LMFDB - Embedded newform 26.5.d.b.5.1

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			5.1
Root			$16.5864i$ of defining polynomial
Character	$\chi$	$=$	26.5
Dual form			26.5.d.b.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 2.00000i) q^{2} -16.5864 q^{3} -8.00000i q^{4} +(-13.5581 + 13.5581i) q^{5} +(-33.1728 + 33.1728i) q^{6} +(-40.1445 - 40.1445i) q^{7} +(-16.0000 - 16.0000i) q^{8} +194.108 q^{9} +O(q^{10})$	\(q+(2.00000 - 2.00000i) q^{2} -16.5864 q^{3} -8.00000i q^{4} +(-13.5581 + 13.5581i) q^{5} +(-33.1728 + 33.1728i) q^{6} +(-40.1445 - 40.1445i) q^{7} +(-16.0000 - 16.0000i) q^{8} +194.108 q^{9} +54.2326i q^{10} +(-12.0598 - 12.0598i) q^{11} +132.691i q^{12} +(-73.6146 - 152.125i) q^{13} -160.578 q^{14} +(224.880 - 224.880i) q^{15} -64.0000 q^{16} +223.703i q^{17} +(388.216 - 388.216i) q^{18} +(-267.563 + 267.563i) q^{19} +(108.465 + 108.465i) q^{20} +(665.852 + 665.852i) q^{21} -48.2392 q^{22} -983.993i q^{23} +(265.382 + 265.382i) q^{24} +257.354i q^{25} +(-451.478 - 157.020i) q^{26} -1876.05 q^{27} +(-321.156 + 321.156i) q^{28} -560.708 q^{29} -899.522i q^{30} +(-139.400 + 139.400i) q^{31} +(-128.000 + 128.000i) q^{32} +(200.028 + 200.028i) q^{33} +(447.405 + 447.405i) q^{34} +1088.57 q^{35} -1552.86i q^{36} +(-700.116 - 700.116i) q^{37} +1070.25i q^{38} +(1221.00 + 2523.20i) q^{39} +433.860 q^{40} +(1872.79 - 1872.79i) q^{41} +2663.41 q^{42} -430.626i q^{43} +(-96.4783 + 96.4783i) q^{44} +(-2631.74 + 2631.74i) q^{45} +(-1967.99 - 1967.99i) q^{46} +(-59.3604 - 59.3604i) q^{47} +1061.53 q^{48} +822.164i q^{49} +(514.708 + 514.708i) q^{50} -3710.42i q^{51} +(-1217.00 + 588.917i) q^{52} +3773.97 q^{53} +(-3752.10 + 3752.10i) q^{54} +327.017 q^{55} +1284.62i q^{56} +(4437.90 - 4437.90i) q^{57} +(-1121.42 + 1121.42i) q^{58} +(924.257 + 924.257i) q^{59} +(-1799.04 - 1799.04i) q^{60} -3935.30 q^{61} +557.601i q^{62} +(-7792.37 - 7792.37i) q^{63} +512.000i q^{64} +(3060.60 + 1064.45i) q^{65} +800.113 q^{66} +(-2992.99 + 2992.99i) q^{67} +1789.62 q^{68} +16320.9i q^{69} +(2177.14 - 2177.14i) q^{70} +(-9.46035 + 9.46035i) q^{71} +(-3105.73 - 3105.73i) q^{72} +(-4922.36 - 4922.36i) q^{73} -2800.47 q^{74} -4268.57i q^{75} +(2140.51 + 2140.51i) q^{76} +968.269i q^{77} +(7488.39 + 2604.39i) q^{78} +1624.91 q^{79} +(867.721 - 867.721i) q^{80} +15394.2 q^{81} -7491.16i q^{82} +(-4406.88 + 4406.88i) q^{83} +(5326.82 - 5326.82i) q^{84} +(-3032.99 - 3032.99i) q^{85} +(-861.252 - 861.252i) q^{86} +9300.11 q^{87} +385.913i q^{88} +(-3715.92 - 3715.92i) q^{89} +10527.0i q^{90} +(-3151.74 + 9062.19i) q^{91} -7871.95 q^{92} +(2312.15 - 2312.15i) q^{93} -237.441 q^{94} -7255.32i q^{95} +(2123.06 - 2123.06i) q^{96} +(-4894.57 + 4894.57i) q^{97} +(1644.33 + 1644.33i) q^{98} +(-2340.90 - 2340.90i) 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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$	−16.5864			−1.84293			−0.921465	−	0.388460i	$-0.873007\pi$
$3$	−16.5864			−1.84293			−0.921465	+	0.388460i	$0.873007\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−13.5581	+	13.5581i	−0.542326	+	0.542326i	−0.924210	−	0.381885i	$-0.875275\pi$
$5$	−13.5581	+	13.5581i	−0.542326	+	0.542326i	0.381885	+	0.924210i	$0.375275\pi$
$6$	−33.1728	+	33.1728i	−0.921465	+	0.921465i
$7$	−40.1445	−	40.1445i	−0.819276	−	0.819276i	0.166727	−	0.986003i	$-0.446680\pi$
$7$	−40.1445	−	40.1445i	−0.819276	−	0.819276i	−0.986003	+	0.166727i	$0.946680\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	194.108			2.39639
$10$			54.2326i			0.542326i
$11$	−12.0598	−	12.0598i	−0.0996677	−	0.0996677i	0.655515	−	0.755182i	$-0.272452\pi$
$11$	−12.0598	−	12.0598i	−0.0996677	−	0.0996677i	−0.755182	+	0.655515i	$0.772452\pi$
$12$			132.691i			0.921465i
$13$	−73.6146	−	152.125i	−0.435589	−	0.900145i
$13$	−73.6146	−	152.125i	−0.435589	−	0.900145i
$14$	−160.578			−0.819276
$15$	224.880	−	224.880i	0.999468	−	0.999468i
$16$	−64.0000			−0.250000
$17$			223.703i			0.774058i	0.922068	+	0.387029i	$0.126499\pi$
$17$			223.703i			0.774058i	−0.922068	+	0.387029i	$0.873501\pi$
$18$	388.216	−	388.216i	1.19820	−	1.19820i
$19$	−267.563	+	267.563i	−0.741172	+	0.741172i	−0.972804	−	0.231631i	$-0.925594\pi$
$19$	−267.563	+	267.563i	−0.741172	+	0.741172i	0.231631	+	0.972804i	$0.425594\pi$
$20$	108.465	+	108.465i	0.271163	+	0.271163i
$21$	665.852	+	665.852i	1.50987	+	1.50987i
$22$	−48.2392			−0.0996677
$23$		−	983.993i		−	1.86010i	−0.367432	−	0.930050i	$-0.619763\pi$
$23$		−	983.993i		−	1.86010i	0.367432	−	0.930050i	$-0.380237\pi$
$24$	265.382	+	265.382i	0.460733	+	0.460733i
$25$			257.354i			0.411766i
$26$	−451.478	−	157.020i	−0.667867	−	0.232278i
$27$	−1876.05			−2.57346
$28$	−321.156	+	321.156i	−0.409638	+	0.409638i
$29$	−560.708			−0.666715			−0.333358	−	0.942800i	$-0.608182\pi$
$29$	−560.708			−0.666715			−0.333358	+	0.942800i	$0.608182\pi$
$30$		−	899.522i		−	0.999468i
$31$	−139.400	+	139.400i	−0.145058	+	0.145058i	−0.775906	−	0.630849i	$-0.782707\pi$
$31$	−139.400	+	139.400i	−0.145058	+	0.145058i	0.630849	+	0.775906i	$0.282707\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	200.028	+	200.028i	0.183681	+	0.183681i
$34$	447.405	+	447.405i	0.387029	+	0.387029i
$35$	1088.57			0.888628
$36$		−	1552.86i		−	1.19820i
$37$	−700.116	−	700.116i	−0.511407	−	0.511407i	0.403550	−	0.914957i	$-0.367776\pi$
$37$	−700.116	−	700.116i	−0.511407	−	0.511407i	−0.914957	+	0.403550i	$0.867776\pi$
$38$			1070.25i			0.741172i
$39$	1221.00	+	2523.20i	0.802761	+	1.65891i
$40$	433.860			0.271163
$41$	1872.79	−	1872.79i	1.11409	−	1.11409i	0.121501	−	0.992591i	$-0.461229\pi$
$41$	1872.79	−	1872.79i	1.11409	−	1.11409i	0.992591	−	0.121501i	$-0.0387707\pi$
$42$	2663.41			1.50987
$43$		−	430.626i		−	0.232897i	−0.993197	−	0.116448i	$-0.962849\pi$
$43$		−	430.626i		−	0.232897i	0.993197	−	0.116448i	$-0.0371510\pi$
$44$	−96.4783	+	96.4783i	−0.0498339	+	0.0498339i
$45$	−2631.74	+	2631.74i	−1.29963	+	1.29963i
$46$	−1967.99	−	1967.99i	−0.930050	−	0.930050i
$47$	−59.3604	−	59.3604i	−0.0268721	−	0.0268721i	0.693543	−	0.720415i	$-0.256049\pi$
$47$	−59.3604	−	59.3604i	−0.0268721	−	0.0268721i	−0.720415	+	0.693543i	$0.756049\pi$
$48$	1061.53			0.460733
$49$			822.164i			0.342426i
$50$	514.708	+	514.708i	0.205883	+	0.205883i
$51$		−	3710.42i		−	1.42653i
$52$	−1217.00	+	588.917i	−0.450073	+	0.217795i
$53$	3773.97			1.34353			0.671763	−	0.740766i	$-0.265537\pi$
$53$	3773.97			1.34353			0.671763	+	0.740766i	$0.265537\pi$
$54$	−3752.10	+	3752.10i	−1.28673	+	1.28673i
$55$	327.017			0.108105
$56$			1284.62i			0.409638i
$57$	4437.90	−	4437.90i	1.36593	−	1.36593i
$58$	−1121.42	+	1121.42i	−0.333358	+	0.333358i
$59$	924.257	+	924.257i	0.265515	+	0.265515i	0.827290	−	0.561775i	$-0.189881\pi$
$59$	924.257	+	924.257i	0.265515	+	0.265515i	−0.561775	+	0.827290i	$0.689881\pi$
$60$	−1799.04	−	1799.04i	−0.499734	−	0.499734i
$61$	−3935.30			−1.05759			−0.528796	−	0.848749i	$-0.677356\pi$
$61$	−3935.30			−1.05759			−0.528796	+	0.848749i	$0.677356\pi$
$62$			557.601i			0.145058i
$63$	−7792.37	−	7792.37i	−1.96331	−	1.96331i
$64$			512.000i			0.125000i
$65$	3060.60	+	1064.45i	0.724403	+	0.251941i
$66$	800.113			0.183681
$67$	−2992.99	+	2992.99i	−0.666738	+	0.666738i	−0.956959	−	0.290222i	$-0.906271\pi$
$67$	−2992.99	+	2992.99i	−0.666738	+	0.666738i	0.290222	+	0.956959i	$0.406271\pi$
$68$	1789.62			0.387029
$69$			16320.9i			3.42804i
$70$	2177.14	−	2177.14i	0.444314	−	0.444314i
$71$	−9.46035	+	9.46035i	−0.00187668	+	0.00187668i	−0.708044	−	0.706168i	$-0.750422\pi$
$71$	−9.46035	+	9.46035i	−0.00187668	+	0.00187668i	0.706168	+	0.708044i	$0.250422\pi$
$72$	−3105.73	−	3105.73i	−0.599099	−	0.599099i
$73$	−4922.36	−	4922.36i	−0.923693	−	0.923693i	0.0735956	−	0.997288i	$-0.476553\pi$
$73$	−4922.36	−	4922.36i	−0.923693	−	0.923693i	−0.997288	+	0.0735956i	$0.976553\pi$
$74$	−2800.47			−0.511407
$75$		−	4268.57i		−	0.758856i
$76$	2140.51	+	2140.51i	0.370586	+	0.370586i
$77$			968.269i			0.163311i
$78$	7488.39	+	2604.39i	1.23083	+	0.428072i
$79$	1624.91			0.260361			0.130180	−	0.991490i	$-0.458444\pi$
$79$	1624.91			0.260361			0.130180	+	0.991490i	$0.458444\pi$
$80$	867.721	−	867.721i	0.135581	−	0.135581i
$81$	15394.2			2.34631
$82$		−	7491.16i		−	1.11409i
$83$	−4406.88	+	4406.88i	−0.639698	+	0.639698i	−0.950481	−	0.310783i	$-0.899409\pi$
$83$	−4406.88	+	4406.88i	−0.639698	+	0.639698i	0.310783	+	0.950481i	$0.399409\pi$
$84$	5326.82	−	5326.82i	0.754934	−	0.754934i
$85$	−3032.99	−	3032.99i	−0.419791	−	0.419791i
$86$	−861.252	−	861.252i	−0.116448	−	0.116448i
$87$	9300.11			1.22871
$88$			385.913i			0.0498339i
$89$	−3715.92	−	3715.92i	−0.469122	−	0.469122i	0.432508	−	0.901630i	$-0.357629\pi$
$89$	−3715.92	−	3715.92i	−0.469122	−	0.469122i	−0.901630	+	0.432508i	$0.857629\pi$
$90$			10527.0i			1.29963i
$91$	−3151.74	+	9062.19i	−0.380599	+	1.09434i
$92$	−7871.95			−0.930050
$93$	2312.15	−	2312.15i	0.267331	−	0.267331i
$94$	−237.441			−0.0268721
$95$		−	7255.32i		−	0.803913i
$96$	2123.06	−	2123.06i	0.230366	−	0.230366i
$97$	−4894.57	+	4894.57i	−0.520201	+	0.520201i	−0.917632	−	0.397431i	$-0.869902\pi$
$97$	−4894.57	+	4894.57i	−0.520201	+	0.520201i	0.397431	+	0.917632i	$0.369902\pi$
$98$	1644.33	+	1644.33i	0.171213	+	0.171213i
$99$	−2340.90	−	2340.90i	−0.238843	−	0.238843i
$100$	2058.83			0.205883
$101$		−	1445.28i		−	0.141681i	−0.997488	−	0.0708403i	$-0.977432\pi$
$101$		−	1445.28i		−	0.141681i	0.997488	−	0.0708403i	$-0.0225681\pi$
$102$	−7420.83	−	7420.83i	−0.713267	−	0.713267i
$103$			4448.97i			0.419358i	0.977770	+	0.209679i	$0.0672420\pi$
$103$			4448.97i			0.419358i	−0.977770	+	0.209679i	$0.932758\pi$
$104$	−1256.16	+	3611.83i	−0.116139	+	0.333934i
$105$	−18055.4			−1.63768
$106$	7547.93	−	7547.93i	0.671763	−	0.671763i
$107$	8104.41			0.707870			0.353935	−	0.935270i	$-0.384843\pi$
$107$	8104.41			0.707870			0.353935	+	0.935270i	$0.384843\pi$
$108$			15008.4i			1.28673i
$109$	−2675.08	+	2675.08i	−0.225156	+	0.225156i	−0.810666	−	0.585509i	$-0.800895\pi$
$109$	−2675.08	+	2675.08i	−0.225156	+	0.225156i	0.585509	+	0.810666i	$0.300895\pi$
$110$	654.033	−	654.033i	0.0540523	−	0.0540523i
$111$	11612.4	+	11612.4i	0.942488	+	0.942488i
$112$	2569.25	+	2569.25i	0.204819	+	0.204819i
$113$	−3008.25			−0.235590			−0.117795	−	0.993038i	$-0.537583\pi$
$113$	−3008.25			−0.235590			−0.117795	+	0.993038i	$0.537583\pi$
$114$		−	17751.6i		−	1.36593i
$115$	13341.1	+	13341.1i	1.00878	+	1.00878i
$116$			4485.66i			0.333358i
$117$	−14289.2	−	29528.6i	−1.04384	−	2.15710i
$118$	3697.03			0.265515
$119$	8980.43	−	8980.43i	0.634167	−	0.634167i
$120$	−7196.17			−0.499734
$121$		−	14350.1i		−	0.980133i
$122$	−7870.60	+	7870.60i	−0.528796	+	0.528796i
$123$	−31062.8	+	31062.8i	−2.05319	+	2.05319i
$124$	1115.20	+	1115.20i	0.0725288	+	0.0725288i
$125$	−11963.1	−	11963.1i	−0.765637	−	0.765637i
$126$	−31169.5			−1.96331
$127$		−	3624.98i		−	0.224749i	−0.993666	−	0.112374i	$-0.964154\pi$
$127$		−	3624.98i		−	0.224749i	0.993666	−	0.112374i	$-0.0358456\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$			7142.53i			0.429213i
$130$	8250.10	−	3992.31i	0.488172	−	0.236231i
$131$	4428.23			0.258040			0.129020	−	0.991642i	$-0.458817\pi$
$131$	4428.23			0.258040			0.129020	+	0.991642i	$0.458817\pi$
$132$	1600.23	−	1600.23i	0.0918404	−	0.0918404i
$133$	21482.4			1.21445
$134$			11971.9i			0.666738i
$135$	25435.8	−	25435.8i	1.39565	−	1.39565i
$136$	3579.24	−	3579.24i	0.193514	−	0.193514i
$137$	977.708	+	977.708i	0.0520916	+	0.0520916i	0.732673	−	0.680581i	$-0.238273\pi$
$137$	977.708	+	977.708i	0.0520916	+	0.0520916i	−0.680581	+	0.732673i	$0.738273\pi$
$138$	32641.8	+	32641.8i	1.71402	+	1.71402i
$139$	36138.6			1.87043			0.935216	−	0.354079i	$-0.115206\pi$
$139$	36138.6			1.87043			0.935216	+	0.354079i	$0.115206\pi$
$140$		−	8708.56i		−	0.444314i
$141$	984.573	+	984.573i	0.0495233	+	0.0495233i
$142$			37.8414i			0.00187668i
$143$	−946.814	+	2722.37i	−0.0463012	+	0.133130i
$144$	−12422.9			−0.599099
$145$	7602.15	−	7602.15i	0.361577	−	0.361577i
$146$	−19689.4			−0.923693
$147$		−	13636.7i		−	0.631067i
$148$	−5600.93	+	5600.93i	−0.255704	+	0.255704i
$149$	12263.5	−	12263.5i	0.552383	−	0.552383i	−0.374745	−	0.927128i	$-0.622270\pi$
$149$	12263.5	−	12263.5i	0.552383	−	0.552383i	0.927128	+	0.374745i	$0.122270\pi$
$150$	−8537.14	−	8537.14i	−0.379428	−	0.379428i
$151$	15818.3	+	15818.3i	0.693756	+	0.693756i	0.963056	−	0.269300i	$-0.0867924\pi$
$151$	15818.3	+	15818.3i	0.693756	+	0.693756i	−0.269300	+	0.963056i	$0.586792\pi$
$152$	8562.02			0.370586
$153$			43422.5i			1.85495i
$154$	1936.54	+	1936.54i	0.0816553	+	0.0816553i
$155$		−	3780.02i		−	0.157337i
$156$	20185.6	−	9768.00i	0.829453	−	0.401381i
$157$	17629.6			0.715225			0.357612	−	0.933870i	$-0.383591\pi$
$157$	17629.6			0.715225			0.357612	+	0.933870i	$0.383591\pi$
$158$	3249.82	−	3249.82i	0.130180	−	0.130180i
$159$	−62596.4			−2.47603
$160$		−	3470.88i		−	0.135581i
$161$	−39501.9	+	39501.9i	−1.52394	+	1.52394i
$162$	30788.3	−	30788.3i	1.17316	−	1.17316i
$163$	−34964.7	−	34964.7i	−1.31600	−	1.31600i	−0.916916	−	0.399080i	$-0.869330\pi$
$163$	−34964.7	−	34964.7i	−1.31600	−	1.31600i	−0.399080	−	0.916916i	$-0.630670\pi$
$164$	−14982.3	−	14982.3i	−0.557046	−	0.557046i
$165$	−5424.02			−0.199229
$166$			17627.5i			0.639698i
$167$	−3546.29	−	3546.29i	−0.127157	−	0.127157i	0.640664	−	0.767821i	$-0.278659\pi$
$167$	−3546.29	−	3546.29i	−0.127157	−	0.127157i	−0.767821	+	0.640664i	$0.778659\pi$
$168$		−	21307.3i		−	0.754934i
$169$	−17722.8	+	22397.2i	−0.620524	+	0.784188i
$170$	−12132.0			−0.419791
$171$	−51936.1	+	51936.1i	−1.77614	+	1.77614i
$172$	−3445.01			−0.116448
$173$		−	38615.8i		−	1.29025i	−0.764078	−	0.645124i	$-0.776806\pi$
$173$		−	38615.8i		−	1.29025i	0.764078	−	0.645124i	$-0.223194\pi$
$174$	18600.2	−	18600.2i	0.614355	−	0.614355i
$175$	10331.3	−	10331.3i	0.337350	−	0.337350i
$176$	771.827	+	771.827i	0.0249169	+	0.0249169i
$177$	−15330.1	−	15330.1i	−0.489326	−	0.489326i
$178$	−14863.7			−0.469122
$179$			4373.46i			0.136496i	0.997668	+	0.0682479i	$0.0217409\pi$
$179$			4373.46i			0.136496i	−0.997668	+	0.0682479i	$0.978259\pi$
$180$	21053.9	+	21053.9i	0.649813	+	0.649813i
$181$		−	25076.9i		−	0.765450i	−0.923862	−	0.382725i	$-0.874986\pi$
$181$		−	25076.9i		−	0.765450i	0.923862	−	0.382725i	$-0.125014\pi$
$182$	11820.9	+	24427.9i	0.356868	+	0.737467i
$183$	65272.4			1.94907
$184$	−15743.9	+	15743.9i	−0.465025	+	0.465025i
$185$	18984.5			0.554698
$186$		−	9248.58i		−	0.267331i
$187$	2697.81	−	2697.81i	0.0771485	−	0.0771485i
$188$	−474.883	+	474.883i	−0.0134360	+	0.0134360i
$189$	75313.2	+	75313.2i	2.10837	+	2.10837i
$190$	−14510.6	−	14510.6i	−0.401957	−	0.401957i
$191$	7846.01			0.215071			0.107536	−	0.994201i	$-0.465704\pi$
$191$	7846.01			0.215071			0.107536	+	0.994201i	$0.465704\pi$
$192$		−	8492.23i		−	0.230366i
$193$	−26725.4	−	26725.4i	−0.717481	−	0.717481i	0.250608	−	0.968089i	$-0.419370\pi$
$193$	−26725.4	−	26725.4i	−0.717481	−	0.717481i	−0.968089	+	0.250608i	$0.919370\pi$
$194$			19578.3i			0.520201i
$195$	−50764.3	−	17655.4i	−1.33502	−	0.464309i
$196$	6577.32			0.171213
$197$	−6777.04	+	6777.04i	−0.174626	+	0.174626i	−0.789008	−	0.614383i	$-0.789405\pi$
$197$	−6777.04	+	6777.04i	−0.174626	+	0.174626i	0.614383	+	0.789008i	$0.289405\pi$
$198$	−9363.61			−0.238843
$199$			61087.0i			1.54256i	0.636495	+	0.771281i	$0.280384\pi$
$199$			61087.0i			1.54256i	−0.636495	+	0.771281i	$0.719616\pi$
$200$	4117.66	−	4117.66i	0.102942	−	0.102942i
$201$	49642.8	−	49642.8i	1.22875	−	1.22875i
$202$	−2890.57	−	2890.57i	−0.0708403	−	0.0708403i
$203$	22509.3	+	22509.3i	0.546224	+	0.546224i
$204$	−29683.3			−0.713267
$205$			50783.1i			1.20840i
$206$	8897.95	+	8897.95i	0.209679	+	0.209679i
$207$		−	191001.i		−	4.45754i
$208$	4711.34	+	9735.97i	0.108897	+	0.225036i
$209$	6453.51			0.147742
$210$	−36110.9	+	36110.9i	−0.818840	+	0.818840i
$211$	−76793.1			−1.72487			−0.862436	−	0.506165i	$-0.831063\pi$
$211$	−76793.1			−1.72487			−0.862436	+	0.506165i	$0.831063\pi$
$212$		−	30191.7i		−	0.671763i
$213$	156.913	−	156.913i	0.00345859	−	0.00345859i
$214$	16208.8	−	16208.8i	0.353935	−	0.353935i
$215$	5838.49	+	5838.49i	0.126306	+	0.126306i
$216$	30016.8	+	30016.8i	0.643365	+	0.643365i
$217$	11192.3			0.237684
$218$			10700.3i			0.225156i
$219$	81644.1	+	81644.1i	1.70230	+	1.70230i
$220$		−	2616.13i		−	0.0540523i
$221$	34030.7	−	16467.8i	0.696764	−	0.337171i
$222$	46449.6			0.942488
$223$	52857.4	−	52857.4i	1.06291	−	1.06291i	0.0650260	−	0.997884i	$-0.479287\pi$
$223$	52857.4	−	52857.4i	1.06291	−	1.06291i	0.997884	−	0.0650260i	$-0.0207130\pi$
$224$	10277.0			0.204819
$225$			49954.4i			0.986754i
$226$	−6016.51	+	6016.51i	−0.117795	+	0.117795i
$227$	−32344.8	+	32344.8i	−0.627700	+	0.627700i	−0.947489	−	0.319788i	$-0.896388\pi$
$227$	−32344.8	+	32344.8i	−0.627700	+	0.627700i	0.319788	+	0.947489i	$0.396388\pi$
$228$	−35503.2	−	35503.2i	−0.682965	−	0.682965i
$229$	−49809.4	−	49809.4i	−0.949818	−	0.949818i	0.0489817	−	0.998800i	$-0.484402\pi$
$229$	−49809.4	−	49809.4i	−0.949818	−	0.949818i	−0.998800	+	0.0489817i	$0.984402\pi$
$230$	53364.5			1.00878
$231$		−	16060.1i		−	0.300970i
$232$	8971.32	+	8971.32i	0.166679	+	0.166679i
$233$			72869.4i			1.34225i	0.741345	+	0.671124i	$0.234188\pi$
$233$			72869.4i			1.34225i	−0.741345	+	0.671124i	$0.765812\pi$
$234$	−87635.6	−	30478.8i	−1.60047	−	0.556630i
$235$	1609.63			0.0291468
$236$	7394.06	−	7394.06i	0.132757	−	0.132757i
$237$	−26951.4			−0.479827
$238$		−	35921.7i		−	0.634167i
$239$	−14223.7	+	14223.7i	−0.249010	+	0.249010i	−0.820564	−	0.571554i	$-0.806341\pi$
$239$	−14223.7	+	14223.7i	−0.249010	+	0.249010i	0.571554	+	0.820564i	$0.306341\pi$
$240$	−14392.3	+	14392.3i	−0.249867	+	0.249867i
$241$	−42338.8	−	42338.8i	−0.728962	−	0.728962i	0.241451	−	0.970413i	$-0.422377\pi$
$241$	−42338.8	−	42338.8i	−0.728962	−	0.728962i	−0.970413	+	0.241451i	$0.922377\pi$
$242$	−28700.2	−	28700.2i	−0.490066	−	0.490066i
$243$	−103373.			−1.75063
$244$			31482.4i			0.528796i
$245$	−11147.0	−	11147.0i	−0.185706	−	0.185706i
$246$			124251.i			2.05319i
$247$	60399.5	+	21006.4i	0.990009	+	0.344316i
$248$	4460.81			0.0725288
$249$	73094.1	−	73094.1i	1.17892	−	1.17892i
$250$	−47852.3			−0.765637
$251$		−	114161.i		−	1.81206i	−0.423216	−	0.906029i	$-0.639099\pi$
$251$		−	114161.i		−	1.81206i	0.423216	−	0.906029i	$-0.360901\pi$
$252$	−62339.0	+	62339.0i	−0.981654	+	0.981654i
$253$	−11866.8	+	11866.8i	−0.185392	+	0.185392i
$254$	−7249.95	−	7249.95i	−0.112374	−	0.112374i
$255$	50306.3	+	50306.3i	0.773646	+	0.773646i
$256$	4096.00			0.0625000
$257$			28776.5i			0.435685i	0.975984	+	0.217842i	$0.0699018\pi$
$257$			28776.5i			0.435685i	−0.975984	+	0.217842i	$0.930098\pi$
$258$	14285.1	+	14285.1i	0.214606	+	0.214606i
$259$			56211.7i			0.837967i
$260$	8515.59	−	24484.8i	0.125970	−	0.362202i
$261$	−108838.			−1.59771
$262$	8856.46	−	8856.46i	0.129020	−	0.129020i
$263$	−41981.1			−0.606936			−0.303468	−	0.952842i	$-0.598144\pi$
$263$	−41981.1			−0.606936			−0.303468	+	0.952842i	$0.598144\pi$
$264$		−	6400.91i		−	0.0918404i
$265$	−51168.0	+	51168.0i	−0.728629	+	0.728629i
$266$	42964.8	−	42964.8i	0.607224	−	0.607224i
$267$	61633.6	+	61633.6i	0.864560	+	0.864560i
$268$	23943.9	+	23943.9i	0.333369	+	0.333369i
$269$	87860.2			1.21419			0.607096	−	0.794628i	$-0.292334\pi$
$269$	87860.2			1.21419			0.607096	+	0.794628i	$0.292334\pi$
$270$		−	101743.i		−	1.39565i
$271$	−59053.1	−	59053.1i	−0.804088	−	0.804088i	0.179643	−	0.983732i	$-0.442506\pi$
$271$	−59053.1	−	59053.1i	−0.804088	−	0.804088i	−0.983732	+	0.179643i	$0.942506\pi$
$272$		−	14317.0i		−	0.193514i
$273$	52276.0	−	150309.i	0.701419	−	2.01678i
$274$	3910.83			0.0520916
$275$	3103.63	−	3103.63i	0.0410398	−	0.0410398i
$276$	130567.			1.71402
$277$			59016.9i			0.769160i	0.923092	+	0.384580i	$0.125654\pi$
$277$			59016.9i			0.769160i	−0.923092	+	0.384580i	$0.874346\pi$
$278$	72277.2	−	72277.2i	0.935216	−	0.935216i
$279$	−27058.7	+	27058.7i	−0.347615	+	0.347615i
$280$	−17417.1	−	17417.1i	−0.222157	−	0.222157i
$281$	73210.7	+	73210.7i	0.927175	+	0.927175i	0.997523	−	0.0703472i	$-0.0224107\pi$
$281$	73210.7	+	73210.7i	0.927175	+	0.927175i	−0.0703472	+	0.997523i	$0.522411\pi$
$282$	3938.29			0.0495233
$283$		−	40778.4i		−	0.509164i	−0.967051	−	0.254582i	$-0.918062\pi$
$283$		−	40778.4i		−	0.509164i	0.967051	−	0.254582i	$-0.0819379\pi$
$284$	75.6828	+	75.6828i	0.000938340	+	0.000938340i
$285$			120339.i			1.48156i
$286$	3551.11	+	7338.36i	0.0434142	+	0.0897154i
$287$	−150364.			−1.82550
$288$	−24845.8	+	24845.8i	−0.299549	+	0.299549i
$289$	33478.1			0.400835
$290$		−	30408.6i		−	0.361577i
$291$	81183.2	−	81183.2i	0.958694	−	0.958694i
$292$	−39378.9	+	39378.9i	−0.461846	+	0.461846i
$293$	41000.3	+	41000.3i	0.477586	+	0.477586i	0.904359	−	0.426773i	$-0.140350\pi$
$293$	41000.3	+	41000.3i	0.477586	+	0.477586i	−0.426773	+	0.904359i	$0.640350\pi$
$294$	−27273.5	−	27273.5i	−0.315534	−	0.315534i
$295$	−25062.4			−0.287991
$296$			22403.7i			0.255704i
$297$	22624.8	+	22624.8i	0.256491	+	0.256491i
$298$		−	49053.9i		−	0.552383i
$299$	−149690.	+	72436.3i	−1.67436	+	0.810240i
$300$	−34148.5			−0.379428
$301$	−17287.3	+	17287.3i	−0.190807	+	0.190807i
$302$	63273.3			0.693756
$303$			23972.0i			0.261107i
$304$	17124.0	−	17124.0i	0.185293	−	0.185293i
$305$	53355.4	−	53355.4i	0.573559	−	0.573559i
$306$	86844.9	+	86844.9i	0.927474	+	0.927474i
$307$	3442.87	+	3442.87i	0.0365295	+	0.0365295i	0.725136	−	0.688606i	$-0.241777\pi$
$307$	3442.87	+	3442.87i	0.0365295	+	0.0365295i	−0.688606	+	0.725136i	$0.741777\pi$
$308$	7746.15			0.0816553
$309$		−	73792.4i		−	0.772849i
$310$	−7560.03	−	7560.03i	−0.0786684	−	0.0786684i
$311$			4606.97i			0.0476316i	0.999716	+	0.0238158i	$0.00758151\pi$
$311$			4606.97i			0.0476316i	−0.999716	+	0.0238158i	$0.992418\pi$
$312$	20835.1	−	59907.1i	0.214036	−	0.615417i
$313$	120038.			1.22527			0.612633	−	0.790368i	$-0.290111\pi$
$313$	120038.			1.22527			0.612633	+	0.790368i	$0.290111\pi$
$314$	35259.1	−	35259.1i	0.357612	−	0.357612i
$315$	211300.			2.12950
$316$		−	12999.3i		−	0.130180i
$317$	−87032.2	+	87032.2i	−0.866087	+	0.866087i	−0.992037	−	0.125950i	$-0.959802\pi$
$317$	−87032.2	+	87032.2i	−0.866087	+	0.866087i	0.125950	+	0.992037i	$0.459802\pi$
$318$	−125193.	+	125193.i	−1.23801	+	1.23801i
$319$	6762.02	+	6762.02i	0.0664500	+	0.0664500i
$320$	−6941.77	−	6941.77i	−0.0677907	−	0.0677907i
$321$	−134423.			−1.30456
$322$			158008.i			1.52394i
$323$	−59854.6	−	59854.6i	−0.573710	−	0.573710i
$324$		−	123153.i		−	1.17316i
$325$	39149.8	−	18945.0i	0.370649	−	0.179361i
$326$	−139859.			−1.31600
$327$	44369.9	−	44369.9i	0.414947	−	0.414947i
$328$	−59929.2			−0.557046
$329$			4765.99i			0.0440312i
$330$	−10848.0	+	10848.0i	−0.0996147	+	0.0996147i
$331$	61566.7	−	61566.7i	0.561940	−	0.561940i	−0.367918	−	0.929858i	$-0.619929\pi$
$331$	61566.7	−	61566.7i	0.561940	−	0.561940i	0.929858	+	0.367918i	$0.119929\pi$
$332$	35255.0	+	35255.0i	0.319849	+	0.319849i
$333$	−135898.	−	135898.i	−1.22553	−	1.22553i
$334$	−14185.1			−0.127157
$335$		−	81158.6i		−	0.723178i
$336$	−42614.5	−	42614.5i	−0.377467	−	0.377467i
$337$			8069.67i			0.0710552i	0.999369	+	0.0355276i	$0.0113112\pi$
$337$			8069.67i			0.0710552i	−0.999369	+	0.0355276i	$0.988689\pi$
$338$	9348.82	+	80239.9i	0.0818321	+	0.702356i
$339$	49896.0			0.434177
$340$	−24263.9	+	24263.9i	−0.209896	+	0.209896i
$341$	3362.28			0.0289151
$342$			207745.i			1.77614i
$343$	−63381.6	+	63381.6i	−0.538735	+	0.538735i
$344$	−6890.02	+	6890.02i	−0.0582242	+	0.0582242i
$345$	−221281.	−	221281.i	−1.85911	−	1.85911i
$346$	−77231.7	−	77231.7i	−0.645124	−	0.645124i
$347$	156363.			1.29860			0.649300	−	0.760533i	$-0.275062\pi$
$347$	156363.			1.29860			0.649300	+	0.760533i	$0.275062\pi$
$348$		−	74400.9i		−	0.614355i
$349$	−141731.	−	141731.i	−1.16363	−	1.16363i	−0.983676	−	0.179951i	$-0.942406\pi$
$349$	−141731.	−	141731.i	−1.16363	−	1.16363i	−0.179951	−	0.983676i	$-0.557594\pi$
$350$		−	41325.4i		−	0.337350i
$351$	138105.	+	285394.i	1.12097	+	2.31649i
$352$	3087.31			0.0249169
$353$	−125248.	+	125248.i	−1.00513	+	1.00513i	−0.00514429	+	0.999987i	$0.501637\pi$
$353$	−125248.	+	125248.i	−1.00513	+	1.00513i	−0.999987	+	0.00514429i	$0.998363\pi$
$354$	−61320.3			−0.489326
$355$		−	256.529i		−	0.00203554i
$356$	−29727.3	+	29727.3i	−0.234561	+	0.234561i
$357$	−148953.	+	148953.i	−1.16873	+	1.16873i
$358$	8746.93	+	8746.93i	0.0682479	+	0.0682479i
$359$	−50595.2	−	50595.2i	−0.392573	−	0.392573i	0.483030	−	0.875604i	$-0.339536\pi$
$359$	−50595.2	−	50595.2i	−0.392573	−	0.392573i	−0.875604	+	0.483030i	$0.839536\pi$
$360$	84215.8			0.649813
$361$		−	12859.1i		−	0.0986722i
$362$	−50153.8	−	50153.8i	−0.382725	−	0.382725i
$363$			238017.i			1.80632i
$364$	72497.5	+	25214.0i	0.547168	+	0.190300i
$365$	133476.			1.00188
$366$	130545.	−	130545.i	0.974535	−	0.974535i
$367$	137759.			1.02279			0.511395	−	0.859346i	$-0.329129\pi$
$367$	137759.			1.02279			0.511395	+	0.859346i	$0.329129\pi$
$368$			62975.6i			0.465025i
$369$	363523.	−	363523.i	2.66980	−	2.66980i
$370$	37969.1	−	37969.1i	0.277349	−	0.277349i
$371$	−151504.	−	151504.i	−1.10072	−	1.10072i
$372$	−18497.2	−	18497.2i	−0.133666	−	0.133666i
$373$	122430.			0.879975			0.439988	−	0.898004i	$-0.354983\pi$
$373$	122430.			0.879975			0.439988	+	0.898004i	$0.354983\pi$
$374$		−	10791.2i		−	0.0771485i
$375$	198424.	+	198424.i	1.41102	+	1.41102i
$376$			1899.53i			0.0134360i
$377$	41276.3	+	85297.4i	0.290414	+	0.600141i
$378$	301253.			2.10837
$379$	−113156.	+	113156.i	−0.787769	+	0.787769i	−0.981128	−	0.193359i	$-0.938062\pi$
$379$	−113156.	+	113156.i	−0.787769	+	0.787769i	0.193359	+	0.981128i	$0.438062\pi$
$380$	−58042.5			−0.401957
$381$			60125.2i			0.414197i
$382$	15692.0	−	15692.0i	0.107536	−	0.107536i
$383$	68319.5	−	68319.5i	0.465744	−	0.465744i	−0.434789	−	0.900532i	$-0.643177\pi$
$383$	68319.5	−	68319.5i	0.465744	−	0.465744i	0.900532	+	0.434789i	$0.143177\pi$
$384$	−16984.5	−	16984.5i	−0.115183	−	0.115183i
$385$	−13127.9	−	13127.9i	−0.0885676	−	0.0885676i
$386$	−106902.			−0.717481
$387$		−	83588.0i		−	0.558113i
$388$	39156.5	+	39156.5i	0.260100	+	0.260100i
$389$		−	85946.1i		−	0.567972i	−0.958828	−	0.283986i	$-0.908343\pi$
$389$		−	85946.1i		−	0.567972i	0.958828	−	0.283986i	$-0.0916569\pi$
$390$	−136839.	+	66217.9i	−0.899667	+	0.435358i
$391$	220122.			1.43983
$392$	13154.6	−	13154.6i	0.0856065	−	0.0856065i
$393$	−73448.3			−0.475551
$394$			27108.2i			0.174626i
$395$	−22030.8	+	22030.8i	−0.141200	+	0.141200i
$396$	−18727.2	+	18727.2i	−0.119422	+	0.119422i
$397$	−49712.1	−	49712.1i	−0.315414	−	0.315414i	0.531589	−	0.847003i	$-0.321595\pi$
$397$	−49712.1	−	49712.1i	−0.315414	−	0.315414i	−0.847003	+	0.531589i	$0.821595\pi$
$398$	122174.	+	122174.i	0.771281	+	0.771281i
$399$	−356315.			−2.23815
$400$		−	16470.6i		−	0.102942i
$401$	55547.8	+	55547.8i	0.345445	+	0.345445i	0.858410	−	0.512965i	$-0.171453\pi$
$401$	55547.8	+	55547.8i	0.345445	+	0.345445i	−0.512965	+	0.858410i	$0.671453\pi$
$402$		−	198571.i		−	1.22875i
$403$	31468.1	+	10944.3i	0.193758	+	0.0673873i
$404$	−11562.3			−0.0708403
$405$	−208716.	+	208716.i	−1.27247	+	1.27247i
$406$	90037.3			0.546224
$407$			16886.5i			0.101942i
$408$	−59366.7	+	59366.7i	−0.356634	+	0.356634i
$409$	77395.2	−	77395.2i	0.462666	−	0.462666i	−0.436862	−	0.899528i	$-0.643910\pi$
$409$	77395.2	−	77395.2i	0.462666	−	0.462666i	0.899528	+	0.436862i	$0.143910\pi$
$410$	101566.	+	101566.i	0.604201	+	0.604201i
$411$	−16216.6	−	16216.6i	−0.0960013	−	0.0960013i
$412$	35591.8			0.209679
$413$		−	74207.7i		−	0.435060i
$414$	−382002.	−	382002.i	−2.22877	−	2.22877i
$415$		−	119498.i		−	0.693849i
$416$	28894.6	+	10049.3i	0.166967	+	0.0580695i
$417$	−599409.			−3.44708
$418$	12907.0	−	12907.0i	0.0738709	−	0.0738709i
$419$	144154.			0.821106			0.410553	−	0.911837i	$-0.365336\pi$
$419$	144154.			0.821106			0.410553	+	0.911837i	$0.365336\pi$
$420$			144443.i			0.818840i
$421$	190864.	−	190864.i	1.07686	−	1.07686i	0.0800732	−	0.996789i	$-0.474485\pi$
$421$	190864.	−	190864.i	1.07686	−	1.07686i	0.996789	−	0.0800732i	$-0.0255154\pi$
$422$	−153586.	+	153586.i	−0.862436	+	0.862436i
$423$	−11522.3	−	11522.3i	−0.0643960	−	0.0643960i
$424$	−60383.5	−	60383.5i	−0.335882	−	0.335882i
$425$	−57570.7			−0.318731
$426$		−	627.651i		−	0.00345859i
$427$	157981.	+	157981.i	0.866460	+	0.866460i
$428$		−	64835.2i		−	0.353935i
$429$	15704.2	−	45154.2i	0.0853300	−	0.245349i
$430$	23354.0			0.126306
$431$	27601.8	−	27601.8i	0.148587	−	0.148587i	−0.628899	−	0.777487i	$-0.716494\pi$
$431$	27601.8	−	27601.8i	0.148587	−	0.148587i	0.777487	+	0.628899i	$0.216494\pi$
$432$	120067.			0.643365
$433$			89204.9i			0.475787i	0.971291	+	0.237894i	$0.0764570\pi$
$433$			89204.9i			0.475787i	−0.971291	+	0.237894i	$0.923543\pi$
$434$	22384.6	−	22384.6i	0.118842	−	0.118842i
$435$	−126092.	+	126092.i	−0.666361	+	0.666361i
$436$	21400.6	+	21400.6i	0.112578	+	0.112578i
$437$	263280.	+	263280.i	1.37865	+	1.37865i
$438$	326576.			1.70230
$439$			7453.00i			0.0386725i	0.999813	+	0.0193362i	$0.00615530\pi$
$439$			7453.00i			0.0386725i	−0.999813	+	0.0193362i	$0.993845\pi$
$440$	−5232.27	−	5232.27i	−0.0270262	−	0.0270262i
$441$			159589.i			0.820587i
$442$	35125.8	−	100997.i	0.179797	−	0.516968i
$443$	−206983.			−1.05470			−0.527349	−	0.849649i	$-0.676814\pi$
$443$	−206983.			−1.05470			−0.527349	+	0.849649i	$0.676814\pi$
$444$	92899.2	−	92899.2i	0.471244	−	0.471244i
$445$	100762.			0.508834
$446$		−	211430.i		−	1.06291i
$447$	−203406.	+	203406.i	−1.01800	+	1.01800i
$448$	20554.0	−	20554.0i	0.102409	−	0.102409i
$449$	201683.	+	201683.i	1.00040	+	1.00040i	1.00000		0.000405082i	$0.000128942\pi$
$449$	201683.	+	201683.i	1.00040	+	1.00040i	0.000405082		1.00000i	$0.499871\pi$
$450$	99908.8	+	99908.8i	0.493377	+	0.493377i
$451$	−45170.9			−0.222078
$452$			24066.0i			0.117795i
$453$	−262369.	−	262369.i	−1.27854	−	1.27854i
$454$			129379.i			0.627700i
$455$	−80134.6	−	165598.i	−0.387077	−	0.799895i
$456$	−142013.			−0.682965
$457$	−254320.	+	254320.i	−1.21772	+	1.21772i	−0.249295	+	0.968428i	$0.580199\pi$
$457$	−254320.	+	254320.i	−1.21772	+	1.21772i	−0.968428	+	0.249295i	$0.919801\pi$
$458$	−199238.			−0.949818
$459$		−	419678.i		−	1.99201i
$460$	106729.	−	106729.i	0.504390	−	0.504390i
$461$	−3957.17	+	3957.17i	−0.0186201	+	0.0186201i	−0.716356	−	0.697735i	$-0.754191\pi$
$461$	−3957.17	+	3957.17i	−0.0186201	+	0.0186201i	0.697735	+	0.716356i	$0.254191\pi$
$462$	−32120.2	−	32120.2i	−0.150485	−	0.150485i
$463$	−154055.	−	154055.i	−0.718642	−	0.718642i	0.249685	−	0.968327i	$-0.419673\pi$
$463$	−154055.	−	154055.i	−0.718642	−	0.718642i	−0.968327	+	0.249685i	$0.919673\pi$
$464$	35885.3			0.166679
$465$			62696.8i			0.289961i
$466$	145739.	+	145739.i	0.671124	+	0.671124i
$467$			56541.9i			0.259261i	0.991562	+	0.129630i	$0.0413790\pi$
$467$			56541.9i			0.259261i	−0.991562	+	0.129630i	$0.958621\pi$
$468$	−236229.	+	114313.i	−1.07855	+	0.521922i
$469$	240304.			1.09248
$470$	3219.26	−	3219.26i	0.0145734	−	0.0145734i
$471$	−292411.			−1.31811
$472$		−	29576.2i		−	0.132757i
$473$	−5193.26	+	5193.26i	−0.0232123	+	0.0232123i
$474$	−53902.8	+	53902.8i	−0.239913	+	0.239913i
$475$	−68858.4	−	68858.4i	−0.305190	−	0.305190i
$476$	−71843.5	−	71843.5i	−0.317083	−	0.317083i
$477$	732557.			3.21962
$478$			56894.9i			0.249010i
$479$	−47534.5	−	47534.5i	−0.207175	−	0.207175i	0.595891	−	0.803066i	$-0.296799\pi$
$479$	−47534.5	−	47534.5i	−0.207175	−	0.207175i	−0.803066	+	0.595891i	$0.796799\pi$
$480$			57569.4i			0.249867i
$481$	−54966.1	+	158044.i	−0.237577	+	0.683104i
$482$	−169355.			−0.728962
$483$	655194.	−	655194.i	2.80851	−	2.80851i
$484$	−114801.			−0.490066
$485$		−	132722.i		−	0.564236i
$486$	−206746.	+	206746.i	−0.875317	+	0.875317i
$487$	−109924.	+	109924.i	−0.463485	+	0.463485i	−0.899796	−	0.436311i	$-0.856285\pi$
$487$	−109924.	+	109924.i	−0.463485	+	0.463485i	0.436311	+	0.899796i	$0.356285\pi$
$488$	62964.8	+	62964.8i	0.264398	+	0.264398i
$489$	579938.	+	579938.i	2.42529	+	2.42529i
$490$	−44588.1			−0.185706
$491$		−	425487.i		−	1.76491i	−0.470396	−	0.882456i	$-0.655889\pi$
$491$		−	425487.i		−	1.76491i	0.470396	−	0.882456i	$-0.344111\pi$
$492$	248502.	+	248502.i	1.02660	+	1.02660i
$493$		−	125432.i		−	0.516076i
$494$	162812.	−	78786.2i	0.667163	−	0.322847i
$495$	63476.5			0.259061
$496$	8921.62	−	8921.62i	0.0362644	−	0.0362644i
$497$	759.562			0.00307504
$498$		−	292377.i		−	1.17892i
$499$	−136551.	+	136551.i	−0.548397	+	0.548397i	−0.925977	−	0.377580i	$-0.876756\pi$
$499$	−136551.	+	136551.i	−0.548397	+	0.548397i	0.377580	+	0.925977i	$0.376756\pi$
$500$	−95704.6	+	95704.6i	−0.382818	+	0.382818i
$501$	58820.0	+	58820.0i	0.234342	+	0.234342i
$502$	−228323.	−	228323.i	−0.906029	−	0.906029i
$503$	−298633.			−1.18033			−0.590164	−	0.807284i	$-0.700937\pi$
$503$	−298633.			−1.18033			−0.590164	+	0.807284i	$0.700937\pi$
$504$			249356.i			0.981654i
$505$	19595.3	+	19595.3i	0.0768370	+	0.0768370i
$506$			47467.0i			0.185392i
$507$	293957.	−	371488.i	1.14358	−	1.44520i
$508$	−28999.8			−0.112374
$509$	242694.	−	242694.i	0.936750	−	0.936750i	−0.0613650	−	0.998115i	$-0.519545\pi$
$509$	242694.	−	242694.i	0.936750	−	0.936750i	0.998115	+	0.0613650i	$0.0195454\pi$
$510$	201225.			0.773646
$511$			395211.i			1.51352i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	501962.	−	501962.i	1.90738	−	1.90738i
$514$	57553.1	+	57553.1i	0.217842	+	0.217842i
$515$	−60319.8	−	60319.8i	−0.227429	−	0.227429i
$516$	57140.2			0.214606
$517$			1431.75i			0.00535655i
$518$	112423.	+	112423.i	0.418983	+	0.418983i
$519$			640497.i			2.37784i
$520$	−31938.5	−	66000.8i	−0.118116	−	0.244086i
$521$	−308799.			−1.13763			−0.568815	−	0.822465i	$-0.692598\pi$
$521$	−308799.			−1.13763			−0.568815	+	0.822465i	$0.692598\pi$
$522$	−217676.	+	217676.i	−0.798857	+	0.798857i
$523$	−196111.			−0.716966			−0.358483	−	0.933536i	$-0.616706\pi$
$523$	−196111.			−0.716966			−0.358483	+	0.933536i	$0.616706\pi$
$524$		−	35425.8i		−	0.129020i
$525$	−171360.	+	171360.i	−0.621713	+	0.621713i
$526$	−83962.3	+	83962.3i	−0.303468	+	0.303468i
$527$	−31184.2	−	31184.2i	−0.112283	−	0.112283i
$528$	−12801.8	−	12801.8i	−0.0459202	−	0.0459202i
$529$	−688402.			−2.45998
$530$			204672.i			0.728629i
$531$	179406.	+	179406.i	0.636278	+	0.636278i
$532$		−	171859.i		−	0.607224i
$533$	−422762.	−	147033.i	−1.48813	−	0.517558i
$534$	246535.			0.864560
$535$	−109881.	+	109881.i	−0.383896	+	0.383896i
$536$	95775.6			0.333369
$537$		−	72539.9i		−	0.251552i
$538$	175720.	−	175720.i	0.607096	−	0.607096i
$539$	9915.13	−	9915.13i	0.0341288	−	0.0341288i
$540$	−203486.	−	203486.i	−0.697826	−	0.697826i
$541$	−47432.2	−	47432.2i	−0.162061	−	0.162061i	0.621418	−	0.783479i	$-0.286557\pi$
$541$	−47432.2	−	47432.2i	−0.162061	−	0.162061i	−0.783479	+	0.621418i	$0.786557\pi$
$542$	−236212.			−0.804088
$543$			415935.i			1.41067i
$544$	−28633.9	−	28633.9i	−0.0967572	−	0.0967572i
$545$		−	72538.2i		−	0.244216i
$546$	−196066.	−	405170.i	−0.657683	−	1.35910i
$547$	478901.			1.60056			0.800278	−	0.599629i	$-0.204685\pi$
$547$	478901.			1.60056			0.800278	+	0.599629i	$0.204685\pi$
$548$	7821.66	−	7821.66i	0.0260458	−	0.0260458i
$549$	−763873.			−2.53441
$550$		−	12414.5i		−	0.0410398i
$551$	150025.	−	150025.i	0.494151	−	0.494151i
$552$	261134.	−	261134.i	0.857009	−	0.857009i
$553$	−65231.2	−	65231.2i	−0.213307	−	0.213307i
$554$	118034.	+	118034.i	0.384580	+	0.384580i
$555$	−314885.			−1.02227
$556$		−	289109.i		−	0.935216i
$557$	303848.	+	303848.i	0.979369	+	0.979369i	0.999791	−	0.0204227i	$-0.00650121\pi$
$557$	303848.	+	303848.i	0.979369	+	0.979369i	−0.0204227	+	0.999791i	$0.506501\pi$
$558$			108235.i			0.347615i
$559$	−65508.8	+	31700.4i	−0.209641	+	0.101447i
$560$	−69668.5			−0.222157
$561$	−44746.9	+	44746.9i	−0.142179	+	0.142179i
$562$	292843.			0.927175
$563$			563388.i			1.77742i	0.458466	+	0.888712i	$0.348399\pi$
$563$			563388.i			1.77742i	−0.458466	+	0.888712i	$0.651601\pi$
$564$	7876.59	−	7876.59i	0.0247617	−	0.0247617i
$565$	40786.3	−	40786.3i	0.127767	−	0.127767i
$566$	−81556.9	−	81556.9i	−0.254582	−	0.254582i
$567$	−617991.	−	617991.i	−1.92228	−	1.92228i
$568$	302.731			0.000938340
$569$			73625.6i			0.227407i	0.993515	+	0.113704i	$0.0362715\pi$
$569$			73625.6i			0.227407i	−0.993515	+	0.113704i	$0.963729\pi$
$570$	240679.	+	240679.i	0.740778	+	0.740778i
$571$		−	551854.i		−	1.69259i	−0.532715	−	0.846295i	$-0.678828\pi$
$571$		−	551854.i		−	1.69259i	0.532715	−	0.846295i	$-0.321172\pi$
$572$	21778.9	+	7574.51i	0.0665648	+	0.0231506i
$573$	−130137.			−0.396361
$574$	−300729.	+	300729.i	−0.912749	+	0.912749i
$575$	253234.			0.765926
$576$			99383.3i			0.299549i
$577$	−171008.	+	171008.i	−0.513647	+	0.513647i	−0.915642	−	0.401995i	$-0.868317\pi$
$577$	−171008.	+	171008.i	−0.513647	+	0.513647i	0.401995	+	0.915642i	$0.368317\pi$
$578$	66956.2	−	66956.2i	0.200417	−	0.200417i
$579$	443278.	+	443278.i	1.32227	+	1.32227i
$580$	−60817.2	−	60817.2i	−0.180788	−	0.180788i
$581$	353824.			1.04818
$582$		−	324733.i		−	0.958694i
$583$	−45513.3	−	45513.3i	−0.133906	−	0.133906i
$584$			157515.i			0.461846i
$585$	594087.	+	206618.i	1.73596	+	0.603749i
$586$	164001.			0.477586
$587$	184791.	−	184791.i	0.536295	−	0.536295i	−0.386143	−	0.922439i	$-0.626193\pi$
$587$	184791.	−	184791.i	0.536295	−	0.536295i	0.922439	+	0.386143i	$0.126193\pi$
$588$	−109094.			−0.315534
$589$		−	74596.8i		−	0.215025i
$590$	−50124.8	+	50124.8i	−0.143995	+	0.143995i
$591$	112407.	−	112407.i	0.321823	−	0.321823i
$592$	44807.4	+	44807.4i	0.127852	+	0.127852i
$593$	56990.3	+	56990.3i	0.162066	+	0.162066i	0.783481	−	0.621415i	$-0.213442\pi$
$593$	56990.3	+	56990.3i	0.162066	+	0.162066i	−0.621415	+	0.783481i	$0.713442\pi$
$594$	90499.2			0.256491
$595$			243516.i			0.687850i
$596$	−98107.7	−	98107.7i	−0.276192	−	0.276192i
$597$		−	1.01321e6i		−	2.84284i
$598$	−154507.	+	444252.i	−0.432060	+	1.24230i
$599$	516301.			1.43896			0.719482	−	0.694511i	$-0.244379\pi$
$599$	516301.			1.43896			0.719482	+	0.694511i	$0.244379\pi$
$600$	−68297.1	+	68297.1i	−0.189714	+	0.189714i
$601$	−295648.			−0.818513			−0.409256	−	0.912419i	$-0.634212\pi$
$601$	−295648.			−0.818513			−0.409256	+	0.912419i	$0.634212\pi$
$602$			69149.1i			0.190807i
$603$	−580962.	+	580962.i	−1.59777	+	1.59777i
$604$	126547.	−	126547.i	0.346878	−	0.346878i
$605$	194561.	+	194561.i	0.531551	+	0.531551i
$606$	47944.0	+	47944.0i	0.130554	+	0.130554i
$607$	−246229.			−0.668285			−0.334142	−	0.942523i	$-0.608447\pi$
$607$	−246229.			−0.668285			−0.334142	+	0.942523i	$0.608447\pi$
$608$		−	68496.2i		−	0.185293i
$609$	−373348.	−	373348.i	−1.00665	−	1.00665i
$610$		−	213421.i		−	0.573559i
$611$	−4660.38	+	13400.0i	−0.0124836	+	0.0358939i
$612$	347380.			0.927474
$613$	−291289.	+	291289.i	−0.775182	+	0.775182i	−0.979007	−	0.203825i	$-0.934663\pi$
$613$	−291289.	+	291289.i	−0.775182	+	0.775182i	0.203825	+	0.979007i	$0.434663\pi$
$614$	13771.5			0.0365295
$615$		−	842307.i		−	2.22700i
$616$	15492.3	−	15492.3i	0.0408277	−	0.0408277i
$617$	229446.	−	229446.i	0.602712	−	0.602712i	−0.338320	−	0.941031i	$-0.609858\pi$
$617$	229446.	−	229446.i	0.602712	−	0.602712i	0.941031	+	0.338320i	$0.109858\pi$
$618$	−147585.	−	147585.i	−0.386424	−	0.386424i
$619$	−180833.	−	180833.i	−0.471951	−	0.471951i	0.430594	−	0.902546i	$-0.358304\pi$
$619$	−180833.	−	180833.i	−0.471951	−	0.471951i	−0.902546	+	0.430594i	$0.858304\pi$
$620$	−30240.1			−0.0786684
$621$			1.84602e6i			4.78689i
$622$	9213.94	+	9213.94i	0.0238158	+	0.0238158i
$623$			298348.i			0.768681i
$624$	−78144.0	−	161485.i	−0.200690	−	0.414726i
$625$	163548.			0.418683
$626$	240076.	−	240076.i	0.612633	−	0.612633i
$627$	−107040.			−0.272278
$628$		−	141037.i		−	0.357612i
$629$	156618.	−	156618.i	0.395859	−	0.395859i
$630$	422600.	−	422600.i	1.06475	−	1.06475i
$631$	272824.	+	272824.i	0.685211	+	0.685211i	0.961170	−	0.275958i	$-0.0889952\pi$
$631$	272824.	+	272824.i	0.685211	+	0.685211i	−0.275958	+	0.961170i	$0.588995\pi$
$632$	−25998.6	−	25998.6i	−0.0650901	−	0.0650901i
$633$	1.27372e6			3.17882
$634$			348129.i			0.866087i
$635$	49147.9	+	49147.9i	0.121887	+	0.121887i
$636$			500772.i			1.23801i
$637$	125071.	−	60523.3i	0.308233	−	0.149157i
$638$	27048.1			0.0664500
$639$	−1836.33	+	1836.33i	−0.00449727	+	0.00449727i
$640$	−27767.1			−0.0677907
$641$		−	165860.i		−	0.403670i	−0.979420	−	0.201835i	$-0.935310\pi$
$641$		−	165860.i		−	0.403670i	0.979420	−	0.201835i	$-0.0646905\pi$
$642$	−268845.	+	268845.i	−0.652278	+	0.652278i
$643$	493796.	−	493796.i	1.19433	−	1.19433i	0.218494	−	0.975838i	$-0.429886\pi$
$643$	493796.	−	493796.i	1.19433	−	1.19433i	0.975838	−	0.218494i	$-0.0701145\pi$
$644$	316016.	+	316016.i	0.761968	+	0.761968i
$645$	−96839.4	−	96839.4i	−0.232773	−	0.232773i
$646$	−239418.			−0.573710
$647$		−	435005.i		−	1.03917i	−0.854420	−	0.519584i	$-0.826087\pi$
$647$		−	435005.i		−	1.03917i	0.854420	−	0.519584i	$-0.173913\pi$
$648$	−246306.	−	246306.i	−0.586578	−	0.586578i
$649$		−	22292.7i		−	0.0529265i
$650$	40409.7	−	116190.i	0.0956442	−	0.275005i
$651$	−185640.			−0.438036
$652$	−279718.	+	279718.i	−0.657998	+	0.657998i
$653$	384248.			0.901125			0.450562	−	0.892745i	$-0.351224\pi$
$653$	384248.			0.901125			0.450562	+	0.892745i	$0.351224\pi$
$654$		−	177480.i		−	0.414947i
$655$	−60038.6	+	60038.6i	−0.139942	+	0.139942i
$656$	−119858.	+	119858.i	−0.278523	+	0.278523i
$657$	−955469.	−	955469.i	−2.21353	−	2.21353i
$658$	9531.97	+	9531.97i	0.0220156	+	0.0220156i
$659$	−549266.			−1.26477			−0.632385	−	0.774654i	$-0.717924\pi$
$659$	−549266.			−1.26477			−0.632385	+	0.774654i	$0.717924\pi$
$660$			43392.2i			0.0996147i
$661$	−492501.	−	492501.i	−1.12721	−	1.12721i	−0.990629	−	0.136580i	$-0.956389\pi$
$661$	−492501.	−	492501.i	−1.12721	−	1.12721i	−0.136580	−	0.990629i	$-0.543611\pi$
$662$		−	246267.i		−	0.561940i
$663$	−564446.	+	273141.i	−1.28409	+	0.621384i
$664$	141020.			0.319849
$665$	−291261.	+	291261.i	−0.658627	+	0.658627i
$666$	−543593.			−1.22553
$667$			551733.i			1.24016i
$668$	−28370.3	+	28370.3i	−0.0635786	+	0.0635786i
$669$	−876713.	+	876713.i	−1.95887	+	1.95887i
$670$	−162317.	−	162317.i	−0.361589	−	0.361589i
$671$	47458.9	+	47458.9i	0.105408	+	0.105408i
$672$	−170458.			−0.377467
$673$		−	606330.i		−	1.33869i	−0.742953	−	0.669343i	$-0.766576\pi$
$673$		−	606330.i		−	1.33869i	0.742953	−	0.669343i	$-0.233424\pi$
$674$	16139.3	+	16139.3i	0.0355276	+	0.0355276i
$675$		−	482809.i		−	1.05966i
$676$	179177.	+	141782.i	0.392094	+	0.310262i
$677$	−364281.			−0.794802			−0.397401	−	0.917645i	$-0.630088\pi$
$677$	−364281.			−0.794802			−0.397401	+	0.917645i	$0.630088\pi$
$678$	99792.1	−	99792.1i	0.217088	−	0.217088i
$679$	392980.			0.852376
$680$			97055.7i			0.209896i
$681$	536483.	−	536483.i	1.15681	−	1.15681i
$682$	6724.55	−	6724.55i	0.0144576	−	0.0144576i
$683$	332608.	+	332608.i	0.713003	+	0.713003i	0.967162	−	0.254160i	$-0.0817989\pi$
$683$	332608.	+	332608.i	0.713003	+	0.713003i	−0.254160	+	0.967162i	$0.581799\pi$
$684$	415489.	+	415489.i	0.888070	+	0.888070i
$685$	−26511.8			−0.0565013
$686$			253526.i			0.538735i
$687$	826158.	+	826158.i	1.75045	+	1.75045i
$688$			27560.1i			0.0582242i
$689$	−277819.	−	574113.i	−0.585226	−	1.20937i
$690$	−885123.			−1.85911
$691$	28649.1	−	28649.1i	0.0600006	−	0.0600006i	−0.676470	−	0.736470i	$-0.736491\pi$
$691$	28649.1	−	28649.1i	0.0600006	−	0.0600006i	0.736470	+	0.676470i	$0.236491\pi$
$692$	−308927.			−0.645124
$693$			187949.i			0.391357i
$694$	312726.	−	312726.i	0.649300	−	0.649300i
$695$	−489972.	+	489972.i	−1.01438	+	1.01438i
$696$	−148802.	−	148802.i	−0.307178	−	0.307178i
$697$	418948.	+	418948.i	0.862372	+	0.862372i
$698$	−566923.			−1.16363
$699$		−	1.20864e6i		−	2.47367i
$700$	−82650.8	−	82650.8i	−0.168675	−	0.168675i
$701$			164808.i			0.335383i	0.985840	+	0.167691i	$0.0536312\pi$
$701$			164808.i			0.335383i	−0.985840	+	0.167691i	$0.946369\pi$
$702$	846997.	+	294577.i	1.71873	+	0.597758i
$703$	374651.			0.758081
$704$	6174.61	−	6174.61i	0.0124585	−	0.0124585i
$705$	−26698.0			−0.0537155
$706$			500994.i			1.00513i
$707$	−58020.2	+	58020.2i	−0.116075	+	0.116075i
$708$	−122641.	+	122641.i	−0.244663	+	0.244663i
$709$	157777.	+	157777.i	0.313870	+	0.313870i	0.846407	−	0.532537i	$-0.178761\pi$
$709$	157777.	+	157777.i	0.313870	+	0.313870i	−0.532537	+	0.846407i	$0.678761\pi$
$710$	−513.059	−	513.059i	−0.00101777	−	0.00101777i
$711$	315408.			0.623927
$712$			118909.i			0.234561i
$713$	137169.	+	137169.i	0.269822	+	0.269822i
$714$			595812.i			1.16873i
$715$	−24073.2	−	49747.3i	−0.0470893	−	0.0973099i
$716$	34987.7			0.0682479
$717$	235920.	−	235920.i	0.458909	−	0.458909i
$718$	−202381.			−0.392573
$719$		−	701282.i		−	1.35655i	−0.734809	−	0.678274i	$-0.762728\pi$
$719$		−	701282.i		−	1.35655i	0.734809	−	0.678274i	$-0.237272\pi$
$720$	168432.	−	168432.i	0.324906	−	0.324906i
$721$	178602.	−	178602.i	0.343570	−	0.343570i
$722$	−25718.1	−	25718.1i	−0.0493361	−	0.0493361i
$723$	702248.	+	702248.i	1.34343	+	1.34343i
$724$	−200615.			−0.382725
$725$		−	144300.i		−	0.274531i
$726$	476033.	+	476033.i	0.903158	+	0.903158i
$727$		−	665420.i		−	1.25900i	−0.776999	−	0.629502i	$-0.783259\pi$
$727$		−	665420.i		−	1.25900i	0.776999	−	0.629502i	$-0.216741\pi$
$728$	195423.	−	94567.1i	0.368734	−	0.178434i
$729$	467659.			0.879983
$730$	266952.	−	266952.i	0.500942	−	0.500942i
$731$	96332.2			0.180276
$732$		−	522179.i		−	0.974535i
$733$	322452.	−	322452.i	0.600146	−	0.600146i	−0.340205	−	0.940351i	$-0.610497\pi$
$733$	322452.	−	322452.i	0.600146	−	0.600146i	0.940351	+	0.340205i	$0.110497\pi$
$734$	275517.	−	275517.i	0.511395	−	0.511395i
$735$	184889.	+	184889.i	0.342244	+	0.342244i
$736$	125951.	+	125951.i	0.232513	+	0.232513i
$737$	72189.6			0.132904
$738$		−	1.45409e6i		−	2.66980i
$739$	50393.5	+	50393.5i	0.0922753	+	0.0922753i	0.751738	−	0.659462i	$-0.229216\pi$
$739$	50393.5	+	50393.5i	0.0922753	+	0.0922753i	−0.659462	+	0.751738i	$0.729216\pi$
$740$		−	151876.i		−	0.277349i
$741$	−1.00181e6	−	348420.i	−1.82452	−	0.634550i
$742$	−606016.			−1.10072
$743$	−585418.	+	585418.i	−1.06045	+	1.06045i	−0.0623941	+	0.998052i	$0.519874\pi$
$743$	−585418.	+	585418.i	−1.06045	+	1.06045i	−0.998052	+	0.0623941i	$0.980126\pi$
$744$	−73988.7			−0.133666
$745$			332540.i			0.599143i
$746$	244860.	−	244860.i	0.439988	−	0.439988i
$747$	−855410.	+	855410.i	−1.53297	+	1.53297i
$748$	−21582.5	−	21582.5i	−0.0385743	−	0.0385743i
$749$	−325347.	−	325347.i	−0.579941	−	0.579941i
$750$	793696.			1.41102
$751$			854251.i			1.51463i	0.653051	+	0.757314i	$0.273489\pi$
$751$			854251.i			1.51463i	−0.653051	+	0.757314i	$0.726511\pi$
$752$	3799.06	+	3799.06i	0.00671801	+	0.00671801i
$753$			1.89353e6i			3.33950i
$754$	253147.	+	88042.3i	0.445278	+	0.154863i
$755$	−428934.			−0.752483
$756$	602505.	−	602505.i	1.05419	−	1.05419i
$757$	−1110.21			−0.00193737			−0.000968684	−	1.00000i	$-0.500308\pi$
$757$	−1110.21			−0.00193737			−0.000968684		1.00000i	$0.500308\pi$
$758$			452624.i			0.787769i
$759$	196827.	−	196827.i	0.341665	−	0.341665i
$760$	−116085.	+	116085.i	−0.200978	+	0.200978i
$761$	−676371.	−	676371.i	−1.16793	−	1.16793i	−0.982695	−	0.185232i	$-0.940696\pi$
$761$	−676371.	−	676371.i	−1.16793	−	1.16793i	−0.185232	−	0.982695i	$-0.559304\pi$
$762$	120250.	+	120250.i	0.207098	+	0.207098i
$763$	214780.			0.368930
$764$		−	62768.1i		−	0.107536i
$765$	−588728.	−	588728.i	−1.00599	−	1.00599i
$766$		−	273278.i		−	0.465744i
$767$	72563.4	−	208641.i	0.123347	−	0.354657i
$768$	−67937.8			−0.115183
$769$	255979.	−	255979.i	0.432864	−	0.432864i	−0.456737	−	0.889602i	$-0.650982\pi$
$769$	255979.	−	255979.i	0.432864	−	0.432864i	0.889602	+	0.456737i	$0.150982\pi$
$770$	−52511.7			−0.0885676
$771$		−	477298.i		−	0.802937i
$772$	−213804.	+	213804.i	−0.358740	+	0.358740i
$773$	−674317.	+	674317.i	−1.12851	+	1.12851i	−0.138090	+	0.990420i	$0.544096\pi$
$773$	−674317.	+	674317.i	−1.12851	+	1.12851i	−0.990420	+	0.138090i	$0.955904\pi$
$774$	−167176.	−	167176.i	−0.279056	−	0.279056i
$775$	−35875.2	−	35875.2i	−0.0597298	−	0.0597298i
$776$	156626.			0.260100
$777$		−	932348.i		−	1.54432i
$778$	−171892.	−	171892.i	−0.283986	−	0.283986i
$779$			1.00218e6i			1.65147i
$780$	−141243.	+	406115.i	−0.232155	+	0.667512i
$781$	228.180			0.000374089
$782$	440244.	−	440244.i	0.719913	−	0.719913i
$783$	1.05192e6			1.71576
$784$		−	52618.5i		−	0.0856065i
$785$	−239024.	+	239024.i	−0.387885	+	0.387885i
$786$	−146897.	+	146897.i	−0.237775	+	0.237775i
$787$	90287.8	+	90287.8i	0.145774	+	0.145774i	0.776227	−	0.630453i	$-0.217131\pi$
$787$	90287.8	+	90287.8i	0.145774	+	0.145774i	−0.630453	+	0.776227i	$0.717131\pi$
$788$	54216.3	+	54216.3i	0.0873128	+	0.0873128i
$789$	696315.			1.11854
$790$			88123.0i			0.141200i
$791$	120765.	+	120765.i	0.193014	+	0.193014i
$792$			74908.9i			0.119422i
$793$	289696.	+	598656.i	0.460676	+	0.951987i
$794$	−198848.			−0.315414
$795$	848691.	−	848691.i	1.34281	−	1.34281i
$796$	488696.			0.771281
$797$			54653.7i			0.0860406i	0.999074	+	0.0430203i	$0.0136980\pi$
$797$			54653.7i			0.0860406i	−0.999074	+	0.0430203i	$0.986302\pi$
$798$	−712630.	+	712630.i	−1.11907	+	1.11907i
$799$	13279.1	−	13279.1i	0.0208005	−	0.0208005i
$800$	−32941.3	−	32941.3i	−0.0514708	−	0.0514708i
$801$	−721289.	−	721289.i	−1.12420	−	1.12420i
$802$	222191.			0.345445
$803$			118725.i			0.184125i
$804$	−397142.	−	397142.i	−0.614376	−	0.614376i
$805$		−	1.07115e6i		−	1.65294i
$806$	84824.8	−	41047.6i	0.130573	−	0.0631855i
$807$	−1.45728e6			−2.23767
$808$	−23124.5	+	23124.5i	−0.0354201	+	0.0354201i
$809$	−596802.			−0.911870			−0.455935	−	0.890013i	$-0.650695\pi$
$809$	−596802.			−0.911870			−0.455935	+	0.890013i	$0.650695\pi$
$810$			834864.i			1.27247i
$811$	198281.	−	198281.i	0.301466	−	0.301466i	−0.540121	−	0.841587i	$-0.681622\pi$
$811$	198281.	−	198281.i	0.301466	−	0.301466i	0.841587	+	0.540121i	$0.181622\pi$
$812$	180075.	−	180075.i	0.273112	−	0.273112i
$813$	979476.	+	979476.i	1.48188	+	1.48188i
$814$	33773.0	+	33773.0i	0.0509708	+	0.0509708i
$815$	948112.			1.42740
$816$			237467.i			0.356634i
$817$	115220.	+	115220.i	0.172617	+	0.172617i
$818$		−	309581.i		−	0.462666i
$819$	−611779.	+	1.75904e6i	−0.912067	+	2.62246i
$820$	406264.			0.604201
$821$	170383.	−	170383.i	0.252779	−	0.252779i	−0.569330	−	0.822109i	$-0.692797\pi$
$821$	170383.	−	170383.i	0.252779	−	0.252779i	0.822109	+	0.569330i	$0.192797\pi$
$822$	−64866.5			−0.0960013
$823$		−	494592.i		−	0.730209i	−0.930967	−	0.365105i	$-0.881033\pi$
$823$		−	494592.i		−	0.730209i	0.930967	−	0.365105i	$-0.118967\pi$
$824$	71183.6	−	71183.6i	0.104840	−	0.104840i
$825$	−51478.0	+	51478.0i	−0.0756335	+	0.0756335i
$826$	−148415.	−	148415.i	−0.217530	−	0.217530i
$827$	−290301.	−	290301.i	−0.424461	−	0.424461i	0.462275	−	0.886737i	$-0.347033\pi$
$827$	−290301.	−	290301.i	−0.424461	−	0.424461i	−0.886737	+	0.462275i	$0.847033\pi$
$828$	−1.52801e6			−2.22877
$829$			731661.i			1.06464i	0.846545	+	0.532318i	$0.178679\pi$
$829$			731661.i			1.06464i	−0.846545	+	0.532318i	$0.821321\pi$
$830$	−238996.	−	238996.i	−0.346924	−	0.346924i
$831$		−	978876.i		−	1.41751i
$832$	77887.8	−	37690.7i	0.112518	−	0.0544487i
$833$	−183920.			−0.265057
$834$	−1.19882e6	+	1.19882e6i	−1.72354	+	1.72354i
$835$	96162.1			0.137921
$836$		−	51628.1i		−	0.0738709i
$837$	261522.	−	261522.i	0.373300	−	0.373300i
$838$	288308.	−	288308.i	0.410553	−	0.410553i
$839$	−580044.	−	580044.i	−0.824019	−	0.824019i	0.162663	−	0.986682i	$-0.447992\pi$
$839$	−580044.	−	580044.i	−0.824019	−	0.824019i	−0.986682	+	0.162663i	$0.947992\pi$
$840$	288887.	+	288887.i	0.409420	+	0.409420i
$841$	−392888.			−0.555491
$842$		−	763456.i		−	1.07686i
$843$	−1.21430e6	−	1.21430e6i	−1.70872	−	1.70872i
$844$			614345.i			0.862436i
$845$	−63376.3	−	543952.i	−0.0887592	−	0.761811i
$846$	−46089.3			−0.0643960
$847$	−576079.	+	576079.i	−0.802999	+	0.802999i
$848$	−241534.			−0.335882
$849$			676367.i			0.938354i
$850$	−115141.	+	115141.i	−0.159365	+	0.159365i
$851$	−688910.	+	688910.i	−0.951269	+	0.951269i
$852$	−1255.30	−	1255.30i	−0.00172930	−	0.00172930i
$853$	−278531.	−	278531.i	−0.382803	−	0.382803i	0.489308	−	0.872111i	$-0.337249\pi$
$853$	−278531.	−	278531.i	−0.382803	−	0.382803i	−0.872111	+	0.489308i	$0.837249\pi$
$854$	631923.			0.866460
$855$		−	1.40831e6i		−	1.92649i
$856$	−129670.	−	129670.i	−0.176968	−	0.176968i
$857$			866031.i			1.17916i	0.807711	+	0.589579i	$0.200706\pi$
$857$			866031.i			1.17916i	−0.807711	+	0.589579i	$0.799294\pi$
$858$	−58900.0	−	121717.i	−0.0800094	−	0.165339i
$859$	422018.			0.571932			0.285966	−	0.958240i	$-0.407686\pi$
$859$	422018.			0.571932			0.285966	+	0.958240i	$0.407686\pi$
$860$	46707.9	−	46707.9i	0.0631529	−	0.0631529i
$861$	2.49400e6			3.36427
$862$		−	110407.i		−	0.148587i
$863$	996621.	−	996621.i	1.33816	−	1.33816i	0.440320	−	0.897841i	$-0.354865\pi$
$863$	996621.	−	996621.i	1.33816	−	1.33816i	0.897841	−	0.440320i	$-0.145135\pi$
$864$	240135.	−	240135.i	0.321682	−	0.321682i
$865$	523559.	+	523559.i	0.699734	+	0.699734i
$866$	178410.	+	178410.i	0.237894	+	0.237894i
$867$	−555281.			−0.738711
$868$		−	89538.5i		−	0.118842i
$869$	−19596.1	−	19596.1i	−0.0259495	−	0.0259495i
$870$			504369.i			0.666361i
$871$	675634.	+	234979.i	0.890585	+	0.309737i
$872$	85602.6			0.112578
$873$	−950075.	+	950075.i	−1.24661	+	1.24661i
$874$	1.05312e6			1.37865
$875$			960504.i			1.25454i
$876$	653153.	−	653153.i	0.851151	−	0.851151i
$877$	913030.	−	913030.i	1.18710	−	1.18710i	0.209229	−	0.977867i	$-0.432904\pi$
$877$	913030.	−	913030.i	1.18710	−	1.18710i	0.977867	−	0.209229i	$-0.0670955\pi$
$878$	14906.0	+	14906.0i	0.0193362	+	0.0193362i
$879$	−680046.	−	680046.i	−0.880158	−	0.880158i
$880$	−20929.1			−0.0270262
$881$			1.11724e6i			1.43945i	0.694260	+	0.719724i	$0.255732\pi$
$881$			1.11724e6i			1.43945i	−0.694260	+	0.719724i	$0.744268\pi$
$882$	319177.	+	319177.i	0.410294	+	0.410294i
$883$		−	839397.i		−	1.07658i	−0.842760	−	0.538289i	$-0.819071\pi$
$883$		−	839397.i		−	1.07658i	0.842760	−	0.538289i	$-0.180929\pi$
$884$	−131742.	−	272245.i	−0.168586	−	0.348382i
$885$	415695.			0.530747
$886$	−413966.	+	413966.i	−0.527349	+	0.527349i
$887$	163002.			0.207179			0.103590	−	0.994620i	$-0.466967\pi$
$887$	163002.			0.207179			0.103590	+	0.994620i	$0.466967\pi$
$888$		−	371597.i		−	0.471244i
$889$	−145523.	+	145523.i	−0.184131	+	0.184131i
$890$	201524.	−	201524.i	0.254417	−	0.254417i
$891$	−185650.	−	185650.i	−0.233852	−	0.233852i
$892$	−422859.	−	422859.i	−0.531455	−	0.531455i
$893$	31765.3			0.0398336
$894$			813626.i			1.01800i
$895$	−59296.0	−	59296.0i	−0.0740252	−	0.0740252i
$896$		−	82216.0i		−	0.102409i
$897$	2.48281e6	−	1.20146e6i	3.08573	−	1.49322i
$898$	806731.			1.00040
$899$	78162.8	−	78162.8i	0.0967121	−	0.0967121i
$900$	399635.			0.493377
$901$			844246.i			1.03997i
$902$	−90341.8	+	90341.8i	−0.111039	+	0.111039i
$903$	286733.	−	286733.i	0.351644	−	0.351644i
$904$	48132.1	+	48132.1i	0.0588976	+	0.0588976i
$905$	339996.	+	339996.i	0.415123	+	0.415123i
$906$	−1.04948e6			−1.27854
$907$			637788.i			0.775285i	0.921810	+	0.387643i	$0.126711\pi$
$907$			637788.i			0.775285i	−0.921810	+	0.387643i	$0.873289\pi$
$908$	258758.	+	258758.i	0.313850	+	0.313850i
$909$		−	280541.i		−	0.339522i
$910$	−491466.	−	170927.i	−0.593486	−	0.206409i
$911$	1.34739e6			1.62352			0.811759	−	0.583993i	$-0.198510\pi$
$911$	1.34739e6			1.62352			0.811759	+	0.583993i	$0.198510\pi$
$912$	−284026.	+	284026.i	−0.341482	+	0.341482i
$913$	106292.			0.127514
$914$			1.01728e6i			1.21772i
$915$	−884972.	+	884972.i	−1.05703	+	1.05703i
$916$	−398475.	+	398475.i	−0.474909	+	0.474909i
$917$	−177769.	−	177769.i	−0.211406	−	0.211406i
$918$	−839355.	−	839355.i	−0.996003	−	0.996003i
$919$	−548840.			−0.649853			−0.324926	−	0.945739i	$-0.605340\pi$
$919$	−548840.			−0.649853			−0.324926	+	0.945739i	$0.605340\pi$
$920$		−	426916.i		−	0.504390i
$921$	−57104.7	−	57104.7i	−0.0673214	−	0.0673214i
$922$			15828.7i			0.0186201i
$923$	2135.57	+	742.731i	0.00250675	+	0.000871823i
$924$	−128481.			−0.150485
$925$	180178.	−	180178.i	0.210580	−	0.210580i
$926$	−616219.			−0.718642
$927$			863581.i			1.00495i
$928$	71770.6	−	71770.6i	0.0833394	−	0.0833394i
$929$	879177.	−	879177.i	1.01870	−	1.01870i	0.0188751	−	0.999822i	$-0.493992\pi$
$929$	879177.	−	879177.i	1.01870	−	1.01870i	0.999822	−	0.0188751i	$-0.00600848\pi$
$930$	125394.	+	125394.i	0.144980	+	0.144980i
$931$	−219981.	−	219981.i	−0.253796	−	0.253796i
$932$	582955.			0.671124
$933$		−	76413.0i		−	0.0877817i
$934$	113084.	+	113084.i	0.129630	+	0.129630i
$935$			73154.5i			0.0836793i
$936$	−243831.	+	701084.i	−0.278315	+	0.800237i
$937$	−406144.			−0.462595			−0.231298	−	0.972883i	$-0.574297\pi$
$937$	−406144.			−0.462595			−0.231298	+	0.972883i	$0.574297\pi$
$938$	480608.	−	480608.i	0.546242	−	0.546242i
$939$	−1.99100e6			−2.25808
$940$		−	12877.1i		−	0.0145734i
$941$	−903964.	+	903964.i	−1.02087	+	1.02087i	−0.0210962	+	0.999777i	$0.506716\pi$
$941$	−903964.	+	903964.i	−1.02087	+	1.02087i	−0.999777	+	0.0210962i	$0.993284\pi$
$942$	−584822.	+	584822.i	−0.659055	+	0.659055i
$943$	−1.84281e6	−	1.84281e6i	−2.07232	−	2.07232i
$944$	−59152.5	−	59152.5i	−0.0663787	−	0.0663787i
$945$	−2.04221e6			−2.28685
$946$			20773.0i			0.0232123i
$947$	−105869.	−	105869.i	−0.118050	−	0.118050i	0.645614	−	0.763664i	$-0.276602\pi$
$947$	−105869.	−	105869.i	−0.118050	−	0.118050i	−0.763664	+	0.645614i	$0.776602\pi$
$948$			215611.i			0.239913i
$949$	−386454.	+	1.11117e6i	−0.429107	+	1.23381i
$950$	−275434.			−0.305190
$951$	1.44355e6	−	1.44355e6i	1.59614	−	1.59614i
$952$	−287374.			−0.317083
$953$		−	857742.i		−	0.944432i	−0.881483	−	0.472216i	$-0.843454\pi$
$953$		−	857742.i		−	0.944432i	0.881483	−	0.472216i	$-0.156546\pi$
$954$	1.46511e6	−	1.46511e6i	1.60981	−	1.60981i
$955$	−106377.	+	106377.i	−0.116639	+	0.116639i
$956$	113790.	+	113790.i	0.124505	+	0.124505i
$957$	−112157.	−	112157.i	−0.122463	−	0.122463i
$958$	−190138.			−0.207175
$959$		−	78499.2i		−	0.0853548i
$960$	115139.	+	115139.i	0.124934	+	0.124934i
$961$			884656.i			0.957917i
$962$	206155.	+	426020.i	0.222764	+	0.460341i
$963$	1.57313e6			1.69634
$964$	−338711.	+	338711.i	−0.364481	+	0.364481i
$965$	724695.			0.778216
$966$		−	2.62078e6i		−	2.80851i
$967$	−620036.	+	620036.i	−0.663077	+	0.663077i	−0.956104	−	0.293027i	$-0.905337\pi$
$967$	−620036.	+	620036.i	−0.663077	+	0.663077i	0.293027	+	0.956104i	$0.405337\pi$
$968$	−229602.	+	229602.i	−0.245033	+	0.245033i
$969$	992771.	+	992771.i	1.05731	+	1.05731i
$970$	−265445.	−	265445.i	−0.282118	−	0.282118i
$971$	623835.			0.661654			0.330827	−	0.943691i	$-0.392672\pi$
$971$	623835.			0.661654			0.330827	+	0.943691i	$0.392672\pi$
$972$			826985.i			0.875317i
$973$	−1.45077e6	−	1.45077e6i	−1.53240	−	1.53240i
$974$			439697.i			0.463485i
$975$	−649354.	+	314229.i	−0.683081	+	0.330550i
$976$	251859.			0.264398
$977$	−214254.	+	214254.i	−0.224461	+	0.224461i	−0.810374	−	0.585913i	$-0.800736\pi$
$977$	−214254.	+	214254.i	−0.224461	+	0.224461i	0.585913	+	0.810374i	$0.300736\pi$
$978$	2.31975e6			2.42529
$979$			89626.4i			0.0935127i
$980$	−89176.1	+	89176.1i	−0.0928531	+	0.0928531i
$981$	−519254.	+	519254.i	−0.539563	+	0.539563i
$982$	−850973.	−	850973.i	−0.882456	−	0.882456i
$983$	1.30014e6	+	1.30014e6i	1.34550	+	1.34550i	0.890479	+	0.455024i	$0.150369\pi$
$983$	1.30014e6	+	1.30014e6i	1.34550	+	1.34550i	0.455024	+	0.890479i	$0.349631\pi$
$984$	994009.			1.02660
$985$		−	183768.i		−	0.189408i
$986$	−250864.	−	250864.i	−0.258038	−	0.258038i
$987$		−	79050.5i		−	0.0811466i
$988$	168051.	−	483196.i	0.172158	−	0.495005i
$989$	−423733.			−0.433211
$990$	126953.	−	126953.i	0.129531	−	0.129531i
$991$	−1.48766e6			−1.51481			−0.757403	−	0.652948i	$-0.773532\pi$
$991$	−1.48766e6			−1.51481			−0.757403	+	0.652948i	$0.773532\pi$
$992$		−	35686.5i		−	0.0362644i
$993$	−1.02117e6	+	1.02117e6i	−1.03562	+	1.03562i
$994$	1519.12	−	1519.12i	0.00153752	−	0.00153752i
$995$	−828226.	−	828226.i	−0.836571	−	0.836571i
$996$	−584753.	−	584753.i	−0.589459	−	0.589459i
$997$	1.29351e6			1.30130			0.650651	−	0.759377i	$-0.274496\pi$
$997$	1.29351e6			1.30130			0.650651	+	0.759377i	$0.274496\pi$
$998$			546205.i			0.548397i
$999$	1.31345e6	+	1.31345e6i	1.31609	+	1.31609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.d.b.5.1	✓	6
3.2	odd	2		234.5.i.a.109.2		6
4.3	odd	2		208.5.t.a.161.3		6
13.5	odd	4		338.5.d.c.99.1		6
13.8	odd	4	inner	26.5.d.b.21.1	yes	6
13.12	even	2		338.5.d.c.239.1		6
39.8	even	4		234.5.i.a.73.2		6
52.47	even	4		208.5.t.a.177.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.d.b.5.1	✓	6	1.1	even	1	trivial
26.5.d.b.21.1	yes	6	13.8	odd	4	inner
208.5.t.a.161.3		6	4.3	odd	2
208.5.t.a.177.3		6	52.47	even	4
234.5.i.a.73.2		6	39.8	even	4
234.5.i.a.109.2		6	3.2	odd	2
338.5.d.c.99.1		6	13.5	odd	4
338.5.d.c.239.1		6	13.12	even	2

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)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} -16.5864 q^{3} -8.00000i q^{4} +(-13.5581 + 13.5581i) q^{5} +(-33.1728 + 33.1728i) q^{6} +(-40.1445 - 40.1445i) q^{7} +(-16.0000 - 16.0000i) q^{8} +194.108 q^{9} +O(q^{10})\)	\(q+(2.00000 - 2.00000i) q^{2} -16.5864 q^{3} -8.00000i q^{4} +(-13.5581 + 13.5581i) q^{5} +(-33.1728 + 33.1728i) q^{6} +(-40.1445 - 40.1445i) q^{7} +(-16.0000 - 16.0000i) q^{8} +194.108 q^{9} +54.2326i q^{10} +(-12.0598 - 12.0598i) q^{11} +132.691i q^{12} +(-73.6146 - 152.125i) q^{13} -160.578 q^{14} +(224.880 - 224.880i) q^{15} -64.0000 q^{16} +223.703i q^{17} +(388.216 - 388.216i) q^{18} +(-267.563 + 267.563i) q^{19} +(108.465 + 108.465i) q^{20} +(665.852 + 665.852i) q^{21} -48.2392 q^{22} -983.993i q^{23} +(265.382 + 265.382i) q^{24} +257.354i q^{25} +(-451.478 - 157.020i) q^{26} -1876.05 q^{27} +(-321.156 + 321.156i) q^{28} -560.708 q^{29} -899.522i q^{30} +(-139.400 + 139.400i) q^{31} +(-128.000 + 128.000i) q^{32} +(200.028 + 200.028i) q^{33} +(447.405 + 447.405i) q^{34} +1088.57 q^{35} -1552.86i q^{36} +(-700.116 - 700.116i) q^{37} +1070.25i q^{38} +(1221.00 + 2523.20i) q^{39} +433.860 q^{40} +(1872.79 - 1872.79i) q^{41} +2663.41 q^{42} -430.626i q^{43} +(-96.4783 + 96.4783i) q^{44} +(-2631.74 + 2631.74i) q^{45} +(-1967.99 - 1967.99i) q^{46} +(-59.3604 - 59.3604i) q^{47} +1061.53 q^{48} +822.164i q^{49} +(514.708 + 514.708i) q^{50} -3710.42i q^{51} +(-1217.00 + 588.917i) q^{52} +3773.97 q^{53} +(-3752.10 + 3752.10i) q^{54} +327.017 q^{55} +1284.62i q^{56} +(4437.90 - 4437.90i) q^{57} +(-1121.42 + 1121.42i) q^{58} +(924.257 + 924.257i) q^{59} +(-1799.04 - 1799.04i) q^{60} -3935.30 q^{61} +557.601i q^{62} +(-7792.37 - 7792.37i) q^{63} +512.000i q^{64} +(3060.60 + 1064.45i) q^{65} +800.113 q^{66} +(-2992.99 + 2992.99i) q^{67} +1789.62 q^{68} +16320.9i q^{69} +(2177.14 - 2177.14i) q^{70} +(-9.46035 + 9.46035i) q^{71} +(-3105.73 - 3105.73i) q^{72} +(-4922.36 - 4922.36i) q^{73} -2800.47 q^{74} -4268.57i q^{75} +(2140.51 + 2140.51i) q^{76} +968.269i q^{77} +(7488.39 + 2604.39i) q^{78} +1624.91 q^{79} +(867.721 - 867.721i) q^{80} +15394.2 q^{81} -7491.16i q^{82} +(-4406.88 + 4406.88i) q^{83} +(5326.82 - 5326.82i) q^{84} +(-3032.99 - 3032.99i) q^{85} +(-861.252 - 861.252i) q^{86} +9300.11 q^{87} +385.913i q^{88} +(-3715.92 - 3715.92i) q^{89} +10527.0i q^{90} +(-3151.74 + 9062.19i) q^{91} -7871.95 q^{92} +(2312.15 - 2312.15i) q^{93} -237.441 q^{94} -7255.32i q^{95} +(2123.06 - 2123.06i) q^{96} +(-4894.57 + 4894.57i) q^{97} +(1644.33 + 1644.33i) q^{98} +(-2340.90 - 2340.90i) 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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