LMFDB - Embedded newform 245.2.e.e.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$1.95633484952$
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			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.2.e.e.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 + 2.09077i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +4.41421 q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(-1.20711 + 2.09077i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +4.41421 q^{8} +(1.41421 - 2.44949i) q^{9} +(1.20711 + 2.09077i) q^{10} +(0.414214 + 0.717439i) q^{11} +(-0.792893 + 1.37333i) q^{12} +4.82843 q^{13} -0.414214 q^{15} +(-1.50000 + 2.59808i) q^{16} +(2.41421 + 4.18154i) q^{17} +(3.41421 + 5.91359i) q^{18} +(1.41421 - 2.44949i) q^{19} -3.82843 q^{20} -2.00000 q^{22} +(-0.207107 + 0.358719i) q^{23} +(-0.914214 - 1.58346i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} -2.41421 q^{27} -1.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(0.792893 + 1.37333i) q^{32} +(0.171573 - 0.297173i) q^{33} -11.6569 q^{34} -10.8284 q^{36} +(3.41421 + 5.91359i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(2.20711 - 3.82282i) q^{40} +7.82843 q^{41} +3.58579 q^{43} +(1.58579 - 2.74666i) q^{44} +(-1.41421 - 2.44949i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.24264 q^{48} +2.41421 q^{50} +(1.00000 - 1.73205i) q^{51} +(-9.24264 - 16.0087i) q^{52} +(0.585786 + 1.01461i) q^{53} +(2.91421 - 5.04757i) q^{54} +0.828427 q^{55} -1.17157 q^{57} +(1.20711 - 2.09077i) q^{58} +(2.24264 + 3.88437i) q^{59} +(0.792893 + 1.37333i) q^{60} +(2.74264 - 4.75039i) q^{61} +14.4853 q^{62} -9.82843 q^{64} +(2.41421 - 4.18154i) q^{65} +(0.414214 + 0.717439i) q^{66} +(-4.79289 - 8.30153i) q^{67} +(9.24264 - 16.0087i) q^{68} +0.171573 q^{69} +4.48528 q^{71} +(6.24264 - 10.8126i) q^{72} +(-0.414214 - 0.717439i) q^{73} +(-0.207107 + 0.358719i) q^{75} -10.8284 q^{76} +4.82843 q^{78} +(-7.41421 + 12.8418i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-3.74264 - 6.48244i) q^{81} +(-9.44975 + 16.3674i) q^{82} -13.7279 q^{83} +4.82843 q^{85} +(-4.32843 + 7.49706i) q^{86} +(0.207107 + 0.358719i) q^{87} +(1.82843 + 3.16693i) q^{88} +(-4.32843 + 7.49706i) q^{89} +6.82843 q^{90} +1.58579 q^{92} +(-1.24264 + 2.15232i) q^{93} +(2.41421 + 4.18154i) q^{94} +(-1.41421 - 2.44949i) q^{95} +(0.328427 - 0.568852i) q^{96} -11.6569 q^{97} +2.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 2 q^{10} - 4 q^{11} - 6 q^{12} + 8 q^{13} + 4 q^{15} - 6 q^{16} + 4 q^{17} + 8 q^{18} - 4 q^{20} - 8 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 4 q^{29} + 2 q^{30} - 12 q^{31} + 6 q^{32} + 12 q^{33} - 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} + 6 q^{40} + 20 q^{41} + 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 4 q^{50} + 4 q^{51} - 20 q^{52} + 8 q^{53} + 6 q^{54} - 8 q^{55} - 16 q^{57} + 2 q^{58} - 8 q^{59} + 6 q^{60} - 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{65} - 4 q^{66} - 22 q^{67} + 20 q^{68} + 12 q^{69} - 16 q^{71} + 8 q^{72} + 4 q^{73} + 2 q^{75} - 32 q^{76} + 8 q^{78} - 24 q^{79} + 6 q^{80} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 8 q^{85} - 6 q^{86} - 2 q^{87} - 4 q^{88} - 6 q^{89} + 16 q^{90} + 12 q^{92} + 12 q^{93} + 4 q^{94} - 10 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 2 * q^10 - 4 * q^11 - 6 * q^12 + 8 * q^13 + 4 * q^15 - 6 * q^16 + 4 * q^17 + 8 * q^18 - 4 * q^20 - 8 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 4 * q^29 + 2 * q^30 - 12 * q^31 + 6 * q^32 + 12 * q^33 - 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 + 6 * q^40 + 20 * q^41 + 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 4 * q^50 + 4 * q^51 - 20 * q^52 + 8 * q^53 + 6 * q^54 - 8 * q^55 - 16 * q^57 + 2 * q^58 - 8 * q^59 + 6 * q^60 - 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^65 - 4 * q^66 - 22 * q^67 + 20 * q^68 + 12 * q^69 - 16 * q^71 + 8 * q^72 + 4 * q^73 + 2 * q^75 - 32 * q^76 + 8 * q^78 - 24 * q^79 + 6 * q^80 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 8 * q^85 - 6 * q^86 - 2 * q^87 - 4 * q^88 - 6 * q^89 + 16 * q^90 + 12 * q^92 + 12 * q^93 + 4 * q^94 - 10 * q^96 - 24 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	$0.492224\pi$
$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	−0.877981	+	0.478696i	$0.841110\pi$
$3$	−0.207107	−	0.358719i	−0.119573	−	0.207107i	0.800025	−	0.599966i	$-0.204819\pi$
$3$	−0.207107	−	0.358719i	−0.119573	−	0.207107i	−0.919599	+	0.392859i	$0.871486\pi$
$4$	−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
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	4.41421			1.56066
$9$	1.41421	−	2.44949i	0.471405	−	0.816497i
$10$	1.20711	+	2.09077i	0.381721	+	0.661160i
$11$	0.414214	+	0.717439i	0.124890	+	0.216316i	0.921690	−	0.387927i	$-0.126809\pi$
$11$	0.414214	+	0.717439i	0.124890	+	0.216316i	−0.796800	+	0.604243i	$0.793476\pi$
$12$	−0.792893	+	1.37333i	−0.228889	+	0.396447i
$13$	4.82843			1.33916			0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843			1.33916			0.669582	+	0.742738i	$0.266473\pi$
$14$		0			0
$15$	−0.414214			−0.106949
$16$	−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	$0.634219\pi$
$18$	3.41421	+	5.91359i	0.804738	+	1.39385i
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	−0.656957	−	0.753928i	$-0.728157\pi$
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	0.981399	+	0.191977i	$0.0614899\pi$
$20$	−3.82843			−0.856062
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−0.207107	+	0.358719i	−0.0431847	+	0.0747982i	−0.886810	−	0.462134i	$-0.847084\pi$
$23$	−0.207107	+	0.358719i	−0.0431847	+	0.0747982i	0.843625	+	0.536933i	$0.180417\pi$
$24$	−0.914214	−	1.58346i	−0.186613	−	0.323223i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.82843	+	10.0951i	−1.14305	+	1.97982i
$27$	−2.41421			−0.464616
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$	0.171573	−	0.297173i	0.0298670	−	0.0517312i
$34$	−11.6569			−1.99913
$35$		0			0
$36$	−10.8284			−1.80474
$37$		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
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	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
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$	−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	$0.120070\pi$
$48$	1.24264			0.179360
$49$		0			0
$50$	2.41421			0.341421
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−9.24264	−	16.0087i	−1.28172	−	2.22001i
$53$	0.585786	+	1.01461i	0.0804640	+	0.139368i	0.903449	−	0.428695i	$-0.141026\pi$
$53$	0.585786	+	1.01461i	0.0804640	+	0.139368i	−0.822985	+	0.568063i	$0.807693\pi$
$54$	2.91421	−	5.04757i	0.396574	−	0.686887i
$55$	0.828427			0.111705
$56$		0			0
$57$	−1.17157			−0.155179
$58$	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	$0.739024\pi$
$60$	0.792893	+	1.37333i	0.102362	+	0.177296i
$61$	2.74264	−	4.75039i	0.351159	−	0.608226i	−0.635294	−	0.772271i	$-0.719121\pi$
$61$	2.74264	−	4.75039i	0.351159	−	0.608226i	0.986453	+	0.164045i	$0.0524543\pi$
$62$	14.4853			1.83963
$63$		0			0
$64$	−9.82843			−1.22855
$65$	2.41421	−	4.18154i	0.299446	−	0.518656i
$66$	0.414214	+	0.717439i	0.0509862	+	0.0883106i
$67$	−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
$69$	0.171573			0.0206549
$70$		0			0
$71$	4.48528			0.532305			0.266152	−	0.963931i	$-0.414248\pi$
$71$	4.48528			0.532305			0.266152	+	0.963931i	$0.414248\pi$
$72$	6.24264	−	10.8126i	0.735702	−	1.27427i
$73$	−0.414214	−	0.717439i	−0.0484800	−	0.0839699i	0.840767	−	0.541397i	$-0.182104\pi$
$73$	−0.414214	−	0.717439i	−0.0484800	−	0.0839699i	−0.889247	+	0.457427i	$0.848771\pi$
$74$		0			0
$75$	−0.207107	+	0.358719i	−0.0239146	+	0.0414214i
$76$	−10.8284			−1.24211
$77$		0			0
$78$	4.82843			0.546712
$79$	−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
$81$	−3.74264	−	6.48244i	−0.415849	−	0.720272i
$82$	−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
$87$	0.207107	+	0.358719i	0.0222042	+	0.0384588i
$88$	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	$0.318392\pi$
$90$	6.82843			0.719779
$91$		0			0
$92$	1.58579			0.165330
$93$	−1.24264	+	2.15232i	−0.128856	+	0.223185i
$94$	2.41421	+	4.18154i	0.249007	+	0.431293i
$95$	−1.41421	−	2.44949i	−0.145095	−	0.251312i
$96$	0.328427	−	0.568852i	0.0335200	−	0.0580583i
$97$	−11.6569			−1.18357			−0.591787	−	0.806094i	$-0.701577\pi$
$97$	−11.6569			−1.18357			−0.591787	+	0.806094i	$0.701577\pi$
$98$		0			0
$99$	2.34315			0.235495
$100$	−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	$-0.338179\pi$
$102$	2.41421	+	4.18154i	0.239043	+	0.414034i
$103$	−1.20711	+	2.09077i	−0.118940	+	0.206010i	−0.919348	−	0.393446i	$-0.871283\pi$
$103$	−1.20711	+	2.09077i	−0.118940	+	0.206010i	0.800408	+	0.599456i	$0.204616\pi$
$104$	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	$0.349543\pi$
$107$	−5.62132	+	9.73641i	−0.543434	+	0.941255i	−0.998704	+	0.0509012i	$0.983791\pi$
$108$	4.62132	+	8.00436i	0.444687	+	0.770220i
$109$	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
$112$		0			0
$113$	−4.48528			−0.421940			−0.210970	−	0.977493i	$-0.567662\pi$
$113$	−4.48528			−0.421940			−0.210970	+	0.977493i	$0.567662\pi$
$114$	1.41421	−	2.44949i	0.132453	−	0.229416i
$115$	0.207107	+	0.358719i	0.0193128	+	0.0334508i
$116$	1.91421	+	3.31552i	0.177730	+	0.307838i
$117$	6.82843	−	11.8272i	0.631288	−	1.09342i
$118$	−10.8284			−0.996838
$119$		0			0
$120$	−1.82843			−0.166912
$121$	5.15685	−	8.93193i	0.468805	−	0.811994i
$122$	6.62132	+	11.4685i	0.599466	+	1.03831i
$123$	−1.62132	−	2.80821i	−0.146190	−	0.253208i
$124$	−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
$129$	−0.742641	−	1.28629i	−0.0653859	−	0.113252i
$130$	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	$0.847026\pi$
$132$	−1.31371			−0.114344
$133$		0			0
$134$	23.1421			1.99918
$135$	−1.20711	+	2.09077i	−0.103891	+	0.179945i
$136$	10.6569	+	18.4582i	0.913818	+	1.58278i
$137$	4.82843	+	8.36308i	0.412520	+	0.714506i	0.995165	−	0.0982211i	$-0.0313152\pi$
$137$	4.82843	+	8.36308i	0.412520	+	0.714506i	−0.582644	+	0.812727i	$0.697982\pi$
$138$	−0.207107	+	0.358719i	−0.0176301	+	0.0305362i
$139$	16.1421			1.36916			0.684579	−	0.728939i	$-0.259986\pi$
$139$	16.1421			1.36916			0.684579	+	0.728939i	$0.259986\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$	−5.41421	+	9.37769i	−0.454351	+	0.786959i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	4.24264	+	7.34847i	0.353553	+	0.612372i
$145$	−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	−0.818117	−	0.575052i	$-0.804982\pi$
$149$	1.08579	−	1.88064i	0.0889511	−	0.154068i	0.907068	+	0.420984i	$0.138315\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−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
$153$	13.6569			1.10409
$154$		0			0
$155$	−6.00000			−0.481932
$156$	−3.82843	+	6.63103i	−0.306519	+	0.530907i
$157$	8.65685	+	14.9941i	0.690892	+	1.19666i	0.971546	+	0.236851i	$0.0761154\pi$
$157$	8.65685	+	14.9941i	0.690892	+	1.19666i	−0.280654	+	0.959809i	$0.590551\pi$
$158$	−17.8995	−	31.0028i	−1.42401	−	2.46645i
$159$	0.242641	−	0.420266i	0.0192427	−	0.0333293i
$160$	1.58579			0.125367
$161$		0			0
$162$	18.0711			1.41980
$163$	−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
$165$	−0.171573	−	0.297173i	−0.0133569	−	0.0231349i
$166$	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
$171$	−4.00000	−	6.92820i	−0.305888	−	0.529813i
$172$	−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	$0.126463\pi$
$174$	−1.00000			−0.0758098
$175$		0			0
$176$	−2.48528			−0.187335
$177$	0.928932	−	1.60896i	0.0698228	−	0.120937i
$178$	−10.4497	−	18.0995i	−0.783242	−	1.35661i
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$	−5.41421	+	9.37769i	−0.403552	+	0.698972i
$181$	−2.65685			−0.197482			−0.0987412	−	0.995113i	$-0.531482\pi$
$181$	−2.65685			−0.197482			−0.0987412	+	0.995113i	$0.531482\pi$
$182$		0			0
$183$	−2.27208			−0.167957
$184$	−0.914214	+	1.58346i	−0.0673967	+	0.116735i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−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	−0.535045	−	0.844824i	$-0.679705\pi$
$191$	6.41421	−	11.1097i	0.464116	−	0.803873i	0.999161	+	0.0409507i	$0.0130387\pi$
$192$	2.03553	+	3.52565i	0.146902	+	0.254442i
$193$	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
$195$	−2.00000			−0.143223
$196$		0			0
$197$	−12.3431			−0.879413			−0.439706	−	0.898142i	$-0.644917\pi$
$197$	−12.3431			−0.879413			−0.439706	+	0.898142i	$0.644917\pi$
$198$	−2.82843	+	4.89898i	−0.201008	+	0.348155i
$199$	−4.82843	−	8.36308i	−0.342278	−	0.592843i	0.642577	−	0.766221i	$-0.277865\pi$
$199$	−4.82843	−	8.36308i	−0.342278	−	0.592843i	−0.984855	+	0.173378i	$0.944532\pi$
$200$	−2.20711	−	3.82282i	−0.156066	−	0.270314i
$201$	−1.98528	+	3.43861i	−0.140031	+	0.242541i
$202$	24.8995			1.75192
$203$		0			0
$204$	−7.65685			−0.536087
$205$	3.91421	−	6.77962i	0.273381	−	0.473509i
$206$	−2.91421	−	5.04757i	−0.203043	−	0.351681i
$207$	0.585786	+	1.01461i	0.0407150	+	0.0705204i
$208$	−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
$213$	−0.928932	−	1.60896i	−0.0636494	−	0.110244i
$214$	−13.5711	−	23.5058i	−0.927699	−	1.60682i
$215$	1.79289	−	3.10538i	0.122274	−	0.211785i
$216$	−10.6569			−0.725107
$217$		0			0
$218$	−32.5563			−2.20499
$219$	−0.171573	+	0.297173i	−0.0115938	+	0.0200811i
$220$	−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	$-0.503657\pi$
$223$	−0.343146			−0.0229787			−0.0114894	+	0.999934i	$0.503657\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$	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	$0.907640\pi$
$228$	2.24264	+	3.88437i	0.148523	+	0.257249i
$229$	−5.82843	+	10.0951i	−0.385153	+	0.667105i	−0.991790	−	0.127874i	$-0.959185\pi$
$229$	−5.82843	+	10.0951i	−0.385153	+	0.667105i	0.606637	+	0.794979i	$0.292518\pi$
$230$	−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	$-0.647491\pi$
$233$	8.41421	−	14.5738i	0.551233	−	0.954764i	0.998186	−	0.0602067i	$-0.0191760\pi$
$234$	16.4853	+	28.5533i	1.07768	+	1.86659i
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	8.58579	−	14.8710i	0.558887	−	0.968021i
$237$	6.14214			0.398975
$238$		0			0
$239$	−21.3137			−1.37867			−0.689335	−	0.724443i	$-0.742097\pi$
$239$	−21.3137			−1.37867			−0.689335	+	0.724443i	$0.742097\pi$
$240$	0.621320	−	1.07616i	0.0401061	−	0.0694657i
$241$	13.8284	+	23.9515i	0.890767	+	1.54285i	0.838957	+	0.544197i	$0.183166\pi$
$241$	13.8284	+	23.9515i	0.890767	+	1.54285i	0.0518100	+	0.998657i	$0.483501\pi$
$242$	12.4497	+	21.5636i	0.800300	+	1.38616i
$243$	−5.17157	+	8.95743i	−0.331757	+	0.574619i
$244$	−21.0000			−1.34439
$245$		0			0
$246$	7.82843			0.499122
$247$	6.82843	−	11.8272i	0.434482	−	0.752546i
$248$	−13.2426	−	22.9369i	−0.840909	−	1.45650i
$249$	2.84315	+	4.92447i	0.180177	+	0.312076i
$250$	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
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	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	$0.103275\pi$
$258$	3.58579			0.223241
$259$		0			0
$260$	−18.4853			−1.14641
$261$	−1.41421	+	2.44949i	−0.0875376	+	0.151620i
$262$	−23.3137	−	40.3805i	−1.44033	−	2.49472i
$263$	14.5208	+	25.1508i	0.895392	+	1.55086i	0.833319	+	0.552793i	$0.186438\pi$
$263$	14.5208	+	25.1508i	0.895392	+	1.55086i	0.0620729	+	0.998072i	$0.480229\pi$
$264$	0.757359	−	1.31178i	0.0466122	−	0.0807348i
$265$	1.17157			0.0719691
$266$		0			0
$267$	3.58579			0.219447
$268$	−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	$0.619000\pi$
$270$	−2.91421	−	5.04757i	−0.177353	−	0.307185i
$271$	8.24264	−	14.2767i	0.500705	−	0.867246i	−0.499295	−	0.866432i	$-0.666408\pi$
$271$	8.24264	−	14.2767i	0.500705	−	0.867246i	1.00000		0.000813982i	$-0.000259099\pi$
$272$	−14.4853			−0.878299
$273$		0			0
$274$	−23.3137			−1.40843
$275$	0.414214	−	0.717439i	0.0249780	−	0.0432632i
$276$	−0.328427	−	0.568852i	−0.0197690	−	0.0342409i
$277$	−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
$279$	−16.9706			−1.01600
$280$		0			0
$281$	−30.2843			−1.80661			−0.903304	−	0.429001i	$-0.858866\pi$
$281$	−30.2843			−1.80661			−0.903304	+	0.429001i	$0.858866\pi$
$282$	1.00000	−	1.73205i	0.0595491	−	0.103142i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	−8.58579	−	14.8710i	−0.509473	−	0.882433i
$285$	−0.585786	+	1.01461i	−0.0346990	+	0.0601004i
$286$	−9.65685			−0.571022
$287$		0			0
$288$	4.48528			0.264298
$289$	−3.15685	+	5.46783i	−0.185697	+	0.321637i
$290$	−1.20711	−	2.09077i	−0.0708838	−	0.122774i
$291$	2.41421	+	4.18154i	0.141524	+	0.245126i
$292$	−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
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	2.62132	+	4.54026i	0.151849	+	0.263010i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$	1.58579			0.0915554
$301$		0			0
$302$	28.1421			1.61940
$303$	−2.13604	+	3.69973i	−0.122712	+	0.212544i
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$	−2.74264	−	4.75039i	−0.157043	−	0.272007i
$306$	−16.4853	+	28.5533i	−0.942401	+	1.63229i
$307$	4.75736			0.271517			0.135758	−	0.990742i	$-0.456653\pi$
$307$	4.75736			0.271517			0.135758	+	0.990742i	$0.456653\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$	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	$0.955157\pi$
$312$	−4.41421	−	7.64564i	−0.249906	−	0.432849i
$313$	−3.17157	+	5.49333i	−0.179268	+	0.310501i	−0.941630	−	0.336650i	$-0.890706\pi$
$313$	−3.17157	+	5.49333i	−0.179268	+	0.310501i	0.762362	+	0.647151i	$0.224040\pi$
$314$	−41.7990			−2.35885
$315$		0			0
$316$	56.7696			3.19354
$317$	6.89949	−	11.9503i	0.387514	−	0.671194i	−0.604600	−	0.796529i	$-0.706667\pi$
$317$	6.89949	−	11.9503i	0.387514	−	0.671194i	0.992115	+	0.125335i	$0.0400005\pi$
$318$	0.585786	+	1.01461i	0.0328493	+	0.0568966i
$319$	−0.414214	−	0.717439i	−0.0231915	−	0.0401689i
$320$	−4.91421	+	8.51167i	−0.274713	+	0.475817i
$321$	4.65685			0.259920
$322$		0			0
$323$	13.6569			0.759888
$324$	−14.3284	+	24.8176i	−0.796024	+	1.37875i
$325$	−2.41421	−	4.18154i	−0.133916	−	0.231950i
$326$	−14.8995	−	25.8067i	−0.825207	−	1.42930i
$327$	2.79289	−	4.83743i	0.154447	−	0.267511i
$328$	34.5563			1.90806
$329$		0			0
$330$	0.828427			0.0456034
$331$	−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
$339$	0.928932	+	1.60896i	0.0504527	+	0.0873866i
$340$	−9.24264	−	16.0087i	−0.501253	−	0.868195i
$341$	2.48528	−	4.30463i	0.134586	−	0.233109i
$342$	19.3137			1.04437
$343$		0			0
$344$	15.8284			0.853412
$345$	0.0857864	−	0.148586i	0.00461859	−	0.00799963i
$346$	4.00000	+	6.92820i	0.215041	+	0.372463i
$347$	−3.96447	−	6.86666i	−0.212824	−	0.368621i	0.739773	−	0.672856i	$-0.234933\pi$
$347$	−3.96447	−	6.86666i	−0.212824	−	0.368621i	−0.952597	+	0.304235i	$0.901599\pi$
$348$	0.792893	−	1.37333i	0.0425035	−	0.0736183i
$349$	15.3431			0.821300			0.410650	−	0.911793i	$-0.365302\pi$
$349$	15.3431			0.821300			0.410650	+	0.911793i	$0.365302\pi$
$350$		0			0
$351$	−11.6569			−0.622197
$352$	−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	$-0.419770\pi$
$354$	2.24264	+	3.88437i	0.119195	+	0.206452i
$355$	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	−0.703382	−	0.710812i	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$	−6.24264	−	10.8126i	−0.329016	−	0.569873i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	3.20711	−	5.55487i	0.168562	−	0.291958i
$363$	−4.27208			−0.224226
$364$		0			0
$365$	−0.828427			−0.0433619
$366$	2.74264	−	4.75039i	0.143360	−	0.248307i
$367$	−1.37868	−	2.38794i	−0.0719665	−	0.124650i	0.827797	−	0.561028i	$-0.189594\pi$
$367$	−1.37868	−	2.38794i	−0.0719665	−	0.124650i	−0.899763	+	0.436379i	$0.856261\pi$
$368$	−0.621320	−	1.07616i	−0.0323886	−	0.0560986i
$369$	11.0711	−	19.1757i	0.576337	−	0.998245i
$370$		0			0
$371$		0			0
$372$	9.51472			0.493315
$373$	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
$375$	0.207107	+	0.358719i	0.0106949	+	0.0185242i
$376$	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
$381$	1.92893	+	3.34101i	0.0988222	+	0.171165i
$382$	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	$0.190268\pi$
$384$	−8.51472			−0.434515
$385$		0			0
$386$	−4.82843			−0.245760
$387$	5.07107	−	8.78335i	0.257777	−	0.446483i
$388$	22.3137	+	38.6485i	1.13281	+	1.96208i
$389$	−11.8284	−	20.4874i	−0.599725	−	1.03875i	−0.992861	−	0.119274i	$-0.961943\pi$
$389$	−11.8284	−	20.4874i	−0.599725	−	1.03875i	0.393136	−	0.919480i	$-0.371390\pi$
$390$	2.41421	−	4.18154i	0.122248	−	0.211741i
$391$	−2.00000			−0.101144
$392$		0			0
$393$	8.00000			0.403547
$394$	14.8995	−	25.8067i	0.750626	−	1.30012i
$395$	7.41421	+	12.8418i	0.373050	+	0.646141i
$396$	−4.48528	−	7.76874i	−0.225394	−	0.390394i
$397$	−8.31371	+	14.3998i	−0.417253	+	0.722704i	−0.995662	−	0.0930434i	$-0.970340\pi$
$397$	−8.31371	+	14.3998i	−0.417253	+	0.722704i	0.578409	+	0.815747i	$0.303674\pi$
$398$	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	$0.439952\pi$
$401$	−15.1569	+	26.2524i	−0.756897	+	1.31098i	−0.944426	+	0.328725i	$0.893381\pi$
$402$	−4.79289	−	8.30153i	−0.239048	−	0.414043i
$403$	−14.4853	−	25.0892i	−0.721563	−	1.24978i
$404$	−19.7426	+	34.1953i	−0.982233	+	1.70128i
$405$	−7.48528			−0.371947
$406$		0			0
$407$		0			0
$408$	4.41421	−	7.64564i	0.218536	−	0.378516i
$409$	−7.39949	−	12.8163i	−0.365881	−	0.633725i	0.623036	−	0.782193i	$-0.285899\pi$
$409$	−7.39949	−	12.8163i	−0.365881	−	0.633725i	−0.988917	+	0.148468i	$0.952566\pi$
$410$	9.44975	+	16.3674i	0.466690	+	0.808330i
$411$	2.00000	−	3.46410i	0.0986527	−	0.170872i
$412$	9.24264			0.455352
$413$		0			0
$414$	−2.82843			−0.139010
$415$	−6.86396	+	11.8887i	−0.336939	+	0.583595i
$416$	3.82843	+	6.63103i	0.187704	+	0.325113i
$417$	−3.34315	−	5.79050i	−0.163715	−	0.283562i
$418$	−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
$423$	−2.82843	−	4.89898i	−0.137523	−	0.238197i
$424$	2.58579	+	4.47871i	0.125577	+	0.217506i
$425$	2.41421	−	4.18154i	0.117107	−	0.202835i
$426$	4.48528			0.217313
$427$		0			0
$428$	43.0416			2.08050
$429$	0.828427	−	1.43488i	0.0399968	−	0.0692766i
$430$	4.32843	+	7.49706i	0.208735	+	0.361540i
$431$	−8.89949	−	15.4144i	−0.428674	−	0.742484i	0.568082	−	0.822972i	$-0.307686\pi$
$431$	−8.89949	−	15.4144i	−0.428674	−	0.742484i	−0.996756	+	0.0804875i	$0.974352\pi$
$432$	3.62132	−	6.27231i	0.174231	−	0.301777i
$433$	−7.79899			−0.374796			−0.187398	−	0.982284i	$-0.560005\pi$
$433$	−7.79899			−0.374796			−0.187398	+	0.982284i	$0.560005\pi$
$434$		0			0
$435$	0.414214			0.0198600
$436$	25.8137	−	44.7107i	1.23625	−	2.14125i
$437$	0.585786	+	1.01461i	0.0280220	+	0.0485355i
$438$	−0.414214	−	0.717439i	−0.0197919	−	0.0342806i
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	0.102930	+	0.994689i	$0.467178\pi$
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	−0.912890	+	0.408205i	$0.866155\pi$
$440$	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	$0.421488\pi$
$443$	−15.1066	+	26.1654i	−0.717736	+	1.24316i	−0.961895	+	0.273420i	$0.911845\pi$
$444$		0			0
$445$	4.32843	+	7.49706i	0.205187	+	0.355395i
$446$	0.414214	−	0.717439i	0.0196136	−	0.0339717i
$447$	−0.899495			−0.0425447
$448$		0			0
$449$	3.82843			0.180675			0.0903373	−	0.995911i	$-0.471205\pi$
$449$	3.82843			0.180675			0.0903373	+	0.995911i	$0.471205\pi$
$450$	3.41421	−	5.91359i	0.160948	−	0.278769i
$451$	3.24264	+	5.61642i	0.152690	+	0.264467i
$452$	8.58579	+	14.8710i	0.403841	+	0.699474i
$453$	−2.41421	+	4.18154i	−0.113430	+	0.196466i
$454$	16.8284			0.789797
$455$		0			0
$456$	−5.17157			−0.242181
$457$	−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
$459$	−5.82843	−	10.0951i	−0.272048	−	0.471200i
$460$	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
$465$	1.24264	+	2.15232i	0.0576261	+	0.0998113i
$466$	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	$0.189521\pi$
$468$	−52.2843			−2.41684
$469$		0			0
$470$	4.82843			0.222719
$471$	3.58579	−	6.21076i	0.165224	−	0.286177i
$472$	9.89949	+	17.1464i	0.455661	+	0.789228i
$473$	1.48528	+	2.57258i	0.0682933	+	0.118287i
$474$	−7.41421	+	12.8418i	−0.340546	+	0.589843i
$475$	−2.82843			−0.129777
$476$		0			0
$477$	3.31371			0.151724
$478$	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	$-0.469711\pi$
$480$	−0.328427	−	0.568852i	−0.0149906	−	0.0259644i
$481$		0			0
$482$	−66.7696			−3.04127
$483$		0			0
$484$	−39.4853			−1.79479
$485$	−5.82843	+	10.0951i	−0.264655	+	0.458396i
$486$	−12.4853	−	21.6251i	−0.566344	−	0.980936i
$487$	−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
$489$	5.11270			0.231204
$490$		0			0
$491$	9.31371			0.420322			0.210161	−	0.977667i	$-0.432601\pi$
$491$	9.31371			0.420322			0.210161	+	0.977667i	$0.432601\pi$
$492$	−6.20711	+	10.7510i	−0.279838	+	0.484694i
$493$	−2.41421	−	4.18154i	−0.108731	−	0.188327i
$494$	16.4853	+	28.5533i	0.741708	+	1.28468i
$495$	1.17157	−	2.02922i	0.0526583	−	0.0912068i
$496$	18.0000			0.808224
$497$		0			0
$498$	−13.7279			−0.615163
$499$	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
$501$	4.64214	+	8.04041i	0.207395	+	0.359219i
$502$	−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
$507$	−2.13604	−	3.69973i	−0.0948648	−	0.164311i
$508$	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	$0.0711097\pi$
$510$	4.82843			0.213806
$511$		0			0
$512$	−31.2426			−1.38074
$513$	−3.41421	+	5.91359i	−0.150741	+	0.261091i
$514$	7.65685	+	13.2621i	0.337729	+	0.584964i
$515$	1.20711	+	2.09077i	0.0531915	+	0.0921303i
$516$	−2.84315	+	4.92447i	−0.125163	+	0.216788i
$517$	1.65685			0.0728684
$518$		0			0
$519$	−1.37258			−0.0602497
$520$	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	$0.726980\pi$
$522$	−3.41421	−	5.91359i	−0.149436	−	0.258831i
$523$	17.8284	−	30.8797i	0.779583	−	1.35028i	−0.152600	−	0.988288i	$-0.548765\pi$
$523$	17.8284	−	30.8797i	0.779583	−	1.35028i	0.932182	−	0.361989i	$-0.117902\pi$
$524$	73.9411			3.23013
$525$		0			0
$526$	−70.1127			−3.05706
$527$	14.4853	−	25.0892i	0.630989	−	1.09290i
$528$	0.514719	+	0.891519i	0.0224003	+	0.0387984i
$529$	11.4142	+	19.7700i	0.496270	+	0.859565i
$530$	−1.41421	+	2.44949i	−0.0614295	+	0.106399i
$531$	12.6863			0.550538
$532$		0			0
$533$	37.7990			1.63726
$534$	−4.32843	+	7.49706i	−0.187309	+	0.324429i
$535$	5.62132	+	9.73641i	0.243031	+	0.420942i
$536$	−21.1569	−	36.6447i	−0.913837	−	1.58281i
$537$	2.07107	−	3.58719i	0.0893732	−	0.154799i
$538$	−49.3848			−2.12913
$539$		0			0
$540$	9.24264			0.397740
$541$	−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
$543$	0.550253	+	0.953065i	0.0236136	+	0.0408999i
$544$	−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
$549$	−7.75736	−	13.4361i	−0.331076	−	0.573441i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−1.41421	+	2.44949i	−0.0602475	+	0.104352i
$552$	0.757359			0.0322354
$553$		0			0
$554$	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	0.527383	−	0.849628i	$-0.323173\pi$
$557$	−11.1421	−	19.2987i	−0.472107	−	0.817714i	−0.999491	+	0.0319135i	$0.989840\pi$
$558$	20.4853	−	35.4815i	0.867211	−	1.50205i
$559$	17.3137			0.732292
$560$		0			0
$561$	1.65685			0.0699524
$562$	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	$0.491337\pi$
$564$	1.58579	+	2.74666i	0.0667737	+	0.115655i
$565$	−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	−0.935047	−	0.354525i	$-0.884643\pi$
$569$	−3.82843	+	6.63103i	−0.160496	+	0.277987i	0.774551	+	0.632512i	$0.217976\pi$
$570$	−1.41421	−	2.44949i	−0.0592349	−	0.102598i
$571$	−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
$573$	−5.31371			−0.221983
$574$		0			0
$575$	0.414214			0.0172739
$576$	−13.8995	+	24.0746i	−0.579146	+	1.00311i
$577$	−21.9706	−	38.0541i	−0.914646	−	1.58421i	−0.807418	−	0.589980i	$-0.799136\pi$
$577$	−21.9706	−	38.0541i	−0.914646	−	1.58421i	−0.107228	−	0.994234i	$-0.534198\pi$
$578$	−7.62132	−	13.2005i	−0.317005	−	0.549069i
$579$	0.414214	−	0.717439i	0.0172141	−	0.0298157i
$580$	3.82843			0.158967
$581$		0			0
$582$	−11.6569			−0.483192
$583$	−0.485281	+	0.840532i	−0.0200983	+	0.0348113i
$584$	−1.82843	−	3.16693i	−0.0756609	−	0.131048i
$585$	−6.82843	−	11.8272i	−0.282321	−	0.488994i
$586$	−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
$591$	2.55635	+	4.42773i	0.105154	+	0.182132i
$592$		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	$0.139176\pi$
$594$	4.82843			0.198113
$595$		0			0
$596$	−8.31371			−0.340543
$597$	−2.00000	+	3.46410i	−0.0818546	+	0.141776i
$598$	−2.41421	−	4.18154i	−0.0987245	−	0.170996i
$599$	−3.17157	−	5.49333i	−0.129587	−	0.224451i	0.793930	−	0.608010i	$-0.208032\pi$
$599$	−3.17157	−	5.49333i	−0.129587	−	0.224451i	−0.923517	+	0.383558i	$0.874698\pi$
$600$	−0.914214	+	1.58346i	−0.0373226	+	0.0646447i
$601$	−19.6569			−0.801820			−0.400910	−	0.916117i	$-0.631306\pi$
$601$	−19.6569			−0.801820			−0.400910	+	0.916117i	$0.631306\pi$
$602$		0			0
$603$	−27.1127			−1.10411
$604$	−22.3137	+	38.6485i	−0.907932	+	1.57258i
$605$	−5.15685	−	8.93193i	−0.209656	−	0.363135i
$606$	−5.15685	−	8.93193i	−0.209483	−	0.362835i
$607$	19.1066	−	33.0936i	0.775513	−	1.34323i	−0.158993	−	0.987280i	$-0.550825\pi$
$607$	19.1066	−	33.0936i	0.775513	−	1.34323i	0.934506	−	0.355948i	$-0.115842\pi$
$608$	4.48528			0.181902
$609$		0			0
$610$	13.2426			0.536179
$611$	4.82843	−	8.36308i	0.195337	−	0.338334i
$612$	−26.1421	−	45.2795i	−1.05673	−	1.83032i
$613$	−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
$615$	−3.24264			−0.130756
$616$		0			0
$617$	11.3137			0.455473			0.227736	−	0.973723i	$-0.426868\pi$
$617$	11.3137			0.455473			0.227736	+	0.973723i	$0.426868\pi$
$618$	−1.20711	+	2.09077i	−0.0485570	+	0.0841031i
$619$	12.7574	+	22.0964i	0.512762	+	0.888129i	0.999890	+	0.0147990i	$0.00471084\pi$
$619$	12.7574	+	22.0964i	0.512762	+	0.888129i	−0.487129	+	0.873330i	$0.661956\pi$
$620$	11.4853	+	19.8931i	0.461260	+	0.798926i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	31.7990			1.27502
$623$		0			0
$624$	6.00000			0.240192
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.65685	−	13.2621i	−0.306029	−	0.530059i
$627$	−0.485281	−	0.840532i	−0.0193803	−	0.0335676i
$628$	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
$633$	−4.24264	−	7.34847i	−0.168630	−	0.292075i
$634$	16.6569	+	28.8505i	0.661528	+	1.14580i
$635$	−4.65685	+	8.06591i	−0.184802	+	0.320086i
$636$	−1.85786			−0.0736691
$637$		0			0
$638$	2.00000			0.0791808
$639$	6.34315	−	10.9867i	0.250931	−	0.434625i
$640$	−10.2782	−	17.8023i	−0.406281	−	0.703699i
$641$	−15.7426	−	27.2671i	−0.621797	−	1.07698i	−0.989151	−	0.146903i	$-0.953070\pi$
$641$	−15.7426	−	27.2671i	−0.621797	−	1.07698i	0.367354	−	0.930081i	$-0.380264\pi$
$642$	−5.62132	+	9.73641i	−0.221856	+	0.384266i
$643$	−26.2843			−1.03655			−0.518275	−	0.855214i	$-0.673426\pi$
$643$	−26.2843			−1.03655			−0.518275	+	0.855214i	$0.673426\pi$
$644$		0			0
$645$	−1.48528			−0.0584829
$646$	−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	$-0.375572\pi$
$648$	−16.5208	−	28.6149i	−0.648999	−	1.12410i
$649$	−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	−0.615224	−	0.788352i	$-0.710935\pi$
$653$	9.58579	−	16.6031i	0.375121	−	0.649728i	0.990345	+	0.138624i	$0.0442679\pi$
$654$	6.74264	+	11.6786i	0.263658	+	0.456669i
$655$	9.65685	+	16.7262i	0.377325	+	0.653545i
$656$	−11.7426	+	20.3389i	−0.458473	+	0.794099i
$657$	−2.34315			−0.0914148
$658$		0			0
$659$	21.1716			0.824727			0.412364	−	0.911019i	$-0.364703\pi$
$659$	21.1716			0.824727			0.412364	+	0.911019i	$0.364703\pi$
$660$	−0.656854	+	1.13770i	−0.0255680	+	0.0442851i
$661$	15.9142	+	27.5642i	0.618991	+	1.07212i	0.989670	+	0.143363i	$0.0457917\pi$
$661$	15.9142	+	27.5642i	0.618991	+	1.07212i	−0.370679	+	0.928761i	$0.620875\pi$
$662$	−27.7279	−	48.0262i	−1.07768	−	1.86659i
$663$	4.82843	−	8.36308i	0.187521	−	0.324795i
$664$	−60.5980			−2.35166
$665$		0			0
$666$		0			0
$667$	0.207107	−	0.358719i	0.00801921	−	0.0138897i
$668$	42.9056	+	74.3147i	1.66007	+	2.87532i
$669$	0.0710678	+	0.123093i	0.00274764	+	0.00475905i
$670$	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
$675$	1.20711	+	2.09077i	0.0464616	+	0.0804738i
$676$	−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	$0.984790\pi$
$678$	−4.48528			−0.172256
$679$		0			0
$680$	21.3137			0.817343
$681$	−1.44365	+	2.50048i	−0.0553208	+	0.0958185i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	17.3787	+	30.1008i	0.664977	+	1.15177i	0.979292	+	0.202455i	$0.0648919\pi$
$683$	17.3787	+	30.1008i	0.664977	+	1.15177i	−0.314315	+	0.949319i	$0.601775\pi$
$684$	−15.3137	+	26.5241i	−0.585534	+	1.01418i
$685$	9.65685			0.368969
$686$		0			0
$687$	4.82843			0.184216
$688$	−5.37868	+	9.31615i	−0.205060	+	0.355175i
$689$	2.82843	+	4.89898i	0.107754	+	0.186636i
$690$	0.207107	+	0.358719i	0.00788442	+	0.0136562i
$691$	0.414214	−	0.717439i	0.0157574	−	0.0272927i	−0.858039	−	0.513584i	$-0.828317\pi$
$691$	0.414214	−	0.717439i	0.0157574	−	0.0272927i	0.873797	+	0.486292i	$0.161651\pi$
$692$	−12.6863			−0.482260
$693$		0			0
$694$	19.1421			0.726626
$695$	8.07107	−	13.9795i	0.306153	−	0.530273i
$696$	0.914214	+	1.58346i	0.0346532	+	0.0600211i
$697$	18.8995	+	32.7349i	0.715869	+	1.23992i
$698$	−18.5208	+	32.0790i	−0.701023	+	1.21421i
$699$	−6.97056			−0.263651
$700$		0			0
$701$	−3.20101			−0.120900			−0.0604502	−	0.998171i	$-0.519254\pi$
$701$	−3.20101			−0.120900			−0.0604502	+	0.998171i	$0.519254\pi$
$702$	14.0711	−	24.3718i	0.531078	−	0.919854i
$703$		0			0
$704$	−4.07107	−	7.05130i	−0.153434	−	0.265756i
$705$	−0.414214	+	0.717439i	−0.0156002	+	0.0270203i
$706$	64.7696			2.43763
$707$		0			0
$708$	−7.11270			−0.267312
$709$	−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
$711$	20.9706	+	36.3221i	0.786458	+	1.36218i
$712$	−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
$717$	4.41421	+	7.64564i	0.164852	+	0.285532i
$718$	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	$0.0378666\pi$
$720$	8.48528			0.316228
$721$		0			0
$722$	−26.5563			−0.988325
$723$	5.72792	−	9.92105i	0.213024	−	0.368968i
$724$	5.08579	+	8.80884i	0.189012	+	0.327378i
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$	5.15685	−	8.93193i	0.191389	−	0.331495i
$727$	37.5858			1.39398			0.696990	−	0.717081i	$-0.254522\pi$
$727$	37.5858			1.39398			0.696990	+	0.717081i	$0.254522\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	8.65685	+	14.9941i	0.320185	+	0.554577i
$732$	4.34924	+	7.53311i	0.160753	+	0.278432i
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$	6.65685			0.245709
$735$		0			0
$736$	−0.656854			−0.0242120
$737$	3.97056	−	6.87722i	0.146258	−	0.253326i
$738$	26.7279	+	46.2941i	0.983868	+	1.70411i
$739$	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
$741$	−5.65685			−0.207810
$742$		0			0
$743$	−16.0711			−0.589590			−0.294795	−	0.955560i	$-0.595251\pi$
$743$	−16.0711			−0.589590			−0.294795	+	0.955560i	$0.595251\pi$
$744$	−5.48528	+	9.50079i	−0.201100	+	0.348316i
$745$	−1.08579	−	1.88064i	−0.0397801	−	0.0689012i
$746$	25.3137	+	43.8446i	0.926801	+	1.60527i
$747$	−19.4142	+	33.6264i	−0.710329	+	1.23033i
$748$	15.3137			0.559925
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	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
$753$	−1.92893	−	3.34101i	−0.0702942	−	0.121753i
$754$	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
$759$	0.0710678	+	0.123093i	0.00257960	+	0.00446800i
$760$	−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	$0.112674\pi$
$762$	−9.31371			−0.337400
$763$		0			0
$764$	−49.1127			−1.77684
$765$	6.82843	−	11.8272i	0.246882	−	0.427613i
$766$	−3.50000	−	6.06218i	−0.126460	−	0.219035i
$767$	10.8284	+	18.7554i	0.390992	+	0.677218i
$768$	6.20711	−	10.7510i	0.223980	−	0.387944i
$769$	0.627417			0.0226252			0.0113126	−	0.999936i	$-0.496399\pi$
$769$	0.627417			0.0226252			0.0113126	+	0.999936i	$0.496399\pi$
$770$		0			0
$771$	−2.62742			−0.0946241
$772$	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	$-0.399270\pi$
$774$	12.2426	+	21.2049i	0.440053	+	0.762194i
$775$	−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
$780$	3.82843	+	6.63103i	0.137080	+	0.237429i
$781$	1.85786	+	3.21792i	0.0664796	+	0.115146i
$782$	2.41421	−	4.18154i	0.0863321	−	0.149532i
$783$	2.41421			0.0862770
$784$		0			0
$785$	17.3137			0.617953
$786$	−9.65685	+	16.7262i	−0.344449	+	0.596602i
$787$	1.27817	+	2.21386i	0.0455620	+	0.0789157i	0.887907	−	0.460023i	$-0.152159\pi$
$787$	1.27817	+	2.21386i	0.0455620	+	0.0789157i	−0.842345	+	0.538939i	$0.818825\pi$
$788$	23.6274	+	40.9239i	0.841692	+	1.45785i
$789$	6.01472	−	10.4178i	0.214130	−	0.370883i
$790$	−35.7990			−1.27367
$791$		0			0
$792$	10.3431			0.367528
$793$	13.2426	−	22.9369i	0.470260	−	0.814514i
$794$	−20.0711	−	34.7641i	−0.712296	−	1.23373i
$795$	−0.242641	−	0.420266i	−0.00860558	−	0.0149053i
$796$	−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
$801$	12.2426	+	21.2049i	0.432572	+	0.749237i
$802$	−36.5919	−	63.3790i	−1.29210	−	2.23799i
$803$	0.343146	−	0.594346i	0.0121094	−	0.0209740i
$804$	15.2010			0.536098
$805$		0			0
$806$	69.9411			2.46357
$807$	4.23654	−	7.33791i	0.149133	−	0.258307i
$808$	−22.7635	−	39.4275i	−0.800816	−	1.38705i
$809$	−17.8137	−	30.8542i	−0.626297	−	1.08478i	−0.988289	−	0.152596i	$-0.951237\pi$
$809$	−17.8137	−	30.8542i	−0.626297	−	1.08478i	0.361992	−	0.932181i	$-0.382097\pi$
$810$	9.03553	−	15.6500i	0.317476	−	0.549885i
$811$	20.6274			0.724327			0.362163	−	0.932115i	$-0.382038\pi$
$811$	20.6274			0.724327			0.362163	+	0.932115i	$0.382038\pi$
$812$		0			0
$813$	−6.82843			−0.239483
$814$		0			0
$815$	6.17157	+	10.6895i	0.216181	+	0.374436i
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	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	$0.482114\pi$
$821$	−23.9706	+	41.5182i	−0.836578	+	1.44900i	−0.892739	+	0.450575i	$0.851219\pi$
$822$	4.82843	+	8.36308i	0.168411	+	0.291696i
$823$	−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
$825$	−0.343146			−0.0119468
$826$		0			0
$827$	−26.2132			−0.911522			−0.455761	−	0.890102i	$-0.650633\pi$
$827$	−26.2132			−0.911522			−0.455761	+	0.890102i	$0.650633\pi$
$828$	2.24264	−	3.88437i	0.0779372	−	0.134991i
$829$	14.6569	+	25.3864i	0.509054	+	0.881707i	0.999945	+	0.0104859i	$0.00333784\pi$
$829$	14.6569	+	25.3864i	0.509054	+	0.881707i	−0.490891	+	0.871221i	$0.663329\pi$
$830$	−16.5711	−	28.7019i	−0.575190	−	0.996259i
$831$	−3.34315	+	5.79050i	−0.115972	+	0.200870i
$832$	−47.4558			−1.64524
$833$		0			0
$834$	16.1421			0.558956
$835$	−11.2071	+	19.4113i	−0.387838	+	0.671755i
$836$	−4.48528	−	7.76874i	−0.155127	−	0.268687i
$837$	7.24264	+	12.5446i	0.250342	+	0.433606i
$838$	−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
$843$	6.27208	+	10.8636i	0.216022	+	0.374161i
$844$	−39.2132	−	67.9193i	−1.34977	−	2.33788i
$845$	5.15685	−	8.93193i	0.177401	−	0.307268i
$846$	13.6569			0.469532
$847$		0			0
$848$	−3.51472			−0.120696
$849$	2.89949	−	5.02207i	0.0995104	−	0.172357i
$850$	5.82843	+	10.0951i	0.199913	+	0.346260i
$851$		0			0
$852$	−3.55635	+	6.15978i	−0.121839	+	0.211030i
$853$	−2.54416			−0.0871102			−0.0435551	−	0.999051i	$-0.513868\pi$
$853$	−2.54416			−0.0871102			−0.0435551	+	0.999051i	$0.513868\pi$
$854$		0			0
$855$	−8.00000			−0.273594
$856$	−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	$0.634206\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	0.686292	−	1.18869i	0.0234160	−	0.0405576i	−0.854080	−	0.520142i	$-0.825879\pi$
$859$	0.686292	−	1.18869i	0.0234160	−	0.0405576i	0.877496	+	0.479584i	$0.159212\pi$
$860$	−13.7279			−0.468118
$861$		0			0
$862$	42.9706			1.46358
$863$	−7.27817	+	12.6062i	−0.247752	+	0.429119i	−0.962902	−	0.269852i	$-0.913025\pi$
$863$	−7.27817	+	12.6062i	−0.247752	+	0.429119i	0.715150	+	0.698971i	$0.246358\pi$
$864$	−1.91421	−	3.31552i	−0.0651229	−	0.112796i
$865$	−1.65685	−	2.86976i	−0.0563347	−	0.0975746i
$866$	9.41421	−	16.3059i	0.319908	−	0.554097i
$867$	2.61522			0.0888177
$868$		0			0
$869$	−12.2843			−0.416715
$870$	−0.500000	+	0.866025i	−0.0169516	+	0.0293610i
$871$	−23.1421	−	40.0834i	−0.784141	−	1.35817i
$872$	29.7635	+	51.5518i	1.00792	+	1.74576i
$873$	−16.4853	+	28.5533i	−0.557942	+	0.966384i
$874$	−2.82843			−0.0956730
$875$		0			0
$876$	1.31371			0.0443861
$877$	−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
$879$	−3.31371	−	5.73951i	−0.111769	−	0.193589i
$880$	−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
$885$	−0.928932	−	1.60896i	−0.0312257	−	0.0540845i
$886$	−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
$889$		0			0
$890$	−20.8995			−0.700553
$891$	3.10051	−	5.37023i	0.103871	−	0.179910i
$892$	0.656854	+	1.13770i	0.0219931	+	0.0380932i
$893$	−2.82843	−	4.89898i	−0.0946497	−	0.163938i
$894$	1.08579	−	1.88064i	0.0363141	−	0.0628979i
$895$	10.0000			0.334263
$896$		0			0
$897$	0.828427			0.0276604
$898$	−4.62132	+	8.00436i	−0.154215	+	0.267109i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$	5.41421	+	9.37769i	0.180474	+	0.312590i
$901$	−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
$906$	−5.82843	−	10.0951i	−0.193637	−	0.335388i
$907$	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
$909$	−29.1716			−0.967560
$910$		0			0
$911$	−10.2010			−0.337975			−0.168987	−	0.985618i	$-0.554050\pi$
$911$	−10.2010			−0.337975			−0.168987	+	0.985618i	$0.554050\pi$
$912$	1.75736	−	3.04384i	0.0581920	−	0.100791i
$913$	−5.68629	−	9.84895i	−0.188189	−	0.325953i
$914$	−29.3137	−	50.7728i	−0.969611	−	1.67942i
$915$	−1.13604	+	1.96768i	−0.0375563	+	0.0650494i
$916$	44.6274			1.47453
$917$		0			0
$918$	28.1421			0.928829
$919$	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
$921$	−0.985281	−	1.70656i	−0.0324661	−	0.0562330i
$922$	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
$927$	3.41421	+	5.91359i	0.112137	+	0.194228i
$928$	−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	$0.137985\pi$
$930$	−6.00000			−0.196748
$931$		0			0
$932$	−64.4264			−2.11036
$933$	−2.72792	+	4.72490i	−0.0893082	+	0.154686i
$934$	−3.74264	−	6.48244i	−0.122463	−	0.212112i
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$	30.1421	−	52.2077i	0.985227	−	1.70646i
$937$	−34.6274			−1.13123			−0.565614	−	0.824670i	$-0.691361\pi$
$937$	−34.6274			−1.13123			−0.565614	+	0.824670i	$0.691361\pi$
$938$		0			0
$939$	2.62742			0.0857425
$940$	−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	$-0.438745\pi$
$942$	8.65685	+	14.9941i	0.282056	+	0.488535i
$943$	−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	$0.347926\pi$
$947$	−16.5919	+	28.7380i	−0.539164	+	0.933859i	−0.998949	+	0.0458290i	$0.985407\pi$
$948$	−11.7574	−	20.3643i	−0.381861	−	0.661403i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	3.41421	−	5.91359i	0.110772	−	0.191862i
$951$	−5.71573			−0.185345
$952$		0			0
$953$	−13.6569			−0.442389			−0.221194	−	0.975230i	$-0.570996\pi$
$953$	−13.6569			−0.442389			−0.221194	+	0.975230i	$0.570996\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$	−6.41421	−	11.1097i	−0.207559	−	0.359503i
$956$	40.7990	+	70.6659i	1.31953	+	2.28550i
$957$	−0.171573	+	0.297173i	−0.00554616	+	0.00960624i
$958$	86.0833			2.78122
$959$		0			0
$960$	4.07107			0.131393
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	15.8995	+	27.5387i	0.512354	+	0.887423i
$964$	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
$969$	−2.82843	−	4.89898i	−0.0908622	−	0.157378i
$970$	−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	$0.292499\pi$
$972$	39.5980			1.27011
$973$		0			0
$974$	10.4853			0.335970
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	8.22792	+	14.2512i	0.263369	+	0.456169i
$977$	0.656854	+	1.13770i	0.0210146	+	0.0363984i	0.876341	−	0.481690i	$-0.159977\pi$
$977$	0.656854	+	1.13770i	0.0210146	+	0.0363984i	−0.855327	+	0.518089i	$0.826644\pi$
$978$	−6.17157	+	10.6895i	−0.197345	+	0.341812i
$979$	−7.17157			−0.229204
$980$		0			0
$981$	38.1421			1.21778
$982$	−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	$0.684782\pi$
$984$	−7.15685	−	12.3960i	−0.228152	−	0.395171i
$985$	−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
$990$	2.82843	+	4.89898i	0.0898933	+	0.155700i
$991$	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
$993$	9.51472			0.301940
$994$		0			0
$995$	−9.65685			−0.306143
$996$	10.8848	−	18.8530i	0.344897	−	0.597380i
$997$	16.7279	+	28.9736i	0.529779	+	0.917603i	0.999397	+	0.0347337i	$0.0110583\pi$
$997$	16.7279	+	28.9736i	0.529779	+	0.917603i	−0.469618	+	0.882870i	$0.655608\pi$
$998$	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	245.2.e.e.226.1		4
7.2	even	3		245.2.a.g.1.2		2
7.3	odd	6		35.2.e.a.11.1	✓	4
7.4	even	3	inner	245.2.e.e.116.1		4
7.5	odd	6		245.2.a.h.1.2		2
7.6	odd	2		35.2.e.a.16.1	yes	4
21.2	odd	6		2205.2.a.q.1.1		2
21.5	even	6		2205.2.a.n.1.1		2
21.17	even	6		315.2.j.e.46.2		4
21.20	even	2		315.2.j.e.226.2		4
28.3	even	6		560.2.q.k.81.1		4
28.19	even	6		3920.2.a.bq.1.2		2
28.23	odd	6		3920.2.a.bv.1.1		2
28.27	even	2		560.2.q.k.401.1		4
35.2	odd	12		1225.2.b.h.99.4		4
35.3	even	12		175.2.k.a.74.1		8
35.9	even	6		1225.2.a.m.1.1		2
35.12	even	12		1225.2.b.g.99.4		4
35.13	even	4		175.2.k.a.149.4		8
35.17	even	12		175.2.k.a.74.4		8
35.19	odd	6		1225.2.a.k.1.1		2
35.23	odd	12		1225.2.b.h.99.1		4
35.24	odd	6		175.2.e.c.151.2		4
35.27	even	4		175.2.k.a.149.1		8
35.33	even	12		1225.2.b.g.99.1		4
35.34	odd	2		175.2.e.c.51.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.1	✓	4	7.3	odd	6
35.2.e.a.16.1	yes	4	7.6	odd	2
175.2.e.c.51.2		4	35.34	odd	2
175.2.e.c.151.2		4	35.24	odd	6
175.2.k.a.74.1		8	35.3	even	12
175.2.k.a.74.4		8	35.17	even	12
175.2.k.a.149.1		8	35.27	even	4
175.2.k.a.149.4		8	35.13	even	4
245.2.a.g.1.2		2	7.2	even	3
245.2.a.h.1.2		2	7.5	odd	6
245.2.e.e.116.1		4	7.4	even	3	inner
245.2.e.e.226.1		4	1.1	even	1	trivial
315.2.j.e.46.2		4	21.17	even	6
315.2.j.e.226.2		4	21.20	even	2
560.2.q.k.81.1		4	28.3	even	6
560.2.q.k.401.1		4	28.27	even	2
1225.2.a.k.1.1		2	35.19	odd	6
1225.2.a.m.1.1		2	35.9	even	6
1225.2.b.g.99.1		4	35.33	even	12
1225.2.b.g.99.4		4	35.12	even	12
1225.2.b.h.99.1		4	35.23	odd	12
1225.2.b.h.99.4		4	35.2	odd	12
2205.2.a.n.1.1		2	21.5	even	6
2205.2.a.q.1.1		2	21.2	odd	6
3920.2.a.bq.1.2		2	28.19	even	6
3920.2.a.bv.1.1		2	28.23	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +4.41421 q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-0.207107 - 0.358719i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +4.41421 q^{8} +(1.41421 - 2.44949i) q^{9} +(1.20711 + 2.09077i) q^{10} +(0.414214 + 0.717439i) q^{11} +(-0.792893 + 1.37333i) q^{12} +4.82843 q^{13} -0.414214 q^{15} +(-1.50000 + 2.59808i) q^{16} +(2.41421 + 4.18154i) q^{17} +(3.41421 + 5.91359i) q^{18} +(1.41421 - 2.44949i) q^{19} -3.82843 q^{20} -2.00000 q^{22} +(-0.207107 + 0.358719i) q^{23} +(-0.914214 - 1.58346i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} -2.41421 q^{27} -1.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(0.792893 + 1.37333i) q^{32} +(0.171573 - 0.297173i) q^{33} -11.6569 q^{34} -10.8284 q^{36} +(3.41421 + 5.91359i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(2.20711 - 3.82282i) q^{40} +7.82843 q^{41} +3.58579 q^{43} +(1.58579 - 2.74666i) q^{44} +(-1.41421 - 2.44949i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.24264 q^{48} +2.41421 q^{50} +(1.00000 - 1.73205i) q^{51} +(-9.24264 - 16.0087i) q^{52} +(0.585786 + 1.01461i) q^{53} +(2.91421 - 5.04757i) q^{54} +0.828427 q^{55} -1.17157 q^{57} +(1.20711 - 2.09077i) q^{58} +(2.24264 + 3.88437i) q^{59} +(0.792893 + 1.37333i) q^{60} +(2.74264 - 4.75039i) q^{61} +14.4853 q^{62} -9.82843 q^{64} +(2.41421 - 4.18154i) q^{65} +(0.414214 + 0.717439i) q^{66} +(-4.79289 - 8.30153i) q^{67} +(9.24264 - 16.0087i) q^{68} +0.171573 q^{69} +4.48528 q^{71} +(6.24264 - 10.8126i) q^{72} +(-0.414214 - 0.717439i) q^{73} +(-0.207107 + 0.358719i) q^{75} -10.8284 q^{76} +4.82843 q^{78} +(-7.41421 + 12.8418i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-3.74264 - 6.48244i) q^{81} +(-9.44975 + 16.3674i) q^{82} -13.7279 q^{83} +4.82843 q^{85} +(-4.32843 + 7.49706i) q^{86} +(0.207107 + 0.358719i) q^{87} +(1.82843 + 3.16693i) q^{88} +(-4.32843 + 7.49706i) q^{89} +6.82843 q^{90} +1.58579 q^{92} +(-1.24264 + 2.15232i) q^{93} +(2.41421 + 4.18154i) q^{94} +(-1.41421 - 2.44949i) q^{95} +(0.328427 - 0.568852i) q^{96} -11.6569 q^{97} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 2 q^{10} - 4 q^{11} - 6 q^{12} + 8 q^{13} + 4 q^{15} - 6 q^{16} + 4 q^{17} + 8 q^{18} - 4 q^{20} - 8 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 4 q^{29} + 2 q^{30} - 12 q^{31} + 6 q^{32} + 12 q^{33} - 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} + 6 q^{40} + 20 q^{41} + 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 4 q^{50} + 4 q^{51} - 20 q^{52} + 8 q^{53} + 6 q^{54} - 8 q^{55} - 16 q^{57} + 2 q^{58} - 8 q^{59} + 6 q^{60} - 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{65} - 4 q^{66} - 22 q^{67} + 20 q^{68} + 12 q^{69} - 16 q^{71} + 8 q^{72} + 4 q^{73} + 2 q^{75} - 32 q^{76} + 8 q^{78} - 24 q^{79} + 6 q^{80} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 8 q^{85} - 6 q^{86} - 2 q^{87} - 4 q^{88} - 6 q^{89} + 16 q^{90} + 12 q^{92} + 12 q^{93} + 4 q^{94} - 10 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 2 * q^10 - 4 * q^11 - 6 * q^12 + 8 * q^13 + 4 * q^15 - 6 * q^16 + 4 * q^17 + 8 * q^18 - 4 * q^20 - 8 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 4 * q^29 + 2 * q^30 - 12 * q^31 + 6 * q^32 + 12 * q^33 - 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 + 6 * q^40 + 20 * q^41 + 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 4 * q^50 + 4 * q^51 - 20 * q^52 + 8 * q^53 + 6 * q^54 - 8 * q^55 - 16 * q^57 + 2 * q^58 - 8 * q^59 + 6 * q^60 - 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^65 - 4 * q^66 - 22 * q^67 + 20 * q^68 + 12 * q^69 - 16 * q^71 + 8 * q^72 + 4 * q^73 + 2 * q^75 - 32 * q^76 + 8 * q^78 - 24 * q^79 + 6 * q^80 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 8 * q^85 - 6 * q^86 - 2 * q^87 - 4 * q^88 - 6 * q^89 + 16 * q^90 + 12 * q^92 + 12 * q^93 + 4 * q^94 - 10 * q^96 - 24 * q^97 + 32 * q^99

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