LMFDB - Embedded newform 99.5.k.c.28.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,5,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$10.2336263453$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			28.8
Character	$\chi$	$=$	99.28
Dual form			99.5.k.c.46.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.29601 - 2.37062i) q^{2} +(34.6676 - 25.1875i) q^{4} +(-2.18122 + 6.71310i) q^{5} +(28.6722 + 39.4639i) q^{7} +(121.078 - 166.650i) q^{8} +O(q^{10})$	\(q+(7.29601 - 2.37062i) q^{2} +(34.6676 - 25.1875i) q^{4} +(-2.18122 + 6.71310i) q^{5} +(28.6722 + 39.4639i) q^{7} +(121.078 - 166.650i) q^{8} +54.1497i q^{10} +(31.5805 - 116.806i) q^{11} +(5.63636 - 1.83136i) q^{13} +(302.746 + 219.958i) q^{14} +(276.455 - 850.842i) q^{16} +(-404.280 - 131.359i) q^{17} +(-347.268 + 477.974i) q^{19} +(93.4686 + 287.667i) q^{20} +(-46.4909 - 927.083i) q^{22} -361.694 q^{23} +(465.328 + 338.080i) q^{25} +(36.7814 - 26.7233i) q^{26} +(1987.99 + 645.938i) q^{28} +(755.357 + 1039.66i) q^{29} +(-36.4276 - 112.113i) q^{31} -3567.27i q^{32} -3261.03 q^{34} +(-327.466 + 106.400i) q^{35} +(-141.071 + 102.494i) q^{37} +(-1400.58 + 4310.54i) q^{38} +(854.640 + 1176.31i) q^{40} +(-1117.70 + 1538.38i) q^{41} -1419.27i q^{43} +(-1847.23 - 4844.82i) q^{44} +(-2638.92 + 857.437i) q^{46} +(177.347 + 128.850i) q^{47} +(6.64598 - 20.4542i) q^{49} +(4196.49 + 1363.52i) q^{50} +(149.272 - 205.455i) q^{52} +(-349.957 - 1077.06i) q^{53} +(715.248 + 466.783i) q^{55} +10048.2 q^{56} +(7975.72 + 5794.70i) q^{58} +(193.695 - 140.727i) q^{59} +(-557.413 - 181.114i) q^{61} +(-531.552 - 731.619i) q^{62} +(-4033.33 - 12413.3i) q^{64} +41.8320i q^{65} +1242.99 q^{67} +(-17324.0 + 5628.92i) q^{68} +(-2136.96 + 1552.59i) q^{70} +(-472.572 + 1454.43i) q^{71} +(-4924.76 - 6778.35i) q^{73} +(-786.279 + 1082.22i) q^{74} +25317.0i q^{76} +(5515.11 - 2102.80i) q^{77} +(-659.926 + 214.423i) q^{79} +(5108.78 + 3711.75i) q^{80} +(-4507.83 + 13873.7i) q^{82} +(-5682.21 - 1846.26i) q^{83} +(1763.65 - 2427.45i) q^{85} +(-3364.53 - 10355.0i) q^{86} +(-15642.0 - 19405.6i) q^{88} +813.300 q^{89} +(233.879 + 169.923i) q^{91} +(-12539.1 + 9110.16i) q^{92} +(1599.38 + 519.670i) q^{94} +(-2451.22 - 3373.82i) q^{95} +(-206.021 - 634.066i) q^{97} -164.989i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	7.29601	−	2.37062i	1.82400	−	0.592654i	0.824355	−	0.566074i	$-0.191538\pi$
$2$	7.29601	−	2.37062i	1.82400	−	0.592654i	0.999647	−	0.0265805i	$-0.00846182\pi$
$3$		0			0
$3$		0			0
$4$	34.6676	−	25.1875i	2.16673	−	1.57422i
$5$	−2.18122	+	6.71310i	−0.0872488	+	0.268524i	−0.985156	−	0.171660i	$-0.945087\pi$
$5$	−2.18122	+	6.71310i	−0.0872488	+	0.268524i	0.897907	+	0.440184i	$0.145087\pi$
$6$		0			0
$7$	28.6722	+	39.4639i	0.585147	+	0.805385i	0.994248	−	0.107104i	$-0.0341577\pi$
$7$	28.6722	+	39.4639i	0.585147	+	0.805385i	−0.409101	+	0.912489i	$0.634158\pi$
$8$	121.078	−	166.650i	1.89185	−	2.60391i
$9$		0			0
$10$			54.1497i			0.541497i
$11$	31.5805	−	116.806i	0.260996	−	0.965340i
$11$	31.5805	−	116.806i	0.260996	−	0.965340i
$12$		0			0
$13$	5.63636	−	1.83136i	0.0333512	−	0.0108365i	−0.292294	−	0.956329i	$-0.594419\pi$
$13$	5.63636	−	1.83136i	0.0333512	−	0.0108365i	0.325645	+	0.945492i	$0.394419\pi$
$14$	302.746	+	219.958i	1.54462	+	1.12223i
$15$		0			0
$16$	276.455	−	850.842i	1.07990	−	3.32360i
$17$	−404.280	−	131.359i	−1.39889	−	0.454528i	−0.490061	−	0.871688i	$-0.663025\pi$
$17$	−404.280	−	131.359i	−1.39889	−	0.454528i	−0.908833	+	0.417160i	$0.863025\pi$
$18$		0			0
$19$	−347.268	+	477.974i	−0.961963	+	1.32403i	−0.0159586	+	0.999873i	$0.505080\pi$
$19$	−347.268	+	477.974i	−0.961963	+	1.32403i	−0.946004	+	0.324155i	$0.894920\pi$
$20$	93.4686	+	287.667i	0.233671	+	0.719167i
$21$		0			0
$22$	−46.4909	−	927.083i	−0.0960556	−	1.91546i
$23$	−361.694			−0.683731			−0.341866	−	0.939749i	$-0.611059\pi$
$23$	−361.694			−0.683731			−0.341866	+	0.939749i	$0.611059\pi$
$24$		0			0
$25$	465.328	+	338.080i	0.744524	+	0.540928i
$26$	36.7814	−	26.7233i	0.0544104	−	0.0395315i
$27$		0			0
$28$	1987.99	+	645.938i	2.53570	+	0.823900i
$29$	755.357	+	1039.66i	0.898165	+	1.23622i	0.971050	+	0.238878i	$0.0767794\pi$
$29$	755.357	+	1039.66i	0.898165	+	1.23622i	−0.0728848	+	0.997340i	$0.523221\pi$
$30$		0			0
$31$	−36.4276	−	112.113i	−0.0379059	−	0.116662i	0.930313	−	0.366766i	$-0.119535\pi$
$31$	−36.4276	−	112.113i	−0.0379059	−	0.116662i	−0.968219	+	0.250104i	$0.919535\pi$
$32$		−	3567.27i		−	3.48366i
$33$		0			0
$34$	−3261.03			−2.82096
$35$	−327.466	+	106.400i	−0.267319	+	0.0868571i
$36$		0			0
$37$	−141.071	+	102.494i	−0.103047	+	0.0748677i	−0.638115	−	0.769941i	$-0.720286\pi$
$37$	−141.071	+	102.494i	−0.103047	+	0.0748677i	0.535069	+	0.844809i	$0.320286\pi$
$38$	−1400.58	+	4310.54i	−0.969931	+	2.98514i
$39$		0			0
$40$	854.640	+	1176.31i	0.534150	+	0.735195i
$41$	−1117.70	+	1538.38i	−0.664902	+	0.915159i	−0.999631	−	0.0271553i	$-0.991355\pi$
$41$	−1117.70	+	1538.38i	−0.664902	+	0.915159i	0.334729	+	0.942314i	$0.391355\pi$
$42$		0			0
$43$		−	1419.27i		−	0.767585i	−0.923419	−	0.383793i	$-0.874618\pi$
$43$		−	1419.27i		−	0.767585i	0.923419	−	0.383793i	$-0.125382\pi$
$44$	−1847.23	−	4844.82i	−0.954149	−	2.50249i
$45$		0			0
$46$	−2638.92	+	857.437i	−1.24713	+	0.405216i
$47$	177.347	+	128.850i	0.0802840	+	0.0583297i	0.627203	−	0.778856i	$-0.284200\pi$
$47$	177.347	+	128.850i	0.0802840	+	0.0583297i	−0.546919	+	0.837185i	$0.684200\pi$
$48$		0			0
$49$	6.64598	−	20.4542i	0.00276800	−	0.00851904i
$50$	4196.49	+	1363.52i	1.67860	+	0.545409i
$51$		0			0
$52$	149.272	−	205.455i	0.0552040	−	0.0759817i
$53$	−349.957	−	1077.06i	−0.124584	−	0.383430i	0.869241	−	0.494389i	$-0.164608\pi$
$53$	−349.957	−	1077.06i	−0.124584	−	0.383430i	−0.993825	+	0.110958i	$0.964608\pi$
$54$		0			0
$55$	715.248	+	466.783i	0.236445	+	0.154308i
$56$	10048.2			3.20416
$57$		0			0
$58$	7975.72	+	5794.70i	2.37090	+	1.72256i
$59$	193.695	−	140.727i	0.0556434	−	0.0404273i	−0.559616	−	0.828752i	$-0.689051\pi$
$59$	193.695	−	140.727i	0.0556434	−	0.0404273i	0.615259	+	0.788325i	$0.289051\pi$
$60$		0			0
$61$	−557.413	−	181.114i	−0.149802	−	0.0486736i	0.233156	−	0.972439i	$-0.425095\pi$
$61$	−557.413	−	181.114i	−0.149802	−	0.0486736i	−0.382958	+	0.923766i	$0.625095\pi$
$62$	−531.552	−	731.619i	−0.138281	−	0.190327i
$63$		0			0
$64$	−4033.33	−	12413.3i	−0.984701	−	3.03060i
$65$			41.8320i			0.00990108i
$66$		0			0
$67$	1242.99			0.276896			0.138448	−	0.990370i	$-0.455789\pi$
$67$	1242.99			0.276896			0.138448	+	0.990370i	$0.455789\pi$
$68$	−17324.0	+	5628.92i	−3.74654	+	1.21733i
$69$		0			0
$70$	−2136.96	+	1552.59i	−0.436114	+	0.316855i
$71$	−472.572	+	1454.43i	−0.0937456	+	0.288519i	−0.986925	−	0.161182i	$-0.948469\pi$
$71$	−472.572	+	1454.43i	−0.0937456	+	0.288519i	0.893179	+	0.449701i	$0.148469\pi$
$72$		0			0
$73$	−4924.76	−	6778.35i	−0.924143	−	1.27197i	−0.962101	−	0.272694i	$-0.912085\pi$
$73$	−4924.76	−	6778.35i	−0.924143	−	1.27197i	0.0379579	−	0.999279i	$-0.487915\pi$
$74$	−786.279	+	1082.22i	−0.143586	+	0.197630i
$75$		0			0
$76$			25317.0i			4.38314i
$77$	5515.11	−	2102.80i	0.930192	−	0.354663i
$78$		0			0
$79$	−659.926	+	214.423i	−0.105741	+	0.0343572i	−0.361409	−	0.932407i	$-0.617704\pi$
$79$	−659.926	+	214.423i	−0.105741	+	0.0343572i	0.255669	+	0.966764i	$0.417704\pi$
$80$	5108.78	+	3711.75i	0.798247	+	0.579960i
$81$		0			0
$82$	−4507.83	+	13873.7i	−0.670409	+	2.06331i
$83$	−5682.21	−	1846.26i	−0.824823	−	0.268001i	−0.133960	−	0.990987i	$-0.542769\pi$
$83$	−5682.21	−	1846.26i	−0.824823	−	0.268001i	−0.690863	+	0.722985i	$0.742769\pi$
$84$		0			0
$85$	1763.65	−	2427.45i	0.244103	−	0.335980i
$86$	−3364.53	−	10355.0i	−0.454913	−	1.40008i
$87$		0			0
$88$	−15642.0	−	19405.6i	−2.01989	−	2.50589i
$89$	813.300			0.102676			0.0513382	−	0.998681i	$-0.483651\pi$
$89$	813.300			0.102676			0.0513382	+	0.998681i	$0.483651\pi$
$90$		0			0
$91$	233.879	+	169.923i	0.0282429	+	0.0205197i
$92$	−12539.1	+	9110.16i	−1.48146	+	1.07634i
$93$		0			0
$94$	1599.38	+	519.670i	0.181007	+	0.0588129i
$95$	−2451.22	−	3373.82i	−0.271603	−	0.373830i
$96$		0			0
$97$	−206.021	−	634.066i	−0.0218961	−	0.0673893i	0.939511	−	0.342518i	$-0.111280\pi$
$97$	−206.021	−	634.066i	−0.0218961	−	0.0673893i	−0.961408	+	0.275128i	$0.911280\pi$
$98$		−	164.989i		−	0.0171792i
$99$		0			0
$100$	24647.2			2.46472
$101$	11016.6	−	3579.49i	1.07995	−	0.350896i	0.285594	−	0.958351i	$-0.407809\pi$
$101$	11016.6	−	3579.49i	1.07995	−	0.350896i	0.794355	+	0.607454i	$0.207809\pi$
$102$		0			0
$103$	7661.96	−	5566.74i	0.722213	−	0.524719i	−0.164877	−	0.986314i	$-0.552723\pi$
$103$	7661.96	−	5566.74i	0.722213	−	0.524719i	0.887091	+	0.461596i	$0.152723\pi$
$104$	377.244	−	1161.04i	0.0348783	−	0.107344i
$105$		0			0
$106$	−5106.57	−	7028.59i	−0.454483	−	0.625542i
$107$	−350.328	+	482.185i	−0.0305990	+	0.0421159i	−0.824042	−	0.566528i	$-0.808286\pi$
$107$	−350.328	+	482.185i	−0.0305990	+	0.0421159i	0.793443	+	0.608644i	$0.208286\pi$
$108$		0			0
$109$		−	14644.6i		−	1.23261i	−0.787508	−	0.616304i	$-0.788629\pi$
$109$		−	14644.6i		−	1.23261i	0.787508	−	0.616304i	$-0.211371\pi$
$110$	6325.01	+	1710.07i	0.522728	+	0.141328i
$111$		0			0
$112$	41504.1	−	13485.5i	3.30868	−	1.07506i
$113$	9602.19	+	6976.40i	0.751992	+	0.546354i	0.896444	−	0.443157i	$-0.146142\pi$
$113$	9602.19	+	6976.40i	0.751992	+	0.546354i	−0.144451	+	0.989512i	$0.546142\pi$
$114$		0			0
$115$	788.934	−	2428.09i	0.0596547	−	0.183598i
$116$	52372.8	+	17017.0i	3.89215	+	1.26464i
$117$		0			0
$118$	1079.59	−	1485.92i	0.0775342	−	0.106717i
$119$	−6407.68	−	19720.8i	−0.452488	−	1.39261i
$120$		0			0
$121$	−12646.3	−	7377.59i	−0.863762	−	0.503900i
$122$	−4496.24			−0.302085
$123$		0			0
$124$	−4086.69	−	2969.16i	−0.265784	−	0.193103i
$125$	−6853.62	+	4979.44i	−0.438631	+	0.318684i
$126$		0			0
$127$	24615.2	+	7997.97i	1.52615	+	0.495875i	0.947514	−	0.319714i	$-0.103587\pi$
$127$	24615.2	+	7997.97i	1.52615	+	0.495875i	0.578632	+	0.815589i	$0.303587\pi$
$128$	−25305.9	−	34830.5i	−1.54455	−	2.12589i
$129$		0			0
$130$	99.1677	+	305.207i	0.00586791	+	0.0180596i
$131$			97.0905i			0.00565763i	0.999996	+	0.00282881i	$0.000900441\pi$
$131$			97.0905i			0.00565763i	−0.999996	+	0.00282881i	$0.999100\pi$
$132$		0			0
$133$	−28819.7			−1.62924
$134$	9068.83	−	2946.64i	0.505059	−	0.164104i
$135$		0			0
$136$	−70840.5	+	51468.6i	−3.83004	+	2.78269i
$137$	9637.37	−	29660.8i	0.513473	−	1.58031i	−0.272571	−	0.962136i	$-0.587874\pi$
$137$	9637.37	−	29660.8i	0.513473	−	1.58031i	0.786044	−	0.618171i	$-0.212126\pi$
$138$		0			0
$139$	4630.83	+	6373.79i	0.239678	+	0.329889i	0.911863	−	0.410494i	$-0.134644\pi$
$139$	4630.83	+	6373.79i	0.239678	+	0.329889i	−0.672185	+	0.740384i	$0.734644\pi$
$140$	−8672.50	+	11936.7i	−0.442474	+	0.609014i
$141$		0			0
$142$			11731.8i			0.581819i
$143$	−35.9154	−	716.196i	−0.00175634	−	0.0350235i
$144$		0			0
$145$	−8626.94	+	2803.06i	−0.410318	+	0.133320i
$146$	−51999.9	−	37780.1i	−2.43948	−	1.77238i
$147$		0			0
$148$	−2309.02	+	7106.43i	−0.105415	+	0.324435i
$149$	−15216.3	−	4944.08i	−0.685389	−	0.222696i	−0.0544356	−	0.998517i	$-0.517336\pi$
$149$	−15216.3	−	4944.08i	−0.685389	−	0.222696i	−0.630953	+	0.775821i	$0.717336\pi$
$150$		0			0
$151$	24390.9	−	33571.2i	1.06973	−	1.47236i	0.199380	−	0.979922i	$-0.436107\pi$
$151$	24390.9	−	33571.2i	1.06973	−	1.47236i	0.870350	−	0.492434i	$-0.163893\pi$
$152$	37607.7	+	115745.i	1.62776	+	5.00972i
$153$		0			0
$154$	35253.3	−	28416.2i	1.48648	−	1.19819i
$155$	832.080			0.0346339
$156$		0			0
$157$	20267.4	+	14725.1i	0.822239	+	0.597391i	0.917353	−	0.398075i	$-0.130322\pi$
$157$	20267.4	+	14725.1i	0.822239	+	0.597391i	−0.0951143	+	0.995466i	$0.530322\pi$
$158$	−4306.51	+	3128.86i	−0.172509	+	0.125335i
$159$		0			0
$160$	23947.4	+	7780.99i	0.935447	+	0.303945i
$161$	−10370.6	−	14273.8i	−0.400083	−	0.550667i
$162$		0			0
$163$	11735.1	+	36117.0i	0.441684	+	1.35936i	0.886079	+	0.463534i	$0.153419\pi$
$163$	11735.1	+	36117.0i	0.441684	+	1.35936i	−0.444395	+	0.895831i	$0.646581\pi$
$164$			81484.1i			3.02960i
$165$		0			0
$166$	−45834.2			−1.66331
$167$	37649.4	−	12233.0i	1.34997	−	0.438633i	0.457291	−	0.889317i	$-0.348820\pi$
$167$	37649.4	−	12233.0i	1.34997	−	0.438633i	0.892684	+	0.450684i	$0.148820\pi$
$168$		0			0
$169$	−23077.9	+	16767.1i	−0.808022	+	0.587062i
$170$	7113.03	−	21891.6i	0.246125	−	0.757496i
$171$		0			0
$172$	−35747.7	−	49202.5i	−1.20835	−	1.66315i
$173$	−16390.6	+	22559.7i	−0.547650	+	0.753775i	−0.989691	−	0.143220i	$-0.954254\pi$
$173$	−16390.6	+	22559.7i	−0.547650	+	0.753775i	0.442041	+	0.896995i	$0.354254\pi$
$174$		0			0
$175$			28057.1i			0.916151i
$176$	−90653.0	−	59161.7i	−2.92656	−	1.90992i
$177$		0			0
$178$	5933.84	−	1928.02i	0.187282	−	0.0608516i
$179$	−941.098	−	683.748i	−0.0293717	−	0.0213398i	0.573003	−	0.819554i	$-0.305778\pi$
$179$	−941.098	−	683.748i	−0.0293717	−	0.0213398i	−0.602374	+	0.798214i	$0.705778\pi$
$180$		0			0
$181$	16079.3	−	49487.0i	0.490806	−	1.51055i	−0.332586	−	0.943073i	$-0.607921\pi$
$181$	16079.3	−	49487.0i	0.490806	−	1.51055i	0.823392	−	0.567473i	$-0.192079\pi$
$182$	2109.21	+	685.323i	0.0636761	+	0.0206896i
$183$		0			0
$184$	−43793.3	+	60276.3i	−1.29352	+	1.78037i
$185$	−380.346	−	1170.58i	−0.0111131	−	0.0342026i
$186$		0			0
$187$	−28110.9	+	43074.0i	−0.803880	+	1.23178i
$188$	9393.62			0.265777
$189$		0			0
$190$	−25882.1	−	18804.5i	−0.716957	−	0.520900i
$191$	−42293.3	+	30727.9i	−1.15932	+	0.842299i	−0.989693	−	0.143208i	$-0.954258\pi$
$191$	−42293.3	+	30727.9i	−1.15932	+	0.842299i	−0.169632	+	0.985507i	$0.554258\pi$
$192$		0			0
$193$	18412.1	+	5982.44i	0.494297	+	0.160607i	0.545549	−	0.838079i	$-0.316321\pi$
$193$	18412.1	+	5982.44i	0.494297	+	0.160607i	−0.0512521	+	0.998686i	$0.516321\pi$
$194$	−3006.26	−	4137.76i	−0.0798771	−	0.109941i
$195$		0			0
$196$	−284.790	−	876.494i	−0.00741332	−	0.0228159i
$197$			10983.7i			0.283019i	0.989937	+	0.141509i	$0.0451956\pi$
$197$			10983.7i			0.283019i	−0.989937	+	0.141509i	$0.954804\pi$
$198$		0			0
$199$	7219.36			0.182302			0.0911512	−	0.995837i	$-0.470945\pi$
$199$	7219.36			0.182302			0.0911512	+	0.995837i	$0.470945\pi$
$200$	112682.	−	36612.7i	2.81705	−	0.915316i
$201$		0			0
$202$	71891.2	−	52232.0i	1.76187	−	1.28007i
$203$	−19371.3	+	59618.6i	−0.470074	+	1.44674i
$204$		0			0
$205$	−7889.37	−	10858.8i	−0.187730	−	0.258389i
$206$	42705.1	−	58778.5i	1.00634	−	1.38511i
$207$		0			0
$208$		−	5301.94i		−	0.122549i
$209$	44863.4	+	55657.7i	1.02707	+	1.27419i
$210$		0			0
$211$	−56058.2	+	18214.4i	−1.25914	+	0.409120i	−0.861188	−	0.508286i	$-0.830279\pi$
$211$	−56058.2	+	18214.4i	−1.25914	+	0.409120i	−0.397953	+	0.917406i	$0.630279\pi$
$212$	−39260.5	−	28524.4i	−0.873542	−	0.634666i
$213$		0			0
$214$	−1412.92	+	4348.52i	−0.0308525	+	0.0949541i
$215$	9527.68	+	3095.73i	0.206115	+	0.0669709i
$216$		0			0
$217$	3379.94	−	4652.09i	0.0717777	−	0.0987936i
$218$	−34716.8	−	106847.i	−0.730511	−	2.24828i
$219$		0			0
$220$	36553.0	−	1833.04i	0.755228	−	0.0378728i
$221$	−2519.23			−0.0515803
$222$		0			0
$223$	−18740.8	−	13616.0i	−0.376858	−	0.273803i	0.383191	−	0.923669i	$-0.374825\pi$
$223$	−18740.8	−	13616.0i	−0.376858	−	0.273803i	−0.760049	+	0.649866i	$0.774825\pi$
$224$	140778.	−	102281.i	2.80569	−	2.03845i
$225$		0			0
$226$	86596.0	+	28136.7i	1.69543	+	0.550880i
$227$	36212.8	+	49842.7i	0.702766	+	0.967274i	0.999923	+	0.0124456i	$0.00396166\pi$
$227$	36212.8	+	49842.7i	0.702766	+	0.967274i	−0.297157	+	0.954829i	$0.596038\pi$
$228$		0			0
$229$	−11972.6	−	36847.9i	−0.228306	−	0.702654i	−0.997939	−	0.0641673i	$-0.979561\pi$
$229$	−11972.6	−	36847.9i	−0.228306	−	0.702654i	0.769633	−	0.638486i	$-0.220439\pi$
$230$		−	19585.6i		−	0.370238i
$231$		0			0
$232$	264717.			4.91819
$233$	−51173.4	+	16627.2i	−0.942610	+	0.306273i	−0.739709	−	0.672927i	$-0.765037\pi$
$233$	−51173.4	+	16627.2i	−0.942610	+	0.306273i	−0.202901	+	0.979199i	$0.565037\pi$
$234$		0			0
$235$	−1251.82	+	909.500i	−0.0226676	+	0.0164690i
$236$	3170.36	−	9757.36i	0.0569226	−	0.175190i
$237$		0			0
$238$	−93500.9	−	128693.i	−1.65068	−	2.27196i
$239$	−17669.2	+	24319.6i	−0.309330	+	0.425756i	−0.935172	−	0.354193i	$-0.884755\pi$
$239$	−17669.2	+	24319.6i	−0.309330	+	0.425756i	0.625842	+	0.779950i	$0.284755\pi$
$240$		0			0
$241$			30542.9i			0.525867i	0.964814	+	0.262933i	$0.0846899\pi$
$241$			30542.9i			0.525867i	−0.964814	+	0.262933i	$0.915310\pi$
$242$	−109757.	−	23847.3i	−1.87414	−	0.407201i
$243$		0			0
$244$	−23886.0	+	7761.03i	−0.401202	+	0.130359i
$245$	122.815	+	89.2302i	0.00204606	+	0.00148655i
$246$		0			0
$247$	−1081.98	+	3330.01i	−0.0177348	+	0.0545822i
$248$	−23094.2	−	7503.75i	−0.375491	−	0.122004i
$249$		0			0
$250$	−38199.7	+	52577.3i	−0.611195	+	0.841237i
$251$	2497.63	+	7686.92i	0.0396443	+	0.122013i	0.968920	−	0.247374i	$-0.0795677\pi$
$251$	2497.63	+	7686.92i	0.0396443	+	0.122013i	−0.929276	+	0.369387i	$0.879568\pi$
$252$		0			0
$253$	−11422.5	+	42248.1i	−0.178451	+	0.660033i
$254$	198553.			3.07758
$255$		0			0
$256$	−98251.1	−	71383.6i	−1.49919	−	1.08923i
$257$	50106.9	−	36404.8i	0.758632	−	0.551178i	−0.139858	−	0.990172i	$-0.544665\pi$
$257$	50106.9	−	36404.8i	0.758632	−	0.551178i	0.898490	+	0.438993i	$0.144665\pi$
$258$		0			0
$259$	−8089.61	−	2628.47i	−0.120595	−	0.0391836i
$260$	1053.64	+	1450.22i	0.0155865	+	0.0214529i
$261$		0			0
$262$	230.164	+	708.373i	0.00335302	+	0.0103195i
$263$			29650.1i			0.428662i	0.976761	+	0.214331i	$0.0687571\pi$
$263$			29650.1i			0.428662i	−0.976761	+	0.214331i	$0.931243\pi$
$264$		0			0
$265$	7993.72			0.113830
$266$	−210268.	+	68320.4i	−2.97174	+	0.965577i
$267$		0			0
$268$	43091.4	−	31307.7i	0.599958	−	0.435895i
$269$	2169.76	−	6677.82i	0.0299852	−	0.0922848i	−0.934944	−	0.354795i	$-0.884550\pi$
$269$	2169.76	−	6677.82i	0.0299852	−	0.0922848i	0.964929	+	0.262511i	$0.0845505\pi$
$270$		0			0
$271$	67057.2	+	92296.3i	0.913076	+	1.25674i	0.966105	+	0.258148i	$0.0831121\pi$
$271$	67057.2	+	92296.3i	0.913076	+	1.25674i	−0.0530299	+	0.998593i	$0.516888\pi$
$272$	−223531.	+	307664.i	−3.02134	+	4.15852i
$273$		0			0
$274$		−	239252.i		−	3.18679i
$275$	54185.1	−	43676.4i	0.716498	−	0.577539i
$276$		0			0
$277$	−86668.9	+	28160.4i	−1.12955	+	0.367012i	−0.813403	−	0.581700i	$-0.802388\pi$
$277$	−86668.9	+	28160.4i	−1.12955	+	0.367012i	−0.316143	+	0.948712i	$0.602388\pi$
$278$	48896.3	+	35525.3i	0.632684	+	0.459672i
$279$		0			0
$280$	−21917.4	+	67454.9i	−0.279559	+	0.860394i
$281$	−54585.7	−	17736.0i	−0.691299	−	0.224617i	−0.0577635	−	0.998330i	$-0.518397\pi$
$281$	−54585.7	−	17736.0i	−0.691299	−	0.224617i	−0.633535	+	0.773714i	$0.718397\pi$
$282$		0			0
$283$	−27052.4	+	37234.4i	−0.337779	+	0.464913i	−0.943791	−	0.330542i	$-0.892768\pi$
$283$	−27052.4	+	37234.4i	−0.337779	+	0.464913i	0.606012	+	0.795455i	$0.292768\pi$
$284$	20250.4	+	62324.4i	0.251071	+	0.772718i
$285$		0			0
$286$	−1959.87	−	5140.23i	−0.0239604	−	0.0628421i
$287$	−92757.5			−1.12612
$288$		0			0
$289$	78617.5	+	57119.0i	0.941290	+	0.683887i
$290$	−56297.2	+	40902.3i	−0.669408	+	0.486353i
$291$		0			0
$292$	−341459.	−	110947.i	−4.00473	−	1.30121i
$293$	−78864.2	−	108547.i	−0.918638	−	1.26440i	−0.964129	−	0.265433i	$-0.914485\pi$
$293$	−78864.2	−	108547.i	−0.918638	−	1.26440i	0.0454910	−	0.998965i	$-0.485515\pi$
$294$		0			0
$295$	522.227	+	1607.25i	0.00600088	+	0.0184688i
$296$			35919.2i			0.409962i
$297$		0			0
$298$	−122739.			−1.38213
$299$	−2038.64	+	662.393i	−0.0228033	+	0.00740923i
$300$		0			0
$301$	56009.7	−	40693.5i	0.618202	−	0.449150i
$302$	98371.7	−	302757.i	1.07859	−	3.31956i
$303$		0			0
$304$	310676.	+	427609.i	3.36171	+	4.62700i
$305$	2431.68	−	3346.92i	0.0261401	−	0.0359787i
$306$		0			0
$307$			59826.1i			0.634766i	0.948297	+	0.317383i	$0.102804\pi$
$307$			59826.1i			0.634766i	−0.948297	+	0.317383i	$0.897196\pi$
$308$	138231.	−	211811.i	1.45715	−	2.23278i
$309$		0			0
$310$	6070.86	−	1972.54i	0.0631724	−	0.0205259i
$311$	90820.7	+	65985.1i	0.938996	+	0.682221i	0.948179	−	0.317737i	$-0.102923\pi$
$311$	90820.7	+	65985.1i	0.938996	+	0.682221i	−0.00918248	+	0.999958i	$0.502923\pi$
$312$		0			0
$313$	45569.0	−	140247.i	0.465136	−	1.43154i	−0.393674	−	0.919250i	$-0.628796\pi$
$313$	45569.0	−	140247.i	0.465136	−	1.43154i	0.858811	−	0.512293i	$-0.171204\pi$
$314$	182778.	+	59388.3i	1.85381	+	0.602340i
$315$		0			0
$316$	−17477.3	+	24055.4i	−0.175025	+	0.240901i
$317$	−45003.3	−	138506.i	−0.447843	−	1.37832i	−0.879335	−	0.476203i	$-0.842013\pi$
$317$	−45003.3	−	138506.i	−0.447843	−	1.37832i	0.431492	−	0.902117i	$-0.357987\pi$
$318$		0			0
$319$	145293.	−	55397.3i	1.42779	−	0.544387i
$320$	92129.5			0.899702
$321$		0			0
$322$	−109501.	−	79557.5i	−1.05611	−	0.767307i
$323$	203180.	−	147619.i	1.94749	−	1.41493i
$324$		0			0
$325$	3241.90	+	1053.36i	0.0306925	+	0.00997261i
$326$	171239.	+	235690.i	1.61127	+	2.21772i
$327$		0			0
$328$	121042.	+	372530.i	1.12509	+	3.46269i
$329$			10693.2i			0.0987910i
$330$		0			0
$331$	−126011.			−1.15015			−0.575074	−	0.818102i	$-0.695027\pi$
$331$	−126011.			−1.15015			−0.575074	+	0.818102i	$0.695027\pi$
$332$	−243491.	+	79115.1i	−2.20906	+	0.717766i
$333$		0			0
$334$	245691.	−	178505.i	2.20240	−	1.60014i
$335$	−2711.23	+	8344.30i	−0.0241588	+	0.0743533i
$336$		0			0
$337$	−41027.9	−	56470.1i	−0.361260	−	0.497232i	0.589239	−	0.807959i	$-0.299428\pi$
$337$	−41027.9	−	56470.1i	−0.361260	−	0.497232i	−0.950499	+	0.310727i	$0.899428\pi$
$338$	−128628.	+	177042.i	−1.12591	+	1.54968i
$339$		0			0
$340$		−	128576.i		−	1.11225i
$341$	−14245.8	+	714.394i	−0.122512	+	0.00614368i
$342$		0			0
$343$	112386.	−	36516.5i	0.955268	−	0.310385i
$344$	−236521.	−	171842.i	−1.99872	−	1.45216i
$345$		0			0
$346$	−66105.5	+	203452.i	−0.552186	+	1.69945i
$347$	85323.7	+	27723.3i	0.708615	+	0.230243i	0.641080	−	0.767474i	$-0.278487\pi$
$347$	85323.7	+	27723.3i	0.708615	+	0.230243i	0.0675350	+	0.997717i	$0.478487\pi$
$348$		0			0
$349$	−24805.4	+	34141.6i	−0.203655	+	0.280307i	−0.898612	−	0.438744i	$-0.855423\pi$
$349$	−24805.4	+	34141.6i	−0.203655	+	0.280307i	0.694957	+	0.719051i	$0.255423\pi$
$350$	66512.7	+	204705.i	0.542961	+	1.67106i
$351$		0			0
$352$	−416679.	−	112656.i	−3.36292	−	0.909221i
$353$	−149772.			−1.20194			−0.600969	−	0.799273i	$-0.705218\pi$
$353$	−149772.			−1.20194			−0.600969	+	0.799273i	$0.705218\pi$
$354$		0			0
$355$	−8732.93	−	6344.85i	−0.0692952	−	0.0503459i
$356$	28195.2	−	20485.0i	0.222472	−	0.161635i
$357$		0			0
$358$	−8487.16	−	2757.64i	−0.0662211	−	0.0215165i
$359$	−21735.4	−	29916.1i	−0.168647	−	0.232122i	0.716325	−	0.697766i	$-0.245823\pi$
$359$	−21735.4	−	29916.1i	−0.168647	−	0.232122i	−0.884972	+	0.465644i	$0.845823\pi$
$360$		0			0
$361$	−67592.4	−	208028.i	−0.518661	−	1.59627i
$362$		−	399175.i		−	3.04612i
$363$		0			0
$364$	12388.0			0.0934970
$365$	56245.7	−	18275.3i	0.422186	−	0.137177i
$366$		0			0
$367$	−160052.	+	116285.i	−1.18831	+	0.863359i	−0.993085	−	0.117399i	$-0.962544\pi$
$367$	−160052.	+	116285.i	−1.18831	+	0.863359i	−0.195227	+	0.980758i	$0.562544\pi$
$368$	−99992.2	+	307744.i	−0.738364	+	2.27245i
$369$		0			0
$370$	−5550.01	−	7638.93i	−0.0405406	−	0.0557994i
$371$	32470.8	−	44692.2i	0.235909	−	0.324701i
$372$		0			0
$373$		−	10284.8i		−	0.0739226i	−0.999317	−	0.0369613i	$-0.988232\pi$
$373$		−	10284.8i		−	0.0739226i	0.999317	−	0.0369613i	$-0.0117678\pi$
$374$	−102985.	+	380908.i	−0.736259	+	2.72319i
$375$		0			0
$376$	42945.8	−	13953.9i	0.303770	−	0.0987009i
$377$	6161.45	+	4476.56i	0.0433511	+	0.0314964i
$378$		0			0
$379$	76040.0	−	234027.i	0.529375	−	1.62925i	−0.226124	−	0.974099i	$-0.572605\pi$
$379$	76040.0	−	234027.i	0.529375	−	1.62925i	0.755499	−	0.655150i	$-0.227395\pi$
$380$	−169956.	−	55222.0i	−1.17698	−	0.382424i
$381$		0			0
$382$	−235728.	+	324452.i	−1.61542	+	2.22343i
$383$	30391.2	+	93534.4i	0.207181	+	0.637637i	0.999617	+	0.0276821i	$0.00881262\pi$
$383$	30391.2	+	93534.4i	0.207181	+	0.637637i	−0.792436	+	0.609955i	$0.791187\pi$
$384$		0			0
$385$	2086.64	+	41610.1i	0.0140775	+	0.280723i
$386$	148517.			0.996783
$387$		0			0
$388$	−23112.8	−	16792.4i	−0.153528	−	0.111545i
$389$	−24234.6	+	17607.5i	−0.160154	+	0.116358i	−0.664976	−	0.746865i	$-0.731558\pi$
$389$	−24234.6	+	17607.5i	−0.160154	+	0.116358i	0.504822	+	0.863223i	$0.331558\pi$
$390$		0			0
$391$	146226.	+	47511.6i	0.956467	+	0.310775i
$392$	−2604.01	−	3584.11i	−0.0169461	−	0.0233244i
$393$		0			0
$394$	26038.1	+	80137.0i	0.167732	+	0.516227i
$395$		−	4897.86i		−	0.0313915i
$396$		0			0
$397$	81038.4			0.514174			0.257087	−	0.966388i	$-0.417237\pi$
$397$	81038.4			0.514174			0.257087	+	0.966388i	$0.417237\pi$
$398$	52672.5	−	17114.3i	0.332520	−	0.108042i
$399$		0			0
$400$	416295.	−	302456.i	2.60185	−	1.89035i
$401$	6022.15	−	18534.3i	0.0374510	−	0.115262i	−0.930583	−	0.366080i	$-0.880700\pi$
$401$	6022.15	−	18534.3i	0.0374510	−	0.115262i	0.968034	+	0.250818i	$0.0806996\pi$
$402$		0			0
$403$	−410.638	−	565.195i	−0.00252842	−	0.00348007i
$404$	291759.	−	401572.i	1.78756	−	2.46037i
$405$		0			0
$406$			480900.i			2.91744i
$407$	7516.83	+	19714.7i	0.0453780	+	0.119015i
$408$		0			0
$409$	−122405.	+	39772.0i	−0.731736	+	0.237755i	−0.651104	−	0.758989i	$-0.725694\pi$
$409$	−122405.	+	39772.0i	−0.731736	+	0.237755i	−0.0806318	+	0.996744i	$0.525694\pi$
$410$	−83302.9	−	60523.1i	−0.495556	−	0.360042i
$411$		0			0
$412$	125410.	−	385971.i	0.738816	−	2.27384i
$413$	11107.3	+	3608.98i	0.0651191	+	0.0211585i
$414$		0			0
$415$	24788.3	−	34118.1i	0.143930	−	0.198102i
$416$	−6532.96	−	20106.4i	−0.0377506	−	0.116184i
$417$		0			0
$418$	459267.	+	299725.i	2.62853	+	1.71542i
$419$	−96456.2			−0.549417			−0.274709	−	0.961528i	$-0.588581\pi$
$419$	−96456.2			−0.549417			−0.274709	+	0.961528i	$0.588581\pi$
$420$		0			0
$421$	−262765.	−	190910.i	−1.48253	−	1.07712i	−0.976731	−	0.214469i	$-0.931198\pi$
$421$	−262765.	−	190910.i	−1.48253	−	1.07712i	−0.505799	−	0.862651i	$-0.668802\pi$
$422$	−365822.	+	265785.i	−2.05421	+	1.49247i
$423$		0			0
$424$	−221863.	−	72087.8i	−1.23411	−	0.400987i
$425$	−143713.	−	197804.i	−0.795643	−	1.09511i
$426$		0			0
$427$	−8834.77	−	27190.6i	−0.0484551	−	0.149129i
$428$			25540.1i			0.139423i
$429$		0			0
$430$	76852.8			0.415645
$431$	−155612.	+	50561.3i	−0.837698	+	0.272185i	−0.696284	−	0.717766i	$-0.745165\pi$
$431$	−155612.	+	50561.3i	−0.837698	+	0.272185i	−0.141414	+	0.989951i	$0.545165\pi$
$432$		0			0
$433$	71769.4	−	52143.5i	0.382793	−	0.278115i	−0.379703	−	0.925108i	$-0.623974\pi$
$433$	71769.4	−	52143.5i	0.382793	−	0.278115i	0.762496	+	0.646993i	$0.223974\pi$
$434$	13631.8	−	41954.2i	0.0723723	−	0.222739i
$435$		0			0
$436$	−368861.	−	507694.i	−1.94040	−	2.67072i
$437$	125605.	−	172880.i	0.657724	−	0.905279i
$438$		0			0
$439$			150259.i			0.779673i	0.920884	+	0.389837i	$0.127469\pi$
$439$			150259.i			0.779673i	−0.920884	+	0.389837i	$0.872531\pi$
$440$	164390.	−	62678.7i	0.849124	−	0.323754i
$441$		0			0
$442$	−18380.3	+	5972.13i	−0.0940825	+	0.0305693i
$443$	159831.	+	116124.i	0.814427	+	0.591716i	0.915111	−	0.403202i	$-0.132103\pi$
$443$	159831.	+	116124.i	0.814427	+	0.591716i	−0.100684	+	0.994919i	$0.532103\pi$
$444$		0			0
$445$	−1773.99	+	5459.77i	−0.00895840	+	0.0275711i
$446$	−169011.	−	54915.0i	−0.849660	−	0.276071i
$447$		0			0
$448$	374234.	−	515088.i	1.86460	−	2.56641i
$449$	98879.8	+	304321.i	0.490473	+	1.50952i	0.823895	+	0.566743i	$0.191797\pi$
$449$	98879.8	+	304321.i	0.490473	+	1.50952i	−0.333422	+	0.942778i	$0.608203\pi$
$450$		0			0
$451$	144395.	+	179137.i	0.709903	+	0.880709i
$452$	508603.			2.48944
$453$		0			0
$454$	382367.	+	277806.i	1.85511	+	1.34781i
$455$	−1650.86	+	1199.42i	−0.00797418	+	0.00579358i
$456$		0			0
$457$	111142.	+	36112.2i	0.532164	+	0.172911i	0.562759	−	0.826621i	$-0.309740\pi$
$457$	111142.	+	36112.2i	0.532164	+	0.172911i	−0.0305945	+	0.999532i	$0.509740\pi$
$458$	−174704.	−	240460.i	−0.832861	−	1.14633i
$459$		0			0
$460$	−33807.0	−	104047.i	−0.159768	−	0.491717i
$461$			249118.i			1.17221i	0.810236	+	0.586103i	$0.199339\pi$
$461$			249118.i			1.17221i	−0.810236	+	0.586103i	$0.800661\pi$
$462$		0			0
$463$	−127754.			−0.595952			−0.297976	−	0.954573i	$-0.596311\pi$
$463$	−127754.			−0.595952			−0.297976	+	0.954573i	$0.596311\pi$
$464$	1.09341e6	−	355270.i	5.07863	−	1.65015i
$465$		0			0
$466$	−333944.	+	242625.i	−1.53781	+	1.11728i
$467$	68328.2	−	210293.i	0.313304	−	0.964251i	−0.663143	−	0.748493i	$-0.730778\pi$
$467$	68328.2	−	210293.i	0.313304	−	0.964251i	0.976447	−	0.215758i	$-0.0692223\pi$
$468$		0			0
$469$	35639.1	+	49053.1i	0.162025	+	0.223008i
$470$	−6977.20	+	9603.30i	−0.0315853	+	0.0434735i
$471$		0			0
$472$		−	49318.2i		−	0.221372i
$473$	−165779.	−	44821.1i	−0.740981	−	0.200337i
$474$		0			0
$475$	−323187.	+	105010.i	−1.43241	+	0.465418i
$476$	−718857.	−	522280.i	−3.17270	−	2.30510i
$477$		0			0
$478$	−71262.4	+	219323.i	−0.311892	+	0.959906i
$479$	73976.1	+	24036.3i	0.322419	+	0.104760i	0.465755	−	0.884914i	$-0.345783\pi$
$479$	73976.1	+	24036.3i	0.322419	+	0.104760i	−0.143336	+	0.989674i	$0.545783\pi$
$480$		0			0
$481$	−607.421	+	836.044i	−0.00262543	+	0.00361359i
$482$	72405.4	+	222841.i	0.311657	+	0.959181i
$483$		0			0
$484$	−624242.	+	62766.1i	−2.66478	+	0.267938i
$485$	4705.93			0.0200061
$486$		0			0
$487$	287065.	+	208565.i	1.21038	+	0.879392i	0.995265	−	0.0971965i	$-0.0309875\pi$
$487$	287065.	+	208565.i	1.21038	+	0.879392i	0.215115	+	0.976589i	$0.430988\pi$
$488$	−97673.3	+	70963.8i	−0.410144	+	0.297987i
$489$		0			0
$490$	1107.59	+	359.877i	0.00461303	+	0.00149886i
$491$	70956.0	+	97662.6i	0.294324	+	0.405103i	0.930413	−	0.366513i	$-0.119449\pi$
$491$	70956.0	+	97662.6i	0.294324	+	0.405103i	−0.636088	+	0.771616i	$0.719449\pi$
$492$		0			0
$493$	−168808.	−	519536.i	−0.694541	−	2.13758i
$494$			26860.7i			0.110069i
$495$		0			0
$496$	−105461.			−0.428674
$497$	−70947.0	+	23052.1i	−0.287224	+	0.0933248i
$498$		0			0
$499$	18127.1	−	13170.1i	0.0727993	−	0.0528918i	−0.550790	−	0.834644i	$-0.685674\pi$
$499$	18127.1	−	13170.1i	0.0727993	−	0.0528918i	0.623590	+	0.781752i	$0.285674\pi$
$500$	−112179.	+	345251.i	−0.448715	+	1.38100i
$501$		0			0
$502$	36445.4	+	50162.9i	0.144622	+	0.199056i
$503$	−254983.	+	350953.i	−1.00780	+	1.38712i	−0.0873863	+	0.996175i	$0.527851\pi$
$503$	−254983.	+	350953.i	−1.00780	+	1.38712i	−0.920414	+	0.390944i	$0.872149\pi$
$504$		0			0
$505$			81762.9i			0.320607i
$506$	16815.5	+	335320.i	0.0656762	+	1.30966i
$507$		0			0
$508$	1.05480e6	−	342725.i	4.08736	−	1.32806i
$509$	12056.0	+	8759.18i	0.0465336	+	0.0338087i	0.610809	−	0.791778i	$-0.290844\pi$
$509$	12056.0	+	8759.18i	0.0465336	+	0.0338087i	−0.564275	+	0.825587i	$0.690844\pi$
$510$		0			0
$511$	126296.	−	388700.i	0.483670	−	1.48858i
$512$	−230931.	−	75034.2i	−0.880934	−	0.286233i
$513$		0			0
$514$	279278.	−	384394.i	1.05709	−	1.45496i
$515$	20657.7	+	63577.8i	0.0778874	+	0.239713i
$516$		0			0
$517$	20651.2	−	16646.1i	0.0772618	−	0.0622775i
$518$	−65253.0			−0.243187
$519$		0			0
$520$	6971.31	+	5064.95i	0.0257815	+	0.0187313i
$521$	230222.	−	167266.i	0.848146	−	0.616214i	−0.0764879	−	0.997071i	$-0.524371\pi$
$521$	230222.	−	167266.i	0.848146	−	0.616214i	0.924634	+	0.380856i	$0.124371\pi$
$522$		0			0
$523$	100173.	+	32548.3i	0.366226	+	0.118994i	0.486348	−	0.873765i	$-0.338329\pi$
$523$	100173.	+	32548.3i	0.366226	+	0.118994i	−0.120122	+	0.992759i	$0.538329\pi$
$524$	2445.47	+	3365.90i	0.00890634	+	0.0122585i
$525$		0			0
$526$	70289.0	+	216327.i	0.254048	+	0.781880i
$527$			50110.0i			0.180428i
$528$		0			0
$529$	−149019.			−0.532511
$530$	58322.2	−	18950.0i	0.207626	−	0.0674619i
$531$		0			0
$532$	−999109.	+	725895.i	−3.53012	+	2.56478i
$533$	−3482.42	+	10717.8i	−0.0122582	+	0.0377269i
$534$		0			0
$535$	−2472.82	−	3403.54i	−0.00863941	−	0.0118911i
$536$	150499.	−	207144.i	0.523845	−	0.721011i
$537$		0			0
$538$		−	53865.1i		−	0.186098i
$539$	−2179.29	−	1422.25i	−0.00750133	−	0.00489550i
$540$		0			0
$541$	−21619.5	+	7024.59i	−0.0738670	+	0.0240009i	−0.345717	−	0.938339i	$-0.612364\pi$
$541$	−21619.5	+	7024.59i	−0.0738670	+	0.0240009i	0.271850	+	0.962340i	$0.412364\pi$
$542$	708049.	+	514427.i	2.41026	+	1.75116i
$543$		0			0
$544$	−468591.	+	1.44218e6i	−1.58342	+	4.87327i
$545$	98310.9	+	31943.1i	0.330985	+	0.107544i
$546$		0			0
$547$	−124939.	+	171963.i	−0.417563	+	0.574726i	−0.965043	−	0.262093i	$-0.915587\pi$
$547$	−124939.	+	171963.i	−0.417563	+	0.574726i	0.547480	+	0.836819i	$0.315587\pi$
$548$	−412976.	−	1.27101e6i	−1.37519	−	4.23241i
$549$		0			0
$550$	291795.	−	447115.i	0.964612	−	1.47807i
$551$	−759242.			−2.50079
$552$		0			0
$553$	−27383.5	−	19895.3i	−0.0895445	−	0.0650579i
$554$	−565579.	+	410918.i	−1.84278	+	1.33886i
$555$		0			0
$556$	321079.	+	104325.i	1.03863	+	0.337473i
$557$	47020.5	+	64718.2i	0.151557	+	0.208601i	0.878044	−	0.478580i	$-0.158848\pi$
$557$	47020.5	+	64718.2i	0.151557	+	0.208601i	−0.726487	+	0.687180i	$0.758848\pi$
$558$		0			0
$559$	−2599.19	−	7999.48i	−0.00831791	−	0.0255999i
$560$			308036.i			0.982259i
$561$		0			0
$562$	−440302.			−1.39405
$563$	−21012.7	+	6827.44i	−0.0662926	+	0.0215398i	−0.341976	−	0.939709i	$-0.611096\pi$
$563$	−21012.7	+	6827.44i	−0.0662926	+	0.0215398i	0.275683	+	0.961249i	$0.411096\pi$
$564$		0			0
$565$	−67777.8	+	49243.4i	−0.212320	+	0.154259i
$566$	−109106.	+	335793.i	−0.340577	+	1.04819i
$567$		0			0
$568$	185162.	+	254854.i	0.573925	+	0.789940i
$569$	145810.	−	200690.i	0.450363	−	0.619871i	−0.522113	−	0.852876i	$-0.674856\pi$
$569$	145810.	−	200690.i	0.450363	−	0.619871i	0.972475	+	0.233006i	$0.0748560\pi$
$570$		0			0
$571$			392725.i			1.20453i	0.798298	+	0.602263i	$0.205734\pi$
$571$			392725.i			1.20453i	−0.798298	+	0.602263i	$0.794266\pi$
$572$	−19284.3	−	23924.2i	−0.0589402	−	0.0731215i
$573$		0			0
$574$	−676759.	+	219892.i	−2.05405	+	0.667400i
$575$	−168306.	−	122282.i	−0.509055	−	0.369850i
$576$		0			0
$577$	85274.3	−	262447.i	0.256134	−	0.788299i	−0.737470	−	0.675379i	$-0.763980\pi$
$577$	85274.3	−	262447.i	0.256134	−	0.788299i	0.993604	−	0.112919i	$-0.0360201\pi$
$578$	709001.	+	230368.i	2.12222	+	0.689552i
$579$		0			0
$580$	−228473.	+	314466.i	−0.679171	+	0.934799i
$581$	−90060.7	−	277178.i	−0.266798	−	0.821121i
$582$		0			0
$583$	−136858.	+	6863.11i	−0.402656	+	0.0201922i
$584$	−1.72589e6			−5.06044
$585$		0			0
$586$	−832717.	−	605005.i	−2.42495	−	1.76183i
$587$	35842.8	−	26041.3i	0.104022	−	0.0755765i	−0.534558	−	0.845132i	$-0.679522\pi$
$587$	35842.8	−	26041.3i	0.104022	−	0.0755765i	0.638580	+	0.769555i	$0.279522\pi$
$588$		0			0
$589$	66237.1	+	21521.7i	0.190928	+	0.0620364i
$590$	7620.34	+	10488.5i	0.0218912	+	0.0301307i
$591$		0			0
$592$	48206.4	+	148364.i	0.137550	+	0.423336i
$593$			376705.i			1.07125i	0.844455	+	0.535627i	$0.179925\pi$
$593$			376705.i			1.07125i	−0.844455	+	0.535627i	$0.820075\pi$
$594$		0			0
$595$	146364.			0.413430
$596$	−652042.	+	211861.i	−1.83562	+	0.596430i
$597$		0			0
$598$	−13303.6	+	9665.64i	−0.0372021	+	0.0270289i
$599$	191096.	−	588134.i	0.532597	−	1.63916i	−0.216189	−	0.976351i	$-0.569363\pi$
$599$	191096.	−	588134.i	0.532597	−	1.63916i	0.748786	−	0.662812i	$-0.230637\pi$
$600$		0			0
$601$	169502.	+	233300.i	0.469274	+	0.645900i	0.976399	−	0.215972i	$-0.0692921\pi$
$601$	169502.	+	233300.i	0.469274	+	0.645900i	−0.507126	+	0.861872i	$0.669292\pi$
$602$	312179.	−	429677.i	0.861411	−	1.18563i
$603$		0			0
$604$		−	1.77818e6i		−	4.87418i
$605$	77111.0	−	68804.1i	0.210671	−	0.187976i
$606$		0			0
$607$	566217.	−	183975.i	1.53676	−	0.499323i	0.586279	−	0.810109i	$-0.300592\pi$
$607$	566217.	−	183975.i	1.53676	−	0.499323i	0.950480	+	0.310786i	$0.100592\pi$
$608$	1.70506e6	+	1.23880e6i	4.61246	+	3.35115i
$609$		0			0
$610$	9807.29	−	30183.7i	0.0263566	−	0.0811172i
$611$	1235.56	+	401.459i	0.00330966	+	0.00107537i
$612$		0			0
$613$	−304577.	+	419214.i	−0.810542	+	1.11562i	0.180697	+	0.983539i	$0.442165\pi$
$613$	−304577.	+	419214.i	−0.810542	+	1.11562i	−0.991239	+	0.132077i	$0.957835\pi$
$614$	141825.	+	436491.i	0.376197	+	1.15781i
$615$		0			0
$616$	317328.	−	1.17370e6i	0.836272	−	3.09310i
$617$	659715.			1.73295			0.866475	−	0.499220i	$-0.166380\pi$
$617$	659715.			1.73295			0.866475	+	0.499220i	$0.166380\pi$
$618$		0			0
$619$	430735.	+	312948.i	1.12416	+	0.816752i	0.984835	−	0.173494i	$-0.0555057\pi$
$619$	430735.	+	312948.i	1.12416	+	0.816752i	0.139328	+	0.990246i	$0.455506\pi$
$620$	28846.2	−	20958.0i	0.0750422	−	0.0545214i
$621$		0			0
$622$	819053.	+	266127.i	2.11705	+	0.687872i
$623$	23319.1	+	32096.0i	0.0600808	+	0.0826941i
$624$		0			0
$625$	92608.8	+	285021.i	0.237079	+	0.729653i
$626$		−	1.13127e6i		−	2.88680i
$627$		0			0
$628$	1.07351e6			2.72199
$629$	70495.6	−	22905.4i	0.178181	−	0.0578944i
$630$		0			0
$631$	−208773.	+	151683.i	−0.524344	+	0.380958i	−0.818238	−	0.574880i	$-0.805049\pi$
$631$	−208773.	+	151683.i	−0.524344	+	0.380958i	0.293894	+	0.955838i	$0.405049\pi$
$632$	−44169.2	+	135939.i	−0.110582	+	0.340337i
$633$		0			0
$634$	−656689.	−	903855.i	−1.63373	−	2.24864i
$635$	−107382.	+	147799.i	−0.266309	+	0.366543i
$636$		0			0
$637$		−	127.458i		−	0.000314116i
$638$	928734.	−	748613.i	2.28165	−	1.83915i
$639$		0			0
$640$	289019.	−	93907.8i	0.705612	−	0.229267i
$641$	239856.	+	174266.i	0.583760	+	0.424127i	0.840078	−	0.542466i	$-0.182509\pi$
$641$	239856.	+	174266.i	0.583760	+	0.424127i	−0.256317	+	0.966593i	$0.582509\pi$
$642$		0			0
$643$	43226.5	−	133038.i	0.104551	−	0.321775i	−0.885074	−	0.465451i	$-0.845892\pi$
$643$	43226.5	−	133038.i	0.104551	−	0.321775i	0.989625	+	0.143676i	$0.0458922\pi$
$644$	−719045.	−	233632.i	−1.73374	−	0.563327i
$645$		0			0
$646$	1.13245e6	−	1.55869e6i	2.71366	−	3.73503i
$647$	−176756.	−	544000.i	−0.422247	−	1.29954i	−0.905606	−	0.424120i	$-0.860584\pi$
$647$	−176756.	−	544000.i	−0.422247	−	1.29954i	0.483360	−	0.875422i	$-0.339416\pi$
$648$		0			0
$649$	−10320.8	−	27069.0i	−0.0245034	−	0.0642661i
$650$	26150.0			0.0618935
$651$		0			0
$652$	1.31652e6	+	956511.i	3.09695	+	2.25006i
$653$	−54049.6	+	39269.3i	−0.126755	+	0.0920931i	−0.649356	−	0.760484i	$-0.724962\pi$
$653$	−54049.6	+	39269.3i	−0.126755	+	0.0920931i	0.522601	+	0.852577i	$0.324962\pi$
$654$		0			0
$655$	−651.779	−	211.776i	−0.00151921	−	0.000493621i
$656$	999926.	+	1.37628e6i	2.32359	+	3.19815i
$657$		0			0
$658$	25349.6	+	78017.9i	0.0585489	+	0.180195i
$659$		−	416882.i		−	0.959937i	−0.877286	−	0.479968i	$-0.840648\pi$
$659$		−	416882.i		−	0.959937i	0.877286	−	0.479968i	$-0.159352\pi$
$660$		0			0
$661$	−570540.			−1.30582			−0.652909	−	0.757436i	$-0.726452\pi$
$661$	−570540.			−1.30582			−0.652909	+	0.757436i	$0.726452\pi$
$662$	−919379.	+	298724.i	−2.09787	+	0.681639i
$663$		0			0
$664$	−995671.	+	723398.i	−2.25829	+	1.64074i
$665$	62862.0	−	193469.i	0.142149	−	0.437491i
$666$		0			0
$667$	−273208.	−	376038.i	−0.614104	−	0.845241i
$668$	997096.	−	1.37239e6i	2.23452	−	3.07555i
$669$		0			0
$670$			67307.3i			0.149938i
$671$	−38758.7	+	59389.6i	−0.0860842	+	0.131906i
$672$		0			0
$673$	−356769.	+	115921.i	−0.787693	+	0.255937i	−0.675121	−	0.737707i	$-0.735909\pi$
$673$	−356769.	+	115921.i	−0.787693	+	0.255937i	−0.112571	+	0.993644i	$0.535909\pi$
$674$	−433209.	−	314745.i	−0.953625	−	0.692849i
$675$		0			0
$676$	−377735.	+	1.16255e6i	−0.826598	+	2.54401i
$677$	−593709.	−	192908.i	−1.29538	−	0.420894i	−0.421407	−	0.906872i	$-0.638464\pi$
$677$	−593709.	−	192908.i	−1.29538	−	0.420894i	−0.873971	+	0.485978i	$0.838464\pi$
$678$		0			0
$679$	19115.7	−	26310.4i	0.0414619	−	0.0570675i
$680$	−190996.	−	587824.i	−0.413053	−	1.27125i
$681$		0			0
$682$	−102244.	+	38983.7i	−0.219821	+	0.0838135i
$683$	534563.			1.14593			0.572965	−	0.819580i	$-0.305793\pi$
$683$	534563.			1.14593			0.572965	+	0.819580i	$0.305793\pi$
$684$		0			0
$685$	178095.	+	129393.i	0.379551	+	0.275760i
$686$	733405.	−	532850.i	1.55846	−	1.13229i
$687$		0			0
$688$	−1.20757e6	−	392364.i	−2.55115	−	0.828918i
$689$	−3944.96	−	5429.77i	−0.00831006	−	0.0114378i
$690$		0			0
$691$	−67881.0	−	208916.i	−0.142165	−	0.437538i	0.854471	−	0.519500i	$-0.173882\pi$
$691$	−67881.0	−	208916.i	−0.142165	−	0.437538i	−0.996636	+	0.0819612i	$0.973882\pi$
$692$			1.19493e6i			2.49534i
$693$		0			0
$694$	688243.			1.42897
$695$	−52888.7	+	17184.6i	−0.109495	+	0.0355770i
$696$		0			0
$697$	653944.	−	475118.i	1.34609	−	0.977993i
$698$	−100043.	+	307902.i	−0.205342	+	0.631977i
$699$		0			0
$700$	706689.	+	972674.i	1.44222	+	1.98505i
$701$	−406735.	+	559823.i	−0.827706	+	1.13924i	0.160640	+	0.987013i	$0.448644\pi$
$701$	−406735.	+	559823.i	−0.827706	+	1.13924i	−0.988346	+	0.152226i	$0.951356\pi$
$702$		0			0
$703$		−	103021.i		−	0.208456i
$704$	−1.57733e6	+	79099.0i	−3.18256	+	0.159597i
$705$		0			0
$706$	−1.09274e6	+	355052.i	−2.19234	+	0.712333i
$707$	457130.	+	332124.i	0.914535	+	0.664449i
$708$		0			0
$709$	−107235.	+	330036.i	−0.213326	+	0.656551i	0.785942	+	0.618301i	$0.212179\pi$
$709$	−107235.	+	330036.i	−0.213326	+	0.656551i	−0.999268	+	0.0382506i	$0.987821\pi$
$710$	−78756.7	−	25589.6i	−0.156232	−	0.0507630i
$711$		0			0
$712$	98473.0	−	135536.i	0.194248	−	0.267360i
$713$	13175.6	+	40550.5i	0.0259175	+	0.0797658i
$714$		0			0
$715$	4886.24	+	1321.08i	0.00955790	+	0.00258414i
$716$	−49847.5			−0.0972338
$717$		0			0
$718$	−229501.	−	166742.i	−0.445180	−	0.323442i
$719$	−153690.	+	111662.i	−0.297295	+	0.215997i	−0.726426	−	0.687245i	$-0.758820\pi$
$719$	−153690.	+	111662.i	−0.297295	+	0.215997i	0.429131	+	0.903242i	$0.358820\pi$
$720$		0			0
$721$	439370.	+	142760.i	0.845201	+	0.274623i
$722$	−986309.	−	1.35754e6i	−1.89208	−	2.60422i
$723$		0			0
$724$	−689023.	−	2.12059e6i	−1.31449	−	4.04558i
$725$			739153.i			1.40624i
$726$		0			0
$727$	−293496.			−0.555307			−0.277654	−	0.960681i	$-0.589557\pi$
$727$	−293496.			−0.555307			−0.277654	+	0.960681i	$0.589557\pi$
$728$	56635.4	−	18402.0i	0.106863	−	0.0347218i
$729$		0			0
$730$	367045.	−	266674.i	0.688770	−	0.500420i
$731$	−186433.	+	573781.i	−0.348889	+	1.07377i
$732$		0			0
$733$	−575175.	−	791660.i	−1.07051	−	1.47343i	−0.869556	−	0.493834i	$-0.835595\pi$
$733$	−575175.	−	791660.i	−1.07051	−	1.47343i	−0.200957	−	0.979600i	$-0.564405\pi$
$734$	−892077.	+	1.22784e6i	−1.65581	+	2.27903i
$735$		0			0
$736$			1.29026e6i			2.38189i
$737$	39254.1	−	145188.i	0.0722687	−	0.267299i
$738$		0			0
$739$	−722504.	+	234756.i	−1.32297	+	0.429860i	−0.883515	−	0.468403i	$-0.844830\pi$
$739$	−722504.	+	234756.i	−1.32297	+	0.429860i	−0.439459	+	0.898263i	$0.644830\pi$
$740$	−42669.8	−	31001.4i	−0.0779214	−	0.0566132i
$741$		0			0
$742$	130959.	−	403050.i	0.237863	−	0.732068i
$743$	849461.	+	276007.i	1.53874	+	0.499967i	0.951029	−	0.309102i	$-0.100029\pi$
$743$	849461.	+	276007.i	1.53874	+	0.499967i	0.587713	+	0.809070i	$0.300029\pi$
$744$		0			0
$745$	66380.2	−	91364.6i	0.119599	−	0.164613i
$746$	−24381.3	−	75037.8i	−0.0438105	−	0.134835i
$747$		0			0
$748$	110390.	+	2.20132e6i	0.197301	+	3.93441i
$749$	−29073.6			−0.0518244
$750$		0			0
$751$	140052.	+	101754.i	0.248318	+	0.180414i	0.704981	−	0.709226i	$-0.250955\pi$
$751$	140052.	+	101754.i	0.248318	+	0.180414i	−0.456663	+	0.889640i	$0.650955\pi$
$752$	158660.	−	115273.i	0.280564	−	0.203841i
$753$		0			0
$754$	55566.2	+	18054.5i	0.0977390	+	0.0317573i
$755$	172165.	+	236965.i	0.302031	+	0.415709i
$756$		0			0
$757$	43580.0	+	134126.i	0.0760494	+	0.234056i	0.981854	−	0.189641i	$-0.0607323\pi$
$757$	43580.0	+	134126.i	0.0760494	+	0.234056i	−0.905804	+	0.423697i	$0.860732\pi$
$758$		−	1.88772e6i		−	3.28549i
$759$		0			0
$760$	−859036.			−1.48725
$761$	152785.	−	49642.8i	0.263822	−	0.0857210i	−0.174119	−	0.984725i	$-0.555708\pi$
$761$	152785.	−	49642.8i	0.263822	−	0.0857210i	0.437941	+	0.899004i	$0.355708\pi$
$762$		0			0
$763$	577934.	−	419894.i	0.992725	−	0.721257i
$764$	−692250.	+	2.13053e6i	−1.18598	+	3.65006i
$765$		0			0
$766$	443468.	+	610382.i	0.755797	+	1.04026i
$767$	834.009	−	1147.91i	0.00141769	−	0.00195128i
$768$		0			0
$769$			418486.i			0.707666i	0.935309	+	0.353833i	$0.115122\pi$
$769$			418486.i			0.707666i	−0.935309	+	0.353833i	$0.884878\pi$
$770$	113866.	+	298641.i	0.192049	+	0.503696i
$771$		0			0
$772$	788985.	−	256357.i	1.32384	−	0.430140i
$773$	−225585.	−	163897.i	−0.377529	−	0.274291i	0.382797	−	0.923832i	$-0.374961\pi$
$773$	−225585.	−	163897.i	−0.377529	−	0.274291i	−0.760326	+	0.649542i	$0.774961\pi$
$774$		0			0
$775$	20952.3	−	64484.6i	0.0348842	−	0.107362i
$776$	−130612.	−	42438.3i	−0.216900	−	0.0704750i
$777$		0			0
$778$	−135075.	+	185915.i	−0.223160	+	0.307154i
$779$	−347165.	−	1.06846e6i	−0.572085	−	1.76070i
$780$		0			0
$781$	154962.	+	101131.i	0.254052	+	0.165799i
$782$	1.17950e6			1.92878
$783$		0			0
$784$	−15566.0	−	11309.4i	−0.0253247	−	0.0183995i
$785$	−143059.	+	103938.i	−0.232153	+	0.168669i
$786$		0			0
$787$	−874562.	−	284163.i	−1.41202	−	0.458794i	−0.498963	−	0.866623i	$-0.666286\pi$
$787$	−874562.	−	284163.i	−1.41202	−	0.458794i	−0.913058	+	0.407830i	$0.866286\pi$
$788$	276651.	+	380778.i	0.445533	+	0.613224i
$789$		0			0
$790$	−11610.9	−	35734.8i	−0.0186043	−	0.0572581i
$791$			578968.i			0.925341i
$792$		0			0
$793$	−3473.46			−0.00552353
$794$	591257.	−	192111.i	0.937854	−	0.304727i
$795$		0			0
$796$	250278.	−	181838.i	0.394999	−	0.286984i
$797$	210515.	−	647900.i	0.331411	−	1.01998i	−0.637052	−	0.770821i	$-0.719846\pi$
$797$	210515.	−	647900.i	0.331411	−	1.01998i	0.968463	−	0.249158i	$-0.0801537\pi$
$798$		0			0
$799$	−54772.4	−	75387.7i	−0.0857962	−	0.118088i
$800$	1.20602e6	−	1.65995e6i	1.88441	−	2.59367i
$801$		0			0
$802$		−	149502.i		−	0.232434i
$803$	−947279.	+	361178.i	−1.46908	+	0.560132i
$804$		0			0
$805$	118442.	−	38484.2i	0.182774	−	0.0593870i
$806$	−4335.88	−	3150.20i	−0.00667432	−	0.00484917i
$807$		0			0
$808$	737343.	−	2.26931e6i	1.12940	−	3.47593i
$809$	−398402.	−	129449.i	−0.608729	−	0.197788i	−0.0115993	−	0.999933i	$-0.503692\pi$
$809$	−398402.	−	129449.i	−0.608729	−	0.197788i	−0.597130	+	0.802145i	$0.703692\pi$
$810$		0			0
$811$	133887.	−	184280.i	0.203563	−	0.280180i	−0.695014	−	0.718996i	$-0.744602\pi$
$811$	133887.	−	184280.i	0.203563	−	0.280180i	0.898577	+	0.438816i	$0.144602\pi$
$812$	830088.	+	2.55475e6i	1.25896	+	3.87468i
$813$		0			0
$814$	101579.	+	126019.i	0.153304	+	0.190190i
$815$	−268054.			−0.403559
$816$		0			0
$817$	678372.	+	492866.i	1.01630	+	0.738388i
$818$	−798787.	+	580353.i	−1.19378	+	0.867332i
$819$		0			0
$820$	−547011.	−	177735.i	−0.813521	−	0.264329i
$821$	337423.	+	464423.i	0.500597	+	0.689013i	0.982298	−	0.187323i	$-0.0599810\pi$
$821$	337423.	+	464423.i	0.500597	+	0.689013i	−0.481701	+	0.876335i	$0.659981\pi$
$822$		0			0
$823$	377294.	+	1.16119e6i	0.557032	+	1.71437i	0.690517	+	0.723317i	$0.257383\pi$
$823$	377294.	+	1.16119e6i	0.557032	+	1.71437i	−0.133485	+	0.991051i	$0.542617\pi$
$824$		−	1.95088e6i		−	2.87326i
$825$		0			0
$826$	89594.4			0.131317
$827$	999806.	−	324857.i	1.46186	−	0.474986i	0.533219	−	0.845977i	$-0.320982\pi$
$827$	999806.	−	324857.i	1.46186	−	0.474986i	0.928636	+	0.370991i	$0.120982\pi$
$828$		0			0
$829$	85881.6	−	62396.7i	0.124966	−	0.0907930i	−0.523547	−	0.851997i	$-0.675391\pi$
$829$	85881.6	−	62396.7i	0.124966	−	0.0907930i	0.648512	+	0.761204i	$0.275391\pi$
$830$	99974.4	−	307690.i	0.145122	−	0.446639i
$831$		0			0
$832$	−45466.6	−	62579.4i	−0.0656819	−	0.0904034i
$833$	−5373.67	+	7396.23i	−0.00774428	+	0.0106591i
$834$		0			0
$835$			279428.i			0.400771i
$836$	2.95719e6	+	799525.i	4.23122	+	1.14398i
$837$		0			0
$838$	−703745.	+	228661.i	−1.00214	+	0.325614i
$839$	−346939.	−	252066.i	−0.492867	−	0.358089i	0.313419	−	0.949615i	$-0.398526\pi$
$839$	−346939.	−	252066.i	−0.492867	−	0.358089i	−0.806286	+	0.591526i	$0.798526\pi$
$840$		0			0
$841$	−291766.	+	897963.i	−0.412518	+	1.26960i
$842$	−2.36971e6	−	769965.i	−3.34250	−	1.08604i
$843$		0			0
$844$	−1.48463e6	+	2.04342e6i	−2.08417	+	2.86861i
$845$	−62221.2	−	191497.i	−0.0871415	−	0.268194i
$846$		0			0
$847$	−71449.9	−	710606.i	−0.0995943	−	0.990517i
$848$	−1.01315e6			−1.40891
$849$		0			0
$850$	−1.51745e6	−	1.10249e6i	−2.10027	−	1.52594i
$851$	51024.4	−	37071.4i	0.0704562	−	0.0511894i
$852$		0			0
$853$	1.05312e6	+	342179.i	1.44737	+	0.470278i	0.924186	−	0.381943i	$-0.124745\pi$
$853$	1.05312e6	+	342179.i	1.44737	+	0.470278i	0.523181	+	0.852221i	$0.324745\pi$
$854$	−128917.	−	177439.i	−0.176764	−	0.243295i
$855$		0			0
$856$	37939.0	+	116764.i	0.0517772	+	0.159354i
$857$			607148.i			0.826672i	0.910579	+	0.413336i	$0.135636\pi$
$857$			607148.i			0.826672i	−0.910579	+	0.413336i	$0.864364\pi$
$858$		0			0
$859$	−358777.			−0.486226			−0.243113	−	0.969998i	$-0.578169\pi$
$859$	−358777.			−0.486226			−0.243113	+	0.969998i	$0.578169\pi$
$860$	408275.	−	132657.i	0.552022	−	0.179363i
$861$		0			0
$862$	−1.01548e6	+	737791.i	−1.36665	+	0.992930i
$863$	27195.8	−	83700.0i	0.0365157	−	0.112384i	−0.931137	−	0.364669i	$-0.881182\pi$
$863$	27195.8	−	83700.0i	0.0365157	−	0.112384i	0.967653	+	0.252285i	$0.0811821\pi$
$864$		0			0
$865$	−115694.	−	159240.i	−0.154625	−	0.212823i
$866$	400018.	−	550577.i	0.533388	−	0.734146i
$867$		0			0
$868$		−	246409.i		−	0.327052i
$869$	4205.12	+	83855.1i	0.00556851	+	0.111043i
$870$		0			0
$871$	7005.91	−	2276.36i	0.00923482	−	0.00300057i
$872$	−2.44053e6	−	1.77315e6i	−3.20960	−	2.33191i
$873$		0			0
$874$	506581.	−	1.55910e6i	0.663172	−	2.04103i
$875$	−393016.	−	127699.i	−0.513328	−	0.166790i
$876$		0			0
$877$	69872.5	−	96171.3i	0.0908463	−	0.125039i	−0.761175	−	0.648547i	$-0.775377\pi$
$877$	69872.5	−	96171.3i	0.0908463	−	0.125039i	0.852021	+	0.523508i	$0.175377\pi$
$878$	356207.	+	1.09629e6i	0.462076	+	1.42212i
$879$		0			0
$880$	594893.	−	479518.i	0.768198	−	0.619212i
$881$	−927640.			−1.19516			−0.597582	−	0.801807i	$-0.703872\pi$
$881$	−927640.			−1.19516			−0.597582	+	0.801807i	$0.703872\pi$
$882$		0			0
$883$	−794142.	−	576978.i	−1.01854	−	0.740010i	−0.0525540	−	0.998618i	$-0.516736\pi$
$883$	−794142.	−	576978.i	−1.01854	−	0.740010i	−0.965982	+	0.258608i	$0.916736\pi$
$884$	−87335.8	+	63453.1i	−0.111760	+	0.0811986i
$885$		0			0
$886$	1.44141e6	+	468342.i	1.83620	+	0.596617i
$887$	311987.	+	429413.i	0.396541	+	0.545792i	0.959872	−	0.280439i	$-0.0904801\pi$
$887$	311987.	+	429413.i	0.396541	+	0.545792i	−0.563330	+	0.826232i	$0.690480\pi$
$888$		0			0
$889$	390141.	+	1.20073e6i	0.493649	+	1.51930i
$890$			44039.9i			0.0555990i
$891$		0			0
$892$	−992650.			−1.24757
$893$	−123174.	+	40021.7i	−0.154460	+	0.0501872i
$894$		0			0
$895$	6642.81	−	4826.28i	0.00829289	−	0.00602513i
$896$	648974.	−	1.99734e6i	0.808372	−	2.48791i
$897$		0			0
$898$	1.44286e6	+	1.98592e6i	1.78925	+	2.46269i
$899$	89043.1	−	122557.i	0.110174	−	0.151642i
$900$		0			0
$901$			481402.i			0.593005i
$902$	1.47817e6	+	964681.i	1.81682	+	1.18569i
$903$		0			0
$904$	2.32523e6	−	755514.i	2.84531	−	0.924498i
$905$	297139.	+	215884.i	0.362796	+	0.263587i
$906$		0			0
$907$	264498.	−	814041.i	0.321520	−	0.989536i	−0.651467	−	0.758677i	$-0.725846\pi$
$907$	264498.	−	814041.i	0.321520	−	0.989536i	0.972987	−	0.230859i	$-0.0741538\pi$
$908$	2.51082e6	+	815816.i	3.04540	+	0.989511i
$909$		0			0
$910$	−9201.29	+	12664.5i	−0.0111113	+	0.0152934i
$911$	64101.0	+	197283.i	0.0772375	+	0.237712i	0.982219	−	0.187738i	$-0.0601156\pi$
$911$	64101.0	+	197283.i	0.0772375	+	0.237712i	−0.904982	+	0.425451i	$0.860116\pi$
$912$		0			0
$913$	−395102.	+	605411.i	−0.473988	+	0.726287i
$914$	896500.			1.07314
$915$		0			0
$916$	−1.34317e6	−	975868.i	−1.60081	−	1.16305i
$917$	−3831.57	+	2783.80i	−0.00455657	+	0.00331054i
$918$		0			0
$919$	−1.42609e6	−	463365.i	−1.68856	−	0.548646i	−0.702017	−	0.712161i	$-0.747717\pi$
$919$	−1.42609e6	−	463365.i	−1.68856	−	0.548646i	−0.986541	+	0.163515i	$0.947717\pi$
$920$	−309118.	−	425465.i	−0.365215	−	0.502676i
$921$		0			0
$922$	590564.	+	1.81757e6i	0.694713	+	2.13811i
$923$			9063.12i			0.0106383i
$924$		0			0
$925$	−100295.			−0.117219
$926$	−932090.	+	302855.i	−1.08702	+	0.353193i
$927$		0			0
$928$	3.70874e6	−	2.69456e6i	4.30656	−	3.12890i
$929$	263539.	−	811090.i	0.305361	−	0.939805i	−0.674181	−	0.738566i	$-0.735503\pi$
$929$	263539.	−	811090.i	0.305361	−	0.939805i	0.979542	−	0.201239i	$-0.0644967\pi$
$930$		0			0
$931$	7468.64	+	10279.7i	0.00861673	+	0.0118599i
$932$	−1.35526e6	+	1.86536e6i	−1.56024	+	2.14748i
$933$		0			0
$934$		−	1.69628e6i		−	1.94448i
$935$	−227844.	−	282665.i	−0.260625	−	0.323332i
$936$		0			0
$937$	1.26471e6	−	410928.i	1.44049	−	0.468044i	0.518440	−	0.855114i	$-0.326513\pi$
$937$	1.26471e6	−	410928.i	1.44049	−	0.468044i	0.922050	+	0.387070i	$0.126513\pi$
$938$	376309.	+	273405.i	0.427700	+	0.310742i
$939$		0			0
$940$	−20489.6	+	63060.4i	−0.0231887	+	0.0713675i
$941$	−743988.	−	241736.i	−0.840208	−	0.273000i	−0.142869	−	0.989742i	$-0.545633\pi$
$941$	−743988.	−	241736.i	−0.840208	−	0.273000i	−0.697339	+	0.716742i	$0.745633\pi$
$942$		0			0
$943$	404265.	−	556424.i	0.454614	−	0.625723i
$944$	−66188.9	−	203708.i	−0.0742747	−	0.228594i
$945$		0			0
$946$	−1.31578e6	+	65982.9i	−1.47028	+	0.0737309i
$947$	−670581.			−0.747741			−0.373870	−	0.927481i	$-0.621970\pi$
$947$	−670581.			−0.747741			−0.373870	+	0.927481i	$0.621970\pi$
$948$		0			0
$949$	−40171.3	−	29186.2i	−0.0446050	−	0.0324074i
$950$	−2.10904e6	+	1.53231e6i	−2.33688	+	1.69785i
$951$		0			0
$952$	−4.06230e6	−	1.31992e6i	−4.48228	−	1.45638i
$953$	70453.4	+	96970.8i	0.0775740	+	0.106771i	0.846041	−	0.533118i	$-0.178980\pi$
$953$	70453.4	+	96970.8i	0.0775740	+	0.106771i	−0.768467	+	0.639890i	$0.778980\pi$
$954$		0			0
$955$	−114029.	−	350944.i	−0.125028	−	0.384796i
$956$			1.28815e6i			1.40945i
$957$		0			0
$958$	596711.			0.650179
$959$	1.44685e6	−	470111.i	1.57321	−	0.511168i
$960$		0			0
$961$	735902.	−	534664.i	0.796844	−	0.578941i
$962$	−2449.81	+	7539.74i	−0.00264717	+	0.00814716i
$963$		0			0
$964$	769298.	+	1.05885e6i	0.827829	+	1.13941i
$965$	−80321.5	+	110553.i	−0.0862536	+	0.118718i
$966$		0			0
$967$		−	1.68698e6i		−	1.80408i	−0.431651	−	0.902041i	$-0.642069\pi$
$967$		−	1.68698e6i		−	1.80408i	0.431651	−	0.902041i	$-0.357931\pi$
$968$	−2.76067e6	+	1.21425e6i	−2.94621	+	1.29585i
$969$		0			0
$970$	34334.5	−	11155.9i	0.0364911	−	0.0118567i
$971$	−1.40294e6	−	1.01930e6i	−1.48799	−	1.08109i	−0.974870	−	0.222775i	$-0.928488\pi$
$971$	−1.40294e6	−	1.01930e6i	−1.48799	−	1.08109i	−0.513123	−	0.858315i	$-0.671512\pi$
$972$		0			0
$973$	−118758.	+	365501.i	−0.125441	+	0.386067i
$974$	2.58885e6	+	841169.i	2.72891	+	0.886677i
$975$		0			0
$976$	−308200.	+	424200.i	−0.323543	+	0.445319i
$977$	321147.	+	988387.i	0.336445	+	1.03547i	0.966006	+	0.258520i	$0.0832348\pi$
$977$	321147.	+	988387.i	0.336445	+	1.03547i	−0.629561	+	0.776951i	$0.716765\pi$
$978$		0			0
$979$	25684.4	−	94998.4i	0.0267981	−	0.0991177i
$980$	6505.18			0.00677341
$981$		0			0
$982$	749216.	+	544337.i	0.776934	+	0.564475i
$983$	205868.	−	149572.i	0.213051	−	0.154790i	−0.476142	−	0.879368i	$-0.657965\pi$
$983$	205868.	−	149572.i	0.213051	−	0.154790i	0.689193	+	0.724578i	$0.257965\pi$
$984$		0			0
$985$	−73734.6	−	23957.8i	−0.0759974	−	0.0246931i
$986$	−2.46324e6	−	3.39036e6i	−2.53369	−	3.48732i
$987$		0			0
$988$	46364.7	+	142696.i	0.0474978	+	0.146183i
$989$			513340.i			0.524822i
$990$		0			0
$991$	−1.22307e6			−1.24538			−0.622692	−	0.782467i	$-0.713961\pi$
$991$	−1.22307e6			−1.24538			−0.622692	+	0.782467i	$0.713961\pi$
$992$	−399936.	+	129947.i	−0.406412	+	0.132051i
$993$		0			0
$994$	−462982.	+	336376.i	−0.468588	+	0.340449i
$995$	−15747.0	+	48464.3i	−0.0159057	+	0.0489526i
$996$		0			0
$997$	−177675.	−	244549.i	−0.178746	−	0.246023i	0.710237	−	0.703962i	$-0.248588\pi$
$997$	−177675.	−	244549.i	−0.178746	−	0.246023i	−0.888983	+	0.457939i	$0.848588\pi$
$998$	101034.	−	139062.i	0.101440	−	0.139620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.5.k.c.28.8		32
3.2	odd	2		33.5.g.a.28.1	yes	32
11.2	odd	10	inner	99.5.k.c.46.8		32
33.2	even	10		33.5.g.a.13.1	✓	32
33.8	even	10		363.5.c.e.241.1		32
33.14	odd	10		363.5.c.e.241.32		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.g.a.13.1	✓	32	33.2	even	10
33.5.g.a.28.1	yes	32	3.2	odd	2
99.5.k.c.28.8		32	1.1	even	1	trivial
99.5.k.c.46.8		32	11.2	odd	10	inner
363.5.c.e.241.1		32	33.8	even	10
363.5.c.e.241.32		32	33.14	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(7.29601 - 2.37062i) q^{2} +(34.6676 - 25.1875i) q^{4} +(-2.18122 + 6.71310i) q^{5} +(28.6722 + 39.4639i) q^{7} +(121.078 - 166.650i) q^{8} +O(q^{10})\)	\(q+(7.29601 - 2.37062i) q^{2} +(34.6676 - 25.1875i) q^{4} +(-2.18122 + 6.71310i) q^{5} +(28.6722 + 39.4639i) q^{7} +(121.078 - 166.650i) q^{8} +54.1497i q^{10} +(31.5805 - 116.806i) q^{11} +(5.63636 - 1.83136i) q^{13} +(302.746 + 219.958i) q^{14} +(276.455 - 850.842i) q^{16} +(-404.280 - 131.359i) q^{17} +(-347.268 + 477.974i) q^{19} +(93.4686 + 287.667i) q^{20} +(-46.4909 - 927.083i) q^{22} -361.694 q^{23} +(465.328 + 338.080i) q^{25} +(36.7814 - 26.7233i) q^{26} +(1987.99 + 645.938i) q^{28} +(755.357 + 1039.66i) q^{29} +(-36.4276 - 112.113i) q^{31} -3567.27i q^{32} -3261.03 q^{34} +(-327.466 + 106.400i) q^{35} +(-141.071 + 102.494i) q^{37} +(-1400.58 + 4310.54i) q^{38} +(854.640 + 1176.31i) q^{40} +(-1117.70 + 1538.38i) q^{41} -1419.27i q^{43} +(-1847.23 - 4844.82i) q^{44} +(-2638.92 + 857.437i) q^{46} +(177.347 + 128.850i) q^{47} +(6.64598 - 20.4542i) q^{49} +(4196.49 + 1363.52i) q^{50} +(149.272 - 205.455i) q^{52} +(-349.957 - 1077.06i) q^{53} +(715.248 + 466.783i) q^{55} +10048.2 q^{56} +(7975.72 + 5794.70i) q^{58} +(193.695 - 140.727i) q^{59} +(-557.413 - 181.114i) q^{61} +(-531.552 - 731.619i) q^{62} +(-4033.33 - 12413.3i) q^{64} +41.8320i q^{65} +1242.99 q^{67} +(-17324.0 + 5628.92i) q^{68} +(-2136.96 + 1552.59i) q^{70} +(-472.572 + 1454.43i) q^{71} +(-4924.76 - 6778.35i) q^{73} +(-786.279 + 1082.22i) q^{74} +25317.0i q^{76} +(5515.11 - 2102.80i) q^{77} +(-659.926 + 214.423i) q^{79} +(5108.78 + 3711.75i) q^{80} +(-4507.83 + 13873.7i) q^{82} +(-5682.21 - 1846.26i) q^{83} +(1763.65 - 2427.45i) q^{85} +(-3364.53 - 10355.0i) q^{86} +(-15642.0 - 19405.6i) q^{88} +813.300 q^{89} +(233.879 + 169.923i) q^{91} +(-12539.1 + 9110.16i) q^{92} +(1599.38 + 519.670i) q^{94} +(-2451.22 - 3373.82i) q^{95} +(-206.021 - 634.066i) q^{97} -164.989i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more