LMFDB - Embedded newform 1148.2.i.e.165.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.8
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.e.821.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.257541 - 0.446074i) q^{3} +(-1.09982 - 1.90494i) q^{5} +(-2.48493 + 0.908374i) q^{7} +(1.36735 + 2.36831i) q^{9} +O(q^{10})$	\(q+(0.257541 - 0.446074i) q^{3} +(-1.09982 - 1.90494i) q^{5} +(-2.48493 + 0.908374i) q^{7} +(1.36735 + 2.36831i) q^{9} +(-2.11080 + 3.65601i) q^{11} +3.63941 q^{13} -1.13299 q^{15} +(3.99349 - 6.91692i) q^{17} +(-0.570070 - 0.987390i) q^{19} +(-0.234768 + 1.34240i) q^{21} +(3.71723 + 6.43843i) q^{23} +(0.0808021 - 0.139953i) q^{25} +2.95383 q^{27} +6.08068 q^{29} +(0.666213 - 1.15392i) q^{31} +(1.08723 + 1.88314i) q^{33} +(4.46336 + 3.73459i) q^{35} +(1.43888 + 2.49222i) q^{37} +(0.937298 - 1.62345i) q^{39} -1.00000 q^{41} +5.14701 q^{43} +(3.00766 - 5.20942i) q^{45} +(-4.06236 - 7.03622i) q^{47} +(5.34971 - 4.51448i) q^{49} +(-2.05697 - 3.56278i) q^{51} +(0.815377 - 1.41227i) q^{53} +9.28598 q^{55} -0.587265 q^{57} +(1.48989 - 2.58057i) q^{59} +(-5.13542 - 8.89481i) q^{61} +(-5.54906 - 4.64302i) q^{63} +(-4.00269 - 6.93287i) q^{65} +(-1.23404 + 2.13742i) q^{67} +3.82935 q^{69} +13.0326 q^{71} +(-5.75997 + 9.97656i) q^{73} +(-0.0416197 - 0.0720874i) q^{75} +(1.92415 - 11.0023i) q^{77} +(-4.53471 - 7.85434i) q^{79} +(-3.34130 + 5.78731i) q^{81} +7.51957 q^{83} -17.5684 q^{85} +(1.56602 - 2.71243i) q^{87} +(8.99097 + 15.5728i) q^{89} +(-9.04367 + 3.30595i) q^{91} +(-0.343154 - 0.594361i) q^{93} +(-1.25395 + 2.17190i) q^{95} +13.2426 q^{97} -11.5448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.257541	−	0.446074i	0.148691	−	0.257541i	−0.782053	−	0.623212i	$-0.785827\pi$
$3$	0.257541	−	0.446074i	0.148691	−	0.257541i	0.930744	+	0.365671i	$0.119161\pi$
$4$		0			0
$5$	−1.09982	−	1.90494i	−0.491853	−	0.851915i	0.508103	−	0.861297i	$-0.330347\pi$
$5$	−1.09982	−	1.90494i	−0.491853	−	0.851915i	−0.999956	+	0.00938144i	$0.997014\pi$
$6$		0			0
$7$	−2.48493	+	0.908374i	−0.939214	+	0.343333i
$7$	−2.48493	+	0.908374i	−0.939214	+	0.343333i
$8$		0			0
$9$	1.36735	+	2.36831i	0.455782	+	0.789437i
$10$		0			0
$11$	−2.11080	+	3.65601i	−0.636430	+	1.10233i	0.349780	+	0.936832i	$0.386256\pi$
$11$	−2.11080	+	3.65601i	−0.636430	+	1.10233i	−0.986210	+	0.165497i	$0.947077\pi$
$12$		0			0
$13$	3.63941			1.00939			0.504696	−	0.863297i	$-0.331605\pi$
$13$	3.63941			1.00939			0.504696	+	0.863297i	$0.331605\pi$
$14$		0			0
$15$	−1.13299			−0.292537
$16$		0			0
$17$	3.99349	−	6.91692i	0.968563	−	1.67760i	0.268842	−	0.963184i	$-0.413359\pi$
$17$	3.99349	−	6.91692i	0.968563	−	1.67760i	0.699721	−	0.714416i	$-0.253308\pi$
$18$		0			0
$19$	−0.570070	−	0.987390i	−0.130783	−	0.226523i	0.793196	−	0.608967i	$-0.208416\pi$
$19$	−0.570070	−	0.987390i	−0.130783	−	0.226523i	−0.923979	+	0.382444i	$0.875082\pi$
$20$		0			0
$21$	−0.234768	+	1.34240i	−0.0512306	+	0.292937i
$22$		0			0
$23$	3.71723	+	6.43843i	0.775096	+	1.34250i	0.934741	+	0.355330i	$0.115632\pi$
$23$	3.71723	+	6.43843i	0.775096	+	1.34250i	−0.159645	+	0.987174i	$0.551035\pi$
$24$		0			0
$25$	0.0808021	−	0.139953i	0.0161604	−	0.0279907i
$26$		0			0
$27$	2.95383			0.568466
$28$		0			0
$29$	6.08068			1.12915			0.564577	−	0.825380i	$-0.309039\pi$
$29$	6.08068			1.12915			0.564577	+	0.825380i	$0.309039\pi$
$30$		0			0
$31$	0.666213	−	1.15392i	0.119655	−	0.207249i	−0.799976	−	0.600032i	$-0.795154\pi$
$31$	0.666213	−	1.15392i	0.119655	−	0.207249i	0.919631	+	0.392783i	$0.128488\pi$
$32$		0			0
$33$	1.08723	+	1.88314i	0.189263	+	0.327813i
$34$		0			0
$35$	4.46336	+	3.73459i	0.754446	+	0.631261i
$36$		0			0
$37$	1.43888	+	2.49222i	0.236551	+	0.409718i	0.959722	−	0.280951i	$-0.0906497\pi$
$37$	1.43888	+	2.49222i	0.236551	+	0.409718i	−0.723172	+	0.690668i	$0.757316\pi$
$38$		0			0
$39$	0.937298	−	1.62345i	0.150088	−	0.259960i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	5.14701			0.784912			0.392456	−	0.919771i	$-0.371626\pi$
$43$	5.14701			0.784912			0.392456	+	0.919771i	$0.371626\pi$
$44$		0			0
$45$	3.00766	−	5.20942i	0.448356	−	0.776575i
$46$		0			0
$47$	−4.06236	−	7.03622i	−0.592557	−	1.02634i	−0.993887	−	0.110405i	$-0.964785\pi$
$47$	−4.06236	−	7.03622i	−0.592557	−	1.02634i	0.401330	−	0.915934i	$-0.368548\pi$
$48$		0			0
$49$	5.34971	−	4.51448i	0.764245	−	0.644926i
$50$		0			0
$51$	−2.05697	−	3.56278i	−0.288034	−	0.498889i
$52$		0			0
$53$	0.815377	−	1.41227i	0.112001	−	0.193991i	−0.804576	−	0.593849i	$-0.797607\pi$
$53$	0.815377	−	1.41227i	0.112001	−	0.193991i	0.916577	+	0.399859i	$0.130941\pi$
$54$		0			0
$55$	9.28598			1.25212
$56$		0			0
$57$	−0.587265			−0.0777852
$58$		0			0
$59$	1.48989	−	2.58057i	0.193967	−	0.335962i	−0.752594	−	0.658485i	$-0.771198\pi$
$59$	1.48989	−	2.58057i	0.193967	−	0.335962i	0.946562	+	0.322523i	$0.104531\pi$
$60$		0			0
$61$	−5.13542	−	8.89481i	−0.657524	−	1.13886i	−0.981255	−	0.192715i	$-0.938271\pi$
$61$	−5.13542	−	8.89481i	−0.657524	−	1.13886i	0.323731	−	0.946149i	$-0.395063\pi$
$62$		0			0
$63$	−5.54906	−	4.64302i	−0.699116	−	0.584965i
$64$		0			0
$65$	−4.00269	−	6.93287i	−0.496473	−	0.859916i
$66$		0			0
$67$	−1.23404	+	2.13742i	−0.150762	+	0.261128i	−0.931508	−	0.363721i	$-0.881506\pi$
$67$	−1.23404	+	2.13742i	−0.150762	+	0.261128i	0.780746	+	0.624849i	$0.214839\pi$
$68$		0			0
$69$	3.82935			0.461000
$70$		0			0
$71$	13.0326			1.54668			0.773342	−	0.633989i	$-0.218584\pi$
$71$	13.0326			1.54668			0.773342	+	0.633989i	$0.218584\pi$
$72$		0			0
$73$	−5.75997	+	9.97656i	−0.674154	+	1.16767i	0.302562	+	0.953130i	$0.402158\pi$
$73$	−5.75997	+	9.97656i	−0.674154	+	1.16767i	−0.976716	+	0.214538i	$0.931175\pi$
$74$		0			0
$75$	−0.0416197	−	0.0720874i	−0.00480583	−	0.00832393i
$76$		0			0
$77$	1.92415	−	11.0023i	0.219278	−	1.25383i
$78$		0			0
$79$	−4.53471	−	7.85434i	−0.510194	−	0.883683i	−0.999930	−	0.0118117i	$-0.996240\pi$
$79$	−4.53471	−	7.85434i	−0.510194	−	0.883683i	0.489736	−	0.871871i	$-0.337093\pi$
$80$		0			0
$81$	−3.34130	+	5.78731i	−0.371256	+	0.643034i
$82$		0			0
$83$	7.51957			0.825380			0.412690	−	0.910872i	$-0.364589\pi$
$83$	7.51957			0.825380			0.412690	+	0.910872i	$0.364589\pi$
$84$		0			0
$85$	−17.5684			−1.90556
$86$		0			0
$87$	1.56602	−	2.71243i	0.167895	−	0.290803i
$88$		0			0
$89$	8.99097	+	15.5728i	0.953041	+	1.65072i	0.738788	+	0.673938i	$0.235399\pi$
$89$	8.99097	+	15.5728i	0.953041	+	1.65072i	0.214254	+	0.976778i	$0.431268\pi$
$90$		0			0
$91$	−9.04367	+	3.30595i	−0.948035	+	0.346558i
$92$		0			0
$93$	−0.343154	−	0.594361i	−0.0355835	−	0.0616323i
$94$		0			0
$95$	−1.25395	+	2.17190i	−0.128652	+	0.222832i
$96$		0			0
$97$	13.2426			1.34459			0.672293	−	0.740285i	$-0.265309\pi$
$97$	13.2426			1.34459			0.672293	+	0.740285i	$0.265309\pi$
$98$		0			0
$99$	−11.5448			−1.16029
$100$		0			0
$101$	−2.95305	+	5.11483i	−0.293839	+	0.508944i	−0.974714	−	0.223455i	$-0.928266\pi$
$101$	−2.95305	+	5.11483i	−0.293839	+	0.508944i	0.680875	+	0.732400i	$0.261600\pi$
$102$		0			0
$103$	2.16437	+	3.74879i	0.213261	+	0.369379i	0.952733	−	0.303808i	$-0.0982581\pi$
$103$	2.16437	+	3.74879i	0.213261	+	0.369379i	−0.739472	+	0.673187i	$0.764925\pi$
$104$		0			0
$105$	2.81540	−	1.02918i	0.274755	−	0.100438i
$106$		0			0
$107$	5.83928	+	10.1139i	0.564504	+	0.977750i	0.997096	+	0.0761599i	$0.0242659\pi$
$107$	5.83928	+	10.1139i	0.564504	+	0.977750i	−0.432591	+	0.901590i	$0.642401\pi$
$108$		0			0
$109$	−7.62328	+	13.2039i	−0.730178	+	1.26470i	0.226629	+	0.973981i	$0.427229\pi$
$109$	−7.62328	+	13.2039i	−0.730178	+	1.26470i	−0.956807	+	0.290724i	$0.906104\pi$
$110$		0			0
$111$	1.48228			0.140692
$112$		0			0
$113$	17.2122			1.61919			0.809594	−	0.586990i	$-0.199687\pi$
$113$	17.2122			1.61919			0.809594	+	0.586990i	$0.199687\pi$
$114$		0			0
$115$	8.17655	−	14.1622i	0.762467	−	1.32063i
$116$		0			0
$117$	4.97634	+	8.61927i	0.460062	+	0.796852i
$118$		0			0
$119$	−3.64037	+	20.8156i	−0.333712	+	1.90817i
$120$		0			0
$121$	−3.41094	−	5.90793i	−0.310086	−	0.537084i
$122$		0			0
$123$	−0.257541	+	0.446074i	−0.0232217	+	0.0402211i
$124$		0			0
$125$	−11.3536			−1.01550
$126$		0			0
$127$	−8.42630			−0.747713			−0.373857	−	0.927487i	$-0.621965\pi$
$127$	−8.42630			−0.747713			−0.373857	+	0.927487i	$0.621965\pi$
$128$		0			0
$129$	1.32557	−	2.29595i	0.116710	−	0.202147i
$130$		0			0
$131$	5.92331	+	10.2595i	0.517522	+	0.896375i	0.999793	+	0.0203524i	$0.00647883\pi$
$131$	5.92331	+	10.2595i	0.517522	+	0.896375i	−0.482271	+	0.876022i	$0.660188\pi$
$132$		0			0
$133$	2.31350	+	1.93575i	0.200606	+	0.167851i
$134$		0			0
$135$	−3.24868	−	5.62688i	−0.279602	−	0.484285i
$136$		0			0
$137$	8.80882	−	15.2573i	0.752589	−	1.30352i	−0.193976	−	0.981006i	$-0.562138\pi$
$137$	8.80882	−	15.2573i	0.752589	−	1.30352i	0.946564	−	0.322515i	$-0.104528\pi$
$138$		0			0
$139$	−3.43664			−0.291492			−0.145746	−	0.989322i	$-0.546558\pi$
$139$	−3.43664			−0.291492			−0.145746	+	0.989322i	$0.546558\pi$
$140$		0			0
$141$	−4.18490			−0.352432
$142$		0			0
$143$	−7.68207	+	13.3057i	−0.642407	+	1.11268i
$144$		0			0
$145$	−6.68764	−	11.5833i	−0.555378	−	0.961943i
$146$		0			0
$147$	−0.636024	−	3.54903i	−0.0524584	−	0.292719i
$148$		0			0
$149$	−10.1427	−	17.5677i	−0.830926	−	1.43921i	−0.897305	−	0.441412i	$-0.854478\pi$
$149$	−10.1427	−	17.5677i	−0.830926	−	1.43921i	0.0663787	−	0.997795i	$-0.478855\pi$
$150$		0			0
$151$	−0.396311	+	0.686431i	−0.0322513	+	0.0558610i	−0.881701	−	0.471809i	$-0.843601\pi$
$151$	−0.396311	+	0.686431i	−0.0322513	+	0.0558610i	0.849449	+	0.527670i	$0.176934\pi$
$152$		0			0
$153$	21.8419			1.76581
$154$		0			0
$155$	−2.93085			−0.235412
$156$		0			0
$157$	−2.64916	+	4.58848i	−0.211426	+	0.366201i	−0.952161	−	0.305597i	$-0.901144\pi$
$157$	−2.64916	+	4.58848i	−0.211426	+	0.366201i	0.740735	+	0.671797i	$0.234477\pi$
$158$		0			0
$159$	−0.419986	−	0.727437i	−0.0333071	−	0.0576895i
$160$		0			0
$161$	−15.0855	−	12.6224i	−1.18891	−	0.994783i
$162$		0			0
$163$	−4.66608	−	8.08189i	−0.365476	−	0.633023i	0.623377	−	0.781922i	$-0.285760\pi$
$163$	−4.66608	−	8.08189i	−0.365476	−	0.633023i	−0.988852	+	0.148899i	$0.952427\pi$
$164$		0			0
$165$	2.39152	−	4.14223i	0.186179	−	0.322472i
$166$		0			0
$167$	5.22005			0.403939			0.201970	−	0.979392i	$-0.435266\pi$
$167$	5.22005			0.403939			0.201970	+	0.979392i	$0.435266\pi$
$168$		0			0
$169$	0.245336			0.0188720
$170$		0			0
$171$	1.55897	−	2.70021i	0.119217	−	0.206490i
$172$		0			0
$173$	0.0939329	+	0.162697i	0.00714158	+	0.0123696i	0.869574	−	0.493802i	$-0.164393\pi$
$173$	0.0939329	+	0.162697i	0.00714158	+	0.0123696i	−0.862433	+	0.506172i	$0.831060\pi$
$174$		0			0
$175$	−0.0736572	+	0.421172i	−0.00556796	+	0.0318376i
$176$		0			0
$177$	−0.767416	−	1.32920i	−0.0576825	−	0.0999091i
$178$		0			0
$179$	−6.69325	+	11.5931i	−0.500277	+	0.866506i	0.499723	+	0.866185i	$0.333435\pi$
$179$	−6.69325	+	11.5931i	−0.500277	+	0.866506i	−1.00000		0.000320215i	$0.999898\pi$
$180$		0			0
$181$	−0.303123			−0.0225309			−0.0112655	−	0.999937i	$-0.503586\pi$
$181$	−0.303123			−0.0225309			−0.0112655	+	0.999937i	$0.503586\pi$
$182$		0			0
$183$	−5.29033			−0.391072
$184$		0			0
$185$	3.16501	−	5.48197i	0.232697	−	0.403042i
$186$		0			0
$187$	16.8589	+	29.2005i	1.23284	+	2.13535i
$188$		0			0
$189$	−7.34006	+	2.68319i	−0.533911	+	0.195173i
$190$		0			0
$191$	0.508917	+	0.881470i	0.0368239	+	0.0637809i	0.883850	−	0.467770i	$-0.154943\pi$
$191$	0.508917	+	0.881470i	0.0368239	+	0.0637809i	−0.847026	+	0.531551i	$0.821609\pi$
$192$		0			0
$193$	−8.55993	+	14.8262i	−0.616157	+	1.06722i	0.374023	+	0.927419i	$0.377978\pi$
$193$	−8.55993	+	14.8262i	−0.616157	+	1.06722i	−0.990180	+	0.139796i	$0.955355\pi$
$194$		0			0
$195$	−4.12343			−0.295285
$196$		0			0
$197$	−4.81082			−0.342757			−0.171379	−	0.985205i	$-0.554822\pi$
$197$	−4.81082			−0.342757			−0.171379	+	0.985205i	$0.554822\pi$
$198$		0			0
$199$	6.27674	−	10.8716i	0.444946	−	0.770669i	−0.553102	−	0.833113i	$-0.686556\pi$
$199$	6.27674	−	10.8716i	0.444946	−	0.770669i	0.998048	+	0.0624441i	$0.0198895\pi$
$200$		0			0
$201$	0.635633	+	1.10095i	0.0448341	+	0.0776549i
$202$		0			0
$203$	−15.1100	+	5.52353i	−1.06052	+	0.387676i
$204$		0			0
$205$	1.09982	+	1.90494i	0.0768146	+	0.133047i
$206$		0			0
$207$	−10.1655	+	17.6071i	−0.706549	+	1.22378i
$208$		0			0
$209$	4.81321			0.332937
$210$		0			0
$211$	20.7515			1.42859			0.714297	−	0.699843i	$-0.246747\pi$
$211$	20.7515			1.42859			0.714297	+	0.699843i	$0.246747\pi$
$212$		0			0
$213$	3.35642	−	5.81350i	0.229978	−	0.398334i
$214$		0			0
$215$	−5.66077	−	9.80475i	−0.386061	−	0.668678i
$216$		0			0
$217$	−0.607304	+	3.47257i	−0.0412265	+	0.235733i
$218$		0			0
$219$	2.96686	+	5.13874i	0.200482	+	0.347244i
$220$		0			0
$221$	14.5340	−	25.1736i	0.977660	−	1.69336i
$222$		0			0
$223$	−11.6034			−0.777022			−0.388511	−	0.921444i	$-0.627010\pi$
$223$	−11.6034			−0.777022			−0.388511	+	0.921444i	$0.627010\pi$
$224$		0			0
$225$	0.441937			0.0294625
$226$		0			0
$227$	0.347298	−	0.601538i	0.0230510	−	0.0399255i	−0.854270	−	0.519830i	$-0.825995\pi$
$227$	0.347298	−	0.601538i	0.0230510	−	0.0399255i	0.877321	+	0.479904i	$0.159329\pi$
$228$		0			0
$229$	−12.5856	−	21.7989i	−0.831681	−	1.44051i	−0.896704	−	0.442630i	$-0.854045\pi$
$229$	−12.5856	−	21.7989i	−0.831681	−	1.44051i	0.0650231	−	0.997884i	$-0.479288\pi$
$230$		0			0
$231$	−4.41230	−	3.69186i	−0.290308	−	0.242907i
$232$		0			0
$233$	−1.47199	−	2.54955i	−0.0964330	−	0.167027i	0.813773	−	0.581183i	$-0.197410\pi$
$233$	−1.47199	−	2.54955i	−0.0964330	−	0.167027i	−0.910206	+	0.414156i	$0.864077\pi$
$234$		0			0
$235$	−8.93572	+	15.4771i	−0.582902	+	1.00962i
$236$		0			0
$237$	−4.67149			−0.303446
$238$		0			0
$239$	7.56259			0.489183			0.244592	−	0.969626i	$-0.421346\pi$
$239$	7.56259			0.489183			0.244592	+	0.969626i	$0.421346\pi$
$240$		0			0
$241$	3.79530	−	6.57365i	0.244477	−	0.423446i	−0.717508	−	0.696551i	$-0.754717\pi$
$241$	3.79530	−	6.57365i	0.244477	−	0.423446i	0.961984	+	0.273105i	$0.0880505\pi$
$242$		0			0
$243$	6.15180	+	10.6552i	0.394638	+	0.683533i
$244$		0			0
$245$	−14.4835	−	5.22577i	−0.925319	−	0.333862i
$246$		0			0
$247$	−2.07472	−	3.59352i	−0.132011	−	0.228650i
$248$		0			0
$249$	1.93660	−	3.35428i	0.122727	−	0.212569i
$250$		0			0
$251$	−23.7549			−1.49940			−0.749698	−	0.661780i	$-0.769801\pi$
$251$	−23.7549			−1.49940			−0.749698	+	0.661780i	$0.769801\pi$
$252$		0			0
$253$	−31.3853			−1.97318
$254$		0			0
$255$	−4.52459	+	7.83682i	−0.283341	+	0.490761i
$256$		0			0
$257$	0.768856	+	1.33170i	0.0479599	+	0.0830690i	0.889009	−	0.457890i	$-0.151395\pi$
$257$	0.768856	+	1.33170i	0.0479599	+	0.0830690i	−0.841049	+	0.540959i	$0.818061\pi$
$258$		0			0
$259$	−5.83938	−	4.88593i	−0.362841	−	0.303597i
$260$		0			0
$261$	8.31439	+	14.4009i	0.514648	+	0.891396i
$262$		0			0
$263$	−8.18633	+	14.1791i	−0.504791	+	0.874323i	0.495194	+	0.868782i	$0.335097\pi$
$263$	−8.18633	+	14.1791i	−0.504791	+	0.874323i	−0.999985	+	0.00554073i	$0.998236\pi$
$264$		0			0
$265$	−3.58707			−0.220352
$266$		0			0
$267$	9.26217			0.566836
$268$		0			0
$269$	−9.32903	+	16.1584i	−0.568801	+	0.985192i	0.427884	+	0.903834i	$0.359259\pi$
$269$	−9.32903	+	16.1584i	−0.568801	+	0.985192i	−0.996685	+	0.0813585i	$0.974074\pi$
$270$		0			0
$271$	−8.16354	−	14.1397i	−0.495900	−	0.858924i	0.504089	−	0.863652i	$-0.331828\pi$
$271$	−8.16354	−	14.1397i	−0.495900	−	0.858924i	−0.999989	+	0.00472805i	$0.998495\pi$
$272$		0			0
$273$	−0.854418	+	4.88556i	−0.0517117	+	0.295688i
$274$		0			0
$275$	0.341114	+	0.590826i	0.0205699	+	0.0356282i
$276$		0			0
$277$	9.62471	−	16.6705i	0.578293	−	1.00163i	−0.417383	−	0.908731i	$-0.637052\pi$
$277$	9.62471	−	16.6705i	0.578293	−	1.00163i	0.995675	−	0.0929015i	$-0.0296142\pi$
$278$		0			0
$279$	3.64378			0.218147
$280$		0			0
$281$	25.4587			1.51874			0.759369	−	0.650660i	$-0.225508\pi$
$281$	25.4587			1.51874			0.759369	+	0.650660i	$0.225508\pi$
$282$		0			0
$283$	3.36268	−	5.82433i	0.199891	−	0.346221i	−0.748602	−	0.663019i	$-0.769275\pi$
$283$	3.36268	−	5.82433i	0.199891	−	0.346221i	0.948493	+	0.316799i	$0.102608\pi$
$284$		0			0
$285$	0.645885	+	1.11871i	0.0382589	+	0.0662664i
$286$		0			0
$287$	2.48493	−	0.908374i	0.146681	−	0.0536196i
$288$		0			0
$289$	−23.3959	−	40.5229i	−1.37623	−	2.38370i
$290$		0			0
$291$	3.41052	−	5.90720i	0.199928	−	0.346286i
$292$		0			0
$293$	−14.0817			−0.822660			−0.411330	−	0.911487i	$-0.634936\pi$
$293$	−14.0817			−0.822660			−0.411330	+	0.911487i	$0.634936\pi$
$294$		0			0
$295$	−6.55444			−0.381614
$296$		0			0
$297$	−6.23495	+	10.7993i	−0.361789	+	0.626636i
$298$		0			0
$299$	13.5285	+	23.4321i	0.782375	+	1.35511i
$300$		0			0
$301$	−12.7899	+	4.67541i	−0.737200	+	0.269486i
$302$		0			0
$303$	1.52106	+	2.63456i	0.0873827	+	0.151351i
$304$		0			0
$305$	−11.2961	+	19.5653i	−0.646810	+	1.12031i
$306$		0			0
$307$	−22.4646			−1.28212			−0.641062	−	0.767489i	$-0.721506\pi$
$307$	−22.4646			−1.28212			−0.641062	+	0.767489i	$0.721506\pi$
$308$		0			0
$309$	2.22965			0.126840
$310$		0			0
$311$	7.56259	−	13.0988i	0.428835	−	0.742764i	−0.567935	−	0.823074i	$-0.692257\pi$
$311$	7.56259	−	13.0988i	0.428835	−	0.742764i	0.996770	+	0.0803091i	$0.0255907\pi$
$312$		0			0
$313$	9.70617	+	16.8116i	0.548625	+	0.950247i	0.998369	+	0.0570894i	$0.0181820\pi$
$313$	9.70617	+	16.8116i	0.548625	+	0.950247i	−0.449744	+	0.893158i	$0.648485\pi$
$314$		0			0
$315$	−2.74171	+	15.6771i	−0.154478	+	0.883305i
$316$		0			0
$317$	−0.881809	−	1.52734i	−0.0495273	−	0.0857838i	0.840199	−	0.542278i	$-0.182438\pi$
$317$	−0.881809	−	1.52734i	−0.0495273	−	0.0857838i	−0.889726	+	0.456494i	$0.849105\pi$
$318$		0			0
$319$	−12.8351	+	22.2310i	−0.718627	+	1.24470i
$320$		0			0
$321$	6.01541			0.335747
$322$		0			0
$323$	−9.10627			−0.506686
$324$		0			0
$325$	0.294072	−	0.509348i	0.0163122	−	0.0282535i
$326$		0			0
$327$	3.92661	+	6.80109i	0.217142	+	0.376101i
$328$		0			0
$329$	16.4862	+	13.7943i	0.908913	+	0.760507i
$330$		0			0
$331$	−6.05882	−	10.4942i	−0.333023	−	0.576812i	0.650080	−	0.759866i	$-0.274735\pi$
$331$	−6.05882	−	10.4942i	−0.333023	−	0.576812i	−0.983103	+	0.183053i	$0.941402\pi$
$332$		0			0
$333$	−3.93490	+	6.81544i	−0.215631	+	0.373484i
$334$		0			0
$335$	5.42889			0.296612
$336$		0			0
$337$	5.78905			0.315349			0.157675	−	0.987491i	$-0.449600\pi$
$337$	5.78905			0.315349			0.157675	+	0.987491i	$0.449600\pi$
$338$		0			0
$339$	4.43285	−	7.67792i	0.240759	−	0.417007i
$340$		0			0
$341$	2.81249	+	4.87137i	0.152305	+	0.263799i
$342$		0			0
$343$	−9.19280	+	16.0777i	−0.496365	+	0.868114i
$344$		0			0
$345$	−4.21159	−	7.29469i	−0.226744	−	0.392733i
$346$		0			0
$347$	−5.96720	+	10.3355i	−0.320336	+	0.554839i	−0.980557	−	0.196233i	$-0.937129\pi$
$347$	−5.96720	+	10.3355i	−0.320336	+	0.554839i	0.660221	+	0.751071i	$0.270463\pi$
$348$		0			0
$349$	−3.41253			−0.182669			−0.0913344	−	0.995820i	$-0.529113\pi$
$349$	−3.41253			−0.182669			−0.0913344	+	0.995820i	$0.529113\pi$
$350$		0			0
$351$	10.7502			0.573805
$352$		0			0
$353$	1.86013	−	3.22184i	0.0990049	−	0.171481i	−0.812268	−	0.583284i	$-0.801767\pi$
$353$	1.86013	−	3.22184i	0.0990049	−	0.171481i	0.911273	+	0.411803i	$0.135101\pi$
$354$		0			0
$355$	−14.3335	−	24.8263i	−0.760742	−	1.31764i
$356$		0			0
$357$	8.34776	+	6.98475i	0.441811	+	0.369672i
$358$		0			0
$359$	−12.6910	−	21.9814i	−0.669803	−	1.16013i	−0.977959	−	0.208797i	$-0.933045\pi$
$359$	−12.6910	−	21.9814i	−0.669803	−	1.16013i	0.308156	−	0.951336i	$-0.400288\pi$
$360$		0			0
$361$	8.85004	−	15.3287i	0.465792	−	0.806775i
$362$		0			0
$363$	−3.51383			−0.184428
$364$		0			0
$365$	25.3397			1.32634
$366$		0			0
$367$	3.83003	−	6.63381i	0.199926	−	0.346282i	−0.748578	−	0.663046i	$-0.769263\pi$
$367$	3.83003	−	6.63381i	0.199926	−	0.346282i	0.948504	+	0.316765i	$0.102597\pi$
$368$		0			0
$369$	−1.36735	−	2.36831i	−0.0711812	−	0.123289i
$370$		0			0
$371$	−0.743278	+	4.25007i	−0.0385891	+	0.220652i
$372$		0			0
$373$	−16.0943	−	27.8761i	−0.833331	−	1.44337i	−0.895382	−	0.445299i	$-0.853097\pi$
$373$	−16.0943	−	27.8761i	−0.833331	−	1.44337i	0.0620506	−	0.998073i	$-0.480236\pi$
$374$		0			0
$375$	−2.92403	+	5.06457i	−0.150996	+	0.261533i
$376$		0			0
$377$	22.1301			1.13976
$378$		0			0
$379$	−4.38797			−0.225395			−0.112697	−	0.993629i	$-0.535949\pi$
$379$	−4.38797			−0.225395			−0.112697	+	0.993629i	$0.535949\pi$
$380$		0			0
$381$	−2.17012	+	3.75875i	−0.111178	+	0.192567i
$382$		0			0
$383$	−2.67692	−	4.63656i	−0.136784	−	0.236917i	0.789493	−	0.613759i	$-0.210343\pi$
$383$	−2.67692	−	4.63656i	−0.136784	−	0.236917i	−0.926278	+	0.376842i	$0.877010\pi$
$384$		0			0
$385$	−23.0750	+	8.43514i	−1.17601	+	0.429895i
$386$		0			0
$387$	7.03774	+	12.1897i	0.357748	+	0.619638i
$388$		0			0
$389$	−0.838099	+	1.45163i	−0.0424933	+	0.0736005i	−0.886490	−	0.462748i	$-0.846863\pi$
$389$	−0.838099	+	1.45163i	−0.0424933	+	0.0736005i	0.843997	+	0.536349i	$0.180197\pi$
$390$		0			0
$391$	59.3788			3.00292
$392$		0			0
$393$	6.10198			0.307804
$394$		0			0
$395$	−9.97470	+	17.2767i	−0.501882	+	0.869285i
$396$		0			0
$397$	−3.92625	−	6.80046i	−0.197053	−	0.341305i	0.750519	−	0.660849i	$-0.229804\pi$
$397$	−3.92625	−	6.80046i	−0.197053	−	0.341305i	−0.947572	+	0.319544i	$0.896470\pi$
$398$		0			0
$399$	1.45931	−	0.533457i	0.0730569	−	0.0267062i
$400$		0			0
$401$	−2.55137	−	4.41910i	−0.127409	−	0.220679i	0.795263	−	0.606265i	$-0.207333\pi$
$401$	−2.55137	−	4.41910i	−0.127409	−	0.220679i	−0.922672	+	0.385585i	$0.874000\pi$
$402$		0			0
$403$	2.42463	−	4.19958i	0.120779	−	0.209196i
$404$		0			0
$405$	14.6993			0.730414
$406$		0			0
$407$	−12.1488			−0.602192
$408$		0			0
$409$	−10.8068	+	18.7178i	−0.534360	+	0.925538i	0.464834	+	0.885398i	$0.346114\pi$
$409$	−10.8068	+	18.7178i	−0.534360	+	0.925538i	−0.999194	+	0.0401404i	$0.987219\pi$
$410$		0			0
$411$	−4.53726	−	7.85877i	−0.223807	−	0.387645i
$412$		0			0
$413$	−1.35815	+	7.76590i	−0.0668302	+	0.382135i
$414$		0			0
$415$	−8.27015	−	14.3243i	−0.405966	−	0.703153i
$416$		0			0
$417$	−0.885077	+	1.53300i	−0.0433424	+	0.0750712i
$418$		0			0
$419$	−29.2736			−1.43011			−0.715054	−	0.699069i	$-0.753598\pi$
$419$	−29.2736			−1.43011			−0.715054	+	0.699069i	$0.753598\pi$
$420$		0			0
$421$	−1.32720			−0.0646837			−0.0323419	−	0.999477i	$-0.510297\pi$
$421$	−1.32720			−0.0646837			−0.0323419	+	0.999477i	$0.510297\pi$
$422$		0			0
$423$	11.1093	−	19.2419i	0.540153	−	0.935573i
$424$		0			0
$425$	−0.645364	−	1.11780i	−0.0313048	−	0.0542214i
$426$		0			0
$427$	20.8410	+	17.4381i	1.00856	+	0.843887i
$428$		0			0
$429$	3.95689	+	6.85354i	0.191041	+	0.330892i
$430$		0			0
$431$	6.63456	−	11.4914i	0.319575	−	0.553521i	−0.660824	−	0.750541i	$-0.729793\pi$
$431$	6.63456	−	11.4914i	0.319575	−	0.553521i	0.980399	+	0.197020i	$0.0631264\pi$
$432$		0			0
$433$	−20.4388			−0.982225			−0.491113	−	0.871096i	$-0.663410\pi$
$433$	−20.4388			−0.982225			−0.491113	+	0.871096i	$0.663410\pi$
$434$		0			0
$435$	−6.88936			−0.330320
$436$		0			0
$437$	4.23816	−	7.34071i	0.202739	−	0.351154i
$438$		0			0
$439$	−0.821249	−	1.42245i	−0.0391961	−	0.0678896i	0.845762	−	0.533561i	$-0.179146\pi$
$439$	−0.821249	−	1.42245i	−0.0391961	−	0.0678896i	−0.884958	+	0.465671i	$0.845813\pi$
$440$		0			0
$441$	18.0066	+	6.49693i	0.857458	+	0.309378i
$442$		0			0
$443$	8.19296	+	14.1906i	0.389259	+	0.674217i	0.992350	−	0.123456i	$-0.0393977\pi$
$443$	8.19296	+	14.1906i	0.389259	+	0.674217i	−0.603091	+	0.797672i	$0.706064\pi$
$444$		0			0
$445$	19.7769	−	34.2545i	0.937513	−	1.62382i
$446$		0			0
$447$	−10.4487			−0.494206
$448$		0			0
$449$	39.6265			1.87009			0.935045	−	0.354528i	$-0.115358\pi$
$449$	39.6265			1.87009			0.935045	+	0.354528i	$0.115358\pi$
$450$		0			0
$451$	2.11080	−	3.65601i	0.0993936	−	0.172155i
$452$		0			0
$453$	0.204133	+	0.353568i	0.00959099	+	0.0166121i
$454$		0			0
$455$	16.2440	+	13.5917i	0.761532	+	0.637190i
$456$		0			0
$457$	−3.60983	−	6.25241i	−0.168861	−	0.292475i	0.769159	−	0.639058i	$-0.220675\pi$
$457$	−3.60983	−	6.25241i	−0.168861	−	0.292475i	−0.938020	+	0.346582i	$0.887342\pi$
$458$		0			0
$459$	11.7961	−	20.4315i	0.550595	−	0.953658i
$460$		0			0
$461$	19.4564			0.906176			0.453088	−	0.891466i	$-0.350322\pi$
$461$	19.4564			0.906176			0.453088	+	0.891466i	$0.350322\pi$
$462$		0			0
$463$	−17.9014			−0.831950			−0.415975	−	0.909376i	$-0.636560\pi$
$463$	−17.9014			−0.831950			−0.415975	+	0.909376i	$0.636560\pi$
$464$		0			0
$465$	−0.754815	+	1.30738i	−0.0350037	+	0.0606282i
$466$		0			0
$467$	0.803008	+	1.39085i	0.0371588	+	0.0643609i	0.884007	−	0.467474i	$-0.154836\pi$
$467$	0.803008	+	1.39085i	0.0371588	+	0.0643609i	−0.846848	+	0.531835i	$0.821503\pi$
$468$		0			0
$469$	1.12492	−	6.43231i	0.0519441	−	0.297017i
$470$		0			0
$471$	1.36454	+	2.36344i	0.0628745	+	0.108902i
$472$		0			0
$473$	−10.8643	+	18.8175i	−0.499541	+	0.865231i
$474$		0			0
$475$	−0.184251			−0.00845403
$476$		0			0
$477$	4.45961			0.204191
$478$		0			0
$479$	−0.966724	+	1.67442i	−0.0441708	+	0.0765060i	−0.887266	−	0.461259i	$-0.847398\pi$
$479$	−0.966724	+	1.67442i	−0.0441708	+	0.0765060i	0.843095	+	0.537765i	$0.180731\pi$
$480$		0			0
$481$	5.23669	+	9.07021i	0.238772	+	0.413566i
$482$		0			0
$483$	−9.51566	+	3.47848i	−0.432977	+	0.158277i
$484$		0			0
$485$	−14.5645	−	25.2264i	−0.661339	−	1.14547i
$486$		0			0
$487$	−15.7670	+	27.3093i	−0.714471	+	1.23750i	0.248692	+	0.968583i	$0.419999\pi$
$487$	−15.7670	+	27.3093i	−0.714471	+	1.23750i	−0.963163	+	0.268918i	$0.913334\pi$
$488$		0			0
$489$	−4.80683			−0.217372
$490$		0			0
$491$	−41.6704			−1.88056			−0.940279	−	0.340404i	$-0.889436\pi$
$491$	−41.6704			−1.88056			−0.940279	+	0.340404i	$0.889436\pi$
$492$		0			0
$493$	24.2831	−	42.0596i	1.09366	−	1.89427i
$494$		0			0
$495$	12.6971	+	21.9921i	0.570694	+	0.988471i
$496$		0			0
$497$	−32.3850	+	11.8385i	−1.45267	+	0.531028i
$498$		0			0
$499$	−2.87599	−	4.98136i	−0.128747	−	0.222996i	0.794444	−	0.607337i	$-0.207762\pi$
$499$	−2.87599	−	4.98136i	−0.128747	−	0.222996i	−0.923191	+	0.384341i	$0.874429\pi$
$500$		0			0
$501$	1.34438	−	2.32853i	0.0600623	−	0.104031i
$502$		0			0
$503$	40.6067			1.81057			0.905283	−	0.424810i	$-0.139659\pi$
$503$	40.6067			1.81057			0.905283	+	0.424810i	$0.139659\pi$
$504$		0			0
$505$	12.9913			0.578103
$506$		0			0
$507$	0.0631840	−	0.109438i	0.00280610	−	0.00486031i
$508$		0			0
$509$	6.58598	+	11.4073i	0.291919	+	0.505618i	0.974263	−	0.225413i	$-0.0723730\pi$
$509$	6.58598	+	11.4073i	0.291919	+	0.505618i	−0.682345	+	0.731030i	$0.739040\pi$
$510$		0			0
$511$	5.25065	−	30.0232i	0.232275	−	1.32815i
$512$		0			0
$513$	−1.68389	−	2.91659i	−0.0743457	−	0.128770i
$514$		0			0
$515$	4.76081	−	8.24597i	0.209787	−	0.363361i
$516$		0			0
$517$	34.2993			1.50848
$518$		0			0
$519$	0.0967662			0.00424757
$520$		0			0
$521$	−17.0978	+	29.6143i	−0.749070	+	1.29743i	0.199199	+	0.979959i	$0.436166\pi$
$521$	−17.0978	+	29.6143i	−0.749070	+	1.29743i	−0.948269	+	0.317468i	$0.897167\pi$
$522$		0			0
$523$	−17.5626	−	30.4194i	−0.767961	−	1.33015i	−0.938667	−	0.344825i	$-0.887938\pi$
$523$	−17.5626	−	30.4194i	−0.767961	−	1.33015i	0.170706	−	0.985322i	$-0.445395\pi$
$524$		0			0
$525$	0.168904	+	0.141326i	0.00737158	+	0.00616795i
$526$		0			0
$527$	−5.32103	−	9.21630i	−0.231788	−	0.401468i
$528$		0			0
$529$	−16.1356	+	27.9476i	−0.701546	+	1.21511i
$530$		0			0
$531$	8.14879			0.353627
$532$		0			0
$533$	−3.63941			−0.157641
$534$		0			0
$535$	12.8443	−	22.2469i	0.555307	−	0.961819i
$536$		0			0
$537$	3.44757	+	5.97137i	0.148774	+	0.257684i
$538$		0			0
$539$	5.21284	+	29.0878i	0.224533	+	1.25290i
$540$		0			0
$541$	−12.0223	−	20.8232i	−0.516878	−	0.895258i	−0.999808	−	0.0195994i	$-0.993761\pi$
$541$	−12.0223	−	20.8232i	−0.516878	−	0.895258i	0.482930	−	0.875659i	$-0.339572\pi$
$542$		0			0
$543$	−0.0780665	+	0.135215i	−0.00335015	+	0.00580264i
$544$		0			0
$545$	33.5369			1.43656
$546$		0			0
$547$	−34.5404			−1.47684			−0.738421	−	0.674340i	$-0.764428\pi$
$547$	−34.5404			−1.47684			−0.738421	+	0.674340i	$0.764428\pi$
$548$		0			0
$549$	14.0438	−	24.3246i	0.599375	−	1.03815i
$550$		0			0
$551$	−3.46641	−	6.00400i	−0.147674	−	0.255779i
$552$		0			0
$553$	18.4031	+	15.3982i	0.782579	+	0.654800i
$554$		0			0
$555$	−1.63024	−	2.82366i	−0.0691999	−	0.119858i
$556$		0			0
$557$	−13.3087	+	23.0514i	−0.563908	+	0.976718i	0.433242	+	0.901278i	$0.357370\pi$
$557$	−13.3087	+	23.0514i	−0.563908	+	0.976718i	−0.997150	+	0.0754402i	$0.975964\pi$
$558$		0			0
$559$	18.7321			0.792283
$560$		0			0
$561$	17.3674			0.733253
$562$		0			0
$563$	19.2357	−	33.3172i	0.810687	−	1.40415i	−0.101696	−	0.994816i	$-0.532427\pi$
$563$	19.2357	−	33.3172i	0.810687	−	1.40415i	0.912384	−	0.409336i	$-0.134240\pi$
$564$		0			0
$565$	−18.9303	−	32.7882i	−0.796403	−	1.37941i
$566$		0			0
$567$	3.04585	−	17.4162i	0.127914	−	0.731411i
$568$		0			0
$569$	11.0989	+	19.2239i	0.465291	+	0.805908i	0.999215	−	0.0396246i	$-0.0126162\pi$
$569$	11.0989	+	19.2239i	0.465291	+	0.805908i	−0.533923	+	0.845533i	$0.679283\pi$
$570$		0			0
$571$	16.1718	−	28.0104i	0.676769	−	1.17220i	−0.299180	−	0.954197i	$-0.596713\pi$
$571$	16.1718	−	28.0104i	0.676769	−	1.17220i	0.975948	−	0.218001i	$-0.0699537\pi$
$572$		0			0
$573$	0.524268			0.0219016
$574$		0			0
$575$	1.20144			0.0501035
$576$		0			0
$577$	−11.7053	+	20.2742i	−0.487299	+	0.844027i	−0.999893	−	0.0146038i	$-0.995351\pi$
$577$	−11.7053	+	20.2742i	−0.487299	+	0.844027i	0.512594	+	0.858631i	$0.328685\pi$
$578$		0			0
$579$	4.40906	+	7.63672i	0.183234	+	0.317371i
$580$		0			0
$581$	−18.6856	+	6.83058i	−0.775208	+	0.283380i
$582$		0			0
$583$	3.44219	+	5.96206i	0.142561	+	0.246923i
$584$		0			0
$585$	10.9461	−	18.9592i	0.452567	−	0.783868i
$586$		0			0
$587$	−6.45509			−0.266430			−0.133215	−	0.991087i	$-0.542530\pi$
$587$	−6.45509			−0.266430			−0.133215	+	0.991087i	$0.542530\pi$
$588$		0			0
$589$	−1.51915			−0.0625956
$590$		0			0
$591$	−1.23898	+	2.14598i	−0.0509650	+	0.0882739i
$592$		0			0
$593$	19.0547	+	33.0038i	0.782484	+	1.35530i	0.930491	+	0.366316i	$0.119381\pi$
$593$	19.0547	+	33.0038i	0.782484	+	1.35530i	−0.148007	+	0.988986i	$0.547286\pi$
$594$		0			0
$595$	43.6563	−	15.9587i	1.78973	−	0.654243i
$596$		0			0
$597$	−3.23303	−	5.59978i	−0.132319	−	0.229184i
$598$		0			0
$599$	8.24749	−	14.2851i	0.336983	−	0.583672i	−0.646880	−	0.762591i	$-0.723927\pi$
$599$	8.24749	−	14.2851i	0.336983	−	0.583672i	0.983864	+	0.178919i	$0.0572600\pi$
$600$		0			0
$601$	4.14054			0.168896			0.0844482	−	0.996428i	$-0.473087\pi$
$601$	4.14054			0.168896			0.0844482	+	0.996428i	$0.473087\pi$
$602$		0			0
$603$	−6.74945			−0.274859
$604$		0			0
$605$	−7.50283	+	12.9953i	−0.305034	+	0.528334i
$606$		0			0
$607$	20.4430	+	35.4083i	0.829756	+	1.43718i	0.898230	+	0.439526i	$0.144854\pi$
$607$	20.4430	+	35.4083i	0.829756	+	1.43718i	−0.0684739	+	0.997653i	$0.521813\pi$
$608$		0			0
$609$	−1.42755	+	8.16273i	−0.0578472	+	0.330771i
$610$		0			0
$611$	−14.7846	−	25.6077i	−0.598122	−	1.03598i
$612$		0			0
$613$	−19.2612	+	33.3613i	−0.777951	+	1.34745i	0.155170	+	0.987888i	$0.450408\pi$
$613$	−19.2612	+	33.3613i	−0.777951	+	1.34745i	−0.933121	+	0.359563i	$0.882926\pi$
$614$		0			0
$615$	1.13299			0.0456867
$616$		0			0
$617$	−26.2855			−1.05822			−0.529108	−	0.848555i	$-0.677473\pi$
$617$	−26.2855			−1.05822			−0.529108	+	0.848555i	$0.677473\pi$
$618$		0			0
$619$	23.6591	−	40.9787i	0.950938	−	1.64707i	0.207535	−	0.978228i	$-0.433456\pi$
$619$	23.6591	−	40.9787i	0.950938	−	1.64707i	0.743402	−	0.668845i	$-0.233211\pi$
$620$		0			0
$621$	10.9801	+	19.0181i	0.440615	+	0.763168i
$622$		0			0
$623$	−36.4879	−	30.5301i	−1.46186	−	1.22316i
$624$		0			0
$625$	12.0829	+	20.9283i	0.483317	+	0.837130i
$626$		0			0
$627$	1.23960	−	2.14705i	0.0495048	−	0.0857448i
$628$		0			0
$629$	22.9846			0.916457
$630$		0			0
$631$	4.48510			0.178549			0.0892746	−	0.996007i	$-0.471545\pi$
$631$	4.48510			0.178549			0.0892746	+	0.996007i	$0.471545\pi$
$632$		0			0
$633$	5.34437	−	9.25671i	0.212419	−	0.367921i
$634$		0			0
$635$	9.26739	+	16.0516i	0.367765	+	0.636988i
$636$		0			0
$637$	19.4698	−	16.4301i	0.771422	−	0.650983i
$638$		0			0
$639$	17.8201	+	30.8652i	0.704950	+	1.22101i
$640$		0			0
$641$	17.8846	−	30.9770i	0.706399	−	1.22352i	−0.259785	−	0.965666i	$-0.583652\pi$
$641$	17.8846	−	30.9770i	0.706399	−	1.22352i	0.966184	−	0.257853i	$-0.0830150\pi$
$642$		0			0
$643$	30.7547			1.21285			0.606424	−	0.795142i	$-0.292603\pi$
$643$	30.7547			1.21285			0.606424	+	0.795142i	$0.292603\pi$
$644$		0			0
$645$	−5.83152			−0.229616
$646$		0			0
$647$	−22.3228	+	38.6643i	−0.877602	+	1.52005i	−0.0236363	+	0.999721i	$0.507524\pi$
$647$	−22.3228	+	38.6643i	−0.877602	+	1.52005i	−0.853965	+	0.520330i	$0.825809\pi$
$648$		0			0
$649$	6.28973	+	10.8941i	0.246893	+	0.427632i
$650$		0			0
$651$	1.39262	+	1.16523i	0.0545809	+	0.0456690i
$652$		0			0
$653$	14.7109	+	25.4799i	0.575680	+	0.997107i	0.995967	+	0.0897162i	$0.0285960\pi$
$653$	14.7109	+	25.4799i	0.575680	+	0.997107i	−0.420287	+	0.907391i	$0.638071\pi$
$654$		0			0
$655$	13.0291	−	22.5671i	0.509090	−	0.881770i
$656$		0			0
$657$	−31.5035			−1.22907
$658$		0			0
$659$	39.7367			1.54792			0.773961	−	0.633234i	$-0.218273\pi$
$659$	39.7367			1.54792			0.773961	+	0.633234i	$0.218273\pi$
$660$		0			0
$661$	4.79493	−	8.30507i	0.186501	−	0.323030i	−0.757580	−	0.652742i	$-0.773618\pi$
$661$	4.79493	−	8.30507i	0.186501	−	0.323030i	0.944081	+	0.329713i	$0.106952\pi$
$662$		0			0
$663$	−7.48618	−	12.9664i	−0.290739	−	0.503575i
$664$		0			0
$665$	1.14307	−	6.53606i	0.0443262	−	0.253457i
$666$		0			0
$667$	22.6033	+	39.1500i	0.875202	+	1.51589i
$668$		0			0
$669$	−2.98835	+	5.17598i	−0.115536	+	0.200115i
$670$		0			0
$671$	43.3594			1.67387
$672$		0			0
$673$	28.1956			1.08686			0.543431	−	0.839454i	$-0.317125\pi$
$673$	28.1956			1.08686			0.543431	+	0.839454i	$0.317125\pi$
$674$		0			0
$675$	0.238676	−	0.413399i	0.00918664	−	0.0159117i
$676$		0			0
$677$	4.64788	+	8.05037i	0.178633	+	0.309401i	0.941412	−	0.337258i	$-0.109499\pi$
$677$	4.64788	+	8.05037i	0.178633	+	0.309401i	−0.762780	+	0.646658i	$0.776166\pi$
$678$		0			0
$679$	−32.9070	+	12.0293i	−1.26285	+	0.461641i
$680$		0			0
$681$	−0.178887	−	0.309841i	−0.00685496	−	0.0118731i
$682$		0			0
$683$	−6.60635	+	11.4425i	−0.252785	+	0.437837i	−0.964292	−	0.264843i	$-0.914680\pi$
$683$	−6.60635	+	11.4425i	−0.252785	+	0.437837i	0.711506	+	0.702680i	$0.248013\pi$
$684$		0			0
$685$	−38.7524			−1.48065
$686$		0			0
$687$	−12.9652			−0.494655
$688$		0			0
$689$	2.96750	−	5.13985i	0.113053	−	0.195813i
$690$		0			0
$691$	3.38749	+	5.86731i	0.128866	+	0.223203i	0.923238	−	0.384230i	$-0.125533\pi$
$691$	3.38749	+	5.86731i	0.128866	+	0.223203i	−0.794371	+	0.607432i	$0.792200\pi$
$692$		0			0
$693$	28.6879	−	10.4870i	1.08976	−	0.398367i
$694$		0			0
$695$	3.77968	+	6.54660i	0.143372	+	0.248327i
$696$		0			0
$697$	−3.99349	+	6.91692i	−0.151264	+	0.261997i
$698$		0			0
$699$	−1.51639			−0.0573550
$700$		0			0
$701$	29.8871			1.12882			0.564410	−	0.825494i	$-0.309104\pi$
$701$	29.8871			1.12882			0.564410	+	0.825494i	$0.309104\pi$
$702$		0			0
$703$	1.64053	−	2.84147i	0.0618736	−	0.107168i
$704$		0			0
$705$	4.60263	+	7.97198i	0.173345	+	0.300242i
$706$		0			0
$707$	2.69193	−	15.3924i	0.101240	−	0.578892i
$708$		0			0
$709$	−2.47683	−	4.29000i	−0.0930194	−	0.161114i	0.815761	−	0.578389i	$-0.196319\pi$
$709$	−2.47683	−	4.29000i	−0.0930194	−	0.161114i	−0.908780	+	0.417275i	$0.862985\pi$
$710$		0			0
$711$	12.4010	−	21.4792i	0.465075	−	0.805533i
$712$		0			0
$713$	9.90587			0.370978
$714$		0			0
$715$	33.7955			1.26388
$716$		0			0
$717$	1.94768	−	3.37347i	0.0727373	−	0.125985i
$718$		0			0
$719$	9.41738	+	16.3114i	0.351209	+	0.608312i	0.986462	−	0.163992i	$-0.0524373\pi$
$719$	9.41738	+	16.3114i	0.351209	+	0.608312i	−0.635252	+	0.772305i	$0.719104\pi$
$720$		0			0
$721$	−8.78359	−	7.34941i	−0.327118	−	0.273706i
$722$		0			0
$723$	−1.95489	−	3.38597i	−0.0727031	−	0.125925i
$724$		0			0
$725$	0.491332	−	0.851011i	0.0182476	−	0.0316058i
$726$		0			0
$727$	−42.1079			−1.56169			−0.780847	−	0.624722i	$-0.785212\pi$
$727$	−42.1079			−1.56169			−0.780847	+	0.624722i	$0.785212\pi$
$728$		0			0
$729$	−13.7105			−0.507795
$730$		0			0
$731$	20.5545	−	35.6015i	0.760237	−	1.31677i
$732$		0			0
$733$	−7.82276	−	13.5494i	−0.288940	−	0.500459i	0.684617	−	0.728903i	$-0.259970\pi$
$733$	−7.82276	−	13.5494i	−0.288940	−	0.500459i	−0.973557	+	0.228444i	$0.926636\pi$
$734$		0			0
$735$	−6.06118	+	5.11488i	−0.223570	+	0.188665i
$736$		0			0
$737$	−5.20963	−	9.02334i	−0.191899	−	0.332379i
$738$		0			0
$739$	−16.0759	+	27.8442i	−0.591360	+	1.02427i	0.402689	+	0.915337i	$0.368076\pi$
$739$	−16.0759	+	27.8442i	−0.591360	+	1.02427i	−0.994049	+	0.108929i	$0.965258\pi$
$740$		0			0
$741$	−2.13730			−0.0785157
$742$		0			0
$743$	−3.81171			−0.139838			−0.0699190	−	0.997553i	$-0.522274\pi$
$743$	−3.81171			−0.139838			−0.0699190	+	0.997553i	$0.522274\pi$
$744$		0			0
$745$	−22.3103	+	38.6426i	−0.817388	+	1.41576i
$746$		0			0
$747$	10.2818	+	17.8087i	0.376193	+	0.651585i
$748$		0			0
$749$	−23.6974	−	19.8281i	−0.865884	−	0.724503i
$750$		0			0
$751$	9.55083	+	16.5425i	0.348515	+	0.603645i	0.985986	−	0.166829i	$-0.0533528\pi$
$751$	9.55083	+	16.5425i	0.348515	+	0.603645i	−0.637471	+	0.770474i	$0.720019\pi$
$752$		0			0
$753$	−6.11786	+	10.5964i	−0.222947	+	0.386156i
$754$		0			0
$755$	1.74348			0.0634517
$756$		0			0
$757$	30.1926			1.09737			0.548684	−	0.836030i	$-0.315129\pi$
$757$	30.1926			1.09737			0.548684	+	0.836030i	$0.315129\pi$
$758$		0			0
$759$	−8.08299	+	14.0002i	−0.293394	+	0.508173i
$760$		0			0
$761$	−25.5386	−	44.2342i	−0.925774	−	1.60349i	−0.790311	−	0.612706i	$-0.790081\pi$
$761$	−25.5386	−	44.2342i	−0.925774	−	1.60349i	−0.135463	−	0.990782i	$-0.543252\pi$
$762$		0			0
$763$	6.94920	−	39.7355i	0.251578	−	1.43852i
$764$		0			0
$765$	−24.0221	−	41.6075i	−0.868522	−	1.50432i
$766$		0			0
$767$	5.42234	−	9.39176i	0.195789	−	0.339117i
$768$		0			0
$769$	−30.8036			−1.11081			−0.555404	−	0.831581i	$-0.687436\pi$
$769$	−30.8036			−1.11081			−0.555404	+	0.831581i	$0.687436\pi$
$770$		0			0
$771$	0.792047			0.0285249
$772$		0			0
$773$	−15.5951	+	27.0114i	−0.560916	+	0.971534i	0.436501	+	0.899704i	$0.356217\pi$
$773$	−15.5951	+	27.0114i	−0.560916	+	0.971534i	−0.997417	+	0.0718306i	$0.977116\pi$
$774$		0			0
$775$	−0.107663	−	0.186478i	−0.00386736	−	0.00669847i
$776$		0			0
$777$	−3.68336	+	1.34647i	−0.132140	+	0.0483043i
$778$		0			0
$779$	0.570070	+	0.987390i	0.0204249	+	0.0353769i
$780$		0			0
$781$	−27.5092	+	47.6473i	−0.984356	+	1.70495i
$782$		0			0
$783$	17.9613			0.641885
$784$		0			0
$785$	11.6544			0.415963
$786$		0			0
$787$	−6.21333	+	10.7618i	−0.221481	+	0.383617i	−0.955258	−	0.295774i	$-0.904423\pi$
$787$	−6.21333	+	10.7618i	−0.221481	+	0.383617i	0.733777	+	0.679391i	$0.237756\pi$
$788$		0			0
$789$	4.21663	+	7.30342i	0.150116	+	0.260009i
$790$		0			0
$791$	−42.7711	+	15.6351i	−1.52076	+	0.555921i
$792$		0			0
$793$	−18.6899	−	32.3719i	−0.663699	−	1.14956i
$794$		0			0
$795$	−0.923816	+	1.60010i	−0.0327644	+	0.0567496i
$796$		0			0
$797$	17.3519			0.614636			0.307318	−	0.951607i	$-0.400568\pi$
$797$	17.3519			0.614636			0.307318	+	0.951607i	$0.400568\pi$
$798$		0			0
$799$	−64.8920			−2.29571
$800$		0			0
$801$	−24.5875	+	42.5869i	−0.868758	+	1.50473i
$802$		0			0
$803$	−24.3163	−	42.1170i	−0.858103	−	1.48628i
$804$		0			0
$805$	−7.45354	+	42.6194i	−0.262703	+	1.50214i
$806$		0			0
$807$	4.80521	+	8.32287i	0.169152	+	0.292979i
$808$		0			0
$809$	−13.0186	+	22.5488i	−0.457708	+	0.792774i	−0.998839	−	0.0481644i	$-0.984663\pi$
$809$	−13.0186	+	22.5488i	−0.457708	+	0.792774i	0.541131	+	0.840938i	$0.317996\pi$
$810$		0			0
$811$	16.2483			0.570557			0.285278	−	0.958445i	$-0.407914\pi$
$811$	16.2483			0.570557			0.285278	+	0.958445i	$0.407914\pi$
$812$		0			0
$813$	−8.40978			−0.294944
$814$		0			0
$815$	−10.2637	+	17.7772i	−0.359521	+	0.622709i
$816$		0			0
$817$	−2.93416	−	5.08211i	−0.102653	−	0.177800i
$818$		0			0
$819$	−20.1953	−	16.8979i	−0.705682	−	0.590459i
$820$		0			0
$821$	−15.2725	−	26.4527i	−0.533013	−	0.923205i	−0.999257	−	0.0385487i	$-0.987727\pi$
$821$	−15.2725	−	26.4527i	−0.533013	−	0.923205i	0.466244	−	0.884656i	$-0.345607\pi$
$822$		0			0
$823$	23.6809	−	41.0165i	0.825464	−	1.42975i	−0.0761005	−	0.997100i	$-0.524247\pi$
$823$	23.6809	−	41.0165i	0.825464	−	1.42975i	0.901564	−	0.432645i	$-0.142420\pi$
$824$		0			0
$825$	0.351403			0.0122343
$826$		0			0
$827$	−49.3914			−1.71751			−0.858754	−	0.512388i	$-0.828761\pi$
$827$	−49.3914			−1.71751			−0.858754	+	0.512388i	$0.828761\pi$
$828$		0			0
$829$	0.874881	−	1.51534i	0.0303859	−	0.0526299i	−0.850433	−	0.526084i	$-0.823660\pi$
$829$	0.874881	−	1.51534i	0.0303859	−	0.0526299i	0.880818	+	0.473454i	$0.156993\pi$
$830$		0			0
$831$	−4.95751	−	8.58666i	−0.171974	−	0.297868i
$832$		0			0
$833$	−9.86233	−	55.0321i	−0.341710	−	1.90675i
$834$		0			0
$835$	−5.74110	−	9.94388i	−0.198679	−	0.344122i
$836$		0			0
$837$	1.96788	−	3.40848i	0.0680200	−	0.117814i
$838$		0			0
$839$	48.9756			1.69083			0.845413	−	0.534113i	$-0.179354\pi$
$839$	48.9756			1.69083			0.845413	+	0.534113i	$0.179354\pi$
$840$		0			0
$841$	7.97468			0.274989
$842$		0			0
$843$	6.55666	−	11.3565i	0.225823	−	0.391137i
$844$		0			0
$845$	−0.269825	−	0.467350i	−0.00928225	−	0.0160773i
$846$		0			0
$847$	13.8426	+	11.5823i	0.475636	+	0.397974i
$848$		0			0
$849$	−1.73206	−	3.00001i	−0.0594440	−	0.102960i
$850$		0			0
$851$	−10.6973	+	18.5283i	−0.366699	+	0.635141i
$852$		0			0
$853$	−26.3270			−0.901420			−0.450710	−	0.892670i	$-0.648829\pi$
$853$	−26.3270			−0.901420			−0.450710	+	0.892670i	$0.648829\pi$
$854$		0			0
$855$	−6.85831			−0.234549
$856$		0			0
$857$	20.6048	−	35.6886i	0.703847	−	1.21910i	−0.263259	−	0.964725i	$-0.584797\pi$
$857$	20.6048	−	35.6886i	0.703847	−	1.21910i	0.967106	−	0.254373i	$-0.0818692\pi$
$858$		0			0
$859$	6.56405	+	11.3693i	0.223962	+	0.387914i	0.956008	−	0.293342i	$-0.0947674\pi$
$859$	6.56405	+	11.3693i	0.223962	+	0.387914i	−0.732045	+	0.681256i	$0.761434\pi$
$860$		0			0
$861$	0.234768	−	1.34240i	0.00800087	−	0.0457490i
$862$		0			0
$863$	16.8527	+	29.1898i	0.573673	+	0.993631i	0.996184	+	0.0872731i	$0.0278153\pi$
$863$	16.8527	+	29.1898i	0.573673	+	0.993631i	−0.422511	+	0.906358i	$0.638851\pi$
$864$		0			0
$865$	0.206618	−	0.357873i	0.00702523	−	0.0121680i
$866$		0			0
$867$	−24.1016			−0.818533
$868$		0			0
$869$	38.2874			1.29881
$870$		0			0
$871$	−4.49119	+	7.77897i	−0.152178	+	0.263580i
$872$		0			0
$873$	18.1073	+	31.3627i	0.612838	+	1.06147i
$874$		0			0
$875$	28.2130	−	10.3134i	0.953773	−	0.348655i
$876$		0			0
$877$	−6.02346	−	10.4329i	−0.203398	−	0.352295i	0.746223	−	0.665696i	$-0.231865\pi$
$877$	−6.02346	−	10.4329i	−0.203398	−	0.352295i	−0.949621	+	0.313401i	$0.898532\pi$
$878$		0			0
$879$	−3.62660	+	6.28146i	−0.122322	+	0.211868i
$880$		0			0
$881$	−25.8023			−0.869302			−0.434651	−	0.900599i	$-0.643128\pi$
$881$	−25.8023			−0.869302			−0.434651	+	0.900599i	$0.643128\pi$
$882$		0			0
$883$	55.2747			1.86014			0.930070	−	0.367381i	$-0.119746\pi$
$883$	55.2747			1.86014			0.930070	+	0.367381i	$0.119746\pi$
$884$		0			0
$885$	−1.68804	+	2.92376i	−0.0567427	+	0.0982813i
$886$		0			0
$887$	−26.2885	−	45.5331i	−0.882682	−	1.52885i	−0.848347	−	0.529440i	$-0.822402\pi$
$887$	−26.2885	−	45.5331i	−0.882682	−	1.52885i	−0.0343352	−	0.999410i	$-0.510931\pi$
$888$		0			0
$889$	20.9387	−	7.65423i	0.702262	−	0.256715i
$890$		0			0
$891$	−14.1056	−	24.4317i	−0.472557	−	0.818492i
$892$		0			0
$893$	−4.63166	+	8.02228i	−0.154993	+	0.268455i
$894$		0			0
$895$	29.4454			0.984252
$896$		0			0
$897$	13.9366			0.465330
$898$		0			0
$899$	4.05103	−	7.01659i	0.135109	−	0.234016i
$900$		0			0
$901$	−6.51240	−	11.2798i	−0.216959	−	0.375785i
$902$		0			0
$903$	−1.20835	+	6.90937i	−0.0402115	+	0.229929i
$904$		0			0
$905$	0.333380	+	0.577431i	0.0110819	+	0.0191944i
$906$		0			0
$907$	17.8980	−	31.0003i	0.594294	−	1.02935i	−0.399352	−	0.916798i	$-0.630765\pi$
$907$	17.8980	−	31.0003i	0.594294	−	1.02935i	0.993646	−	0.112550i	$-0.0359019\pi$
$908$		0			0
$909$	−16.1513			−0.535706
$910$		0			0
$911$	5.12715			0.169870			0.0849350	−	0.996386i	$-0.472932\pi$
$911$	5.12715			0.169870			0.0849350	+	0.996386i	$0.472932\pi$
$912$		0			0
$913$	−15.8723	+	27.4916i	−0.525296	+	0.909840i
$914$		0			0
$915$	5.81839	+	10.0778i	0.192350	+	0.333160i
$916$		0			0
$917$	−24.0384	−	20.1135i	−0.793819	−	0.664205i
$918$		0			0
$919$	−1.36857	−	2.37043i	−0.0451449	−	0.0781932i	0.842570	−	0.538587i	$-0.181042\pi$
$919$	−1.36857	−	2.37043i	−0.0451449	−	0.0781932i	−0.887715	+	0.460394i	$0.847708\pi$
$920$		0			0
$921$	−5.78556	+	10.0209i	−0.190641	+	0.330199i
$922$		0			0
$923$	47.4310			1.56121
$924$		0			0
$925$	0.465058			0.0152910
$926$		0			0
$927$	−5.91887	+	10.2518i	−0.194401	+	0.336713i
$928$		0			0
$929$	−6.83348	−	11.8359i	−0.224199	−	0.388325i	0.731880	−	0.681434i	$-0.238643\pi$
$929$	−6.83348	−	11.8359i	−0.224199	−	0.388325i	−0.956079	+	0.293109i	$0.905310\pi$
$930$		0			0
$931$	−7.50727	−	2.70868i	−0.246041	−	0.0887735i
$932$		0			0
$933$	−3.89535	−	6.74695i	−0.127528	−	0.220885i
$934$		0			0
$935$	37.0834	−	64.2304i	1.21276	−	2.10056i
$936$		0			0
$937$	6.96389			0.227500			0.113750	−	0.993509i	$-0.463714\pi$
$937$	6.96389			0.227500			0.113750	+	0.993509i	$0.463714\pi$
$938$		0			0
$939$	9.99895			0.326303
$940$		0			0
$941$	11.2749	−	19.5287i	0.367551	−	0.636617i	−0.621631	−	0.783310i	$-0.713530\pi$
$941$	11.2749	−	19.5287i	0.367551	−	0.636617i	0.989182	+	0.146693i	$0.0468631\pi$
$942$		0			0
$943$	−3.71723	−	6.43843i	−0.121050	−	0.209664i
$944$		0			0
$945$	13.1840	+	11.0314i	0.428877	+	0.358850i
$946$		0			0
$947$	21.9884	+	38.0851i	0.714528	+	1.23760i	0.963141	+	0.268996i	$0.0866918\pi$
$947$	21.9884	+	38.0851i	0.714528	+	1.23760i	−0.248613	+	0.968603i	$0.579975\pi$
$948$		0			0
$949$	−20.9629	+	36.3088i	−0.680485	+	1.17863i
$950$		0			0
$951$	−0.908407			−0.0294571
$952$		0			0
$953$	6.89729			0.223425			0.111713	−	0.993741i	$-0.464366\pi$
$953$	6.89729			0.223425			0.111713	+	0.993741i	$0.464366\pi$
$954$		0			0
$955$	1.11943	−	1.93891i	0.0362240	−	0.0627417i
$956$		0			0
$957$	6.61112	+	11.4508i	0.213707	+	0.370152i
$958$		0			0
$959$	−8.02991	+	45.9150i	−0.259299	+	1.48267i
$960$		0			0
$961$	14.6123	+	25.3093i	0.471365	+	0.816428i
$962$		0			0
$963$	−15.9686	+	27.6585i	−0.514581	+	0.891281i
$964$		0			0
$965$	37.6574			1.21224
$966$		0			0
$967$	24.7226			0.795025			0.397512	−	0.917597i	$-0.369874\pi$
$967$	24.7226			0.795025			0.397512	+	0.917597i	$0.369874\pi$
$968$		0			0
$969$	−2.34524	+	4.06207i	−0.0753399	+	0.130492i
$970$		0			0
$971$	−25.9239	−	44.9015i	−0.831937	−	1.44096i	−0.896500	−	0.443043i	$-0.853899\pi$
$971$	−25.9239	−	44.9015i	−0.831937	−	1.44096i	0.0645639	−	0.997914i	$-0.479434\pi$
$972$		0			0
$973$	8.53981	−	3.12176i	0.273774	−	0.100079i
$974$		0			0
$975$	−0.151471	−	0.262356i	−0.00485096	−	0.00840211i
$976$		0			0
$977$	−4.99945	+	8.65931i	−0.159947	+	0.277036i	−0.934849	−	0.355045i	$-0.884466\pi$
$977$	−4.99945	+	8.65931i	−0.159947	+	0.277036i	0.774903	+	0.632081i	$0.217799\pi$
$978$		0			0
$979$	−75.9126			−2.42618
$980$		0			0
$981$	−41.6946			−1.33121
$982$		0			0
$983$	−0.613835	+	1.06319i	−0.0195783	+	0.0339106i	−0.875649	−	0.482949i	$-0.839566\pi$
$983$	−0.613835	+	1.06319i	−0.0195783	+	0.0339106i	0.856070	+	0.516859i	$0.172899\pi$
$984$		0			0
$985$	5.29103	+	9.16433i	0.168586	+	0.292000i
$986$		0			0
$987$	10.3992	−	3.80145i	0.331009	−	0.121002i
$988$		0			0
$989$	19.1326	+	33.1386i	0.608382	+	1.05375i
$990$		0			0
$991$	−21.8599	+	37.8625i	−0.694403	+	1.20274i	0.275979	+	0.961164i	$0.410998\pi$
$991$	−21.8599	+	37.8625i	−0.694403	+	1.20274i	−0.970382	+	0.241577i	$0.922335\pi$
$992$		0			0
$993$	−6.24157			−0.198070
$994$		0			0
$995$	−27.6131			−0.875393
$996$		0			0
$997$	−2.89602	+	5.01606i	−0.0917180	+	0.158860i	−0.908234	−	0.418462i	$-0.862569\pi$
$997$	−2.89602	+	5.01606i	−0.0917180	+	0.158860i	0.816516	+	0.577323i	$0.195902\pi$
$998$		0			0
$999$	4.25022	+	7.36159i	0.134471	+	0.232911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.165.8	✓	30
7.2	even	3	inner	1148.2.i.e.821.8	yes	30
7.3	odd	6		8036.2.a.r.1.8		15
7.4	even	3		8036.2.a.q.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.8	✓	30	1.1	even	1	trivial
1148.2.i.e.821.8	yes	30	7.2	even	3	inner
8036.2.a.q.1.8		15	7.4	even	3
8036.2.a.r.1.8		15	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.257541 - 0.446074i) q^{3} +(-1.09982 - 1.90494i) q^{5} +(-2.48493 + 0.908374i) q^{7} +(1.36735 + 2.36831i) q^{9} +O(q^{10})\)	\(q+(0.257541 - 0.446074i) q^{3} +(-1.09982 - 1.90494i) q^{5} +(-2.48493 + 0.908374i) q^{7} +(1.36735 + 2.36831i) q^{9} +(-2.11080 + 3.65601i) q^{11} +3.63941 q^{13} -1.13299 q^{15} +(3.99349 - 6.91692i) q^{17} +(-0.570070 - 0.987390i) q^{19} +(-0.234768 + 1.34240i) q^{21} +(3.71723 + 6.43843i) q^{23} +(0.0808021 - 0.139953i) q^{25} +2.95383 q^{27} +6.08068 q^{29} +(0.666213 - 1.15392i) q^{31} +(1.08723 + 1.88314i) q^{33} +(4.46336 + 3.73459i) q^{35} +(1.43888 + 2.49222i) q^{37} +(0.937298 - 1.62345i) q^{39} -1.00000 q^{41} +5.14701 q^{43} +(3.00766 - 5.20942i) q^{45} +(-4.06236 - 7.03622i) q^{47} +(5.34971 - 4.51448i) q^{49} +(-2.05697 - 3.56278i) q^{51} +(0.815377 - 1.41227i) q^{53} +9.28598 q^{55} -0.587265 q^{57} +(1.48989 - 2.58057i) q^{59} +(-5.13542 - 8.89481i) q^{61} +(-5.54906 - 4.64302i) q^{63} +(-4.00269 - 6.93287i) q^{65} +(-1.23404 + 2.13742i) q^{67} +3.82935 q^{69} +13.0326 q^{71} +(-5.75997 + 9.97656i) q^{73} +(-0.0416197 - 0.0720874i) q^{75} +(1.92415 - 11.0023i) q^{77} +(-4.53471 - 7.85434i) q^{79} +(-3.34130 + 5.78731i) q^{81} +7.51957 q^{83} -17.5684 q^{85} +(1.56602 - 2.71243i) q^{87} +(8.99097 + 15.5728i) q^{89} +(-9.04367 + 3.30595i) q^{91} +(-0.343154 - 0.594361i) q^{93} +(-1.25395 + 2.17190i) q^{95} +13.2426 q^{97} -11.5448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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