LMFDB - Embedded newform 315.2.bf.c.109.8

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			109.8
Root			$0.733576 + 2.11231i$ of defining polynomial
Character	$\chi$	$=$	315.109
Dual form			315.2.bf.c.289.8

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.456284	−	0.889834i	$-0.349180\pi$
$2$	2.05774	−	1.18804i	1.45505	−	0.840071i	0.998761	+	0.0497633i	$0.0158467\pi$
$3$		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	−0.453748	−	0.891130i	$-0.649913\pi$
$11$	1.80712	−	3.13003i	0.544867	−	0.943738i	0.998615	−	0.0526080i	$-0.0167534\pi$
$12$		0			0
$13$			3.36961i			0.934561i	0.884109	+	0.467280i	$0.154766\pi$
$13$			3.36961i			0.934561i	−0.884109	+	0.467280i	$0.845234\pi$
$14$	−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	−0.196307	−	0.980543i	$-0.562895\pi$
$17$	−4.71533	−	2.72240i	−1.14363	−	0.660278i	−0.947328	+	0.320265i	$0.896228\pi$
$18$		0			0
$19$	2.32288	+	4.02334i	0.532904	+	0.923017i	0.999262	+	0.0384208i	$0.0122327\pi$
$19$	2.32288	+	4.02334i	0.532904	+	0.923017i	−0.466357	+	0.884596i	$0.654434\pi$
$20$	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	−0.561232	−	0.827658i	$-0.689672\pi$
$23$	−0.599838	+	0.346317i	−0.125075	+	0.0722120i	0.436157	+	0.899870i	$0.356339\pi$
$24$		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	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	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	−0.823131	−	0.567851i	$-0.807775\pi$
$37$	−4.51902	+	2.60906i	−0.742923	+	0.428927i	0.0802083	+	0.996778i	$0.474441\pi$
$38$	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	$-0.762078\pi$
$43$		−	8.91514i		−	1.35955i	0.733422	−	0.679773i	$-0.237922\pi$
$44$	−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	−0.232246	−	0.972657i	$-0.574607\pi$
$47$	3.38654	−	1.95522i	0.493977	−	0.285198i	0.726223	+	0.687459i	$0.241274\pi$
$48$		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	0.0657253	−	0.997838i	$-0.479064\pi$
$53$	−5.57340	−	3.21780i	−0.765565	−	0.441999i	−0.831290	+	0.555839i	$0.812397\pi$
$54$		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	−0.839594	−	0.543215i	$-0.817207\pi$
$59$	0.388984	−	0.673739i	0.0506414	−	0.0877134i	0.890235	+	0.455502i	$0.150540\pi$
$60$		0			0
$61$	−2.82288	−	4.88936i	−0.361432	−	0.626019i	0.626765	−	0.779209i	$-0.284379\pi$
$61$	−2.82288	−	4.88936i	−0.361432	−	0.626019i	−0.988197	+	0.153190i	$0.951045\pi$
$62$			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	0.999043	−	0.0437409i	$-0.0139276\pi$
$67$	11.9562	+	6.90292i	1.46068	+	0.843326i	0.461641	+	0.887067i	$0.347261\pi$
$68$	−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	0.575105	−	0.818080i	$-0.304961\pi$
$73$	1.31731	+	0.760548i	0.154179	+	0.0890154i	−0.420926	+	0.907095i	$0.638295\pi$
$74$	−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	−0.997579	−	0.0695415i	$-0.977846\pi$
$79$	−4.96863	−	8.60591i	−0.559014	−	0.968241i	0.438565	−	0.898700i	$-0.355487\pi$
$80$	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	$-0.933815\pi$
$83$		−	3.76135i		−	0.412861i	0.978461	−	0.206431i	$-0.0661848\pi$
$84$		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	0.754211	−	0.656632i	$-0.228020\pi$
$89$	−1.80712	−	3.13003i	−0.191554	−	0.331782i	−0.945766	+	0.324850i	$0.894686\pi$
$90$		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	$0.214356\pi$
$97$			12.2847i			1.24733i	−0.781693	+	0.623664i	$0.785644\pi$
$98$	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	−0.0583461	−	0.998296i	$-0.518583\pi$
$101$	8.39544	−	14.5413i	0.835377	−	1.44692i	0.893723	−	0.448619i	$-0.148084\pi$
$102$		0			0
$103$	−10.3554	+	5.97867i	−1.02034	+	0.589095i	−0.914203	−	0.405256i	$-0.867182\pi$
$103$	−10.3554	+	5.97867i	−1.02034	+	0.589095i	−0.106140	+	0.994351i	$0.533849\pi$
$104$	13.1766			1.29207
$105$		0			0
$106$	−15.2915			−1.48524
$107$	6.90219	−	3.98498i	0.667260	−	0.385243i	−0.127778	−	0.991803i	$-0.540784\pi$
$107$	6.90219	−	3.98498i	0.667260	−	0.385243i	0.795038	+	0.606560i	$0.207451\pi$
$108$		0			0
$109$	6.61438	−	11.4564i	0.633543	−	1.09733i	−0.353279	−	0.935518i	$-0.614933\pi$
$109$	6.61438	−	11.4564i	0.633543	−	1.09733i	0.986822	−	0.161810i	$-0.0517332\pi$
$110$	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	$-0.793009\pi$
$113$		−	12.8712i		−	1.21082i	0.795913	−	0.605411i	$-0.206991\pi$
$114$		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	$0.0477671\pi$
$127$			3.36961i			0.299004i	−0.988761	+	0.149502i	$0.952233\pi$
$128$	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	−0.999961	−	0.00885883i	$-0.997180\pi$
$131$	−5.81035	−	10.0638i	−0.507652	−	0.879280i	0.492308	−	0.870421i	$-0.336153\pi$
$132$		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	0.614296	−	0.789076i	$-0.289440\pi$
$137$	2.78670	+	1.60890i	0.238084	+	0.137458i	−0.376212	+	0.926534i	$0.622774\pi$
$138$		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	0.941850	−	0.336033i	$-0.109085\pi$
$149$	2.19610	+	3.80376i	0.179912	+	0.311617i	−0.761938	+	0.647650i	$0.775752\pi$
$150$		0			0
$151$	−3.46863	+	6.00784i	−0.282273	+	0.488911i	−0.971944	−	0.235212i	$-0.924422\pi$
$151$	−3.46863	+	6.00784i	−0.282273	+	0.488911i	0.689671	+	0.724123i	$0.257755\pi$
$152$	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	−0.0755249	−	0.997144i	$-0.524063\pi$
$157$	−12.2398	−	7.06663i	−0.976839	−	0.563978i	−0.901314	+	0.433165i	$0.857397\pi$
$158$	−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	−0.102374	−	0.994746i	$-0.532644\pi$
$163$	9.03805	−	5.21812i	0.707914	−	0.408715i	0.810288	+	0.586031i	$0.199310\pi$
$164$	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	$-0.840384\pi$
$167$		−	12.4239i		−	0.961393i	0.876887	−	0.480697i	$-0.159616\pi$
$168$		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	−0.632950	+	0.774193i	$0.718156\pi$
$173$	−21.3064	+	12.3013i	−1.61990	+	0.935247i	−0.986945	+	0.161055i	$0.948510\pi$
$174$		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	−0.893634	−	0.448796i	$-0.851853\pi$
$179$	−0.777967	+	1.34748i	−0.0581480	+	0.100715i	0.835486	+	0.549512i	$0.185186\pi$
$180$		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	0.966645	−	0.256119i	$-0.0824438\pi$
$191$	3.61424	+	6.26005i	0.261517	+	0.452961i	−0.705128	+	0.709080i	$0.749110\pi$
$192$		0			0
$193$	16.7588	+	9.67569i	1.20632	+	0.696471i	0.961954	−	0.273211i	$-0.0880857\pi$
$193$	16.7588	+	9.67569i	1.20632	+	0.696471i	0.244370	+	0.969682i	$0.421419\pi$
$194$	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	$0.167606\pi$
$197$			14.1074i			1.00511i	−0.864545	+	0.502555i	$0.832394\pi$
$198$		0			0
$199$	6.17712	−	10.6991i	0.437885	−	0.758439i	−0.559641	−	0.828735i	$-0.689061\pi$
$199$	6.17712	−	10.6991i	0.437885	−	0.758439i	0.997526	+	0.0702963i	$0.0223945\pi$
$200$	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	0.989246	−	0.146261i	$-0.0467239\pi$
$227$	20.4483	+	11.8059i	1.35720	+	0.783582i	0.367957	+	0.929843i	$0.380057\pi$
$228$		0			0
$229$	4.14575	+	7.18065i	0.273959	+	0.474511i	0.969872	−	0.243615i	$-0.0783334\pi$
$229$	4.14575	+	7.18065i	0.273959	+	0.474511i	−0.695913	+	0.718126i	$0.745000\pi$
$230$	−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	−0.288777	−	0.957396i	$-0.593249\pi$
$233$	6.04412	−	3.48957i	0.395963	−	0.228610i	0.684741	+	0.728787i	$0.259915\pi$
$234$		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	−0.893139	−	0.449781i	$-0.851502\pi$
$241$	−0.885622	+	1.53394i	−0.0570479	+	0.0988099i	0.836091	+	0.548591i	$0.184835\pi$
$242$	−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	−0.660097	−	0.751180i	$-0.729485\pi$
$257$	−5.44428	+	3.14326i	−0.339605	+	0.196071i	0.320492	+	0.947251i	$0.396152\pi$
$258$		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	0.634689	−	0.772767i	$-0.281128\pi$
$263$	4.58621	+	2.64785i	0.282798	+	0.163273i	−0.351891	+	0.936041i	$0.614461\pi$
$264$		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	−0.977667	−	0.210160i	$-0.932602\pi$
$269$	−5.03238	+	8.71634i	−0.306830	+	0.531444i	0.670837	+	0.741604i	$0.265935\pi$
$270$		0			0
$271$	2.11438	+	3.66221i	0.128439	+	0.222463i	0.923072	−	0.384627i	$-0.125670\pi$
$271$	2.11438	+	3.66221i	0.128439	+	0.222463i	−0.794633	+	0.607090i	$0.792337\pi$
$272$			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	0.699270	−	0.714858i	$-0.253508\pi$
$277$	7.15364	+	4.13015i	0.429820	+	0.248157i	−0.269450	+	0.963014i	$0.586842\pi$
$278$	−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	−0.327429	−	0.944876i	$-0.606182\pi$
$283$	−22.0280	−	12.7179i	−1.30943	−	0.755999i	−0.982001	+	0.188877i	$0.939515\pi$
$284$	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	$0.294942\pi$
$293$			27.3730i			1.59915i	−0.600566	+	0.799575i	$0.705058\pi$
$294$		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	$0.159648\pi$
$307$			16.8480i			0.961568i	−0.876839	+	0.480784i	$0.840352\pi$
$308$	−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	−0.523562	−	0.851987i	$-0.675397\pi$
$311$	8.39544	−	14.5413i	0.476061	−	0.824563i	0.999624	+	0.0274247i	$0.00873065\pi$
$312$		0			0
$313$	1.31731	−	0.760548i	0.0744586	−	0.0429887i	−0.462308	−	0.886719i	$-0.652979\pi$
$313$	1.31731	−	0.760548i	0.0744586	−	0.0429887i	0.536767	+	0.843730i	$0.319645\pi$
$314$	−33.5817			−1.89513
$315$		0			0
$316$	−36.2288			−2.03803
$317$	−17.3200	+	9.99972i	−0.972790	+	0.561640i	−0.900086	−	0.435713i	$-0.856496\pi$
$317$	−17.3200	+	9.99972i	−0.972790	+	0.561640i	−0.0727041	+	0.997354i	$0.523163\pi$
$318$		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	0.911051	−	0.412293i	$-0.135272\pi$
$331$	1.79150	+	3.10297i	0.0984699	+	0.170555i	−0.812582	+	0.582847i	$0.801939\pi$
$332$	−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	$0.0887875\pi$
$337$			10.1088i			0.550663i	−0.961349	+	0.275331i	$0.911212\pi$
$338$	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	0.973304	−	0.229521i	$-0.0737160\pi$
$347$	23.4933	+	13.5638i	1.26118	+	0.728145i	0.287881	+	0.957666i	$0.407049\pi$
$348$		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	0.637838	−	0.770171i	$-0.279829\pi$
$353$	5.44428	+	3.14326i	0.289770	+	0.167299i	−0.348068	+	0.937469i	$0.613162\pi$
$354$		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	0.768275	−	0.640120i	$-0.221115\pi$
$359$	−3.22526	−	5.58631i	−0.170223	−	0.294834i	−0.938498	+	0.345286i	$0.887782\pi$
$360$		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	0.967741	−	0.251949i	$-0.0810714\pi$
$367$	23.6289	+	13.6421i	1.23342	+	0.712114i	0.265676	+	0.964062i	$0.414405\pi$
$368$	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	−0.587509	−	0.809218i	$-0.699891\pi$
$373$	−3.48527	+	2.01222i	−0.180460	+	0.104189i	0.407049	+	0.913406i	$0.366558\pi$
$374$	−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	−0.0251859	−	0.999683i	$-0.508018\pi$
$383$	16.2037	−	9.35523i	0.827972	−	0.478030i	0.853158	+	0.521653i	$0.174684\pi$
$384$		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	−0.689982	−	0.723826i	$-0.742382\pi$
$389$	5.55916	−	9.62875i	0.281861	−	0.488197i	0.971843	+	0.235629i	$0.0757151\pi$
$390$		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	−0.994233	−	0.107246i	$-0.965797\pi$
$397$	−27.8643	+	16.0875i	−1.39847	+	0.807408i	−0.404239	+	0.914654i	$0.632463\pi$
$398$		−	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	0.975456	−	0.220192i	$-0.0706685\pi$
$401$	5.94814	+	10.3025i	0.297036	+	0.514482i	−0.678420	+	0.734674i	$0.737335\pi$
$402$		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	−0.806245	−	0.591582i	$-0.798503\pi$
$409$	2.20850	−	3.82523i	0.109203	−	0.189145i	0.915448	+	0.402437i	$0.131837\pi$
$410$	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	0.211799	+	0.977313i	$0.432068\pi$
$431$	−15.3727	+	26.6264i	−0.740478	+	1.28255i	−0.952278	+	0.305233i	$0.901266\pi$
$432$		0			0
$433$			7.72146i			0.371070i	0.982638	+	0.185535i	$0.0594018\pi$
$433$			7.72146i			0.371070i	−0.982638	+	0.185535i	$0.940598\pi$
$434$	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	0.907509	−	0.420032i	$-0.137981\pi$
$439$	1.88562	+	3.26599i	0.0899958	+	0.155877i	−0.817513	+	0.575910i	$0.804648\pi$
$440$	−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	−0.584079	−	0.811697i	$-0.698544\pi$
$443$	−3.64477	+	2.10431i	−0.173168	+	0.0999787i	0.410911	+	0.911676i	$0.365211\pi$
$444$		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	−0.444002	−	0.896026i	$-0.646442\pi$
$457$	2.35106	−	1.35739i	0.109978	−	0.0634959i	0.553980	+	0.832530i	$0.313108\pi$
$458$	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	$-0.836039\pi$
$463$		−	21.1999i		−	0.985242i	0.870244	−	0.492621i	$-0.163961\pi$
$464$	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	−0.720401	−	0.693557i	$-0.756042\pi$
$467$	−10.3721	+	5.98833i	−0.479964	+	0.277107i	0.240438	+	0.970665i	$0.422709\pi$
$468$		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	−0.355979	−	0.934494i	$-0.615853\pi$
$479$	13.8168	−	23.9314i	0.631306	−	1.09345i	0.987285	−	0.158960i	$-0.0508140\pi$
$480$		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	0.418951	−	0.908009i	$-0.362398\pi$
$487$	−3.48527	−	2.01222i	−0.157933	−	0.0911824i	−0.576883	+	0.816827i	$0.695731\pi$
$488$	−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	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$	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	$-0.907359\pi$
$503$		−	12.8712i		−	0.573899i	0.957946	−	0.286949i	$-0.0926412\pi$
$504$		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	0.660173	−	0.751114i	$-0.270483\pi$
$509$	−7.22848	−	12.5201i	−0.320397	−	0.554944i	−0.980570	+	0.196170i	$0.937150\pi$
$510$		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	−0.882564	−	0.470192i	$-0.844185\pi$
$521$	−0.777967	+	1.34748i	−0.0340834	+	0.0590341i	0.848481	+	0.529227i	$0.177518\pi$
$522$		0			0
$523$	11.9562	−	6.90292i	0.522809	−	0.301844i	−0.215274	−	0.976554i	$-0.569065\pi$
$523$	11.9562	−	6.90292i	0.522809	−	0.301844i	0.738083	+	0.674710i	$0.235731\pi$
$524$	−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	0.761263	−	0.648444i	$-0.224580\pi$
$541$	−4.20850	−	7.28933i	−0.180937	−	0.313393i	−0.942200	+	0.335051i	$0.891246\pi$
$542$	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	$-0.804498\pi$
$547$		−	26.9569i		−	1.15259i	0.817241	−	0.576296i	$-0.195502\pi$
$548$	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	0.976609	+	0.215023i	$0.0689825\pi$
$557$	38.9680	+	22.4982i	1.65113	+	0.953280i	0.674520	+	0.738257i	$0.264351\pi$
$558$		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	0.186608	−	0.982435i	$-0.440251\pi$
$563$	−13.5461	−	7.82087i	−0.570902	−	0.329610i	−0.757509	+	0.652824i	$0.773584\pi$
$564$		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	0.999642	−	0.0267732i	$-0.00852318\pi$
$569$	11.3695	+	19.6926i	0.476635	+	0.825555i	−0.523007	+	0.852328i	$0.675190\pi$
$570$		0			0
$571$	16.2601	−	28.1634i	0.680465	−	1.17860i	−0.294374	−	0.955690i	$-0.595111\pi$
$571$	16.2601	−	28.1634i	0.680465	−	1.17860i	0.974839	−	0.222910i	$-0.0715556\pi$
$572$	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	0.379944	−	0.925009i	$-0.375943\pi$
$577$	−5.55278	−	3.20590i	−0.231165	−	0.133463i	−0.611109	+	0.791546i	$0.709276\pi$
$578$	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	$-0.911370\pi$
$587$		−	13.3185i		−	0.549712i	0.961485	−	0.274856i	$-0.0886302\pi$
$588$		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	−0.250278	−	0.968174i	$-0.580522\pi$
$593$	11.2759	−	6.51015i	0.463046	−	0.267340i	0.713324	+	0.700834i	$0.247189\pi$
$594$		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	−0.950329	−	0.311246i	$-0.899254\pi$
$599$	−5.03238	+	8.71634i	−0.205617	+	0.356140i	0.744712	+	0.667386i	$0.232587\pi$
$600$		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	0.0631807	−	0.998002i	$-0.479876\pi$
$607$	23.6289	−	13.6421i	0.959066	−	0.553717i	0.895886	+	0.444285i	$0.146542\pi$
$608$			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	0.785586	−	0.618753i	$-0.212362\pi$
$613$	15.9081	+	9.18456i	0.642523	+	0.370961i	−0.143063	+	0.989714i	$0.545695\pi$
$614$	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	$-0.792040\pi$
$617$		−	30.1964i		−	1.21566i	0.794067	−	0.607831i	$-0.207960\pi$
$618$		0			0
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	−0.705319	−	0.708890i	$-0.749196\pi$
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	0.966576	+	0.256379i	$0.0825296\pi$
$620$	−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	−0.885634	−	0.464384i	$-0.846276\pi$
$641$	−1.02915	+	1.78255i	−0.0406491	+	0.0704064i	0.844985	+	0.534790i	$0.179609\pi$
$642$		0			0
$643$		−	39.0302i		−	1.53920i	−0.638526	−	0.769600i	$-0.720456\pi$
$643$		−	39.0302i		−	1.53920i	0.638526	−	0.769600i	$-0.279544\pi$
$644$	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	−0.391038	−	0.920374i	$-0.627884\pi$
$647$	−35.1942	−	20.3194i	−1.38362	−	0.798836i	−0.992587	+	0.121538i	$0.961217\pi$
$648$		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	−0.716150	−	0.697946i	$-0.754098\pi$
$653$	−12.0049	+	6.93101i	−0.469787	+	0.271231i	0.246364	+	0.969177i	$0.420764\pi$
$654$		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	−0.966164	−	0.257928i	$-0.916960\pi$
$661$	−6.67712	+	11.5651i	−0.259710	+	0.449831i	0.706454	+	0.707759i	$0.250294\pi$
$662$	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	$0.0624165\pi$
$673$			10.1088i			0.389666i	−0.980836	+	0.194833i	$0.937583\pi$
$674$	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	−0.512658	+	0.858593i	$0.671339\pi$
$677$	−39.3554	+	22.7218i	−1.51255	+	0.873271i	−0.999892	+	0.0146783i	$0.995328\pi$
$678$		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	0.0420428	−	0.999116i	$-0.486613\pi$
$683$	−20.9648	−	12.1040i	−0.802196	−	0.463148i	−0.844238	+	0.535968i	$0.819947\pi$
$684$		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	0.828599	−	0.559843i	$-0.189139\pi$
$691$	−1.85425	−	3.21165i	−0.0705389	−	0.122177i	−0.899138	+	0.437666i	$0.855805\pi$
$692$			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	0.735723	−	0.677283i	$-0.236843\pi$
$709$	−5.82288	−	10.0855i	−0.218683	−	0.378770i	−0.954405	+	0.298513i	$0.903509\pi$
$710$	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	0.805225	−	0.592969i	$-0.202045\pi$
$719$	−2.97407	−	5.15124i	−0.110914	−	0.192109i	−0.916139	+	0.400861i	$0.868711\pi$
$720$		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	$0.120983\pi$
$727$			20.0062i			0.741989i	−0.928635	+	0.370995i	$0.879017\pi$
$728$	−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	−0.134020	−	0.990979i	$-0.542789\pi$
$733$	17.7925	−	10.2725i	0.657182	−	0.379424i	0.791203	+	0.611554i	$0.209455\pi$
$734$	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	−0.899960	−	0.435972i	$-0.856405\pi$
$739$	−1.96863	+	3.40976i	−0.0724171	+	0.125430i	0.827543	+	0.561402i	$0.189738\pi$
$740$	−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	$0.0286562\pi$
$743$			4.90125i			0.179809i	−0.995950	+	0.0899047i	$0.971344\pi$
$744$		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	0.999178	−	0.0405415i	$-0.0129083\pi$
$751$	12.7288	+	22.0469i	0.464479	+	0.804501i	−0.534699	+	0.845043i	$0.679575\pi$
$752$	−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	$0.209777\pi$
$757$			33.6961i			1.22470i	−0.790585	+	0.612352i	$0.790223\pi$
$758$	−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	0.945976	+	0.324237i	$0.105108\pi$
$761$	20.7941	+	36.0164i	0.753785	+	1.30559i	−0.192191	+	0.981358i	$0.561559\pi$
$762$		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	0.826563	−	0.562845i	$-0.190293\pi$
$773$	20.9191	+	12.0776i	0.752406	+	0.434402i	−0.0741565	+	0.997247i	$0.523626\pi$
$774$		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	0.821435	−	0.570302i	$-0.193174\pi$
$787$	20.7107	+	11.9573i	0.738257	+	0.426233i	−0.0831783	+	0.996535i	$0.526507\pi$
$788$	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	$-0.862666\pi$
$797$		−	23.6117i		−	0.836369i	0.908362	−	0.418185i	$-0.137334\pi$
$798$		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	0.00191780	−	0.999998i	$-0.499390\pi$
$809$	24.6595	−	42.7115i	0.866983	−	1.50166i	0.865065	−	0.501660i	$-0.167277\pi$
$810$		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	0.718202	−	0.695835i	$-0.244965\pi$
$821$	−6.97730	−	12.0850i	−0.243509	−	0.421771i	−0.961711	+	0.274064i	$0.911632\pi$
$822$		0			0
$823$	−32.4838	−	18.7545i	−1.13231	−	0.653742i	−0.187799	−	0.982208i	$-0.560135\pi$
$823$	−32.4838	−	18.7545i	−1.13231	−	0.653742i	−0.944516	+	0.328465i	$0.893469\pi$
$824$	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	$-0.918866\pi$
$827$		−	14.5018i		−	0.504278i	0.967691	−	0.252139i	$-0.0811341\pi$
$828$		0			0
$829$	−13.5516	+	23.4721i	−0.470668	+	0.815220i	−0.999437	−	0.0335452i	$-0.989320\pi$
$829$	−13.5516	+	23.4721i	−0.470668	+	0.815220i	0.528770	+	0.848765i	$0.322654\pi$
$830$	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	$0.0863619\pi$
$853$			15.6544i			0.535995i	−0.963420	+	0.267997i	$0.913638\pi$
$854$	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	0.848947	−	0.528478i	$-0.177237\pi$
$857$	23.8806	+	13.7875i	0.815746	+	0.470971i	−0.0332013	+	0.999449i	$0.510570\pi$
$858$		0			0
$859$	16.4686	+	28.5245i	0.561902	+	0.973243i	0.997330	+	0.0730199i	$0.0232636\pi$
$859$	16.4686	+	28.5245i	0.561902	+	0.973243i	−0.435428	+	0.900223i	$0.643403\pi$
$860$	−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	−0.941193	−	0.337869i	$-0.890294\pi$
$863$	−32.8782	+	18.9822i	−1.11919	+	0.646162i	−0.177993	+	0.984032i	$0.556960\pi$
$864$		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	−0.151036	−	0.988528i	$-0.548261\pi$
$877$	18.6432	−	10.7637i	0.629536	−	0.363463i	0.780572	+	0.625065i	$0.214928\pi$
$878$	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	$0.206265\pi$
$883$			35.8720i			1.20719i	−0.797292	+	0.603594i	$0.793735\pi$
$884$	−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	−0.936521	−	0.350612i	$-0.885973\pi$
$887$	−32.7948	+	18.9341i	−1.10114	+	0.635744i	−0.164621	+	0.986357i	$0.552640\pi$
$888$		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	0.423094	−	0.906086i	$-0.360944\pi$
$907$	−4.51902	−	2.60906i	−0.150052	−	0.0866324i	−0.573146	+	0.819453i	$0.694277\pi$
$908$	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	0.990665	−	0.136315i	$-0.0435260\pi$
$919$	11.4373	+	19.8099i	0.377280	+	0.653468i	−0.613385	+	0.789784i	$0.710193\pi$
$920$	−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	0.829555	+	0.558425i	$0.188594\pi$
$929$	27.3824	+	47.4277i	0.898388	+	1.55605i	0.0688327	+	0.997628i	$0.478073\pi$
$930$		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	$-0.659416\pi$
$937$		−	53.7023i		−	1.75438i	0.480146	−	0.877188i	$-0.340584\pi$
$938$	−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	0.409416	+	0.912348i	$0.365732\pi$
$941$	−17.9578	+	31.1039i	−0.585408	+	1.01396i	−0.994824	+	0.101609i	$0.967601\pi$
$942$		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	−0.772462	−	0.635061i	$-0.780975\pi$
$947$	−18.7322	+	10.8150i	−0.608715	+	0.351442i	0.163748	+	0.986502i	$0.447642\pi$
$948$		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	$-0.888527\pi$
$953$		−	21.1828i		−	0.686178i	0.939303	−	0.343089i	$-0.111473\pi$
$954$		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	$0.180970\pi$
$967$			33.4846i			1.07679i	−0.842692	+	0.538397i	$0.819030\pi$
$968$	−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	−0.729061	−	0.684449i	$-0.760043\pi$
$971$	−29.8297	−	51.6666i	−0.957281	−	1.65806i	−0.228220	−	0.973610i	$-0.573291\pi$
$972$		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	0.855211	−	0.518280i	$-0.173428\pi$
$977$	26.0675	+	15.0501i	0.833972	+	0.481494i	−0.0212386	+	0.999774i	$0.506761\pi$
$978$		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	−0.158253	−	0.987399i	$-0.550586\pi$
$983$	−34.2527	−	19.7758i	−1.09249	−	0.630750i	−0.934239	+	0.356648i	$0.883919\pi$
$984$		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	0.0641128	+	0.997943i	$0.479578\pi$
$991$	−26.1974	+	45.3752i	−0.832187	+	1.44139i	−0.896300	+	0.443448i	$0.853755\pi$
$992$	−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	−0.0109997	−	0.999940i	$-0.503501\pi$
$997$	−27.8643	−	16.0875i	−0.882473	−	0.509496i	−0.871473	+	0.490444i	$0.836835\pi$
$998$	−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.109.8	yes	16
3.2	odd	2	inner	315.2.bf.c.109.1	✓	16
5.4	even	2	inner	315.2.bf.c.109.2	yes	16
7.2	even	3	inner	315.2.bf.c.289.2	yes	16
7.3	odd	6		2205.2.d.r.1324.8		8
7.4	even	3		2205.2.d.p.1324.7		8
15.14	odd	2	inner	315.2.bf.c.109.7	yes	16
21.2	odd	6	inner	315.2.bf.c.289.7	yes	16
21.11	odd	6		2205.2.d.p.1324.2		8
21.17	even	6		2205.2.d.r.1324.1		8
35.4	even	6		2205.2.d.p.1324.1		8
35.9	even	6	inner	315.2.bf.c.289.8	yes	16
35.24	odd	6		2205.2.d.r.1324.2		8
105.44	odd	6	inner	315.2.bf.c.289.1	yes	16
105.59	even	6		2205.2.d.r.1324.7		8
105.74	odd	6		2205.2.d.p.1324.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bf.c.109.1	✓	16	3.2	odd	2	inner
315.2.bf.c.109.2	yes	16	5.4	even	2	inner
315.2.bf.c.109.7	yes	16	15.14	odd	2	inner
315.2.bf.c.109.8	yes	16	1.1	even	1	trivial
315.2.bf.c.289.1	yes	16	105.44	odd	6	inner
315.2.bf.c.289.2	yes	16	7.2	even	3	inner
315.2.bf.c.289.7	yes	16	21.2	odd	6	inner
315.2.bf.c.289.8	yes	16	35.9	even	6	inner
2205.2.d.p.1324.1		8	35.4	even	6
2205.2.d.p.1324.2		8	21.11	odd	6
2205.2.d.p.1324.7		8	7.4	even	3
2205.2.d.p.1324.8		8	105.74	odd	6
2205.2.d.r.1324.1		8	21.17	even	6
2205.2.d.r.1324.2		8	35.24	odd	6
2205.2.d.r.1324.7		8	105.59	even	6
2205.2.d.r.1324.8		8	7.3	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

Introduction

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