LMFDB - Embedded newform 338.5.d.e.99.1

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			99.1
Root			$-2.16680 + 2.16680i$ of defining polynomial
Character	$\chi$	$=$	338.99
Dual form			338.5.d.e.239.1

$q$-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 $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−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	−0.992773	−	0.120006i	$-0.961709\pi$
$5$	−27.8195	−	27.8195i	−1.11278	−	1.11278i	−0.120006	−	0.992773i	$-0.538291\pi$
$6$	23.9709	+	23.9709i	0.665859	+	0.665859i
$7$	49.1528	−	49.1528i	1.00312	−	1.00312i	0.00312281	−	0.999995i	$-0.499006\pi$
$7$	49.1528	−	49.1528i	1.00312	−	1.00312i	0.999995	−	0.00312281i	$-0.000994022\pi$
$8$	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	−0.419407	−	0.907798i	$-0.637762\pi$
$11$	59.0953	−	59.0953i	0.488391	−	0.488391i	0.907798	+	0.419407i	$0.137762\pi$
$12$		−	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	$0.256402\pi$
$17$			416.844i			1.44237i	−0.692744	+	0.721184i	$0.743598\pi$
$18$	−125.303	−	125.303i	−0.386737	−	0.386737i
$19$	−3.74806	−	3.74806i	−0.0103824	−	0.0103824i	0.701897	−	0.712279i	$-0.252337\pi$
$19$	−3.74806	−	3.74806i	−0.0103824	−	0.0103824i	−0.712279	+	0.701897i	$0.752337\pi$
$20$	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	$0.143868\pi$
$23$			462.074i			0.873486i	−0.899586	+	0.436743i	$0.856132\pi$
$24$	−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	0.671019	−	0.741440i	$-0.265857\pi$
$31$	−67.6743	−	67.6743i	−0.0704208	−	0.0704208i	−0.741440	+	0.671019i	$0.765857\pi$
$32$	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	−0.761247	−	0.648461i	$-0.775413\pi$
$37$	−154.404	+	154.404i	−0.112786	+	0.112786i	0.648461	+	0.761247i	$0.275413\pi$
$38$			14.9922i			0.0103824i
$39$		0			0
$40$	−890.223			−0.556389
$41$	2081.41	+	2081.41i	1.23820	+	1.23820i	0.960738	+	0.277458i	$0.0894920\pi$
$41$	2081.41	+	2081.41i	1.23820	+	1.23820i	0.277458	+	0.960738i	$0.410508\pi$
$42$	2356.48			1.33587
$43$		−	1407.69i		−	0.761327i	−0.924714	−	0.380663i	$-0.875696\pi$
$43$		−	1407.69i		−	0.761327i	0.924714	−	0.380663i	$-0.124304\pi$
$44$	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	−0.324293	−	0.945957i	$-0.605126\pi$
$47$	1373.25	−	1373.25i	0.621664	−	0.621664i	0.945957	+	0.324293i	$0.105126\pi$
$48$	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	−0.760582	−	0.649242i	$-0.775086\pi$
$59$	−387.572	+	387.572i	−0.111339	+	0.111339i	0.649242	+	0.760582i	$0.275086\pi$
$60$	−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	0.923645	−	0.383250i	$-0.125195\pi$
$67$	2425.83	+	2425.83i	0.540394	+	0.540394i	−0.383250	+	0.923645i	$0.625195\pi$
$68$	−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	0.999912	−	0.0132789i	$-0.00422694\pi$
$71$	4973.62	+	4973.62i	0.986633	+	0.986633i	−0.0132789	+	0.999912i	$0.504227\pi$
$72$	1002.42	−	1002.42i	0.193368	−	0.193368i
$73$	−1208.41	+	1208.41i	−0.226762	+	0.226762i	−0.811338	−	0.584577i	$-0.801261\pi$
$73$	−1208.41	+	1208.41i	−0.226762	+	0.226762i	0.584577	+	0.811338i	$0.301261\pi$
$74$	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	0.825781	−	0.563991i	$-0.190735\pi$
$83$	1803.48	+	1803.48i	0.261791	+	0.261791i	−0.563991	+	0.825781i	$0.690735\pi$
$84$	−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	−0.866867	−	0.498539i	$-0.833870\pi$
$89$	−2917.53	+	2917.53i	−0.368329	+	0.368329i	0.498539	+	0.866867i	$0.333870\pi$
$90$			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	−0.993110	−	0.117188i	$-0.962612\pi$
$97$	−10446.8	−	10446.8i	−1.11030	−	1.11030i	−0.117188	−	0.993110i	$-0.537388\pi$
$98$	−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	$-0.981825\pi$
$101$		−	1164.32i		−	0.114138i	0.998370	−	0.0570688i	$-0.0181754\pi$
$102$	−9992.15	+	9992.15i	−0.960414	+	0.960414i
$103$		−	13334.2i		−	1.25688i	−0.777860	−	0.628438i	$-0.783695\pi$
$103$		−	13334.2i		−	1.25688i	0.777860	−	0.628438i	$-0.216305\pi$
$104$		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	−0.952269	−	0.305259i	$-0.901257\pi$
$109$	−14940.7	−	14940.7i	−1.25753	−	1.25753i	−0.305259	−	0.952269i	$-0.598743\pi$
$110$	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	$0.369058\pi$
$127$			29566.9i			1.83315i	−0.399863	+	0.916575i	$0.630942\pi$
$128$	−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	−0.471070	−	0.882096i	$-0.656132\pi$
$137$	7714.53	−	7714.53i	0.411025	−	0.411025i	0.882096	+	0.471070i	$0.156132\pi$
$138$	−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	0.990365	−	0.138480i	$-0.0442215\pi$
$149$	18912.7	+	18912.7i	0.851886	+	0.851886i	−0.138480	+	0.990365i	$0.544222\pi$
$150$	−22121.5	+	22121.5i	−0.983177	+	0.983177i
$151$	10548.8	−	10548.8i	0.462645	−	0.462645i	−0.436877	−	0.899521i	$-0.643915\pi$
$151$	10548.8	−	10548.8i	0.462645	−	0.462645i	0.899521	+	0.436877i	$0.143915\pi$
$152$	−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	−0.864762	−	0.502181i	$-0.832531\pi$
$163$	−9633.41	+	9633.41i	−0.362581	+	0.362581i	0.502181	+	0.864762i	$0.332531\pi$
$164$	−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	−0.00397084	−	0.999992i	$-0.501264\pi$
$167$	27778.0	−	27778.0i	0.996021	−	0.996021i	0.999992	+	0.00397084i	$0.00126396\pi$
$168$			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	$3.46788e-5\pi$
$173$			6.52133i			0.000217893i	−1.00000		0.000108947i	$0.999965\pi$
$174$	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	$0.129423\pi$
$179$			25343.4i			0.790969i	−0.918473	+	0.395485i	$0.870577\pi$
$180$	13943.4	−	13943.4i	0.430353	−	0.430353i
$181$		−	13510.0i		−	0.412380i	−0.978512	−	0.206190i	$-0.933894\pi$
$181$		−	13510.0i		−	0.412380i	0.978512	−	0.206190i	$-0.0661065\pi$
$182$		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	−0.525340	−	0.850892i	$-0.676062\pi$
$193$	12126.5	−	12126.5i	0.325552	−	0.325552i	0.850892	+	0.525340i	$0.176062\pi$
$194$			41787.2i			1.11030i
$195$		0			0
$196$	19447.9			0.506246
$197$	−349.848	−	349.848i	−0.00901462	−	0.00901462i	0.702585	−	0.711600i	$-0.252029\pi$
$197$	−349.848	−	349.848i	−0.00901462	−	0.00901462i	−0.711600	+	0.702585i	$0.752029\pi$
$198$	−14809.6			−0.377758
$199$			56143.5i			1.41773i	0.705344	+	0.708865i	$0.250793\pi$
$199$			56143.5i			1.41773i	−0.705344	+	0.708865i	$0.749207\pi$
$200$	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	0.377577	−	0.925978i	$-0.376757\pi$
$223$	−27271.4	−	27271.4i	−0.548401	−	0.548401i	−0.925978	+	0.377577i	$0.876757\pi$
$224$	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	0.986750	−	0.162250i	$-0.0518750\pi$
$227$	42485.7	+	42485.7i	0.824500	+	0.824500i	−0.162250	+	0.986750i	$0.551875\pi$
$228$	−359.378	+	359.378i	−0.00691324	+	0.00691324i
$229$	28796.6	−	28796.6i	0.549124	−	0.549124i	−0.377063	−	0.926188i	$-0.623066\pi$
$229$	28796.6	−	28796.6i	0.549124	−	0.549124i	0.926188	+	0.377063i	$0.123066\pi$
$230$	−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	$-0.832765\pi$
$233$		−	54456.8i		−	1.00309i	0.865131	−	0.501546i	$-0.167235\pi$
$234$		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	0.368031	−	0.929813i	$-0.380032\pi$
$239$	−32089.5	−	32089.5i	−0.561782	−	0.561782i	−0.929813	+	0.368031i	$0.880032\pi$
$240$	−21339.5	−	21339.5i	−0.370477	−	0.370477i
$241$	−69395.6	+	69395.6i	−1.19481	+	1.19481i	−0.219105	+	0.975701i	$0.570314\pi$
$241$	−69395.6	+	69395.6i	−1.19481	+	1.19481i	−0.975701	+	0.219105i	$0.929686\pi$
$242$	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	$-0.924179\pi$
$251$		−	29730.6i		−	0.471906i	0.971764	−	0.235953i	$-0.0758212\pi$
$252$	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	$-0.969019\pi$
$257$		−	12836.7i		−	0.194352i	0.995267	−	0.0971759i	$-0.0309809\pi$
$258$	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	−0.973436	−	0.228958i	$-0.926468\pi$
$271$	−54675.2	+	54675.2i	−0.744478	+	0.744478i	0.228958	+	0.973436i	$0.426468\pi$
$272$		−	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	$0.116566\pi$
$277$			54949.1i			0.716145i	−0.933694	+	0.358073i	$0.883434\pi$
$278$	−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	−0.531469	−	0.847078i	$-0.678360\pi$
$281$	24920.8	−	24920.8i	0.315609	−	0.315609i	0.847078	+	0.531469i	$0.178360\pi$
$282$	65836.4			0.827881
$283$		−	40742.6i		−	0.508716i	−0.967110	−	0.254358i	$-0.918136\pi$
$283$		−	40742.6i		−	0.508716i	0.967110	−	0.254358i	$-0.0818642\pi$
$284$	−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	0.00594591	−	0.999982i	$-0.498107\pi$
$293$	86357.9	−	86357.9i	1.00593	−	1.00593i	0.999982	−	0.00594591i	$-0.00189265\pi$
$294$	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	−0.612178	−	0.790720i	$-0.709706\pi$
$307$	16827.4	−	16827.4i	0.178542	−	0.178542i	0.790720	+	0.612178i	$0.209706\pi$
$308$	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	$0.157134\pi$
$311$			91661.6i			0.947691i	−0.880608	+	0.473845i	$0.842866\pi$
$312$		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	0.635284	−	0.772278i	$-0.280883\pi$
$317$	−13766.4	−	13766.4i	−0.136994	−	0.136994i	−0.772278	+	0.635284i	$0.780883\pi$
$318$	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	0.858216	−	0.513288i	$-0.171573\pi$
$331$	37790.7	+	37790.7i	0.344928	+	0.344928i	−0.513288	+	0.858216i	$0.671573\pi$
$332$	−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	$-0.981645\pi$
$337$		−	13090.4i		−	0.115264i	0.998338	−	0.0576319i	$-0.0183550\pi$
$338$		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	0.0815455	−	0.996670i	$-0.474014\pi$
$349$	131328.	−	131328.i	1.07822	−	1.07822i	0.996670	−	0.0815455i	$-0.0259856\pi$
$350$		−	181442.i		−	1.48116i
$351$		0			0
$352$	15128.4			0.122098
$353$	−137041.	−	137041.i	−1.09977	−	1.09977i	−0.994437	−	0.105333i	$-0.966409\pi$
$353$	−137041.	−	137041.i	−1.09977	−	1.09977i	−0.105333	−	0.994437i	$-0.533591\pi$
$354$	−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	−0.604433	−	0.796656i	$-0.706600\pi$
$359$	24773.9	−	24773.9i	0.192223	−	0.192223i	0.796656	+	0.604433i	$0.206600\pi$
$360$	−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	0.119165	−	0.992874i	$-0.461978\pi$
$379$	−125500.	−	125500.i	−0.873709	−	0.873709i	−0.992874	+	0.119165i	$0.961978\pi$
$380$	−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	0.634773	−	0.772698i	$-0.281093\pi$
$383$	−20232.1	−	20232.1i	−0.137925	−	0.137925i	−0.772698	+	0.634773i	$0.781093\pi$
$384$	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	$0.152201\pi$
$389$			139258.i			0.920283i	−0.887846	+	0.460141i	$0.847799\pi$
$390$		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	−0.784190	−	0.620521i	$-0.786921\pi$
$397$	−25795.6	+	25795.6i	−0.163668	+	0.163668i	0.620521	+	0.784190i	$0.286921\pi$
$398$	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	−0.347254	−	0.937771i	$-0.612886\pi$
$401$	94955.8	−	94955.8i	0.590517	−	0.590517i	0.937771	+	0.347254i	$0.112886\pi$
$402$			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	0.682431	−	0.730950i	$-0.260923\pi$
$409$	−8116.40	−	8116.40i	−0.0485195	−	0.0485195i	−0.730950	+	0.682431i	$0.760923\pi$
$410$	−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	0.923195	+	0.384333i	$0.125568\pi$
$421$	231747.	+	231747.i	1.30753	+	1.30753i	0.384333	+	0.923195i	$0.374432\pi$
$422$	−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	0.993557	+	0.113330i	$0.0361516\pi$
$431$	205616.	+	205616.i	1.10689	+	1.10689i	0.113330	+	0.993557i	$0.463848\pi$
$432$	−14074.7			−0.0754173
$433$		−	222253.i		−	1.18542i	−0.805416	−	0.592710i	$-0.798058\pi$
$433$		−	222253.i		−	1.18542i	0.805416	−	0.592710i	$-0.201942\pi$
$434$	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	$0.288762\pi$
$439$			303638.i			1.57553i	−0.615975	+	0.787765i	$0.711238\pi$
$440$	−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	−0.678703	−	0.734413i	$-0.737458\pi$
$449$	11231.3	−	11231.3i	0.0557104	−	0.0557104i	0.734413	+	0.678703i	$0.237458\pi$
$450$	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	0.979517	−	0.201362i	$-0.0645368\pi$
$457$	162517.	+	162517.i	0.778155	+	0.778155i	−0.201362	+	0.979517i	$0.564537\pi$
$458$	−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	0.789345	−	0.613950i	$-0.210420\pi$
$461$	37275.2	+	37275.2i	0.175396	+	0.175396i	−0.613950	+	0.789345i	$0.710420\pi$
$462$	139257.	−	139257.i	0.652427	−	0.652427i
$463$	137439.	−	137439.i	0.641134	−	0.641134i	−0.309700	−	0.950834i	$-0.600229\pi$
$463$	137439.	−	137439.i	0.641134	−	0.641134i	0.950834	+	0.309700i	$0.100229\pi$
$464$	−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	$-0.964077\pi$
$467$		−	49120.0i		−	0.225229i	0.993639	−	0.112615i	$-0.0359225\pi$
$468$		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	−0.155875	+	0.987777i	$0.549820\pi$
$479$	−262401.	+	262401.i	−1.14365	+	1.14365i	−0.987777	+	0.155875i	$0.950180\pi$
$480$			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	0.809521	−	0.587090i	$-0.199727\pi$
$487$	52753.7	+	52753.7i	0.222431	+	0.222431i	−0.587090	+	0.809521i	$0.699727\pi$
$488$	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	$-0.988566\pi$
$491$		−	17315.8i		−	0.0718258i	0.999355	−	0.0359129i	$-0.0114339\pi$
$492$	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	0.843527	−	0.537087i	$-0.180475\pi$
$499$	76303.8	+	76303.8i	0.306440	+	0.306440i	−0.537087	+	0.843527i	$0.680475\pi$
$500$	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	0.478020	−	0.878349i	$-0.341355\pi$
$509$	−103718.	−	103718.i	−0.400330	−	0.400330i	−0.878349	+	0.478020i	$0.841355\pi$
$510$	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	−0.0842501	−	0.996445i	$-0.526849\pi$
$541$	266982.	−	266982.i	0.912194	−	0.912194i	0.996445	+	0.0842501i	$0.0268495\pi$
$542$	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	−0.903990	−	0.427553i	$-0.859376\pi$
$557$	−147814.	+	147814.i	−0.476438	+	0.476438i	0.427553	+	0.903990i	$0.359376\pi$
$558$			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	$0.109332\pi$
$563$			213487.i			0.673527i	−0.941589	+	0.336763i	$0.890668\pi$
$564$	−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	$0.231399\pi$
$569$			430345.i			1.32921i	−0.747196	+	0.664603i	$0.768601\pi$
$570$	−4998.85	+	4998.85i	−0.0153858	+	0.0153858i
$571$		−	413840.i		−	1.26929i	−0.772805	−	0.634644i	$-0.781147\pi$
$571$		−	413840.i		−	1.26929i	0.772805	−	0.634644i	$-0.218853\pi$
$572$		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	0.998755	+	0.0498841i	$0.0158852\pi$
$577$	349122.	+	349122.i	1.04864	+	1.04864i	0.0498841	+	0.998755i	$0.484115\pi$
$578$	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	0.698921	−	0.715199i	$-0.253664\pi$
$587$	−5609.16	−	5609.16i	−0.0162788	−	0.0162788i	−0.715199	+	0.698921i	$0.753664\pi$
$588$	−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	−0.487312	−	0.873228i	$-0.662022\pi$
$593$	135707.	−	135707.i	0.385917	−	0.385917i	0.873228	+	0.487312i	$0.162022\pi$
$594$	−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	0.740674	−	0.671865i	$-0.234506\pi$
$613$	25856.4	+	25856.4i	0.0688093	+	0.0688093i	−0.671865	+	0.740674i	$0.734506\pi$
$614$	−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	0.995772	−	0.0918557i	$-0.0292799\pi$
$617$	344111.	+	344111.i	0.903917	+	0.903917i	−0.0918557	+	0.995772i	$0.529280\pi$
$618$	319633.	−	319633.i	0.836902	−	0.836902i
$619$	112057.	−	112057.i	0.292453	−	0.292453i	−0.545596	−	0.838049i	$-0.683697\pi$
$619$	112057.	−	112057.i	0.292453	−	0.292453i	0.838049	+	0.545596i	$0.183697\pi$
$620$	−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	−0.777453	−	0.628941i	$-0.783489\pi$
$631$	−59131.7	+	59131.7i	−0.148512	+	0.148512i	0.628941	+	0.777453i	$0.283489\pi$
$632$	−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	$-0.923427\pi$
$641$		−	195783.i		−	0.476496i	0.971204	−	0.238248i	$-0.0765731\pi$
$642$	390734.	+	390734.i	0.948007	+	0.948007i
$643$	241575.	+	241575.i	0.584293	+	0.584293i	0.936080	−	0.351787i	$-0.114426\pi$
$643$	241575.	+	241575.i	0.584293	+	0.584293i	−0.351787	+	0.936080i	$0.614426\pi$
$644$	−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	$0.379711\pi$
$647$			778145.i			1.85888i	−0.368970	+	0.929441i	$0.620289\pi$
$648$	−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	0.0567313	−	0.998389i	$-0.481932\pi$
$661$	461004.	−	461004.i	1.05512	−	1.05512i	0.998389	−	0.0567313i	$-0.0180678\pi$
$662$		−	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	$-0.698954\pi$
$673$		−	734600.i		−	1.62189i	0.585124	−	0.810944i	$-0.301046\pi$
$674$	−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	−0.685351	−	0.728213i	$-0.740351\pi$
$683$	19994.2	−	19994.2i	0.0428611	−	0.0428611i	0.728213	+	0.685351i	$0.240351\pi$
$684$	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	0.421013	−	0.907055i	$-0.361675\pi$
$691$	−232076.	−	232076.i	−0.486042	−	0.486042i	−0.907055	+	0.421013i	$0.861675\pi$
$692$	−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	$-0.771980\pi$
$701$		−	645341.i		−	1.31327i	0.754209	−	0.656634i	$-0.228020\pi$
$702$		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	−0.637351	−	0.770574i	$-0.719970\pi$
$709$	66968.7	−	66968.7i	0.133223	−	0.133223i	0.770574	+	0.637351i	$0.219970\pi$
$710$	−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	$-0.776599\pi$
$719$		−	667521.i		−	1.29124i	0.763659	−	0.645620i	$-0.223401\pi$
$720$	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	$-0.936739\pi$
$727$		−	208700.i		−	0.394870i	0.980316	−	0.197435i	$-0.0632611\pi$
$728$		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	0.299550	−	0.954080i	$-0.403163\pi$
$733$	−351672.	−	351672.i	−0.654530	−	0.654530i	−0.954080	+	0.299550i	$0.903163\pi$
$734$	−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	−0.951053	−	0.309029i	$-0.899996\pi$
$739$	−350623.	+	350623.i	−0.642024	+	0.642024i	0.309029	+	0.951053i	$0.399996\pi$
$740$			68727.0i			0.125506i
$741$		0			0
$742$	−495418.			−0.899837
$743$	619690.	+	619690.i	1.12253	+	1.12253i	0.991360	+	0.131166i	$0.0418722\pi$
$743$	619690.	+	619690.i	1.12253	+	1.12253i	0.131166	+	0.991360i	$0.458128\pi$
$744$	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	$0.0728831\pi$
$751$			256027.i			0.453947i	−0.973901	+	0.226974i	$0.927117\pi$
$752$	−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	−0.904253	−	0.426996i	$-0.859572\pi$
$761$	−276390.	+	276390.i	−0.477257	+	0.477257i	0.426996	+	0.904253i	$0.359572\pi$
$762$	−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	0.810491	−	0.585751i	$-0.199200\pi$
$769$	132903.	+	132903.i	0.224740	+	0.224740i	−0.585751	+	0.810491i	$0.699200\pi$
$770$	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	0.323133	−	0.946354i	$-0.395264\pi$
$773$	−372392.	−	372392.i	−0.623221	−	0.623221i	−0.946354	+	0.323133i	$0.895264\pi$
$774$	−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	−0.451002	−	0.892523i	$-0.648933\pi$
$787$	273464.	−	273464.i	0.441521	−	0.441521i	0.892523	+	0.451002i	$0.148933\pi$
$788$	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	$0.229569\pi$
$797$			838853.i			1.32059i	−0.751005	+	0.660297i	$0.770431\pi$
$798$	−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	0.705451	−	0.708759i	$-0.250745\pi$
$811$	−2176.16	−	2176.16i	−0.00330863	−	0.00330863i	−0.708759	+	0.705451i	$0.750745\pi$
$812$	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	0.645700	−	0.763591i	$-0.276566\pi$
$821$	−79463.3	−	79463.3i	−0.117891	−	0.117891i	−0.763591	+	0.645700i	$0.776566\pi$
$822$	369849.			0.547370
$823$		−	651622.i		−	0.962047i	−0.876708	−	0.481023i	$-0.840265\pi$
$823$		−	651622.i		−	0.962047i	0.876708	−	0.481023i	$-0.159735\pi$
$824$	−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	−0.957923	−	0.287026i	$-0.907333\pi$
$827$	−458846.	+	458846.i	−0.670897	+	0.670897i	0.287026	+	0.957923i	$0.407333\pi$
$828$	−231597.			−0.337809
$829$		−	1.22076e6i		−	1.77631i	−0.459540	−	0.888157i	$-0.651986\pi$
$829$		−	1.22076e6i		−	1.77631i	0.459540	−	0.888157i	$-0.348014\pi$
$830$	−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	−0.127160	−	0.991882i	$-0.540586\pi$
$839$	608696.	−	608696.i	0.864722	−	0.864722i	0.991882	+	0.127160i	$0.0405862\pi$
$840$	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	0.161579	−	0.986860i	$-0.448341\pi$
$853$	835615.	−	835615.i	1.14844	−	1.14844i	0.986860	−	0.161579i	$-0.0516588\pi$
$854$	−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	$0.240795\pi$
$857$			1.00820e6i			1.37273i	−0.727256	+	0.686366i	$0.759205\pi$
$858$		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	0.831687	−	0.555245i	$-0.187375\pi$
$863$	205886.	+	205886.i	0.276442	+	0.276442i	−0.555245	+	0.831687i	$0.687375\pi$
$864$	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	−0.985616	−	0.169001i	$-0.945946\pi$
$877$	−888049.	−	888049.i	−1.15462	−	1.15462i	−0.169001	−	0.985616i	$-0.554054\pi$
$878$	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	$0.0778256\pi$
$881$			375767.i			0.484136i	−0.970259	+	0.242068i	$0.922174\pi$
$882$	−304610.	+	304610.i	−0.391568	+	0.391568i
$883$			420890.i			0.539818i	0.962886	+	0.269909i	$0.0869936\pi$
$883$			420890.i			0.539818i	−0.962886	+	0.269909i	$0.913006\pi$
$884$		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	$-0.759646\pi$
$907$		−	1.12762e6i		−	1.37071i	0.728207	−	0.685357i	$-0.240354\pi$
$908$	−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	0.490241	−	0.871587i	$-0.336909\pi$
$929$	−329117.	−	329117.i	−0.381346	−	0.381346i	−0.871587	+	0.490241i	$0.836909\pi$
$930$	−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	−0.994094	−	0.108525i	$-0.965387\pi$
$941$	−976348.	−	976348.i	−1.10262	−	1.10262i	−0.108525	−	0.994094i	$-0.534613\pi$
$942$	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	−0.664239	−	0.747520i	$-0.731244\pi$
$947$	74686.8	−	74686.8i	0.0832806	−	0.0832806i	0.747520	+	0.664239i	$0.231244\pi$
$948$			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	$-0.769736\pi$
$953$		−	1.20235e6i		−	1.32387i	0.749562	−	0.661935i	$-0.230264\pi$
$954$	−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	0.275140	−	0.961404i	$-0.411276\pi$
$967$	−641718.	−	641718.i	−0.686264	−	0.686264i	−0.961404	+	0.275140i	$0.911276\pi$
$968$	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	−0.952134	−	0.305680i	$-0.901116\pi$
$977$	−1.20062e6	−	1.20062e6i	−1.25781	−	1.25781i	−0.305680	−	0.952134i	$-0.598884\pi$
$978$	−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	−0.783291	−	0.621655i	$-0.786461\pi$
$983$	−156188.	+	156188.i	−0.161637	+	0.161637i	0.621655	+	0.783291i	$0.286461\pi$
$984$	−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.99.1		8
13.4	even	6		26.5.f.a.11.2	✓	8
13.5	odd	4	inner	338.5.d.e.239.1		8
13.8	odd	4		338.5.d.h.239.1		8
13.11	odd	12		26.5.f.a.19.2	yes	8
13.12	even	2		338.5.d.h.99.1		8
39.11	even	12		234.5.bb.c.19.1		8
39.17	odd	6		234.5.bb.c.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.11.2	✓	8	13.4	even	6
26.5.f.a.19.2	yes	8	13.11	odd	12
234.5.bb.c.19.1		8	39.11	even	12
234.5.bb.c.37.1		8	39.17	odd	6
338.5.d.e.99.1		8	1.1	even	1	trivial
338.5.d.e.239.1		8	13.5	odd	4	inner
338.5.d.h.99.1		8	13.12	even	2
338.5.d.h.239.1		8	13.8	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
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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