LMFDB - Embedded newform 315.2.bf.c.289.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 26x^{12} - 96x^{10} - 781x^{8} - 2400x^{6} + 16250x^{4} + 125000x^{2} + 390625 $ x^16 + 8x^14 + 26x^12 - 96x^10 - 781x^8 - 2400x^6 + 16250x^4 + 125000*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.8
Root			$0.733576 - 2.11231i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.c.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05774 + 1.18804i) q^{2} +(1.82288 + 3.15731i) q^{4} +(1.46253 - 1.69145i) q^{5} +(-2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +O(q^{10})$	\(q+(2.05774 + 1.18804i) q^{2} +(1.82288 + 3.15731i) q^{4} +(1.46253 - 1.69145i) q^{5} +(-2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +(5.01902 - 1.74303i) q^{10} +(1.80712 + 3.13003i) q^{11} -3.36961i q^{13} +(-6.19933 + 1.04334i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(-4.71533 + 2.72240i) q^{17} +(2.32288 - 4.02334i) q^{19} +(8.00645 + 1.53436i) q^{20} +8.58772i q^{22} +(-0.599838 - 0.346317i) q^{23} +(-0.722018 - 4.94759i) q^{25} +(4.00323 - 6.93379i) q^{26} +(-9.03805 - 3.36961i) q^{28} -8.00645 q^{29} +(-2.50000 - 4.33013i) q^{31} +(2.65758 - 1.53436i) q^{32} -12.9373 q^{34} +(-0.133738 + 5.91457i) q^{35} +(-4.51902 - 2.60906i) q^{37} +(9.55977 - 5.51934i) q^{38} +(6.61431 + 5.71912i) q^{40} +5.17018 q^{41} +8.91514i q^{43} +(-6.58831 + 11.4113i) q^{44} +(-0.822876 - 1.42526i) q^{46} +(3.38654 + 1.95522i) q^{47} +(1.32288 - 6.87386i) q^{49} +(4.39221 - 11.0387i) q^{50} +(10.6389 - 6.14237i) q^{52} +(-5.57340 + 3.21780i) q^{53} +(7.93725 + 1.52110i) q^{55} +(-6.58831 - 7.97713i) q^{56} +(-16.4752 - 9.51198i) q^{58} +(0.388984 + 0.673739i) q^{59} +(-2.82288 + 4.88936i) q^{61} -11.8804i q^{62} +11.2915 q^{64} +(-5.69953 - 4.92815i) q^{65} +(11.9562 - 6.90292i) q^{67} +(-17.1909 - 9.92518i) q^{68} +(-7.30194 + 12.0118i) q^{70} +8.00645 q^{71} +(1.31731 - 0.760548i) q^{73} +(-6.19933 - 10.7376i) q^{74} +16.9373 q^{76} +(-8.95993 - 3.34048i) q^{77} +(-4.96863 + 8.60591i) q^{79} +(1.46715 + 4.22463i) q^{80} +(10.6389 + 6.14237i) q^{82} +3.76135i q^{83} +(-2.29150 + 11.9573i) q^{85} +(-10.5915 + 18.3451i) q^{86} +(-12.2398 + 7.06663i) q^{88} +(-1.80712 + 3.13003i) q^{89} +(5.67712 + 6.87386i) q^{91} -2.52517i q^{92} +(4.64575 + 8.04668i) q^{94} +(-3.40801 - 9.81328i) q^{95} -12.2847i q^{97} +(10.8886 - 12.5730i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 8 q^{10} - 16 q^{16} + 16 q^{19} - 16 q^{25} - 40 q^{31} - 80 q^{34} + 8 q^{40} + 8 q^{46} - 24 q^{61} + 96 q^{64} - 56 q^{70} + 144 q^{76} - 16 q^{79} + 48 q^{85} + 112 q^{91} + 32 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^10 - 16 * q^16 + 16 * q^19 - 16 * q^25 - 40 * q^31 - 80 * q^34 + 8 * q^40 + 8 * q^46 - 24 * q^61 + 96 * q^64 - 56 * q^70 + 144 * q^76 - 16 * q^79 + 48 * q^85 + 112 * q^91 + 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.05774	+	1.18804i	1.45505	+	0.840071i	0.998761	−	0.0497633i	$-0.0158467\pi$
$2$	2.05774	+	1.18804i	1.45505	+	0.840071i	0.456284	+	0.889834i	$0.349180\pi$
$3$		0			0
$3$		0			0
$4$	1.82288	+	3.15731i	0.911438	+	1.57866i
$5$	1.46253	−	1.69145i	0.654063	−	0.756440i
$5$	1.46253	−	1.69145i	0.654063	−	0.756440i
$6$		0			0
$7$	−2.03996	+	1.68480i	−0.771033	+	0.636796i
$7$	−2.03996	+	1.68480i	−0.771033	+	0.636796i
$8$			3.91044i			1.38255i
$9$		0			0
$10$	5.01902	−	1.74303i	1.58715	−	0.551196i
$11$	1.80712	+	3.13003i	0.544867	+	0.943738i	0.998615	+	0.0526080i	$0.0167534\pi$
$11$	1.80712	+	3.13003i	0.544867	+	0.943738i	−0.453748	+	0.891130i	$0.649913\pi$
$12$		0			0
$13$		−	3.36961i		−	0.934561i	−0.884109	−	0.467280i	$-0.845234\pi$
$13$		−	3.36961i		−	0.934561i	0.884109	−	0.467280i	$-0.154766\pi$
$14$	−6.19933	+	1.04334i	−1.65684	+	0.278845i
$15$		0			0
$16$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$17$	−4.71533	+	2.72240i	−1.14363	+	0.660278i	−0.947328	−	0.320265i	$-0.896228\pi$
$17$	−4.71533	+	2.72240i	−1.14363	+	0.660278i	−0.196307	+	0.980543i	$0.562895\pi$
$18$		0			0
$19$	2.32288	−	4.02334i	0.532904	−	0.923017i	−0.466357	−	0.884596i	$-0.654434\pi$
$19$	2.32288	−	4.02334i	0.532904	−	0.923017i	0.999262	−	0.0384208i	$-0.0122327\pi$
$20$	8.00645	+	1.53436i	1.79030	+	0.343092i
$21$		0			0
$22$			8.58772i			1.83091i
$23$	−0.599838	−	0.346317i	−0.125075	−	0.0722120i	0.436157	−	0.899870i	$-0.356339\pi$
$23$	−0.599838	−	0.346317i	−0.125075	−	0.0722120i	−0.561232	+	0.827658i	$0.689672\pi$
$24$		0			0
$25$	−0.722018	−	4.94759i	−0.144404	−	0.989519i
$26$	4.00323	−	6.93379i	0.785097	−	1.35983i
$27$		0			0
$28$	−9.03805	−	3.36961i	−1.70803	−	0.636796i
$29$	−8.00645			−1.48676			−0.743380	−	0.668869i	$-0.766779\pi$
$29$	−8.00645			−1.48676			−0.743380	+	0.668869i	$0.766779\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	2.65758	−	1.53436i	0.469799	−	0.271238i
$33$		0			0
$34$	−12.9373			−2.21872
$35$	−0.133738	+	5.91457i	−0.0226058	+	0.999744i
$36$		0			0
$37$	−4.51902	−	2.60906i	−0.742923	−	0.428927i	0.0802083	−	0.996778i	$-0.474441\pi$
$37$	−4.51902	−	2.60906i	−0.742923	−	0.428927i	−0.823131	+	0.567851i	$0.807775\pi$
$38$	9.55977	−	5.51934i	1.55080	−	0.895355i
$39$		0			0
$40$	6.61431	+	5.71912i	1.04581	+	0.904273i
$41$	5.17018			0.807446			0.403723	−	0.914881i	$-0.367716\pi$
$41$	5.17018			0.807446			0.403723	+	0.914881i	$0.367716\pi$
$42$		0			0
$43$			8.91514i			1.35955i	0.733422	+	0.679773i	$0.237922\pi$
$43$			8.91514i			1.35955i	−0.733422	+	0.679773i	$0.762078\pi$
$44$	−6.58831	+	11.4113i	−0.993226	+	1.72032i
$45$		0			0
$46$	−0.822876	−	1.42526i	−0.121326	−	0.210143i
$47$	3.38654	+	1.95522i	0.493977	+	0.285198i	0.726223	−	0.687459i	$-0.241274\pi$
$47$	3.38654	+	1.95522i	0.493977	+	0.285198i	−0.232246	+	0.972657i	$0.574607\pi$
$48$		0			0
$49$	1.32288	−	6.87386i	0.188982	−	0.981981i
$50$	4.39221	−	11.0387i	0.621152	−	1.56110i
$51$		0			0
$52$	10.6389	−	6.14237i	1.47535	−	0.851794i
$53$	−5.57340	+	3.21780i	−0.765565	+	0.441999i	−0.831290	−	0.555839i	$-0.812397\pi$
$53$	−5.57340	+	3.21780i	−0.765565	+	0.441999i	0.0657253	+	0.997838i	$0.479064\pi$
$54$		0			0
$55$	7.93725	+	1.52110i	1.07026	+	0.205104i
$56$	−6.58831	−	7.97713i	−0.880400	−	1.06599i
$57$		0			0
$58$	−16.4752	−	9.51198i	−2.16330	−	1.24898i
$59$	0.388984	+	0.673739i	0.0506414	+	0.0877134i	0.890235	−	0.455502i	$-0.150540\pi$
$59$	0.388984	+	0.673739i	0.0506414	+	0.0877134i	−0.839594	+	0.543215i	$0.817207\pi$
$60$		0			0
$61$	−2.82288	+	4.88936i	−0.361432	+	0.626019i	−0.988197	−	0.153190i	$-0.951045\pi$
$61$	−2.82288	+	4.88936i	−0.361432	+	0.626019i	0.626765	+	0.779209i	$0.284379\pi$
$62$		−	11.8804i		−	1.50881i
$63$		0			0
$64$	11.2915			1.41144
$65$	−5.69953	−	4.92815i	−0.706939	−	0.611261i
$66$		0			0
$67$	11.9562	−	6.90292i	1.46068	−	0.843326i	0.461641	−	0.887067i	$-0.347261\pi$
$67$	11.9562	−	6.90292i	1.46068	−	0.843326i	0.999043	+	0.0437409i	$0.0139276\pi$
$68$	−17.1909	−	9.92518i	−2.08470	−	1.20360i
$69$		0			0
$70$	−7.30194	+	12.0118i	−0.872749	+	1.43568i
$71$	8.00645			0.950191			0.475095	−	0.879934i	$-0.342414\pi$
$71$	8.00645			0.950191			0.475095	+	0.879934i	$0.342414\pi$
$72$		0			0
$73$	1.31731	−	0.760548i	0.154179	−	0.0890154i	−0.420926	−	0.907095i	$-0.638295\pi$
$73$	1.31731	−	0.760548i	0.154179	−	0.0890154i	0.575105	+	0.818080i	$0.304961\pi$
$74$	−6.19933	−	10.7376i	−0.720658	−	1.24822i
$75$		0			0
$76$	16.9373			1.94284
$77$	−8.95993	−	3.34048i	−1.02108	−	0.380683i
$78$		0			0
$79$	−4.96863	+	8.60591i	−0.559014	+	0.968241i	0.438565	+	0.898700i	$0.355487\pi$
$79$	−4.96863	+	8.60591i	−0.559014	+	0.968241i	−0.997579	+	0.0695415i	$0.977846\pi$
$80$	1.46715	+	4.22463i	0.164032	+	0.472328i
$81$		0			0
$82$	10.6389	+	6.14237i	1.17487	+	0.678312i
$83$			3.76135i			0.412861i	0.978461	+	0.206431i	$0.0661848\pi$
$83$			3.76135i			0.412861i	−0.978461	+	0.206431i	$0.933815\pi$
$84$		0			0
$85$	−2.29150	+	11.9573i	−0.248548	+	1.29695i
$86$	−10.5915	+	18.3451i	−1.14212	+	1.97820i
$87$		0			0
$88$	−12.2398	+	7.06663i	−1.30476	+	0.753305i
$89$	−1.80712	+	3.13003i	−0.191554	+	0.331782i	−0.945766	−	0.324850i	$-0.894686\pi$
$89$	−1.80712	+	3.13003i	−0.191554	+	0.331782i	0.754211	+	0.656632i	$0.228020\pi$
$90$		0			0
$91$	5.67712	+	6.87386i	0.595124	+	0.720577i
$92$		−	2.52517i		−	0.263267i
$93$		0			0
$94$	4.64575	+	8.04668i	0.479173	+	0.829951i
$95$	−3.40801	−	9.81328i	−0.349654	−	1.00682i
$96$		0			0
$97$		−	12.2847i		−	1.24733i	−0.781693	−	0.623664i	$-0.785644\pi$
$97$		−	12.2847i		−	1.24733i	0.781693	−	0.623664i	$-0.214356\pi$
$98$	10.8886	−	12.5730i	1.09991	−	1.27007i
$99$		0			0
$100$	14.3050	−	11.2985i	1.43050	−	1.12985i
$101$	8.39544	+	14.5413i	0.835377	+	1.44692i	0.893723	+	0.448619i	$0.148084\pi$
$101$	8.39544	+	14.5413i	0.835377	+	1.44692i	−0.0583461	+	0.998296i	$0.518583\pi$
$102$		0			0
$103$	−10.3554	−	5.97867i	−1.02034	−	0.589095i	−0.106140	−	0.994351i	$-0.533849\pi$
$103$	−10.3554	−	5.97867i	−1.02034	−	0.589095i	−0.914203	+	0.405256i	$0.867182\pi$
$104$	13.1766			1.29207
$105$		0			0
$106$	−15.2915			−1.48524
$107$	6.90219	+	3.98498i	0.667260	+	0.385243i	0.795038	−	0.606560i	$-0.207451\pi$
$107$	6.90219	+	3.98498i	0.667260	+	0.385243i	−0.127778	+	0.991803i	$0.540784\pi$
$108$		0			0
$109$	6.61438	+	11.4564i	0.633543	+	1.09733i	0.986822	+	0.161810i	$0.0517332\pi$
$109$	6.61438	+	11.4564i	0.633543	+	1.09733i	−0.353279	+	0.935518i	$0.614933\pi$
$110$	14.5257	+	12.5598i	1.38497	+	1.19753i
$111$		0			0
$112$	−0.878205	−	5.21812i	−0.0829825	−	0.493066i
$113$			12.8712i			1.21082i	0.795913	+	0.605411i	$0.206991\pi$
$113$			12.8712i			1.21082i	−0.795913	+	0.605411i	$0.793009\pi$
$114$		0			0
$115$	−1.46306	+	0.508099i	−0.136431	+	0.0473805i
$116$	−14.5948	−	25.2789i	−1.35509	−	2.34708i
$117$		0			0
$118$			1.84851i			0.170169i
$119$	5.03238	−	13.4980i	0.461317	−	1.23736i
$120$		0			0
$121$	−1.03137	+	1.78639i	−0.0937612	+	0.162399i
$122$	−11.6175	+	6.70738i	−1.05180	+	0.607257i
$123$		0			0
$124$	9.11438	−	15.7866i	0.818495	−	1.41768i
$125$	−9.42459	−	6.01474i	−0.842961	−	0.537975i
$126$		0			0
$127$		−	3.36961i		−	0.299004i	−0.988761	−	0.149502i	$-0.952233\pi$
$127$		−	3.36961i		−	0.299004i	0.988761	−	0.149502i	$-0.0477671\pi$
$128$	17.9199	+	10.3460i	1.58391	+	0.914469i
$129$		0			0
$130$	−5.87334	−	16.9121i	−0.515126	−	1.48329i
$131$	−5.81035	+	10.0638i	−0.507652	+	0.879280i	0.492308	+	0.870421i	$0.336153\pi$
$131$	−5.81035	+	10.0638i	−0.507652	+	0.879280i	−0.999961	+	0.00885883i	$0.997180\pi$
$132$		0			0
$133$	2.03996	+	12.1210i	0.176887	+	1.05103i
$134$	32.8038			2.83381
$135$		0			0
$136$	−10.6458	−	18.4390i	−0.912866	−	1.58113i
$137$	2.78670	−	1.60890i	0.238084	−	0.137458i	−0.376212	−	0.926534i	$-0.622774\pi$
$137$	2.78670	−	1.60890i	0.238084	−	0.137458i	0.614296	+	0.789076i	$0.289440\pi$
$138$		0			0
$139$	−19.2288			−1.63096			−0.815481	−	0.578784i	$-0.803527\pi$
$139$	−19.2288			−1.63096			−0.815481	+	0.578784i	$0.803527\pi$
$140$	−18.9179	+	10.3593i	−1.59886	+	0.875518i
$141$		0			0
$142$	16.4752	+	9.51198i	1.38257	+	0.798228i
$143$	10.5470	−	6.08929i	0.881981	−	0.509212i
$144$		0			0
$145$	−11.7097	+	13.5425i	−0.972435	+	1.12465i
$146$	3.61424			0.299117
$147$		0			0
$148$		−	19.0240i		−	1.56376i
$149$	2.19610	−	3.80376i	0.179912	−	0.311617i	−0.761938	−	0.647650i	$-0.775752\pi$
$149$	2.19610	−	3.80376i	0.179912	−	0.311617i	0.941850	+	0.336033i	$0.109085\pi$
$150$		0			0
$151$	−3.46863	−	6.00784i	−0.282273	−	0.488911i	0.689671	−	0.724123i	$-0.257755\pi$
$151$	−3.46863	−	6.00784i	−0.282273	−	0.488911i	−0.971944	+	0.235212i	$0.924422\pi$
$152$	15.7330	+	9.08345i	1.27612	+	0.736765i
$153$		0			0
$154$	−14.4686	−	17.5186i	−1.16592	−	1.41169i
$155$	−10.9805	−	2.10431i	−0.881977	−	0.169022i
$156$		0			0
$157$	−12.2398	+	7.06663i	−0.976839	+	0.563978i	−0.901314	−	0.433165i	$-0.857397\pi$
$157$	−12.2398	+	7.06663i	−0.976839	+	0.563978i	−0.0755249	+	0.997144i	$0.524063\pi$
$158$	−20.4483	+	11.8059i	−1.62678	+	0.939223i
$159$		0			0
$160$	1.29150	−	6.73921i	0.102102	−	0.532782i
$161$	1.80712	−	0.304137i	0.142421	−	0.0239693i
$162$		0			0
$163$	9.03805	+	5.21812i	0.707914	+	0.408715i	0.810288	−	0.586031i	$-0.199310\pi$
$163$	9.03805	+	5.21812i	0.707914	+	0.408715i	−0.102374	+	0.994746i	$0.532644\pi$
$164$	9.42459	+	16.3239i	0.735937	+	1.27468i
$165$		0			0
$166$	−4.46863	+	7.73989i	−0.346833	+	0.600732i
$167$			12.4239i			0.961393i	0.876887	+	0.480697i	$0.159616\pi$
$167$			12.4239i			0.961393i	−0.876887	+	0.480697i	$0.840384\pi$
$168$		0			0
$169$	1.64575			0.126596
$170$	−18.9211	+	21.8827i	−1.45118	+	1.67833i
$171$		0			0
$172$	−28.1479	+	16.2512i	−2.14626	+	1.23914i
$173$	−21.3064	−	12.3013i	−1.61990	−	0.935247i	−0.986945	−	0.161055i	$-0.948510\pi$
$173$	−21.3064	−	12.3013i	−1.61990	−	0.935247i	−0.632950	−	0.774193i	$-0.718156\pi$
$174$		0			0
$175$	9.80861	+	8.87644i	0.741461	+	0.670996i
$176$	−7.22848			−0.544867
$177$		0			0
$178$	−7.43719	+	4.29386i	−0.557441	+	0.321839i
$179$	−0.777967	−	1.34748i	−0.0581480	−	0.100715i	0.835486	−	0.549512i	$-0.185186\pi$
$179$	−0.777967	−	1.34748i	−0.0581480	−	0.100715i	−0.893634	+	0.448796i	$0.851853\pi$
$180$		0			0
$181$	7.35425			0.546637			0.273319	−	0.961924i	$-0.411879\pi$
$181$	7.35425			0.546637			0.273319	+	0.961924i	$0.411879\pi$
$182$	3.51565	+	20.8893i	0.260597	+	1.54842i
$183$		0			0
$184$	1.35425	−	2.34563i	0.0998365	−	0.172922i
$185$	−11.0223	+	3.82788i	−0.810376	+	0.281432i
$186$		0			0
$187$	−17.0423	−	9.83940i	−1.24626	−	0.719528i
$188$			14.2565i			1.03976i
$189$		0			0
$190$	4.64575	−	24.2421i	0.337038	−	1.75871i
$191$	3.61424	−	6.26005i	0.261517	−	0.452961i	−0.705128	−	0.709080i	$-0.749110\pi$
$191$	3.61424	−	6.26005i	0.261517	−	0.452961i	0.966645	+	0.256119i	$0.0824438\pi$
$192$		0			0
$193$	16.7588	−	9.67569i	1.20632	−	0.696471i	0.244370	−	0.969682i	$-0.421419\pi$
$193$	16.7588	−	9.67569i	1.20632	−	0.696471i	0.961954	+	0.273211i	$0.0880857\pi$
$194$	14.5948	−	25.2789i	1.04784	−	1.81492i
$195$		0			0
$196$	24.1144	−	8.35347i	1.72246	−	0.596676i
$197$		−	14.1074i		−	1.00511i	−0.864545	−	0.502555i	$-0.832394\pi$
$197$		−	14.1074i		−	1.00511i	0.864545	−	0.502555i	$-0.167606\pi$
$198$		0			0
$199$	6.17712	+	10.6991i	0.437885	+	0.758439i	0.997526	−	0.0702963i	$-0.0223945\pi$
$199$	6.17712	+	10.6991i	0.437885	+	0.758439i	−0.559641	+	0.828735i	$0.689061\pi$
$200$	19.3472	−	2.82340i	1.36806	−	0.199645i
$201$		0			0
$202$			39.8964i			2.80710i
$203$	16.3328	−	13.4893i	1.14634	−	0.946763i
$204$		0			0
$205$	7.56153	−	8.74510i	0.528120	−	0.610785i
$206$	−14.2058	−	24.6051i	−0.989764	−	1.71432i
$207$		0			0
$208$	5.83633	+	3.36961i	0.404677	+	0.233640i
$209$	16.7909			1.16145
$210$		0			0
$211$	0.937254			0.0645232			0.0322616	−	0.999479i	$-0.489729\pi$
$211$	0.937254			0.0645232			0.0322616	+	0.999479i	$0.489729\pi$
$212$	−20.3192	−	11.7313i	−1.39553	−	0.805709i
$213$		0			0
$214$	9.46863	+	16.4001i	0.647262	+	1.12109i
$215$	15.0795	+	13.0387i	1.02842	+	0.889229i
$216$		0			0
$217$	12.3953	+	4.62128i	0.841449	+	0.313713i
$218$			31.4326i			2.12888i
$219$		0			0
$220$	9.66605	+	27.8332i	0.651685	+	1.87651i
$221$	9.17340	+	15.8888i	0.617070	+	1.06880i
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	−2.83627	+	7.60753i	−0.189507	+	0.508299i
$225$		0			0
$226$	−15.2915	+	26.4857i	−1.01718	+	1.76180i
$227$	20.4483	−	11.8059i	1.35720	−	0.783582i	0.367957	−	0.929843i	$-0.380057\pi$
$227$	20.4483	−	11.8059i	1.35720	−	0.783582i	0.989246	+	0.146261i	$0.0467239\pi$
$228$		0			0
$229$	4.14575	−	7.18065i	0.273959	−	0.474511i	−0.695913	−	0.718126i	$-0.745000\pi$
$229$	4.14575	−	7.18065i	0.273959	−	0.474511i	0.969872	+	0.243615i	$0.0783334\pi$
$230$	−3.61424	−	0.692633i	−0.238316	−	0.0456709i
$231$		0			0
$232$		−	31.3087i		−	2.05552i
$233$	6.04412	+	3.48957i	0.395963	+	0.228610i	0.684741	−	0.728787i	$-0.259915\pi$
$233$	6.04412	+	3.48957i	0.395963	+	0.228610i	−0.288777	+	0.957396i	$0.593249\pi$
$234$		0			0
$235$	8.26006	−	2.86860i	0.538827	−	0.187127i
$236$	−1.41814	+	2.45629i	−0.0923129	+	0.159891i
$237$		0			0
$238$	26.3915	−	21.7967i	1.71071	−	1.41287i
$239$	−13.1766			−0.852325			−0.426163	−	0.904647i	$-0.640135\pi$
$239$	−13.1766			−0.852325			−0.426163	+	0.904647i	$0.640135\pi$
$240$		0			0
$241$	−0.885622	−	1.53394i	−0.0570479	−	0.0988099i	0.836091	−	0.548591i	$-0.184835\pi$
$241$	−0.885622	−	1.53394i	−0.0570479	−	0.0988099i	−0.893139	+	0.449781i	$0.851502\pi$
$242$	−4.24460	+	2.45062i	−0.272854	+	0.157532i
$243$		0			0
$244$	−20.5830			−1.31769
$245$	−9.69206	−	12.2908i	−0.619203	−	0.785231i
$246$		0			0
$247$	−13.5571	−	7.82718i	−0.862616	−	0.498031i
$248$	16.9327	−	9.77609i	1.07523	−	0.620782i
$249$		0			0
$250$	−12.2476	−	23.5736i	−0.774609	−	1.49092i
$251$	10.8427			0.684387			0.342193	−	0.939630i	$-0.388830\pi$
$251$	10.8427			0.684387			0.342193	+	0.939630i	$0.388830\pi$
$252$		0			0
$253$		−	2.50334i		−	0.157384i
$254$	4.00323	−	6.93379i	0.251185	−	0.435065i
$255$		0			0
$256$	13.2915	+	23.0216i	0.830719	+	1.43885i
$257$	−5.44428	−	3.14326i	−0.339605	−	0.196071i	0.320492	−	0.947251i	$-0.396152\pi$
$257$	−5.44428	−	3.14326i	−0.339605	−	0.196071i	−0.660097	+	0.751180i	$0.729485\pi$
$258$		0			0
$259$	13.6144	−	2.29129i	0.845956	−	0.142374i
$260$	5.17018	−	26.9786i	0.320641	−	1.67314i
$261$		0			0
$262$	−23.9124	+	13.8058i	−1.47731	+	0.852928i
$263$	4.58621	−	2.64785i	0.282798	−	0.163273i	−0.351891	−	0.936041i	$-0.614461\pi$
$263$	4.58621	−	2.64785i	0.282798	−	0.163273i	0.634689	+	0.772767i	$0.281128\pi$
$264$		0			0
$265$	−2.70850	+	14.1333i	−0.166382	+	0.868199i
$266$	−10.2026	+	27.3656i	−0.625559	+	1.67789i
$267$		0			0
$268$	43.5894	+	25.1663i	2.66264	+	1.53728i
$269$	−5.03238	−	8.71634i	−0.306830	−	0.531444i	0.670837	−	0.741604i	$-0.265935\pi$
$269$	−5.03238	−	8.71634i	−0.306830	−	0.531444i	−0.977667	+	0.210160i	$0.932602\pi$
$270$		0			0
$271$	2.11438	−	3.66221i	0.128439	−	0.222463i	−0.794633	−	0.607090i	$-0.792337\pi$
$271$	2.11438	−	3.66221i	0.128439	−	0.222463i	0.923072	+	0.384627i	$0.125670\pi$
$272$		−	10.8896i		−	0.660278i
$273$		0			0
$274$	7.64575			0.461897
$275$	14.1813	−	11.2008i	0.855166	−	0.675436i
$276$		0			0
$277$	7.15364	−	4.13015i	0.429820	−	0.248157i	−0.269450	−	0.963014i	$-0.586842\pi$
$277$	7.15364	−	4.13015i	0.429820	−	0.248157i	0.699270	+	0.714858i	$0.253508\pi$
$278$	−39.5679	−	22.8445i	−2.37312	−	1.37012i
$279$		0			0
$280$	−23.1285	−	0.522972i	−1.38219	−	0.0312536i
$281$	−29.1895			−1.74130			−0.870651	−	0.491902i	$-0.836302\pi$
$281$	−29.1895			−1.74130			−0.870651	+	0.491902i	$0.836302\pi$
$282$		0			0
$283$	−22.0280	+	12.7179i	−1.30943	+	0.755999i	−0.982001	−	0.188877i	$-0.939515\pi$
$283$	−22.0280	+	12.7179i	−1.30943	+	0.755999i	−0.327429	+	0.944876i	$0.606182\pi$
$284$	14.5948	+	25.2789i	0.866040	+	1.50003i
$285$		0			0
$286$	28.9373			1.71110
$287$	−10.5470	+	8.71073i	−0.622567	+	0.514178i
$288$		0			0
$289$	6.32288	−	10.9515i	0.371934	−	0.644208i
$290$	−40.1846	+	13.9555i	−2.35972	+	0.819496i
$291$		0			0
$292$	4.80257	+	2.77277i	0.281049	+	0.162264i
$293$		−	27.3730i		−	1.59915i	−0.600566	−	0.799575i	$-0.705058\pi$
$293$		−	27.3730i		−	1.59915i	0.600566	−	0.799575i	$-0.294942\pi$
$294$		0			0
$295$	1.70850	+	0.327416i	0.0994726	+	0.0190629i
$296$	10.2026	−	17.6713i	0.593012	−	1.02713i
$297$		0			0
$298$	9.03805	−	5.21812i	0.523560	−	0.302277i
$299$	−1.16695	+	2.02122i	−0.0674865	+	0.116890i
$300$		0			0
$301$	−15.0203	−	18.1865i	−0.865753	−	1.04825i
$302$		−	16.4835i		−	0.948517i
$303$		0			0
$304$	4.64575	+	8.04668i	0.266452	+	0.461509i
$305$	4.14159	+	11.9256i	0.237147	+	0.682858i
$306$		0			0
$307$		−	16.8480i		−	0.961568i	−0.876839	−	0.480784i	$-0.840352\pi$
$307$		−	16.8480i		−	0.961568i	0.876839	−	0.480784i	$-0.159648\pi$
$308$	−5.78589	−	34.3786i	−0.329682	−	1.95890i
$309$		0			0
$310$	−20.0951	−	17.3754i	−1.14133	−	0.986858i
$311$	8.39544	+	14.5413i	0.476061	+	0.824563i	0.999624	−	0.0274247i	$-0.00873065\pi$
$311$	8.39544	+	14.5413i	0.476061	+	0.824563i	−0.523562	+	0.851987i	$0.675397\pi$
$312$		0			0
$313$	1.31731	+	0.760548i	0.0744586	+	0.0429887i	0.536767	−	0.843730i	$-0.319645\pi$
$313$	1.31731	+	0.760548i	0.0744586	+	0.0429887i	−0.462308	+	0.886719i	$0.652979\pi$
$314$	−33.5817			−1.89513
$315$		0			0
$316$	−36.2288			−2.03803
$317$	−17.3200	−	9.99972i	−0.972790	−	0.561640i	−0.0727041	−	0.997354i	$-0.523163\pi$
$317$	−17.3200	−	9.99972i	−0.972790	−	0.561640i	−0.900086	+	0.435713i	$0.856496\pi$
$318$		0			0
$319$	−14.4686	−	25.0604i	−0.810088	−	1.40311i
$320$	16.5142	−	19.0990i	0.923169	−	1.06767i
$321$		0			0
$322$	4.07992	+	1.52110i	0.227365	+	0.0847673i
$323$			25.2951i			1.40746i
$324$		0			0
$325$	−16.6714	+	2.43292i	−0.924765	+	0.134954i
$326$	12.3987	+	21.4751i	0.686698	+	1.18940i
$327$		0			0
$328$			20.2176i			1.11633i
$329$	−10.2026	+	1.71708i	−0.562485	+	0.0946657i
$330$		0			0
$331$	1.79150	−	3.10297i	0.0984699	−	0.170555i	−0.812582	−	0.582847i	$-0.801939\pi$
$331$	1.79150	−	3.10297i	0.0984699	−	0.170555i	0.911051	+	0.412293i	$0.135272\pi$
$332$	−11.8757	+	6.85647i	−0.651766	+	0.376297i
$333$		0			0
$334$	−14.7601	+	25.5653i	−0.807638	+	1.39887i
$335$	5.81035	−	30.3191i	0.317453	−	1.65651i
$336$		0			0
$337$		−	10.1088i		−	0.550663i	−0.961349	−	0.275331i	$-0.911212\pi$
$337$		−	10.1088i		−	0.550663i	0.961349	−	0.275331i	$-0.0887875\pi$
$338$	3.38654	+	1.95522i	0.184203	+	0.106350i
$339$		0			0
$340$	−41.9302	+	14.5617i	−2.27398	+	0.789721i
$341$	9.03561	−	15.6501i	0.489305	−	0.847502i
$342$		0			0
$343$	8.88249	+	16.2512i	0.479610	+	0.877482i
$344$	−34.8621			−1.87964
$345$		0			0
$346$	−29.2288	−	50.6257i	−1.57135	−	2.72165i
$347$	23.4933	−	13.5638i	1.26118	−	0.728145i	0.287881	−	0.957666i	$-0.407049\pi$
$347$	23.4933	−	13.5638i	1.26118	−	0.728145i	0.973304	+	0.229521i	$0.0737160\pi$
$348$		0			0
$349$	5.87451			0.314455			0.157228	−	0.987562i	$-0.449744\pi$
$349$	5.87451			0.314455			0.157228	+	0.987562i	$0.449744\pi$
$350$	9.63806	+	29.9185i	0.515176	+	1.59921i
$351$		0			0
$352$	9.60515	+	5.54553i	0.511956	+	0.295578i
$353$	5.44428	−	3.14326i	0.289770	−	0.167299i	−0.348068	−	0.937469i	$-0.613162\pi$
$353$	5.44428	−	3.14326i	0.289770	−	0.167299i	0.637838	+	0.770171i	$0.279829\pi$
$354$		0			0
$355$	11.7097	−	13.5425i	0.621485	−	0.718763i
$356$	−13.1766			−0.698360
$357$		0			0
$358$		−	3.69702i		−	0.195394i
$359$	−3.22526	+	5.58631i	−0.170223	+	0.294834i	−0.938498	−	0.345286i	$-0.887782\pi$
$359$	−3.22526	+	5.58631i	−0.170223	+	0.294834i	0.768275	+	0.640120i	$0.221115\pi$
$360$		0			0
$361$	−1.29150	−	2.23695i	−0.0679738	−	0.117734i
$362$	15.1332	+	8.73714i	0.795382	+	0.459214i
$363$		0			0
$364$	−11.3542	+	30.4547i	−0.595124	+	1.59626i
$365$	0.640170	−	3.34048i	0.0335080	−	0.174849i
$366$		0			0
$367$	23.6289	−	13.6421i	1.23342	−	0.712114i	0.265676	−	0.964062i	$-0.414405\pi$
$367$	23.6289	−	13.6421i	1.23342	−	0.712114i	0.967741	+	0.251949i	$0.0810714\pi$
$368$	1.19968	−	0.692633i	0.0625374	−	0.0361060i
$369$		0			0
$370$	−27.2288	−	5.21812i	−1.41556	−	0.271277i
$371$	5.94814	−	15.9543i	0.308812	−	0.828304i
$372$		0			0
$373$	−3.48527	−	2.01222i	−0.180460	−	0.104189i	0.407049	−	0.913406i	$-0.366558\pi$
$373$	−3.48527	−	2.01222i	−0.180460	−	0.104189i	−0.587509	+	0.809218i	$0.699891\pi$
$374$	−23.3792	−	40.4939i	−1.20891	−	2.09389i
$375$		0			0
$376$	−7.64575	+	13.2428i	−0.394300	+	0.682947i
$377$			26.9786i			1.38947i
$378$		0			0
$379$	−8.29150			−0.425906			−0.212953	−	0.977062i	$-0.568308\pi$
$379$	−8.29150			−0.425906			−0.212953	+	0.977062i	$0.568308\pi$
$380$	24.7712	−	28.6485i	1.27074	−	1.46964i
$381$		0			0
$382$	14.8744	−	8.58772i	0.761039	−	0.439386i
$383$	16.2037	+	9.35523i	0.827972	+	0.478030i	0.853158	−	0.521653i	$-0.174684\pi$
$383$	16.2037	+	9.35523i	0.827972	+	0.478030i	−0.0251859	+	0.999683i	$0.508018\pi$
$384$		0			0
$385$	−18.7544	+	10.2697i	−0.955814	+	0.523394i
$386$	45.9804			2.34034
$387$		0			0
$388$	38.7868	−	22.3936i	1.96910	−	1.13686i
$389$	5.55916	+	9.62875i	0.281861	+	0.488197i	0.971843	−	0.235629i	$-0.0757151\pi$
$389$	5.55916	+	9.62875i	0.281861	+	0.488197i	−0.689982	+	0.723826i	$0.742382\pi$
$390$		0			0
$391$	3.77124			0.190720
$392$	26.8798	+	5.17302i	1.35763	+	0.261277i
$393$		0			0
$394$	16.7601	−	29.0294i	0.844363	−	1.46248i
$395$	7.28973	+	20.9906i	0.366786	+	1.05615i
$396$		0			0
$397$	−27.8643	−	16.0875i	−1.39847	−	0.807408i	−0.404239	−	0.914654i	$-0.632463\pi$
$397$	−27.8643	−	16.0875i	−1.39847	−	0.807408i	−0.994233	+	0.107246i	$0.965797\pi$
$398$			29.3547i			1.47142i
$399$		0			0
$400$	9.29150	+	3.69702i	0.464575	+	0.184851i
$401$	5.94814	−	10.3025i	0.297036	−	0.514482i	−0.678420	−	0.734674i	$-0.737335\pi$
$401$	5.94814	−	10.3025i	0.297036	−	0.514482i	0.975456	+	0.220192i	$0.0706685\pi$
$402$		0			0
$403$	−14.5908	+	8.42402i	−0.726821	+	0.419630i
$404$	−30.6077	+	53.0140i	−1.52279	+	2.63755i
$405$		0			0
$406$	49.6346	−	8.35347i	2.46333	−	0.414576i
$407$		−	18.8595i		−	0.934833i
$408$		0			0
$409$	2.20850	+	3.82523i	0.109203	+	0.189145i	0.915448	−	0.402437i	$-0.131837\pi$
$409$	2.20850	+	3.82523i	0.109203	+	0.189145i	−0.806245	+	0.591582i	$0.798503\pi$
$410$	25.9492	−	9.01179i	1.28154	−	0.445061i
$411$		0			0
$412$		−	43.5935i		−	2.14770i
$413$	−1.92863	−	0.719041i	−0.0949016	−	0.0353817i
$414$		0			0
$415$	6.36213	+	5.50108i	0.312305	+	0.270037i
$416$	−5.17018	−	8.95501i	−0.253489	−	0.439055i
$417$		0			0
$418$	34.5513	+	19.9482i	1.68996	+	0.975699i
$419$	−26.3533			−1.28744			−0.643720	−	0.765261i	$-0.722610\pi$
$419$	−26.3533			−1.28744			−0.643720	+	0.765261i	$0.722610\pi$
$420$		0			0
$421$	17.2288			0.839678			0.419839	−	0.907599i	$-0.362086\pi$
$421$	17.2288			0.839678			0.419839	+	0.907599i	$0.362086\pi$
$422$	1.92863	+	1.11349i	0.0938842	+	0.0542041i
$423$		0			0
$424$	−12.5830	−	21.7944i	−0.611085	−	1.05843i
$425$	16.8739	+	21.3639i	0.818502	+	1.03630i
$426$		0			0
$427$	−2.47906	−	14.7301i	−0.119970	−	0.712839i
$428$			29.0565i			1.40450i
$429$		0			0
$430$	15.5394	+	44.7453i	0.749376	+	2.15781i
$431$	−15.3727	−	26.6264i	−0.740478	−	1.28255i	−0.952278	−	0.305233i	$-0.901266\pi$
$431$	−15.3727	−	26.6264i	−0.740478	−	1.28255i	0.211799	−	0.977313i	$-0.432068\pi$
$432$		0			0
$433$		−	7.72146i		−	0.371070i	−0.982638	−	0.185535i	$-0.940598\pi$
$433$		−	7.72146i		−	0.371070i	0.982638	−	0.185535i	$-0.0594018\pi$
$434$	20.0161	+	24.2355i	0.960805	+	1.16334i
$435$		0			0
$436$	−24.1144	+	41.7673i	−1.15487	+	2.00029i
$437$	−2.78670	+	1.60890i	−0.133306	+	0.0769642i
$438$		0			0
$439$	1.88562	−	3.26599i	0.0899958	−	0.155877i	−0.817513	−	0.575910i	$-0.804648\pi$
$439$	1.88562	−	3.26599i	0.0899958	−	0.155877i	0.907509	+	0.420032i	$0.137981\pi$
$440$	−5.94814	+	31.0381i	−0.283567	+	1.47968i
$441$		0			0
$442$			43.5935i			2.07353i
$443$	−3.64477	−	2.10431i	−0.173168	−	0.0999787i	0.410911	−	0.911676i	$-0.365211\pi$
$443$	−3.64477	−	2.10431i	−0.173168	−	0.0999787i	−0.584079	+	0.811697i	$0.698544\pi$
$444$		0			0
$445$	2.65132	+	7.63441i	0.125685	+	0.361906i
$446$		0			0
$447$		0			0
$448$	−23.0342	+	19.0240i	−1.08826	+	0.898798i
$449$	−10.3404			−0.487991			−0.243996	−	0.969776i	$-0.578458\pi$
$449$	−10.3404			−0.487991			−0.243996	+	0.969776i	$0.578458\pi$
$450$		0			0
$451$	9.34313	+	16.1828i	0.439951	+	0.762018i
$452$	−40.6384	+	23.4626i	−1.91147	+	1.10359i
$453$		0			0
$454$	56.1033			2.63306
$455$	19.9298	+	0.450643i	0.934322	+	0.0211265i
$456$		0			0
$457$	2.35106	+	1.35739i	0.109978	+	0.0634959i	0.553980	−	0.832530i	$-0.313108\pi$
$457$	2.35106	+	1.35739i	0.109978	+	0.0634959i	−0.444002	+	0.896026i	$0.646442\pi$
$458$	17.0618	−	9.85063i	0.797245	−	0.460290i
$459$		0			0
$460$	−4.27120	−	3.69313i	−0.199146	−	0.172193i
$461$	−10.8427			−0.504996			−0.252498	−	0.967597i	$-0.581252\pi$
$461$	−10.8427			−0.504996			−0.252498	+	0.967597i	$0.581252\pi$
$462$		0			0
$463$			21.1999i			0.985242i	0.870244	+	0.492621i	$0.163961\pi$
$463$			21.1999i			0.985242i	−0.870244	+	0.492621i	$0.836039\pi$
$464$	8.00645	−	13.8676i	0.371690	−	0.643786i
$465$		0			0
$466$	8.29150	+	14.3613i	0.384096	+	0.665275i
$467$	−10.3721	−	5.98833i	−0.479964	−	0.277107i	0.240438	−	0.970665i	$-0.422709\pi$
$467$	−10.3721	−	5.98833i	−0.479964	−	0.277107i	−0.720401	+	0.693557i	$0.756042\pi$
$468$		0			0
$469$	−12.7601	+	34.2255i	−0.589208	+	1.58039i
$470$	20.4051	+	3.91044i	0.941218	+	0.180375i
$471$		0			0
$472$	−2.63461	+	1.52110i	−0.121268	+	0.0700141i
$473$	−27.9046	+	16.1107i	−1.28306	+	0.740773i
$474$		0			0
$475$	−21.5830	−	8.58772i	−0.990296	−	0.394032i
$476$	51.7907	−	8.71634i	2.37383	−	0.399513i
$477$		0			0
$478$	−27.1141	−	15.6544i	−1.24017	−	0.716014i
$479$	13.8168	+	23.9314i	0.631306	+	1.09345i	0.987285	+	0.158960i	$0.0508140\pi$
$479$	13.8168	+	23.9314i	0.631306	+	1.09345i	−0.355979	+	0.934494i	$0.615853\pi$
$480$		0			0
$481$	−8.79150	+	15.2273i	−0.400858	+	0.694306i
$482$		−	4.20861i		−	0.191697i
$483$		0			0
$484$	−7.52026			−0.341830
$485$	−20.7791	−	17.9668i	−0.943528	−	0.815830i
$486$		0			0
$487$	−3.48527	+	2.01222i	−0.157933	+	0.0911824i	−0.576883	−	0.816827i	$-0.695731\pi$
$487$	−3.48527	+	2.01222i	−0.157933	+	0.0911824i	0.418951	+	0.908009i	$0.362398\pi$
$488$	−19.1195	−	11.0387i	−0.865501	−	0.499697i
$489$		0			0
$490$	−5.34183	−	36.8059i	−0.241319	−	1.66272i
$491$	−7.50408			−0.338654			−0.169327	−	0.985560i	$-0.554159\pi$
$491$	−7.50408			−0.338654			−0.169327	+	0.985560i	$0.554159\pi$
$492$		0			0
$493$	37.7530	−	21.7967i	1.70031	−	0.981675i
$494$	−18.5980	−	32.2127i	−0.836763	−	1.44932i
$495$		0			0
$496$	10.0000			0.449013
$497$	−16.3328	+	13.4893i	−0.732628	+	0.605078i
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	1.81057	−	40.7205i	0.0809712	−	1.82108i
$501$		0			0
$502$	22.3116	+	12.8816i	0.995814	+	0.574933i
$503$			12.8712i			0.573899i	0.957946	+	0.286949i	$0.0926412\pi$
$503$			12.8712i			0.573899i	−0.957946	+	0.286949i	$0.907359\pi$
$504$		0			0
$505$	36.8745	+	7.06663i	1.64089	+	0.314461i
$506$	2.97407	−	5.15124i	0.132214	−	0.229001i
$507$		0			0
$508$	10.6389	−	6.14237i	0.472025	−	0.272524i
$509$	−7.22848	+	12.5201i	−0.320397	+	0.554944i	−0.980570	−	0.196170i	$-0.937150\pi$
$509$	−7.22848	+	12.5201i	−0.320397	+	0.554944i	0.660173	+	0.751114i	$0.270483\pi$
$510$		0			0
$511$	−1.40588	+	3.77089i	−0.0621925	+	0.166814i
$512$			21.7792i			0.962512i
$513$		0			0
$514$	−7.46863	−	12.9360i	−0.329427	−	0.570584i
$515$	−25.2576	+	8.77161i	−1.11298	+	0.386523i
$516$		0			0
$517$			14.1333i			0.621580i
$518$	30.7371	+	11.4595i	1.35051	+	0.503503i
$519$		0			0
$520$	19.2712	−	22.2876i	0.845098	−	0.977377i
$521$	−0.777967	−	1.34748i	−0.0340834	−	0.0590341i	0.848481	−	0.529227i	$-0.177518\pi$
$521$	−0.777967	−	1.34748i	−0.0340834	−	0.0590341i	−0.882564	+	0.470192i	$0.844185\pi$
$522$		0			0
$523$	11.9562	+	6.90292i	0.522809	+	0.301844i	0.738083	−	0.674710i	$-0.235731\pi$
$523$	11.9562	+	6.90292i	0.522809	+	0.301844i	−0.215274	+	0.976554i	$0.569065\pi$
$524$	−42.3662			−1.85077
$525$		0			0
$526$	12.5830			0.548645
$527$	23.5766	+	13.6120i	1.02701	+	0.592947i
$528$		0			0
$529$	−11.2601	−	19.5031i	−0.489571	−	0.847962i
$530$	−22.3643	+	25.8648i	−0.971442	+	1.12350i
$531$		0			0
$532$	−34.5513	+	28.5359i	−1.49799	+	1.23719i
$533$		−	17.4215i		−	0.754607i
$534$		0			0
$535$	16.8351	−	5.84657i	0.727843	−	0.252769i
$536$	26.9934	+	46.7540i	1.16594	+	2.01946i
$537$		0			0
$538$		−	23.9147i		−	1.03103i
$539$	23.9060	−	8.28127i	1.02970	−	0.356700i
$540$		0			0
$541$	−4.20850	+	7.28933i	−0.180937	+	0.313393i	−0.942200	−	0.335051i	$-0.891246\pi$
$541$	−4.20850	+	7.28933i	−0.180937	+	0.313393i	0.761263	+	0.648444i	$0.224580\pi$
$542$	8.70170	−	5.02393i	0.373770	−	0.215796i
$543$		0			0
$544$	−8.35425	+	14.4700i	−0.358185	+	0.620395i
$545$	29.0517	+	5.56747i	1.24444	+	0.238484i
$546$		0			0
$547$			26.9569i			1.15259i	0.817241	+	0.576296i	$0.195502\pi$
$547$			26.9569i			1.15259i	−0.817241	+	0.576296i	$0.804498\pi$
$548$	10.1596	+	5.86565i	0.433997	+	0.250568i
$549$		0			0
$550$	42.4886	−	6.20049i	1.81172	−	0.264390i
$551$	−18.5980	+	32.2127i	−0.792301	+	1.37231i
$552$		0			0
$553$	−4.36347	−	25.9269i	−0.185554	−	1.10252i
$554$	19.6271			0.833877
$555$		0			0
$556$	−35.0516	−	60.7112i	−1.48652	−	2.57473i
$557$	38.9680	−	22.4982i	1.65113	−	0.953280i	0.674520	−	0.738257i	$-0.264351\pi$
$557$	38.9680	−	22.4982i	1.65113	−	0.953280i	0.976609	−	0.215023i	$-0.0689825\pi$
$558$		0			0
$559$	30.0405			1.27058
$560$	−10.1106	−	6.14621i	−0.427251	−	0.259725i
$561$		0			0
$562$	−60.0646	−	34.6783i	−2.53367	−	1.46282i
$563$	−13.5461	+	7.82087i	−0.570902	+	0.329610i	−0.757509	−	0.652824i	$-0.773584\pi$
$563$	−13.5461	+	7.82087i	−0.570902	+	0.329610i	0.186608	+	0.982435i	$0.440251\pi$
$564$		0			0
$565$	21.7710	+	18.8245i	0.915914	+	0.791953i
$566$	−60.4374			−2.54037
$567$		0			0
$568$			31.3087i			1.31368i
$569$	11.3695	−	19.6926i	0.476635	−	0.825555i	−0.523007	−	0.852328i	$-0.675190\pi$
$569$	11.3695	−	19.6926i	0.476635	−	0.825555i	0.999642	+	0.0267732i	$0.00852318\pi$
$570$		0			0
$571$	16.2601	+	28.1634i	0.680465	+	1.17860i	0.974839	+	0.222910i	$0.0715556\pi$
$571$	16.2601	+	28.1634i	0.680465	+	1.17860i	−0.294374	+	0.955690i	$0.595111\pi$
$572$	38.4516	+	22.2000i	1.60774	+	0.928230i
$573$		0			0
$574$	−32.0516	+	5.39426i	−1.33781	+	0.225152i
$575$	−1.28034	+	3.21780i	−0.0533939	+	0.134192i
$576$		0			0
$577$	−5.55278	+	3.20590i	−0.231165	+	0.133463i	−0.611109	−	0.791546i	$-0.709276\pi$
$577$	−5.55278	+	3.20590i	−0.231165	+	0.133463i	0.379944	+	0.925009i	$0.375943\pi$
$578$	26.0217	−	15.0237i	1.08236	−	0.624902i
$579$		0			0
$580$	−64.1033	−	12.2847i	−2.66174	−	0.510096i
$581$	−6.33713	−	7.67300i	−0.262908	−	0.318329i
$582$		0			0
$583$	−20.1436	−	11.6299i	−0.834263	−	0.481662i
$584$	2.97407	+	5.15124i	0.123068	+	0.213160i
$585$		0			0
$586$	32.5203	−	56.3267i	1.34340	−	2.32684i
$587$			13.3185i			0.549712i	0.961485	+	0.274856i	$0.0886302\pi$
$587$			13.3185i			0.549712i	−0.961485	+	0.274856i	$0.911370\pi$
$588$		0			0
$589$	−23.2288			−0.957124
$590$	3.12667	+	2.70350i	0.128723	+	0.111301i
$591$		0			0
$592$	9.03805	−	5.21812i	0.371461	−	0.214463i
$593$	11.2759	+	6.51015i	0.463046	+	0.267340i	0.713324	−	0.700834i	$-0.247189\pi$
$593$	11.2759	+	6.51015i	0.463046	+	0.267340i	−0.250278	+	0.968174i	$0.580522\pi$
$594$		0			0
$595$	−15.4712	−	28.2532i	−0.634256	−	1.15827i
$596$	16.0129			0.655914
$597$		0			0
$598$	−4.80257	+	2.77277i	−0.196392	+	0.113387i
$599$	−5.03238	−	8.71634i	−0.205617	−	0.356140i	0.744712	−	0.667386i	$-0.232587\pi$
$599$	−5.03238	−	8.71634i	−0.205617	−	0.356140i	−0.950329	+	0.311246i	$0.899254\pi$
$600$		0			0
$601$	−35.1033			−1.43189			−0.715946	−	0.698156i	$-0.754004\pi$
$601$	−35.1033			−1.43189			−0.715946	+	0.698156i	$0.754004\pi$
$602$	−9.30154	−	55.2679i	−0.379102	−	2.25255i
$603$		0			0
$604$	12.6458	−	21.9031i	0.514548	−	0.891224i
$605$	1.51318	+	4.35717i	0.0615195	+	0.177144i
$606$		0			0
$607$	23.6289	+	13.6421i	0.959066	+	0.553717i	0.895886	−	0.444285i	$-0.146542\pi$
$607$	23.6289	+	13.6421i	0.959066	+	0.553717i	0.0631807	+	0.998002i	$0.479876\pi$
$608$		−	14.2565i		−	0.578176i
$609$		0			0
$610$	−5.64575	+	29.4602i	−0.228590	+	1.19281i
$611$	6.58831	−	11.4113i	0.266535	−	0.461652i
$612$		0			0
$613$	15.9081	−	9.18456i	0.642523	−	0.370961i	−0.143063	−	0.989714i	$-0.545695\pi$
$613$	15.9081	−	9.18456i	0.642523	−	0.370961i	0.785586	+	0.618753i	$0.212362\pi$
$614$	20.0161	−	34.6690i	0.807785	−	1.39913i
$615$		0			0
$616$	13.0627	−	35.0372i	0.526313	−	1.41169i
$617$			30.1964i			1.21566i	0.794067	+	0.607831i	$0.207960\pi$
$617$			30.1964i			1.21566i	−0.794067	+	0.607831i	$0.792040\pi$
$618$		0			0
$619$	6.50000	+	11.2583i	0.261257	+	0.452510i	0.966576	−	0.256379i	$-0.0825296\pi$
$619$	6.50000	+	11.2583i	0.261257	+	0.452510i	−0.705319	+	0.708890i	$0.749196\pi$
$620$	−13.3722	−	38.5048i	−0.537039	−	1.54639i
$621$		0			0
$622$			39.8964i			1.59970i
$623$	−1.58702	−	9.42977i	−0.0635827	−	0.377796i
$624$		0			0
$625$	−23.9574	+	7.14450i	−0.958295	+	0.285780i
$626$	1.80712	+	3.13003i	0.0722271	+	0.125101i
$627$		0			0
$628$	−44.6231	−	25.7632i	−1.78066	−	1.02806i
$629$	28.4116			1.13284
$630$		0			0
$631$	−39.1660			−1.55917			−0.779587	−	0.626294i	$-0.784571\pi$
$631$	−39.1660			−1.55917			−0.779587	+	0.626294i	$0.784571\pi$
$632$	−33.6529	−	19.4295i	−1.33864	−	0.772864i
$633$		0			0
$634$	−23.7601	−	41.1538i	−0.943635	−	1.63442i
$635$	−5.69953	−	4.92815i	−0.226179	−	0.195568i
$636$		0			0
$637$	−23.1622	−	4.45757i	−0.917720	−	0.176615i
$638$		−	68.7572i		−	2.72212i
$639$		0			0
$640$	43.7081	−	15.1792i	1.72772	−	0.600011i
$641$	−1.02915	−	1.78255i	−0.0406491	−	0.0704064i	0.844985	−	0.534790i	$-0.179609\pi$
$641$	−1.02915	−	1.78255i	−0.0406491	−	0.0704064i	−0.885634	+	0.464384i	$0.846276\pi$
$642$		0			0
$643$			39.0302i			1.53920i	0.638526	+	0.769600i	$0.279544\pi$
$643$			39.0302i			1.53920i	−0.638526	+	0.769600i	$0.720456\pi$
$644$	4.25441	+	5.15124i	0.167647	+	0.202987i
$645$		0			0
$646$	−30.0516	+	52.0510i	−1.18237	+	2.04792i
$647$	−35.1942	+	20.3194i	−1.38362	+	0.798836i	−0.992587	−	0.121538i	$-0.961217\pi$
$647$	−35.1942	+	20.3194i	−1.38362	+	0.798836i	−0.391038	+	0.920374i	$0.627884\pi$
$648$		0			0
$649$	−1.40588	+	2.43506i	−0.0551857	+	0.0955844i
$650$	−37.1960	−	14.8000i	−1.45895	−	0.580504i
$651$		0			0
$652$			38.0479i			1.49007i
$653$	−12.0049	−	6.93101i	−0.469787	−	0.271231i	0.246364	−	0.969177i	$-0.420764\pi$
$653$	−12.0049	−	6.93101i	−0.469787	−	0.271231i	−0.716150	+	0.697946i	$0.754098\pi$
$654$		0			0
$655$	8.52466	+	24.5465i	0.333086	+	0.959113i
$656$	−5.17018	+	8.95501i	−0.201861	+	0.349634i
$657$		0			0
$658$	−23.0342	−	8.58772i	−0.897967	−	0.334784i
$659$	26.3533			1.02658			0.513289	−	0.858216i	$-0.328427\pi$
$659$	26.3533			1.02658			0.513289	+	0.858216i	$0.328427\pi$
$660$		0			0
$661$	−6.67712	−	11.5651i	−0.259710	−	0.449831i	0.706454	−	0.707759i	$-0.250294\pi$
$661$	−6.67712	−	11.5651i	−0.259710	−	0.449831i	−0.966164	+	0.257928i	$0.916960\pi$
$662$	7.37291	−	4.25675i	0.286556	−	0.165443i
$663$		0			0
$664$	−14.7085			−0.570800
$665$	23.4857	+	14.2769i	0.910735	+	0.553634i
$666$		0			0
$667$	4.80257	+	2.77277i	0.185956	+	0.107362i
$668$	−39.2263	+	22.6473i	−1.51771	+	0.876250i
$669$		0			0
$670$	47.9765	−	55.4860i	1.85349	−	2.14361i
$671$	−20.4051			−0.787731
$672$		0			0
$673$		−	10.1088i		−	0.389666i	−0.980836	−	0.194833i	$-0.937583\pi$
$673$		−	10.1088i		−	0.389666i	0.980836	−	0.194833i	$-0.0624165\pi$
$674$	12.0097	−	20.8014i	0.462595	−	0.801239i
$675$		0			0
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	−39.3554	−	22.7218i	−1.51255	−	0.873271i	−0.999892	−	0.0146783i	$-0.995328\pi$
$677$	−39.3554	−	22.7218i	−1.51255	−	0.873271i	−0.512658	−	0.858593i	$-0.671339\pi$
$678$		0			0
$679$	20.6974	+	25.0604i	0.794293	+	0.961730i
$680$	−46.7584	−	8.96077i	−1.79310	−	0.343630i
$681$		0			0
$682$	37.1859	−	21.4693i	1.42392	−	0.822102i
$683$	−20.9648	+	12.1040i	−0.802196	+	0.463148i	−0.844238	−	0.535968i	$-0.819947\pi$
$683$	−20.9648	+	12.1040i	−0.802196	+	0.463148i	0.0420428	+	0.999116i	$0.486613\pi$
$684$		0			0
$685$	1.35425	−	7.06663i	0.0517432	−	0.270002i
$686$	−1.02915	+	43.9936i	−0.0392933	+	1.67968i
$687$		0			0
$688$	−15.4415	−	8.91514i	−0.588701	−	0.339887i
$689$	10.8427	+	18.7802i	0.413075	+	0.715467i
$690$		0			0
$691$	−1.85425	+	3.21165i	−0.0705389	+	0.122177i	−0.899138	−	0.437666i	$-0.855805\pi$
$691$	−1.85425	+	3.21165i	−0.0705389	+	0.122177i	0.828599	+	0.559843i	$0.189139\pi$
$692$		−	89.6946i		−	3.40968i
$693$		0			0
$694$	64.4575			2.44677
$695$	−28.1226	+	32.5245i	−1.06675	+	1.23373i
$696$		0			0
$697$	−24.3791	+	14.0753i	−0.923423	+	0.533139i
$698$	12.0882	+	6.97915i	0.457547	+	0.264165i
$699$		0			0
$700$	−10.1458	+	47.1495i	−0.383476	+	1.78208i
$701$	−42.8685			−1.61912			−0.809561	−	0.587036i	$-0.800295\pi$
$701$	−42.8685			−1.61912			−0.809561	+	0.587036i	$0.800295\pi$
$702$		0			0
$703$	−20.9943	+	12.1210i	−0.791813	+	0.457154i
$704$	20.4051	+	35.3427i	0.769047	+	1.33203i
$705$		0			0
$706$	14.9373			0.562171
$707$	−41.6256	−	15.5191i	−1.56549	−	0.583654i
$708$		0			0
$709$	−5.82288	+	10.0855i	−0.218683	+	0.378770i	−0.954405	−	0.298513i	$-0.903509\pi$
$709$	−5.82288	+	10.0855i	−0.218683	+	0.378770i	0.735723	+	0.677283i	$0.236843\pi$
$710$	40.1846	−	13.9555i	1.50810	−	0.523741i
$711$		0			0
$712$	−12.2398	−	7.06663i	−0.458704	−	0.264833i
$713$			3.46317i			0.129697i
$714$		0			0
$715$	5.12549	−	26.7454i	0.191683	−	1.00022i
$716$	2.83627	−	4.91257i	0.105997	−	0.183591i
$717$		0			0
$718$	−13.2735	+	7.66347i	−0.495363	+	0.285998i
$719$	−2.97407	+	5.15124i	−0.110914	+	0.192109i	−0.916139	−	0.400861i	$-0.868711\pi$
$719$	−2.97407	+	5.15124i	−0.110914	+	0.192109i	0.805225	+	0.592969i	$0.202045\pi$
$720$		0			0
$721$	31.1974	−	5.25049i	1.16185	−	0.195539i
$722$		−	6.13742i		−	0.228411i
$723$		0			0
$724$	13.4059	+	23.2197i	0.498226	+	0.862952i
$725$	5.78080	+	39.6127i	0.214694	+	1.47118i
$726$		0			0
$727$		−	20.0062i		−	0.741989i	−0.928635	−	0.370995i	$-0.879017\pi$
$727$		−	20.0062i		−	0.741989i	0.928635	−	0.370995i	$-0.120983\pi$
$728$	−26.8798	+	22.2000i	−0.996232	+	0.822788i
$729$		0			0
$730$	5.28593	−	6.11332i	0.195641	−	0.226264i
$731$	−24.2705	−	42.0378i	−0.897678	−	1.55482i
$732$		0			0
$733$	17.7925	+	10.2725i	0.657182	+	0.379424i	0.791203	−	0.611554i	$-0.209455\pi$
$733$	17.7925	+	10.2725i	0.657182	+	0.379424i	−0.134020	+	0.990979i	$0.542789\pi$
$734$	64.8296			2.39290
$735$		0			0
$736$	−2.12549			−0.0783467
$737$	43.2126	+	24.9488i	1.59176	+	0.919002i
$738$		0			0
$739$	−1.96863	−	3.40976i	−0.0724171	−	0.125430i	0.827543	−	0.561402i	$-0.189738\pi$
$739$	−1.96863	−	3.40976i	−0.0724171	−	0.125430i	−0.899960	+	0.435972i	$0.856405\pi$
$740$	−32.1781	−	27.8231i	−1.18289	−	1.02280i
$741$		0			0
$742$	31.1941	−	25.7632i	1.14517	−	0.945796i
$743$		−	4.90125i		−	0.179809i	−0.995950	−	0.0899047i	$-0.971344\pi$
$743$		−	4.90125i		−	0.179809i	0.995950	−	0.0899047i	$-0.0286562\pi$
$744$		0			0
$745$	−3.22202	−	9.27772i	−0.118046	−	0.339909i
$746$	−4.78119	−	8.28127i	−0.175052	−	0.303199i
$747$		0			0
$748$		−	71.7440i		−	2.62322i
$749$	−20.7941	+	3.49963i	−0.759800	+	0.127874i
$750$		0			0
$751$	12.7288	−	22.0469i	0.464479	−	0.804501i	−0.534699	−	0.845043i	$-0.679575\pi$
$751$	12.7288	−	22.0469i	0.464479	−	0.804501i	0.999178	+	0.0405415i	$0.0129083\pi$
$752$	−6.77307	+	3.91044i	−0.246989	+	0.142599i
$753$		0			0
$754$	−32.0516	+	55.5151i	−1.16725	+	2.02174i
$755$	−15.2349	−	2.91962i	−0.554456	−	0.106256i
$756$		0			0
$757$		−	33.6961i		−	1.22470i	−0.790585	−	0.612352i	$-0.790223\pi$
$757$		−	33.6961i		−	1.22470i	0.790585	−	0.612352i	$-0.209777\pi$
$758$	−17.0618	−	9.85063i	−0.619712	−	0.357791i
$759$		0			0
$760$	38.3742	−	13.3268i	1.39198	−	0.483414i
$761$	20.7941	−	36.0164i	0.753785	−	1.30559i	−0.192191	−	0.981358i	$-0.561559\pi$
$761$	20.7941	−	36.0164i	0.753785	−	1.30559i	0.945976	−	0.324237i	$-0.105108\pi$
$762$		0			0
$763$	−32.7949	−	12.2268i	−1.18726	−	0.442638i
$764$	26.3533			0.953427
$765$		0			0
$766$	22.2288	+	38.5013i	0.803158	+	1.39111i
$767$	2.27024	−	1.31072i	0.0819735	−	0.0473274i
$768$		0			0
$769$	19.3542			0.697932			0.348966	−	0.937135i	$-0.386533\pi$
$769$	19.3542			0.697932			0.348966	+	0.937135i	$0.386533\pi$
$770$	−50.7927	−	1.14850i	−1.83044	−	0.0413891i
$771$		0			0
$772$	61.0984	+	35.2752i	2.19898	+	1.26958i
$773$	20.9191	−	12.0776i	0.752406	−	0.434402i	−0.0741565	−	0.997247i	$-0.523626\pi$
$773$	20.9191	−	12.0776i	0.752406	−	0.434402i	0.826563	+	0.562845i	$0.190293\pi$
$774$		0			0
$775$	−19.6187	+	15.4954i	−0.704723	+	0.556612i
$776$	48.0387			1.72449
$777$		0			0
$778$			26.4180i			0.947131i
$779$	12.0097	−	20.8014i	0.430291	−	0.745286i
$780$		0			0
$781$	14.4686	+	25.0604i	0.517728	+	0.896732i
$782$	7.76026	+	4.48039i	0.277506	+	0.160218i
$783$		0			0
$784$	10.5830	+	9.16515i	0.377964	+	0.327327i
$785$	−5.94814	+	31.0381i	−0.212298	+	1.10780i
$786$		0			0
$787$	20.7107	−	11.9573i	0.738257	−	0.426233i	−0.0831783	−	0.996535i	$-0.526507\pi$
$787$	20.7107	−	11.9573i	0.738257	−	0.426233i	0.821435	+	0.570302i	$0.193174\pi$
$788$	44.5414	−	25.7160i	1.58672	−	0.916095i
$789$		0			0
$790$	−9.93725	+	51.8538i	−0.353552	+	1.84487i
$791$	−21.6855	−	26.2568i	−0.771046	−	0.933583i
$792$		0			0
$793$	16.4752	+	9.51198i	0.585053	+	0.337780i
$794$	−38.2251	−	66.2079i	−1.35656	−	2.34963i
$795$		0			0
$796$	−22.5203	+	39.0062i	−0.798209	+	1.38254i
$797$			23.6117i			0.836369i	0.908362	+	0.418185i	$0.137334\pi$
$797$			23.6117i			0.836369i	−0.908362	+	0.418185i	$0.862666\pi$
$798$		0			0
$799$	−21.2915			−0.753239
$800$	−9.51019	−	12.0408i	−0.336236	−	0.425707i
$801$		0			0
$802$	24.4795	−	14.1333i	0.864402	−	0.499063i
$803$	4.76107	+	2.74880i	0.168014	+	0.0970032i
$804$		0			0
$805$	2.12853	−	3.50147i	0.0750210	−	0.123410i
$806$	−40.0323			−1.41008
$807$		0			0
$808$	−56.8629	+	32.8298i	−2.00043	+	1.15495i
$809$	24.6595	+	42.7115i	0.866983	+	1.50166i	0.865065	+	0.501660i	$0.167277\pi$
$809$	24.6595	+	42.7115i	0.866983	+	1.50166i	0.00191780	+	0.999998i	$0.499390\pi$
$810$		0			0
$811$	13.7712			0.483574			0.241787	−	0.970329i	$-0.422267\pi$
$811$	13.7712			0.483574			0.241787	+	0.970329i	$0.422267\pi$
$812$	72.3627	+	26.9786i	2.53943	+	0.946763i
$813$		0			0
$814$	22.4059	−	38.8081i	0.785326	−	1.36022i
$815$	22.0446	−	7.65577i	0.772189	−	0.268170i
$816$		0			0
$817$	35.8686	+	20.7088i	1.25488	+	0.724508i
$818$			10.4951i			0.366954i
$819$		0			0
$820$	41.3948	+	7.93289i	1.44557	+	0.277029i
$821$	−6.97730	+	12.0850i	−0.243509	+	0.421771i	−0.961711	−	0.274064i	$-0.911632\pi$
$821$	−6.97730	+	12.0850i	−0.243509	+	0.421771i	0.718202	+	0.695835i	$0.244965\pi$
$822$		0			0
$823$	−32.4838	+	18.7545i	−1.13231	+	0.653742i	−0.944516	−	0.328465i	$-0.893469\pi$
$823$	−32.4838	+	18.7545i	−1.13231	+	0.653742i	−0.187799	+	0.982208i	$0.560135\pi$
$824$	23.3792	−	40.4939i	0.814452	−	1.41067i
$825$		0			0
$826$	−3.11438	−	3.77089i	−0.108363	−	0.131206i
$827$			14.5018i			0.504278i	0.967691	+	0.252139i	$0.0811341\pi$
$827$			14.5018i			0.504278i	−0.967691	+	0.252139i	$0.918866\pi$
$828$		0			0
$829$	−13.5516	−	23.4721i	−0.470668	−	0.815220i	0.528770	−	0.848765i	$-0.322654\pi$
$829$	−13.5516	−	23.4721i	−0.470668	−	0.815220i	−0.999437	+	0.0335452i	$0.989320\pi$
$830$	6.55615	+	18.8783i	0.227567	+	0.655275i
$831$		0			0
$832$		−	38.0479i		−	1.31907i
$833$	12.4756	+	36.0139i	0.432253	+	1.24781i
$834$		0			0
$835$	21.0145	+	18.1704i	0.727236	+	0.628812i
$836$	30.6077	+	53.0140i	1.05859	+	1.83353i
$837$		0			0
$838$	−54.2283	−	31.3087i	−1.87328	−	1.08154i
$839$	28.6872			0.990391			0.495195	−	0.868782i	$-0.335096\pi$
$839$	28.6872			0.990391			0.495195	+	0.868782i	$0.335096\pi$
$840$		0			0
$841$	35.1033			1.21046
$842$	35.4524	+	20.4684i	1.22177	+	0.705389i
$843$		0			0
$844$	1.70850	+	2.95920i	0.0588089	+	0.101860i
$845$	2.40696	−	2.78371i	0.0828019	−	0.0957625i
$846$		0			0
$847$	−0.905757	−	5.38183i	−0.0311222	−	0.184922i
$848$		−	12.8712i		−	0.441999i
$849$		0			0
$850$	9.34093	+	64.0083i	0.320391	+	2.19547i
$851$	1.80712	+	3.13003i	0.0619473	+	0.107296i
$852$		0			0
$853$		−	15.6544i		−	0.535995i	−0.963420	−	0.267997i	$-0.913638\pi$
$853$		−	15.6544i		−	0.535995i	0.963420	−	0.267997i	$-0.0863619\pi$
$854$	12.3987	−	33.2560i	0.424273	−	1.13800i
$855$		0			0
$856$	−15.5830	+	26.9906i	−0.532616	+	0.922518i
$857$	23.8806	−	13.7875i	0.815746	−	0.470971i	−0.0332013	−	0.999449i	$-0.510570\pi$
$857$	23.8806	−	13.7875i	0.815746	−	0.470971i	0.848947	+	0.528478i	$0.177237\pi$
$858$		0			0
$859$	16.4686	−	28.5245i	0.561902	−	0.973243i	−0.435428	−	0.900223i	$-0.643403\pi$
$859$	16.4686	−	28.5245i	0.561902	−	0.973243i	0.997330	−	0.0730199i	$-0.0232636\pi$
$860$	−13.6790	+	71.3786i	−0.466450	+	2.43399i
$861$		0			0
$862$		−	73.0537i		−	2.48822i
$863$	−32.8782	−	18.9822i	−1.11919	−	0.646162i	−0.177993	−	0.984032i	$-0.556960\pi$
$863$	−32.8782	−	18.9822i	−1.11919	−	0.646162i	−0.941193	+	0.337869i	$0.890294\pi$
$864$		0			0
$865$	−51.9682	+	18.0478i	−1.76697	+	0.613644i
$866$	9.17340	−	15.8888i	0.311725	−	0.539923i
$867$		0			0
$868$	8.00429	+	47.5599i	0.271683	+	1.61429i
$869$	−35.9156			−1.21835
$870$		0			0
$871$	−23.2601	−	40.2877i	−0.788139	−	1.36510i
$872$	−44.7997	+	25.8651i	−1.51711	+	0.875903i
$873$		0			0
$874$	−7.64575			−0.258621
$875$	29.3594	−	3.60874i	0.992530	−	0.121998i
$876$		0			0
$877$	18.6432	+	10.7637i	0.629536	+	0.363463i	0.780572	−	0.625065i	$-0.214928\pi$
$877$	18.6432	+	10.7637i	0.629536	+	0.363463i	−0.151036	+	0.988528i	$0.548261\pi$
$878$	7.76026	−	4.48039i	0.261896	−	0.151206i
$879$		0			0
$880$	−10.5719	+	12.2266i	−0.356378	+	0.412160i
$881$	24.5217			0.826158			0.413079	−	0.910695i	$-0.364453\pi$
$881$	24.5217			0.826158			0.413079	+	0.910695i	$0.364453\pi$
$882$		0			0
$883$		−	35.8720i		−	1.20719i	−0.797292	−	0.603594i	$-0.793735\pi$
$883$		−	35.8720i		−	1.20719i	0.797292	−	0.603594i	$-0.206265\pi$
$884$	−33.4439	+	57.9266i	−1.12484	+	1.94828i
$885$		0			0
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	−32.7948	−	18.9341i	−1.10114	−	0.635744i	−0.164621	−	0.986357i	$-0.552640\pi$
$887$	−32.7948	−	18.9341i	−1.10114	−	0.635744i	−0.936521	+	0.350612i	$0.885973\pi$
$888$		0			0
$889$	5.67712	+	6.87386i	0.190405	+	0.230542i
$890$	−3.61424	+	18.8595i	−0.121150	+	0.632173i
$891$		0			0
$892$		0			0
$893$	15.7330	−	9.08345i	0.526485	−	0.303966i
$894$		0			0
$895$	−3.41699	−	0.654833i	−0.114218	−	0.0218886i
$896$	−53.9869	+	9.08594i	−1.80357	+	0.303540i
$897$		0			0
$898$	−21.2778	−	12.2847i	−0.710050	−	0.409947i
$899$	20.0161	+	34.6690i	0.667575	+	1.15627i
$900$		0			0
$901$	17.5203	−	30.3460i	0.583684	−	1.01097i
$902$			44.4001i			1.47836i
$903$		0			0
$904$	−50.3320			−1.67402
$905$	10.7558	−	12.4394i	0.357535	−	0.413498i
$906$		0			0
$907$	−4.51902	+	2.60906i	−0.150052	+	0.0866324i	−0.573146	−	0.819453i	$-0.694277\pi$
$907$	−4.51902	+	2.60906i	−0.150052	+	0.0866324i	0.423094	+	0.906086i	$0.360944\pi$
$908$	74.5495	+	43.0412i	2.47401	+	1.42837i
$909$		0			0
$910$	40.4750	+	24.6047i	1.34173	+	0.815637i
$911$	37.1960			1.23236			0.616179	−	0.787606i	$-0.288680\pi$
$911$	37.1960			1.23236			0.616179	+	0.787606i	$0.288680\pi$
$912$		0			0
$913$	−11.7731	+	6.79721i	−0.389633	+	0.224955i
$914$	3.22526	+	5.58631i	0.106682	+	0.184779i
$915$		0			0
$916$	30.2288			0.998786
$917$	−5.10267	−	30.3191i	−0.168505	−	1.00122i
$918$		0			0
$919$	11.4373	−	19.8099i	0.377280	−	0.653468i	−0.613385	−	0.789784i	$-0.710193\pi$
$919$	11.4373	−	19.8099i	0.377280	−	0.653468i	0.990665	+	0.136315i	$0.0435260\pi$
$920$	−1.98689	−	5.72119i	−0.0655057	−	0.188622i
$921$		0			0
$922$	−22.3116	−	12.8816i	−0.734792	−	0.424232i
$923$		−	26.9786i		−	0.888011i
$924$		0			0
$925$	−9.64575	+	24.2421i	−0.317150	+	0.797075i
$926$	−25.1863	+	43.6240i	−0.827673	+	1.43357i
$927$		0			0
$928$	−21.2778	+	12.2847i	−0.698478	+	0.403267i
$929$	27.3824	−	47.4277i	0.898388	−	1.55605i	0.0688327	−	0.997628i	$-0.478073\pi$
$929$	27.3824	−	47.4277i	0.898388	−	1.55605i	0.829555	−	0.558425i	$-0.188594\pi$
$930$		0			0
$931$	−24.5830	−	21.2895i	−0.805675	−	0.697735i
$932$			25.4442i			0.833454i
$933$		0			0
$934$	−14.2288	−	24.6449i	−0.465579	−	0.806407i
$935$	−41.5678	+	14.4359i	−1.35941	+	0.472104i
$936$		0			0
$937$			53.7023i			1.75438i	0.480146	+	0.877188i	$0.340584\pi$
$937$			53.7023i			1.75438i	−0.480146	+	0.877188i	$0.659416\pi$
$938$	−66.9184	+	55.2679i	−2.18496	+	1.80456i
$939$		0			0
$940$	24.1141	+	20.8505i	0.786516	+	0.680069i
$941$	−17.9578	−	31.1039i	−0.585408	−	1.01396i	−0.994824	−	0.101609i	$-0.967601\pi$
$941$	−17.9578	−	31.1039i	−0.585408	−	1.01396i	0.409416	−	0.912348i	$-0.365732\pi$
$942$		0			0
$943$	−3.10127	−	1.79052i	−0.100991	−	0.0583073i
$944$	−1.55593			−0.0506414
$945$		0			0
$946$	−76.5608			−2.48921
$947$	−18.7322	−	10.8150i	−0.608715	−	0.351442i	0.163748	−	0.986502i	$-0.447642\pi$
$947$	−18.7322	−	10.8150i	−0.608715	−	0.351442i	−0.772462	+	0.635061i	$0.780975\pi$
$948$		0			0
$949$	−2.56275	−	4.43881i	−0.0831903	−	0.144090i
$950$	−34.2098	−	43.3128i	−1.10991	−	1.40525i
$951$		0			0
$952$	52.7830	+	19.6788i	1.71071	+	0.637793i
$953$			21.1828i			0.686178i	0.939303	+	0.343089i	$0.111473\pi$
$953$			21.1828i			0.686178i	−0.939303	+	0.343089i	$0.888527\pi$
$954$		0			0
$955$	−5.30264	−	15.2688i	−0.171589	−	0.494087i
$956$	−24.0194	−	41.6027i	−0.776841	−	1.34553i
$957$		0			0
$958$			65.6596i			2.12137i
$959$	−2.97407	+	7.97713i	−0.0960378	+	0.257595i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	−36.1813	+	20.8893i	−1.16653	+	0.673498i
$963$		0			0
$964$	3.22876	−	5.59237i	0.103991	−	0.180118i
$965$	8.14425	−	42.4976i	0.262173	−	1.36805i
$966$		0			0
$967$		−	33.4846i		−	1.07679i	−0.842692	−	0.538397i	$-0.819030\pi$
$967$		−	33.4846i		−	1.07679i	0.842692	−	0.538397i	$-0.180970\pi$
$968$	−6.98556	−	4.03312i	−0.224525	−	0.129629i
$969$		0			0
$970$	−21.4127	−	61.6574i	−0.687521	−	1.97970i
$971$	−29.8297	+	51.6666i	−0.957281	+	1.65806i	−0.228220	+	0.973610i	$0.573291\pi$
$971$	−29.8297	+	51.6666i	−0.957281	+	1.65806i	−0.729061	+	0.684449i	$0.760043\pi$
$972$		0			0
$973$	39.2259	−	32.3967i	1.25752	−	1.03859i
$974$	−9.56239			−0.306399
$975$		0			0
$976$	−5.64575	−	9.77873i	−0.180716	−	0.313009i
$977$	26.0675	−	15.0501i	0.833972	−	0.481494i	−0.0212386	−	0.999774i	$-0.506761\pi$
$977$	26.0675	−	15.0501i	0.833972	−	0.481494i	0.855211	+	0.518280i	$0.173428\pi$
$978$		0			0
$979$	−13.0627			−0.417487
$980$	21.1385	−	53.0055i	0.675244	−	1.69320i
$981$		0			0
$982$	−15.4415	−	8.91514i	−0.492757	−	0.284494i
$983$	−34.2527	+	19.7758i	−1.09249	+	0.630750i	−0.934239	−	0.356648i	$-0.883919\pi$
$983$	−34.2527	+	19.7758i	−1.09249	+	0.630750i	−0.158253	+	0.987399i	$0.550586\pi$
$984$		0			0
$985$	−23.8620	−	20.6325i	−0.760305	−	0.657405i
$986$	103.581			3.29871
$987$		0			0
$988$		−	57.0719i		−	1.81570i
$989$	3.08746	−	5.34764i	0.0981756	−	0.170045i
$990$		0			0
$991$	−26.1974	−	45.3752i	−0.832187	−	1.44139i	−0.896300	−	0.443448i	$-0.853755\pi$
$991$	−26.1974	−	45.3752i	−0.832187	−	1.44139i	0.0641128	−	0.997943i	$-0.479578\pi$
$992$	−13.2879	−	7.67178i	−0.421892	−	0.243579i
$993$		0			0
$994$	−49.6346	+	8.35347i	−1.57432	+	0.264956i
$995$	27.1312	+	5.19943i	0.860118	+	0.164833i
$996$		0			0
$997$	−27.8643	+	16.0875i	−0.882473	+	0.509496i	−0.871473	−	0.490444i	$-0.836835\pi$
$997$	−27.8643	+	16.0875i	−0.882473	+	0.509496i	−0.0109997	+	0.999940i	$0.503501\pi$
$998$	−10.2887	+	5.94020i	−0.325684	+	0.188034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.c.289.8	yes	16
3.2	odd	2	inner	315.2.bf.c.289.1	yes	16
5.4	even	2	inner	315.2.bf.c.289.2	yes	16
7.2	even	3		2205.2.d.p.1324.1		8
7.4	even	3	inner	315.2.bf.c.109.2	yes	16
7.5	odd	6		2205.2.d.r.1324.2		8
15.14	odd	2	inner	315.2.bf.c.289.7	yes	16
21.2	odd	6		2205.2.d.p.1324.8		8
21.5	even	6		2205.2.d.r.1324.7		8
21.11	odd	6	inner	315.2.bf.c.109.7	yes	16
35.4	even	6	inner	315.2.bf.c.109.8	yes	16
35.9	even	6		2205.2.d.p.1324.7		8
35.19	odd	6		2205.2.d.r.1324.8		8
105.44	odd	6		2205.2.d.p.1324.2		8
105.74	odd	6	inner	315.2.bf.c.109.1	✓	16
105.89	even	6		2205.2.d.r.1324.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bf.c.109.1	✓	16	105.74	odd	6	inner
315.2.bf.c.109.2	yes	16	7.4	even	3	inner
315.2.bf.c.109.7	yes	16	21.11	odd	6	inner
315.2.bf.c.109.8	yes	16	35.4	even	6	inner
315.2.bf.c.289.1	yes	16	3.2	odd	2	inner
315.2.bf.c.289.2	yes	16	5.4	even	2	inner
315.2.bf.c.289.7	yes	16	15.14	odd	2	inner
315.2.bf.c.289.8	yes	16	1.1	even	1	trivial
2205.2.d.p.1324.1		8	7.2	even	3
2205.2.d.p.1324.2		8	105.44	odd	6
2205.2.d.p.1324.7		8	35.9	even	6
2205.2.d.p.1324.8		8	21.2	odd	6
2205.2.d.r.1324.1		8	105.89	even	6
2205.2.d.r.1324.2		8	7.5	odd	6
2205.2.d.r.1324.7		8	21.5	even	6
2205.2.d.r.1324.8		8	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05774 + 1.18804i) q^{2} +(1.82288 + 3.15731i) q^{4} +(1.46253 - 1.69145i) q^{5} +(-2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +O(q^{10})\)	\(q+(2.05774 + 1.18804i) q^{2} +(1.82288 + 3.15731i) q^{4} +(1.46253 - 1.69145i) q^{5} +(-2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +(5.01902 - 1.74303i) q^{10} +(1.80712 + 3.13003i) q^{11} -3.36961i q^{13} +(-6.19933 + 1.04334i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(-4.71533 + 2.72240i) q^{17} +(2.32288 - 4.02334i) q^{19} +(8.00645 + 1.53436i) q^{20} +8.58772i q^{22} +(-0.599838 - 0.346317i) q^{23} +(-0.722018 - 4.94759i) q^{25} +(4.00323 - 6.93379i) q^{26} +(-9.03805 - 3.36961i) q^{28} -8.00645 q^{29} +(-2.50000 - 4.33013i) q^{31} +(2.65758 - 1.53436i) q^{32} -12.9373 q^{34} +(-0.133738 + 5.91457i) q^{35} +(-4.51902 - 2.60906i) q^{37} +(9.55977 - 5.51934i) q^{38} +(6.61431 + 5.71912i) q^{40} +5.17018 q^{41} +8.91514i q^{43} +(-6.58831 + 11.4113i) q^{44} +(-0.822876 - 1.42526i) q^{46} +(3.38654 + 1.95522i) q^{47} +(1.32288 - 6.87386i) q^{49} +(4.39221 - 11.0387i) q^{50} +(10.6389 - 6.14237i) q^{52} +(-5.57340 + 3.21780i) q^{53} +(7.93725 + 1.52110i) q^{55} +(-6.58831 - 7.97713i) q^{56} +(-16.4752 - 9.51198i) q^{58} +(0.388984 + 0.673739i) q^{59} +(-2.82288 + 4.88936i) q^{61} -11.8804i q^{62} +11.2915 q^{64} +(-5.69953 - 4.92815i) q^{65} +(11.9562 - 6.90292i) q^{67} +(-17.1909 - 9.92518i) q^{68} +(-7.30194 + 12.0118i) q^{70} +8.00645 q^{71} +(1.31731 - 0.760548i) q^{73} +(-6.19933 - 10.7376i) q^{74} +16.9373 q^{76} +(-8.95993 - 3.34048i) q^{77} +(-4.96863 + 8.60591i) q^{79} +(1.46715 + 4.22463i) q^{80} +(10.6389 + 6.14237i) q^{82} +3.76135i q^{83} +(-2.29150 + 11.9573i) q^{85} +(-10.5915 + 18.3451i) q^{86} +(-12.2398 + 7.06663i) q^{88} +(-1.80712 + 3.13003i) q^{89} +(5.67712 + 6.87386i) q^{91} -2.52517i q^{92} +(4.64575 + 8.04668i) q^{94} +(-3.40801 - 9.81328i) q^{95} -12.2847i q^{97} +(10.8886 - 12.5730i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 8 q^{10} - 16 q^{16} + 16 q^{19} - 16 q^{25} - 40 q^{31} - 80 q^{34} + 8 q^{40} + 8 q^{46} - 24 q^{61} + 96 q^{64} - 56 q^{70} + 144 q^{76} - 16 q^{79} + 48 q^{85} + 112 q^{91} + 32 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^10 - 16 * q^16 + 16 * q^19 - 16 * q^25 - 40 * q^31 - 80 * q^34 + 8 * q^40 + 8 * q^46 - 24 * q^61 + 96 * q^64 - 56 * q^70 + 144 * q^76 - 16 * q^79 + 48 * q^85 + 112 * q^91 + 32 * q^94

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