LMFDB - Embedded newform 2070.2.j.j.737.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.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:	$16.5290332184$
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} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 $ x^20 - 20x^18 + 187x^16 - 1012x^14 + 3533x^12 - 7896x^10 + 10837x^8 - 5668x^6 - 4125x^4 + 8700*x^2 + 3721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.8
Root			$-1.75570 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.j.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.967383 - 2.01598i) q^{5} +(0.545849 + 0.545849i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.967383 - 2.01598i) q^{5} +(0.545849 + 0.545849i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.741469 - 2.10956i) q^{10} +0.823770i q^{11} +(3.43352 - 3.43352i) q^{13} +0.771946 q^{14} -1.00000 q^{16} +(-0.823770 + 0.823770i) q^{17} -3.38410i q^{19} +(-2.01598 - 0.967383i) q^{20} +(0.582493 + 0.582493i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-3.12834 - 3.90045i) q^{25} -4.85573i q^{26} +(0.545849 - 0.545849i) q^{28} +9.51219 q^{29} -6.25668 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.16499i q^{34} +(1.62846 - 0.572375i) q^{35} +(-2.43100 - 2.43100i) q^{37} +(-2.39292 - 2.39292i) q^{38} +(-2.10956 + 0.741469i) q^{40} -0.0889676i q^{41} +(1.12834 - 1.12834i) q^{43} +0.823770 q^{44} +1.00000 q^{46} +(1.57664 - 1.57664i) q^{47} -6.40410i q^{49} +(-4.97010 - 0.545960i) q^{50} +(-3.43352 - 3.43352i) q^{52} +(3.37555 + 3.37555i) q^{53} +(1.66070 + 0.796900i) q^{55} -0.771946i q^{56} +(6.72613 - 6.72613i) q^{58} -13.3268 q^{59} +15.2076 q^{61} +(-4.42414 + 4.42414i) q^{62} +1.00000i q^{64} +(-3.60037 - 10.2434i) q^{65} +(-6.25575 - 6.25575i) q^{67} +(0.823770 + 0.823770i) q^{68} +(0.746768 - 1.55623i) q^{70} +0.428017i q^{71} +(-7.35876 + 7.35876i) q^{73} -3.43795 q^{74} -3.38410 q^{76} +(-0.449653 + 0.449653i) q^{77} -1.82787i q^{79} +(-0.967383 + 2.01598i) q^{80} +(-0.0629096 - 0.0629096i) q^{82} +(3.05325 + 3.05325i) q^{83} +(0.863802 + 2.45760i) q^{85} -1.59572i q^{86} +(0.582493 - 0.582493i) q^{88} -5.58696 q^{89} +3.74836 q^{91} +(0.707107 - 0.707107i) q^{92} -2.22971i q^{94} +(-6.82227 - 3.27372i) q^{95} +(-9.10678 - 9.10678i) q^{97} +(-4.52838 - 4.52838i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{7}+O(q^{10}) $ 20 * q - 16 * q^7	$ 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) $ 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.967383	−	2.01598i	0.432627	−	0.901573i
$5$	0.967383	−	2.01598i	0.432627	−	0.901573i
$6$		0			0
$7$	0.545849	+	0.545849i	0.206311	+	0.206311i	0.802698	−	0.596386i	$-0.203397\pi$
$7$	0.545849	+	0.545849i	0.206311	+	0.206311i	−0.596386	+	0.802698i	$0.703397\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.741469	−	2.10956i	−0.234473	−	0.667100i
$11$			0.823770i			0.248376i	0.992259	+	0.124188i	$0.0396326\pi$
$11$			0.823770i			0.248376i	−0.992259	+	0.124188i	$0.960367\pi$
$12$		0			0
$13$	3.43352	−	3.43352i	0.952286	−	0.952286i	−0.0466260	−	0.998912i	$-0.514847\pi$
$13$	3.43352	−	3.43352i	0.952286	−	0.952286i	0.998912	+	0.0466260i	$0.0148469\pi$
$14$	0.771946			0.206311
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.823770	+	0.823770i	−0.199793	+	0.199793i	−0.799911	−	0.600118i	$-0.795120\pi$
$17$	−0.823770	+	0.823770i	−0.199793	+	0.199793i	0.600118	+	0.799911i	$0.295120\pi$
$18$		0			0
$19$		−	3.38410i		−	0.776365i	−0.921583	−	0.388182i	$-0.873103\pi$
$19$		−	3.38410i		−	0.776365i	0.921583	−	0.388182i	$-0.126897\pi$
$20$	−2.01598	−	0.967383i	−0.450787	−	0.216313i
$21$		0			0
$22$	0.582493	+	0.582493i	0.124188	+	0.124188i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−3.12834	−	3.90045i	−0.625668	−	0.780089i
$26$		−	4.85573i		−	0.952286i
$27$		0			0
$28$	0.545849	−	0.545849i	0.103156	−	0.103156i
$29$	9.51219			1.76637			0.883185	−	0.469025i	$-0.155395\pi$
$29$	9.51219			1.76637			0.883185	+	0.469025i	$0.155395\pi$
$30$		0			0
$31$	−6.25668			−1.12373			−0.561867	−	0.827228i	$-0.689917\pi$
$31$	−6.25668			−1.12373			−0.561867	+	0.827228i	$0.689917\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			1.16499i			0.199793i
$35$	1.62846	−	0.572375i	0.275261	−	0.0967490i
$36$		0			0
$37$	−2.43100	−	2.43100i	−0.399653	−	0.399653i	0.478458	−	0.878111i	$-0.341196\pi$
$37$	−2.43100	−	2.43100i	−0.399653	−	0.399653i	−0.878111	+	0.478458i	$0.841196\pi$
$38$	−2.39292	−	2.39292i	−0.388182	−	0.388182i
$39$		0			0
$40$	−2.10956	+	0.741469i	−0.333550	+	0.117237i
$41$		−	0.0889676i		−	0.0138944i	−0.999976	−	0.00694720i	$-0.997789\pi$
$41$		−	0.0889676i		−	0.0138944i	0.999976	−	0.00694720i	$-0.00221138\pi$
$42$		0			0
$43$	1.12834	−	1.12834i	0.172070	−	0.172070i	−0.615818	−	0.787888i	$-0.711174\pi$
$43$	1.12834	−	1.12834i	0.172070	−	0.172070i	0.787888	+	0.615818i	$0.211174\pi$
$44$	0.823770			0.124188
$45$		0			0
$46$	1.00000			0.147442
$47$	1.57664	−	1.57664i	0.229977	−	0.229977i	−0.582706	−	0.812683i	$-0.698006\pi$
$47$	1.57664	−	1.57664i	0.229977	−	0.229977i	0.812683	+	0.582706i	$0.198006\pi$
$48$		0			0
$49$		−	6.40410i		−	0.914871i
$50$	−4.97010	−	0.545960i	−0.702879	−	0.0772104i
$51$		0			0
$52$	−3.43352	−	3.43352i	−0.476143	−	0.476143i
$53$	3.37555	+	3.37555i	0.463667	+	0.463667i	0.899855	−	0.436188i	$-0.143672\pi$
$53$	3.37555	+	3.37555i	0.463667	+	0.463667i	−0.436188	+	0.899855i	$0.643672\pi$
$54$		0			0
$55$	1.66070	+	0.796900i	0.223929	+	0.107454i
$56$		−	0.771946i		−	0.103156i
$57$		0			0
$58$	6.72613	−	6.72613i	0.883185	−	0.883185i
$59$	−13.3268			−1.73500			−0.867502	−	0.497434i	$-0.834276\pi$
$59$	−13.3268			−1.73500			−0.867502	+	0.497434i	$0.834276\pi$
$60$		0			0
$61$	15.2076			1.94713			0.973567	−	0.228401i	$-0.0733498\pi$
$61$	15.2076			1.94713			0.973567	+	0.228401i	$0.0733498\pi$
$62$	−4.42414	+	4.42414i	−0.561867	+	0.561867i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−3.60037	−	10.2434i	−0.446571	−	1.27054i
$66$		0			0
$67$	−6.25575	−	6.25575i	−0.764262	−	0.764262i	0.212828	−	0.977090i	$-0.431733\pi$
$67$	−6.25575	−	6.25575i	−0.764262	−	0.764262i	−0.977090	+	0.212828i	$0.931733\pi$
$68$	0.823770	+	0.823770i	0.0998967	+	0.0998967i
$69$		0			0
$70$	0.746768	−	1.55623i	0.0892558	−	0.186005i
$71$			0.428017i			0.0507963i	0.999677	+	0.0253981i	$0.00808535\pi$
$71$			0.428017i			0.0507963i	−0.999677	+	0.0253981i	$0.991915\pi$
$72$		0			0
$73$	−7.35876	+	7.35876i	−0.861278	+	0.861278i	−0.991487	−	0.130209i	$-0.958435\pi$
$73$	−7.35876	+	7.35876i	−0.861278	+	0.861278i	0.130209	+	0.991487i	$0.458435\pi$
$74$	−3.43795			−0.399653
$75$		0			0
$76$	−3.38410			−0.388182
$77$	−0.449653	+	0.449653i	−0.0512428	+	0.0512428i
$78$		0			0
$79$		−	1.82787i		−	0.205651i	−0.994699	−	0.102826i	$-0.967212\pi$
$79$		−	1.82787i		−	0.205651i	0.994699	−	0.102826i	$-0.0327884\pi$
$80$	−0.967383	+	2.01598i	−0.108157	+	0.225393i
$81$		0			0
$82$	−0.0629096	−	0.0629096i	−0.00694720	−	0.00694720i
$83$	3.05325	+	3.05325i	0.335138	+	0.335138i	0.854534	−	0.519396i	$-0.173843\pi$
$83$	3.05325	+	3.05325i	0.335138	+	0.335138i	−0.519396	+	0.854534i	$0.673843\pi$
$84$		0			0
$85$	0.863802	+	2.45760i	0.0936924	+	0.266564i
$86$		−	1.59572i		−	0.172070i
$87$		0			0
$88$	0.582493	−	0.582493i	0.0620940	−	0.0620940i
$89$	−5.58696			−0.592217			−0.296108	−	0.955154i	$-0.595689\pi$
$89$	−5.58696			−0.592217			−0.296108	+	0.955154i	$0.595689\pi$
$90$		0			0
$91$	3.74836			0.392935
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$		−	2.22971i		−	0.229977i
$95$	−6.82227	−	3.27372i	−0.699950	−	0.335876i
$96$		0			0
$97$	−9.10678	−	9.10678i	−0.924653	−	0.924653i	0.0727005	−	0.997354i	$-0.476838\pi$
$97$	−9.10678	−	9.10678i	−0.924653	−	0.924653i	−0.997354	+	0.0727005i	$0.976838\pi$
$98$	−4.52838	−	4.52838i	−0.457436	−	0.457436i
$99$		0			0
$100$	−3.90045	+	3.12834i	−0.390045	+	0.312834i
$101$		−	0.235403i		−	0.0234235i	−0.999931	−	0.0117118i	$-0.996272\pi$
$101$		−	0.235403i		−	0.0234235i	0.999931	−	0.0117118i	$-0.00372805\pi$
$102$		0			0
$103$	12.9841	−	12.9841i	1.27936	−	1.27936i	0.338331	−	0.941027i	$-0.390138\pi$
$103$	12.9841	−	12.9841i	1.27936	−	1.27936i	0.941027	−	0.338331i	$-0.109862\pi$
$104$	−4.85573			−0.476143
$105$		0			0
$106$	4.77374			0.463667
$107$	−8.07141	+	8.07141i	−0.780292	+	0.780292i	−0.979880	−	0.199588i	$-0.936040\pi$
$107$	−8.07141	+	8.07141i	−0.780292	+	0.780292i	0.199588	+	0.979880i	$0.436040\pi$
$108$		0			0
$109$			0.689192i			0.0660127i	0.999455	+	0.0330063i	$0.0105082\pi$
$109$			0.689192i			0.0660127i	−0.999455	+	0.0330063i	$0.989492\pi$
$110$	1.73779	−	0.610800i	0.165692	−	0.0582375i
$111$		0			0
$112$	−0.545849	−	0.545849i	−0.0515778	−	0.0515778i
$113$	5.98479	+	5.98479i	0.563002	+	0.563002i	0.930159	−	0.367157i	$-0.119669\pi$
$113$	5.98479	+	5.98479i	0.563002	+	0.563002i	−0.367157	+	0.930159i	$0.619669\pi$
$114$		0			0
$115$	2.10956	−	0.741469i	0.196717	−	0.0691424i
$116$		−	9.51219i		−	0.883185i
$117$		0			0
$118$	−9.42348	+	9.42348i	−0.867502	+	0.867502i
$119$	−0.899307			−0.0824393
$120$		0			0
$121$	10.3214			0.938309
$122$	10.7534	−	10.7534i	0.973567	−	0.973567i
$123$		0			0
$124$			6.25668i			0.561867i
$125$	−10.8895	+	2.53345i	−0.973988	+	0.226598i
$126$		0			0
$127$	−11.3994	−	11.3994i	−1.01153	−	1.01153i	−0.999933	−	0.0116001i	$-0.996307\pi$
$127$	−11.3994	−	11.3994i	−1.01153	−	1.01153i	−0.0116001	−	0.999933i	$-0.503693\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−9.78904	−	4.69735i	−0.858556	−	0.411985i
$131$			13.5764i			1.18618i	0.805137	+	0.593088i	$0.202092\pi$
$131$			13.5764i			1.18618i	−0.805137	+	0.593088i	$0.797908\pi$
$132$		0			0
$133$	1.84720	−	1.84720i	0.160173	−	0.160173i
$134$	−8.84697			−0.764262
$135$		0			0
$136$	1.16499			0.0998967
$137$	1.83112	−	1.83112i	0.156443	−	0.156443i	−0.624545	−	0.780988i	$-0.714716\pi$
$137$	1.83112	−	1.83112i	0.156443	−	0.156443i	0.780988	+	0.624545i	$0.214716\pi$
$138$		0			0
$139$			12.9152i			1.09545i	0.836657	+	0.547727i	$0.184507\pi$
$139$			12.9152i			1.09545i	−0.836657	+	0.547727i	$0.815493\pi$
$140$	−0.572375	−	1.62846i	−0.0483745	−	0.137630i
$141$		0			0
$142$	0.302654	+	0.302654i	0.0253981	+	0.0253981i
$143$	2.82843	+	2.82843i	0.236525	+	0.236525i
$144$		0			0
$145$	9.20193	−	19.1764i	0.764178	−	1.59251i
$146$			10.4069i			0.861278i
$147$		0			0
$148$	−2.43100	+	2.43100i	−0.199827	+	0.199827i
$149$	11.8391			0.969900			0.484950	−	0.874542i	$-0.338838\pi$
$149$	11.8391			0.969900			0.484950	+	0.874542i	$0.338838\pi$
$150$		0			0
$151$	−6.05321			−0.492604			−0.246302	−	0.969193i	$-0.579215\pi$
$151$	−6.05321			−0.492604			−0.246302	+	0.969193i	$0.579215\pi$
$152$	−2.39292	+	2.39292i	−0.194091	+	0.194091i
$153$		0			0
$154$			0.635906i			0.0512428i
$155$	−6.05261	+	12.6133i	−0.486157	+	1.01313i
$156$		0			0
$157$	9.88326	+	9.88326i	0.788770	+	0.788770i	0.981293	−	0.192522i	$-0.0616668\pi$
$157$	9.88326	+	9.88326i	0.788770	+	0.788770i	−0.192522	+	0.981293i	$0.561667\pi$
$158$	−1.29250	−	1.29250i	−0.102826	−	0.102826i
$159$		0			0
$160$	0.741469	+	2.10956i	0.0586183	+	0.166775i
$161$			0.771946i			0.0608379i
$162$		0			0
$163$	10.3875	−	10.3875i	0.813615	−	0.813615i	−0.171558	−	0.985174i	$-0.554880\pi$
$163$	10.3875	−	10.3875i	0.813615	−	0.813615i	0.985174	+	0.171558i	$0.0548802\pi$
$164$	−0.0889676			−0.00694720
$165$		0			0
$166$	4.31795			0.335138
$167$	−12.0791	+	12.0791i	−0.934710	+	0.934710i	−0.997995	−	0.0632853i	$-0.979842\pi$
$167$	−12.0791	+	12.0791i	−0.934710	+	0.934710i	0.0632853	+	0.997995i	$0.479842\pi$
$168$		0			0
$169$		−	10.5781i		−	0.813699i
$170$	2.34859	+	1.12699i	0.180128	+	0.0864360i
$171$		0			0
$172$	−1.12834	−	1.12834i	−0.0860352	−	0.0860352i
$173$	6.80191	+	6.80191i	0.517140	+	0.517140i	0.916705	−	0.399565i	$-0.130839\pi$
$173$	6.80191	+	6.80191i	0.517140	+	0.517140i	−0.399565	+	0.916705i	$0.630839\pi$
$174$		0			0
$175$	0.421452	−	3.83665i	0.0318588	−	0.290024i
$176$		−	0.823770i		−	0.0620940i
$177$		0			0
$178$	−3.95058	+	3.95058i	−0.296108	+	0.296108i
$179$	−8.62964			−0.645010			−0.322505	−	0.946568i	$-0.604525\pi$
$179$	−8.62964			−0.645010			−0.322505	+	0.946568i	$0.604525\pi$
$180$		0			0
$181$	−18.4075			−1.36822			−0.684111	−	0.729378i	$-0.739810\pi$
$181$	−18.4075			−1.36822			−0.684111	+	0.729378i	$0.739810\pi$
$182$	2.65049	−	2.65049i	0.196468	−	0.196468i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−7.25254	+	2.54913i	−0.533217	+	0.187416i
$186$		0			0
$187$	−0.678596	−	0.678596i	−0.0496239	−	0.0496239i
$188$	−1.57664	−	1.57664i	−0.114988	−	0.114988i
$189$		0			0
$190$	−7.13894	+	2.50920i	−0.517913	+	0.182037i
$191$		−	6.86973i		−	0.497076i	−0.968622	−	0.248538i	$-0.920050\pi$
$191$		−	6.86973i		−	0.497076i	0.968622	−	0.248538i	$-0.0799501\pi$
$192$		0			0
$193$	7.83501	−	7.83501i	0.563977	−	0.563977i	−0.366458	−	0.930435i	$-0.619430\pi$
$193$	7.83501	−	7.83501i	0.563977	−	0.563977i	0.930435	+	0.366458i	$0.119430\pi$
$194$	−12.8789			−0.924653
$195$		0			0
$196$	−6.40410			−0.457436
$197$	14.0985	−	14.0985i	1.00447	−	1.00447i	0.00448323	−	0.999990i	$-0.498573\pi$
$197$	14.0985	−	14.0985i	1.00447	−	1.00447i	0.999990	−	0.00448323i	$-0.00142706\pi$
$198$		0			0
$199$			17.8854i			1.26787i	0.773388	+	0.633933i	$0.218560\pi$
$199$			17.8854i			1.26787i	−0.773388	+	0.633933i	$0.781440\pi$
$200$	−0.545960	+	4.97010i	−0.0386052	+	0.351439i
$201$		0			0
$202$	−0.166455	−	0.166455i	−0.0117118	−	0.0117118i
$203$	5.19222	+	5.19222i	0.364422	+	0.364422i
$204$		0			0
$205$	−0.179357	−	0.0860657i	−0.0125268	−	0.00601109i
$206$		−	18.3622i		−	1.27936i
$207$		0			0
$208$	−3.43352	+	3.43352i	−0.238072	+	0.238072i
$209$	2.78772			0.192830
$210$		0			0
$211$	8.68986			0.598235			0.299117	−	0.954216i	$-0.403308\pi$
$211$	8.68986			0.598235			0.299117	+	0.954216i	$0.403308\pi$
$212$	3.37555	−	3.37555i	0.231834	−	0.231834i
$213$		0			0
$214$			11.4147i			0.780292i
$215$	−1.18317	−	3.36625i	−0.0806918	−	0.229576i
$216$		0			0
$217$	−3.41520	−	3.41520i	−0.231839	−	0.231839i
$218$	0.487333	+	0.487333i	0.0330063	+	0.0330063i
$219$		0			0
$220$	0.796900	−	1.66070i	0.0537270	−	0.111964i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	2.43171	−	2.43171i	0.162839	−	0.162839i	−0.620984	−	0.783823i	$-0.713267\pi$
$223$	2.43171	−	2.43171i	0.162839	−	0.162839i	0.783823	+	0.620984i	$0.213267\pi$
$224$	−0.771946			−0.0515778
$225$		0			0
$226$	8.46377			0.563002
$227$	15.5944	−	15.5944i	1.03504	−	1.03504i	0.0356765	−	0.999363i	$-0.488641\pi$
$227$	15.5944	−	15.5944i	1.03504	−	1.03504i	0.999363	−	0.0356765i	$-0.0113586\pi$
$228$		0			0
$229$			1.17054i			0.0773513i	0.999252	+	0.0386756i	$0.0123139\pi$
$229$			1.17054i			0.0773513i	−0.999252	+	0.0386756i	$0.987686\pi$
$230$	0.967383	−	2.01598i	0.0637873	−	0.132930i
$231$		0			0
$232$	−6.72613	−	6.72613i	−0.441592	−	0.441592i
$233$	−0.391179	−	0.391179i	−0.0256270	−	0.0256270i	0.694177	−	0.719804i	$-0.255768\pi$
$233$	−0.391179	−	0.391179i	−0.0256270	−	0.0256270i	−0.719804	+	0.694177i	$0.755768\pi$
$234$		0			0
$235$	−1.65326	−	4.70369i	−0.107847	−	0.306835i
$236$			13.3268i			0.867502i
$237$		0			0
$238$	−0.635906	+	0.635906i	−0.0412197	+	0.0412197i
$239$	4.90654			0.317378			0.158689	−	0.987329i	$-0.449273\pi$
$239$	4.90654			0.317378			0.158689	+	0.987329i	$0.449273\pi$
$240$		0			0
$241$	25.4617			1.64013			0.820065	−	0.572270i	$-0.193937\pi$
$241$	25.4617			1.64013			0.820065	+	0.572270i	$0.193937\pi$
$242$	7.29833	−	7.29833i	0.469155	−	0.469155i
$243$		0			0
$244$		−	15.2076i		−	0.973567i
$245$	−12.9105	−	6.19521i	−0.824823	−	0.395798i
$246$		0			0
$247$	−11.6194	−	11.6194i	−0.739322	−	0.739322i
$248$	4.42414	+	4.42414i	0.280933	+	0.280933i
$249$		0			0
$250$	−5.90864	+	9.49147i	−0.373695	+	0.600293i
$251$		−	6.16290i		−	0.388999i	−0.980903	−	0.194500i	$-0.937692\pi$
$251$		−	6.16290i		−	0.388999i	0.980903	−	0.194500i	$-0.0623083\pi$
$252$		0			0
$253$	−0.582493	+	0.582493i	−0.0366210	+	0.0366210i
$254$	−16.1212			−1.01153
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.598408	+	0.598408i	−0.0373277	+	0.0373277i	−0.725524	−	0.688197i	$-0.758403\pi$
$257$	−0.598408	+	0.598408i	−0.0373277	+	0.0373277i	0.688197	+	0.725524i	$0.258403\pi$
$258$		0			0
$259$		−	2.65391i		−	0.164906i
$260$	−10.2434	+	3.60037i	−0.635270	+	0.223286i
$261$		0			0
$262$	9.59997	+	9.59997i	0.593088	+	0.593088i
$263$	6.40765	+	6.40765i	0.395112	+	0.395112i	0.876505	−	0.481393i	$-0.159869\pi$
$263$	6.40765	+	6.40765i	0.395112	+	0.395112i	−0.481393	+	0.876505i	$0.659869\pi$
$264$		0			0
$265$	10.0705	−	3.53959i	0.618624	−	0.217435i
$266$		−	2.61234i		−	0.160173i
$267$		0			0
$268$	−6.25575	+	6.25575i	−0.382131	+	0.382131i
$269$	−21.4121			−1.30552			−0.652760	−	0.757565i	$-0.726389\pi$
$269$	−21.4121			−1.30552			−0.652760	+	0.757565i	$0.726389\pi$
$270$		0			0
$271$	24.2617			1.47380			0.736898	−	0.676004i	$-0.236290\pi$
$271$	24.2617			1.47380			0.736898	+	0.676004i	$0.236290\pi$
$272$	0.823770	−	0.823770i	0.0499484	−	0.0499484i
$273$		0			0
$274$		−	2.58959i		−	0.156443i
$275$	3.21307	−	2.57703i	0.193755	−	0.155401i
$276$		0			0
$277$	13.0367	+	13.0367i	0.783301	+	0.783301i	0.980386	−	0.197085i	$-0.0631476\pi$
$277$	13.0367	+	13.0367i	0.783301	+	0.783301i	−0.197085	+	0.980386i	$0.563148\pi$
$278$	9.13243	+	9.13243i	0.547727	+	0.547727i
$279$		0			0
$280$	−1.55623	−	0.746768i	−0.0930024	−	0.0446279i
$281$			6.37847i			0.380507i	0.981735	+	0.190254i	$0.0609311\pi$
$281$			6.37847i			0.380507i	−0.981735	+	0.190254i	$0.939069\pi$
$282$		0			0
$283$	−5.26980	+	5.26980i	−0.313257	+	0.313257i	−0.846170	−	0.532913i	$-0.821097\pi$
$283$	−5.26980	+	5.26980i	−0.313257	+	0.313257i	0.532913	+	0.846170i	$0.321097\pi$
$284$	0.428017			0.0253981
$285$		0			0
$286$	4.00000			0.236525
$287$	0.0485629	−	0.0485629i	0.00286657	−	0.00286657i
$288$		0			0
$289$			15.6428i			0.920165i
$290$	−7.05300	−	20.0665i	−0.414166	−	1.17834i
$291$		0			0
$292$	7.35876	+	7.35876i	0.430639	+	0.430639i
$293$	17.2056	+	17.2056i	1.00516	+	1.00516i	0.999987	+	0.00517573i	$0.00164749\pi$
$293$	17.2056	+	17.2056i	1.00516	+	1.00516i	0.00517573	+	0.999987i	$0.498353\pi$
$294$		0			0
$295$	−12.8921	+	26.8666i	−0.750609	+	1.56423i
$296$			3.43795i			0.199827i
$297$		0			0
$298$	8.37154	−	8.37154i	0.484950	−	0.484950i
$299$	4.85573			0.280814
$300$		0			0
$301$	1.23181			0.0710002
$302$	−4.28027	+	4.28027i	−0.246302	+	0.246302i
$303$		0			0
$304$			3.38410i			0.194091i
$305$	14.7116	−	30.6582i	0.842382	−	1.75548i
$306$		0			0
$307$	4.42881	+	4.42881i	0.252766	+	0.252766i	0.822104	−	0.569338i	$-0.192800\pi$
$307$	4.42881	+	4.42881i	0.252766	+	0.252766i	−0.569338	+	0.822104i	$0.692800\pi$
$308$	0.449653	+	0.449653i	0.0256214	+	0.0256214i
$309$		0			0
$310$	4.63914	+	13.1988i	0.263485	+	0.749643i
$311$			33.7161i			1.91186i	0.293591	+	0.955931i	$0.405149\pi$
$311$			33.7161i			1.91186i	−0.293591	+	0.955931i	$0.594851\pi$
$312$		0			0
$313$	−11.4623	+	11.4623i	−0.647888	+	0.647888i	−0.952482	−	0.304594i	$-0.901479\pi$
$313$	−11.4623	+	11.4623i	−0.647888	+	0.647888i	0.304594	+	0.952482i	$0.401479\pi$
$314$	13.9770			0.788770
$315$		0			0
$316$	−1.82787			−0.102826
$317$	5.06949	−	5.06949i	0.284731	−	0.284731i	−0.550261	−	0.834992i	$-0.685472\pi$
$317$	5.06949	−	5.06949i	0.284731	−	0.284731i	0.834992	+	0.550261i	$0.185472\pi$
$318$		0			0
$319$			7.83585i			0.438723i
$320$	2.01598	+	0.967383i	0.112697	+	0.0540783i
$321$		0			0
$322$	0.545849	+	0.545849i	0.0304190	+	0.0304190i
$323$	2.78772	+	2.78772i	0.155113	+	0.155113i
$324$		0			0
$325$	−24.1335	−	2.65103i	−1.33868	−	0.147053i
$326$		−	14.6902i		−	0.813615i
$327$		0			0
$328$	−0.0629096	+	0.0629096i	−0.00347360	+	0.00347360i
$329$	1.72121			0.0948936
$330$		0			0
$331$	13.5511			0.744836			0.372418	−	0.928065i	$-0.378529\pi$
$331$	13.5511			0.744836			0.372418	+	0.928065i	$0.378529\pi$
$332$	3.05325	−	3.05325i	0.167569	−	0.167569i
$333$		0			0
$334$			17.0825i			0.934710i
$335$	−18.6632	+	6.55976i	−1.01968	+	0.358398i
$336$		0			0
$337$	−11.7603	−	11.7603i	−0.640622	−	0.640622i	0.310086	−	0.950708i	$-0.399642\pi$
$337$	−11.7603	−	11.7603i	−0.640622	−	0.640622i	−0.950708	+	0.310086i	$0.899642\pi$
$338$	−7.47984	−	7.47984i	−0.406849	−	0.406849i
$339$		0			0
$340$	2.45760	−	0.863802i	0.133282	−	0.0468462i
$341$		−	5.15406i		−	0.279108i
$342$		0			0
$343$	7.31661	−	7.31661i	0.395060	−	0.395060i
$344$	−1.59572			−0.0860352
$345$		0			0
$346$	9.61935			0.517140
$347$	−14.7814	+	14.7814i	−0.793509	+	0.793509i	−0.982063	−	0.188554i	$-0.939620\pi$
$347$	−14.7814	+	14.7814i	−0.793509	+	0.793509i	0.188554	+	0.982063i	$0.439620\pi$
$348$		0			0
$349$			14.3329i			0.767223i	0.923495	+	0.383612i	$0.125320\pi$
$349$			14.3329i			0.767223i	−0.923495	+	0.383612i	$0.874680\pi$
$350$	−2.41491	−	3.01094i	−0.129082	−	0.160941i
$351$		0			0
$352$	−0.582493	−	0.582493i	−0.0310470	−	0.0310470i
$353$	−1.89228	−	1.89228i	−0.100716	−	0.100716i	0.654953	−	0.755669i	$-0.272688\pi$
$353$	−1.89228	−	1.89228i	−0.100716	−	0.100716i	−0.755669	+	0.654953i	$0.772688\pi$
$354$		0			0
$355$	0.862873	+	0.414056i	0.0457966	+	0.0219758i
$356$			5.58696i			0.296108i
$357$		0			0
$358$	−6.10208	+	6.10208i	−0.322505	+	0.322505i
$359$	18.9501			1.00015			0.500074	−	0.865983i	$-0.333306\pi$
$359$	18.9501			1.00015			0.500074	+	0.865983i	$0.333306\pi$
$360$		0			0
$361$	7.54789			0.397257
$362$	−13.0161	+	13.0161i	−0.684111	+	0.684111i
$363$		0			0
$364$		−	3.74836i		−	0.196468i
$365$	7.71637	+	21.9538i	0.403893	+	1.14912i
$366$		0			0
$367$	0.190323	+	0.190323i	0.00993477	+	0.00993477i	0.712057	−	0.702122i	$-0.247764\pi$
$367$	0.190323	+	0.190323i	0.00993477	+	0.00993477i	−0.702122	+	0.712057i	$0.747764\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	−3.32581	+	6.93083i	−0.172901	+	0.360317i
$371$			3.68508i			0.191320i
$372$		0			0
$373$	−7.01623	+	7.01623i	−0.363287	+	0.363287i	−0.865021	−	0.501735i	$-0.832695\pi$
$373$	−7.01623	+	7.01623i	−0.363287	+	0.363287i	0.501735	+	0.865021i	$0.332695\pi$
$374$	−0.959680			−0.0496239
$375$		0			0
$376$	−2.22971			−0.114988
$377$	32.6603	−	32.6603i	1.68209	−	1.68209i
$378$		0			0
$379$			29.6158i			1.52126i	0.649184	+	0.760631i	$0.275110\pi$
$379$			29.6158i			1.52126i	−0.649184	+	0.760631i	$0.724890\pi$
$380$	−3.27372	+	6.82227i	−0.167938	+	0.349975i
$381$		0			0
$382$	−4.85763	−	4.85763i	−0.248538	−	0.248538i
$383$	7.39104	+	7.39104i	0.377665	+	0.377665i	0.870259	−	0.492594i	$-0.163951\pi$
$383$	7.39104	+	7.39104i	0.377665	+	0.377665i	−0.492594	+	0.870259i	$0.663951\pi$
$384$		0			0
$385$	0.471505	+	1.34148i	0.0240301	+	0.0683681i
$386$		−	11.0804i		−	0.563977i
$387$		0			0
$388$	−9.10678	+	9.10678i	−0.462327	+	0.462327i
$389$	14.7314			0.746911			0.373455	−	0.927648i	$-0.378173\pi$
$389$	14.7314			0.746911			0.373455	+	0.927648i	$0.378173\pi$
$390$		0			0
$391$	−1.16499			−0.0589159
$392$	−4.52838	+	4.52838i	−0.228718	+	0.228718i
$393$		0			0
$394$		−	19.9382i		−	1.00447i
$395$	−3.68494	−	1.76825i	−0.185410	−	0.0889702i
$396$		0			0
$397$	−6.42637	−	6.42637i	−0.322530	−	0.322530i	0.527207	−	0.849737i	$-0.323239\pi$
$397$	−6.42637	−	6.42637i	−0.322530	−	0.322530i	−0.849737	+	0.527207i	$0.823239\pi$
$398$	12.6469	+	12.6469i	0.633933	+	0.633933i
$399$		0			0
$400$	3.12834	+	3.90045i	0.156417	+	0.195022i
$401$			1.21263i			0.0605558i	0.999542	+	0.0302779i	$0.00963923\pi$
$401$			1.21263i			0.0605558i	−0.999542	+	0.0302779i	$0.990361\pi$
$402$		0			0
$403$	−21.4824	+	21.4824i	−1.07012	+	1.07012i
$404$	−0.235403			−0.0117118
$405$		0			0
$406$	7.34290			0.364422
$407$	2.00258	−	2.00258i	0.0992642	−	0.0992642i
$408$		0			0
$409$			17.2113i			0.851044i	0.904948	+	0.425522i	$0.139909\pi$
$409$			17.2113i			0.851044i	−0.904948	+	0.425522i	$0.860091\pi$
$410$	−0.187682	+	0.0659668i	−0.00926896	+	0.00325787i
$411$		0			0
$412$	−12.9841	−	12.9841i	−0.639679	−	0.639679i
$413$	−7.27442	−	7.27442i	−0.357951	−	0.357951i
$414$		0			0
$415$	9.10896	−	3.20163i	0.447141	−	0.157162i
$416$			4.85573i			0.238072i
$417$		0			0
$418$	1.97121	−	1.97121i	0.0964152	−	0.0964152i
$419$	10.0536			0.491150			0.245575	−	0.969378i	$-0.421023\pi$
$419$	10.0536			0.491150			0.245575	+	0.969378i	$0.421023\pi$
$420$		0			0
$421$	−3.81796			−0.186076			−0.0930379	−	0.995663i	$-0.529658\pi$
$421$	−3.81796			−0.186076			−0.0930379	+	0.995663i	$0.529658\pi$
$422$	6.14466	−	6.14466i	0.299117	−	0.299117i
$423$		0			0
$424$		−	4.77374i		−	0.231834i
$425$	5.79010	+	0.636036i	0.280861	+	0.0308523i
$426$		0			0
$427$	8.30105	+	8.30105i	0.401716	+	0.401716i
$428$	8.07141	+	8.07141i	0.390146	+	0.390146i
$429$		0			0
$430$	−3.21693	−	1.54367i	−0.155134	−	0.0744423i
$431$			35.8552i			1.72708i	0.504278	+	0.863541i	$0.331759\pi$
$431$			35.8552i			1.72708i	−0.504278	+	0.863541i	$0.668241\pi$
$432$		0			0
$433$	4.52198	−	4.52198i	0.217313	−	0.217313i	−0.590052	−	0.807365i	$-0.700893\pi$
$433$	4.52198	−	4.52198i	0.217313	−	0.217313i	0.807365	+	0.590052i	$0.200893\pi$
$434$	−4.82982			−0.231839
$435$		0			0
$436$	0.689192			0.0330063
$437$	2.39292	−	2.39292i	0.114469	−	0.114469i
$438$		0			0
$439$			35.3661i			1.68793i	0.536396	+	0.843966i	$0.319785\pi$
$439$			35.3661i			1.68793i	−0.536396	+	0.843966i	$0.680215\pi$
$440$	−0.610800	−	1.73779i	−0.0291187	−	0.0828458i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	−17.5186	−	17.5186i	−0.832336	−	0.832336i	0.155500	−	0.987836i	$-0.450301\pi$
$443$	−17.5186	−	17.5186i	−0.832336	−	0.832336i	−0.987836	+	0.155500i	$0.950301\pi$
$444$		0			0
$445$	−5.40473	+	11.2632i	−0.256209	+	0.533927i
$446$		−	3.43895i		−	0.162839i
$447$		0			0
$448$	−0.545849	+	0.545849i	−0.0257889	+	0.0257889i
$449$	−4.05598			−0.191413			−0.0957067	−	0.995410i	$-0.530511\pi$
$449$	−4.05598			−0.191413			−0.0957067	+	0.995410i	$0.530511\pi$
$450$		0			0
$451$	0.0732888			0.00345104
$452$	5.98479	−	5.98479i	0.281501	−	0.281501i
$453$		0			0
$454$		−	22.0539i		−	1.03504i
$455$	3.62610	−	7.55662i	0.169994	−	0.354260i
$456$		0			0
$457$	−24.1765	−	24.1765i	−1.13093	−	1.13093i	−0.990023	−	0.140908i	$-0.954998\pi$
$457$	−24.1765	−	24.1765i	−1.13093	−	1.13093i	−0.140908	−	0.990023i	$-0.545002\pi$
$458$	0.827695	+	0.827695i	0.0386756	+	0.0386756i
$459$		0			0
$460$	−0.741469	−	2.10956i	−0.0345712	−	0.0983585i
$461$			10.8730i			0.506407i	0.967413	+	0.253204i	$0.0814843\pi$
$461$			10.8730i			0.506407i	−0.967413	+	0.253204i	$0.918516\pi$
$462$		0			0
$463$	20.2413	−	20.2413i	0.940694	−	0.940694i	−0.0576437	−	0.998337i	$-0.518359\pi$
$463$	20.2413	−	20.2413i	0.940694	−	0.940694i	0.998337	+	0.0576437i	$0.0183587\pi$
$464$	−9.51219			−0.441592
$465$		0			0
$466$	−0.553211			−0.0256270
$467$	−3.11096	+	3.11096i	−0.143958	+	0.143958i	−0.775413	−	0.631455i	$-0.782458\pi$
$467$	−3.11096	+	3.11096i	−0.143958	+	0.143958i	0.631455	+	0.775413i	$0.282458\pi$
$468$		0			0
$469$		−	6.82939i		−	0.315352i
$470$	−4.49504	−	2.15698i	−0.207341	−	0.0994940i
$471$		0			0
$472$	9.42348	+	9.42348i	0.433751	+	0.433751i
$473$	0.929493	+	0.929493i	0.0427382	+	0.0427382i
$474$		0			0
$475$	−13.1995	+	10.5866i	−0.605634	+	0.485747i
$476$			0.899307i			0.0412197i
$477$		0			0
$478$	3.46945	−	3.46945i	0.158689	−	0.158689i
$479$	39.1662			1.78955			0.894774	−	0.446520i	$-0.147337\pi$
$479$	39.1662			1.78955			0.894774	+	0.446520i	$0.147337\pi$
$480$		0			0
$481$	−16.6937			−0.761169
$482$	18.0041	−	18.0041i	0.820065	−	0.820065i
$483$		0			0
$484$		−	10.3214i		−	0.469155i
$485$	−27.1688	+	9.54933i	−1.23367	+	0.433613i
$486$		0			0
$487$	−4.07985	−	4.07985i	−0.184876	−	0.184876i	0.608601	−	0.793476i	$-0.291731\pi$
$487$	−4.07985	−	4.07985i	−0.184876	−	0.184876i	−0.793476	+	0.608601i	$0.791731\pi$
$488$	−10.7534	−	10.7534i	−0.486784	−	0.486784i
$489$		0			0
$490$	−13.5098	+	4.74844i	−0.610311	+	0.214513i
$491$			34.5406i			1.55879i	0.626530	+	0.779397i	$0.284475\pi$
$491$			34.5406i			1.55879i	−0.626530	+	0.779397i	$0.715525\pi$
$492$		0			0
$493$	−7.83585	+	7.83585i	−0.352909	+	0.352909i
$494$	−16.4322			−0.739322
$495$		0			0
$496$	6.25668			0.280933
$497$	−0.233632	+	0.233632i	−0.0104798	+	0.0104798i
$498$		0			0
$499$		−	7.67978i		−	0.343794i	−0.985115	−	0.171897i	$-0.945010\pi$
$499$		−	7.67978i		−	0.343794i	0.985115	−	0.171897i	$-0.0549896\pi$
$500$	2.53345	+	10.8895i	0.113299	+	0.486994i
$501$		0			0
$502$	−4.35783	−	4.35783i	−0.194500	−	0.194500i
$503$	−7.02025	−	7.02025i	−0.313018	−	0.313018i	0.533060	−	0.846077i	$-0.321042\pi$
$503$	−7.02025	−	7.02025i	−0.313018	−	0.313018i	−0.846077	+	0.533060i	$0.821042\pi$
$504$		0			0
$505$	−0.474568	−	0.227725i	−0.0211180	−	0.0101336i
$506$			0.823770i			0.0366210i
$507$		0			0
$508$	−11.3994	+	11.3994i	−0.505766	+	0.505766i
$509$	29.8928			1.32497			0.662487	−	0.749074i	$-0.269501\pi$
$509$	29.8928			1.32497			0.662487	+	0.749074i	$0.269501\pi$
$510$		0			0
$511$	−8.03354			−0.355383
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			0.846277i			0.0373277i
$515$	−13.6150	−	38.7362i	−0.599951	−	1.70692i
$516$		0			0
$517$	1.29879	+	1.29879i	0.0571207	+	0.0571207i
$518$	−1.87660	−	1.87660i	−0.0824530	−	0.0824530i
$519$		0			0
$520$	−4.69735	+	9.78904i	−0.205992	+	0.429278i
$521$			7.33613i			0.321402i	0.987003	+	0.160701i	$0.0513755\pi$
$521$			7.33613i			0.321402i	−0.987003	+	0.160701i	$0.948625\pi$
$522$		0			0
$523$	−0.119339	+	0.119339i	−0.00521834	+	0.00521834i	−0.709711	−	0.704493i	$-0.751175\pi$
$523$	−0.119339	+	0.119339i	−0.00521834	+	0.00521834i	0.704493	+	0.709711i	$0.251175\pi$
$524$	13.5764			0.593088
$525$		0			0
$526$	9.06178			0.395112
$527$	5.15406	−	5.15406i	0.224515	−	0.224515i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	4.61804	−	9.62377i	0.200595	−	0.418030i
$531$		0			0
$532$	−1.84720	−	1.84720i	−0.0800865	−	0.0800865i
$533$	−0.305472	−	0.305472i	−0.0132315	−	0.0132315i
$534$		0			0
$535$	8.46365	+	24.0799i	0.365915	+	1.04107i
$536$			8.84697i			0.382131i
$537$		0			0
$538$	−15.1407	+	15.1407i	−0.652760	+	0.652760i
$539$	5.27550			0.227232
$540$		0			0
$541$	−25.8485			−1.11132			−0.555658	−	0.831411i	$-0.687533\pi$
$541$	−25.8485			−1.11132			−0.555658	+	0.831411i	$0.687533\pi$
$542$	17.1556	−	17.1556i	0.736898	−	0.736898i
$543$		0			0
$544$		−	1.16499i		−	0.0499484i
$545$	1.38940	+	0.666713i	0.0595152	+	0.0285588i
$546$		0			0
$547$	0.355526	+	0.355526i	0.0152012	+	0.0152012i	0.714667	−	0.699465i	$-0.246578\pi$
$547$	0.355526	+	0.355526i	0.0152012	+	0.0152012i	−0.699465	+	0.714667i	$0.746578\pi$
$548$	−1.83112	−	1.83112i	−0.0782215	−	0.0782215i
$549$		0			0
$550$	0.449745	−	4.09422i	0.0191772	−	0.174578i
$551$		−	32.1902i		−	1.37135i
$552$		0			0
$553$	0.997739	−	0.997739i	0.0424282	−	0.0424282i
$554$	18.4367			0.783301
$555$		0			0
$556$	12.9152			0.547727
$557$	28.7593	−	28.7593i	1.21857	−	1.21857i	0.250438	−	0.968133i	$-0.419426\pi$
$557$	28.7593	−	28.7593i	1.21857	−	1.21857i	0.968133	−	0.250438i	$-0.0805745\pi$
$558$		0			0
$559$		−	7.74836i		−	0.327721i
$560$	−1.62846	+	0.572375i	−0.0688152	+	0.0241872i
$561$		0			0
$562$	4.51026	+	4.51026i	0.190254	+	0.190254i
$563$	2.05030	+	2.05030i	0.0864099	+	0.0864099i	0.748991	−	0.662581i	$-0.230539\pi$
$563$	2.05030	+	2.05030i	0.0864099	+	0.0864099i	−0.662581	+	0.748991i	$0.730539\pi$
$564$		0			0
$565$	17.8548	−	6.27563i	0.751157	−	0.264018i
$566$			7.45263i			0.313257i
$567$		0			0
$568$	0.302654	−	0.302654i	0.0126991	−	0.0126991i
$569$	17.8381			0.747813			0.373907	−	0.927466i	$-0.378018\pi$
$569$	17.8381			0.747813			0.373907	+	0.927466i	$0.378018\pi$
$570$		0			0
$571$	25.3891			1.06250			0.531251	−	0.847214i	$-0.321722\pi$
$571$	25.3891			1.06250			0.531251	+	0.847214i	$0.321722\pi$
$572$	2.82843	−	2.82843i	0.118262	−	0.118262i
$573$		0			0
$574$		−	0.0686782i		−	0.00286657i
$575$	0.545960	−	4.97010i	0.0227681	−	0.207268i
$576$		0			0
$577$	−22.7672	−	22.7672i	−0.947812	−	0.947812i	0.0508924	−	0.998704i	$-0.483793\pi$
$577$	−22.7672	−	22.7672i	−0.947812	−	0.947812i	−0.998704	+	0.0508924i	$0.983793\pi$
$578$	11.0611	+	11.0611i	0.460083	+	0.460083i
$579$		0			0
$580$	−19.1764	−	9.20193i	−0.796256	−	0.382089i
$581$			3.33323i			0.138286i
$582$		0			0
$583$	−2.78067	+	2.78067i	−0.115164	+	0.115164i
$584$	10.4069			0.430639
$585$		0			0
$586$	24.3324			1.00516
$587$	6.18537	−	6.18537i	0.255298	−	0.255298i	−0.567841	−	0.823138i	$-0.692221\pi$
$587$	6.18537	−	6.18537i	0.255298	−	0.255298i	0.823138	+	0.567841i	$0.192221\pi$
$588$		0			0
$589$			21.1732i			0.872427i
$590$	9.88143	+	28.1136i	0.406812	+	1.15742i
$591$		0			0
$592$	2.43100	+	2.43100i	0.0999133	+	0.0999133i
$593$	32.3700	+	32.3700i	1.32927	+	1.32927i	0.906002	+	0.423273i	$0.139119\pi$
$593$	32.3700	+	32.3700i	1.32927	+	1.32927i	0.423273	+	0.906002i	$0.360881\pi$
$594$		0			0
$595$	−0.869974	+	1.81298i	−0.0356655	+	0.0743251i
$596$		−	11.8391i		−	0.484950i
$597$		0			0
$598$	3.43352	−	3.43352i	0.140407	−	0.140407i
$599$	−35.6565			−1.45688			−0.728442	−	0.685108i	$-0.759755\pi$
$599$	−35.6565			−1.45688			−0.728442	+	0.685108i	$0.759755\pi$
$600$		0			0
$601$	−13.3509			−0.544594			−0.272297	−	0.962213i	$-0.587783\pi$
$601$	−13.3509			−0.544594			−0.272297	+	0.962213i	$0.587783\pi$
$602$	0.871019	−	0.871019i	0.0355001	−	0.0355001i
$603$		0			0
$604$			6.05321i			0.246302i
$605$	9.98475	−	20.8077i	0.405938	−	0.845955i
$606$		0			0
$607$	10.1614	+	10.1614i	0.412439	+	0.412439i	0.882587	−	0.470148i	$-0.155800\pi$
$607$	10.1614	+	10.1614i	0.412439	+	0.412439i	−0.470148	+	0.882587i	$0.655800\pi$
$608$	2.39292	+	2.39292i	0.0970456	+	0.0970456i
$609$		0			0
$610$	−11.2760	−	32.0813i	−0.456551	−	1.29893i
$611$		−	10.8268i		−	0.438007i
$612$		0			0
$613$	−7.45520	+	7.45520i	−0.301113	+	0.301113i	−0.841449	−	0.540336i	$-0.818297\pi$
$613$	−7.45520	+	7.45520i	−0.301113	+	0.301113i	0.540336	+	0.841449i	$0.318297\pi$
$614$	6.26329			0.252766
$615$		0			0
$616$	0.635906			0.0256214
$617$	−6.27790	+	6.27790i	−0.252739	+	0.252739i	−0.822093	−	0.569354i	$-0.807193\pi$
$617$	−6.27790	+	6.27790i	−0.252739	+	0.252739i	0.569354	+	0.822093i	$0.307193\pi$
$618$		0			0
$619$			30.0408i			1.20744i	0.797196	+	0.603720i	$0.206316\pi$
$619$			30.0408i			1.20744i	−0.797196	+	0.603720i	$0.793684\pi$
$620$	12.6133	+	6.05261i	0.506564	+	0.243079i
$621$		0			0
$622$	23.8409	+	23.8409i	0.955931	+	0.955931i
$623$	−3.04964	−	3.04964i	−0.122181	−	0.122181i
$624$		0			0
$625$	−5.42696	+	24.4039i	−0.217078	+	0.976154i
$626$			16.2101i			0.647888i
$627$		0			0
$628$	9.88326	−	9.88326i	0.394385	−	0.394385i
$629$	4.00516			0.159696
$630$		0			0
$631$	−2.75693			−0.109752			−0.0548758	−	0.998493i	$-0.517476\pi$
$631$	−2.75693			−0.109752			−0.0548758	+	0.998493i	$0.517476\pi$
$632$	−1.29250	+	1.29250i	−0.0514128	+	0.0514128i
$633$		0			0
$634$		−	7.16935i		−	0.284731i
$635$	−34.0085	+	11.9534i	−1.34959	+	0.474355i
$636$		0			0
$637$	−21.9886	−	21.9886i	−0.871219	−	0.871219i
$638$	5.54078	+	5.54078i	0.219362	+	0.219362i
$639$		0			0
$640$	2.10956	−	0.741469i	0.0833875	−	0.0293092i
$641$		−	32.3276i		−	1.27686i	−0.769679	−	0.638431i	$-0.779584\pi$
$641$		−	32.3276i		−	1.27686i	0.769679	−	0.638431i	$-0.220416\pi$
$642$		0			0
$643$	22.3690	−	22.3690i	0.882149	−	0.882149i	−0.111604	−	0.993753i	$-0.535599\pi$
$643$	22.3690	−	22.3690i	0.882149	−	0.882149i	0.993753	+	0.111604i	$0.0355987\pi$
$644$	0.771946			0.0304190
$645$		0			0
$646$	3.94242			0.155113
$647$	28.3388	−	28.3388i	1.11411	−	1.11411i	0.121523	−	0.992589i	$-0.461222\pi$
$647$	28.3388	−	28.3388i	1.11411	−	1.11411i	0.992589	−	0.121523i	$-0.0387779\pi$
$648$		0			0
$649$		−	10.9782i		−	0.430933i
$650$	−18.9395	+	15.1904i	−0.742868	+	0.595815i
$651$		0			0
$652$	−10.3875	−	10.3875i	−0.406808	−	0.406808i
$653$	8.22997	+	8.22997i	0.322064	+	0.322064i	0.849558	−	0.527495i	$-0.176869\pi$
$653$	8.22997	+	8.22997i	0.322064	+	0.322064i	−0.527495	+	0.849558i	$0.676869\pi$
$654$		0			0
$655$	27.3698	+	13.1336i	1.06942	+	0.513172i
$656$			0.0889676i			0.00347360i
$657$		0			0
$658$	1.21708	−	1.21708i	0.0474468	−	0.0474468i
$659$	−17.5863			−0.685066			−0.342533	−	0.939506i	$-0.611285\pi$
$659$	−17.5863			−0.685066			−0.342533	+	0.939506i	$0.611285\pi$
$660$		0			0
$661$	−47.1567			−1.83418			−0.917092	−	0.398675i	$-0.869470\pi$
$661$	−47.1567			−1.83418			−0.917092	+	0.398675i	$0.869470\pi$
$662$	9.58208	−	9.58208i	0.372418	−	0.372418i
$663$		0			0
$664$		−	4.31795i		−	0.167569i
$665$	−1.93697	−	5.51088i	−0.0751125	−	0.213703i
$666$		0			0
$667$	6.72613	+	6.72613i	0.260437	+	0.260437i
$668$	12.0791	+	12.0791i	0.467355	+	0.467355i
$669$		0			0
$670$	−8.55841	+	17.8353i	−0.330640	+	0.689038i
$671$			12.5276i			0.483621i
$672$		0			0
$673$	−10.0202	+	10.0202i	−0.386251	+	0.386251i	−0.873348	−	0.487097i	$-0.838056\pi$
$673$	−10.0202	+	10.0202i	−0.386251	+	0.386251i	0.487097	+	0.873348i	$0.338056\pi$
$674$	−16.6315			−0.640622
$675$		0			0
$676$	−10.5781			−0.406849
$677$	17.2224	−	17.2224i	0.661909	−	0.661909i	−0.293921	−	0.955830i	$-0.594960\pi$
$677$	17.2224	−	17.2224i	0.661909	−	0.661909i	0.955830	+	0.293921i	$0.0949601\pi$
$678$		0			0
$679$		−	9.94185i		−	0.381533i
$680$	1.12699	−	2.34859i	0.0432180	−	0.0900642i
$681$		0			0
$682$	−3.64447	−	3.64447i	−0.139554	−	0.139554i
$683$	5.97392	+	5.97392i	0.228586	+	0.228586i	0.812102	−	0.583516i	$-0.198323\pi$
$683$	5.97392	+	5.97392i	0.228586	+	0.228586i	−0.583516	+	0.812102i	$0.698323\pi$
$684$		0			0
$685$	−1.92010	−	5.46289i	−0.0733634	−	0.208726i
$686$		−	10.3472i		−	0.395060i
$687$		0			0
$688$	−1.12834	+	1.12834i	−0.0430176	+	0.0430176i
$689$	23.1800			0.883088
$690$		0			0
$691$	−32.4935			−1.23611			−0.618056	−	0.786134i	$-0.712080\pi$
$691$	−32.4935			−1.23611			−0.618056	+	0.786134i	$0.712080\pi$
$692$	6.80191	−	6.80191i	0.258570	−	0.258570i
$693$		0			0
$694$			20.9041i			0.793509i
$695$	26.0368	+	12.4939i	0.987631	+	0.473922i
$696$		0			0
$697$	0.0732888	+	0.0732888i	0.00277601	+	0.00277601i
$698$	10.1349	+	10.1349i	0.383612	+	0.383612i
$699$		0			0
$700$	−3.83665	−	0.421452i	−0.145012	−	0.0159294i
$701$		−	20.7760i		−	0.784698i	−0.919816	−	0.392349i	$-0.871663\pi$
$701$		−	20.7760i		−	0.784698i	0.919816	−	0.392349i	$-0.128337\pi$
$702$		0			0
$703$	−8.22672	+	8.22672i	−0.310277	+	0.310277i
$704$	−0.823770			−0.0310470
$705$		0			0
$706$	−2.67609			−0.100716
$707$	0.128495	−	0.128495i	0.00483254	−	0.00483254i
$708$		0			0
$709$			18.1760i			0.682613i	0.939952	+	0.341307i	$0.110869\pi$
$709$			18.1760i			0.682613i	−0.939952	+	0.341307i	$0.889131\pi$
$710$	0.902925	−	0.317362i	0.0338862	−	0.0119104i
$711$		0			0
$712$	3.95058	+	3.95058i	0.148054	+	0.148054i
$713$	−4.42414	−	4.42414i	−0.165685	−	0.165685i
$714$		0			0
$715$	8.43822	−	2.96588i	0.315572	−	0.110918i
$716$			8.62964i			0.322505i
$717$		0			0
$718$	13.3997	−	13.3997i	0.500074	−	0.500074i
$719$	−33.5991			−1.25304			−0.626518	−	0.779407i	$-0.715520\pi$
$719$	−33.5991			−1.25304			−0.626518	+	0.779407i	$0.715520\pi$
$720$		0			0
$721$	14.1747			0.527892
$722$	5.33717	−	5.33717i	0.198629	−	0.198629i
$723$		0			0
$724$			18.4075i			0.684111i
$725$	−29.7574	−	37.1018i	−1.10516	−	1.37793i
$726$		0			0
$727$	5.35893	+	5.35893i	0.198752	+	0.198752i	0.799465	−	0.600713i	$-0.205117\pi$
$727$	5.35893	+	5.35893i	0.198752	+	0.198752i	−0.600713	+	0.799465i	$0.705117\pi$
$728$	−2.65049	−	2.65049i	−0.0982338	−	0.0982338i
$729$		0			0
$730$	20.9800	+	10.0674i	0.776505	+	0.372612i
$731$			1.85899i			0.0687571i
$732$		0			0
$733$	21.1434	−	21.1434i	0.780949	−	0.780949i	−0.199042	−	0.979991i	$-0.563783\pi$
$733$	21.1434	−	21.1434i	0.780949	−	0.780949i	0.979991	+	0.199042i	$0.0637830\pi$
$734$	0.269157			0.00993477
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	5.15330	−	5.15330i	0.189824	−	0.189824i
$738$		0			0
$739$		−	9.67003i		−	0.355718i	−0.984056	−	0.177859i	$-0.943083\pi$
$739$		−	9.67003i		−	0.355718i	0.984056	−	0.177859i	$-0.0569171\pi$
$740$	2.54913	+	7.25254i	0.0937080	+	0.266609i
$741$		0			0
$742$	2.60574	+	2.60574i	0.0956598	+	0.0956598i
$743$	−11.5881	−	11.5881i	−0.425124	−	0.425124i	0.461839	−	0.886964i	$-0.347190\pi$
$743$	−11.5881	−	11.5881i	−0.425124	−	0.425124i	−0.886964	+	0.461839i	$0.847190\pi$
$744$		0			0
$745$	11.4530	−	23.8675i	0.419605	−	0.874436i
$746$			9.92244i			0.363287i
$747$		0			0
$748$	−0.678596	+	0.678596i	−0.0248119	+	0.0248119i
$749$	−8.81153			−0.321966
$750$		0			0
$751$	30.0545			1.09670			0.548351	−	0.836248i	$-0.315256\pi$
$751$	30.0545			1.09670			0.548351	+	0.836248i	$0.315256\pi$
$752$	−1.57664	+	1.57664i	−0.0574942	+	0.0574942i
$753$		0			0
$754$		−	46.1886i		−	1.68209i
$755$	−5.85577	+	12.2032i	−0.213113	+	0.444118i
$756$		0			0
$757$	−38.1394	−	38.1394i	−1.38620	−	1.38620i	−0.833141	−	0.553060i	$-0.813460\pi$
$757$	−38.1394	−	38.1394i	−1.38620	−	1.38620i	−0.553060	−	0.833141i	$-0.686540\pi$
$758$	20.9415	+	20.9415i	0.760631	+	0.760631i
$759$		0			0
$760$	2.50920	+	7.13894i	0.0910184	+	0.258956i
$761$		−	1.74371i		−	0.0632093i	−0.999500	−	0.0316046i	$-0.989938\pi$
$761$		−	1.74371i		−	0.0632093i	0.999500	−	0.0316046i	$-0.0100617\pi$
$762$		0			0
$763$	−0.376195	+	0.376195i	−0.0136192	+	0.0136192i
$764$	−6.86973			−0.248538
$765$		0			0
$766$	10.4525			0.377665
$767$	−45.7578	+	45.7578i	−1.65222	+	1.65222i
$768$		0			0
$769$		−	25.8398i		−	0.931808i	−0.884835	−	0.465904i	$-0.845729\pi$
$769$		−	25.8398i		−	0.931808i	0.884835	−	0.465904i	$-0.154271\pi$
$770$	1.28197	+	0.615164i	0.0461991	+	0.0221690i
$771$		0			0
$772$	−7.83501	−	7.83501i	−0.281988	−	0.281988i
$773$	−31.7741	−	31.7741i	−1.14284	−	1.14284i	−0.987929	−	0.154906i	$-0.950493\pi$
$773$	−31.7741	−	31.7741i	−1.14284	−	1.14284i	−0.154906	−	0.987929i	$-0.549507\pi$
$774$		0			0
$775$	19.5730	+	24.4039i	0.703084	+	0.876612i
$776$			12.8789i			0.462327i
$777$		0			0
$778$	10.4167	−	10.4167i	0.373455	−	0.373455i
$779$	−0.301075			−0.0107871
$780$		0			0
$781$	−0.352587			−0.0126166
$782$	−0.823770	+	0.823770i	−0.0294579	+	0.0294579i
$783$		0			0
$784$			6.40410i			0.228718i
$785$	29.4853	−	10.3636i	1.05238	−	0.369891i
$786$		0			0
$787$	−34.8573	−	34.8573i	−1.24253	−	1.24253i	−0.958949	−	0.283580i	$-0.908478\pi$
$787$	−34.8573	−	34.8573i	−1.24253	−	1.24253i	−0.283580	−	0.958949i	$-0.591522\pi$
$788$	−14.0985	−	14.0985i	−0.502237	−	0.502237i
$789$		0			0
$790$	−3.85599	+	1.35531i	−0.137190	+	0.0482197i
$791$			6.53358i			0.232307i
$792$		0			0
$793$	52.2156	−	52.2156i	1.85423	−	1.85423i
$794$	−9.08826			−0.322530
$795$		0			0
$796$	17.8854			0.633933
$797$	2.33267	−	2.33267i	0.0826275	−	0.0826275i	−0.664585	−	0.747213i	$-0.731392\pi$
$797$	2.33267	−	2.33267i	0.0826275	−	0.0826275i	0.747213	+	0.664585i	$0.231392\pi$
$798$		0			0
$799$			2.59758i			0.0918957i
$800$	4.97010	+	0.545960i	0.175720	+	0.0193026i
$801$		0			0
$802$	0.857459	+	0.857459i	0.0302779	+	0.0302779i
$803$	−6.06192	−	6.06192i	−0.213921	−	0.213921i
$804$		0			0
$805$	1.55623	+	0.746768i	0.0548498	+	0.0263201i
$806$			30.3807i			1.07012i
$807$		0			0
$808$	−0.166455	+	0.166455i	−0.00585588	+	0.00585588i
$809$	−21.7674			−0.765303			−0.382651	−	0.923893i	$-0.624989\pi$
$809$	−21.7674			−0.765303			−0.382651	+	0.923893i	$0.624989\pi$
$810$		0			0
$811$	6.82577			0.239685			0.119843	−	0.992793i	$-0.461761\pi$
$811$	6.82577			0.239685			0.119843	+	0.992793i	$0.461761\pi$
$812$	5.19222	−	5.19222i	0.182211	−	0.182211i
$813$		0			0
$814$		−	2.83208i		−	0.0992642i
$815$	−10.8923	−	30.9898i	−0.381542	−	1.08553i
$816$		0			0
$817$	−3.81842	−	3.81842i	−0.133589	−	0.133589i
$818$	12.1702	+	12.1702i	0.425522	+	0.425522i
$819$		0			0
$820$	−0.0860657	+	0.179357i	−0.00300555	+	0.00626341i
$821$			8.55784i			0.298671i	0.988787	+	0.149335i	$0.0477134\pi$
$821$			8.55784i			0.298671i	−0.988787	+	0.149335i	$0.952287\pi$
$822$		0			0
$823$	−20.3021	+	20.3021i	−0.707687	+	0.707687i	−0.966048	−	0.258361i	$-0.916818\pi$
$823$	−20.3021	+	20.3021i	−0.707687	+	0.707687i	0.258361	+	0.966048i	$0.416818\pi$
$824$	−18.3622			−0.639679
$825$		0			0
$826$	−10.2876			−0.357951
$827$	17.5394	−	17.5394i	0.609906	−	0.609906i	−0.333016	−	0.942921i	$-0.608066\pi$
$827$	17.5394	−	17.5394i	0.609906	−	0.609906i	0.942921	+	0.333016i	$0.108066\pi$
$828$		0			0
$829$			10.9440i			0.380101i	0.981774	+	0.190050i	$0.0608652\pi$
$829$			10.9440i			0.380101i	−0.981774	+	0.190050i	$0.939135\pi$
$830$	4.17711	−	8.70490i	0.144990	−	0.302152i
$831$		0			0
$832$	3.43352	+	3.43352i	0.119036	+	0.119036i
$833$	5.27550	+	5.27550i	0.182785	+	0.182785i
$834$		0			0
$835$	12.6661	+	36.0364i	0.438329	+	1.24709i
$836$		−	2.78772i		−	0.0964152i
$837$		0			0
$838$	7.10896	−	7.10896i	0.245575	−	0.245575i
$839$	−50.9037			−1.75739			−0.878696	−	0.477382i	$-0.841586\pi$
$839$	−50.9037			−1.75739			−0.878696	+	0.477382i	$0.841586\pi$
$840$		0			0
$841$	61.4818			2.12006
$842$	−2.69970	+	2.69970i	−0.0930379	+	0.0930379i
$843$		0			0
$844$		−	8.68986i		−	0.299117i
$845$	−21.3252	−	10.2331i	−0.733609	−	0.352028i
$846$		0			0
$847$	5.63392	+	5.63392i	0.193584	+	0.193584i
$848$	−3.37555	−	3.37555i	−0.115917	−	0.115917i
$849$		0			0
$850$	4.54396	−	3.64447i	0.155857	−	0.125004i
$851$		−	3.43795i		−	0.117851i
$852$		0			0
$853$	−6.76417	+	6.76417i	−0.231601	+	0.231601i	−0.813361	−	0.581760i	$-0.802364\pi$
$853$	−6.76417	+	6.76417i	−0.231601	+	0.231601i	0.581760	+	0.813361i	$0.302364\pi$
$854$	11.7395			0.401716
$855$		0			0
$856$	11.4147			0.390146
$857$	−5.91490	+	5.91490i	−0.202049	+	0.202049i	−0.800877	−	0.598828i	$-0.795633\pi$
$857$	−5.91490	+	5.91490i	−0.202049	+	0.202049i	0.598828	+	0.800877i	$0.295633\pi$
$858$		0			0
$859$			4.86410i			0.165961i	0.996551	+	0.0829804i	$0.0264439\pi$
$859$			4.86410i			0.165961i	−0.996551	+	0.0829804i	$0.973556\pi$
$860$	−3.36625	+	1.18317i	−0.114788	+	0.0403459i
$861$		0			0
$862$	25.3534	+	25.3534i	0.863541	+	0.863541i
$863$	−4.84105	−	4.84105i	−0.164791	−	0.164791i	0.619894	−	0.784685i	$-0.287176\pi$
$863$	−4.84105	−	4.84105i	−0.164791	−	0.164791i	−0.784685	+	0.619894i	$0.787176\pi$
$864$		0			0
$865$	20.2926	−	7.13246i	0.689968	−	0.242511i
$866$		−	6.39505i		−	0.217313i
$867$		0			0
$868$	−3.41520	+	3.41520i	−0.115919	+	0.115919i
$869$	1.50574			0.0510788
$870$		0			0
$871$	−42.9585			−1.45559
$872$	0.487333	−	0.487333i	0.0165032	−	0.0165032i
$873$		0			0
$874$		−	3.38410i		−	0.114469i
$875$	−7.32691	−	4.56115i	−0.247695	−	0.154195i
$876$		0			0
$877$	−35.1613	−	35.1613i	−1.18731	−	1.18731i	−0.977808	−	0.209504i	$-0.932815\pi$
$877$	−35.1613	−	35.1613i	−1.18731	−	1.18731i	−0.209504	−	0.977808i	$-0.567185\pi$
$878$	25.0076	+	25.0076i	0.843966	+	0.843966i
$879$		0			0
$880$	−1.66070	−	0.796900i	−0.0559822	−	0.0268635i
$881$			33.2817i			1.12129i	0.828057	+	0.560644i	$0.189447\pi$
$881$			33.2817i			1.12129i	−0.828057	+	0.560644i	$0.810553\pi$
$882$		0			0
$883$	9.99858	−	9.99858i	0.336479	−	0.336479i	−0.518561	−	0.855040i	$-0.673532\pi$
$883$	9.99858	−	9.99858i	0.336479	−	0.336479i	0.855040	+	0.518561i	$0.173532\pi$
$884$	5.65685			0.190261
$885$		0			0
$886$	−24.7751			−0.832336
$887$	−37.4673	+	37.4673i	−1.25803	+	1.25803i	−0.305997	+	0.952032i	$0.598990\pi$
$887$	−37.4673	+	37.4673i	−1.25803	+	1.25803i	−0.952032	+	0.305997i	$0.901010\pi$
$888$		0			0
$889$		−	12.4447i		−	0.417381i
$890$	4.14256	+	11.7860i	0.138859	+	0.395068i
$891$		0			0
$892$	−2.43171	−	2.43171i	−0.0814196	−	0.0814196i
$893$	−5.33550	−	5.33550i	−0.178546	−	0.178546i
$894$		0			0
$895$	−8.34816	+	17.3972i	−0.279048	+	0.581523i
$896$			0.771946i			0.0257889i
$897$		0			0
$898$	−2.86801	+	2.86801i	−0.0957067	+	0.0957067i
$899$	−59.5148			−1.98493
$900$		0			0
$901$	−5.56135			−0.185275
$902$	0.0518230	−	0.0518230i	0.00172552	−	0.00172552i
$903$		0			0
$904$		−	8.46377i		−	0.281501i
$905$	−17.8071	+	37.1092i	−0.591929	+	1.23355i
$906$		0			0
$907$	42.0280	+	42.0280i	1.39552	+	1.39552i	0.812359	+	0.583157i	$0.198183\pi$
$907$	42.0280	+	42.0280i	1.39552	+	1.39552i	0.583157	+	0.812359i	$0.301817\pi$
$908$	−15.5944	−	15.5944i	−0.517520	−	0.517520i
$909$		0			0
$910$	−2.77930	−	7.90738i	−0.0921328	−	0.262127i
$911$			35.4560i			1.17471i	0.809329	+	0.587355i	$0.199831\pi$
$911$			35.4560i			1.17471i	−0.809329	+	0.587355i	$0.800169\pi$
$912$		0			0
$913$	−2.51518	+	2.51518i	−0.0832402	+	0.0832402i
$914$	−34.1908			−1.13093
$915$		0			0
$916$	1.17054			0.0386756
$917$	−7.41067	+	7.41067i	−0.244722	+	0.244722i
$918$		0			0
$919$		−	12.6463i		−	0.417163i	−0.978005	−	0.208581i	$-0.933115\pi$
$919$		−	12.6463i		−	0.417163i	0.978005	−	0.208581i	$-0.0668846\pi$
$920$	−2.01598	−	0.967383i	−0.0664649	−	0.0318937i
$921$		0			0
$922$	7.68839	+	7.68839i	0.253204	+	0.253204i
$923$	1.46960	+	1.46960i	0.0483726	+	0.0483726i
$924$		0			0
$925$	−1.87698	+	17.0869i	−0.0617148	+	0.561815i
$926$		−	28.6255i		−	0.940694i
$927$		0			0
$928$	−6.72613	+	6.72613i	−0.220796	+	0.220796i
$929$	6.96583			0.228541			0.114271	−	0.993450i	$-0.463547\pi$
$929$	6.96583			0.228541			0.114271	+	0.993450i	$0.463547\pi$
$930$		0			0
$931$	−21.6721			−0.710274
$932$	−0.391179	+	0.391179i	−0.0128135	+	0.0128135i
$933$		0			0
$934$			4.39957i			0.143958i
$935$	−2.02450	+	0.711573i	−0.0662082	+	0.0232709i
$936$		0			0
$937$	4.21026	+	4.21026i	0.137543	+	0.137543i	0.772526	−	0.634983i	$-0.218993\pi$
$937$	4.21026	+	4.21026i	0.137543	+	0.137543i	−0.634983	+	0.772526i	$0.718993\pi$
$938$	−4.82911	−	4.82911i	−0.157676	−	0.157676i
$939$		0			0
$940$	−4.70369	+	1.65326i	−0.153417	+	0.0539234i
$941$			2.55988i			0.0834498i	0.999129	+	0.0417249i	$0.0132853\pi$
$941$			2.55988i			0.0834498i	−0.999129	+	0.0417249i	$0.986715\pi$
$942$		0			0
$943$	0.0629096	−	0.0629096i	0.00204862	−	0.00204862i
$944$	13.3268			0.433751
$945$		0			0
$946$	1.31450			0.0427382
$947$	−12.5991	+	12.5991i	−0.409416	+	0.409416i	−0.881535	−	0.472119i	$-0.843489\pi$
$947$	−12.5991	+	12.5991i	−0.409416	+	0.409416i	0.472119	+	0.881535i	$0.343489\pi$
$948$		0			0
$949$			50.5329i			1.64037i
$950$	−1.84758	+	16.8193i	−0.0599435	+	0.545690i
$951$		0			0
$952$	0.635906	+	0.635906i	0.0206098	+	0.0206098i
$953$	5.29171	+	5.29171i	0.171415	+	0.171415i	0.787601	−	0.616186i	$-0.211323\pi$
$953$	5.29171	+	5.29171i	0.171415	+	0.171415i	−0.616186	+	0.787601i	$0.711323\pi$
$954$		0			0
$955$	−13.8492	−	6.64565i	−0.448150	−	0.215048i
$956$		−	4.90654i		−	0.158689i
$957$		0			0
$958$	27.6947	−	27.6947i	0.894774	−	0.894774i
$959$	1.99903			0.0645520
$960$		0			0
$961$	8.14608			0.262777
$962$	−11.8042	+	11.8042i	−0.380584	+	0.380584i
$963$		0			0
$964$		−	25.4617i		−	0.820065i
$965$	−8.21577	−	23.3747i	−0.264475	−	0.752458i
$966$		0			0
$967$	21.0727	+	21.0727i	0.677651	+	0.677651i	0.959468	−	0.281817i	$-0.0909372\pi$
$967$	21.0727	+	21.0727i	0.677651	+	0.677651i	−0.281817	+	0.959468i	$0.590937\pi$
$968$	−7.29833	−	7.29833i	−0.234577	−	0.234577i
$969$		0			0
$970$	−12.4589	+	25.9637i	−0.400030	+	0.833643i
$971$		−	34.5438i		−	1.10856i	−0.832329	−	0.554282i	$-0.812993\pi$
$971$		−	34.5438i		−	1.10856i	0.832329	−	0.554282i	$-0.187007\pi$
$972$		0			0
$973$	−7.04975	+	7.04975i	−0.226004	+	0.226004i
$974$	−5.76978			−0.184876
$975$		0			0
$976$	−15.2076			−0.486784
$977$	−29.6333	+	29.6333i	−0.948053	+	0.948053i	−0.998716	−	0.0506632i	$-0.983866\pi$
$977$	−29.6333	+	29.6333i	−0.948053	+	0.948053i	0.0506632	+	0.998716i	$0.483866\pi$
$978$		0			0
$979$		−	4.60237i		−	0.147092i
$980$	−6.19521	+	12.9105i	−0.197899	+	0.412412i
$981$		0			0
$982$	24.4239	+	24.4239i	0.779397	+	0.779397i
$983$	−40.1893	−	40.1893i	−1.28184	−	1.28184i	−0.939620	−	0.342221i	$-0.888821\pi$
$983$	−40.1893	−	40.1893i	−1.28184	−	1.28184i	−0.342221	−	0.939620i	$-0.611179\pi$
$984$		0			0
$985$	−14.7836	−	42.0608i	−0.471044	−	1.34017i
$986$			11.0816i			0.352909i
$987$		0			0
$988$	−11.6194	+	11.6194i	−0.369661	+	0.369661i
$989$	1.59572			0.0507408
$990$		0			0
$991$	−42.1900			−1.34021			−0.670105	−	0.742266i	$-0.733751\pi$
$991$	−42.1900			−1.34021			−0.670105	+	0.742266i	$0.733751\pi$
$992$	4.42414	−	4.42414i	0.140467	−	0.140467i
$993$		0			0
$994$			0.330406i			0.0104798i
$995$	36.0567	+	17.3021i	1.14307	+	0.548512i
$996$		0			0
$997$	−4.72432	−	4.72432i	−0.149621	−	0.149621i	0.628328	−	0.777949i	$-0.283740\pi$
$997$	−4.72432	−	4.72432i	−0.149621	−	0.149621i	−0.777949	+	0.628328i	$0.783740\pi$
$998$	−5.43042	−	5.43042i	−0.171897	−	0.171897i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.j.737.8	yes	20
3.2	odd	2	inner	2070.2.j.j.737.3	yes	20
5.3	odd	4	inner	2070.2.j.j.323.3	✓	20
15.8	even	4	inner	2070.2.j.j.323.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.j.323.3	✓	20	5.3	odd	4	inner
2070.2.j.j.323.8	yes	20	15.8	even	4	inner
2070.2.j.j.737.3	yes	20	3.2	odd	2	inner
2070.2.j.j.737.8	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.967383 - 2.01598i) q^{5} +(0.545849 + 0.545849i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.967383 - 2.01598i) q^{5} +(0.545849 + 0.545849i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.741469 - 2.10956i) q^{10} +0.823770i q^{11} +(3.43352 - 3.43352i) q^{13} +0.771946 q^{14} -1.00000 q^{16} +(-0.823770 + 0.823770i) q^{17} -3.38410i q^{19} +(-2.01598 - 0.967383i) q^{20} +(0.582493 + 0.582493i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-3.12834 - 3.90045i) q^{25} -4.85573i q^{26} +(0.545849 - 0.545849i) q^{28} +9.51219 q^{29} -6.25668 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.16499i q^{34} +(1.62846 - 0.572375i) q^{35} +(-2.43100 - 2.43100i) q^{37} +(-2.39292 - 2.39292i) q^{38} +(-2.10956 + 0.741469i) q^{40} -0.0889676i q^{41} +(1.12834 - 1.12834i) q^{43} +0.823770 q^{44} +1.00000 q^{46} +(1.57664 - 1.57664i) q^{47} -6.40410i q^{49} +(-4.97010 - 0.545960i) q^{50} +(-3.43352 - 3.43352i) q^{52} +(3.37555 + 3.37555i) q^{53} +(1.66070 + 0.796900i) q^{55} -0.771946i q^{56} +(6.72613 - 6.72613i) q^{58} -13.3268 q^{59} +15.2076 q^{61} +(-4.42414 + 4.42414i) q^{62} +1.00000i q^{64} +(-3.60037 - 10.2434i) q^{65} +(-6.25575 - 6.25575i) q^{67} +(0.823770 + 0.823770i) q^{68} +(0.746768 - 1.55623i) q^{70} +0.428017i q^{71} +(-7.35876 + 7.35876i) q^{73} -3.43795 q^{74} -3.38410 q^{76} +(-0.449653 + 0.449653i) q^{77} -1.82787i q^{79} +(-0.967383 + 2.01598i) q^{80} +(-0.0629096 - 0.0629096i) q^{82} +(3.05325 + 3.05325i) q^{83} +(0.863802 + 2.45760i) q^{85} -1.59572i q^{86} +(0.582493 - 0.582493i) q^{88} -5.58696 q^{89} +3.74836 q^{91} +(0.707107 - 0.707107i) q^{92} -2.22971i q^{94} +(-6.82227 - 3.27372i) q^{95} +(-9.10678 - 9.10678i) q^{97} +(-4.52838 - 4.52838i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{7}+O(q^{10}) \) 20 * q - 16 * q^7	\( 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) \) 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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