LMFDB - Embedded newform 360.2.w.d.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 5x^{12} + 28x^{8} + 80x^{4} + 256 $ x^16 + 5x^12 + 28x^8 + 80*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.6
Root			$-1.17431 - 0.788026i$ of defining polynomial
Character	$\chi$	$=$	360.163
Dual form			360.2.w.d.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.788026 - 1.17431i) q^{2} +(-0.758030 - 1.85078i) q^{4} +(0.386289 - 2.20245i) q^{5} +(-1.51606 - 1.51606i) q^{7} +(-2.77075 - 0.568298i) q^{8} +O(q^{10})$	\(q+(0.788026 - 1.17431i) q^{2} +(-0.758030 - 1.85078i) q^{4} +(0.386289 - 2.20245i) q^{5} +(-1.51606 - 1.51606i) q^{7} +(-2.77075 - 0.568298i) q^{8} +(-2.28196 - 2.18921i) q^{10} +3.92468 q^{11} +(-3.56393 + 3.56393i) q^{13} +(-2.97503 + 0.585637i) q^{14} +(-2.85078 + 2.80590i) q^{16} +(-1.37670 + 1.37670i) q^{17} -4.00000i q^{19} +(-4.36907 + 0.954587i) q^{20} +(3.09275 - 4.60881i) q^{22} +(5.17748 - 5.17748i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(1.37670 + 6.99364i) q^{26} +(-1.65668 + 3.95511i) q^{28} +5.95005 q^{29} -7.12785i q^{31} +(1.04851 + 5.55883i) q^{32} +(0.531805 + 2.70156i) q^{34} +(-3.92468 + 2.75341i) q^{35} +(3.56393 + 3.56393i) q^{37} +(-4.69726 - 3.15210i) q^{38} +(-2.32196 + 5.88290i) q^{40} +2.75341 q^{41} +(5.40312 + 5.40312i) q^{43} +(-2.97503 - 7.26373i) q^{44} +(-2.00000 - 10.1600i) q^{46} +(1.54515 + 1.54515i) q^{47} -2.40312i q^{49} +(-5.70312 + 4.18024i) q^{50} +(9.29761 + 3.89448i) q^{52} +(1.81616 - 1.81616i) q^{53} +(1.51606 - 8.64391i) q^{55} +(3.33904 + 5.06219i) q^{56} +(4.68880 - 6.98723i) q^{58} +3.92468i q^{59} +13.1921i q^{61} +(-8.37034 - 5.61693i) q^{62} +(7.35408 + 3.14922i) q^{64} +(6.47266 + 9.22607i) q^{65} +(-5.40312 + 5.40312i) q^{67} +(3.59156 + 1.50439i) q^{68} +(0.140616 + 6.77857i) q^{70} +(5.00000 + 5.00000i) q^{73} +(6.99364 - 1.37670i) q^{74} +(-7.40312 + 3.03212i) q^{76} +(-5.95005 - 5.95005i) q^{77} +7.12785 q^{79} +(5.07862 + 7.36259i) q^{80} +(2.16976 - 3.23337i) q^{82} +(-6.67809 - 6.67809i) q^{83} +(2.50031 + 3.56393i) q^{85} +(10.6028 - 2.08717i) q^{86} +(-10.8743 - 2.23039i) q^{88} -18.4521i q^{89} +10.8062 q^{91} +(-13.5071 - 5.65769i) q^{92} +(3.03212 - 0.596876i) q^{94} +(-8.80980 - 1.54515i) q^{95} +(-10.4031 + 10.4031i) q^{97} +(-2.82202 - 1.89372i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 20 * q^16 + 36 * q^22 - 24 * q^25 + 44 * q^28 + 32 * q^40 - 16 * q^43 - 32 * q^46 - 8 * q^52 - 44 * q^58 + 16 * q^67 - 44 * q^70 + 80 * q^73 - 16 * q^76 - 8 * q^82 - 28 * q^88 - 32 * q^91 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.788026	−	1.17431i	0.557219	−	0.830366i
$2$	0.788026	−	1.17431i	0.557219	−	0.830366i
$3$		0			0
$3$		0			0
$4$	−0.758030	−	1.85078i	−0.379015	−	0.925391i
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$6$		0			0
$7$	−1.51606	−	1.51606i	−0.573017	−	0.573017i	0.359953	−	0.932970i	$-0.382793\pi$
$7$	−1.51606	−	1.51606i	−0.573017	−	0.573017i	−0.932970	+	0.359953i	$0.882793\pi$
$8$	−2.77075	−	0.568298i	−0.979607	−	0.200924i
$9$		0			0
$10$	−2.28196	−	2.18921i	−0.721620	−	0.692289i
$11$	3.92468			1.18334			0.591668	−	0.806182i	$-0.298470\pi$
$11$	3.92468			1.18334			0.591668	+	0.806182i	$0.298470\pi$
$12$		0			0
$13$	−3.56393	+	3.56393i	−0.988455	+	0.988455i	−0.999934	−	0.0114791i	$-0.996346\pi$
$13$	−3.56393	+	3.56393i	−0.988455	+	0.988455i	0.0114791	+	0.999934i	$0.496346\pi$
$14$	−2.97503	+	0.585637i	−0.795109	+	0.156518i
$15$		0			0
$16$	−2.85078	+	2.80590i	−0.712695	+	0.701474i
$17$	−1.37670	+	1.37670i	−0.333900	+	0.333900i	−0.854065	−	0.520166i	$-0.825870\pi$
$17$	−1.37670	+	1.37670i	−0.333900	+	0.333900i	0.520166	+	0.854065i	$0.325870\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−4.36907	+	0.954587i	−0.976954	+	0.213452i
$21$		0			0
$22$	3.09275	−	4.60881i	0.659377	−	0.982602i
$23$	5.17748	−	5.17748i	1.07958	−	1.07958i	0.0830312	−	0.996547i	$-0.473540\pi$
$23$	5.17748	−	5.17748i	1.07958	−	1.07958i	0.996547	−	0.0830312i	$-0.0264601\pi$
$24$		0			0
$25$	−4.70156	−	1.70156i	−0.940312	−	0.340312i
$26$	1.37670	+	6.99364i	0.269994	+	1.37156i
$27$		0			0
$28$	−1.65668	+	3.95511i	−0.313082	+	0.747446i
$29$	5.95005			1.10490			0.552449	−	0.833547i	$-0.313694\pi$
$29$	5.95005			1.10490			0.552449	+	0.833547i	$0.313694\pi$
$30$		0			0
$31$		−	7.12785i		−	1.28020i	−0.768292	−	0.640100i	$-0.778893\pi$
$31$		−	7.12785i		−	1.28020i	0.768292	−	0.640100i	$-0.221107\pi$
$32$	1.04851	+	5.55883i	0.185353	+	0.982672i
$33$		0			0
$34$	0.531805	+	2.70156i	0.0912038	+	0.463314i
$35$	−3.92468	+	2.75341i	−0.663392	+	0.465411i
$36$		0			0
$37$	3.56393	+	3.56393i	0.585906	+	0.585906i	0.936520	−	0.350614i	$-0.114027\pi$
$37$	3.56393	+	3.56393i	0.585906	+	0.585906i	−0.350614	+	0.936520i	$0.614027\pi$
$38$	−4.69726	−	3.15210i	−0.761996	−	0.511339i
$39$		0			0
$40$	−2.32196	+	5.88290i	−0.367133	+	0.930168i
$41$	2.75341			0.430010			0.215005	−	0.976613i	$-0.431023\pi$
$41$	2.75341			0.430010			0.215005	+	0.976613i	$0.431023\pi$
$42$		0			0
$43$	5.40312	+	5.40312i	0.823969	+	0.823969i	0.986675	−	0.162706i	$-0.0520222\pi$
$43$	5.40312	+	5.40312i	0.823969	+	0.823969i	−0.162706	+	0.986675i	$0.552022\pi$
$44$	−2.97503	−	7.26373i	−0.448502	−	1.09505i
$45$		0			0
$46$	−2.00000	−	10.1600i	−0.294884	−	1.49801i
$47$	1.54515	+	1.54515i	0.225384	+	0.225384i	0.810761	−	0.585377i	$-0.199054\pi$
$47$	1.54515	+	1.54515i	0.225384	+	0.225384i	−0.585377	+	0.810761i	$0.699054\pi$
$48$		0			0
$49$		−	2.40312i		−	0.343303i
$50$	−5.70312	+	4.18024i	−0.806543	+	0.591175i
$51$		0			0
$52$	9.29761	+	3.89448i	1.28935	+	0.540068i
$53$	1.81616	−	1.81616i	0.249469	−	0.249469i	−0.571284	−	0.820753i	$-0.693554\pi$
$53$	1.81616	−	1.81616i	0.249469	−	0.249469i	0.820753	+	0.571284i	$0.193554\pi$
$54$		0			0
$55$	1.51606	−	8.64391i	0.204425	−	1.16554i
$56$	3.33904	+	5.06219i	0.446199	+	0.676464i
$57$		0			0
$58$	4.68880	−	6.98723i	0.615669	−	0.917469i
$59$			3.92468i			0.510950i	0.966816	+	0.255475i	$0.0822318\pi$
$59$			3.92468i			0.510950i	−0.966816	+	0.255475i	$0.917768\pi$
$60$		0			0
$61$			13.1921i			1.68907i	0.535497	+	0.844537i	$0.320124\pi$
$61$			13.1921i			1.68907i	−0.535497	+	0.844537i	$0.679876\pi$
$62$	−8.37034	−	5.61693i	−1.06303	−	0.713351i
$63$		0			0
$64$	7.35408	+	3.14922i	0.919259	+	0.393652i
$65$	6.47266	+	9.22607i	0.802835	+	1.14435i
$66$		0			0
$67$	−5.40312	+	5.40312i	−0.660097	+	0.660097i	−0.955403	−	0.295306i	$-0.904578\pi$
$67$	−5.40312	+	5.40312i	−0.660097	+	0.660097i	0.295306	+	0.955403i	$0.404578\pi$
$68$	3.59156	+	1.50439i	0.435541	+	0.182435i
$69$		0			0
$70$	0.140616	+	6.77857i	0.0168068	+	0.810194i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	0.936329	−	0.351123i	$-0.114200\pi$
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	6.99364	−	1.37670i	0.812994	−	0.160039i
$75$		0			0
$76$	−7.40312	+	3.03212i	−0.849197	+	0.347808i
$77$	−5.95005	−	5.95005i	−0.678071	−	0.678071i
$78$		0			0
$79$	7.12785			0.801946			0.400973	−	0.916090i	$-0.368672\pi$
$79$	7.12785			0.801946			0.400973	+	0.916090i	$0.368672\pi$
$80$	5.07862	+	7.36259i	0.567807	+	0.823162i
$81$		0			0
$82$	2.16976	−	3.23337i	0.239610	−	0.357066i
$83$	−6.67809	−	6.67809i	−0.733016	−	0.733016i	0.238200	−	0.971216i	$-0.423442\pi$
$83$	−6.67809	−	6.67809i	−0.733016	−	0.733016i	−0.971216	+	0.238200i	$0.923442\pi$
$84$		0			0
$85$	2.50031	+	3.56393i	0.271197	+	0.386562i
$86$	10.6028	−	2.08717i	1.14333	−	0.225065i
$87$		0			0
$88$	−10.8743	−	2.23039i	−1.15920	−	0.237760i
$89$		−	18.4521i		−	1.95592i	−0.208787	−	0.977961i	$-0.566952\pi$
$89$		−	18.4521i		−	1.95592i	0.208787	−	0.977961i	$-0.433048\pi$
$90$		0			0
$91$	10.8062			1.13280
$92$	−13.5071	−	5.65769i	−1.40821	−	0.589855i
$93$		0			0
$94$	3.03212	−	0.596876i	0.312739	−	0.0615630i
$95$	−8.80980	−	1.54515i	−0.903866	−	0.158530i
$96$		0			0
$97$	−10.4031	+	10.4031i	−1.05628	+	1.05628i	−0.0579582	+	0.998319i	$0.518459\pi$
$97$	−10.4031	+	10.4031i	−1.05628	+	1.05628i	−0.998319	+	0.0579582i	$0.981541\pi$
$98$	−2.82202	−	1.89372i	−0.285067	−	0.191295i
$99$		0			0
$100$	0.414706	+	9.99140i	0.0414706	+	0.999140i
$101$			8.03722i			0.799733i	0.916573	+	0.399867i	$0.130944\pi$
$101$			8.03722i			0.799733i	−0.916573	+	0.399867i	$0.869056\pi$
$102$		0			0
$103$	5.61179	−	5.61179i	0.552946	−	0.552946i	−0.374344	−	0.927290i	$-0.622132\pi$
$103$	5.61179	−	5.61179i	0.552946	−	0.552946i	0.927290	+	0.374344i	$0.122132\pi$
$104$	11.9001	−	7.84936i	1.16690	−	0.769693i
$105$		0			0
$106$	−0.701562	−	3.56393i	−0.0681417	−	0.346159i
$107$	3.92468	−	3.92468i	0.379413	−	0.379413i	−0.491477	−	0.870890i	$-0.663543\pi$
$107$	3.92468	−	3.92468i	0.379413	−	0.379413i	0.870890	+	0.491477i	$0.163543\pi$
$108$		0			0
$109$	6.06424			0.580849			0.290424	−	0.956898i	$-0.406204\pi$
$109$	6.06424			0.580849			0.290424	+	0.956898i	$0.406204\pi$
$110$	−8.95598	−	8.59196i	−0.853919	−	0.819211i
$111$		0			0
$112$	8.57586	+	0.0680498i	0.810343	+	0.00643010i
$113$	−1.37670	−	1.37670i	−0.129509	−	0.129509i	0.639381	−	0.768890i	$-0.279191\pi$
$113$	−1.37670	−	1.37670i	−0.129509	−	0.129509i	−0.768890	+	0.639381i	$0.779191\pi$
$114$		0			0
$115$	−9.40312	−	13.4031i	−0.876846	−	1.24985i
$116$	−4.51032	−	11.0122i	−0.418773	−	1.02246i
$117$		0			0
$118$	4.60881	+	3.09275i	0.424275	+	0.284711i
$119$	4.17433			0.382660
$120$		0			0
$121$	4.40312			0.400284
$122$	15.4917	+	10.3957i	1.40255	+	0.941183i
$123$		0			0
$124$	−13.1921	+	5.40312i	−1.18468	+	0.485215i
$125$	−5.56376	+	9.69766i	−0.497638	+	0.867385i
$126$		0			0
$127$	−11.6760	−	11.6760i	−1.03608	−	1.03608i	−0.999324	−	0.0367559i	$-0.988298\pi$
$127$	−11.6760	−	11.6760i	−1.03608	−	1.03608i	−0.0367559	−	0.999324i	$-0.511702\pi$
$128$	9.49338	−	6.15433i	0.839104	−	0.543971i
$129$		0			0
$130$	15.9349	−	0.330558i	1.39759	−	0.0289918i
$131$	17.2809			1.50984			0.754918	−	0.655819i	$-0.227677\pi$
$131$	17.2809			1.50984			0.754918	+	0.655819i	$0.227677\pi$
$132$		0			0
$133$	−6.06424	+	6.06424i	−0.525836	+	0.525836i
$134$	2.08717	+	10.6028i	0.180304	+	0.915940i
$135$		0			0
$136$	4.59688	−	3.03212i	0.394179	−	0.260002i
$137$	−14.3220	+	14.3220i	−1.22361	+	1.22361i	−0.257275	+	0.966338i	$0.582824\pi$
$137$	−14.3220	+	14.3220i	−1.22361	+	1.22361i	−0.966338	+	0.257275i	$0.917176\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	8.07098	+	5.17656i	0.682122	+	0.437499i
$141$		0			0
$142$		0			0
$143$	−13.9873	+	13.9873i	−1.16967	+	1.16967i
$144$		0			0
$145$	2.29844	−	13.1047i	0.190875	−	1.08828i
$146$	9.81170	−	1.93144i	0.812022	−	0.159847i
$147$		0			0
$148$	3.89448	−	9.29761i	0.320125	−	0.764259i
$149$	−8.03722			−0.658435			−0.329217	−	0.944254i	$-0.606785\pi$
$149$	−8.03722			−0.658435			−0.329217	+	0.944254i	$0.606785\pi$
$150$		0			0
$151$			10.1600i			0.826807i	0.910548	+	0.413403i	$0.135660\pi$
$151$			10.1600i			0.826807i	−0.910548	+	0.413403i	$0.864340\pi$
$152$	−2.27319	+	11.0830i	−0.184380	+	0.898949i
$153$		0			0
$154$	−11.6760	+	2.29844i	−0.940881	+	0.185213i
$155$	−15.6987	−	2.75341i	−1.26095	−	0.221159i
$156$		0			0
$157$	−9.62817	−	9.62817i	−0.768411	−	0.768411i	0.209416	−	0.977827i	$-0.432844\pi$
$157$	−9.62817	−	9.62817i	−0.768411	−	0.768411i	−0.977827	+	0.209416i	$0.932844\pi$
$158$	5.61693	−	8.37034i	0.446859	−	0.665908i
$159$		0			0
$160$	12.6481	−	0.161985i	0.999918	−	0.0128060i
$161$	−15.6987			−1.23723
$162$		0			0
$163$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$163$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$164$	−2.08717	−	5.09596i	−0.162980	−	0.397927i
$165$		0			0
$166$	−13.1047	+	2.57967i	−1.01712	+	0.200221i
$167$	−1.54515	−	1.54515i	−0.119568	−	0.119568i	0.644791	−	0.764359i	$-0.276944\pi$
$167$	−1.54515	−	1.54515i	−0.119568	−	0.119568i	−0.764359	+	0.644791i	$0.776944\pi$
$168$		0			0
$169$		−	12.4031i		−	0.954086i
$170$	6.15548	−	0.127691i	0.472104	−	0.00979343i
$171$		0			0
$172$	5.90427	−	14.0957i	0.450196	−	1.07479i
$173$	−4.13389	+	4.13389i	−0.314294	+	0.314294i	−0.846571	−	0.532277i	$-0.821337\pi$
$173$	−4.13389	+	4.13389i	−0.314294	+	0.314294i	0.532277	+	0.846571i	$0.321337\pi$
$174$		0			0
$175$	4.54818	+	9.70752i	0.343810	+	0.733820i
$176$	−11.1884	+	11.0122i	−0.843358	+	0.830079i
$177$		0			0
$178$	−21.6686	−	14.5408i	−1.62413	−	1.08988i
$179$			14.1166i			1.05512i	0.849517	+	0.527562i	$0.176894\pi$
$179$			14.1166i			1.05512i	−0.849517	+	0.527562i	$0.823106\pi$
$180$		0			0
$181$		−	6.06424i		−	0.450751i	−0.974272	−	0.225376i	$-0.927639\pi$
$181$		−	6.06424i		−	0.450751i	0.974272	−	0.225376i	$-0.0723610\pi$
$182$	8.51560	−	12.6899i	0.631219	−	0.940641i
$183$		0			0
$184$	−17.2878	+	11.4031i	−1.27448	+	0.840649i
$185$	9.22607	−	6.47266i	0.678314	−	0.475879i
$186$		0			0
$187$	−5.40312	+	5.40312i	−0.395116	+	0.395116i
$188$	1.68847	−	4.03102i	0.123144	−	0.293992i
$189$		0			0
$190$	−8.75685	+	9.12785i	−0.635288	+	0.662204i
$191$			23.8002i			1.72212i	0.508501	+	0.861061i	$0.330200\pi$
$191$			23.8002i			1.72212i	−0.508501	+	0.861061i	$0.669800\pi$
$192$		0			0
$193$	0.403124	+	0.403124i	0.0290175	+	0.0290175i	0.721467	−	0.692449i	$-0.243468\pi$
$193$	0.403124	+	0.403124i	0.0290175	+	0.0290175i	−0.692449	+	0.721467i	$0.743468\pi$
$194$	4.01861	+	20.4145i	0.288519	+	1.46567i
$195$		0			0
$196$	−4.44766	+	1.82164i	−0.317690	+	0.130117i
$197$	5.44848	+	5.44848i	0.388188	+	0.388188i	0.874041	−	0.485853i	$-0.161491\pi$
$197$	5.44848	+	5.44848i	0.388188	+	0.388188i	−0.485853	+	0.874041i	$0.661491\pi$
$198$		0			0
$199$	−18.3514			−1.30090			−0.650449	−	0.759550i	$-0.725419\pi$
$199$	−18.3514			−1.30090			−0.650449	+	0.759550i	$0.725419\pi$
$200$	12.0598	+	7.38649i	0.852760	+	0.522303i
$201$		0			0
$202$	9.43822	+	6.33354i	0.664071	+	0.445626i
$203$	−9.02064	−	9.02064i	−0.633125	−	0.633125i
$204$		0			0
$205$	1.06361	−	6.06424i	0.0742858	−	0.423545i
$206$	−2.16777	−	11.0122i	−0.151036	−	0.767259i
$207$		0			0
$208$	0.159970	−	20.1600i	0.0110919	−	1.39784i
$209$		−	15.6987i		−	1.08590i
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−4.73802	−	1.98461i	−0.325408	−	0.136304i
$213$		0			0
$214$	−1.51606	−	7.70156i	−0.103636	−	0.526468i
$215$	13.9873	−	9.81294i	0.953924	−	0.669237i
$216$		0			0
$217$	−10.8062	+	10.8062i	−0.733576	+	0.733576i
$218$	4.77878	−	7.12133i	0.323660	−	0.482317i
$219$		0			0
$220$	−17.1472	+	3.74645i	−1.15606	+	0.252585i
$221$		−	9.81294i		−	0.660090i
$222$		0			0
$223$	−11.6760	+	11.6760i	−0.781885	+	0.781885i	−0.980149	−	0.198264i	$-0.936470\pi$
$223$	−11.6760	+	11.6760i	−0.781885	+	0.781885i	0.198264	+	0.980149i	$0.436470\pi$
$224$	6.83791	−	10.0171i	0.456877	−	0.669298i
$225$		0			0
$226$	−2.70156	+	0.531805i	−0.179705	+	0.0353752i
$227$	12.9453	−	12.9453i	0.859211	−	0.859211i	−0.132034	−	0.991245i	$-0.542151\pi$
$227$	12.9453	−	12.9453i	0.859211	−	0.859211i	0.991245	+	0.132034i	$0.0421509\pi$
$228$		0			0
$229$	−13.1921			−0.871758			−0.435879	−	0.900005i	$-0.643562\pi$
$229$	−13.1921			−0.871758			−0.435879	+	0.900005i	$0.643562\pi$
$230$	−23.1494	+	0.480216i	−1.52643	+	0.0316645i
$231$		0			0
$232$	−16.4861	−	3.38140i	−1.08236	−	0.222000i
$233$	14.3220	+	14.3220i	0.938267	+	0.938267i	0.998202	−	0.0599354i	$-0.0190895\pi$
$233$	14.3220	+	14.3220i	0.938267	+	0.938267i	−0.0599354	+	0.998202i	$0.519089\pi$
$234$		0			0
$235$	4.00000	−	2.80625i	0.260931	−	0.183059i
$236$	7.26373	−	2.97503i	0.472828	−	0.193658i
$237$		0			0
$238$	3.28948	−	4.90198i	0.213225	−	0.317748i
$239$	−27.9745			−1.80952			−0.904761	−	0.425919i	$-0.859951\pi$
$239$	−27.9745			−1.80952			−0.904761	+	0.425919i	$0.859951\pi$
$240$		0			0
$241$	18.8062			1.21142			0.605708	−	0.795687i	$-0.292890\pi$
$241$	18.8062			1.21142			0.605708	+	0.795687i	$0.292890\pi$
$242$	3.46978	−	5.17065i	0.223046	−	0.332382i
$243$		0			0
$244$	24.4157	−	10.0000i	1.56305	−	0.640184i
$245$	−5.29276	−	0.928300i	−0.338142	−	0.0593069i
$246$		0			0
$247$	14.2557	+	14.2557i	0.907068	+	0.907068i
$248$	−4.05074	+	19.7495i	−0.257222	+	1.25409i
$249$		0			0
$250$	7.00371	+	14.1756i	0.442953	+	0.896545i
$251$	−1.58213			−0.0998634			−0.0499317	−	0.998753i	$-0.515900\pi$
$251$	−1.58213			−0.0998634			−0.0499317	+	0.998753i	$0.515900\pi$
$252$		0			0
$253$	20.3199	−	20.3199i	1.27750	−	1.27750i
$254$	−22.9123	+	4.51032i	−1.43765	+	0.283003i
$255$		0			0
$256$	0.253905	−	15.9980i	0.0158691	−	0.999874i
$257$	4.13011	−	4.13011i	0.257629	−	0.257629i	−0.566460	−	0.824089i	$-0.691687\pi$
$257$	4.13011	−	4.13011i	0.257629	−	0.257629i	0.824089	+	0.566460i	$0.191687\pi$
$258$		0			0
$259$		−	10.8062i		−	0.671468i
$260$	12.1690	−	18.9731i	0.754687	−	1.17666i
$261$		0			0
$262$	13.6178	−	20.2932i	0.841308	−	1.25372i
$263$	19.1647	−	19.1647i	1.18175	−	1.18175i	0.202458	−	0.979291i	$-0.435107\pi$
$263$	19.1647	−	19.1647i	1.18175	−	1.18175i	0.979291	−	0.202458i	$-0.0648929\pi$
$264$		0			0
$265$	−3.29844	−	4.70156i	−0.202621	−	0.288815i
$266$	2.34255	+	11.9001i	0.143631	+	0.729642i
$267$		0			0
$268$	14.0957	+	5.90427i	0.861034	+	0.360661i
$269$	3.86289			0.235524			0.117762	−	0.993042i	$-0.462428\pi$
$269$	3.86289			0.235524			0.117762	+	0.993042i	$0.462428\pi$
$270$		0			0
$271$			16.2242i			0.985551i	0.870157	+	0.492775i	$0.164018\pi$
$271$			16.2242i			0.985551i	−0.870157	+	0.492775i	$0.835982\pi$
$272$	0.0617947	−	7.78757i	0.00374685	−	0.472191i
$273$		0			0
$274$	5.53243	+	28.1047i	0.334227	+	1.69787i
$275$	−18.4521	−	6.67809i	−1.11271	−	0.402704i
$276$		0			0
$277$	−10.6918	−	10.6918i	−0.642407	−	0.642407i	0.308740	−	0.951146i	$-0.400093\pi$
$277$	−10.6918	−	10.6918i	−0.642407	−	0.642407i	−0.951146	+	0.308740i	$0.900093\pi$
$278$	4.69726	+	3.15210i	0.281723	+	0.189051i
$279$		0			0
$280$	12.4391	−	5.39861i	0.743376	−	0.322629i
$281$	−8.26022			−0.492764			−0.246382	−	0.969173i	$-0.579242\pi$
$281$	−8.26022			−0.492764			−0.246382	+	0.969173i	$0.579242\pi$
$282$		0			0
$283$	−5.40312	−	5.40312i	−0.321182	−	0.321182i	0.528038	−	0.849221i	$-0.322928\pi$
$283$	−5.40312	−	5.40312i	−0.321182	−	0.321182i	−0.849221	+	0.528038i	$0.822928\pi$
$284$		0			0
$285$		0			0
$286$	5.40312	+	27.4478i	0.319493	+	1.62302i
$287$	−4.17433	−	4.17433i	−0.246403	−	0.246403i
$288$		0			0
$289$			13.2094i			0.777022i
$290$	−13.5778	−	13.0259i	−0.797316	−	0.764909i
$291$		0			0
$292$	5.46376	−	13.0441i	0.319742	−	0.763346i
$293$	−1.81616	+	1.81616i	−0.106101	+	0.106101i	−0.758165	−	0.652063i	$-0.773904\pi$
$293$	−1.81616	+	1.81616i	−0.106101	+	0.106101i	0.652063	+	0.758165i	$0.273904\pi$
$294$		0			0
$295$	8.64391	+	1.51606i	0.503268	+	0.0882684i
$296$	−7.84936	−	11.9001i	−0.456235	−	0.691680i
$297$		0			0
$298$	−6.33354	+	9.43822i	−0.366892	+	0.546742i
$299$			36.9043i			2.13423i
$300$		0			0
$301$		−	16.3829i		−	0.944296i
$302$	11.9310	+	8.00632i	0.686552	+	0.460712i
$303$		0			0
$304$	11.2236	+	11.4031i	0.643716	+	0.654014i
$305$	29.0549	+	5.09596i	1.66368	+	0.291794i
$306$		0			0
$307$	−20.0000	+	20.0000i	−1.14146	+	1.14146i	−0.153277	+	0.988183i	$0.548983\pi$
$307$	−20.0000	+	20.0000i	−1.14146	+	1.14146i	−0.988183	+	0.153277i	$0.951017\pi$
$308$	−6.50193	+	15.5226i	−0.370482	+	0.884480i
$309$		0			0
$310$	−15.6044	+	16.2655i	−0.886269	+	0.923818i
$311$		−	27.9745i		−	1.58629i	−0.609032	−	0.793145i	$-0.708442\pi$
$311$		−	27.9745i		−	1.58629i	0.609032	−	0.793145i	$-0.291558\pi$
$312$		0			0
$313$	5.80625	+	5.80625i	0.328189	+	0.328189i	0.851897	−	0.523709i	$-0.175452\pi$
$313$	5.80625	+	5.80625i	0.328189	+	0.328189i	−0.523709	+	0.851897i	$0.675452\pi$
$314$	−18.8937	+	3.71925i	−1.06624	+	0.209889i
$315$		0			0
$316$	−5.40312	−	13.1921i	−0.303949	−	0.742113i
$317$	11.3985	+	11.3985i	0.640205	+	0.640205i	0.950606	−	0.310400i	$-0.100463\pi$
$317$	11.3985	+	11.3985i	0.640205	+	0.640205i	−0.310400	+	0.950606i	$0.600463\pi$
$318$		0			0
$319$	23.3521			1.30746
$320$	9.77679	−	14.9805i	0.546539	−	0.837434i
$321$		0			0
$322$	−12.3710	+	18.4352i	−0.689409	+	1.02736i
$323$	5.50682	+	5.50682i	0.306407	+	0.306407i
$324$		0			0
$325$	22.8203	−	10.6918i	1.26584	−	0.593073i
$326$		0			0
$327$		0			0
$328$	−7.62900	−	1.56476i	−0.421241	−	0.0863992i
$329$		−	4.68509i		−	0.258298i
$330$		0			0
$331$	−22.8062			−1.25354			−0.626772	−	0.779202i	$-0.715624\pi$
$331$	−22.8062			−1.25354			−0.626772	+	0.779202i	$0.715624\pi$
$332$	−7.29749	+	17.4219i	−0.400502	+	0.956149i
$333$		0			0
$334$	−3.03212	+	0.596876i	−0.165910	+	0.0326596i
$335$	9.81294	+	13.9873i	0.536138	+	0.764206i
$336$		0			0
$337$	10.4031	−	10.4031i	0.566694	−	0.566694i	−0.364507	−	0.931201i	$-0.618762\pi$
$337$	10.4031	−	10.4031i	0.566694	−	0.566694i	0.931201	+	0.364507i	$0.118762\pi$
$338$	−14.5652	−	9.77398i	−0.792241	−	0.531635i
$339$		0			0
$340$	4.70073	−	7.32910i	0.254933	−	0.397476i
$341$		−	27.9745i		−	1.51491i
$342$		0			0
$343$	−14.2557	+	14.2557i	−0.769735	+	0.769735i
$344$	−11.9001	−	18.0413i	−0.641611	−	0.972720i
$345$		0			0
$346$	1.59688	+	8.11211i	0.0858486	+	0.436109i
$347$	18.4521	−	18.4521i	0.990562	−	0.990562i	−0.00939345	−	0.999956i	$-0.502990\pi$
$347$	18.4521	−	18.4521i	0.990562	−	0.990562i	0.999956	+	0.00939345i	$0.00299007\pi$
$348$		0			0
$349$	13.1921			0.706156			0.353078	−	0.935594i	$-0.385135\pi$
$349$	13.1921			0.706156			0.353078	+	0.935594i	$0.385135\pi$
$350$	14.9838	+	2.30878i	0.800916	+	0.123410i
$351$		0			0
$352$	4.11508	+	21.8166i	0.219335	+	1.16283i
$353$	4.13011	+	4.13011i	0.219824	+	0.219824i	0.808424	−	0.588600i	$-0.200321\pi$
$353$	4.13011	+	4.13011i	0.219824	+	0.219824i	−0.588600	+	0.808424i	$0.700321\pi$
$354$		0			0
$355$		0			0
$356$	−34.1509	+	13.9873i	−1.80999	+	0.741324i
$357$		0			0
$358$	16.5773	+	11.1242i	0.876139	+	0.587934i
$359$	32.1489			1.69675			0.848376	−	0.529394i	$-0.177581\pi$
$359$	32.1489			1.69675			0.848376	+	0.529394i	$0.177581\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−7.12133	−	4.77878i	−0.374289	−	0.251167i
$363$		0			0
$364$	−8.19146	−	20.0000i	−0.429349	−	1.04828i
$365$	12.9437	−	9.08080i	0.677504	−	0.475311i
$366$		0			0
$367$	7.58030	+	7.58030i	0.395688	+	0.395688i	0.876709	−	0.481021i	$-0.159734\pi$
$367$	7.58030	+	7.58030i	0.395688	+	0.395688i	−0.481021	+	0.876709i	$0.659734\pi$
$368$	−0.232396	+	29.2873i	−0.0121145	+	1.52671i
$369$		0			0
$370$	−0.330558	−	15.9349i	−0.0171849	−	0.828418i
$371$	−5.50682			−0.285900
$372$		0			0
$373$	−2.50031	+	2.50031i	−0.129461	+	0.129461i	−0.768868	−	0.639407i	$-0.779180\pi$
$373$	−2.50031	+	2.50031i	−0.129461	+	0.129461i	0.639407	+	0.768868i	$0.279180\pi$
$374$	2.08717	+	10.6028i	0.107925	+	0.548256i
$375$		0			0
$376$	−3.40312	−	5.15934i	−0.175503	−	0.266073i
$377$	−21.2055	+	21.2055i	−1.09214	+	1.09214i
$378$		0			0
$379$		−	6.80625i		−	0.349614i	−0.984603	−	0.174807i	$-0.944070\pi$
$379$		−	6.80625i		−	0.349614i	0.984603	−	0.174807i	$-0.0559301\pi$
$380$	3.81835	+	17.4763i	0.195877	+	0.896514i
$381$		0			0
$382$	27.9489	+	18.7552i	1.42999	+	0.959599i
$383$	−9.35181	+	9.35181i	−0.477855	+	0.477855i	−0.904445	−	0.426590i	$-0.859715\pi$
$383$	−9.35181	+	9.35181i	−0.477855	+	0.477855i	0.426590	+	0.904445i	$0.359715\pi$
$384$		0			0
$385$	−15.4031	+	10.8062i	−0.785016	+	0.550737i
$386$	0.791067	−	0.155722i	0.0402643	−	0.00792606i
$387$		0			0
$388$	27.1398	+	11.3680i	1.37781	+	0.577124i
$389$	27.6631			1.40257			0.701287	−	0.712879i	$-0.252609\pi$
$389$	27.6631			1.40257			0.701287	+	0.712879i	$0.252609\pi$
$390$		0			0
$391$			14.2557i			0.720942i
$392$	−1.36569	+	6.65845i	−0.0689778	+	0.336302i
$393$		0			0
$394$	10.6918	−	2.10469i	0.538644	−	0.106033i
$395$	2.75341	−	15.6987i	0.138539	−	0.789889i
$396$		0			0
$397$	4.62754	+	4.62754i	0.232249	+	0.232249i	0.813631	−	0.581382i	$-0.197488\pi$
$397$	4.62754	+	4.62754i	0.232249	+	0.232249i	−0.581382	+	0.813631i	$0.697488\pi$
$398$	−14.4614	+	21.5504i	−0.724885	+	1.08022i
$399$		0			0
$400$	18.1775	−	8.34131i	0.908876	−	0.417065i
$401$	−31.3975			−1.56791			−0.783957	−	0.620815i	$-0.786802\pi$
$401$	−31.3975			−1.56791			−0.783957	+	0.620815i	$0.786802\pi$
$402$		0			0
$403$	25.4031	+	25.4031i	1.26542	+	1.26542i
$404$	14.8751	−	6.09245i	0.740065	−	0.303111i
$405$		0			0
$406$	−17.7016	+	3.48457i	−0.878514	+	0.172936i
$407$	13.9873	+	13.9873i	0.693323	+	0.693323i
$408$		0			0
$409$			9.40312i			0.464955i	0.972602	+	0.232477i	$0.0746831\pi$
$409$			9.40312i			0.464955i	−0.972602	+	0.232477i	$0.925317\pi$
$410$	−6.28317	−	6.02779i	−0.310304	−	0.297691i
$411$		0			0
$412$	−14.6401	−	6.13229i	−0.721266	−	0.302116i
$413$	5.95005	−	5.95005i	0.292783	−	0.292783i
$414$		0			0
$415$	−17.2878	+	12.1285i	−0.848626	+	0.595364i
$416$	−23.5481	−	16.0744i	−1.15454	−	0.788114i
$417$		0			0
$418$	−18.4352	−	12.3710i	−0.901697	−	0.605086i
$419$			22.7877i			1.11325i	0.830764	+	0.556625i	$0.187904\pi$
$419$			22.7877i			1.11325i	−0.830764	+	0.556625i	$0.812096\pi$
$420$		0			0
$421$		−	25.3206i		−	1.23405i	−0.786944	−	0.617025i	$-0.788338\pi$
$421$		−	25.3206i		−	1.23405i	0.786944	−	0.617025i	$-0.211662\pi$
$422$	9.45631	−	14.0918i	0.460326	−	0.685977i
$423$		0			0
$424$	−6.06424	+	4.00000i	−0.294506	+	0.194257i
$425$	8.81521	−	4.13011i	0.427600	−	0.200340i
$426$		0			0
$427$	20.0000	−	20.0000i	0.967868	−	0.967868i
$428$	−10.2388	−	4.28870i	−0.494909	−	0.207302i
$429$		0			0
$430$	−0.501146	−	24.1583i	−0.0241674	−	1.16502i
$431$		−	4.17433i		−	0.201070i	−0.994933	−	0.100535i	$-0.967944\pi$
$431$		−	4.17433i		−	0.201070i	0.994933	−	0.100535i	$-0.0320555\pi$
$432$		0			0
$433$	−0.403124	−	0.403124i	−0.0193729	−	0.0193729i	0.697354	−	0.716727i	$-0.254361\pi$
$433$	−0.403124	−	0.403124i	−0.0193729	−	0.0193729i	−0.716727	+	0.697354i	$0.754361\pi$
$434$	4.17433	+	21.2055i	0.200374	+	1.01790i
$435$		0			0
$436$	−4.59688	−	11.2236i	−0.220150	−	0.537512i
$437$	−20.7099	−	20.7099i	−0.990689	−	0.990689i
$438$		0			0
$439$	4.09573			0.195479			0.0977393	−	0.995212i	$-0.468839\pi$
$439$	4.09573			0.195479			0.0977393	+	0.995212i	$0.468839\pi$
$440$	−9.11293	+	23.0885i	−0.434442	+	1.10070i
$441$		0			0
$442$	−11.5235	−	7.73285i	−0.548116	−	0.367814i
$443$	12.9453	+	12.9453i	0.615051	+	0.615051i	0.944258	−	0.329207i	$-0.106781\pi$
$443$	12.9453	+	12.9453i	0.615051	+	0.615051i	−0.329207	+	0.944258i	$0.606781\pi$
$444$		0			0
$445$	−40.6399	−	7.12785i	−1.92652	−	0.337893i
$446$	4.51032	+	22.9123i	0.213570	+	1.08493i
$447$		0			0
$448$	−6.37481	−	15.9236i	−0.301182	−	0.752321i
$449$		−	15.6987i		−	0.740869i	−0.928859	−	0.370434i	$-0.879209\pi$
$449$		−	15.6987i		−	0.740869i	0.928859	−	0.370434i	$-0.120791\pi$
$450$		0			0
$451$	10.8062			0.508846
$452$	−1.50439	+	3.59156i	−0.0707608	+	0.168933i
$453$		0			0
$454$	−5.00063	−	25.4031i	−0.234691	−	1.19223i
$455$	4.17433	−	23.8002i	0.195696	−	1.11577i
$456$		0			0
$457$	15.8062	−	15.8062i	0.739385	−	0.739385i	−0.233074	−	0.972459i	$-0.574878\pi$
$457$	15.8062	−	15.8062i	0.739385	−	0.739385i	0.972459	+	0.233074i	$0.0748784\pi$
$458$	−10.3957	+	15.4917i	−0.485760	+	0.723878i
$459$		0			0
$460$	−17.6784	+	27.5631i	−0.824260	+	1.28514i
$461$			3.86289i			0.179913i	0.995946	+	0.0899563i	$0.0286727\pi$
$461$			3.86289i			0.179913i	−0.995946	+	0.0899563i	$0.971327\pi$
$462$		0			0
$463$	7.58030	−	7.58030i	0.352286	−	0.352286i	−0.508673	−	0.860960i	$-0.669864\pi$
$463$	7.58030	−	7.58030i	0.352286	−	0.352286i	0.860960	+	0.508673i	$0.169864\pi$
$464$	−16.9623	+	16.6952i	−0.787455	+	0.775056i
$465$		0			0
$466$	28.1047	−	5.53243i	1.30192	−	0.256285i
$467$	−1.17127	+	1.17127i	−0.0542001	+	0.0542001i	−0.733687	−	0.679487i	$-0.762202\pi$
$467$	−1.17127	+	1.17127i	−0.0542001	+	0.0542001i	0.679487	+	0.733687i	$0.262202\pi$
$468$		0			0
$469$	16.3829			0.756493
$470$	−0.143315	−	6.90866i	−0.00661062	−	0.318673i
$471$		0			0
$472$	2.23039	−	10.8743i	0.102662	−	0.500530i
$473$	21.2055	+	21.2055i	0.975032	+	0.975032i
$474$		0			0
$475$	−6.80625	+	18.8062i	−0.312292	+	0.862890i
$476$	−3.16427	−	7.72577i	−0.145034	−	0.354110i
$477$		0			0
$478$	−22.0447	+	32.8509i	−1.00830	+	1.50257i
$479$	−27.9745			−1.27819			−0.639095	−	0.769128i	$-0.720691\pi$
$479$	−27.9745			−1.27819			−0.639095	+	0.769128i	$0.720691\pi$
$480$		0			0
$481$	−25.4031			−1.15828
$482$	14.8198	−	22.0845i	0.675024	−	1.00592i
$483$		0			0
$484$	−3.33770	−	8.14922i	−0.151714	−	0.370419i
$485$	18.8937	+	26.9310i	0.857921	+	1.22287i
$486$		0			0
$487$	−8.64391	−	8.64391i	−0.391693	−	0.391693i	0.483598	−	0.875290i	$-0.339330\pi$
$487$	−8.64391	−	8.64391i	−0.391693	−	0.391693i	−0.875290	+	0.483598i	$0.839330\pi$
$488$	7.49704	−	36.5519i	0.339375	−	1.65463i
$489$		0			0
$490$	−5.26095	+	5.48384i	−0.237665	+	0.247735i
$491$	27.4728			1.23983			0.619914	−	0.784669i	$-0.287167\pi$
$491$	27.4728			1.23983			0.619914	+	0.784669i	$0.287167\pi$
$492$		0			0
$493$	−8.19146	+	8.19146i	−0.368925	+	0.368925i
$494$	27.9745	−	5.50682i	1.25863	−	0.247763i
$495$		0			0
$496$	20.0000	+	20.3199i	0.898027	+	0.912392i
$497$		0			0
$498$		0			0
$499$			6.80625i			0.304690i	0.988327	+	0.152345i	$0.0486824\pi$
$499$			6.80625i			0.304690i	−0.988327	+	0.152345i	$0.951318\pi$
$500$	22.1657	+	2.94619i	0.991282	+	0.131758i
$501$		0			0
$502$	−1.24676	+	1.85792i	−0.0556458	+	0.0829232i
$503$	8.80980	−	8.80980i	0.392809	−	0.392809i	−0.482878	−	0.875688i	$-0.660409\pi$
$503$	8.80980	−	8.80980i	0.392809	−	0.392809i	0.875688	+	0.482878i	$0.160409\pi$
$504$		0			0
$505$	17.7016	+	3.10469i	0.787709	+	0.138157i
$506$	−7.84936	−	39.8746i	−0.348947	−	1.77264i
$507$		0			0
$508$	−12.7590	+	30.4606i	−0.566089	+	1.35147i
$509$	−22.0245			−0.976218			−0.488109	−	0.872783i	$-0.662313\pi$
$509$	−22.0245			−0.976218			−0.488109	+	0.872783i	$0.662313\pi$
$510$		0			0
$511$		−	15.1606i		−	0.670665i
$512$	−18.5866	−	12.9050i	−0.821419	−	0.570326i
$513$		0			0
$514$	−1.59542	−	8.10469i	−0.0703708	−	0.357482i
$515$	−10.1919	−	14.5275i	−0.449109	−	0.640156i
$516$		0			0
$517$	6.06424	+	6.06424i	0.266705	+	0.266705i
$518$	−12.6899	−	8.51560i	−0.557564	−	0.374154i
$519$		0			0
$520$	−12.6909	−	29.2415i	−0.556535	−	1.28232i
$521$	−15.6987			−0.687774			−0.343887	−	0.939011i	$-0.611744\pi$
$521$	−15.6987			−0.687774			−0.343887	+	0.939011i	$0.611744\pi$
$522$		0			0
$523$	−30.8062	−	30.8062i	−1.34706	−	1.34706i	−0.888834	−	0.458229i	$-0.848484\pi$
$523$	−30.8062	−	30.8062i	−1.34706	−	1.34706i	−0.458229	−	0.888834i	$-0.651516\pi$
$524$	−13.0994	−	31.9831i	−0.572250	−	1.39719i
$525$		0			0
$526$	−7.40312	−	37.6078i	−0.322792	−	1.63978i
$527$	9.81294	+	9.81294i	0.427458	+	0.427458i
$528$		0			0
$529$		−	30.6125i		−	1.33098i
$530$	−8.12037	+	0.168451i	−0.352726	+	0.00731703i
$531$		0			0
$532$	15.8205	+	6.62670i	0.685904	+	0.287304i
$533$	−9.81294	+	9.81294i	−0.425046	+	0.425046i
$534$		0			0
$535$	−7.12785	−	10.1600i	−0.308164	−	0.439254i
$536$	18.0413	−	11.9001i	0.779264	−	0.514006i
$537$		0			0
$538$	3.04406	−	4.53624i	0.131239	−	0.195571i
$539$		−	9.43150i		−	0.406243i
$540$		0			0
$541$			34.5756i			1.48652i	0.669001	+	0.743261i	$0.266722\pi$
$541$			34.5756i			1.48652i	−0.669001	+	0.743261i	$0.733278\pi$
$542$	19.0523	+	12.7851i	0.818368	+	0.549167i
$543$		0			0
$544$	−9.09636	−	6.20937i	−0.390003	−	0.266225i
$545$	2.34255	−	13.3562i	0.100344	−	0.572116i
$546$		0			0
$547$	16.2094	−	16.2094i	0.693063	−	0.693063i	−0.269842	−	0.962905i	$-0.586971\pi$
$547$	16.2094	−	16.2094i	0.693063	−	0.693063i	0.962905	+	0.269842i	$0.0869714\pi$
$548$	37.3634	+	15.6504i	1.59609	+	0.668552i
$549$		0			0
$550$	−22.3829	+	16.4061i	−0.954412	+	0.699559i
$551$		−	23.8002i		−	1.01392i
$552$		0			0
$553$	−10.8062	−	10.8062i	−0.459528	−	0.459528i
$554$	−20.9809	+	4.13011i	−0.891393	+	0.175472i
$555$		0			0
$556$	7.40312	−	3.03212i	0.313962	−	0.128591i
$557$	−15.2614	−	15.2614i	−0.646647	−	0.646647i	0.305534	−	0.952181i	$-0.401165\pi$
$557$	−15.2614	−	15.2614i	−0.646647	−	0.646647i	−0.952181	+	0.305534i	$0.901165\pi$
$558$		0			0
$559$	−38.5127			−1.62891
$560$	3.46263	−	18.8616i	0.146323	−	0.797048i
$561$		0			0
$562$	−6.50927	+	9.70010i	−0.274577	+	0.409174i
$563$	−18.4521	−	18.4521i	−0.777665	−	0.777665i	0.201769	−	0.979433i	$-0.435331\pi$
$563$	−18.4521	−	18.4521i	−0.777665	−	0.777665i	−0.979433	+	0.201769i	$0.935331\pi$
$564$		0			0
$565$	−3.56393	+	2.50031i	−0.149935	+	0.105189i
$566$	−10.6028	+	2.08717i	−0.445668	+	0.0877301i
$567$		0			0
$568$		0			0
$569$		−	11.0136i		−	0.461715i	−0.972988	−	0.230858i	$-0.925847\pi$
$569$		−	11.0136i		−	0.461715i	0.972988	−	0.230858i	$-0.0741532\pi$
$570$		0			0
$571$	−33.6125			−1.40664			−0.703320	−	0.710874i	$-0.748300\pi$
$571$	−33.6125			−1.40664			−0.703320	+	0.710874i	$0.748300\pi$
$572$	36.4901	+	15.2846i	1.52573	+	0.639081i
$573$		0			0
$574$	−8.19146	+	1.61250i	−0.341905	+	0.0673043i
$575$	−33.1520	+	15.5324i	−1.38253	+	0.647747i
$576$		0			0
$577$	−0.403124	+	0.403124i	−0.0167823	+	0.0167823i	−0.715448	−	0.698666i	$-0.753777\pi$
$577$	−0.403124	+	0.403124i	−0.0167823	+	0.0167823i	0.698666	+	0.715448i	$0.253777\pi$
$578$	15.5120	+	10.4093i	0.645212	+	0.432971i
$579$		0			0
$580$	−25.9962	+	5.67984i	−1.07943	+	0.235843i
$581$			20.2488i			0.840060i
$582$		0			0
$583$	7.12785	−	7.12785i	0.295205	−	0.295205i
$584$	−11.0122	−	16.6952i	−0.455690	−	0.690853i
$585$		0			0
$586$	0.701562	+	3.56393i	0.0289813	+	0.147224i
$587$	−3.92468	+	3.92468i	−0.161989	+	0.161989i	−0.783447	−	0.621458i	$-0.786541\pi$
$587$	−3.92468	+	3.92468i	−0.161989	+	0.161989i	0.621458	+	0.783447i	$0.286541\pi$
$588$		0			0
$589$	−28.5114			−1.17479
$590$	8.59196	−	8.95598i	0.353725	−	0.368712i
$591$		0			0
$592$	−20.1600	−	0.159970i	−0.828570	−	0.00657473i
$593$	1.37670	+	1.37670i	0.0565345	+	0.0565345i	0.734809	−	0.678274i	$-0.237272\pi$
$593$	1.37670	+	1.37670i	0.0565345	+	0.0565345i	−0.678274	+	0.734809i	$0.737272\pi$
$594$		0			0
$595$	1.61250	−	9.19375i	0.0661059	−	0.376907i
$596$	6.09245	+	14.8751i	0.249557	+	0.609309i
$597$		0			0
$598$	43.3372	+	29.0815i	1.77219	+	1.18923i
$599$	4.17433			0.170559			0.0852793	−	0.996357i	$-0.472822\pi$
$599$	4.17433			0.170559			0.0852793	+	0.996357i	$0.472822\pi$
$600$		0			0
$601$	−18.2094			−0.742776			−0.371388	−	0.928478i	$-0.621118\pi$
$601$	−18.2094			−0.742776			−0.371388	+	0.928478i	$0.621118\pi$
$602$	−19.2387	−	12.9102i	−0.784111	−	0.526179i
$603$		0			0
$604$	18.8039	−	7.70156i	0.765119	−	0.313372i
$605$	1.70088	−	9.69766i	0.0691505	−	0.394266i
$606$		0			0
$607$	9.70752	+	9.70752i	0.394016	+	0.394016i	0.876116	−	0.482100i	$-0.160126\pi$
$607$	9.70752	+	9.70752i	0.394016	+	0.394016i	−0.482100	+	0.876116i	$0.660126\pi$
$608$	22.2353	−	4.19406i	0.901762	−	0.170091i
$609$		0			0
$610$	28.8803	−	30.1039i	1.16933	−	1.21887i
$611$	−11.0136			−0.445564
$612$		0			0
$613$	−4.62754	+	4.62754i	−0.186904	+	0.186904i	−0.794356	−	0.607452i	$-0.792192\pi$
$613$	−4.62754	+	4.62754i	−0.186904	+	0.186904i	0.607452	+	0.794356i	$0.292192\pi$
$614$	7.72577	+	39.2468i	0.311787	+	1.58387i
$615$		0			0
$616$	13.1047	+	19.8675i	0.528003	+	0.800484i
$617$	19.8288	−	19.8288i	0.798279	−	0.798279i	−0.184545	−	0.982824i	$-0.559081\pi$
$617$	19.8288	−	19.8288i	0.798279	−	0.798279i	0.982824	+	0.184545i	$0.0590812\pi$
$618$		0			0
$619$			14.8062i			0.595113i	0.954704	+	0.297557i	$0.0961717\pi$
$619$			14.8062i			0.595113i	−0.954704	+	0.297557i	$0.903828\pi$
$620$	6.80415	+	31.1421i	0.273261	+	1.25070i
$621$		0			0
$622$	−32.8509	−	22.0447i	−1.31720	−	0.883911i
$623$	−27.9745	+	27.9745i	−1.12078	+	1.12078i
$624$		0			0
$625$	19.2094	+	16.0000i	0.768375	+	0.640000i
$626$	11.3938	−	2.24289i	0.455389	−	0.0896438i
$627$		0			0
$628$	−10.5212	+	25.1181i	−0.419841	+	1.00232i
$629$	−9.81294			−0.391268
$630$		0			0
$631$		−	35.6393i		−	1.41878i	−0.704818	−	0.709388i	$-0.748971\pi$
$631$		−	35.6393i		−	1.41878i	0.704818	−	0.709388i	$-0.251029\pi$
$632$	−19.7495	−	4.05074i	−0.785592	−	0.161130i
$633$		0			0
$634$	22.3678	−	4.40312i	0.888339	−	0.174870i
$635$	−30.2262	+	21.2055i	−1.19949	+	0.841516i
$636$		0			0
$637$	8.56455	+	8.56455i	0.339340	+	0.339340i
$638$	18.4020	−	27.4227i	0.728543	−	1.08567i
$639$		0			0
$640$	−9.88742	−	23.2860i	−0.390834	−	0.920461i
$641$	18.4521			0.728815			0.364408	−	0.931240i	$-0.381271\pi$
$641$	18.4521			0.728815			0.364408	+	0.931240i	$0.381271\pi$
$642$		0			0
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$	11.9001	+	29.0549i	0.468930	+	1.14492i
$645$		0			0
$646$	10.8062	−	2.12722i	0.425166	−	0.0836944i
$647$	5.71949	+	5.71949i	0.224856	+	0.224856i	0.810540	−	0.585684i	$-0.199174\pi$
$647$	5.71949	+	5.71949i	0.224856	+	0.224856i	−0.585684	+	0.810540i	$0.699174\pi$
$648$		0			0
$649$			15.4031i			0.604626i
$650$	5.42745	−	35.2236i	0.212882	−	1.38158i
$651$		0			0
$652$		0			0
$653$	−5.67905	+	5.67905i	−0.222238	+	0.222238i	−0.809440	−	0.587202i	$-0.800229\pi$
$653$	−5.67905	+	5.67905i	−0.222238	+	0.222238i	0.587202	+	0.809440i	$0.300229\pi$
$654$		0			0
$655$	6.67540	−	38.0602i	0.260829	−	1.48714i
$656$	−7.84936	+	7.72577i	−0.306466	+	0.301641i
$657$		0			0
$658$	−5.50178	−	3.69198i	−0.214482	−	0.143928i
$659$			11.7740i			0.458652i	0.973350	+	0.229326i	$0.0736521\pi$
$659$			11.7740i			0.458652i	−0.973350	+	0.229326i	$0.926348\pi$
$660$		0			0
$661$			15.3193i			0.595852i	0.954589	+	0.297926i	$0.0962949\pi$
$661$			15.3193i			0.595852i	−0.954589	+	0.297926i	$0.903705\pi$
$662$	−17.9719	+	26.7817i	−0.698498	+	1.04090i
$663$		0			0
$664$	14.7082	+	22.2984i	0.570787	+	0.865347i
$665$	11.0136	+	15.6987i	0.427090	+	0.608770i
$666$		0			0
$667$	30.8062	−	30.8062i	1.19282	−	1.19282i
$668$	−1.68847	+	4.03102i	−0.0653288	+	0.155965i
$669$		0			0
$670$	24.1583	−	0.501146i	0.933317	−	0.0193609i
$671$			51.7748i			1.99874i
$672$		0			0
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$	−4.01861	−	20.4145i	−0.154791	−	0.786336i
$675$		0			0
$676$	−22.9555	+	9.40194i	−0.882903	+	0.361613i
$677$	13.4857	+	13.4857i	0.518298	+	0.518298i	0.917056	−	0.398758i	$-0.130559\pi$
$677$	13.4857	+	13.4857i	0.518298	+	0.518298i	−0.398758	+	0.917056i	$0.630559\pi$
$678$		0			0
$679$	31.5435			1.21053
$680$	−4.90237	−	11.2957i	−0.187997	−	0.433169i
$681$		0			0
$682$	−32.8509	−	22.0447i	−1.25793	−	0.844134i
$683$	−22.3768	−	22.3768i	−0.856225	−	0.856225i	0.134666	−	0.990891i	$-0.457004\pi$
$683$	−22.3768	−	22.3768i	−0.856225	−	0.856225i	−0.990891	+	0.134666i	$0.957004\pi$
$684$		0			0
$685$	26.0111	+	37.0760i	0.993833	+	1.41660i
$686$	5.50682	+	27.9745i	0.210251	+	1.06807i
$687$		0			0
$688$	−30.5637	−	0.242524i	−1.16523	−	0.00924616i
$689$			12.9453i			0.493177i
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	10.7845	+	4.51732i	0.409967	+	0.171723i
$693$		0			0
$694$	−7.12785	−	36.2094i	−0.270569	−	1.37449i
$695$	8.80980	+	1.54515i	0.334175	+	0.0586111i
$696$		0			0
$697$	−3.79063	+	3.79063i	−0.143580	+	0.143580i
$698$	10.3957	−	15.4917i	0.393483	−	0.586368i
$699$		0			0
$700$	14.5188	−	15.7763i	0.548761	−	0.596287i
$701$			33.9246i			1.28131i	0.767827	+	0.640657i	$0.221338\pi$
$701$			33.9246i			1.28131i	−0.767827	+	0.640657i	$0.778662\pi$
$702$		0			0
$703$	14.2557	−	14.2557i	0.537664	−	0.537664i
$704$	28.8624	+	12.3597i	1.08779	+	0.465823i
$705$		0			0
$706$	8.10469	−	1.59542i	0.305024	−	0.0600443i
$707$	12.1849	−	12.1849i	0.458261	−	0.458261i
$708$		0			0
$709$	−15.3193			−0.575329			−0.287664	−	0.957731i	$-0.592879\pi$
$709$	−15.3193			−0.575329			−0.287664	+	0.957731i	$0.592879\pi$
$710$		0			0
$711$		0			0
$712$	−10.4863	+	51.1262i	−0.392991	+	1.91603i
$713$	−36.9043	−	36.9043i	−1.38208	−	1.38208i
$714$		0			0
$715$	25.4031	+	36.2094i	0.950023	+	1.35415i
$716$	26.1267	−	10.7008i	0.976401	−	0.399908i
$717$		0			0
$718$	25.3341	−	37.7529i	0.945462	−	1.40893i
$719$	−27.9745			−1.04327			−0.521637	−	0.853167i	$-0.674679\pi$
$719$	−27.9745			−1.04327			−0.521637	+	0.853167i	$0.674679\pi$
$720$		0			0
$721$	−17.0156			−0.633695
$722$	2.36408	−	3.52294i	0.0879819	−	0.131110i
$723$		0			0
$724$	−11.2236	+	4.59688i	−0.417121	+	0.170842i
$725$	−27.9745	−	10.1244i	−1.03895	−	0.376010i
$726$		0			0
$727$	−10.7711	−	10.7711i	−0.399479	−	0.399479i	0.478570	−	0.878049i	$-0.341155\pi$
$727$	−10.7711	−	10.7711i	−0.399479	−	0.399479i	−0.878049	+	0.478570i	$0.841155\pi$
$728$	−29.9414	−	6.14117i	−1.10970	−	0.227607i
$729$		0			0
$730$	−0.463755	−	22.3559i	−0.0171644	−	0.827428i
$731$	−14.8770			−0.550246
$732$		0			0
$733$	−3.56393	+	3.56393i	−0.131637	+	0.131637i	−0.769855	−	0.638219i	$-0.779672\pi$
$733$	−3.56393	+	3.56393i	−0.131637	+	0.131637i	0.638219	+	0.769855i	$0.279672\pi$
$734$	14.8751	−	2.92818i	0.549051	−	0.108081i
$735$		0			0
$736$	34.2094	+	23.3521i	1.26097	+	0.860768i
$737$	−21.2055	+	21.2055i	−0.781116	+	0.781116i
$738$		0			0
$739$			28.4187i			1.04540i	0.852517	+	0.522700i	$0.175075\pi$
$739$			28.4187i			1.04540i	−0.852517	+	0.522700i	$0.824925\pi$
$740$	−18.9731	−	12.1690i	−0.697465	−	0.447340i
$741$		0			0
$742$	−4.33951	+	6.46673i	−0.159309	+	0.237401i
$743$	22.7971	−	22.7971i	0.836343	−	0.836343i	−0.152032	−	0.988376i	$-0.548582\pi$
$743$	22.7971	−	22.7971i	0.836343	−	0.836343i	0.988376	+	0.152032i	$0.0485818\pi$
$744$		0			0
$745$	−3.10469	+	17.7016i	−0.113747	+	0.648535i
$746$	0.965843	+	4.90647i	0.0353620	+	0.179639i
$747$		0			0
$748$	14.0957	+	5.90427i	0.515391	+	0.215881i
$749$	−11.9001			−0.434820
$750$		0			0
$751$		−	21.3836i		−	0.780297i	−0.920752	−	0.390148i	$-0.872424\pi$
$751$		−	21.3836i		−	0.780297i	0.920752	−	0.390148i	$-0.127576\pi$
$752$	−8.74044	−	0.0693557i	−0.318731	−	0.00252914i
$753$		0			0
$754$	8.19146	+	41.6125i	0.298315	+	1.51544i
$755$	22.3768	+	3.92468i	0.814376	+	0.142834i
$756$		0			0
$757$	29.9481	+	29.9481i	1.08848	+	1.08848i	0.995685	+	0.0927974i	$0.0295809\pi$
$757$	29.9481	+	29.9481i	1.08848	+	1.08848i	0.0927974	+	0.995685i	$0.470419\pi$
$758$	−7.99268	−	5.36350i	−0.290307	−	0.194811i
$759$		0			0
$760$	23.5316	+	9.28782i	0.853581	+	0.336905i
$761$	−4.68509			−0.169835			−0.0849173	−	0.996388i	$-0.527063\pi$
$761$	−4.68509			−0.169835			−0.0849173	+	0.996388i	$0.527063\pi$
$762$		0			0
$763$	−9.19375	−	9.19375i	−0.332836	−	0.332836i
$764$	44.0490	−	18.0413i	1.59364	−	0.652710i
$765$		0			0
$766$	3.61250	+	18.3514i	0.130525	+	0.663064i
$767$	−13.9873	−	13.9873i	−0.505051	−	0.505051i
$768$		0			0
$769$			11.4031i			0.411207i	0.978635	+	0.205604i	$0.0659157\pi$
$769$			11.4031i			0.411207i	−0.978635	+	0.205604i	$0.934084\pi$
$770$	0.551874	+	26.6037i	0.0198881	+	0.958732i
$771$		0			0
$772$	0.440514	−	1.05167i	0.0158545	−	0.0378506i
$773$	−11.9405	+	11.9405i	−0.429472	+	0.429472i	−0.888448	−	0.458977i	$-0.848216\pi$
$773$	−11.9405	+	11.9405i	−0.429472	+	0.429472i	0.458977	+	0.888448i	$0.348216\pi$
$774$		0			0
$775$	−12.1285	+	33.5120i	−0.435668	+	1.20379i
$776$	34.7365	−	22.9123i	1.24697	−	0.822505i
$777$		0			0
$778$	21.7992	−	32.4852i	0.781541	−	1.16465i
$779$		−	11.0136i		−	0.394604i
$780$		0			0
$781$		0			0
$782$	16.7407	+	11.2339i	0.598645	+	0.401722i
$783$		0			0
$784$	6.74291	+	6.85078i	0.240818	+	0.244671i
$785$	−24.9248	+	17.4863i	−0.889604	+	0.624112i
$786$		0			0
$787$	−20.0000	+	20.0000i	−0.712923	+	0.712923i	−0.967146	−	0.254223i	$-0.918180\pi$
$787$	−20.0000	+	20.0000i	−0.712923	+	0.712923i	0.254223	+	0.967146i	$0.418180\pi$
$788$	5.95383	−	14.2141i	0.212097	−	0.506355i
$789$		0			0
$790$	−16.2655	−	15.6044i	−0.578700	−	0.555179i
$791$			4.17433i			0.148422i
$792$		0			0
$793$	−47.0156	−	47.0156i	−1.66957	−	1.66957i
$794$	9.08080	−	1.78756i	0.322266	−	0.0634383i
$795$		0			0
$796$	13.9109	+	33.9645i	0.493060	+	1.20384i
$797$	28.4761	+	28.4761i	1.00868	+	1.00868i	0.999962	+	0.00871364i	$0.00277367\pi$
$797$	28.4761	+	28.4761i	1.00868	+	1.00868i	0.00871364	+	0.999962i	$0.497226\pi$
$798$		0			0
$799$	−4.25444			−0.150511
$800$	4.52904	−	27.9193i	0.160126	−	0.987097i
$801$		0			0
$802$	−24.7420	+	36.8705i	−0.873671	+	1.30194i
$803$	19.6234	+	19.6234i	0.692495	+	0.692495i
$804$		0			0
$805$	−6.06424	+	34.5756i	−0.213736	+	1.21863i
$806$	49.8496	−	9.81294i	1.75588	−	0.345646i
$807$		0			0
$808$	4.56753	−	22.2691i	0.160685	−	0.783424i
$809$		−	18.4521i		−	0.648742i	−0.945930	−	0.324371i	$-0.894847\pi$
$809$		−	18.4521i		−	0.648742i	0.945930	−	0.324371i	$-0.105153\pi$
$810$		0			0
$811$	−17.1938			−0.603754			−0.301877	−	0.953347i	$-0.597613\pi$
$811$	−17.1938			−0.603754			−0.301877	+	0.953347i	$0.597613\pi$
$812$	−9.85731	+	23.5331i	−0.345924	+	0.825851i
$813$		0			0
$814$	27.4478	−	5.40312i	0.962045	−	0.189379i
$815$		0			0
$816$		0			0
$817$	21.6125	−	21.6125i	0.756126	−	0.756126i
$818$	11.0422	+	7.40991i	0.386082	+	0.259081i
$819$		0			0
$820$	−12.0298	+	2.62837i	−0.420100	+	0.0917865i
$821$		−	26.1988i		−	0.914345i	−0.889378	−	0.457173i	$-0.848862\pi$
$821$		−	26.1988i		−	0.914345i	0.889378	−	0.457173i	$-0.151138\pi$
$822$		0			0
$823$	31.9960	−	31.9960i	1.11531	−	1.11531i	0.122889	−	0.992420i	$-0.460784\pi$
$823$	31.9960	−	31.9960i	1.11531	−	1.11531i	0.992420	−	0.122889i	$-0.0392159\pi$
$824$	−18.7380	+	12.3597i	−0.652770	+	0.430570i
$825$		0			0
$826$	−2.29844	−	11.6760i	−0.0799729	−	0.406261i
$827$	−11.0136	+	11.0136i	−0.382981	+	0.382981i	−0.872175	−	0.489194i	$-0.837291\pi$
$827$	−11.0136	+	11.0136i	−0.382981	+	0.382981i	0.489194	+	0.872175i	$0.337291\pi$
$828$		0			0
$829$	34.5756			1.20086			0.600431	−	0.799677i	$-0.294996\pi$
$829$	34.5756			1.20086			0.600431	+	0.799677i	$0.294996\pi$
$830$	0.619400	+	29.8589i	0.0214997	+	1.03642i
$831$		0			0
$832$	−37.4330	+	14.9858i	−1.29775	+	0.519539i
$833$	3.30839	+	3.30839i	0.114629	+	0.114629i
$834$		0			0
$835$	−4.00000	+	2.80625i	−0.138426	+	0.0971142i
$836$	−29.0549	+	11.9001i	−1.00488	+	0.411574i
$837$		0			0
$838$	26.7599	+	17.9573i	0.924405	+	0.620324i
$839$	4.17433			0.144114			0.0720570	−	0.997401i	$-0.477044\pi$
$839$	4.17433			0.144114			0.0720570	+	0.997401i	$0.477044\pi$
$840$		0			0
$841$	6.40312			0.220797
$842$	−29.7343	−	19.9533i	−1.02471	−	0.687635i
$843$		0			0
$844$	−9.09636	−	22.2094i	−0.313110	−	0.764478i
$845$	−27.3172	−	4.79119i	−0.939742	−	0.164822i
$846$		0			0
$847$	−6.67540	−	6.67540i	−0.229369	−	0.229369i
$848$	−0.0815201	+	10.2734i	−0.00279941	+	0.352791i
$849$		0			0
$850$	2.09656	−	13.6065i	0.0719114	−	0.466698i
$851$	36.9043			1.26506
$852$		0			0
$853$	−2.50031	+	2.50031i	−0.0856091	+	0.0856091i	−0.748615	−	0.663005i	$-0.769281\pi$
$853$	−2.50031	+	2.50031i	−0.0856091	+	0.0856091i	0.663005	+	0.748615i	$0.269281\pi$
$854$	−7.72577	−	39.2468i	−0.264371	−	1.34300i
$855$		0			0
$856$	−13.1047	+	8.64391i	−0.447909	+	0.295443i
$857$	4.13011	−	4.13011i	0.141082	−	0.141082i	−0.633038	−	0.774120i	$-0.718193\pi$
$857$	4.13011	−	4.13011i	0.141082	−	0.141082i	0.774120	+	0.633038i	$0.218193\pi$
$858$		0			0
$859$			25.6125i			0.873887i	0.899489	+	0.436944i	$0.143939\pi$
$859$			25.6125i			0.873887i	−0.899489	+	0.436944i	$0.856061\pi$
$860$	−28.7644	−	18.4489i	−0.980857	−	0.629101i
$861$		0			0
$862$	−4.90198	−	3.28948i	−0.166962	−	0.112040i
$863$	−4.63546	+	4.63546i	−0.157793	+	0.157793i	−0.781588	−	0.623795i	$-0.785590\pi$
$863$	−4.63546	+	4.63546i	−0.157793	+	0.157793i	0.623795	+	0.781588i	$0.285590\pi$
$864$		0			0
$865$	7.50781	+	10.7016i	0.255273	+	0.363864i
$866$	−0.791067	+	0.155722i	−0.0268816	+	0.00529166i
$867$		0			0
$868$	28.1915	+	11.8085i	0.956881	+	0.400808i
$869$	27.9745			0.948971
$870$		0			0
$871$		−	38.5127i		−	1.30495i
$872$	−16.8025	−	3.44629i	−0.569004	−	0.116706i
$873$		0			0
$874$	−40.6399	+	8.00000i	−1.37466	+	0.270604i
$875$	23.1372	−	6.26723i	0.782181	−	0.211871i
$876$		0			0
$877$	2.50031	+	2.50031i	0.0844296	+	0.0844296i	0.748060	−	0.663631i	$-0.230985\pi$
$877$	2.50031	+	2.50031i	0.0844296	+	0.0844296i	−0.663631	+	0.748060i	$0.730985\pi$
$878$	3.22754	−	4.80968i	0.108924	−	0.162319i
$879$		0			0
$880$	19.9320	+	28.8958i	0.671906	+	0.974077i
$881$	38.8360			1.30842			0.654208	−	0.756314i	$-0.273002\pi$
$881$	38.8360			1.30842			0.654208	+	0.756314i	$0.273002\pi$
$882$		0			0
$883$	−10.8062	−	10.8062i	−0.363659	−	0.363659i	0.501499	−	0.865158i	$-0.332782\pi$
$883$	−10.8062	−	10.8062i	−0.363659	−	0.363659i	−0.865158	+	0.501499i	$0.832782\pi$
$884$	−18.1616	+	7.43850i	−0.610841	+	0.250184i
$885$		0			0
$886$	25.4031	−	5.00063i	0.853435	−	0.167999i
$887$	−25.3454	−	25.3454i	−0.851014	−	0.851014i	0.139244	−	0.990258i	$-0.455533\pi$
$887$	−25.3454	−	25.3454i	−0.851014	−	0.851014i	−0.990258	+	0.139244i	$0.955533\pi$
$888$		0			0
$889$			35.4031i			1.18738i
$890$	−40.3956	+	42.1071i	−1.35406	+	1.41143i
$891$		0			0
$892$	30.4606	+	12.7590i	1.01989	+	0.427203i
$893$	6.18062	−	6.18062i	0.206827	−	0.206827i
$894$		0			0
$895$	31.0911	+	5.45308i	1.03926	+	0.182276i
$896$	−23.7229	−	5.06219i	−0.792525	−	0.169116i
$897$		0			0
$898$	−18.4352	−	12.3710i	−0.615192	−	0.412826i
$899$		−	42.4111i		−	1.41449i
$900$		0			0
$901$			5.00063i			0.166595i
$902$	8.51560	−	12.6899i	0.283539	−	0.422529i
$903$		0			0
$904$	3.03212	+	4.59688i	0.100847	+	0.152890i
$905$	−13.3562	−	2.34255i	−0.443974	−	0.0778689i
$906$		0			0
$907$	25.4031	−	25.4031i	0.843497	−	0.843497i	−0.145815	−	0.989312i	$-0.546580\pi$
$907$	25.4031	−	25.4031i	0.843497	−	0.843497i	0.989312	+	0.145815i	$0.0465804\pi$
$908$	−33.7719	−	14.1460i	−1.12076	−	0.469452i
$909$		0			0
$910$	−24.6595	−	23.6572i	−0.817453	−	0.784227i
$911$			4.17433i			0.138302i	0.997606	+	0.0691509i	$0.0220290\pi$
$911$			4.17433i			0.138302i	−0.997606	+	0.0691509i	$0.977971\pi$
$912$		0			0
$913$	−26.2094	−	26.2094i	−0.867404	−	0.867404i
$914$	−6.10577	−	31.0172i	−0.201961	−	1.02596i
$915$		0			0
$916$	10.0000	+	24.4157i	0.330409	+	0.806716i
$917$	−26.1988	−	26.1988i	−0.865161	−	0.865161i
$918$		0			0
$919$	−17.1291			−0.565037			−0.282519	−	0.959262i	$-0.591170\pi$
$919$	−17.1291			−0.565037			−0.282519	+	0.959262i	$0.591170\pi$
$920$	18.4367	+	42.4804i	0.607840	+	1.40054i
$921$		0			0
$922$	4.53624	+	3.04406i	0.149393	+	0.100251i
$923$		0			0
$924$		0			0
$925$	−10.6918	−	22.8203i	−0.351543	−	0.750325i
$926$	−2.92818	−	14.8751i	−0.0962261	−	0.488827i
$927$		0			0
$928$	6.23871	+	33.0753i	0.204796	+	1.08575i
$929$		−	4.68509i		−	0.153713i	−0.997042	−	0.0768565i	$-0.975512\pi$
$929$		−	4.68509i		−	0.153713i	0.997042	−	0.0768565i	$-0.0244883\pi$
$930$		0			0
$931$	−9.61250			−0.315037
$932$	15.6504	−	37.3634i	0.512646	−	1.22388i
$933$		0			0
$934$	0.452450	+	2.29844i	0.0148046	+	0.0752072i
$935$	9.81294	+	13.9873i	0.320917	+	0.457433i
$936$		0			0
$937$	9.59688	−	9.59688i	0.313516	−	0.313516i	−0.532754	−	0.846270i	$-0.678843\pi$
$937$	9.59688	−	9.59688i	0.313516	−	0.313516i	0.846270	+	0.532754i	$0.178843\pi$
$938$	12.9102	−	19.2387i	0.421532	−	0.628166i
$939$		0			0
$940$	−8.22587	−	5.27590i	−0.268298	−	0.172081i
$941$		−	31.8374i		−	1.03787i	−0.854814	−	0.518935i	$-0.826329\pi$
$941$		−	31.8374i		−	1.03787i	0.854814	−	0.518935i	$-0.173671\pi$
$942$		0			0
$943$	14.2557	−	14.2557i	0.464229	−	0.464229i
$944$	−11.0122	−	11.1884i	−0.358418	−	0.364152i
$945$		0			0
$946$	41.6125	−	8.19146i	1.35294	−	0.266327i
$947$	−5.50682	+	5.50682i	−0.178947	+	0.178947i	−0.790897	−	0.611949i	$-0.790386\pi$
$947$	−5.50682	+	5.50682i	−0.178947	+	0.178947i	0.611949	+	0.790897i	$0.290386\pi$
$948$		0			0
$949$	−35.6393			−1.15690
$950$	16.7210	+	22.8125i	0.542499	+	0.740135i
$951$		0			0
$952$	−11.5660	−	2.37226i	−0.374857	−	0.0768855i
$953$	−17.0754	−	17.0754i	−0.553127	−	0.553127i	0.374215	−	0.927342i	$-0.377912\pi$
$953$	−17.0754	−	17.0754i	−0.553127	−	0.553127i	−0.927342	+	0.374215i	$0.877912\pi$
$954$		0			0
$955$	52.4187	+	9.19375i	1.69623	+	0.297503i
$956$	21.2055	+	51.7748i	0.685836	+	1.67452i
$957$		0			0
$958$	−22.0447	+	32.8509i	−0.712231	+	1.06136i
$959$	43.4261			1.40230
$960$		0			0
$961$	−19.8062			−0.638911
$962$	−20.0183	+	29.8313i	−0.645417	+	0.961798i
$963$		0			0
$964$	−14.2557	−	34.8062i	−0.459145	−	1.12103i
$965$	1.04358	−	0.732138i	0.0335941	−	0.0235684i
$966$		0			0
$967$	−8.64391	−	8.64391i	−0.277969	−	0.277969i	0.554329	−	0.832298i	$-0.312975\pi$
$967$	−8.64391	−	8.64391i	−0.277969	−	0.277969i	−0.832298	+	0.554329i	$0.812975\pi$
$968$	−12.1999	−	2.50229i	−0.392121	−	0.0804265i
$969$		0			0
$970$	46.5142	−	0.964901i	1.49348	−	0.0309811i
$971$	7.08895			0.227495			0.113748	−	0.993510i	$-0.463714\pi$
$971$	7.08895			0.227495			0.113748	+	0.993510i	$0.463714\pi$
$972$		0			0
$973$	6.06424	−	6.06424i	0.194411	−	0.194411i
$974$	−16.9623	+	3.33904i	−0.543507	+	0.106990i
$975$		0			0
$976$	−37.0156	−	37.6078i	−1.18484	−	1.20380i
$977$	−19.8288	+	19.8288i	−0.634381	+	0.634381i	−0.949164	−	0.314783i	$-0.898068\pi$
$977$	−19.8288	+	19.8288i	−0.634381	+	0.634381i	0.314783	+	0.949164i	$0.398068\pi$
$978$		0			0
$979$		−	72.4187i		−	2.31451i
$980$	2.29399	+	10.4994i	0.0732788	+	0.335392i
$981$		0			0
$982$	21.6493	−	32.2617i	0.690856	−	1.02951i
$983$	22.7971	−	22.7971i	0.727113	−	0.727113i	−0.242930	−	0.970044i	$-0.578109\pi$
$983$	22.7971	−	22.7971i	0.727113	−	0.727113i	0.970044	+	0.242930i	$0.0781086\pi$
$984$		0			0
$985$	14.1047	−	9.89531i	0.449413	−	0.315291i
$986$	3.16427	+	16.0744i	0.100771	+	0.511914i
$987$		0			0
$988$	15.5779	−	37.1904i	0.495600	−	1.18319i
$989$	55.9491			1.77908
$990$		0			0
$991$			26.5429i			0.843163i	0.906791	+	0.421581i	$0.138525\pi$
$991$			26.5429i			0.843163i	−0.906791	+	0.421581i	$0.861475\pi$
$992$	39.6225	−	7.47365i	1.25802	−	0.237289i
$993$		0			0
$994$		0			0
$995$	−7.08895	+	40.4181i	−0.224735	+	1.28134i
$996$		0			0
$997$	3.56393	+	3.56393i	0.112871	+	0.112871i	0.761286	−	0.648416i	$-0.224568\pi$
$997$	3.56393	+	3.56393i	0.112871	+	0.112871i	−0.648416	+	0.761286i	$0.724568\pi$
$998$	7.99268	+	5.36350i	0.253004	+	0.169779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.d.163.6	yes	16
3.2	odd	2	inner	360.2.w.d.163.3	yes	16
4.3	odd	2		1440.2.bi.d.1423.6		16
5.2	odd	4	inner	360.2.w.d.307.7	yes	16
8.3	odd	2	inner	360.2.w.d.163.7	yes	16
8.5	even	2		1440.2.bi.d.1423.3		16
12.11	even	2		1440.2.bi.d.1423.4		16
15.2	even	4	inner	360.2.w.d.307.2	yes	16
20.7	even	4		1440.2.bi.d.847.3		16
24.5	odd	2		1440.2.bi.d.1423.5		16
24.11	even	2	inner	360.2.w.d.163.2	✓	16
40.27	even	4	inner	360.2.w.d.307.6	yes	16
40.37	odd	4		1440.2.bi.d.847.6		16
60.47	odd	4		1440.2.bi.d.847.5		16
120.77	even	4		1440.2.bi.d.847.4		16
120.107	odd	4	inner	360.2.w.d.307.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.w.d.163.2	✓	16	24.11	even	2	inner
360.2.w.d.163.3	yes	16	3.2	odd	2	inner
360.2.w.d.163.6	yes	16	1.1	even	1	trivial
360.2.w.d.163.7	yes	16	8.3	odd	2	inner
360.2.w.d.307.2	yes	16	15.2	even	4	inner
360.2.w.d.307.3	yes	16	120.107	odd	4	inner
360.2.w.d.307.6	yes	16	40.27	even	4	inner
360.2.w.d.307.7	yes	16	5.2	odd	4	inner
1440.2.bi.d.847.3		16	20.7	even	4
1440.2.bi.d.847.4		16	120.77	even	4
1440.2.bi.d.847.5		16	60.47	odd	4
1440.2.bi.d.847.6		16	40.37	odd	4
1440.2.bi.d.1423.3		16	8.5	even	2
1440.2.bi.d.1423.4		16	12.11	even	2
1440.2.bi.d.1423.5		16	24.5	odd	2
1440.2.bi.d.1423.6		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.788026 - 1.17431i) q^{2} +(-0.758030 - 1.85078i) q^{4} +(0.386289 - 2.20245i) q^{5} +(-1.51606 - 1.51606i) q^{7} +(-2.77075 - 0.568298i) q^{8} +O(q^{10})\)	\(q+(0.788026 - 1.17431i) q^{2} +(-0.758030 - 1.85078i) q^{4} +(0.386289 - 2.20245i) q^{5} +(-1.51606 - 1.51606i) q^{7} +(-2.77075 - 0.568298i) q^{8} +(-2.28196 - 2.18921i) q^{10} +3.92468 q^{11} +(-3.56393 + 3.56393i) q^{13} +(-2.97503 + 0.585637i) q^{14} +(-2.85078 + 2.80590i) q^{16} +(-1.37670 + 1.37670i) q^{17} -4.00000i q^{19} +(-4.36907 + 0.954587i) q^{20} +(3.09275 - 4.60881i) q^{22} +(5.17748 - 5.17748i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(1.37670 + 6.99364i) q^{26} +(-1.65668 + 3.95511i) q^{28} +5.95005 q^{29} -7.12785i q^{31} +(1.04851 + 5.55883i) q^{32} +(0.531805 + 2.70156i) q^{34} +(-3.92468 + 2.75341i) q^{35} +(3.56393 + 3.56393i) q^{37} +(-4.69726 - 3.15210i) q^{38} +(-2.32196 + 5.88290i) q^{40} +2.75341 q^{41} +(5.40312 + 5.40312i) q^{43} +(-2.97503 - 7.26373i) q^{44} +(-2.00000 - 10.1600i) q^{46} +(1.54515 + 1.54515i) q^{47} -2.40312i q^{49} +(-5.70312 + 4.18024i) q^{50} +(9.29761 + 3.89448i) q^{52} +(1.81616 - 1.81616i) q^{53} +(1.51606 - 8.64391i) q^{55} +(3.33904 + 5.06219i) q^{56} +(4.68880 - 6.98723i) q^{58} +3.92468i q^{59} +13.1921i q^{61} +(-8.37034 - 5.61693i) q^{62} +(7.35408 + 3.14922i) q^{64} +(6.47266 + 9.22607i) q^{65} +(-5.40312 + 5.40312i) q^{67} +(3.59156 + 1.50439i) q^{68} +(0.140616 + 6.77857i) q^{70} +(5.00000 + 5.00000i) q^{73} +(6.99364 - 1.37670i) q^{74} +(-7.40312 + 3.03212i) q^{76} +(-5.95005 - 5.95005i) q^{77} +7.12785 q^{79} +(5.07862 + 7.36259i) q^{80} +(2.16976 - 3.23337i) q^{82} +(-6.67809 - 6.67809i) q^{83} +(2.50031 + 3.56393i) q^{85} +(10.6028 - 2.08717i) q^{86} +(-10.8743 - 2.23039i) q^{88} -18.4521i q^{89} +10.8062 q^{91} +(-13.5071 - 5.65769i) q^{92} +(3.03212 - 0.596876i) q^{94} +(-8.80980 - 1.54515i) q^{95} +(-10.4031 + 10.4031i) q^{97} +(-2.82202 - 1.89372i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 20 * q^16 + 36 * q^22 - 24 * q^25 + 44 * q^28 + 32 * q^40 - 16 * q^43 - 32 * q^46 - 8 * q^52 - 44 * q^58 + 16 * q^67 - 44 * q^70 + 80 * q^73 - 16 * q^76 - 8 * q^82 - 28 * q^88 - 32 * q^91 - 64 * q^97

Introduction

L-functions

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