LMFDB - Embedded newform 338.5.d.e.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,5,Mod(99,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("338.99");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	338.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:	$34.9390475223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.120336834816.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 46x^{5} + 445x^{4} + 68x^{3} + 32x^{2} + 1136x + 20164 $ x^8 - 2x^7 + 2x^6 + 46x^5 + 445x^4 + 68x^3 + 32x^2 + 1136*x + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.1
Root			$-2.16680 - 2.16680i$ of defining polynomial
Character	$\chi$	$=$	338.239
Dual form			338.5.d.e.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} -11.9855 q^{3} -8.00000i q^{4} +(-27.8195 + 27.8195i) q^{5} +(23.9709 - 23.9709i) q^{6} +(49.1528 + 49.1528i) q^{7} +(16.0000 + 16.0000i) q^{8} +62.6514 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} -11.9855 q^{3} -8.00000i q^{4} +(-27.8195 + 27.8195i) q^{5} +(23.9709 - 23.9709i) q^{6} +(49.1528 + 49.1528i) q^{7} +(16.0000 + 16.0000i) q^{8} +62.6514 q^{9} -111.278i q^{10} +(59.0953 + 59.0953i) q^{11} +95.8837i q^{12} -196.611 q^{14} +(333.429 - 333.429i) q^{15} -64.0000 q^{16} -416.844i q^{17} +(-125.303 + 125.303i) q^{18} +(-3.74806 + 3.74806i) q^{19} +(222.556 + 222.556i) q^{20} +(-589.119 - 589.119i) q^{21} -236.381 q^{22} -462.074i q^{23} +(-191.767 - 191.767i) q^{24} -922.846i q^{25} +219.917 q^{27} +(393.222 - 393.222i) q^{28} +918.874 q^{29} +1333.72i q^{30} +(-67.6743 + 67.6743i) q^{31} +(128.000 - 128.000i) q^{32} +(-708.285 - 708.285i) q^{33} +(833.689 + 833.689i) q^{34} -2734.81 q^{35} -501.211i q^{36} +(-154.404 - 154.404i) q^{37} -14.9922i q^{38} -890.223 q^{40} +(2081.41 - 2081.41i) q^{41} +2356.48 q^{42} +1407.69i q^{43} +(472.762 - 472.762i) q^{44} +(-1742.93 + 1742.93i) q^{45} +(924.149 + 924.149i) q^{46} +(1373.25 + 1373.25i) q^{47} +767.070 q^{48} +2430.99i q^{49} +(1845.69 + 1845.69i) q^{50} +4996.07i q^{51} +2519.79 q^{53} +(-439.834 + 439.834i) q^{54} -3288.00 q^{55} +1572.89i q^{56} +(44.9222 - 44.9222i) q^{57} +(-1837.75 + 1837.75i) q^{58} +(-387.572 - 387.572i) q^{59} +(-2667.43 - 2667.43i) q^{60} +2705.62 q^{61} -270.697i q^{62} +(3079.49 + 3079.49i) q^{63} +512.000i q^{64} +2833.14 q^{66} +(2425.83 - 2425.83i) q^{67} -3334.75 q^{68} +5538.18i q^{69} +(5469.62 - 5469.62i) q^{70} +(4973.62 - 4973.62i) q^{71} +(1002.42 + 1002.42i) q^{72} +(-1208.41 - 1208.41i) q^{73} +617.616 q^{74} +11060.7i q^{75} +(29.9845 + 29.9845i) q^{76} +5809.40i q^{77} -3300.68 q^{79} +(1780.45 - 1780.45i) q^{80} -7710.57 q^{81} +8325.63i q^{82} +(1803.48 - 1803.48i) q^{83} +(-4712.95 + 4712.95i) q^{84} +(11596.4 + 11596.4i) q^{85} +(-2815.39 - 2815.39i) q^{86} -11013.1 q^{87} +1891.05i q^{88} +(-2917.53 - 2917.53i) q^{89} -6971.71i q^{90} -3696.59 q^{92} +(811.109 - 811.109i) q^{93} -5493.02 q^{94} -208.538i q^{95} +(-1534.14 + 1534.14i) q^{96} +(-10446.8 + 10446.8i) q^{97} +(-4861.98 - 4861.98i) q^{98} +(3702.40 + 3702.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{2} - 30 q^{5} + 86 q^{7} + 128 q^{8} - 180 q^{9}+O(q^{10}) $ 8 * q - 16 * q^2 - 30 * q^5 + 86 * q^7 + 128 * q^8 - 180 * q^9	$ 8 q - 16 q^{2} - 30 q^{5} + 86 q^{7} + 128 q^{8} - 180 q^{9} + 474 q^{11} - 344 q^{14} + 1128 q^{15} - 512 q^{16} + 360 q^{18} + 518 q^{19} + 240 q^{20} - 1914 q^{21} - 1896 q^{22} - 2268 q^{27} + 688 q^{28} + 504 q^{29} + 3376 q^{31} + 1024 q^{32} + 246 q^{33} - 1080 q^{34} - 12948 q^{35} + 5056 q^{37} - 960 q^{40} + 4392 q^{41} + 7656 q^{42} + 3792 q^{44} - 2898 q^{45} - 24 q^{46} - 4848 q^{47} + 3152 q^{50} - 6840 q^{53} + 4536 q^{54} - 588 q^{55} + 4434 q^{57} - 1008 q^{58} + 3510 q^{59} - 9024 q^{60} - 17340 q^{61} + 3276 q^{63} - 984 q^{66} + 7334 q^{67} + 4320 q^{68} + 25896 q^{70} + 7998 q^{71} - 2880 q^{72} - 19294 q^{73} - 20224 q^{74} - 4144 q^{76} - 11328 q^{79} + 1920 q^{80} - 12096 q^{81} - 10344 q^{83} - 15312 q^{84} + 20670 q^{85} - 13536 q^{86} - 36744 q^{87} - 1998 q^{89} + 96 q^{92} + 12744 q^{93} + 19392 q^{94} - 13694 q^{97} - 24640 q^{98} - 9504 q^{99}+O(q^{100}) $ 8 * q - 16 * q^2 - 30 * q^5 + 86 * q^7 + 128 * q^8 - 180 * q^9 + 474 * q^11 - 344 * q^14 + 1128 * q^15 - 512 * q^16 + 360 * q^18 + 518 * q^19 + 240 * q^20 - 1914 * q^21 - 1896 * q^22 - 2268 * q^27 + 688 * q^28 + 504 * q^29 + 3376 * q^31 + 1024 * q^32 + 246 * q^33 - 1080 * q^34 - 12948 * q^35 + 5056 * q^37 - 960 * q^40 + 4392 * q^41 + 7656 * q^42 + 3792 * q^44 - 2898 * q^45 - 24 * q^46 - 4848 * q^47 + 3152 * q^50 - 6840 * q^53 + 4536 * q^54 - 588 * q^55 + 4434 * q^57 - 1008 * q^58 + 3510 * q^59 - 9024 * q^60 - 17340 * q^61 + 3276 * q^63 - 984 * q^66 + 7334 * q^67 + 4320 * q^68 + 25896 * q^70 + 7998 * q^71 - 2880 * q^72 - 19294 * q^73 - 20224 * q^74 - 4144 * q^76 - 11328 * q^79 + 1920 * q^80 - 12096 * q^81 - 10344 * q^83 - 15312 * q^84 + 20670 * q^85 - 13536 * q^86 - 36744 * q^87 - 1998 * q^89 + 96 * q^92 + 12744 * q^93 + 19392 * q^94 - 13694 * q^97 - 24640 * q^98 - 9504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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
$3$	−11.9855			−1.33172			−0.665859	−	0.746077i	$-0.731935\pi$
$3$	−11.9855			−1.33172			−0.665859	+	0.746077i	$0.731935\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−27.8195	+	27.8195i	−1.11278	+	1.11278i	−0.120006	+	0.992773i	$0.538291\pi$
$5$	−27.8195	+	27.8195i	−1.11278	+	1.11278i	−0.992773	+	0.120006i	$0.961709\pi$
$6$	23.9709	−	23.9709i	0.665859	−	0.665859i
$7$	49.1528	+	49.1528i	1.00312	+	1.00312i	0.999995	+	0.00312281i	$0.000994022\pi$
$7$	49.1528	+	49.1528i	1.00312	+	1.00312i	0.00312281	+	0.999995i	$0.499006\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	62.6514			0.773474
$10$		−	111.278i		−	1.11278i
$11$	59.0953	+	59.0953i	0.488391	+	0.488391i	0.907798	−	0.419407i	$-0.137762\pi$
$11$	59.0953	+	59.0953i	0.488391	+	0.488391i	−0.419407	+	0.907798i	$0.637762\pi$
$12$			95.8837i			0.665859i
$13$		0			0
$13$		0			0
$14$	−196.611			−1.00312
$15$	333.429	−	333.429i	1.48191	−	1.48191i
$16$	−64.0000			−0.250000
$17$		−	416.844i		−	1.44237i	−0.692744	−	0.721184i	$-0.743598\pi$
$17$		−	416.844i		−	1.44237i	0.692744	−	0.721184i	$-0.256402\pi$
$18$	−125.303	+	125.303i	−0.386737	+	0.386737i
$19$	−3.74806	+	3.74806i	−0.0103824	+	0.0103824i	−0.712279	−	0.701897i	$-0.752337\pi$
$19$	−3.74806	+	3.74806i	−0.0103824	+	0.0103824i	0.701897	+	0.712279i	$0.252337\pi$
$20$	222.556	+	222.556i	0.556389	+	0.556389i
$21$	−589.119	−	589.119i	−1.33587	−	1.33587i
$22$	−236.381			−0.488391
$23$		−	462.074i		−	0.873486i	−0.899586	−	0.436743i	$-0.856132\pi$
$23$		−	462.074i		−	0.873486i	0.899586	−	0.436743i	$-0.143868\pi$
$24$	−191.767	−	191.767i	−0.332930	−	0.332930i
$25$		−	922.846i		−	1.47655i
$26$		0			0
$27$	219.917			0.301669
$28$	393.222	−	393.222i	0.501559	−	0.501559i
$29$	918.874			1.09260			0.546298	−	0.837591i	$-0.316037\pi$
$29$	918.874			1.09260			0.546298	+	0.837591i	$0.316037\pi$
$30$			1333.72i			1.48191i
$31$	−67.6743	+	67.6743i	−0.0704208	+	0.0704208i	−0.741440	−	0.671019i	$-0.765857\pi$
$31$	−67.6743	+	67.6743i	−0.0704208	+	0.0704208i	0.671019	+	0.741440i	$0.265857\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−708.285	−	708.285i	−0.650399	−	0.650399i
$34$	833.689	+	833.689i	0.721184	+	0.721184i
$35$	−2734.81			−2.23250
$36$		−	501.211i		−	0.386737i
$37$	−154.404	−	154.404i	−0.112786	−	0.112786i	0.648461	−	0.761247i	$-0.275413\pi$
$37$	−154.404	−	154.404i	−0.112786	−	0.112786i	−0.761247	+	0.648461i	$0.775413\pi$
$38$		−	14.9922i		−	0.0103824i
$39$		0			0
$40$	−890.223			−0.556389
$41$	2081.41	−	2081.41i	1.23820	−	1.23820i	0.277458	−	0.960738i	$-0.410508\pi$
$41$	2081.41	−	2081.41i	1.23820	−	1.23820i	0.960738	−	0.277458i	$-0.0894920\pi$
$42$	2356.48			1.33587
$43$			1407.69i			0.761327i	0.924714	+	0.380663i	$0.124304\pi$
$43$			1407.69i			0.761327i	−0.924714	+	0.380663i	$0.875696\pi$
$44$	472.762	−	472.762i	0.244195	−	0.244195i
$45$	−1742.93	+	1742.93i	−0.860705	+	0.860705i
$46$	924.149	+	924.149i	0.436743	+	0.436743i
$47$	1373.25	+	1373.25i	0.621664	+	0.621664i	0.945957	−	0.324293i	$-0.105126\pi$
$47$	1373.25	+	1373.25i	0.621664	+	0.621664i	−0.324293	+	0.945957i	$0.605126\pi$
$48$	767.070			0.332930
$49$			2430.99i			1.01249i
$50$	1845.69	+	1845.69i	0.738277	+	0.738277i
$51$			4996.07i			1.92083i
$52$		0			0
$53$	2519.79			0.897040			0.448520	−	0.893773i	$-0.351951\pi$
$53$	2519.79			0.897040			0.448520	+	0.893773i	$0.351951\pi$
$54$	−439.834	+	439.834i	−0.150835	+	0.150835i
$55$	−3288.00			−1.08694
$56$			1572.89i			0.501559i
$57$	44.9222	−	44.9222i	0.0138265	−	0.0138265i
$58$	−1837.75	+	1837.75i	−0.546298	+	0.546298i
$59$	−387.572	−	387.572i	−0.111339	−	0.111339i	0.649242	−	0.760582i	$-0.275086\pi$
$59$	−387.572	−	387.572i	−0.111339	−	0.111339i	−0.760582	+	0.649242i	$0.775086\pi$
$60$	−2667.43	−	2667.43i	−0.740954	−	0.740954i
$61$	2705.62			0.727123			0.363562	−	0.931570i	$-0.381561\pi$
$61$	2705.62			0.727123			0.363562	+	0.931570i	$0.381561\pi$
$62$		−	270.697i		−	0.0704208i
$63$	3079.49	+	3079.49i	0.775885	+	0.775885i
$64$			512.000i			0.125000i
$65$		0			0
$66$	2833.14			0.650399
$67$	2425.83	−	2425.83i	0.540394	−	0.540394i	−0.383250	−	0.923645i	$-0.625195\pi$
$67$	2425.83	−	2425.83i	0.540394	−	0.540394i	0.923645	+	0.383250i	$0.125195\pi$
$68$	−3334.75			−0.721184
$69$			5538.18i			1.16324i
$70$	5469.62	−	5469.62i	1.11625	−	1.11625i
$71$	4973.62	−	4973.62i	0.986633	−	0.986633i	−0.0132789	−	0.999912i	$-0.504227\pi$
$71$	4973.62	−	4973.62i	0.986633	−	0.986633i	0.999912	+	0.0132789i	$0.00422694\pi$
$72$	1002.42	+	1002.42i	0.193368	+	0.193368i
$73$	−1208.41	−	1208.41i	−0.226762	−	0.226762i	0.584577	−	0.811338i	$-0.301261\pi$
$73$	−1208.41	−	1208.41i	−0.226762	−	0.226762i	−0.811338	+	0.584577i	$0.801261\pi$
$74$	617.616			0.112786
$75$			11060.7i			1.96635i
$76$	29.9845	+	29.9845i	0.00519122	+	0.00519122i
$77$			5809.40i			0.979827i
$78$		0			0
$79$	−3300.68			−0.528870			−0.264435	−	0.964403i	$-0.585186\pi$
$79$	−3300.68			−0.528870			−0.264435	+	0.964403i	$0.585186\pi$
$80$	1780.45	−	1780.45i	0.278195	−	0.278195i
$81$	−7710.57			−1.17521
$82$			8325.63i			1.23820i
$83$	1803.48	−	1803.48i	0.261791	−	0.261791i	−0.563991	−	0.825781i	$-0.690735\pi$
$83$	1803.48	−	1803.48i	0.261791	−	0.261791i	0.825781	+	0.563991i	$0.190735\pi$
$84$	−4712.95	+	4712.95i	−0.667935	+	0.667935i
$85$	11596.4	+	11596.4i	1.60504	+	1.60504i
$86$	−2815.39	−	2815.39i	−0.380663	−	0.380663i
$87$	−11013.1			−1.45503
$88$			1891.05i			0.244195i
$89$	−2917.53	−	2917.53i	−0.368329	−	0.368329i	0.498539	−	0.866867i	$-0.333870\pi$
$89$	−2917.53	−	2917.53i	−0.368329	−	0.368329i	−0.866867	+	0.498539i	$0.833870\pi$
$90$		−	6971.71i		−	0.860705i
$91$		0			0
$92$	−3696.59			−0.436743
$93$	811.109	−	811.109i	0.0937806	−	0.0937806i
$94$	−5493.02			−0.621664
$95$		−	208.538i		−	0.0231067i
$96$	−1534.14	+	1534.14i	−0.166465	+	0.166465i
$97$	−10446.8	+	10446.8i	−1.11030	+	1.11030i	−0.117188	+	0.993110i	$0.537388\pi$
$97$	−10446.8	+	10446.8i	−1.11030	+	1.11030i	−0.993110	+	0.117188i	$0.962612\pi$
$98$	−4861.98	−	4861.98i	−0.506246	−	0.506246i
$99$	3702.40	+	3702.40i	0.377758	+	0.377758i
$100$	−7382.77			−0.738277
$101$			1164.32i			0.114138i	0.998370	+	0.0570688i	$0.0181754\pi$
$101$			1164.32i			0.114138i	−0.998370	+	0.0570688i	$0.981825\pi$
$102$	−9992.15	−	9992.15i	−0.960414	−	0.960414i
$103$			13334.2i			1.25688i	0.777860	+	0.628438i	$0.216305\pi$
$103$			13334.2i			1.25688i	−0.777860	+	0.628438i	$0.783695\pi$
$104$		0			0
$105$	32778.0			2.97306
$106$	−5039.57	+	5039.57i	−0.448520	+	0.448520i
$107$	16300.3			1.42374			0.711868	−	0.702314i	$-0.247850\pi$
$107$	16300.3			1.42374			0.711868	+	0.702314i	$0.247850\pi$
$108$		−	1759.33i		−	0.150835i
$109$	−14940.7	+	14940.7i	−1.25753	+	1.25753i	−0.305259	+	0.952269i	$0.598743\pi$
$109$	−14940.7	+	14940.7i	−1.25753	+	1.25753i	−0.952269	+	0.305259i	$0.901257\pi$
$110$	6576.00	−	6576.00i	0.543471	−	0.543471i
$111$	1850.60	+	1850.60i	0.150199	+	0.150199i
$112$	−3145.78	−	3145.78i	−0.250779	−	0.250779i
$113$	2940.09			0.230252			0.115126	−	0.993351i	$-0.463273\pi$
$113$	2940.09			0.230252			0.115126	+	0.993351i	$0.463273\pi$
$114$			179.689i			0.0138265i
$115$	12854.7	+	12854.7i	0.971997	+	0.971997i
$116$		−	7350.99i		−	0.546298i
$117$		0			0
$118$	1550.29			0.111339
$119$	20489.1	−	20489.1i	1.44687	−	1.44687i
$120$	10669.7			0.740954
$121$		−	7656.49i		−	0.522949i
$122$	−5411.25	+	5411.25i	−0.363562	+	0.363562i
$123$	−24946.6	+	24946.6i	−1.64893	+	1.64893i
$124$	541.395	+	541.395i	0.0352104	+	0.0352104i
$125$	8285.92	+	8285.92i	0.530299	+	0.530299i
$126$	−12318.0			−0.775885
$127$		−	29566.9i		−	1.83315i	−0.399863	−	0.916575i	$-0.630942\pi$
$127$		−	29566.9i		−	1.83315i	0.399863	−	0.916575i	$-0.369058\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$		−	16871.9i		−	1.01387i
$130$		0			0
$131$	−16053.2			−0.935446			−0.467723	−	0.883875i	$-0.654925\pi$
$131$	−16053.2			−0.935446			−0.467723	+	0.883875i	$0.654925\pi$
$132$	−5666.28	+	5666.28i	−0.325200	+	0.325200i
$133$	−368.455			−0.0208296
$134$			9703.32i			0.540394i
$135$	−6117.97	+	6117.97i	−0.335691	+	0.335691i
$136$	6669.51	−	6669.51i	0.360592	−	0.360592i
$137$	7714.53	+	7714.53i	0.411025	+	0.411025i	0.882096	−	0.471070i	$-0.156132\pi$
$137$	7714.53	+	7714.53i	0.411025	+	0.411025i	−0.471070	+	0.882096i	$0.656132\pi$
$138$	−11076.4	−	11076.4i	−0.581619	−	0.581619i
$139$	13585.1			0.703129			0.351564	−	0.936164i	$-0.385650\pi$
$139$	13585.1			0.703129			0.351564	+	0.936164i	$0.385650\pi$
$140$			21878.5i			1.11625i
$141$	−16459.1	−	16459.1i	−0.827881	−	0.827881i
$142$			19894.5i			0.986633i
$143$		0			0
$144$	−4009.69			−0.193368
$145$	−25562.6	+	25562.6i	−1.21582	+	1.21582i
$146$	4833.65			0.226762
$147$		−	29136.6i		−	1.34835i
$148$	−1235.23	+	1235.23i	−0.0563930	+	0.0563930i
$149$	18912.7	−	18912.7i	0.851886	−	0.851886i	−0.138480	−	0.990365i	$-0.544222\pi$
$149$	18912.7	−	18912.7i	0.851886	−	0.851886i	0.990365	+	0.138480i	$0.0442215\pi$
$150$	−22121.5	−	22121.5i	−0.983177	−	0.983177i
$151$	10548.8	+	10548.8i	0.462645	+	0.462645i	0.899521	−	0.436877i	$-0.143915\pi$
$151$	10548.8	+	10548.8i	0.462645	+	0.462645i	−0.436877	+	0.899521i	$0.643915\pi$
$152$	−119.938			−0.00519122
$153$		−	26115.9i		−	1.11563i
$154$	−11618.8	−	11618.8i	−0.489914	−	0.489914i
$155$		−	3765.33i		−	0.156725i
$156$		0			0
$157$	4252.07			0.172505			0.0862524	−	0.996273i	$-0.472511\pi$
$157$	4252.07			0.172505			0.0862524	+	0.996273i	$0.472511\pi$
$158$	6601.36	−	6601.36i	0.264435	−	0.264435i
$159$	−30200.8			−1.19460
$160$			7121.78i			0.278195i
$161$	22712.2	−	22712.2i	0.876210	−	0.876210i
$162$	15421.1	−	15421.1i	0.587606	−	0.587606i
$163$	−9633.41	−	9633.41i	−0.362581	−	0.362581i	0.502181	−	0.864762i	$-0.332531\pi$
$163$	−9633.41	−	9633.41i	−0.362581	−	0.362581i	−0.864762	+	0.502181i	$0.832531\pi$
$164$	−16651.3	−	16651.3i	−0.619098	−	0.619098i
$165$	39408.2			1.44750
$166$			7213.90i			0.261791i
$167$	27778.0	+	27778.0i	0.996021	+	0.996021i	0.999992	−	0.00397084i	$-0.00126396\pi$
$167$	27778.0	+	27778.0i	0.996021	+	0.996021i	−0.00397084	+	0.999992i	$0.501264\pi$
$168$		−	18851.8i		−	0.667935i
$169$		0			0
$170$	−46385.6			−1.60504
$171$	−234.821	+	234.821i	−0.00803054	+	0.00803054i
$172$	11261.5			0.380663
$173$		−	6.52133i		−	0.000217893i	−1.00000		0.000108947i	$-0.999965\pi$
$173$		−	6.52133i		−	0.000217893i	1.00000		0.000108947i	$-3.46788e-5\pi$
$174$	22026.3	−	22026.3i	0.727515	−	0.727515i
$175$	45360.4	−	45360.4i	1.48116	−	1.48116i
$176$	−3782.10	−	3782.10i	−0.122098	−	0.122098i
$177$	4645.23	+	4645.23i	0.148272	+	0.148272i
$178$	11670.1			0.368329
$179$		−	25343.4i		−	0.790969i	−0.918473	−	0.395485i	$-0.870577\pi$
$179$		−	25343.4i		−	0.790969i	0.918473	−	0.395485i	$-0.129423\pi$
$180$	13943.4	+	13943.4i	0.430353	+	0.430353i
$181$			13510.0i			0.412380i	0.978512	+	0.206190i	$0.0661065\pi$
$181$			13510.0i			0.412380i	−0.978512	+	0.206190i	$0.933894\pi$
$182$		0			0
$183$	−32428.2			−0.968323
$184$	7393.19	−	7393.19i	0.218372	−	0.218372i
$185$	8590.88			0.251012
$186$			3244.43i			0.0937806i
$187$	24633.5	−	24633.5i	0.704439	−	0.704439i
$188$	10986.0	−	10986.0i	0.310832	−	0.310832i
$189$	10809.5	+	10809.5i	0.302610	+	0.302610i
$190$	417.076	+	417.076i	0.0115534	+	0.0115534i
$191$	−12999.2			−0.356329			−0.178165	−	0.984001i	$-0.557016\pi$
$191$	−12999.2			−0.356329			−0.178165	+	0.984001i	$0.557016\pi$
$192$		−	6136.56i		−	0.166465i
$193$	12126.5	+	12126.5i	0.325552	+	0.325552i	0.850892	−	0.525340i	$-0.176062\pi$
$193$	12126.5	+	12126.5i	0.325552	+	0.325552i	−0.525340	+	0.850892i	$0.676062\pi$
$194$		−	41787.2i		−	1.11030i
$195$		0			0
$196$	19447.9			0.506246
$197$	−349.848	+	349.848i	−0.00901462	+	0.00901462i	−0.711600	−	0.702585i	$-0.752029\pi$
$197$	−349.848	+	349.848i	−0.00901462	+	0.00901462i	0.702585	+	0.711600i	$0.252029\pi$
$198$	−14809.6			−0.377758
$199$		−	56143.5i		−	1.41773i	−0.705344	−	0.708865i	$-0.749207\pi$
$199$		−	56143.5i		−	1.41773i	0.705344	−	0.708865i	$-0.250793\pi$
$200$	14765.5	−	14765.5i	0.369138	−	0.369138i
$201$	−29074.7	+	29074.7i	−0.719653	+	0.719653i
$202$	−2328.63	−	2328.63i	−0.0570688	−	0.0570688i
$203$	45165.2	+	45165.2i	1.09600	+	1.09600i
$204$	39968.6			0.960414
$205$			115807.i			2.75568i
$206$	−26668.4	−	26668.4i	−0.628438	−	0.628438i
$207$		−	28949.6i		−	0.675619i
$208$		0			0
$209$	−442.985			−0.0101414
$210$	−65555.9	+	65555.9i	−1.48653	+	1.48653i
$211$	10570.7			0.237431			0.118716	−	0.992928i	$-0.462122\pi$
$211$	10570.7			0.237431			0.118716	+	0.992928i	$0.462122\pi$
$212$		−	20158.3i		−	0.448520i
$213$	−59611.1	+	59611.1i	−1.31392	+	1.31392i
$214$	−32600.7	+	32600.7i	−0.711868	+	0.711868i
$215$	−39161.3	−	39161.3i	−0.847189	−	0.847189i
$216$	3518.67	+	3518.67i	0.0754173	+	0.0754173i
$217$	−6652.76			−0.141281
$218$		−	59762.8i		−	1.25753i
$219$	14483.4	+	14483.4i	0.301983	+	0.301983i
$220$			26304.0i			0.543471i
$221$		0			0
$222$	−7402.42			−0.150199
$223$	−27271.4	+	27271.4i	−0.548401	+	0.548401i	−0.925978	−	0.377577i	$-0.876757\pi$
$223$	−27271.4	+	27271.4i	−0.548401	+	0.548401i	0.377577	+	0.925978i	$0.376757\pi$
$224$	12583.1			0.250779
$225$		−	57817.6i		−	1.14208i
$226$	−5880.18	+	5880.18i	−0.115126	+	0.115126i
$227$	42485.7	−	42485.7i	0.824500	−	0.824500i	−0.162250	−	0.986750i	$-0.551875\pi$
$227$	42485.7	−	42485.7i	0.824500	−	0.824500i	0.986750	+	0.162250i	$0.0518750\pi$
$228$	−359.378	−	359.378i	−0.00691324	−	0.00691324i
$229$	28796.6	+	28796.6i	0.549124	+	0.549124i	0.926188	−	0.377063i	$-0.123066\pi$
$229$	28796.6	+	28796.6i	0.549124	+	0.549124i	−0.377063	+	0.926188i	$0.623066\pi$
$230$	−51418.6			−0.971997
$231$		−	69628.3i		−	1.30485i
$232$	14702.0	+	14702.0i	0.273149	+	0.273149i
$233$			54456.8i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$233$			54456.8i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$234$		0			0
$235$	−76406.4			−1.38355
$236$	−3100.57	+	3100.57i	−0.0556696	+	0.0556696i
$237$	39560.2			0.704307
$238$			81956.2i			1.44687i
$239$	−32089.5	+	32089.5i	−0.561782	+	0.561782i	−0.929813	−	0.368031i	$-0.880032\pi$
$239$	−32089.5	+	32089.5i	−0.561782	+	0.561782i	0.368031	+	0.929813i	$0.380032\pi$
$240$	−21339.5	+	21339.5i	−0.370477	+	0.370477i
$241$	−69395.6	−	69395.6i	−1.19481	−	1.19481i	−0.975701	−	0.219105i	$-0.929686\pi$
$241$	−69395.6	−	69395.6i	−1.19481	−	1.19481i	−0.219105	−	0.975701i	$-0.570314\pi$
$242$	15313.0	+	15313.0i	0.261474	+	0.261474i
$243$	74601.5			1.26338
$244$		−	21645.0i		−	0.363562i
$245$	−67628.9	−	67628.9i	−1.12668	−	1.12668i
$246$		−	99786.5i		−	1.64893i
$247$		0			0
$248$	−2165.58			−0.0352104
$249$	−21615.5	+	21615.5i	−0.348631	+	0.348631i
$250$	−33143.7			−0.530299
$251$			29730.6i			0.471906i	0.971764	+	0.235953i	$0.0758212\pi$
$251$			29730.6i			0.471906i	−0.971764	+	0.235953i	$0.924179\pi$
$252$	24635.9	−	24635.9i	0.387943	−	0.387943i
$253$	27306.4	−	27306.4i	0.426603	−	0.426603i
$254$	59133.8	+	59133.8i	0.916575	+	0.916575i
$255$	−138988.	−	138988.i	−2.13746	−	2.13746i
$256$	4096.00			0.0625000
$257$			12836.7i			0.194352i	0.995267	+	0.0971759i	$0.0309809\pi$
$257$			12836.7i			0.194352i	−0.995267	+	0.0971759i	$0.969019\pi$
$258$	33743.7	+	33743.7i	0.506937	+	0.506937i
$259$		−	15178.8i		−	0.226275i
$260$		0			0
$261$	57568.7			0.845095
$262$	32106.4	−	32106.4i	0.467723	−	0.467723i
$263$	59850.0			0.865272			0.432636	−	0.901569i	$-0.357584\pi$
$263$	59850.0			0.865272			0.432636	+	0.901569i	$0.357584\pi$
$264$		−	22665.1i		−	0.325200i
$265$	−70099.1	+	70099.1i	−0.998207	+	0.998207i
$266$	736.910	−	736.910i	0.0104148	−	0.0104148i
$267$	34968.0	+	34968.0i	0.490510	+	0.490510i
$268$	−19406.6	−	19406.6i	−0.270197	−	0.270197i
$269$	−80657.7			−1.11466			−0.557329	−	0.830292i	$-0.688174\pi$
$269$	−80657.7			−1.11466			−0.557329	+	0.830292i	$0.688174\pi$
$270$		−	24471.9i		−	0.335691i
$271$	−54675.2	−	54675.2i	−0.744478	−	0.744478i	0.228958	−	0.973436i	$-0.426468\pi$
$271$	−54675.2	−	54675.2i	−0.744478	−	0.744478i	−0.973436	+	0.228958i	$0.926468\pi$
$272$			26678.0i			0.360592i
$273$		0			0
$274$	−30858.1			−0.411025
$275$	54535.9	−	54535.9i	0.721135	−	0.721135i
$276$	44305.4			0.581619
$277$		−	54949.1i		−	0.716145i	−0.933694	−	0.358073i	$-0.883434\pi$
$277$		−	54949.1i		−	0.716145i	0.933694	−	0.358073i	$-0.116566\pi$
$278$	−27170.3	+	27170.3i	−0.351564	+	0.351564i
$279$	−4239.89	+	4239.89i	−0.0544686	+	0.0544686i
$280$	−43756.9	−	43756.9i	−0.558124	−	0.558124i
$281$	24920.8	+	24920.8i	0.315609	+	0.315609i	0.847078	−	0.531469i	$-0.178360\pi$
$281$	24920.8	+	24920.8i	0.315609	+	0.315609i	−0.531469	+	0.847078i	$0.678360\pi$
$282$	65836.4			0.827881
$283$			40742.6i			0.508716i	0.967110	+	0.254358i	$0.0818642\pi$
$283$			40742.6i			0.508716i	−0.967110	+	0.254358i	$0.918136\pi$
$284$	−39788.9	−	39788.9i	−0.493316	−	0.493316i
$285$			2499.43i			0.0307716i
$286$		0			0
$287$	204614.			2.48411
$288$	8019.38	−	8019.38i	0.0966842	−	0.0966842i
$289$	−90238.2			−1.08043
$290$		−	102250.i		−	1.21582i
$291$	125210.	−	125210.i	1.47860	−	1.47860i
$292$	−9667.31	+	9667.31i	−0.113381	+	0.113381i
$293$	86357.9	+	86357.9i	1.00593	+	1.00593i	0.999982	+	0.00594591i	$0.00189265\pi$
$293$	86357.9	+	86357.9i	1.00593	+	1.00593i	0.00594591	+	0.999982i	$0.498107\pi$
$294$	58273.1	+	58273.1i	0.674177	+	0.674177i
$295$	21564.1			0.247792
$296$		−	4940.93i		−	0.0563930i
$297$	12996.1	+	12996.1i	0.147333	+	0.147333i
$298$			75650.9i			0.851886i
$299$		0			0
$300$	88485.9			0.983177
$301$	−69192.0	+	69192.0i	−0.763701	+	0.763701i
$302$	−42195.1			−0.462645
$303$		−	13954.9i		−	0.151999i
$304$	239.876	−	239.876i	0.00259561	−	0.00259561i
$305$	−75269.1	+	75269.1i	−0.809127	+	0.809127i
$306$	52231.7	+	52231.7i	0.557817	+	0.557817i
$307$	16827.4	+	16827.4i	0.178542	+	0.178542i	0.790720	−	0.612178i	$-0.209706\pi$
$307$	16827.4	+	16827.4i	0.178542	+	0.178542i	−0.612178	+	0.790720i	$0.709706\pi$
$308$	46475.2			0.489914
$309$		−	159817.i		−	1.67380i
$310$	7530.66	+	7530.66i	0.0783627	+	0.0783627i
$311$		−	91661.6i		−	0.947691i	−0.880608	−	0.473845i	$-0.842866\pi$
$311$		−	91661.6i		−	0.947691i	0.880608	−	0.473845i	$-0.157134\pi$
$312$		0			0
$313$	−97693.4			−0.997186			−0.498593	−	0.866836i	$-0.666150\pi$
$313$	−97693.4			−0.997186			−0.498593	+	0.866836i	$0.666150\pi$
$314$	−8504.14	+	8504.14i	−0.0862524	+	0.0862524i
$315$	−171340.			−1.72678
$316$			26405.4i			0.264435i
$317$	−13766.4	+	13766.4i	−0.136994	+	0.136994i	−0.772278	−	0.635284i	$-0.780883\pi$
$317$	−13766.4	+	13766.4i	−0.136994	+	0.136994i	0.635284	+	0.772278i	$0.280883\pi$
$318$	60401.6	−	60401.6i	0.597302	−	0.597302i
$319$	54301.1	+	54301.1i	0.533614	+	0.533614i
$320$	−14243.6	−	14243.6i	−0.139097	−	0.139097i
$321$	−195367.			−1.89601
$322$			90848.9i			0.876210i
$323$	1562.36	+	1562.36i	0.0149753	+	0.0149753i
$324$			61684.5i			0.587606i
$325$		0			0
$326$	38533.7			0.362581
$327$	179071.	−	179071.i	1.67467	−	1.67467i
$328$	66605.0			0.619098
$329$			134999.i			1.24720i
$330$	−78816.4	+	78816.4i	−0.723750	+	0.723750i
$331$	37790.7	−	37790.7i	0.344928	−	0.344928i	−0.513288	−	0.858216i	$-0.671573\pi$
$331$	37790.7	−	37790.7i	0.344928	−	0.344928i	0.858216	+	0.513288i	$0.171573\pi$
$332$	−14427.8	−	14427.8i	−0.130895	−	0.130895i
$333$	−9673.63	−	9673.63i	−0.0872370	−	0.0872370i
$334$	−111112.			−0.996021
$335$			134971.i			1.20268i
$336$	37703.6	+	37703.6i	0.333968	+	0.333968i
$337$			13090.4i			0.115264i	0.998338	+	0.0576319i	$0.0183550\pi$
$337$			13090.4i			0.115264i	−0.998338	+	0.0576319i	$0.981645\pi$
$338$		0			0
$339$	−35238.4			−0.306631
$340$	92771.1	−	92771.1i	0.802518	−	0.802518i
$341$	−7998.47			−0.0687857
$342$		−	939.284i		−	0.00803054i
$343$	−1474.16	+	1474.16i	−0.0125301	+	0.0125301i
$344$	−22523.1	+	22523.1i	−0.190332	+	0.190332i
$345$	−154069.	−	154069.i	−1.29443	−	1.29443i
$346$	13.0427	+	13.0427i	0.000108947	+	0.000108947i
$347$	61798.8			0.513241			0.256620	−	0.966512i	$-0.417391\pi$
$347$	61798.8			0.513241			0.256620	+	0.966512i	$0.417391\pi$
$348$			88105.0i			0.727515i
$349$	131328.	+	131328.i	1.07822	+	1.07822i	0.996670	+	0.0815455i	$0.0259856\pi$
$349$	131328.	+	131328.i	1.07822	+	1.07822i	0.0815455	+	0.996670i	$0.474014\pi$
$350$			181442.i			1.48116i
$351$		0			0
$352$	15128.4			0.122098
$353$	−137041.	+	137041.i	−1.09977	+	1.09977i	−0.105333	+	0.994437i	$0.533591\pi$
$353$	−137041.	+	137041.i	−1.09977	+	1.09977i	−0.994437	+	0.105333i	$0.966409\pi$
$354$	−18580.9			−0.148272
$355$			276727.i			2.19581i
$356$	−23340.2	+	23340.2i	−0.184164	+	0.184164i
$357$	−245571.	+	245571.i	−1.92682	+	1.92682i
$358$	50686.9	+	50686.9i	0.395485	+	0.395485i
$359$	24773.9	+	24773.9i	0.192223	+	0.192223i	0.796656	−	0.604433i	$-0.206600\pi$
$359$	24773.9	+	24773.9i	0.192223	+	0.192223i	−0.604433	+	0.796656i	$0.706600\pi$
$360$	−55773.7			−0.430353
$361$			130293.i			0.999784i
$362$	−27020.0	−	27020.0i	−0.206190	−	0.206190i
$363$			91766.6i			0.696420i
$364$		0			0
$365$	67234.9			0.504671
$366$	64856.3	−	64856.3i	0.484162	−	0.484162i
$367$	168676.			1.25234			0.626169	−	0.779687i	$-0.284622\pi$
$367$	168676.			1.25234			0.626169	+	0.779687i	$0.284622\pi$
$368$			29572.8i			0.218372i
$369$	130403.	−	130403.i	0.957712	−	0.957712i
$370$	−17181.8	+	17181.8i	−0.125506	+	0.125506i
$371$	123854.	+	123854.i	0.899837	+	0.899837i
$372$	−6488.87	−	6488.87i	−0.0468903	−	0.0468903i
$373$	104703.			0.752559			0.376279	−	0.926506i	$-0.377203\pi$
$373$	104703.			0.752559			0.376279	+	0.926506i	$0.377203\pi$
$374$			98534.2i			0.704439i
$375$	−99310.6	−	99310.6i	−0.706209	−	0.706209i
$376$			43944.2i			0.310832i
$377$		0			0
$378$	−43238.1			−0.302610
$379$	−125500.	+	125500.i	−0.873709	+	0.873709i	−0.992874	−	0.119165i	$-0.961978\pi$
$379$	−125500.	+	125500.i	−0.873709	+	0.873709i	0.119165	+	0.992874i	$0.461978\pi$
$380$	−1668.30			−0.0115534
$381$			354373.i			2.44124i
$382$	25998.5	−	25998.5i	0.178165	−	0.178165i
$383$	−20232.1	+	20232.1i	−0.137925	+	0.137925i	−0.772698	−	0.634773i	$-0.781093\pi$
$383$	−20232.1	+	20232.1i	−0.137925	+	0.137925i	0.634773	+	0.772698i	$0.281093\pi$
$384$	12273.1	+	12273.1i	0.0832324	+	0.0832324i
$385$	−161614.	−	161614.i	−1.09033	−	1.09033i
$386$	−48506.0			−0.325552
$387$			88193.9i			0.588866i
$388$	83574.3	+	83574.3i	0.555149	+	0.555149i
$389$		−	139258.i		−	0.920283i	−0.887846	−	0.460141i	$-0.847799\pi$
$389$		−	139258.i		−	0.920283i	0.887846	−	0.460141i	$-0.152201\pi$
$390$		0			0
$391$	−192613.			−1.25989
$392$	−38895.9	+	38895.9i	−0.253123	+	0.253123i
$393$	192405.			1.24575
$394$		−	1399.39i		−	0.00901462i
$395$	91823.2	−	91823.2i	0.588516	−	0.588516i
$396$	29619.2	−	29619.2i	0.188879	−	0.188879i
$397$	−25795.6	−	25795.6i	−0.163668	−	0.163668i	0.620521	−	0.784190i	$-0.286921\pi$
$397$	−25795.6	−	25795.6i	−0.163668	−	0.163668i	−0.784190	+	0.620521i	$0.786921\pi$
$398$	112287.	+	112287.i	0.708865	+	0.708865i
$399$	4416.10			0.0277392
$400$			59062.1i			0.369138i
$401$	94955.8	+	94955.8i	0.590517	+	0.590517i	0.937771	−	0.347254i	$-0.112886\pi$
$401$	94955.8	+	94955.8i	0.590517	+	0.590517i	−0.347254	+	0.937771i	$0.612886\pi$
$402$		−	116299.i		−	0.719653i
$403$		0			0
$404$	9314.54			0.0570688
$405$	214504.	−	214504.i	1.30775	−	1.30775i
$406$	−180661.			−1.09600
$407$		−	18249.1i		−	0.110167i
$408$	−79937.2	+	79937.2i	−0.480207	+	0.480207i
$409$	−8116.40	+	8116.40i	−0.0485195	+	0.0485195i	−0.730950	−	0.682431i	$-0.760923\pi$
$409$	−8116.40	+	8116.40i	−0.0485195	+	0.0485195i	0.682431	+	0.730950i	$0.260923\pi$
$410$	−231615.	−	231615.i	−1.37784	−	1.37784i
$411$	−92462.3	−	92462.3i	−0.547370	−	0.547370i
$412$	106674.			0.628438
$413$		−	38100.4i		−	0.223373i
$414$	57899.2	+	57899.2i	0.337809	+	0.337809i
$415$			100343.i			0.582630i
$416$		0			0
$417$	−162824.			−0.936369
$418$	885.971	−	885.971i	0.00507069	−	0.00507069i
$419$	−223820.			−1.27488			−0.637441	−	0.770499i	$-0.720007\pi$
$419$	−223820.			−1.27488			−0.637441	+	0.770499i	$0.720007\pi$
$420$		−	262224.i		−	1.48653i
$421$	231747.	−	231747.i	1.30753	−	1.30753i	0.384333	−	0.923195i	$-0.374432\pi$
$421$	231747.	−	231747.i	1.30753	−	1.30753i	0.923195	−	0.384333i	$-0.125568\pi$
$422$	−21141.3	+	21141.3i	−0.118716	+	0.118716i
$423$	86036.3	+	86036.3i	0.480840	+	0.480840i
$424$	40316.6	+	40316.6i	0.224260	+	0.224260i
$425$	−384683.			−2.12973
$426$		−	238444.i		−	1.31392i
$427$	132989.	+	132989.i	0.729390	+	0.729390i
$428$		−	130403.i		−	0.711868i
$429$		0			0
$430$	156645.			0.847189
$431$	205616.	−	205616.i	1.10689	−	1.10689i	0.113330	−	0.993557i	$-0.463848\pi$
$431$	205616.	−	205616.i	1.10689	−	1.10689i	0.993557	−	0.113330i	$-0.0361516\pi$
$432$	−14074.7			−0.0754173
$433$			222253.i			1.18542i	0.805416	+	0.592710i	$0.201942\pi$
$433$			222253.i			1.18542i	−0.805416	+	0.592710i	$0.798058\pi$
$434$	13305.5	−	13305.5i	0.0706403	−	0.0706403i
$435$	306379.	−	306379.i	1.61913	−	1.61913i
$436$	119526.	+	119526.i	0.628764	+	0.628764i
$437$	1731.88	+	1731.88i	0.00906891	+	0.00906891i
$438$	−57933.6			−0.301983
$439$		−	303638.i		−	1.57553i	−0.615975	−	0.787765i	$-0.711238\pi$
$439$		−	303638.i		−	1.57553i	0.615975	−	0.787765i	$-0.288762\pi$
$440$	−52608.0	−	52608.0i	−0.271736	−	0.271736i
$441$			152305.i			0.783135i
$442$		0			0
$443$	103827.			0.529060			0.264530	−	0.964377i	$-0.414783\pi$
$443$	103827.			0.529060			0.264530	+	0.964377i	$0.414783\pi$
$444$	14804.8	−	14804.8i	0.0750996	−	0.0750996i
$445$	162328.			0.819736
$446$		−	109086.i		−	0.548401i
$447$	−226678.	+	226678.i	−1.13447	+	1.13447i
$448$	−25166.2	+	25166.2i	−0.125390	+	0.125390i
$449$	11231.3	+	11231.3i	0.0557104	+	0.0557104i	0.734413	−	0.678703i	$-0.237458\pi$
$449$	11231.3	+	11231.3i	0.0557104	+	0.0557104i	−0.678703	+	0.734413i	$0.737458\pi$
$450$	115635.	+	115635.i	0.571038	+	0.571038i
$451$	246003.			1.20945
$452$		−	23520.7i		−	0.115126i
$453$	−126432.	−	126432.i	−0.616113	−	0.616113i
$454$			169943.i			0.824500i
$455$		0			0
$456$	1437.51			0.00691324
$457$	162517.	−	162517.i	0.778155	−	0.778155i	−0.201362	−	0.979517i	$-0.564537\pi$
$457$	162517.	−	162517.i	0.778155	−	0.778155i	0.979517	+	0.201362i	$0.0645368\pi$
$458$	−115187.			−0.549124
$459$		−	91671.1i		−	0.435118i
$460$	102837.	−	102837.i	0.485999	−	0.485999i
$461$	37275.2	−	37275.2i	0.175396	−	0.175396i	−0.613950	−	0.789345i	$-0.710420\pi$
$461$	37275.2	−	37275.2i	0.175396	−	0.175396i	0.789345	+	0.613950i	$0.210420\pi$
$462$	139257.	+	139257.i	0.652427	+	0.652427i
$463$	137439.	+	137439.i	0.641134	+	0.641134i	0.950834	−	0.309700i	$-0.100229\pi$
$463$	137439.	+	137439.i	0.641134	+	0.641134i	−0.309700	+	0.950834i	$0.600229\pi$
$464$	−58807.9			−0.273149
$465$			45129.2i			0.208714i
$466$	−108914.	−	108914.i	−0.501546	−	0.501546i
$467$			49120.0i			0.225229i	0.993639	+	0.112615i	$0.0359225\pi$
$467$			49120.0i			0.225229i	−0.993639	+	0.112615i	$0.964077\pi$
$468$		0			0
$469$	238473.			1.08416
$470$	152813.	−	152813.i	0.691774	−	0.691774i
$471$	−50963.0			−0.229728
$472$		−	12402.3i		−	0.0556696i
$473$	−83188.1	+	83188.1i	−0.371825	+	0.371825i
$474$	−79120.4	+	79120.4i	−0.352153	+	0.352153i
$475$	3458.88	+	3458.88i	0.0153302	+	0.0153302i
$476$	−163912.	−	163912.i	−0.723433	−	0.723433i
$477$	157868.			0.693837
$478$		−	128358.i		−	0.561782i
$479$	−262401.	−	262401.i	−1.14365	−	1.14365i	−0.987777	−	0.155875i	$-0.950180\pi$
$479$	−262401.	−	262401.i	−1.14365	−	1.14365i	−0.155875	−	0.987777i	$-0.549820\pi$
$480$		−	85357.9i		−	0.370477i
$481$		0			0
$482$	277582.			1.19481
$483$	−272217.	+	272217.i	−1.16686	+	1.16686i
$484$	−61251.9			−0.261474
$485$		−	581248.i		−	2.47103i
$486$	−149203.	+	149203.i	−0.631691	+	0.631691i
$487$	52753.7	−	52753.7i	0.222431	−	0.222431i	−0.587090	−	0.809521i	$-0.699727\pi$
$487$	52753.7	−	52753.7i	0.222431	−	0.222431i	0.809521	+	0.587090i	$0.199727\pi$
$488$	43290.0	+	43290.0i	0.181781	+	0.181781i
$489$	115461.	+	115461.i	0.482856	+	0.482856i
$490$	270516.			1.12668
$491$			17315.8i			0.0718258i	0.999355	+	0.0359129i	$0.0114339\pi$
$491$			17315.8i			0.0718258i	−0.999355	+	0.0359129i	$0.988566\pi$
$492$	199573.	+	199573.i	0.824464	+	0.824464i
$493$		−	383027.i		−	1.57593i
$494$		0			0
$495$	−205998.			−0.840721
$496$	4331.16	−	4331.16i	0.0176052	−	0.0176052i
$497$	488934.			1.97942
$498$		−	86462.0i		−	0.348631i
$499$	76303.8	−	76303.8i	0.306440	−	0.306440i	−0.537087	−	0.843527i	$-0.680475\pi$
$499$	76303.8	−	76303.8i	0.306440	−	0.306440i	0.843527	+	0.537087i	$0.180475\pi$
$500$	66287.4	−	66287.4i	0.265149	−	0.265149i
$501$	−332933.	−	332933.i	−1.32642	−	1.32642i
$502$	−59461.1	−	59461.1i	−0.235953	−	0.235953i
$503$	−332406.			−1.31381			−0.656906	−	0.753973i	$-0.728135\pi$
$503$	−332406.			−1.31381			−0.656906	+	0.753973i	$0.728135\pi$
$504$			98543.6i			0.387943i
$505$	−32390.7	−	32390.7i	−0.127010	−	0.127010i
$506$			109226.i			0.426603i
$507$		0			0
$508$	−236535.			−0.916575
$509$	−103718.	+	103718.i	−0.400330	+	0.400330i	−0.878349	−	0.478020i	$-0.841355\pi$
$509$	−103718.	+	103718.i	−0.400330	+	0.400330i	0.478020	+	0.878349i	$0.341355\pi$
$510$	555952.			2.13746
$511$		−	118794.i		−	0.454938i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−824.261	+	824.261i	−0.00313206	+	0.00313206i
$514$	−25673.5	−	25673.5i	−0.0971759	−	0.0971759i
$515$	−370950.	−	370950.i	−1.39862	−	1.39862i
$516$	−134975.			−0.506937
$517$			162306.i			0.607230i
$518$	30357.6	+	30357.6i	0.113138	+	0.113138i
$519$			78.1612i			0.000290173i
$520$		0			0
$521$	−510268.			−1.87985			−0.939923	−	0.341385i	$-0.889104\pi$
$521$	−510268.			−1.87985			−0.939923	+	0.341385i	$0.889104\pi$
$522$	−115137.	+	115137.i	−0.422547	+	0.422547i
$523$	−531190.			−1.94199			−0.970993	−	0.239108i	$-0.923145\pi$
$523$	−531190.			−1.94199			−0.970993	+	0.239108i	$0.923145\pi$
$524$			128425.i			0.467723i
$525$	−543666.	+	543666.i	−1.97248	+	1.97248i
$526$	−119700.	+	119700.i	−0.432636	+	0.432636i
$527$	28209.7	+	28209.7i	0.101573	+	0.101573i
$528$	45330.2	+	45330.2i	0.162600	+	0.162600i
$529$	66328.4			0.237022
$530$		−	280396.i		−	0.998207i
$531$	−24281.9	−	24281.9i	−0.0861179	−	0.0861179i
$532$			2947.64i			0.0104148i
$533$		0			0
$534$	−139872.			−0.490510
$535$	−453467.	+	453467.i	−1.58430	+	1.58430i
$536$	77626.6			0.270197
$537$			303753.i			1.05335i
$538$	161315.	−	161315.i	0.557329	−	0.557329i
$539$	−143660.	+	143660.i	−0.494491	+	0.494491i
$540$	48943.8	+	48943.8i	0.167846	+	0.167846i
$541$	266982.	+	266982.i	0.912194	+	0.912194i	0.996445	−	0.0842501i	$-0.0268495\pi$
$541$	266982.	+	266982.i	0.912194	+	0.912194i	−0.0842501	+	0.996445i	$0.526849\pi$
$542$	218701.			0.744478
$543$		−	161923.i		−	0.549174i
$544$	−53356.1	−	53356.1i	−0.180296	−	0.180296i
$545$		−	831284.i		−	2.79870i
$546$		0			0
$547$	412153.			1.37748			0.688738	−	0.725010i	$-0.258165\pi$
$547$	412153.			1.37748			0.688738	+	0.725010i	$0.258165\pi$
$548$	61716.3	−	61716.3i	0.205513	−	0.205513i
$549$	169511.			0.562411
$550$			218143.i			0.721135i
$551$	−3443.99	+	3443.99i	−0.0113438	+	0.0113438i
$552$	−88610.8	+	88610.8i	−0.290809	+	0.290809i
$553$	−162238.	−	162238.i	−0.530519	−	0.530519i
$554$	109898.	+	109898.i	0.358073	+	0.358073i
$555$	−102966.			−0.334277
$556$		−	108681.i		−	0.351564i
$557$	−147814.	−	147814.i	−0.476438	−	0.476438i	0.427553	−	0.903990i	$-0.359376\pi$
$557$	−147814.	−	147814.i	−0.476438	−	0.476438i	−0.903990	+	0.427553i	$0.859376\pi$
$558$		−	16959.6i		−	0.0544686i
$559$		0			0
$560$	175028.			0.558124
$561$	−295244.	+	295244.i	−0.938115	+	0.938115i
$562$	−99683.1			−0.315609
$563$		−	213487.i		−	0.673527i	−0.941589	−	0.336763i	$-0.890668\pi$
$563$		−	213487.i		−	0.673527i	0.941589	−	0.336763i	$-0.109332\pi$
$564$	−131673.	+	131673.i	−0.413940	+	0.413940i
$565$	−81791.8	+	81791.8i	−0.256220	+	0.256220i
$566$	−81485.2	−	81485.2i	−0.254358	−	0.254358i
$567$	−378996.	−	378996.i	−1.17888	−	1.17888i
$568$	159156.			0.493316
$569$		−	430345.i		−	1.32921i	−0.747196	−	0.664603i	$-0.768601\pi$
$569$		−	430345.i		−	1.32921i	0.747196	−	0.664603i	$-0.231399\pi$
$570$	−4998.85	−	4998.85i	−0.0153858	−	0.0153858i
$571$			413840.i			1.26929i	0.772805	+	0.634644i	$0.218853\pi$
$571$			413840.i			1.26929i	−0.772805	+	0.634644i	$0.781147\pi$
$572$		0			0
$573$	155802.			0.474530
$574$	−409228.	+	409228.i	−1.24206	+	1.24206i
$575$	−426423.			−1.28975
$576$			32077.5i			0.0966842i
$577$	349122.	−	349122.i	1.04864	−	1.04864i	0.0498841	−	0.998755i	$-0.484115\pi$
$577$	349122.	−	349122.i	1.04864	−	1.04864i	0.998755	−	0.0498841i	$-0.0158852\pi$
$578$	180476.	−	180476.i	0.540213	−	0.540213i
$579$	−145342.	−	145342.i	−0.433544	−	0.433544i
$580$	204501.	+	204501.i	0.607909	+	0.607909i
$581$	177292.			0.525214
$582$			500838.i			1.47860i
$583$	148908.	+	148908.i	0.438106	+	0.438106i
$584$		−	38669.2i		−	0.113381i
$585$		0			0
$586$	−345432.			−1.00593
$587$	−5609.16	+	5609.16i	−0.0162788	+	0.0162788i	−0.715199	−	0.698921i	$-0.753664\pi$
$587$	−5609.16	+	5609.16i	−0.0162788	+	0.0162788i	0.698921	+	0.715199i	$0.253664\pi$
$588$	−233092.			−0.674177
$589$		−	507.295i		−	0.00146228i
$590$	−43128.2	+	43128.2i	−0.123896	+	0.123896i
$591$	4193.09	−	4193.09i	0.0120049	−	0.0120049i
$592$	9881.86	+	9881.86i	0.0281965	+	0.0281965i
$593$	135707.	+	135707.i	0.385917	+	0.385917i	0.873228	−	0.487312i	$-0.162022\pi$
$593$	135707.	+	135707.i	0.385917	+	0.385917i	−0.487312	+	0.873228i	$0.662022\pi$
$594$	−51984.2			−0.147333
$595$			1.13999e6i			3.22008i
$596$	−151302.	−	151302.i	−0.425943	−	0.425943i
$597$			672907.i			1.88802i
$598$		0			0
$599$	43856.1			0.122230			0.0611149	−	0.998131i	$-0.480534\pi$
$599$	43856.1			0.122230			0.0611149	+	0.998131i	$0.480534\pi$
$600$	−176972.	+	176972.i	−0.491588	+	0.491588i
$601$	−239364.			−0.662690			−0.331345	−	0.943510i	$-0.607502\pi$
$601$	−239364.			−0.662690			−0.331345	+	0.943510i	$0.607502\pi$
$602$		−	276768.i		−	0.763701i
$603$	151982.	−	151982.i	0.417981	−	0.417981i
$604$	84390.1	−	84390.1i	0.231322	−	0.231322i
$605$	213000.	+	213000.i	0.581926	+	0.581926i
$606$	27909.8	+	27909.8i	0.0759995	+	0.0759995i
$607$	713286.			1.93591			0.967957	−	0.251116i	$-0.0807975\pi$
$607$	713286.			1.93591			0.967957	+	0.251116i	$0.0807975\pi$
$608$			959.503i			0.00259561i
$609$	−541326.	−	541326.i	−1.45957	−	1.45957i
$610$		−	301076.i		−	0.809127i
$611$		0			0
$612$	−208927.			−0.557817
$613$	25856.4	−	25856.4i	0.0688093	−	0.0688093i	−0.671865	−	0.740674i	$-0.734506\pi$
$613$	25856.4	−	25856.4i	0.0688093	−	0.0688093i	0.740674	+	0.671865i	$0.234506\pi$
$614$	−67309.7			−0.178542
$615$		−	1.38800e6i		−	3.66978i
$616$	−92950.3	+	92950.3i	−0.244957	+	0.244957i
$617$	344111.	−	344111.i	0.903917	−	0.903917i	−0.0918557	−	0.995772i	$-0.529280\pi$
$617$	344111.	−	344111.i	0.903917	−	0.903917i	0.995772	+	0.0918557i	$0.0292799\pi$
$618$	319633.	+	319633.i	0.836902	+	0.836902i
$619$	112057.	+	112057.i	0.292453	+	0.292453i	0.838049	−	0.545596i	$-0.183697\pi$
$619$	112057.	+	112057.i	0.292453	+	0.292453i	−0.545596	+	0.838049i	$0.683697\pi$
$620$	−30122.6			−0.0783627
$621$		−	101618.i		−	0.263504i
$622$	183323.	+	183323.i	0.473845	+	0.473845i
$623$		−	286809.i		−	0.738954i
$624$		0			0
$625$	115759.			0.296343
$626$	195387.	−	195387.i	0.498593	−	0.498593i
$627$	5309.38			0.0135055
$628$		−	34016.6i		−	0.0862524i
$629$	−64362.5	+	64362.5i	−0.162679	+	0.162679i
$630$	342679.	−	342679.i	0.863389	−	0.863389i
$631$	−59131.7	−	59131.7i	−0.148512	−	0.148512i	0.628941	−	0.777453i	$-0.283489\pi$
$631$	−59131.7	−	59131.7i	−0.148512	−	0.148512i	−0.777453	+	0.628941i	$0.783489\pi$
$632$	−52810.9	−	52810.9i	−0.132218	−	0.132218i
$633$	−126694.			−0.316191
$634$		−	55065.5i		−	0.136994i
$635$	822535.	+	822535.i	2.03989	+	2.03989i
$636$			241606.i			0.597302i
$637$		0			0
$638$	−217204.			−0.533614
$639$	311604.	−	311604.i	0.763135	−	0.763135i
$640$	56974.3			0.139097
$641$			195783.i			0.476496i	0.971204	+	0.238248i	$0.0765731\pi$
$641$			195783.i			0.476496i	−0.971204	+	0.238248i	$0.923427\pi$
$642$	390734.	−	390734.i	0.948007	−	0.948007i
$643$	241575.	−	241575.i	0.584293	−	0.584293i	−0.351787	−	0.936080i	$-0.614426\pi$
$643$	241575.	−	241575.i	0.584293	−	0.584293i	0.936080	+	0.351787i	$0.114426\pi$
$644$	−181698.	−	181698.i	−0.438105	−	0.438105i
$645$	469366.	+	469366.i	1.12822	+	1.12822i
$646$	−6249.43			−0.0149753
$647$		−	778145.i		−	1.85888i	−0.368970	−	0.929441i	$-0.620289\pi$
$647$		−	778145.i		−	1.85888i	0.368970	−	0.929441i	$-0.379711\pi$
$648$	−123369.	−	123369.i	−0.293803	−	0.293803i
$649$		−	45807.3i		−	0.108754i
$650$		0			0
$651$	79736.5			0.188146
$652$	−77067.3	+	77067.3i	−0.181290	+	0.181290i
$653$	542695.			1.27271			0.636355	−	0.771396i	$-0.280441\pi$
$653$	542695.			1.27271			0.636355	+	0.771396i	$0.280441\pi$
$654$			716285.i			1.67467i
$655$	446591.	−	446591.i	1.04094	−	1.04094i
$656$	−133210.	+	133210.i	−0.309549	+	0.309549i
$657$	−75708.8	−	75708.8i	−0.175394	−	0.175394i
$658$	−269997.	−	269997.i	−0.623602	−	0.623602i
$659$	776835.			1.78878			0.894392	−	0.447284i	$-0.147609\pi$
$659$	776835.			1.78878			0.894392	+	0.447284i	$0.147609\pi$
$660$		−	315266.i		−	0.723750i
$661$	461004.	+	461004.i	1.05512	+	1.05512i	0.998389	+	0.0567313i	$0.0180678\pi$
$661$	461004.	+	461004.i	1.05512	+	1.05512i	0.0567313	+	0.998389i	$0.481932\pi$
$662$			151163.i			0.344928i
$663$		0			0
$664$	57711.2			0.130895
$665$	10250.2	−	10250.2i	0.0231788	−	0.0231788i
$666$	38694.5			0.0872370
$667$		−	424588.i		−	0.954368i
$668$	222224.	−	222224.i	0.498011	−	0.498011i
$669$	326861.	−	326861.i	0.730316	−	0.730316i
$670$	−269941.	−	269941.i	−0.601339	−	0.601339i
$671$	159890.	+	159890.i	0.355120	+	0.355120i
$672$	−150814.			−0.333968
$673$			734600.i			1.62189i	0.585124	+	0.810944i	$0.301046\pi$
$673$			734600.i			1.62189i	−0.585124	+	0.810944i	$0.698954\pi$
$674$	−26180.8	−	26180.8i	−0.0576319	−	0.0576319i
$675$		−	202949.i		−	0.445431i
$676$		0			0
$677$	−275668.			−0.601464			−0.300732	−	0.953709i	$-0.597231\pi$
$677$	−275668.			−0.601464			−0.300732	+	0.953709i	$0.597231\pi$
$678$	70476.7	−	70476.7i	0.153316	−	0.153316i
$679$	−1.02698e6			−2.22752
$680$			371084.i			0.802518i
$681$	−509210.	+	509210.i	−1.09800	+	1.09800i
$682$	15996.9	−	15996.9i	0.0343929	−	0.0343929i
$683$	19994.2	+	19994.2i	0.0428611	+	0.0428611i	0.728213	−	0.685351i	$-0.240351\pi$
$683$	19994.2	+	19994.2i	0.0428611	+	0.0428611i	−0.685351	+	0.728213i	$0.740351\pi$
$684$	1878.57	+	1878.57i	0.00401527	+	0.00401527i
$685$	−429228.			−0.914760
$686$		−	5896.62i		−	0.0125301i
$687$	−345141.	−	345141.i	−0.731279	−	0.731279i
$688$		−	90092.4i		−	0.190332i
$689$		0			0
$690$	616276.			1.29443
$691$	−232076.	+	232076.i	−0.486042	+	0.486042i	−0.907055	−	0.421013i	$-0.861675\pi$
$691$	−232076.	+	232076.i	−0.486042	+	0.486042i	0.421013	+	0.907055i	$0.361675\pi$
$692$	−52.1707			−0.000108947
$693$			363967.i			0.757871i
$694$	−123598.	+	123598.i	−0.256620	+	0.256620i
$695$	−377932.	+	377932.i	−0.782427	+	0.782427i
$696$	−176210.	−	176210.i	−0.363758	−	0.363758i
$697$	−867623.	−	867623.i	−1.78593	−	1.78593i
$698$	−525311.			−1.07822
$699$		−	652691.i		−	1.33584i
$700$	−362884.	−	362884.i	−0.740579	−	0.740579i
$701$			645341.i			1.31327i	0.754209	+	0.656634i	$0.228020\pi$
$701$			645341.i			1.31327i	−0.754209	+	0.656634i	$0.771980\pi$
$702$		0			0
$703$	1157.43			0.00234199
$704$	−30256.8	+	30256.8i	−0.0610489	+	0.0610489i
$705$	915767.			1.84250
$706$		−	548165.i		−	1.09977i
$707$	−57229.4	+	57229.4i	−0.114493	+	0.114493i
$708$	37161.8	−	37161.8i	0.0741362	−	0.0741362i
$709$	66968.7	+	66968.7i	0.133223	+	0.133223i	0.770574	−	0.637351i	$-0.219970\pi$
$709$	66968.7	+	66968.7i	0.133223	+	0.133223i	−0.637351	+	0.770574i	$0.719970\pi$
$710$	−553454.	−	553454.i	−1.09790	−	1.09790i
$711$	−206792.			−0.409067
$712$		−	93361.0i		−	0.184164i
$713$	31270.6	+	31270.6i	0.0615116	+	0.0615116i
$714$		−	982284.i		−	1.92682i
$715$		0			0
$716$	−202748.			−0.395485
$717$	384608.	−	384608.i	0.748135	−	0.748135i
$718$	−99095.8			−0.192223
$719$			667521.i			1.29124i	0.763659	+	0.645620i	$0.223401\pi$
$719$			667521.i			1.29124i	−0.763659	+	0.645620i	$0.776599\pi$
$720$	111547.	−	111547.i	0.215176	−	0.215176i
$721$	−655413.	+	655413.i	−1.26079	+	1.26079i
$722$	−260586.	−	260586.i	−0.499892	−	0.499892i
$723$	831738.	+	831738.i	1.59115	+	1.59115i
$724$	108080.			0.206190
$725$		−	847979.i		−	1.61328i
$726$	−183533.	−	183533.i	−0.348210	−	0.348210i
$727$			208700.i			0.394870i	0.980316	+	0.197435i	$0.0632611\pi$
$727$			208700.i			0.394870i	−0.980316	+	0.197435i	$0.936739\pi$
$728$		0			0
$729$	−269577.			−0.507257
$730$	−134470.	+	134470.i	−0.252336	+	0.252336i
$731$	586789.			1.09811
$732$			259425.i			0.484162i
$733$	−351672.	+	351672.i	−0.654530	+	0.654530i	−0.954080	−	0.299550i	$-0.903163\pi$
$733$	−351672.	+	351672.i	−0.654530	+	0.654530i	0.299550	+	0.954080i	$0.403163\pi$
$734$	−337352.	+	337352.i	−0.626169	+	0.626169i
$735$	810564.	+	810564.i	1.50042	+	1.50042i
$736$	−59145.5	−	59145.5i	−0.109186	−	0.109186i
$737$	286710.			0.527847
$738$			521612.i			0.957712i
$739$	−350623.	−	350623.i	−0.642024	−	0.642024i	0.309029	−	0.951053i	$-0.399996\pi$
$739$	−350623.	−	350623.i	−0.642024	−	0.642024i	−0.951053	+	0.309029i	$0.899996\pi$
$740$		−	68727.0i		−	0.125506i
$741$		0			0
$742$	−495418.			−0.899837
$743$	619690.	−	619690.i	1.12253	−	1.12253i	0.131166	−	0.991360i	$-0.458128\pi$
$743$	619690.	−	619690.i	1.12253	−	1.12253i	0.991360	−	0.131166i	$-0.0418722\pi$
$744$	25955.5			0.0468903
$745$			1.05228e6i			1.89592i
$746$	−209405.	+	209405.i	−0.376279	+	0.376279i
$747$	112990.	−	112990.i	0.202488	−	0.202488i
$748$	−197068.	−	197068.i	−0.352220	−	0.352220i
$749$	801207.	+	801207.i	1.42817	+	1.42817i
$750$	397242.			0.706209
$751$		−	256027.i		−	0.453947i	−0.973901	−	0.226974i	$-0.927117\pi$
$751$		−	256027.i		−	0.453947i	0.973901	−	0.226974i	$-0.0728831\pi$
$752$	−87888.3	−	87888.3i	−0.155416	−	0.155416i
$753$		−	356335.i		−	0.628446i
$754$		0			0
$755$	−586922.			−1.02964
$756$	86476.2	−	86476.2i	0.151305	−	0.151305i
$757$	963391.			1.68117			0.840583	−	0.541683i	$-0.182213\pi$
$757$	963391.			1.68117			0.840583	+	0.541683i	$0.182213\pi$
$758$		−	502002.i		−	0.873709i
$759$	−327280.	+	327280.i	−0.568115	+	0.568115i
$760$	3336.61	−	3336.61i	0.00577668	−	0.00577668i
$761$	−276390.	−	276390.i	−0.477257	−	0.477257i	0.426996	−	0.904253i	$-0.359572\pi$
$761$	−276390.	−	276390.i	−0.477257	−	0.477257i	−0.904253	+	0.426996i	$0.859572\pi$
$762$	−708746.	−	708746.i	−1.22062	−	1.22062i
$763$	−1.46875e6			−2.52290
$764$			103994.i			0.178165i
$765$	726530.	+	726530.i	1.24145	+	1.24145i
$766$		−	80928.3i		−	0.137925i
$767$		0			0
$768$	−49092.5			−0.0832324
$769$	132903.	−	132903.i	0.224740	−	0.224740i	−0.585751	−	0.810491i	$-0.699200\pi$
$769$	132903.	−	132903.i	0.224740	−	0.224740i	0.810491	+	0.585751i	$0.199200\pi$
$770$	646457.			1.09033
$771$		−	153854.i		−	0.258822i
$772$	97011.9	−	97011.9i	0.162776	−	0.162776i
$773$	−372392.	+	372392.i	−0.623221	+	0.623221i	−0.946354	−	0.323133i	$-0.895264\pi$
$773$	−372392.	+	372392.i	−0.623221	+	0.623221i	0.323133	+	0.946354i	$0.395264\pi$
$774$	−176388.	−	176388.i	−0.294433	−	0.294433i
$775$	62453.0	+	62453.0i	0.103980	+	0.103980i
$776$	−334297.			−0.555149
$777$			181925.i			0.301335i
$778$	278516.	+	278516.i	0.460141	+	0.460141i
$779$			15602.5i			0.0257110i
$780$		0			0
$781$	587835.			0.963725
$782$	385226.	−	385226.i	0.629944	−	0.629944i
$783$	202076.			0.329603
$784$		−	155583.i		−	0.253123i
$785$	−118290.	+	118290.i	−0.191960	+	0.191960i
$786$	−384810.	+	384810.i	−0.622875	+	0.622875i
$787$	273464.	+	273464.i	0.441521	+	0.441521i	0.892523	−	0.451002i	$-0.148933\pi$
$787$	273464.	+	273464.i	0.441521	+	0.441521i	−0.451002	+	0.892523i	$0.648933\pi$
$788$	2798.79	+	2798.79i	0.00450731	+	0.00450731i
$789$	−717330.			−1.15230
$790$			367293.i			0.588516i
$791$	144514.	+	144514.i	0.230970	+	0.230970i
$792$			118477.i			0.188879i
$793$		0			0
$794$	103182.			0.163668
$795$	840170.	−	840170.i	1.32933	−	1.32933i
$796$	−449148.			−0.708865
$797$		−	838853.i		−	1.32059i	−0.751005	−	0.660297i	$-0.770431\pi$
$797$		−	838853.i		−	1.32059i	0.751005	−	0.660297i	$-0.229569\pi$
$798$	−8832.21	+	8832.21i	−0.0138696	+	0.0138696i
$799$	572433.	−	572433.i	0.896668	−	0.896668i
$800$	−118124.	−	118124.i	−0.184569	−	0.184569i
$801$	−182787.	−	182787.i	−0.284892	−	0.284892i
$802$	−379823.			−0.590517
$803$		−	142823.i		−	0.221497i
$804$	232598.	+	232598.i	0.359826	+	0.359826i
$805$			1.26368e6i			1.95006i
$806$		0			0
$807$	966720.			1.48441
$808$	−18629.1	+	18629.1i	−0.0285344	+	0.0285344i
$809$	−560469.			−0.856356			−0.428178	−	0.903694i	$-0.640844\pi$
$809$	−560469.			−0.856356			−0.428178	+	0.903694i	$0.640844\pi$
$810$			858016.i			1.30775i
$811$	−2176.16	+	2176.16i	−0.00330863	+	0.00330863i	−0.708759	−	0.705451i	$-0.750745\pi$
$811$	−2176.16	+	2176.16i	−0.00330863	+	0.00330863i	0.705451	+	0.708759i	$0.250745\pi$
$812$	361322.	−	361322.i	0.548002	−	0.548002i
$813$	655308.	+	655308.i	0.991436	+	0.991436i
$814$	36498.2	+	36498.2i	0.0550837	+	0.0550837i
$815$	535993.			0.806945
$816$		−	319749.i		−	0.480207i
$817$	−5276.12	−	5276.12i	−0.00790443	−	0.00790443i
$818$		−	32465.6i		−	0.0485195i
$819$		0			0
$820$	926458.			1.37784
$821$	−79463.3	+	79463.3i	−0.117891	+	0.117891i	−0.763591	−	0.645700i	$-0.776566\pi$
$821$	−79463.3	+	79463.3i	−0.117891	+	0.117891i	0.645700	+	0.763591i	$0.276566\pi$
$822$	369849.			0.547370
$823$			651622.i			0.962047i	0.876708	+	0.481023i	$0.159735\pi$
$823$			651622.i			0.962047i	−0.876708	+	0.481023i	$0.840265\pi$
$824$	−213347.	+	213347.i	−0.314219	+	0.314219i
$825$	−653638.	+	653638.i	−0.960349	+	0.960349i
$826$	76200.9	+	76200.9i	0.111686	+	0.111686i
$827$	−458846.	−	458846.i	−0.670897	−	0.670897i	0.287026	−	0.957923i	$-0.407333\pi$
$827$	−458846.	−	458846.i	−0.670897	−	0.670897i	−0.957923	+	0.287026i	$0.907333\pi$
$828$	−231597.			−0.337809
$829$			1.22076e6i			1.77631i	0.459540	+	0.888157i	$0.348014\pi$
$829$			1.22076e6i			1.77631i	−0.459540	+	0.888157i	$0.651986\pi$
$830$	−200687.	−	200687.i	−0.291315	−	0.291315i
$831$			658590.i			0.953703i
$832$		0			0
$833$	1.01334e6			1.46038
$834$	325649.	−	325649.i	0.468185	−	0.468185i
$835$	−1.54554e6			−2.21670
$836$			3543.88i			0.00507069i
$837$	−14882.7	+	14882.7i	−0.0212438	+	0.0212438i
$838$	447639.	−	447639.i	0.637441	−	0.637441i
$839$	608696.	+	608696.i	0.864722	+	0.864722i	0.991882	−	0.127160i	$-0.0405862\pi$
$839$	608696.	+	608696.i	0.864722	+	0.864722i	−0.127160	+	0.991882i	$0.540586\pi$
$840$	524447.	+	524447.i	0.743264	+	0.743264i
$841$	137048.			0.193767
$842$			926990.i			1.30753i
$843$	−298687.	−	298687.i	−0.420302	−	0.420302i
$844$		−	84565.3i		−	0.118716i
$845$		0			0
$846$	−344145.			−0.480840
$847$	376338.	−	376338.i	0.524579	−	0.524579i
$848$	−161266.			−0.224260
$849$		−	488319.i		−	0.677467i
$850$	769366.	−	769366.i	1.06487	−	1.06487i
$851$	−71346.1	+	71346.1i	−0.0985171	+	0.0985171i
$852$	476889.	+	476889.i	0.656959	+	0.656959i
$853$	835615.	+	835615.i	1.14844	+	1.14844i	0.986860	+	0.161579i	$0.0516588\pi$
$853$	835615.	+	835615.i	1.14844	+	1.14844i	0.161579	+	0.986860i	$0.448341\pi$
$854$	−531956.			−0.729390
$855$		−	13065.2i		−	0.0178724i
$856$	260805.	+	260805.i	0.355934	+	0.355934i
$857$		−	1.00820e6i		−	1.37273i	−0.727256	−	0.686366i	$-0.759205\pi$
$857$		−	1.00820e6i		−	1.37273i	0.727256	−	0.686366i	$-0.240795\pi$
$858$		0			0
$859$	−766118.			−1.03827			−0.519134	−	0.854693i	$-0.673745\pi$
$859$	−766118.			−1.03827			−0.519134	+	0.854693i	$0.673745\pi$
$860$	−313290.	+	313290.i	−0.423594	+	0.423594i
$861$	−2.45239e6			−3.30814
$862$			822466.i			1.10689i
$863$	205886.	−	205886.i	0.276442	−	0.276442i	−0.555245	−	0.831687i	$-0.687375\pi$
$863$	205886.	−	205886.i	0.276442	−	0.276442i	0.831687	+	0.555245i	$0.187375\pi$
$864$	28149.4	−	28149.4i	0.0377087	−	0.0377087i
$865$	181.420	+	181.420i	0.000242467	+	0.000242467i
$866$	−444506.	−	444506.i	−0.592710	−	0.592710i
$867$	1.08155e6			1.43882
$868$			53222.1i			0.0706403i
$869$	−195055.	−	195055.i	−0.258296	−	0.258296i
$870$			1.22552e6i			1.61913i
$871$		0			0
$872$	−478102.			−0.628764
$873$	−654506.	+	654506.i	−0.858786	+	0.858786i
$874$	−6927.53			−0.00906891
$875$			814552.i			1.06390i
$876$	115867.	−	115867.i	0.150991	−	0.150991i
$877$	−888049.	+	888049.i	−1.15462	+	1.15462i	−0.169001	+	0.985616i	$0.554054\pi$
$877$	−888049.	+	888049.i	−1.15462	+	1.15462i	−0.985616	+	0.169001i	$0.945946\pi$
$878$	607276.	+	607276.i	0.787765	+	0.787765i
$879$	−1.03504e6	−	1.03504e6i	−1.33961	−	1.33961i
$880$	210432.			0.271736
$881$		−	375767.i		−	0.484136i	−0.970259	−	0.242068i	$-0.922174\pi$
$881$		−	375767.i		−	0.484136i	0.970259	−	0.242068i	$-0.0778256\pi$
$882$	−304610.	−	304610.i	−0.391568	−	0.391568i
$883$		−	420890.i		−	0.539818i	−0.962886	−	0.269909i	$-0.913006\pi$
$883$		−	420890.i		−	0.539818i	0.962886	−	0.269909i	$-0.0869936\pi$
$884$		0			0
$885$	−258456.			−0.329989
$886$	−207655.	+	207655.i	−0.264530	+	0.264530i
$887$	1.04182e6			1.32417			0.662086	−	0.749428i	$-0.269671\pi$
$887$	1.04182e6			1.32417			0.662086	+	0.749428i	$0.269671\pi$
$888$			59219.3i			0.0750996i
$889$	1.45329e6	−	1.45329e6i	1.83887	−	1.83887i
$890$	−324657.	+	324657.i	−0.409868	+	0.409868i
$891$	−455658.	−	455658.i	−0.573963	−	0.573963i
$892$	218171.	+	218171.i	0.274201	+	0.274201i
$893$	−10294.1			−0.0129088
$894$		−	906711.i		−	1.13447i
$895$	705041.	+	705041.i	0.880174	+	0.880174i
$896$		−	100665.i		−	0.125390i
$897$		0			0
$898$	−44925.1			−0.0557104
$899$	−62184.2	+	62184.2i	−0.0769415	+	0.0769415i
$900$	−462541.			−0.571038
$901$		−	1.05036e6i		−	1.29386i
$902$	−492006.	+	492006.i	−0.604724	+	0.604724i
$903$	829299.	−	829299.i	1.01703	−	1.01703i
$904$	47041.5	+	47041.5i	0.0575631	+	0.0575631i
$905$	−375840.	−	375840.i	−0.458888	−	0.458888i
$906$	505727.			0.616113
$907$			1.12762e6i			1.37071i	0.728207	+	0.685357i	$0.240354\pi$
$907$			1.12762e6i			1.37071i	−0.728207	+	0.685357i	$0.759646\pi$
$908$	−339885.	−	339885.i	−0.412250	−	0.412250i
$909$			72946.1i			0.0882824i
$910$		0			0
$911$	621926.			0.749380			0.374690	−	0.927150i	$-0.377749\pi$
$911$	621926.			0.749380			0.374690	+	0.927150i	$0.377749\pi$
$912$	−2875.02	+	2875.02i	−0.00345662	+	0.00345662i
$913$	213154.			0.255712
$914$			650068.i			0.778155i
$915$	902135.	−	902135.i	1.07753	−	1.07753i
$916$	230373.	−	230373.i	0.274562	−	0.274562i
$917$	−789058.	−	789058.i	−0.938362	−	0.938362i
$918$	183342.	+	183342.i	0.217559	+	0.217559i
$919$	212127.			0.251169			0.125584	−	0.992083i	$-0.459919\pi$
$919$	212127.			0.251169			0.125584	+	0.992083i	$0.459919\pi$
$920$			411349.i			0.485999i
$921$	−201685.	−	201685.i	−0.237768	−	0.237768i
$922$			149101.i			0.175396i
$923$		0			0
$924$	−557027.			−0.652427
$925$	−142491.	+	142491.i	−0.166535	+	0.166535i
$926$	−549757.			−0.641134
$927$			835406.i			0.972160i
$928$	117616.	−	117616.i	0.136575	−	0.136575i
$929$	−329117.	+	329117.i	−0.381346	+	0.381346i	−0.871587	−	0.490241i	$-0.836909\pi$
$929$	−329117.	+	329117.i	−0.381346	+	0.381346i	0.490241	+	0.871587i	$0.336909\pi$
$930$	−90258.4	−	90258.4i	−0.104357	−	0.104357i
$931$	−9111.50	−	9111.50i	−0.0105121	−	0.0105121i
$932$	435655.			0.501546
$933$			1.09861e6i			1.26206i
$934$	−98240.0	−	98240.0i	−0.112615	−	0.112615i
$935$			1.37058e6i			1.56777i
$936$		0			0
$937$	860175.			0.979733			0.489867	−	0.871797i	$-0.337045\pi$
$937$	860175.			0.979733			0.489867	+	0.871797i	$0.337045\pi$
$938$	−476945.	+	476945.i	−0.542079	+	0.542079i
$939$	1.17090e6			1.32797
$940$			611252.i			0.691774i
$941$	−976348.	+	976348.i	−1.10262	+	1.10262i	−0.108525	+	0.994094i	$0.534613\pi$
$941$	−976348.	+	976348.i	−1.10262	+	1.10262i	−0.994094	+	0.108525i	$0.965387\pi$
$942$	101926.	−	101926.i	0.114864	−	0.114864i
$943$	−961765.	−	961765.i	−1.08155	−	1.08155i
$944$	24804.6	+	24804.6i	0.0278348	+	0.0278348i
$945$	−601431.			−0.673476
$946$		−	332752.i		−	0.371825i
$947$	74686.8	+	74686.8i	0.0832806	+	0.0832806i	0.747520	−	0.664239i	$-0.231244\pi$
$947$	74686.8	+	74686.8i	0.0832806	+	0.0832806i	−0.664239	+	0.747520i	$0.731244\pi$
$948$		−	316482.i		−	0.352153i
$949$		0			0
$950$	−13835.5			−0.0153302
$951$	164996.	−	164996.i	0.182437	−	0.182437i
$952$	655650.			0.723433
$953$			1.20235e6i			1.32387i	0.749562	+	0.661935i	$0.230264\pi$
$953$			1.20235e6i			1.32387i	−0.749562	+	0.661935i	$0.769736\pi$
$954$	−315736.	+	315736.i	−0.346918	+	0.346918i
$955$	361632.	−	361632.i	0.396515	−	0.396515i
$956$	256716.	+	256716.i	0.280891	+	0.280891i
$957$	−650824.	−	650824.i	−0.710624	−	0.710624i
$958$	1.04960e6			1.14365
$959$			758381.i			0.824614i
$960$	170716.	+	170716.i	0.185239	+	0.185239i
$961$			914361.i			0.990082i
$962$		0			0
$963$	1.02124e6			1.10122
$964$	−555164.	+	555164.i	−0.597403	+	0.597403i
$965$	−674705.			−0.724535
$966$		−	1.08887e6i		−	1.16686i
$967$	−641718.	+	641718.i	−0.686264	+	0.686264i	−0.961404	−	0.275140i	$-0.911276\pi$
$967$	−641718.	+	641718.i	−0.686264	+	0.686264i	0.275140	+	0.961404i	$0.411276\pi$
$968$	122504.	−	122504.i	0.130737	−	0.130737i
$969$	−18725.6	−	18725.6i	−0.0199429	−	0.0199429i
$970$	1.16250e6	+	1.16250e6i	1.23552	+	1.23552i
$971$	−260542.			−0.276337			−0.138168	−	0.990409i	$-0.544121\pi$
$971$	−260542.			−0.276337			−0.138168	+	0.990409i	$0.544121\pi$
$972$		−	596812.i		−	0.631691i
$973$	667748.	+	667748.i	0.705321	+	0.705321i
$974$			211015.i			0.222431i
$975$		0			0
$976$	−173160.			−0.181781
$977$	−1.20062e6	+	1.20062e6i	−1.25781	+	1.25781i	−0.305680	+	0.952134i	$0.598884\pi$
$977$	−1.20062e6	+	1.20062e6i	−1.25781	+	1.25781i	−0.952134	+	0.305680i	$0.901116\pi$
$978$	−461844.			−0.482856
$979$		−	344825.i		−	0.359777i
$980$	−541031.	+	541031.i	−0.563339	+	0.563339i
$981$	−936055.	+	936055.i	−0.972665	+	0.972665i
$982$	−34631.7	−	34631.7i	−0.0359129	−	0.0359129i
$983$	−156188.	−	156188.i	−0.161637	−	0.161637i	0.621655	−	0.783291i	$-0.286461\pi$
$983$	−156188.	−	156188.i	−0.161637	−	0.161637i	−0.783291	+	0.621655i	$0.786461\pi$
$984$	−798292.			−0.824464
$985$		−	19465.2i		−	0.0200625i
$986$	766055.	+	766055.i	0.787963	+	0.787963i
$987$		−	1.61802e6i		−	1.66092i
$988$		0			0
$989$	650459.			0.665009
$990$	411995.	−	411995.i	0.420361	−	0.420361i
$991$	440953.			0.448998			0.224499	−	0.974474i	$-0.427925\pi$
$991$	440953.			0.448998			0.224499	+	0.974474i	$0.427925\pi$
$992$			17324.6i			0.0176052i
$993$	−452939.	+	452939.i	−0.459347	+	0.459347i
$994$	−977868.	+	977868.i	−0.989709	+	0.989709i
$995$	1.56188e6	+	1.56188e6i	1.57762	+	1.57762i
$996$	172924.	+	172924.i	0.174316	+	0.174316i
$997$	−853876.			−0.859023			−0.429511	−	0.903061i	$-0.641314\pi$
$997$	−853876.			−0.859023			−0.429511	+	0.903061i	$0.641314\pi$
$998$			305215.i			0.306440i
$999$	−33956.1	−	33956.1i	−0.0340241	−	0.0340241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.5.d.e.239.1		8
13.5	odd	4		338.5.d.h.99.1		8
13.6	odd	12		26.5.f.a.11.2	✓	8
13.8	odd	4	inner	338.5.d.e.99.1		8
13.10	even	6		26.5.f.a.19.2	yes	8
13.12	even	2		338.5.d.h.239.1		8
39.23	odd	6		234.5.bb.c.19.1		8
39.32	even	12		234.5.bb.c.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.11.2	✓	8	13.6	odd	12
26.5.f.a.19.2	yes	8	13.10	even	6
234.5.bb.c.19.1		8	39.23	odd	6
234.5.bb.c.37.1		8	39.32	even	12
338.5.d.e.99.1		8	13.8	odd	4	inner
338.5.d.e.239.1		8	1.1	even	1	trivial
338.5.d.h.99.1		8	13.5	odd	4
338.5.d.h.239.1		8	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	338.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} -11.9855 q^{3} -8.00000i q^{4} +(-27.8195 + 27.8195i) q^{5} +(23.9709 - 23.9709i) q^{6} +(49.1528 + 49.1528i) q^{7} +(16.0000 + 16.0000i) q^{8} +62.6514 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} -11.9855 q^{3} -8.00000i q^{4} +(-27.8195 + 27.8195i) q^{5} +(23.9709 - 23.9709i) q^{6} +(49.1528 + 49.1528i) q^{7} +(16.0000 + 16.0000i) q^{8} +62.6514 q^{9} -111.278i q^{10} +(59.0953 + 59.0953i) q^{11} +95.8837i q^{12} -196.611 q^{14} +(333.429 - 333.429i) q^{15} -64.0000 q^{16} -416.844i q^{17} +(-125.303 + 125.303i) q^{18} +(-3.74806 + 3.74806i) q^{19} +(222.556 + 222.556i) q^{20} +(-589.119 - 589.119i) q^{21} -236.381 q^{22} -462.074i q^{23} +(-191.767 - 191.767i) q^{24} -922.846i q^{25} +219.917 q^{27} +(393.222 - 393.222i) q^{28} +918.874 q^{29} +1333.72i q^{30} +(-67.6743 + 67.6743i) q^{31} +(128.000 - 128.000i) q^{32} +(-708.285 - 708.285i) q^{33} +(833.689 + 833.689i) q^{34} -2734.81 q^{35} -501.211i q^{36} +(-154.404 - 154.404i) q^{37} -14.9922i q^{38} -890.223 q^{40} +(2081.41 - 2081.41i) q^{41} +2356.48 q^{42} +1407.69i q^{43} +(472.762 - 472.762i) q^{44} +(-1742.93 + 1742.93i) q^{45} +(924.149 + 924.149i) q^{46} +(1373.25 + 1373.25i) q^{47} +767.070 q^{48} +2430.99i q^{49} +(1845.69 + 1845.69i) q^{50} +4996.07i q^{51} +2519.79 q^{53} +(-439.834 + 439.834i) q^{54} -3288.00 q^{55} +1572.89i q^{56} +(44.9222 - 44.9222i) q^{57} +(-1837.75 + 1837.75i) q^{58} +(-387.572 - 387.572i) q^{59} +(-2667.43 - 2667.43i) q^{60} +2705.62 q^{61} -270.697i q^{62} +(3079.49 + 3079.49i) q^{63} +512.000i q^{64} +2833.14 q^{66} +(2425.83 - 2425.83i) q^{67} -3334.75 q^{68} +5538.18i q^{69} +(5469.62 - 5469.62i) q^{70} +(4973.62 - 4973.62i) q^{71} +(1002.42 + 1002.42i) q^{72} +(-1208.41 - 1208.41i) q^{73} +617.616 q^{74} +11060.7i q^{75} +(29.9845 + 29.9845i) q^{76} +5809.40i q^{77} -3300.68 q^{79} +(1780.45 - 1780.45i) q^{80} -7710.57 q^{81} +8325.63i q^{82} +(1803.48 - 1803.48i) q^{83} +(-4712.95 + 4712.95i) q^{84} +(11596.4 + 11596.4i) q^{85} +(-2815.39 - 2815.39i) q^{86} -11013.1 q^{87} +1891.05i q^{88} +(-2917.53 - 2917.53i) q^{89} -6971.71i q^{90} -3696.59 q^{92} +(811.109 - 811.109i) q^{93} -5493.02 q^{94} -208.538i q^{95} +(-1534.14 + 1534.14i) q^{96} +(-10446.8 + 10446.8i) q^{97} +(-4861.98 - 4861.98i) q^{98} +(3702.40 + 3702.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{2} - 30 q^{5} + 86 q^{7} + 128 q^{8} - 180 q^{9}+O(q^{10}) \) 8 * q - 16 * q^2 - 30 * q^5 + 86 * q^7 + 128 * q^8 - 180 * q^9	\( 8 q - 16 q^{2} - 30 q^{5} + 86 q^{7} + 128 q^{8} - 180 q^{9} + 474 q^{11} - 344 q^{14} + 1128 q^{15} - 512 q^{16} + 360 q^{18} + 518 q^{19} + 240 q^{20} - 1914 q^{21} - 1896 q^{22} - 2268 q^{27} + 688 q^{28} + 504 q^{29} + 3376 q^{31} + 1024 q^{32} + 246 q^{33} - 1080 q^{34} - 12948 q^{35} + 5056 q^{37} - 960 q^{40} + 4392 q^{41} + 7656 q^{42} + 3792 q^{44} - 2898 q^{45} - 24 q^{46} - 4848 q^{47} + 3152 q^{50} - 6840 q^{53} + 4536 q^{54} - 588 q^{55} + 4434 q^{57} - 1008 q^{58} + 3510 q^{59} - 9024 q^{60} - 17340 q^{61} + 3276 q^{63} - 984 q^{66} + 7334 q^{67} + 4320 q^{68} + 25896 q^{70} + 7998 q^{71} - 2880 q^{72} - 19294 q^{73} - 20224 q^{74} - 4144 q^{76} - 11328 q^{79} + 1920 q^{80} - 12096 q^{81} - 10344 q^{83} - 15312 q^{84} + 20670 q^{85} - 13536 q^{86} - 36744 q^{87} - 1998 q^{89} + 96 q^{92} + 12744 q^{93} + 19392 q^{94} - 13694 q^{97} - 24640 q^{98} - 9504 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 30 * q^5 + 86 * q^7 + 128 * q^8 - 180 * q^9 + 474 * q^11 - 344 * q^14 + 1128 * q^15 - 512 * q^16 + 360 * q^18 + 518 * q^19 + 240 * q^20 - 1914 * q^21 - 1896 * q^22 - 2268 * q^27 + 688 * q^28 + 504 * q^29 + 3376 * q^31 + 1024 * q^32 + 246 * q^33 - 1080 * q^34 - 12948 * q^35 + 5056 * q^37 - 960 * q^40 + 4392 * q^41 + 7656 * q^42 + 3792 * q^44 - 2898 * q^45 - 24 * q^46 - 4848 * q^47 + 3152 * q^50 - 6840 * q^53 + 4536 * q^54 - 588 * q^55 + 4434 * q^57 - 1008 * q^58 + 3510 * q^59 - 9024 * q^60 - 17340 * q^61 + 3276 * q^63 - 984 * q^66 + 7334 * q^67 + 4320 * q^68 + 25896 * q^70 + 7998 * q^71 - 2880 * q^72 - 19294 * q^73 - 20224 * q^74 - 4144 * q^76 - 11328 * q^79 + 1920 * q^80 - 12096 * q^81 - 10344 * q^83 - 15312 * q^84 + 20670 * q^85 - 13536 * q^86 - 36744 * q^87 - 1998 * q^89 + 96 * q^92 + 12744 * q^93 + 19392 * q^94 - 13694 * q^97 - 24640 * q^98 - 9504 * q^99

Introduction

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