LMFDB - Embedded newform 495.2.bj.a.343.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			343.3
Character	$\chi$	$=$	495.343
Dual form			495.2.bj.a.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930933 - 0.474334i) q^{2} +(-0.533928 + 0.734888i) q^{4} +(1.77672 - 1.35766i) q^{5} +(0.0860119 + 0.543058i) q^{7} +(-0.475357 + 3.00128i) q^{8} +O(q^{10})$	\(q+(0.930933 - 0.474334i) q^{2} +(-0.533928 + 0.734888i) q^{4} +(1.77672 - 1.35766i) q^{5} +(0.0860119 + 0.543058i) q^{7} +(-0.475357 + 3.00128i) q^{8} +(1.01002 - 2.10665i) q^{10} +(3.29961 + 0.335528i) q^{11} +(1.47301 + 2.89095i) q^{13} +(0.337662 + 0.464752i) q^{14} +(0.419681 + 1.29165i) q^{16} +(2.57079 - 5.04545i) q^{17} +(-1.25925 + 0.914902i) q^{19} +(0.0490901 + 2.03059i) q^{20} +(3.23087 - 1.25276i) q^{22} +(0.803543 + 0.803543i) q^{23} +(1.31349 - 4.82439i) q^{25} +(2.74255 + 1.99258i) q^{26} +(-0.445011 - 0.226744i) q^{28} +(3.44380 + 2.50207i) q^{29} +(-0.509209 + 1.56718i) q^{31} +(-3.29400 - 3.29400i) q^{32} -5.91638i q^{34} +(0.890110 + 0.848089i) q^{35} +(-0.945121 + 0.149692i) q^{37} +(-0.738312 + 1.44902i) q^{38} +(3.23016 + 5.97783i) q^{40} +(-5.25869 - 7.23797i) q^{41} +(-2.55312 + 2.55312i) q^{43} +(-2.00833 + 2.24570i) q^{44} +(1.12919 + 0.366897i) q^{46} +(-0.636959 + 4.02160i) q^{47} +(6.36988 - 2.06970i) q^{49} +(-1.06560 - 5.11422i) q^{50} +(-2.91101 - 0.461058i) q^{52} +(-6.27685 + 3.19821i) q^{53} +(6.31803 - 3.88362i) q^{55} -1.67076 q^{56} +(4.39276 + 0.695746i) q^{58} +(3.97760 - 5.47470i) q^{59} +(-8.75080 + 2.84331i) q^{61} +(0.269329 + 1.70048i) q^{62} +(-7.21224 - 2.34340i) q^{64} +(6.54208 + 3.13656i) q^{65} +(-2.62254 + 2.62254i) q^{67} +(2.33523 + 4.58314i) q^{68} +(1.23091 + 0.367304i) q^{70} +(-2.11802 - 6.51858i) q^{71} +(-9.96541 + 1.57837i) q^{73} +(-0.808840 + 0.587656i) q^{74} -1.41390i q^{76} +(0.101594 + 1.82074i) q^{77} +(-1.28746 + 3.96241i) q^{79} +(2.49928 + 1.72511i) q^{80} +(-8.32870 - 4.24369i) q^{82} +(-10.0947 - 5.14352i) q^{83} +(-2.28245 - 12.4546i) q^{85} +(-1.16575 + 3.58782i) q^{86} +(-2.57551 + 9.74357i) q^{88} -3.64860i q^{89} +(-1.44326 + 1.04859i) q^{91} +(-1.01955 + 0.161481i) q^{92} +(1.31462 + 4.04597i) q^{94} +(-0.995217 + 3.33517i) q^{95} +(-7.56722 - 14.8515i) q^{97} +(4.94820 - 4.94820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8}+O(q^{10}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40} - 40 q^{41} + 60 q^{46} + 28 q^{47} + 50 q^{50} - 50 q^{52} + 24 q^{53} - 64 q^{55} + 80 q^{56} - 50 q^{58} - 60 q^{61} - 100 q^{62} - 8 q^{67} + 30 q^{68} + 30 q^{70} - 24 q^{71} + 50 q^{73} - 70 q^{77} - 98 q^{80} - 10 q^{82} - 90 q^{83} + 30 q^{85} - 100 q^{86} + 170 q^{88} + 20 q^{91} + 68 q^{92} + 40 q^{95} - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.930933	−	0.474334i	0.658269	−	0.335405i	−0.0927463	−	0.995690i	$-0.529565\pi$
$2$	0.930933	−	0.474334i	0.658269	−	0.335405i	0.751015	+	0.660285i	$0.229565\pi$
$3$		0			0
$3$		0			0
$4$	−0.533928	+	0.734888i	−0.266964	+	0.367444i
$5$	1.77672	−	1.35766i	0.794575	−	0.607166i
$5$	1.77672	−	1.35766i	0.794575	−	0.607166i
$6$		0			0
$7$	0.0860119	+	0.543058i	0.0325095	+	0.205257i	0.998597	−	0.0529594i	$-0.0168654\pi$
$7$	0.0860119	+	0.543058i	0.0325095	+	0.205257i	−0.966087	+	0.258216i	$0.916865\pi$
$8$	−0.475357	+	3.00128i	−0.168064	+	1.06111i
$9$		0			0
$10$	1.01002	−	2.10665i	0.319398	−	0.666183i
$11$	3.29961	+	0.335528i	0.994870	+	0.101166i
$11$	3.29961	+	0.335528i	0.994870	+	0.101166i
$12$		0			0
$13$	1.47301	+	2.89095i	0.408540	+	0.801805i	0.999990	−	0.00453687i	$-0.00144414\pi$
$13$	1.47301	+	2.89095i	0.408540	+	0.801805i	−0.591450	+	0.806342i	$0.701444\pi$
$14$	0.337662	+	0.464752i	0.0902440	+	0.124210i
$15$		0			0
$16$	0.419681	+	1.29165i	0.104920	+	0.322912i
$17$	2.57079	−	5.04545i	0.623507	−	1.22370i	−0.335959	−	0.941877i	$-0.609060\pi$
$17$	2.57079	−	5.04545i	0.623507	−	1.22370i	0.959466	−	0.281825i	$-0.0909397\pi$
$18$		0			0
$19$	−1.25925	+	0.914902i	−0.288893	+	0.209893i	−0.722787	−	0.691071i	$-0.757139\pi$
$19$	−1.25925	+	0.914902i	−0.288893	+	0.209893i	0.433894	+	0.900964i	$0.357139\pi$
$20$	0.0490901	+	2.03059i	0.0109769	+	0.454053i
$21$		0			0
$22$	3.23087	−	1.25276i	0.688823	−	0.267090i
$23$	0.803543	+	0.803543i	0.167550	+	0.167550i	0.785902	−	0.618351i	$-0.212199\pi$
$23$	0.803543	+	0.803543i	0.167550	+	0.167550i	−0.618351	+	0.785902i	$0.712199\pi$
$24$		0			0
$25$	1.31349	−	4.82439i	0.262699	−	0.964878i
$26$	2.74255	+	1.99258i	0.537858	+	0.390777i
$27$		0			0
$28$	−0.445011	−	0.226744i	−0.0840992	−	0.0428507i
$29$	3.44380	+	2.50207i	0.639498	+	0.464623i	0.859678	−	0.510837i	$-0.170664\pi$
$29$	3.44380	+	2.50207i	0.639498	+	0.464623i	−0.220180	+	0.975459i	$0.570664\pi$
$30$		0			0
$31$	−0.509209	+	1.56718i	−0.0914566	+	0.281475i	−0.986314	−	0.164878i	$-0.947277\pi$
$31$	−0.509209	+	1.56718i	−0.0914566	+	0.281475i	0.894857	+	0.446352i	$0.147277\pi$
$32$	−3.29400	−	3.29400i	−0.582302	−	0.582302i
$33$		0			0
$34$		−	5.91638i		−	1.01465i
$35$	0.890110	+	0.848089i	0.150456	+	0.143353i
$36$		0			0
$37$	−0.945121	+	0.149692i	−0.155377	+	0.0246093i	−0.233638	−	0.972324i	$-0.575063\pi$
$37$	−0.945121	+	0.149692i	−0.155377	+	0.0246093i	0.0782613	+	0.996933i	$0.475063\pi$
$38$	−0.738312	+	1.44902i	−0.119770	+	0.235062i
$39$		0			0
$40$	3.23016	+	5.97783i	0.510733	+	0.945178i
$41$	−5.25869	−	7.23797i	−0.821270	−	1.13038i	−0.989486	−	0.144631i	$-0.953801\pi$
$41$	−5.25869	−	7.23797i	−0.821270	−	1.13038i	0.168216	−	0.985750i	$-0.446199\pi$
$42$		0			0
$43$	−2.55312	+	2.55312i	−0.389348	+	0.389348i	−0.874455	−	0.485107i	$-0.838781\pi$
$43$	−2.55312	+	2.55312i	−0.389348	+	0.389348i	0.485107	+	0.874455i	$0.338781\pi$
$44$	−2.00833	+	2.24570i	−0.302767	+	0.338551i
$45$		0			0
$46$	1.12919	+	0.366897i	0.166490	+	0.0540960i
$47$	−0.636959	+	4.02160i	−0.0929101	+	0.586611i	0.896678	+	0.442683i	$0.145973\pi$
$47$	−0.636959	+	4.02160i	−0.0929101	+	0.586611i	−0.989588	+	0.143928i	$0.954027\pi$
$48$		0			0
$49$	6.36988	−	2.06970i	0.909983	−	0.295671i
$50$	−1.06560	−	5.11422i	−0.150698	−	0.723259i
$51$		0			0
$52$	−2.91101	−	0.461058i	−0.403684	−	0.0639373i
$53$	−6.27685	+	3.19821i	−0.862192	+	0.439309i	−0.828411	−	0.560121i	$-0.810755\pi$
$53$	−6.27685	+	3.19821i	−0.862192	+	0.439309i	−0.0337806	+	0.999429i	$0.510755\pi$
$54$		0			0
$55$	6.31803	−	3.88362i	0.851923	−	0.523667i
$56$	−1.67076			−0.223264
$57$		0			0
$58$	4.39276	+	0.695746i	0.576798	+	0.0913559i
$59$	3.97760	−	5.47470i	0.517839	−	0.712745i	−0.467377	−	0.884058i	$-0.654801\pi$
$59$	3.97760	−	5.47470i	0.517839	−	0.712745i	0.985217	+	0.171313i	$0.0548010\pi$
$60$		0			0
$61$	−8.75080	+	2.84331i	−1.12043	+	0.364048i	−0.809930	−	0.586526i	$-0.800495\pi$
$61$	−8.75080	+	2.84331i	−1.12043	+	0.364048i	−0.310496	+	0.950575i	$0.600495\pi$
$62$	0.269329	+	1.70048i	0.0342048	+	0.215961i
$63$		0			0
$64$	−7.21224	−	2.34340i	−0.901530	−	0.292925i
$65$	6.54208	+	3.13656i	0.811445	+	0.389043i
$66$		0			0
$67$	−2.62254	+	2.62254i	−0.320394	+	0.320394i	−0.848918	−	0.528524i	$-0.822746\pi$
$67$	−2.62254	+	2.62254i	−0.320394	+	0.320394i	0.528524	+	0.848918i	$0.322746\pi$
$68$	2.33523	+	4.58314i	0.283188	+	0.555788i
$69$		0			0
$70$	1.23091	+	0.367304i	0.147122	+	0.0439012i
$71$	−2.11802	−	6.51858i	−0.251362	−	0.773613i	−0.994525	−	0.104502i	$-0.966675\pi$
$71$	−2.11802	−	6.51858i	−0.251362	−	0.773613i	0.743162	−	0.669111i	$-0.233325\pi$
$72$		0			0
$73$	−9.96541	+	1.57837i	−1.16636	+	0.184734i	−0.709436	−	0.704770i	$-0.751050\pi$
$73$	−9.96541	+	1.57837i	−1.16636	+	0.184734i	−0.456928	+	0.889504i	$0.651050\pi$
$74$	−0.808840	+	0.587656i	−0.0940257	+	0.0683137i
$75$		0			0
$76$		−	1.41390i		−	0.162186i
$77$	0.101594	+	1.82074i	0.0115778	+	0.207492i
$78$		0			0
$79$	−1.28746	+	3.96241i	−0.144851	+	0.445806i	−0.996992	−	0.0775069i	$-0.975304\pi$
$79$	−1.28746	+	3.96241i	−0.144851	+	0.445806i	0.852141	+	0.523313i	$0.175304\pi$
$80$	2.49928	+	1.72511i	0.279428	+	0.192873i
$81$		0			0
$82$	−8.32870	−	4.24369i	−0.919751	−	0.468637i
$83$	−10.0947	−	5.14352i	−1.10804	−	0.564574i	−0.198462	−	0.980109i	$-0.563595\pi$
$83$	−10.0947	−	5.14352i	−1.10804	−	0.564574i	−0.909577	+	0.415534i	$0.863595\pi$
$84$		0			0
$85$	−2.28245	−	12.4546i	−0.247567	−	1.35089i
$86$	−1.16575	+	3.58782i	−0.125706	+	0.386884i
$87$		0			0
$88$	−2.57551	+	9.74357i	−0.274550	+	1.03867i
$89$		−	3.64860i		−	0.386750i	−0.981125	−	0.193375i	$-0.938057\pi$
$89$		−	3.64860i		−	0.386750i	0.981125	−	0.193375i	$-0.0619435\pi$
$90$		0			0
$91$	−1.44326	+	1.04859i	−0.151294	+	0.109922i
$92$	−1.01955	+	0.161481i	−0.106295	+	0.0168355i
$93$		0			0
$94$	1.31462	+	4.04597i	0.135592	+	0.417310i
$95$	−0.995217	+	3.33517i	−0.102107	+	0.342182i
$96$		0			0
$97$	−7.56722	−	14.8515i	−0.768335	−	1.50794i	−0.858952	−	0.512057i	$-0.828884\pi$
$97$	−7.56722	−	14.8515i	−0.768335	−	1.50794i	0.0906166	−	0.995886i	$-0.471116\pi$
$98$	4.94820	−	4.94820i	0.499844	−	0.499844i
$99$		0			0
$100$	2.84408	+	3.54115i	0.284408	+	0.354115i
$101$	0.608855	+	0.197829i	0.0605834	+	0.0196847i	0.339152	−	0.940732i	$-0.389860\pi$
$101$	0.608855	+	0.197829i	0.0605834	+	0.0196847i	−0.278569	+	0.960416i	$0.589860\pi$
$102$		0			0
$103$	−0.323199	−	2.04060i	−0.0318457	−	0.201066i	0.966636	−	0.256155i	$-0.0824558\pi$
$103$	−0.323199	−	2.04060i	−0.0318457	−	0.201066i	−0.998481	+	0.0550890i	$0.982456\pi$
$104$	−9.37677	+	3.04670i	−0.919468	+	0.298753i
$105$		0			0
$106$	−4.32630	+	5.95465i	−0.420208	+	0.578366i
$107$	−8.82790	−	1.39820i	−0.853425	−	0.135169i	−0.285631	−	0.958340i	$-0.592203\pi$
$107$	−8.82790	−	1.39820i	−0.853425	−	0.135169i	−0.567794	+	0.823171i	$0.692203\pi$
$108$		0			0
$109$	4.48044			0.429148			0.214574	−	0.976708i	$-0.431164\pi$
$109$	4.48044			0.429148			0.214574	+	0.976708i	$0.431164\pi$
$110$	4.03953	−	6.61225i	0.385154	−	0.630453i
$111$		0			0
$112$	−0.665341	+	0.339008i	−0.0628688	+	0.0320333i
$113$	1.41806	+	0.224599i	0.133400	+	0.0211285i	0.222778	−	0.974869i	$-0.428488\pi$
$113$	1.41806	+	0.224599i	0.133400	+	0.0211285i	−0.0893772	+	0.995998i	$0.528488\pi$
$114$		0			0
$115$	2.51862	+	0.336732i	0.234862	+	0.0314004i
$116$	−3.67748	+	1.19489i	−0.341446	+	0.110942i
$117$		0			0
$118$	1.10604	−	6.98328i	0.101820	−	0.642863i
$119$	2.96109	+	0.962116i	0.271443	+	0.0881971i
$120$		0			0
$121$	10.7748	+	2.21422i	0.979531	+	0.201293i
$122$	−6.79773	+	6.79773i	−0.615438	+	0.615438i
$123$		0			0
$124$	−0.879824	−	1.21097i	−0.0790106	−	0.108749i
$125$	−4.21619	−	10.3549i	−0.377107	−	0.926170i
$126$		0			0
$127$	−5.36790	+	10.5351i	−0.476324	+	0.934838i	0.520397	+	0.853924i	$0.325784\pi$
$127$	−5.36790	+	10.5351i	−0.476324	+	0.934838i	−0.996721	+	0.0809136i	$0.974216\pi$
$128$	1.37647	−	0.218011i	0.121664	−	0.0192696i
$129$		0			0
$130$	7.57801	−	0.183201i	0.664635	−	0.0160678i
$131$			7.94436i			0.694102i	0.937846	+	0.347051i	$0.112817\pi$
$131$			7.94436i			0.694102i	−0.937846	+	0.347051i	$0.887183\pi$
$132$		0			0
$133$	−0.605156	−	0.605156i	−0.0524737	−	0.0524737i
$134$	−1.19745	+	3.68537i	−0.103444	+	0.318367i
$135$		0			0
$136$	13.9208	+	10.1140i	1.19370	+	0.867272i
$137$	−3.98714	−	2.03155i	−0.340644	−	0.173567i	0.275297	−	0.961359i	$-0.411224\pi$
$137$	−3.98714	−	2.03155i	−0.340644	−	0.173567i	−0.615941	+	0.787792i	$0.711224\pi$
$138$		0			0
$139$	18.2968	+	13.2934i	1.55192	+	1.12753i	0.942267	+	0.334862i	$0.108690\pi$
$139$	18.2968	+	13.2934i	1.55192	+	1.12753i	0.609650	+	0.792671i	$0.291310\pi$
$140$	−1.09850	+	0.201314i	−0.0928406	+	0.0170141i
$141$		0			0
$142$	−5.06371	−	5.06371i	−0.424937	−	0.424937i
$143$	3.89037	+	10.0332i	0.325329	+	0.839022i
$144$		0			0
$145$	9.51566	−	0.230044i	0.790232	−	0.0191041i
$146$	−8.52846	+	6.19629i	−0.705820	+	0.512808i
$147$		0			0
$148$	0.394619	−	0.774483i	0.0324375	−	0.0636621i
$149$	4.56892	+	14.0617i	0.374301	+	1.15198i	0.943949	+	0.330091i	$0.107079\pi$
$149$	4.56892	+	14.0617i	0.374301	+	1.15198i	−0.569648	+	0.821888i	$0.692921\pi$
$150$		0			0
$151$	3.90602	+	5.37617i	0.317867	+	0.437507i	0.937815	−	0.347137i	$-0.112846\pi$
$151$	3.90602	+	5.37617i	0.317867	+	0.437507i	−0.619947	+	0.784644i	$0.712846\pi$
$152$	−2.14729	−	4.21429i	−0.174168	−	0.341824i
$153$		0			0
$154$	0.958216	+	1.64680i	0.0772152	+	0.132703i
$155$	1.22299	+	3.47579i	0.0982327	+	0.279182i
$156$		0			0
$157$	0.252536	−	1.59445i	0.0201545	−	0.127251i	−0.975560	−	0.219735i	$-0.929481\pi$
$157$	0.252536	−	1.59445i	0.0201545	−	0.127251i	0.995714	+	0.0924842i	$0.0294808\pi$
$158$	0.680962	+	4.29942i	0.0541744	+	0.342044i
$159$		0			0
$160$	−10.3247	−	1.38038i	−0.816237	−	0.109129i
$161$	−0.367256	+	0.505485i	−0.0289438	+	0.0398378i
$162$		0			0
$163$	−9.02548	+	4.59871i	−0.706930	+	0.360199i	−0.770204	−	0.637797i	$-0.779846\pi$
$163$	−9.02548	+	4.59871i	−0.706930	+	0.360199i	0.0632741	+	0.997996i	$0.479846\pi$
$164$	8.12686			0.634601
$165$		0			0
$166$	−11.8372			−0.918749
$167$	12.7574	−	6.50021i	0.987195	−	0.503001i	0.115636	−	0.993292i	$-0.463109\pi$
$167$	12.7574	−	6.50021i	0.987195	−	0.503001i	0.871559	+	0.490290i	$0.163109\pi$
$168$		0			0
$169$	1.45339	−	2.00041i	0.111799	−	0.153878i
$170$	−8.03247	−	10.5118i	−0.616062	−	0.806217i
$171$		0			0
$172$	−0.513077	−	3.23944i	−0.0391218	−	0.247005i
$173$	2.59199	−	16.3652i	0.197066	−	1.24422i	−0.668608	−	0.743615i	$-0.733110\pi$
$173$	2.59199	−	16.3652i	0.197066	−	1.24422i	0.865674	−	0.500609i	$-0.166890\pi$
$174$		0			0
$175$	2.73290	+	0.298348i	0.206588	+	0.0225530i
$176$	0.951401	+	4.40274i	0.0717145	+	0.331869i
$177$		0			0
$178$	−1.73065	−	3.39660i	−0.129718	−	0.254586i
$179$	−11.7477	−	16.1694i	−0.878066	−	1.20855i	−0.976953	−	0.213455i	$-0.931528\pi$
$179$	−11.7477	−	16.1694i	−0.878066	−	1.20855i	0.0988868	−	0.995099i	$-0.468472\pi$
$180$		0			0
$181$	−8.30476	−	25.5594i	−0.617288	−	1.89982i	−0.355370	−	0.934726i	$-0.615645\pi$
$181$	−8.30476	−	25.5594i	−0.617288	−	1.89982i	−0.261918	−	0.965090i	$-0.584355\pi$
$182$	−0.846194	+	1.66075i	−0.0627241	+	0.123103i
$183$		0			0
$184$	−2.79363	+	2.02969i	−0.205949	+	0.149631i
$185$	−1.47599	+	1.54912i	−0.108517	+	0.113894i
$186$		0			0
$187$	10.1755	−	15.7854i	0.744105	−	1.15435i
$188$	−2.61534	−	2.61534i	−0.190743	−	0.190743i
$189$		0			0
$190$	0.655506	+	3.57689i	0.0475554	+	0.259495i
$191$	10.4691	+	7.60626i	0.757519	+	0.550370i	0.898148	−	0.439693i	$-0.144913\pi$
$191$	10.4691	+	7.60626i	0.757519	+	0.550370i	−0.140629	+	0.990062i	$0.544913\pi$
$192$		0			0
$193$	6.68068	+	3.40398i	0.480886	+	0.245024i	0.677591	−	0.735439i	$-0.263024\pi$
$193$	6.68068	+	3.40398i	0.480886	+	0.245024i	−0.196705	+	0.980463i	$0.563024\pi$
$194$	−14.0892	−	10.2364i	−1.01154	−	0.734928i
$195$		0			0
$196$	−1.88006	+	5.78622i	−0.134290	+	0.413301i
$197$	−2.73095	−	2.73095i	−0.194572	−	0.194572i	0.603096	−	0.797668i	$-0.293933\pi$
$197$	−2.73095	−	2.73095i	−0.194572	−	0.194572i	−0.797668	+	0.603096i	$0.793933\pi$
$198$		0			0
$199$		−	12.3835i		−	0.877842i	−0.898526	−	0.438921i	$-0.855361\pi$
$199$		−	12.3835i		−	0.877842i	0.898526	−	0.438921i	$-0.144639\pi$
$200$	13.8550	+	6.23547i	0.979696	+	0.440915i
$201$		0			0
$202$	0.660640	−	0.104635i	0.0464825	−	0.00736210i
$203$	−1.06256	+	2.08539i	−0.0745771	+	0.146366i
$204$		0			0
$205$	−19.1700	−	5.72033i	−1.33889	−	0.399525i
$206$	−1.26880	−	1.74635i	−0.0884015	−	0.121674i
$207$		0			0
$208$	−3.11589	+	3.11589i	−0.216048	+	0.216048i
$209$	−4.46202	+	2.59630i	−0.308645	+	0.179590i
$210$		0			0
$211$	12.8931	+	4.18923i	0.887599	+	0.288398i	0.717109	−	0.696961i	$-0.245465\pi$
$211$	12.8931	+	4.18923i	0.887599	+	0.288398i	0.170490	+	0.985359i	$0.445465\pi$
$212$	1.00105	−	6.32040i	0.0687526	−	0.434087i
$213$		0			0
$214$	−8.88139	+	2.88574i	−0.607119	+	0.197265i
$215$	−1.06991	+	8.00248i	−0.0729672	+	0.545765i
$216$		0			0
$217$	−0.894870	−	0.141733i	−0.0607477	−	0.00962149i
$218$	4.17099	−	2.12522i	0.282495	−	0.143938i
$219$		0			0
$220$	−0.519341	+	6.71662i	−0.0350140	+	0.452834i
$221$	18.3729			1.23590
$222$		0			0
$223$	−5.17593	−	0.819786i	−0.346606	−	0.0548969i	−0.0192953	−	0.999814i	$-0.506142\pi$
$223$	−5.17593	−	0.819786i	−0.346606	−	0.0548969i	−0.327310	+	0.944917i	$0.606142\pi$
$224$	1.50551	−	2.07216i	0.100591	−	0.138452i
$225$		0			0
$226$	1.42666	−	0.463549i	0.0948999	−	0.0308348i
$227$	2.35763	+	14.8855i	0.156481	+	0.987984i	0.933518	+	0.358530i	$0.116722\pi$
$227$	2.35763	+	14.8855i	0.156481	+	0.987984i	−0.777037	+	0.629455i	$0.783278\pi$
$228$		0			0
$229$	14.1396	+	4.59424i	0.934371	+	0.303596i	0.736349	−	0.676602i	$-0.236548\pi$
$229$	14.1396	+	4.59424i	0.934371	+	0.303596i	0.198022	+	0.980198i	$0.436548\pi$
$230$	2.50438	−	0.881190i	0.165134	−	0.0581040i
$231$		0			0
$232$	−9.14646	+	9.14646i	−0.600494	+	0.600494i
$233$	−2.51466	−	4.93530i	−0.164741	−	0.323322i	0.793848	−	0.608117i	$-0.208075\pi$
$233$	−2.51466	−	4.93530i	−0.164741	−	0.323322i	−0.958589	+	0.284794i	$0.908075\pi$
$234$		0			0
$235$	4.32829	+	8.01005i	0.282346	+	0.522518i
$236$	1.89954	+	5.84618i	0.123649	+	0.380554i
$237$		0			0
$238$	3.21294	−	0.508880i	0.208264	−	0.0329858i
$239$	19.9985	−	14.5297i	1.29359	−	0.939850i	0.293721	−	0.955891i	$-0.405106\pi$
$239$	19.9985	−	14.5297i	1.29359	−	0.939850i	0.999871	+	0.0160415i	$0.00510638\pi$
$240$		0			0
$241$		−	5.19700i		−	0.334768i	−0.985892	−	0.167384i	$-0.946468\pi$
$241$		−	5.19700i		−	0.334768i	0.985892	−	0.167384i	$-0.0535320\pi$
$242$	11.0809	−	3.04958i	0.712309	−	0.196034i
$243$		0			0
$244$	2.58278	−	7.94898i	0.165346	−	0.508882i
$245$	8.50756	−	12.3254i	0.543528	−	0.787444i
$246$		0			0
$247$	−4.49983	−	2.29278i	−0.286318	−	0.145886i
$248$	−4.46151	−	2.27325i	−0.283306	−	0.144352i
$249$		0			0
$250$	−8.83666	−	7.63982i	−0.558880	−	0.483185i
$251$	−3.85860	+	11.8755i	−0.243553	+	0.749578i	0.752319	+	0.658799i	$0.228935\pi$
$251$	−3.85860	+	11.8755i	−0.243553	+	0.749578i	−0.995871	+	0.0907782i	$0.971065\pi$
$252$		0			0
$253$	2.38177	+	2.92099i	0.149740	+	0.183641i
$254$			12.3536i			0.775136i
$255$		0			0
$256$	13.4482	−	9.77068i	0.840511	−	0.610667i
$257$	−12.5983	+	1.99537i	−0.785859	+	0.124468i	−0.536452	−	0.843931i	$-0.680236\pi$
$257$	−12.5983	+	1.99537i	−0.785859	+	0.124468i	−0.249407	+	0.968399i	$0.580236\pi$
$258$		0			0
$259$	−0.162583	−	0.500380i	−0.0101024	−	0.0310921i
$260$	−5.79802	+	3.13300i	−0.359578	+	0.194300i
$261$		0			0
$262$	3.76828	+	7.39566i	0.232805	+	0.456906i
$263$	−13.6161	+	13.6161i	−0.839605	+	0.839605i	−0.988807	−	0.149202i	$-0.952330\pi$
$263$	−13.6161	+	13.6161i	−0.839605	+	0.839605i	0.149202	+	0.988807i	$0.452330\pi$
$264$		0			0
$265$	−6.81012	+	14.2042i	−0.418343	+	0.872557i
$266$	−0.850405	−	0.276313i	−0.0521417	−	0.0169419i
$267$		0			0
$268$	−0.527027	−	3.32752i	−0.0321933	−	0.203261i
$269$	16.5446	−	5.37566i	1.00874	−	0.327760i	0.242387	−	0.970180i	$-0.422070\pi$
$269$	16.5446	−	5.37566i	1.00874	−	0.327760i	0.766353	+	0.642420i	$0.222070\pi$
$270$		0			0
$271$	−18.6755	+	25.7046i	−1.13445	+	1.56144i	−0.355133	+	0.934816i	$0.615564\pi$
$271$	−18.6755	+	25.7046i	−1.13445	+	1.56144i	−0.779321	+	0.626625i	$0.784436\pi$
$272$	7.59585	+	1.20306i	0.460566	+	0.0729465i
$273$		0			0
$274$	−4.67539			−0.282451
$275$	5.95273	−	15.4779i	0.358963	−	0.933352i
$276$		0			0
$277$	6.46840	−	3.29581i	0.388649	−	0.198026i	−0.248738	−	0.968571i	$-0.580016\pi$
$277$	6.46840	−	3.29581i	0.388649	−	0.198026i	0.637386	+	0.770545i	$0.280016\pi$
$278$	23.3386	+	3.69648i	1.39976	+	0.221700i
$279$		0			0
$280$	−2.96848	+	2.26833i	−0.177400	+	0.135559i
$281$	5.27301	−	1.71330i	0.314561	−	0.102207i	−0.147481	−	0.989065i	$-0.547117\pi$
$281$	5.27301	−	1.71330i	0.314561	−	0.102207i	0.462043	+	0.886858i	$0.347117\pi$
$282$		0			0
$283$	2.16199	−	13.6503i	0.128517	−	0.811425i	−0.836255	−	0.548340i	$-0.815260\pi$
$283$	2.16199	−	13.6503i	0.128517	−	0.811425i	0.964773	−	0.263085i	$-0.0847401\pi$
$284$	5.92130	+	1.92395i	0.351364	+	0.114165i
$285$		0			0
$286$	8.38078	+	7.49494i	0.495566	+	0.443185i
$287$	3.47833	−	3.47833i	0.205319	−	0.205319i
$288$		0			0
$289$	−8.85528	−	12.1882i	−0.520899	−	0.716956i
$290$	8.74932	−	4.72775i	0.513778	−	0.277623i
$291$		0			0
$292$	4.16089	−	8.16620i	0.243497	−	0.477891i
$293$	6.71571	−	1.06366i	0.392336	−	0.0621400i	0.0428502	−	0.999082i	$-0.486356\pi$
$293$	6.71571	−	1.06366i	0.392336	−	0.0621400i	0.349486	+	0.936942i	$0.386356\pi$
$294$		0			0
$295$	−0.365707	−	15.1273i	−0.0212923	−	0.880743i
$296$		−	2.90773i		−	0.169009i
$297$		0			0
$298$	10.9233	+	10.9233i	0.632770	+	0.632770i
$299$	−1.13937	+	3.50663i	−0.0658917	+	0.202794i
$300$		0			0
$301$	−1.60609	−	1.16689i	−0.0925737	−	0.0672587i
$302$	6.18634	+	3.15210i	0.355984	+	0.181383i
$303$		0			0
$304$	−1.71022	−	1.24254i	−0.0980876	−	0.0712648i
$305$	−11.6875	+	16.9324i	−0.669224	+	0.969548i
$306$		0			0
$307$	5.54209	+	5.54209i	0.316304	+	0.316304i	0.847346	−	0.531042i	$-0.178199\pi$
$307$	5.54209	+	5.54209i	0.316304	+	0.316304i	−0.531042	+	0.847346i	$0.678199\pi$
$308$	−1.39228	−	0.897482i	−0.0793327	−	0.0511388i
$309$		0			0
$310$	2.78720	+	2.65562i	0.158302	+	0.150829i
$311$	13.4223	−	9.75186i	0.761108	−	0.552977i	−0.138142	−	0.990412i	$-0.544113\pi$
$311$	13.4223	−	9.75186i	0.761108	−	0.552977i	0.899250	+	0.437435i	$0.144113\pi$
$312$		0			0
$313$	−4.32355	+	8.48544i	−0.244381	+	0.479625i	−0.980318	−	0.197425i	$-0.936742\pi$
$313$	−4.32355	+	8.48544i	−0.244381	+	0.479625i	0.735937	+	0.677050i	$0.236742\pi$
$314$	−0.521207	−	1.60411i	−0.0294134	−	0.0905251i
$315$		0			0
$316$	−2.22451	−	3.06178i	−0.125139	−	0.172239i
$317$	−10.9490	−	21.4887i	−0.614960	−	1.20693i	−0.963014	−	0.269452i	$-0.913157\pi$
$317$	−10.9490	−	21.4887i	−0.614960	−	1.20693i	0.348054	−	0.937474i	$-0.386843\pi$
$318$		0			0
$319$	10.5237	+	9.41134i	0.589213	+	0.526934i
$320$	−15.9957	+	5.62823i	−0.894187	+	0.314628i
$321$		0			0
$322$	−0.102122	+	0.644774i	−0.00569105	+	0.0359319i
$323$	1.37882	+	8.70552i	0.0767196	+	0.484388i
$324$		0			0
$325$	15.8819	−	3.30914i	0.880967	−	0.183558i
$326$	−6.22079	+	8.56218i	−0.344538	+	0.474215i
$327$		0			0
$328$	24.2230	−	12.3422i	1.33749	−	0.681485i
$329$	−2.23875			−0.123426
$330$		0			0
$331$	12.5641			0.690587			0.345294	−	0.938495i	$-0.387779\pi$
$331$	12.5641			0.690587			0.345294	+	0.938495i	$0.387779\pi$
$332$	9.16976	−	4.67222i	0.503256	−	0.256422i
$333$		0			0
$334$	8.79299	−	12.1025i	0.481131	−	0.662220i
$335$	−1.09900	+	8.22006i	−0.0600447	+	0.449110i
$336$		0			0
$337$	2.57734	+	16.2727i	0.140397	+	0.886430i	0.952858	+	0.303415i	$0.0981269\pi$
$337$	2.57734	+	16.2727i	0.140397	+	0.886430i	−0.812462	+	0.583015i	$0.801873\pi$
$338$	0.404140	−	2.55164i	0.0219823	−	0.138791i
$339$		0			0
$340$	10.3714	+	4.97252i	0.562470	+	0.269673i
$341$	−2.20603	+	5.00024i	−0.119463	+	0.270778i
$342$		0			0
$343$	3.41917	+	6.71049i	0.184618	+	0.362333i
$344$	−6.44901	−	8.87630i	−0.347707	−	0.478578i
$345$		0			0
$346$	−5.34960	−	16.4644i	−0.287596	−	0.885130i
$347$	−6.46480	+	12.6879i	−0.347049	+	0.681121i	−0.996878	−	0.0789590i	$-0.974840\pi$
$347$	−6.46480	+	12.6879i	−0.347049	+	0.681121i	0.649829	+	0.760080i	$0.274840\pi$
$348$		0			0
$349$	−13.4408	+	9.76528i	−0.719467	+	0.522724i	−0.886214	−	0.463276i	$-0.846674\pi$
$349$	−13.4408	+	9.76528i	−0.719467	+	0.522724i	0.166747	+	0.986000i	$0.446674\pi$
$350$	2.68566	−	1.01856i	0.143555	−	0.0544446i
$351$		0			0
$352$	−9.76368	−	11.9741i	−0.520406	−	0.638224i
$353$	−7.78082	−	7.78082i	−0.414131	−	0.414131i	0.469044	−	0.883175i	$-0.344599\pi$
$353$	−7.78082	−	7.78082i	−0.414131	−	0.414131i	−0.883175	+	0.469044i	$0.844599\pi$
$354$		0			0
$355$	−12.6132	−	8.70616i	−0.669438	−	0.462075i
$356$	2.68131	+	1.94809i	0.142109	+	0.103248i
$357$		0			0
$358$	−18.6060	−	9.48024i	−0.983358	−	0.501046i
$359$	10.6626	+	7.74686i	0.562753	+	0.408864i	0.832465	−	0.554077i	$-0.186929\pi$
$359$	10.6626	+	7.74686i	0.562753	+	0.408864i	−0.269713	+	0.962941i	$0.586929\pi$
$360$		0			0
$361$	−5.12265	+	15.7659i	−0.269613	+	0.829783i
$362$	−19.8549	−	19.8549i	−1.04355	−	1.04355i
$363$		0			0
$364$		−	1.62050i		−	0.0849374i
$365$	−15.5629	+	16.3340i	−0.814599	+	0.854961i
$366$		0			0
$367$	27.4601	−	4.34925i	1.43341	−	0.227029i	0.609064	−	0.793121i	$-0.291545\pi$
$367$	27.4601	−	4.34925i	1.43341	−	0.227029i	0.824342	+	0.566092i	$0.191545\pi$
$368$	−0.700661	+	1.37513i	−0.0365245	+	0.0716834i
$369$		0			0
$370$	−0.639244	+	2.14224i	−0.0332327	+	0.111370i
$371$	−2.27670	−	3.13361i	−0.118200	−	0.162689i
$372$		0			0
$373$	−6.02155	+	6.02155i	−0.311784	+	0.311784i	−0.845600	−	0.533816i	$-0.820757\pi$
$373$	−6.02155	+	6.02155i	−0.311784	+	0.311784i	0.533816	+	0.845600i	$0.320757\pi$
$374$	1.98511	−	19.5218i	0.102648	−	1.00945i
$375$		0			0
$376$	−11.7672	−	3.82339i	−0.606847	−	0.197176i
$377$	−2.16059	+	13.6414i	−0.111276	+	0.702570i
$378$		0			0
$379$	4.14195	−	1.34580i	0.212758	−	0.0691292i	−0.200699	−	0.979653i	$-0.564321\pi$
$379$	4.14195	−	1.34580i	0.212758	−	0.0691292i	0.413457	+	0.910524i	$0.364321\pi$
$380$	−1.91961	−	2.51211i	−0.0984737	−	0.128869i
$381$		0			0
$382$	13.3540	+	2.11506i	0.683248	+	0.108216i
$383$	6.04488	−	3.08002i	0.308879	−	0.157382i	−0.292679	−	0.956211i	$-0.594547\pi$
$383$	6.04488	−	3.08002i	0.308879	−	0.157382i	0.601558	+	0.798829i	$0.294547\pi$
$384$		0			0
$385$	2.65246	+	3.09702i	0.135182	+	0.157839i
$386$	7.83388			0.398734
$387$		0			0
$388$	14.9545	+	2.36857i	0.759202	+	0.120246i
$389$	−14.4727	+	19.9200i	−0.733797	+	1.00998i	0.265155	+	0.964206i	$0.414577\pi$
$389$	−14.4727	+	19.9200i	−0.733797	+	1.00998i	−0.998952	+	0.0457786i	$0.985423\pi$
$390$		0			0
$391$	6.11997	−	1.98850i	0.309500	−	0.100563i
$392$	3.18379	+	20.1017i	0.160806	+	1.01529i
$393$		0			0
$394$	−3.83771	−	1.24695i	−0.193341	−	0.0628203i
$395$	3.09215	+	8.78805i	0.155583	+	0.442175i
$396$		0			0
$397$	−20.7876	+	20.7876i	−1.04330	+	1.04330i	−0.0442826	+	0.999019i	$0.514100\pi$
$397$	−20.7876	+	20.7876i	−1.04330	+	1.04330i	−0.999019	+	0.0442826i	$0.985900\pi$
$398$	−5.87390	−	11.5282i	−0.294432	−	0.577856i
$399$		0			0
$400$	6.78265	−	0.328138i	0.339133	−	0.0164069i
$401$	−7.65264	−	23.5524i	−0.382155	−	1.17615i	−0.938523	−	0.345216i	$-0.887806\pi$
$401$	−7.65264	−	23.5524i	−0.382155	−	1.17615i	0.556369	−	0.830935i	$-0.312194\pi$
$402$		0			0
$403$	−5.28072	+	0.836384i	−0.263051	+	0.0416633i
$404$	−0.470467	+	0.341814i	−0.0234066	+	0.0170059i
$405$		0			0
$406$			2.44537i			0.121362i
$407$	−3.16876	+	0.176812i	−0.157069	+	0.00876424i
$408$		0			0
$409$	−3.09442	+	9.52366i	−0.153009	+	0.470915i	−0.997954	−	0.0639396i	$-0.979633\pi$
$409$	−3.09442	+	9.52366i	−0.153009	+	0.470915i	0.844944	+	0.534854i	$0.179633\pi$
$410$	−20.5593	+	3.76773i	−1.01535	+	0.186075i
$411$		0			0
$412$	1.67218	+	0.852016i	0.0823822	+	0.0419758i
$413$	3.31520	+	1.68918i	0.163130	+	0.0831190i
$414$		0			0
$415$	−24.9187	+	4.56664i	−1.22321	+	0.224167i
$416$	4.67068	−	14.3749i	0.228999	−	0.704787i
$417$		0			0
$418$	−2.92233	+	4.53347i	−0.142936	+	0.221739i
$419$			7.65743i			0.374090i	0.982351	+	0.187045i	$0.0598910\pi$
$419$			7.65743i			0.374090i	−0.982351	+	0.187045i	$0.940109\pi$
$420$		0			0
$421$	17.5332	−	12.7386i	0.854517	−	0.620843i	−0.0718707	−	0.997414i	$-0.522897\pi$
$421$	17.5332	−	12.7386i	0.854517	−	0.620843i	0.926388	+	0.376571i	$0.122897\pi$
$422$	13.9897	−	2.21575i	0.681009	−	0.107861i
$423$		0			0
$424$	−6.61501	−	20.3589i	−0.321253	−	0.988716i
$425$	−20.9645	−	19.0296i	−1.01693	−	0.923073i
$426$		0			0
$427$	−2.29676	−	4.50764i	−0.111148	−	0.218140i
$428$	5.74098	−	5.74098i	0.277501	−	0.277501i
$429$		0			0
$430$	2.79983	+	7.95726i	0.135020	+	0.383733i
$431$	−27.0858	−	8.80070i	−1.30468	−	0.423915i	−0.427470	−	0.904030i	$-0.640595\pi$
$431$	−27.0858	−	8.80070i	−1.30468	−	0.423915i	−0.877206	+	0.480115i	$0.840595\pi$
$432$		0			0
$433$	1.95098	+	12.3180i	0.0937582	+	0.591966i	0.989175	+	0.146738i	$0.0468774\pi$
$433$	1.95098	+	12.3180i	0.0937582	+	0.591966i	−0.895417	+	0.445228i	$0.853123\pi$
$434$	−0.900293	+	0.292523i	−0.0432154	+	0.0140415i
$435$		0			0
$436$	−2.39223	+	3.29262i	−0.114567	+	0.157688i
$437$	−1.74703	−	0.276702i	−0.0835717	−	0.0132365i
$438$		0			0
$439$	−16.9147			−0.807294			−0.403647	−	0.914915i	$-0.632258\pi$
$439$	−16.9147			−0.807294			−0.403647	+	0.914915i	$0.632258\pi$
$440$	8.65254	+	20.8083i	0.412494	+	0.991997i
$441$		0			0
$442$	17.1040	−	8.71491i	0.813553	−	0.414526i
$443$	−10.9258	−	1.73048i	−0.519102	−	0.0822176i	−0.108614	−	0.994084i	$-0.534641\pi$
$443$	−10.9258	−	1.73048i	−0.519102	−	0.0822176i	−0.410487	+	0.911866i	$0.634641\pi$
$444$		0			0
$445$	−4.95357	−	6.48255i	−0.234822	−	0.307302i
$446$	−5.20729	+	1.69195i	−0.246572	+	0.0801162i
$447$		0			0
$448$	0.652263	−	4.11822i	0.0308165	−	0.194568i
$449$	−4.29754	−	1.39635i	−0.202813	−	0.0658980i	0.205849	−	0.978584i	$-0.434005\pi$
$449$	−4.29754	−	1.39635i	−0.202813	−	0.0658980i	−0.408662	+	0.912686i	$0.634005\pi$
$450$		0			0
$451$	−14.9231	−	25.6469i	−0.702701	−	1.20767i
$452$	−0.922199	+	0.922199i	−0.0433766	+	0.0433766i
$453$		0			0
$454$	9.25549	+	12.7391i	0.434381	+	0.597875i
$455$	−1.14064	+	3.82251i	−0.0534739	+	0.179202i
$456$		0			0
$457$	−14.8120	+	29.0702i	−0.692877	+	1.35985i	0.229405	+	0.973331i	$0.426322\pi$
$457$	−14.8120	+	29.0702i	−0.692877	+	1.35985i	−0.922282	+	0.386517i	$0.873678\pi$
$458$	15.3422	−	2.42997i	0.716895	−	0.113545i
$459$		0			0
$460$	−1.59222	+	1.67111i	−0.0742376	+	0.0779159i
$461$		−	23.4279i		−	1.09114i	−0.838064	−	0.545572i	$-0.816312\pi$
$461$		−	23.4279i		−	1.09114i	0.838064	−	0.545572i	$-0.183688\pi$
$462$		0			0
$463$	−29.2123	−	29.2123i	−1.35761	−	1.35761i	−0.876851	−	0.480762i	$-0.840360\pi$
$463$	−29.2123	−	29.2123i	−1.35761	−	1.35761i	−0.480762	−	0.876851i	$-0.659640\pi$
$464$	−1.78649	+	5.49825i	−0.0829356	+	0.255250i
$465$		0			0
$466$	−4.68196	−	3.40165i	−0.216888	−	0.157578i
$467$	25.3107	+	12.8965i	1.17124	+	0.596777i	0.927778	−	0.373133i	$-0.121716\pi$
$467$	25.3107	+	12.8965i	1.17124	+	0.596777i	0.243463	+	0.969910i	$0.421716\pi$
$468$		0			0
$469$	−1.64976	−	1.19862i	−0.0761789	−	0.0553472i
$470$	7.82878	+	5.40377i	0.361115	+	0.249257i
$471$		0			0
$472$	14.5403	+	14.5403i	0.669273	+	0.669273i
$473$	−9.28095	+	7.56766i	−0.426739	+	0.347962i
$474$		0			0
$475$	2.75982	+	7.27685i	0.126629	+	0.333885i
$476$	−2.28806	+	1.66237i	−0.104873	+	0.0761946i
$477$		0			0
$478$	11.7253	−	23.0121i	0.536301	−	1.05255i
$479$	9.69547	+	29.8396i	0.442998	+	1.36341i	0.884665	+	0.466227i	$0.154387\pi$
$479$	9.69547	+	29.8396i	0.442998	+	1.36341i	−0.441667	+	0.897179i	$0.645613\pi$
$480$		0			0
$481$	−1.82493	−	2.51180i	−0.0832096	−	0.114528i
$482$	−2.46511	−	4.83806i	−0.112283	−	0.220367i
$483$		0			0
$484$	−7.38019	+	6.73607i	−0.335463	+	0.306185i
$485$	−33.6082	−	16.1133i	−1.52607	−	0.731666i
$486$		0			0
$487$	−1.07518	+	6.78843i	−0.0487211	+	0.307613i	−1.00000		0.000719535i	$-0.999771\pi$
$487$	−1.07518	+	6.78843i	−0.0487211	+	0.307613i	0.951279	+	0.308333i	$0.0997710\pi$
$488$	−4.37382	−	27.6152i	−0.197994	−	1.25008i
$489$		0			0
$490$	2.07359	−	15.5096i	0.0936752	−	0.700652i
$491$	−8.65794	+	11.9166i	−0.390728	+	0.537790i	−0.958387	−	0.285473i	$-0.907849\pi$
$491$	−8.65794	+	11.9166i	−0.390728	+	0.537790i	0.567659	+	0.823264i	$0.307849\pi$
$492$		0			0
$493$	21.4773	−	10.9433i	0.967291	−	0.492859i
$494$	−5.27658			−0.237405
$495$		0			0
$496$	−2.23795			−0.100487
$497$	3.35779	−	1.71088i	0.150618	−	0.0767435i
$498$		0			0
$499$	−15.5610	+	21.4179i	−0.696607	+	0.958797i	0.303376	+	0.952871i	$0.401886\pi$
$499$	−15.5610	+	21.4179i	−0.696607	+	0.958797i	−0.999982	+	0.00592589i	$0.998114\pi$
$500$	9.86083	+	2.43033i	0.440990	+	0.108688i
$501$		0			0
$502$	2.04088	+	12.8856i	0.0910888	+	0.575112i
$503$	−4.76166	+	30.0639i	−0.212312	+	1.34049i	0.619312	+	0.785145i	$0.287412\pi$
$503$	−4.76166	+	30.0639i	−0.212312	+	1.34049i	−0.831624	+	0.555340i	$0.812588\pi$
$504$		0			0
$505$	1.35035	−	0.475134i	0.0600899	−	0.0211432i
$506$	3.60279	+	1.58949i	0.160163	+	0.0706615i
$507$		0			0
$508$	−4.87604	−	9.56978i	−0.216339	−	0.424590i
$509$	2.38516	+	3.28290i	0.105721	+	0.145512i	0.858599	−	0.512648i	$-0.171335\pi$
$509$	2.38516	+	3.28290i	0.105721	+	0.145512i	−0.752879	+	0.658159i	$0.771335\pi$
$510$		0			0
$511$	−1.71429	−	5.27604i	−0.0758357	−	0.233398i
$512$	6.61940	−	12.9913i	0.292539	−	0.574140i
$513$		0			0
$514$	−10.7817	+	7.83334i	−0.475559	+	0.345514i
$515$	−3.34468	−	3.18678i	−0.147384	−	0.140426i
$516$		0			0
$517$	−3.45108	+	13.0560i	−0.151778	+	0.574202i
$518$	−0.388701	−	0.388701i	−0.0170786	−	0.0170786i
$519$		0			0
$520$	−12.5235	+	18.1436i	−0.549193	+	0.795652i
$521$	14.1602	+	10.2880i	0.620370	+	0.450725i	0.853051	−	0.521828i	$-0.174750\pi$
$521$	14.1602	+	10.2880i	0.620370	+	0.450725i	−0.232681	+	0.972553i	$0.574750\pi$
$522$		0			0
$523$	15.4819	+	7.88844i	0.676978	+	0.344938i	0.758444	−	0.651739i	$-0.225960\pi$
$523$	15.4819	+	7.88844i	0.676978	+	0.344938i	−0.0814656	+	0.996676i	$0.525960\pi$
$524$	−5.83821	−	4.24171i	−0.255044	−	0.185300i
$525$		0			0
$526$	−6.21710	+	19.1343i	−0.271078	+	0.834293i
$527$	6.59808	+	6.59808i	0.287417	+	0.287417i
$528$		0			0
$529$		−	21.7086i		−	0.943854i
$530$	0.397767	+	16.4534i	0.0172779	+	0.714691i
$531$		0			0
$532$	0.767831	−	0.121612i	0.0332897	−	0.00527257i
$533$	13.1785	−	25.8642i	0.570823	−	1.12030i
$534$		0			0
$535$	−17.5830	+	9.50110i	−0.760180	+	0.410769i
$536$	−6.62435	−	9.11763i	−0.286128	−	0.393822i
$537$		0			0
$538$	12.8520	−	12.8520i	0.554090	−	0.554090i
$539$	21.7126	−	4.69193i	0.935226	−	0.202096i
$540$		0			0
$541$	−35.0319	−	11.3826i	−1.50614	−	0.489375i	−0.564339	−	0.825543i	$-0.690869\pi$
$541$	−35.0319	−	11.3826i	−1.50614	−	0.489375i	−0.941802	+	0.336169i	$0.890869\pi$
$542$	−5.19305	+	32.7876i	−0.223061	+	1.40835i
$543$		0			0
$544$	−25.0879	+	8.15154i	−1.07563	+	0.349495i
$545$	7.96050	−	6.08293i	0.340990	−	0.260564i
$546$		0			0
$547$	−8.55820	−	1.35549i	−0.365922	−	0.0579564i	−0.0292340	−	0.999573i	$-0.509307\pi$
$547$	−8.55820	−	1.35549i	−0.365922	−	0.0579564i	−0.336688	+	0.941616i	$0.609307\pi$
$548$	3.62180	−	1.84540i	0.154716	−	0.0788316i
$549$		0			0
$550$	−1.80009	−	17.2325i	−0.0767562	−	0.734794i
$551$	−6.62577			−0.282267
$552$		0			0
$553$	−2.26256	−	0.358354i	−0.0962136	−	0.0152387i
$554$	4.45833	−	6.13636i	0.189416	−	0.260709i
$555$		0			0
$556$	−19.5384	+	6.34840i	−0.828611	+	0.269232i
$557$	1.31040	+	8.27356i	0.0555236	+	0.350562i	0.999772	+	0.0213297i	$0.00678998\pi$
$557$	1.31040	+	8.27356i	0.0555236	+	0.350562i	−0.944249	+	0.329232i	$0.893210\pi$
$558$		0			0
$559$	−11.1417	−	3.62017i	−0.471245	−	0.153117i
$560$	−0.721868	+	1.50563i	−0.0305045	+	0.0636247i
$561$		0			0
$562$	4.09614	−	4.09614i	0.172785	−	0.172785i
$563$	−13.6849	−	26.8581i	−0.576748	−	1.13193i	−0.976542	−	0.215327i	$-0.930918\pi$
$563$	−13.6849	−	26.8581i	−0.576748	−	1.13193i	0.399794	−	0.916605i	$-0.369082\pi$
$564$		0			0
$565$	2.82444	−	1.52621i	0.118825	−	0.0642079i
$566$	−4.46212	−	13.7330i	−0.187557	−	0.577241i
$567$		0			0
$568$	20.5709	−	3.25812i	0.863137	−	0.136708i
$569$	−21.9297	+	15.9329i	−0.919341	+	0.667940i	−0.943360	−	0.331771i	$-0.892354\pi$
$569$	−21.9297	+	15.9329i	−0.919341	+	0.667940i	0.0240192	+	0.999711i	$0.492354\pi$
$570$		0			0
$571$		−	6.30511i		−	0.263861i	−0.991259	−	0.131930i	$-0.957883\pi$
$571$		−	6.30511i		−	0.263861i	0.991259	−	0.131930i	$-0.0421175\pi$
$572$	−9.45049	−	2.49804i	−0.395145	−	0.104448i
$573$		0			0
$574$	1.58820	−	4.88797i	0.0662902	−	0.204020i
$575$	4.93205	−	2.82116i	0.205681	−	0.117650i
$576$		0			0
$577$	21.1889	+	10.7963i	0.882107	+	0.449456i	0.835521	−	0.549458i	$-0.185166\pi$
$577$	21.1889	+	10.7963i	0.882107	+	0.449456i	0.0465858	+	0.998914i	$0.485166\pi$
$578$	−14.0250	−	7.14608i	−0.583362	−	0.297238i
$579$		0			0
$580$	−4.91161	+	7.11577i	−0.203944	+	0.295466i
$581$	1.92496	−	5.92442i	0.0798608	−	0.245786i
$582$		0			0
$583$	−21.7842	+	8.44680i	−0.902211	+	0.349831i
$584$		−	30.6593i		−	1.26869i
$585$		0			0
$586$	5.74735	−	4.17569i	0.237421	−	0.172496i
$587$	−10.7795	+	1.70730i	−0.444917	+	0.0704680i	−0.374874	−	0.927076i	$-0.622314\pi$
$587$	−10.7795	+	1.70730i	−0.444917	+	0.0704680i	−0.0700437	+	0.997544i	$0.522314\pi$
$588$		0			0
$589$	−0.792596	−	2.43936i	−0.0326584	−	0.100512i
$590$	−7.51582	−	13.9090i	−0.309422	−	0.572624i
$591$		0			0
$592$	−0.589999	−	1.15794i	−0.0242488	−	0.0475910i
$593$	−26.5198	+	26.5198i	−1.08904	+	1.08904i	−0.0934112	+	0.995628i	$0.529777\pi$
$593$	−26.5198	+	26.5198i	−1.08904	+	1.08904i	−0.995628	+	0.0934112i	$0.970223\pi$
$594$		0			0
$595$	6.56727	−	2.31075i	0.269232	−	0.0947316i
$596$	−12.7732	−	4.15028i	−0.523213	−	0.170002i
$597$		0			0
$598$	0.602634	+	3.80488i	0.0246435	+	0.155593i
$599$	−42.0288	+	13.6560i	−1.71725	+	0.557968i	−0.991513	−	0.130006i	$-0.958500\pi$
$599$	−42.0288	+	13.6560i	−1.71725	+	0.557968i	−0.725735	+	0.687974i	$0.758500\pi$
$600$		0			0
$601$	21.8365	−	30.0554i	0.890730	−	1.22599i	−0.0826012	−	0.996583i	$-0.526323\pi$
$601$	21.8365	−	30.0554i	0.890730	−	1.22599i	0.973332	−	0.229403i	$-0.0736772\pi$
$602$	−2.04866	−	0.324476i	−0.0834972	−	0.0132247i
$603$		0			0
$604$	−6.03642			−0.245618
$605$	22.1501	−	10.6946i	0.900529	−	0.434796i
$606$		0			0
$607$	40.2449	−	20.5058i	1.63349	−	0.832306i	0.635295	−	0.772269i	$-0.280878\pi$
$607$	40.2449	−	20.5058i	1.63349	−	0.832306i	0.998196	−	0.0600364i	$-0.0191217\pi$
$608$	7.16167	+	1.13430i	0.290444	+	0.0460018i
$609$		0			0
$610$	−2.84865	+	21.3067i	−0.115338	+	0.862684i
$611$	−12.5645	+	4.08245i	−0.508305	+	0.165158i
$612$		0			0
$613$	2.20539	−	13.9243i	0.0890749	−	0.562397i	−0.902276	−	0.431159i	$-0.858105\pi$
$613$	2.20539	−	13.9243i	0.0890749	−	0.562397i	0.991351	−	0.131238i	$-0.0418952\pi$
$614$	7.78811	+	2.53051i	0.314302	+	0.102123i
$615$		0			0
$616$	−5.51285	−	0.560586i	−0.222119	−	0.0225867i
$617$	17.9495	−	17.9495i	0.722618	−	0.722618i	−0.246520	−	0.969138i	$-0.579287\pi$
$617$	17.9495	−	17.9495i	0.722618	−	0.722618i	0.969138	+	0.246520i	$0.0792870\pi$
$618$		0			0
$619$	15.8217	+	21.7768i	0.635930	+	0.875282i	0.998390	−	0.0567171i	$-0.0180633\pi$
$619$	15.8217	+	21.7768i	0.635930	+	0.875282i	−0.362461	+	0.931999i	$0.618063\pi$
$620$	−3.20730	−	0.957060i	−0.128808	−	0.0384365i
$621$		0			0
$622$	7.86961	−	15.4450i	0.315543	−	0.619287i
$623$	1.98140	−	0.313823i	0.0793831	−	0.0125730i
$624$		0			0
$625$	−21.5495	−	12.6736i	−0.861979	−	0.506944i
$626$			9.95017i			0.397689i
$627$		0			0
$628$	1.03690	+	1.03690i	0.0413770	+	0.0413770i
$629$	−1.67444	+	5.15339i	−0.0667642	+	0.205479i
$630$		0			0
$631$	4.56785	+	3.31874i	0.181843	+	0.132117i	0.674983	−	0.737833i	$-0.264151\pi$
$631$	4.56785	+	3.31874i	0.181843	+	0.132117i	−0.493140	+	0.869950i	$0.664151\pi$
$632$	−11.2803	−	5.74761i	−0.448707	−	0.228628i
$633$		0			0
$634$	−20.3857	−	14.8110i	−0.809618	−	0.588222i
$635$	4.76585	+	26.0057i	0.189127	+	1.03201i
$636$		0			0
$637$	15.3663	+	15.3663i	0.608835	+	0.608835i
$638$	14.2610	+	3.76958i	0.564597	+	0.149239i
$639$		0			0
$640$	2.14962	−	2.25613i	0.0849711	−	0.0891813i
$641$	27.9714	−	20.3224i	1.10480	−	0.802686i	0.122965	−	0.992411i	$-0.460760\pi$
$641$	27.9714	−	20.3224i	1.10480	−	0.802686i	0.981837	+	0.189725i	$0.0607597\pi$
$642$		0			0
$643$	−8.79786	+	17.2668i	−0.346954	+	0.680935i	−0.996869	−	0.0790717i	$-0.974804\pi$
$643$	−8.79786	+	17.2668i	−0.346954	+	0.680935i	0.649915	+	0.760007i	$0.274804\pi$
$644$	−0.175387	−	0.539784i	−0.00691120	−	0.0212705i
$645$		0			0
$646$	5.41291	+	7.45023i	0.212968	+	0.293126i
$647$	−9.41683	−	18.4816i	−0.370214	−	0.726586i	0.628472	−	0.777832i	$-0.283681\pi$
$647$	−9.41683	−	18.4816i	−0.370214	−	0.726586i	−0.998686	+	0.0512465i	$0.983681\pi$
$648$		0			0
$649$	14.9614	−	16.7298i	0.587288	−	0.656700i
$650$	13.2153	−	10.6139i	0.518347	−	0.416311i
$651$		0			0
$652$	1.43941	−	9.08810i	0.0563718	−	0.355917i
$653$	5.13133	+	32.3979i	0.200804	+	1.26783i	0.857820	+	0.513951i	$0.171819\pi$
$653$	5.13133	+	32.3979i	0.200804	+	1.26783i	−0.657015	+	0.753877i	$0.728181\pi$
$654$		0			0
$655$	10.7858	+	14.1149i	0.421435	+	0.551516i
$656$	7.14192	−	9.83001i	0.278845	−	0.383797i
$657$		0			0
$658$	−2.08413	+	1.06191i	−0.0812477	+	0.0413978i
$659$	3.99211			0.155511			0.0777553	−	0.996972i	$-0.475225\pi$
$659$	3.99211			0.155511			0.0777553	+	0.996972i	$0.475225\pi$
$660$		0			0
$661$	42.4892			1.65264			0.826318	−	0.563204i	$-0.190431\pi$
$661$	42.4892			1.65264			0.826318	+	0.563204i	$0.190431\pi$
$662$	11.6964	−	5.95960i	0.454592	−	0.231626i
$663$		0			0
$664$	20.2358	−	27.8521i	0.785299	−	1.08087i
$665$	−1.89679	−	0.253596i	−0.0735545	−	0.00983403i
$666$		0			0
$667$	0.756723	+	4.77776i	0.0293004	+	0.184996i
$668$	−2.03459	+	12.8459i	−0.0787206	+	0.497022i
$669$		0			0
$670$	2.87596	+	8.17361i	0.111108	+	0.315774i
$671$	−29.8282	+	6.44567i	−1.15151	+	0.248832i
$672$		0			0
$673$	0.287000	+	0.563270i	0.0110631	+	0.0217125i	0.896472	−	0.443101i	$-0.146122\pi$
$673$	0.287000	+	0.563270i	0.0110631	+	0.0217125i	−0.885409	+	0.464813i	$0.846122\pi$
$674$	10.1180	+	13.9263i	0.389731	+	0.536419i
$675$		0			0
$676$	0.694078	+	2.13615i	0.0266953	+	0.0821597i
$677$	−2.17477	+	4.26823i	−0.0835833	+	0.164041i	−0.929015	−	0.370042i	$-0.879343\pi$
$677$	−2.17477	+	4.26823i	−0.0835833	+	0.164041i	0.845432	+	0.534084i	$0.179343\pi$
$678$		0			0
$679$	7.41436	−	5.38685i	0.284537	−	0.206728i
$680$	38.4649	−	0.929901i	1.47506	−	0.0356601i
$681$		0			0
$682$	0.318123	+	5.70128i	0.0121816	+	0.218313i
$683$	6.48359	+	6.48359i	0.248088	+	0.248088i	0.820186	−	0.572098i	$-0.193870\pi$
$683$	6.48359	+	6.48359i	0.248088	+	0.248088i	−0.572098	+	0.820186i	$0.693870\pi$
$684$		0			0
$685$	−9.84220	+	1.80370i	−0.376051	+	0.0689157i
$686$	6.36603	+	4.62519i	0.243056	+	0.176591i
$687$		0			0
$688$	−4.36923	−	2.22623i	−0.166575	−	0.0848744i
$689$	−18.4918	−	13.4350i	−0.704480	−	0.511834i
$690$		0			0
$691$	9.76613	−	30.0571i	0.371521	−	1.14342i	−0.574275	−	0.818663i	$-0.694716\pi$
$691$	9.76613	−	30.0571i	0.371521	−	1.14342i	0.945796	−	0.324762i	$-0.105284\pi$
$692$	10.6427	+	10.6427i	0.404573	+	0.404573i
$693$		0			0
$694$			14.8780i			0.564762i
$695$	50.5564	−	1.22222i	1.91771	−	0.0463614i
$696$		0			0
$697$	−50.0378	+	7.92520i	−1.89532	+	0.300189i
$698$	−7.88044	+	15.4662i	−0.298279	+	0.585405i
$699$		0			0
$700$	−1.67842	+	1.84908i	−0.0634384	+	0.0698886i
$701$	−9.60255	−	13.2168i	−0.362683	−	0.499191i	0.588211	−	0.808708i	$-0.299833\pi$
$701$	−9.60255	−	13.2168i	−0.362683	−	0.499191i	−0.950894	+	0.309517i	$0.899833\pi$
$702$		0			0
$703$	1.05319	−	1.05319i	0.0397220	−	0.0397220i
$704$	−23.0113	−	10.1522i	−0.867271	−	0.382626i
$705$		0			0
$706$	−10.9341	−	3.55271i	−0.411511	−	0.133708i
$707$	−0.0550638	+	0.347659i	−0.00207089	+	0.0130751i
$708$		0			0
$709$	18.1917	−	5.91083i	0.683202	−	0.221986i	0.0532052	−	0.998584i	$-0.483056\pi$
$709$	18.1917	−	5.91083i	0.683202	−	0.221986i	0.629997	+	0.776598i	$0.283056\pi$
$710$	−15.8716	−	2.12199i	−0.595652	−	0.0796370i
$711$		0			0
$712$	10.9505	+	1.73438i	0.410386	+	0.0649988i
$713$	−1.66847	+	0.850128i	−0.0624847	+	0.0318376i
$714$		0			0
$715$	20.5339	+	12.5445i	0.767924	+	0.469137i
$716$	18.1551			0.678488
$717$		0			0
$718$	13.6008	+	2.15415i	0.507577	+	0.0803923i
$719$	8.94663	−	12.3140i	0.333653	−	0.459234i	−0.608921	−	0.793231i	$-0.708397\pi$
$719$	8.94663	−	12.3140i	0.333653	−	0.459234i	0.942574	+	0.333997i	$0.108397\pi$
$720$		0			0
$721$	1.08036	−	0.351031i	0.0402348	−	0.0130731i
$722$	2.70945	+	17.1068i	0.100835	+	0.636650i
$723$		0			0
$724$	23.2174	+	7.54381i	0.862870	+	0.280363i
$725$	16.5944	−	13.3278i	0.616299	−	0.494982i
$726$		0			0
$727$	5.98783	−	5.98783i	0.222076	−	0.222076i	−0.587296	−	0.809372i	$-0.699808\pi$
$727$	5.98783	−	5.98783i	0.222076	−	0.222076i	0.809372	+	0.587296i	$0.199808\pi$
$728$	−2.46105	−	4.83008i	−0.0912125	−	0.179015i
$729$		0			0
$730$	−6.74023	+	22.5879i	−0.249467	+	0.836015i
$731$	6.31812	+	19.4452i	0.233684	+	0.719206i
$732$		0			0
$733$	28.8912	−	4.57591i	1.06712	−	0.169015i	0.401915	−	0.915677i	$-0.368345\pi$
$733$	28.8912	−	4.57591i	1.06712	−	0.169015i	0.665204	+	0.746662i	$0.268345\pi$
$734$	23.5005	−	17.0741i	0.867420	−	0.630217i
$735$		0			0
$736$		−	5.29374i		−	0.195130i
$737$	−9.53329	+	7.77342i	−0.351163	+	0.286338i
$738$		0			0
$739$	−13.4702	+	41.4569i	−0.495508	+	1.52502i	0.320656	+	0.947196i	$0.396097\pi$
$739$	−13.4702	+	41.4569i	−0.495508	+	1.52502i	−0.816164	+	0.577821i	$0.803903\pi$
$740$	−0.350360	−	1.91180i	−0.0128795	−	0.0702793i
$741$		0			0
$742$	−3.60583	−	1.83726i	−0.132374	−	0.0674480i
$743$	40.9991	+	20.8901i	1.50411	+	0.766384i	0.995513	−	0.0946199i	$-0.0301636\pi$
$743$	40.9991	+	20.8901i	1.50411	+	0.766384i	0.508599	+	0.861004i	$0.330164\pi$
$744$		0			0
$745$	27.2088	+	18.7807i	0.996853	+	0.688071i
$746$	−2.74943	+	8.46188i	−0.100664	+	0.309811i
$747$		0			0
$748$	6.16757	+	15.9061i	0.225509	+	0.581585i
$749$		−	4.91432i		−	0.179565i
$750$		0			0
$751$	2.65295	−	1.92748i	0.0968077	−	0.0703349i	−0.538328	−	0.842735i	$-0.680944\pi$
$751$	2.65295	−	1.92748i	0.0968077	−	0.0703349i	0.635136	+	0.772400i	$0.280944\pi$
$752$	−5.46181	+	0.865065i	−0.199172	+	0.0315457i
$753$		0			0
$754$	4.45923	+	13.7241i	0.162396	+	0.499802i
$755$	14.2390	+	4.24891i	0.518209	+	0.154634i
$756$		0			0
$757$	8.47970	+	16.6423i	0.308200	+	0.604876i	0.992207	−	0.124599i	$-0.0397644\pi$
$757$	8.47970	+	16.6423i	0.308200	+	0.604876i	−0.684007	+	0.729475i	$0.739764\pi$
$758$	3.21752	−	3.21752i	0.116866	−	0.116866i
$759$		0			0
$760$	−9.53672	−	4.57233i	−0.345933	−	0.165856i
$761$	3.30619	+	1.07424i	0.119849	+	0.0389413i	0.368328	−	0.929696i	$-0.379931\pi$
$761$	3.30619	+	1.07424i	0.119849	+	0.0389413i	−0.248478	+	0.968637i	$0.579931\pi$
$762$		0			0
$763$	0.385371	+	2.43314i	0.0139514	+	0.0880855i
$764$	−11.1795	+	3.63244i	−0.404460	+	0.131417i
$765$		0			0
$766$	4.16642	−	5.73459i	0.150539	−	0.207199i
$767$	21.6861	+	3.43474i	0.783040	+	0.124021i
$768$		0			0
$769$	−40.6658			−1.46645			−0.733223	−	0.679989i	$-0.761985\pi$
$769$	−40.6658			−1.46645			−0.733223	+	0.679989i	$0.761985\pi$
$770$	3.93828	+	1.62496i	0.141926	+	0.0585596i
$771$		0			0
$772$	−6.06854	+	3.09208i	−0.218412	+	0.111286i
$773$	42.5790	+	6.74385i	1.53146	+	0.242559i	0.864538	−	0.502568i	$-0.167611\pi$
$773$	42.5790	+	6.74385i	1.53146	+	0.242559i	0.666922	+	0.745128i	$0.267611\pi$
$774$		0			0
$775$	6.89186	+	4.51511i	0.247563	+	0.162187i
$776$	48.1707	−	15.6516i	1.72923	−	0.561861i
$777$		0			0
$778$	−4.02440	+	25.4091i	−0.144282	+	0.910960i
$779$	13.2441	+	4.30326i	0.474518	+	0.154180i
$780$		0			0
$781$	−4.80146	−	22.2194i	−0.171810	−	0.795074i
$782$	4.75407	−	4.75407i	0.170005	−	0.170005i
$783$		0			0
$784$	5.34664	+	7.35902i	0.190951	+	0.262822i
$785$	−1.71604	−	3.17575i	−0.0612481	−	0.113347i
$786$		0			0
$787$	11.9320	−	23.4179i	0.425331	−	0.834758i	−0.574537	−	0.818479i	$-0.694818\pi$
$787$	11.9320	−	23.4179i	0.425331	−	0.834758i	0.999867	−	0.0162795i	$-0.00518216\pi$
$788$	3.46507	−	0.548813i	0.123438	−	0.0195506i
$789$		0			0
$790$	7.04706	+	6.71437i	0.250723	+	0.238887i
$791$			0.789410i			0.0280682i
$792$		0			0
$793$	−21.1099	−	21.1099i	−0.749635	−	0.749635i
$794$	−9.49161	+	29.2122i	−0.336845	+	1.03670i
$795$		0			0
$796$	9.10047	+	6.61188i	0.322558	+	0.234352i
$797$	39.7780	+	20.2679i	1.40901	+	0.717925i	0.982448	−	0.186534i	$-0.0597255\pi$
$797$	39.7780	+	20.2679i	1.40901	+	0.717925i	0.426560	+	0.904459i	$0.359725\pi$
$798$		0			0
$799$	18.6533	+	13.5524i	0.659907	+	0.479450i
$800$	−20.2182	+	11.5649i	−0.714821	+	0.408881i
$801$		0			0
$802$	−18.2958	−	18.2958i	−0.646047	−	0.646047i
$803$	−33.4116	+	1.86432i	−1.17907	+	0.0657902i
$804$		0			0
$805$	0.0337661	+	1.39672i	0.00119010	+	0.0492278i
$806$	−4.51927	+	3.28344i	−0.159185	+	0.115654i
$807$		0			0
$808$	−0.883165	+	1.73331i	−0.0310696	+	0.0609776i
$809$	−17.0236	−	52.3932i	−0.598517	−	1.84205i	−0.536376	−	0.843979i	$-0.680207\pi$
$809$	−17.0236	−	52.3932i	−0.598517	−	1.84205i	−0.0621416	−	0.998067i	$-0.519793\pi$
$810$		0			0
$811$	7.83988	+	10.7907i	0.275295	+	0.378912i	0.924168	−	0.381985i	$-0.124759\pi$
$811$	7.83988	+	10.7907i	0.275295	+	0.378912i	−0.648873	+	0.760897i	$0.724759\pi$
$812$	−0.965200	−	1.89431i	−0.0338719	−	0.0664773i
$813$		0			0
$814$	−2.86603	+	1.66765i	−0.100454	+	0.0584510i
$815$	−9.79228	+	20.4242i	−0.343008	+	0.715429i
$816$		0			0
$817$	0.879175	−	5.55089i	0.0307584	−	0.194201i
$818$	1.63669	+	10.3337i	0.0572256	+	0.361309i
$819$		0			0
$820$	14.4392	−	11.0335i	0.504238	−	0.385308i
$821$	4.26813	−	5.87458i	0.148959	−	0.205024i	−0.728016	−	0.685560i	$-0.759558\pi$
$821$	4.26813	−	5.87458i	0.148959	−	0.205024i	0.876975	+	0.480535i	$0.159558\pi$
$822$		0			0
$823$	−42.8940	+	21.8556i	−1.49519	+	0.761837i	−0.994594	−	0.103844i	$-0.966886\pi$
$823$	−42.8940	+	21.8556i	−1.49519	+	0.761837i	−0.500596	+	0.865681i	$0.666886\pi$
$824$	6.27805			0.218706
$825$		0			0
$826$	3.88746			0.135262
$827$	32.9554	−	16.7916i	1.14597	−	0.583901i	0.225318	−	0.974285i	$-0.427658\pi$
$827$	32.9554	−	16.7916i	1.14597	−	0.583901i	0.920652	+	0.390384i	$0.127658\pi$
$828$		0			0
$829$	12.5416	−	17.2620i	0.435586	−	0.599533i	−0.533638	−	0.845713i	$-0.679175\pi$
$829$	12.5416	−	17.2620i	0.435586	−	0.599533i	0.969224	+	0.246180i	$0.0791754\pi$
$830$	−21.0315	+	16.0710i	−0.730015	+	0.557833i
$831$		0			0
$832$	−3.84907	−	24.3021i	−0.133442	−	0.842523i
$833$	5.93303	−	37.4597i	0.205567	−	1.29790i
$834$		0			0
$835$	13.8412	−	28.8693i	0.478995	−	0.999064i
$836$	0.474404	−	4.66533i	0.0164076	−	0.161354i
$837$		0			0
$838$	3.63218	+	7.12855i	0.125471	+	0.246252i
$839$	−12.5857	−	17.3228i	−0.434507	−	0.598048i	0.534473	−	0.845186i	$-0.320510\pi$
$839$	−12.5857	−	17.3228i	−0.434507	−	0.598048i	−0.968980	+	0.247137i	$0.920510\pi$
$840$		0			0
$841$	−3.36207	−	10.3474i	−0.115933	−	0.356806i
$842$	10.2799	−	20.1754i	0.354268	−	0.695291i
$843$		0			0
$844$	−9.96260	+	7.23825i	−0.342927	+	0.249151i
$845$	−0.133626	−	5.52739i	−0.00459689	−	0.190148i
$846$		0			0
$847$	−0.275687	+	6.04181i	−0.00947272	+	0.207599i
$848$	−6.76524	−	6.76524i	−0.232319	−	0.232319i
$849$		0			0
$850$	−28.5429	−	7.77113i	−0.979015	−	0.266548i
$851$	−0.879730	−	0.639161i	−0.0301567	−	0.0219102i
$852$		0			0
$853$	26.1306	+	13.3142i	0.894696	+	0.455871i	0.839971	−	0.542631i	$-0.182572\pi$
$853$	26.1306	+	13.3142i	0.894696	+	0.455871i	0.0547251	+	0.998501i	$0.482572\pi$
$854$	−4.27625	−	3.10688i	−0.146330	−	0.106315i
$855$		0			0
$856$	8.39280	−	25.8304i	0.286860	−	0.882864i
$857$	14.3622	+	14.3622i	0.490604	+	0.490604i	0.908496	−	0.417893i	$-0.137231\pi$
$857$	14.3622	+	14.3622i	0.490604	+	0.490604i	−0.417893	+	0.908496i	$0.637231\pi$
$858$		0			0
$859$		−	21.7404i		−	0.741772i	−0.928678	−	0.370886i	$-0.879054\pi$
$859$		−	21.7404i		−	0.741772i	0.928678	−	0.370886i	$-0.120946\pi$
$860$	−5.30967	−	5.05901i	−0.181058	−	0.172511i
$861$		0			0
$862$	−29.3895	+	4.65484i	−1.00101	+	0.158544i
$863$	11.7043	−	22.9709i	0.398417	−	0.781938i	−0.601438	−	0.798919i	$-0.705405\pi$
$863$	11.7043	−	22.9709i	0.398417	−	0.781938i	0.999856	+	0.0169810i	$0.00540549\pi$
$864$		0			0
$865$	−17.6132	−	32.5955i	−0.598867	−	1.10828i
$866$	7.65908	+	10.5418i	0.260266	+	0.358226i
$867$		0			0
$868$	0.581954	−	0.581954i	0.0197528	−	0.0197528i
$869$	−5.57763	+	12.6424i	−0.189208	+	0.428865i
$870$		0			0
$871$	−11.4447	−	3.71860i	−0.387788	−	0.126000i
$872$	−2.12981	+	13.4471i	−0.0721244	+	0.455375i
$873$		0			0
$874$	−1.75761	+	0.571084i	−0.0594522	+	0.0193172i
$875$	5.26066	−	3.18028i	0.177843	−	0.107513i
$876$		0			0
$877$	45.4978	+	7.20614i	1.53635	+	0.243334i	0.866506	−	0.499167i	$-0.166361\pi$
$877$	45.4978	+	7.20614i	1.53635	+	0.243334i	0.669845	+	0.742501i	$0.266361\pi$
$878$	−15.7464	+	8.02321i	−0.531417	+	0.270770i
$879$		0			0
$880$	7.66782	+	6.53077i	0.258482	+	0.220152i
$881$	−3.73181			−0.125728			−0.0628640	−	0.998022i	$-0.520023\pi$
$881$	−3.73181			−0.125728			−0.0628640	+	0.998022i	$0.520023\pi$
$882$		0			0
$883$	−24.7590	−	3.92144i	−0.833207	−	0.131967i	−0.274766	−	0.961511i	$-0.588600\pi$
$883$	−24.7590	−	3.92144i	−0.833207	−	0.131967i	−0.558441	+	0.829544i	$0.688600\pi$
$884$	−9.80982	+	13.5021i	−0.329940	+	0.454123i
$885$		0			0
$886$	−10.9920	+	3.57153i	−0.369285	+	0.119988i
$887$	−2.22501	−	14.0482i	−0.0747087	−	0.471692i	−0.996471	−	0.0839369i	$-0.973251\pi$
$887$	−2.22501	−	14.0482i	−0.0747087	−	0.471692i	0.921762	−	0.387755i	$-0.126749\pi$
$888$		0			0
$889$	−6.18287	−	2.00893i	−0.207367	−	0.0673775i
$890$	−7.68633	−	3.68517i	−0.257646	−	0.123527i
$891$		0			0
$892$	3.36602	−	3.36602i	0.112703	−	0.112703i
$893$	−2.87728	−	5.64698i	−0.0962845	−	0.188969i
$894$		0			0
$895$	−42.8250	−	12.7790i	−1.43148	−	0.427155i
$896$	0.236785	+	0.728751i	0.00791045	+	0.0243458i
$897$		0			0
$898$	−4.66306	+	0.738556i	−0.155608	+	0.0246459i
$899$	−5.67482	+	4.12300i	−0.189266	+	0.137510i
$900$		0			0
$901$			39.8915i			1.32898i
$902$	−26.0576	−	16.7970i	−0.867623	−	0.559279i
$903$		0			0
$904$	−1.34817	+	4.14925i	−0.0448396	+	0.138002i
$905$	−49.4564	−	34.1369i	−1.64399	−	1.13475i
$906$		0			0
$907$	43.8334	+	22.3342i	1.45547	+	0.741597i	0.989679	−	0.143301i	$-0.0457717\pi$
$907$	43.8334	+	22.3342i	1.45547	+	0.741597i	0.465786	+	0.884897i	$0.345772\pi$
$908$	−12.1980	−	6.21518i	−0.404804	−	0.206258i
$909$		0			0
$910$	0.751288	+	4.09954i	0.0249049	+	0.135898i
$911$	−13.4007	+	41.2430i	−0.443984	+	1.36644i	0.439610	+	0.898189i	$0.355117\pi$
$911$	−13.4007	+	41.2430i	−0.443984	+	1.36644i	−0.883594	+	0.468254i	$0.844883\pi$
$912$		0			0
$913$	−31.5828	−	20.3587i	−1.04524	−	0.673773i
$914$			34.0883i			1.12754i
$915$		0			0
$916$	−10.9258	+	7.93804i	−0.360998	+	0.262280i
$917$	−4.31425	+	0.683310i	−0.142469	+	0.0225649i
$918$		0			0
$919$	7.23415	+	22.2644i	0.238633	+	0.734435i	0.996619	+	0.0821649i	$0.0261834\pi$
$919$	7.23415	+	22.2644i	0.238633	+	0.734435i	−0.757986	+	0.652271i	$0.773817\pi$
$920$	−2.20787	+	7.39902i	−0.0727913	+	0.243938i
$921$		0			0
$922$	−11.1126	−	21.8098i	−0.365975	−	0.718267i
$923$	15.7250	−	15.7250i	0.517596	−	0.517596i
$924$		0			0
$925$	−0.519235	+	4.75625i	−0.0170723	+	0.156385i
$926$	−41.0511	−	13.3383i	−1.34902	−	0.438324i
$927$		0			0
$928$	−3.10207	−	19.5857i	−0.101830	−	0.642932i
$929$	12.0399	−	3.91200i	0.395017	−	0.128349i	−0.104772	−	0.994496i	$-0.533411\pi$
$929$	12.0399	−	3.91200i	0.395017	−	0.128349i	0.499788	+	0.866148i	$0.333411\pi$
$930$		0			0
$931$	−6.12773	+	8.43410i	−0.200828	+	0.276416i
$932$	4.96954	+	0.787098i	0.162783	+	0.0257823i
$933$		0			0
$934$	29.6798			0.971153
$935$	−3.35233	−	41.8613i	−0.109633	−	1.36901i
$936$		0			0
$937$	−23.6950	+	12.0732i	−0.774082	+	0.394414i	−0.795962	−	0.605346i	$-0.793035\pi$
$937$	−23.6950	+	12.0732i	−0.774082	+	0.394414i	0.0218805	+	0.999761i	$0.493035\pi$
$938$	−2.10436	−	0.333298i	−0.0687099	−	0.0108826i
$939$		0			0
$940$	−8.19749	−	1.09598i	−0.267373	−	0.0357470i
$941$	−22.7044	+	7.37710i	−0.740141	+	0.240487i	−0.654734	−	0.755860i	$-0.727219\pi$
$941$	−22.7044	+	7.37710i	−0.740141	+	0.240487i	−0.0854076	+	0.996346i	$0.527219\pi$
$942$		0			0
$943$	1.59043	−	10.0416i	0.0517916	−	0.327000i
$944$	8.74069	+	2.84002i	0.284485	+	0.0924349i
$945$		0			0
$946$	−5.05034	+	11.4473i	−0.164201	+	0.372182i
$947$	−38.6416	+	38.6416i	−1.25568	+	1.25568i	−0.302548	+	0.953134i	$0.597837\pi$
$947$	−38.6416	+	38.6416i	−1.25568	+	1.25568i	−0.953134	+	0.302548i	$0.902163\pi$
$948$		0			0
$949$	−19.2422	−	26.4846i	−0.624627	−	0.859725i
$950$	6.02087	+	5.46518i	0.195343	+	0.177314i
$951$		0			0
$952$	−4.29516	+	8.42973i	−0.139207	+	0.273209i
$953$	15.8000	−	2.50247i	0.511811	−	0.0810628i	0.104813	−	0.994492i	$-0.466576\pi$
$953$	15.8000	−	2.50247i	0.511811	−	0.0810628i	0.406998	+	0.913429i	$0.366576\pi$
$954$		0			0
$955$	28.9275	−	0.699331i	0.936071	−	0.0226298i
$956$			22.4544i			0.726229i
$957$		0			0
$958$	23.1798	+	23.1798i	0.748904	+	0.748904i
$959$	0.760307	−	2.33998i	0.0245516	−	0.0755620i
$960$		0			0
$961$	22.8828	+	16.6253i	0.738153	+	0.536300i
$962$	−2.89032	−	1.47269i	−0.0931875	−	0.0474814i
$963$		0			0
$964$	3.81921	+	2.77482i	0.123009	+	0.0893710i
$965$	16.4912	−	3.02220i	0.530870	−	0.0972880i
$966$		0			0
$967$	−37.1649	−	37.1649i	−1.19514	−	1.19514i	−0.975604	−	0.219539i	$-0.929545\pi$
$967$	−37.1649	−	37.1649i	−1.19514	−	1.19514i	−0.219539	−	0.975604i	$-0.570455\pi$
$968$	−11.7674	+	31.2858i	−0.378219	+	1.00556i
$969$		0			0
$970$	−38.9301	+	0.941147i	−1.24997	+	0.0302184i
$971$	17.7106	−	12.8675i	0.568359	−	0.412937i	−0.266149	−	0.963932i	$-0.585751\pi$
$971$	17.7106	−	12.8675i	0.568359	−	0.412937i	0.834509	+	0.550994i	$0.185751\pi$
$972$		0			0
$973$	−5.64535	+	11.0796i	−0.180982	+	0.355197i
$974$	2.21906	+	6.82956i	0.0711033	+	0.218833i
$975$		0			0
$976$	−7.34510	−	10.1097i	−0.235111	−	0.323602i
$977$	0.0465411	+	0.0913420i	0.00148898	+	0.00292229i	0.891750	−	0.452529i	$-0.149478\pi$
$977$	0.0465411	+	0.0913420i	0.00148898	+	0.00292229i	−0.890261	+	0.455451i	$0.849478\pi$
$978$		0			0
$979$	1.22421	−	12.0389i	0.0391258	−	0.384766i
$980$	4.51541	+	12.8330i	0.144239	+	0.409935i
$981$		0			0
$982$	−2.40750	+	15.2003i	−0.0768264	+	0.485062i
$983$	−7.11481	−	44.9211i	−0.226927	−	1.43276i	−0.793410	−	0.608688i	$-0.791696\pi$
$983$	−7.11481	−	44.9211i	−0.226927	−	1.43276i	0.566483	−	0.824074i	$-0.308304\pi$
$984$		0			0
$985$	−8.55985	−	1.14443i	−0.272739	−	0.0364645i
$986$	14.8032	−	20.3749i	0.471430	−	0.648868i
$987$		0			0
$988$	4.08752	−	2.08270i	0.130041	−	0.0662594i
$989$	−4.10309			−0.130471
$990$		0			0
$991$	−7.25030			−0.230313			−0.115157	−	0.993347i	$-0.536737\pi$
$991$	−7.25030			−0.230313			−0.115157	+	0.993347i	$0.536737\pi$
$992$	6.83964	−	3.48497i	0.217159	−	0.110648i
$993$		0			0
$994$	2.31435	−	3.18543i	0.0734067	−	0.101036i
$995$	−16.8126	−	22.0020i	−0.532996	−	0.697511i
$996$		0			0
$997$	−4.36575	−	27.5642i	−0.138265	−	0.872968i	−0.955140	−	0.296154i	$-0.904296\pi$
$997$	−4.36575	−	27.5642i	−0.138265	−	0.872968i	0.816876	−	0.576814i	$-0.195704\pi$
$998$	−4.32702	+	27.3197i	−0.136969	+	0.864791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.343.3		32
3.2	odd	2		55.2.l.a.13.2	yes	32
5.2	odd	4	inner	495.2.bj.a.442.3		32
11.6	odd	10	inner	495.2.bj.a.28.3		32
12.11	even	2		880.2.cm.a.673.4		32
15.2	even	4		55.2.l.a.2.2	✓	32
15.8	even	4		275.2.bm.b.57.3		32
15.14	odd	2		275.2.bm.b.68.3		32
33.2	even	10		605.2.m.d.118.2		32
33.5	odd	10		605.2.m.e.578.3		32
33.8	even	10		605.2.m.c.403.2		32
33.14	odd	10		605.2.m.d.403.3		32
33.17	even	10		55.2.l.a.28.2	yes	32
33.20	odd	10		605.2.m.c.118.3		32
33.26	odd	10		605.2.e.b.483.6		32
33.29	even	10		605.2.e.b.483.11		32
33.32	even	2		605.2.m.e.233.3		32
55.17	even	20	inner	495.2.bj.a.127.3		32
60.47	odd	4		880.2.cm.a.497.4		32
132.83	odd	10		880.2.cm.a.193.4		32
165.2	odd	20		605.2.m.d.602.3		32
165.17	odd	20		55.2.l.a.17.2	yes	32
165.32	odd	4		605.2.m.e.112.3		32
165.47	even	20		605.2.m.d.282.2		32
165.62	odd	20		605.2.e.b.362.6		32
165.83	odd	20		275.2.bm.b.182.3		32
165.92	even	20		605.2.e.b.362.11		32
165.107	odd	20		605.2.m.c.282.3		32
165.137	even	20		605.2.m.e.457.3		32
165.149	even	10		275.2.bm.b.193.3		32
165.152	even	20		605.2.m.c.602.2		32
660.347	even	20		880.2.cm.a.17.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.2	✓	32	15.2	even	4
55.2.l.a.13.2	yes	32	3.2	odd	2
55.2.l.a.17.2	yes	32	165.17	odd	20
55.2.l.a.28.2	yes	32	33.17	even	10
275.2.bm.b.57.3		32	15.8	even	4
275.2.bm.b.68.3		32	15.14	odd	2
275.2.bm.b.182.3		32	165.83	odd	20
275.2.bm.b.193.3		32	165.149	even	10
495.2.bj.a.28.3		32	11.6	odd	10	inner
495.2.bj.a.127.3		32	55.17	even	20	inner
495.2.bj.a.343.3		32	1.1	even	1	trivial
495.2.bj.a.442.3		32	5.2	odd	4	inner
605.2.e.b.362.6		32	165.62	odd	20
605.2.e.b.362.11		32	165.92	even	20
605.2.e.b.483.6		32	33.26	odd	10
605.2.e.b.483.11		32	33.29	even	10
605.2.m.c.118.3		32	33.20	odd	10
605.2.m.c.282.3		32	165.107	odd	20
605.2.m.c.403.2		32	33.8	even	10
605.2.m.c.602.2		32	165.152	even	20
605.2.m.d.118.2		32	33.2	even	10
605.2.m.d.282.2		32	165.47	even	20
605.2.m.d.403.3		32	33.14	odd	10
605.2.m.d.602.3		32	165.2	odd	20
605.2.m.e.112.3		32	165.32	odd	4
605.2.m.e.233.3		32	33.32	even	2
605.2.m.e.457.3		32	165.137	even	20
605.2.m.e.578.3		32	33.5	odd	10
880.2.cm.a.17.4		32	660.347	even	20
880.2.cm.a.193.4		32	132.83	odd	10
880.2.cm.a.497.4		32	60.47	odd	4
880.2.cm.a.673.4		32	12.11	even	2

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930933 - 0.474334i) q^{2} +(-0.533928 + 0.734888i) q^{4} +(1.77672 - 1.35766i) q^{5} +(0.0860119 + 0.543058i) q^{7} +(-0.475357 + 3.00128i) q^{8} +O(q^{10})\)	\(q+(0.930933 - 0.474334i) q^{2} +(-0.533928 + 0.734888i) q^{4} +(1.77672 - 1.35766i) q^{5} +(0.0860119 + 0.543058i) q^{7} +(-0.475357 + 3.00128i) q^{8} +(1.01002 - 2.10665i) q^{10} +(3.29961 + 0.335528i) q^{11} +(1.47301 + 2.89095i) q^{13} +(0.337662 + 0.464752i) q^{14} +(0.419681 + 1.29165i) q^{16} +(2.57079 - 5.04545i) q^{17} +(-1.25925 + 0.914902i) q^{19} +(0.0490901 + 2.03059i) q^{20} +(3.23087 - 1.25276i) q^{22} +(0.803543 + 0.803543i) q^{23} +(1.31349 - 4.82439i) q^{25} +(2.74255 + 1.99258i) q^{26} +(-0.445011 - 0.226744i) q^{28} +(3.44380 + 2.50207i) q^{29} +(-0.509209 + 1.56718i) q^{31} +(-3.29400 - 3.29400i) q^{32} -5.91638i q^{34} +(0.890110 + 0.848089i) q^{35} +(-0.945121 + 0.149692i) q^{37} +(-0.738312 + 1.44902i) q^{38} +(3.23016 + 5.97783i) q^{40} +(-5.25869 - 7.23797i) q^{41} +(-2.55312 + 2.55312i) q^{43} +(-2.00833 + 2.24570i) q^{44} +(1.12919 + 0.366897i) q^{46} +(-0.636959 + 4.02160i) q^{47} +(6.36988 - 2.06970i) q^{49} +(-1.06560 - 5.11422i) q^{50} +(-2.91101 - 0.461058i) q^{52} +(-6.27685 + 3.19821i) q^{53} +(6.31803 - 3.88362i) q^{55} -1.67076 q^{56} +(4.39276 + 0.695746i) q^{58} +(3.97760 - 5.47470i) q^{59} +(-8.75080 + 2.84331i) q^{61} +(0.269329 + 1.70048i) q^{62} +(-7.21224 - 2.34340i) q^{64} +(6.54208 + 3.13656i) q^{65} +(-2.62254 + 2.62254i) q^{67} +(2.33523 + 4.58314i) q^{68} +(1.23091 + 0.367304i) q^{70} +(-2.11802 - 6.51858i) q^{71} +(-9.96541 + 1.57837i) q^{73} +(-0.808840 + 0.587656i) q^{74} -1.41390i q^{76} +(0.101594 + 1.82074i) q^{77} +(-1.28746 + 3.96241i) q^{79} +(2.49928 + 1.72511i) q^{80} +(-8.32870 - 4.24369i) q^{82} +(-10.0947 - 5.14352i) q^{83} +(-2.28245 - 12.4546i) q^{85} +(-1.16575 + 3.58782i) q^{86} +(-2.57551 + 9.74357i) q^{88} -3.64860i q^{89} +(-1.44326 + 1.04859i) q^{91} +(-1.01955 + 0.161481i) q^{92} +(1.31462 + 4.04597i) q^{94} +(-0.995217 + 3.33517i) q^{95} +(-7.56722 - 14.8515i) q^{97} +(4.94820 - 4.94820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8}+O(q^{10}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40} - 40 q^{41} + 60 q^{46} + 28 q^{47} + 50 q^{50} - 50 q^{52} + 24 q^{53} - 64 q^{55} + 80 q^{56} - 50 q^{58} - 60 q^{61} - 100 q^{62} - 8 q^{67} + 30 q^{68} + 30 q^{70} - 24 q^{71} + 50 q^{73} - 70 q^{77} - 98 q^{80} - 10 q^{82} - 90 q^{83} + 30 q^{85} - 100 q^{86} + 170 q^{88} + 20 q^{91} + 68 q^{92} + 40 q^{95} - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

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