LMFDB - Embedded newform 1450.2.j.j.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(157,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1450.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 36 x^{18} + 534 x^{16} + 4248 x^{14} + 19701 x^{12} + 54104 x^{10} + 85176 x^{8} + 70068 x^{6} + \cdots + 100 $ x^20 + 36x^18 + 534x^16 + 4248x^14 + 19701x^12 + 54104x^10 + 85176x^8 + 70068x^6 + 24828x^4 + 3384*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.3
Root			$-1.41267i$ of defining polynomial
Character	$\chi$	$=$	1450.157
Dual form			1450.2.j.j.1293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.41267 q^{3} -1.00000 q^{4} +1.41267i q^{6} +(-2.52368 - 2.52368i) q^{7} +1.00000i q^{8} -1.00435 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.41267 q^{3} -1.00000 q^{4} +1.41267i q^{6} +(-2.52368 - 2.52368i) q^{7} +1.00000i q^{8} -1.00435 q^{9} +(-3.45447 - 3.45447i) q^{11} +1.41267 q^{12} +(-0.440183 - 0.440183i) q^{13} +(-2.52368 + 2.52368i) q^{14} +1.00000 q^{16} -6.19134i q^{17} +1.00435i q^{18} +(-1.83551 + 1.83551i) q^{19} +(3.56514 + 3.56514i) q^{21} +(-3.45447 + 3.45447i) q^{22} +(5.35712 - 5.35712i) q^{23} -1.41267i q^{24} +(-0.440183 + 0.440183i) q^{26} +5.65684 q^{27} +(2.52368 + 2.52368i) q^{28} +(1.02579 + 5.28656i) q^{29} +(7.06123 + 7.06123i) q^{31} -1.00000i q^{32} +(4.88004 + 4.88004i) q^{33} -6.19134 q^{34} +1.00435 q^{36} -11.8561 q^{37} +(1.83551 + 1.83551i) q^{38} +(0.621836 + 0.621836i) q^{39} +(-6.15956 + 6.15956i) q^{41} +(3.56514 - 3.56514i) q^{42} -0.682361 q^{43} +(3.45447 + 3.45447i) q^{44} +(-5.35712 - 5.35712i) q^{46} -0.628279 q^{47} -1.41267 q^{48} +5.73796i q^{49} +8.74634i q^{51} +(0.440183 + 0.440183i) q^{52} +(-5.28335 + 5.28335i) q^{53} -5.65684i q^{54} +(2.52368 - 2.52368i) q^{56} +(2.59298 - 2.59298i) q^{57} +(5.28656 - 1.02579i) q^{58} -12.2371i q^{59} +(-0.427953 - 0.427953i) q^{61} +(7.06123 - 7.06123i) q^{62} +(2.53466 + 2.53466i) q^{63} -1.00000 q^{64} +(4.88004 - 4.88004i) q^{66} +(-3.94698 + 3.94698i) q^{67} +6.19134i q^{68} +(-7.56787 + 7.56787i) q^{69} +14.5967i q^{71} -1.00435i q^{72} +11.5283i q^{73} +11.8561i q^{74} +(1.83551 - 1.83551i) q^{76} +17.4360i q^{77} +(0.621836 - 0.621836i) q^{78} +(9.54037 - 9.54037i) q^{79} -4.97823 q^{81} +(6.15956 + 6.15956i) q^{82} +(5.35735 - 5.35735i) q^{83} +(-3.56514 - 3.56514i) q^{84} +0.682361i q^{86} +(-1.44910 - 7.46819i) q^{87} +(3.45447 - 3.45447i) q^{88} +(-1.84859 + 1.84859i) q^{89} +2.22177i q^{91} +(-5.35712 + 5.35712i) q^{92} +(-9.97523 - 9.97523i) q^{93} +0.628279i q^{94} +1.41267i q^{96} +13.5465 q^{97} +5.73796 q^{98} +(3.46950 + 3.46950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{3} - 20 q^{4} - 8 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + 8 * q^3 - 20 * q^4 - 8 * q^7 + 12 * q^9	$ 20 q + 8 q^{3} - 20 q^{4} - 8 q^{7} + 12 q^{9} - 8 q^{11} - 8 q^{12} + 4 q^{13} - 8 q^{14} + 20 q^{16} + 4 q^{19} + 4 q^{21} - 8 q^{22} + 12 q^{23} + 4 q^{26} + 32 q^{27} + 8 q^{28} - 8 q^{29} + 28 q^{31} + 16 q^{34} - 12 q^{36} - 20 q^{37} - 4 q^{38} + 24 q^{39} + 24 q^{41} + 4 q^{42} + 8 q^{43} + 8 q^{44} - 12 q^{46} - 28 q^{47} + 8 q^{48} - 4 q^{52} + 8 q^{56} + 8 q^{57} + 8 q^{58} + 24 q^{61} + 28 q^{62} - 20 q^{63} - 20 q^{64} - 12 q^{67} + 28 q^{69} - 4 q^{76} + 24 q^{78} - 32 q^{79} - 12 q^{81} - 24 q^{82} - 20 q^{83} - 4 q^{84} - 36 q^{87} + 8 q^{88} - 4 q^{89} - 12 q^{92} - 12 q^{93} + 48 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) $ 20 * q + 8 * q^3 - 20 * q^4 - 8 * q^7 + 12 * q^9 - 8 * q^11 - 8 * q^12 + 4 * q^13 - 8 * q^14 + 20 * q^16 + 4 * q^19 + 4 * q^21 - 8 * q^22 + 12 * q^23 + 4 * q^26 + 32 * q^27 + 8 * q^28 - 8 * q^29 + 28 * q^31 + 16 * q^34 - 12 * q^36 - 20 * q^37 - 4 * q^38 + 24 * q^39 + 24 * q^41 + 4 * q^42 + 8 * q^43 + 8 * q^44 - 12 * q^46 - 28 * q^47 + 8 * q^48 - 4 * q^52 + 8 * q^56 + 8 * q^57 + 8 * q^58 + 24 * q^61 + 28 * q^62 - 20 * q^63 - 20 * q^64 - 12 * q^67 + 28 * q^69 - 4 * q^76 + 24 * q^78 - 32 * q^79 - 12 * q^81 - 24 * q^82 - 20 * q^83 - 4 * q^84 - 36 * q^87 + 8 * q^88 - 4 * q^89 - 12 * q^92 - 12 * q^93 + 48 * q^97 + 20 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.41267			−0.815608			−0.407804	−	0.913069i	$-0.633705\pi$
$3$	−1.41267			−0.815608			−0.407804	+	0.913069i	$0.633705\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			1.41267i			0.576722i
$7$	−2.52368	−	2.52368i	−0.953863	−	0.953863i	0.0451189	−	0.998982i	$-0.485633\pi$
$7$	−2.52368	−	2.52368i	−0.953863	−	0.953863i	−0.998982	+	0.0451189i	$0.985633\pi$
$8$			1.00000i			0.353553i
$9$	−1.00435			−0.334784
$10$		0			0
$11$	−3.45447	−	3.45447i	−1.04156	−	1.04156i	−0.999098	−	0.0424627i	$-0.986480\pi$
$11$	−3.45447	−	3.45447i	−1.04156	−	1.04156i	−0.0424627	−	0.999098i	$-0.513520\pi$
$12$	1.41267			0.407804
$13$	−0.440183	−	0.440183i	−0.122085	−	0.122085i	0.643425	−	0.765509i	$-0.277513\pi$
$13$	−0.440183	−	0.440183i	−0.122085	−	0.122085i	−0.765509	+	0.643425i	$0.777513\pi$
$14$	−2.52368	+	2.52368i	−0.674483	+	0.674483i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.19134i		−	1.50162i	−0.660518	−	0.750810i	$-0.729663\pi$
$17$		−	6.19134i		−	1.50162i	0.660518	−	0.750810i	$-0.270337\pi$
$18$			1.00435i			0.236728i
$19$	−1.83551	+	1.83551i	−0.421096	+	0.421096i	−0.885581	−	0.464485i	$-0.846239\pi$
$19$	−1.83551	+	1.83551i	−0.421096	+	0.421096i	0.464485	+	0.885581i	$0.346239\pi$
$20$		0			0
$21$	3.56514	+	3.56514i	0.777978	+	0.777978i
$22$	−3.45447	+	3.45447i	−0.736495	+	0.736495i
$23$	5.35712	−	5.35712i	1.11704	−	1.11704i	0.124864	−	0.992174i	$-0.460151\pi$
$23$	5.35712	−	5.35712i	1.11704	−	1.11704i	0.992174	−	0.124864i	$-0.0398493\pi$
$24$		−	1.41267i		−	0.288361i
$25$		0			0
$26$	−0.440183	+	0.440183i	−0.0863271	+	0.0863271i
$27$	5.65684			1.08866
$28$	2.52368	+	2.52368i	0.476931	+	0.476931i
$29$	1.02579	+	5.28656i	0.190484	+	0.981690i
$29$	1.02579	+	5.28656i	0.190484	+	0.981690i
$30$		0			0
$31$	7.06123	+	7.06123i	1.26824	+	1.26824i	0.946999	+	0.321236i	$0.104098\pi$
$31$	7.06123	+	7.06123i	1.26824	+	1.26824i	0.321236	+	0.946999i	$0.395902\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.88004	+	4.88004i	0.849505	+	0.849505i
$34$	−6.19134			−1.06181
$35$		0			0
$36$	1.00435			0.167392
$37$	−11.8561			−1.94913			−0.974565	−	0.224103i	$-0.928055\pi$
$37$	−11.8561			−1.94913			−0.974565	+	0.224103i	$0.928055\pi$
$38$	1.83551	+	1.83551i	0.297760	+	0.297760i
$39$	0.621836	+	0.621836i	0.0995734	+	0.0995734i
$40$		0			0
$41$	−6.15956	+	6.15956i	−0.961961	+	0.961961i	−0.999303	−	0.0373414i	$-0.988111\pi$
$41$	−6.15956	+	6.15956i	−0.961961	+	0.961961i	0.0373414	+	0.999303i	$0.488111\pi$
$42$	3.56514	−	3.56514i	0.550114	−	0.550114i
$43$	−0.682361			−0.104059			−0.0520295	−	0.998646i	$-0.516569\pi$
$43$	−0.682361			−0.104059			−0.0520295	+	0.998646i	$0.516569\pi$
$44$	3.45447	+	3.45447i	0.520780	+	0.520780i
$45$		0			0
$46$	−5.35712	−	5.35712i	−0.789865	−	0.789865i
$47$	−0.628279			−0.0916439			−0.0458219	−	0.998950i	$-0.514591\pi$
$47$	−0.628279			−0.0916439			−0.0458219	+	0.998950i	$0.514591\pi$
$48$	−1.41267			−0.203902
$49$			5.73796i			0.819708i
$50$		0			0
$51$			8.74634i			1.22473i
$52$	0.440183	+	0.440183i	0.0610424	+	0.0610424i
$53$	−5.28335	+	5.28335i	−0.725724	+	0.725724i	−0.969765	−	0.244041i	$-0.921527\pi$
$53$	−5.28335	+	5.28335i	−0.725724	+	0.725724i	0.244041	+	0.969765i	$0.421527\pi$
$54$		−	5.65684i		−	0.769799i
$55$		0			0
$56$	2.52368	−	2.52368i	0.337241	−	0.337241i
$57$	2.59298	−	2.59298i	0.343449	−	0.343449i
$58$	5.28656	−	1.02579i	0.694160	−	0.134692i
$59$		−	12.2371i		−	1.59314i	−0.604547	−	0.796569i	$-0.706646\pi$
$59$		−	12.2371i		−	1.59314i	0.604547	−	0.796569i	$-0.293354\pi$
$60$		0			0
$61$	−0.427953	−	0.427953i	−0.0547938	−	0.0547938i	0.679179	−	0.733973i	$-0.262336\pi$
$61$	−0.427953	−	0.427953i	−0.0547938	−	0.0547938i	−0.733973	+	0.679179i	$0.762336\pi$
$62$	7.06123	−	7.06123i	0.896778	−	0.896778i
$63$	2.53466	+	2.53466i	0.319338	+	0.319338i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.88004	−	4.88004i	0.600691	−	0.600691i
$67$	−3.94698	+	3.94698i	−0.482200	+	0.482200i	−0.905834	−	0.423633i	$-0.860755\pi$
$67$	−3.94698	+	3.94698i	−0.482200	+	0.482200i	0.423633	+	0.905834i	$0.360755\pi$
$68$			6.19134i			0.750810i
$69$	−7.56787	+	7.56787i	−0.911065	+	0.911065i
$70$		0			0
$71$			14.5967i			1.73231i	0.499773	+	0.866156i	$0.333417\pi$
$71$			14.5967i			1.73231i	−0.499773	+	0.866156i	$0.666583\pi$
$72$		−	1.00435i		−	0.118364i
$73$			11.5283i			1.34928i	0.738146	+	0.674641i	$0.235701\pi$
$73$			11.5283i			1.34928i	−0.738146	+	0.674641i	$0.764299\pi$
$74$			11.8561i			1.37824i
$75$		0			0
$76$	1.83551	−	1.83551i	0.210548	−	0.210548i
$77$			17.4360i			1.98701i
$78$	0.621836	−	0.621836i	0.0704090	−	0.0704090i
$79$	9.54037	−	9.54037i	1.07338	−	1.07338i	0.0762893	−	0.997086i	$-0.475693\pi$
$79$	9.54037	−	9.54037i	1.07338	−	1.07338i	0.997086	−	0.0762893i	$-0.0243073\pi$
$80$		0			0
$81$	−4.97823			−0.553136
$82$	6.15956	+	6.15956i	0.680209	+	0.680209i
$83$	5.35735	−	5.35735i	0.588046	−	0.588046i	−0.349056	−	0.937102i	$-0.613498\pi$
$83$	5.35735	−	5.35735i	0.588046	−	0.588046i	0.937102	+	0.349056i	$0.113498\pi$
$84$	−3.56514	−	3.56514i	−0.388989	−	0.388989i
$85$		0			0
$86$			0.682361i			0.0735809i
$87$	−1.44910	−	7.46819i	−0.155360	−	0.800674i
$88$	3.45447	−	3.45447i	0.368247	−	0.368247i
$89$	−1.84859	+	1.84859i	−0.195950	+	0.195950i	−0.798261	−	0.602311i	$-0.794247\pi$
$89$	−1.84859	+	1.84859i	−0.195950	+	0.195950i	0.602311	+	0.798261i	$0.294247\pi$
$90$		0			0
$91$			2.22177i			0.232904i
$92$	−5.35712	+	5.35712i	−0.558519	+	0.558519i
$93$	−9.97523	−	9.97523i	−1.03438	−	1.03438i
$94$			0.628279i			0.0648020i
$95$		0			0
$96$			1.41267i			0.144180i
$97$	13.5465			1.37544			0.687720	−	0.725976i	$-0.258612\pi$
$97$	13.5465			1.37544			0.687720	+	0.725976i	$0.258612\pi$
$98$	5.73796			0.579621
$99$	3.46950	+	3.46950i	0.348697	+	0.348697i
$100$		0			0
$101$	4.34239	+	4.34239i	0.432084	+	0.432084i	0.889337	−	0.457253i	$-0.151166\pi$
$101$	4.34239	+	4.34239i	0.432084	+	0.432084i	−0.457253	+	0.889337i	$0.651166\pi$
$102$	8.74634			0.866017
$103$	4.53579	−	4.53579i	0.446925	−	0.446925i	−0.447406	−	0.894331i	$-0.647652\pi$
$103$	4.53579	−	4.53579i	0.446925	−	0.446925i	0.894331	+	0.447406i	$0.147652\pi$
$104$	0.440183	−	0.440183i	0.0431635	−	0.0431635i
$105$		0			0
$106$	5.28335	+	5.28335i	0.513164	+	0.513164i
$107$	−2.20738	−	2.20738i	−0.213396	−	0.213396i	0.592313	−	0.805708i	$-0.298215\pi$
$107$	−2.20738	−	2.20738i	−0.213396	−	0.213396i	−0.805708	+	0.592313i	$0.798215\pi$
$108$	−5.65684			−0.544330
$109$	−15.0643			−1.44290			−0.721451	−	0.692465i	$-0.756525\pi$
$109$	−15.0643			−1.44290			−0.721451	+	0.692465i	$0.756525\pi$
$110$		0			0
$111$	16.7488			1.58973
$112$	−2.52368	−	2.52368i	−0.238466	−	0.238466i
$113$		−	0.652119i		−	0.0613462i	−0.999529	−	0.0306731i	$-0.990235\pi$
$113$		−	0.652119i		−	0.0613462i	0.999529	−	0.0306731i	$-0.00976509\pi$
$114$	−2.59298	−	2.59298i	−0.242855	−	0.242855i
$115$		0			0
$116$	−1.02579	−	5.28656i	−0.0952419	−	0.490845i
$117$	0.442099	+	0.442099i	0.0408720	+	0.0408720i
$118$	−12.2371			−1.12652
$119$	−15.6250	+	15.6250i	−1.43234	+	1.43234i
$120$		0			0
$121$			12.8667i			1.16970i
$122$	−0.427953	+	0.427953i	−0.0387451	+	0.0387451i
$123$	8.70145	−	8.70145i	0.784583	−	0.784583i
$124$	−7.06123	−	7.06123i	−0.634118	−	0.634118i
$125$		0			0
$126$	2.53466	−	2.53466i	0.225806	−	0.225806i
$127$			4.76046i			0.422423i	0.977440	+	0.211211i	$0.0677409\pi$
$127$			4.76046i			0.422423i	−0.977440	+	0.211211i	$0.932259\pi$
$128$			1.00000i			0.0883883i
$129$	0.963954			0.0848714
$130$		0			0
$131$	4.80985	−	4.80985i	0.420239	−	0.420239i	−0.465047	−	0.885286i	$-0.653963\pi$
$131$	4.80985	−	4.80985i	0.420239	−	0.420239i	0.885286	+	0.465047i	$0.153963\pi$
$132$	−4.88004	−	4.88004i	−0.424753	−	0.424753i
$133$	9.26451			0.803335
$134$	3.94698	+	3.94698i	0.340967	+	0.340967i
$135$		0			0
$136$	6.19134			0.530903
$137$		−	6.97103i		−	0.595575i	−0.954632	−	0.297788i	$-0.903751\pi$
$137$		−	6.97103i		−	0.595575i	0.954632	−	0.297788i	$-0.0962487\pi$
$138$	7.56787	+	7.56787i	0.644220	+	0.644220i
$139$		−	4.02888i		−	0.341725i	−0.985295	−	0.170863i	$-0.945345\pi$
$139$		−	4.02888i		−	0.341725i	0.985295	−	0.170863i	$-0.0546554\pi$
$140$		0			0
$141$	0.887553			0.0747455
$142$	14.5967			1.22493
$143$			3.04120i			0.254318i
$144$	−1.00435			−0.0836959
$145$		0			0
$146$	11.5283			0.954086
$147$		−	8.10587i		−	0.668561i
$148$	11.8561			0.974565
$149$	21.4142			1.75432			0.877160	−	0.480198i	$-0.159435\pi$
$149$	21.4142			1.75432			0.877160	+	0.480198i	$0.159435\pi$
$150$		0			0
$151$			0.705021i			0.0573738i	0.999588	+	0.0286869i	$0.00913257\pi$
$151$			0.705021i			0.0573738i	−0.999588	+	0.0286869i	$0.990867\pi$
$152$	−1.83551	−	1.83551i	−0.148880	−	0.148880i
$153$			6.21827i			0.502718i
$154$	17.4360			1.40503
$155$		0			0
$156$	−0.621836	−	0.621836i	−0.0497867	−	0.0497867i
$157$	−10.6135			−0.847052			−0.423526	−	0.905884i	$-0.639208\pi$
$157$	−10.6135			−0.847052			−0.423526	+	0.905884i	$0.639208\pi$
$158$	−9.54037	−	9.54037i	−0.758991	−	0.758991i
$159$	7.46365	−	7.46365i	0.591906	−	0.591906i
$160$		0			0
$161$	−27.0394			−2.13100
$162$			4.97823i			0.391126i
$163$			1.01388i			0.0794134i	0.999211	+	0.0397067i	$0.0126424\pi$
$163$			1.01388i			0.0794134i	−0.999211	+	0.0397067i	$0.987358\pi$
$164$	6.15956	−	6.15956i	0.480981	−	0.480981i
$165$		0			0
$166$	−5.35735	−	5.35735i	−0.415811	−	0.415811i
$167$	−12.1290	+	12.1290i	−0.938571	+	0.938571i	−0.998219	−	0.0596480i	$-0.981002\pi$
$167$	−12.1290	+	12.1290i	−0.938571	+	0.938571i	0.0596480	+	0.998219i	$0.481002\pi$
$168$	−3.56514	+	3.56514i	−0.275057	+	0.275057i
$169$		−	12.6125i		−	0.970191i
$170$		0			0
$171$	1.84350	−	1.84350i	0.140976	−	0.140976i
$172$	0.682361			0.0520295
$173$	−3.52527	−	3.52527i	−0.268021	−	0.268021i	0.560281	−	0.828303i	$-0.310693\pi$
$173$	−3.52527	−	3.52527i	−0.268021	−	0.268021i	−0.828303	+	0.560281i	$0.810693\pi$
$174$	−7.46819	+	1.44910i	−0.566162	+	0.109856i
$175$		0			0
$176$	−3.45447	−	3.45447i	−0.260390	−	0.260390i
$177$			17.2871i			1.29938i
$178$	1.84859	+	1.84859i	0.138557	+	0.138557i
$179$	6.72909			0.502956			0.251478	−	0.967863i	$-0.419083\pi$
$179$	6.72909			0.502956			0.251478	+	0.967863i	$0.419083\pi$
$180$		0			0
$181$	−3.82115			−0.284024			−0.142012	−	0.989865i	$-0.545357\pi$
$181$	−3.82115			−0.284024			−0.142012	+	0.989865i	$0.545357\pi$
$182$	2.22177			0.164688
$183$	0.604559	+	0.604559i	0.0446903	+	0.0446903i
$184$	5.35712	+	5.35712i	0.394932	+	0.394932i
$185$		0			0
$186$	−9.97523	+	9.97523i	−0.731419	+	0.731419i
$187$	−21.3878	+	21.3878i	−1.56403	+	1.56403i
$188$	0.628279			0.0458219
$189$	−14.2761	−	14.2761i	−1.03843	−	1.03843i
$190$		0			0
$191$	−14.7012	−	14.7012i	−1.06374	−	1.06374i	−0.997825	−	0.0659169i	$-0.979003\pi$
$191$	−14.7012	−	14.7012i	−1.06374	−	1.06374i	−0.0659169	−	0.997825i	$-0.520997\pi$
$192$	1.41267			0.101951
$193$	6.62222			0.476678			0.238339	−	0.971182i	$-0.423397\pi$
$193$	6.62222			0.476678			0.238339	+	0.971182i	$0.423397\pi$
$194$		−	13.5465i		−	0.972582i
$195$		0			0
$196$		−	5.73796i		−	0.409854i
$197$	14.2096	+	14.2096i	1.01239	+	1.01239i	0.999922	+	0.0124689i	$0.00396909\pi$
$197$	14.2096	+	14.2096i	1.01239	+	1.01239i	0.0124689	+	0.999922i	$0.496031\pi$
$198$	3.46950	−	3.46950i	0.246566	−	0.246566i
$199$		−	7.66685i		−	0.543489i	−0.962369	−	0.271744i	$-0.912399\pi$
$199$		−	7.66685i		−	0.543489i	0.962369	−	0.271744i	$-0.0876005\pi$
$200$		0			0
$201$	5.57580	−	5.57580i	0.393287	−	0.393287i
$202$	4.34239	−	4.34239i	0.305530	−	0.305530i
$203$	10.7529	−	15.9304i	0.754703	−	1.11809i
$204$		−	8.74634i		−	0.612367i
$205$		0			0
$206$	−4.53579	−	4.53579i	−0.316024	−	0.316024i
$207$	−5.38043	+	5.38043i	−0.373966	+	0.373966i
$208$	−0.440183	−	0.440183i	−0.0305212	−	0.0305212i
$209$	12.6814			0.877194
$210$		0			0
$211$	5.01654	−	5.01654i	0.345353	−	0.345353i	−0.513023	−	0.858375i	$-0.671474\pi$
$211$	5.01654	−	5.01654i	0.345353	−	0.345353i	0.858375	+	0.513023i	$0.171474\pi$
$212$	5.28335	−	5.28335i	0.362862	−	0.362862i
$213$		−	20.6204i		−	1.41289i
$214$	−2.20738	+	2.20738i	−0.150893	+	0.150893i
$215$		0			0
$216$			5.65684i			0.384899i
$217$		−	35.6406i		−	2.41944i
$218$			15.0643i			1.02029i
$219$		−	16.2857i		−	1.10048i
$220$		0			0
$221$	−2.72532	+	2.72532i	−0.183325	+	0.183325i
$222$		−	16.7488i		−	1.12411i
$223$	−7.10101	+	7.10101i	−0.475519	+	0.475519i	−0.903695	−	0.428176i	$-0.859156\pi$
$223$	−7.10101	+	7.10101i	−0.475519	+	0.475519i	0.428176	+	0.903695i	$0.359156\pi$
$224$	−2.52368	+	2.52368i	−0.168621	+	0.168621i
$225$		0			0
$226$	−0.652119			−0.0433783
$227$	−4.06690	−	4.06690i	−0.269929	−	0.269929i	0.559142	−	0.829072i	$-0.311131\pi$
$227$	−4.06690	−	4.06690i	−0.269929	−	0.269929i	−0.829072	+	0.559142i	$0.811131\pi$
$228$	−2.59298	+	2.59298i	−0.171725	+	0.171725i
$229$	3.49894	+	3.49894i	0.231217	+	0.231217i	0.813200	−	0.581984i	$-0.197723\pi$
$229$	3.49894	+	3.49894i	0.231217	+	0.231217i	−0.581984	+	0.813200i	$0.697723\pi$
$230$		0			0
$231$		−	24.6313i		−	1.62062i
$232$	−5.28656	+	1.02579i	−0.347080	+	0.0673462i
$233$	−6.60871	+	6.60871i	−0.432951	+	0.432951i	−0.889631	−	0.456680i	$-0.849038\pi$
$233$	−6.60871	+	6.60871i	−0.432951	+	0.432951i	0.456680	+	0.889631i	$0.349038\pi$
$234$	0.442099	−	0.442099i	0.0289009	−	0.0289009i
$235$		0			0
$236$			12.2371i			0.796569i
$237$	−13.4774	+	13.4774i	−0.875453	+	0.875453i
$238$	15.6250	+	15.6250i	1.01282	+	1.01282i
$239$			13.4285i			0.868617i	0.900764	+	0.434308i	$0.143007\pi$
$239$			13.4285i			0.868617i	−0.900764	+	0.434308i	$0.856993\pi$
$240$		0			0
$241$			5.06604i			0.326332i	0.986599	+	0.163166i	$0.0521706\pi$
$241$			5.06604i			0.326332i	−0.986599	+	0.163166i	$0.947829\pi$
$242$	12.8667			0.827101
$243$	−9.93792			−0.637518
$244$	0.427953	+	0.427953i	0.0273969	+	0.0273969i
$245$		0			0
$246$	−8.70145	−	8.70145i	−0.554784	−	0.554784i
$247$	1.61593			0.102819
$248$	−7.06123	+	7.06123i	−0.448389	+	0.448389i
$249$	−7.56820	+	7.56820i	−0.479615	+	0.479615i
$250$		0			0
$251$	−19.2823	−	19.2823i	−1.21709	−	1.21709i	−0.968647	−	0.248441i	$-0.920082\pi$
$251$	−19.2823	−	19.2823i	−1.21709	−	1.21709i	−0.248441	−	0.968647i	$-0.579918\pi$
$252$	−2.53466	−	2.53466i	−0.159669	−	0.159669i
$253$	−37.0120			−2.32692
$254$	4.76046			0.298698
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.83466	+	5.83466i	0.363956	+	0.363956i	0.865267	−	0.501311i	$-0.167149\pi$
$257$	5.83466	+	5.83466i	0.363956	+	0.363956i	−0.501311	+	0.865267i	$0.667149\pi$
$258$		−	0.963954i		−	0.0600132i
$259$	29.9210	+	29.9210i	1.85920	+	1.85920i
$260$		0			0
$261$	−1.03025	−	5.30957i	−0.0637708	−	0.328654i
$262$	−4.80985	−	4.80985i	−0.297154	−	0.297154i
$263$	18.8063			1.15964			0.579822	−	0.814743i	$-0.303122\pi$
$263$	18.8063			1.15964			0.579822	+	0.814743i	$0.303122\pi$
$264$	−4.88004	+	4.88004i	−0.300345	+	0.300345i
$265$		0			0
$266$		−	9.26451i		−	0.568044i
$267$	2.61145	−	2.61145i	0.159818	−	0.159818i
$268$	3.94698	−	3.94698i	0.241100	−	0.241100i
$269$	4.07821	+	4.07821i	0.248653	+	0.248653i	0.820418	−	0.571765i	$-0.193741\pi$
$269$	4.07821	+	4.07821i	0.248653	+	0.248653i	−0.571765	+	0.820418i	$0.693741\pi$
$270$		0			0
$271$	−5.55071	+	5.55071i	−0.337182	+	0.337182i	−0.855306	−	0.518124i	$-0.826631\pi$
$271$	−5.55071	+	5.55071i	−0.337182	+	0.337182i	0.518124	+	0.855306i	$0.326631\pi$
$272$		−	6.19134i		−	0.375405i
$273$		−	3.13863i		−	0.189959i
$274$	−6.97103			−0.421135
$275$		0			0
$276$	7.56787	−	7.56787i	0.455532	−	0.455532i
$277$	−17.6329	−	17.6329i	−1.05946	−	1.05946i	−0.998117	−	0.0613400i	$-0.980463\pi$
$277$	−17.6329	−	17.6329i	−1.05946	−	1.05946i	−0.0613400	−	0.998117i	$-0.519537\pi$
$278$	−4.02888			−0.241636
$279$	−7.09196	−	7.09196i	−0.424584	−	0.424584i
$280$		0			0
$281$	12.1013			0.721904			0.360952	−	0.932584i	$-0.382452\pi$
$281$	12.1013			0.721904			0.360952	+	0.932584i	$0.382452\pi$
$282$		−	0.887553i		−	0.0528530i
$283$	−19.9355	−	19.9355i	−1.18504	−	1.18504i	−0.978421	−	0.206620i	$-0.933754\pi$
$283$	−19.9355	−	19.9355i	−1.18504	−	1.18504i	−0.206620	−	0.978421i	$-0.566246\pi$
$284$		−	14.5967i		−	0.866156i
$285$		0			0
$286$	3.04120			0.179830
$287$	31.0895			1.83516
$288$			1.00435i			0.0591819i
$289$	−21.3327			−1.25486
$290$		0			0
$291$	−19.1368			−1.12182
$292$		−	11.5283i		−	0.674641i
$293$	−16.5160			−0.964875			−0.482438	−	0.875930i	$-0.660248\pi$
$293$	−16.5160			−0.964875			−0.482438	+	0.875930i	$0.660248\pi$
$294$	−8.10587			−0.472744
$295$		0			0
$296$		−	11.8561i		−	0.689122i
$297$	−19.5414	−	19.5414i	−1.13391	−	1.13391i
$298$		−	21.4142i		−	1.24049i
$299$	−4.71623			−0.272747
$300$		0			0
$301$	1.72206	+	1.72206i	0.0992581	+	0.0992581i
$302$	0.705021			0.0405694
$303$	−6.13439	−	6.13439i	−0.352411	−	0.352411i
$304$	−1.83551	+	1.83551i	−0.105274	+	0.105274i
$305$		0			0
$306$	6.21827			0.355475
$307$			24.7544i			1.41281i	0.707809	+	0.706404i	$0.249684\pi$
$307$			24.7544i			1.41281i	−0.707809	+	0.706404i	$0.750316\pi$
$308$		−	17.4360i		−	0.993506i
$309$	−6.40760	+	6.40760i	−0.364515	+	0.364515i
$310$		0			0
$311$	12.2930	+	12.2930i	0.697070	+	0.697070i	0.963777	−	0.266708i	$-0.0859359\pi$
$311$	12.2930	+	12.2930i	0.697070	+	0.697070i	−0.266708	+	0.963777i	$0.585936\pi$
$312$	−0.621836	+	0.621836i	−0.0352045	+	0.0352045i
$313$	−10.2575	+	10.2575i	−0.579787	+	0.579787i	−0.934844	−	0.355058i	$-0.884461\pi$
$313$	−10.2575	+	10.2575i	−0.579787	+	0.579787i	0.355058	+	0.934844i	$0.384461\pi$
$314$			10.6135i			0.598956i
$315$		0			0
$316$	−9.54037	+	9.54037i	−0.536688	+	0.536688i
$317$	3.24824			0.182440			0.0912198	−	0.995831i	$-0.470923\pi$
$317$	3.24824			0.182440			0.0912198	+	0.995831i	$0.470923\pi$
$318$	−7.46365	−	7.46365i	−0.418541	−	0.418541i
$319$	14.7187	−	21.8058i	0.824090	−	1.22089i
$320$		0			0
$321$	3.11831	+	3.11831i	0.174047	+	0.174047i
$322$			27.0394i			1.50685i
$323$	11.3643	+	11.3643i	0.632326	+	0.632326i
$324$	4.97823			0.276568
$325$		0			0
$326$	1.01388			0.0561538
$327$	21.2810			1.17684
$328$	−6.15956	−	6.15956i	−0.340105	−	0.340105i
$329$	1.58558	+	1.58558i	0.0874157	+	0.0874157i
$330$		0			0
$331$	−11.6868	+	11.6868i	−0.642365	+	0.642365i	−0.951136	−	0.308772i	$-0.900082\pi$
$331$	−11.6868	+	11.6868i	−0.642365	+	0.642365i	0.308772	+	0.951136i	$0.400082\pi$
$332$	−5.35735	+	5.35735i	−0.294023	+	0.294023i
$333$	11.9077			0.652537
$334$	12.1290	+	12.1290i	0.663670	+	0.663670i
$335$		0			0
$336$	3.56514	+	3.56514i	0.194495	+	0.194495i
$337$	−29.7531			−1.62075			−0.810377	−	0.585909i	$-0.800738\pi$
$337$	−29.7531			−1.62075			−0.810377	+	0.585909i	$0.800738\pi$
$338$	−12.6125			−0.686028
$339$			0.921232i			0.0500345i
$340$		0			0
$341$		−	48.7856i		−	2.64189i
$342$	−1.84350	−	1.84350i	−0.0996851	−	0.0996851i
$343$	−3.18500	+	3.18500i	−0.171974	+	0.171974i
$344$		−	0.682361i		−	0.0367904i
$345$		0			0
$346$	−3.52527	+	3.52527i	−0.189520	+	0.189520i
$347$	8.90390	−	8.90390i	0.477987	−	0.477987i	−0.426501	−	0.904487i	$-0.640254\pi$
$347$	8.90390	−	8.90390i	0.477987	−	0.477987i	0.904487	+	0.426501i	$0.140254\pi$
$348$	1.44910	+	7.46819i	0.0776800	+	0.400337i
$349$			14.3912i			0.770344i	0.922845	+	0.385172i	$0.125858\pi$
$349$			14.3912i			0.770344i	−0.922845	+	0.385172i	$0.874142\pi$
$350$		0			0
$351$	−2.49005	−	2.49005i	−0.132909	−	0.132909i
$352$	−3.45447	+	3.45447i	−0.184124	+	0.184124i
$353$	−14.6585	−	14.6585i	−0.780195	−	0.780195i	0.199668	−	0.979864i	$-0.436013\pi$
$353$	−14.6585	−	14.6585i	−0.780195	−	0.780195i	−0.979864	+	0.199668i	$0.936013\pi$
$354$	17.2871			0.918798
$355$		0			0
$356$	1.84859	−	1.84859i	0.0979749	−	0.0979749i
$357$	22.0730	−	22.0730i	1.16823	−	1.16823i
$358$		−	6.72909i		−	0.355643i
$359$	−11.7160	+	11.7160i	−0.618349	+	0.618349i	−0.945108	−	0.326759i	$-0.894044\pi$
$359$	−11.7160	+	11.7160i	−0.618349	+	0.618349i	0.326759	+	0.945108i	$0.394044\pi$
$360$		0			0
$361$			12.2618i			0.645357i
$362$			3.82115i			0.200835i
$363$		−	18.1764i		−	0.954015i
$364$		−	2.22177i		−	0.116452i
$365$		0			0
$366$	0.604559	−	0.604559i	0.0316008	−	0.0316008i
$367$		−	16.2434i		−	0.847897i	−0.905686	−	0.423948i	$-0.860644\pi$
$367$		−	16.2434i		−	0.847897i	0.905686	−	0.423948i	$-0.139356\pi$
$368$	5.35712	−	5.35712i	0.279259	−	0.279259i
$369$	6.18636	−	6.18636i	0.322049	−	0.322049i
$370$		0			0
$371$	26.6670			1.38448
$372$	9.97523	+	9.97523i	0.517191	+	0.517191i
$373$	−13.1251	+	13.1251i	−0.679594	+	0.679594i	−0.959908	−	0.280314i	$-0.909561\pi$
$373$	−13.1251	+	13.1251i	−0.679594	+	0.679594i	0.280314	+	0.959908i	$0.409561\pi$
$374$	21.3878	+	21.3878i	1.10593	+	1.10593i
$375$		0			0
$376$		−	0.628279i		−	0.0324010i
$377$	1.87552	−	2.77859i	0.0965944	−	0.143105i
$378$	−14.2761	+	14.2761i	−0.734283	+	0.734283i
$379$	−4.88454	+	4.88454i	−0.250902	+	0.250902i	−0.821340	−	0.570438i	$-0.806773\pi$
$379$	−4.88454	+	4.88454i	−0.250902	+	0.250902i	0.570438	+	0.821340i	$0.306773\pi$
$380$		0			0
$381$		−	6.72499i		−	0.344531i
$382$	−14.7012	+	14.7012i	−0.752179	+	0.752179i
$383$	13.3373	+	13.3373i	0.681502	+	0.681502i	0.960339	−	0.278836i	$-0.0899487\pi$
$383$	13.3373	+	13.3373i	0.681502	+	0.681502i	−0.278836	+	0.960339i	$0.589949\pi$
$384$		−	1.41267i		−	0.0720902i
$385$		0			0
$386$		−	6.62222i		−	0.337062i
$387$	0.685330			0.0348373
$388$	−13.5465			−0.687720
$389$	13.7513	+	13.7513i	0.697217	+	0.697217i	0.963809	−	0.266593i	$-0.0858978\pi$
$389$	13.7513	+	13.7513i	0.697217	+	0.697217i	−0.266593	+	0.963809i	$0.585898\pi$
$390$		0			0
$391$	−33.1678	−	33.1678i	−1.67737	−	1.67737i
$392$	−5.73796			−0.289811
$393$	−6.79476	+	6.79476i	−0.342750	+	0.342750i
$394$	14.2096	−	14.2096i	0.715869	−	0.715869i
$395$		0			0
$396$	−3.46950	−	3.46950i	−0.174349	−	0.174349i
$397$	−17.2435	−	17.2435i	−0.865427	−	0.865427i	0.126535	−	0.991962i	$-0.459614\pi$
$397$	−17.2435	−	17.2435i	−0.865427	−	0.865427i	−0.991962	+	0.126535i	$0.959614\pi$
$398$	−7.66685			−0.384305
$399$	−13.0877			−0.655207
$400$		0			0
$401$	13.4475			0.671539			0.335769	−	0.941944i	$-0.391004\pi$
$401$	13.4475			0.671539			0.335769	+	0.941944i	$0.391004\pi$
$402$	−5.57580	−	5.57580i	−0.278096	−	0.278096i
$403$		−	6.21648i		−	0.309665i
$404$	−4.34239	−	4.34239i	−0.216042	−	0.216042i
$405$		0			0
$406$	−15.9304	−	10.7529i	−0.790611	−	0.533655i
$407$	40.9565	+	40.9565i	2.03014	+	2.03014i
$408$	−8.74634			−0.433009
$409$	7.23090	−	7.23090i	0.357545	−	0.357545i	−0.505362	−	0.862907i	$-0.668641\pi$
$409$	7.23090	−	7.23090i	0.357545	−	0.357545i	0.862907	+	0.505362i	$0.168641\pi$
$410$		0			0
$411$			9.84780i			0.485756i
$412$	−4.53579	+	4.53579i	−0.223462	+	0.223462i
$413$	−30.8826	+	30.8826i	−1.51964	+	1.51964i
$414$	5.38043	+	5.38043i	0.264434	+	0.264434i
$415$		0			0
$416$	−0.440183	+	0.440183i	−0.0215818	+	0.0215818i
$417$			5.69150i			0.278714i
$418$		−	12.6814i		−	0.620270i
$419$	17.1690			0.838761			0.419380	−	0.907811i	$-0.362247\pi$
$419$	17.1690			0.838761			0.419380	+	0.907811i	$0.362247\pi$
$420$		0			0
$421$	−17.6568	+	17.6568i	−0.860542	+	0.860542i	−0.991401	−	0.130859i	$-0.958227\pi$
$421$	−17.6568	+	17.6568i	−0.860542	+	0.860542i	0.130859	+	0.991401i	$0.458227\pi$
$422$	−5.01654	−	5.01654i	−0.244201	−	0.244201i
$423$	0.631012			0.0306809
$424$	−5.28335	−	5.28335i	−0.256582	−	0.256582i
$425$		0			0
$426$	−20.6204			−0.999062
$427$			2.16004i			0.104532i
$428$	2.20738	+	2.20738i	0.106698	+	0.106698i
$429$		−	4.29622i		−	0.207424i
$430$		0			0
$431$	−10.6981			−0.515311			−0.257656	−	0.966237i	$-0.582950\pi$
$431$	−10.6981			−0.515311			−0.257656	+	0.966237i	$0.582950\pi$
$432$	5.65684			0.272165
$433$			18.2193i			0.875566i	0.899081	+	0.437783i	$0.144236\pi$
$433$			18.2193i			0.875566i	−0.899081	+	0.437783i	$0.855764\pi$
$434$	−35.6406			−1.71081
$435$		0			0
$436$	15.0643			0.721451
$437$			19.6662i			0.940760i
$438$	−16.2857			−0.778160
$439$	11.3312			0.540810			0.270405	−	0.962747i	$-0.412842\pi$
$439$	11.3312			0.540810			0.270405	+	0.962747i	$0.412842\pi$
$440$		0			0
$441$		−	5.76292i		−	0.274425i
$442$	2.72532	+	2.72532i	0.129630	+	0.129630i
$443$			18.5707i			0.882321i	0.897428	+	0.441161i	$0.145433\pi$
$443$			18.5707i			0.882321i	−0.897428	+	0.441161i	$0.854567\pi$
$444$	−16.7488			−0.794863
$445$		0			0
$446$	7.10101	+	7.10101i	0.336243	+	0.336243i
$447$	−30.2513			−1.43084
$448$	2.52368	+	2.52368i	0.119233	+	0.119233i
$449$	−6.14011	+	6.14011i	−0.289770	+	0.289770i	−0.836989	−	0.547220i	$-0.815686\pi$
$449$	−6.14011	+	6.14011i	−0.289770	+	0.289770i	0.547220	+	0.836989i	$0.315686\pi$
$450$		0			0
$451$	42.5560			2.00388
$452$			0.652119i			0.0306731i
$453$		−	0.995965i		−	0.0467945i
$454$	−4.06690	+	4.06690i	−0.190869	+	0.190869i
$455$		0			0
$456$	2.59298	+	2.59298i	0.121428	+	0.121428i
$457$	3.69886	−	3.69886i	0.173026	−	0.173026i	−0.615282	−	0.788307i	$-0.710958\pi$
$457$	3.69886	−	3.69886i	0.173026	−	0.173026i	0.788307	+	0.615282i	$0.210958\pi$
$458$	3.49894	−	3.49894i	0.163495	−	0.163495i
$459$		−	35.0234i		−	1.63475i
$460$		0			0
$461$	3.58100	−	3.58100i	0.166784	−	0.166784i	−0.618780	−	0.785564i	$-0.712373\pi$
$461$	3.58100	−	3.58100i	0.166784	−	0.166784i	0.785564	+	0.618780i	$0.212373\pi$
$462$	−24.6313			−1.14595
$463$	−20.2620	−	20.2620i	−0.941656	−	0.941656i	0.0567334	−	0.998389i	$-0.481932\pi$
$463$	−20.2620	−	20.2620i	−0.941656	−	0.941656i	−0.998389	+	0.0567334i	$0.981932\pi$
$464$	1.02579	+	5.28656i	0.0476209	+	0.245423i
$465$		0			0
$466$	6.60871	+	6.60871i	0.306142	+	0.306142i
$467$			38.6995i			1.79080i	0.445264	+	0.895399i	$0.353110\pi$
$467$			38.6995i			1.79080i	−0.445264	+	0.895399i	$0.646890\pi$
$468$	−0.442099	−	0.442099i	−0.0204360	−	0.0204360i
$469$	19.9219			0.919906
$470$		0			0
$471$	14.9935			0.690862
$472$	12.2371			0.563260
$473$	2.35719	+	2.35719i	0.108384	+	0.108384i
$474$	13.4774	+	13.4774i	0.619039	+	0.619039i
$475$		0			0
$476$	15.6250	−	15.6250i	0.716170	−	0.716170i
$477$	5.30634	−	5.30634i	0.242961	−	0.242961i
$478$	13.4285			0.614205
$479$	5.09240	+	5.09240i	0.232678	+	0.232678i	0.813809	−	0.581132i	$-0.197390\pi$
$479$	5.09240	+	5.09240i	0.232678	+	0.232678i	−0.581132	+	0.813809i	$0.697390\pi$
$480$		0			0
$481$	5.21886	+	5.21886i	0.237959	+	0.237959i
$482$	5.06604			0.230752
$483$	38.1978			1.73806
$484$		−	12.8667i		−	0.584849i
$485$		0			0
$486$			9.93792i			0.450793i
$487$	−10.3418	−	10.3418i	−0.468633	−	0.468633i	0.432839	−	0.901471i	$-0.357512\pi$
$487$	−10.3418	−	10.3418i	−0.468633	−	0.468633i	−0.901471	+	0.432839i	$0.857512\pi$
$488$	0.427953	−	0.427953i	0.0193725	−	0.0193725i
$489$		−	1.43229i		−	0.0647702i
$490$		0			0
$491$	−29.3949	+	29.3949i	−1.32657	+	1.32657i	−0.418237	+	0.908338i	$0.637352\pi$
$491$	−29.3949	+	29.3949i	−1.32657	+	1.32657i	−0.908338	+	0.418237i	$0.862648\pi$
$492$	−8.70145	+	8.70145i	−0.392292	+	0.392292i
$493$	32.7309	−	6.35099i	1.47413	−	0.286034i
$494$		−	1.61593i		−	0.0727039i
$495$		0			0
$496$	7.06123	+	7.06123i	0.317059	+	0.317059i
$497$	36.8375	−	36.8375i	1.65239	−	1.65239i
$498$	7.56820	+	7.56820i	0.339139	+	0.339139i
$499$	−26.9799			−1.20779			−0.603893	−	0.797065i	$-0.706385\pi$
$499$	−26.9799			−1.20779			−0.603893	+	0.797065i	$0.706385\pi$
$500$		0			0
$501$	17.1344	−	17.1344i	0.765506	−	0.765506i
$502$	−19.2823	+	19.2823i	−0.860611	+	0.860611i
$503$		−	13.2891i		−	0.592532i	−0.955105	−	0.296266i	$-0.904258\pi$
$503$		−	13.2891i		−	0.592532i	0.955105	−	0.296266i	$-0.0957416\pi$
$504$	−2.53466	+	2.53466i	−0.112903	+	0.112903i
$505$		0			0
$506$			37.0120i			1.64538i
$507$			17.8173i			0.791295i
$508$		−	4.76046i		−	0.211211i
$509$		−	11.3278i		−	0.502098i	−0.967974	−	0.251049i	$-0.919224\pi$
$509$		−	11.3278i		−	0.502098i	0.967974	−	0.251049i	$-0.0807755\pi$
$510$		0			0
$511$	29.0937	−	29.0937i	1.28703	−	1.28703i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.3832	+	10.3832i	−0.458430	+	0.458430i
$514$	5.83466	−	5.83466i	0.257356	−	0.257356i
$515$		0			0
$516$	−0.963954			−0.0424357
$517$	2.17037	+	2.17037i	0.0954526	+	0.0954526i
$518$	29.9210	−	29.9210i	1.31466	−	1.31466i
$519$	4.98006	+	4.98006i	0.218600	+	0.218600i
$520$		0			0
$521$			26.6394i			1.16709i	0.812080	+	0.583546i	$0.198335\pi$
$521$			26.6394i			1.16709i	−0.812080	+	0.583546i	$0.801665\pi$
$522$	−5.30957	+	1.03025i	−0.232393	+	0.0450928i
$523$	6.84266	−	6.84266i	0.299209	−	0.299209i	−0.541495	−	0.840704i	$-0.682142\pi$
$523$	6.84266	−	6.84266i	0.299209	−	0.299209i	0.840704	+	0.541495i	$0.182142\pi$
$524$	−4.80985	+	4.80985i	−0.210119	+	0.210119i
$525$		0			0
$526$		−	18.8063i		−	0.819993i
$527$	43.7185	−	43.7185i	1.90441	−	1.90441i
$528$	4.88004	+	4.88004i	0.212376	+	0.212376i
$529$		−	34.3975i		−	1.49555i
$530$		0			0
$531$			12.2904i			0.533357i
$532$	−9.26451			−0.401668
$533$	5.42267			0.234882
$534$	−2.61145	−	2.61145i	−0.113009	−	0.113009i
$535$		0			0
$536$	−3.94698	−	3.94698i	−0.170484	−	0.170484i
$537$	−9.50601			−0.410215
$538$	4.07821	−	4.07821i	0.175824	−	0.175824i
$539$	19.8216	−	19.8216i	0.853776	−	0.853776i
$540$		0			0
$541$	14.5237	+	14.5237i	0.624421	+	0.624421i	0.946659	−	0.322237i	$-0.104435\pi$
$541$	14.5237	+	14.5237i	0.624421	+	0.624421i	−0.322237	+	0.946659i	$0.604435\pi$
$542$	5.55071	+	5.55071i	0.238423	+	0.238423i
$543$	5.39804			0.231652
$544$	−6.19134			−0.265451
$545$		0			0
$546$	−3.13863			−0.134321
$547$	−18.1185	−	18.1185i	−0.774689	−	0.774689i	0.204233	−	0.978922i	$-0.434530\pi$
$547$	−18.1185	−	18.1185i	−0.774689	−	0.774689i	−0.978922	+	0.204233i	$0.934530\pi$
$548$			6.97103i			0.297788i
$549$	0.429815	+	0.429815i	0.0183441	+	0.0183441i
$550$		0			0
$551$	−11.5864	−	7.82072i	−0.493598	−	0.333174i
$552$	−7.56787	−	7.56787i	−0.322110	−	0.322110i
$553$	−48.1537			−2.04770
$554$	−17.6329	+	17.6329i	−0.749149	+	0.749149i
$555$		0			0
$556$			4.02888i			0.170863i
$557$	4.48520	−	4.48520i	0.190044	−	0.190044i	−0.605671	−	0.795715i	$-0.707095\pi$
$557$	4.48520	−	4.48520i	0.190044	−	0.190044i	0.795715	+	0.605671i	$0.207095\pi$
$558$	−7.09196	+	7.09196i	−0.300227	+	0.300227i
$559$	0.300364	+	0.300364i	0.0127040	+	0.0127040i
$560$		0			0
$561$	30.2139	−	30.2139i	1.27563	−	1.27563i
$562$		−	12.1013i		−	0.510463i
$563$			38.6483i			1.62883i	0.580282	+	0.814416i	$0.302942\pi$
$563$			38.6483i			1.62883i	−0.580282	+	0.814416i	$0.697058\pi$
$564$	−0.887553			−0.0373727
$565$		0			0
$566$	−19.9355	+	19.9355i	−0.837951	+	0.837951i
$567$	12.5635	+	12.5635i	0.527616	+	0.527616i
$568$	−14.5967			−0.612465
$569$	7.32708	+	7.32708i	0.307167	+	0.307167i	0.843810	−	0.536642i	$-0.180308\pi$
$569$	7.32708	+	7.32708i	0.307167	+	0.307167i	−0.536642	+	0.843810i	$0.680308\pi$
$570$		0			0
$571$	4.30547			0.180178			0.0900892	−	0.995934i	$-0.471285\pi$
$571$	4.30547			0.180178			0.0900892	+	0.995934i	$0.471285\pi$
$572$		−	3.04120i		−	0.127159i
$573$	20.7680	+	20.7680i	0.867596	+	0.867596i
$574$		−	31.0895i		−	1.29765i
$575$		0			0
$576$	1.00435			0.0418480
$577$	16.7579			0.697640			0.348820	−	0.937190i	$-0.386582\pi$
$577$	16.7579			0.697640			0.348820	+	0.937190i	$0.386582\pi$
$578$			21.3327i			0.887321i
$579$	−9.35505			−0.388782
$580$		0			0
$581$	−27.0405			−1.12183
$582$			19.1368i			0.793246i
$583$	36.5023			1.51177
$584$	−11.5283			−0.477043
$585$		0			0
$586$			16.5160i			0.682270i
$587$	−7.79616	−	7.79616i	−0.321782	−	0.321782i	0.527668	−	0.849450i	$-0.323066\pi$
$587$	−7.79616	−	7.79616i	−0.321782	−	0.321782i	−0.849450	+	0.527668i	$0.823066\pi$
$588$			8.10587i			0.334280i
$589$	−25.9220			−1.06810
$590$		0			0
$591$	−20.0735	−	20.0735i	−0.825714	−	0.825714i
$592$	−11.8561			−0.487283
$593$	−27.1434	−	27.1434i	−1.11465	−	1.11465i	−0.992514	−	0.122133i	$-0.961026\pi$
$593$	−27.1434	−	27.1434i	−1.11465	−	1.11465i	−0.122133	−	0.992514i	$-0.538974\pi$
$594$	−19.5414	+	19.5414i	−0.801792	+	0.801792i
$595$		0			0
$596$	−21.4142			−0.877160
$597$			10.8308i			0.443274i
$598$			4.71623i			0.192861i
$599$	15.0238	−	15.0238i	0.613854	−	0.613854i	−0.330094	−	0.943948i	$-0.607080\pi$
$599$	15.0238	−	15.0238i	0.613854	−	0.613854i	0.943948	+	0.330094i	$0.107080\pi$
$600$		0			0
$601$	−1.85265	−	1.85265i	−0.0755713	−	0.0755713i	0.668311	−	0.743882i	$-0.267018\pi$
$601$	−1.85265	−	1.85265i	−0.0755713	−	0.0755713i	−0.743882	+	0.668311i	$0.767018\pi$
$602$	1.72206	−	1.72206i	0.0701861	−	0.0701861i
$603$	3.96415	−	3.96415i	0.161433	−	0.161433i
$604$		−	0.705021i		−	0.0286869i
$605$		0			0
$606$	−6.13439	+	6.13439i	−0.249193	+	0.249193i
$607$	−17.9074			−0.726838			−0.363419	−	0.931626i	$-0.618391\pi$
$607$	−17.9074			−0.726838			−0.363419	+	0.931626i	$0.618391\pi$
$608$	1.83551	+	1.83551i	0.0744399	+	0.0744399i
$609$	−15.1903	+	22.5044i	−0.615541	+	0.911926i
$610$		0			0
$611$	0.276558	+	0.276558i	0.0111883	+	0.0111883i
$612$		−	6.21827i		−	0.251359i
$613$	2.62429	+	2.62429i	0.105994	+	0.105994i	0.758115	−	0.652121i	$-0.226121\pi$
$613$	2.62429	+	2.62429i	0.105994	+	0.105994i	−0.652121	+	0.758115i	$0.726121\pi$
$614$	24.7544			0.999006
$615$		0			0
$616$	−17.4360			−0.702515
$617$	−11.4843			−0.462340			−0.231170	−	0.972913i	$-0.574255\pi$
$617$	−11.4843			−0.462340			−0.231170	+	0.972913i	$0.574255\pi$
$618$	6.40760	+	6.40760i	0.257751	+	0.257751i
$619$	−15.0527	−	15.0527i	−0.605021	−	0.605021i	0.336620	−	0.941641i	$-0.390716\pi$
$619$	−15.0527	−	15.0527i	−0.605021	−	0.605021i	−0.941641	+	0.336620i	$0.890716\pi$
$620$		0			0
$621$	30.3044	−	30.3044i	1.21607	−	1.21607i
$622$	12.2930	−	12.2930i	0.492903	−	0.492903i
$623$	9.33050			0.373818
$624$	0.621836	+	0.621836i	0.0248934	+	0.0248934i
$625$		0			0
$626$	10.2575	+	10.2575i	0.409971	+	0.409971i
$627$	−17.9148			−0.715446
$628$	10.6135			0.423526
$629$			73.4051i			2.92685i
$630$		0			0
$631$		−	10.3261i		−	0.411074i	−0.978649	−	0.205537i	$-0.934106\pi$
$631$		−	10.3261i		−	0.411074i	0.978649	−	0.205537i	$-0.0658940\pi$
$632$	9.54037	+	9.54037i	0.379495	+	0.379495i
$633$	−7.08673	+	7.08673i	−0.281672	+	0.281672i
$634$		−	3.24824i		−	0.129004i
$635$		0			0
$636$	−7.46365	+	7.46365i	−0.295953	+	0.295953i
$637$	2.52575	−	2.52575i	0.100074	−	0.100074i
$638$	−21.8058	−	14.7187i	−0.863300	−	0.582719i
$639$		−	14.6602i		−	0.579950i
$640$		0			0
$641$	26.4206	+	26.4206i	1.04355	+	1.04355i	0.999007	+	0.0445450i	$0.0141838\pi$
$641$	26.4206	+	26.4206i	1.04355	+	1.04355i	0.0445450	+	0.999007i	$0.485816\pi$
$642$	3.11831	−	3.11831i	0.123070	−	0.123070i
$643$	−6.22674	−	6.22674i	−0.245559	−	0.245559i	0.573586	−	0.819145i	$-0.305552\pi$
$643$	−6.22674	−	6.22674i	−0.245559	−	0.245559i	−0.819145	+	0.573586i	$0.805552\pi$
$644$	27.0394			1.06550
$645$		0			0
$646$	11.3643	−	11.3643i	0.447122	−	0.447122i
$647$	12.5127	−	12.5127i	0.491925	−	0.491925i	−0.416987	−	0.908912i	$-0.636914\pi$
$647$	12.5127	−	12.5127i	0.491925	−	0.491925i	0.908912	+	0.416987i	$0.136914\pi$
$648$		−	4.97823i		−	0.195563i
$649$	−42.2728	+	42.2728i	−1.65935	+	1.65935i
$650$		0			0
$651$			50.3486i			1.97332i
$652$		−	1.01388i		−	0.0397067i
$653$		−	30.3079i		−	1.18604i	−0.805188	−	0.593020i	$-0.797936\pi$
$653$		−	30.3079i		−	1.18604i	0.805188	−	0.593020i	$-0.202064\pi$
$654$		−	21.2810i		−	0.832153i
$655$		0			0
$656$	−6.15956	+	6.15956i	−0.240490	+	0.240490i
$657$		−	11.5784i		−	0.451717i
$658$	1.58558	−	1.58558i	0.0618122	−	0.0618122i
$659$	−6.40338	+	6.40338i	−0.249440	+	0.249440i	−0.820741	−	0.571301i	$-0.806439\pi$
$659$	−6.40338	+	6.40338i	−0.249440	+	0.249440i	0.571301	+	0.820741i	$0.306439\pi$
$660$		0			0
$661$	−19.3728			−0.753514			−0.376757	−	0.926312i	$-0.622961\pi$
$661$	−19.3728			−0.753514			−0.376757	+	0.926312i	$0.622961\pi$
$662$	11.6868	+	11.6868i	0.454220	+	0.454220i
$663$	3.84999	−	3.84999i	0.149521	−	0.149521i
$664$	5.35735	+	5.35735i	0.207906	+	0.207906i
$665$		0			0
$666$		−	11.9077i		−	0.461413i
$667$	33.8160	+	22.8255i	1.30936	+	0.883807i
$668$	12.1290	−	12.1290i	0.469286	−	0.469286i
$669$	10.0314	−	10.0314i	0.387837	−	0.387837i
$670$		0			0
$671$			2.95670i			0.114142i
$672$	3.56514	−	3.56514i	0.137528	−	0.137528i
$673$	12.6978	+	12.6978i	0.489462	+	0.489462i	0.908137	−	0.418674i	$-0.137505\pi$
$673$	12.6978	+	12.6978i	0.489462	+	0.489462i	−0.418674	+	0.908137i	$0.637505\pi$
$674$			29.7531i			1.14605i
$675$		0			0
$676$			12.6125i			0.485095i
$677$	−6.32220			−0.242982			−0.121491	−	0.992593i	$-0.538768\pi$
$677$	−6.32220			−0.242982			−0.121491	+	0.992593i	$0.538768\pi$
$678$	0.921232			0.0353797
$679$	−34.1871	−	34.1871i	−1.31198	−	1.31198i
$680$		0			0
$681$	5.74520	+	5.74520i	0.220157	+	0.220157i
$682$	−48.7856			−1.86810
$683$	0.141971	−	0.141971i	0.00543238	−	0.00543238i	−0.704385	−	0.709818i	$-0.748777\pi$
$683$	0.141971	−	0.141971i	0.00543238	−	0.00543238i	0.709818	+	0.704385i	$0.248777\pi$
$684$	−1.84350	+	1.84350i	−0.0704880	+	0.0704880i
$685$		0			0
$686$	3.18500	+	3.18500i	0.121604	+	0.121604i
$687$	−4.94287	−	4.94287i	−0.188582	−	0.188582i
$688$	−0.682361			−0.0260148
$689$	4.65129			0.177200
$690$		0			0
$691$	−25.8224			−0.982329			−0.491164	−	0.871067i	$-0.663429\pi$
$691$	−25.8224			−0.982329			−0.491164	+	0.871067i	$0.663429\pi$
$692$	3.52527	+	3.52527i	0.134011	+	0.134011i
$693$		−	17.5118i		−	0.665219i
$694$	−8.90390	−	8.90390i	−0.337988	−	0.337988i
$695$		0			0
$696$	7.46819	−	1.44910i	0.283081	−	0.0549281i
$697$	38.1359	+	38.1359i	1.44450	+	1.44450i
$698$	14.3912			0.544715
$699$	9.33595	−	9.33595i	0.353118	−	0.353118i
$700$		0			0
$701$			30.9580i			1.16927i	0.811298	+	0.584633i	$0.198762\pi$
$701$			30.9580i			1.16927i	−0.811298	+	0.584633i	$0.801238\pi$
$702$	−2.49005	+	2.49005i	−0.0939808	+	0.0939808i
$703$	21.7620	−	21.7620i	0.820771	−	0.820771i
$704$	3.45447	+	3.45447i	0.130195	+	0.130195i
$705$		0			0
$706$	−14.6585	+	14.6585i	−0.551681	+	0.551681i
$707$		−	21.9177i		−	0.824298i
$708$		−	17.2871i		−	0.649688i
$709$	−10.1056			−0.379524			−0.189762	−	0.981830i	$-0.560772\pi$
$709$	−10.1056			−0.379524			−0.189762	+	0.981830i	$0.560772\pi$
$710$		0			0
$711$	−9.58187	+	9.58187i	−0.359348	+	0.359348i
$712$	−1.84859	−	1.84859i	−0.0692787	−	0.0692787i
$713$	75.6558			2.83333
$714$	−22.0730	−	22.0730i	−0.826061	−	0.826061i
$715$		0			0
$716$	−6.72909			−0.251478
$717$		−	18.9701i		−	0.708451i
$718$	11.7160	+	11.7160i	0.437239	+	0.437239i
$719$		−	42.6599i		−	1.59095i	−0.605988	−	0.795474i	$-0.707222\pi$
$719$		−	42.6599i		−	1.59095i	0.605988	−	0.795474i	$-0.292778\pi$
$720$		0			0
$721$	−22.8938			−0.852610
$722$	12.2618			0.456336
$723$		−	7.15666i		−	0.266159i
$724$	3.82115			0.142012
$725$		0			0
$726$	−18.1764			−0.674590
$727$		−	7.52696i		−	0.279159i	−0.990211	−	0.139580i	$-0.955425\pi$
$727$		−	7.52696i		−	0.279159i	0.990211	−	0.139580i	$-0.0445752\pi$
$728$	−2.22177			−0.0823442
$729$	28.9737			1.07310
$730$		0			0
$731$			4.22473i			0.156257i
$732$	−0.604559	−	0.604559i	−0.0223451	−	0.0223451i
$733$		−	1.73837i		−	0.0642080i	−0.999485	−	0.0321040i	$-0.989779\pi$
$733$		−	1.73837i		−	0.0642080i	0.999485	−	0.0321040i	$-0.0102208\pi$
$734$	−16.2434			−0.599553
$735$		0			0
$736$	−5.35712	−	5.35712i	−0.197466	−	0.197466i
$737$	27.2694			1.00448
$738$	−6.18636	−	6.18636i	−0.227723	−	0.227723i
$739$	−10.4108	+	10.4108i	−0.382969	+	0.382969i	−0.872171	−	0.489202i	$-0.837288\pi$
$739$	−10.4108	+	10.4108i	−0.382969	+	0.382969i	0.489202	+	0.872171i	$0.337288\pi$
$740$		0			0
$741$	−2.28278			−0.0838599
$742$		−	26.6670i		−	0.978977i
$743$			32.1457i			1.17931i	0.807655	+	0.589656i	$0.200737\pi$
$743$			32.1457i			1.17931i	−0.807655	+	0.589656i	$0.799263\pi$
$744$	9.97523	−	9.97523i	0.365710	−	0.365710i
$745$		0			0
$746$	13.1251	+	13.1251i	0.480546	+	0.480546i
$747$	−5.38066	+	5.38066i	−0.196868	+	0.196868i
$748$	21.3878	−	21.3878i	0.782014	−	0.782014i
$749$			11.1415i			0.407100i
$750$		0			0
$751$	33.4144	−	33.4144i	1.21931	−	1.21931i	0.251435	−	0.967874i	$-0.419098\pi$
$751$	33.4144	−	33.4144i	1.21931	−	1.21931i	0.967874	−	0.251435i	$-0.0809025\pi$
$752$	−0.628279			−0.0229110
$753$	27.2396	+	27.2396i	0.992666	+	0.992666i
$754$	−2.77859	−	1.87552i	−0.101190	−	0.0683025i
$755$		0			0
$756$	14.2761	+	14.2761i	0.519216	+	0.519216i
$757$		−	6.67498i		−	0.242606i	−0.992616	−	0.121303i	$-0.961293\pi$
$757$		−	6.67498i		−	0.242606i	0.992616	−	0.121303i	$-0.0387073\pi$
$758$	4.88454	+	4.88454i	0.177415	+	0.177415i
$759$	52.2859			1.89786
$760$		0			0
$761$	14.0010			0.507535			0.253767	−	0.967265i	$-0.418330\pi$
$761$	14.0010			0.507535			0.253767	+	0.967265i	$0.418330\pi$
$762$	−6.72499			−0.243621
$763$	38.0176	+	38.0176i	1.37633	+	1.37633i
$764$	14.7012	+	14.7012i	0.531871	+	0.531871i
$765$		0			0
$766$	13.3373	−	13.3373i	0.481895	−	0.481895i
$767$	−5.38658	+	5.38658i	−0.194498	+	0.194498i
$768$	−1.41267			−0.0509755
$769$	32.7401	+	32.7401i	1.18064	+	1.18064i	0.979579	+	0.201060i	$0.0644386\pi$
$769$	32.7401	+	32.7401i	1.18064	+	1.18064i	0.201060	+	0.979579i	$0.435561\pi$
$770$		0			0
$771$	−8.24248	−	8.24248i	−0.296846	−	0.296846i
$772$	−6.62222			−0.238339
$773$	31.0937			1.11836			0.559182	−	0.829045i	$-0.311115\pi$
$773$	31.0937			1.11836			0.559182	+	0.829045i	$0.311115\pi$
$774$		−	0.685330i		−	0.0246337i
$775$		0			0
$776$			13.5465i			0.486291i
$777$	−42.2687	−	42.2687i	−1.51638	−	1.51638i
$778$	13.7513	−	13.7513i	0.493007	−	0.493007i
$779$		−	22.6119i		−	0.810156i
$780$		0			0
$781$	50.4239	−	50.4239i	1.80431	−	1.80431i
$782$	−33.1678	+	33.1678i	−1.18608	+	1.18608i
$783$	5.80271	+	29.9053i	0.207372	+	1.06873i
$784$			5.73796i			0.204927i
$785$		0			0
$786$	6.79476	+	6.79476i	0.242361	+	0.242361i
$787$	3.26907	−	3.26907i	0.116530	−	0.116530i	−0.646437	−	0.762967i	$-0.723742\pi$
$787$	3.26907	−	3.26907i	0.116530	−	0.116530i	0.762967	+	0.646437i	$0.223742\pi$
$788$	−14.2096	−	14.2096i	−0.506196	−	0.506196i
$789$	−26.5672			−0.945816
$790$		0			0
$791$	−1.64574	+	1.64574i	−0.0585159	+	0.0585159i
$792$	−3.46950	+	3.46950i	−0.123283	+	0.123283i
$793$			0.376756i			0.0133790i
$794$	−17.2435	+	17.2435i	−0.611949	+	0.611949i
$795$		0			0
$796$			7.66685i			0.271744i
$797$		−	4.09662i		−	0.145110i	−0.997364	−	0.0725548i	$-0.976885\pi$
$797$		−	4.09662i		−	0.145110i	0.997364	−	0.0725548i	$-0.0231152\pi$
$798$			13.0877i			0.463301i
$799$			3.88988i			0.137614i
$800$		0			0
$801$	1.85663	−	1.85663i	0.0656008	−	0.0656008i
$802$		−	13.4475i		−	0.474849i
$803$	39.8240	−	39.8240i	1.40536	−	1.40536i
$804$	−5.57580	+	5.57580i	−0.196643	+	0.196643i
$805$		0			0
$806$	−6.21648			−0.218966
$807$	−5.76118	−	5.76118i	−0.202803	−	0.202803i
$808$	−4.34239	+	4.34239i	−0.152765	+	0.152765i
$809$	2.27681	+	2.27681i	0.0800484	+	0.0800484i	0.745997	−	0.665949i	$-0.231973\pi$
$809$	2.27681	+	2.27681i	0.0800484	+	0.0800484i	−0.665949	+	0.745997i	$0.731973\pi$
$810$		0			0
$811$		−	17.9110i		−	0.628942i	−0.949267	−	0.314471i	$-0.898173\pi$
$811$		−	17.9110i		−	0.628942i	0.949267	−	0.314471i	$-0.101827\pi$
$812$	−10.7529	+	15.9304i	−0.377351	+	0.559047i
$813$	7.84135	−	7.84135i	0.275008	−	0.275008i
$814$	40.9565	−	40.9565i	1.43552	−	1.43552i
$815$		0			0
$816$			8.74634i			0.306183i
$817$	1.25248	−	1.25248i	0.0438189	−	0.0438189i
$818$	−7.23090	−	7.23090i	−0.252823	−	0.252823i
$819$		−	2.23143i		−	0.0779726i
$820$		0			0
$821$		−	3.20679i		−	0.111918i	−0.998433	−	0.0559588i	$-0.982178\pi$
$821$		−	3.20679i		−	0.111918i	0.998433	−	0.0559588i	$-0.0178216\pi$
$822$	9.84780			0.343481
$823$	1.89800			0.0661602			0.0330801	−	0.999453i	$-0.489468\pi$
$823$	1.89800			0.0661602			0.0330801	+	0.999453i	$0.489468\pi$
$824$	4.53579	+	4.53579i	0.158012	+	0.158012i
$825$		0			0
$826$	30.8826	+	30.8826i	1.07454	+	1.07454i
$827$	−17.2862			−0.601100			−0.300550	−	0.953766i	$-0.597170\pi$
$827$	−17.2862			−0.601100			−0.300550	+	0.953766i	$0.597170\pi$
$828$	5.38043	−	5.38043i	0.186983	−	0.186983i
$829$	−39.7835	+	39.7835i	−1.38174	+	1.38174i	−0.540204	+	0.841534i	$0.681653\pi$
$829$	−39.7835	+	39.7835i	−1.38174	+	1.38174i	−0.841534	+	0.540204i	$0.818347\pi$
$830$		0			0
$831$	24.9095	+	24.9095i	0.864102	+	0.864102i
$832$	0.440183	+	0.440183i	0.0152606	+	0.0152606i
$833$	35.5256			1.23089
$834$	5.69150			0.197080
$835$		0			0
$836$	−12.6814			−0.438597
$837$	39.9443	+	39.9443i	1.38068	+	1.38068i
$838$		−	17.1690i		−	0.593093i
$839$	−19.4112	−	19.4112i	−0.670150	−	0.670150i	0.287600	−	0.957750i	$-0.407142\pi$
$839$	−19.4112	−	19.4112i	−0.670150	−	0.670150i	−0.957750	+	0.287600i	$0.907142\pi$
$840$		0			0
$841$	−26.8955	+	10.8458i	−0.927432	+	0.373992i
$842$	17.6568	+	17.6568i	0.608495	+	0.608495i
$843$	−17.0952			−0.588791
$844$	−5.01654	+	5.01654i	−0.172676	+	0.172676i
$845$		0			0
$846$		−	0.631012i		−	0.0216946i
$847$	32.4714	−	32.4714i	1.11573	−	1.11573i
$848$	−5.28335	+	5.28335i	−0.181431	+	0.181431i
$849$	28.1623	+	28.1623i	0.966529	+	0.966529i
$850$		0			0
$851$	−63.5146	+	63.5146i	−2.17725	+	2.17725i
$852$			20.6204i			0.706444i
$853$			45.3339i			1.55220i	0.630608	+	0.776101i	$0.282806\pi$
$853$			45.3339i			1.55220i	−0.630608	+	0.776101i	$0.717194\pi$
$854$	2.16004			0.0739150
$855$		0			0
$856$	2.20738	−	2.20738i	0.0754467	−	0.0754467i
$857$	−24.2867	−	24.2867i	−0.829617	−	0.829617i	0.157846	−	0.987464i	$-0.449545\pi$
$857$	−24.2867	−	24.2867i	−0.829617	−	0.829617i	−0.987464	+	0.157846i	$0.949545\pi$
$858$	−4.29622			−0.146671
$859$	−36.7875	−	36.7875i	−1.25517	−	1.25517i	−0.953370	−	0.301803i	$-0.902411\pi$
$859$	−36.7875	−	36.7875i	−1.25517	−	1.25517i	−0.301803	−	0.953370i	$-0.597589\pi$
$860$		0			0
$861$	−43.9194			−1.49677
$862$			10.6981i			0.364380i
$863$	−10.6313	−	10.6313i	−0.361893	−	0.361893i	0.502616	−	0.864510i	$-0.332371\pi$
$863$	−10.6313	−	10.6313i	−0.361893	−	0.361893i	−0.864510	+	0.502616i	$0.832371\pi$
$864$		−	5.65684i		−	0.192450i
$865$		0			0
$866$	18.2193			0.619118
$867$	30.1361			1.02348
$868$			35.6406i			1.20972i
$869$	−65.9137			−2.23597
$870$		0			0
$871$	3.47479			0.117739
$872$		−	15.0643i		−	0.510143i
$873$	−13.6054			−0.460475
$874$	19.6662			0.665218
$875$		0			0
$876$			16.2857i			0.550242i
$877$	−7.88593	−	7.88593i	−0.266289	−	0.266289i	0.561314	−	0.827603i	$-0.310296\pi$
$877$	−7.88593	−	7.88593i	−0.266289	−	0.266289i	−0.827603	+	0.561314i	$0.810296\pi$
$878$		−	11.3312i		−	0.382411i
$879$	23.3317			0.786960
$880$		0			0
$881$	−19.0632	−	19.0632i	−0.642255	−	0.642255i	0.308854	−	0.951109i	$-0.400054\pi$
$881$	−19.0632	−	19.0632i	−0.642255	−	0.642255i	−0.951109	+	0.308854i	$0.900054\pi$
$882$	−5.76292			−0.194048
$883$	−0.177670	−	0.177670i	−0.00597907	−	0.00597907i	0.704111	−	0.710090i	$-0.251346\pi$
$883$	−0.177670	−	0.177670i	−0.00597907	−	0.00597907i	−0.710090	+	0.704111i	$0.751346\pi$
$884$	2.72532	−	2.72532i	0.0916625	−	0.0916625i
$885$		0			0
$886$	18.5707			0.623895
$887$			55.5736i			1.86598i	0.359902	+	0.932990i	$0.382810\pi$
$887$			55.5736i			1.86598i	−0.359902	+	0.932990i	$0.617190\pi$
$888$			16.7488i			0.562053i
$889$	12.0139	−	12.0139i	0.402933	−	0.402933i
$890$		0			0
$891$	17.1971	+	17.1971i	0.576125	+	0.576125i
$892$	7.10101	−	7.10101i	0.237759	−	0.237759i
$893$	1.15321	−	1.15321i	0.0385909	−	0.0385909i
$894$			30.2513i			1.01176i
$895$		0			0
$896$	2.52368	−	2.52368i	0.0843104	−	0.0843104i
$897$	6.66250			0.222454
$898$	6.14011	+	6.14011i	0.204898	+	0.204898i
$899$	−30.0864	+	44.5730i	−1.00344	+	1.48659i
$900$		0			0
$901$	32.7110	+	32.7110i	1.08976	+	1.08976i
$902$		−	42.5560i		−	1.41696i
$903$	−2.43272	−	2.43272i	−0.0809557	−	0.0809557i
$904$	0.652119			0.0216892
$905$		0			0
$906$	−0.995965			−0.0330887
$907$	37.9565			1.26032			0.630162	−	0.776464i	$-0.282988\pi$
$907$	37.9565			1.26032			0.630162	+	0.776464i	$0.282988\pi$
$908$	4.06690	+	4.06690i	0.134965	+	0.134965i
$909$	−4.36129	−	4.36129i	−0.144655	−	0.144655i
$910$		0			0
$911$	19.0278	−	19.0278i	0.630418	−	0.630418i	−0.317755	−	0.948173i	$-0.602929\pi$
$911$	19.0278	−	19.0278i	0.630418	−	0.630418i	0.948173	+	0.317755i	$0.102929\pi$
$912$	2.59298	−	2.59298i	0.0858623	−	0.0858623i
$913$	−37.0136			−1.22497
$914$	−3.69886	−	3.69886i	−0.122348	−	0.122348i
$915$		0			0
$916$	−3.49894	−	3.49894i	−0.115608	−	0.115608i
$917$	−24.2771			−0.801700
$918$	−35.0234			−1.15595
$919$			34.8187i			1.14856i	0.818658	+	0.574281i	$0.194718\pi$
$919$			34.8187i			1.14856i	−0.818658	+	0.574281i	$0.805282\pi$
$920$		0			0
$921$		−	34.9699i		−	1.15230i
$922$	−3.58100	−	3.58100i	−0.117934	−	0.117934i
$923$	6.42523	−	6.42523i	0.211489	−	0.211489i
$924$			24.6313i			0.810311i
$925$		0			0
$926$	−20.2620	+	20.2620i	−0.665851	+	0.665851i
$927$	−4.55553	+	4.55553i	−0.149623	+	0.149623i
$928$	5.28656	−	1.02579i	0.173540	−	0.0336731i
$929$		−	14.7794i		−	0.484895i	−0.970164	−	0.242448i	$-0.922050\pi$
$929$		−	14.7794i		−	0.484895i	0.970164	−	0.242448i	$-0.0779503\pi$
$930$		0			0
$931$	−10.5321	−	10.5321i	−0.345176	−	0.345176i
$932$	6.60871	−	6.60871i	0.216475	−	0.216475i
$933$	−17.3659	−	17.3659i	−0.568535	−	0.568535i
$934$	38.6995			1.26629
$935$		0			0
$936$	−0.442099	+	0.442099i	−0.0144504	+	0.0144504i
$937$	−20.4397	+	20.4397i	−0.667734	+	0.667734i	−0.957191	−	0.289457i	$-0.906525\pi$
$937$	−20.4397	+	20.4397i	−0.667734	+	0.667734i	0.289457	+	0.957191i	$0.406525\pi$
$938$		−	19.9219i		−	0.650472i
$939$	14.4905	−	14.4905i	0.472879	−	0.472879i
$940$		0			0
$941$		−	41.7298i		−	1.36035i	−0.733048	−	0.680177i	$-0.761903\pi$
$941$		−	41.7298i		−	1.36035i	0.733048	−	0.680177i	$-0.238097\pi$
$942$		−	14.9935i		−	0.488513i
$943$			65.9950i			2.14909i
$944$		−	12.2371i		−	0.398285i
$945$		0			0
$946$	2.35719	−	2.35719i	0.0766390	−	0.0766390i
$947$			30.3409i			0.985947i	0.870044	+	0.492974i	$0.164090\pi$
$947$			30.3409i			0.985947i	−0.870044	+	0.492974i	$0.835910\pi$
$948$	13.4774	−	13.4774i	0.437727	−	0.437727i
$949$	5.07455	−	5.07455i	0.164727	−	0.164727i
$950$		0			0
$951$	−4.58871			−0.148799
$952$	−15.6250	−	15.6250i	−0.506408	−	0.506408i
$953$	−20.9109	+	20.9109i	−0.677369	+	0.677369i	−0.959404	−	0.282035i	$-0.908991\pi$
$953$	−20.9109	+	20.9109i	−0.677369	+	0.677369i	0.282035	+	0.959404i	$0.408991\pi$
$954$	−5.30634	−	5.30634i	−0.171799	−	0.171799i
$955$		0			0
$956$		−	13.4285i		−	0.434308i
$957$	−20.7928	+	30.8045i	−0.672134	+	0.995768i
$958$	5.09240	−	5.09240i	0.164528	−	0.164528i
$959$	−17.5927	+	17.5927i	−0.568097	+	0.568097i
$960$		0			0
$961$			68.7221i			2.21684i
$962$	5.21886	−	5.21886i	0.168263	−	0.168263i
$963$	2.21699	+	2.21699i	0.0714413	+	0.0714413i
$964$		−	5.06604i		−	0.163166i
$965$		0			0
$966$		−	38.1978i		−	1.22899i
$967$	3.51863			0.113151			0.0565757	−	0.998398i	$-0.481982\pi$
$967$	3.51863			0.113151			0.0565757	+	0.998398i	$0.481982\pi$
$968$	−12.8667			−0.413551
$969$	−16.0540	−	16.0540i	−0.515730	−	0.515730i
$970$		0			0
$971$	−4.23753	−	4.23753i	−0.135989	−	0.135989i	0.635836	−	0.771824i	$-0.280656\pi$
$971$	−4.23753	−	4.23753i	−0.135989	−	0.135989i	−0.771824	+	0.635836i	$0.780656\pi$
$972$	9.93792			0.318759
$973$	−10.1676	+	10.1676i	−0.325959	+	0.325959i
$974$	−10.3418	+	10.3418i	−0.331373	+	0.331373i
$975$		0			0
$976$	−0.427953	−	0.427953i	−0.0136985	−	0.0136985i
$977$	16.4965	+	16.4965i	0.527771	+	0.527771i	0.919907	−	0.392136i	$-0.128264\pi$
$977$	16.4965	+	16.4965i	0.527771	+	0.527771i	−0.392136	+	0.919907i	$0.628264\pi$
$978$	−1.43229			−0.0457995
$979$	12.7718			0.408187
$980$		0			0
$981$	15.1299			0.483060
$982$	29.3949	+	29.3949i	0.938030	+	0.938030i
$983$			24.4121i			0.778624i	0.921106	+	0.389312i	$0.127287\pi$
$983$			24.4121i			0.778624i	−0.921106	+	0.389312i	$0.872713\pi$
$984$	8.70145	+	8.70145i	0.277392	+	0.277392i
$985$		0			0
$986$	−6.35099	−	32.7309i	−0.202257	−	1.04236i
$987$	−2.23990	−	2.23990i	−0.0712969	−	0.0712969i
$988$	−1.61593			−0.0514094
$989$	−3.65549	+	3.65549i	−0.116238	+	0.116238i
$990$		0			0
$991$			50.0549i			1.59005i	0.606579	+	0.795023i	$0.292541\pi$
$991$			50.0549i			1.59005i	−0.606579	+	0.795023i	$0.707459\pi$
$992$	7.06123	−	7.06123i	0.224194	−	0.224194i
$993$	16.5096	−	16.5096i	0.523918	−	0.523918i
$994$	−36.8375	−	36.8375i	−1.16841	−	1.16841i
$995$		0			0
$996$	7.56820	−	7.56820i	0.239808	−	0.239808i
$997$		−	2.68348i		−	0.0849867i	−0.999097	−	0.0424933i	$-0.986470\pi$
$997$		−	2.68348i		−	0.0849867i	0.999097	−	0.0424933i	$-0.0135301\pi$
$998$			26.9799i			0.854034i
$999$	−67.0681			−2.12194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.j.j.157.3	yes	20
5.2	odd	4		1450.2.e.j.1143.8	yes	20
5.3	odd	4		1450.2.e.i.1143.3	yes	20
5.4	even	2		1450.2.j.i.157.8	yes	20
29.17	odd	4		1450.2.e.i.307.8	✓	20
145.17	even	4		1450.2.j.i.1293.8	yes	20
145.104	odd	4		1450.2.e.j.307.3	yes	20
145.133	even	4	inner	1450.2.j.j.1293.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.e.i.307.8	✓	20	29.17	odd	4
1450.2.e.i.1143.3	yes	20	5.3	odd	4
1450.2.e.j.307.3	yes	20	145.104	odd	4
1450.2.e.j.1143.8	yes	20	5.2	odd	4
1450.2.j.i.157.8	yes	20	5.4	even	2
1450.2.j.i.1293.8	yes	20	145.17	even	4
1450.2.j.j.157.3	yes	20	1.1	even	1	trivial
1450.2.j.j.1293.3	yes	20	145.133	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.41267 q^{3} -1.00000 q^{4} +1.41267i q^{6} +(-2.52368 - 2.52368i) q^{7} +1.00000i q^{8} -1.00435 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.41267 q^{3} -1.00000 q^{4} +1.41267i q^{6} +(-2.52368 - 2.52368i) q^{7} +1.00000i q^{8} -1.00435 q^{9} +(-3.45447 - 3.45447i) q^{11} +1.41267 q^{12} +(-0.440183 - 0.440183i) q^{13} +(-2.52368 + 2.52368i) q^{14} +1.00000 q^{16} -6.19134i q^{17} +1.00435i q^{18} +(-1.83551 + 1.83551i) q^{19} +(3.56514 + 3.56514i) q^{21} +(-3.45447 + 3.45447i) q^{22} +(5.35712 - 5.35712i) q^{23} -1.41267i q^{24} +(-0.440183 + 0.440183i) q^{26} +5.65684 q^{27} +(2.52368 + 2.52368i) q^{28} +(1.02579 + 5.28656i) q^{29} +(7.06123 + 7.06123i) q^{31} -1.00000i q^{32} +(4.88004 + 4.88004i) q^{33} -6.19134 q^{34} +1.00435 q^{36} -11.8561 q^{37} +(1.83551 + 1.83551i) q^{38} +(0.621836 + 0.621836i) q^{39} +(-6.15956 + 6.15956i) q^{41} +(3.56514 - 3.56514i) q^{42} -0.682361 q^{43} +(3.45447 + 3.45447i) q^{44} +(-5.35712 - 5.35712i) q^{46} -0.628279 q^{47} -1.41267 q^{48} +5.73796i q^{49} +8.74634i q^{51} +(0.440183 + 0.440183i) q^{52} +(-5.28335 + 5.28335i) q^{53} -5.65684i q^{54} +(2.52368 - 2.52368i) q^{56} +(2.59298 - 2.59298i) q^{57} +(5.28656 - 1.02579i) q^{58} -12.2371i q^{59} +(-0.427953 - 0.427953i) q^{61} +(7.06123 - 7.06123i) q^{62} +(2.53466 + 2.53466i) q^{63} -1.00000 q^{64} +(4.88004 - 4.88004i) q^{66} +(-3.94698 + 3.94698i) q^{67} +6.19134i q^{68} +(-7.56787 + 7.56787i) q^{69} +14.5967i q^{71} -1.00435i q^{72} +11.5283i q^{73} +11.8561i q^{74} +(1.83551 - 1.83551i) q^{76} +17.4360i q^{77} +(0.621836 - 0.621836i) q^{78} +(9.54037 - 9.54037i) q^{79} -4.97823 q^{81} +(6.15956 + 6.15956i) q^{82} +(5.35735 - 5.35735i) q^{83} +(-3.56514 - 3.56514i) q^{84} +0.682361i q^{86} +(-1.44910 - 7.46819i) q^{87} +(3.45447 - 3.45447i) q^{88} +(-1.84859 + 1.84859i) q^{89} +2.22177i q^{91} +(-5.35712 + 5.35712i) q^{92} +(-9.97523 - 9.97523i) q^{93} +0.628279i q^{94} +1.41267i q^{96} +13.5465 q^{97} +5.73796 q^{98} +(3.46950 + 3.46950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{3} - 20 q^{4} - 8 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + 8 * q^3 - 20 * q^4 - 8 * q^7 + 12 * q^9	\( 20 q + 8 q^{3} - 20 q^{4} - 8 q^{7} + 12 q^{9} - 8 q^{11} - 8 q^{12} + 4 q^{13} - 8 q^{14} + 20 q^{16} + 4 q^{19} + 4 q^{21} - 8 q^{22} + 12 q^{23} + 4 q^{26} + 32 q^{27} + 8 q^{28} - 8 q^{29} + 28 q^{31} + 16 q^{34} - 12 q^{36} - 20 q^{37} - 4 q^{38} + 24 q^{39} + 24 q^{41} + 4 q^{42} + 8 q^{43} + 8 q^{44} - 12 q^{46} - 28 q^{47} + 8 q^{48} - 4 q^{52} + 8 q^{56} + 8 q^{57} + 8 q^{58} + 24 q^{61} + 28 q^{62} - 20 q^{63} - 20 q^{64} - 12 q^{67} + 28 q^{69} - 4 q^{76} + 24 q^{78} - 32 q^{79} - 12 q^{81} - 24 q^{82} - 20 q^{83} - 4 q^{84} - 36 q^{87} + 8 q^{88} - 4 q^{89} - 12 q^{92} - 12 q^{93} + 48 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) \) 20 * q + 8 * q^3 - 20 * q^4 - 8 * q^7 + 12 * q^9 - 8 * q^11 - 8 * q^12 + 4 * q^13 - 8 * q^14 + 20 * q^16 + 4 * q^19 + 4 * q^21 - 8 * q^22 + 12 * q^23 + 4 * q^26 + 32 * q^27 + 8 * q^28 - 8 * q^29 + 28 * q^31 + 16 * q^34 - 12 * q^36 - 20 * q^37 - 4 * q^38 + 24 * q^39 + 24 * q^41 + 4 * q^42 + 8 * q^43 + 8 * q^44 - 12 * q^46 - 28 * q^47 + 8 * q^48 - 4 * q^52 + 8 * q^56 + 8 * q^57 + 8 * q^58 + 24 * q^61 + 28 * q^62 - 20 * q^63 - 20 * q^64 - 12 * q^67 + 28 * q^69 - 4 * q^76 + 24 * q^78 - 32 * q^79 - 12 * q^81 - 24 * q^82 - 20 * q^83 - 4 * q^84 - 36 * q^87 + 8 * q^88 - 4 * q^89 - 12 * q^92 - 12 * q^93 + 48 * q^97 + 20 * q^98 - 8 * q^99

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