LMFDB - Embedded newform 26.5.d.b.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(5,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("26.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 522x^{4} + 68121x^{2} + 54756 $ x^6 + 522x^4 + 68121x^2 + 54756
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.2
Root			$0.899339i$ of defining polynomial
Character	$\chi$	$=$	26.21
Dual form			26.5.d.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +0.899339 q^{3} +8.00000i q^{4} +(23.4155 + 23.4155i) q^{5} +(1.79868 + 1.79868i) q^{6} +(14.3149 - 14.3149i) q^{7} +(-16.0000 + 16.0000i) q^{8} -80.1912 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +0.899339 q^{3} +8.00000i q^{4} +(23.4155 + 23.4155i) q^{5} +(1.79868 + 1.79868i) q^{6} +(14.3149 - 14.3149i) q^{7} +(-16.0000 + 16.0000i) q^{8} -80.1912 q^{9} +93.6621i q^{10} +(100.863 - 100.863i) q^{11} +7.19471i q^{12} +(-75.6169 - 151.139i) q^{13} +57.2595 q^{14} +(21.0585 + 21.0585i) q^{15} -64.0000 q^{16} -132.270i q^{17} +(-160.382 - 160.382i) q^{18} +(-153.172 - 153.172i) q^{19} +(-187.324 + 187.324i) q^{20} +(12.8739 - 12.8739i) q^{21} +403.454 q^{22} +428.455i q^{23} +(-14.3894 + 14.3894i) q^{24} +471.574i q^{25} +(151.045 - 453.512i) q^{26} -144.965 q^{27} +(114.519 + 114.519i) q^{28} +37.8112 q^{29} +84.2340i q^{30} +(1255.05 + 1255.05i) q^{31} +(-128.000 - 128.000i) q^{32} +(90.7104 - 90.7104i) q^{33} +(264.539 - 264.539i) q^{34} +670.380 q^{35} -641.530i q^{36} +(-1356.70 + 1356.70i) q^{37} -612.688i q^{38} +(-68.0052 - 135.925i) q^{39} -749.297 q^{40} +(-1823.91 - 1823.91i) q^{41} +51.4957 q^{42} -1409.65i q^{43} +(806.908 + 806.908i) q^{44} +(-1877.72 - 1877.72i) q^{45} +(-856.910 + 856.910i) q^{46} +(1703.90 - 1703.90i) q^{47} -57.5577 q^{48} +1991.17i q^{49} +(-943.148 + 943.148i) q^{50} -118.955i q^{51} +(1209.11 - 604.935i) q^{52} -722.399 q^{53} +(-289.931 - 289.931i) q^{54} +4723.54 q^{55} +458.076i q^{56} +(-137.754 - 137.754i) q^{57} +(75.6224 + 75.6224i) q^{58} +(-2103.18 + 2103.18i) q^{59} +(-168.468 + 168.468i) q^{60} +2495.71 q^{61} +5020.21i q^{62} +(-1147.93 + 1147.93i) q^{63} -512.000i q^{64} +(1768.40 - 5309.62i) q^{65} +362.842 q^{66} +(5336.90 + 5336.90i) q^{67} +1058.16 q^{68} +385.326i q^{69} +(1340.76 + 1340.76i) q^{70} +(-6408.17 - 6408.17i) q^{71} +(1283.06 - 1283.06i) q^{72} +(-6706.04 + 6706.04i) q^{73} -5426.80 q^{74} +424.105i q^{75} +(1225.38 - 1225.38i) q^{76} -2887.69i q^{77} +(135.841 - 407.861i) q^{78} -1750.23 q^{79} +(-1498.59 - 1498.59i) q^{80} +6365.11 q^{81} -7295.63i q^{82} +(2133.32 + 2133.32i) q^{83} +(102.991 + 102.991i) q^{84} +(3097.16 - 3097.16i) q^{85} +(2819.30 - 2819.30i) q^{86} +34.0051 q^{87} +3227.63i q^{88} +(-5954.76 + 5954.76i) q^{89} -7510.88i q^{90} +(-3245.98 - 1081.09i) q^{91} -3427.64 q^{92} +(1128.72 + 1128.72i) q^{93} +6815.59 q^{94} -7173.21i q^{95} +(-115.115 - 115.115i) q^{96} +(-2812.03 - 2812.03i) q^{97} +(-3982.34 + 3982.34i) q^{98} +(-8088.36 + 8088.36i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9	$ 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9} - 66 q^{11} - 294 q^{13} - 360 q^{14} - 288 q^{15} - 384 q^{16} + 1116 q^{18} - 318 q^{19} + 240 q^{20} + 756 q^{21} - 264 q^{22} + 84 q^{26} - 1404 q^{27} - 720 q^{28} - 276 q^{29} + 3282 q^{31} - 768 q^{32} - 3240 q^{33} + 2280 q^{34} + 5424 q^{35} - 3006 q^{37} + 2376 q^{39} + 960 q^{40} - 894 q^{41} + 3024 q^{42} - 528 q^{44} - 17226 q^{45} - 4848 q^{46} + 1566 q^{47} - 3300 q^{50} + 2688 q^{52} - 1356 q^{53} - 2808 q^{54} + 22212 q^{55} + 16812 q^{57} - 552 q^{58} + 5178 q^{59} + 2304 q^{60} + 2172 q^{61} - 24210 q^{63} + 1146 q^{65} - 12960 q^{66} + 1134 q^{67} + 9120 q^{68} + 10848 q^{70} - 18498 q^{71} - 8928 q^{72} - 13278 q^{73} - 12024 q^{74} + 2544 q^{76} + 25992 q^{78} - 13596 q^{79} + 1920 q^{80} + 58158 q^{81} - 11490 q^{83} + 6048 q^{84} - 10512 q^{85} - 7128 q^{86} + 30744 q^{87} - 28038 q^{89} - 6402 q^{91} - 19392 q^{92} + 23364 q^{93} + 6264 q^{94} - 27378 q^{97} - 11340 q^{98} - 61074 q^{99}+O(q^{100}) $ 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9 - 66 * q^11 - 294 * q^13 - 360 * q^14 - 288 * q^15 - 384 * q^16 + 1116 * q^18 - 318 * q^19 + 240 * q^20 + 756 * q^21 - 264 * q^22 + 84 * q^26 - 1404 * q^27 - 720 * q^28 - 276 * q^29 + 3282 * q^31 - 768 * q^32 - 3240 * q^33 + 2280 * q^34 + 5424 * q^35 - 3006 * q^37 + 2376 * q^39 + 960 * q^40 - 894 * q^41 + 3024 * q^42 - 528 * q^44 - 17226 * q^45 - 4848 * q^46 + 1566 * q^47 - 3300 * q^50 + 2688 * q^52 - 1356 * q^53 - 2808 * q^54 + 22212 * q^55 + 16812 * q^57 - 552 * q^58 + 5178 * q^59 + 2304 * q^60 + 2172 * q^61 - 24210 * q^63 + 1146 * q^65 - 12960 * q^66 + 1134 * q^67 + 9120 * q^68 + 10848 * q^70 - 18498 * q^71 - 8928 * q^72 - 13278 * q^73 - 12024 * q^74 + 2544 * q^76 + 25992 * q^78 - 13596 * q^79 + 1920 * q^80 + 58158 * q^81 - 11490 * q^83 + 6048 * q^84 - 10512 * q^85 - 7128 * q^86 + 30744 * q^87 - 28038 * q^89 - 6402 * q^91 - 19392 * q^92 + 23364 * q^93 + 6264 * q^94 - 27378 * q^97 - 11340 * q^98 - 61074 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	0.899339			0.0999265			0.0499633	−	0.998751i	$-0.484090\pi$
$3$	0.899339			0.0999265			0.0499633	+	0.998751i	$0.484090\pi$
$4$			8.00000i			0.500000i
$5$	23.4155	+	23.4155i	0.936621	+	0.936621i	0.998108	−	0.0614867i	$-0.0195842\pi$
$5$	23.4155	+	23.4155i	0.936621	+	0.936621i	−0.0614867	+	0.998108i	$0.519584\pi$
$6$	1.79868	+	1.79868i	0.0499633	+	0.0499633i
$7$	14.3149	−	14.3149i	0.292140	−	0.292140i	−0.545785	−	0.837925i	$-0.683768\pi$
$7$	14.3149	−	14.3149i	0.292140	−	0.292140i	0.837925	+	0.545785i	$0.183768\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−80.1912			−0.990015
$10$			93.6621i			0.936621i
$11$	100.863	−	100.863i	0.833582	−	0.833582i	−0.154423	−	0.988005i	$-0.549352\pi$
$11$	100.863	−	100.863i	0.833582	−	0.833582i	0.988005	+	0.154423i	$0.0493518\pi$
$12$			7.19471i			0.0499633i
$13$	−75.6169	−	151.139i	−0.447437	−	0.894315i
$13$	−75.6169	−	151.139i	−0.447437	−	0.894315i
$14$	57.2595			0.292140
$15$	21.0585	+	21.0585i	0.0935933	+	0.0935933i
$16$	−64.0000			−0.250000
$17$		−	132.270i		−	0.457680i	−0.973464	−	0.228840i	$-0.926507\pi$
$17$		−	132.270i		−	0.457680i	0.973464	−	0.228840i	$-0.0734933\pi$
$18$	−160.382	−	160.382i	−0.495007	−	0.495007i
$19$	−153.172	−	153.172i	−0.424299	−	0.424299i	0.462382	−	0.886681i	$-0.346995\pi$
$19$	−153.172	−	153.172i	−0.424299	−	0.424299i	−0.886681	+	0.462382i	$0.846995\pi$
$20$	−187.324	+	187.324i	−0.468311	+	0.468311i
$21$	12.8739	−	12.8739i	0.0291925	−	0.0291925i
$22$	403.454			0.833582
$23$			428.455i			0.809934i	0.914331	+	0.404967i	$0.132717\pi$
$23$			428.455i			0.809934i	−0.914331	+	0.404967i	$0.867283\pi$
$24$	−14.3894	+	14.3894i	−0.0249816	+	0.0249816i
$25$			471.574i			0.754518i
$26$	151.045	−	453.512i	0.223439	−	0.670876i
$27$	−144.965			−0.198855
$28$	114.519	+	114.519i	0.146070	+	0.146070i
$29$	37.8112			0.0449598			0.0224799	−	0.999747i	$-0.492844\pi$
$29$	37.8112			0.0449598			0.0224799	+	0.999747i	$0.492844\pi$
$30$			84.2340i			0.0935933i
$31$	1255.05	+	1255.05i	1.30599	+	1.30599i	0.924286	+	0.381701i	$0.124662\pi$
$31$	1255.05	+	1255.05i	1.30599	+	1.30599i	0.381701	+	0.924286i	$0.375338\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	90.7104	−	90.7104i	0.0832970	−	0.0832970i
$34$	264.539	−	264.539i	0.228840	−	0.228840i
$35$	670.380			0.547249
$36$		−	641.530i		−	0.495007i
$37$	−1356.70	+	1356.70i	−0.991015	+	0.991015i	−0.999960	−	0.00894472i	$-0.997153\pi$
$37$	−1356.70	+	1356.70i	−0.991015	+	0.991015i	0.00894472	+	0.999960i	$0.497153\pi$
$38$		−	612.688i		−	0.424299i
$39$	−68.0052	−	135.925i	−0.0447108	−	0.0893658i
$40$	−749.297			−0.468311
$41$	−1823.91	−	1823.91i	−1.08501	−	1.08501i	−0.996033	−	0.0889804i	$-0.971639\pi$
$41$	−1823.91	−	1823.91i	−1.08501	−	1.08501i	−0.0889804	−	0.996033i	$-0.528361\pi$
$42$	51.4957			0.0291925
$43$		−	1409.65i		−	0.762385i	−0.924496	−	0.381192i	$-0.875514\pi$
$43$		−	1409.65i		−	0.762385i	0.924496	−	0.381192i	$-0.124486\pi$
$44$	806.908	+	806.908i	0.416791	+	0.416791i
$45$	−1877.72	−	1877.72i	−0.927269	−	0.927269i
$46$	−856.910	+	856.910i	−0.404967	+	0.404967i
$47$	1703.90	−	1703.90i	0.771343	−	0.771343i	−0.206998	−	0.978341i	$-0.566369\pi$
$47$	1703.90	−	1703.90i	0.771343	−	0.771343i	0.978341	+	0.206998i	$0.0663695\pi$
$48$	−57.5577			−0.0249816
$49$			1991.17i			0.829308i
$50$	−943.148	+	943.148i	−0.377259	+	0.377259i
$51$		−	118.955i		−	0.0457344i
$52$	1209.11	−	604.935i	0.447158	−	0.223718i
$53$	−722.399			−0.257173			−0.128587	−	0.991698i	$-0.541044\pi$
$53$	−722.399			−0.257173			−0.128587	+	0.991698i	$0.541044\pi$
$54$	−289.931	−	289.931i	−0.0994276	−	0.0994276i
$55$	4723.54			1.56150
$56$			458.076i			0.146070i
$57$	−137.754	−	137.754i	−0.0423987	−	0.0423987i
$58$	75.6224	+	75.6224i	0.0224799	+	0.0224799i
$59$	−2103.18	+	2103.18i	−0.604188	+	0.604188i	−0.941421	−	0.337233i	$-0.890509\pi$
$59$	−2103.18	+	2103.18i	−0.604188	+	0.604188i	0.337233	+	0.941421i	$0.390509\pi$
$60$	−168.468	+	168.468i	−0.0467966	+	0.0467966i
$61$	2495.71			0.670709			0.335354	−	0.942092i	$-0.391144\pi$
$61$	2495.71			0.670709			0.335354	+	0.942092i	$0.391144\pi$
$62$			5020.21i			1.30599i
$63$	−1147.93	+	1147.93i	−0.289223	+	0.289223i
$64$		−	512.000i		−	0.125000i
$65$	1768.40	−	5309.62i	0.418556	−	1.25671i
$66$	362.842			0.0832970
$67$	5336.90	+	5336.90i	1.18888	+	1.18888i	0.977376	+	0.211507i	$0.0678371\pi$
$67$	5336.90	+	5336.90i	1.18888	+	1.18888i	0.211507	+	0.977376i	$0.432163\pi$
$68$	1058.16			0.228840
$69$			385.326i			0.0809338i
$70$	1340.76	+	1340.76i	0.273625	+	0.273625i
$71$	−6408.17	−	6408.17i	−1.27121	−	1.27121i	−0.945454	−	0.325757i	$-0.894381\pi$
$71$	−6408.17	−	6408.17i	−1.27121	−	1.27121i	−0.325757	−	0.945454i	$-0.605619\pi$
$72$	1283.06	−	1283.06i	0.247504	−	0.247504i
$73$	−6706.04	+	6706.04i	−1.25841	+	1.25841i	−0.306551	+	0.951854i	$0.599175\pi$
$73$	−6706.04	+	6706.04i	−1.25841	+	1.25841i	−0.951854	+	0.306551i	$0.900825\pi$
$74$	−5426.80			−0.991015
$75$			424.105i			0.0753964i
$76$	1225.38	−	1225.38i	0.212150	−	0.212150i
$77$		−	2887.69i		−	0.487046i
$78$	135.841	−	407.861i	0.0223275	−	0.0670383i
$79$	−1750.23			−0.280441			−0.140220	−	0.990120i	$-0.544781\pi$
$79$	−1750.23			−0.280441			−0.140220	+	0.990120i	$0.544781\pi$
$80$	−1498.59	−	1498.59i	−0.234155	−	0.234155i
$81$	6365.11			0.970144
$82$		−	7295.63i		−	1.08501i
$83$	2133.32	+	2133.32i	0.309671	+	0.309671i	0.844782	−	0.535111i	$-0.179730\pi$
$83$	2133.32	+	2133.32i	0.309671	+	0.309671i	−0.535111	+	0.844782i	$0.679730\pi$
$84$	102.991	+	102.991i	0.0145963	+	0.0145963i
$85$	3097.16	−	3097.16i	0.428673	−	0.428673i
$86$	2819.30	−	2819.30i	0.381192	−	0.381192i
$87$	34.0051			0.00449268
$88$			3227.63i			0.416791i
$89$	−5954.76	+	5954.76i	−0.751769	+	0.751769i	−0.974809	−	0.223040i	$-0.928402\pi$
$89$	−5954.76	+	5954.76i	−0.751769	+	0.751769i	0.223040	+	0.974809i	$0.428402\pi$
$90$		−	7510.88i		−	0.927269i
$91$	−3245.98	−	1081.09i	−0.391980	−	0.130551i
$92$	−3427.64			−0.404967
$93$	1128.72	+	1128.72i	0.130503	+	0.130503i
$94$	6815.59			0.771343
$95$		−	7173.21i		−	0.794815i
$96$	−115.115	−	115.115i	−0.0124908	−	0.0124908i
$97$	−2812.03	−	2812.03i	−0.298866	−	0.298866i	0.541704	−	0.840570i	$-0.317780\pi$
$97$	−2812.03	−	2812.03i	−0.298866	−	0.298866i	−0.840570	+	0.541704i	$0.817780\pi$
$98$	−3982.34	+	3982.34i	−0.414654	+	0.414654i
$99$	−8088.36	+	8088.36i	−0.825259	+	0.825259i
$100$	−3772.59			−0.377259
$101$			6324.21i			0.619960i	0.950743	+	0.309980i	$0.100322\pi$
$101$			6324.21i			0.619960i	−0.950743	+	0.309980i	$0.899678\pi$
$102$	237.910	−	237.910i	0.0228672	−	0.0228672i
$103$		−	2270.07i		−	0.213976i	−0.994260	−	0.106988i	$-0.965879\pi$
$103$		−	2270.07i		−	0.213976i	0.994260	−	0.106988i	$-0.0341206\pi$
$104$	3628.10	+	1208.36i	0.335438	+	0.111720i
$105$	602.899			0.0546847
$106$	−1444.80	−	1444.80i	−0.128587	−	0.128587i
$107$	12776.7			1.11597			0.557983	−	0.829852i	$-0.311575\pi$
$107$	12776.7			1.11597			0.557983	+	0.829852i	$0.311575\pi$
$108$		−	1159.72i		−	0.0994276i
$109$	−1909.32	−	1909.32i	−0.160704	−	0.160704i	0.622175	−	0.782878i	$-0.286249\pi$
$109$	−1909.32	−	1909.32i	−0.160704	−	0.160704i	−0.782878	+	0.622175i	$0.786249\pi$
$110$	9447.08	+	9447.08i	0.780751	+	0.780751i
$111$	−1220.13	+	1220.13i	−0.0990287	+	0.0990287i
$112$	−916.152	+	916.152i	−0.0730350	+	0.0730350i
$113$	21363.7			1.67309			0.836544	−	0.547899i	$-0.184572\pi$
$113$	21363.7			1.67309			0.836544	+	0.547899i	$0.184572\pi$
$114$		−	551.014i		−	0.0423987i
$115$	−10032.5	+	10032.5i	−0.758601	+	0.758601i
$116$			302.490i			0.0224799i
$117$	6063.81	+	12120.0i	0.442969	+	0.885385i
$118$	−8412.72			−0.604188
$119$	−1893.42	−	1893.42i	−0.133707	−	0.133707i
$120$	−673.872			−0.0467966
$121$		−	5705.87i		−	0.389718i
$122$	4991.42	+	4991.42i	0.335354	+	0.335354i
$123$	−1640.31	−	1640.31i	−0.108422	−	0.108422i
$124$	−10040.4	+	10040.4i	−0.652994	+	0.652994i
$125$	3592.55	−	3592.55i	0.229923	−	0.229923i
$126$	−4591.71			−0.289223
$127$		−	26936.1i		−	1.67004i	−0.550219	−	0.835020i	$-0.685456\pi$
$127$		−	26936.1i		−	1.67004i	0.550219	−	0.835020i	$-0.314544\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	1267.75i		−	0.0761824i
$130$	14156.0	−	7082.43i	0.837635	−	0.419079i
$131$	−864.611			−0.0503823			−0.0251912	−	0.999683i	$-0.508019\pi$
$131$	−864.611			−0.0503823			−0.0251912	+	0.999683i	$0.508019\pi$
$132$	725.683	+	725.683i	0.0416485	+	0.0416485i
$133$	−4385.27			−0.247910
$134$			21347.6i			1.18888i
$135$	−3394.44	−	3394.44i	−0.186252	−	0.186252i
$136$	2116.31	+	2116.31i	0.114420	+	0.114420i
$137$	18425.3	−	18425.3i	0.981686	−	0.981686i	−0.0181495	−	0.999835i	$-0.505777\pi$
$137$	18425.3	−	18425.3i	0.981686	−	0.981686i	0.999835	+	0.0181495i	$0.00577747\pi$
$138$	−770.652	+	770.652i	−0.0404669	+	0.0404669i
$139$	−26640.4			−1.37883			−0.689415	−	0.724366i	$-0.742132\pi$
$139$	−26640.4			−1.37883			−0.689415	+	0.724366i	$0.742132\pi$
$140$			5363.04i			0.273625i
$141$	1532.38	−	1532.38i	0.0770776	−	0.0770776i
$142$		−	25632.7i		−	1.27121i
$143$	−22871.4	−	7617.46i	−1.11846	−	0.372510i
$144$	5132.24			0.247504
$145$	885.370	+	885.370i	0.0421103	+	0.0421103i
$146$	−26824.2			−1.25841
$147$			1790.74i			0.0828699i
$148$	−10853.6	−	10853.6i	−0.495508	−	0.495508i
$149$	−17262.7	−	17262.7i	−0.777566	−	0.777566i	0.201850	−	0.979416i	$-0.435304\pi$
$149$	−17262.7	−	17262.7i	−0.777566	−	0.777566i	−0.979416	+	0.201850i	$0.935304\pi$
$150$	−848.209	+	848.209i	−0.0376982	+	0.0376982i
$151$	5649.38	−	5649.38i	0.247769	−	0.247769i	−0.572285	−	0.820055i	$-0.693943\pi$
$151$	5649.38	−	5649.38i	0.247769	−	0.247769i	0.820055	+	0.572285i	$0.193943\pi$
$152$	4901.51			0.212150
$153$			10606.9i			0.453110i
$154$	5775.39	−	5775.39i	0.243523	−	0.243523i
$155$			58775.5i			2.44643i
$156$	1087.40	−	544.041i	0.0446829	−	0.0223554i
$157$	27471.0			1.11449			0.557244	−	0.830349i	$-0.311859\pi$
$157$	27471.0			1.11449			0.557244	+	0.830349i	$0.311859\pi$
$158$	−3500.46	−	3500.46i	−0.140220	−	0.140220i
$159$	−649.682			−0.0256984
$160$		−	5994.38i		−	0.234155i
$161$	6133.27	+	6133.27i	0.236614	+	0.236614i
$162$	12730.2	+	12730.2i	0.485072	+	0.485072i
$163$	4856.58	−	4856.58i	0.182791	−	0.182791i	−0.609780	−	0.792571i	$-0.708742\pi$
$163$	4856.58	−	4856.58i	0.182791	−	0.182791i	0.792571	+	0.609780i	$0.208742\pi$
$164$	14591.3	−	14591.3i	0.542507	−	0.542507i
$165$	4248.06			0.156035
$166$			8533.29i			0.309671i
$167$	25898.8	−	25898.8i	0.928637	−	0.928637i	−0.0689808	−	0.997618i	$-0.521975\pi$
$167$	25898.8	−	25898.8i	0.928637	−	0.928637i	0.997618	+	0.0689808i	$0.0219747\pi$
$168$			411.965i			0.0145963i
$169$	−17125.2	+	22857.4i	−0.599600	+	0.800300i
$170$	12388.7			0.428673
$171$	12283.0	+	12283.0i	0.420063	+	0.420063i
$172$	11277.2			0.381192
$173$			26273.0i			0.877846i	0.898525	+	0.438923i	$0.144640\pi$
$173$			26273.0i			0.877846i	−0.898525	+	0.438923i	$0.855360\pi$
$174$	68.0102	+	68.0102i	0.00224634	+	0.00224634i
$175$	6750.52	+	6750.52i	0.220425	+	0.220425i
$176$	−6455.26	+	6455.26i	−0.208396	+	0.208396i
$177$	−1891.47	+	1891.47i	−0.0603744	+	0.0603744i
$178$	−23819.0			−0.751769
$179$		−	2843.94i		−	0.0887594i	−0.999015	−	0.0443797i	$-0.985869\pi$
$179$		−	2843.94i		−	0.0887594i	0.999015	−	0.0443797i	$-0.0141311\pi$
$180$	15021.8	−	15021.8i	0.463634	−	0.463634i
$181$			38206.1i			1.16621i	0.812398	+	0.583104i	$0.198162\pi$
$181$			38206.1i			1.16621i	−0.812398	+	0.583104i	$0.801838\pi$
$182$	−4329.78	−	8654.16i	−0.130714	−	0.261265i
$183$	2244.49			0.0670216
$184$	−6855.28	−	6855.28i	−0.202483	−	0.202483i
$185$	−63535.7			−1.85641
$186$			4514.87i			0.130503i
$187$	−13341.2	−	13341.2i	−0.381514	−	0.381514i
$188$	13631.2	+	13631.2i	0.385671	+	0.385671i
$189$	−2075.16	+	2075.16i	−0.0580936	+	0.0580936i
$190$	14346.4	−	14346.4i	0.397408	−	0.397408i
$191$	45700.9			1.25273			0.626366	−	0.779529i	$-0.284541\pi$
$191$	45700.9			1.25273			0.626366	+	0.779529i	$0.284541\pi$
$192$		−	460.461i		−	0.0124908i
$193$	18312.4	−	18312.4i	0.491622	−	0.491622i	−0.417195	−	0.908817i	$-0.636987\pi$
$193$	18312.4	−	18312.4i	0.491622	−	0.491622i	0.908817	+	0.417195i	$0.136987\pi$
$194$		−	11248.1i		−	0.298866i
$195$	1590.39	−	4775.14i	0.0418248	−	0.125579i
$196$	−15929.4			−0.414654
$197$	−19840.7	−	19840.7i	−0.511241	−	0.511241i	0.403666	−	0.914907i	$-0.367736\pi$
$197$	−19840.7	−	19840.7i	−0.511241	−	0.511241i	−0.914907	+	0.403666i	$0.867736\pi$
$198$	−32353.4			−0.825259
$199$			36306.4i			0.916806i	0.888745	+	0.458403i	$0.151578\pi$
$199$			36306.4i			0.916806i	−0.888745	+	0.458403i	$0.848422\pi$
$200$	−7545.18	−	7545.18i	−0.188630	−	0.188630i
$201$	4799.68	+	4799.68i	0.118801	+	0.118801i
$202$	−12648.4	+	12648.4i	−0.309980	+	0.309980i
$203$	541.263	−	541.263i	0.0131346	−	0.0131346i
$204$	951.641			0.0228672
$205$		−	85415.5i		−	2.03249i
$206$	4540.14	−	4540.14i	0.106988	−	0.106988i
$207$		−	34358.3i		−	0.801846i
$208$	4839.48	+	9672.92i	0.111859	+	0.223579i
$209$	−30898.9			−0.707377
$210$	1205.80	+	1205.80i	0.0273424	+	0.0273424i
$211$	−57831.8			−1.29898			−0.649489	−	0.760371i	$-0.725017\pi$
$211$	−57831.8			−1.29898			−0.649489	+	0.760371i	$0.725017\pi$
$212$		−	5779.19i		−	0.128587i
$213$	−5763.12	−	5763.12i	−0.127028	−	0.127028i
$214$	25553.4	+	25553.4i	0.557983	+	0.557983i
$215$	33007.7	−	33007.7i	0.714066	−	0.714066i
$216$	2319.45	−	2319.45i	0.0497138	−	0.0497138i
$217$	35931.9			0.763062
$218$		−	7637.28i		−	0.160704i
$219$	−6031.00	+	6031.00i	−0.125748	+	0.125748i
$220$			37788.3i			0.780751i
$221$	−19991.1	+	10001.8i	−0.409311	+	0.204783i
$222$	−4880.53			−0.0990287
$223$	5324.82	+	5324.82i	0.107077	+	0.107077i	0.758615	−	0.651539i	$-0.225876\pi$
$223$	5324.82	+	5324.82i	0.107077	+	0.107077i	−0.651539	+	0.758615i	$0.725876\pi$
$224$	−3664.61			−0.0730350
$225$		−	37816.1i		−	0.746984i
$226$	42727.3	+	42727.3i	0.836544	+	0.836544i
$227$	32210.0	+	32210.0i	0.625085	+	0.625085i	0.946827	−	0.321742i	$-0.104269\pi$
$227$	32210.0	+	32210.0i	0.625085	+	0.625085i	−0.321742	+	0.946827i	$0.604269\pi$
$228$	1102.03	−	1102.03i	0.0211994	−	0.0211994i
$229$	10785.6	−	10785.6i	0.205671	−	0.205671i	−0.596754	−	0.802425i	$-0.703543\pi$
$229$	10785.6	−	10785.6i	0.205671	−	0.205671i	0.802425	+	0.596754i	$0.203543\pi$
$230$	−40130.0			−0.758601
$231$		−	2597.01i		−	0.0486688i
$232$	−604.979	+	604.979i	−0.0112400	+	0.0112400i
$233$		−	7221.98i		−	0.133029i	−0.997785	−	0.0665143i	$-0.978812\pi$
$233$		−	7221.98i		−	0.133029i	0.997785	−	0.0665143i	$-0.0211878\pi$
$234$	−12112.5	+	36367.7i	−0.221208	+	0.664177i
$235$	79795.3			1.44491
$236$	−16825.4	−	16825.4i	−0.302094	−	0.302094i
$237$	−1574.05			−0.0280235
$238$		−	7573.69i		−	0.133707i
$239$	−34149.7	−	34149.7i	−0.597849	−	0.597849i	0.341891	−	0.939740i	$-0.388933\pi$
$239$	−34149.7	−	34149.7i	−0.597849	−	0.597849i	−0.939740	+	0.341891i	$0.888933\pi$
$240$	−1347.74	−	1347.74i	−0.0233983	−	0.0233983i
$241$	−26853.3	+	26853.3i	−0.462342	+	0.462342i	−0.899423	−	0.437080i	$-0.856013\pi$
$241$	−26853.3	+	26853.3i	−0.462342	+	0.462342i	0.437080	+	0.899423i	$0.356013\pi$
$242$	11411.7	−	11411.7i	0.194859	−	0.194859i
$243$	17466.6			0.295798
$244$			19965.7i			0.335354i
$245$	−46624.3	+	46624.3i	−0.776748	+	0.776748i
$246$		−	6561.24i		−	0.108422i
$247$	−11567.9	+	34732.7i	−0.189610	+	0.569305i
$248$	−40161.7			−0.652994
$249$	1918.58	+	1918.58i	0.0309443	+	0.0309443i
$250$	14370.2			0.229923
$251$			48510.9i			0.770003i	0.922916	+	0.385001i	$0.125799\pi$
$251$			48510.9i			0.770003i	−0.922916	+	0.385001i	$0.874201\pi$
$252$	−9183.41	−	9183.41i	−0.144612	−	0.144612i
$253$	43215.4	+	43215.4i	0.675146	+	0.675146i
$254$	53872.2	−	53872.2i	0.835020	−	0.835020i
$255$	2785.40	−	2785.40i	0.0428358	−	0.0428358i
$256$	4096.00			0.0625000
$257$		−	19329.8i		−	0.292659i	−0.989236	−	0.146329i	$-0.953254\pi$
$257$		−	19329.8i		−	0.292659i	0.989236	−	0.146329i	$-0.0467460\pi$
$258$	2535.50	−	2535.50i	0.0380912	−	0.0380912i
$259$			38842.0i			0.579031i
$260$	42476.9	+	14147.2i	0.628357	+	0.209278i
$261$	−3032.13			−0.0445109
$262$	−1729.22	−	1729.22i	−0.0251912	−	0.0251912i
$263$	69941.4			1.01117			0.505583	−	0.862778i	$-0.331277\pi$
$263$	69941.4			1.01117			0.505583	+	0.862778i	$0.331277\pi$
$264$			2902.73i			0.0416485i
$265$	−16915.4	−	16915.4i	−0.240874	−	0.240874i
$266$	−8770.55	−	8770.55i	−0.123955	−	0.123955i
$267$	−5355.35	+	5355.35i	−0.0751216	+	0.0751216i
$268$	−42695.2	+	42695.2i	−0.594442	+	0.594442i
$269$	−86473.3			−1.19503			−0.597513	−	0.801859i	$-0.703845\pi$
$269$	−86473.3			−1.19503			−0.597513	+	0.801859i	$0.703845\pi$
$270$		−	13577.8i		−	0.186252i
$271$	72727.2	−	72727.2i	0.990281	−	0.990281i	−0.00967257	−	0.999953i	$-0.503079\pi$
$271$	72727.2	−	72727.2i	0.990281	−	0.990281i	0.999953	+	0.00967257i	$0.00307892\pi$
$272$			8465.25i			0.114420i
$273$	−2919.24	−	972.270i	−0.0391692	−	0.0130455i
$274$	73701.0			0.981686
$275$	47564.6	+	47564.6i	0.628953	+	0.628953i
$276$	−3082.61			−0.0404669
$277$		−	1030.11i		−	0.0134254i	−0.999977	−	0.00671268i	$-0.997863\pi$
$277$		−	1030.11i		−	0.0134254i	0.999977	−	0.00671268i	$-0.00213673\pi$
$278$	−53280.8	−	53280.8i	−0.689415	−	0.689415i
$279$	−100644.	−	100644.i	−1.29295	−	1.29295i
$280$	−10726.1	+	10726.1i	−0.136812	+	0.136812i
$281$	−28924.5	+	28924.5i	−0.366314	+	0.366314i	−0.866131	−	0.499817i	$-0.833401\pi$
$281$	−28924.5	+	28924.5i	−0.366314	+	0.366314i	0.499817	+	0.866131i	$0.333401\pi$
$282$	6129.52			0.0770776
$283$			51585.0i			0.644095i	0.946723	+	0.322048i	$0.104371\pi$
$283$			51585.0i			0.644095i	−0.946723	+	0.322048i	$0.895629\pi$
$284$	51265.4	−	51265.4i	0.635605	−	0.635605i
$285$		−	6451.14i		−	0.0794231i
$286$	−30507.9	−	60977.7i	−0.372975	−	0.745485i
$287$	−52218.0			−0.633952
$288$	10264.5	+	10264.5i	0.123752	+	0.123752i
$289$	66025.8			0.790529
$290$			3541.48i			0.0421103i
$291$	−2528.97	−	2528.97i	−0.0298646	−	0.0298646i
$292$	−53648.3	−	53648.3i	−0.629203	−	0.629203i
$293$	−498.956	+	498.956i	−0.00581202	+	0.00581202i	−0.710007	−	0.704195i	$-0.751308\pi$
$293$	−498.956	+	498.956i	−0.00581202	+	0.00581202i	0.704195	+	0.710007i	$0.251308\pi$
$294$	−3581.47	+	3581.47i	−0.0414349	+	0.0414349i
$295$	−98494.1			−1.13179
$296$		−	43414.4i		−	0.495508i
$297$	−14621.7	+	14621.7i	−0.165762	+	0.165762i
$298$		−	69051.0i		−	0.777566i
$299$	64756.4	−	32398.4i	0.724336	−	0.362394i
$300$	−3392.84			−0.0376982
$301$	−20178.9	−	20178.9i	−0.222723	−	0.222723i
$302$	22597.5			0.247769
$303$			5687.61i			0.0619504i
$304$	9803.01	+	9803.01i	0.106075	+	0.106075i
$305$	58438.3	+	58438.3i	0.628200	+	0.628200i
$306$	−21213.7	+	21213.7i	−0.226555	+	0.226555i
$307$	−94497.9	+	94497.9i	−1.00264	+	1.00264i	−0.00264458	+	0.999997i	$0.500842\pi$
$307$	−94497.9	+	94497.9i	−1.00264	+	1.00264i	−0.999997	+	0.00264458i	$0.999158\pi$
$308$	23101.5			0.243523
$309$		−	2041.56i		−	0.0213819i
$310$	−117551.	+	117551.i	−1.22322	+	1.22322i
$311$		−	172167.i		−	1.78004i	−0.455922	−	0.890019i	$-0.650691\pi$
$311$		−	172167.i		−	1.78004i	0.455922	−	0.890019i	$-0.349309\pi$
$312$	3262.89	+	1086.72i	0.0335192	+	0.0111638i
$313$	4771.90			0.0487083			0.0243541	−	0.999703i	$-0.492247\pi$
$313$	4771.90			0.0487083			0.0243541	+	0.999703i	$0.492247\pi$
$314$	54942.0	+	54942.0i	0.557244	+	0.557244i
$315$	−53758.6			−0.541785
$316$		−	14001.9i		−	0.140220i
$317$	46466.8	+	46466.8i	0.462407	+	0.462407i	0.899444	−	0.437037i	$-0.143972\pi$
$317$	46466.8	+	46466.8i	0.462407	+	0.462407i	−0.437037	+	0.899444i	$0.643972\pi$
$318$	−1299.36	−	1299.36i	−0.0128492	−	0.0128492i
$319$	3813.77	−	3813.77i	0.0374777	−	0.0374777i
$320$	11988.8	−	11988.8i	0.117078	−	0.117078i
$321$	11490.6			0.111515
$322$			24533.1i			0.236614i
$323$	−20260.0	+	20260.0i	−0.194193	+	0.194193i
$324$			50920.9i			0.485072i
$325$	71273.4	−	35658.9i	0.674777	−	0.337599i
$326$	19426.3			0.182791
$327$	−1717.13	−	1717.13i	−0.0160586	−	0.0160586i
$328$	58365.1			0.542507
$329$		−	48782.1i		−	0.450681i
$330$	8496.13	+	8496.13i	0.0780177	+	0.0780177i
$331$	−12366.7	−	12366.7i	−0.112875	−	0.112875i	0.648414	−	0.761288i	$-0.275433\pi$
$331$	−12366.7	−	12366.7i	−0.112875	−	0.112875i	−0.761288	+	0.648414i	$0.775433\pi$
$332$	−17066.6	+	17066.6i	−0.154835	+	0.154835i
$333$	108795.	−	108795.i	0.981120	−	0.981120i
$334$	103595.			0.928637
$335$			249933.i			2.22707i
$336$	−823.931	+	823.931i	−0.00729814	+	0.00729814i
$337$			16853.8i			0.148401i	0.997243	+	0.0742005i	$0.0236405\pi$
$337$			16853.8i			0.148401i	−0.997243	+	0.0742005i	$0.976360\pi$
$338$	−79965.1	+	11464.3i	−0.699950	+	0.100350i
$339$	19213.2			0.167186
$340$	24777.3	+	24777.3i	0.214337	+	0.214337i
$341$	253178.			2.17729
$342$			49132.2i			0.420063i
$343$	62873.3	+	62873.3i	0.534414	+	0.534414i
$344$	22554.4	+	22554.4i	0.190596	+	0.190596i
$345$	−9022.61	+	9022.61i	−0.0758044	+	0.0758044i
$346$	−52546.1	+	52546.1i	−0.438923	+	0.438923i
$347$	−77846.5			−0.646518			−0.323259	−	0.946311i	$-0.604778\pi$
$347$	−77846.5			−0.646518			−0.323259	+	0.946311i	$0.604778\pi$
$348$			272.041i			0.00224634i
$349$	−63844.8	+	63844.8i	−0.524173	+	0.524173i	−0.918829	−	0.394656i	$-0.870864\pi$
$349$	−63844.8	+	63844.8i	−0.524173	+	0.524173i	0.394656	+	0.918829i	$0.370864\pi$
$350$			27002.1i			0.220425i
$351$	10961.8	+	21910.0i	0.0889752	+	0.177839i
$352$	−25821.0			−0.208396
$353$	−48651.9	−	48651.9i	−0.390437	−	0.390437i	0.484406	−	0.874843i	$-0.339036\pi$
$353$	−48651.9	−	48651.9i	−0.390437	−	0.390437i	−0.874843	+	0.484406i	$0.839036\pi$
$354$	−7565.88			−0.0603744
$355$		−	300101.i		−	2.38128i
$356$	−47638.1	−	47638.1i	−0.375884	−	0.375884i
$357$	−1702.83	−	1702.83i	−0.0133609	−	0.0133609i
$358$	5687.88	−	5687.88i	0.0443797	−	0.0443797i
$359$	3002.18	−	3002.18i	0.0232942	−	0.0232942i	−0.695364	−	0.718658i	$-0.744757\pi$
$359$	3002.18	−	3002.18i	0.0232942	−	0.0232942i	0.718658	+	0.695364i	$0.244757\pi$
$360$	60087.0			0.463634
$361$		−	83397.7i		−	0.639940i
$362$	−76412.3	+	76412.3i	−0.583104	+	0.583104i
$363$		−	5131.51i		−	0.0389432i
$364$	8648.75	−	25967.9i	0.0652756	−	0.195990i
$365$	−314051.			−2.35730
$366$	4488.97	+	4488.97i	0.0335108	+	0.0335108i
$367$	−108842.			−0.808102			−0.404051	−	0.914737i	$-0.632398\pi$
$367$	−108842.			−0.808102			−0.404051	+	0.914737i	$0.632398\pi$
$368$		−	27421.1i		−	0.202483i
$369$	146261.	+	146261.i	1.07418	+	1.07418i
$370$	−127071.	−	127071.i	−0.928206	−	0.928206i
$371$	−10341.0	+	10341.0i	−0.0751306	+	0.0751306i
$372$	−9029.75	+	9029.75i	−0.0652514	+	0.0652514i
$373$	163850.			1.17768			0.588840	−	0.808249i	$-0.299585\pi$
$373$	163850.			1.17768			0.588840	+	0.808249i	$0.299585\pi$
$374$		−	53364.7i		−	0.381514i
$375$	3230.92	−	3230.92i	0.0229754	−	0.0229754i
$376$			54524.7i			0.385671i
$377$	−2859.17	−	5714.76i	−0.0201167	−	0.0402083i
$378$	−8300.65			−0.0580936
$379$	−185064.	−	185064.i	−1.28838	−	1.28838i	−0.935770	−	0.352612i	$-0.885294\pi$
$379$	−185064.	−	185064.i	−1.28838	−	1.28838i	−0.352612	−	0.935770i	$-0.614706\pi$
$380$	57385.7			0.397408
$381$		−	24224.7i		−	0.166881i
$382$	91401.9	+	91401.9i	0.626366	+	0.626366i
$383$	−52515.7	−	52515.7i	−0.358007	−	0.358007i	0.505071	−	0.863078i	$-0.331466\pi$
$383$	−52515.7	−	52515.7i	−0.358007	−	0.358007i	−0.863078	+	0.505071i	$0.831466\pi$
$384$	920.923	−	920.923i	0.00624541	−	0.00624541i
$385$	67616.9	−	67616.9i	0.456177	−	0.456177i
$386$	73249.8			0.491622
$387$			113041.i			0.754772i
$388$	22496.2	−	22496.2i	0.149433	−	0.149433i
$389$		−	178815.i		−	1.18169i	−0.806785	−	0.590846i	$-0.798794\pi$
$389$		−	178815.i		−	1.18169i	0.806785	−	0.590846i	$-0.201206\pi$
$390$	12731.1	−	6369.51i	0.0837019	−	0.0418771i
$391$	56671.6			0.370691
$392$	−31858.7	−	31858.7i	−0.207327	−	0.207327i
$393$	−777.578			−0.00503453
$394$		−	79363.0i		−	0.511241i
$395$	−40982.6	−	40982.6i	−0.262667	−	0.262667i
$396$	−64706.9	−	64706.9i	−0.412629	−	0.412629i
$397$	−176697.	+	176697.i	−1.12111	+	1.12111i	−0.129533	+	0.991575i	$0.541348\pi$
$397$	−176697.	+	176697.i	−1.12111	+	1.12111i	−0.991575	+	0.129533i	$0.958652\pi$
$398$	−72612.8	+	72612.8i	−0.458403	+	0.458403i
$399$	−3943.85			−0.0247728
$400$		−	30180.7i		−	0.188630i
$401$	−112038.	+	112038.i	−0.696748	+	0.696748i	−0.963708	−	0.266959i	$-0.913981\pi$
$401$	−112038.	+	112038.i	−0.696748	+	0.696748i	0.266959	+	0.963708i	$0.413981\pi$
$402$			19198.7i			0.118801i
$403$	94784.7	−	284591.i	0.583617	−	1.75231i
$404$	−50593.7			−0.309980
$405$	149042.	+	149042.i	0.908657	+	0.908657i
$406$	2165.05			0.0131346
$407$			273683.i			1.65219i
$408$	1903.28	+	1903.28i	0.0114336	+	0.0114336i
$409$	45789.4	+	45789.4i	0.273727	+	0.273727i	0.830599	−	0.556872i	$-0.187998\pi$
$409$	45789.4	+	45789.4i	0.273727	+	0.273727i	−0.556872	+	0.830599i	$0.687998\pi$
$410$	170831.	−	170831.i	1.01625	−	1.01625i
$411$	16570.5	−	16570.5i	0.0980964	−	0.0980964i
$412$	18160.6			0.106988
$413$			60213.5i			0.353015i
$414$	68716.6	−	68716.6i	0.400923	−	0.400923i
$415$			99905.7i			0.580089i
$416$	−9666.87	+	29024.8i	−0.0558598	+	0.167719i
$417$	−23958.7			−0.137782
$418$	−61797.8	−	61797.8i	−0.353688	−	0.353688i
$419$	166004.			0.945562			0.472781	−	0.881180i	$-0.343250\pi$
$419$	166004.			0.945562			0.472781	+	0.881180i	$0.343250\pi$
$420$			4823.19i			0.0273424i
$421$	34739.8	+	34739.8i	0.196003	+	0.196003i	0.798284	−	0.602281i	$-0.205741\pi$
$421$	34739.8	+	34739.8i	0.196003	+	0.196003i	−0.602281	+	0.798284i	$0.705741\pi$
$422$	−115664.	−	115664.i	−0.649489	−	0.649489i
$423$	−136637.	+	136637.i	−0.763641	+	0.763641i
$424$	11558.4	−	11558.4i	0.0642933	−	0.0642933i
$425$	62374.9			0.345328
$426$		−	23052.5i		−	0.127028i
$427$	35725.7	−	35725.7i	0.195941	−	0.195941i
$428$			102214.i			0.557983i
$429$	−20569.1	−	6850.67i	−0.111764	−	0.0372236i
$430$	132031.			0.714066
$431$	186629.	+	186629.i	1.00467	+	1.00467i	0.999989	+	0.00468572i	$0.00149151\pi$
$431$	186629.	+	186629.i	1.00467	+	1.00467i	0.00468572	+	0.999989i	$0.498508\pi$
$432$	9277.79			0.0497138
$433$			58721.8i			0.313201i	0.987662	+	0.156601i	$0.0500535\pi$
$433$			58721.8i			0.313201i	−0.987662	+	0.156601i	$0.949946\pi$
$434$	71863.7	+	71863.7i	0.381531	+	0.381531i
$435$	796.247	+	796.247i	0.00420794	+	0.00420794i
$436$	15274.6	−	15274.6i	0.0803518	−	0.0803518i
$437$	65627.3	−	65627.3i	0.343654	−	0.343654i
$438$	−24124.0			−0.125748
$439$			231617.i			1.20183i	0.799314	+	0.600914i	$0.205197\pi$
$439$			231617.i			1.20183i	−0.799314	+	0.600914i	$0.794803\pi$
$440$	−75576.7	+	75576.7i	−0.390375	+	0.390375i
$441$		−	159674.i		−	0.821027i
$442$	−59985.9	−	19978.7i	−0.307047	−	0.102264i
$443$	260788.			1.32886			0.664430	−	0.747350i	$-0.268674\pi$
$443$	260788.			1.32886			0.664430	+	0.747350i	$0.268674\pi$
$444$	−9761.06	−	9761.06i	−0.0495144	−	0.0495144i
$445$	−278868.			−1.40825
$446$			21299.3i			0.107077i
$447$	−15525.0	−	15525.0i	−0.0776995	−	0.0776995i
$448$	−7329.21	−	7329.21i	−0.0365175	−	0.0365175i
$449$	1466.56	−	1466.56i	0.00727456	−	0.00727456i	−0.703460	−	0.710735i	$-0.748363\pi$
$449$	1466.56	−	1466.56i	0.00727456	−	0.00727456i	0.710735	+	0.703460i	$0.248363\pi$
$450$	75632.2	−	75632.2i	0.373492	−	0.373492i
$451$	−367931.			−1.80890
$452$			170909.i			0.836544i
$453$	5080.71	−	5080.71i	0.0247587	−	0.0247587i
$454$			128840.i			0.625085i
$455$	−50692.1	−	101321.i	−0.244860	−	0.489414i
$456$	4408.11			0.0211994
$457$	−175321.	−	175321.i	−0.839461	−	0.839461i	0.149327	−	0.988788i	$-0.452289\pi$
$457$	−175321.	−	175321.i	−0.839461	−	0.839461i	−0.988788	+	0.149327i	$0.952289\pi$
$458$	43142.4			0.205671
$459$			19174.5i			0.0910121i
$460$	−80260.0	−	80260.0i	−0.379300	−	0.379300i
$461$	1644.37	+	1644.37i	0.00773744	+	0.00773744i	0.710965	−	0.703227i	$-0.248258\pi$
$461$	1644.37	+	1644.37i	0.00773744	+	0.00773744i	−0.703227	+	0.710965i	$0.748258\pi$
$462$	5194.03	−	5194.03i	0.0243344	−	0.0243344i
$463$	5625.83	−	5625.83i	0.0262437	−	0.0262437i	−0.693863	−	0.720107i	$-0.744093\pi$
$463$	5625.83	−	5625.83i	0.0262437	−	0.0262437i	0.720107	+	0.693863i	$0.244093\pi$
$464$	−2419.92			−0.0112400
$465$			52859.1i			0.244463i
$466$	14444.0	−	14444.0i	0.0665143	−	0.0665143i
$467$			24956.5i			0.114433i	0.998362	+	0.0572164i	$0.0182225\pi$
$467$			24956.5i			0.114433i	−0.998362	+	0.0572164i	$0.981778\pi$
$468$	−96960.3	+	48510.4i	−0.442693	+	0.221485i
$469$	152794.			0.694641
$470$	159591.	+	159591.i	0.722456	+	0.722456i
$471$	24705.7			0.111367
$472$		−	67301.8i		−	0.302094i
$473$	−142182.	−	142182.i	−0.635510	−	0.635510i
$474$	−3148.10	−	3148.10i	−0.0140117	−	0.0140117i
$475$	72231.9	−	72231.9i	0.320142	−	0.320142i
$476$	15147.4	−	15147.4i	0.0668534	−	0.0668534i
$477$	57930.1			0.254605
$478$		−	136599.i		−	0.597849i
$479$	298404.	−	298404.i	1.30057	−	1.30057i	0.372559	−	0.928008i	$-0.378480\pi$
$479$	298404.	−	298404.i	1.30057	−	1.30057i	0.928008	−	0.372559i	$-0.121520\pi$
$480$		−	5390.97i		−	0.0233983i
$481$	307640.	+	102461.i	1.32970	+	0.442863i
$482$	−107413.			−0.462342
$483$	5515.89	+	5515.89i	0.0236440	+	0.0236440i
$484$	45646.9			0.194859
$485$		−	131690.i		−	0.559848i
$486$	34933.2	+	34933.2i	0.147899	+	0.147899i
$487$	59226.0	+	59226.0i	0.249721	+	0.249721i	0.820856	−	0.571135i	$-0.193497\pi$
$487$	59226.0	+	59226.0i	0.249721	+	0.249721i	−0.571135	+	0.820856i	$0.693497\pi$
$488$	−39931.3	+	39931.3i	−0.167677	+	0.167677i
$489$	4367.71	−	4367.71i	0.0182657	−	0.0182657i
$490$	−186497.			−0.776748
$491$		−	298924.i		−	1.23993i	−0.784629	−	0.619965i	$-0.787147\pi$
$491$		−	298924.i		−	1.23993i	0.784629	−	0.619965i	$-0.212853\pi$
$492$	13122.5	−	13122.5i	0.0542108	−	0.0542108i
$493$		−	5001.27i		−	0.0205772i
$494$	−92601.3	+	46329.5i	−0.379457	+	0.189847i
$495$	−378786.			−1.54591
$496$	−80323.4	−	80323.4i	−0.326497	−	0.326497i
$497$	−183464.			−0.742743
$498$			7674.32i			0.0309443i
$499$	−26413.7	−	26413.7i	−0.106079	−	0.106079i	0.652075	−	0.758154i	$-0.273899\pi$
$499$	−26413.7	−	26413.7i	−0.106079	−	0.106079i	−0.758154	+	0.652075i	$0.773899\pi$
$500$	28740.4	+	28740.4i	0.114962	+	0.114962i
$501$	23291.8	−	23291.8i	0.0927955	−	0.0927955i
$502$	−97021.9	+	97021.9i	−0.385001	+	0.385001i
$503$	51867.6			0.205003			0.102501	−	0.994733i	$-0.467315\pi$
$503$	51867.6			0.205003			0.102501	+	0.994733i	$0.467315\pi$
$504$		−	36733.6i		−	0.144612i
$505$	−148085.	+	148085.i	−0.580668	+	0.580668i
$506$			172862.i			0.675146i
$507$	−15401.3	+	20556.5i	−0.0599160	+	0.0799712i
$508$	215489.			0.835020
$509$	−282072.	−	282072.i	−1.08874	−	1.08874i	−0.995659	−	0.0930803i	$-0.970329\pi$
$509$	−282072.	−	282072.i	−1.08874	−	1.08874i	−0.0930803	−	0.995659i	$-0.529671\pi$
$510$	11141.6			0.0428358
$511$			191992.i			0.735262i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	22204.7	+	22204.7i	0.0843741	+	0.0843741i
$514$	38659.7	−	38659.7i	0.146329	−	0.146329i
$515$	53154.9	−	53154.9i	0.200414	−	0.200414i
$516$	10142.0			0.0380912
$517$		−	343722.i		−	1.28596i
$518$	−77683.9	+	77683.9i	−0.289515	+	0.289515i
$519$			23628.4i			0.0877201i
$520$	56659.5	+	113248.i	0.209539	+	0.418817i
$521$	−276996.			−1.02047			−0.510233	−	0.860036i	$-0.670441\pi$
$521$	−276996.			−1.02047			−0.510233	+	0.860036i	$0.670441\pi$
$522$	−6064.25	−	6064.25i	−0.0222554	−	0.0222554i
$523$	138350.			0.505797			0.252899	−	0.967493i	$-0.418616\pi$
$523$	138350.			0.505797			0.252899	+	0.967493i	$0.418616\pi$
$524$		−	6916.89i		−	0.0251912i
$525$	6071.00	+	6071.00i	0.0220263	+	0.0220263i
$526$	139883.	+	139883.i	0.505583	+	0.505583i
$527$	166005.	−	166005.i	0.597725	−	0.597725i
$528$	−5805.47	+	5805.47i	−0.0208242	+	0.0208242i
$529$	96267.4			0.344008
$530$		−	67661.4i		−	0.240874i
$531$	168656.	−	168656.i	0.598155	−	0.598155i
$532$		−	35082.2i		−	0.123955i
$533$	−137746.	+	413582.i	−0.484869	+	1.45582i
$534$	−21421.4			−0.0751216
$535$	299173.	+	299173.i	1.04524	+	1.04524i
$536$	−170781.			−0.594442
$537$		−	2557.67i		−	0.00886942i
$538$	−172947.	−	172947.i	−0.597513	−	0.597513i
$539$	200836.	+	200836.i	0.691297	+	0.691297i
$540$	27155.5	−	27155.5i	0.0931260	−	0.0931260i
$541$	−342753.	+	342753.i	−1.17108	+	1.17108i	−0.189129	+	0.981952i	$0.560566\pi$
$541$	−342753.	+	342753.i	−1.17108	+	1.17108i	−0.981952	+	0.189129i	$0.939434\pi$
$542$	290909.			0.990281
$543$			34360.3i			0.116535i
$544$	−16930.5	+	16930.5i	−0.0572100	+	0.0572100i
$545$		−	89415.5i		−	0.301037i
$546$	−3893.94	−	7783.02i	−0.0130618	−	0.0261073i
$547$	552138.			1.84533			0.922663	−	0.385608i	$-0.126008\pi$
$547$	552138.			1.84533			0.922663	+	0.385608i	$0.126008\pi$
$548$	147402.	+	147402.i	0.490843	+	0.490843i
$549$	−200134.			−0.664012
$550$			190258.i			0.628953i
$551$	−5791.62	−	5791.62i	−0.0190764	−	0.0190764i
$552$	−6165.22	−	6165.22i	−0.0202335	−	0.0202335i
$553$	−25054.3	+	25054.3i	−0.0819281	+	0.0819281i
$554$	2060.23	−	2060.23i	0.00671268	−	0.00671268i
$555$	−57140.1			−0.185505
$556$		−	213123.i		−	0.689415i
$557$	9408.68	−	9408.68i	0.0303262	−	0.0303262i	−0.691781	−	0.722107i	$-0.743174\pi$
$557$	9408.68	−	9408.68i	0.0303262	−	0.0303262i	0.722107	+	0.691781i	$0.243174\pi$
$558$		−	402577.i		−	1.29295i
$559$	−213053.	+	106593.i	−0.681812	+	0.341119i
$560$	−42904.3			−0.136812
$561$	−11998.2	−	11998.2i	−0.0381234	−	0.0381234i
$562$	−115698.			−0.366314
$563$			166105.i			0.524041i	0.965062	+	0.262020i	$0.0843887\pi$
$563$			166105.i			0.524041i	−0.965062	+	0.262020i	$0.915611\pi$
$564$	12259.0	+	12259.0i	0.0385388	+	0.0385388i
$565$	500242.	+	500242.i	1.56705	+	1.56705i
$566$	−103170.	+	103170.i	−0.322048	+	0.322048i
$567$	91115.8	−	91115.8i	0.283418	−	0.283418i
$568$	205061.			0.635605
$569$		−	183793.i		−	0.567682i	−0.958871	−	0.283841i	$-0.908391\pi$
$569$		−	183793.i		−	0.567682i	0.958871	−	0.283841i	$-0.0916088\pi$
$570$	12902.3	−	12902.3i	0.0397116	−	0.0397116i
$571$			254738.i			0.781308i	0.920538	+	0.390654i	$0.127751\pi$
$571$			254738.i			0.781308i	−0.920538	+	0.390654i	$0.872249\pi$
$572$	60939.6	−	182971.i	0.186255	−	0.559230i
$573$	41100.6			0.125181
$574$	−104436.	−	104436.i	−0.316976	−	0.316976i
$575$	−202048.			−0.611110
$576$			41057.9i			0.123752i
$577$	−41922.1	−	41922.1i	−0.125919	−	0.125919i	0.641339	−	0.767258i	$-0.278379\pi$
$577$	−41922.1	−	41922.1i	−0.125919	−	0.125919i	−0.767258	+	0.641339i	$0.778379\pi$
$578$	132052.	+	132052.i	0.395264	+	0.395264i
$579$	16469.1	−	16469.1i	0.0491261	−	0.0491261i
$580$	−7082.96	+	7082.96i	−0.0210552	+	0.0210552i
$581$	61076.5			0.180935
$582$		−	10115.9i		−	0.0298646i
$583$	−72863.7	+	72863.7i	−0.214375	+	0.214375i
$584$		−	214593.i		−	0.629203i
$585$	−141810.	+	425784.i	−0.414376	+	1.24417i
$586$	−1995.83			−0.00581202
$587$	56243.0	+	56243.0i	0.163227	+	0.163227i	0.783995	−	0.620768i	$-0.213179\pi$
$587$	56243.0	+	56243.0i	0.163227	+	0.163227i	−0.620768	+	0.783995i	$0.713179\pi$
$588$	−14325.9			−0.0414349
$589$		−	384478.i		−	1.10826i
$590$	−196988.	−	196988.i	−0.565896	−	0.565896i
$591$	−17843.6	−	17843.6i	−0.0510865	−	0.0510865i
$592$	86828.8	−	86828.8i	0.247754	−	0.247754i
$593$	259490.	−	259490.i	0.737922	−	0.737922i	−0.234253	−	0.972176i	$-0.575265\pi$
$593$	259490.	−	259490.i	0.737922	−	0.737922i	0.972176	+	0.234253i	$0.0752645\pi$
$594$	−58486.9			−0.165762
$595$		−	88670.9i		−	0.250465i
$596$	138102.	−	138102.i	0.388783	−	0.388783i
$597$			32651.8i			0.0916132i
$598$	194310.	+	64715.9i	0.543365	+	0.180971i
$599$	−307613.			−0.857336			−0.428668	−	0.903462i	$-0.641017\pi$
$599$	−307613.			−0.857336			−0.428668	+	0.903462i	$0.641017\pi$
$600$	−6785.68	−	6785.68i	−0.0188491	−	0.0188491i
$601$	171093.			0.473678			0.236839	−	0.971549i	$-0.423889\pi$
$601$	171093.			0.473678			0.236839	+	0.971549i	$0.423889\pi$
$602$		−	80715.8i		−	0.222723i
$603$	−427972.	−	427972.i	−1.17701	−	1.17701i
$604$	45195.1	+	45195.1i	0.123885	+	0.123885i
$605$	133606.	−	133606.i	0.365018	−	0.365018i
$606$	−11375.2	+	11375.2i	−0.0309752	+	0.0309752i
$607$	−625686.			−1.69816			−0.849080	−	0.528264i	$-0.822843\pi$
$607$	−625686.			−1.69816			−0.849080	+	0.528264i	$0.822843\pi$
$608$			39212.0i			0.106075i
$609$	486.778	−	486.778i	0.00131249	−	0.00131249i
$610$			233753.i			0.628200i
$611$	−386369.	−	128682.i	−1.03495	−	0.344697i
$612$	−84854.9			−0.226555
$613$	−283280.	−	283280.i	−0.753868	−	0.753868i	0.221331	−	0.975199i	$-0.428960\pi$
$613$	−283280.	−	283280.i	−0.753868	−	0.753868i	−0.975199	+	0.221331i	$0.928960\pi$
$614$	−377992.			−1.00264
$615$		−	76817.5i		−	0.203100i
$616$	46203.1	+	46203.1i	0.121761	+	0.121761i
$617$	−213778.	−	213778.i	−0.561557	−	0.561557i	0.368193	−	0.929750i	$-0.379977\pi$
$617$	−213778.	−	213778.i	−0.561557	−	0.561557i	−0.929750	+	0.368193i	$0.879977\pi$
$618$	4083.12	−	4083.12i	0.0106909	−	0.0106909i
$619$	−270488.	+	270488.i	−0.705939	+	0.705939i	−0.965679	−	0.259740i	$-0.916363\pi$
$619$	−270488.	+	270488.i	−0.705939	+	0.705939i	0.259740	+	0.965679i	$0.416363\pi$
$620$	−470204.			−1.22322
$621$		−	62111.2i		−	0.161060i
$622$	344334.	−	344334.i	0.890019	−	0.890019i
$623$			170483.i			0.439244i
$624$	4352.33	+	8699.23i	0.0111777	+	0.0223415i
$625$	462977.			1.18522
$626$	9543.80	+	9543.80i	0.0243541	+	0.0243541i
$627$	−27788.6			−0.0706857
$628$			219768.i			0.557244i
$629$	179450.	+	179450.i	0.453568	+	0.453568i
$630$	−107517.	−	107517.i	−0.270892	−	0.270892i
$631$	93538.3	−	93538.3i	0.234926	−	0.234926i	−0.579819	−	0.814745i	$-0.696877\pi$
$631$	93538.3	−	93538.3i	0.234926	−	0.234926i	0.814745	+	0.579819i	$0.196877\pi$
$632$	28003.7	−	28003.7i	0.0701102	−	0.0701102i
$633$	−52010.4			−0.129802
$634$			185867.i			0.462407i
$635$	630723.	−	630723.i	1.56420	−	1.56420i
$636$		−	5197.45i		−	0.0128492i
$637$	300944.	−	150566.i	0.741663	−	0.371063i
$638$	15255.1			0.0374777
$639$	513879.	+	513879.i	1.25852	+	1.25852i
$640$	47955.0			0.117078
$641$			548028.i			1.33379i	0.745153	+	0.666894i	$0.232376\pi$
$641$			548028.i			1.33379i	−0.745153	+	0.666894i	$0.767624\pi$
$642$	22981.2	+	22981.2i	0.0557573	+	0.0557573i
$643$	−225103.	−	225103.i	−0.544451	−	0.544451i	0.380380	−	0.924830i	$-0.375793\pi$
$643$	−225103.	−	225103.i	−0.544451	−	0.544451i	−0.924830	+	0.380380i	$0.875793\pi$
$644$	−49066.2	+	49066.2i	−0.118307	+	0.118307i
$645$	29685.1	−	29685.1i	0.0713541	−	0.0713541i
$646$	−81040.0			−0.194193
$647$			225097.i			0.537727i	0.963178	+	0.268863i	$0.0866481\pi$
$647$			225097.i			0.537727i	−0.963178	+	0.268863i	$0.913352\pi$
$648$	−101842.	+	101842.i	−0.242536	+	0.242536i
$649$			424268.i			1.00728i
$650$	213865.	+	71228.9i	0.506188	+	0.168589i
$651$	32314.9			0.0762502
$652$	38852.7	+	38852.7i	0.0913957	+	0.0913957i
$653$	−348036.			−0.816202			−0.408101	−	0.912937i	$-0.633809\pi$
$653$	−348036.			−0.816202			−0.408101	+	0.912937i	$0.633809\pi$
$654$		−	6868.50i		−	0.0160586i
$655$	−20245.3	−	20245.3i	−0.0471892	−	0.0471892i
$656$	116730.	+	116730.i	0.271253	+	0.271253i
$657$	537766.	−	537766.i	1.24584	−	1.24584i
$658$	97564.2	−	97564.2i	0.225340	−	0.225340i
$659$	68570.8			0.157895			0.0789475	−	0.996879i	$-0.474844\pi$
$659$	68570.8			0.157895			0.0789475	+	0.996879i	$0.474844\pi$
$660$			33984.5i			0.0780177i
$661$	−170311.	+	170311.i	−0.389799	+	0.389799i	−0.874616	−	0.484817i	$-0.838886\pi$
$661$	−170311.	+	170311.i	−0.389799	+	0.389799i	0.484817	+	0.874616i	$0.338886\pi$
$662$		−	49466.6i		−	0.112875i
$663$	−17978.8	+	8995.02i	−0.0409010	+	0.0204633i
$664$	−68266.3			−0.154835
$665$	−102684.	−	102684.i	−0.232197	−	0.232197i
$666$	435182.			0.981120
$667$			16200.4i			0.0364145i
$668$	207190.	+	207190.i	0.464319	+	0.464319i
$669$	4788.81	+	4788.81i	0.0106998	+	0.0106998i
$670$	−499865.	+	499865.i	−1.11353	+	1.11353i
$671$	251726.	−	251726.i	0.559091	−	0.559091i
$672$	−3295.72			−0.00729814
$673$		−	294958.i		−	0.651224i	−0.945503	−	0.325612i	$-0.894430\pi$
$673$		−	294958.i		−	0.651224i	0.945503	−	0.325612i	$-0.105570\pi$
$674$	−33707.5	+	33707.5i	−0.0742005	+	0.0742005i
$675$		−	68361.9i		−	0.150040i
$676$	−182859.	−	137001.i	−0.400150	−	0.299800i
$677$	128070.			0.279428			0.139714	−	0.990192i	$-0.455382\pi$
$677$	128070.			0.279428			0.139714	+	0.990192i	$0.455382\pi$
$678$	38426.3	+	38426.3i	0.0835930	+	0.0835930i
$679$	−80507.7			−0.174621
$680$			99109.2i			0.214337i
$681$	28967.7	+	28967.7i	0.0624625	+	0.0624625i
$682$	506356.	+	506356.i	1.08865	+	1.08865i
$683$	−506688.	+	506688.i	−1.08617	+	1.08617i	−0.0902553	+	0.995919i	$0.528768\pi$
$683$	−506688.	+	506688.i	−1.08617	+	1.08617i	−0.995919	+	0.0902553i	$0.971232\pi$
$684$	−98264.4	+	98264.4i	−0.210031	+	0.210031i
$685$	862874.			1.83894
$686$			251493.i			0.534414i
$687$	9699.90	−	9699.90i	0.0205520	−	0.0205520i
$688$			90217.5i			0.190596i
$689$	54625.6	+	109183.i	0.115069	+	0.229994i
$690$	−36090.5			−0.0758044
$691$	−111016.	−	111016.i	−0.232503	−	0.232503i	0.581234	−	0.813737i	$-0.302570\pi$
$691$	−111016.	−	111016.i	−0.232503	−	0.232503i	−0.813737	+	0.581234i	$0.802570\pi$
$692$	−210184.			−0.438923
$693$			231568.i			0.482182i
$694$	−155693.	−	155693.i	−0.323259	−	0.323259i
$695$	−623799.	−	623799.i	−1.29144	−	1.29144i
$696$	−544.081	+	544.081i	−0.00112317	+	0.00112317i
$697$	−241248.	+	241248.i	−0.496589	+	0.496589i
$698$	−255379.			−0.524173
$699$		−	6495.01i		−	0.0132931i
$700$	−54004.2	+	54004.2i	−0.110213	+	0.110213i
$701$			9708.12i			0.0197560i	0.999951	+	0.00987800i	$0.00314432\pi$
$701$			9708.12i			0.0197560i	−0.999951	+	0.00987800i	$0.996856\pi$
$702$	−21896.3	+	65743.6i	−0.0444321	+	0.133407i
$703$	415617.			0.840974
$704$	−51642.1	−	51642.1i	−0.104198	−	0.104198i
$705$	71763.0			0.144385
$706$		−	194608.i		−	0.390437i
$707$	90530.2	+	90530.2i	0.181115	+	0.181115i
$708$	−15131.8	−	15131.8i	−0.0301872	−	0.0301872i
$709$	189439.	−	189439.i	0.376857	−	0.376857i	−0.493110	−	0.869967i	$-0.664140\pi$
$709$	189439.	−	189439.i	0.376857	−	0.376857i	0.869967	+	0.493110i	$0.164140\pi$
$710$	600203.	−	600203.i	1.19064	−	1.19064i
$711$	140353.			0.277641
$712$		−	190552.i		−	0.375884i
$713$	−537734.	+	537734.i	−1.05776	+	1.05776i
$714$		−	6811.31i		−	0.0133609i
$715$	−357179.	−	713913.i	−0.698673	−	1.39647i
$716$	22751.5			0.0443797
$717$	−30712.2	−	30712.2i	−0.0597409	−	0.0597409i
$718$	12008.7			0.0232942
$719$			369870.i			0.715469i	0.933823	+	0.357734i	$0.116451\pi$
$719$			369870.i			0.715469i	−0.933823	+	0.357734i	$0.883549\pi$
$720$	120174.	+	120174.i	0.231817	+	0.231817i
$721$	−32495.8	−	32495.8i	−0.0625110	−	0.0625110i
$722$	166795.	−	166795.i	0.319970	−	0.319970i
$723$	−24150.2	+	24150.2i	−0.0462003	+	0.0462003i
$724$	−305649.			−0.583104
$725$			17830.8i			0.0339230i
$726$	10263.0	−	10263.0i	0.0194716	−	0.0194716i
$727$			6926.71i			0.0131056i	0.999979	+	0.00655282i	$0.00208584\pi$
$727$			6926.71i			0.0131056i	−0.999979	+	0.00655282i	$0.997914\pi$
$728$	69233.3	−	34638.2i	0.130633	−	0.0653572i
$729$	−499866.			−0.940586
$730$	−628102.	−	628102.i	−1.17865	−	1.17865i
$731$	−186454.			−0.348928
$732$			17955.9i			0.0335108i
$733$	−70822.5	−	70822.5i	−0.131815	−	0.131815i	0.638121	−	0.769936i	$-0.279712\pi$
$733$	−70822.5	−	70822.5i	−0.131815	−	0.131815i	−0.769936	+	0.638121i	$0.779712\pi$
$734$	−217685.	−	217685.i	−0.404051	−	0.404051i
$735$	−41931.0	+	41931.0i	−0.0776177	+	0.0776177i
$736$	54842.2	−	54842.2i	0.101242	−	0.101242i
$737$	1.07660e6			1.98206
$738$			585045.i			1.07418i
$739$	−592256.	+	592256.i	−1.08448	+	1.08448i	−0.0883920	+	0.996086i	$0.528173\pi$
$739$	−592256.	+	592256.i	−1.08448	+	1.08448i	−0.996086	+	0.0883920i	$0.971827\pi$
$740$		−	508286.i		−	0.928206i
$741$	−10403.5	+	31236.5i	−0.0189471	+	0.0568886i
$742$	−41364.2			−0.0751306
$743$	47680.1	+	47680.1i	0.0863693	+	0.0863693i	0.748972	−	0.662602i	$-0.230548\pi$
$743$	47680.1	+	47680.1i	0.0863693	+	0.0863693i	−0.662602	+	0.748972i	$0.730548\pi$
$744$	−36119.0			−0.0652514
$745$		−	808432.i		−	1.45657i
$746$	327699.	+	327699.i	0.588840	+	0.588840i
$747$	−171074.	−	171074.i	−0.306579	−	0.306579i
$748$	106729.	−	106729.i	0.190757	−	0.190757i
$749$	182897.	−	182897.i	0.326019	−	0.326019i
$750$	12923.7			0.0229754
$751$		−	763332.i		−	1.35342i	−0.736248	−	0.676711i	$-0.763404\pi$
$751$		−	763332.i		−	1.35342i	0.736248	−	0.676711i	$-0.236596\pi$
$752$	−109049.	+	109049.i	−0.192836	+	0.192836i
$753$			43627.8i			0.0769437i
$754$	5711.19	−	17147.9i	0.0100458	−	0.0301625i
$755$	264567.			0.464132
$756$	−16601.3	−	16601.3i	−0.0290468	−	0.0290468i
$757$	739066.			1.28971			0.644854	−	0.764306i	$-0.276918\pi$
$757$	739066.			1.28971			0.644854	+	0.764306i	$0.276918\pi$
$758$		−	740258.i		−	1.28838i
$759$	38865.3	+	38865.3i	0.0674650	+	0.0674650i
$760$	114771.	+	114771.i	0.198704	+	0.198704i
$761$	−485218.	+	485218.i	−0.837853	+	0.837853i	−0.988576	−	0.150723i	$-0.951840\pi$
$761$	−485218.	+	485218.i	−0.837853	+	0.837853i	0.150723	+	0.988576i	$0.451840\pi$
$762$	48449.3	−	48449.3i	0.0834407	−	0.0834407i
$763$	−54663.3			−0.0938960
$764$			365607.i			0.626366i
$765$	−248365.	+	248365.i	−0.424393	+	0.424393i
$766$		−	210063.i		−	0.358007i
$767$	476909.	+	158837.i	0.810671	+	0.269999i
$768$	3683.69			0.00624541
$769$	−130843.	−	130843.i	−0.221257	−	0.221257i	0.587771	−	0.809028i	$-0.300006\pi$
$769$	−130843.	−	130843.i	−0.221257	−	0.221257i	−0.809028	+	0.587771i	$0.800006\pi$
$770$	270467.			0.456177
$771$		−	17384.1i		−	0.0292444i
$772$	146500.	+	146500.i	0.245811	+	0.245811i
$773$	−109787.	−	109787.i	−0.183734	−	0.183734i	0.609246	−	0.792981i	$-0.291472\pi$
$773$	−109787.	−	109787.i	−0.183734	−	0.183734i	−0.792981	+	0.609246i	$0.791472\pi$
$774$	−226083.	+	226083.i	−0.377386	+	0.377386i
$775$	−591851.	+	591851.i	−0.985391	+	0.985391i
$776$	89984.9			0.149433
$777$			34932.1i			0.0578605i
$778$	357629.	−	357629.i	0.590846	−	0.590846i
$779$			558743.i			0.920741i
$780$	38201.1	+	12723.1i	0.0627895	+	0.0209124i
$781$	−1.29270e6			−2.11932
$782$	113343.	+	113343.i	0.185345	+	0.185345i
$783$	−5481.32			−0.00894050
$784$		−	127435.i		−	0.207327i
$785$	643248.	+	643248.i	1.04385	+	1.04385i
$786$	−1555.16	−	1555.16i	−0.00251727	−	0.00251727i
$787$	−17028.1	+	17028.1i	−0.0274927	+	0.0274927i	−0.720720	−	0.693227i	$-0.756188\pi$
$787$	−17028.1	+	17028.1i	−0.0274927	+	0.0274927i	0.693227	+	0.720720i	$0.256188\pi$
$788$	158726.	−	158726.i	0.255620	−	0.255620i
$789$	62901.0			0.101042
$790$		−	163930.i		−	0.262667i
$791$	305818.	−	305818.i	0.488776	−	0.488776i
$792$		−	258827.i		−	0.412629i
$793$	−188718.	−	377200.i	−0.300100	−	0.599825i
$794$	−706787.			−1.12111
$795$	−15212.6	−	15212.6i	−0.0240697	−	0.0240697i
$796$	−290451.			−0.458403
$797$		−	160080.i		−	0.252012i	−0.992030	−	0.126006i	$-0.959784\pi$
$797$		−	160080.i		−	0.252012i	0.992030	−	0.126006i	$-0.0402158\pi$
$798$	−7887.69	−	7887.69i	−0.0123864	−	0.0123864i
$799$	−225374.	−	225374.i	−0.353028	−	0.353028i
$800$	60361.5	−	60361.5i	0.0943148	−	0.0943148i
$801$	477519.	−	477519.i	0.744262	−	0.744262i
$802$	−448151.			−0.696748
$803$			1.35279e6i			2.09797i
$804$	−38397.4	+	38397.4i	−0.0594005	+	0.0594005i
$805$			287228.i			0.443236i
$806$	758752.	−	379613.i	1.16796	−	0.584347i
$807$	−77768.8			−0.119415
$808$	−101187.	−	101187.i	−0.154990	−	0.154990i
$809$	424616.			0.648782			0.324391	−	0.945923i	$-0.394841\pi$
$809$	424616.			0.648782			0.324391	+	0.945923i	$0.394841\pi$
$810$			596170.i			0.908657i
$811$	368459.	+	368459.i	0.560206	+	0.560206i	0.929366	−	0.369160i	$-0.120354\pi$
$811$	368459.	+	368459.i	0.560206	+	0.560206i	−0.369160	+	0.929366i	$0.620354\pi$
$812$	4330.10	+	4330.10i	0.00656729	+	0.00656729i
$813$	65406.4	−	65406.4i	0.0989553	−	0.0989553i
$814$	−547366.	+	547366.i	−0.826093	+	0.826093i
$815$	227439.			0.342412
$816$			7613.13i			0.0114336i
$817$	−215919.	+	215919.i	−0.323479	+	0.323479i
$818$			183157.i			0.273727i
$819$	260299.	+	86694.2i	0.388066	+	0.129248i
$820$	683324.			1.01625
$821$	567077.	+	567077.i	0.841309	+	0.841309i	0.989029	−	0.147720i	$-0.0471935\pi$
$821$	567077.	+	567077.i	0.841309	+	0.841309i	−0.147720	+	0.989029i	$0.547194\pi$
$822$	66282.2			0.0980964
$823$		−	1.04414e6i		−	1.54156i	−0.637101	−	0.770780i	$-0.719867\pi$
$823$		−	1.04414e6i		−	1.54156i	0.637101	−	0.770780i	$-0.280133\pi$
$824$	36321.1	+	36321.1i	0.0534940	+	0.0534940i
$825$	42776.7	+	42776.7i	0.0628491	+	0.0628491i
$826$	−120427.	+	120427.i	−0.176508	+	0.176508i
$827$	−611298.	+	611298.i	−0.893804	+	0.893804i	−0.994879	−	0.101075i	$-0.967772\pi$
$827$	−611298.	+	611298.i	−0.893804	+	0.893804i	0.101075	+	0.994879i	$0.467772\pi$
$828$	274866.			0.400923
$829$			212198.i			0.308767i	0.988011	+	0.154384i	$0.0493392\pi$
$829$			212198.i			0.308767i	−0.988011	+	0.154384i	$0.950661\pi$
$830$	−199811.	+	199811.i	−0.290044	+	0.290044i
$831$		−	926.422i		−	0.00134155i
$832$	−77383.3	+	38715.8i	−0.111789	+	0.0559296i
$833$	263371.			0.379558
$834$	−47917.4	−	47917.4i	−0.0688909	−	0.0688909i
$835$	1.21287e6			1.73956
$836$		−	247191.i		−	0.353688i
$837$	−181939.	−	181939.i	−0.259702	−	0.259702i
$838$	332008.	+	332008.i	0.472781	+	0.472781i
$839$	565990.	−	565990.i	0.804054	−	0.804054i	−0.179673	−	0.983726i	$-0.557504\pi$
$839$	565990.	−	565990.i	0.804054	−	0.804054i	0.983726	+	0.179673i	$0.0575038\pi$
$840$	−9646.38	+	9646.38i	−0.0136712	+	0.0136712i
$841$	−705851.			−0.997979
$842$			138959.i			0.196003i
$843$	−26012.9	+	26012.9i	−0.0366045	+	0.0366045i
$844$		−	462654.i		−	0.649489i
$845$	−936212.	+	134222.i	−1.31118	+	0.187979i
$846$	−546550.			−0.763641
$847$	−81678.7	−	81678.7i	−0.113852	−	0.113852i
$848$	46233.5			0.0642933
$849$			46392.3i			0.0643622i
$850$	124750.	+	124750.i	0.172664	+	0.172664i
$851$	−581285.	−	581285.i	−0.802657	−	0.802657i
$852$	46104.9	−	46104.9i	0.0635138	−	0.0635138i
$853$	195603.	−	195603.i	0.268829	−	0.268829i	−0.559799	−	0.828628i	$-0.689122\pi$
$853$	195603.	−	195603.i	0.268829	−	0.268829i	0.828628	+	0.559799i	$0.189122\pi$
$854$	142903.			0.195941
$855$			575228.i			0.786879i
$856$	−204427.	+	204427.i	−0.278992	+	0.278992i
$857$		−	1.30446e6i		−	1.77611i	−0.459740	−	0.888053i	$-0.652057\pi$
$857$		−	1.30446e6i		−	1.77611i	0.459740	−	0.888053i	$-0.347943\pi$
$858$	−27436.9	−	54839.6i	−0.0372701	−	0.0744938i
$859$	1.21936e6			1.65251			0.826257	−	0.563293i	$-0.190466\pi$
$859$	1.21936e6			1.65251			0.826257	+	0.563293i	$0.190466\pi$
$860$	264061.	+	264061.i	0.357033	+	0.357033i
$861$	−46961.7			−0.0633486
$862$			746518.i			1.00467i
$863$	−508482.	−	508482.i	−0.682738	−	0.682738i	0.277878	−	0.960616i	$-0.410369\pi$
$863$	−508482.	−	508482.i	−0.682738	−	0.682738i	−0.960616	+	0.277878i	$0.910369\pi$
$864$	18555.6	+	18555.6i	0.0248569	+	0.0248569i
$865$	−615197.	+	615197.i	−0.822209	+	0.822209i
$866$	−117444.	+	117444.i	−0.156601	+	0.156601i
$867$	59379.5			0.0789948
$868$			287455.i			0.381531i
$869$	−176534.	+	176534.i	−0.233771	+	0.233771i
$870$			3184.99i			0.00420794i
$871$	403056.	−	1.21017e6i	0.531286	−	1.59519i
$872$	61098.3			0.0803518
$873$	225500.	+	225500.i	0.295882	+	0.295882i
$874$	262509.			0.343654
$875$		−	102854.i		−	0.134340i
$876$	−48248.0	−	48248.0i	−0.0628740	−	0.0628740i
$877$	−708919.	−	708919.i	−0.921716	−	0.921716i	0.0754343	−	0.997151i	$-0.475966\pi$
$877$	−708919.	−	708919.i	−0.921716	−	0.921716i	−0.997151	+	0.0754343i	$0.975966\pi$
$878$	−463235.	+	463235.i	−0.600914	+	0.600914i
$879$	−448.731	+	448.731i	−0.000580775	+	0.000580775i
$880$	−302307.			−0.390375
$881$		−	899711.i		−	1.15918i	−0.814908	−	0.579591i	$-0.803212\pi$
$881$		−	899711.i		−	1.15918i	0.814908	−	0.579591i	$-0.196788\pi$
$882$	319348.	−	319348.i	0.410514	−	0.410514i
$883$		−	134270.i		−	0.172209i	−0.996286	−	0.0861045i	$-0.972558\pi$
$883$		−	134270.i		−	0.172209i	0.996286	−	0.0861045i	$-0.0274419\pi$
$884$	−80014.5	−	159929.i	−0.102392	−	0.204655i
$885$	−88579.6			−0.113096
$886$	521575.	+	521575.i	0.664430	+	0.664430i
$887$	252983.			0.321546			0.160773	−	0.986991i	$-0.448601\pi$
$887$	252983.			0.321546			0.160773	+	0.986991i	$0.448601\pi$
$888$		−	39044.2i		−	0.0495144i
$889$	−385586.	−	385586.i	−0.487886	−	0.487886i
$890$	−557735.	−	557735.i	−0.704123	−	0.704123i
$891$	642007.	−	642007.i	0.808695	−	0.808695i
$892$	−42598.5	+	42598.5i	−0.0535383	+	0.0535383i
$893$	−521979.			−0.654561
$894$		−	62100.2i		−	0.0776995i
$895$	66592.4	−	66592.4i	0.0831339	−	0.0831339i
$896$		−	29316.8i		−	0.0365175i
$897$	58237.9	−	29137.1i	0.0723804	−	0.0362128i
$898$	5866.24			0.00727456
$899$	47455.1	+	47455.1i	0.0587170	+	0.0587170i
$900$	302529.			0.373492
$901$			95551.5i			0.117703i
$902$	−735863.	−	735863.i	−0.904448	−	0.904448i
$903$	−18147.7	−	18147.7i	−0.0222560	−	0.0222560i
$904$	−341819.	+	341819.i	−0.418272	+	0.418272i
$905$	−894617.	+	894617.i	−1.09229	+	1.09229i
$906$	20322.8			0.0247587
$907$			1.17704e6i			1.43079i	0.698719	+	0.715396i	$0.253754\pi$
$907$			1.17704e6i			1.43079i	−0.698719	+	0.715396i	$0.746246\pi$
$908$	−257680.	+	257680.i	−0.312542	+	0.312542i
$909$		−	507146.i		−	0.613769i
$910$	101258.	−	304026.i	0.122277	−	0.367137i
$911$	−47172.9			−0.0568403			−0.0284201	−	0.999596i	$-0.509048\pi$
$911$	−47172.9			−0.0568403			−0.0284201	+	0.999596i	$0.509048\pi$
$912$	8816.23	+	8816.23i	0.0105997	+	0.0105997i
$913$	430348.			0.516272
$914$		−	701282.i		−	0.839461i
$915$	52555.8	+	52555.8i	0.0627739	+	0.0627739i
$916$	86284.7	+	86284.7i	0.102836	+	0.102836i
$917$	−12376.8	+	12376.8i	−0.0147187	+	0.0147187i
$918$	−38349.1	+	38349.1i	−0.0455061	+	0.0455061i
$919$	−391165.			−0.463158			−0.231579	−	0.972816i	$-0.574389\pi$
$919$	−391165.			−0.463158			−0.231579	+	0.972816i	$0.574389\pi$
$920$		−	321040.i		−	0.379300i
$921$	−84985.6	+	84985.6i	−0.100190	+	0.100190i
$922$			6577.48i			0.00773744i
$923$	−483961.	+	1.45309e6i	−0.568076	+	1.70565i
$924$	20776.1			0.0243344
$925$	−639784.	−	639784.i	−0.747739	−	0.747739i
$926$	22503.3			0.0262437
$927$			182040.i			0.211839i
$928$	−4839.84	−	4839.84i	−0.00561998	−	0.00561998i
$929$	29541.2	+	29541.2i	0.0342292	+	0.0342292i	0.724014	−	0.689785i	$-0.242295\pi$
$929$	29541.2	+	29541.2i	0.0342292	+	0.0342292i	−0.689785	+	0.724014i	$0.742295\pi$
$930$	−105718.	+	105718.i	−0.122232	+	0.122232i
$931$	304991.	−	304991.i	0.351875	−	0.351875i
$932$	57775.9			0.0665143
$933$		−	154837.i		−	0.177873i
$934$	−49913.1	+	49913.1i	−0.0572164	+	0.0572164i
$935$		−	624781.i		−	0.714668i
$936$	−290942.	−	96899.8i	−0.332089	−	0.110604i
$937$	−674412.			−0.768150			−0.384075	−	0.923302i	$-0.625480\pi$
$937$	−674412.			−0.768150			−0.384075	+	0.923302i	$0.625480\pi$
$938$	305588.	+	305588.i	0.347321	+	0.347321i
$939$	4291.55			0.00486725
$940$			638362.i			0.722456i
$941$	791946.	+	791946.i	0.894368	+	0.894368i	0.994931	−	0.100563i	$-0.0320642\pi$
$941$	791946.	+	791946.i	0.894368	+	0.894368i	−0.100563	+	0.994931i	$0.532064\pi$
$942$	49411.5	+	49411.5i	0.0556834	+	0.0556834i
$943$	781462.	−	781462.i	0.878789	−	0.878789i
$944$	134604.	−	134604.i	0.151047	−	0.151047i
$945$	−97182.0			−0.108823
$946$		−	568728.i		−	0.635510i
$947$	−29113.6	+	29113.6i	−0.0324635	+	0.0324635i	−0.723152	−	0.690689i	$-0.757308\pi$
$947$	−29113.6	+	29113.6i	−0.0324635	+	0.0324635i	0.690689	+	0.723152i	$0.257308\pi$
$948$		−	12592.4i		−	0.0140117i
$949$	1.52064e6	+	506457.i	1.68847	+	0.562354i
$950$	288928.			0.320142
$951$	41789.4	+	41789.4i	0.0462067	+	0.0462067i
$952$	60589.5			0.0668534
$953$		−	625479.i		−	0.688695i	−0.938842	−	0.344348i	$-0.888100\pi$
$953$		−	625479.i		−	0.688695i	0.938842	−	0.344348i	$-0.111900\pi$
$954$	115860.	+	115860.i	0.127303	+	0.127303i
$955$	1.07011e6	+	1.07011e6i	1.17334	+	1.17334i
$956$	273198.	−	273198.i	0.298924	−	0.298924i
$957$	3429.87	−	3429.87i	0.00374502	−	0.00374502i
$958$	1.19361e6			1.30057
$959$		−	527510.i		−	0.573580i
$960$	10781.9	−	10781.9i	0.0116992	−	0.0116992i
$961$			2.22680e6i			2.41120i
$962$	410358.	+	820203.i	0.443417	+	0.886280i
$963$	−1.02458e6			−1.10482
$964$	−214826.	−	214826.i	−0.231171	−	0.231171i
$965$	857591.			0.920928
$966$			22063.6i			0.0236440i
$967$	720716.	+	720716.i	0.770746	+	0.770746i	0.978237	−	0.207491i	$-0.0665298\pi$
$967$	720716.	+	720716.i	0.770746	+	0.770746i	−0.207491	+	0.978237i	$0.566530\pi$
$968$	91293.9	+	91293.9i	0.0974296	+	0.0974296i
$969$	−18220.6	+	18220.6i	−0.0194051	+	0.0194051i
$970$	263381.	−	263381.i	0.279924	−	0.279924i
$971$	−395523.			−0.419501			−0.209751	−	0.977755i	$-0.567265\pi$
$971$	−395523.			−0.419501			−0.209751	+	0.977755i	$0.567265\pi$
$972$			139733.i			0.147899i
$973$	−381354.	+	381354.i	−0.402812	+	0.402812i
$974$			236904.i			0.249721i
$975$	64098.9	−	32069.5i	0.0674282	−	0.0337351i
$976$	−159725.			−0.167677
$977$	63841.5	+	63841.5i	0.0668827	+	0.0668827i	0.739757	−	0.672874i	$-0.234940\pi$
$977$	63841.5	+	63841.5i	0.0668827	+	0.0668827i	−0.672874	+	0.739757i	$0.734940\pi$
$978$	17470.8			0.0182657
$979$			1.20124e6i			1.25332i
$980$	−372994.	−	372994.i	−0.388374	−	0.388374i
$981$	153111.	+	153111.i	0.159099	+	0.159099i
$982$	597847.	−	597847.i	0.619965	−	0.619965i
$983$	−282438.	+	282438.i	−0.292291	+	0.292291i	−0.837985	−	0.545694i	$-0.816266\pi$
$983$	−282438.	+	282438.i	−0.292291	+	0.292291i	0.545694	+	0.837985i	$0.316266\pi$
$984$	52490.0			0.0542108
$985$		−	929163.i		−	0.957678i
$986$	10002.5	−	10002.5i	0.0102886	−	0.0102886i
$987$		−	43871.6i		−	0.0450349i
$988$	−277862.	−	92543.4i	−0.284652	−	0.0948051i
$989$	603971.			0.617481
$990$	−757573.	−	757573.i	−0.772955	−	0.772955i
$991$	−651035.			−0.662914			−0.331457	−	0.943470i	$-0.607540\pi$
$991$	−651035.			−0.662914			−0.331457	+	0.943470i	$0.607540\pi$
$992$		−	321294.i		−	0.326497i
$993$	−11121.8	−	11121.8i	−0.0112792	−	0.0112792i
$994$	−366928.	−	366928.i	−0.371372	−	0.371372i
$995$	−850134.	+	850134.i	−0.858700	+	0.858700i
$996$	−15348.6	+	15348.6i	−0.0154722	+	0.0154722i
$997$	−181923.			−0.183020			−0.0915100	−	0.995804i	$-0.529169\pi$
$997$	−181923.			−0.183020			−0.0915100	+	0.995804i	$0.529169\pi$
$998$		−	105655.i		−	0.106079i
$999$	196675.	−	196675.i	0.197069	−	0.197069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.d.b.21.2	yes	6
3.2	odd	2		234.5.i.a.73.1		6
4.3	odd	2		208.5.t.a.177.2		6
13.5	odd	4	inner	26.5.d.b.5.2	✓	6
13.8	odd	4		338.5.d.c.239.2		6
13.12	even	2		338.5.d.c.99.2		6
39.5	even	4		234.5.i.a.109.1		6
52.31	even	4		208.5.t.a.161.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.d.b.5.2	✓	6	13.5	odd	4	inner
26.5.d.b.21.2	yes	6	1.1	even	1	trivial
208.5.t.a.161.2		6	52.31	even	4
208.5.t.a.177.2		6	4.3	odd	2
234.5.i.a.73.1		6	3.2	odd	2
234.5.i.a.109.1		6	39.5	even	4
338.5.d.c.99.2		6	13.12	even	2
338.5.d.c.239.2		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +0.899339 q^{3} +8.00000i q^{4} +(23.4155 + 23.4155i) q^{5} +(1.79868 + 1.79868i) q^{6} +(14.3149 - 14.3149i) q^{7} +(-16.0000 + 16.0000i) q^{8} -80.1912 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +0.899339 q^{3} +8.00000i q^{4} +(23.4155 + 23.4155i) q^{5} +(1.79868 + 1.79868i) q^{6} +(14.3149 - 14.3149i) q^{7} +(-16.0000 + 16.0000i) q^{8} -80.1912 q^{9} +93.6621i q^{10} +(100.863 - 100.863i) q^{11} +7.19471i q^{12} +(-75.6169 - 151.139i) q^{13} +57.2595 q^{14} +(21.0585 + 21.0585i) q^{15} -64.0000 q^{16} -132.270i q^{17} +(-160.382 - 160.382i) q^{18} +(-153.172 - 153.172i) q^{19} +(-187.324 + 187.324i) q^{20} +(12.8739 - 12.8739i) q^{21} +403.454 q^{22} +428.455i q^{23} +(-14.3894 + 14.3894i) q^{24} +471.574i q^{25} +(151.045 - 453.512i) q^{26} -144.965 q^{27} +(114.519 + 114.519i) q^{28} +37.8112 q^{29} +84.2340i q^{30} +(1255.05 + 1255.05i) q^{31} +(-128.000 - 128.000i) q^{32} +(90.7104 - 90.7104i) q^{33} +(264.539 - 264.539i) q^{34} +670.380 q^{35} -641.530i q^{36} +(-1356.70 + 1356.70i) q^{37} -612.688i q^{38} +(-68.0052 - 135.925i) q^{39} -749.297 q^{40} +(-1823.91 - 1823.91i) q^{41} +51.4957 q^{42} -1409.65i q^{43} +(806.908 + 806.908i) q^{44} +(-1877.72 - 1877.72i) q^{45} +(-856.910 + 856.910i) q^{46} +(1703.90 - 1703.90i) q^{47} -57.5577 q^{48} +1991.17i q^{49} +(-943.148 + 943.148i) q^{50} -118.955i q^{51} +(1209.11 - 604.935i) q^{52} -722.399 q^{53} +(-289.931 - 289.931i) q^{54} +4723.54 q^{55} +458.076i q^{56} +(-137.754 - 137.754i) q^{57} +(75.6224 + 75.6224i) q^{58} +(-2103.18 + 2103.18i) q^{59} +(-168.468 + 168.468i) q^{60} +2495.71 q^{61} +5020.21i q^{62} +(-1147.93 + 1147.93i) q^{63} -512.000i q^{64} +(1768.40 - 5309.62i) q^{65} +362.842 q^{66} +(5336.90 + 5336.90i) q^{67} +1058.16 q^{68} +385.326i q^{69} +(1340.76 + 1340.76i) q^{70} +(-6408.17 - 6408.17i) q^{71} +(1283.06 - 1283.06i) q^{72} +(-6706.04 + 6706.04i) q^{73} -5426.80 q^{74} +424.105i q^{75} +(1225.38 - 1225.38i) q^{76} -2887.69i q^{77} +(135.841 - 407.861i) q^{78} -1750.23 q^{79} +(-1498.59 - 1498.59i) q^{80} +6365.11 q^{81} -7295.63i q^{82} +(2133.32 + 2133.32i) q^{83} +(102.991 + 102.991i) q^{84} +(3097.16 - 3097.16i) q^{85} +(2819.30 - 2819.30i) q^{86} +34.0051 q^{87} +3227.63i q^{88} +(-5954.76 + 5954.76i) q^{89} -7510.88i q^{90} +(-3245.98 - 1081.09i) q^{91} -3427.64 q^{92} +(1128.72 + 1128.72i) q^{93} +6815.59 q^{94} -7173.21i q^{95} +(-115.115 - 115.115i) q^{96} +(-2812.03 - 2812.03i) q^{97} +(-3982.34 + 3982.34i) q^{98} +(-8088.36 + 8088.36i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9	\( 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9} - 66 q^{11} - 294 q^{13} - 360 q^{14} - 288 q^{15} - 384 q^{16} + 1116 q^{18} - 318 q^{19} + 240 q^{20} + 756 q^{21} - 264 q^{22} + 84 q^{26} - 1404 q^{27} - 720 q^{28} - 276 q^{29} + 3282 q^{31} - 768 q^{32} - 3240 q^{33} + 2280 q^{34} + 5424 q^{35} - 3006 q^{37} + 2376 q^{39} + 960 q^{40} - 894 q^{41} + 3024 q^{42} - 528 q^{44} - 17226 q^{45} - 4848 q^{46} + 1566 q^{47} - 3300 q^{50} + 2688 q^{52} - 1356 q^{53} - 2808 q^{54} + 22212 q^{55} + 16812 q^{57} - 552 q^{58} + 5178 q^{59} + 2304 q^{60} + 2172 q^{61} - 24210 q^{63} + 1146 q^{65} - 12960 q^{66} + 1134 q^{67} + 9120 q^{68} + 10848 q^{70} - 18498 q^{71} - 8928 q^{72} - 13278 q^{73} - 12024 q^{74} + 2544 q^{76} + 25992 q^{78} - 13596 q^{79} + 1920 q^{80} + 58158 q^{81} - 11490 q^{83} + 6048 q^{84} - 10512 q^{85} - 7128 q^{86} + 30744 q^{87} - 28038 q^{89} - 6402 q^{91} - 19392 q^{92} + 23364 q^{93} + 6264 q^{94} - 27378 q^{97} - 11340 q^{98} - 61074 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9 - 66 * q^11 - 294 * q^13 - 360 * q^14 - 288 * q^15 - 384 * q^16 + 1116 * q^18 - 318 * q^19 + 240 * q^20 + 756 * q^21 - 264 * q^22 + 84 * q^26 - 1404 * q^27 - 720 * q^28 - 276 * q^29 + 3282 * q^31 - 768 * q^32 - 3240 * q^33 + 2280 * q^34 + 5424 * q^35 - 3006 * q^37 + 2376 * q^39 + 960 * q^40 - 894 * q^41 + 3024 * q^42 - 528 * q^44 - 17226 * q^45 - 4848 * q^46 + 1566 * q^47 - 3300 * q^50 + 2688 * q^52 - 1356 * q^53 - 2808 * q^54 + 22212 * q^55 + 16812 * q^57 - 552 * q^58 + 5178 * q^59 + 2304 * q^60 + 2172 * q^61 - 24210 * q^63 + 1146 * q^65 - 12960 * q^66 + 1134 * q^67 + 9120 * q^68 + 10848 * q^70 - 18498 * q^71 - 8928 * q^72 - 13278 * q^73 - 12024 * q^74 + 2544 * q^76 + 25992 * q^78 - 13596 * q^79 + 1920 * q^80 + 58158 * q^81 - 11490 * q^83 + 6048 * q^84 - 10512 * q^85 - 7128 * q^86 + 30744 * q^87 - 28038 * q^89 - 6402 * q^91 - 19392 * q^92 + 23364 * q^93 + 6264 * q^94 - 27378 * q^97 - 11340 * q^98 - 61074 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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