LMFDB - Embedded newform 1530.2.m.h.647.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1530.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.17364600040304039428096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 20 x^{14} - 40 x^{13} + 104 x^{12} - 180 x^{11} + 242 x^{10} - 132 x^{9} - 302 x^{8} + \cdots + 1 $ x^16 - 4x^15 + 20x^14 - 40x^13 + 104x^12 - 180x^11 + 242x^10 - 132x^9 - 302x^8 + 416x^7 + 296x^6 - 416x^5 + 2x^4 + 32x^3 + 46x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.8
Root			$1.25829 + 0.521201i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.h.953.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.16023 - 0.577419i) q^{5} +(1.51658 + 1.51658i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.16023 - 0.577419i) q^{5} +(1.51658 + 1.51658i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11922 - 1.93581i) q^{10} +5.47530i q^{11} +(1.53844 - 1.53844i) q^{13} +2.14477 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +8.66635i q^{19} +(-0.577419 - 2.16023i) q^{20} +(3.87162 + 3.87162i) q^{22} +(4.15186 + 4.15186i) q^{23} +(4.33317 - 2.49472i) q^{25} -2.17569i q^{26} +(1.51658 - 1.51658i) q^{28} +3.13470 q^{29} -9.82789 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(4.15186 + 2.40046i) q^{35} +(-4.21657 - 4.21657i) q^{37} +(6.12803 + 6.12803i) q^{38} +(-1.93581 - 1.11922i) q^{40} -3.48117i q^{41} +(6.41006 - 6.41006i) q^{43} +5.47530 q^{44} +5.87162 q^{46} +(-2.96242 + 2.96242i) q^{47} -2.39997i q^{49} +(1.29999 - 4.82805i) q^{50} +(-1.53844 - 1.53844i) q^{52} +(3.58990 + 3.58990i) q^{53} +(3.16154 + 11.8279i) q^{55} -2.14477i q^{56} +(2.21657 - 2.21657i) q^{58} -11.1574 q^{59} +4.75100 q^{61} +(-6.94937 + 6.94937i) q^{62} +1.00000i q^{64} +(2.43506 - 4.21172i) q^{65} +(-2.86153 - 2.86153i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(4.63319 - 1.23843i) q^{70} -1.20241i q^{71} +(-0.699986 + 0.699986i) q^{73} -5.96312 q^{74} +8.66635 q^{76} +(-8.30372 + 8.30372i) q^{77} -12.2149i q^{79} +(-2.16023 + 0.577419i) q^{80} +(-2.46156 - 2.46156i) q^{82} +(5.76559 + 5.76559i) q^{83} +(1.11922 - 1.93581i) q^{85} -9.06520i q^{86} +(3.87162 - 3.87162i) q^{88} +9.65609 q^{89} +4.66635 q^{91} +(4.15186 - 4.15186i) q^{92} +4.18949i q^{94} +(5.00412 + 18.7213i) q^{95} +(-9.41006 - 9.41006i) q^{97} +(-1.69704 - 1.69704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$5$	2.16023	−	0.577419i	0.966084	−	0.258230i
$5$	2.16023	−	0.577419i	0.966084	−	0.258230i
$6$		0			0
$7$	1.51658	+	1.51658i	0.573213	+	0.573213i	0.933025	−	0.359812i	$-0.117159\pi$
$7$	1.51658	+	1.51658i	0.573213	+	0.573213i	−0.359812	+	0.933025i	$0.617159\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.11922	−	1.93581i	0.353927	−	0.612157i
$11$			5.47530i			1.65086i	0.564502	+	0.825432i	$0.309068\pi$
$11$			5.47530i			1.65086i	−0.564502	+	0.825432i	$0.690932\pi$
$12$		0			0
$13$	1.53844	−	1.53844i	0.426688	−	0.426688i	−0.460811	−	0.887498i	$-0.652441\pi$
$13$	1.53844	−	1.53844i	0.426688	−	0.426688i	0.887498	+	0.460811i	$0.152441\pi$
$14$	2.14477			0.573213
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$			8.66635i			1.98820i	0.108483	+	0.994098i	$0.465401\pi$
$19$			8.66635i			1.98820i	−0.108483	+	0.994098i	$0.534599\pi$
$20$	−0.577419	−	2.16023i	−0.129115	−	0.483042i
$21$		0			0
$22$	3.87162	+	3.87162i	0.825432	+	0.825432i
$23$	4.15186	+	4.15186i	0.865723	+	0.865723i	0.991996	−	0.126273i	$-0.0403014\pi$
$23$	4.15186	+	4.15186i	0.865723	+	0.865723i	−0.126273	+	0.991996i	$0.540301\pi$
$24$		0			0
$25$	4.33317	−	2.49472i	0.866635	−	0.498943i
$26$		−	2.17569i		−	0.426688i
$27$		0			0
$28$	1.51658	−	1.51658i	0.286607	−	0.286607i
$29$	3.13470			0.582099			0.291049	−	0.956708i	$-0.405996\pi$
$29$	3.13470			0.582099			0.291049	+	0.956708i	$0.405996\pi$
$30$		0			0
$31$	−9.82789			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$31$	−9.82789			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.00000i		−	0.171499i
$35$	4.15186	+	2.40046i	0.701793	+	0.405751i
$36$		0			0
$37$	−4.21657	−	4.21657i	−0.693199	−	0.693199i	0.269735	−	0.962934i	$-0.413064\pi$
$37$	−4.21657	−	4.21657i	−0.693199	−	0.693199i	−0.962934	+	0.269735i	$0.913064\pi$
$38$	6.12803	+	6.12803i	0.994098	+	0.994098i
$39$		0			0
$40$	−1.93581	−	1.11922i	−0.306078	−	0.176963i
$41$		−	3.48117i		−	0.543667i	−0.962344	−	0.271833i	$-0.912370\pi$
$41$		−	3.48117i		−	0.543667i	0.962344	−	0.271833i	$-0.0876299\pi$
$42$		0			0
$43$	6.41006	−	6.41006i	0.977525	−	0.977525i	−0.0222275	−	0.999753i	$-0.507076\pi$
$43$	6.41006	−	6.41006i	0.977525	−	0.977525i	0.999753	+	0.0222275i	$0.00707581\pi$
$44$	5.47530			0.825432
$45$		0			0
$46$	5.87162			0.865723
$47$	−2.96242	+	2.96242i	−0.432113	+	0.432113i	−0.889347	−	0.457234i	$-0.848840\pi$
$47$	−2.96242	+	2.96242i	−0.432113	+	0.432113i	0.457234	+	0.889347i	$0.348840\pi$
$48$		0			0
$49$		−	2.39997i		−	0.342853i
$50$	1.29999	−	4.82805i	0.183846	−	0.682789i
$51$		0			0
$52$	−1.53844	−	1.53844i	−0.213344	−	0.213344i
$53$	3.58990	+	3.58990i	0.493111	+	0.493111i	0.909285	−	0.416174i	$-0.136629\pi$
$53$	3.58990	+	3.58990i	0.493111	+	0.493111i	−0.416174	+	0.909285i	$0.636629\pi$
$54$		0			0
$55$	3.16154	+	11.8279i	0.426302	+	1.59487i
$56$		−	2.14477i		−	0.286607i
$57$		0			0
$58$	2.21657	−	2.21657i	0.291049	−	0.291049i
$59$	−11.1574			−1.45257			−0.726285	−	0.687394i	$-0.758755\pi$
$59$	−11.1574			−1.45257			−0.726285	+	0.687394i	$0.758755\pi$
$60$		0			0
$61$	4.75100			0.608303			0.304152	−	0.952624i	$-0.401627\pi$
$61$	4.75100			0.608303			0.304152	+	0.952624i	$0.401627\pi$
$62$	−6.94937	+	6.94937i	−0.882570	+	0.882570i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.43506	−	4.21172i	0.302033	−	0.522399i
$66$		0			0
$67$	−2.86153	−	2.86153i	−0.349591	−	0.349591i	0.510366	−	0.859957i	$-0.329510\pi$
$67$	−2.86153	−	2.86153i	−0.349591	−	0.349591i	−0.859957	+	0.510366i	$0.829510\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	4.63319	−	1.23843i	0.553772	−	0.148021i
$71$		−	1.20241i		−	0.142700i	−0.997451	−	0.0713499i	$-0.977269\pi$
$71$		−	1.20241i		−	0.142700i	0.997451	−	0.0713499i	$-0.0227307\pi$
$72$		0			0
$73$	−0.699986	+	0.699986i	−0.0819271	+	0.0819271i	−0.746883	−	0.664956i	$-0.768450\pi$
$73$	−0.699986	+	0.699986i	−0.0819271	+	0.0819271i	0.664956	+	0.746883i	$0.268450\pi$
$74$	−5.96312			−0.693199
$75$		0			0
$76$	8.66635			0.994098
$77$	−8.30372	+	8.30372i	−0.946297	+	0.946297i
$78$		0			0
$79$		−	12.2149i		−	1.37428i	−0.726524	−	0.687141i	$-0.758865\pi$
$79$		−	12.2149i		−	1.37428i	0.726524	−	0.687141i	$-0.241135\pi$
$80$	−2.16023	+	0.577419i	−0.241521	+	0.0645574i
$81$		0			0
$82$	−2.46156	−	2.46156i	−0.271833	−	0.271833i
$83$	5.76559	+	5.76559i	0.632856	+	0.632856i	0.948783	−	0.315927i	$-0.102316\pi$
$83$	5.76559	+	5.76559i	0.632856	+	0.632856i	−0.315927	+	0.948783i	$0.602316\pi$
$84$		0			0
$85$	1.11922	−	1.93581i	0.121396	−	0.209968i
$86$		−	9.06520i		−	0.977525i
$87$		0			0
$88$	3.87162	−	3.87162i	0.412716	−	0.412716i
$89$	9.65609			1.02354			0.511772	−	0.859121i	$-0.328989\pi$
$89$	9.65609			1.02354			0.511772	+	0.859121i	$0.328989\pi$
$90$		0			0
$91$	4.66635			0.489166
$92$	4.15186	−	4.15186i	0.432861	−	0.432861i
$93$		0			0
$94$			4.18949i			0.432113i
$95$	5.00412	+	18.7213i	0.513411	+	1.92076i
$96$		0			0
$97$	−9.41006	−	9.41006i	−0.955447	−	0.955447i	0.0436018	−	0.999049i	$-0.486117\pi$
$97$	−9.41006	−	9.41006i	−0.955447	−	0.955447i	−0.999049	+	0.0436018i	$0.986117\pi$
$98$	−1.69704	−	1.69704i	−0.171427	−	0.171427i
$99$		0			0
$100$	−2.49472	−	4.33317i	−0.249472	−	0.433317i
$101$			9.11209i			0.906687i	0.891336	+	0.453344i	$0.149769\pi$
$101$			9.11209i			0.906687i	−0.891336	+	0.453344i	$0.850231\pi$
$102$		0			0
$103$	10.8610	−	10.8610i	1.07017	−	1.07017i	0.0728263	−	0.997345i	$-0.476798\pi$
$103$	10.8610	−	10.8610i	1.07017	−	1.07017i	0.997345	−	0.0728263i	$-0.0232019\pi$
$104$	−2.17569			−0.213344
$105$		0			0
$106$	5.07689			0.493111
$107$	3.63680	−	3.63680i	0.351582	−	0.351582i	−0.509116	−	0.860698i	$-0.670027\pi$
$107$	3.63680	−	3.63680i	0.351582	−	0.351582i	0.860698	+	0.509116i	$0.170027\pi$
$108$		0			0
$109$		−	18.1274i		−	1.73629i	−0.496309	−	0.868146i	$-0.665312\pi$
$109$		−	18.1274i		−	1.73629i	0.496309	−	0.868146i	$-0.334688\pi$
$110$	10.5991	+	6.12803i	1.01059	+	0.584285i
$111$		0			0
$112$	−1.51658	−	1.51658i	−0.143303	−	0.143303i
$113$	−4.19507	−	4.19507i	−0.394639	−	0.394639i	0.481698	−	0.876337i	$-0.340020\pi$
$113$	−4.19507	−	4.19507i	−0.394639	−	0.394639i	−0.876337	+	0.481698i	$0.840020\pi$
$114$		0			0
$115$	11.3663	+	6.57160i	1.05992	+	0.612805i
$116$		−	3.13470i		−	0.291049i
$117$		0			0
$118$	−7.88947	+	7.88947i	−0.726285	+	0.726285i
$119$	2.14477			0.196611
$120$		0			0
$121$	−18.9789			−1.72535
$122$	3.35946	−	3.35946i	0.304152	−	0.304152i
$123$		0			0
$124$			9.82789i			0.882570i
$125$	7.92015	−	7.89121i	0.708400	−	0.705812i
$126$		0			0
$127$	−14.5817	−	14.5817i	−1.29392	−	1.29392i	−0.932344	−	0.361572i	$-0.882240\pi$
$127$	−14.5817	−	14.5817i	−1.29392	−	1.29392i	−0.361572	−	0.932344i	$-0.617760\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−1.25628	−	4.69999i	−0.110183	−	0.412216i
$131$		−	11.9807i		−	1.04676i	−0.852099	−	0.523380i	$-0.824671\pi$
$131$		−	11.9807i		−	1.04676i	0.852099	−	0.523380i	$-0.175329\pi$
$132$		0			0
$133$	−13.1432	+	13.1432i	−1.13966	+	1.13966i
$134$	−4.04681			−0.349591
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	−6.98397	+	6.98397i	−0.596681	+	0.596681i	−0.939428	−	0.342747i	$-0.888643\pi$
$137$	−6.98397	+	6.98397i	−0.596681	+	0.596681i	0.342747	+	0.939428i	$0.388643\pi$
$138$		0			0
$139$		−	3.55375i		−	0.301425i	−0.988578	−	0.150713i	$-0.951843\pi$
$139$		−	3.55375i		−	0.301425i	0.988578	−	0.150713i	$-0.0481568\pi$
$140$	2.40046	−	4.15186i	0.202876	−	0.350896i
$141$		0			0
$142$	−0.850232	−	0.850232i	−0.0713499	−	0.0713499i
$143$	8.42344	+	8.42344i	0.704403	+	0.704403i
$144$		0			0
$145$	6.77166	−	1.81003i	0.562356	−	0.150315i
$146$			0.989929i			0.0819271i
$147$		0			0
$148$	−4.21657	+	4.21657i	−0.346600	+	0.346600i
$149$	3.97399			0.325562			0.162781	−	0.986662i	$-0.447954\pi$
$149$	3.97399			0.325562			0.162781	+	0.986662i	$0.447954\pi$
$150$		0			0
$151$	19.2095			1.56325			0.781625	−	0.623749i	$-0.214391\pi$
$151$	19.2095			1.56325			0.781625	+	0.623749i	$0.214391\pi$
$152$	6.12803	−	6.12803i	0.497049	−	0.497049i
$153$		0			0
$154$			11.7432i			0.946297i
$155$	−21.2305	+	5.67481i	−1.70527	+	0.455812i
$156$		0			0
$157$	7.49472	+	7.49472i	0.598143	+	0.598143i	0.939818	−	0.341675i	$-0.110994\pi$
$157$	7.49472	+	7.49472i	0.598143	+	0.598143i	−0.341675	+	0.939818i	$0.610994\pi$
$158$	−8.63723	−	8.63723i	−0.687141	−	0.687141i
$159$		0			0
$160$	−1.11922	+	1.93581i	−0.0884817	+	0.153039i
$161$			12.5933i			0.992488i
$162$		0			0
$163$	−10.2201	+	10.2201i	−0.800500	+	0.800500i	−0.983174	−	0.182674i	$-0.941525\pi$
$163$	−10.2201	+	10.2201i	−0.800500	+	0.800500i	0.182674	+	0.983174i	$0.441525\pi$
$164$	−3.48117			−0.271833
$165$		0			0
$166$	8.15378			0.632856
$167$	0.821334	−	0.821334i	0.0635567	−	0.0635567i	−0.674614	−	0.738171i	$-0.735690\pi$
$167$	0.821334	−	0.821334i	0.0635567	−	0.0635567i	0.738171	+	0.674614i	$0.235690\pi$
$168$		0			0
$169$			8.26638i			0.635875i
$170$	−0.577419	−	2.16023i	−0.0442860	−	0.165682i
$171$		0			0
$172$	−6.41006	−	6.41006i	−0.488763	−	0.488763i
$173$	6.05390	+	6.05390i	0.460270	+	0.460270i	0.898744	−	0.438474i	$-0.144481\pi$
$173$	6.05390	+	6.05390i	0.460270	+	0.460270i	−0.438474	+	0.898744i	$0.644481\pi$
$174$		0			0
$175$	10.3550	+	2.78817i	0.782767	+	0.210766i
$176$		−	5.47530i		−	0.412716i
$177$		0			0
$178$	6.82789	−	6.82789i	0.511772	−	0.511772i
$179$	3.07115			0.229549			0.114774	−	0.993392i	$-0.463385\pi$
$179$	3.07115			0.229549			0.114774	+	0.993392i	$0.463385\pi$
$180$		0			0
$181$	21.6506			1.60927			0.804637	−	0.593767i	$-0.202360\pi$
$181$	21.6506			1.60927			0.804637	+	0.593767i	$0.202360\pi$
$182$	3.29961	−	3.29961i	0.244583	−	0.244583i
$183$		0			0
$184$		−	5.87162i		−	0.432861i
$185$	−11.5435	−	6.67402i	−0.848693	−	0.490684i
$186$		0			0
$187$	3.87162	+	3.87162i	0.283121	+	0.283121i
$188$	2.96242	+	2.96242i	0.216056	+	0.216056i
$189$		0			0
$190$	16.7764	+	9.69951i	1.21709	+	0.703676i
$191$			2.98406i			0.215919i	0.994155	+	0.107959i	$0.0344317\pi$
$191$			2.98406i			0.215919i	−0.994155	+	0.107959i	$0.965568\pi$
$192$		0			0
$193$	5.88692	−	5.88692i	0.423750	−	0.423750i	−0.462743	−	0.886493i	$-0.653135\pi$
$193$	5.88692	−	5.88692i	0.423750	−	0.423750i	0.886493	+	0.462743i	$0.153135\pi$
$194$	−13.3078			−0.955447
$195$		0			0
$196$	−2.39997			−0.171427
$197$	−5.59700	+	5.59700i	−0.398769	+	0.398769i	−0.877799	−	0.479029i	$-0.840989\pi$
$197$	−5.59700	+	5.59700i	−0.398769	+	0.398769i	0.479029	+	0.877799i	$0.340989\pi$
$198$		0			0
$199$		−	1.35103i		−	0.0957719i	−0.998853	−	0.0478859i	$-0.984752\pi$
$199$		−	1.35103i		−	0.0957719i	0.998853	−	0.0478859i	$-0.0152484\pi$
$200$	−4.82805	−	1.29999i	−0.341394	−	0.0919229i
$201$		0			0
$202$	6.44322	+	6.44322i	0.453344	+	0.453344i
$203$	4.75402	+	4.75402i	0.333667	+	0.333667i
$204$		0			0
$205$	−2.01009	−	7.52011i	−0.140391	−	0.525227i
$206$		−	15.3598i		−	1.07017i
$207$		0			0
$208$	−1.53844	+	1.53844i	−0.106672	+	0.106672i
$209$	−47.4508			−3.28224
$210$		0			0
$211$	−13.4202			−0.923882			−0.461941	−	0.886911i	$-0.652847\pi$
$211$	−13.4202			−0.923882			−0.461941	+	0.886911i	$0.652847\pi$
$212$	3.58990	−	3.58990i	0.246556	−	0.246556i
$213$		0			0
$214$		−	5.14321i		−	0.351582i
$215$	10.1459	−	17.5485i	0.691945	−	1.19680i
$216$		0			0
$217$	−14.9048	−	14.9048i	−1.01180	−	1.01180i
$218$	−12.8180	−	12.8180i	−0.868146	−	0.868146i
$219$		0			0
$220$	11.8279	−	3.16154i	0.797436	−	0.213151i
$221$		−	2.17569i		−	0.146353i
$222$		0			0
$223$	−16.2812	+	16.2812i	−1.09027	+	1.09027i	−0.0947709	+	0.995499i	$0.530212\pi$
$223$	−16.2812	+	16.2812i	−1.09027	+	1.09027i	−0.995499	+	0.0947709i	$0.969788\pi$
$224$	−2.14477			−0.143303
$225$		0			0
$226$	−5.93272			−0.394639
$227$	8.77490	−	8.77490i	0.582411	−	0.582411i	−0.353154	−	0.935565i	$-0.614891\pi$
$227$	8.77490	−	8.77490i	0.582411	−	0.582411i	0.935565	+	0.353154i	$0.114891\pi$
$228$		0			0
$229$			6.47686i			0.428003i	0.976833	+	0.214001i	$0.0686497\pi$
$229$			6.47686i			0.428003i	−0.976833	+	0.214001i	$0.931350\pi$
$230$	12.6840	−	3.39039i	0.836361	−	0.223555i
$231$		0			0
$232$	−2.21657	−	2.21657i	−0.145525	−	0.145525i
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	0.899716	−	0.436475i	$-0.143773\pi$
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	−0.436475	+	0.899716i	$0.643773\pi$
$234$		0			0
$235$	−4.68894	+	8.11005i	−0.305873	+	0.529041i
$236$			11.1574i			0.726285i
$237$		0			0
$238$	1.51658	−	1.51658i	0.0983053	−	0.0983053i
$239$	−6.84999			−0.443089			−0.221544	−	0.975150i	$-0.571110\pi$
$239$	−6.84999			−0.443089			−0.221544	+	0.975150i	$0.571110\pi$
$240$		0			0
$241$	−29.4865			−1.89939			−0.949695	−	0.313175i	$-0.898607\pi$
$241$	−29.4865			−1.89939			−0.949695	+	0.313175i	$0.898607\pi$
$242$	−13.4201	+	13.4201i	−0.862675	+	0.862675i
$243$		0			0
$244$		−	4.75100i		−	0.304152i
$245$	−1.38579	−	5.18449i	−0.0885349	−	0.331225i
$246$		0			0
$247$	13.3327	+	13.3327i	0.848339	+	0.848339i
$248$	6.94937	+	6.94937i	0.441285	+	0.441285i
$249$		0			0
$250$	0.0204612	−	11.1803i	0.00129408	−	0.707106i
$251$		−	24.9438i		−	1.57444i	−0.616673	−	0.787219i	$-0.711520\pi$
$251$		−	24.9438i		−	1.57444i	0.616673	−	0.787219i	$-0.288480\pi$
$252$		0			0
$253$	−22.7327	+	22.7327i	−1.42919	+	1.42919i
$254$	−20.6216			−1.29392
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.8635	+	10.8635i	−0.677646	+	0.677646i	−0.959467	−	0.281821i	$-0.909062\pi$
$257$	−10.8635	+	10.8635i	−0.677646	+	0.677646i	0.281821	+	0.959467i	$0.409062\pi$
$258$		0			0
$259$		−	12.7895i		−	0.794702i
$260$	−4.21172	−	2.43506i	−0.261200	−	0.151016i
$261$		0			0
$262$	−8.47165	−	8.47165i	−0.523380	−	0.523380i
$263$	20.0484	+	20.0484i	1.23624	+	1.23624i	0.961527	+	0.274711i	$0.0885823\pi$
$263$	20.0484	+	20.0484i	1.23624	+	1.23624i	0.274711	+	0.961527i	$0.411418\pi$
$264$		0			0
$265$	9.82789	+	5.68213i	0.603722	+	0.349051i
$266$			18.5873i			1.13966i
$267$		0			0
$268$	−2.86153	+	2.86153i	−0.174796	+	0.174796i
$269$	−26.6426			−1.62443			−0.812215	−	0.583358i	$-0.801738\pi$
$269$	−26.6426			−1.62443			−0.812215	+	0.583358i	$0.801738\pi$
$270$		0			0
$271$	−20.4096			−1.23979			−0.619897	−	0.784683i	$-0.712826\pi$
$271$	−20.4096			−1.23979			−0.619897	+	0.784683i	$0.712826\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$		0			0
$274$			9.87683i			0.596681i
$275$	13.6593	+	23.7254i	0.823687	+	1.43070i
$276$		0			0
$277$	−3.09073	−	3.09073i	−0.185704	−	0.185704i	0.608132	−	0.793836i	$-0.291919\pi$
$277$	−3.09073	−	3.09073i	−0.185704	−	0.185704i	−0.793836	+	0.608132i	$0.791919\pi$
$278$	−2.51288	−	2.51288i	−0.150713	−	0.150713i
$279$		0			0
$280$	−1.23843	−	4.63319i	−0.0740104	−	0.276886i
$281$		−	16.7122i		−	0.996967i	−0.866899	−	0.498484i	$-0.833890\pi$
$281$		−	16.7122i		−	0.996967i	0.866899	−	0.498484i	$-0.166110\pi$
$282$		0			0
$283$	−13.0332	+	13.0332i	−0.774741	+	0.774741i	−0.978931	−	0.204190i	$-0.934544\pi$
$283$	−13.0332	+	13.0332i	−0.774741	+	0.774741i	0.204190	+	0.978931i	$0.434544\pi$
$284$	−1.20241			−0.0713499
$285$		0			0
$286$	11.9125			0.704403
$287$	5.27946	−	5.27946i	0.311637	−	0.311637i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	3.50840	−	6.06818i	0.206020	−	0.356336i
$291$		0			0
$292$	0.699986	+	0.699986i	0.0409636	+	0.0409636i
$293$	−12.1214	−	12.1214i	−0.708140	−	0.708140i	0.258004	−	0.966144i	$-0.416935\pi$
$293$	−12.1214	−	12.1214i	−0.708140	−	0.708140i	−0.966144	+	0.258004i	$0.916935\pi$
$294$		0			0
$295$	−24.1025	+	6.44250i	−1.40330	+	0.375097i
$296$			5.96312i			0.346600i
$297$		0			0
$298$	2.81003	−	2.81003i	0.162781	−	0.162781i
$299$	12.7748			0.738787
$300$		0			0
$301$	19.4427			1.12066
$302$	13.5832	−	13.5832i	0.781625	−	0.781625i
$303$		0			0
$304$		−	8.66635i		−	0.497049i
$305$	10.2632	−	2.74332i	0.587672	−	0.157082i
$306$		0			0
$307$	5.96381	+	5.96381i	0.340373	+	0.340373i	0.856507	−	0.516135i	$-0.172630\pi$
$307$	5.96381	+	5.96381i	0.340373	+	0.340373i	−0.516135	+	0.856507i	$0.672630\pi$
$308$	8.30372	+	8.30372i	0.473149	+	0.473149i
$309$		0			0
$310$	−10.9995	+	19.0249i	−0.624731	+	1.08054i
$311$		−	13.0954i		−	0.742570i	−0.928519	−	0.371285i	$-0.878917\pi$
$311$		−	13.0954i		−	0.742570i	0.928519	−	0.371285i	$-0.121083\pi$
$312$		0			0
$313$	−1.22058	+	1.22058i	−0.0689910	+	0.0689910i	−0.740760	−	0.671769i	$-0.765535\pi$
$313$	−1.22058	+	1.22058i	−0.0689910	+	0.0689910i	0.671769	+	0.740760i	$0.265535\pi$
$314$	10.5991			0.598143
$315$		0			0
$316$	−12.2149			−0.687141
$317$	−15.0556	+	15.0556i	−0.845604	+	0.845604i	−0.989581	−	0.143977i	$-0.954011\pi$
$317$	−15.0556	+	15.0556i	−0.845604	+	0.845604i	0.143977	+	0.989581i	$0.454011\pi$
$318$		0			0
$319$			17.1634i			0.960965i
$320$	0.577419	+	2.16023i	0.0322787	+	0.120760i
$321$		0			0
$322$	8.90478	+	8.90478i	0.496244	+	0.496244i
$323$	6.12803	+	6.12803i	0.340973	+	0.340973i
$324$		0			0
$325$	2.82837	−	10.5043i	0.156890	−	0.582675i
$326$			14.4534i			0.800500i
$327$		0			0
$328$	−2.46156	+	2.46156i	−0.135917	+	0.135917i
$329$	−8.98548			−0.495385
$330$		0			0
$331$	−13.9327			−0.765812			−0.382906	−	0.923787i	$-0.625077\pi$
$331$	−13.9327			−0.765812			−0.382906	+	0.923787i	$0.625077\pi$
$332$	5.76559	−	5.76559i	0.316428	−	0.316428i
$333$		0			0
$334$		−	1.16154i		−	0.0635567i
$335$	−7.83385	−	4.52925i	−0.428009	−	0.247459i
$336$		0			0
$337$	6.09996	+	6.09996i	0.332286	+	0.332286i	0.853454	−	0.521168i	$-0.174504\pi$
$337$	6.09996	+	6.09996i	0.332286	+	0.332286i	−0.521168	+	0.853454i	$0.674504\pi$
$338$	5.84521	+	5.84521i	0.317938	+	0.317938i
$339$		0			0
$340$	−1.93581	−	1.11922i	−0.104984	−	0.0606980i
$341$		−	53.8106i		−	2.91401i
$342$		0			0
$343$	14.2558	−	14.2558i	0.769741	−	0.769741i
$344$	−9.06520			−0.488763
$345$		0			0
$346$	8.56151			0.460270
$347$	−17.7171	+	17.7171i	−0.951103	+	0.951103i	−0.998859	−	0.0477558i	$-0.984793\pi$
$347$	−17.7171	+	17.7171i	−0.951103	+	0.951103i	0.0477558	+	0.998859i	$0.484793\pi$
$348$		0			0
$349$		−	3.74419i		−	0.200422i	−0.994966	−	0.100211i	$-0.968048\pi$
$349$		−	3.74419i		−	0.200422i	0.994966	−	0.100211i	$-0.0319518\pi$
$350$	9.29365	−	5.35058i	0.496767	−	0.286001i
$351$		0			0
$352$	−3.87162	−	3.87162i	−0.206358	−	0.206358i
$353$	8.36557	+	8.36557i	0.445254	+	0.445254i	0.893773	−	0.448519i	$-0.148048\pi$
$353$	8.36557	+	8.36557i	0.445254	+	0.445254i	−0.448519	+	0.893773i	$0.648048\pi$
$354$		0			0
$355$	−0.694294	−	2.59748i	−0.0368493	−	0.137860i
$356$		−	9.65609i		−	0.511772i
$357$		0			0
$358$	2.17163	−	2.17163i	0.114774	−	0.114774i
$359$	−17.6954			−0.933930			−0.466965	−	0.884276i	$-0.654653\pi$
$359$	−17.6954			−0.933930			−0.466965	+	0.884276i	$0.654653\pi$
$360$		0			0
$361$	−56.1056			−2.95293
$362$	15.3093	−	15.3093i	0.804637	−	0.804637i
$363$		0			0
$364$		−	4.66635i		−	0.244583i
$365$	−1.10794	+	1.91631i	−0.0579924	+	0.100304i
$366$		0			0
$367$	−20.7157	−	20.7157i	−1.08135	−	1.08135i	−0.996384	−	0.0849659i	$-0.972922\pi$
$367$	−20.7157	−	20.7157i	−1.08135	−	1.08135i	−0.0849659	−	0.996384i	$-0.527078\pi$
$368$	−4.15186	−	4.15186i	−0.216431	−	0.216431i
$369$		0			0
$370$	−12.8817	+	3.44322i	−0.669688	+	0.179005i
$371$			10.8887i			0.565316i
$372$		0			0
$373$	25.6249	−	25.6249i	1.32681	−	1.32681i	0.418672	−	0.908138i	$-0.362496\pi$
$373$	25.6249	−	25.6249i	1.32681	−	1.32681i	0.908138	−	0.418672i	$-0.137504\pi$
$374$	5.47530			0.283121
$375$		0			0
$376$	4.18949			0.216056
$377$	4.82256	−	4.82256i	0.248374	−	0.248374i
$378$		0			0
$379$			9.14321i			0.469655i	0.972037	+	0.234828i	$0.0754525\pi$
$379$			9.14321i			0.469655i	−0.972037	+	0.234828i	$0.924547\pi$
$380$	18.7213	−	5.00412i	0.960382	−	0.256706i
$381$		0			0
$382$	2.11005	+	2.11005i	0.107959	+	0.107959i
$383$	18.2501	+	18.2501i	0.932537	+	0.932537i	0.997864	−	0.0653267i	$-0.0208090\pi$
$383$	18.2501	+	18.2501i	0.932537	+	0.932537i	−0.0653267	+	0.997864i	$0.520809\pi$
$384$		0			0
$385$	−13.1432	+	22.7327i	−0.669840	+	1.15856i
$386$		−	8.32537i		−	0.423750i
$387$		0			0
$388$	−9.41006	+	9.41006i	−0.477724	+	0.477724i
$389$	16.2301			0.822896			0.411448	−	0.911433i	$-0.365023\pi$
$389$	16.2301			0.822896			0.411448	+	0.911433i	$0.365023\pi$
$390$		0			0
$391$	5.87162			0.296941
$392$	−1.69704	+	1.69704i	−0.0857133	+	0.0857133i
$393$		0			0
$394$			7.91535i			0.398769i
$395$	−7.05311	−	26.3869i	−0.354880	−	1.32767i
$396$		0			0
$397$	12.0007	+	12.0007i	0.602299	+	0.602299i	0.940922	−	0.338623i	$-0.109961\pi$
$397$	12.0007	+	12.0007i	0.602299	+	0.602299i	−0.338623	+	0.940922i	$0.609961\pi$
$398$	−0.955321	−	0.955321i	−0.0478859	−	0.0478859i
$399$		0			0
$400$	−4.33317	+	2.49472i	−0.216659	+	0.124736i
$401$		−	1.01586i		−	0.0507294i	−0.999678	−	0.0253647i	$-0.991925\pi$
$401$		−	1.01586i		−	0.0507294i	0.999678	−	0.0253647i	$-0.00807470\pi$
$402$		0			0
$403$	−15.1197	+	15.1197i	−0.753164	+	0.753164i
$404$	9.11209			0.453344
$405$		0			0
$406$	6.72320			0.333667
$407$	23.0869	−	23.0869i	1.14438	−	1.14438i
$408$		0			0
$409$			11.7423i			0.580618i	0.956933	+	0.290309i	$0.0937582\pi$
$409$			11.7423i			0.580618i	−0.956933	+	0.290309i	$0.906242\pi$
$410$	−6.73887	−	3.89617i	−0.332809	−	0.192418i
$411$		0			0
$412$	−10.8610	−	10.8610i	−0.535085	−	0.535085i
$413$	−16.9211	−	16.9211i	−0.832632	−	0.832632i
$414$		0			0
$415$	15.7842	+	9.12583i	0.774814	+	0.447969i
$416$			2.17569i			0.106672i
$417$		0			0
$418$	−33.5528	+	33.5528i	−1.64112	+	1.64112i
$419$	−1.57742			−0.0770621			−0.0385310	−	0.999257i	$-0.512268\pi$
$419$	−1.57742			−0.0770621			−0.0385310	+	0.999257i	$0.512268\pi$
$420$		0			0
$421$	24.3739			1.18791			0.593955	−	0.804498i	$-0.297566\pi$
$421$	24.3739			1.18791			0.593955	+	0.804498i	$0.297566\pi$
$422$	−9.48948	+	9.48948i	−0.461941	+	0.461941i
$423$		0			0
$424$		−	5.07689i		−	0.246556i
$425$	1.29999	−	4.82805i	0.0630586	−	0.234195i
$426$		0			0
$427$	7.20527	+	7.20527i	0.348687	+	0.348687i
$428$	−3.63680	−	3.63680i	−0.175791	−	0.175791i
$429$		0			0
$430$	−5.23442	−	19.5829i	−0.252426	−	0.944371i
$431$		−	24.8155i		−	1.19532i	−0.801750	−	0.597660i	$-0.796097\pi$
$431$		−	24.8155i		−	1.19532i	0.801750	−	0.597660i	$-0.203903\pi$
$432$		0			0
$433$	16.6374	−	16.6374i	0.799545	−	0.799545i	−0.183479	−	0.983024i	$-0.558736\pi$
$433$	16.6374	−	16.6374i	0.799545	−	0.799545i	0.983024	+	0.183479i	$0.0587359\pi$
$434$	−21.0785			−1.01180
$435$		0			0
$436$	−18.1274			−0.868146
$437$	−35.9815	+	35.9815i	−1.72123	+	1.72123i
$438$		0			0
$439$			23.0253i			1.09894i	0.835515	+	0.549468i	$0.185169\pi$
$439$			23.0253i			1.09894i	−0.835515	+	0.549468i	$0.814831\pi$
$440$	6.12803	−	10.5991i	0.292143	−	0.505294i
$441$		0			0
$442$	−1.53844	−	1.53844i	−0.0731763	−	0.0731763i
$443$	−18.5621	−	18.5621i	−0.881910	−	0.881910i	0.111819	−	0.993729i	$-0.464332\pi$
$443$	−18.5621	−	18.5621i	−0.881910	−	0.881910i	−0.993729	+	0.111819i	$0.964332\pi$
$444$		0			0
$445$	20.8594	−	5.57561i	0.988829	−	0.264309i
$446$			23.0251i			1.09027i
$447$		0			0
$448$	−1.51658	+	1.51658i	−0.0716517	+	0.0716517i
$449$	21.7559			1.02672			0.513361	−	0.858173i	$-0.328400\pi$
$449$	21.7559			1.02672			0.513361	+	0.858173i	$0.328400\pi$
$450$		0			0
$451$	19.0604			0.897520
$452$	−4.19507	+	4.19507i	−0.197319	+	0.197319i
$453$		0			0
$454$		−	12.4096i		−	0.582411i
$455$	10.0804	−	2.69444i	0.472575	−	0.126317i
$456$		0			0
$457$	17.7712	+	17.7712i	0.831301	+	0.831301i	0.987695	−	0.156394i	$-0.0499869\pi$
$457$	17.7712	+	17.7712i	0.831301	+	0.831301i	−0.156394	+	0.987695i	$0.549987\pi$
$458$	4.57983	+	4.57983i	0.214001	+	0.214001i
$459$		0			0
$460$	6.57160	−	11.3663i	0.306403	−	0.529958i
$461$			5.98715i			0.278849i	0.990233	+	0.139425i	$0.0445253\pi$
$461$			5.98715i			0.278849i	−0.990233	+	0.139425i	$0.955475\pi$
$462$		0			0
$463$	−7.95908	+	7.95908i	−0.369890	+	0.369890i	−0.867437	−	0.497547i	$-0.834234\pi$
$463$	−7.95908	+	7.95908i	−0.369890	+	0.369890i	0.497547	+	0.867437i	$0.334234\pi$
$464$	−3.13470			−0.145525
$465$		0			0
$466$	10.0000			0.463241
$467$	21.4157	−	21.4157i	0.991002	−	0.991002i	−0.00895805	−	0.999960i	$-0.502851\pi$
$467$	21.4157	−	21.4157i	0.991002	−	0.991002i	0.999960	+	0.00895805i	$0.00285147\pi$
$468$		0			0
$469$		−	8.67947i		−	0.400781i
$470$	2.41909	+	9.05025i	0.111584	+	0.417457i
$471$		0			0
$472$	7.88947	+	7.88947i	0.363142	+	0.363142i
$473$	35.0970	+	35.0970i	1.61376	+	1.61376i
$474$		0			0
$475$	21.6201	+	37.5528i	0.991997	+	1.72304i
$476$		−	2.14477i		−	0.0983053i
$477$		0			0
$478$	−4.84367	+	4.84367i	−0.221544	+	0.221544i
$479$	2.48933			0.113740			0.0568702	−	0.998382i	$-0.481888\pi$
$479$	2.48933			0.113740			0.0568702	+	0.998382i	$0.481888\pi$
$480$		0			0
$481$	−12.9739			−0.591559
$482$	−20.8501	+	20.8501i	−0.949695	+	0.949695i
$483$		0			0
$484$			18.9789i			0.862675i
$485$	−25.7614	−	14.8943i	−1.16977	−	0.676317i
$486$		0			0
$487$	1.46764	+	1.46764i	0.0665050	+	0.0665050i	0.739577	−	0.673072i	$-0.235026\pi$
$487$	1.46764	+	1.46764i	0.0665050	+	0.0665050i	−0.673072	+	0.739577i	$0.735026\pi$
$488$	−3.35946	−	3.35946i	−0.152076	−	0.152076i
$489$		0			0
$490$	−4.64589	−	2.68608i	−0.209880	−	0.121345i
$491$		−	41.5512i		−	1.87518i	−0.347741	−	0.937591i	$-0.613051\pi$
$491$		−	41.5512i		−	1.87518i	0.347741	−	0.937591i	$-0.386949\pi$
$492$		0			0
$493$	2.21657	−	2.21657i	0.0998291	−	0.0998291i
$494$	18.8553			0.848339
$495$		0			0
$496$	9.82789			0.441285
$497$	1.82355	−	1.82355i	0.0817974	−	0.0817974i
$498$		0			0
$499$			0.122212i			0.00547097i	0.999996	+	0.00273548i	$0.000870732\pi$
$499$			0.122212i			0.00547097i	−0.999996	+	0.00273548i	$0.999129\pi$
$500$	−7.89121	−	7.92015i	−0.352906	−	0.354200i
$501$		0			0
$502$	−17.6379	−	17.6379i	−0.787219	−	0.787219i
$503$	14.8345	+	14.8345i	0.661437	+	0.661437i	0.955719	−	0.294282i	$-0.0950805\pi$
$503$	14.8345	+	14.8345i	0.661437	+	0.661437i	−0.294282	+	0.955719i	$0.595080\pi$
$504$		0			0
$505$	5.26150	+	19.6842i	0.234134	+	0.875936i
$506$			32.1488i			1.42919i
$507$		0			0
$508$	−14.5817	+	14.5817i	−0.646958	+	0.646958i
$509$	9.22444			0.408866			0.204433	−	0.978881i	$-0.434465\pi$
$509$	9.22444			0.408866			0.204433	+	0.978881i	$0.434465\pi$
$510$		0			0
$511$	−2.12317			−0.0939234
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			15.3633i			0.677646i
$515$	17.1910	−	29.7337i	0.757525	−	1.31022i
$516$		0			0
$517$	−16.2201	−	16.2201i	−0.713359	−	0.713359i
$518$	−9.04355	−	9.04355i	−0.397351	−	0.397351i
$519$		0			0
$520$	−4.69999	+	1.25628i	−0.206108	+	0.0550917i
$521$			15.5916i			0.683080i	0.939867	+	0.341540i	$0.110948\pi$
$521$			15.5916i			0.683080i	−0.939867	+	0.341540i	$0.889052\pi$
$522$		0			0
$523$	−12.6405	+	12.6405i	−0.552729	+	0.552729i	−0.927228	−	0.374498i	$-0.877815\pi$
$523$	−12.6405	+	12.6405i	−0.552729	+	0.552729i	0.374498	+	0.927228i	$0.377815\pi$
$524$	−11.9807			−0.523380
$525$		0			0
$526$	28.3527			1.23624
$527$	−6.94937	+	6.94937i	−0.302719	+	0.302719i
$528$		0			0
$529$			11.4759i			0.498952i
$530$	10.9672	−	2.93149i	0.476386	−	0.127336i
$531$		0			0
$532$	13.1432	+	13.1432i	0.569830	+	0.569830i
$533$	−5.35558	−	5.35558i	−0.231976	−	0.231976i
$534$		0			0
$535$	5.75636	−	9.95627i	0.248869	−	0.430447i
$536$			4.04681i			0.174796i
$537$		0			0
$538$	−18.8392	+	18.8392i	−0.812215	+	0.812215i
$539$	13.1406			0.566004
$540$		0			0
$541$	−19.3450			−0.831705			−0.415853	−	0.909432i	$-0.636517\pi$
$541$	−19.3450			−0.831705			−0.415853	+	0.909432i	$0.636517\pi$
$542$	−14.4318	+	14.4318i	−0.619897	+	0.619897i
$543$		0			0
$544$			1.00000i			0.0428746i
$545$	−10.4671	−	39.1594i	−0.448362	−	1.67740i
$546$		0			0
$547$	−1.86881	−	1.86881i	−0.0799046	−	0.0799046i	0.666025	−	0.745930i	$-0.267994\pi$
$547$	−1.86881	−	1.86881i	−0.0799046	−	0.0799046i	−0.745930	+	0.666025i	$0.767994\pi$
$548$	6.98397	+	6.98397i	0.298341	+	0.298341i
$549$		0			0
$550$	26.4350	+	7.11781i	1.12719	+	0.303505i
$551$			27.1664i			1.15733i
$552$		0			0
$553$	18.5248	−	18.5248i	0.787757	−	0.787757i
$554$	−4.37096			−0.185704
$555$		0			0
$556$	−3.55375			−0.150713
$557$	−5.50792	+	5.50792i	−0.233378	+	0.233378i	−0.814101	−	0.580723i	$-0.802770\pi$
$557$	−5.50792	+	5.50792i	−0.233378	+	0.233378i	0.580723	+	0.814101i	$0.302770\pi$
$558$		0			0
$559$		−	19.7231i		−	0.834196i
$560$	−4.15186	−	2.40046i	−0.175448	−	0.101438i
$561$		0			0
$562$	−11.8173	−	11.8173i	−0.498484	−	0.498484i
$563$	27.7001	+	27.7001i	1.16742	+	1.16742i	0.982813	+	0.184606i	$0.0591010\pi$
$563$	27.7001	+	27.7001i	1.16742	+	1.16742i	0.184606	+	0.982813i	$0.440899\pi$
$564$		0			0
$565$	−11.4846	−	6.64000i	−0.483162	−	0.279347i
$566$			18.4317i			0.774741i
$567$		0			0
$568$	−0.850232	+	0.850232i	−0.0356749	+	0.0356749i
$569$	−13.4010			−0.561797			−0.280899	−	0.959737i	$-0.590632\pi$
$569$	−13.4010			−0.561797			−0.280899	+	0.959737i	$0.590632\pi$
$570$		0			0
$571$	−1.17987			−0.0493762			−0.0246881	−	0.999695i	$-0.507859\pi$
$571$	−1.17987			−0.0493762			−0.0246881	+	0.999695i	$0.507859\pi$
$572$	8.42344	−	8.42344i	0.352202	−	0.352202i
$573$		0			0
$574$		−	7.46629i		−	0.311637i
$575$	28.3484	+	7.63303i	1.18221	+	0.318319i
$576$		0			0
$577$	4.11260	+	4.11260i	0.171210	+	0.171210i	0.787511	−	0.616301i	$-0.211370\pi$
$577$	4.11260	+	4.11260i	0.171210	+	0.171210i	−0.616301	+	0.787511i	$0.711370\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	−1.81003	−	6.77166i	−0.0751576	−	0.281178i
$581$			17.4880i			0.725523i
$582$		0			0
$583$	−19.6558	+	19.6558i	−0.814059	+	0.814059i
$584$	0.989929			0.0409636
$585$		0			0
$586$	−17.1423			−0.708140
$587$	−0.761476	+	0.761476i	−0.0314295	+	0.0314295i	−0.722647	−	0.691217i	$-0.757075\pi$
$587$	−0.761476	+	0.761476i	−0.0314295	+	0.0314295i	0.691217	+	0.722647i	$0.257075\pi$
$588$		0			0
$589$		−	85.1719i		−	3.50945i
$590$	−12.4875	+	21.5986i	−0.514104	+	0.889200i
$591$		0			0
$592$	4.21657	+	4.21657i	0.173300	+	0.173300i
$593$	12.8001	+	12.8001i	0.525636	+	0.525636i	0.919268	−	0.393632i	$-0.128782\pi$
$593$	12.8001	+	12.8001i	0.525636	+	0.525636i	−0.393632	+	0.919268i	$0.628782\pi$
$594$		0			0
$595$	4.63319	−	1.23843i	0.189942	−	0.0507707i
$596$		−	3.97399i		−	0.162781i
$597$		0			0
$598$	9.03316	−	9.03316i	0.369393	−	0.369393i
$599$	−12.9809			−0.530387			−0.265194	−	0.964195i	$-0.585436\pi$
$599$	−12.9809			−0.530387			−0.265194	+	0.964195i	$0.585436\pi$
$600$		0			0
$601$	23.6709			0.965555			0.482777	−	0.875743i	$-0.339628\pi$
$601$	23.6709			0.965555			0.482777	+	0.875743i	$0.339628\pi$
$602$	13.7481	−	13.7481i	0.560331	−	0.560331i
$603$		0			0
$604$		−	19.2095i		−	0.781625i
$605$	−40.9987	+	10.9588i	−1.66683	+	0.445537i
$606$		0			0
$607$	−10.6108	−	10.6108i	−0.430681	−	0.430681i	0.458179	−	0.888860i	$-0.348502\pi$
$607$	−10.6108	−	10.6108i	−0.430681	−	0.430681i	−0.888860	+	0.458179i	$0.848502\pi$
$608$	−6.12803	−	6.12803i	−0.248525	−	0.248525i
$609$		0			0
$610$	5.31739	−	9.19703i	0.215295	−	0.372377i
$611$			9.11502i			0.368754i
$612$		0			0
$613$	−11.5506	+	11.5506i	−0.466525	+	0.466525i	−0.900787	−	0.434262i	$-0.857009\pi$
$613$	−11.5506	+	11.5506i	−0.466525	+	0.466525i	0.434262	+	0.900787i	$0.357009\pi$
$614$	8.43410			0.340373
$615$		0			0
$616$	11.7432			0.473149
$617$	27.7791	−	27.7791i	1.11835	−	1.11835i	0.126361	−	0.991984i	$-0.459670\pi$
$617$	27.7791	−	27.7791i	1.11835	−	1.11835i	0.991984	−	0.126361i	$-0.0403297\pi$
$618$		0			0
$619$			31.8759i			1.28120i	0.767875	+	0.640600i	$0.221314\pi$
$619$			31.8759i			1.28120i	−0.767875	+	0.640600i	$0.778686\pi$
$620$	5.67481	+	21.2305i	0.227906	+	0.852637i
$621$		0			0
$622$	−9.25982	−	9.25982i	−0.371285	−	0.371285i
$623$	14.6442	+	14.6442i	0.586709	+	0.586709i
$624$		0			0
$625$	12.5528	−	21.6201i	0.502112	−	0.864803i
$626$			1.72615i			0.0689910i
$627$		0			0
$628$	7.49472	−	7.49472i	0.299072	−	0.299072i
$629$	−5.96312			−0.237765
$630$		0			0
$631$	18.1990			0.724489			0.362245	−	0.932083i	$-0.382011\pi$
$631$	18.1990			0.724489			0.362245	+	0.932083i	$0.382011\pi$
$632$	−8.63723	+	8.63723i	−0.343570	+	0.343570i
$633$		0			0
$634$			21.2918i			0.845604i
$635$	−39.9195	−	23.0800i	−1.58416	−	0.915904i
$636$		0			0
$637$	−3.69222	−	3.69222i	−0.146291	−	0.146291i
$638$	12.1364	+	12.1364i	0.480483	+	0.480483i
$639$		0			0
$640$	1.93581	+	1.11922i	0.0765196	+	0.0442409i
$641$			6.04162i			0.238630i	0.992856	+	0.119315i	$0.0380698\pi$
$641$			6.04162i			0.238630i	−0.992856	+	0.119315i	$0.961930\pi$
$642$		0			0
$643$	11.5326	−	11.5326i	0.454802	−	0.454802i	−0.442143	−	0.896945i	$-0.645782\pi$
$643$	11.5326	−	11.5326i	0.454802	−	0.454802i	0.896945	+	0.442143i	$0.145782\pi$
$644$	12.5933			0.496244
$645$		0			0
$646$	8.66635			0.340973
$647$	21.9591	−	21.9591i	0.863300	−	0.863300i	−0.128420	−	0.991720i	$-0.540991\pi$
$647$	21.9591	−	21.9591i	0.863300	−	0.863300i	0.991720	+	0.128420i	$0.0409907\pi$
$648$		0			0
$649$		−	61.0901i		−	2.39799i
$650$	−5.42772	−	9.42764i	−0.212893	−	0.369782i
$651$		0			0
$652$	10.2201	+	10.2201i	0.400250	+	0.400250i
$653$	−27.6758	−	27.6758i	−1.08304	−	1.08304i	−0.996225	−	0.0868117i	$-0.972332\pi$
$653$	−27.6758	−	27.6758i	−1.08304	−	1.08304i	−0.0868117	−	0.996225i	$-0.527668\pi$
$654$		0			0
$655$	−6.91790	−	25.8811i	−0.270305	−	1.01126i
$656$			3.48117i			0.135917i
$657$		0			0
$658$	−6.35369	+	6.35369i	−0.247693	+	0.247693i
$659$	−14.5159			−0.565460			−0.282730	−	0.959200i	$-0.591240\pi$
$659$	−14.5159			−0.565460			−0.282730	+	0.959200i	$0.591240\pi$
$660$		0			0
$661$	2.62968			0.102283			0.0511414	−	0.998691i	$-0.483714\pi$
$661$	2.62968			0.102283			0.0511414	+	0.998691i	$0.483714\pi$
$662$	−9.85192	+	9.85192i	−0.382906	+	0.382906i
$663$		0			0
$664$		−	8.15378i		−	0.316428i
$665$	−20.8032	+	35.9815i	−0.806713	+	1.39530i
$666$		0			0
$667$	13.0148	+	13.0148i	0.503936	+	0.503936i
$668$	−0.821334	−	0.821334i	−0.0317784	−	0.0317784i
$669$		0			0
$670$	−8.74203	+	2.33671i	−0.337734	+	0.0902748i
$671$			26.0131i			1.00423i
$672$		0			0
$673$	26.5227	−	26.5227i	1.02237	−	1.02237i	0.0226295	−	0.999744i	$-0.492796\pi$
$673$	26.5227	−	26.5227i	1.02237	−	1.02237i	0.999744	−	0.0226295i	$-0.00720382\pi$
$674$	8.62664			0.332286
$675$		0			0
$676$	8.26638			0.317938
$677$	−28.3811	+	28.3811i	−1.09077	+	1.09077i	−0.0953272	+	0.995446i	$0.530390\pi$
$677$	−28.3811	+	28.3811i	−1.09077	+	1.09077i	−0.995446	+	0.0953272i	$0.969610\pi$
$678$		0			0
$679$		−	28.5422i		−	1.09535i
$680$	−2.16023	+	0.577419i	−0.0828410	+	0.0221430i
$681$		0			0
$682$	−38.0498	−	38.0498i	−1.45700	−	1.45700i
$683$	−27.3479	−	27.3479i	−1.04644	−	1.04644i	−0.998868	−	0.0475718i	$-0.984852\pi$
$683$	−27.3479	−	27.3479i	−1.04644	−	1.04644i	−0.0475718	−	0.998868i	$-0.515148\pi$
$684$		0			0
$685$	−11.0543	+	19.1197i	−0.422363	+	0.730525i
$686$		−	20.1608i		−	0.769741i
$687$		0			0
$688$	−6.41006	+	6.41006i	−0.244381	+	0.244381i
$689$	11.0457			0.420809
$690$		0			0
$691$	−8.60950			−0.327521			−0.163760	−	0.986500i	$-0.552362\pi$
$691$	−8.60950			−0.327521			−0.163760	+	0.986500i	$0.552362\pi$
$692$	6.05390	−	6.05390i	0.230135	−	0.230135i
$693$		0			0
$694$			25.0557i			0.951103i
$695$	−2.05200	−	7.67691i	−0.0778369	−	0.291202i
$696$		0			0
$697$	−2.46156	−	2.46156i	−0.0932381	−	0.0932381i
$698$	−2.64754	−	2.64754i	−0.100211	−	0.100211i
$699$		0			0
$700$	2.78817	−	10.3550i	0.105383	−	0.391384i
$701$		−	6.64678i		−	0.251046i	−0.992091	−	0.125523i	$-0.959939\pi$
$701$		−	6.64678i		−	0.251046i	0.992091	−	0.125523i	$-0.0400608\pi$
$702$		0			0
$703$	36.5422	−	36.5422i	1.37822	−	1.37822i
$704$	−5.47530			−0.206358
$705$		0			0
$706$	11.8307			0.445254
$707$	−13.8192	+	13.8192i	−0.519725	+	0.519725i
$708$		0			0
$709$		−	0.974460i		−	0.0365966i	−0.999833	−	0.0182983i	$-0.994175\pi$
$709$		−	0.974460i		−	0.0365966i	0.999833	−	0.0182983i	$-0.00582486\pi$
$710$	−2.32764	−	1.34575i	−0.0873546	−	0.0505053i
$711$		0			0
$712$	−6.82789	−	6.82789i	−0.255886	−	0.255886i
$713$	−40.8040	−	40.8040i	−1.52812	−	1.52812i
$714$		0			0
$715$	23.0604	+	13.3327i	0.862410	+	0.498615i
$716$		−	3.07115i		−	0.114774i
$717$		0			0
$718$	−12.5126	+	12.5126i	−0.466965	+	0.466965i
$719$	32.9116			1.22739			0.613697	−	0.789542i	$-0.289682\pi$
$719$	32.9116			1.22739			0.613697	+	0.789542i	$0.289682\pi$
$720$		0			0
$721$	32.9433			1.22687
$722$	−39.6726	+	39.6726i	−1.47646	+	1.47646i
$723$		0			0
$724$		−	21.6506i		−	0.804637i
$725$	13.5832	−	7.82018i	0.504467	−	0.290434i
$726$		0			0
$727$	24.8375	+	24.8375i	0.921172	+	0.921172i	0.997112	−	0.0759404i	$-0.0241959\pi$
$727$	24.8375	+	24.8375i	0.921172	+	0.921172i	−0.0759404	+	0.997112i	$0.524196\pi$
$728$	−3.29961	−	3.29961i	−0.122292	−	0.122292i
$729$		0			0
$730$	0.571604	+	2.13847i	0.0211560	+	0.0791484i
$731$		−	9.06520i		−	0.335288i
$732$		0			0
$733$	1.57415	−	1.57415i	0.0581427	−	0.0581427i	−0.677438	−	0.735580i	$-0.736910\pi$
$733$	1.57415	−	1.57415i	0.0581427	−	0.0581427i	0.735580	+	0.677438i	$0.236910\pi$
$734$	−29.2964			−1.08135
$735$		0			0
$736$	−5.87162			−0.216431
$737$	15.6677	−	15.6677i	0.577127	−	0.577127i
$738$		0			0
$739$		−	16.8507i		−	0.619864i	−0.950759	−	0.309932i	$-0.899694\pi$
$739$		−	16.8507i		−	0.619864i	0.950759	−	0.309932i	$-0.100306\pi$
$740$	−6.67402	+	11.5435i	−0.245342	+	0.424346i
$741$		0			0
$742$	7.69951	+	7.69951i	0.282658	+	0.282658i
$743$	0.763460	+	0.763460i	0.0280086	+	0.0280086i	0.720972	−	0.692964i	$-0.243695\pi$
$743$	0.763460	+	0.763460i	0.0280086	+	0.0280086i	−0.692964	+	0.720972i	$0.743695\pi$
$744$		0			0
$745$	8.58472	−	2.29466i	0.314520	−	0.0840698i
$746$		−	36.2391i		−	1.32681i
$747$		0			0
$748$	3.87162	−	3.87162i	0.141560	−	0.141560i
$749$	11.0310			0.403064
$750$		0			0
$751$	−10.7233			−0.391299			−0.195650	−	0.980674i	$-0.562682\pi$
$751$	−10.7233			−0.391299			−0.195650	+	0.980674i	$0.562682\pi$
$752$	2.96242	−	2.96242i	0.108028	−	0.108028i
$753$		0			0
$754$		−	6.82013i		−	0.248374i
$755$	41.4970	−	11.0920i	1.51023	−	0.403677i
$756$		0			0
$757$	3.48429	+	3.48429i	0.126639	+	0.126639i	0.767585	−	0.640947i	$-0.221458\pi$
$757$	3.48429	+	3.48429i	0.126639	+	0.126639i	−0.640947	+	0.767585i	$0.721458\pi$
$758$	6.46522	+	6.46522i	0.234828	+	0.234828i
$759$		0			0
$760$	9.69951	−	16.7764i	0.351838	−	0.608544i
$761$			9.41404i			0.341259i	0.985335	+	0.170629i	$0.0545801\pi$
$761$			9.41404i			0.341259i	−0.985335	+	0.170629i	$0.945420\pi$
$762$		0			0
$763$	27.4917	−	27.4917i	0.995266	−	0.995266i
$764$	2.98406			0.107959
$765$		0			0
$766$	25.8096			0.932537
$767$	−17.1650	+	17.1650i	−0.619794	+	0.619794i
$768$		0			0
$769$		−	38.7740i		−	1.39823i	−0.715011	−	0.699113i	$-0.753578\pi$
$769$		−	38.7740i		−	1.39823i	0.715011	−	0.699113i	$-0.246422\pi$
$770$	6.78077	+	25.3681i	0.244362	+	0.914202i
$771$		0			0
$772$	−5.88692	−	5.88692i	−0.211875	−	0.211875i
$773$	22.2710	+	22.2710i	0.801032	+	0.801032i	0.983257	−	0.182225i	$-0.0583299\pi$
$773$	22.2710	+	22.2710i	0.801032	+	0.801032i	−0.182225	+	0.983257i	$0.558330\pi$
$774$		0			0
$775$	−42.5860	+	24.5178i	−1.52973	+	0.880705i
$776$			13.3078i			0.477724i
$777$		0			0
$778$	11.4764	−	11.4764i	0.411448	−	0.411448i
$779$	30.1690			1.08092
$780$		0			0
$781$	6.58355			0.235578
$782$	4.15186	−	4.15186i	0.148470	−	0.148470i
$783$		0			0
$784$			2.39997i			0.0857133i
$785$	20.5179	+	11.8627i	0.732315	+	0.423398i
$786$		0			0
$787$	−1.47431	−	1.47431i	−0.0525535	−	0.0525535i	0.680342	−	0.732895i	$-0.261831\pi$
$787$	−1.47431	−	1.47431i	−0.0525535	−	0.0525535i	−0.732895	+	0.680342i	$0.761831\pi$
$788$	5.59700	+	5.59700i	0.199385	+	0.199385i
$789$		0			0
$790$	−23.6457	−	13.6711i	−0.841276	−	0.486395i
$791$		−	12.7243i		−	0.452425i
$792$		0			0
$793$	7.30915	−	7.30915i	0.259556	−	0.259556i
$794$	16.9716			0.602299
$795$		0			0
$796$	−1.35103			−0.0478859
$797$	−6.46590	+	6.46590i	−0.229034	+	0.229034i	−0.812289	−	0.583255i	$-0.801779\pi$
$797$	−6.46590	+	6.46590i	−0.229034	+	0.229034i	0.583255	+	0.812289i	$0.301779\pi$
$798$		0			0
$799$			4.18949i			0.148213i
$800$	−1.29999	+	4.82805i	−0.0459615	+	0.170697i
$801$		0			0
$802$	−0.718318	−	0.718318i	−0.0253647	−	0.0253647i
$803$	−3.83263	−	3.83263i	−0.135251	−	0.135251i
$804$		0			0
$805$	7.27159	+	27.2043i	0.256290	+	0.958826i
$806$			21.3824i			0.753164i
$807$		0			0
$808$	6.44322	−	6.44322i	0.226672	−	0.226672i
$809$	8.21041			0.288663			0.144331	−	0.989529i	$-0.453897\pi$
$809$	8.21041			0.288663			0.144331	+	0.989529i	$0.453897\pi$
$810$		0			0
$811$	12.9843			0.455942			0.227971	−	0.973668i	$-0.426791\pi$
$811$	12.9843			0.455942			0.227971	+	0.973668i	$0.426791\pi$
$812$	4.75402	−	4.75402i	0.166833	−	0.166833i
$813$		0			0
$814$		−	32.6499i		−	1.14438i
$815$	−16.1765	+	27.9790i	−0.566637	+	0.980063i
$816$		0			0
$817$	55.5518	+	55.5518i	1.94351	+	1.94351i
$818$	8.30305	+	8.30305i	0.290309	+	0.290309i
$819$		0			0
$820$	−7.52011	+	2.01009i	−0.262614	+	0.0701955i
$821$			8.75223i			0.305455i	0.988268	+	0.152727i	$0.0488057\pi$
$821$			8.75223i			0.305455i	−0.988268	+	0.152727i	$0.951194\pi$
$822$		0			0
$823$	−28.7844	+	28.7844i	−1.00336	+	1.00336i	−0.00336700	+	0.999994i	$0.501072\pi$
$823$	−28.7844	+	28.7844i	−1.00336	+	1.00336i	−0.999994	+	0.00336700i	$0.998928\pi$
$824$	−15.3598			−0.535085
$825$		0			0
$826$	−23.9300			−0.832632
$827$	−0.812652	+	0.812652i	−0.0282587	+	0.0282587i	−0.721095	−	0.692836i	$-0.756361\pi$
$827$	−0.812652	+	0.812652i	−0.0282587	+	0.0282587i	0.692836	+	0.721095i	$0.256361\pi$
$828$		0			0
$829$		−	14.3382i		−	0.497985i	−0.968505	−	0.248993i	$-0.919901\pi$
$829$		−	14.3382i		−	0.497985i	0.968505	−	0.248993i	$-0.0800995\pi$
$830$	17.6140	−	4.70815i	0.611392	−	0.163422i
$831$		0			0
$832$	1.53844	+	1.53844i	0.0533360	+	0.0533360i
$833$	−1.69704	−	1.69704i	−0.0587988	−	0.0587988i
$834$		0			0
$835$	1.30001	−	2.24852i	0.0449889	−	0.0778133i
$836$			47.4508i			1.64112i
$837$		0			0
$838$	−1.11541	+	1.11541i	−0.0385310	+	0.0385310i
$839$	−9.56797			−0.330323			−0.165162	−	0.986267i	$-0.552815\pi$
$839$	−9.56797			−0.330323			−0.165162	+	0.986267i	$0.552815\pi$
$840$		0			0
$841$	−19.1737			−0.661161
$842$	17.2349	−	17.2349i	0.593955	−	0.593955i
$843$		0			0
$844$			13.4202i			0.461941i
$845$	4.77317	+	17.8573i	0.164202	+	0.614308i
$846$		0			0
$847$	−28.7830	−	28.7830i	−0.988994	−	0.988994i
$848$	−3.58990	−	3.58990i	−0.123278	−	0.123278i
$849$		0			0
$850$	−2.49472	−	4.33317i	−0.0855680	−	0.148627i
$851$		−	35.0132i		−	1.20024i
$852$		0			0
$853$	−12.7517	+	12.7517i	−0.436611	+	0.436611i	−0.890870	−	0.454259i	$-0.849904\pi$
$853$	−12.7517	+	12.7517i	−0.436611	+	0.436611i	0.454259	+	0.890870i	$0.349904\pi$
$854$	10.1898			0.348687
$855$		0			0
$856$	−5.14321			−0.175791
$857$	−16.3790	+	16.3790i	−0.559496	+	0.559496i	−0.929164	−	0.369668i	$-0.879471\pi$
$857$	−16.3790	+	16.3790i	−0.559496	+	0.559496i	0.369668	+	0.929164i	$0.379471\pi$
$858$		0			0
$859$		−	12.1336i		−	0.413993i	−0.978342	−	0.206996i	$-0.933631\pi$
$859$		−	12.1336i		−	0.413993i	0.978342	−	0.206996i	$-0.0663689\pi$
$860$	−17.5485	−	10.1459i	−0.598399	−	0.345973i
$861$		0			0
$862$	−17.5472	−	17.5472i	−0.597660	−	0.597660i
$863$	1.59510	+	1.59510i	0.0542977	+	0.0542977i	0.733734	−	0.679437i	$-0.237776\pi$
$863$	1.59510	+	1.59510i	0.0542977	+	0.0542977i	−0.679437	+	0.733734i	$0.737776\pi$
$864$		0			0
$865$	16.5735	+	9.58217i	0.563514	+	0.325804i
$866$		−	23.5289i		−	0.799545i
$867$		0			0
$868$	−14.9048	+	14.9048i	−0.505901	+	0.505901i
$869$	66.8801			2.26875
$870$		0			0
$871$	−8.80460			−0.298333
$872$	−12.8180	+	12.8180i	−0.434073	+	0.434073i
$873$		0			0
$874$			50.8855i			1.72123i
$875$	23.9792	+	0.0438846i	0.810645	+	0.00148357i
$876$		0			0
$877$	26.2960	+	26.2960i	0.887953	+	0.887953i	0.994326	−	0.106373i	$-0.0339239\pi$
$877$	26.2960	+	26.2960i	0.887953	+	0.887953i	−0.106373	+	0.994326i	$0.533924\pi$
$878$	16.2813	+	16.2813i	0.549468	+	0.549468i
$879$		0			0
$880$	−3.16154	−	11.8279i	−0.106576	−	0.398718i
$881$			9.51113i			0.320438i	0.987081	+	0.160219i	$0.0512200\pi$
$881$			9.51113i			0.320438i	−0.987081	+	0.160219i	$0.948780\pi$
$882$		0			0
$883$	33.3586	−	33.3586i	1.12261	−	1.12261i	0.131257	−	0.991348i	$-0.458099\pi$
$883$	33.3586	−	33.3586i	1.12261	−	1.12261i	0.991348	−	0.131257i	$-0.0419013\pi$
$884$	−2.17569			−0.0731763
$885$		0			0
$886$	−26.2507			−0.881910
$887$	−16.8315	+	16.8315i	−0.565148	+	0.565148i	−0.930765	−	0.365618i	$-0.880858\pi$
$887$	−16.8315	+	16.8315i	−0.565148	+	0.565148i	0.365618	+	0.930765i	$0.380858\pi$
$888$		0			0
$889$		−	44.2286i		−	1.48338i
$890$	10.8072	−	18.6924i	0.362260	−	0.626569i
$891$		0			0
$892$	16.2812	+	16.2812i	0.545135	+	0.545135i
$893$	−25.6733	−	25.6733i	−0.859125	−	0.859125i
$894$		0			0
$895$	6.63439	−	1.77334i	0.221763	−	0.0592763i
$896$			2.14477i			0.0716517i
$897$		0			0
$898$	15.3837	−	15.3837i	0.513361	−	0.513361i
$899$	−30.8075			−1.02749
$900$		0			0
$901$	5.07689			0.169136
$902$	13.4777	−	13.4777i	0.448760	−	0.448760i
$903$		0			0
$904$			5.93272i			0.197319i
$905$	46.7702	−	12.5015i	1.55469	−	0.415562i
$906$		0			0
$907$	5.65337	+	5.65337i	0.187717	+	0.187717i	0.794708	−	0.606991i	$-0.207624\pi$
$907$	5.65337	+	5.65337i	0.187717	+	0.187717i	−0.606991	+	0.794708i	$0.707624\pi$
$908$	−8.77490	−	8.77490i	−0.291205	−	0.291205i
$909$		0			0
$910$	5.22265	−	9.03316i	0.173129	−	0.299446i
$911$			19.2205i			0.636802i	0.947956	+	0.318401i	$0.103146\pi$
$911$			19.2205i			0.636802i	−0.947956	+	0.318401i	$0.896854\pi$
$912$		0			0
$913$	−31.5683	+	31.5683i	−1.04476	+	1.04476i
$914$	25.1322			0.831301
$915$		0			0
$916$	6.47686			0.214001
$917$	18.1697	−	18.1697i	0.600017	−	0.600017i
$918$		0			0
$919$			19.1991i			0.633320i	0.948539	+	0.316660i	$0.102561\pi$
$919$			19.1991i			0.633320i	−0.948539	+	0.316660i	$0.897439\pi$
$920$	−3.39039	−	12.6840i	−0.111778	−	0.418180i
$921$		0			0
$922$	4.23355	+	4.23355i	0.139425	+	0.139425i
$923$	−1.84984	−	1.84984i	−0.0608882	−	0.0608882i
$924$		0			0
$925$	−28.7902	−	7.75198i	−0.946617	−	0.254884i
$926$			11.2558i			0.369890i
$927$		0			0
$928$	−2.21657	+	2.21657i	−0.0727623	+	0.0727623i
$929$	−34.0772			−1.11804			−0.559018	−	0.829156i	$-0.688822\pi$
$929$	−34.0772			−1.11804			−0.559018	+	0.829156i	$0.688822\pi$
$930$		0			0
$931$	20.7990			0.681659
$932$	7.07107	−	7.07107i	0.231621	−	0.231621i
$933$		0			0
$934$		−	30.2864i		−	0.991002i
$935$	10.5991	+	6.12803i	0.346629	+	0.200408i
$936$		0			0
$937$	10.6690	+	10.6690i	0.348541	+	0.348541i	0.859566	−	0.511025i	$-0.170734\pi$
$937$	10.6690	+	10.6690i	0.348541	+	0.348541i	−0.511025	+	0.859566i	$0.670734\pi$
$938$	−6.13731	−	6.13731i	−0.200390	−	0.200390i
$939$		0			0
$940$	8.11005	+	4.68894i	0.264521	+	0.152936i
$941$		−	46.7455i		−	1.52386i	−0.647659	−	0.761930i	$-0.724252\pi$
$941$		−	46.7455i		−	1.52386i	0.647659	−	0.761930i	$-0.275748\pi$
$942$		0			0
$943$	14.4533	−	14.4533i	0.470665	−	0.470665i
$944$	11.1574			0.363142
$945$		0			0
$946$	49.6346			1.61376
$947$	19.5659	−	19.5659i	0.635806	−	0.635806i	−0.313712	−	0.949518i	$-0.601573\pi$
$947$	19.5659	−	19.5659i	0.635806	−	0.635806i	0.949518	+	0.313712i	$0.101573\pi$
$948$		0			0
$949$			2.15378i			0.0699146i
$950$	41.8415	+	11.2661i	1.35752	+	0.365522i
$951$		0			0
$952$	−1.51658	−	1.51658i	−0.0491526	−	0.0491526i
$953$	−29.6071	−	29.6071i	−0.959068	−	0.959068i	0.0401263	−	0.999195i	$-0.487224\pi$
$953$	−29.6071	−	29.6071i	−0.959068	−	0.959068i	−0.999195	+	0.0401263i	$0.987224\pi$
$954$		0			0
$955$	1.72305	+	6.44625i	0.0557567	+	0.208596i
$956$			6.84999i			0.221544i
$957$		0			0
$958$	1.76022	−	1.76022i	0.0568702	−	0.0568702i
$959$	−21.1835			−0.684051
$960$		0			0
$961$	65.5874			2.11572
$962$	−9.17394	+	9.17394i	−0.295780	+	0.295780i
$963$		0			0
$964$			29.4865i			0.949695i
$965$	9.31788	−	16.1163i	0.299953	−	0.518803i
$966$		0			0
$967$	−29.7371	−	29.7371i	−0.956280	−	0.956280i	0.0428039	−	0.999083i	$-0.486371\pi$
$967$	−29.7371	−	29.7371i	−0.956280	−	0.956280i	−0.999083	+	0.0428039i	$0.986371\pi$
$968$	13.4201	+	13.4201i	0.431338	+	0.431338i
$969$		0			0
$970$	−28.7480	+	7.68420i	−0.923042	+	0.246725i
$971$		−	9.67909i		−	0.310617i	−0.987866	−	0.155308i	$-0.950363\pi$
$971$		−	9.67909i		−	0.310617i	0.987866	−	0.155308i	$-0.0496371\pi$
$972$		0			0
$973$	5.38954	−	5.38954i	0.172781	−	0.172781i
$974$	2.07555			0.0665050
$975$		0			0
$976$	−4.75100			−0.152076
$977$	−34.8100	+	34.8100i	−1.11367	+	1.11367i	−0.121020	+	0.992650i	$0.538617\pi$
$977$	−34.8100	+	34.8100i	−1.11367	+	1.11367i	−0.992650	+	0.121020i	$0.961383\pi$
$978$		0			0
$979$			52.8700i			1.68973i
$980$	−5.18449	+	1.38579i	−0.165612	+	0.0442674i
$981$		0			0
$982$	−29.3812	−	29.3812i	−0.937591	−	0.937591i
$983$	13.1207	+	13.1207i	0.418485	+	0.418485i	0.884681	−	0.466196i	$-0.154376\pi$
$983$	13.1207	+	13.1207i	0.418485	+	0.418485i	−0.466196	+	0.884681i	$0.654376\pi$
$984$		0			0
$985$	−8.85898	+	15.3226i	−0.282270	+	0.488219i
$986$		−	3.13470i		−	0.0998291i
$987$		0			0
$988$	13.3327	−	13.3327i	0.424170	−	0.424170i
$989$	53.2274			1.69253
$990$		0			0
$991$	39.3459			1.24986			0.624932	−	0.780679i	$-0.285127\pi$
$991$	39.3459			1.24986			0.624932	+	0.780679i	$0.285127\pi$
$992$	6.94937	−	6.94937i	0.220643	−	0.220643i
$993$		0			0
$994$		−	2.57889i		−	0.0817974i
$995$	−0.780110	−	2.91853i	−0.0247311	−	0.0925236i
$996$		0			0
$997$	−24.2104	−	24.2104i	−0.766751	−	0.766751i	0.210782	−	0.977533i	$-0.432399\pi$
$997$	−24.2104	−	24.2104i	−0.766751	−	0.766751i	−0.977533	+	0.210782i	$0.932399\pi$
$998$	0.0864170	+	0.0864170i	0.00273548	+	0.00273548i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.h.647.8	yes	16
3.2	odd	2	inner	1530.2.m.h.647.1	✓	16
5.3	odd	4	inner	1530.2.m.h.953.1	yes	16
15.8	even	4	inner	1530.2.m.h.953.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.h.647.1	✓	16	3.2	odd	2	inner
1530.2.m.h.647.8	yes	16	1.1	even	1	trivial
1530.2.m.h.953.1	yes	16	5.3	odd	4	inner
1530.2.m.h.953.8	yes	16	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.16023 - 0.577419i) q^{5} +(1.51658 + 1.51658i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.16023 - 0.577419i) q^{5} +(1.51658 + 1.51658i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11922 - 1.93581i) q^{10} +5.47530i q^{11} +(1.53844 - 1.53844i) q^{13} +2.14477 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +8.66635i q^{19} +(-0.577419 - 2.16023i) q^{20} +(3.87162 + 3.87162i) q^{22} +(4.15186 + 4.15186i) q^{23} +(4.33317 - 2.49472i) q^{25} -2.17569i q^{26} +(1.51658 - 1.51658i) q^{28} +3.13470 q^{29} -9.82789 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(4.15186 + 2.40046i) q^{35} +(-4.21657 - 4.21657i) q^{37} +(6.12803 + 6.12803i) q^{38} +(-1.93581 - 1.11922i) q^{40} -3.48117i q^{41} +(6.41006 - 6.41006i) q^{43} +5.47530 q^{44} +5.87162 q^{46} +(-2.96242 + 2.96242i) q^{47} -2.39997i q^{49} +(1.29999 - 4.82805i) q^{50} +(-1.53844 - 1.53844i) q^{52} +(3.58990 + 3.58990i) q^{53} +(3.16154 + 11.8279i) q^{55} -2.14477i q^{56} +(2.21657 - 2.21657i) q^{58} -11.1574 q^{59} +4.75100 q^{61} +(-6.94937 + 6.94937i) q^{62} +1.00000i q^{64} +(2.43506 - 4.21172i) q^{65} +(-2.86153 - 2.86153i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(4.63319 - 1.23843i) q^{70} -1.20241i q^{71} +(-0.699986 + 0.699986i) q^{73} -5.96312 q^{74} +8.66635 q^{76} +(-8.30372 + 8.30372i) q^{77} -12.2149i q^{79} +(-2.16023 + 0.577419i) q^{80} +(-2.46156 - 2.46156i) q^{82} +(5.76559 + 5.76559i) q^{83} +(1.11922 - 1.93581i) q^{85} -9.06520i q^{86} +(3.87162 - 3.87162i) q^{88} +9.65609 q^{89} +4.66635 q^{91} +(4.15186 - 4.15186i) q^{92} +4.18949i q^{94} +(5.00412 + 18.7213i) q^{95} +(-9.41006 - 9.41006i) q^{97} +(-1.69704 - 1.69704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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