LMFDB - Embedded newform 308.2.i.a.221.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(177,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("308.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	308.221
Dual form			308.2.i.a.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.296790 - 0.514055i) q^{3} +(0.933463 + 1.61680i) q^{5} +(0.0665372 - 2.64491i) q^{7} +(1.32383 + 2.29294i) q^{9} +(0.500000 - 0.866025i) q^{11} +4.32743 q^{13} +1.10817 q^{15} +(-0.230252 + 0.398809i) q^{17} +(-0.769748 - 1.33324i) q^{19} +(-1.33988 - 0.819187i) q^{21} +(1.73025 + 2.99689i) q^{23} +(0.757295 - 1.31167i) q^{25} +3.35234 q^{27} -5.78794 q^{29} +(0.487547 - 0.844456i) q^{31} +(-0.296790 - 0.514055i) q^{33} +(4.33842 - 2.36135i) q^{35} +(0.133074 + 0.230492i) q^{37} +(1.28434 - 2.22454i) q^{39} +0.485411 q^{41} -3.70175 q^{43} +(-2.47150 + 4.28076i) q^{45} +(-3.23025 - 5.59496i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(0.136673 + 0.236725i) q^{51} +(-6.21780 + 10.7695i) q^{53} +1.86693 q^{55} -0.913813 q^{57} +(-2.39037 + 4.14024i) q^{59} +(-4.64766 - 8.04999i) q^{61} +(6.15272 - 3.34886i) q^{63} +(4.03950 + 6.99661i) q^{65} +(-6.51459 + 11.2836i) q^{67} +2.05408 q^{69} -6.46050 q^{71} +(-3.20321 + 5.54812i) q^{73} +(-0.449514 - 0.778582i) q^{75} +(-2.25729 - 1.38008i) q^{77} +(-7.54163 - 13.0625i) q^{79} +(-2.97656 + 5.15555i) q^{81} +6.83482 q^{83} -0.859728 q^{85} +(-1.71780 + 2.97532i) q^{87} +(-1.30039 - 2.25234i) q^{89} +(0.287935 - 11.4457i) q^{91} +(-0.289398 - 0.501252i) q^{93} +(1.43706 - 2.48906i) q^{95} -5.35661 q^{97} +2.64766 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{5} + 4 q^{7} - 4 q^{9} + 3 q^{11} + 6 q^{13} - 30 q^{15} + 5 q^{17} - 11 q^{19} - 10 q^{21} + 4 q^{23} - 11 q^{25} + 44 q^{27} - 2 q^{29} - 19 q^{31} + q^{33} - 17 q^{35} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 6 * q - q^3 + 2 * q^5 + 4 * q^7 - 4 * q^9 + 3 * q^11 + 6 * q^13 - 30 * q^15 + 5 * q^17 - 11 * q^19 - 10 * q^21 + 4 * q^23 - 11 * q^25 + 44 * q^27 - 2 * q^29 - 19 * q^31 + q^33 - 17 * q^35 + 8 * q^37 - 17 * q^39 + 34 * q^41 + 20 * q^43 + 21 * q^45 - 13 * q^47 - 12 * q^49 - 9 * q^53 + 4 * q^55 + 4 * q^57 - 6 * q^59 - 4 * q^61 + 50 * q^63 + 37 * q^65 - 8 * q^67 - 6 * q^69 - 26 * q^71 - 22 * q^73 - 13 * q^75 + 2 * q^77 - 5 * q^79 - 19 * q^81 + 6 * q^83 - 14 * q^85 + 18 * q^87 + 3 * q^89 - 31 * q^91 - 14 * q^93 - 3 * q^95 + 50 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.296790	−	0.514055i	0.171352	−	0.296790i	−0.767541	−	0.641000i	$-0.778520\pi$
$3$	0.296790	−	0.514055i	0.171352	−	0.296790i	0.938893	+	0.344210i	$0.111853\pi$
$4$		0			0
$5$	0.933463	+	1.61680i	0.417457	+	0.723057i	0.995683	−	0.0928197i	$-0.0295880\pi$
$5$	0.933463	+	1.61680i	0.417457	+	0.723057i	−0.578226	+	0.815877i	$0.696255\pi$
$6$		0			0
$7$	0.0665372	−	2.64491i	0.0251487	−	0.999684i
$7$	0.0665372	−	2.64491i	0.0251487	−	0.999684i
$8$		0			0
$9$	1.32383	+	2.29294i	0.441277	+	0.764315i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	4.32743			1.20021			0.600107	−	0.799920i	$-0.295125\pi$
$13$	4.32743			1.20021			0.600107	+	0.799920i	$0.295125\pi$
$14$		0			0
$15$	1.10817			0.286128
$16$		0			0
$17$	−0.230252	+	0.398809i	−0.0558444	+	0.0967254i	−0.892596	−	0.450857i	$-0.851118\pi$
$17$	−0.230252	+	0.398809i	−0.0558444	+	0.0967254i	0.836752	+	0.547582i	$0.184452\pi$
$18$		0			0
$19$	−0.769748	−	1.33324i	−0.176592	−	0.305867i	0.764119	−	0.645075i	$-0.223174\pi$
$19$	−0.769748	−	1.33324i	−0.176592	−	0.305867i	−0.940711	+	0.339209i	$0.889841\pi$
$20$		0			0
$21$	−1.33988	−	0.819187i	−0.292387	−	0.178761i
$22$		0			0
$23$	1.73025	+	2.99689i	0.360783	+	0.624894i	0.988090	−	0.153878i	$-0.0491763\pi$
$23$	1.73025	+	2.99689i	0.360783	+	0.624894i	−0.627307	+	0.778772i	$0.715843\pi$
$24$		0			0
$25$	0.757295	−	1.31167i	0.151459	−	0.262335i
$26$		0			0
$27$	3.35234			0.645157
$28$		0			0
$29$	−5.78794			−1.07479			−0.537396	−	0.843330i	$-0.680592\pi$
$29$	−5.78794			−1.07479			−0.537396	+	0.843330i	$0.680592\pi$
$30$		0			0
$31$	0.487547	−	0.844456i	0.0875660	−	0.151669i	−0.818916	−	0.573914i	$-0.805424\pi$
$31$	0.487547	−	0.844456i	0.0875660	−	0.151669i	0.906482	+	0.422245i	$0.138758\pi$
$32$		0			0
$33$	−0.296790	−	0.514055i	−0.0516645	−	0.0894855i
$34$		0			0
$35$	4.33842	−	2.36135i	0.733327	−	0.399141i
$36$		0			0
$37$	0.133074	+	0.230492i	0.0218773	+	0.0378926i	0.876757	−	0.480934i	$-0.159702\pi$
$37$	0.133074	+	0.230492i	0.0218773	+	0.0378926i	−0.854879	+	0.518827i	$0.826369\pi$
$38$		0			0
$39$	1.28434	−	2.22454i	0.205658	−	0.356211i
$40$		0			0
$41$	0.485411			0.0758084			0.0379042	−	0.999281i	$-0.487932\pi$
$41$	0.485411			0.0758084			0.0379042	+	0.999281i	$0.487932\pi$
$42$		0			0
$43$	−3.70175			−0.564511			−0.282256	−	0.959339i	$-0.591083\pi$
$43$	−3.70175			−0.564511			−0.282256	+	0.959339i	$0.591083\pi$
$44$		0			0
$45$	−2.47150	+	4.28076i	−0.368429	+	0.638137i
$46$		0			0
$47$	−3.23025	−	5.59496i	−0.471181	−	0.816109i	0.528276	−	0.849073i	$-0.322839\pi$
$47$	−3.23025	−	5.59496i	−0.471181	−	0.816109i	−0.999457	+	0.0329638i	$0.989505\pi$
$48$		0			0
$49$	−6.99115	−	0.351971i	−0.998735	−	0.0502815i
$50$		0			0
$51$	0.136673	+	0.236725i	0.0191381	+	0.0331481i
$52$		0			0
$53$	−6.21780	+	10.7695i	−0.854080	+	1.47931i	0.0234151	+	0.999726i	$0.492546\pi$
$53$	−6.21780	+	10.7695i	−0.854080	+	1.47931i	−0.877495	+	0.479585i	$0.840787\pi$
$54$		0			0
$55$	1.86693			0.251736
$56$		0			0
$57$	−0.913813			−0.121037
$58$		0			0
$59$	−2.39037	+	4.14024i	−0.311200	+	0.539013i	−0.978622	−	0.205666i	$-0.934064\pi$
$59$	−2.39037	+	4.14024i	−0.311200	+	0.539013i	0.667423	+	0.744679i	$0.267397\pi$
$60$		0			0
$61$	−4.64766	−	8.04999i	−0.595072	−	1.03070i	−0.993537	−	0.113512i	$-0.963790\pi$
$61$	−4.64766	−	8.04999i	−0.595072	−	1.03070i	0.398464	−	0.917184i	$-0.369543\pi$
$62$		0			0
$63$	6.15272	−	3.34886i	0.775170	−	0.421916i
$64$		0			0
$65$	4.03950	+	6.99661i	0.501038	+	0.867823i
$66$		0			0
$67$	−6.51459	+	11.2836i	−0.795884	+	1.37851i	0.126393	+	0.991980i	$0.459660\pi$
$67$	−6.51459	+	11.2836i	−0.795884	+	1.37851i	−0.922277	+	0.386531i	$0.873673\pi$
$68$		0			0
$69$	2.05408			0.247283
$70$		0			0
$71$	−6.46050			−0.766721			−0.383360	−	0.923599i	$-0.625233\pi$
$71$	−6.46050			−0.766721			−0.383360	+	0.923599i	$0.625233\pi$
$72$		0			0
$73$	−3.20321	+	5.54812i	−0.374907	+	0.649359i	−0.990313	−	0.138852i	$-0.955659\pi$
$73$	−3.20321	+	5.54812i	−0.374907	+	0.649359i	0.615406	+	0.788210i	$0.288992\pi$
$74$		0			0
$75$	−0.449514	−	0.778582i	−0.0519055	−	0.0899029i
$76$		0			0
$77$	−2.25729	−	1.38008i	−0.257243	−	0.157275i
$78$		0			0
$79$	−7.54163	−	13.0625i	−0.848500	−	1.46964i	−0.882547	−	0.470225i	$-0.844173\pi$
$79$	−7.54163	−	13.0625i	−0.848500	−	1.46964i	0.0340470	−	0.999420i	$-0.489160\pi$
$80$		0			0
$81$	−2.97656	+	5.15555i	−0.330729	+	0.572839i
$82$		0			0
$83$	6.83482			0.750219			0.375110	−	0.926980i	$-0.377605\pi$
$83$	6.83482			0.750219			0.375110	+	0.926980i	$0.377605\pi$
$84$		0			0
$85$	−0.859728			−0.0932506
$86$		0			0
$87$	−1.71780	+	2.97532i	−0.184167	+	0.318987i
$88$		0			0
$89$	−1.30039	−	2.25234i	−0.137841	−	0.238747i	0.788838	−	0.614601i	$-0.210683\pi$
$89$	−1.30039	−	2.25234i	−0.137841	−	0.238747i	−0.926679	+	0.375853i	$0.877350\pi$
$90$		0			0
$91$	0.287935	−	11.4457i	0.0301838	−	1.19983i
$92$		0			0
$93$	−0.289398	−	0.501252i	−0.0300092	−	0.0519774i
$94$		0			0
$95$	1.43706	−	2.48906i	0.147439	−	0.255373i
$96$		0			0
$97$	−5.35661			−0.543881			−0.271941	−	0.962314i	$-0.587665\pi$
$97$	−5.35661			−0.543881			−0.271941	+	0.962314i	$0.587665\pi$
$98$		0			0
$99$	2.64766			0.266100
$100$		0			0
$101$	9.29893	−	16.1062i	0.925278	−	1.60263i	0.134164	−	0.990959i	$-0.457165\pi$
$101$	9.29893	−	16.1062i	0.925278	−	1.60263i	0.791114	−	0.611669i	$-0.209501\pi$
$102$		0			0
$103$	−8.43200	−	14.6047i	−0.830830	−	1.43904i	−0.897381	−	0.441256i	$-0.854533\pi$
$103$	−8.43200	−	14.6047i	−0.830830	−	1.43904i	0.0665515	−	0.997783i	$-0.478800\pi$
$104$		0			0
$105$	0.0737345	−	2.93101i	0.00719575	−	0.286037i
$106$		0			0
$107$	5.31498	+	9.20581i	0.513818	+	0.889959i	0.999872	+	0.0160301i	$0.00510277\pi$
$107$	5.31498	+	9.20581i	0.513818	+	0.889959i	−0.486053	+	0.873929i	$0.661564\pi$
$108$		0			0
$109$	−5.12062	+	8.86918i	−0.490467	+	0.849513i	−0.999940	−	0.0109735i	$-0.996507\pi$
$109$	−5.12062	+	8.86918i	−0.490467	+	0.849513i	0.509473	+	0.860487i	$0.329840\pi$
$110$		0			0
$111$	0.157981			0.0149948
$112$		0			0
$113$	8.67684			0.816249			0.408124	−	0.912926i	$-0.366183\pi$
$113$	8.67684			0.816249			0.408124	+	0.912926i	$0.366183\pi$
$114$		0			0
$115$	−3.23025	+	5.59496i	−0.301223	+	0.521733i
$116$		0			0
$117$	5.72879	+	9.92256i	0.529627	+	0.917341i
$118$		0			0
$119$	1.03950	+	0.635534i	0.0952904	+	0.0582593i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	0.144065	−	0.249528i	0.0129899	−	0.0224992i
$124$		0			0
$125$	12.1623			1.08782
$126$		0			0
$127$	1.32743			0.117790			0.0588952	−	0.998264i	$-0.481242\pi$
$127$	1.32743			0.117790			0.0588952	+	0.998264i	$0.481242\pi$
$128$		0			0
$129$	−1.09864	+	1.90290i	−0.0967299	+	0.167541i
$130$		0			0
$131$	5.13521	+	8.89445i	0.448665	+	0.777111i	0.998299	−	0.0582942i	$-0.0185662\pi$
$131$	5.13521	+	8.89445i	0.448665	+	0.777111i	−0.549634	+	0.835406i	$0.685233\pi$
$132$		0			0
$133$	−3.57753	+	1.94721i	−0.310211	+	0.168844i
$134$		0			0
$135$	3.12928	+	5.42007i	0.269326	+	0.466486i
$136$		0			0
$137$	−7.71780	+	13.3676i	−0.659376	+	1.14207i	0.321401	+	0.946943i	$0.395846\pi$
$137$	−7.71780	+	13.3676i	−0.659376	+	1.14207i	−0.980777	+	0.195130i	$0.937487\pi$
$138$		0			0
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$		0			0
$141$	−3.83482			−0.322950
$142$		0			0
$143$	2.16372	−	3.74766i	0.180939	−	0.313395i
$144$		0			0
$145$	−5.40282	−	9.35796i	−0.448680	−	0.777136i
$146$		0			0
$147$	−2.25583	+	3.48937i	−0.186058	+	0.287798i
$148$		0			0
$149$	7.28794	+	12.6231i	0.597051	+	1.03412i	0.993254	+	0.115960i	$0.0369943\pi$
$149$	7.28794	+	12.6231i	0.597051	+	1.03412i	−0.396203	+	0.918163i	$0.629672\pi$
$150$		0			0
$151$	2.97656	−	5.15555i	0.242229	−	0.419552i	−0.719120	−	0.694886i	$-0.755455\pi$
$151$	2.97656	−	5.15555i	0.242229	−	0.419552i	0.961349	+	0.275333i	$0.0887882\pi$
$152$		0			0
$153$	−1.21926			−0.0985715
$154$		0			0
$155$	1.82043			0.146220
$156$		0			0
$157$	12.0146	−	20.8099i	0.958869	−	1.66081i	0.233613	−	0.972330i	$-0.424945\pi$
$157$	12.0146	−	20.8099i	0.958869	−	1.66081i	0.725256	−	0.688479i	$-0.241721\pi$
$158$		0			0
$159$	3.69076	+	6.39258i	0.292696	+	0.506965i
$160$		0			0
$161$	8.04163	−	4.37697i	0.633769	−	0.344953i
$162$		0			0
$163$	−0.421010	−	0.729210i	−0.0329760	−	0.0571162i	0.849066	−	0.528286i	$-0.177165\pi$
$163$	−0.421010	−	0.729210i	−0.0329760	−	0.0571162i	−0.882042	+	0.471170i	$0.843832\pi$
$164$		0			0
$165$	0.554084	−	0.959702i	0.0431354	−	0.0747127i
$166$		0			0
$167$	15.5218			1.20111			0.600556	−	0.799583i	$-0.294946\pi$
$167$	15.5218			1.20111			0.600556	+	0.799583i	$0.294946\pi$
$168$		0			0
$169$	5.72665			0.440512
$170$		0			0
$171$	2.03803	−	3.52998i	0.155852	−	0.269944i
$172$		0			0
$173$	−6.67830	−	11.5672i	−0.507742	−	0.879435i	−0.999960	−	0.00896297i	$-0.997147\pi$
$173$	−6.67830	−	11.5672i	−0.507742	−	0.879435i	0.492218	−	0.870472i	$-0.336186\pi$
$174$		0			0
$175$	−3.41887	−	2.09025i	−0.258443	−	0.158008i
$176$		0			0
$177$	1.41887	+	2.45756i	0.106649	+	0.184722i
$178$		0			0
$179$	4.53064	−	7.84730i	0.338636	−	0.586535i	−0.645540	−	0.763726i	$-0.723368\pi$
$179$	4.53064	−	7.84730i	0.338636	−	0.586535i	0.984176	+	0.177191i	$0.0567012\pi$
$180$		0			0
$181$	20.1986			1.50135			0.750676	−	0.660670i	$-0.229728\pi$
$181$	20.1986			1.50135			0.750676	+	0.660670i	$0.229728\pi$
$182$		0			0
$183$	−5.51751			−0.407866
$184$		0			0
$185$	−0.248440	+	0.430311i	−0.0182657	+	0.0316371i
$186$		0			0
$187$	0.230252	+	0.398809i	0.0168377	+	0.0291638i
$188$		0			0
$189$	0.223055	−	8.86664i	0.0162249	−	0.644953i
$190$		0			0
$191$	−7.03950	−	12.1928i	−0.509360	−	0.882237i	−0.999941	−	0.0108419i	$-0.996549\pi$
$191$	−7.03950	−	12.1928i	−0.509360	−	0.882237i	0.490581	−	0.871395i	$-0.336784\pi$
$192$		0			0
$193$	8.21780	−	14.2336i	0.591530	−	1.02456i	−0.402496	−	0.915422i	$-0.631857\pi$
$193$	8.21780	−	14.2336i	0.591530	−	1.02456i	0.994027	−	0.109139i	$-0.0348093\pi$
$194$		0			0
$195$	4.79552			0.343414
$196$		0			0
$197$	−8.48968			−0.604865			−0.302432	−	0.953171i	$-0.597799\pi$
$197$	−8.48968			−0.604865			−0.302432	+	0.953171i	$0.597799\pi$
$198$		0			0
$199$	−13.7288	+	23.7790i	−0.973208	+	1.68565i	−0.287482	+	0.957786i	$0.592818\pi$
$199$	−13.7288	+	23.7790i	−0.973208	+	1.68565i	−0.685726	+	0.727860i	$0.740515\pi$
$200$		0			0
$201$	3.86693	+	6.69771i	0.272752	+	0.472420i
$202$		0			0
$203$	−0.385113	+	15.3086i	−0.0270296	+	1.07445i
$204$		0			0
$205$	0.453113	+	0.784815i	0.0316468	+	0.0548138i
$206$		0			0
$207$	−4.58113	+	7.93474i	−0.318410	+	0.551503i
$208$		0			0
$209$	−1.53950			−0.106489
$210$		0			0
$211$	8.49688			0.584949			0.292475	−	0.956273i	$-0.405521\pi$
$211$	8.49688			0.584949			0.292475	+	0.956273i	$0.405521\pi$
$212$		0			0
$213$	−1.91741	+	3.32105i	−0.131379	+	0.227555i
$214$		0			0
$215$	−3.45544	−	5.98500i	−0.235659	−	0.408174i
$216$		0			0
$217$	−2.20107	−	1.34571i	−0.149419	−	0.0913526i
$218$		0			0
$219$	1.90136	+	3.29325i	0.128482	+	0.222537i
$220$		0			0
$221$	−0.996401	+	1.72582i	−0.0670252	+	0.116091i
$222$		0			0
$223$	−13.9210			−0.932220			−0.466110	−	0.884727i	$-0.654345\pi$
$223$	−13.9210			−0.932220			−0.466110	+	0.884727i	$0.654345\pi$
$224$		0			0
$225$	4.01012			0.267341
$226$		0			0
$227$	−12.8224	+	22.2090i	−0.851051	+	1.47406i	0.0292106	+	0.999573i	$0.490701\pi$
$227$	−12.8224	+	22.2090i	−0.851051	+	1.47406i	−0.880261	+	0.474489i	$0.842633\pi$
$228$		0			0
$229$	5.82743	+	10.0934i	0.385087	+	0.666991i	0.991781	−	0.127945i	$-0.0408380\pi$
$229$	5.82743	+	10.0934i	0.385087	+	0.666991i	−0.606694	+	0.794936i	$0.707505\pi$
$230$		0			0
$231$	−1.37938	+	0.750780i	−0.0907564	+	0.0493977i
$232$		0			0
$233$	−6.55408	−	11.3520i	−0.429372	−	0.743695i	0.567445	−	0.823411i	$-0.307932\pi$
$233$	−6.55408	−	11.3520i	−0.429372	−	0.743695i	−0.996818	+	0.0797164i	$0.974599\pi$
$234$		0			0
$235$	6.03064	−	10.4454i	0.393396	−	0.681381i
$236$		0			0
$237$	−8.95311			−0.581567
$238$		0			0
$239$	−18.3346			−1.18597			−0.592984	−	0.805214i	$-0.702050\pi$
$239$	−18.3346			−1.18597			−0.592984	+	0.805214i	$0.702050\pi$
$240$		0			0
$241$	8.03803	−	13.9223i	0.517775	−	0.896813i	−0.482012	−	0.876165i	$-0.660094\pi$
$241$	8.03803	−	13.9223i	0.517775	−	0.896813i	0.999787	−	0.0206481i	$-0.00657297\pi$
$242$		0			0
$243$	6.79533	+	11.7699i	0.435920	+	0.755036i
$244$		0			0
$245$	−5.95691	−	11.6319i	−0.380573	−	0.743133i
$246$		0			0
$247$	−3.33103	−	5.76951i	−0.211948	−	0.367105i
$248$		0			0
$249$	2.02850	−	3.51347i	0.128551	−	0.222657i
$250$		0			0
$251$	6.03638			0.381013			0.190506	−	0.981686i	$-0.438987\pi$
$251$	6.03638			0.381013			0.190506	+	0.981686i	$0.438987\pi$
$252$		0			0
$253$	3.46050			0.217560
$254$		0			0
$255$	−0.255158	+	0.441947i	−0.0159786	+	0.0276758i
$256$		0			0
$257$	8.40856	+	14.5640i	0.524511	+	0.908480i	0.999593	+	0.0285384i	$0.00908530\pi$
$257$	8.40856	+	14.5640i	0.524511	+	0.908480i	−0.475081	+	0.879942i	$0.657581\pi$
$258$		0			0
$259$	0.618485	−	0.336634i	0.0384308	−	0.0209174i
$260$		0			0
$261$	−7.66225	−	13.2714i	−0.474282	−	0.821480i
$262$		0			0
$263$	−7.24484	+	12.5484i	−0.446736	+	0.773770i	−0.998171	−	0.0604481i	$-0.980747\pi$
$263$	−7.24484	+	12.5484i	−0.446736	+	0.773770i	0.551435	+	0.834218i	$0.314080\pi$
$264$		0			0
$265$	−23.2163			−1.42617
$266$		0			0
$267$	−1.54377			−0.0944770
$268$		0			0
$269$	2.24630	−	3.89071i	0.136960	−	0.237221i	−0.789385	−	0.613899i	$-0.789600\pi$
$269$	2.24630	−	3.89071i	0.136960	−	0.237221i	0.926344	+	0.376678i	$0.122934\pi$
$270$		0			0
$271$	−11.7484	−	20.3489i	−0.713667	−	1.23611i	−0.963471	−	0.267811i	$-0.913700\pi$
$271$	−11.7484	−	20.3489i	−0.713667	−	1.23611i	0.249805	−	0.968296i	$-0.419634\pi$
$272$		0			0
$273$	−5.79825	−	3.54498i	−0.350926	−	0.214552i
$274$		0			0
$275$	−0.757295	−	1.31167i	−0.0456666	−	0.0790968i
$276$		0			0
$277$	3.53064	−	6.11525i	0.212136	−	0.367430i	−0.740247	−	0.672335i	$-0.765291\pi$
$277$	3.53064	−	6.11525i	0.212136	−	0.367430i	0.952383	+	0.304905i	$0.0986248\pi$
$278$		0			0
$279$	2.58172			0.154564
$280$		0			0
$281$	−4.88171			−0.291218			−0.145609	−	0.989342i	$-0.546514\pi$
$281$	−4.88171			−0.291218			−0.145609	+	0.989342i	$0.546514\pi$
$282$		0			0
$283$	−11.7053	+	20.2743i	−0.695811	+	1.20518i	0.274096	+	0.961702i	$0.411621\pi$
$283$	−11.7053	+	20.2743i	−0.695811	+	1.20518i	−0.969907	+	0.243477i	$0.921712\pi$
$284$		0			0
$285$	−0.853010	−	1.47746i	−0.0505279	−	0.0875170i
$286$		0			0
$287$	0.0322979	−	1.28387i	0.00190648	−	0.0757845i
$288$		0			0
$289$	8.39397	+	14.5388i	0.493763	+	0.855222i
$290$		0			0
$291$	−1.58979	+	2.75359i	−0.0931949	+	0.161418i
$292$		0			0
$293$	−18.0875			−1.05669			−0.528343	−	0.849031i	$-0.677186\pi$
$293$	−18.0875			−1.05669			−0.528343	+	0.849031i	$0.677186\pi$
$294$		0			0
$295$	−8.92528			−0.519650
$296$		0			0
$297$	1.67617	−	2.90321i	0.0972611	−	0.168461i
$298$		0			0
$299$	7.48755	+	12.9688i	0.433016	+	0.750006i
$300$		0			0
$301$	−0.246304	+	9.79081i	−0.0141967	+	0.564333i
$302$		0			0
$303$	−5.51965	−	9.56031i	−0.317096	−	0.549226i
$304$		0			0
$305$	8.67684	−	15.0287i	0.496835	−	0.860543i
$306$		0			0
$307$	−11.8171			−0.674438			−0.337219	−	0.941426i	$-0.609486\pi$
$307$	−11.8171			−0.674438			−0.337219	+	0.941426i	$0.609486\pi$
$308$		0			0
$309$	−10.0101			−0.569456
$310$		0			0
$311$	5.98755	−	10.3707i	0.339523	−	0.588070i	−0.644820	−	0.764334i	$-0.723068\pi$
$311$	5.98755	−	10.3707i	0.339523	−	0.588070i	0.984343	+	0.176264i	$0.0564011\pi$
$312$		0			0
$313$	−6.01099	−	10.4113i	−0.339761	−	0.588484i	0.644626	−	0.764498i	$-0.277013\pi$
$313$	−6.01099	−	10.4113i	−0.339761	−	0.588484i	−0.984388	+	0.176014i	$0.943680\pi$
$314$		0			0
$315$	11.1578	+	6.82172i	0.628670	+	0.384361i
$316$		0			0
$317$	10.4445	+	18.0903i	0.586619	+	1.01605i	0.994671	+	0.103095i	$0.0328747\pi$
$317$	10.4445	+	18.0903i	0.586619	+	1.01605i	−0.408053	+	0.912958i	$0.633792\pi$
$318$		0			0
$319$	−2.89397	+	5.01250i	−0.162031	+	0.280646i
$320$		0			0
$321$	6.30972			0.352174
$322$		0			0
$323$	0.708945			0.0394468
$324$		0			0
$325$	3.27714	−	5.67617i	0.181783	−	0.314857i
$326$		0			0
$327$	3.03950	+	5.26456i	0.168084	+	0.291131i
$328$		0			0
$329$	−15.0131	+	8.17147i	−0.827700	+	0.450508i
$330$		0			0
$331$	3.01459	+	5.22142i	0.165697	+	0.286995i	0.936903	−	0.349591i	$-0.113679\pi$
$331$	3.01459	+	5.22142i	0.165697	+	0.286995i	−0.771206	+	0.636586i	$0.780346\pi$
$332$		0			0
$333$	−0.352336	+	0.610265i	−0.0193079	+	0.0334423i
$334$		0			0
$335$	−24.3245			−1.32899
$336$		0			0
$337$	21.2091			1.15534			0.577668	−	0.816272i	$-0.303963\pi$
$337$	21.2091			1.15534			0.577668	+	0.816272i	$0.303963\pi$
$338$		0			0
$339$	2.57520	−	4.46037i	0.139866	−	0.242254i
$340$		0			0
$341$	−0.487547	−	0.844456i	−0.0264021	−	0.0457299i
$342$		0			0
$343$	−1.39610	+	18.4676i	−0.0753825	+	0.997155i
$344$		0			0
$345$	1.91741	+	3.32105i	0.103230	+	0.178800i
$346$		0			0
$347$	−6.05622	+	10.4897i	−0.325115	+	0.563116i	−0.981536	−	0.191279i	$-0.938736\pi$
$347$	−6.05622	+	10.4897i	−0.325115	+	0.563116i	0.656421	+	0.754395i	$0.272070\pi$
$348$		0			0
$349$	−17.1082			−0.915779			−0.457890	−	0.889009i	$-0.651395\pi$
$349$	−17.1082			−0.915779			−0.457890	+	0.889009i	$0.651395\pi$
$350$		0			0
$351$	14.5070			0.774327
$352$		0			0
$353$	11.8186	−	20.4704i	0.629039	−	1.08953i	−0.358706	−	0.933451i	$-0.616782\pi$
$353$	11.8186	−	20.4704i	0.629039	−	1.08953i	0.987745	−	0.156077i	$-0.0498849\pi$
$354$		0			0
$355$	−6.03064	−	10.4454i	−0.320073	−	0.554383i
$356$		0			0
$357$	0.635211	−	0.345738i	0.0336189	−	0.0182984i
$358$		0			0
$359$	−17.8384	−	30.8971i	−0.941476	−	1.63068i	−0.762658	−	0.646802i	$-0.776106\pi$
$359$	−17.8384	−	30.8971i	−0.941476	−	1.63068i	−0.178818	−	0.983882i	$-0.557227\pi$
$360$		0			0
$361$	8.31498	−	14.4020i	0.437630	−	0.757998i
$362$		0			0
$363$	−0.593579			−0.0311548
$364$		0			0
$365$	−11.9603			−0.626031
$366$		0			0
$367$	−5.51245	+	9.54785i	−0.287748	+	0.498394i	−0.973272	−	0.229656i	$-0.926240\pi$
$367$	−5.51245	+	9.54785i	−0.287748	+	0.498394i	0.685524	+	0.728050i	$0.259573\pi$
$368$		0			0
$369$	0.642602	+	1.11302i	0.0334525	+	0.0579415i
$370$		0			0
$371$	28.0708	+	17.1621i	1.45736	+	0.891013i
$372$		0			0
$373$	11.9897	+	20.7667i	0.620802	+	1.07526i	0.989337	+	0.145647i	$0.0465264\pi$
$373$	11.9897	+	20.7667i	0.620802	+	1.07526i	−0.368534	+	0.929614i	$0.620140\pi$
$374$		0			0
$375$	3.60963	−	6.25206i	0.186401	−	0.322855i
$376$		0			0
$377$	−25.0469			−1.28998
$378$		0			0
$379$	−3.53950			−0.181812			−0.0909058	−	0.995859i	$-0.528976\pi$
$379$	−3.53950			−0.181812			−0.0909058	+	0.995859i	$0.528976\pi$
$380$		0			0
$381$	0.393968	−	0.682372i	0.0201836	−	0.0349590i
$382$		0			0
$383$	5.84348	+	10.1212i	0.298588	+	0.517170i	0.975813	−	0.218606i	$-0.0701510\pi$
$383$	5.84348	+	10.1212i	0.298588	+	0.517170i	−0.677225	+	0.735776i	$0.736818\pi$
$384$		0			0
$385$	0.124220	−	4.93786i	0.00633084	−	0.251657i
$386$		0			0
$387$	−4.90049	−	8.48790i	−0.249106	−	0.431464i
$388$		0			0
$389$	0.591443	−	1.02441i	0.0299874	−	0.0519396i	−0.850642	−	0.525745i	$-0.823787\pi$
$389$	0.591443	−	1.02441i	0.0299874	−	0.0519396i	0.880630	+	0.473805i	$0.157120\pi$
$390$		0			0
$391$	−1.59358			−0.0805908
$392$		0			0
$393$	6.09631			0.307518
$394$		0			0
$395$	14.0797	−	24.3867i	0.708425	−	1.22703i
$396$		0			0
$397$	3.32023	+	5.75081i	0.166638	+	0.288625i	0.937236	−	0.348697i	$-0.113376\pi$
$397$	3.32023	+	5.75081i	0.166638	+	0.288625i	−0.770598	+	0.637322i	$0.780042\pi$
$398$		0			0
$399$	−0.0608026	+	2.41696i	−0.00304394	+	0.120999i
$400$		0			0
$401$	−8.26449	−	14.3145i	−0.412709	−	0.714833i	0.582476	−	0.812848i	$-0.302084\pi$
$401$	−8.26449	−	14.3145i	−0.412709	−	0.714833i	−0.995185	+	0.0980150i	$0.968751\pi$
$402$		0			0
$403$	2.10983	−	3.65433i	0.105098	−	0.182035i
$404$		0			0
$405$	−11.1140			−0.552260
$406$		0			0
$407$	0.266149			0.0131925
$408$		0			0
$409$	−14.6747	+	25.4173i	−0.725617	+	1.25681i	0.233102	+	0.972452i	$0.425112\pi$
$409$	−14.6747	+	25.4173i	−0.725617	+	1.25681i	−0.958719	+	0.284354i	$0.908221\pi$
$410$		0			0
$411$	4.58113	+	7.93474i	0.225970	+	0.391392i
$412$		0			0
$413$	10.7915	+	6.59780i	0.531017	+	0.324657i
$414$		0			0
$415$	6.38005	+	11.0506i	0.313184	+	0.542451i
$416$		0			0
$417$	3.26469	−	5.65460i	0.159872	−	0.276907i
$418$		0			0
$419$	12.6840			0.619656			0.309828	−	0.950793i	$-0.399729\pi$
$419$	12.6840			0.619656			0.309828	+	0.950793i	$0.399729\pi$
$420$		0			0
$421$	30.5835			1.49055			0.745273	−	0.666759i	$-0.232319\pi$
$421$	30.5835			1.49055			0.745273	+	0.666759i	$0.232319\pi$
$422$		0			0
$423$	8.55262	−	14.8136i	0.415843	−	0.720261i
$424$		0			0
$425$	0.348738	+	0.604032i	0.0169163	+	0.0292998i
$426$		0			0
$427$	−21.6008	+	11.7570i	−1.04533	+	0.568963i
$428$		0			0
$429$	−1.28434	−	2.22454i	−0.0620084	−	0.107402i
$430$		0			0
$431$	13.8743	−	24.0310i	0.668302	−	1.15753i	−0.310076	−	0.950712i	$-0.600355\pi$
$431$	13.8743	−	24.0310i	0.668302	−	1.15753i	0.978379	−	0.206822i	$-0.0663121\pi$
$432$		0			0
$433$	13.7778			0.662119			0.331060	−	0.943610i	$-0.392594\pi$
$433$	13.7778			0.662119			0.331060	+	0.943610i	$0.392594\pi$
$434$		0			0
$435$	−6.41401			−0.307528
$436$		0			0
$437$	2.66372	−	4.61369i	0.127423	−	0.220703i
$438$		0			0
$439$	−0.402822	−	0.697708i	−0.0192256	−	0.0332998i	0.856253	−	0.516557i	$-0.172787\pi$
$439$	−0.402822	−	0.697708i	−0.0192256	−	0.0332998i	−0.875478	+	0.483258i	$0.839453\pi$
$440$		0			0
$441$	−8.44805	−	16.4963i	−0.402288	−	0.785536i
$442$		0			0
$443$	6.19961	+	10.7380i	0.294552	+	0.510180i	0.974881	−	0.222728i	$-0.0714961\pi$
$443$	6.19961	+	10.7380i	0.294552	+	0.510180i	−0.680328	+	0.732908i	$0.738163\pi$
$444$		0			0
$445$	2.42773	−	4.20495i	0.115085	−	0.199334i
$446$		0			0
$447$	8.65194			0.409223
$448$		0			0
$449$	40.1957			1.89695			0.948476	−	0.316848i	$-0.102625\pi$
$449$	40.1957			1.89695			0.948476	+	0.316848i	$0.102625\pi$
$450$		0			0
$451$	0.242705	−	0.420378i	0.0114286	−	0.0197948i
$452$		0			0
$453$	−1.76682	−	3.06023i	−0.0830126	−	0.143782i
$454$		0			0
$455$	18.7742	−	10.2186i	0.880149	−	0.479055i
$456$		0			0
$457$	11.6908	+	20.2490i	0.546871	+	0.947208i	0.998487	+	0.0549952i	$0.0175144\pi$
$457$	11.6908	+	20.2490i	0.546871	+	0.947208i	−0.451616	+	0.892212i	$0.649152\pi$
$458$		0			0
$459$	−0.771884	+	1.33694i	−0.0360284	+	0.0624031i
$460$		0			0
$461$	−34.9430			−1.62746			−0.813729	−	0.581245i	$-0.802566\pi$
$461$	−34.9430			−1.62746			−0.813729	+	0.581245i	$0.802566\pi$
$462$		0			0
$463$	40.5510			1.88456			0.942282	−	0.334822i	$-0.108676\pi$
$463$	40.5510			1.88456			0.942282	+	0.334822i	$0.108676\pi$
$464$		0			0
$465$	0.540284	−	0.935800i	0.0250551	−	0.0433967i
$466$		0			0
$467$	−0.572272	−	0.991204i	−0.0264816	−	0.0458675i	0.852481	−	0.522758i	$-0.175097\pi$
$467$	−0.572272	−	0.991204i	−0.0264816	−	0.0458675i	−0.878962	+	0.476891i	$0.841764\pi$
$468$		0			0
$469$	29.4107	+	17.9813i	1.35806	+	0.830300i
$470$		0			0
$471$	−7.13161	−	12.3523i	−0.328607	−	0.569165i
$472$		0			0
$473$	−1.85087	+	3.20581i	−0.0851033	+	0.147403i
$474$		0			0
$475$	−2.33170			−0.106986
$476$		0			0
$477$	−32.9253			−1.50755
$478$		0			0
$479$	0.940855	−	1.62961i	0.0429887	−	0.0744587i	−0.843730	−	0.536767i	$-0.819645\pi$
$479$	0.940855	−	1.62961i	0.0429887	−	0.0744587i	0.886719	+	0.462308i	$0.152979\pi$
$480$		0			0
$481$	0.575871	+	0.997437i	0.0262574	+	0.0454792i
$482$		0			0
$483$	0.136673	−	5.43288i	0.00621884	−	0.247204i
$484$		0			0
$485$	−5.00019	−	8.66059i	−0.227047	−	0.393257i
$486$		0			0
$487$	−5.44445	+	9.43007i	−0.246712	+	0.427317i	−0.962611	−	0.270886i	$-0.912683\pi$
$487$	−5.44445	+	9.43007i	−0.246712	+	0.427317i	0.715900	+	0.698203i	$0.246017\pi$
$488$		0			0
$489$	−0.499805			−0.0226020
$490$		0			0
$491$	−12.5615			−0.566891			−0.283446	−	0.958988i	$-0.591478\pi$
$491$	−12.5615			−0.566891			−0.283446	+	0.958988i	$0.591478\pi$
$492$		0			0
$493$	1.33269	−	2.30828i	0.0600212	−	0.103960i
$494$		0			0
$495$	2.47150	+	4.28076i	0.111085	+	0.192406i
$496$		0			0
$497$	−0.429864	+	17.0875i	−0.0192820	+	0.766478i
$498$		0			0
$499$	−19.2434	−	33.3305i	−0.861452	−	1.49208i	−0.870528	−	0.492120i	$-0.836222\pi$
$499$	−19.2434	−	33.3305i	−0.861452	−	1.49208i	0.00907557	−	0.999959i	$-0.497111\pi$
$500$		0			0
$501$	4.60671	−	7.97905i	0.205812	−	0.356478i
$502$		0			0
$503$	32.6519			1.45588			0.727939	−	0.685642i	$-0.240478\pi$
$503$	32.6519			1.45588			0.727939	+	0.685642i	$0.240478\pi$
$504$		0			0
$505$	34.7208			1.54506
$506$		0			0
$507$	1.69961	−	2.94381i	0.0754824	−	0.130739i
$508$		0			0
$509$	17.1046	+	29.6260i	0.758147	+	1.31315i	0.943795	+	0.330532i	$0.107228\pi$
$509$	17.1046	+	29.6260i	0.758147	+	1.31315i	−0.185648	+	0.982616i	$0.559438\pi$
$510$		0			0
$511$	14.4612	+	8.84137i	0.639725	+	0.391119i
$512$		0			0
$513$	−2.58045	−	4.46948i	−0.113930	−	0.197332i
$514$		0			0
$515$	15.7419	−	27.2658i	0.693672	−	1.20147i
$516$		0			0
$517$	−6.46050			−0.284133
$518$		0			0
$519$	−7.92821			−0.348010
$520$		0			0
$521$	−4.81644	+	8.34232i	−0.211012	+	0.365484i	−0.952032	−	0.306000i	$-0.901009\pi$
$521$	−4.81644	+	8.34232i	−0.211012	+	0.365484i	0.741019	+	0.671484i	$0.234343\pi$
$522$		0			0
$523$	11.2915	+	19.5575i	0.493744	+	0.855190i	0.999974	−	0.00720846i	$-0.00229454\pi$
$523$	11.2915	+	19.5575i	0.493744	+	0.855190i	−0.506230	+	0.862399i	$0.668961\pi$
$524$		0			0
$525$	−2.08919	+	1.13712i	−0.0911798	+	0.0496281i
$526$		0			0
$527$	0.224518	+	0.388876i	0.00978015	+	0.0169397i
$528$		0			0
$529$	5.51245	−	9.54785i	0.239672	−	0.415124i
$530$		0			0
$531$	−12.6578			−0.549301
$532$		0			0
$533$	2.10058			0.0909863
$534$		0			0
$535$	−9.92267	+	17.1866i	−0.428994	+	0.743040i
$536$		0			0
$537$	−2.68929	−	4.65800i	−0.116052	−	0.201007i
$538$		0			0
$539$	−3.80039	+	5.87852i	−0.163694	+	0.253206i
$540$		0			0
$541$	0.972958	+	1.68521i	0.0418307	+	0.0724529i	0.886183	−	0.463336i	$-0.153348\pi$
$541$	0.972958	+	1.68521i	0.0418307	+	0.0724529i	−0.844352	+	0.535789i	$0.820014\pi$
$542$		0			0
$543$	5.99474	−	10.3832i	0.257259	−	0.445586i
$544$		0			0
$545$	−19.1196			−0.818995
$546$		0			0
$547$	−2.29533			−0.0981411			−0.0490706	−	0.998795i	$-0.515626\pi$
$547$	−2.29533			−0.0981411			−0.0490706	+	0.998795i	$0.515626\pi$
$548$		0			0
$549$	12.3054	−	21.3137i	0.525184	−	0.909645i
$550$		0			0
$551$	4.45525	+	7.71672i	0.189800	+	0.328743i
$552$		0			0
$553$	−35.0510	+	19.0778i	−1.49052	+	0.811272i
$554$		0			0
$555$	0.147469	+	0.255424i	0.00625971	+	0.0108421i
$556$		0			0
$557$	−5.73911	+	9.94042i	−0.243174	+	0.421189i	−0.961617	−	0.274397i	$-0.911522\pi$
$557$	−5.73911	+	9.94042i	−0.243174	+	0.421189i	0.718443	+	0.695586i	$0.244855\pi$
$558$		0			0
$559$	−16.0191			−0.677534
$560$		0			0
$561$	0.273346			0.0115407
$562$		0			0
$563$	−20.9377	+	36.2652i	−0.882420	+	1.52840i	−0.0337782	+	0.999429i	$0.510754\pi$
$563$	−20.9377	+	36.2652i	−0.882420	+	1.52840i	−0.848642	+	0.528967i	$0.822579\pi$
$564$		0			0
$565$	8.09951	+	14.0288i	0.340749	+	0.590194i
$566$		0			0
$567$	13.4379	+	8.21577i	0.564340	+	0.345030i
$568$		0			0
$569$	−15.5723	−	26.9720i	−0.652824	−	1.13072i	−0.982435	−	0.186607i	$-0.940251\pi$
$569$	−15.5723	−	26.9720i	−0.652824	−	1.13072i	0.329611	−	0.944117i	$-0.393082\pi$
$570$		0			0
$571$	13.2594	−	22.9660i	0.554890	−	0.961098i	−0.443022	−	0.896511i	$-0.646094\pi$
$571$	13.2594	−	22.9660i	0.554890	−	0.961098i	0.997912	−	0.0645869i	$-0.0205730\pi$
$572$		0			0
$573$	−8.35700			−0.349119
$574$		0			0
$575$	5.24124			0.218575
$576$		0			0
$577$	−1.80185	+	3.12090i	−0.0750120	+	0.129925i	−0.901092	−	0.433629i	$-0.857233\pi$
$577$	−1.80185	+	3.12090i	−0.0750120	+	0.129925i	0.826079	+	0.563554i	$0.190566\pi$
$578$		0			0
$579$	−4.87792	−	8.44880i	−0.202719	−	0.351120i
$580$		0			0
$581$	0.454770	−	18.0775i	0.0188670	−	0.749982i
$582$		0			0
$583$	6.21780	+	10.7695i	0.257515	+	0.446029i
$584$		0			0
$585$	−10.6952	+	18.5247i	−0.442193	+	0.765901i
$586$		0			0
$587$	−21.1111			−0.871348			−0.435674	−	0.900105i	$-0.643490\pi$
$587$	−21.1111			−0.871348			−0.435674	+	0.900105i	$0.643490\pi$
$588$		0			0
$589$	−1.50115			−0.0618539
$590$		0			0
$591$	−2.51965	+	4.36416i	−0.103645	+	0.179518i
$592$		0			0
$593$	−11.8078	−	20.4517i	−0.484887	−	0.839850i	0.514962	−	0.857213i	$-0.327806\pi$
$593$	−11.8078	−	20.4517i	−0.484887	−	0.839850i	−0.999849	+	0.0173635i	$0.994473\pi$
$594$		0			0
$595$	−0.0572039	+	2.27391i	−0.00234513	+	0.0932211i
$596$		0			0
$597$	8.14913	+	14.1147i	0.333522	+	0.577676i
$598$		0			0
$599$	11.7001	−	20.2652i	0.478053	−	0.828012i	−0.521631	−	0.853171i	$-0.674676\pi$
$599$	11.7001	−	20.2652i	0.478053	−	0.828012i	0.999683	+	0.0251597i	$0.00800944\pi$
$600$		0			0
$601$	23.4868			0.958045			0.479022	−	0.877803i	$-0.340991\pi$
$601$	23.4868			0.958045			0.479022	+	0.877803i	$0.340991\pi$
$602$		0			0
$603$	−34.4969			−1.40482
$604$		0			0
$605$	0.933463	−	1.61680i	0.0379507	−	0.0657325i
$606$		0			0
$607$	3.99854	+	6.92567i	0.162296	+	0.281104i	0.935692	−	0.352819i	$-0.114777\pi$
$607$	3.99854	+	6.92567i	0.162296	+	0.281104i	−0.773396	+	0.633923i	$0.781444\pi$
$608$		0			0
$609$	7.75516	+	4.74140i	0.314255	+	0.192131i
$610$		0			0
$611$	−13.9787	−	24.2118i	−0.565517	−	0.979505i
$612$		0			0
$613$	7.35234	−	12.7346i	0.296958	−	0.514346i	−0.678480	−	0.734618i	$-0.737361\pi$
$613$	7.35234	−	12.7346i	0.296958	−	0.514346i	0.975438	+	0.220272i	$0.0706945\pi$
$614$		0			0
$615$	0.537917			0.0216909
$616$		0			0
$617$	−17.5261			−0.705573			−0.352786	−	0.935704i	$-0.614766\pi$
$617$	−17.5261			−0.705573			−0.352786	+	0.935704i	$0.614766\pi$
$618$		0			0
$619$	4.32743	−	7.49533i	0.173934	−	0.301263i	−0.765858	−	0.643010i	$-0.777685\pi$
$619$	4.32743	−	7.49533i	0.173934	−	0.301263i	0.939792	+	0.341747i	$0.111019\pi$
$620$		0			0
$621$	5.80039	+	10.0466i	0.232762	+	0.403155i
$622$		0			0
$623$	−6.04377	+	3.28955i	−0.242138	+	0.131793i
$624$		0			0
$625$	7.56654	+	13.1056i	0.302661	+	0.524225i
$626$		0			0
$627$	−0.456906	+	0.791385i	−0.0182471	+	0.0316049i
$628$		0			0
$629$	−0.122563			−0.00488690
$630$		0			0
$631$	−34.1488			−1.35944			−0.679721	−	0.733470i	$-0.737899\pi$
$631$	−34.1488			−1.35944			−0.679721	+	0.733470i	$0.737899\pi$
$632$		0			0
$633$	2.52179	−	4.36786i	0.100232	−	0.173607i
$634$		0			0
$635$	1.23911	+	2.14620i	0.0491725	+	0.0851692i
$636$		0			0
$637$	−30.2537	−	1.52313i	−1.19870	−	0.0603485i
$638$		0			0
$639$	−8.55262	−	14.8136i	−0.338336	−	0.586016i
$640$		0			0
$641$	−23.5708	+	40.8258i	−0.930991	+	1.61252i	−0.149360	+	0.988783i	$0.547721\pi$
$641$	−23.5708	+	40.8258i	−0.930991	+	1.61252i	−0.781631	+	0.623741i	$0.785612\pi$
$642$		0			0
$643$	30.6050			1.20695			0.603473	−	0.797384i	$-0.293783\pi$
$643$	30.6050			1.20695			0.603473	+	0.797384i	$0.293783\pi$
$644$		0			0
$645$	−4.10216			−0.161522
$646$		0			0
$647$	21.0512	−	36.4617i	0.827606	−	1.43346i	−0.0723044	−	0.997383i	$-0.523035\pi$
$647$	21.0512	−	36.4617i	0.827606	−	1.43346i	0.899911	−	0.436074i	$-0.143631\pi$
$648$		0			0
$649$	2.39037	+	4.14024i	0.0938302	+	0.162519i
$650$		0			0
$651$	−1.34502	+	0.732081i	−0.0527156	+	0.0286925i
$652$		0			0
$653$	−3.24271	−	5.61653i	−0.126897	−	0.219792i	0.795576	−	0.605854i	$-0.207168\pi$
$653$	−3.24271	−	5.61653i	−0.126897	−	0.219792i	−0.922473	+	0.386062i	$0.873835\pi$
$654$		0			0
$655$	−9.58706	+	16.6053i	−0.374597	+	0.648821i
$656$		0			0
$657$	−16.9620			−0.661752
$658$		0			0
$659$	7.74105			0.301548			0.150774	−	0.988568i	$-0.451823\pi$
$659$	7.74105			0.301548			0.150774	+	0.988568i	$0.451823\pi$
$660$		0			0
$661$	20.2360	−	35.0498i	0.787089	−	1.36328i	−0.140655	−	0.990059i	$-0.544921\pi$
$661$	20.2360	−	35.0498i	0.787089	−	1.36328i	0.927743	−	0.373219i	$-0.121746\pi$
$662$		0			0
$663$	0.591443	+	1.02441i	0.0229698	+	0.0397848i
$664$		0			0
$665$	−6.48774	−	3.96652i	−0.251584	−	0.153815i
$666$		0			0
$667$	−10.0146	−	17.3458i	−0.387766	−	0.671631i
$668$		0			0
$669$	−4.13161	+	7.15616i	−0.159737	+	0.276673i
$670$		0			0
$671$	−9.29533			−0.358842
$672$		0			0
$673$	−8.23073			−0.317271			−0.158636	−	0.987337i	$-0.550710\pi$
$673$	−8.23073			−0.317271			−0.158636	+	0.987337i	$0.550710\pi$
$674$		0			0
$675$	2.53871	−	4.39717i	0.0977148	−	0.169247i
$676$		0			0
$677$	11.1120	+	19.2465i	0.427067	+	0.739702i	0.996611	−	0.0822587i	$-0.0262134\pi$
$677$	11.1120	+	19.2465i	0.427067	+	0.739702i	−0.569544	+	0.821961i	$0.692880\pi$
$678$		0			0
$679$	−0.356414	+	14.1678i	−0.0136779	+	0.543709i
$680$		0			0
$681$	7.61109	+	13.1828i	0.291658	+	0.505166i
$682$		0			0
$683$	14.5452	−	25.1931i	0.556558	−	0.963986i	−0.441223	−	0.897398i	$-0.645455\pi$
$683$	14.5452	−	25.1931i	0.556558	−	0.963986i	0.997781	−	0.0665887i	$-0.0212115\pi$
$684$		0			0
$685$	−28.8171			−1.10105
$686$		0			0
$687$	6.91808			0.263941
$688$		0			0
$689$	−26.9071	+	46.6045i	−1.02508	+	1.77549i
$690$		0			0
$691$	−21.9502	−	38.0188i	−0.835025	−	1.44630i	−0.894010	−	0.448046i	$-0.852120\pi$
$691$	−21.9502	−	38.0188i	−0.835025	−	1.44630i	0.0589860	−	0.998259i	$-0.481213\pi$
$692$		0			0
$693$	0.176168	−	7.00284i	0.00669208	−	0.266016i
$694$		0			0
$695$	10.2681	+	17.7849i	0.389491	+	0.674618i
$696$		0			0
$697$	−0.111767	+	0.193586i	−0.00423348	+	0.00733260i
$698$		0			0
$699$	−7.78074			−0.294295
$700$		0			0
$701$	−26.1800			−0.988803			−0.494402	−	0.869234i	$-0.664613\pi$
$701$	−26.1800			−0.988803			−0.494402	+	0.869234i	$0.664613\pi$
$702$		0			0
$703$	0.204868	−	0.354841i	0.00772672	−	0.0133831i
$704$		0			0
$705$	−3.57966	−	6.20016i	−0.134818	−	0.233512i
$706$		0			0
$707$	−41.9808	−	25.6665i	−1.57885	−	0.965289i
$708$		0			0
$709$	8.60291	+	14.9007i	0.323089	+	0.559607i	0.981124	−	0.193381i	$-0.0619453\pi$
$709$	8.60291	+	14.9007i	0.323089	+	0.559607i	−0.658035	+	0.752988i	$0.728612\pi$
$710$		0			0
$711$	19.9677	−	34.5851i	0.748847	−	1.29704i
$712$		0			0
$713$	3.37432			0.126369
$714$		0			0
$715$	8.07899			0.302137
$716$		0			0
$717$	−5.44153	+	9.42500i	−0.203218	+	0.351983i
$718$		0			0
$719$	−2.44085	−	4.22768i	−0.0910285	−	0.157666i	0.816916	−	0.576757i	$-0.195682\pi$
$719$	−2.44085	−	4.22768i	−0.0910285	−	0.157666i	−0.907944	+	0.419091i	$0.862349\pi$
$720$		0			0
$721$	−39.1891	+	21.3302i	−1.45948	+	0.794377i
$722$		0			0
$723$	−4.77121	−	8.26398i	−0.177443	−	0.307341i
$724$		0			0
$725$	−4.38317	+	7.59188i	−0.162787	+	0.281955i
$726$		0			0
$727$	5.17704			0.192006			0.0960028	−	0.995381i	$-0.469394\pi$
$727$	5.17704			0.192006			0.0960028	+	0.995381i	$0.469394\pi$
$728$		0			0
$729$	−9.79221			−0.362674
$730$		0			0
$731$	0.852336	−	1.47629i	0.0315248	−	0.0546026i
$732$		0			0
$733$	5.85301	+	10.1377i	0.216186	+	0.374445i	0.953639	−	0.300954i	$-0.0973050\pi$
$733$	5.85301	+	10.1377i	0.216186	+	0.374445i	−0.737453	+	0.675399i	$0.763972\pi$
$734$		0			0
$735$	−7.74737	−	0.390043i	−0.285766	−	0.0143869i
$736$		0			0
$737$	6.51459	+	11.2836i	0.239968	+	0.415637i
$738$		0			0
$739$	−11.3435	+	19.6475i	−0.417277	+	0.722745i	−0.995664	−	0.0930175i	$-0.970349\pi$
$739$	−11.3435	+	19.6475i	−0.417277	+	0.722745i	0.578388	+	0.815762i	$0.303682\pi$
$740$		0			0
$741$	−3.95446			−0.145271
$742$		0			0
$743$	−28.5949			−1.04905			−0.524523	−	0.851396i	$-0.675756\pi$
$743$	−28.5949			−1.04905			−0.524523	+	0.851396i	$0.675756\pi$
$744$		0			0
$745$	−13.6060	+	23.5663i	−0.498486	+	0.863404i
$746$		0			0
$747$	9.04815	+	15.6719i	0.331055	+	0.573404i
$748$		0			0
$749$	24.7022	−	13.4451i	0.902600	−	0.491274i
$750$		0			0
$751$	19.3298	+	33.4801i	0.705353	+	1.22171i	0.966564	+	0.256426i	$0.0825448\pi$
$751$	19.3298	+	33.4801i	0.705353	+	1.22171i	−0.261211	+	0.965282i	$0.584122\pi$
$752$		0			0
$753$	1.79153	−	3.10303i	0.0652871	−	0.113081i
$754$		0			0
$755$	11.1140			0.404481
$756$		0			0
$757$	37.9253			1.37842			0.689209	−	0.724563i	$-0.257958\pi$
$757$	37.9253			1.37842			0.689209	+	0.724563i	$0.257958\pi$
$758$		0			0
$759$	1.02704	−	1.77889i	0.0372793	−	0.0645696i
$760$		0			0
$761$	−4.51819	−	7.82573i	−0.163784	−	0.283683i	0.772439	−	0.635089i	$-0.219037\pi$
$761$	−4.51819	−	7.82573i	−0.163784	−	0.283683i	−0.936223	+	0.351407i	$0.885703\pi$
$762$		0			0
$763$	23.1175	+	14.1337i	0.836910	+	0.511676i
$764$		0			0
$765$	−1.13814	−	1.97131i	−0.0411494	−	0.0712728i
$766$		0			0
$767$	−10.3442	+	17.9166i	−0.373506	+	0.646931i
$768$		0			0
$769$	30.9148			1.11482			0.557408	−	0.830239i	$-0.311796\pi$
$769$	30.9148			1.11482			0.557408	+	0.830239i	$0.311796\pi$
$770$		0			0
$771$	9.98229			0.359503
$772$		0			0
$773$	11.8707	−	20.5607i	0.426960	−	0.739517i	−0.569641	−	0.821894i	$-0.692918\pi$
$773$	11.8707	−	20.5607i	0.426960	−	0.739517i	0.996601	+	0.0823770i	$0.0262511\pi$
$774$		0			0
$775$	−0.738433	−	1.27900i	−0.0265253	−	0.0459432i
$776$		0			0
$777$	0.0105116	−	0.417845i	0.000377101	−	0.0149901i
$778$		0			0
$779$	−0.373644	−	0.647170i	−0.0133872	−	0.0231873i
$780$		0			0
$781$	−3.23025	+	5.59496i	−0.115588	+	0.200203i
$782$		0			0
$783$	−19.4031			−0.693410
$784$		0			0
$785$	44.8607			1.60115
$786$		0			0
$787$	−1.49115	+	2.58274i	−0.0531536	+	0.0920647i	−0.891378	−	0.453261i	$-0.850261\pi$
$787$	−1.49115	+	2.58274i	−0.0531536	+	0.0920647i	0.838224	+	0.545326i	$0.183594\pi$
$788$		0			0
$789$	4.30039	+	7.44849i	0.153098	+	0.265173i
$790$		0			0
$791$	0.577333	−	22.9495i	0.0205276	−	0.815990i
$792$		0			0
$793$	−20.1124	−	34.8358i	−0.714214	−	1.23705i
$794$		0			0
$795$	−6.89037	+	11.9345i	−0.244376	+	0.423272i
$796$		0			0
$797$	−25.7410			−0.911795			−0.455897	−	0.890032i	$-0.650682\pi$
$797$	−25.7410			−0.911795			−0.455897	+	0.890032i	$0.650682\pi$
$798$		0			0
$799$	2.97509			0.105251
$800$		0			0
$801$	3.44299	−	5.96343i	0.121652	−	0.210708i
$802$		0			0
$803$	3.20321	+	5.54812i	0.113039	+	0.195789i
$804$		0			0
$805$	14.5833	+	8.91601i	0.513992	+	0.314248i
$806$		0			0
$807$	−1.33336	−	2.30945i	−0.0469365	−	0.0812964i
$808$		0			0
$809$	−9.42821	+	16.3301i	−0.331478	+	0.574137i	−0.982802	−	0.184663i	$-0.940881\pi$
$809$	−9.42821	+	16.3301i	−0.331478	+	0.574137i	0.651324	+	0.758800i	$0.274214\pi$
$810$		0			0
$811$	37.0541			1.30114			0.650572	−	0.759444i	$-0.274529\pi$
$811$	37.0541			1.30114			0.650572	+	0.759444i	$0.274529\pi$
$812$		0			0
$813$	−13.9473			−0.489152
$814$		0			0
$815$	0.785994	−	1.36138i	0.0275322	−	0.0476871i
$816$		0			0
$817$	2.84941	+	4.93533i	0.0996883	+	0.172665i
$818$		0			0
$819$	26.6255	−	14.4919i	0.930370	−	0.506389i
$820$		0			0
$821$	−18.3982	−	31.8667i	−0.642103	−	1.11216i	−0.984962	−	0.172768i	$-0.944729\pi$
$821$	−18.3982	−	31.8667i	−0.642103	−	1.11216i	0.342859	−	0.939387i	$-0.388605\pi$
$822$		0			0
$823$	−7.62782	+	13.2118i	−0.265889	+	0.460533i	−0.967796	−	0.251735i	$-0.918999\pi$
$823$	−7.62782	+	13.2118i	−0.265889	+	0.460533i	0.701907	+	0.712268i	$0.252332\pi$
$824$		0			0
$825$	−0.899029			−0.0313002
$826$		0			0
$827$	19.4792			0.677357			0.338679	−	0.940902i	$-0.390020\pi$
$827$	19.4792			0.677357			0.338679	+	0.940902i	$0.390020\pi$
$828$		0			0
$829$	−16.5995	+	28.7512i	−0.576525	+	0.998570i	0.419349	+	0.907825i	$0.362258\pi$
$829$	−16.5995	+	28.7512i	−0.576525	+	0.998570i	−0.995874	+	0.0907453i	$0.971075\pi$
$830$		0			0
$831$	−2.09572	−	3.62989i	−0.0726996	−	0.125919i
$832$		0			0
$833$	1.75010	−	2.70709i	0.0606373	−	0.0937951i
$834$		0			0
$835$	14.4890	+	25.0957i	0.501413	+	0.868473i
$836$		0			0
$837$	1.63442	−	2.83090i	0.0564939	−	0.0978503i
$838$		0			0
$839$	−20.1416			−0.695366			−0.347683	−	0.937612i	$-0.613031\pi$
$839$	−20.1416			−0.695366			−0.347683	+	0.937612i	$0.613031\pi$
$840$		0			0
$841$	4.50019			0.155179
$842$		0			0
$843$	−1.44884	+	2.50947i	−0.0499007	+	0.0864306i
$844$		0			0
$845$	5.34562	+	9.25888i	0.183895	+	0.318515i
$846$		0			0
$847$	−2.32383	+	1.26483i	−0.0798478	+	0.0434602i
$848$		0			0
$849$	6.94805	+	12.0344i	0.238457	+	0.413019i
$850$		0			0
$851$	−0.460505	+	0.797618i	−0.0157859	+	0.0273420i
$852$		0			0
$853$	46.0669			1.57730			0.788650	−	0.614842i	$-0.210780\pi$
$853$	46.0669			1.57730			0.788650	+	0.614842i	$0.210780\pi$
$854$		0			0
$855$	7.60971			0.260247
$856$		0			0
$857$	26.6513	−	46.1613i	0.910390	−	1.57684i	0.0968754	−	0.995297i	$-0.469115\pi$
$857$	26.6513	−	46.1613i	0.910390	−	1.57684i	0.813514	−	0.581545i	$-0.197552\pi$
$858$		0			0
$859$	−26.6855	−	46.2206i	−0.910498	−	1.57703i	−0.813363	−	0.581757i	$-0.802366\pi$
$859$	−26.6855	−	46.2206i	−0.910498	−	1.57703i	−0.0971348	−	0.995271i	$-0.530968\pi$
$860$		0			0
$861$	−0.650394	−	0.397642i	−0.0221654	−	0.0135516i
$862$		0			0
$863$	−8.55195	−	14.8124i	−0.291112	−	0.504220i	0.682961	−	0.730455i	$-0.260692\pi$
$863$	−8.55195	−	14.8124i	−0.291112	−	0.504220i	−0.974073	+	0.226234i	$0.927358\pi$
$864$		0			0
$865$	12.4679	−	21.5950i	0.423921	−	0.734253i
$866$		0			0
$867$	9.96497			0.338428
$868$		0			0
$869$	−15.0833			−0.511665
$870$		0			0
$871$	−28.1914	+	48.8290i	−0.955230	+	1.65451i
$872$		0			0
$873$	−7.09125	−	12.2824i	−0.240002	−	0.415696i
$874$		0			0
$875$	0.809243	−	32.1681i	0.0273574	−	1.08748i
$876$		0			0
$877$	−22.6211	−	39.1809i	−0.763860	−	1.32304i	−0.940847	−	0.338832i	$-0.889968\pi$
$877$	−22.6211	−	39.1809i	−0.763860	−	1.32304i	0.176987	−	0.984213i	$-0.443365\pi$
$878$		0			0
$879$	−5.36819	+	9.29798i	−0.181065	+	0.313613i
$880$		0			0
$881$	31.6313			1.06569			0.532843	−	0.846214i	$-0.321124\pi$
$881$	31.6313			1.06569			0.532843	+	0.846214i	$0.321124\pi$
$882$		0			0
$883$	20.0613			0.675116			0.337558	−	0.941305i	$-0.390399\pi$
$883$	20.0613			0.675116			0.337558	+	0.941305i	$0.390399\pi$
$884$		0			0
$885$	−2.64893	+	4.58808i	−0.0890429	+	0.154227i
$886$		0			0
$887$	−1.94971	−	3.37700i	−0.0654648	−	0.113388i	0.831435	−	0.555622i	$-0.187520\pi$
$887$	−1.94971	−	3.37700i	−0.0654648	−	0.113388i	−0.896900	+	0.442233i	$0.854186\pi$
$888$		0			0
$889$	0.0883236	−	3.51094i	0.00296228	−	0.117753i
$890$		0			0
$891$	2.97656	+	5.15555i	0.0997184	+	0.172717i
$892$		0			0
$893$	−4.97296	+	8.61342i	−0.166414	+	0.288237i
$894$		0			0
$895$	16.9167			0.565464
$896$		0			0
$897$	8.88891			0.296792
$898$		0			0
$899$	−2.82189	+	4.88766i	−0.0941153	+	0.163013i
$900$		0			0
$901$	−2.86333	−	4.95943i	−0.0953912	−	0.165222i
$902$		0			0
$903$	4.95991	+	3.03242i	0.165055	+	0.100913i
$904$		0			0
$905$	18.8547	+	32.6572i	0.626750	+	1.08556i
$906$		0			0
$907$	18.6986	−	32.3870i	0.620878	−	1.07539i	−0.368445	−	0.929650i	$-0.620110\pi$
$907$	18.6986	−	32.3870i	0.620878	−	1.07539i	0.989323	−	0.145742i	$-0.0465570\pi$
$908$		0			0
$909$	49.2409			1.63322
$910$		0			0
$911$	37.3432			1.23723			0.618617	−	0.785693i	$-0.287693\pi$
$911$	37.3432			1.23723			0.618617	+	0.785693i	$0.287693\pi$
$912$		0			0
$913$	3.41741	−	5.91913i	0.113100	−	0.195895i
$914$		0			0
$915$	−5.15039	−	8.92074i	−0.170267	−	0.294911i
$916$		0			0
$917$	23.8667	−	12.9904i	0.788149	−	0.428980i
$918$		0			0
$919$	8.64027	+	14.9654i	0.285016	+	0.493663i	0.972613	−	0.232430i	$-0.0746677\pi$
$919$	8.64027	+	14.9654i	0.285016	+	0.493663i	−0.687597	+	0.726093i	$0.741334\pi$
$920$		0			0
$921$	−3.50720	+	6.07464i	−0.115566	+	0.200166i
$922$		0			0
$923$	−27.9574			−0.920229
$924$		0			0
$925$	0.403106			0.0132541
$926$		0			0
$927$	22.3251	−	38.6682i	0.733252	−	1.27003i
$928$		0			0
$929$	−20.2901	−	35.1434i	−0.665696	−	1.15302i	−0.979096	−	0.203398i	$-0.934802\pi$
$929$	−20.2901	−	35.1434i	−0.665696	−	1.15302i	0.313401	−	0.949621i	$-0.398532\pi$
$930$		0			0
$931$	4.91216	+	9.59182i	0.160989	+	0.314359i
$932$		0			0
$933$	−3.55408	−	6.15585i	−0.116355	−	0.201534i
$934$		0			0
$935$	−0.429864	+	0.744547i	−0.0140581	+	0.0243493i
$936$		0			0
$937$	−2.98949			−0.0976623			−0.0488312	−	0.998807i	$-0.515550\pi$
$937$	−2.98949			−0.0976623			−0.0488312	+	0.998807i	$0.515550\pi$
$938$		0			0
$939$	−7.13600			−0.232875
$940$		0			0
$941$	−1.35827	+	2.35259i	−0.0442782	+	0.0766921i	−0.887315	−	0.461164i	$-0.847432\pi$
$941$	−1.35827	+	2.35259i	−0.0442782	+	0.0766921i	0.843037	+	0.537856i	$0.180765\pi$
$942$		0			0
$943$	0.839883	+	1.45472i	0.0273504	+	0.0473722i
$944$		0			0
$945$	14.5438	−	7.91604i	0.473111	−	0.257509i
$946$		0			0
$947$	21.1498	+	36.6325i	0.687276	+	1.19040i	0.972716	+	0.232000i	$0.0745271\pi$
$947$	21.1498	+	36.6325i	0.687276	+	1.19040i	−0.285440	+	0.958397i	$0.592140\pi$
$948$		0			0
$949$	−13.8617	+	24.0091i	−0.449969	+	0.779369i
$950$		0			0
$951$	12.3992			0.402072
$952$		0			0
$953$	−54.7500			−1.77353			−0.886763	−	0.462225i	$-0.847051\pi$
$953$	−54.7500			−1.77353			−0.886763	+	0.462225i	$0.847051\pi$
$954$		0			0
$955$	13.1422	−	22.7630i	0.425272	−	0.736593i
$956$		0			0
$957$	1.71780	+	2.97532i	0.0555286	+	0.0961783i
$958$		0			0
$959$	34.8427	+	21.3024i	1.12513	+	0.687889i
$960$		0			0
$961$	15.0246	+	26.0234i	0.484664	+	0.839463i
$962$		0			0
$963$	−14.0723	+	24.3739i	−0.453473	+	0.785438i
$964$		0			0
$965$	30.6840			0.987754
$966$		0			0
$967$	11.4356			0.367744			0.183872	−	0.982950i	$-0.441137\pi$
$967$	11.4356			0.367744			0.183872	+	0.982950i	$0.441137\pi$
$968$		0			0
$969$	0.210408	−	0.364437i	0.00675926	−	0.0117074i
$970$		0			0
$971$	18.9069	+	32.7477i	0.606751	+	1.05092i	0.991772	+	0.128016i	$0.0408609\pi$
$971$	18.9069	+	32.7477i	0.606751	+	1.05092i	−0.385021	+	0.922908i	$0.625806\pi$
$972$		0			0
$973$	0.731910	−	29.0941i	0.0234639	−	0.932713i
$974$		0			0
$975$	−1.94524	−	3.36926i	−0.0622976	−	0.107903i
$976$		0			0
$977$	−9.93181	+	17.2024i	−0.317747	+	0.550353i	−0.980018	−	0.198911i	$-0.936259\pi$
$977$	−9.93181	+	17.2024i	−0.317747	+	0.550353i	0.662271	+	0.749264i	$0.269593\pi$
$978$		0			0
$979$	−2.60078			−0.0831212
$980$		0			0
$981$	−27.1154			−0.865727
$982$		0			0
$983$	−13.7542	+	23.8229i	−0.438690	+	0.759833i	−0.997589	−	0.0694025i	$-0.977891\pi$
$983$	−13.7542	+	23.8229i	−0.438690	+	0.759833i	0.558899	+	0.829236i	$0.311224\pi$
$984$		0			0
$985$	−7.92480	−	13.7262i	−0.252505	−	0.437352i
$986$		0			0
$987$	−0.255158	+	10.1428i	−0.00812178	+	0.322848i
$988$		0			0
$989$	−6.40496	−	11.0937i	−0.203666	−	0.352760i
$990$		0			0
$991$	−16.5400	+	28.6481i	−0.525410	+	0.910036i	0.474152	+	0.880443i	$0.342755\pi$
$991$	−16.5400	+	28.6481i	−0.525410	+	0.910036i	−0.999562	+	0.0295933i	$0.990579\pi$
$992$		0			0
$993$	3.57880			0.113570
$994$		0			0
$995$	−51.2613			−1.62509
$996$		0			0
$997$	1.04835	−	1.81579i	0.0332016	−	0.0575068i	−0.848947	−	0.528478i	$-0.822763\pi$
$997$	1.04835	−	1.81579i	0.0332016	−	0.0575068i	0.882149	+	0.470971i	$0.156096\pi$
$998$		0			0
$999$	0.446110	+	0.772686i	0.0141143	+	0.0244467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.i.a.221.2	yes	6
3.2	odd	2		2772.2.s.f.2377.2		6
4.3	odd	2		1232.2.q.l.529.2		6
7.2	even	3	inner	308.2.i.a.177.2	✓	6
7.3	odd	6		2156.2.a.h.1.2		3
7.4	even	3		2156.2.a.i.1.2		3
7.5	odd	6		2156.2.i.l.177.2		6
7.6	odd	2		2156.2.i.l.1145.2		6
21.2	odd	6		2772.2.s.f.793.2		6
28.3	even	6		8624.2.a.cn.1.2		3
28.11	odd	6		8624.2.a.ci.1.2		3
28.23	odd	6		1232.2.q.l.177.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.a.177.2	✓	6	7.2	even	3	inner
308.2.i.a.221.2	yes	6	1.1	even	1	trivial
1232.2.q.l.177.2		6	28.23	odd	6
1232.2.q.l.529.2		6	4.3	odd	2
2156.2.a.h.1.2		3	7.3	odd	6
2156.2.a.i.1.2		3	7.4	even	3
2156.2.i.l.177.2		6	7.5	odd	6
2156.2.i.l.1145.2		6	7.6	odd	2
2772.2.s.f.793.2		6	21.2	odd	6
2772.2.s.f.2377.2		6	3.2	odd	2
8624.2.a.ci.1.2		3	28.11	odd	6
8624.2.a.cn.1.2		3	28.3	even	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.296790 - 0.514055i) q^{3} +(0.933463 + 1.61680i) q^{5} +(0.0665372 - 2.64491i) q^{7} +(1.32383 + 2.29294i) q^{9} +(0.500000 - 0.866025i) q^{11} +4.32743 q^{13} +1.10817 q^{15} +(-0.230252 + 0.398809i) q^{17} +(-0.769748 - 1.33324i) q^{19} +(-1.33988 - 0.819187i) q^{21} +(1.73025 + 2.99689i) q^{23} +(0.757295 - 1.31167i) q^{25} +3.35234 q^{27} -5.78794 q^{29} +(0.487547 - 0.844456i) q^{31} +(-0.296790 - 0.514055i) q^{33} +(4.33842 - 2.36135i) q^{35} +(0.133074 + 0.230492i) q^{37} +(1.28434 - 2.22454i) q^{39} +0.485411 q^{41} -3.70175 q^{43} +(-2.47150 + 4.28076i) q^{45} +(-3.23025 - 5.59496i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(0.136673 + 0.236725i) q^{51} +(-6.21780 + 10.7695i) q^{53} +1.86693 q^{55} -0.913813 q^{57} +(-2.39037 + 4.14024i) q^{59} +(-4.64766 - 8.04999i) q^{61} +(6.15272 - 3.34886i) q^{63} +(4.03950 + 6.99661i) q^{65} +(-6.51459 + 11.2836i) q^{67} +2.05408 q^{69} -6.46050 q^{71} +(-3.20321 + 5.54812i) q^{73} +(-0.449514 - 0.778582i) q^{75} +(-2.25729 - 1.38008i) q^{77} +(-7.54163 - 13.0625i) q^{79} +(-2.97656 + 5.15555i) q^{81} +6.83482 q^{83} -0.859728 q^{85} +(-1.71780 + 2.97532i) q^{87} +(-1.30039 - 2.25234i) q^{89} +(0.287935 - 11.4457i) q^{91} +(-0.289398 - 0.501252i) q^{93} +(1.43706 - 2.48906i) q^{95} -5.35661 q^{97} +2.64766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{5} + 4 q^{7} - 4 q^{9} + 3 q^{11} + 6 q^{13} - 30 q^{15} + 5 q^{17} - 11 q^{19} - 10 q^{21} + 4 q^{23} - 11 q^{25} + 44 q^{27} - 2 q^{29} - 19 q^{31} + q^{33} - 17 q^{35} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^5 + 4 * q^7 - 4 * q^9 + 3 * q^11 + 6 * q^13 - 30 * q^15 + 5 * q^17 - 11 * q^19 - 10 * q^21 + 4 * q^23 - 11 * q^25 + 44 * q^27 - 2 * q^29 - 19 * q^31 + q^33 - 17 * q^35 + 8 * q^37 - 17 * q^39 + 34 * q^41 + 20 * q^43 + 21 * q^45 - 13 * q^47 - 12 * q^49 - 9 * q^53 + 4 * q^55 + 4 * q^57 - 6 * q^59 - 4 * q^61 + 50 * q^63 + 37 * q^65 - 8 * q^67 - 6 * q^69 - 26 * q^71 - 22 * q^73 - 13 * q^75 + 2 * q^77 - 5 * q^79 - 19 * q^81 + 6 * q^83 - 14 * q^85 + 18 * q^87 + 3 * q^89 - 31 * q^91 - 14 * q^93 - 3 * q^95 + 50 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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