.170996i
$599$	3.17157	+	5.49333i	0.129587	+	0.224451i	0.923517	−	0.383558i	$-0.125302\pi$
$599$	3.17157	+	5.49333i	0.129587	+	0.224451i	−0.793930	+	0.608010i	$0.791968\pi$
$600$		0			0
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$	8.65685	−	21.2049i	0.352827	−	0.864246i
$603$		0			0
$604$	−22.3137	+	38.6485i	−0.907932	+	1.57258i
$605$	−5.15685	−	8.93193i	−0.209656	−	0.363135i
$606$		0			0
$607$	−19.1066	+	33.0936i	−0.775513	+	1.34323i	0.158993	+	0.987280i	$0.449175\pi$
$607$	−19.1066	+	33.0936i	−0.775513	+	1.34323i	−0.934506	+	0.355948i	$0.884158\pi$
$608$	4.48528			0.181902
$609$		0			0
$610$	13.2426			0.536179
$611$	−4.82843	+	8.36308i	−0.195337	+	0.338334i
$612$		0			0
$613$	−17.7279	−	30.7057i	−0.716024	−	1.24019i	−0.962563	−	0.271057i	$-0.912627\pi$
$613$	−17.7279	−	30.7057i	−0.716024	−	1.24019i	0.246539	−	0.969133i	$-0.420707\pi$
$614$	−5.74264	+	9.94655i	−0.231754	+	0.401410i
$615$		0			0
$616$	5.92893	+	7.64564i	0.238883	+	0.308052i
$617$	−11.3137			−0.455473			−0.227736	−	0.973723i	$-0.573132\pi$
$617$	−11.3137			−0.455473			−0.227736	+	0.973723i	$0.573132\pi$
$618$		0			0
$619$	−12.7574	−	22.0964i	−0.512762	−	0.888129i	−0.999890	−	0.0147990i	$-0.995289\pi$
$619$	−12.7574	−	22.0964i	−0.512762	−	0.888129i	0.487129	−	0.873330i	$-0.338044\pi$
$620$	−11.4853	−	19.8931i	−0.461260	−	0.798926i
$621$		0			0
$622$	−31.7990			−1.27502
$623$	−8.65685	+	21.2049i	−0.346830	+	0.849555i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.65685	−	13.2621i	−0.306029	−	0.530059i
$627$		0			0
$628$	−33.1421	+	57.4039i	−1.32252	+	2.29066i
$629$		0			0
$630$		0			0
$631$	−20.1421			−0.801846			−0.400923	−	0.916112i	$-0.631310\pi$
$631$	−20.1421			−0.801846			−0.400923	+	0.916112i	$0.631310\pi$
$632$	32.7279	−	56.6864i	1.30185	−	2.25486i
$633$		0			0
$634$	16.6569	+	28.8505i	0.661528	+	1.14580i
$635$	−4.65685	+	8.06591i	−0.184802	+	0.320086i
$636$		0			0
$637$	−32.5563	+	9.08052i	−1.28993	+	0.359783i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	10.2782	+	17.8023i	0.406281	+	0.703699i
$641$	15.7426	+	27.2671i	0.621797	+	1.07698i	0.989151	+	0.146903i	$0.0469304\pi$
$641$	15.7426	+	27.2671i	0.621797	+	1.07698i	−0.367354	+	0.930081i	$0.619736\pi$
$642$		0			0
$643$	26.2843			1.03655			0.518275	−	0.855214i	$-0.326574\pi$
$643$	26.2843			1.03655			0.518275	+	0.855214i	$0.326574\pi$
$644$	−4.15685	+	0.568852i	−0.163803	+	0.0224159i
$645$		0			0
$646$	−16.4853	+	28.5533i	−0.648605	+	1.12342i
$647$	−15.5208	−	26.8828i	−0.610186	−	1.05687i	−0.991209	−	0.132308i	$-0.957761\pi$
$647$	−15.5208	−	26.8828i	−0.610186	−	1.05687i	0.381022	−	0.924566i	$-0.375572\pi$
$648$		0			0
$649$	1.85786	−	3.21792i	0.0729276	−	0.126314i
$650$	11.6569			0.457219
$651$		0			0
$652$	47.2548			1.85064
$653$	−9.58579	+	16.6031i	−0.375121	+	0.649728i	−0.990345	−	0.138624i	$-0.955732\pi$
$653$	−9.58579	+	16.6031i	−0.375121	+	0.649728i	0.615224	+	0.788352i	$0.289065\pi$
$654$		0			0
$655$	9.65685	+	16.7262i	0.377325	+	0.653545i
$656$	−11.7426	+	20.3389i	−0.458473	+	0.794099i
$657$		0			0
$658$	−7.82843	−	10.0951i	−0.305184	−	0.393549i
$659$	−21.1716			−0.824727			−0.412364	−	0.911019i	$-0.635297\pi$
$659$	−21.1716			−0.824727			−0.412364	+	0.911019i	$0.635297\pi$
$660$		0			0
$661$	−15.9142	−	27.5642i	−0.618991	−	1.07212i	−0.989670	−	0.143363i	$-0.954208\pi$
$661$	−15.9142	−	27.5642i	−0.618991	−	1.07212i	0.370679	−	0.928761i	$-0.379125\pi$
$662$	27.7279	+	48.0262i	1.07768	+	1.86659i
$663$		0			0
$664$	60.5980			2.35166
$665$	4.58579	+	5.91359i	0.177829	+	0.229319i
$666$		0			0
$667$	0.207107	−	0.358719i	0.00801921	−	0.0138897i
$668$	42.9056	+	74.3147i	1.66007	+	2.87532i
$669$		0			0
$670$	−11.5711	+	20.0417i	−0.447029	+	0.774278i
$671$	4.54416			0.175425
$672$		0			0
$673$	29.6569			1.14319			0.571594	−	0.820537i	$-0.306325\pi$
$673$	29.6569			1.14319			0.571594	+	0.820537i	$0.306325\pi$
$674$	11.0711	−	19.1757i	0.426442	−	0.738619i
$675$		0			0
$676$	−19.7426	−	34.1953i	−0.759332	−	1.31520i
$677$	−14.0711	+	24.3718i	−0.540795	+	0.936685i	0.458064	+	0.888919i	$0.348543\pi$
$677$	−14.0711	+	24.3718i	−0.540795	+	0.936685i	−0.998859	+	0.0477651i	$0.984790\pi$
$678$		0			0
$679$	30.5563	−	4.18154i	1.17265	−	0.160473i
$680$	−21.3137			−0.817343
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−17.3787	−	30.1008i	−0.664977	−	1.15177i	−0.979292	−	0.202455i	$-0.935108\pi$
$683$	−17.3787	−	30.1008i	−0.664977	−	1.15177i	0.314315	−	0.949319i	$-0.398225\pi$
$684$		0			0
$685$	−9.65685			−0.368969
$686$	5.15685	−	44.4135i	0.196890	−	1.69571i
$687$		0			0
$688$	−5.37868	+	9.31615i	−0.205060	+	0.355175i
$689$	2.82843	+	4.89898i	0.107754	+	0.186636i
$690$		0			0
$691$	−0.414214	+	0.717439i	−0.0157574	+	0.0272927i	−0.873797	−	0.486292i	$-0.838349\pi$
$691$	−0.414214	+	0.717439i	−0.0157574	+	0.0272927i	0.858039	+	0.513584i	$0.171683\pi$
$692$	−12.6863			−0.482260
$693$		0			0
$694$	19.1421			0.726626
$695$	−8.07107	+	13.9795i	−0.306153	+	0.530273i
$696$		0			0
$697$	18.8995	+	32.7349i	0.715869	+	1.23992i
$698$	−18.5208	+	32.0790i	−0.701023	+	1.21421i
$699$		0			0
$700$	−3.82843	+	9.37769i	−0.144701	+	0.354443i
$701$	3.20101			0.120900			0.0604502	−	0.998171i	$-0.480746\pi$
$701$	3.20101			0.120900			0.0604502	+	0.998171i	$0.480746\pi$
$702$		0			0
$703$		0			0
$704$	4.07107	+	7.05130i	0.153434	+	0.265756i
$705$		0			0
$706$	−64.7696			−2.43763
$707$	−16.7218	−	21.5636i	−0.628889	−	0.810982i
$708$		0			0
$709$	−7.84315	+	13.5847i	−0.294556	+	0.510185i	−0.974881	−	0.222725i	$-0.928505\pi$
$709$	−7.84315	+	13.5847i	−0.294556	+	0.510185i	0.680326	+	0.732910i	$0.261838\pi$
$710$	5.41421	+	9.37769i	0.203192	+	0.351939i
$711$		0			0
$712$	19.1066	−	33.0936i	0.716050	−	1.24024i
$713$	2.48528			0.0930745
$714$		0			0
$715$	4.00000			0.149592
$716$	−19.1421	+	33.1552i	−0.715375	+	1.23907i
$717$		0			0
$718$	12.0711	+	20.9077i	0.450488	+	0.780269i
$719$	10.5563	−	18.2841i	0.393685	−	0.681883i	−0.599247	−	0.800564i	$-0.704533\pi$
$719$	10.5563	−	18.2841i	0.393685	−	0.681883i	0.992932	+	0.118681i	$0.0378666\pi$
$720$		0			0
$721$	2.41421	−	5.91359i	0.0899100	−	0.220234i
$722$	26.5563			0.988325
$723$		0			0
$724$	−5.08579	−	8.80884i	−0.189012	−	0.327378i
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	−37.5858			−1.39398			−0.696990	−	0.717081i	$-0.745478\pi$
$727$	−37.5858			−1.39398			−0.696990	+	0.717081i	$0.745478\pi$
$728$	55.8701	−	7.64564i	2.07068	−	0.283366i
$729$		0			0
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	8.65685	+	14.9941i	0.320185	+	0.554577i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	6.65685			0.245709
$735$		0			0
$736$	−0.656854			−0.0242120
$737$	−3.97056	+	6.87722i	−0.146258	+	0.253326i
$738$		0			0
$739$	10.5563	+	18.2841i	0.388322	+	0.672593i	0.992224	−	0.124466i	$-0.0397216\pi$
$739$	10.5563	+	18.2841i	0.388322	+	0.672593i	−0.603902	+	0.797058i	$0.706388\pi$
$740$		0			0
$741$		0			0
$742$	−7.41421	+	1.01461i	−0.272184	+	0.0372476i
$743$	16.0711			0.589590			0.294795	−	0.955560i	$-0.404749\pi$
$743$	16.0711			0.589590			0.294795	+	0.955560i	$0.404749\pi$
$744$		0			0
$745$	1.08579	+	1.88064i	0.0397801	+	0.0689012i
$746$	−25.3137	−	43.8446i	−0.926801	−	1.60527i
$747$		0			0
$748$	−15.3137			−0.559925
$749$	11.2426	−	27.5387i	0.410797	−	1.00624i
$750$		0			0
$751$	15.1716	−	26.2779i	0.553619	−	0.958895i	−0.444391	−	0.895833i	$-0.646580\pi$
$751$	15.1716	−	26.2779i	0.553619	−	0.958895i	0.998010	−	0.0630625i	$-0.0200868\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	−5.82843	+	10.0951i	−0.212259	+	0.367643i
$755$	−11.6569			−0.424236
$756$		0			0
$757$	−31.4558			−1.14328			−0.571641	−	0.820504i	$-0.693693\pi$
$757$	−31.4558			−1.14328			−0.571641	+	0.820504i	$0.693693\pi$
$758$	32.3848	−	56.0921i	1.17627	−	2.03736i
$759$		0			0
$760$	−6.24264	−	10.8126i	−0.226444	−	0.392213i
$761$	4.65685	−	8.06591i	0.168811	−	0.292389i	−0.769191	−	0.639019i	$-0.779341\pi$
$761$	4.65685	−	8.06591i	0.168811	−	0.292389i	0.938002	+	0.346630i	$0.112674\pi$
$762$		0			0
$763$	21.8640	+	28.1946i	0.791529	+	1.02071i
$764$	49.1127			1.77684
$765$		0			0
$766$	3.50000	+	6.06218i	0.126460	+	0.219035i
$767$	−10.8284	−	18.7554i	−0.390992	−	0.677218i
$768$		0			0
$769$	−0.627417			−0.0226252			−0.0113126	−	0.999936i	$-0.503601\pi$
$769$	−0.627417			−0.0226252			−0.0113126	+	0.999936i	$0.503601\pi$
$770$	−2.00000	+	4.89898i	−0.0720750	+	0.176547i
$771$		0			0
$772$	3.82843	−	6.63103i	0.137788	−	0.238656i
$773$	−18.5563	−	32.1405i	−0.667425	−	1.15601i	−0.978622	−	0.205669i	$-0.934063\pi$
$773$	−18.5563	−	32.1405i	−0.667425	−	1.15601i	0.311196	−	0.950346i	$-0.399270\pi$
$774$		0			0
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	−51.4558			−1.84716
$777$		0			0
$778$	57.1127			2.04759
$779$	−11.0711	+	19.1757i	−0.396662	+	0.687039i
$780$		0			0
$781$	1.85786	+	3.21792i	0.0664796	+	0.115146i
$782$	2.41421	−	4.18154i	0.0863321	−	0.149532i
$783$		0			0
$784$	−5.22792	+	20.3389i	−0.186712	+	0.726388i
$785$	−17.3137			−0.617953
$786$		0			0
$787$	−1.27817	−	2.21386i	−0.0455620	−	0.0789157i	0.842345	−	0.538939i	$-0.181175\pi$
$787$	−1.27817	−	2.21386i	−0.0455620	−	0.0789157i	−0.887907	+	0.460023i	$0.847841\pi$
$788$	−23.6274	−	40.9239i	−0.841692	−	1.45785i
$789$		0			0
$790$	35.7990			1.27367
$791$	11.7574	−	1.60896i	0.418044	−	0.0572080i
$792$		0			0
$793$	13.2426	−	22.9369i	0.470260	−	0.814514i
$794$	−20.0711	−	34.7641i	−0.712296	−	1.23373i
$795$		0			0
$796$	18.4853	−	32.0174i	0.655193	−	1.13483i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$	9.65685			0.341635
$800$	−0.792893	+	1.37333i	−0.0280330	+	0.0485546i
$801$		0			0
$802$	−36.5919	−	63.3790i	−1.29210	−	2.23799i
$803$	0.343146	−	0.594346i	0.0121094	−	0.0209740i
$804$		0			0
$805$	−0.671573	−	0.866025i	−0.0236698	−	0.0305234i
$806$	−69.9411			−2.46357
$807$		0			0
$808$	22.7635	+	39.4275i	0.800816	+	1.38705i
$809$	17.8137	+	30.8542i	0.626297	+	1.08478i	0.988289	+	0.152596i	$0.0487634\pi$
$809$	17.8137	+	30.8542i	0.626297	+	1.08478i	−0.361992	+	0.932181i	$0.617903\pi$
$810$		0			0
$811$	−20.6274			−0.724327			−0.362163	−	0.932115i	$-0.617962\pi$
$811$	−20.6274			−0.724327			−0.362163	+	0.932115i	$0.617962\pi$
$812$	−6.20711	−	8.00436i	−0.217827	−	0.280898i
$813$		0			0
$814$		0			0
$815$	6.17157	+	10.6895i	0.216181	+	0.374436i
$816$		0			0
$817$	−5.07107	+	8.78335i	−0.177414	+	0.307290i
$818$	35.7279			1.24920
$819$		0			0
$820$	−29.9706			−1.04662
$821$	23.9706	−	41.5182i	0.836578	−	1.44900i	−0.0561604	−	0.998422i	$-0.517886\pi$
$821$	23.9706	−	41.5182i	0.836578	−	1.44900i	0.892739	−	0.450575i	$-0.148781\pi$
$822$		0			0
$823$	−1.03553	−	1.79360i	−0.0360964	−	0.0625209i	0.847413	−	0.530935i	$-0.178159\pi$
$823$	−1.03553	−	1.79360i	−0.0360964	−	0.0625209i	−0.883509	+	0.468414i	$0.844826\pi$
$824$	−5.32843	+	9.22911i	−0.185625	+	0.321511i
$825$		0			0
$826$	28.3848	−	3.88437i	0.987633	−	0.135154i
$827$	26.2132			0.911522			0.455761	−	0.890102i	$-0.349367\pi$
$827$	26.2132			0.911522			0.455761	+	0.890102i	$0.349367\pi$
$828$		0			0
$829$	−14.6569	−	25.3864i	−0.509054	−	0.881707i	−0.999945	−	0.0104859i	$-0.996662\pi$
$829$	−14.6569	−	25.3864i	−0.509054	−	0.881707i	0.490891	−	0.871221i	$-0.336671\pi$
$830$	16.5711	+	28.7019i	0.575190	+	0.996259i
$831$		0			0
$832$	47.4558			1.64524
$833$	24.1421	+	23.6544i	0.836475	+	0.819575i
$834$		0			0
$835$	−11.2071	+	19.4113i	−0.387838	+	0.671755i
$836$	−4.48528	−	7.76874i	−0.155127	−	0.268687i
$837$		0			0
$838$	0.828427	−	1.43488i	0.0286175	−	0.0495670i
$839$	−15.1716			−0.523781			−0.261890	−	0.965098i	$-0.584346\pi$
$839$	−15.1716			−0.523781			−0.261890	+	0.965098i	$0.584346\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	16.2782	−	28.1946i	0.560983	−	0.971651i
$843$		0			0
$844$	−39.2132	−	67.9193i	−1.34977	−	2.33788i
$845$	5.15685	−	8.93193i	0.177401	−	0.307268i
$846$		0			0
$847$	10.3137	−	25.2633i	0.354383	−	0.868058i
$848$	3.51472			0.120696
$849$		0			0
$850$	−5.82843	−	10.0951i	−0.199913	−	0.346260i
$851$		0			0
$852$		0			0
$853$	2.54416			0.0871102			0.0435551	−	0.999051i	$-0.486132\pi$
$853$	2.54416			0.0871102			0.0435551	+	0.999051i	$0.486132\pi$
$854$	21.4706	+	27.6873i	0.734708	+	0.947441i
$855$		0			0
$856$	−24.8137	+	42.9786i	−0.848115	+	1.46898i
$857$	17.1421	+	29.6910i	0.585564	+	1.01423i	0.994805	+	0.101800i	$0.0324603\pi$
$857$	17.1421	+	29.6910i	0.585564	+	1.01423i	−0.409241	+	0.912426i	$0.634206\pi$
$858$		0			0
$859$	−0.686292	+	1.18869i	−0.0234160	+	0.0405576i	−0.877496	−	0.479584i	$-0.840788\pi$
$859$	−0.686292	+	1.18869i	−0.0234160	+	0.0405576i	0.854080	+	0.520142i	$0.174121\pi$
$860$	−13.7279			−0.468118
$861$		0			0
$862$	42.9706			1.46358
$863$	7.27817	−	12.6062i	0.247752	−	0.429119i	−0.715150	−	0.698971i	$-0.753642\pi$
$863$	7.27817	−	12.6062i	0.247752	−	0.429119i	0.962902	+	0.269852i	$0.0869749\pi$
$864$		0			0
$865$	−1.65685	−	2.86976i	−0.0563347	−	0.0975746i
$866$	9.41421	−	16.3059i	0.319908	−	0.554097i
$867$		0			0
$868$	22.9706	−	56.2662i	0.779672	−	1.90980i
$869$	12.2843			0.416715
$870$		0			0
$871$	23.1421	+	40.0834i	0.784141	+	1.35817i
$872$	−29.7635	−	51.5518i	−1.00792	−	1.74576i
$873$		0			0
$874$	2.82843			0.0956730
$875$	−2.62132	+	0.358719i	−0.0886168	+	0.0121269i
$876$		0			0
$877$	−12.5858	+	21.7992i	−0.424992	+	0.736107i	−0.996420	−	0.0845449i	$-0.973056\pi$
$877$	−12.5858	+	21.7992i	−0.424992	+	0.736107i	0.571428	+	0.820652i	$0.306390\pi$
$878$	−40.9706	−	70.9631i	−1.38269	−	2.39489i
$879$		0			0
$880$	1.24264	−	2.15232i	0.0418894	−	0.0725546i
$881$	−1.82843			−0.0616013			−0.0308006	−	0.999526i	$-0.509806\pi$
$881$	−1.82843			−0.0616013			−0.0308006	+	0.999526i	$0.509806\pi$
$882$		0			0
$883$	18.2843			0.615315			0.307657	−	0.951497i	$-0.400455\pi$
$883$	18.2843			0.615315			0.307657	+	0.951497i	$0.400455\pi$
$884$	−44.6274	+	77.2970i	−1.50098	+	2.59978i
$885$		0			0
$886$	−36.4706	−	63.1689i	−1.22525	−	2.12220i
$887$	14.9645	−	25.9192i	0.502458	−	0.870282i	−0.497538	−	0.867442i	$-0.665763\pi$
$887$	14.9645	−	25.9192i	0.502458	−	0.870282i	0.999996	−	0.00284012i	$-0.000904038\pi$
$888$		0			0
$889$	−24.4142	+	3.34101i	−0.818826	+	0.112054i
$890$	20.8995			0.700553
$891$		0			0
$892$	−0.656854	−	1.13770i	−0.0219931	−	0.0380932i
$893$	2.82843	+	4.89898i	0.0946497	+	0.163938i
$894$		0			0
$895$	−10.0000			−0.334263
$896$	−20.5563	+	50.3526i	−0.686739	+	1.68216i
$897$		0			0
$898$	−4.62132	+	8.00436i	−0.154215	+	0.267109i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	2.82843	−	4.89898i	0.0942286	−	0.163209i
$902$	−15.6569			−0.521316
$903$		0			0
$904$	−19.7990			−0.658505
$905$	1.32843	−	2.30090i	0.0441584	−	0.0764846i
$906$		0			0
$907$	7.10660	+	12.3090i	0.235971	+	0.408713i	0.959554	−	0.281523i	$-0.0908397\pi$
$907$	7.10660	+	12.3090i	0.235971	+	0.408713i	−0.723584	+	0.690237i	$0.757506\pi$
$908$	−13.3431	+	23.1110i	−0.442808	+	0.766966i
$909$		0			0
$910$	18.8995	+	24.3718i	0.626512	+	0.807917i
$911$	10.2010			0.337975			0.168987	−	0.985618i	$-0.445950\pi$
$911$	10.2010			0.337975			0.168987	+	0.985618i	$0.445950\pi$
$912$		0			0
$913$	5.68629	+	9.84895i	0.188189	+	0.325953i
$914$	29.3137	+	50.7728i	0.969611	+	1.67942i
$915$		0			0
$916$	−44.6274			−1.47453
$917$	−19.3137	+	47.3087i	−0.637795	+	1.56227i
$918$		0			0
$919$	21.5563	−	37.3367i	0.711078	−	1.23162i	−0.253374	−	0.967368i	$-0.581540\pi$
$919$	21.5563	−	37.3367i	0.711078	−	1.23162i	0.964453	−	0.264256i	$-0.0851262\pi$
$920$	0.914214	+	1.58346i	0.0301407	+	0.0522053i
$921$		0			0
$922$	−49.8701	+	86.3775i	−1.64238	+	2.84469i
$923$	21.6569			0.712844
$924$		0			0
$925$		0			0
$926$	−44.7132	+	77.4455i	−1.46937	+	2.54502i
$927$		0			0
$928$	−0.792893	−	1.37333i	−0.0260280	−	0.0450818i
$929$	2.74264	−	4.75039i	0.0899831	−	0.155855i	−0.817521	−	0.575899i	$-0.804652\pi$
$929$	2.74264	−	4.75039i	0.0899831	−	0.155855i	0.907504	+	0.420044i	$0.137985\pi$
$930$		0			0
$931$	−4.92893	+	19.1757i	−0.161539	+	0.628457i
$932$	64.4264			2.11036
$933$		0			0
$934$	3.74264	+	6.48244i	0.122463	+	0.212112i
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$		0			0
$937$	34.6274			1.13123			0.565614	−	0.824670i	$-0.308639\pi$
$937$	34.6274			1.13123			0.565614	+	0.824670i	$0.308639\pi$
$938$	−60.6630	+	8.30153i	−1.98072	+	0.271055i
$939$		0			0
$940$	−3.82843	+	6.63103i	−0.124870	+	0.216280i
$941$	−23.1421	−	40.0834i	−0.754412	−	1.30668i	−0.945666	−	0.325139i	$-0.894589\pi$
$941$	−23.1421	−	40.0834i	−0.754412	−	1.30668i	0.191254	−	0.981541i	$-0.438745\pi$
$942$		0			0
$943$	1.62132	−	2.80821i	0.0527975	−	0.0914479i
$944$	−13.4558			−0.437950
$945$		0			0
$946$	−7.17157			−0.233168
$947$	16.5919	−	28.7380i	0.539164	−	0.933859i	−0.459786	−	0.888030i	$-0.652074\pi$
$947$	16.5919	−	28.7380i	0.539164	−	0.933859i	0.998949	−	0.0458290i	$-0.0145929\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	3.41421	−	5.91359i	0.110772	−	0.191862i
$951$		0			0
$952$	−34.5563	−	44.5621i	−1.11998	−	1.44426i
$953$	13.6569			0.442389			0.221194	−	0.975230i	$-0.429004\pi$
$953$	13.6569			0.442389			0.221194	+	0.975230i	$0.429004\pi$
$954$		0			0
$955$	6.41421	+	11.1097i	0.207559	+	0.359503i
$956$	−40.7990	−	70.6659i	−1.31953	−	2.28550i
$957$		0			0
$958$	−86.0833			−2.78122
$959$	−15.6569	−	20.1903i	−0.505586	−	0.651978i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$		0			0
$964$	−52.9411	+	91.6967i	−1.70512	+	2.95335i
$965$	2.00000			0.0643823
$966$		0			0
$967$	37.5269			1.20678			0.603392	−	0.797445i	$-0.293815\pi$
$967$	37.5269			1.20678			0.603392	+	0.797445i	$0.293815\pi$
$968$	−22.7635	+	39.4275i	−0.731645	+	1.26725i
$969$		0			0
$970$	−14.0711	−	24.3718i	−0.451795	−	0.782531i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$		0			0
$973$	−42.3137	+	5.79050i	−1.35652	+	0.185635i
$974$	−10.4853			−0.335970
$975$		0			0
$976$	−8.22792	−	14.2512i	−0.263369	−	0.456169i
$977$	−0.656854	−	1.13770i	−0.0210146	−	0.0363984i	0.855327	−	0.518089i	$-0.173356\pi$
$977$	−0.656854	−	1.13770i	−0.0210146	−	0.0363984i	−0.876341	+	0.481690i	$0.840023\pi$
$978$		0			0
$979$	7.17157			0.229204
$980$	−25.8137	+	7.19988i	−0.824589	+	0.229992i
$981$		0			0
$982$	−11.2426	+	19.4728i	−0.358767	+	0.621403i
$983$	14.1066	+	24.4334i	0.449931	+	0.779303i	0.998381	−	0.0568803i	$-0.0181153\pi$
$983$	14.1066	+	24.4334i	0.449931	+	0.779303i	−0.548450	+	0.836183i	$0.684782\pi$
$984$		0			0
$985$	6.17157	−	10.6895i	0.196643	−	0.340595i
$986$	11.6569			0.371230
$987$		0			0
$988$	−52.2843			−1.66338
$989$	0.742641	−	1.28629i	0.0236146	−	0.0409017i
$990$		0			0
$991$	2.17157	+	3.76127i	0.0689823	+	0.119481i	0.898454	−	0.439069i	$-0.144691\pi$
$991$	2.17157	+	3.76127i	0.0689823	+	0.119481i	−0.829471	+	0.558549i	$0.811358\pi$
$992$	4.75736	−	8.23999i	0.151046	−	0.261620i
$993$		0			0
$994$	−10.8284	+	26.5241i	−0.343457	+	0.841294i
$995$	9.65685			0.306143
$996$		0			0
$997$	−16.7279	−	28.9736i	−0.529779	−	0.917603i	−0.999397	−	0.0347337i	$-0.988942\pi$
$997$	−16.7279	−	28.9736i	−0.529779	−	0.917603i	0.469618	−	0.882870i	$-0.344392\pi$
$998$	−1.00000	−	1.73205i	−0.0316544	−	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.e.226.2		4
3.2	odd	2		35.2.e.a.16.1	yes	4
7.2	even	3		2205.2.a.n.1.1		2
7.4	even	3	inner	315.2.j.e.46.2		4
7.5	odd	6		2205.2.a.q.1.1		2
12.11	even	2		560.2.q.k.401.1		4
15.2	even	4		175.2.k.a.149.1		8
15.8	even	4		175.2.k.a.149.4		8
15.14	odd	2		175.2.e.c.51.2		4
21.2	odd	6		245.2.a.h.1.2		2
21.5	even	6		245.2.a.g.1.2		2
21.11	odd	6		35.2.e.a.11.1	✓	4
21.17	even	6		245.2.e.e.116.1		4
21.20	even	2		245.2.e.e.226.1		4
84.11	even	6		560.2.q.k.81.1		4
84.23	even	6		3920.2.a.bq.1.2		2
84.47	odd	6		3920.2.a.bv.1.1		2
105.2	even	12		1225.2.b.g.99.4		4
105.23	even	12		1225.2.b.g.99.1		4
105.32	even	12		175.2.k.a.74.4		8
105.44	odd	6		1225.2.a.k.1.1		2
105.47	odd	12		1225.2.b.h.99.4		4
105.53	even	12		175.2.k.a.74.1		8
105.68	odd	12		1225.2.b.h.99.1		4
105.74	odd	6		175.2.e.c.151.2		4
105.89	even	6		1225.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.1	✓	4	21.11	odd	6
35.2.e.a.16.1	yes	4	3.2	odd	2
175.2.e.c.51.2		4	15.14	odd	2
175.2.e.c.151.2		4	105.74	odd	6
175.2.k.a.74.1		8	105.53	even	12
175.2.k.a.74.4		8	105.32	even	12
175.2.k.a.149.1		8	15.2	even	4
175.2.k.a.149.4		8	15.8	even	4
245.2.a.g.1.2		2	21.5	even	6
245.2.a.h.1.2		2	21.2	odd	6
245.2.e.e.116.1		4	21.17	even	6
245.2.e.e.226.1		4	21.20	even	2
315.2.j.e.46.2		4	7.4	even	3	inner
315.2.j.e.226.2		4	1.1	even	1	trivial
560.2.q.k.81.1		4	84.11	even	6
560.2.q.k.401.1		4	12.11	even	2
1225.2.a.k.1.1		2	105.44	odd	6
1225.2.a.m.1.1		2	105.89	even	6
1225.2.b.g.99.1		4	105.23	even	12
1225.2.b.g.99.4		4	105.2	even	12
1225.2.b.h.99.1		4	105.68	odd	12
1225.2.b.h.99.4		4	105.47	odd	12
2205.2.a.n.1.1		2	7.2	even	3
2205.2.a.q.1.1		2	7.5	odd	6
3920.2.a.bq.1.2		2	84.23	even	6
3920.2.a.bv.1.1		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 - 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +O(q^{10})\)	\(q+(1.20711 - 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} -4.41421 q^{8} +(-1.20711 - 2.09077i) q^{10} +(-0.414214 - 0.717439i) q^{11} -4.82843 q^{13} +(2.41421 - 5.91359i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(2.41421 + 4.18154i) q^{17} +(-1.41421 + 2.44949i) q^{19} -3.82843 q^{20} -2.00000 q^{22} +(0.207107 - 0.358719i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} +(-6.20711 - 8.00436i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-0.792893 - 1.37333i) q^{32} +11.6569 q^{34} +(1.00000 - 2.44949i) q^{35} +(3.41421 + 5.91359i) q^{38} +(-2.20711 + 3.82282i) q^{40} +7.82843 q^{41} +3.58579 q^{43} +(-1.58579 + 2.74666i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +(6.74264 - 1.88064i) q^{49} -2.41421 q^{50} +(9.24264 + 16.0087i) q^{52} +(-0.585786 - 1.01461i) q^{53} -0.828427 q^{55} +(-11.5711 + 1.58346i) q^{56} +(1.20711 - 2.09077i) q^{58} +(2.24264 + 3.88437i) q^{59} +(-2.74264 + 4.75039i) q^{61} +14.4853 q^{62} -9.82843 q^{64} +(-2.41421 + 4.18154i) q^{65} +(-4.79289 - 8.30153i) q^{67} +(9.24264 - 16.0087i) q^{68} +(-3.91421 - 5.04757i) q^{70} -4.48528 q^{71} +(0.414214 + 0.717439i) q^{73} +10.8284 q^{76} +(-1.34315 - 1.73205i) q^{77} +(-7.41421 + 12.8418i) q^{79} +(1.50000 + 2.59808i) q^{80} +(9.44975 - 16.3674i) q^{82} -13.7279 q^{83} +4.82843 q^{85} +(4.32843 - 7.49706i) q^{86} +(1.82843 + 3.16693i) q^{88} +(-4.32843 + 7.49706i) q^{89} +(-12.6569 + 1.73205i) q^{91} -1.58579 q^{92} +(-2.41421 - 4.18154i) q^{94} +(1.41421 + 2.44949i) q^{95} +11.6569 q^{97} +(4.20711 - 16.3674i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 2 q^{10} + 4 q^{11} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{20} - 8 q^{22} - 2 q^{23} - 2 q^{25} - 12 q^{26} - 22 q^{28} + 4 q^{29} + 12 q^{31} - 6 q^{32} + 24 q^{34} + 4 q^{35} + 8 q^{38} - 6 q^{40} + 20 q^{41} + 20 q^{43} - 12 q^{44} - 2 q^{46} + 4 q^{47} + 10 q^{49} - 4 q^{50} + 20 q^{52} - 8 q^{53} + 8 q^{55} - 18 q^{56} + 2 q^{58} - 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} - 4 q^{65} - 22 q^{67} + 20 q^{68} - 10 q^{70} + 16 q^{71} - 4 q^{73} + 32 q^{76} - 28 q^{77} - 24 q^{79} + 6 q^{80} + 18 q^{82} - 4 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 12 q^{92} - 4 q^{94} + 24 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 2 * q^10 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^20 - 8 * q^22 - 2 * q^23 - 2 * q^25 - 12 * q^26 - 22 * q^28 + 4 * q^29 + 12 * q^31 - 6 * q^32 + 24 * q^34 + 4 * q^35 + 8 * q^38 - 6 * q^40 + 20 * q^41 + 20 * q^43 - 12 * q^44 - 2 * q^46 + 4 * q^47 + 10 * q^49 - 4 * q^50 + 20 * q^52 - 8 * q^53 + 8 * q^55 - 18 * q^56 + 2 * q^58 - 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 - 4 * q^65 - 22 * q^67 + 20 * q^68 - 10 * q^70 + 16 * q^71 - 4 * q^73 + 32 * q^76 - 28 * q^77 - 24 * q^79 + 6 * q^80 + 18 * q^82 - 4 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 12 * q^92 - 4 * q^94 + 24 * q^97 + 14 * q^98

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