LMFDB - Embedded newform 95.5.f.a.58.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,5,Mod(58,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.58"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.82014649297$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			58.17
Character	$\chi$	$=$	95.58
Dual form			95.5.f.a.77.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.248255 + 0.248255i) q^{2} +(-4.68699 - 4.68699i) q^{3} +15.8767i q^{4} +(-20.9216 + 13.6853i) q^{5} +2.32714 q^{6} +(9.28930 - 9.28930i) q^{7} +(-7.91356 - 7.91356i) q^{8} -37.0643i q^{9} +(1.79645 - 8.59133i) q^{10} +157.199 q^{11} +(74.4141 - 74.4141i) q^{12} +(-163.427 - 163.427i) q^{13} +4.61223i q^{14} +(162.202 + 33.9166i) q^{15} -250.099 q^{16} +(207.129 - 207.129i) q^{17} +(9.20138 + 9.20138i) q^{18} -82.8191i q^{19} +(-217.277 - 332.167i) q^{20} -87.0777 q^{21} +(-39.0255 + 39.0255i) q^{22} +(-517.395 - 517.395i) q^{23} +74.1815i q^{24} +(250.427 - 572.636i) q^{25} +81.1429 q^{26} +(-553.366 + 553.366i) q^{27} +(147.484 + 147.484i) q^{28} -129.178i q^{29} +(-48.6874 + 31.8475i) q^{30} +1459.75 q^{31} +(188.705 - 188.705i) q^{32} +(-736.791 - 736.791i) q^{33} +102.841i q^{34} +(-67.2204 + 321.473i) q^{35} +588.460 q^{36} +(1650.27 - 1650.27i) q^{37} +(20.5602 + 20.5602i) q^{38} +1531.96i q^{39} +(273.863 + 57.2651i) q^{40} -2053.53 q^{41} +(21.6175 - 21.6175i) q^{42} +(-174.030 - 174.030i) q^{43} +2495.81i q^{44} +(507.234 + 775.444i) q^{45} +256.892 q^{46} +(-1168.66 + 1168.66i) q^{47} +(1172.21 + 1172.21i) q^{48} +2228.42i q^{49} +(79.9899 + 204.329i) q^{50} -1941.62 q^{51} +(2594.68 - 2594.68i) q^{52} +(-1448.10 - 1448.10i) q^{53} -274.752i q^{54} +(-3288.86 + 2151.31i) q^{55} -147.023 q^{56} +(-388.172 + 388.172i) q^{57} +(32.0690 + 32.0690i) q^{58} -1919.33i q^{59} +(-538.485 + 2575.24i) q^{60} -3903.95 q^{61} +(-362.391 + 362.391i) q^{62} +(-344.301 - 344.301i) q^{63} -3907.88i q^{64} +(5655.69 + 1182.61i) q^{65} +365.824 q^{66} +(546.347 - 546.347i) q^{67} +(3288.53 + 3288.53i) q^{68} +4850.05i q^{69} +(-63.1196 - 96.4952i) q^{70} -2485.36 q^{71} +(-293.310 + 293.310i) q^{72} +(6502.33 + 6502.33i) q^{73} +819.377i q^{74} +(-3857.68 + 1510.19i) q^{75} +1314.90 q^{76} +(1460.27 - 1460.27i) q^{77} +(-380.316 - 380.316i) q^{78} -4966.63i q^{79} +(5232.46 - 3422.67i) q^{80} +2185.04 q^{81} +(509.798 - 509.798i) q^{82} +(-6514.60 - 6514.60i) q^{83} -1382.51i q^{84} +(-1498.85 + 7168.07i) q^{85} +86.4076 q^{86} +(-605.455 + 605.455i) q^{87} +(-1244.00 - 1244.00i) q^{88} +8157.92i q^{89} +(-318.431 - 66.5842i) q^{90} -3036.24 q^{91} +(8214.54 - 8214.54i) q^{92} +(-6841.85 - 6841.85i) q^{93} -580.253i q^{94} +(1133.40 + 1732.71i) q^{95} -1768.92 q^{96} +(10378.0 - 10378.0i) q^{97} +(-553.216 - 553.216i) q^{98} -5826.47i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 20 q^{3} - 66 q^{5} - 128 q^{6} + 130 q^{7} + 16 q^{10} + 312 q^{11} - 80 q^{12} - 760 q^{13} + 1184 q^{15} - 3504 q^{16} + 1110 q^{17} + 960 q^{20} - 2840 q^{21} + 720 q^{22} + 300 q^{23} - 2322 q^{25}+ \cdots - 31440 q^{98}+O(q^{100}) $ 72 * q + 20 * q^3 - 66 * q^5 - 128 * q^6 + 130 * q^7 + 16 * q^10 + 312 * q^11 - 80 * q^12 - 760 * q^13 + 1184 * q^15 - 3504 * q^16 + 1110 * q^17 + 960 * q^20 - 2840 * q^21 + 720 * q^22 + 300 * q^23 - 2322 * q^25 - 192 * q^26 + 2060 * q^27 - 1120 * q^28 - 1160 * q^30 - 584 * q^31 - 6600 * q^32 + 3200 * q^33 - 4602 * q^35 + 10160 * q^36 + 2280 * q^37 + 11736 * q^40 + 6984 * q^41 - 8800 * q^42 - 8110 * q^43 - 8748 * q^45 + 11312 * q^46 - 3870 * q^47 - 660 * q^48 + 588 * q^50 + 7224 * q^51 + 2340 * q^52 + 13380 * q^53 - 5048 * q^55 - 13416 * q^56 + 5280 * q^58 - 9684 * q^60 + 10952 * q^61 - 1800 * q^62 + 17830 * q^63 + 852 * q^65 - 37928 * q^66 + 13780 * q^67 - 39000 * q^68 + 26500 * q^70 + 28680 * q^71 + 52900 * q^72 + 24070 * q^73 - 10208 * q^75 - 13530 * q^77 + 9400 * q^78 + 60240 * q^80 - 78720 * q^81 - 40360 * q^82 - 1740 * q^83 - 10112 * q^85 + 6432 * q^86 + 9720 * q^87 - 48180 * q^88 - 52736 * q^90 - 34232 * q^91 - 25800 * q^92 + 23800 * q^93 - 6498 * q^95 + 88440 * q^96 + 38060 * q^97 - 31440 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.248255	+	0.248255i	−0.0620637	+	0.0620637i	−0.737457	−	0.675394i	$-0.763974\pi$
$2$	−0.248255	+	0.248255i	−0.0620637	+	0.0620637i	0.675394	+	0.737457i	$0.263974\pi$
$3$	−4.68699	−	4.68699i	−0.520777	−	0.520777i	0.397029	−	0.917806i	$-0.370041\pi$
$3$	−4.68699	−	4.68699i	−0.520777	−	0.520777i	−0.917806	+	0.397029i	$0.870041\pi$
$4$			15.8767i			0.992296i
$5$	−20.9216	+	13.6853i	−0.836864	+	0.547411i
$5$	−20.9216	+	13.6853i	−0.836864	+	0.547411i
$6$	2.32714			0.0646427
$7$	9.28930	−	9.28930i	0.189577	−	0.189577i	−0.605936	−	0.795513i	$-0.707201\pi$
$7$	9.28930	−	9.28930i	0.189577	−	0.189577i	0.795513	+	0.605936i	$0.207201\pi$
$8$	−7.91356	−	7.91356i	−0.123649	−	0.123649i
$9$		−	37.0643i		−	0.457583i
$10$	1.79645	−	8.59133i	0.0179645	−	0.0859133i
$11$	157.199			1.29917			0.649583	−	0.760291i	$-0.274943\pi$
$11$	157.199			1.29917			0.649583	+	0.760291i	$0.274943\pi$
$12$	74.4141	−	74.4141i	0.516765	−	0.516765i
$13$	−163.427	−	163.427i	−0.967022	−	0.967022i	0.0324517	−	0.999473i	$-0.489668\pi$
$13$	−163.427	−	163.427i	−0.967022	−	0.967022i	−0.999473	+	0.0324517i	$0.989668\pi$
$14$			4.61223i			0.0235318i
$15$	162.202	+	33.9166i	0.720898	+	0.150740i
$16$	−250.099			−0.976948
$17$	207.129	−	207.129i	0.716708	−	0.716708i	−0.251222	−	0.967930i	$-0.580832\pi$
$17$	207.129	−	207.129i	0.716708	−	0.716708i	0.967930	+	0.251222i	$0.0808323\pi$
$18$	9.20138	+	9.20138i	0.0283993	+	0.0283993i
$19$		−	82.8191i		−	0.229416i
$19$		−	82.8191i		−	0.229416i
$20$	−217.277	−	332.167i	−0.543194	−	0.830417i
$21$	−87.0777			−0.197455
$22$	−39.0255	+	39.0255i	−0.0806311	+	0.0806311i
$23$	−517.395	−	517.395i	−0.978062	−	0.978062i	0.0217022	−	0.999764i	$-0.493091\pi$
$23$	−517.395	−	517.395i	−0.978062	−	0.978062i	−0.999764	+	0.0217022i	$0.993091\pi$
$24$			74.1815i			0.128787i
$25$	250.427	−	572.636i	0.400683	−	0.916217i
$26$	81.1429			0.120034
$27$	−553.366	+	553.366i	−0.759075	+	0.759075i
$28$	147.484	+	147.484i	0.188117	+	0.188117i
$29$		−	129.178i		−	0.153600i	−0.997047	−	0.0768001i	$-0.975530\pi$
$29$		−	129.178i		−	0.153600i	0.997047	−	0.0768001i	$-0.0244703\pi$
$30$	−48.6874	+	31.8475i	−0.0540971	+	0.0353861i
$31$	1459.75			1.51899			0.759497	−	0.650511i	$-0.225445\pi$
$31$	1459.75			1.51899			0.759497	+	0.650511i	$0.225445\pi$
$32$	188.705	−	188.705i	0.184282	−	0.184282i
$33$	−736.791	−	736.791i	−0.676575	−	0.676575i
$34$			102.841i			0.0889631i
$35$	−67.2204	+	321.473i	−0.0548738	+	0.262427i
$36$	588.460			0.454058
$37$	1650.27	−	1650.27i	1.20546	−	1.20546i	0.232977	−	0.972482i	$-0.425153\pi$
$37$	1650.27	−	1650.27i	1.20546	−	1.20546i	0.972482	−	0.232977i	$-0.0748468\pi$
$38$	20.5602	+	20.5602i	0.0142384	+	0.0142384i
$39$			1531.96i			1.00720i
$40$	273.863	+	57.2651i	0.171165	+	0.0357907i
$41$	−2053.53			−1.22161			−0.610805	−	0.791781i	$-0.709154\pi$
$41$	−2053.53			−1.22161			−0.610805	+	0.791781i	$0.709154\pi$
$42$	21.6175	−	21.6175i	0.0122548	−	0.0122548i
$43$	−174.030	−	174.030i	−0.0941211	−	0.0941211i	0.658478	−	0.752600i	$-0.271200\pi$
$43$	−174.030	−	174.030i	−0.0941211	−	0.0941211i	−0.752600	+	0.658478i	$0.771200\pi$
$44$			2495.81i			1.28916i
$45$	507.234	+	775.444i	0.250486	+	0.382935i
$46$	256.892			0.121404
$47$	−1168.66	+	1168.66i	−0.529046	+	0.529046i	−0.920288	−	0.391242i	$-0.872046\pi$
$47$	−1168.66	+	1168.66i	−0.529046	+	0.529046i	0.391242	+	0.920288i	$0.372046\pi$
$48$	1172.21	+	1172.21i	0.508772	+	0.508772i
$49$			2228.42i			0.928121i
$50$	79.9899	+	204.329i	0.0319960	+	0.0817317i
$51$	−1941.62			−0.746490
$52$	2594.68	−	2594.68i	0.959572	−	0.959572i
$53$	−1448.10	−	1448.10i	−0.515522	−	0.515522i	0.400691	−	0.916213i	$-0.368770\pi$
$53$	−1448.10	−	1448.10i	−0.515522	−	0.515522i	−0.916213	+	0.400691i	$0.868770\pi$
$54$		−	274.752i		−	0.0942221i
$55$	−3288.86	+	2151.31i	−1.08723	+	0.711178i
$56$	−147.023			−0.0468823
$57$	−388.172	+	388.172i	−0.119474	+	0.119474i
$58$	32.0690	+	32.0690i	0.00953300	+	0.00953300i
$59$		−	1919.33i		−	0.551374i	−0.961247	−	0.275687i	$-0.911095\pi$
$59$		−	1919.33i		−	0.551374i	0.961247	−	0.275687i	$-0.0889054\pi$
$60$	−538.485	+	2575.24i	−0.149579	+	0.715344i
$61$	−3903.95			−1.04917			−0.524583	−	0.851359i	$-0.675779\pi$
$61$	−3903.95			−1.04917			−0.524583	+	0.851359i	$0.675779\pi$
$62$	−362.391	+	362.391i	−0.0942745	+	0.0942745i
$63$	−344.301	−	344.301i	−0.0867475	−	0.0867475i
$64$		−	3907.88i		−	0.954073i
$65$	5655.69	+	1182.61i	1.33862	+	0.279907i
$66$	365.824			0.0839816
$67$	546.347	−	546.347i	0.121708	−	0.121708i	−0.643629	−	0.765337i	$-0.722572\pi$
$67$	546.347	−	546.347i	0.121708	−	0.121708i	0.765337	+	0.643629i	$0.222572\pi$
$68$	3288.53	+	3288.53i	0.711187	+	0.711187i
$69$			4850.05i			1.01870i
$70$	−63.1196	−	96.4952i	−0.0128815	−	0.0196929i
$71$	−2485.36			−0.493029			−0.246514	−	0.969139i	$-0.579285\pi$
$71$	−2485.36			−0.493029			−0.246514	+	0.969139i	$0.579285\pi$
$72$	−293.310	+	293.310i	−0.0565799	+	0.0565799i
$73$	6502.33	+	6502.33i	1.22018	+	1.22018i	0.967568	+	0.252611i	$0.0812893\pi$
$73$	6502.33	+	6502.33i	1.22018	+	1.22018i	0.252611	+	0.967568i	$0.418711\pi$
$74$			819.377i			0.149631i
$75$	−3857.68	+	1510.19i	−0.685811	+	0.268478i
$76$	1314.90			0.227648
$77$	1460.27	−	1460.27i	0.246293	−	0.246293i
$78$	−380.316	−	380.316i	−0.0625109	−	0.0625109i
$79$		−	4966.63i		−	0.795807i	−0.917427	−	0.397904i	$-0.869738\pi$
$79$		−	4966.63i		−	0.795807i	0.917427	−	0.397904i	$-0.130262\pi$
$80$	5232.46	−	3422.67i	0.817573	−	0.534792i
$81$	2185.04			0.333034
$82$	509.798	−	509.798i	0.0758176	−	0.0758176i
$83$	−6514.60	−	6514.60i	−0.945653	−	0.945653i	0.0529445	−	0.998597i	$-0.483139\pi$
$83$	−6514.60	−	6514.60i	−0.945653	−	0.945653i	−0.998597	+	0.0529445i	$0.983139\pi$
$84$		−	1382.51i		−	0.195934i
$85$	−1498.85	+	7168.07i	−0.207453	+	0.992121i
$86$	86.4076			0.0116830
$87$	−605.455	+	605.455i	−0.0799914	+	0.0799914i
$88$	−1244.00	−	1244.00i	−0.160641	−	0.160641i
$89$			8157.92i			1.02991i	0.857217	+	0.514955i	$0.172191\pi$
$89$			8157.92i			1.02991i	−0.857217	+	0.514955i	$0.827809\pi$
$90$	−318.431	−	66.5842i	−0.0393125	−	0.00822028i
$91$	−3036.24			−0.366651
$92$	8214.54	−	8214.54i	0.970527	−	0.970527i
$93$	−6841.85	−	6841.85i	−0.791057	−	0.791057i
$94$		−	580.253i		−	0.0656692i
$95$	1133.40	+	1732.71i	0.125585	+	0.191990i
$96$	−1768.92			−0.191940
$97$	10378.0	−	10378.0i	1.10298	−	1.10298i	0.108933	−	0.994049i	$-0.465257\pi$
$97$	10378.0	−	10378.0i	1.10298	−	1.10298i	0.994049	−	0.108933i	$-0.0347433\pi$
$98$	−553.216	−	553.216i	−0.0576026	−	0.0576026i
$99$		−	5826.47i		−	0.594477i
$100$	9091.59	+	3975.96i	0.909159	+	0.397596i
$101$	−18748.3			−1.83789			−0.918944	−	0.394387i	$-0.870957\pi$
$101$	−18748.3			−1.83789			−0.918944	+	0.394387i	$0.870957\pi$
$102$	482.017	−	482.017i	0.0463299	−	0.0463299i
$103$	−6033.54	−	6033.54i	−0.568719	−	0.568719i	0.363051	−	0.931769i	$-0.381735\pi$
$103$	−6033.54	−	6033.54i	−0.568719	−	0.568719i	−0.931769	+	0.363051i	$0.881735\pi$
$104$			2586.57i			0.239143i
$105$	1821.80	−	1191.68i	0.165243	−	0.108089i
$106$	718.996			0.0639904
$107$	4811.26	−	4811.26i	0.420234	−	0.420234i	−0.465050	−	0.885284i	$-0.653964\pi$
$107$	4811.26	−	4811.26i	0.420234	−	0.420234i	0.885284	+	0.465050i	$0.153964\pi$
$108$	−8785.65	−	8785.65i	−0.753228	−	0.753228i
$109$		−	22913.7i		−	1.92860i	−0.264816	−	0.964299i	$-0.585311\pi$
$109$		−	22913.7i		−	1.92860i	0.264816	−	0.964299i	$-0.414689\pi$
$110$	282.401	−	1350.55i	0.0233389	−	0.111616i
$111$	−15469.6			−1.25555
$112$	−2323.24	+	2323.24i	−0.185207	+	0.185207i
$113$	−4979.45	−	4979.45i	−0.389964	−	0.389964i	0.484711	−	0.874675i	$-0.338925\pi$
$113$	−4979.45	−	4979.45i	−0.389964	−	0.389964i	−0.874675	+	0.484711i	$0.838925\pi$
$114$		−	192.731i		−	0.0148300i
$115$	17905.4	+	3744.04i	1.35391	+	0.283103i
$116$	2050.92			0.152417
$117$	−6057.29	+	6057.29i	−0.442493	+	0.442493i
$118$	476.484	+	476.484i	0.0342204	+	0.0342204i
$119$		−	3848.16i		−	0.271743i
$120$	−1015.19	−	1552.00i	−0.0704996	−	0.107778i
$121$	10070.6			0.687833
$122$	969.174	−	969.174i	0.0651151	−	0.0651151i
$123$	9624.85	+	9624.85i	0.636186	+	0.636186i
$124$			23176.1i			1.50729i
$125$	2597.35	+	15407.6i	0.166230	+	0.986087i
$126$	170.949			0.0107677
$127$	−5902.45	+	5902.45i	−0.365953	+	0.365953i	−0.865999	−	0.500046i	$-0.833316\pi$
$127$	−5902.45	+	5902.45i	−0.365953	+	0.365953i	0.500046	+	0.865999i	$0.333316\pi$
$128$	3989.43	+	3989.43i	0.243496	+	0.243496i
$129$			1631.35i			0.0980322i
$130$	−1697.64	+	1110.46i	−0.100452	+	0.0657079i
$131$	3107.32			0.181069			0.0905343	−	0.995893i	$-0.471143\pi$
$131$	3107.32			0.181069			0.0905343	+	0.995893i	$0.471143\pi$
$132$	11697.8	−	11697.8i	0.671363	−	0.671363i
$133$	−769.331	−	769.331i	−0.0434921	−	0.0434921i
$134$			271.267i			0.0151073i
$135$	4004.34	−	19150.3i	0.219717	−	1.05077i
$136$	−3278.25			−0.177241
$137$	−840.684	+	840.684i	−0.0447911	+	0.0447911i	−0.729148	−	0.684356i	$-0.760083\pi$
$137$	−840.684	+	840.684i	−0.0447911	+	0.0447911i	0.684356	+	0.729148i	$0.260083\pi$
$138$	−1204.05	−	1204.05i	−0.0632246	−	0.0632246i
$139$			18274.4i			0.945832i	0.881108	+	0.472916i	$0.156799\pi$
$139$			18274.4i			0.945832i	−0.881108	+	0.472916i	$0.843201\pi$
$140$	−5103.95	−	1067.24i	−0.260406	−	0.0544511i
$141$	10955.0			0.551030
$142$	617.003	−	617.003i	0.0305992	−	0.0305992i
$143$	−25690.5	−	25690.5i	−1.25632	−	1.25632i
$144$			9269.72i			0.447035i
$145$	1767.83	+	2702.60i	0.0840824	+	0.128542i
$146$	−3228.47			−0.151458
$147$	10444.6	−	10444.6i	0.483344	−	0.483344i
$148$	26201.0	+	26201.0i	1.19617	+	1.19617i
$149$			27053.7i			1.21858i	0.792947	+	0.609290i	$0.208546\pi$
$149$			27053.7i			1.21858i	−0.792947	+	0.609290i	$0.791454\pi$
$150$	582.777	−	1332.60i	0.0259012	−	0.0592267i
$151$	28593.6			1.25405			0.627026	−	0.778999i	$-0.284272\pi$
$151$	28593.6			1.25405			0.627026	+	0.778999i	$0.284272\pi$
$152$	−655.394	+	655.394i	−0.0283671	+	0.0283671i
$153$	−7677.07	−	7677.07i	−0.327954	−	0.327954i
$154$			725.038i			0.0305717i
$155$	−30540.4	+	19977.1i	−1.27119	+	0.831514i
$156$	−24322.5			−0.999445
$157$	−19455.1	+	19455.1i	−0.789284	+	0.789284i	−0.981377	−	0.192093i	$-0.938473\pi$
$157$	−19455.1	+	19455.1i	−0.789284	+	0.789284i	0.192093	+	0.981377i	$0.438473\pi$
$158$	1232.99	+	1232.99i	0.0493908	+	0.0493908i
$159$			13574.5i			0.536943i
$160$	−1365.53	+	6530.49i	−0.0533411	+	0.255097i
$161$	−9612.47			−0.370837
$162$	−542.446	+	542.446i	−0.0206693	+	0.0206693i
$163$	−13734.3	−	13734.3i	−0.516930	−	0.516930i	0.399711	−	0.916641i	$-0.369110\pi$
$163$	−13734.3	−	13734.3i	−0.516930	−	0.516930i	−0.916641	+	0.399711i	$0.869110\pi$
$164$		−	32603.3i		−	1.21220i
$165$	25498.0	+	5331.66i	0.936566	+	0.195837i
$166$	3234.56			0.117381
$167$	13747.7	−	13747.7i	0.492945	−	0.492945i	−0.416288	−	0.909233i	$-0.636669\pi$
$167$	13747.7	−	13747.7i	0.492945	−	0.492945i	0.909233	+	0.416288i	$0.136669\pi$
$168$	689.094	+	689.094i	0.0244152	+	0.0244152i
$169$			24855.5i			0.870262i
$170$	−1407.41	−	2151.61i	−0.0486994	−	0.0744500i
$171$	−3069.63			−0.104977
$172$	2763.03	−	2763.03i	0.0933960	−	0.0933960i
$173$	−7211.83	−	7211.83i	−0.240965	−	0.240965i	0.576284	−	0.817249i	$-0.304502\pi$
$173$	−7211.83	−	7211.83i	−0.240965	−	0.240965i	−0.817249	+	0.576284i	$0.804502\pi$
$174$		−	300.614i		−	0.00992912i
$175$	−2993.09	−	7645.67i	−0.0977337	−	0.249654i
$176$	−39315.3			−1.26922
$177$	−8995.90	+	8995.90i	−0.287143	+	0.287143i
$178$	−2025.24	−	2025.24i	−0.0639201	−	0.0639201i
$179$			11251.0i			0.351145i	0.984466	+	0.175573i	$0.0561777\pi$
$179$			11251.0i			0.351145i	−0.984466	+	0.175573i	$0.943822\pi$
$180$	−12311.5	+	8053.23i	−0.379985	+	0.248556i
$181$	41802.9			1.27599			0.637997	−	0.770039i	$-0.279763\pi$
$181$	41802.9			1.27599			0.637997	+	0.770039i	$0.279763\pi$
$182$	753.761	−	753.761i	0.0227557	−	0.0227557i
$183$	18297.8	+	18297.8i	0.546381	+	0.546381i
$184$			8188.87i			0.241873i
$185$	−11941.9	+	57110.8i	−0.348924	+	1.66869i
$186$	3397.05			0.0981919
$187$	32560.4	−	32560.4i	0.931123	−	0.931123i
$188$	−18554.6	−	18554.6i	−0.524971	−	0.524971i
$189$			10280.8i			0.287807i
$190$	−711.526	−	148.781i	−0.0197099	−	0.00412135i
$191$	55641.4			1.52522			0.762608	−	0.646861i	$-0.223919\pi$
$191$	55641.4			1.52522			0.762608	+	0.646861i	$0.223919\pi$
$192$	−18316.2	+	18316.2i	−0.496859	+	0.496859i
$193$	20190.8	+	20190.8i	0.542050	+	0.542050i	0.924129	−	0.382079i	$-0.124792\pi$
$193$	20190.8	+	20190.8i	0.542050	+	0.542050i	−0.382079	+	0.924129i	$0.624792\pi$
$194$			5152.76i			0.136910i
$195$	−20965.3	−	32051.0i	−0.551355	−	0.842893i
$196$	−35380.0			−0.920971
$197$	−3696.82	+	3696.82i	−0.0952568	+	0.0952568i	−0.753129	−	0.657873i	$-0.771457\pi$
$197$	−3696.82	+	3696.82i	−0.0952568	+	0.0952568i	0.657873	+	0.753129i	$0.271457\pi$
$198$	1446.45	+	1446.45i	0.0368955	+	0.0368955i
$199$		−	39057.2i		−	0.986267i	−0.869954	−	0.493133i	$-0.835851\pi$
$199$		−	39057.2i		−	0.986267i	0.869954	−	0.493133i	$-0.164149\pi$
$200$	−6513.35	+	2549.82i	−0.162834	+	0.0637455i
$201$	−5121.45			−0.126765
$202$	4654.36	−	4654.36i	0.114066	−	0.114066i
$203$	−1199.97	−	1199.97i	−0.0291191	−	0.0291191i
$204$		−	30826.6i		−	0.740739i
$205$	42963.0	−	28103.1i	1.02232	−	0.668722i
$206$	2995.71			0.0705936
$207$	−19176.9	+	19176.9i	−0.447545	+	0.447545i
$208$	40872.8	+	40872.8i	0.944730	+	0.944730i
$209$		−	13019.1i		−	0.298049i
$210$	−156.431	+	748.113i	−0.00354719	+	0.0169640i
$211$	−3966.35			−0.0890894			−0.0445447	−	0.999007i	$-0.514184\pi$
$211$	−3966.35			−0.0890894			−0.0445447	+	0.999007i	$0.514184\pi$
$212$	22991.1	−	22991.1i	0.511550	−	0.511550i
$213$	11648.9	+	11648.9i	0.256758	+	0.256758i
$214$			2388.84i			0.0521626i
$215$	6022.63	+	1259.34i	0.130290	+	0.0272437i
$216$	8758.19			0.187718
$217$	13560.1	−	13560.1i	0.287967	−	0.287967i
$218$	5688.43	+	5688.43i	0.119696	+	0.119696i
$219$		−	60952.7i		−	1.27088i
$220$	−34155.8	−	52216.3i	−0.705699	−	1.07885i
$221$	−67700.7			−1.38614
$222$	3840.41	−	3840.41i	0.0779241	−	0.0779241i
$223$	−5079.73	−	5079.73i	−0.102148	−	0.102148i	0.654186	−	0.756334i	$-0.273011\pi$
$223$	−5079.73	−	5079.73i	−0.102148	−	0.102148i	−0.756334	+	0.654186i	$0.773011\pi$
$224$		−	3505.88i		−	0.0698716i
$225$	−21224.3	−	9281.88i	−0.419246	−	0.183346i
$226$	2472.35			0.0484052
$227$	−12949.7	+	12949.7i	−0.251309	+	0.251309i	−0.821507	−	0.570198i	$-0.806866\pi$
$227$	−12949.7	+	12949.7i	−0.251309	+	0.251309i	0.570198	+	0.821507i	$0.306866\pi$
$228$	−6162.91	−	6162.91i	−0.118554	−	0.118554i
$229$			20233.3i			0.385829i	0.981216	+	0.192915i	$0.0617940\pi$
$229$			20233.3i			0.385829i	−0.981216	+	0.192915i	$0.938206\pi$
$230$	−5374.58	+	3515.63i	−0.101599	+	0.0664581i
$231$	−13688.5			−0.256527
$232$	−1022.26	+	1022.26i	−0.0189926	+	0.0189926i
$233$	17200.6	+	17200.6i	0.316834	+	0.316834i	0.847550	−	0.530716i	$-0.178077\pi$
$233$	17200.6	+	17200.6i	0.316834	+	0.316834i	−0.530716	+	0.847550i	$0.678077\pi$
$234$		−	3007.50i		−	0.0549255i
$235$	8456.83	−	40443.8i	0.153134	−	0.732345i
$236$	30472.8			0.547127
$237$	−23278.6	+	23278.6i	−0.414438	+	0.414438i
$238$	955.324	+	955.324i	0.0168654	+	0.0168654i
$239$		−	46419.9i		−	0.812660i	−0.913726	−	0.406330i	$-0.866808\pi$
$239$		−	46419.9i		−	0.812660i	0.913726	−	0.406330i	$-0.133192\pi$
$240$	−40566.5	−	8482.50i	−0.704280	−	0.147266i
$241$	53296.3			0.917619			0.458810	−	0.888535i	$-0.348276\pi$
$241$	53296.3			0.917619			0.458810	+	0.888535i	$0.348276\pi$
$242$	−2500.07	+	2500.07i	−0.0426895	+	0.0426895i
$243$	34581.4	+	34581.4i	0.585639	+	0.585639i
$244$		−	61981.9i		−	1.04108i
$245$	−30496.5	−	46622.1i	−0.508063	−	0.776711i
$246$	−4778.83			−0.0789681
$247$	−13534.8	+	13534.8i	−0.221850	+	0.221850i
$248$	−11551.8	−	11551.8i	−0.187823	−	0.187823i
$249$			61067.8i			0.984948i
$250$	−4469.82	−	3180.21i	−0.0715171	−	0.0508834i
$251$	−21974.2			−0.348791			−0.174396	−	0.984676i	$-0.555797\pi$
$251$	−21974.2			−0.348791			−0.174396	+	0.984676i	$0.555797\pi$
$252$	5466.37	−	5466.37i	0.0860792	−	0.0860792i
$253$	−81334.0	−	81334.0i	−1.27067	−	1.27067i
$254$		−	2930.62i		−	0.0454248i
$255$	40621.8	−	26571.6i	0.624710	−	0.408636i
$256$	60545.4			0.923849
$257$	−48244.3	+	48244.3i	−0.730432	+	0.730432i	−0.970705	−	0.240273i	$-0.922763\pi$
$257$	−48244.3	+	48244.3i	−0.730432	+	0.730432i	0.240273	+	0.970705i	$0.422763\pi$
$258$	−404.991	−	404.991i	−0.00608424	−	0.00608424i
$259$		−	30659.8i		−	0.457056i
$260$	−18776.0	+	89793.8i	−0.277751	+	1.32831i
$261$	−4787.88			−0.0702849
$262$	−771.407	+	771.407i	−0.0112378	+	0.0112378i
$263$	−9037.53	−	9037.53i	−0.130659	−	0.130659i	0.638753	−	0.769412i	$-0.279451\pi$
$263$	−9037.53	−	9037.53i	−0.130659	−	0.130659i	−0.769412	+	0.638753i	$0.779451\pi$
$264$			11661.3i			0.167316i
$265$	50114.2	+	10478.9i	0.713624	+	0.149219i
$266$	381.980			0.00539856
$267$	38236.1	−	38236.1i	0.536353	−	0.536353i
$268$	8674.21	+	8674.21i	0.120770	+	0.120770i
$269$		−	34416.7i		−	0.475624i	−0.971311	−	0.237812i	$-0.923570\pi$
$269$		−	34416.7i		−	0.475624i	0.971311	−	0.237812i	$-0.0764303\pi$
$270$	3760.05	+	5748.24i	0.0515782	+	0.0788511i
$271$	136084.			1.85297			0.926483	−	0.376335i	$-0.122816\pi$
$271$	136084.			1.85297			0.926483	+	0.376335i	$0.122816\pi$
$272$	−51802.6	+	51802.6i	−0.700186	+	0.700186i
$273$	14230.8	+	14230.8i	0.190943	+	0.190943i
$274$		−	417.408i		−	0.00555981i
$275$	39366.9	−	90017.8i	0.520553	−	1.19032i
$276$	−77003.0			−1.01086
$277$	−5638.98	+	5638.98i	−0.0734921	+	0.0734921i	−0.742897	−	0.669405i	$-0.766549\pi$
$277$	−5638.98	+	5638.98i	−0.0734921	+	0.0734921i	0.669405	+	0.742897i	$0.266549\pi$
$278$	−4536.71	−	4536.71i	−0.0587019	−	0.0587019i
$279$		−	54104.7i		−	0.695067i
$280$	3075.95	−	2012.05i	0.0392341	−	0.0256639i
$281$	140527.			1.77970			0.889850	−	0.456252i	$-0.150809\pi$
$281$	140527.			1.77970			0.889850	+	0.456252i	$0.150809\pi$
$282$	−2719.64	+	2719.64i	−0.0341990	+	0.0341990i
$283$	16772.2	+	16772.2i	0.209419	+	0.209419i	0.804020	−	0.594602i	$-0.202690\pi$
$283$	16772.2	+	16772.2i	0.209419	+	0.209419i	−0.594602	+	0.804020i	$0.702690\pi$
$284$		−	39459.4i		−	0.489231i
$285$	2808.94	−	13433.4i	0.0345822	−	0.165385i
$286$	12755.6			0.155944
$287$	−19075.8	+	19075.8i	−0.231590	+	0.231590i
$288$	−6994.22	−	6994.22i	−0.0843245	−	0.0843245i
$289$		−	2283.52i		−	0.0273406i
$290$	−1109.81	−	232.062i	−0.0131963	−	0.00275936i
$291$	−97282.7			−1.14881
$292$	−103236.	+	103236.i	−1.21078	+	1.21078i
$293$	57532.1	+	57532.1i	0.670154	+	0.670154i	0.957751	−	0.287597i	$-0.0928564\pi$
$293$	57532.1	+	57532.1i	0.670154	+	0.670154i	−0.287597	+	0.957751i	$0.592856\pi$
$294$			5185.83i			0.0599962i
$295$	26266.6	+	40155.5i	0.301828	+	0.461425i
$296$	−26119.1			−0.298109
$297$	−86988.6	+	86988.6i	−0.986165	+	0.986165i
$298$	−6716.22	−	6716.22i	−0.0756297	−	0.0756297i
$299$			169112.i			1.89161i
$300$	−23976.9	−	61247.4i	−0.266410	−	0.680527i
$301$	−3233.23			−0.0356865
$302$	−7098.51	+	7098.51i	−0.0778311	+	0.0778311i
$303$	87873.1	+	87873.1i	0.957129	+	0.957129i
$304$			20712.9i			0.224127i
$305$	81676.8	−	53426.6i	0.878009	−	0.574325i
$306$	3811.74			0.0407081
$307$	−101772.	+	101772.i	−1.07982	+	1.07982i	−0.0833001	+	0.996525i	$0.526546\pi$
$307$	−101772.	+	101772.i	−1.07982	+	1.07982i	−0.996525	+	0.0833001i	$0.973454\pi$
$308$	23184.3	+	23184.3i	0.244395	+	0.244395i
$309$			56558.2i			0.592351i
$310$	2622.38	−	12541.2i	0.0272880	−	0.130502i
$311$	−172013.			−1.77845			−0.889225	−	0.457471i	$-0.848755\pi$
$311$	−172013.			−1.77845			−0.889225	+	0.457471i	$0.848755\pi$
$312$	12123.2	−	12123.2i	0.124540	−	0.124540i
$313$	1006.84	+	1006.84i	0.0102771	+	0.0102771i	0.712227	−	0.701950i	$-0.247687\pi$
$313$	1006.84	+	1006.84i	0.0102771	+	0.0102771i	−0.701950	+	0.712227i	$0.747687\pi$
$314$		−	9659.63i		−	0.0979718i
$315$	11915.2	+	2491.47i	0.120082	+	0.0251093i
$316$	78853.9			0.789676
$317$	86837.9	−	86837.9i	0.864153	−	0.864153i	−0.127664	−	0.991817i	$-0.540748\pi$
$317$	86837.9	−	86837.9i	0.864153	−	0.864153i	0.991817	+	0.127664i	$0.0407479\pi$
$318$	−3369.93	−	3369.93i	−0.0333247	−	0.0333247i
$319$		−	20306.6i		−	0.199552i
$320$	53480.5	+	81759.2i	0.522270	+	0.798430i
$321$	−45100.6			−0.437696
$322$	2386.34	−	2386.34i	0.0230155	−	0.0230155i
$323$	−17154.2	−	17154.2i	−0.164424	−	0.164424i
$324$			34691.3i			0.330468i
$325$	−134510.	+	52657.5i	−1.27347	+	0.498533i
$326$	6819.22			0.0641652
$327$	−107396.	+	107396.i	−1.00437	+	1.00437i
$328$	16250.7	+	16250.7i	0.151051	+	0.151051i
$329$			21712.1i			0.200590i
$330$	−7653.62	+	5006.40i	−0.0702812	+	0.0459724i
$331$	45645.6			0.416623			0.208311	−	0.978063i	$-0.433203\pi$
$331$	45645.6			0.416623			0.208311	+	0.978063i	$0.433203\pi$
$332$	103431.	−	103431.i	0.938368	−	0.938368i
$333$	−61166.2	−	61166.2i	−0.551598	−	0.551598i
$334$			6825.88i			0.0611880i
$335$	−3953.55	+	18907.4i	−0.0352288	+	0.168477i
$336$	21778.0			0.192903
$337$	−18075.0	+	18075.0i	−0.159155	+	0.159155i	−0.782192	−	0.623037i	$-0.785898\pi$
$337$	−18075.0	+	18075.0i	−0.159155	+	0.159155i	0.623037	+	0.782192i	$0.285898\pi$
$338$	−6170.51	−	6170.51i	−0.0540117	−	0.0540117i
$339$			46677.3i			0.406168i
$340$	−113806.	−	23796.9i	−0.984478	−	0.205855i
$341$	229472.			1.97343
$342$	762.050	−	762.050i	0.00651525	−	0.00651525i
$343$	43004.0	+	43004.0i	0.365528	+	0.365528i
$344$			2754.39i			0.0232760i
$345$	−66374.2	−	101471.i	−0.557650	−	0.852517i
$346$	3580.75			0.0299103
$347$	−33288.8	+	33288.8i	−0.276464	+	0.276464i	−0.831696	−	0.555231i	$-0.812630\pi$
$347$	−33288.8	+	33288.8i	−0.276464	+	0.276464i	0.555231	+	0.831696i	$0.312630\pi$
$348$	−9612.64	−	9612.64i	−0.0793751	−	0.0793751i
$349$		−	14607.1i		−	0.119926i	−0.998201	−	0.0599628i	$-0.980902\pi$
$349$		−	14607.1i		−	0.119926i	0.998201	−	0.0599628i	$-0.0190982\pi$
$350$	2641.12	+	1155.02i	0.0215602	+	0.00942877i
$351$	180869.			1.46808
$352$	29664.3	−	29664.3i	0.239413	−	0.239413i
$353$	79407.0	+	79407.0i	0.637249	+	0.637249i	0.949876	−	0.312627i	$-0.101209\pi$
$353$	79407.0	+	79407.0i	0.637249	+	0.637249i	−0.312627	+	0.949876i	$0.601209\pi$
$354$		−	4466.55i		−	0.0356423i
$355$	51997.7	−	34012.8i	0.412598	−	0.269889i
$356$	−129521.			−1.02198
$357$	−18036.3	+	18036.3i	−0.141518	+	0.141518i
$358$	−2793.13	−	2793.13i	−0.0217934	−	0.0217934i
$359$		−	207880.i		−	1.61296i	−0.591263	−	0.806479i	$-0.701371\pi$
$359$		−	207880.i		−	1.61296i	0.591263	−	0.806479i	$-0.298629\pi$
$360$	2122.49	−	10150.5i	0.0163772	−	0.0783221i
$361$	−6859.00			−0.0526316
$362$	−10377.8	+	10377.8i	−0.0791930	+	0.0791930i
$363$	−47200.6	−	47200.6i	−0.358207	−	0.358207i
$364$		−	48205.5i		−	0.363826i
$365$	−225025.	−	47053.0i	−1.68906	−	0.353185i
$366$	−9085.01			−0.0678209
$367$	112184.	−	112184.i	0.832914	−	0.832914i	−0.155001	−	0.987914i	$-0.549538\pi$
$367$	112184.	−	112184.i	0.832914	−	0.832914i	0.987914	+	0.155001i	$0.0495379\pi$
$368$	129400.	+	129400.i	0.955516	+	0.955516i
$369$			76112.4i			0.558988i
$370$	−11213.4	−	17142.7i	−0.0819094	−	0.125220i
$371$	−26903.7			−0.195463
$372$	108626.	−	108626.i	0.784963	−	0.784963i
$373$	−33527.0	−	33527.0i	−0.240978	−	0.240978i	0.576277	−	0.817255i	$-0.304505\pi$
$373$	−33527.0	−	33527.0i	−0.240978	−	0.240978i	−0.817255	+	0.576277i	$0.804505\pi$
$374$			16166.6i			0.115578i
$375$	60041.6	−	84389.0i	0.426962	−	0.600100i
$376$	18496.6			0.130832
$377$	−21111.1	+	21111.1i	−0.148535	+	0.148535i
$378$	−2552.25	−	2552.25i	−0.0178624	−	0.0178624i
$379$		−	66372.9i		−	0.462075i	−0.972945	−	0.231037i	$-0.925788\pi$
$379$		−	66372.9i		−	0.462075i	0.972945	−	0.231037i	$-0.0742120\pi$
$380$	−27509.7	+	17994.7i	−0.190511	+	0.124617i
$381$	55329.4			0.381159
$382$	−13813.3	+	13813.3i	−0.0946606	+	0.0946606i
$383$	−197523.	−	197523.i	−1.34655	−	1.34655i	−0.889383	−	0.457163i	$-0.848866\pi$
$383$	−197523.	−	197523.i	−1.34655	−	1.34655i	−0.457163	−	0.889383i	$-0.651134\pi$
$384$		−	37396.9i		−	0.253614i
$385$	−10567.0	+	50535.3i	−0.0712902	+	0.340937i
$386$	−10024.9			−0.0672833
$387$	−6450.29	+	6450.29i	−0.0430683	+	0.0430683i
$388$	164768.	+	164768.i	1.09448	+	1.09448i
$389$			92818.4i			0.613387i	0.951808	+	0.306694i	$0.0992227\pi$
$389$			92818.4i			0.613387i	−0.951808	+	0.306694i	$0.900777\pi$
$390$	13161.6	+	2752.09i	0.0865322	+	0.0180940i
$391$	−214335.			−1.40197
$392$	17634.7	−	17634.7i	0.114762	−	0.114762i
$393$	−14564.0	−	14564.0i	−0.0942963	−	0.0942963i
$394$		−	1835.51i		−	0.0118240i
$395$	67969.7	+	103910.i	0.435634	+	0.665982i
$396$	92505.3			0.589897
$397$	−182774.	+	182774.i	−1.15967	+	1.15967i	−0.175118	+	0.984547i	$0.556031\pi$
$397$	−182774.	+	182774.i	−1.15967	+	1.15967i	−0.984547	+	0.175118i	$0.943969\pi$
$398$	9696.13	+	9696.13i	0.0612114	+	0.0612114i
$399$			7211.69i			0.0452993i
$400$	−62631.4	+	143215.i	−0.391446	+	0.895096i
$401$	−59399.7			−0.369399			−0.184699	−	0.982795i	$-0.559131\pi$
$401$	−59399.7			−0.369399			−0.184699	+	0.982795i	$0.559131\pi$
$402$	1271.42	−	1271.42i	0.00786753	−	0.00786753i
$403$	−238563.	−	238563.i	−1.46890	−	1.46890i
$404$		−	297662.i		−	1.82373i
$405$	−45714.5	+	29902.8i	−0.278704	+	0.182306i
$406$	595.797			0.00361448
$407$	259422.	−	259422.i	1.56609	−	1.56609i
$408$	15365.1	+	15365.1i	0.0923029	+	0.0923029i
$409$			102623.i			0.613479i	0.951794	+	0.306739i	$0.0992380\pi$
$409$			102623.i			0.613479i	−0.951794	+	0.306739i	$0.900762\pi$
$410$	−3689.06	+	17642.5i	−0.0219457	+	0.104952i
$411$	7880.56			0.0466523
$412$	95792.9	−	95792.9i	0.564337	−	0.564337i
$413$	−17829.3	−	17829.3i	−0.104528	−	0.104528i
$414$		−	9521.50i		−	0.0555526i
$415$	225450.	+	47141.8i	1.30904	+	0.273722i
$416$	−61678.9			−0.356410
$417$	85652.0	−	85652.0i	0.492567	−	0.492567i
$418$	3232.05	+	3232.05i	0.0184980	+	0.0184980i
$419$		−	26028.0i		−	0.148256i	−0.997249	−	0.0741282i	$-0.976383\pi$
$419$		−	26028.0i		−	0.148256i	0.997249	−	0.0741282i	$-0.0236174\pi$
$420$	18920.0	+	28924.3i	0.107256	+	0.163970i
$421$	−115120.			−0.649509			−0.324754	−	0.945798i	$-0.605282\pi$
$421$	−115120.			−0.649509			−0.324754	+	0.945798i	$0.605282\pi$
$422$	984.665	−	984.665i	0.00552922	−	0.00552922i
$423$	43315.6	+	43315.6i	0.242083	+	0.242083i
$424$			22919.3i			0.127488i
$425$	−66738.7	−	170480.i	−0.369487	−	0.943832i
$426$	−5783.77			−0.0318707
$427$	−36264.9	+	36264.9i	−0.198898	+	0.198898i
$428$	76387.1	+	76387.1i	0.416996	+	0.416996i
$429$			240822.i			1.30853i
$430$	−1807.78	+	1182.51i	−0.00977710	+	0.00639541i
$431$	−299940.			−1.61465			−0.807326	−	0.590105i	$-0.799086\pi$
$431$	−299940.			−1.61465			−0.807326	+	0.590105i	$0.799086\pi$
$432$	138396.	−	138396.i	0.741577	−	0.741577i
$433$	39418.3	+	39418.3i	0.210244	+	0.210244i	0.804371	−	0.594127i	$-0.202503\pi$
$433$	39418.3	+	39418.3i	0.210244	+	0.210244i	−0.594127	+	0.804371i	$0.702503\pi$
$434$			6732.71i			0.0357446i
$435$	4381.27	−	20952.9i	0.0231537	−	0.110730i
$436$	363794.			1.91374
$437$	−42850.2	+	42850.2i	−0.224383	+	0.224383i
$438$	15131.8	+	15131.8i	0.0788756	+	0.0788756i
$439$		−	102240.i		−	0.530507i	−0.964179	−	0.265254i	$-0.914544\pi$
$439$		−	102240.i		−	0.530507i	0.964179	−	0.265254i	$-0.0854557\pi$
$440$	43051.1	+	9002.02i	0.222371	+	0.0464981i
$441$	82594.7			0.424693
$442$	16807.0	−	16807.0i	0.0860293	−	0.0860293i
$443$	−88705.8	−	88705.8i	−0.452007	−	0.452007i	0.444013	−	0.896020i	$-0.353554\pi$
$443$	−88705.8	−	88705.8i	−0.452007	−	0.452007i	−0.896020	+	0.444013i	$0.853554\pi$
$444$		−	245607.i		−	1.24588i
$445$	−111643.	−	170677.i	−0.563784	−	0.861895i
$446$	2522.14			0.0126794
$447$	126800.	−	126800.i	0.634608	−	0.634608i
$448$	−36301.5	−	36301.5i	−0.180871	−	0.180871i
$449$			211182.i			1.04752i	0.851865	+	0.523762i	$0.175472\pi$
$449$			211182.i			1.04752i	−0.851865	+	0.523762i	$0.824528\pi$
$450$	7573.31	−	2964.77i	0.0373991	−	0.0146408i
$451$	−322812.			−1.58707
$452$	79057.4	−	79057.4i	0.386960	−	0.386960i
$453$	−134018.	−	134018.i	−0.653080	−	0.653080i
$454$		−	6429.65i		−	0.0311943i
$455$	63522.9	−	41551.7i	0.306837	−	0.200709i
$456$	6143.65			0.0295458
$457$	151599.	−	151599.i	0.725879	−	0.725879i	−0.243917	−	0.969796i	$-0.578432\pi$
$457$	151599.	−	151599.i	0.725879	−	0.725879i	0.969796	+	0.243917i	$0.0784324\pi$
$458$	−5023.01	−	5023.01i	−0.0239460	−	0.0239460i
$459$			229236.i			1.08807i
$460$	−59443.1	+	284280.i	−0.280922	+	1.34348i
$461$	391022.			1.83992			0.919960	−	0.392011i	$-0.128221\pi$
$461$	391022.			1.83992			0.919960	+	0.392011i	$0.128221\pi$
$462$	3398.25	−	3398.25i	0.0159210	−	0.0159210i
$463$	−68273.2	−	68273.2i	−0.318485	−	0.318485i	0.529700	−	0.848185i	$-0.322304\pi$
$463$	−68273.2	−	68273.2i	−0.318485	−	0.318485i	−0.848185	+	0.529700i	$0.822304\pi$
$464$			32307.2i			0.150059i
$465$	236775.	+	49509.9i	1.09504	+	0.228974i
$466$	−8540.26			−0.0393278
$467$	−276950.	+	276950.i	−1.26990	+	1.26990i	−0.323754	+	0.946141i	$0.604945\pi$
$467$	−276950.	+	276950.i	−1.26990	+	1.26990i	−0.946141	+	0.323754i	$0.895055\pi$
$468$	−96170.0	−	96170.0i	−0.439084	−	0.439084i
$469$		−	10150.4i		−	0.0461462i
$470$	7940.92	+	12139.8i	0.0359480	+	0.0549562i
$471$	182371.			0.822082
$472$	−15188.8	+	15188.8i	−0.0681771	+	0.0681771i
$473$	−27357.4	−	27357.4i	−0.122279	−	0.122279i
$474$		−	11558.0i		−	0.0514431i
$475$	−47425.1	−	20740.1i	−0.210195	−	0.0919229i
$476$	61096.2			0.269650
$477$	−53672.8	+	53672.8i	−0.235894	+	0.235894i
$478$	11524.0	+	11524.0i	0.0504367	+	0.0504367i
$479$		−	218272.i		−	0.951321i	−0.879629	−	0.475660i	$-0.842209\pi$
$479$		−	218272.i		−	0.951321i	0.879629	−	0.475660i	$-0.157791\pi$
$480$	37008.6	−	24208.1i	0.160628	−	0.105070i
$481$	−539398.			−2.33141
$482$	−13231.1	+	13231.1i	−0.0569509	+	0.0569509i
$483$	45053.5	+	45053.5i	0.193123	+	0.193123i
$484$			159888.i			0.682534i
$485$	−75098.3	+	359149.i	−0.319262	+	1.52683i
$486$	−17170.0			−0.0726939
$487$	−171921.	+	171921.i	−0.724888	+	0.724888i	−0.969597	−	0.244709i	$-0.921308\pi$
$487$	−171921.	+	171921.i	−0.724888	+	0.724888i	0.244709	+	0.969597i	$0.421308\pi$
$488$	30894.1	+	30894.1i	0.129729	+	0.129729i
$489$			128745.i			0.538410i
$490$	19145.1	+	4003.25i	0.0797379	+	0.0166733i
$491$	129722.			0.538084			0.269042	−	0.963128i	$-0.413293\pi$
$491$	129722.			0.538084			0.269042	+	0.963128i	$0.413293\pi$
$492$	−152811.	+	152811.i	−0.631285	+	0.631285i
$493$	−26756.4	−	26756.4i	−0.110086	−	0.110086i
$494$		−	6720.18i		−	0.0275377i
$495$	79736.8	+	121899.i	0.325423	+	0.497496i
$496$	−365082.			−1.48398
$497$	−23087.2	+	23087.2i	−0.0934672	+	0.0934672i
$498$	−15160.4	−	15160.4i	−0.0611295	−	0.0611295i
$499$		−	82384.6i		−	0.330861i	−0.986221	−	0.165430i	$-0.947099\pi$
$499$		−	82384.6i		−	0.330861i	0.986221	−	0.165430i	$-0.0529013\pi$
$500$	−244623.	+	41237.4i	−0.978490	+	0.164950i
$501$	−128871.			−0.513428
$502$	5455.20	−	5455.20i	0.0216473	−	0.0216473i
$503$	182880.	+	182880.i	0.722820	+	0.722820i	0.969179	−	0.246359i	$-0.0792342\pi$
$503$	182880.	+	182880.i	0.722820	+	0.722820i	−0.246359	+	0.969179i	$0.579234\pi$
$504$			5449.29i			0.0214525i
$505$	392244.	−	256576.i	1.53806	−	1.00608i
$506$	40383.1			0.157724
$507$	116498.	−	116498.i	0.453212	−	0.453212i
$508$	−93711.7	−	93711.7i	−0.363133	−	0.363133i
$509$			107517.i			0.414994i	0.978236	+	0.207497i	$0.0665317\pi$
$509$			107517.i			0.414994i	−0.978236	+	0.207497i	$0.933468\pi$
$510$	−3488.03	+	16681.1i	−0.0134103	+	0.0641333i
$511$	120804.			0.462637
$512$	−78861.6	+	78861.6i	−0.300833	+	0.300833i
$513$	45829.3	+	45829.3i	0.174144	+	0.174144i
$514$		−	23953.8i		−	0.0906667i
$515$	208802.	+	43660.6i	0.787263	+	0.164617i
$516$	−25900.6			−0.0972769
$517$	−183713.	+	183713.i	−0.687319	+	0.687319i
$518$	7611.44	+	7611.44i	0.0283666	+	0.0283666i
$519$			67603.6i			0.250978i
$520$	−35397.9	−	54115.2i	−0.130910	−	0.200130i
$521$	79248.0			0.291953			0.145977	−	0.989288i	$-0.453368\pi$
$521$	79248.0			0.291953			0.145977	+	0.989288i	$0.453368\pi$
$522$	1188.61	−	1188.61i	0.00436214	−	0.00436214i
$523$	−261877.	−	261877.i	−0.957402	−	0.957402i	0.0417269	−	0.999129i	$-0.486714\pi$
$523$	−261877.	−	261877.i	−0.957402	−	0.957402i	−0.999129	+	0.0417269i	$0.986714\pi$
$524$			49334.1i			0.179674i
$525$	−21806.6	+	49863.8i	−0.0791168	+	0.180912i
$526$	4487.22			0.0162183
$527$	302357.	−	302357.i	1.08868	−	1.08868i
$528$	184270.	+	184270.i	0.660979	+	0.660979i
$529$			255554.i			0.913212i
$530$	−15042.6	+	9839.66i	−0.0535513	+	0.0350290i
$531$	−71138.7			−0.252300
$532$	12214.5	−	12214.5i	0.0431570	−	0.0431570i
$533$	335601.	+	335601.i	1.18132	+	1.18132i
$534$			18984.6i			0.0665762i
$535$	−34815.8	+	166503.i	−0.121638	+	0.581719i
$536$	−8647.10			−0.0300982
$537$	52733.5	−	52733.5i	0.182868	−	0.182868i
$538$	8544.10	+	8544.10i	0.0295190	+	0.0295190i
$539$			350305.i			1.20578i
$540$	304044.	+	63575.8i	1.04267	+	0.218024i
$541$	−99539.3			−0.340095			−0.170047	−	0.985436i	$-0.554392\pi$
$541$	−99539.3			−0.340095			−0.170047	+	0.985436i	$0.554392\pi$
$542$	−33783.5	+	33783.5i	−0.115002	+	0.115002i
$543$	−195930.	−	195930.i	−0.664508	−	0.664508i
$544$		−	78172.5i		−	0.264153i
$545$	313580.	+	479391.i	1.05574	+	1.61397i
$546$	−7065.74			−0.0237013
$547$	195631.	−	195631.i	0.653826	−	0.653826i	−0.300086	−	0.953912i	$-0.597015\pi$
$547$	195631.	−	195631.i	0.653826	−	0.653826i	0.953912	+	0.300086i	$0.0970153\pi$
$548$	−13347.3	−	13347.3i	−0.0444461	−	0.0444461i
$549$			144697.i			0.480081i
$550$	12574.3	+	32120.4i	0.0415681	+	0.106183i
$551$	−10698.4			−0.0352383
$552$	38381.1	−	38381.1i	0.125962	−	0.125962i
$553$	−46136.5	−	46136.5i	−0.150867	−	0.150867i
$554$		−	2799.81i		−	0.00912239i
$555$	323649.	−	211706.i	1.05072	−	0.687302i
$556$	−290138.			−0.938545
$557$	28641.4	−	28641.4i	0.0923174	−	0.0923174i	−0.659440	−	0.751757i	$-0.729207\pi$
$557$	28641.4	−	28641.4i	0.0923174	−	0.0923174i	0.751757	+	0.659440i	$0.229207\pi$
$558$	13431.8	+	13431.8i	0.0431384	+	0.0431384i
$559$			56882.3i			0.182034i
$560$	16811.7	−	80400.1i	0.0536088	−	0.256378i
$561$	−305221.			−0.969814
$562$	−34886.5	+	34886.5i	−0.110455	+	0.110455i
$563$	−188251.	−	188251.i	−0.593911	−	0.593911i	0.344774	−	0.938686i	$-0.387955\pi$
$563$	−188251.	−	188251.i	−0.593911	−	0.593911i	−0.938686	+	0.344774i	$0.887955\pi$
$564$			173930.i			0.546785i
$565$	172323.	+	36032.9i	0.539817	+	0.112876i
$566$	−8327.54			−0.0259946
$567$	20297.4	−	20297.4i	0.0631357	−	0.0631357i
$568$	19668.0	+	19668.0i	0.0609627	+	0.0609627i
$569$		−	449285.i		−	1.38771i	−0.720117	−	0.693853i	$-0.755912\pi$
$569$		−	449285.i		−	1.38771i	0.720117	−	0.693853i	$-0.244088\pi$
$570$	2637.58	+	4032.25i	0.00811813	+	0.0124107i
$571$	183720.			0.563487			0.281743	−	0.959490i	$-0.409087\pi$
$571$	183720.			0.563487			0.281743	+	0.959490i	$0.409087\pi$
$572$	407882.	−	407882.i	1.24664	−	1.24664i
$573$	−260791.	−	260791.i	−0.794297	−	0.794297i
$574$		−	9471.33i		−	0.0287466i
$575$	−425848.	+	166709.i	−1.28801	+	0.504225i
$576$	−144843.			−0.436568
$577$	227559.	−	227559.i	0.683508	−	0.683508i	−0.277281	−	0.960789i	$-0.589433\pi$
$577$	227559.	−	227559.i	0.683508	−	0.683508i	0.960789	+	0.277281i	$0.0894334\pi$
$578$	566.894	+	566.894i	0.00169686	+	0.00169686i
$579$		−	189268.i		−	0.564574i
$580$	−42908.5	+	28067.4i	−0.127552	+	0.0834346i
$581$	−121032.			−0.358549
$582$	24150.9	−	24150.9i	0.0712997	−	0.0712997i
$583$	−227640.	−	227640.i	−0.669749	−	0.669749i
$584$		−	102913.i		−	0.301749i
$585$	43832.5	−	209624.i	0.128081	−	0.612532i
$586$	−28565.2			−0.0831846
$587$	−24060.1	+	24060.1i	−0.0698266	+	0.0698266i	−0.741158	−	0.671331i	$-0.765723\pi$
$587$	−24060.1	+	24060.1i	−0.0698266	+	0.0698266i	0.671331	+	0.741158i	$0.265723\pi$
$588$	165826.	+	165826.i	0.479620	+	0.479620i
$589$		−	120895.i		−	0.348481i
$590$	−16489.6	−	3448.00i	−0.0473704	−	0.00990519i
$591$	34653.9			0.0992150
$592$	−412731.	+	412731.i	−1.17767	+	1.17767i
$593$	299276.	+	299276.i	0.851065	+	0.851065i	0.990264	−	0.139199i	$-0.0444528\pi$
$593$	299276.	+	299276.i	0.851065	+	0.851065i	−0.139199	+	0.990264i	$0.544453\pi$
$594$		−	43190.7i		−	0.122410i
$595$	52663.1	+	80509.6i	0.148755	+	0.227412i
$596$	−429525.			−1.20919
$597$	−183061.	+	183061.i	−0.513625	+	0.513625i
$598$	−41982.9	−	41982.9i	−0.117401	−	0.117401i
$599$		−	57413.4i		−	0.160014i	−0.996794	−	0.0800072i	$-0.974506\pi$
$599$		−	57413.4i		−	0.160014i	0.996794	−	0.0800072i	$-0.0254943\pi$
$600$	42479.0	+	18577.0i	0.117997	+	0.0516029i
$601$	179956.			0.498215			0.249108	−	0.968476i	$-0.419863\pi$
$601$	179956.			0.498215			0.249108	+	0.968476i	$0.419863\pi$
$602$	802.666	−	802.666i	0.00221484	−	0.00221484i
$603$	−20249.9	−	20249.9i	−0.0556915	−	0.0556915i
$604$			453973.i			1.24439i
$605$	−210692.	+	137818.i	−0.575623	+	0.376527i
$606$	−43629.9			−0.118806
$607$	159650.	−	159650.i	0.433304	−	0.433304i	−0.456447	−	0.889751i	$-0.650878\pi$
$607$	159650.	−	159650.i	0.433304	−	0.433304i	0.889751	+	0.456447i	$0.150878\pi$
$608$	−15628.4	−	15628.4i	−0.0422773	−	0.0422773i
$609$			11248.5i			0.0303291i
$610$	−7013.26	+	33540.1i	−0.0188478	+	0.0901372i
$611$	381981.			1.02320
$612$	121887.	−	121887.i	0.325427	−	0.325427i
$613$	−195334.	−	195334.i	−0.519824	−	0.519824i	0.397694	−	0.917518i	$-0.369811\pi$
$613$	−195334.	−	195334.i	−0.519824	−	0.519824i	−0.917518	+	0.397694i	$0.869811\pi$
$614$		−	50531.0i		−	0.134036i
$615$	−333086.	−	69648.6i	−0.880656	−	0.184146i
$616$	−23111.8			−0.0609078
$617$	−128140.	+	128140.i	−0.336601	+	0.336601i	−0.855087	−	0.518485i	$-0.826496\pi$
$617$	−128140.	+	128140.i	−0.336601	+	0.336601i	0.518485	+	0.855087i	$0.326496\pi$
$618$	−14040.9	−	14040.9i	−0.0367635	−	0.0367635i
$619$			323639.i			0.844656i	0.906443	+	0.422328i	$0.138787\pi$
$619$			323639.i			0.844656i	−0.906443	+	0.422328i	$0.861213\pi$
$620$	−317172.	−	484882.i	−0.825108	−	1.26140i
$621$	572617.			1.48485
$622$	42703.2	−	42703.2i	0.110377	−	0.110377i
$623$	75781.3	+	75781.3i	0.195248	+	0.195248i
$624$		−	383141.i		−	0.983986i
$625$	−265198.	−	286806.i	−0.678907	−	0.734224i
$626$	−499.904			−0.00127567
$627$	−61020.3	+	61020.3i	−0.155217	+	0.155217i
$628$	−308883.	−	308883.i	−0.783204	−	0.783204i
$629$		−	683638.i		−	1.72792i
$630$	−3576.52	+	2339.48i	−0.00901114	+	0.00589438i
$631$	−258991.			−0.650469			−0.325235	−	0.945633i	$-0.605443\pi$
$631$	−258991.			−0.650469			−0.325235	+	0.945633i	$0.605443\pi$
$632$	−39303.7	+	39303.7i	−0.0984010	+	0.0984010i
$633$	18590.2	+	18590.2i	0.0463957	+	0.0463957i
$634$			43115.9i			0.107265i
$635$	42712.1	−	204265.i	0.105926	−	0.506579i
$636$	−215518.			−0.532807
$637$	364183.	−	364183.i	0.897513	−	0.897513i
$638$	5041.22	+	5041.22i	0.0123849	+	0.0123849i
$639$			92118.0i			0.225602i
$640$	−138062.	−	28868.9i	−0.337065	−	0.0704806i
$641$	329545.			0.802044			0.401022	−	0.916068i	$-0.368655\pi$
$641$	329545.			0.802044			0.401022	+	0.916068i	$0.368655\pi$
$642$	11196.5	−	11196.5i	0.0271650	−	0.0271650i
$643$	−138718.	−	138718.i	−0.335513	−	0.335513i	0.519162	−	0.854676i	$-0.326244\pi$
$643$	−138718.	−	138718.i	−0.335513	−	0.335513i	−0.854676	+	0.519162i	$0.826244\pi$
$644$		−	152615.i		−	0.367980i
$645$	−22325.5	−	34130.5i	−0.0536639	−	0.0820396i
$646$	8517.23			0.0204095
$647$	28159.5	−	28159.5i	0.0672691	−	0.0672691i	−0.672672	−	0.739941i	$-0.734853\pi$
$647$	28159.5	−	28159.5i	0.0672691	−	0.0672691i	0.739941	+	0.672672i	$0.234853\pi$
$648$	−17291.4	−	17291.4i	−0.0411794	−	0.0411794i
$649$		−	301718.i		−	0.716327i
$650$	20320.4	−	46465.3i	0.0480955	−	0.109977i
$651$	−127112.			−0.299933
$652$	218056.	−	218056.i	0.512947	−	0.512947i
$653$	320164.	+	320164.i	0.750838	+	0.750838i	0.974636	−	0.223797i	$-0.0718453\pi$
$653$	320164.	+	320164.i	0.750838	+	0.750838i	−0.223797	+	0.974636i	$0.571845\pi$
$654$		−	53323.2i		−	0.124670i
$655$	−65010.1	+	42524.5i	−0.151530	+	0.0991190i
$656$	513584.			1.19345
$657$	241004.	−	241004.i	0.558334	−	0.558334i
$658$	−5390.14	−	5390.14i	−0.0124494	−	0.0124494i
$659$		−	57520.3i		−	0.132449i	−0.997805	−	0.0662247i	$-0.978905\pi$
$659$		−	57520.3i		−	0.132449i	0.997805	−	0.0662247i	$-0.0210954\pi$
$660$	−84649.4	+	404825.i	−0.194328	+	0.929351i
$661$	279342.			0.639341			0.319671	−	0.947529i	$-0.396428\pi$
$661$	279342.			0.639341			0.319671	+	0.947529i	$0.396428\pi$
$662$	−11331.7	+	11331.7i	−0.0258572	+	0.0258572i
$663$	317312.	+	317312.i	0.721872	+	0.721872i
$664$			103107.i			0.233859i
$665$	26624.1	+	5567.13i	0.0602050	+	0.0125889i
$666$	30369.6			0.0684685
$667$	−66835.9	+	66835.9i	−0.150230	+	0.150230i
$668$	218269.	+	218269.i	0.489147	+	0.489147i
$669$			47617.3i			0.106393i
$670$	−3712.36	−	5675.33i	−0.00826990	−	0.0126428i
$671$	−613697.			−1.36304
$672$	−16432.0	+	16432.0i	−0.0363875	+	0.0363875i
$673$	138656.	+	138656.i	0.306131	+	0.306131i	0.843407	−	0.537276i	$-0.180547\pi$
$673$	138656.	+	138656.i	0.306131	+	0.306131i	−0.537276	+	0.843407i	$0.680547\pi$
$674$		−	8974.43i		−	0.0197555i
$675$	178299.	+	455455.i	0.391329	+	0.999626i
$676$	−394625.			−0.863557
$677$	164080.	−	164080.i	0.357996	−	0.357996i	−0.505078	−	0.863074i	$-0.668536\pi$
$677$	164080.	−	164080.i	0.357996	−	0.357996i	0.863074	+	0.505078i	$0.168536\pi$
$678$	−11587.9	−	11587.9i	−0.0252083	−	0.0252083i
$679$		−	192808.i		−	0.418201i
$680$	68586.2	−	44863.7i	0.148327	−	0.0970236i
$681$	121390.			0.261751
$682$	−56967.5	+	56967.5i	−0.122478	+	0.122478i
$683$	461783.	+	461783.i	0.989912	+	0.989912i	0.999950	−	0.0100381i	$-0.00319527\pi$
$683$	461783.	+	461783.i	0.989912	+	0.989912i	−0.0100381	+	0.999950i	$0.503195\pi$
$684$		−	48735.7i		−	0.104168i
$685$	6083.47	−	29093.5i	0.0129649	−	0.0620032i
$686$	−21351.9			−0.0453721
$687$	94833.1	−	94833.1i	0.200931	−	0.200931i
$688$	43524.7	+	43524.7i	0.0919514	+	0.0919514i
$689$			473317.i			0.997042i
$690$	41668.4	+	8712.89i	0.0875202	+	0.0183005i
$691$	850196.			1.78059			0.890293	−	0.455389i	$-0.150500\pi$
$691$	850196.			1.78059			0.890293	+	0.455389i	$0.150500\pi$
$692$	114500.	−	114500.i	0.239108	−	0.239108i
$693$	−54123.8	−	54123.8i	−0.112699	−	0.112699i
$694$		−	16528.2i		−	0.0343168i
$695$	−250090.	−	382330.i	−0.517759	−	0.791533i
$696$	9582.60			0.0197818
$697$	−425344.	+	425344.i	−0.875537	+	0.875537i
$698$	3626.28	+	3626.28i	0.00744304	+	0.00744304i
$699$		−	161238.i		−	0.329999i
$700$	121388.	−	47520.6i	0.247731	−	0.0969807i
$701$	48696.2			0.0990967			0.0495483	−	0.998772i	$-0.484222\pi$
$701$	48696.2			0.0990967			0.0495483	+	0.998772i	$0.484222\pi$
$702$	−44901.7	+	44901.7i	−0.0911148	+	0.0911148i
$703$	−136674.	−	136674.i	−0.276551	−	0.276551i
$704$		−	614316.i		−	1.23950i
$705$	−229197.	+	149922.i	−0.461137	+	0.301640i
$706$	−39426.4			−0.0791001
$707$	−174159.	+	174159.i	−0.348422	+	0.348422i
$708$	−142826.	−	142826.i	−0.284931	−	0.284931i
$709$			782089.i			1.55584i	0.628366	+	0.777918i	$0.283724\pi$
$709$			782089.i			1.55584i	−0.628366	+	0.777918i	$0.716276\pi$
$710$	−4464.83	+	21352.5i	−0.00885704	+	0.0423577i
$711$	−184085.			−0.364148
$712$	64558.2	−	64558.2i	0.127348	−	0.127348i
$713$	−755269.	−	755269.i	−1.48567	−	1.48567i
$714$		−	8955.19i		−	0.0175662i
$715$	889069.	+	185905.i	1.73909	+	0.363646i
$716$	−178630.			−0.348440
$717$	−217570.	+	217570.i	−0.423214	+	0.423214i
$718$	51607.1	+	51607.1i	0.100106	+	0.100106i
$719$		−	29385.1i		−	0.0568419i	−0.999596	−	0.0284210i	$-0.990952\pi$
$719$		−	29385.1i		−	0.0568419i	0.999596	−	0.0284210i	$-0.00904789\pi$
$720$	−126859.	−	193937.i	−0.244712	−	0.374108i
$721$	−112095.			−0.215632
$722$	1702.78	−	1702.78i	0.00326651	−	0.00326651i
$723$	−249799.	−	249799.i	−0.477875	−	0.477875i
$724$			663693.i			1.26616i
$725$	−73971.7	−	32349.5i	−0.140731	−	0.0615449i
$726$	23435.6			0.0444634
$727$	−534010.	+	534010.i	−1.01037	+	1.01037i	−0.0104254	+	0.999946i	$0.503319\pi$
$727$	−534010.	+	534010.i	−1.01037	+	1.01037i	−0.999946	+	0.0104254i	$0.996681\pi$
$728$	24027.4	+	24027.4i	0.0453362	+	0.0453362i
$729$		−	501153.i		−	0.943008i
$730$	67544.8	−	44182.5i	0.126750	−	0.0829096i
$731$	−72093.2			−0.134915
$732$	−290509.	+	290509.i	−0.542172	+	0.542172i
$733$	66096.1	+	66096.1i	0.123018	+	0.123018i	0.765935	−	0.642918i	$-0.222276\pi$
$733$	66096.1	+	66096.1i	0.123018	+	0.123018i	−0.642918	+	0.765935i	$0.722276\pi$
$734$			55700.6i			0.103387i
$735$	−75580.4	+	361454.i	−0.139905	+	0.669080i
$736$	−195270.			−0.360479
$737$	85885.3	−	85885.3i	0.158119	−	0.158119i
$738$	−18895.3	−	18895.3i	−0.0346929	−	0.0346929i
$739$			34601.2i			0.0633581i	0.999498	+	0.0316791i	$0.0100854\pi$
$739$			34601.2i			0.0633581i	−0.999498	+	0.0316791i	$0.989915\pi$
$740$	−906734.	−	189599.i	−1.65583	−	0.346236i
$741$	126875.			0.231069
$742$	6678.97	−	6678.97i	0.0121311	−	0.0121311i
$743$	543119.	+	543119.i	0.983823	+	0.983823i	0.999871	−	0.0160481i	$-0.00510849\pi$
$743$	543119.	+	543119.i	0.983823	+	0.983823i	−0.0160481	+	0.999871i	$0.505108\pi$
$744$			108287.i			0.195627i
$745$	−370237.	−	566007.i	−0.667064	−	1.01979i
$746$	16646.5			0.0299120
$747$	−241459.	+	241459.i	−0.432715	+	0.432715i
$748$	516954.	+	516954.i	0.923950	+	0.923950i
$749$		−	89386.4i		−	0.159334i
$750$	6044.38	+	35855.6i	0.0107456	+	0.0637433i
$751$	825649.			1.46391			0.731957	−	0.681351i	$-0.238607\pi$
$751$	825649.			1.46391			0.731957	+	0.681351i	$0.238607\pi$
$752$	292281.	−	292281.i	0.516851	−	0.516851i
$753$	102993.	+	102993.i	0.181642	+	0.181642i
$754$		−	10481.9i		−	0.0184372i
$755$	−598224.	+	391311.i	−1.04947	+	0.686481i
$756$	−163225.			−0.285590
$757$	417342.	−	417342.i	0.728284	−	0.728284i	−0.241994	−	0.970278i	$-0.577801\pi$
$757$	417342.	−	417342.i	0.728284	−	0.728284i	0.970278	+	0.241994i	$0.0778014\pi$
$758$	16477.4	+	16477.4i	0.0286781	+	0.0286781i
$759$			762424.i			1.32347i
$760$	4742.64	−	22681.1i	0.00821095	−	0.0392679i
$761$	211728.			0.365602			0.182801	−	0.983150i	$-0.441484\pi$
$761$	211728.			0.365602			0.182801	+	0.983150i	$0.441484\pi$
$762$	−13735.8	+	13735.8i	−0.0236562	+	0.0236562i
$763$	−212852.	−	212852.i	−0.365619	−	0.365619i
$764$			883404.i			1.51347i
$765$	265679.	+	55553.8i	0.453978	+	0.0949272i
$766$	98072.3			0.167143
$767$	−313670.	+	313670.i	−0.533191	+	0.533191i
$768$	−283775.	−	283775.i	−0.481119	−	0.481119i
$769$			33206.1i			0.0561519i	0.999606	+	0.0280760i	$0.00893803\pi$
$769$			33206.1i			0.0561519i	−0.999606	+	0.0280760i	$0.991062\pi$
$770$	−9922.34	−	15169.0i	−0.0167353	−	0.0255843i
$771$	452241.			0.760784
$772$	−320564.	+	320564.i	−0.537874	+	0.537874i
$773$	−501896.	−	501896.i	−0.839953	−	0.839953i	0.148899	−	0.988852i	$-0.452427\pi$
$773$	−501896.	−	501896.i	−0.839953	−	0.839953i	−0.988852	+	0.148899i	$0.952427\pi$
$774$		−	3202.63i		−	0.00534595i
$775$	365561.	−	835907.i	0.608635	−	1.39173i
$776$	−164253.			−0.272766
$777$	−143702.	+	143702.i	−0.238024	+	0.238024i
$778$	−23042.6	−	23042.6i	−0.0380691	−	0.0380691i
$779$			170071.i			0.280256i
$780$	508866.	−	332860.i	0.836400	−	0.547107i
$781$	−390696.			−0.640527
$782$	53209.6	−	53209.6i	0.0870115	−	0.0870115i
$783$	71482.5	+	71482.5i	0.116594	+	0.116594i
$784$		−	557324.i		−	0.906726i
$785$	140783.	−	673279.i	0.228461	−	1.09259i
$786$	7231.16			0.0117048
$787$	−481658.	+	481658.i	−0.777659	+	0.777659i	−0.979432	−	0.201773i	$-0.935330\pi$
$787$	−481658.	+	481658.i	−0.777659	+	0.777659i	0.201773	+	0.979432i	$0.435330\pi$
$788$	−58693.5	−	58693.5i	−0.0945229	−	0.0945229i
$789$			84717.7i			0.136088i
$790$	−42670.0	−	8922.33i	−0.0683704	−	0.0142963i
$791$	−92511.2			−0.147857
$792$	−46108.1	+	46108.1i	−0.0735067	+	0.0735067i
$793$	638009.	+	638009.i	1.01457	+	1.01457i
$794$		−	90748.9i		−	0.143946i
$795$	−185770.	−	284000.i	−0.293929	−	0.449349i
$796$	620100.			0.978669
$797$	−426608.	+	426608.i	−0.671603	+	0.671603i	−0.958085	−	0.286483i	$-0.907514\pi$
$797$	−426608.	+	426608.i	−0.671603	+	0.671603i	0.286483	+	0.958085i	$0.407514\pi$
$798$	−1790.34	−	1790.34i	−0.00281144	−	0.00281144i
$799$			484127.i			0.758343i
$800$	−60802.5	−	155316.i	−0.0950039	−	0.242681i
$801$	302367.			0.471270
$802$	14746.3	−	14746.3i	0.0229263	−	0.0229263i
$803$	1.02216e6	+	1.02216e6i	1.58522	+	1.58522i
$804$		−	81311.9i		−	0.125789i
$805$	201108.	−	131549.i	0.310340	−	0.203000i
$806$	118449.			0.182331
$807$	−161311.	+	161311.i	−0.247694	+	0.247694i
$808$	148366.	+	148366.i	0.227254	+	0.227254i
$809$		−	41317.1i		−	0.0631296i	−0.999502	−	0.0315648i	$-0.989951\pi$
$809$		−	41317.1i		−	0.0631296i	0.999502	−	0.0315648i	$-0.0100491\pi$
$810$	3925.32	−	18772.4i	0.00598280	−	0.0286120i
$811$	−6536.31			−0.00993782			−0.00496891	−	0.999988i	$-0.501582\pi$
$811$	−6536.31			−0.00993782			−0.00496891	+	0.999988i	$0.501582\pi$
$812$	19051.6	−	19051.6i	0.0288948	−	0.0288948i
$813$	−637823.	−	637823.i	−0.964982	−	0.964982i
$814$			128805.i			0.194395i
$815$	475301.	+	99385.9i	0.715573	+	0.149627i
$816$	485596.			0.729281
$817$	−14413.0	+	14413.0i	−0.0215929	+	0.0215929i
$818$	−25476.7	−	25476.7i	−0.0380748	−	0.0380748i
$819$			112536.i			0.167773i
$820$	446185.	+	682113.i	0.663571	+	1.01445i
$821$	610375.			0.905546			0.452773	−	0.891626i	$-0.350435\pi$
$821$	610375.			0.905546			0.452773	+	0.891626i	$0.350435\pi$
$822$	−1956.39	+	1956.39i	−0.00289542	+	0.00289542i
$823$	736149.	+	736149.i	1.08684	+	1.08684i	0.995852	+	0.0909885i	$0.0290026\pi$
$823$	736149.	+	736149.i	1.08684	+	1.08684i	0.0909885	+	0.995852i	$0.470997\pi$
$824$			95493.5i			0.140643i
$825$	−606425.	+	237400.i	−0.890982	+	0.348798i
$826$	8852.41			0.0129748
$827$	−456101.	+	456101.i	−0.666884	+	0.666884i	−0.956993	−	0.290109i	$-0.906308\pi$
$827$	−456101.	+	456101.i	−0.666884	+	0.666884i	0.290109	+	0.956993i	$0.406308\pi$
$828$	−304466.	−	304466.i	−0.444097	−	0.444097i
$829$		−	1.20651e6i		−	1.75558i	−0.479045	−	0.877790i	$-0.659017\pi$
$829$		−	1.20651e6i		−	1.75558i	0.479045	−	0.877790i	$-0.340983\pi$
$830$	−67672.3	+	44265.9i	−0.0982323	+	0.0642559i
$831$	52859.7			0.0765460
$832$	−638653.	+	638653.i	−0.922610	+	0.922610i
$833$	461569.	+	461569.i	0.665192	+	0.665192i
$834$			42527.1i			0.0611411i
$835$	−99483.1	+	475766.i	−0.142684	+	0.682371i
$836$	206701.			0.295753
$837$	−807778.	+	807778.i	−1.15303	+	1.15303i
$838$	6461.59	+	6461.59i	0.00920135	+	0.00920135i
$839$		−	994094.i		−	1.41222i	−0.708100	−	0.706112i	$-0.750447\pi$
$839$		−	994094.i		−	1.41222i	0.708100	−	0.706112i	$-0.249553\pi$
$840$	−23847.4	−	4986.51i	−0.0337973	−	0.00706705i
$841$	690594.			0.976407
$842$	28579.0	−	28579.0i	0.0403109	−	0.0403109i
$843$	−658648.	−	658648.i	−0.926827	−	0.926827i
$844$		−	62972.7i		−	0.0884030i
$845$	−340155.	−	520018.i	−0.476391	−	0.728291i
$846$	−21506.6			−0.0300491
$847$	93548.5	−	93548.5i	0.130398	−	0.130398i
$848$	362168.	+	362168.i	0.503638	+	0.503638i
$849$		−	157222.i		−	0.218121i
$850$	58890.6	+	25754.2i	0.0815095	+	0.0356460i
$851$	−1.70769e6			−2.35803
$852$	−184946.	+	184946.i	−0.254780	+	0.254780i
$853$	−548127.	−	548127.i	−0.753326	−	0.753326i	0.221772	−	0.975098i	$-0.428816\pi$
$853$	−548127.	−	548127.i	−0.753326	−	0.753326i	−0.975098	+	0.221772i	$0.928816\pi$
$854$		−	18005.9i		−	0.0246887i
$855$	64221.5	−	42008.7i	0.0878513	−	0.0574655i
$856$	−76148.3			−0.103923
$857$	242614.	−	242614.i	0.330334	−	0.330334i	−0.522379	−	0.852713i	$-0.674955\pi$
$857$	242614.	−	242614.i	0.330334	−	0.330334i	0.852713	+	0.522379i	$0.174955\pi$
$858$	−59785.4	−	59785.4i	−0.0812120	−	0.0812120i
$859$		−	1.12681e6i		−	1.52708i	−0.645758	−	0.763542i	$-0.723459\pi$
$859$		−	1.12681e6i		−	1.52708i	0.645758	−	0.763542i	$-0.276541\pi$
$860$	−19994.2	+	95619.8i	−0.0270338	+	0.129286i
$861$	178816.			0.241213
$862$	74461.5	−	74461.5i	0.100211	−	0.100211i
$863$	419926.	+	419926.i	0.563834	+	0.563834i	0.930394	−	0.366560i	$-0.119465\pi$
$863$	419926.	+	419926.i	0.563834	+	0.563834i	−0.366560	+	0.930394i	$0.619465\pi$
$864$			208846.i			0.279768i
$865$	249579.	+	52187.2i	0.333561	+	0.0697480i
$866$	−19571.6			−0.0260970
$867$	−10702.8	+	10702.8i	−0.0142384	+	0.0142384i
$868$	215290.	+	215290.i	0.285749	+	0.285749i
$869$		−	780750.i		−	1.03389i
$870$	4113.99	+	6289.33i	0.00543531	+	0.00830933i
$871$	−178575.			−0.235388
$872$	−181329.	+	181329.i	−0.238470	+	0.238470i
$873$	−384651.	−	384651.i	−0.504706	−	0.504706i
$874$		−	21275.5i		−	0.0278521i
$875$	167253.	+	118998.i	0.218453	+	0.155426i
$876$	967731.			1.26109
$877$	106338.	−	106338.i	0.138257	−	0.138257i	−0.634591	−	0.772848i	$-0.718831\pi$
$877$	106338.	−	106338.i	0.138257	−	0.138257i	0.772848	+	0.634591i	$0.218831\pi$
$878$	25381.6	+	25381.6i	0.0329253	+	0.0329253i
$879$		−	539305.i		−	0.698001i
$880$	822539.	−	538040.i	1.06216	−	0.694784i
$881$	−1.11980e6			−1.44274			−0.721368	−	0.692552i	$-0.756486\pi$
$881$	−1.11980e6			−1.44274			−0.721368	+	0.692552i	$0.756486\pi$
$882$	−20504.5	+	20504.5i	−0.0263580	+	0.0263580i
$883$	−505487.	−	505487.i	−0.648319	−	0.648319i	0.304268	−	0.952587i	$-0.401588\pi$
$883$	−505487.	−	505487.i	−0.648319	−	0.648319i	−0.952587	+	0.304268i	$0.901588\pi$
$884$		−	1.07487e6i		−	1.37547i
$885$	65097.3	−	311320.i	0.0831144	−	0.397485i
$886$	44043.3			0.0561064
$887$	735861.	−	735861.i	0.935295	−	0.935295i	−0.0627352	−	0.998030i	$-0.519982\pi$
$887$	735861.	−	735861.i	0.935295	−	0.935295i	0.998030	+	0.0627352i	$0.0199823\pi$
$888$	122420.	+	122420.i	0.155248	+	0.155248i
$889$			109659.i			0.138753i
$890$	70087.4	+	14655.3i	0.0884830	+	0.0185019i
$891$	343486.			0.432667
$892$	80649.6	−	80649.6i	0.101361	−	0.101361i
$893$	96787.6	+	96787.6i	0.121372	+	0.121372i
$894$			62957.7i			0.0787723i
$895$	−153974.	−	235390.i	−0.192221	−	0.293861i
$896$	74118.1			0.0923226
$897$	792627.	−	792627.i	0.985109	−	0.985109i
$898$	−52427.0	−	52427.0i	−0.0650133	−	0.0650133i
$899$		−	188568.i		−	0.233318i
$900$	147366.	−	336973.i	0.181933	−	0.416016i
$901$	−599886.			−0.738957
$902$	80139.8	−	80139.8i	0.0984997	−	0.0984997i
$903$	15154.1	+	15154.1i	0.0185847	+	0.0185847i
$904$			78810.3i			0.0964376i
$905$	−874583.	+	572083.i	−1.06783	+	0.698493i
$906$	66541.3			0.0810652
$907$	536931.	−	536931.i	0.652685	−	0.652685i	−0.300954	−	0.953639i	$-0.597305\pi$
$907$	536931.	−	536931.i	0.652685	−	0.652685i	0.953639	+	0.300954i	$0.0973049\pi$
$908$	−205599.	−	205599.i	−0.249373	−	0.249373i
$909$			694892.i			0.840987i
$910$	−5454.46	+	26085.3i	−0.00658672	+	0.0315002i
$911$	−1.39379e6			−1.67943			−0.839714	−	0.543028i	$-0.817278\pi$
$911$	−1.39379e6			−1.67943			−0.839714	+	0.543028i	$0.817278\pi$
$912$	97081.3	−	97081.3i	0.116720	−	0.116720i
$913$	−1.02409e6	−	1.02409e6i	−1.22856	−	1.22856i
$914$			75270.5i			0.0901015i
$915$	−633228.	−	132409.i	−0.756341	−	0.158152i
$916$	−321238.			−0.382857
$917$	28864.8	−	28864.8i	0.0343265	−	0.0343265i
$918$	−56908.9	−	56908.9i	−0.0675297	−	0.0675297i
$919$			428803.i			0.507722i	0.967241	+	0.253861i	$0.0817006\pi$
$919$			428803.i			0.507722i	−0.967241	+	0.253861i	$0.918299\pi$
$920$	−112067.	−	171324.i	−0.132404	−	0.202415i
$921$	954012.			1.12469
$922$	−97073.1	+	97073.1i	−0.114192	+	0.114192i
$923$	406174.	+	406174.i	0.476770	+	0.476770i
$924$		−	217329.i		−	0.254551i
$925$	−531733.	−	1.35828e6i	−0.621456	−	1.58747i
$926$	33898.3			0.0395327
$927$	−223629.	+	223629.i	−0.260236	+	0.260236i
$928$	−24376.5	−	24376.5i	−0.0283058	−	0.0283058i
$929$		−	172289.i		−	0.199630i	−0.995006	−	0.0998150i	$-0.968175\pi$
$929$		−	172289.i		−	0.199630i	0.995006	−	0.0998150i	$-0.0318251\pi$
$930$	−71071.6	+	46489.5i	−0.0821732	+	0.0537513i
$931$	184556.			0.212926
$932$	−273089.	+	273089.i	−0.314393	+	0.314393i
$933$	806225.	+	806225.i	0.926175	+	0.926175i
$934$		−	137509.i		−	0.157629i
$935$	−235618.	+	1.12681e6i	−0.269516	+	1.28893i
$936$	95869.4			0.109428
$937$	600969.	−	600969.i	0.684499	−	0.684499i	−0.276512	−	0.961011i	$-0.589178\pi$
$937$	600969.	−	600969.i	0.684499	−	0.684499i	0.961011	+	0.276512i	$0.0891784\pi$
$938$	2519.88	+	2519.88i	0.00286400	+	0.00286400i
$939$		−	9438.05i		−	0.0107041i
$940$	642115.	+	134267.i	0.726704	+	0.151954i
$941$	−85999.8			−0.0971222			−0.0485611	−	0.998820i	$-0.515464\pi$
$941$	−85999.8			−0.0971222			−0.0485611	+	0.998820i	$0.515464\pi$
$942$	−45274.6	+	45274.6i	−0.0510214	+	0.0510214i
$943$	1.06248e6	+	1.06248e6i	1.19481	+	1.19481i
$944$			480023.i			0.538664i
$945$	−140695.	−	215090.i	−0.157549	−	0.240855i
$946$	13583.2			0.0151782
$947$	−497776.	+	497776.i	−0.555052	+	0.555052i	−0.927895	−	0.372842i	$-0.878383\pi$
$947$	−497776.	+	497776.i	−0.555052	+	0.555052i	0.372842	+	0.927895i	$0.378383\pi$
$948$	−369588.	−	369588.i	−0.411245	−	0.411245i
$949$		−	2.12531e6i		−	2.35988i
$950$	16922.4	−	6624.69i	0.0187505	−	0.00734038i
$951$	−814017.			−0.900062
$952$	−30452.6	+	30452.6i	−0.0336009	+	0.0336009i
$953$	674086.	+	674086.i	0.742214	+	0.742214i	0.973004	−	0.230789i	$-0.0741308\pi$
$953$	674086.	+	674086.i	0.742214	+	0.742214i	−0.230789	+	0.973004i	$0.574131\pi$
$954$		−	26649.1i		−	0.0292810i
$955$	−1.16411e6	+	761468.i	−1.27640	+	0.834920i
$956$	736997.			0.806399
$957$	−95176.9	+	95176.9i	−0.103922	+	0.103922i
$958$	54187.1	+	54187.1i	0.0590425	+	0.0590425i
$959$			15618.7i			0.0169828i
$960$	132542.	−	633867.i	0.143817	−	0.687790i
$961$	1.20736e6			1.30734
$962$	133908.	−	133908.i	0.144696	−	0.144696i
$963$	−178326.	−	178326.i	−0.192292	−	0.192292i
$964$			846171.i			0.910550i
$965$	−698741.	−	146107.i	−0.750346	−	0.156898i
$966$	−22369.5			−0.0239719
$967$	799383.	−	799383.i	0.854874	−	0.854874i	−0.135855	−	0.990729i	$-0.543378\pi$
$967$	799383.	−	799383.i	0.854874	−	0.854874i	0.990729	+	0.135855i	$0.0433780\pi$
$968$	−79694.0	−	79694.0i	−0.0850501	−	0.0850501i
$969$			160803.i			0.171256i
$970$	−70516.9	−	107804.i	−0.0749462	−	0.114575i
$971$	−527096.			−0.559051			−0.279526	−	0.960138i	$-0.590177\pi$
$971$	−527096.			−0.559051			−0.279526	+	0.960138i	$0.590177\pi$
$972$	−549040.	+	549040.i	−0.581127	+	0.581127i
$973$	169756.	+	169756.i	0.179308	+	0.179308i
$974$		−	85360.5i		−	0.0899785i
$975$	877254.	+	383643.i	0.922818	+	0.403569i
$976$	976372.			1.02498
$977$	513566.	−	513566.i	0.538031	−	0.538031i	−0.384919	−	0.922950i	$-0.625771\pi$
$977$	513566.	−	513566.i	0.538031	−	0.538031i	0.922950	+	0.384919i	$0.125771\pi$
$978$	−31961.6	−	31961.6i	−0.0334157	−	0.0334157i
$979$			1.28242e6i			1.33802i
$980$	740206.	−	484185.i	0.770727	−	0.504149i
$981$	−849278.			−0.882494
$982$	−32204.1	+	32204.1i	−0.0333955	+	0.0333955i
$983$	500717.	+	500717.i	0.518186	+	0.518186i	0.917022	−	0.398836i	$-0.130586\pi$
$983$	500717.	+	500717.i	0.518186	+	0.518186i	−0.398836	+	0.917022i	$0.630586\pi$
$984$		−	152334.i		−	0.157328i
$985$	26751.4	−	127935.i	0.0275724	−	0.131862i
$986$	13284.8			0.0136647
$987$	101764.	−	101764.i	0.104463	−	0.104463i
$988$	−214889.	−	214889.i	−0.220141	−	0.220141i
$989$			180084.i			0.184113i
$990$	−50057.1	−	10467.0i	−0.0510735	−	0.0106795i
$991$	1.11137e6			1.13165			0.565825	−	0.824525i	$-0.308558\pi$
$991$	1.11137e6			1.13165			0.565825	+	0.824525i	$0.308558\pi$
$992$	275463.	−	275463.i	0.279924	−	0.279924i
$993$	−213940.	−	213940.i	−0.216967	−	0.216967i
$994$		−	11463.0i		−	0.0116018i
$995$	534508.	+	817138.i	0.539893	+	0.825371i
$996$	−969557.			−0.977360
$997$	−705180.	+	705180.i	−0.709430	+	0.709430i	−0.966415	−	0.256986i	$-0.917271\pi$
$997$	−705180.	+	705180.i	−0.709430	+	0.709430i	0.256986	+	0.966415i	$0.417271\pi$
$998$	20452.4	+	20452.4i	0.0205344	+	0.0205344i
$999$			1.82641e6i			1.83007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.f.a.58.17	✓	72
5.2	odd	4	inner	95.5.f.a.77.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.f.a.58.17	✓	72	1.1	even	1	trivial
95.5.f.a.77.17	yes	72	5.2	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248255 + 0.248255i) q^{2} +(-4.68699 - 4.68699i) q^{3} +15.8767i q^{4} +(-20.9216 + 13.6853i) q^{5} +2.32714 q^{6} +(9.28930 - 9.28930i) q^{7} +(-7.91356 - 7.91356i) q^{8} -37.0643i q^{9} +(1.79645 - 8.59133i) q^{10} +157.199 q^{11} +(74.4141 - 74.4141i) q^{12} +(-163.427 - 163.427i) q^{13} +4.61223i q^{14} +(162.202 + 33.9166i) q^{15} -250.099 q^{16} +(207.129 - 207.129i) q^{17} +(9.20138 + 9.20138i) q^{18} -82.8191i q^{19} +(-217.277 - 332.167i) q^{20} -87.0777 q^{21} +(-39.0255 + 39.0255i) q^{22} +(-517.395 - 517.395i) q^{23} +74.1815i q^{24} +(250.427 - 572.636i) q^{25} +81.1429 q^{26} +(-553.366 + 553.366i) q^{27} +(147.484 + 147.484i) q^{28} -129.178i q^{29} +(-48.6874 + 31.8475i) q^{30} +1459.75 q^{31} +(188.705 - 188.705i) q^{32} +(-736.791 - 736.791i) q^{33} +102.841i q^{34} +(-67.2204 + 321.473i) q^{35} +588.460 q^{36} +(1650.27 - 1650.27i) q^{37} +(20.5602 + 20.5602i) q^{38} +1531.96i q^{39} +(273.863 + 57.2651i) q^{40} -2053.53 q^{41} +(21.6175 - 21.6175i) q^{42} +(-174.030 - 174.030i) q^{43} +2495.81i q^{44} +(507.234 + 775.444i) q^{45} +256.892 q^{46} +(-1168.66 + 1168.66i) q^{47} +(1172.21 + 1172.21i) q^{48} +2228.42i q^{49} +(79.9899 + 204.329i) q^{50} -1941.62 q^{51} +(2594.68 - 2594.68i) q^{52} +(-1448.10 - 1448.10i) q^{53} -274.752i q^{54} +(-3288.86 + 2151.31i) q^{55} -147.023 q^{56} +(-388.172 + 388.172i) q^{57} +(32.0690 + 32.0690i) q^{58} -1919.33i q^{59} +(-538.485 + 2575.24i) q^{60} -3903.95 q^{61} +(-362.391 + 362.391i) q^{62} +(-344.301 - 344.301i) q^{63} -3907.88i q^{64} +(5655.69 + 1182.61i) q^{65} +365.824 q^{66} +(546.347 - 546.347i) q^{67} +(3288.53 + 3288.53i) q^{68} +4850.05i q^{69} +(-63.1196 - 96.4952i) q^{70} -2485.36 q^{71} +(-293.310 + 293.310i) q^{72} +(6502.33 + 6502.33i) q^{73} +819.377i q^{74} +(-3857.68 + 1510.19i) q^{75} +1314.90 q^{76} +(1460.27 - 1460.27i) q^{77} +(-380.316 - 380.316i) q^{78} -4966.63i q^{79} +(5232.46 - 3422.67i) q^{80} +2185.04 q^{81} +(509.798 - 509.798i) q^{82} +(-6514.60 - 6514.60i) q^{83} -1382.51i q^{84} +(-1498.85 + 7168.07i) q^{85} +86.4076 q^{86} +(-605.455 + 605.455i) q^{87} +(-1244.00 - 1244.00i) q^{88} +8157.92i q^{89} +(-318.431 - 66.5842i) q^{90} -3036.24 q^{91} +(8214.54 - 8214.54i) q^{92} +(-6841.85 - 6841.85i) q^{93} -580.253i q^{94} +(1133.40 + 1732.71i) q^{95} -1768.92 q^{96} +(10378.0 - 10378.0i) q^{97} +(-553.216 - 553.216i) q^{98} -5826.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 20 q^{3} - 66 q^{5} - 128 q^{6} + 130 q^{7} + 16 q^{10} + 312 q^{11} - 80 q^{12} - 760 q^{13} + 1184 q^{15} - 3504 q^{16} + 1110 q^{17} + 960 q^{20} - 2840 q^{21} + 720 q^{22} + 300 q^{23} - 2322 q^{25}+ \cdots - 31440 q^{98}+O(q^{100}) \) 72 * q + 20 * q^3 - 66 * q^5 - 128 * q^6 + 130 * q^7 + 16 * q^10 + 312 * q^11 - 80 * q^12 - 760 * q^13 + 1184 * q^15 - 3504 * q^16 + 1110 * q^17 + 960 * q^20 - 2840 * q^21 + 720 * q^22 + 300 * q^23 - 2322 * q^25 - 192 * q^26 + 2060 * q^27 - 1120 * q^28 - 1160 * q^30 - 584 * q^31 - 6600 * q^32 + 3200 * q^33 - 4602 * q^35 + 10160 * q^36 + 2280 * q^37 + 11736 * q^40 + 6984 * q^41 - 8800 * q^42 - 8110 * q^43 - 8748 * q^45 + 11312 * q^46 - 3870 * q^47 - 660 * q^48 + 588 * q^50 + 7224 * q^51 + 2340 * q^52 + 13380 * q^53 - 5048 * q^55 - 13416 * q^56 + 5280 * q^58 - 9684 * q^60 + 10952 * q^61 - 1800 * q^62 + 17830 * q^63 + 852 * q^65 - 37928 * q^66 + 13780 * q^67 - 39000 * q^68 + 26500 * q^70 + 28680 * q^71 + 52900 * q^72 + 24070 * q^73 - 10208 * q^75 - 13530 * q^77 + 9400 * q^78 + 60240 * q^80 - 78720 * q^81 - 40360 * q^82 - 1740 * q^83 - 10112 * q^85 + 6432 * q^86 + 9720 * q^87 - 48180 * q^88 - 52736 * q^90 - 34232 * q^91 - 25800 * q^92 + 23800 * q^93 - 6498 * q^95 + 88440 * q^96 + 38060 * q^97 - 31440 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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