LMFDB - Embedded newform 125.2.d.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(26,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("125.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.d (of order $5$, degree $4$, not 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.2
Root			$0.0566033 + 1.17421i$ of defining polynomial
Character	$\chi$	$=$	125.101
Dual form			125.2.d.b.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0566033 + 0.174207i) q^{2} +(1.19083 + 0.865190i) q^{3} +(1.59089 + 1.15585i) q^{4} +(-0.218127 + 0.158479i) q^{6} -3.26086 q^{7} +(-0.587785 + 0.427051i) q^{8} +(-0.257524 - 0.792578i) q^{9} +O(q^{10})$	\(q+(-0.0566033 + 0.174207i) q^{2} +(1.19083 + 0.865190i) q^{3} +(1.59089 + 1.15585i) q^{4} +(-0.218127 + 0.158479i) q^{6} -3.26086 q^{7} +(-0.587785 + 0.427051i) q^{8} +(-0.257524 - 0.792578i) q^{9} +(0.618034 - 1.90211i) q^{11} +(0.894453 + 2.75284i) q^{12} +(-0.0915860 - 0.281873i) q^{13} +(0.184575 - 0.568064i) q^{14} +(1.17421 + 3.61384i) q^{16} +(4.17693 - 3.03472i) q^{17} +0.152649 q^{18} +(-1.39991 + 1.01709i) q^{19} +(-3.88313 - 2.82126i) q^{21} +(0.296379 + 0.215332i) q^{22} +(0.271685 - 0.836161i) q^{23} -1.06943 q^{24} +0.0542883 q^{26} +(1.74363 - 5.36635i) q^{27} +(-5.18766 - 3.76906i) q^{28} +(-4.78304 - 3.47508i) q^{29} +(-4.93462 + 3.58521i) q^{31} -2.14910 q^{32} +(2.38166 - 1.73038i) q^{33} +(0.292241 + 0.899425i) q^{34} +(0.506408 - 1.55856i) q^{36} +(2.49933 + 7.69215i) q^{37} +(-0.0979452 - 0.301444i) q^{38} +(0.134810 - 0.414902i) q^{39} +(-0.313697 - 0.965461i) q^{41} +(0.711281 - 0.516776i) q^{42} -3.24199 q^{43} +(3.18178 - 2.31170i) q^{44} +(0.130287 + 0.0946589i) q^{46} +(-3.41402 - 2.48043i) q^{47} +(-1.72837 + 5.31939i) q^{48} +3.63318 q^{49} +7.59963 q^{51} +(0.180099 - 0.554288i) q^{52} +(6.55362 + 4.76148i) q^{53} +(0.836161 + 0.607507i) q^{54} +(1.91668 - 1.39255i) q^{56} -2.54703 q^{57} +(0.876119 - 0.636538i) q^{58} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(-0.345253 - 1.06258i) q^{62} +(0.839749 + 2.58448i) q^{63} +(-2.22677 + 6.85329i) q^{64} +(0.166634 + 0.512848i) q^{66} +(-5.57255 + 4.04870i) q^{67} +10.1527 q^{68} +(1.04697 - 0.760668i) q^{69} +(4.82884 + 3.50836i) q^{71} +(0.489840 + 0.355890i) q^{72} +(2.72967 - 8.40107i) q^{73} -1.48150 q^{74} -3.40270 q^{76} +(-2.01532 + 6.20252i) q^{77} +(0.0646482 + 0.0469697i) q^{78} +(6.27851 + 4.56161i) q^{79} +(4.69667 - 3.41233i) q^{81} +0.185946 q^{82} +(-11.7432 + 8.53192i) q^{83} +(-2.91668 - 8.97663i) q^{84} +(0.183507 - 0.564778i) q^{86} +(-2.68919 - 8.27647i) q^{87} +(0.449028 + 1.38197i) q^{88} +(2.32579 - 7.15805i) q^{89} +(0.298649 + 0.919147i) q^{91} +(1.39870 - 1.01621i) q^{92} -8.97820 q^{93} +(0.625353 - 0.454345i) q^{94} +(-2.55922 - 1.85938i) q^{96} +(5.44184 + 3.95373i) q^{97} +(-0.205650 + 0.632925i) q^{98} -1.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	$ 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46} - 28 q^{49} - 8 q^{51} + 10 q^{54} + 20 q^{56} - 18 q^{61} - 8 q^{64} + 24 q^{66} - 34 q^{69} + 12 q^{71} + 24 q^{74} - 40 q^{76} - 30 q^{79} + 56 q^{81} - 36 q^{84} - 18 q^{86} + 50 q^{89} + 12 q^{91} + 54 q^{94} + 32 q^{96} + 16 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9 - 8 * q^11 - 26 * q^14 + 6 * q^16 + 10 * q^19 - 8 * q^21 + 40 * q^24 + 12 * q^26 + 10 * q^29 - 18 * q^31 - 26 * q^34 + 46 * q^36 + 6 * q^39 - 8 * q^41 + 4 * q^44 - 38 * q^46 - 28 * q^49 - 8 * q^51 + 10 * q^54 + 20 * q^56 - 18 * q^61 - 8 * q^64 + 24 * q^66 - 34 * q^69 + 12 * q^71 + 24 * q^74 - 40 * q^76 - 30 * q^79 + 56 * q^81 - 36 * q^84 - 18 * q^86 + 50 * q^89 + 12 * q^91 + 54 * q^94 + 32 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.0566033	+	0.174207i	−0.0400246	+	0.123183i	−0.969072	−	0.246777i	$-0.920629\pi$
$2$	−0.0566033	+	0.174207i	−0.0400246	+	0.123183i	0.929048	+	0.369960i	$0.120629\pi$
$3$	1.19083	+	0.865190i	0.687527	+	0.499518i	0.875846	−	0.482590i	$-0.160304\pi$
$3$	1.19083	+	0.865190i	0.687527	+	0.499518i	−0.188319	+	0.982108i	$0.560304\pi$
$4$	1.59089	+	1.15585i	0.795445	+	0.577925i
$5$		0			0
$5$		0			0
$6$	−0.218127	+	0.158479i	−0.0890500	+	0.0646986i
$7$	−3.26086			−1.23249			−0.616244	−	0.787555i	$-0.711346\pi$
$7$	−3.26086			−1.23249			−0.616244	+	0.787555i	$0.711346\pi$
$8$	−0.587785	+	0.427051i	−0.207813	+	0.150985i
$9$	−0.257524	−	0.792578i	−0.0858414	−	0.264193i
$10$		0			0
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	0.894453	+	2.75284i	0.258206	+	0.794678i
$13$	−0.0915860	−	0.281873i	−0.0254014	−	0.0781775i	0.937552	−	0.347845i	$-0.113086\pi$
$13$	−0.0915860	−	0.281873i	−0.0254014	−	0.0781775i	−0.962954	+	0.269667i	$0.913086\pi$
$14$	0.184575	−	0.568064i	0.0493298	−	0.151821i
$15$		0			0
$16$	1.17421	+	3.61384i	0.293552	+	0.903459i
$17$	4.17693	−	3.03472i	1.01305	−	0.736027i	0.0482067	−	0.998837i	$-0.484649\pi$
$17$	4.17693	−	3.03472i	1.01305	−	0.736027i	0.964847	+	0.262810i	$0.0846494\pi$
$18$	0.152649			0.0359798
$19$	−1.39991	+	1.01709i	−0.321161	+	0.233337i	−0.736671	−	0.676252i	$-0.763603\pi$
$19$	−1.39991	+	1.01709i	−0.321161	+	0.233337i	0.415510	+	0.909589i	$0.363603\pi$
$20$		0			0
$21$	−3.88313	−	2.82126i	−0.847369	−	0.615649i
$22$	0.296379	+	0.215332i	0.0631881	+	0.0459089i
$23$	0.271685	−	0.836161i	0.0566503	−	0.174352i	−0.918728	−	0.394892i	$-0.870782\pi$
$23$	0.271685	−	0.836161i	0.0566503	−	0.174352i	0.975378	+	0.220540i	$0.0707820\pi$
$24$	−1.06943			−0.218297
$25$		0			0
$26$	0.0542883			0.0106468
$27$	1.74363	−	5.36635i	0.335563	−	1.03276i
$28$	−5.18766	−	3.76906i	−0.980376	−	0.712285i
$29$	−4.78304	−	3.47508i	−0.888188	−	0.645306i	0.0472171	−	0.998885i	$-0.484965\pi$
$29$	−4.78304	−	3.47508i	−0.888188	−	0.645306i	−0.935405	+	0.353578i	$0.884965\pi$
$30$		0			0
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	−0.934907	−	0.354894i	$-0.884517\pi$
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	0.0486220	+	0.998817i	$0.484517\pi$
$32$	−2.14910			−0.379912
$33$	2.38166	−	1.73038i	0.414594	−	0.301220i
$34$	0.292241	+	0.899425i	0.0501189	+	0.154250i
$35$		0			0
$36$	0.506408	−	1.55856i	0.0844013	−	0.259761i
$37$	2.49933	+	7.69215i	0.410887	+	1.26458i	0.915878	+	0.401457i	$0.131496\pi$
$37$	2.49933	+	7.69215i	0.410887	+	1.26458i	−0.504991	+	0.863125i	$0.668504\pi$
$38$	−0.0979452	−	0.301444i	−0.0158888	−	0.0489007i
$39$	0.134810	−	0.414902i	0.0215869	−	0.0664376i
$40$		0			0
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	0.923568	−	0.383434i	$-0.125259\pi$
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	−0.972559	+	0.232655i	$0.925259\pi$
$42$	0.711281	−	0.516776i	0.109753	−	0.0797403i
$43$	−3.24199			−0.494399			−0.247200	−	0.968965i	$-0.579510\pi$
$43$	−3.24199			−0.494399			−0.247200	+	0.968965i	$0.579510\pi$
$44$	3.18178	−	2.31170i	0.479671	−	0.348502i
$45$		0			0
$46$	0.130287	+	0.0946589i	0.0192097	+	0.0139567i
$47$	−3.41402	−	2.48043i	−0.497986	−	0.361808i	0.310261	−	0.950651i	$-0.399583\pi$
$47$	−3.41402	−	2.48043i	−0.497986	−	0.361808i	−0.808247	+	0.588844i	$0.799583\pi$
$48$	−1.72837	+	5.31939i	−0.249469	+	0.767787i
$49$	3.63318			0.519026
$50$		0			0
$51$	7.59963			1.06416
$52$	0.180099	−	0.554288i	0.0249753	−	0.0768660i
$53$	6.55362	+	4.76148i	0.900209	+	0.654040i	0.938520	−	0.345226i	$-0.112198\pi$
$53$	6.55362	+	4.76148i	0.900209	+	0.654040i	−0.0383106	+	0.999266i	$0.512198\pi$
$54$	0.836161	+	0.607507i	0.113787	+	0.0826712i
$55$		0			0
$56$	1.91668	−	1.39255i	0.256128	−	0.186088i
$57$	−2.54703			−0.337363
$58$	0.876119	−	0.636538i	0.115040	−	0.0835815i
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	0.996591	+	0.0824976i	$0.0262897\pi$
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	−0.757768	+	0.652524i	$0.773710\pi$
$60$		0			0
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	−0.931308	−	0.364233i	$-0.881331\pi$
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	0.967535	+	0.252738i	$0.0813312\pi$
$62$	−0.345253	−	1.06258i	−0.0438472	−	0.134948i
$63$	0.839749	+	2.58448i	0.105798	+	0.325614i
$64$	−2.22677	+	6.85329i	−0.278346	+	0.856661i
$65$		0			0
$66$	0.166634	+	0.512848i	0.0205113	+	0.0631272i
$67$	−5.57255	+	4.04870i	−0.680796	+	0.494627i	−0.873622	−	0.486606i	$-0.838235\pi$
$67$	−5.57255	+	4.04870i	−0.680796	+	0.494627i	0.192826	+	0.981233i	$0.438235\pi$
$68$	10.1527			1.23120
$69$	1.04697	−	0.760668i	0.126040	−	0.0915737i
$70$		0			0
$71$	4.82884	+	3.50836i	0.573078	+	0.416366i	0.836222	−	0.548391i	$-0.184759\pi$
$71$	4.82884	+	3.50836i	0.573078	+	0.416366i	−0.263144	+	0.964757i	$0.584759\pi$
$72$	0.489840	+	0.355890i	0.0577282	+	0.0419420i
$73$	2.72967	−	8.40107i	0.319484	−	0.983271i	−0.654385	−	0.756161i	$-0.727072\pi$
$73$	2.72967	−	8.40107i	0.319484	−	0.983271i	0.973869	−	0.227110i	$-0.0729276\pi$
$74$	−1.48150			−0.172220
$75$		0			0
$76$	−3.40270			−0.390317
$77$	−2.01532	+	6.20252i	−0.229667	+	0.706842i
$78$	0.0646482	+	0.0469697i	0.00731997	+	0.00531827i
$79$	6.27851	+	4.56161i	0.706388	+	0.513221i	0.882006	−	0.471237i	$-0.156192\pi$
$79$	6.27851	+	4.56161i	0.706388	+	0.513221i	−0.175618	+	0.984458i	$0.556192\pi$
$80$		0			0
$81$	4.69667	−	3.41233i	0.521852	−	0.379148i
$82$	0.185946			0.0205343
$83$	−11.7432	+	8.53192i	−1.28898	+	0.936500i	−0.999784	−	0.0207694i	$-0.993388\pi$
$83$	−11.7432	+	8.53192i	−1.28898	+	0.936500i	−0.289197	+	0.957269i	$0.593388\pi$
$84$	−2.91668	−	8.97663i	−0.318236	−	0.979430i
$85$		0			0
$86$	0.183507	−	0.564778i	0.0197881	−	0.0609015i
$87$	−2.68919	−	8.27647i	−0.288311	−	0.887331i
$88$	0.449028	+	1.38197i	0.0478665	+	0.147318i
$89$	2.32579	−	7.15805i	0.246534	−	0.758752i	−0.748847	−	0.662743i	$-0.769392\pi$
$89$	2.32579	−	7.15805i	0.246534	−	0.758752i	0.995380	−	0.0960092i	$-0.0306078\pi$
$90$		0			0
$91$	0.298649	+	0.919147i	0.0313069	+	0.0963528i
$92$	1.39870	−	1.01621i	0.145824	−	0.105948i
$93$	−8.97820			−0.930996
$94$	0.625353	−	0.454345i	0.0645002	−	0.0468621i
$95$		0			0
$96$	−2.55922	−	1.85938i	−0.261200	−	0.189773i
$97$	5.44184	+	3.95373i	0.552535	+	0.401440i	0.828719	−	0.559664i	$-0.189070\pi$
$97$	5.44184	+	3.95373i	0.552535	+	0.401440i	−0.276184	+	0.961105i	$0.589070\pi$
$98$	−0.205650	+	0.632925i	−0.0207738	+	0.0639351i
$99$	−1.66673			−0.167513
$100$		0			0
$101$	−12.1955			−1.21350			−0.606748	−	0.794894i	$-0.707526\pi$
$101$	−12.1955			−1.21350			−0.606748	+	0.794894i	$0.707526\pi$
$102$	−0.430164	+	1.32391i	−0.0425926	+	0.131086i
$103$	−1.11758	−	0.811969i	−0.110118	−	0.0800057i	0.531363	−	0.847144i	$-0.321680\pi$
$103$	−1.11758	−	0.811969i	−0.110118	−	0.0800057i	−0.641482	+	0.767138i	$0.721680\pi$
$104$	0.174207	+	0.126569i	0.0170824	+	0.0124111i
$105$		0			0
$106$	−1.20044	+	0.872171i	−0.116597	+	0.0847127i
$107$	15.8285			1.53020			0.765101	−	0.643911i	$-0.222689\pi$
$107$	15.8285			1.53020			0.765101	+	0.643911i	$0.222689\pi$
$108$	8.97663	−	6.52190i	0.863776	−	0.627570i
$109$	−0.619199	−	1.90570i	−0.0593085	−	0.182533i	0.917013	−	0.398857i	$-0.130593\pi$
$109$	−0.619199	−	1.90570i	−0.0593085	−	0.182533i	−0.976322	+	0.216324i	$0.930593\pi$
$110$		0			0
$111$	−3.67889	+	11.3225i	−0.349185	+	1.07468i
$112$	−3.82892	−	11.7842i	−0.361799	−	1.11350i
$113$	−3.22227	−	9.91713i	−0.303126	−	0.932925i	−0.980370	−	0.197167i	$-0.936826\pi$
$113$	−3.22227	−	9.91713i	−0.303126	−	0.932925i	0.677244	−	0.735758i	$-0.263174\pi$
$114$	0.144170	−	0.443711i	0.0135028	−	0.0415573i
$115$		0			0
$116$	−3.59262	−	11.0569i	−0.333566	−	1.02661i
$117$	−0.199821	+	0.145178i	−0.0184734	+	0.0134217i
$118$	−1.08737			−0.100101
$119$	−13.6204	+	9.89577i	−1.24858	+	0.907144i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	0.135684	+	0.0985805i	0.0122843	+	0.00892506i
$123$	0.461746	−	1.42111i	0.0416343	−	0.128137i
$124$	−11.9944			−1.07713
$125$		0			0
$126$	−0.497767			−0.0443446
$127$	−1.80777	+	5.56375i	−0.160414	+	0.493703i	−0.998669	−	0.0515752i	$-0.983576\pi$
$127$	−1.80777	+	5.56375i	−0.160414	+	0.493703i	0.838255	+	0.545278i	$0.183576\pi$
$128$	−4.54517	−	3.30226i	−0.401740	−	0.291881i
$129$	−3.86067	−	2.80494i	−0.339913	−	0.246961i
$130$		0			0
$131$	1.21081	−	0.879704i	0.105789	−	0.0768601i	−0.533633	−	0.845716i	$-0.679174\pi$
$131$	1.21081	−	0.879704i	0.105789	−	0.0768601i	0.639422	+	0.768856i	$0.279174\pi$
$132$	5.78902			0.503870
$133$	4.56489	−	3.31659i	0.395827	−	0.287585i
$134$	−0.389887	−	1.19995i	−0.0336811	−	0.103660i
$135$		0			0
$136$	−1.15916	+	3.56752i	−0.0993970	+	0.305913i
$137$	−2.42543	−	7.46472i	−0.207219	−	0.637754i	−0.999615	−	0.0277472i	$-0.991167\pi$
$137$	−2.42543	−	7.46472i	−0.207219	−	0.637754i	0.792396	−	0.610007i	$-0.208833\pi$
$138$	0.0732518	+	0.225446i	0.00623560	+	0.0191912i
$139$	1.66607	−	5.12764i	0.141314	−	0.434921i	−0.855204	−	0.518291i	$-0.826568\pi$
$139$	1.66607	−	5.12764i	0.141314	−	0.434921i	0.996519	+	0.0833702i	$0.0265684\pi$
$140$		0			0
$141$	−1.91948	−	5.90755i	−0.161649	−	0.497505i
$142$	−0.884509	+	0.642634i	−0.0742264	+	0.0539286i
$143$	−0.592757			−0.0495689
$144$	2.56186	−	1.86130i	0.213488	−	0.155108i
$145$		0			0
$146$	1.30902	+	0.951057i	0.108335	+	0.0787100i
$147$	4.32651	+	3.14339i	0.356844	+	0.259262i
$148$	−4.91480	+	15.1262i	−0.403994	+	1.24337i
$149$	18.8229			1.54203			0.771015	−	0.636817i	$-0.219749\pi$
$149$	18.8229			1.54203			0.771015	+	0.636817i	$0.219749\pi$
$150$		0			0
$151$	−3.88797			−0.316398			−0.158199	−	0.987407i	$-0.550569\pi$
$151$	−3.88797			−0.316398			−0.158199	+	0.987407i	$0.550569\pi$
$152$	0.388495	−	1.19566i	0.0315111	−	0.0969811i
$153$	−3.48091	−	2.52903i	−0.281415	−	0.204460i
$154$	−0.966448	−	0.702166i	−0.0778786	−	0.0565821i
$155$		0			0
$156$	0.694033	−	0.504244i	0.0555671	−	0.0403718i
$157$	4.28378			0.341883			0.170941	−	0.985281i	$-0.445319\pi$
$157$	4.28378			0.341883			0.170941	+	0.985281i	$0.445319\pi$
$158$	−1.15005	+	0.835559i	−0.0914930	+	0.0664735i
$159$	3.68467	+	11.3403i	0.292214	+	0.899341i
$160$		0			0
$161$	−0.885926	+	2.72660i	−0.0698208	+	0.214886i
$162$	0.328605	+	1.01134i	0.0258176	+	0.0794585i
$163$	4.85970	+	14.9566i	0.380641	+	1.17149i	0.939593	+	0.342293i	$0.111204\pi$
$163$	4.85970	+	14.9566i	0.380641	+	1.17149i	−0.558952	+	0.829200i	$0.688796\pi$
$164$	0.616869	−	1.89853i	0.0481694	−	0.148250i
$165$		0			0
$166$	−0.821618	−	2.52868i	−0.0637699	−	0.196264i
$167$	−17.0161	+	12.3629i	−1.31674	+	0.956670i	−0.316777	+	0.948500i	$0.602601\pi$
$167$	−17.0161	+	12.3629i	−1.31674	+	0.956670i	−0.999967	+	0.00816967i	$0.997399\pi$
$168$	3.48727			0.269049
$169$	10.4462	−	7.58958i	0.803551	−	0.583814i
$170$		0			0
$171$	1.16663	+	0.847609i	0.0892148	+	0.0648183i
$172$	−5.15765	−	3.74725i	−0.393267	−	0.285725i
$173$	2.21461	−	6.81587i	0.168374	−	0.518201i	−0.830895	−	0.556429i	$-0.812171\pi$
$173$	2.21461	−	6.81587i	0.168374	−	0.518201i	0.999269	+	0.0382277i	$0.0121712\pi$
$174$	1.59404			0.120844
$175$		0			0
$176$	7.59963			0.572843
$177$	−2.70019	+	8.31034i	−0.202959	+	0.624643i
$178$	1.11534	+	0.810339i	0.0835979	+	0.0607375i
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	0.317565	−	0.948237i	$-0.397135\pi$
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	−0.803694	+	0.595043i	$0.797135\pi$
$180$		0			0
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.242200	−	0.970226i	$-0.422131\pi$
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.997584	+	0.0694707i	$0.0221310\pi$
$182$	−0.177026			−0.0131221
$183$	1.09034	−	0.792181i	0.0806005	−	0.0585597i
$184$	0.197391	+	0.607507i	0.0145518	+	0.0447860i
$185$		0			0
$186$	0.508196	−	1.56407i	0.0372627	−	0.114683i
$187$	−3.19089	−	9.82055i	−0.233341	−	0.718150i
$188$	−2.56432	−	7.89218i	−0.187023	−	0.575596i
$189$	−5.68574	+	17.4989i	−0.413577	+	1.27286i
$190$		0			0
$191$	5.57167	+	17.1478i	0.403152	+	1.24077i	0.922429	+	0.386167i	$0.126201\pi$
$191$	5.57167	+	17.1478i	0.403152	+	1.24077i	−0.519277	+	0.854606i	$0.673799\pi$
$192$	−8.58110	+	6.23453i	−0.619288	+	0.449939i
$193$	6.78859			0.488653			0.244327	−	0.969693i	$-0.421433\pi$
$193$	6.78859			0.488653			0.244327	+	0.969693i	$0.421433\pi$
$194$	−0.996793	+	0.724213i	−0.0715656	+	0.0519955i
$195$		0			0
$196$	5.77999	+	4.19941i	0.412856	+	0.299958i
$197$	−6.46839	−	4.69956i	−0.460854	−	0.334830i	0.333012	−	0.942923i	$-0.391935\pi$
$197$	−6.46839	−	4.69956i	−0.460854	−	0.334830i	−0.793866	+	0.608092i	$0.791935\pi$
$198$	0.0943425	−	0.290356i	0.00670463	−	0.0206347i
$199$	−5.20485			−0.368962			−0.184481	−	0.982836i	$-0.559060\pi$
$199$	−5.20485			−0.368962			−0.184481	+	0.982836i	$0.559060\pi$
$200$		0			0
$201$	−10.1389			−0.715141
$202$	0.690305	−	2.12454i	0.0485697	−	0.149482i
$203$	15.5968	+	11.3317i	1.09468	+	0.795332i
$204$	12.0902	+	8.78402i	0.846481	+	0.615005i
$205$		0			0
$206$	0.204709	−	0.148730i	0.0142628	−	0.0103625i
$207$	−0.732688			−0.0509254
$208$	0.911102	−	0.661954i	0.0631735	−	0.0458983i
$209$	1.06943	+	3.29138i	0.0739743	+	0.227669i
$210$		0			0
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	−0.603872	−	0.797082i	$-0.706376\pi$
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	0.957055	−	0.289906i	$-0.0936239\pi$
$212$	4.92253	+	15.1500i	0.338081	+	1.04051i
$213$	2.71494	+	8.35573i	0.186025	+	0.572525i
$214$	−0.895947	+	2.75744i	−0.0612456	+	0.188495i
$215$		0			0
$216$	1.26682	+	3.89889i	0.0861965	+	0.265286i
$217$	16.0911	−	11.6909i	1.09233	−	0.793628i
$218$	0.367035			0.0248587
$219$	10.5191	−	7.64258i	0.710815	−	0.516438i
$220$		0			0
$221$	−1.23795	−	0.899425i	−0.0832737	−	0.0605019i
$222$	−1.76421	−	1.28178i	−0.118406	−	0.0860272i
$223$	2.04819	−	6.30368i	0.137157	−	0.422126i	−0.858762	−	0.512374i	$-0.828766\pi$
$223$	2.04819	−	6.30368i	0.137157	−	0.422126i	0.995919	+	0.0902485i	$0.0287661\pi$
$224$	7.00792			0.468236
$225$		0			0
$226$	1.91002			0.127053
$227$	4.13833	−	12.7365i	0.274671	−	0.845350i	−0.714636	−	0.699497i	$-0.753407\pi$
$227$	4.13833	−	12.7365i	0.274671	−	0.845350i	0.989306	−	0.145853i	$-0.0465926\pi$
$228$	−4.05205	−	2.94398i	−0.268353	−	0.194970i
$229$	−8.16032	−	5.92882i	−0.539249	−	0.391788i	0.284557	−	0.958659i	$-0.408154\pi$
$229$	−8.16032	−	5.92882i	−0.539249	−	0.391788i	−0.823806	+	0.566872i	$0.808154\pi$
$230$		0			0
$231$	−7.76626	+	5.64252i	−0.510983	+	0.371251i
$232$	4.29544			0.282009
$233$	−17.8028	+	12.9345i	−1.16630	+	0.847368i	−0.990562	−	0.137069i	$-0.956232\pi$
$233$	−17.8028	+	12.9345i	−1.16630	+	0.847368i	−0.175740	+	0.984437i	$0.556232\pi$
$234$	−0.0139805	−	0.0430277i	−0.000913937	−	0.00281281i
$235$		0			0
$236$	−3.60732	+	11.1022i	−0.234816	+	0.722691i
$237$	3.53000	+	10.8642i	0.229298	+	0.705707i
$238$	−0.952956	−	2.93290i	−0.0617709	−	0.190111i
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	−0.846627	−	0.532187i	$-0.821371\pi$
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	0.997747	+	0.0670870i	$0.0213705\pi$
$240$		0			0
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	−0.920087	−	0.391713i	$-0.871883\pi$
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	0.514123	−	0.857716i	$-0.328117\pi$
$242$	−1.03733	+	0.753661i	−0.0666818	+	0.0484472i
$243$	−8.38230			−0.537725
$244$	1.45664	−	1.05831i	0.0932520	−	0.0677515i
$245$		0			0
$246$	0.221431	+	0.160879i	0.0141179	+	0.0102573i
$247$	0.414902	+	0.301444i	0.0263996	+	0.0191804i
$248$	1.36943	−	4.21467i	0.0869589	−	0.267632i
$249$	−21.3659			−1.35401
$250$		0			0
$251$	10.5717			0.667278			0.333639	−	0.942701i	$-0.391723\pi$
$251$	10.5717			0.667278			0.333639	+	0.942701i	$0.391723\pi$
$252$	−1.65132	+	5.08225i	−0.104024	+	0.320152i
$253$	−1.42256	−	1.03355i	−0.0894357	−	0.0649789i
$254$	−0.866918	−	0.629853i	−0.0543953	−	0.0395205i
$255$		0			0
$256$	−10.8270	+	7.86625i	−0.676685	+	0.491640i
$257$	−20.2700			−1.26441			−0.632205	−	0.774801i	$-0.717850\pi$
$257$	−20.2700			−1.26441			−0.632205	+	0.774801i	$0.717850\pi$
$258$	0.707166	−	0.513786i	0.0440263	−	0.0319869i
$259$	−8.14996	−	25.0830i	−0.506414	−	1.55858i
$260$		0			0
$261$	−1.52252	+	4.68585i	−0.0942419	+	0.290047i
$262$	0.0847148	+	0.260725i	0.00523370	+	0.0161077i
$263$	−8.68056	−	26.7160i	−0.535267	−	1.64738i	−0.743072	−	0.669211i	$-0.766632\pi$
$263$	−8.68056	−	26.7160i	−0.535267	−	1.64738i	0.207806	−	0.978170i	$-0.433368\pi$
$264$	−0.660946	+	2.03418i	−0.0406784	+	0.125195i
$265$		0			0
$266$	0.319385	+	0.982966i	0.0195828	+	0.0602695i
$267$	8.96271	−	6.51179i	0.548509	−	0.398515i
$268$	−13.5450			−0.827393
$269$	−16.4416	+	11.9455i	−1.00246	+	0.728333i	−0.962615	−	0.270873i	$-0.912688\pi$
$269$	−16.4416	+	11.9455i	−1.00246	+	0.728333i	−0.0398490	+	0.999206i	$0.512688\pi$
$270$		0			0
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.946816	−	0.321777i	$-0.895720\pi$
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.598610	−	0.801041i	$-0.704280\pi$
$272$	15.8716	+	11.5314i	0.962354	+	0.699191i
$273$	−0.439596	+	1.35294i	−0.0266056	+	0.0818835i
$274$	1.43769			0.0868543
$275$		0			0
$276$	2.54483			0.153181
$277$	4.30475	−	13.2487i	0.258648	−	0.796035i	−0.734441	−	0.678672i	$-0.762556\pi$
$277$	4.30475	−	13.2487i	0.258648	−	0.796035i	0.993089	−	0.117363i	$-0.0374442\pi$
$278$	0.798966	+	0.580483i	0.0479188	+	0.0348150i
$279$	4.11235	+	2.98779i	0.246200	+	0.178875i
$280$		0			0
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.998158	−	0.0606690i	$-0.980677\pi$
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.250748	+	0.968052i	$0.580677\pi$
$282$	1.13778			0.0677541
$283$	19.1993	−	13.9491i	1.14128	−	0.829188i	0.153983	−	0.988074i	$-0.450790\pi$
$283$	19.1993	−	13.9491i	1.14128	−	0.829188i	0.987297	+	0.158885i	$0.0507899\pi$
$284$	3.62702	+	11.1628i	0.215224	+	0.662392i
$285$		0			0
$286$	0.0335520	−	0.103262i	0.00198397	−	0.00610604i
$287$	1.02292	+	3.14823i	0.0603811	+	0.185834i
$288$	0.553446	+	1.70333i	0.0326121	+	0.100370i
$289$	2.98394	−	9.18363i	0.175526	−	0.540214i
$290$		0			0
$291$	3.05959	+	9.41645i	0.179356	+	0.552002i
$292$	14.0530	−	10.2101i	0.822389	−	0.597500i
$293$	12.3029			0.718742			0.359371	−	0.933195i	$-0.382991\pi$
$293$	12.3029			0.718742			0.359371	+	0.933195i	$0.382991\pi$
$294$	−0.792495	+	0.575781i	−0.0462193	+	0.0335803i
$295$		0			0
$296$	−4.75401	−	3.45399i	−0.276321	−	0.200759i
$297$	−9.12979	−	6.63318i	−0.529764	−	0.384896i
$298$	−1.06544	+	3.27908i	−0.0617191	+	0.189952i
$299$	−0.260574			−0.0150694
$300$		0			0
$301$	10.5717			0.609341
$302$	0.220072	−	0.677311i	0.0126637	−	0.0389749i
$303$	−14.5228	−	10.5514i	−0.834311	−	0.606163i
$304$	−5.31939	−	3.86476i	−0.305088	−	0.221659i
$305$		0			0
$306$	0.637605	−	0.463247i	0.0364495	−	0.0264821i
$307$	−4.28249			−0.244415			−0.122207	−	0.992505i	$-0.538997\pi$
$307$	−4.28249			−0.244415			−0.122207	+	0.992505i	$0.538997\pi$
$308$	−10.3753	+	7.53811i	−0.591189	+	0.429524i
$309$	−0.628342	−	1.93384i	−0.0357451	−	0.110012i
$310$		0			0
$311$	7.92526	−	24.3915i	0.449400	−	1.38311i	−0.428185	−	0.903691i	$-0.640847\pi$
$311$	7.92526	−	24.3915i	0.449400	−	1.38311i	0.877585	−	0.479421i	$-0.159153\pi$
$312$	0.0979452	+	0.301444i	0.00554505	+	0.0170659i
$313$	6.90692	+	21.2573i	0.390402	+	1.20153i	0.932485	+	0.361209i	$0.117636\pi$
$313$	6.90692	+	21.2573i	0.390402	+	1.20153i	−0.542083	+	0.840325i	$0.682364\pi$
$314$	−0.242476	+	0.746264i	−0.0136837	+	0.0421141i
$315$		0			0
$316$	4.71589	+	14.5140i	0.265290	+	0.816478i
$317$	17.7360	−	12.8859i	0.996151	−	0.723746i	0.0348911	−	0.999391i	$-0.488892\pi$
$317$	17.7360	−	12.8859i	0.996151	−	0.723746i	0.961259	+	0.275645i	$0.0888916\pi$
$318$	−2.18412			−0.122479
$319$	−9.56608	+	6.95016i	−0.535597	+	0.389134i
$320$		0			0
$321$	18.8491	+	13.6947i	1.05205	+	0.764363i
$322$	−0.424847	−	0.308669i	−0.0236758	−	0.0172015i
$323$	−2.76073	+	8.49664i	−0.153611	+	0.472766i
$324$	11.4160			0.634224
$325$		0			0
$326$	−2.88062			−0.159543
$327$	0.911429	−	2.80509i	0.0504021	−	0.155122i
$328$	0.596687	+	0.433519i	0.0329466	+	0.0239371i
$329$	11.1326	+	8.08832i	0.613761	+	0.445923i
$330$		0			0
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	−0.370393	−	0.928875i	$-0.620777\pi$
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	0.768955	+	0.639303i	$0.220777\pi$
$332$	−28.5437			−1.56654
$333$	5.45299	−	3.96183i	0.298822	−	0.217107i
$334$	−1.19054	−	3.66410i	−0.0651433	−	0.200491i
$335$		0			0
$336$	5.63597	−	17.3457i	0.307468	−	0.946288i
$337$	8.98731	+	27.6601i	0.489570	+	1.50674i	0.825251	+	0.564766i	$0.191034\pi$
$337$	8.98731	+	27.6601i	0.489570	+	1.50674i	−0.335681	+	0.941976i	$0.608966\pi$
$338$	0.730871	+	2.24939i	0.0397541	+	0.122351i
$339$	4.74302	−	14.5975i	0.257605	−	0.792828i
$340$		0			0
$341$	3.76972	+	11.6020i	0.204142	+	0.628283i
$342$	−0.213695	+	0.155258i	−0.0115553	+	0.00839541i
$343$	10.9787			0.592795
$344$	1.90559	−	1.38450i	0.102743	−	0.0746470i
$345$		0			0
$346$	1.06202	+	0.771601i	0.0570944	+	0.0414815i
$347$	11.5667	+	8.40368i	0.620931	+	0.451133i	0.853247	−	0.521508i	$-0.174630\pi$
$347$	11.5667	+	8.40368i	0.620931	+	0.451133i	−0.232315	+	0.972641i	$0.574630\pi$
$348$	5.28815	−	16.2753i	0.283475	−	0.872445i
$349$	5.62382			0.301036			0.150518	−	0.988607i	$-0.451906\pi$
$349$	5.62382			0.301036			0.150518	+	0.988607i	$0.451906\pi$
$350$		0			0
$351$	−1.67232			−0.0892620
$352$	−1.32822	+	4.08784i	−0.0707944	+	0.217883i
$353$	1.54520	+	1.12265i	0.0822427	+	0.0597529i	0.628147	−	0.778095i	$-0.283814\pi$
$353$	1.54520	+	1.12265i	0.0822427	+	0.0597529i	−0.545904	+	0.837848i	$0.683814\pi$
$354$	−1.29488	−	0.940785i	−0.0688221	−	0.0500022i
$355$		0			0
$356$	11.9737	−	8.69941i	0.634605	−	0.461068i
$357$	−24.7813			−1.31156
$358$	1.19134	−	0.865562i	0.0629645	−	0.0457464i
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	0.951751	+	0.306870i	$0.0992818\pi$
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	−0.589609	+	0.807689i	$0.700718\pi$
$360$		0			0
$361$	−4.94606	+	15.2224i	−0.260319	+	0.801179i
$362$	1.16700	+	3.59164i	0.0613359	+	0.188773i
$363$	3.18400	+	9.79935i	0.167117	+	0.514332i
$364$	−0.587277	+	1.80745i	−0.0307817	+	0.0947363i
$365$		0			0
$366$	0.0762864	+	0.234786i	0.00398756	+	0.0122724i
$367$	−17.3493	+	12.6050i	−0.905629	+	0.657978i	−0.939906	−	0.341435i	$-0.889087\pi$
$367$	−17.3493	+	12.6050i	−0.905629	+	0.657978i	0.0342768	+	0.999412i	$0.489087\pi$
$368$	3.34077			0.174149
$369$	−0.684418	+	0.497259i	−0.0356294	+	0.0258863i
$370$		0			0
$371$	−21.3704	−	15.5265i	−1.10950	−	0.806096i
$372$	−14.2833	−	10.3774i	−0.740556	−	0.538045i
$373$	−7.15063	+	22.0074i	−0.370245	+	1.13950i	0.576385	+	0.817178i	$0.304463\pi$
$373$	−7.15063	+	22.0074i	−0.370245	+	1.13950i	−0.946631	+	0.322320i	$0.895537\pi$
$374$	1.89142			0.0978032
$375$		0			0
$376$	3.06598			0.158116
$377$	−0.541471	+	1.66648i	−0.0278872	+	0.0858279i
$378$	−2.72660	−	1.98099i	−0.140241	−	0.101891i
$379$	17.5153	+	12.7256i	0.899702	+	0.653672i	0.938390	−	0.345579i	$-0.112318\pi$
$379$	17.5153	+	12.7256i	0.899702	+	0.653672i	−0.0386872	+	0.999251i	$0.512318\pi$
$380$		0			0
$381$	−6.96645	+	5.06142i	−0.356902	+	0.259304i
$382$	−3.30265			−0.168978
$383$	4.57484	−	3.32381i	0.233763	−	0.169839i	−0.464737	−	0.885449i	$-0.653851\pi$
$383$	4.57484	−	3.32381i	0.233763	−	0.169839i	0.698500	+	0.715610i	$0.253851\pi$
$384$	−2.55545	−	7.86488i	−0.130407	−	0.401353i
$385$		0			0
$386$	−0.384257	+	1.18262i	−0.0195581	+	0.0601938i
$387$	0.834891	+	2.56953i	0.0424399	+	0.130617i
$388$	4.08746	+	12.5799i	0.207509	+	0.638647i
$389$	−2.51109	+	7.72833i	−0.127317	+	0.391842i	−0.994316	−	0.106468i	$-0.966046\pi$
$389$	−2.51109	+	7.72833i	−0.127317	+	0.391842i	0.866999	+	0.498310i	$0.166046\pi$
$390$		0			0
$391$	−1.40270	−	4.31707i	−0.0709377	−	0.218324i
$392$	−2.13553	+	1.55155i	−0.107861	+	0.0783653i
$393$	2.20298			0.111126
$394$	1.18483	−	0.860829i	0.0596908	−	0.0433679i
$395$		0			0
$396$	−2.65159	−	1.92649i	−0.133247	−	0.0968098i
$397$	−16.8024	−	12.2076i	−0.843287	−	0.612684i	0.0799998	−	0.996795i	$-0.474508\pi$
$397$	−16.8024	−	12.2076i	−0.843287	−	0.612684i	−0.923287	+	0.384111i	$0.874508\pi$
$398$	0.294611	−	0.906721i	0.0147675	−	0.0454498i
$399$	8.30550			0.415795
$400$		0			0
$401$	30.1195			1.50410			0.752049	−	0.659107i	$-0.229066\pi$
$401$	30.1195			1.50410			0.752049	+	0.659107i	$0.229066\pi$
$402$	0.573893	−	1.76626i	0.0286232	−	0.0880931i
$403$	1.46252	+	1.06258i	0.0728532	+	0.0529309i
$404$	−19.4017	−	14.0961i	−0.965269	−	0.701309i
$405$		0			0
$406$	−2.85690	+	2.07566i	−0.141785	+	0.103013i
$407$	16.1760			0.801815
$408$	−4.46695	+	3.24543i	−0.221147	+	0.160673i
$409$	3.41317	+	10.5046i	0.168770	+	0.519421i	0.999294	−	0.0375613i	$-0.0119589\pi$
$409$	3.41317	+	10.5046i	0.168770	+	0.519421i	−0.830524	+	0.556983i	$0.811959\pi$
$410$		0			0
$411$	3.57012	−	10.9877i	0.176101	−	0.541983i
$412$	−0.839433	−	2.58351i	−0.0413559	−	0.127280i
$413$	−5.98182	−	18.4102i	−0.294346	−	0.905905i
$414$	0.0414726	−	0.127639i	0.00203827	−	0.00627314i
$415$		0			0
$416$	0.196828	+	0.605774i	0.00965029	+	0.0297005i
$417$	6.42039	−	4.66469i	0.314408	−	0.228431i
$418$	−0.633915			−0.0310058
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.301179	−	0.953568i	$-0.402620\pi$
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.999966	+	0.00823011i	$0.00261975\pi$
$420$		0			0
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	0.910626	−	0.413231i	$-0.135600\pi$
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	−0.111607	+	0.993752i	$0.535600\pi$
$422$	2.46023	+	1.78746i	0.119762	+	0.0870124i
$423$	−1.08674	+	3.34464i	−0.0528392	+	0.162622i
$424$	−5.88552			−0.285826
$425$		0			0
$426$	−1.60930			−0.0779709
$427$	−0.922629	+	2.83956i	−0.0446491	+	0.137416i
$428$	25.1814	+	18.2954i	1.21719	+	0.884341i
$429$	−0.705874	−	0.512848i	−0.0340799	−	0.0247605i
$430$		0			0
$431$	−5.78873	+	4.20576i	−0.278833	+	0.202584i	−0.718408	−	0.695622i	$-0.755129\pi$
$431$	−5.78873	+	4.20576i	−0.278833	+	0.202584i	0.439575	+	0.898206i	$0.355129\pi$
$432$	21.4405			1.03156
$433$	−4.43555	+	3.22262i	−0.213159	+	0.154869i	−0.689242	−	0.724531i	$-0.742056\pi$
$433$	−4.43555	+	3.22262i	−0.213159	+	0.154869i	0.476083	+	0.879400i	$0.342056\pi$
$434$	1.12582	+	3.46492i	0.0540412	+	0.166322i
$435$		0			0
$436$	1.21762	−	3.74746i	0.0583135	−	0.179471i
$437$	0.470119	+	1.44688i	0.0224888	+	0.0692135i
$438$	0.735975	+	2.26510i	0.0351662	+	0.108231i
$439$	−9.50415	+	29.2508i	−0.453609	+	1.39606i	0.419153	+	0.907916i	$0.362327\pi$
$439$	−9.50415	+	29.2508i	−0.453609	+	1.39606i	−0.872761	+	0.488148i	$0.837673\pi$
$440$		0			0
$441$	−0.935631	−	2.87958i	−0.0445539	−	0.137123i
$442$	0.226758	−	0.164750i	0.0107858	−	0.00783634i
$443$	−11.3527			−0.539381			−0.269691	−	0.962947i	$-0.586921\pi$
$443$	−11.3527			−0.539381			−0.269691	+	0.962947i	$0.586921\pi$
$444$	−18.9397	+	13.7605i	−0.898841	+	0.653046i
$445$		0			0
$446$	0.982211	+	0.713618i	0.0465090	+	0.0337908i
$447$	22.4149	+	16.2854i	1.06019	+	0.770271i
$448$	7.26117	−	22.3476i	0.343058	−	1.05582i
$449$	−15.7661			−0.744050			−0.372025	−	0.928223i	$-0.621336\pi$
$449$	−15.7661			−0.744050			−0.372025	+	0.928223i	$0.621336\pi$
$450$		0			0
$451$	−2.03029			−0.0956027
$452$	6.33643	−	19.5015i	0.298040	−	0.917274i
$453$	−4.62992	−	3.36383i	−0.217532	−	0.158047i
$454$	1.98454	+	1.44185i	0.0931391	+	0.0676695i
$455$		0			0
$456$	1.49711	−	1.08771i	0.0701085	−	0.0509368i
$457$	4.16714			0.194931			0.0974653	−	0.995239i	$-0.468926\pi$
$457$	4.16714			0.194931			0.0974653	+	0.995239i	$0.468926\pi$
$458$	1.49474	−	1.08599i	0.0698448	−	0.0507452i
$459$	−9.00233	−	27.7063i	−0.420193	−	1.29322i
$460$		0			0
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	0.616576	+	0.787296i	$0.288519\pi$
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	−0.961581	+	0.274521i	$0.911481\pi$
$462$	−0.543370	−	1.67232i	−0.0252799	−	0.0778035i
$463$	−12.7700	−	39.3021i	−0.593473	−	1.82652i	−0.562183	−	0.827013i	$-0.690038\pi$
$463$	−12.7700	−	39.3021i	−0.593473	−	1.82652i	−0.0312899	−	0.999510i	$-0.509962\pi$
$464$	6.94210	−	21.3656i	0.322279	−	0.991872i
$465$		0			0
$466$	−1.24558	−	3.83351i	−0.0577005	−	0.177584i
$467$	−8.41102	+	6.11096i	−0.389216	+	0.282782i	−0.765134	−	0.643871i	$-0.777327\pi$
$467$	−8.41102	+	6.11096i	−0.389216	+	0.282782i	0.375918	+	0.926653i	$0.377327\pi$
$468$	−0.485697			−0.0224513
$469$	18.1713	−	13.2022i	0.839072	−	0.609622i
$470$		0			0
$471$	5.10126	+	3.70628i	0.235054	+	0.170776i
$472$	−3.48930	−	2.53512i	−0.160608	−	0.116689i
$473$	−2.00366	+	6.16663i	−0.0921284	+	0.283542i
$474$	−2.09243			−0.0961086
$475$		0			0
$476$	−33.1065			−1.51743
$477$	2.08613	−	6.42045i	0.0955174	−	0.293972i
$478$	1.12035	+	0.813985i	0.0512438	+	0.0372308i
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.999723	−	0.0235349i	$-0.992508\pi$
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.331314	−	0.943520i	$-0.607492\pi$
$480$		0			0
$481$	1.93930	−	1.40899i	0.0884246	−	0.0642443i
$482$	3.73571			0.170157
$483$	−3.41402	+	2.48043i	−0.155343	+	0.112863i
$484$	4.25366	+	13.0914i	0.193348	+	0.595065i
$485$		0			0
$486$	0.474466	−	1.46025i	0.0215222	−	0.0662385i
$487$	−3.28726	−	10.1172i	−0.148960	−	0.458452i	0.848539	−	0.529133i	$-0.177483\pi$
$487$	−3.28726	−	10.1172i	−0.148960	−	0.458452i	−0.997499	+	0.0706809i	$0.977483\pi$
$488$	0.205568	+	0.632674i	0.00930564	+	0.0286398i
$489$	−7.15323	+	22.0154i	−0.323480	+	0.995570i
$490$		0			0
$491$	−5.46010	−	16.8045i	−0.246411	−	0.758375i	−0.995401	−	0.0957938i	$-0.969461\pi$
$491$	−5.46010	−	16.8045i	−0.246411	−	0.758375i	0.748990	−	0.662581i	$-0.230539\pi$
$492$	2.37718	−	1.72712i	0.107171	−	0.0778645i
$493$	−30.5243			−1.37475
$494$	−0.0759986	+	0.0552162i	−0.00341934	+	0.00248429i
$495$		0			0
$496$	−18.7507	−	13.6231i	−0.841929	−	0.611697i
$497$	−15.7462	−	11.4403i	−0.706312	−	0.513166i
$498$	1.20938	−	3.72209i	0.0541936	−	0.166791i
$499$	−9.41734			−0.421578			−0.210789	−	0.977532i	$-0.567603\pi$
$499$	−9.41734			−0.421578			−0.210789	+	0.977532i	$0.567603\pi$
$500$		0			0
$501$	−30.9595			−1.38317
$502$	−0.598391	+	1.84166i	−0.0267075	+	0.0821972i
$503$	−14.5730	−	10.5879i	−0.649780	−	0.472093i	0.213416	−	0.976961i	$-0.431541\pi$
$503$	−14.5730	−	10.5879i	−0.649780	−	0.472093i	−0.863196	+	0.504869i	$0.831541\pi$
$504$	−1.59730	−	1.16050i	−0.0711493	−	0.0516930i
$505$		0			0
$506$	0.260574	−	0.189318i	0.0115839	−	0.00841621i
$507$	19.0060			0.844088
$508$	−9.30681	+	6.76180i	−0.412923	+	0.300006i
$509$	−4.95926	−	15.2630i	−0.219815	−	0.676522i	−0.998777	−	0.0494500i	$-0.984253\pi$
$509$	−4.95926	−	15.2630i	−0.219815	−	0.676522i	0.778961	−	0.627072i	$-0.215747\pi$
$510$		0			0
$511$	−8.90107	+	27.3947i	−0.393760	+	1.21187i
$512$	−4.22972	−	13.0177i	−0.186929	−	0.575308i
$513$	3.01715	+	9.28583i	0.133210	+	0.409980i
$514$	1.14735	−	3.53118i	0.0506075	−	0.155754i
$515$		0			0
$516$	−2.89981	−	8.92470i	−0.127657	−	0.392888i
$517$	−6.82803	+	4.96086i	−0.300297	+	0.218178i
$518$	4.83095			0.212260
$519$	8.53425	−	6.20050i	0.374612	−	0.272172i
$520$		0			0
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	0.626102	−	0.779741i	$-0.284649\pi$
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	−0.548102	+	0.836412i	$0.684649\pi$
$522$	−0.730127	−	0.530469i	−0.0319568	−	0.0232180i
$523$	2.29781	−	7.07194i	0.100476	−	0.309234i	−0.888166	−	0.459523i	$-0.848020\pi$
$523$	2.29781	−	7.07194i	0.100476	−	0.309234i	0.988642	+	0.150289i	$0.0480203\pi$
$524$	2.94307			0.128569
$525$		0			0
$526$	5.14547			0.224353
$527$	−9.73147	+	29.9504i	−0.423909	+	1.30466i
$528$	9.04988	+	6.57512i	0.393845	+	0.286145i
$529$	17.9820	+	13.0647i	0.781828	+	0.568031i
$530$		0			0
$531$	4.00233	−	2.90786i	0.173686	−	0.126190i
$532$	11.0957			0.481061
$533$	−0.243407	+	0.176845i	−0.0105431	+	0.00766003i
$534$	0.627080	+	1.92995i	0.0271364	+	0.0835173i
$535$		0			0
$536$	1.54646	−	4.75953i	0.0667971	−	0.205580i
$537$	−3.65675	−	11.2543i	−0.157800	−	0.485660i
$538$	−1.15035	−	3.54040i	−0.0495950	−	0.152638i
$539$	2.24543	−	6.91072i	0.0967174	−	0.297666i
$540$		0			0
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	0.989400	+	0.145216i	$0.0463878\pi$
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	−0.715085	+	0.699037i	$0.753612\pi$
$542$	4.66007	−	3.38574i	0.200167	−	0.145430i
$543$	30.3473			1.30233
$544$	−8.97666	+	6.52192i	−0.384871	+	0.279625i
$545$		0			0
$546$	−0.210809	−	0.153161i	−0.00902177	−	0.00655470i
$547$	25.3839	+	18.4424i	1.08534	+	0.788542i	0.978605	−	0.205746i	$-0.0659621\pi$
$547$	25.3839	+	18.4424i	1.08534	+	0.788542i	0.106730	+	0.994288i	$0.465962\pi$
$548$	4.76949	−	14.6790i	0.203743	−	0.627055i
$549$	−0.763042			−0.0325658
$550$		0			0
$551$	10.2303			0.435825
$552$	−0.290549	+	0.894219i	−0.0123666	+	0.0380605i
$553$	−20.4733	−	14.8747i	−0.870615	−	0.632538i
$554$	2.06435	+	1.49984i	0.0877057	+	0.0637219i
$555$		0			0
$556$	8.57732	−	6.23178i	0.363759	−	0.264287i
$557$	22.3515			0.947064			0.473532	−	0.880776i	$-0.342979\pi$
$557$	22.3515			0.947064			0.473532	+	0.880776i	$0.342979\pi$
$558$	−0.753267	+	0.547280i	−0.0318883	+	0.0231682i
$559$	0.296921	+	0.913829i	0.0125584	+	0.0386509i
$560$		0			0
$561$	4.69683	−	14.4554i	0.198300	−	0.610305i
$562$	−1.46476	−	4.50807i	−0.0617872	−	0.190162i
$563$	10.6198	+	32.6843i	0.447570	+	1.37748i	0.879640	+	0.475639i	$0.157783\pi$
$563$	10.6198	+	32.6843i	0.447570	+	1.37748i	−0.432070	+	0.901840i	$0.642217\pi$
$564$	3.77455	−	11.6169i	0.158937	−	0.489159i
$565$		0			0
$566$	1.34329	+	4.13422i	0.0564626	+	0.173774i
$567$	−15.3152	+	11.1271i	−0.643177	+	0.467295i
$568$	−4.33657			−0.181958
$569$	−26.0230	+	18.9068i	−1.09094	+	0.792615i	−0.979558	−	0.201162i	$-0.935528\pi$
$569$	−26.0230	+	18.9068i	−1.09094	+	0.792615i	−0.111383	+	0.993778i	$0.535528\pi$
$570$		0			0
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	0.943466	−	0.331468i	$-0.107544\pi$
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	−0.0236979	+	0.999719i	$0.507544\pi$
$572$	−0.943012	−	0.685138i	−0.0394293	−	0.0286471i
$573$	−8.20121	+	25.2407i	−0.342610	+	1.05445i
$574$	−0.606344			−0.0253083
$575$		0			0
$576$	6.00521			0.250217
$577$	−4.27998	+	13.1724i	−0.178178	+	0.548375i	−0.999764	−	0.0217089i	$-0.993089\pi$
$577$	−4.27998	+	13.1724i	−0.178178	+	0.548375i	0.821586	+	0.570084i	$0.193089\pi$
$578$	1.43095	+	1.03965i	0.0595198	+	0.0432436i
$579$	8.08407	+	5.87342i	0.335963	+	0.244091i
$580$		0			0
$581$	38.2928	−	27.8214i	1.58865	−	1.15422i
$582$	−1.81360			−0.0751759
$583$	13.1072	−	9.52297i	0.542847	−	0.394401i
$584$	1.98322	+	6.10374i	0.0820664	+	0.252574i
$585$		0			0
$586$	−0.696383	+	2.14325i	−0.0287673	+	0.0885367i
$587$	−13.6431	−	41.9890i	−0.563110	−	1.73307i	−0.673502	−	0.739185i	$-0.735211\pi$
$587$	−13.6431	−	41.9890i	−0.563110	−	1.73307i	0.110392	−	0.993888i	$-0.464789\pi$
$588$	3.24971	+	10.0016i	0.134016	+	0.412458i
$589$	3.26152	−	10.0379i	0.134389	−	0.413606i
$590$		0			0
$591$	−3.63675	−	11.1928i	−0.149596	−	0.460409i
$592$	−24.8634	+	18.0643i	−1.02188	+	0.742440i
$593$	16.2531			0.667437			0.333718	−	0.942673i	$-0.391697\pi$
$593$	16.2531			0.667437			0.333718	+	0.942673i	$0.391697\pi$
$594$	1.67232	−	1.21501i	0.0686162	−	0.0498526i
$595$		0			0
$596$	29.9451	+	21.7564i	1.22660	+	0.891177i
$597$	−6.19810	−	4.50318i	−0.253671	−	0.184303i
$598$	0.0147493	−	0.0453938i	0.000603145	−	0.00185629i
$599$	30.4822			1.24547			0.622734	−	0.782433i	$-0.286022\pi$
$599$	30.4822			1.24547			0.622734	+	0.782433i	$0.286022\pi$
$600$		0			0
$601$	−28.9162			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$601$	−28.9162			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$602$	−0.598391	+	1.84166i	−0.0243886	+	0.0750604i
$603$	4.64398	+	3.37405i	0.189117	+	0.137402i
$604$	−6.18533	−	4.49390i	−0.251677	−	0.182854i
$605$		0			0
$606$	2.66017	−	1.93272i	0.108062	−	0.0785115i
$607$	−8.23276			−0.334157			−0.167079	−	0.985944i	$-0.553433\pi$
$607$	−8.23276			−0.334157			−0.167079	+	0.985944i	$0.553433\pi$
$608$	3.00855	−	2.18584i	0.122013	−	0.0886474i
$609$	8.76906	+	26.9884i	0.355340	+	1.09362i
$610$		0			0
$611$	−0.386489	+	1.18949i	−0.0156357	+	0.0481217i
$612$	−2.61457	−	8.04681i	−0.105688	−	0.325273i
$613$	−1.48270	−	4.56327i	−0.0598856	−	0.184309i	0.916638	−	0.399717i	$-0.130892\pi$
$613$	−1.48270	−	4.56327i	−0.0598856	−	0.184309i	−0.976524	+	0.215408i	$0.930892\pi$
$614$	0.242403	−	0.746040i	0.00978259	−	0.0301077i
$615$		0			0
$616$	−1.46422	−	4.50639i	−0.0589949	−	0.181568i
$617$	−1.64379	+	1.19428i	−0.0661765	+	0.0480800i	−0.620382	−	0.784300i	$-0.713022\pi$
$617$	−1.64379	+	1.19428i	−0.0661765	+	0.0480800i	0.554205	+	0.832380i	$0.313022\pi$
$618$	0.372454			0.0149823
$619$	−6.58621	+	4.78516i	−0.264722	+	0.192332i	−0.712226	−	0.701950i	$-0.752313\pi$
$619$	−6.58621	+	4.78516i	−0.264722	+	0.192332i	0.447504	+	0.894282i	$0.352313\pi$
$620$		0			0
$621$	−4.01342	−	2.91592i	−0.161053	−	0.117012i
$622$	3.80057	+	2.76127i	0.152389	+	0.110717i
$623$	−7.58408	+	23.3414i	−0.303850	+	0.935153i
$624$	1.65769			0.0663605
$625$		0			0
$626$	−4.09413			−0.163634
$627$	−1.57415	+	4.84474i	−0.0628656	+	0.193480i
$628$	6.81502	+	4.95140i	0.271949	+	0.197582i
$629$	33.7830	+	24.5448i	1.34702	+	0.978665i
$630$		0			0
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.976268	−	0.216567i	$-0.930514\pi$
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.0957154	+	0.995409i	$0.530514\pi$
$632$	−5.63846			−0.224286
$633$	19.7701	−	14.3638i	0.785793	−	0.570912i
$634$	1.24091	+	3.81911i	0.0492826	+	0.151676i
$635$		0			0
$636$	−7.24572	+	22.3000i	−0.287311	+	0.884253i
$637$	−0.332749	−	1.02409i	−0.0131840	−	0.0405761i
$638$	−0.669295	−	2.05988i	−0.0264977	−	0.0815514i
$639$	1.53710	−	4.73072i	0.0608069	−	0.187144i
$640$		0			0
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	−0.826394	−	0.563092i	$-0.809612\pi$
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	0.337590	−	0.941293i	$-0.390388\pi$
$642$	−3.45263	+	2.50848i	−0.136264	+	0.0990019i
$643$	11.6870			0.460890			0.230445	−	0.973085i	$-0.425982\pi$
$643$	11.6870			0.460890			0.230445	+	0.973085i	$0.425982\pi$
$644$	−4.56095	+	3.31372i	−0.179727	+	0.130579i
$645$		0			0
$646$	−1.32391	−	0.961876i	−0.0520885	−	0.0378445i
$647$	−6.43117	−	4.67252i	−0.252835	−	0.183696i	0.454147	−	0.890927i	$-0.349944\pi$
$647$	−6.43117	−	4.67252i	−0.252835	−	0.183696i	−0.706982	+	0.707231i	$0.749944\pi$
$648$	−1.30339	+	4.01144i	−0.0512022	+	0.157584i
$649$	11.8727			0.466044
$650$		0			0
$651$	29.2766			1.14744
$652$	−9.55635	+	29.4114i	−0.374256	+	1.15184i
$653$	2.69998	+	1.96165i	0.105658	+	0.0767653i	0.639360	−	0.768908i	$-0.279199\pi$
$653$	2.69998	+	1.96165i	0.105658	+	0.0767653i	−0.533702	+	0.845673i	$0.679199\pi$
$654$	0.437077	+	0.317555i	0.0170910	+	0.0124174i
$655$		0			0
$656$	3.12067	−	2.26730i	0.121842	−	0.0885232i
$657$	−7.36146			−0.287198
$658$	−2.03918	+	1.48155i	−0.0794957	+	0.0577570i
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	−0.951998	−	0.306105i	$-0.900974\pi$
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	0.590259	−	0.807214i	$-0.299026\pi$
$660$		0			0
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	−0.982796	−	0.184693i	$-0.940871\pi$
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	0.903659	+	0.428253i	$0.140871\pi$
$662$	0.507335	+	1.56142i	0.0197181	+	0.0606862i
$663$	−0.696020	−	2.14213i	−0.0270312	−	0.0831934i
$664$	3.25890	−	10.0299i	0.126470	−	0.389235i
$665$		0			0
$666$	0.381521	+	1.17420i	0.0147836	+	0.0454994i
$667$	−4.20521	+	3.05526i	−0.162826	+	0.118300i
$668$	−41.3603			−1.60028
$669$	7.89293	−	5.73455i	0.305158	−	0.221711i
$670$		0			0
$671$	−1.48150	−	1.07637i	−0.0571925	−	0.0415528i
$672$	8.34526	+	6.06318i	0.321925	+	0.233892i
$673$	−2.08012	+	6.40194i	−0.0801826	+	0.246777i	−0.983110	−	0.183017i	$-0.941414\pi$
$673$	−2.08012	+	6.40194i	−0.0801826	+	0.246777i	0.902927	+	0.429794i	$0.141414\pi$
$674$	−5.32730			−0.205200
$675$		0			0
$676$	25.3911			0.976580
$677$	−4.21741	+	12.9799i	−0.162088	+	0.498857i	−0.998810	−	0.0487718i	$-0.984469\pi$
$677$	−4.21741	+	12.9799i	−0.162088	+	0.498857i	0.836722	+	0.547629i	$0.184469\pi$
$678$	2.27452	+	1.65253i	0.0873523	+	0.0634652i
$679$	−17.7451	−	12.8925i	−0.680993	−	0.494770i
$680$		0			0
$681$	15.9475	−	11.5866i	0.611111	−	0.443998i
$682$	−2.23453			−0.0855645
$683$	0.948329	−	0.689001i	0.0362868	−	0.0263639i	−0.569494	−	0.821995i	$-0.692861\pi$
$683$	0.948329	−	0.689001i	0.0362868	−	0.0263639i	0.605781	+	0.795632i	$0.292861\pi$
$684$	0.876278	+	2.69691i	0.0335053	+	0.103119i
$685$		0			0
$686$	−0.621431	+	1.91257i	−0.0237264	+	0.0730222i
$687$	−4.58802	−	14.1205i	−0.175044	−	0.538729i
$688$	−3.80677	−	11.7160i	−0.145132	−	0.446669i
$689$	0.741913	−	2.28337i	0.0282646	−	0.0869896i
$690$		0			0
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	0.996909	−	0.0785709i	$-0.0250357\pi$
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	−0.852699	+	0.522403i	$0.825036\pi$
$692$	11.4013	−	8.28354i	0.433413	−	0.314893i
$693$	5.43497			0.206457
$694$	−2.11869	+	1.53932i	−0.0804244	+	0.0584317i
$695$		0			0
$696$	5.11514	+	3.71637i	0.193889	+	0.140869i
$697$	−4.24019	−	3.08068i	−0.160609	−	0.116689i
$698$	−0.318327	+	0.979709i	−0.0120488	+	0.0370825i
$699$	−32.3910			−1.22514
$700$		0			0
$701$	−20.0271			−0.756415			−0.378207	−	0.925721i	$-0.623459\pi$
$701$	−20.0271			−0.756415			−0.378207	+	0.925721i	$0.623459\pi$
$702$	0.0946589	−	0.291330i	0.00357267	−	0.0109956i
$703$	−11.3225	−	8.22624i	−0.427034	−	0.310259i
$704$	11.6595	+	8.47113i	0.439434	+	0.319268i
$705$		0			0
$706$	−0.283038	+	0.205639i	−0.0106523	+	0.00773932i
$707$	39.7677			1.49562
$708$	−13.9012	+	10.0998i	−0.522439	+	0.379574i
$709$	−1.35816	−	4.17998i	−0.0510067	−	0.156983i	0.922309	−	0.386454i	$-0.126300\pi$
$709$	−1.35816	−	4.17998i	−0.0510067	−	0.156983i	−0.973315	+	0.229471i	$0.926300\pi$
$710$		0			0
$711$	1.99856	−	6.15094i	0.0749519	−	0.230678i
$712$	1.68979	+	5.20063i	0.0633275	+	0.194902i
$713$	1.65715	+	5.10019i	0.0620608	+	0.191004i
$714$	1.40270	−	4.31707i	0.0524948	−	0.161562i
$715$		0			0
$716$	−4.88523	−	15.0352i	−0.182570	−	0.561892i
$717$	9.00303	−	6.54109i	0.336224	−	0.244281i
$718$	−4.06727			−0.151789
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	−0.410591	−	0.911819i	$-0.634678\pi$
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	0.740312	+	0.672263i	$0.234678\pi$
$720$		0			0
$721$	3.64427	+	2.64772i	0.135720	+	0.0986061i
$722$	−2.37189	−	1.72328i	−0.0882725	−	0.0641337i
$723$	9.27661	−	28.5505i	0.345001	−	1.06180i
$724$	40.5425			1.50675
$725$		0			0
$726$	−1.88734			−0.0700458
$727$	10.1677	−	31.2928i	0.377097	−	1.16059i	−0.564955	−	0.825122i	$-0.691107\pi$
$727$	10.1677	−	31.2928i	0.377097	−	1.16059i	0.942053	−	0.335465i	$-0.108893\pi$
$728$	−0.568064	−	0.412723i	−0.0210538	−	0.0152965i
$729$	−24.0719	−	17.4893i	−0.891553	−	0.647751i
$730$		0			0
$731$	−13.5416	+	9.83853i	−0.500853	+	0.363891i
$732$	2.65026			0.0979564
$733$	−11.1238	+	8.08190i	−0.410866	+	0.298512i	−0.773952	−	0.633244i	$-0.781723\pi$
$733$	−11.1238	+	8.08190i	−0.410866	+	0.298512i	0.363086	+	0.931756i	$0.381723\pi$
$734$	−1.21386	−	3.73586i	−0.0448042	−	0.137893i
$735$		0			0
$736$	−0.583880	+	1.79700i	−0.0215221	+	0.0662382i
$737$	4.25705	+	13.1019i	0.156811	+	0.482613i
$738$	−0.0478857	−	0.147377i	−0.00176270	−	0.00542502i
$739$	−13.3462	+	41.0754i	−0.490949	+	1.51098i	0.332228	+	0.943199i	$0.392200\pi$
$739$	−13.3462	+	41.0754i	−0.490949	+	1.51098i	−0.823177	+	0.567785i	$0.807800\pi$
$740$		0			0
$741$	0.233273	+	0.717939i	0.00856948	+	0.0263741i
$742$	3.91446	−	2.84402i	0.143704	−	0.104407i
$743$	31.8479			1.16838			0.584192	−	0.811615i	$-0.301411\pi$
$743$	31.8479			1.16838			0.584192	+	0.811615i	$0.301411\pi$
$744$	5.27725	−	3.83415i	0.193473	−	0.140567i
$745$		0			0
$746$	−3.42909	−	2.49138i	−0.125548	−	0.0912158i
$747$	9.78637	+	7.11021i	0.358064	+	0.260149i
$748$	6.27472	−	19.3116i	0.229426	−	0.706102i
$749$	−51.6145			−1.88595
$750$		0			0
$751$	−29.5952			−1.07995			−0.539973	−	0.841682i	$-0.681565\pi$
$751$	−29.5952			−1.07995			−0.539973	+	0.841682i	$0.681565\pi$
$752$	4.95510	−	15.2502i	0.180694	−	0.556119i
$753$	12.5891	+	9.14650i	0.458771	+	0.333317i
$754$	−0.259663	−	0.188656i	−0.00945637	−	0.00687045i
$755$		0			0
$756$	−29.2715	+	21.2670i	−1.06459	+	0.773473i
$757$	−0.0984401			−0.00357786			−0.00178893	−	0.999998i	$-0.500569\pi$
$757$	−0.0984401			−0.00357786			−0.00178893	+	0.999998i	$0.500569\pi$
$758$	−3.20832	+	2.33098i	−0.116531	+	0.0846651i
$759$	−0.799814	−	2.46157i	−0.0290314	−	0.0893495i
$760$		0			0
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	−0.968942	−	0.247287i	$-0.920461\pi$
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	0.929243	+	0.369470i	$0.120461\pi$
$762$	−0.487411	−	1.50010i	−0.0176570	−	0.0543428i
$763$	2.01912	+	6.21421i	0.0730970	+	0.224969i
$764$	−10.9564	+	33.7203i	−0.396388	+	1.21996i
$765$		0			0
$766$	0.320081	+	0.985108i	0.0115650	+	0.0355934i
$767$	1.42339	−	1.03415i	0.0513957	−	0.0373411i
$768$	−19.6989			−0.710822
$769$	−1.15494	+	0.839116i	−0.0416484	+	0.0302593i	−0.608415	−	0.793619i	$-0.708194\pi$
$769$	−1.15494	+	0.839116i	−0.0416484	+	0.0302593i	0.566766	+	0.823879i	$0.308194\pi$
$770$		0			0
$771$	−24.1382	−	17.5374i	−0.869316	−	0.631595i
$772$	10.7999	+	7.84659i	0.388697	+	0.282405i
$773$	10.4388	−	32.1274i	0.375458	−	1.15554i	−0.567711	−	0.823228i	$-0.692171\pi$
$773$	10.4388	−	32.1274i	0.375458	−	1.15554i	0.943169	−	0.332313i	$-0.107829\pi$
$774$	−0.494888			−0.0177884
$775$		0			0
$776$	−4.88708			−0.175436
$777$	11.9963	−	36.9209i	0.430366	−	1.32453i
$778$	−1.20419	−	0.874898i	−0.0431725	−	0.0313666i
$779$	1.42111	+	1.03250i	0.0509165	+	0.0369930i
$780$		0			0
$781$	9.65769	−	7.01672i	0.345579	−	0.251078i
$782$	0.831462			0.0297330
$783$	−26.9884	+	19.6082i	−0.964486	+	0.700740i
$784$	4.26610	+	13.1297i	0.152361	+	0.468919i
$785$		0			0
$786$	−0.124696	+	0.383775i	−0.00444776	+	0.0136888i
$787$	0.673749	+	2.07358i	0.0240165	+	0.0739153i	0.962346	−	0.271826i	$-0.0876275\pi$
$787$	0.673749	+	2.07358i	0.0240165	+	0.0739153i	−0.938330	+	0.345741i	$0.887627\pi$
$788$	−4.85852	−	14.9530i	−0.173077	−	0.532678i
$789$	12.7773	−	39.3246i	0.454886	−	1.39999i
$790$		0			0
$791$	10.5074	+	32.3383i	0.373599	+	1.14982i
$792$	0.979680	−	0.711779i	0.0348114	−	0.0252920i
$793$	−0.271369			−0.00963659
$794$	3.07773	−	2.23610i	0.109224	−	0.0793562i
$795$		0			0
$796$	−8.28034	−	6.01602i	−0.293489	−	0.213232i
$797$	−19.0053	−	13.8082i	−0.673203	−	0.489110i	0.197893	−	0.980224i	$-0.436590\pi$
$797$	−19.0053	−	13.8082i	−0.673203	−	0.489110i	−0.871096	+	0.491113i	$0.836590\pi$
$798$	−0.470119	+	1.44688i	−0.0166420	+	0.0512189i
$799$	−21.7875			−0.770787
$800$		0			0
$801$	−6.27226			−0.221620
$802$	−1.70486	+	5.24703i	−0.0602009	+	0.185279i
$803$	−14.2928	−	10.3843i	−0.504380	−	0.366454i
$804$	−16.1298	−	11.7190i	−0.568855	−	0.413297i
$805$		0			0
$806$	−0.267892	+	0.194635i	−0.00943610	+	0.00685573i
$807$	−29.9144			−1.05304
$808$	7.16833	−	5.20809i	0.252181	−	0.183220i
$809$	−11.7893	−	36.2837i	−0.414489	−	1.27567i	−0.912707	−	0.408615i	$-0.866012\pi$
$809$	−11.7893	−	36.2837i	−0.414489	−	1.27567i	0.498217	−	0.867052i	$-0.333988\pi$
$810$		0			0
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	−0.254458	−	0.967084i	$-0.581897\pi$
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	0.774298	−	0.632821i	$-0.218103\pi$
$812$	11.7150	+	36.0551i	0.411116	+	1.26529i
$813$	−14.3038	−	44.0224i	−0.501655	−	1.54393i
$814$	−0.915615	+	2.81797i	−0.0320923	+	0.0987699i
$815$		0			0
$816$	8.92354	+	27.4638i	0.312386	+	0.961426i
$817$	4.53849	−	3.29740i	0.158782	−	0.115362i
$818$	−2.02318			−0.0707388
$819$	0.651586	−	0.473405i	0.0227683	−	0.0165421i
$820$		0			0
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	0.286647	−	0.958036i	$-0.407459\pi$
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	−0.822568	+	0.568667i	$0.807459\pi$
$822$	1.71205	+	1.24388i	0.0597147	+	0.0433852i
$823$	−6.85033	+	21.0831i	−0.238787	+	0.734912i	0.757809	+	0.652476i	$0.226270\pi$
$823$	−6.85033	+	21.0831i	−0.238787	+	0.734912i	−0.996596	+	0.0824356i	$0.973730\pi$
$824$	1.00365			0.0349638
$825$		0			0
$826$	3.54577			0.123373
$827$	−1.46146	+	4.49790i	−0.0508199	+	0.156407i	−0.973246	−	0.229767i	$-0.926204\pi$
$827$	−1.46146	+	4.49790i	−0.0508199	+	0.156407i	0.922426	+	0.386174i	$0.126204\pi$
$828$	−1.16563	−	0.846877i	−0.0405083	−	0.0294310i
$829$	−13.3003	−	9.66320i	−0.461937	−	0.335617i	0.332354	−	0.943155i	$-0.392157\pi$
$829$	−13.3003	−	9.66320i	−0.461937	−	0.335617i	−0.794291	+	0.607538i	$0.792157\pi$
$830$		0			0
$831$	16.5889	−	12.0525i	0.575461	−	0.418097i
$832$	2.13570			0.0740419
$833$	15.1755	−	11.0257i	0.525801	−	0.382017i
$834$	0.449206	+	1.38251i	0.0155547	+	0.0478726i
$835$		0			0
$836$	−2.10299	+	6.47232i	−0.0727333	+	0.223850i
$837$	10.6354	+	32.7322i	0.367611	+	1.13139i
$838$	1.86345	+	5.73510i	0.0643717	+	0.198116i
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	−0.976477	−	0.215620i	$-0.930823\pi$
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	0.916725	+	0.399519i	$0.130823\pi$
$840$		0			0
$841$	1.83977	+	5.66224i	0.0634405	+	0.195250i
$842$	−3.00302	+	2.18182i	−0.103491	+	0.0751904i
$843$	−38.0906			−1.31191
$844$	26.4119	−	19.1894i	0.909135	−	0.660525i
$845$		0			0
$846$	−0.521147	−	0.378636i	−0.0179174	−	0.0130178i
$847$	−18.4666	−	13.4168i	−0.634520	−	0.461006i
$848$	−9.51192	+	29.2747i	−0.326641	+	1.00530i
$849$	34.9318			1.19886
$850$		0			0
$851$	7.11091			0.243759
$852$	−5.33879	+	16.4311i	−0.182904	+	0.562921i
$853$	14.4737	+	10.5158i	0.495571	+	0.360053i	0.807323	−	0.590110i	$-0.200916\pi$
$853$	14.4737	+	10.5158i	0.495571	+	0.360053i	−0.311752	+	0.950164i	$0.600916\pi$
$854$	−0.442447	−	0.321457i	−0.0151402	−	0.0110000i
$855$		0			0
$856$	−9.30377	+	6.75959i	−0.317996	+	0.231038i
$857$	3.19536			0.109151			0.0545757	−	0.998510i	$-0.482619\pi$
$857$	3.19536			0.109151			0.0545757	+	0.998510i	$0.482619\pi$
$858$	0.129296	−	0.0939394i	0.00441411	−	0.00320704i
$859$	13.4174	+	41.2945i	0.457795	+	1.40895i	0.867822	+	0.496875i	$0.165519\pi$
$859$	13.4174	+	41.2945i	0.457795	+	1.40895i	−0.410027	+	0.912073i	$0.634481\pi$
$860$		0			0
$861$	−1.50569	+	4.63403i	−0.0513137	+	0.157927i
$862$	−0.405011	−	1.24650i	−0.0137947	−	0.0424558i
$863$	13.3719	+	41.1545i	0.455185	+	1.40091i	0.870918	+	0.491428i	$0.163525\pi$
$863$	13.3719	+	41.1545i	0.455185	+	1.40091i	−0.415734	+	0.909486i	$0.636475\pi$
$864$	−3.74725	+	11.5329i	−0.127484	+	0.392356i
$865$		0			0
$866$	−0.310336	−	0.955115i	−0.0105456	−	0.0324561i
$867$	11.4990	−	8.35449i	0.390525	−	0.283733i
$868$	39.1120			1.32755
$869$	12.5570	−	9.12322i	0.425968	−	0.309484i
$870$		0			0
$871$	1.65159	+	1.19995i	0.0559619	+	0.0406587i
$872$	1.17779	+	0.855712i	0.0398849	+	0.0289781i
$873$	1.73223	−	5.33126i	0.0586272	−	0.180436i
$874$	−0.278666			−0.00942603
$875$		0			0
$876$	25.5684			0.863876
$877$	10.5789	−	32.5584i	0.357223	−	1.09942i	−0.597487	−	0.801879i	$-0.703834\pi$
$877$	10.5789	−	32.5584i	0.357223	−	1.09942i	0.954709	−	0.297540i	$-0.0961661\pi$
$878$	−4.55772	−	3.31138i	−0.153816	−	0.111754i
$879$	14.6507	+	10.6443i	0.494154	+	0.359024i
$880$		0			0
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	−0.896760	−	0.442517i	$-0.854086\pi$
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	0.143744	+	0.989615i	$0.454086\pi$
$882$	0.554602			0.0186744
$883$	−20.9527	+	15.2231i	−0.705116	+	0.512297i	−0.881594	−	0.472008i	$-0.843529\pi$
$883$	−20.9527	+	15.2231i	−0.705116	+	0.512297i	0.176478	+	0.984305i	$0.443529\pi$
$884$	−0.929846	−	2.86177i	−0.0312741	−	0.0962518i
$885$		0			0
$886$	0.642598	−	1.97771i	0.0215885	−	0.0664425i
$887$	5.32897	+	16.4009i	0.178929	+	0.550688i	0.999791	−	0.0204392i	$-0.00650644\pi$
$887$	5.32897	+	16.4009i	0.178929	+	0.550688i	−0.820862	+	0.571127i	$0.806506\pi$
$888$	−2.67287	−	8.22624i	−0.0896956	−	0.276055i
$889$	5.89488	−	18.1426i	0.197708	−	0.608482i
$890$		0			0
$891$	−3.58794	−	11.0425i	−0.120200	−	0.369939i
$892$	10.5445	−	7.66106i	0.353058	−	0.256511i
$893$	7.30213			0.244356
$894$	−4.10578	+	2.98302i	−0.137318	+	0.0997673i
$895$		0			0
$896$	14.8212	+	10.7682i	0.495140	+	0.359740i
$897$	−0.310299	−	0.225446i	−0.0103606	−	0.00752741i
$898$	0.892415	−	2.74657i	0.0297803	−	0.0916543i
$899$	36.0614			1.20271
$900$		0			0
$901$	41.8238			1.39335
$902$	0.114921	−	0.353691i	0.00382645	−	0.0117766i
$903$	12.5891	+	9.14650i	0.418938	+	0.304376i
$904$	6.12912	+	4.45307i	0.203852	+	0.148107i
$905$		0			0
$906$	0.848071	−	0.616160i	0.0281753	−	0.0204705i
$907$	−57.0465			−1.89420			−0.947099	−	0.320940i	$-0.896001\pi$
$907$	−57.0465			−1.89420			−0.947099	+	0.320940i	$0.896001\pi$
$908$	21.3051	−	15.4790i	0.707034	−	0.513690i
$909$	3.14063	+	9.66587i	0.104168	+	0.320597i
$910$		0			0
$911$	6.13965	−	18.8959i	0.203416	−	0.626049i	−0.796359	−	0.604824i	$-0.793243\pi$
$911$	6.13965	−	18.8959i	0.203416	−	0.626049i	0.999775	−	0.0212248i	$-0.00675656\pi$
$912$	−2.99074	−	9.20456i	−0.0990334	−	0.304793i
$913$	8.97099	+	27.6099i	0.296897	+	0.913754i
$914$	−0.235874	+	0.725945i	−0.00780201	+	0.0240121i
$915$		0			0
$916$	−6.12935	−	18.8642i	−0.202519	−	0.623291i
$917$	−3.94827	+	2.86859i	−0.130383	+	0.0947291i
$918$	5.33620			0.176121
$919$	−22.6350	+	16.4453i	−0.746661	+	0.542481i	−0.894790	−	0.446487i	$-0.852675\pi$
$919$	−22.6350	+	16.4453i	−0.746661	+	0.542481i	0.148129	+	0.988968i	$0.452675\pi$
$920$		0			0
$921$	−5.09972	−	3.70517i	−0.168042	−	0.122089i
$922$	−3.55231	−	2.58090i	−0.116989	−	0.0849975i
$923$	0.546657	−	1.68244i	0.0179934	−	0.0553781i
$924$	−18.8772			−0.621013
$925$		0			0
$926$	7.56952			0.248750
$927$	−0.355745	+	1.09487i	−0.0116842	+	0.0359603i
$928$	10.2792	+	7.46831i	0.337433	+	0.245159i
$929$	11.4273	+	8.30242i	0.374918	+	0.272394i	0.759247	−	0.650802i	$-0.225567\pi$
$929$	11.4273	+	8.30242i	0.374918	+	0.272394i	−0.384329	+	0.923196i	$0.625567\pi$
$930$		0			0
$931$	−5.08611	+	3.69528i	−0.166691	+	0.121108i
$932$	−43.2727			−1.41744
$933$	30.5409	−	22.1893i	0.999864	−	0.726444i
$934$	−0.588481	−	1.81116i	−0.0192557	−	0.0592629i
$935$		0			0
$936$	0.0554531	−	0.170667i	0.00181254	−	0.00557843i
$937$	11.1106	+	34.1949i	0.362967	+	1.11710i	0.951244	+	0.308438i	$0.0998063\pi$
$937$	11.1106	+	34.1949i	0.362967	+	1.11710i	−0.588277	+	0.808659i	$0.700194\pi$
$938$	1.27136	+	3.91286i	0.0415115	+	0.127759i
$939$	−10.1666	+	31.2897i	−0.331776	+	1.02110i
$940$		0			0
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	0.990758	+	0.135641i	$0.0433094\pi$
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	−0.721812	+	0.692089i	$0.756691\pi$
$942$	−0.934408	+	0.678887i	−0.0304447	+	0.0221193i
$943$	−0.892508			−0.0290640
$944$	−18.2490	+	13.2587i	−0.593955	+	0.431534i
$945$		0			0
$946$	−0.960857	−	0.698104i	−0.0312402	−	0.0226973i
$947$	−14.0042	−	10.1747i	−0.455077	−	0.330633i	0.336520	−	0.941676i	$-0.390750\pi$
$947$	−14.0042	−	10.1747i	−0.455077	−	0.330633i	−0.791597	+	0.611044i	$0.790750\pi$
$948$	−6.94156	+	21.3639i	−0.225451	+	0.693868i
$949$	−2.61803			−0.0849850
$950$		0			0
$951$	32.2693			1.04640
$952$	3.77985	−	11.6332i	0.122506	−	0.377034i
$953$	−19.6286	−	14.2610i	−0.635831	−	0.461959i	0.222584	−	0.974913i	$-0.428551\pi$
$953$	−19.6286	−	14.2610i	−0.635831	−	0.461959i	−0.858416	+	0.512955i	$0.828551\pi$
$954$	1.00041	+	0.726837i	0.0323893	+	0.0235322i
$955$		0			0
$956$	12.0276	−	8.73855i	0.389000	−	0.282625i
$957$	−17.4048			−0.562617
$958$	5.33602	−	3.87684i	0.172399	−	0.125255i
$959$	7.90899	+	24.3414i	0.255395	+	0.786024i
$960$		0			0
$961$	1.91722	−	5.90061i	0.0618460	−	0.190342i
$962$	0.135684	+	0.417594i	0.00437464	+	0.0134638i
$963$	−4.07623	−	12.5453i	−0.131355	−	0.404268i
$964$	12.3931	−	38.1419i	0.399154	−	1.22847i
$965$		0			0
$966$	−0.238863	−	0.735146i	−0.00768531	−	0.0236529i
$967$	25.1720	−	18.2885i	0.809477	−	0.588120i	−0.104202	−	0.994556i	$-0.533229\pi$
$967$	25.1720	−	18.2885i	0.809477	−	0.588120i	0.913679	+	0.406437i	$0.133229\pi$
$968$	−5.08580			−0.163464
$969$	−10.6388	+	7.72952i	−0.341767	+	0.248308i
$970$		0			0
$971$	14.0543	+	10.2111i	0.451025	+	0.327689i	0.790000	−	0.613106i	$-0.210080\pi$
$971$	14.0543	+	10.2111i	0.451025	+	0.327689i	−0.338975	+	0.940795i	$0.610080\pi$
$972$	−13.3353	−	9.68867i	−0.427730	−	0.310764i
$973$	−5.43282	+	16.7205i	−0.174168	+	0.536034i
$974$	1.94855			0.0624356
$975$		0			0
$976$	3.47917			0.111365
$977$	−13.2546	+	40.7936i	−0.424054	+	1.30510i	0.479844	+	0.877354i	$0.340693\pi$
$977$	−13.2546	+	40.7936i	−0.424054	+	1.30510i	−0.903898	+	0.427749i	$0.859307\pi$
$978$	−3.43034	−	2.49229i	−0.109690	−	0.0796945i
$979$	−12.1780	−	8.84784i	−0.389211	−	0.282778i
$980$		0			0
$981$	−1.35096	+	0.981527i	−0.0431327	+	0.0313377i
$982$	3.23651			0.103281
$983$	30.3003	−	22.0145i	0.966431	−	0.702153i	0.0117954	−	0.999930i	$-0.496245\pi$
$983$	30.3003	−	22.0145i	0.966431	−	0.702153i	0.954635	+	0.297777i	$0.0962453\pi$
$984$	0.335478	+	1.03250i	0.0106947	+	0.0329148i
$985$		0			0
$986$	1.72778	−	5.31755i	0.0550236	−	0.169345i
$987$	6.25914	+	19.2637i	0.199231	+	0.613169i
$988$	0.311640	+	0.959129i	0.00991459	+	0.0305140i
$989$	−0.880801	+	2.71083i	−0.0280078	+	0.0861993i
$990$		0			0
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	0.999002	−	0.0446564i	$-0.0142193\pi$
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	−0.834458	+	0.551071i	$0.814219\pi$
$992$	10.6050	−	7.70500i	0.336710	−	0.244634i
$993$	13.1931			0.418669
$994$	2.88426	−	2.09554i	0.0914831	−	0.0664663i
$995$		0			0
$996$	−33.9908	−	24.6957i	−1.07704	−	0.782515i
$997$	48.4273	+	35.1845i	1.53371	+	1.11430i	0.954132	+	0.299388i	$0.0967824\pi$
$997$	48.4273	+	35.1845i	1.53371	+	1.11430i	0.579577	+	0.814917i	$0.303218\pi$
$998$	0.533052	−	1.64057i	0.0168735	−	0.0519312i
$999$	45.6367			1.44388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.d.b.101.2		16
5.2	odd	4		125.2.e.b.24.1		8
5.3	odd	4		25.2.e.a.4.2	✓	8
5.4	even	2	inner	125.2.d.b.101.3		16
15.8	even	4		225.2.m.a.154.1		8
20.3	even	4		400.2.y.c.129.2		8
25.2	odd	20		625.2.e.i.249.1		8
25.3	odd	20		625.2.e.i.374.1		8
25.4	even	10		625.2.d.o.251.2		16
25.6	even	5	inner	125.2.d.b.26.2		16
25.8	odd	20		125.2.e.b.99.1		8
25.9	even	10		625.2.a.f.1.5		8
25.11	even	5		625.2.d.o.376.3		16
25.12	odd	20		625.2.b.c.624.4		8
25.13	odd	20		625.2.b.c.624.5		8
25.14	even	10		625.2.d.o.376.2		16
25.16	even	5		625.2.a.f.1.4		8
25.17	odd	20		25.2.e.a.19.2	yes	8
25.19	even	10	inner	125.2.d.b.26.3		16
25.21	even	5		625.2.d.o.251.3		16
25.22	odd	20		625.2.e.a.374.2		8
25.23	odd	20		625.2.e.a.249.2		8
75.17	even	20		225.2.m.a.19.1		8
75.41	odd	10		5625.2.a.x.1.5		8
75.59	odd	10		5625.2.a.x.1.4		8
100.59	odd	10		10000.2.a.bj.1.3		8
100.67	even	20		400.2.y.c.369.2		8
100.91	odd	10		10000.2.a.bj.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.2	✓	8	5.3	odd	4
25.2.e.a.19.2	yes	8	25.17	odd	20
125.2.d.b.26.2		16	25.6	even	5	inner
125.2.d.b.26.3		16	25.19	even	10	inner
125.2.d.b.101.2		16	1.1	even	1	trivial
125.2.d.b.101.3		16	5.4	even	2	inner
125.2.e.b.24.1		8	5.2	odd	4
125.2.e.b.99.1		8	25.8	odd	20
225.2.m.a.19.1		8	75.17	even	20
225.2.m.a.154.1		8	15.8	even	4
400.2.y.c.129.2		8	20.3	even	4
400.2.y.c.369.2		8	100.67	even	20
625.2.a.f.1.4		8	25.16	even	5
625.2.a.f.1.5		8	25.9	even	10
625.2.b.c.624.4		8	25.12	odd	20
625.2.b.c.624.5		8	25.13	odd	20
625.2.d.o.251.2		16	25.4	even	10
625.2.d.o.251.3		16	25.21	even	5
625.2.d.o.376.2		16	25.14	even	10
625.2.d.o.376.3		16	25.11	even	5
625.2.e.a.249.2		8	25.23	odd	20
625.2.e.a.374.2		8	25.22	odd	20
625.2.e.i.249.1		8	25.2	odd	20
625.2.e.i.374.1		8	25.3	odd	20
5625.2.a.x.1.4		8	75.59	odd	10
5625.2.a.x.1.5		8	75.41	odd	10
10000.2.a.bj.1.3		8	100.59	odd	10
10000.2.a.bj.1.6		8	100.91	odd	10

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0566033 + 0.174207i) q^{2} +(1.19083 + 0.865190i) q^{3} +(1.59089 + 1.15585i) q^{4} +(-0.218127 + 0.158479i) q^{6} -3.26086 q^{7} +(-0.587785 + 0.427051i) q^{8} +(-0.257524 - 0.792578i) q^{9} +O(q^{10})\)	\(q+(-0.0566033 + 0.174207i) q^{2} +(1.19083 + 0.865190i) q^{3} +(1.59089 + 1.15585i) q^{4} +(-0.218127 + 0.158479i) q^{6} -3.26086 q^{7} +(-0.587785 + 0.427051i) q^{8} +(-0.257524 - 0.792578i) q^{9} +(0.618034 - 1.90211i) q^{11} +(0.894453 + 2.75284i) q^{12} +(-0.0915860 - 0.281873i) q^{13} +(0.184575 - 0.568064i) q^{14} +(1.17421 + 3.61384i) q^{16} +(4.17693 - 3.03472i) q^{17} +0.152649 q^{18} +(-1.39991 + 1.01709i) q^{19} +(-3.88313 - 2.82126i) q^{21} +(0.296379 + 0.215332i) q^{22} +(0.271685 - 0.836161i) q^{23} -1.06943 q^{24} +0.0542883 q^{26} +(1.74363 - 5.36635i) q^{27} +(-5.18766 - 3.76906i) q^{28} +(-4.78304 - 3.47508i) q^{29} +(-4.93462 + 3.58521i) q^{31} -2.14910 q^{32} +(2.38166 - 1.73038i) q^{33} +(0.292241 + 0.899425i) q^{34} +(0.506408 - 1.55856i) q^{36} +(2.49933 + 7.69215i) q^{37} +(-0.0979452 - 0.301444i) q^{38} +(0.134810 - 0.414902i) q^{39} +(-0.313697 - 0.965461i) q^{41} +(0.711281 - 0.516776i) q^{42} -3.24199 q^{43} +(3.18178 - 2.31170i) q^{44} +(0.130287 + 0.0946589i) q^{46} +(-3.41402 - 2.48043i) q^{47} +(-1.72837 + 5.31939i) q^{48} +3.63318 q^{49} +7.59963 q^{51} +(0.180099 - 0.554288i) q^{52} +(6.55362 + 4.76148i) q^{53} +(0.836161 + 0.607507i) q^{54} +(1.91668 - 1.39255i) q^{56} -2.54703 q^{57} +(0.876119 - 0.636538i) q^{58} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(-0.345253 - 1.06258i) q^{62} +(0.839749 + 2.58448i) q^{63} +(-2.22677 + 6.85329i) q^{64} +(0.166634 + 0.512848i) q^{66} +(-5.57255 + 4.04870i) q^{67} +10.1527 q^{68} +(1.04697 - 0.760668i) q^{69} +(4.82884 + 3.50836i) q^{71} +(0.489840 + 0.355890i) q^{72} +(2.72967 - 8.40107i) q^{73} -1.48150 q^{74} -3.40270 q^{76} +(-2.01532 + 6.20252i) q^{77} +(0.0646482 + 0.0469697i) q^{78} +(6.27851 + 4.56161i) q^{79} +(4.69667 - 3.41233i) q^{81} +0.185946 q^{82} +(-11.7432 + 8.53192i) q^{83} +(-2.91668 - 8.97663i) q^{84} +(0.183507 - 0.564778i) q^{86} +(-2.68919 - 8.27647i) q^{87} +(0.449028 + 1.38197i) q^{88} +(2.32579 - 7.15805i) q^{89} +(0.298649 + 0.919147i) q^{91} +(1.39870 - 1.01621i) q^{92} -8.97820 q^{93} +(0.625353 - 0.454345i) q^{94} +(-2.55922 - 1.85938i) q^{96} +(5.44184 + 3.95373i) q^{97} +(-0.205650 + 0.632925i) q^{98} -1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46} - 28 q^{49} - 8 q^{51} + 10 q^{54} + 20 q^{56} - 18 q^{61} - 8 q^{64} + 24 q^{66} - 34 q^{69} + 12 q^{71} + 24 q^{74} - 40 q^{76} - 30 q^{79} + 56 q^{81} - 36 q^{84} - 18 q^{86} + 50 q^{89} + 12 q^{91} + 54 q^{94} + 32 q^{96} + 16 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9 - 8 * q^11 - 26 * q^14 + 6 * q^16 + 10 * q^19 - 8 * q^21 + 40 * q^24 + 12 * q^26 + 10 * q^29 - 18 * q^31 - 26 * q^34 + 46 * q^36 + 6 * q^39 - 8 * q^41 + 4 * q^44 - 38 * q^46 - 28 * q^49 - 8 * q^51 + 10 * q^54 + 20 * q^56 - 18 * q^61 - 8 * q^64 + 24 * q^66 - 34 * q^69 + 12 * q^71 + 24 * q^74 - 40 * q^76 - 30 * q^79 + 56 * q^81 - 36 * q^84 - 18 * q^86 + 50 * q^89 + 12 * q^91 + 54 * q^94 + 32 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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