LMFDB - Embedded newform 65.5.g.a.34.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (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:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.17
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96266 - 1.96266i) q^{2} -11.7087i q^{3} +8.29597i q^{4} +(14.8937 - 20.0793i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(-49.2380 - 49.2380i) q^{7} +(47.6846 + 47.6846i) q^{8} -56.0939 q^{9} +O(q^{10})$	\(q+(1.96266 - 1.96266i) q^{2} -11.7087i q^{3} +8.29597i q^{4} +(14.8937 - 20.0793i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(-49.2380 - 49.2380i) q^{7} +(47.6846 + 47.6846i) q^{8} -56.0939 q^{9} +(-10.1776 - 68.6399i) q^{10} +(36.9838 - 36.9838i) q^{11} +97.1351 q^{12} +(-167.514 + 22.3654i) q^{13} -193.275 q^{14} +(-235.103 - 174.386i) q^{15} +54.4414 q^{16} -2.83570 q^{17} +(-110.093 + 110.093i) q^{18} +(-74.4440 - 74.4440i) q^{19} +(166.577 + 123.558i) q^{20} +(-576.514 + 576.514i) q^{21} -145.173i q^{22} +858.183 q^{23} +(558.325 - 558.325i) q^{24} +(-181.357 - 598.109i) q^{25} +(-284.876 + 372.667i) q^{26} -291.618i q^{27} +(408.477 - 408.477i) q^{28} +1280.13 q^{29} +(-803.685 + 119.166i) q^{30} +(975.637 + 975.637i) q^{31} +(-656.104 + 656.104i) q^{32} +(-433.033 - 433.033i) q^{33} +(-5.56551 + 5.56551i) q^{34} +(-1722.00 + 255.330i) q^{35} -465.353i q^{36} +(-573.577 - 573.577i) q^{37} -292.216 q^{38} +(261.869 + 1961.37i) q^{39} +(1667.67 - 247.274i) q^{40} +(276.665 + 276.665i) q^{41} +2263.00i q^{42} +3340.52 q^{43} +(306.817 + 306.817i) q^{44} +(-835.445 + 1126.33i) q^{45} +(1684.32 - 1684.32i) q^{46} +(-345.914 - 345.914i) q^{47} -637.439i q^{48} +2447.77i q^{49} +(-1529.82 - 817.942i) q^{50} +33.2024i q^{51} +(-185.542 - 1389.69i) q^{52} +1606.43i q^{53} +(-572.346 - 572.346i) q^{54} +(-191.784 - 1293.43i) q^{55} -4695.79i q^{56} +(-871.644 + 871.644i) q^{57} +(2512.45 - 2512.45i) q^{58} +(-641.576 + 641.576i) q^{59} +(1446.70 - 1950.40i) q^{60} -5200.73 q^{61} +3829.68 q^{62} +(2761.95 + 2761.95i) q^{63} +3446.47i q^{64} +(-2045.81 + 3696.66i) q^{65} -1699.79 q^{66} +(-2958.39 + 2958.39i) q^{67} -23.5249i q^{68} -10048.2i q^{69} +(-2878.57 + 3880.82i) q^{70} +(-1343.74 - 1343.74i) q^{71} +(-2674.82 - 2674.82i) q^{72} +(-1183.61 - 1183.61i) q^{73} -2251.47 q^{74} +(-7003.09 + 2123.45i) q^{75} +(617.585 - 617.585i) q^{76} -3642.02 q^{77} +(4363.45 + 3335.53i) q^{78} +2812.08 q^{79} +(810.833 - 1093.15i) q^{80} -7958.08 q^{81} +1086.00 q^{82} +(7138.41 - 7138.41i) q^{83} +(-4782.74 - 4782.74i) q^{84} +(-42.2340 + 56.9389i) q^{85} +(6556.29 - 6556.29i) q^{86} -14988.7i q^{87} +3527.12 q^{88} +(-1031.96 + 1031.96i) q^{89} +(570.901 + 3850.28i) q^{90} +(9349.26 + 7146.81i) q^{91} +7119.46i q^{92} +(11423.4 - 11423.4i) q^{93} -1357.82 q^{94} +(-2603.53 + 386.039i) q^{95} +(7682.13 + 7682.13i) q^{96} +(-8066.83 + 8066.83i) q^{97} +(4804.12 + 4804.12i) q^{98} +(-2074.57 + 2074.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.96266	−	1.96266i	0.490664	−	0.490664i	−0.417852	−	0.908515i	$-0.637217\pi$
$2$	1.96266	−	1.96266i	0.490664	−	0.490664i	0.908515	+	0.417852i	$0.137217\pi$
$3$		−	11.7087i		−	1.30097i	−0.759520	−	0.650484i	$-0.774566\pi$
$3$		−	11.7087i		−	1.30097i	0.759520	−	0.650484i	$-0.225434\pi$
$4$			8.29597i			0.518498i
$5$	14.8937	−	20.0793i	0.595747	−	0.803172i
$5$	14.8937	−	20.0793i	0.595747	−	0.803172i
$6$	−22.9802	−	22.9802i	−0.638338	−	0.638338i
$7$	−49.2380	−	49.2380i	−1.00486	−	1.00486i	−0.999988	−	0.00486952i	$-0.998450\pi$
$7$	−49.2380	−	49.2380i	−1.00486	−	1.00486i	−0.00486952	−	0.999988i	$-0.501550\pi$
$8$	47.6846	+	47.6846i	0.745072	+	0.745072i
$9$	−56.0939			−0.692517
$10$	−10.1776	−	68.6399i	−0.101776	−	0.686399i
$11$	36.9838	−	36.9838i	0.305652	−	0.305652i	−0.537569	−	0.843220i	$-0.680657\pi$
$11$	36.9838	−	36.9838i	0.305652	−	0.305652i	0.843220	+	0.537569i	$0.180657\pi$
$12$	97.1351			0.674549
$13$	−167.514	+	22.3654i	−0.991204	+	0.132339i
$13$	−167.514	+	22.3654i	−0.991204	+	0.132339i
$14$	−193.275			−0.986095
$15$	−235.103	−	174.386i	−1.04490	−	0.775048i
$16$	54.4414			0.212662
$17$	−2.83570			−0.00981212			−0.00490606	−	0.999988i	$-0.501562\pi$
$17$	−2.83570			−0.00981212			−0.00490606	+	0.999988i	$0.501562\pi$
$18$	−110.093	+	110.093i	−0.339793	+	0.339793i
$19$	−74.4440	−	74.4440i	−0.206216	−	0.206216i	0.596441	−	0.802657i	$-0.296581\pi$
$19$	−74.4440	−	74.4440i	−0.206216	−	0.206216i	−0.802657	+	0.596441i	$0.796581\pi$
$20$	166.577	+	123.558i	0.416443	+	0.308894i
$21$	−576.514	+	576.514i	−1.30729	+	1.30729i
$22$		−	145.173i		−	0.299944i
$23$	858.183			1.62227			0.811137	−	0.584856i	$-0.198849\pi$
$23$	858.183			1.62227			0.811137	+	0.584856i	$0.198849\pi$
$24$	558.325	−	558.325i	0.969315	−	0.969315i
$25$	−181.357	−	598.109i	−0.290171	−	0.956975i
$26$	−284.876	+	372.667i	−0.421414	+	0.551282i
$27$		−	291.618i		−	0.400025i
$28$	408.477	−	408.477i	0.521017	−	0.521017i
$29$	1280.13			1.52215			0.761076	−	0.648663i	$-0.224671\pi$
$29$	1280.13			1.52215			0.761076	+	0.648663i	$0.224671\pi$
$30$	−803.685	+	119.166i	−0.892983	+	0.132407i
$31$	975.637	+	975.637i	1.01523	+	1.01523i	0.999882	+	0.0153483i	$0.00488572\pi$
$31$	975.637	+	975.637i	1.01523	+	1.01523i	0.0153483	+	0.999882i	$0.495114\pi$
$32$	−656.104	+	656.104i	−0.640727	+	0.640727i
$33$	−433.033	−	433.033i	−0.397643	−	0.397643i
$34$	−5.56551	+	5.56551i	−0.00481445	+	0.00481445i
$35$	−1722.00	+	255.330i	−1.40571	+	0.208432i
$36$		−	465.353i		−	0.359069i
$37$	−573.577	−	573.577i	−0.418975	−	0.418975i	0.465875	−	0.884850i	$-0.345740\pi$
$37$	−573.577	−	573.577i	−0.418975	−	0.418975i	−0.884850	+	0.465875i	$0.845740\pi$
$38$	−292.216			−0.202366
$39$	261.869	+	1961.37i	0.172169	+	1.28953i
$40$	1667.67	−	247.274i	1.04230	−	0.154546i
$41$	276.665	+	276.665i	0.164584	+	0.164584i	0.784594	−	0.620010i	$-0.212872\pi$
$41$	276.665	+	276.665i	0.164584	+	0.164584i	−0.620010	+	0.784594i	$0.712872\pi$
$42$			2263.00i			1.28288i
$43$	3340.52			1.80666			0.903332	−	0.428942i	$-0.141113\pi$
$43$	3340.52			1.80666			0.903332	+	0.428942i	$0.141113\pi$
$44$	306.817	+	306.817i	0.158480	+	0.158480i
$45$	−835.445	+	1126.33i	−0.412565	+	0.556211i
$46$	1684.32	−	1684.32i	0.795991	−	0.795991i
$47$	−345.914	−	345.914i	−0.156593	−	0.156593i	0.624462	−	0.781055i	$-0.285318\pi$
$47$	−345.914	−	345.914i	−0.156593	−	0.156593i	−0.781055	+	0.624462i	$0.785318\pi$
$48$		−	637.439i		−	0.276666i
$49$			2447.77i			1.01948i
$50$	−1529.82	−	817.942i	−0.611929	−	0.327177i
$51$			33.2024i			0.0127652i
$52$	−185.542	−	1389.69i	−0.0686177	−	0.513938i
$53$			1606.43i			0.571888i	0.958246	+	0.285944i	$0.0923071\pi$
$53$			1606.43i			0.571888i	−0.958246	+	0.285944i	$0.907693\pi$
$54$	−572.346	−	572.346i	−0.196278	−	0.196278i
$55$	−191.784	−	1293.43i	−0.0633997	−	0.427582i
$56$		−	4695.79i		−	1.49738i
$57$	−871.644	+	871.644i	−0.268281	+	0.268281i
$58$	2512.45	−	2512.45i	0.746865	−	0.746865i
$59$	−641.576	+	641.576i	−0.184308	+	0.184308i	−0.793230	−	0.608922i	$-0.791602\pi$
$59$	−641.576	+	641.576i	−0.184308	+	0.184308i	0.608922	+	0.793230i	$0.291602\pi$
$60$	1446.70	−	1950.40i	0.401861	−	0.541779i
$61$	−5200.73			−1.39767			−0.698836	−	0.715282i	$-0.746298\pi$
$61$	−5200.73			−1.39767			−0.698836	+	0.715282i	$0.746298\pi$
$62$	3829.68			0.996274
$63$	2761.95	+	2761.95i	0.695881	+	0.695881i
$64$			3446.47i			0.841424i
$65$	−2045.81	+	3696.66i	−0.484216	+	0.874948i
$66$	−1699.79			−0.390218
$67$	−2958.39	+	2958.39i	−0.659031	+	0.659031i	−0.955151	−	0.296119i	$-0.904307\pi$
$67$	−2958.39	+	2958.39i	−0.659031	+	0.659031i	0.296119	+	0.955151i	$0.404307\pi$
$68$		−	23.5249i		−	0.00508756i
$69$		−	10048.2i		−	2.11053i
$70$	−2878.57	+	3880.82i	−0.587463	+	0.792004i
$71$	−1343.74	−	1343.74i	−0.266562	−	0.266562i	0.561151	−	0.827713i	$-0.310359\pi$
$71$	−1343.74	−	1343.74i	−0.266562	−	0.266562i	−0.827713	+	0.561151i	$0.810359\pi$
$72$	−2674.82	−	2674.82i	−0.515975	−	0.515975i
$73$	−1183.61	−	1183.61i	−0.222107	−	0.222107i	0.587278	−	0.809385i	$-0.300200\pi$
$73$	−1183.61	−	1183.61i	−0.222107	−	0.222107i	−0.809385	+	0.587278i	$0.800200\pi$
$74$	−2251.47			−0.411152
$75$	−7003.09	+	2123.45i	−1.24499	+	0.377503i
$76$	617.585	−	617.585i	0.106923	−	0.106923i
$77$	−3642.02			−0.614273
$78$	4363.45	+	3335.53i	0.717201	+	0.548246i
$79$	2812.08			0.450581			0.225291	−	0.974292i	$-0.427667\pi$
$79$	2812.08			0.450581			0.225291	+	0.974292i	$0.427667\pi$
$80$	810.833	−	1093.15i	0.126693	−	0.170804i
$81$	−7958.08			−1.21294
$82$	1086.00			0.161511
$83$	7138.41	−	7138.41i	1.03620	−	1.03620i	0.0368852	−	0.999320i	$-0.488256\pi$
$83$	7138.41	−	7138.41i	1.03620	−	1.03620i	0.999320	−	0.0368852i	$-0.0117436\pi$
$84$	−4782.74	−	4782.74i	−0.677826	−	0.677826i
$85$	−42.2340	+	56.9389i	−0.00584554	+	0.00788082i
$86$	6556.29	−	6556.29i	0.886465	−	0.886465i
$87$		−	14988.7i		−	1.98027i
$88$	3527.12			0.455465
$89$	−1031.96	+	1031.96i	−0.130282	+	0.130282i	−0.769241	−	0.638959i	$-0.779365\pi$
$89$	−1031.96	+	1031.96i	−0.130282	+	0.130282i	0.638959	+	0.769241i	$0.279365\pi$
$90$	570.901	+	3850.28i	0.0704815	+	0.475343i
$91$	9349.26	+	7146.81i	1.12900	+	0.863037i
$92$			7119.46i			0.841146i
$93$	11423.4	−	11423.4i	1.32078	−	1.32078i
$94$	−1357.82			−0.153669
$95$	−2603.53	+	386.039i	−0.288480	+	0.0427744i
$96$	7682.13	+	7682.13i	0.833565	+	0.833565i
$97$	−8066.83	+	8066.83i	−0.857353	+	0.857353i	−0.991026	−	0.133673i	$-0.957323\pi$
$97$	−8066.83	+	8066.83i	−0.857353	+	0.857353i	0.133673	+	0.991026i	$0.457323\pi$
$98$	4804.12	+	4804.12i	0.500221	+	0.500221i
$99$	−2074.57	+	2074.57i	−0.211669	+	0.211669i
$100$	4961.90	−	1504.53i	0.496190	−	0.150453i
$101$		−	3934.27i		−	0.385675i	−0.981231	−	0.192838i	$-0.938231\pi$
$101$		−	3934.27i		−	0.385675i	0.981231	−	0.192838i	$-0.0617691\pi$
$102$	65.1649	+	65.1649i	0.00626345	+	0.00626345i
$103$	−15584.3			−1.46897			−0.734485	−	0.678625i	$-0.762576\pi$
$103$	−15584.3			−1.46897			−0.734485	+	0.678625i	$0.762576\pi$
$104$	−9054.30	−	6921.34i	−0.837121	−	0.639916i
$105$	2989.58	+	20162.4i	0.271164	+	1.82879i
$106$	3152.87	+	3152.87i	0.280605	+	0.280605i
$107$			4354.40i			0.380330i	0.981752	+	0.190165i	$0.0609024\pi$
$107$			4354.40i			0.380330i	−0.981752	+	0.190165i	$0.939098\pi$
$108$	2419.26			0.207412
$109$	14256.5	+	14256.5i	1.19994	+	1.19994i	0.974185	+	0.225752i	$0.0724840\pi$
$109$	14256.5	+	14256.5i	1.19994	+	1.19994i	0.225752	+	0.974185i	$0.427516\pi$
$110$	−2914.97	−	2162.16i	−0.240907	−	0.178691i
$111$	−6715.85	+	6715.85i	−0.545073	+	0.545073i
$112$	−2680.59	−	2680.59i	−0.213695	−	0.213695i
$113$			18625.6i			1.45866i	0.684162	+	0.729330i	$0.260168\pi$
$113$			18625.6i			1.45866i	−0.684162	+	0.729330i	$0.739832\pi$
$114$			3421.47i			0.263271i
$115$	12781.5	−	17231.7i	0.966465	−	1.30297i
$116$			10619.9i			0.789233i
$117$	9396.49	−	1254.56i	0.686426	−	0.0916473i
$118$			2518.38i			0.180866i
$119$	139.624	+	139.624i	0.00985978	+	0.00985978i
$120$	−2895.26	−	19526.3i	−0.201060	−	1.35599i
$121$			11905.4i			0.813154i
$122$	−10207.2	+	10207.2i	−0.685787	+	0.685787i
$123$	3239.39	−	3239.39i	0.214118	−	0.214118i
$124$	−8093.85	+	8093.85i	−0.526395	+	0.526395i
$125$	−14710.7	−	5266.54i	−0.941484	−	0.337058i
$126$	10841.5			0.682888
$127$	20800.0			1.28961			0.644803	−	0.764349i	$-0.276940\pi$
$127$	20800.0			1.28961			0.644803	+	0.764349i	$0.276940\pi$
$128$	−3733.42	−	3733.42i	−0.227870	−	0.227870i
$129$		−	39113.2i		−	2.35041i
$130$	3240.04	+	11270.5i	0.191718	+	0.666893i
$131$	7041.46			0.410317			0.205159	−	0.978729i	$-0.434229\pi$
$131$	7041.46			0.410317			0.205159	+	0.978729i	$0.434229\pi$
$132$	3592.43	−	3592.43i	0.206177	−	0.206177i
$133$			7330.95i			0.414436i
$134$			11612.6i			0.646726i
$135$	−5855.49	−	4343.27i	−0.321289	−	0.238314i
$136$	−135.219	−	135.219i	−0.00731073	−	0.00731073i
$137$	−15382.9	−	15382.9i	−0.819591	−	0.819591i	0.166457	−	0.986049i	$-0.446767\pi$
$137$	−15382.9	−	15382.9i	−0.819591	−	0.819591i	−0.986049	+	0.166457i	$0.946767\pi$
$138$	−19721.2	−	19721.2i	−1.03556	−	1.03556i
$139$	14481.8			0.749539			0.374769	−	0.927118i	$-0.377722\pi$
$139$	14481.8			0.749539			0.374769	+	0.927118i	$0.377722\pi$
$140$	−2118.21	−	14285.7i	−0.108072	−	0.728860i
$141$	−4050.21	+	4050.21i	−0.203722	+	0.203722i
$142$	−5274.60			−0.261585
$143$	−5368.14	+	7022.45i	−0.262513	+	0.343413i
$144$	−3053.83			−0.147272
$145$	19065.8	−	25704.1i	0.906818	−	1.22255i
$146$	−4646.03			−0.217960
$147$	28660.2			1.32631
$148$	4758.38	−	4758.38i	0.217238	−	0.217238i
$149$	−12147.7	−	12147.7i	−0.547170	−	0.547170i	0.378451	−	0.925621i	$-0.376457\pi$
$149$	−12147.7	−	12147.7i	−0.547170	−	0.547170i	−0.925621	+	0.378451i	$0.876457\pi$
$150$	−9577.05	+	17912.3i	−0.425646	+	0.796100i
$151$	−6761.45	+	6761.45i	−0.296542	+	0.296542i	−0.839658	−	0.543116i	$-0.817244\pi$
$151$	−6761.45	+	6761.45i	−0.296542	+	0.296542i	0.543116	+	0.839658i	$0.317244\pi$
$152$		−	7099.67i		−	0.307292i
$153$	159.066			0.00679506
$154$	−7148.03	+	7148.03i	−0.301401	+	0.301401i
$155$	34120.9	−	5059.28i	1.42023	−	0.210584i
$156$	−16271.4	+	2172.46i	−0.668616	+	0.0892694i
$157$			12263.3i			0.497519i	0.968565	+	0.248759i	$0.0800228\pi$
$157$			12263.3i			0.497519i	−0.968565	+	0.248759i	$0.919977\pi$
$158$	5519.14	−	5519.14i	0.221084	−	0.221084i
$159$	18809.3			0.744008
$160$	3402.31	+	22945.9i	0.132903	+	0.896325i
$161$	−42255.2	−	42255.2i	−1.63015	−	1.63015i
$162$	−15619.0	+	15619.0i	−0.595144	+	0.595144i
$163$	−2052.00	−	2052.00i	−0.0772329	−	0.0772329i	0.667435	−	0.744668i	$-0.267392\pi$
$163$	−2052.00	−	2052.00i	−0.0772329	−	0.0772329i	−0.744668	+	0.667435i	$0.767392\pi$
$164$	−2295.21	+	2295.21i	−0.0853364	+	0.0853364i
$165$	−15144.5	+	2245.54i	−0.556270	+	0.0824810i
$166$		−	28020.5i		−	1.01686i
$167$	−21065.0	−	21065.0i	−0.755316	−	0.755316i	0.220150	−	0.975466i	$-0.429345\pi$
$167$	−21065.0	−	21065.0i	−0.755316	−	0.755316i	−0.975466	+	0.220150i	$0.929345\pi$
$168$	−54981.7			−1.94805
$169$	27560.6	−	7493.00i	0.964973	−	0.262351i
$170$	28.8606	+	194.642i	0.000998637	+	0.00673503i
$171$	4175.86	+	4175.86i	0.142808	+	0.142808i
$172$			27712.9i			0.936752i
$173$	6229.06			0.208128			0.104064	−	0.994571i	$-0.466815\pi$
$173$	6229.06			0.208128			0.104064	+	0.994571i	$0.466815\pi$
$174$	−29417.6	−	29417.6i	−0.971647	−	0.971647i
$175$	−20520.1	+	38379.4i	−0.670043	+	1.25320i
$176$	2013.45	−	2013.45i	0.0650004	−	0.0650004i
$177$	7512.03	+	7512.03i	0.239779	+	0.239779i
$178$			4050.78i			0.127849i
$179$			38292.2i			1.19510i	0.801832	+	0.597549i	$0.203859\pi$
$179$			38292.2i			1.19510i	−0.801832	+	0.597549i	$0.796141\pi$
$180$	−9343.97	−	6930.82i	−0.288394	−	0.213914i
$181$		−	38251.7i		−	1.16760i	−0.811898	−	0.583800i	$-0.801565\pi$
$181$		−	38251.7i		−	1.16760i	0.811898	−	0.583800i	$-0.198435\pi$
$182$	32376.1	−	4322.65i	0.977421	−	0.130499i
$183$			60893.9i			1.81833i
$184$	40922.1	+	40922.1i	1.20871	+	1.20871i
$185$	−20059.7	+	2974.35i	−0.586113	+	0.0869059i
$186$		−	44840.6i		−	1.29612i
$187$	−104.875	+	104.875i	−0.00299909	+	0.00299909i
$188$	2869.69	−	2869.69i	0.0811931	−	0.0811931i
$189$	−14358.7	+	14358.7i	−0.401968	+	0.401968i
$190$	−4352.17	+	5867.49i	−0.120559	+	0.162534i
$191$	58381.3			1.60032			0.800160	−	0.599786i	$-0.204748\pi$
$191$	58381.3			1.60032			0.800160	+	0.599786i	$0.204748\pi$
$192$	40353.8			1.09467
$193$	−18900.7	−	18900.7i	−0.507414	−	0.507414i	0.406318	−	0.913732i	$-0.366813\pi$
$193$	−18900.7	−	18900.7i	−0.507414	−	0.507414i	−0.913732	+	0.406318i	$0.866813\pi$
$194$			31664.8i			0.841344i
$195$	43283.1	+	23953.8i	1.13828	+	0.629949i
$196$	−20306.6			−0.528597
$197$	41161.7	−	41161.7i	1.06062	−	1.06062i	0.0625830	−	0.998040i	$-0.480066\pi$
$197$	41161.7	−	41161.7i	1.06062	−	1.06062i	0.998040	−	0.0625830i	$-0.0199338\pi$
$198$			8143.32i			0.207717i
$199$			7371.87i			0.186154i	0.995659	+	0.0930768i	$0.0296702\pi$
$199$			7371.87i			0.186154i	−0.995659	+	0.0930768i	$0.970330\pi$
$200$	19872.7	−	37168.5i	0.496817	−	0.929213i
$201$	34639.0	+	34639.0i	0.857379	+	0.857379i
$202$	−7721.62	−	7721.62i	−0.189237	−	0.189237i
$203$	−63031.1	−	63031.1i	−1.52955	−	1.52955i
$204$	−275.446			−0.00661876
$205$	9675.81	−	1434.68i	0.230239	−	0.0341388i
$206$	−30586.6	+	30586.6i	−0.720770	+	0.720770i
$207$	−48138.8			−1.12345
$208$	−9119.67	+	1217.60i	−0.210791	+	0.0281435i
$209$	−5506.45			−0.126061
$210$	45439.4	+	33704.3i	1.03037	+	0.764271i
$211$	−20922.5			−0.469946			−0.234973	−	0.972002i	$-0.575500\pi$
$211$	−20922.5			−0.469946			−0.234973	+	0.972002i	$0.575500\pi$
$212$	−13326.9			−0.296523
$213$	−15733.5	+	15733.5i	−0.346789	+	0.346789i
$214$	8546.19	+	8546.19i	0.186614	+	0.186614i
$215$	49752.7	−	67075.4i	1.07632	−	1.45106i
$216$	13905.7	−	13905.7i	0.298047	−	0.298047i
$217$		−	96076.8i		−	2.04032i
$218$	55961.0			1.17753
$219$	−13858.5	+	13858.5i	−0.288954	+	0.288954i
$220$	10730.3	−	1591.04i	0.221700	−	0.0328726i
$221$	475.018	−	63.4215i	0.00972581	−	0.00129853i
$222$			26361.8i			0.534896i
$223$	−34337.0	+	34337.0i	−0.690483	+	0.690483i	−0.962338	−	0.271855i	$-0.912363\pi$
$223$	−34337.0	+	34337.0i	−0.690483	+	0.690483i	0.271855	+	0.962338i	$0.412363\pi$
$224$	64610.5			1.28768
$225$	10173.0	+	33550.3i	0.200948	+	0.662722i
$226$	36555.7	+	36555.7i	0.715712	+	0.715712i
$227$	−37503.4	+	37503.4i	−0.727812	+	0.727812i	−0.970184	−	0.242371i	$-0.922075\pi$
$227$	−37503.4	+	37503.4i	−0.727812	+	0.727812i	0.242371	+	0.970184i	$0.422075\pi$
$228$	−7231.13	−	7231.13i	−0.139103	−	0.139103i
$229$	5100.19	−	5100.19i	0.0972557	−	0.0972557i	−0.656805	−	0.754061i	$-0.728092\pi$
$229$	5100.19	−	5100.19i	0.0972557	−	0.0972557i	0.754061	+	0.656805i	$0.228092\pi$
$230$	−8734.23	−	58905.6i	−0.165108	−	1.11353i
$231$			42643.4i			0.799149i
$232$	61042.5	+	61042.5i	1.13411	+	1.13411i
$233$	−61062.0			−1.12476			−0.562379	−	0.826880i	$-0.690114\pi$
$233$	−61062.0			−1.12476			−0.562379	+	0.826880i	$0.690114\pi$
$234$	15979.8	−	20904.3i	0.291837	−	0.381773i
$235$	−12097.6	+	1793.78i	−0.219061	+	0.0324813i
$236$	−5322.49	−	5322.49i	−0.0955633	−	0.0955633i
$237$		−	32925.8i		−	0.586192i
$238$	548.069			0.00967568
$239$	−14053.0	−	14053.0i	−0.246021	−	0.246021i	0.573315	−	0.819335i	$-0.305657\pi$
$239$	−14053.0	−	14053.0i	−0.246021	−	0.246021i	−0.819335	+	0.573315i	$0.805657\pi$
$240$	−12799.3	−	9493.81i	−0.222210	−	0.164823i
$241$	18222.3	−	18222.3i	0.313739	−	0.313739i	−0.532617	−	0.846356i	$-0.678792\pi$
$241$	18222.3	−	18222.3i	0.313739	−	0.313739i	0.846356	+	0.532617i	$0.178792\pi$
$242$	23366.2	+	23366.2i	0.398985	+	0.398985i
$243$			69557.8i			1.17797i
$244$		−	43145.1i		−	0.724690i
$245$	49149.4	+	36456.2i	0.818816	+	0.607351i
$246$		−	12715.6i		−	0.210120i
$247$	14135.4	+	10805.4i	0.231693	+	0.177112i
$248$			93045.7i			1.51284i
$249$	−83581.6	−	83581.6i	−1.34807	−	1.34807i
$250$	−39208.4	+	18535.6i	−0.627334	+	0.296570i
$251$			117416.i			1.86372i	0.362821	+	0.931859i	$0.381814\pi$
$251$			117416.i			1.86372i	−0.362821	+	0.931859i	$0.618186\pi$
$252$	−22913.1	+	22913.1i	−0.360813	+	0.360813i
$253$	31738.9	−	31738.9i	0.495851	−	0.495851i
$254$	40823.3	−	40823.3i	0.632763	−	0.632763i
$255$	666.681	+	494.506i	0.0102527	+	0.00760486i
$256$	−69798.4			−1.06504
$257$	−66273.8			−1.00340			−0.501701	−	0.865041i	$-0.667292\pi$
$257$	−66273.8			−1.00340			−0.501701	+	0.865041i	$0.667292\pi$
$258$	−76765.8	−	76765.8i	−1.15326	−	1.15326i
$259$			56483.6i			0.842021i
$260$	−30667.4	−	16972.0i	−0.453659	−	0.251065i
$261$	−71807.5			−1.05412
$262$	13819.9	−	13819.9i	0.201328	−	0.201328i
$263$			20370.0i			0.294496i	0.989100	+	0.147248i	$0.0470415\pi$
$263$			20370.0i			0.294496i	−0.989100	+	0.147248i	$0.952958\pi$
$264$		−	41298.0i		−	0.592545i
$265$	32256.1	+	23925.7i	0.459324	+	0.340701i
$266$	14388.1	+	14388.1i	0.203349	+	0.203349i
$267$	12083.0	+	12083.0i	0.169493	+	0.169493i
$268$	−24542.7	−	24542.7i	−0.341707	−	0.341707i
$269$	−24183.0			−0.334199			−0.167099	−	0.985940i	$-0.553440\pi$
$269$	−24183.0			−0.334199			−0.167099	+	0.985940i	$0.553440\pi$
$270$	−20016.6	+	2967.97i	−0.274577	+	0.0407129i
$271$	45864.2	−	45864.2i	0.624504	−	0.624504i	−0.322176	−	0.946680i	$-0.604414\pi$
$271$	45864.2	−	45864.2i	0.624504	−	0.624504i	0.946680	+	0.322176i	$0.104414\pi$
$272$	−154.380			−0.00208666
$273$	83679.9	−	109468.i	1.12278	−	1.46879i
$274$	−60382.7			−0.804287
$275$	−28827.6	−	15413.1i	−0.381192	−	0.203810i
$276$	83359.7			1.09430
$277$	91774.5			1.19609			0.598043	−	0.801464i	$-0.295945\pi$
$277$	91774.5			1.19609			0.598043	+	0.801464i	$0.295945\pi$
$278$	28422.9	−	28422.9i	0.367772	−	0.367772i
$279$	−54727.3	−	54727.3i	−0.703065	−	0.703065i
$280$	−94288.2	−	69937.6i	−1.20266	−	0.892062i
$281$	4584.41	−	4584.41i	0.0580591	−	0.0580591i	−0.677481	−	0.735540i	$-0.736928\pi$
$281$	4584.41	−	4584.41i	0.0580591	−	0.0580591i	0.735540	+	0.677481i	$0.236928\pi$
$282$			15898.3i			0.199918i
$283$	104879.			1.30953			0.654766	−	0.755832i	$-0.272767\pi$
$283$	104879.			1.30953			0.654766	+	0.755832i	$0.272767\pi$
$284$	11147.6	−	11147.6i	0.138212	−	0.138212i
$285$	4520.01	+	30484.0i	0.0556481	+	0.375303i
$286$	3246.85	+	24318.4i	0.0396944	+	0.297306i
$287$		−	27244.9i		−	0.330767i
$288$	36803.4	−	36803.4i	0.443714	−	0.443714i
$289$	−83513.0			−0.999904
$290$	−13028.6	−	87868.0i	−0.154918	−	1.04480i
$291$	94452.2	+	94452.2i	1.11539	+	1.11539i
$292$	9819.19	−	9819.19i	0.115162	−	0.115162i
$293$	110200.	+	110200.i	1.28365	+	1.28365i	0.938574	+	0.345078i	$0.112148\pi$
$293$	110200.	+	110200.i	1.28365	+	1.28365i	0.345078	+	0.938574i	$0.387852\pi$
$294$	56250.1	−	56250.1i	0.650771	−	0.650771i
$295$	3326.97	+	22437.8i	0.0382300	+	0.257832i
$296$		−	54701.6i		−	0.624334i
$297$	−10785.2	−	10785.2i	−0.122268	−	0.122268i
$298$	−47683.6			−0.536954
$299$	−143757.	+	19193.6i	−1.60801	+	0.214691i
$300$	−17616.1	−	58097.4i	−0.195734	−	0.645527i
$301$	−164481.	−	164481.i	−1.81544	−	1.81544i
$302$			26540.8i			0.291005i
$303$	−46065.3			−0.501751
$304$	−4052.84	−	4052.84i	−0.0438543	−	0.0438543i
$305$	−77458.1	+	104427.i	−0.832659	+	1.12257i
$306$	312.191	−	312.191i	0.00333409	−	0.00333409i
$307$	−86941.0	−	86941.0i	−0.922461	−	0.922461i	0.0747419	−	0.997203i	$-0.476187\pi$
$307$	−86941.0	−	86941.0i	−0.922461	−	0.922461i	−0.997203	+	0.0747419i	$0.976187\pi$
$308$		−	30214.1i		−	0.318499i
$309$			182472.i			1.91108i
$310$	57038.0	−	76897.2i	0.593527	−	0.800179i
$311$			97359.6i			1.00660i	0.864111	+	0.503301i	$0.167881\pi$
$311$			97359.6i			1.00660i	−0.864111	+	0.503301i	$0.832119\pi$
$312$	−81039.9	+	106014.i	−0.832511	+	1.08907i
$313$		−	43692.2i		−	0.445979i	−0.974821	−	0.222990i	$-0.928418\pi$
$313$		−	43692.2i		−	0.445979i	0.974821	−	0.222990i	$-0.0715816\pi$
$314$	24068.7	+	24068.7i	0.244114	+	0.244114i
$315$	96593.7	−	14322.4i	0.973482	−	0.144343i
$316$			23328.9i			0.233626i
$317$	−72240.4	+	72240.4i	−0.718889	+	0.718889i	−0.968378	−	0.249489i	$-0.919737\pi$
$317$	−72240.4	+	72240.4i	−0.718889	+	0.718889i	0.249489	+	0.968378i	$0.419737\pi$
$318$	36916.1	−	36916.1i	0.365058	−	0.365058i
$319$	47344.1	−	47344.1i	0.465248	−	0.465248i
$320$	69202.8	+	51330.7i	0.675809	+	0.501276i
$321$	50984.4			0.494798
$322$	−165865.			−1.59972
$323$	211.101	+	211.101i	0.00202342	+	0.00202342i
$324$		−	66020.0i		−	0.628906i
$325$	43756.6	+	96135.3i	0.414264	+	0.910157i
$326$	−8054.74			−0.0757908
$327$	166925.	−	166925.i	1.56108	−	1.56108i
$328$			26385.4i			0.245254i
$329$			34064.2i			0.314707i
$330$	−25316.1	+	34130.6i	−0.232471	+	0.313412i
$331$	−86768.0	−	86768.0i	−0.791961	−	0.791961i	0.189852	−	0.981813i	$-0.439199\pi$
$331$	−86768.0	−	86768.0i	−0.791961	−	0.791961i	−0.981813	+	0.189852i	$0.939199\pi$
$332$	59220.1	+	59220.1i	0.537270	+	0.537270i
$333$	32174.2	+	32174.2i	0.290148	+	0.290148i
$334$	−82686.7			−0.741213
$335$	15341.1	+	103464.i	0.136699	+	0.921932i
$336$	−31386.2	+	31386.2i	−0.278010	+	0.278010i
$337$	3730.58			0.0328486			0.0164243	−	0.999865i	$-0.494772\pi$
$337$	3730.58			0.0328486			0.0164243	+	0.999865i	$0.494772\pi$
$338$	39385.7	−	68798.1i	0.344751	−	0.602203i
$339$	218082.			1.89767
$340$	−472.363	−	350.372i	−0.00408619	−	0.00303090i
$341$	72165.6			0.620614
$342$	16391.5			0.140142
$343$	2302.68	−	2302.68i	0.0195725	−	0.0195725i
$344$	159292.	+	159292.i	1.34610	+	1.34610i
$345$	−201761.	−	149655.i	−1.69512	−	1.25734i
$346$	12225.5	−	12225.5i	0.102121	−	0.102121i
$347$		−	34660.7i		−	0.287858i	−0.989588	−	0.143929i	$-0.954026\pi$
$347$		−	34660.7i		−	0.287858i	0.989588	−	0.143929i	$-0.0459737\pi$
$348$	124346.			1.02677
$349$	−7412.49	+	7412.49i	−0.0608574	+	0.0608574i	−0.736880	−	0.676023i	$-0.763702\pi$
$349$	−7412.49	+	7412.49i	−0.0608574	+	0.0608574i	0.676023	+	0.736880i	$0.263702\pi$
$350$	35051.6	+	115599.i	0.286136	+	0.943668i
$351$	6522.14	+	48850.0i	0.0529391	+	0.396507i
$352$			48530.5i			0.391678i
$353$	−95189.5	+	95189.5i	−0.763906	+	0.763906i	−0.977026	−	0.213120i	$-0.931637\pi$
$353$	−95189.5	+	95189.5i	−0.763906	+	0.763906i	0.213120	+	0.977026i	$0.431637\pi$
$354$	29487.0			0.235301
$355$	−46994.6	+	6968.12i	−0.372899	+	0.0552916i
$356$	−8561.14	−	8561.14i	−0.0675509	−	0.0675509i
$357$	1634.82	−	1634.82i	0.0128273	−	0.0128273i
$358$	75154.3	+	75154.3i	0.586392	+	0.586392i
$359$	74820.5	−	74820.5i	0.580539	−	0.580539i	−0.354512	−	0.935051i	$-0.615353\pi$
$359$	74820.5	−	74820.5i	0.580539	−	0.580539i	0.935051	+	0.354512i	$0.115353\pi$
$360$	−93546.3	+	13870.6i	−0.721808	+	0.107026i
$361$		−	119237.i		−	0.914950i
$362$	−75075.0	−	75075.0i	−0.572899	−	0.572899i
$363$	139397.			1.05789
$364$	−59289.7	+	77561.2i	−0.447483	+	0.585385i
$365$	−41394.3	+	6137.75i	−0.310710	+	0.0460705i
$366$	119514.	+	119514.i	0.892186	+	0.892186i
$367$		−	77746.8i		−	0.577232i	−0.957445	−	0.288616i	$-0.906805\pi$
$367$		−	77746.8i		−	0.577232i	0.957445	−	0.288616i	$-0.0931951\pi$
$368$	46720.7			0.344996
$369$	−15519.2	−	15519.2i	−0.113977	−	0.113977i
$370$	−33532.7	+	45207.9i	−0.244943	+	0.330226i
$371$	79097.6	−	79097.6i	0.574666	−	0.574666i
$372$	94768.6	+	94768.6i	0.684823	+	0.684823i
$373$			228528.i			1.64257i	0.570522	+	0.821283i	$0.306741\pi$
$373$			228528.i			1.64257i	−0.570522	+	0.821283i	$0.693259\pi$
$374$			411.667i			0.00294309i
$375$	−61664.3	+	172243.i	−0.438502	+	1.22484i
$376$		−	32989.5i		−	0.233346i
$377$	−214439.	+	28630.6i	−1.50876	+	0.201441i
$378$			56362.4i			0.394462i
$379$	104576.	+	104576.i	0.728039	+	0.728039i	0.970229	−	0.242190i	$-0.0778656\pi$
$379$	104576.	+	104576.i	0.728039	+	0.728039i	−0.242190	+	0.970229i	$0.577866\pi$
$380$	−3202.56	−	21598.8i	−0.0221784	−	0.149576i
$381$		−	243542.i		−	1.67773i
$382$	114582.	−	114582.i	0.785219	−	0.785219i
$383$	188674.	−	188674.i	1.28622	−	1.28622i	0.349152	−	0.937066i	$-0.386470\pi$
$383$	188674.	−	188674.i	1.28622	−	1.28622i	0.937066	−	0.349152i	$-0.113530\pi$
$384$	−43713.6	+	43713.6i	−0.296452	+	0.296452i
$385$	−54243.1	+	73129.3i	−0.365951	+	0.493367i
$386$	−74191.0			−0.497939
$387$	−187383.			−1.25115
$388$	−66922.2	−	66922.2i	−0.444536	−	0.444536i
$389$		−	19213.2i		−	0.126970i	−0.997983	−	0.0634849i	$-0.979779\pi$
$389$		−	19213.2i		−	0.126970i	0.997983	−	0.0634849i	$-0.0202215\pi$
$390$	131963.	−	37936.7i	0.867606	−	0.249419i
$391$	−2433.55			−0.0159179
$392$	−116721.	+	116721.i	−0.759584	+	0.759584i
$393$		−	82446.4i		−	0.533810i
$394$		−	161572.i		−	1.04082i
$395$	41882.2	−	56464.6i	0.268433	−	0.361894i
$396$	−17210.5	−	17210.5i	−0.109750	−	0.109750i
$397$	124954.	+	124954.i	0.792808	+	0.792808i	0.981950	−	0.189142i	$-0.0605705\pi$
$397$	124954.	+	124954.i	0.792808	+	0.792808i	−0.189142	+	0.981950i	$0.560570\pi$
$398$	14468.4	+	14468.4i	0.0913388	+	0.0913388i
$399$	85836.0			0.539168
$400$	−9873.31	−	32561.9i	−0.0617082	−	0.203512i
$401$	59134.8	−	59134.8i	0.367752	−	0.367752i	−0.498905	−	0.866657i	$-0.666264\pi$
$401$	59134.8	−	59134.8i	0.367752	−	0.367752i	0.866657	+	0.498905i	$0.166264\pi$
$402$	135969.			0.841369
$403$	−185253.	−	141612.i	−1.14066	−	0.871946i
$404$	32638.6			0.199972
$405$	−118525.	+	159793.i	−0.722604	+	0.974197i
$406$	−247417.			−1.50099
$407$	−42426.2			−0.256121
$408$	−1583.24	+	1583.24i	−0.00951103	+	0.00951103i
$409$	75924.7	+	75924.7i	0.453875	+	0.453875i	0.896639	−	0.442763i	$-0.146002\pi$
$409$	75924.7	+	75924.7i	0.453875	+	0.453875i	−0.442763	+	0.896639i	$0.646002\pi$
$410$	16174.5	−	21806.1i	0.0962195	−	0.129721i
$411$	−180114.	+	180114.i	−1.06626	+	1.06626i
$412$		−	129287.i		−	0.761658i
$413$	63179.9			0.370407
$414$	−94479.9	+	94479.9i	−0.551238	+	0.551238i
$415$	−37017.1	−	249652.i	−0.214935	−	1.44957i
$416$	95232.3	−	124580.i	0.550298	−	0.719884i
$417$		−	169564.i		−	0.975126i
$418$	−10807.3	+	10807.3i	−0.0618534	+	0.0618534i
$419$	−115602.			−0.658473			−0.329236	−	0.944248i	$-0.606791\pi$
$419$	−115602.			−0.658473			−0.329236	+	0.944248i	$0.606791\pi$
$420$	−167267.	+	24801.5i	−0.948224	+	0.140598i
$421$	−54540.6	−	54540.6i	−0.307720	−	0.307720i	0.536305	−	0.844024i	$-0.319820\pi$
$421$	−54540.6	−	54540.6i	−0.307720	−	0.307720i	−0.844024	+	0.536305i	$0.819820\pi$
$422$	−41063.6	+	41063.6i	−0.230586	+	0.230586i
$423$	19403.7	+	19403.7i	0.108443	+	0.108443i
$424$	−76602.1	+	76602.1i	−0.426098	+	0.426098i
$425$	514.273	+	1696.06i	0.00284719	+	0.00938995i
$426$			61758.7i			0.340313i
$427$	256074.	+	256074.i	1.40446	+	1.40446i
$428$	−36124.0			−0.197201
$429$	82223.8	+	62854.0i	0.446769	+	0.341522i
$430$	−33998.5	−	229293.i	−0.183875	−	1.24009i
$431$	134785.	+	134785.i	0.725583	+	0.725583i	0.969736	−	0.244154i	$-0.0785102\pi$
$431$	134785.	+	134785.i	0.725583	+	0.725583i	−0.244154	+	0.969736i	$0.578510\pi$
$432$		−	15876.1i		−	0.0850700i
$433$	42349.4			0.225877			0.112938	−	0.993602i	$-0.463974\pi$
$433$	42349.4			0.225877			0.112938	+	0.993602i	$0.463974\pi$
$434$	−188566.	−	188566.i	−1.00111	−	1.00111i
$435$	−300962.	−	223237.i	−1.59050	−	1.17974i
$436$	−118271.	+	118271.i	−0.622165	+	0.622165i
$437$	−63886.6	−	63886.6i	−0.334539	−	0.334539i
$438$			54399.1i			0.283559i
$439$		−	293456.i		−	1.52270i	−0.648342	−	0.761350i	$-0.724537\pi$
$439$		−	293456.i		−	1.52270i	0.648342	−	0.761350i	$-0.275463\pi$
$440$	52531.8	−	70822.1i	0.271342	−	0.365817i
$441$		−	137305.i		−	0.706006i
$442$	807.823	−	1056.77i	0.00413496	−	0.00540925i
$443$		−	239583.i		−	1.22081i	−0.792088	−	0.610406i	$-0.791006\pi$
$443$		−	239583.i		−	1.22081i	0.792088	−	0.610406i	$-0.208994\pi$
$444$	−55714.5	−	55714.5i	−0.282619	−	0.282619i
$445$	5351.37	+	36090.8i	0.0270237	+	0.182254i
$446$			134783.i			0.677590i
$447$	−142234.	+	142234.i	−0.711851	+	0.711851i
$448$	169698.	−	169698.i	0.845512	−	0.845512i
$449$	−195773.	+	195773.i	−0.971091	+	0.971091i	−0.999594	−	0.0285030i	$-0.990926\pi$
$449$	−195773.	+	195773.i	−0.971091	+	0.971091i	0.0285030	+	0.999594i	$0.490926\pi$
$450$	85813.7	+	45881.6i	0.423772	+	0.226576i
$451$	20464.3			0.100611
$452$	−154518.			−0.756312
$453$	79167.9	+	79167.9i	0.385791	+	0.385791i
$454$			147213.i			0.714222i
$455$	282748.	−	81284.3i	1.36577	−	0.392631i
$456$	−83128.0			−0.399777
$457$	87988.1	−	87988.1i	0.421300	−	0.421300i	−0.464351	−	0.885651i	$-0.653712\pi$
$457$	87988.1	−	87988.1i	0.421300	−	0.421300i	0.885651	+	0.464351i	$0.153712\pi$
$458$		−	20019.8i		−	0.0954397i
$459$			826.942i			0.00392509i
$460$	142954.	+	106035.i	0.675585	+	0.501110i
$461$	56098.7	+	56098.7i	0.263968	+	0.263968i	0.826664	−	0.562696i	$-0.190236\pi$
$461$	56098.7	+	56098.7i	0.263968	+	0.263968i	−0.562696	+	0.826664i	$0.690236\pi$
$462$	83694.3	+	83694.3i	0.392113	+	0.392113i
$463$	21715.3	+	21715.3i	0.101299	+	0.101299i	0.755940	−	0.654641i	$-0.227180\pi$
$463$	21715.3	+	21715.3i	0.101299	+	0.101299i	−0.654641	+	0.755940i	$0.727180\pi$
$464$	69692.1			0.323704
$465$	−59237.7	−	399512.i	−0.273963	−	1.84767i
$466$	−119844.	+	119844.i	−0.551878	+	0.551878i
$467$	114586.			0.525409			0.262705	−	0.964876i	$-0.415386\pi$
$467$	114586.			0.525409			0.262705	+	0.964876i	$0.415386\pi$
$468$	10407.8	+	77953.0i	0.0475190	+	0.355911i
$469$	291331.			1.32447
$470$	−20222.9	+	27264.1i	−0.0915479	+	0.123423i
$471$	143588.			0.647256
$472$	−61186.6			−0.274645
$473$	123545.	−	123545.i	0.552210	−	0.552210i
$474$	−64622.0	−	64622.0i	−0.287623	−	0.287623i
$475$	−31024.8	+	58026.6i	−0.137506	+	0.257182i
$476$	−1158.32	+	1158.32i	−0.00511228	+	0.00511228i
$477$		−	90111.1i		−	0.396042i
$478$	−55162.2			−0.241427
$479$	258343.	−	258343.i	1.12597	−	1.12597i	0.135142	−	0.990826i	$-0.456851\pi$
$479$	258343.	−	258343.i	1.12597	−	1.12597i	0.990826	−	0.135142i	$-0.0431492\pi$
$480$	268667.	−	39836.6i	1.16609	−	0.172902i
$481$	108910.	+	83253.7i	0.470737	+	0.359843i
$482$		−	71528.0i		−	0.307880i
$483$	−494754.	+	494754.i	−2.12078	+	2.12078i
$484$	−98766.8			−0.421619
$485$	41831.5	+	282121.i	0.177836	+	1.19937i
$486$	136518.	+	136518.i	0.577986	+	0.577986i
$487$	7983.76	−	7983.76i	0.0336628	−	0.0336628i	−0.690075	−	0.723738i	$-0.742423\pi$
$487$	7983.76	−	7983.76i	0.0336628	−	0.0336628i	0.723738	+	0.690075i	$0.242423\pi$
$488$	−247995.	−	247995.i	−1.04137	−	1.04137i
$489$	−24026.3	+	24026.3i	−0.100478	+	0.100478i
$490$	168014.	−	24912.4i	0.699769	−	0.103758i
$491$			16818.2i			0.0697618i	0.999391	+	0.0348809i	$0.0111052\pi$
$491$			16818.2i			0.0697618i	−0.999391	+	0.0348809i	$0.988895\pi$
$492$	26873.9	+	26873.9i	0.111020	+	0.111020i
$493$	−3630.07			−0.0149355
$494$	48950.1	−	6535.51i	0.200586	−	0.0267809i
$495$	10757.9	+	72553.8i	0.0439054	+	0.296108i
$496$	53115.0	+	53115.0i	0.215901	+	0.215901i
$497$			132326.i			0.535714i
$498$	−328084.			−1.32290
$499$	−280657.	−	280657.i	−1.12713	−	1.12713i	−0.990641	−	0.136492i	$-0.956417\pi$
$499$	−280657.	−	280657.i	−1.12713	−	1.12713i	−0.136492	−	0.990641i	$-0.543583\pi$
$500$	43691.0	−	122039.i	0.174764	−	0.488158i
$501$	−246644.	+	246644.i	−0.982642	+	0.982642i
$502$	230447.	+	230447.i	0.914459	+	0.914459i
$503$			314884.i			1.24456i	0.782797	+	0.622278i	$0.213793\pi$
$503$			314884.i			1.24456i	−0.782797	+	0.622278i	$0.786207\pi$
$504$			263405.i			1.03696i
$505$	−78997.5	−	58595.8i	−0.309764	−	0.229765i
$506$		−	124585.i		−	0.486592i
$507$	−87733.4	−	322699.i	−0.341310	−	1.25540i
$508$			172556.i			0.668658i
$509$	−177611.	−	177611.i	−0.685544	−	0.685544i	0.275700	−	0.961244i	$-0.411090\pi$
$509$	−177611.	−	177611.i	−0.685544	−	0.685544i	−0.961244	+	0.275700i	$0.911090\pi$
$510$	2279.01	−	337.920i	0.00876205	−	0.00129919i
$511$			116557.i			0.446372i
$512$	−77255.5	+	77255.5i	−0.294706	+	0.294706i
$513$	−21709.2	+	21709.2i	−0.0824916	+	0.0824916i
$514$	−130073.	+	130073.i	−0.492334	+	0.492334i
$515$	−232107.	+	312922.i	−0.875134	+	1.17983i
$516$	324482.			1.21868
$517$	−25586.4			−0.0957258
$518$	110858.	+	110858.i	0.413149	+	0.413149i
$519$		−	72934.3i		−	0.270768i
$520$	−273827.	+	78719.9i	−1.01268	+	0.291124i
$521$	336979.			1.24144			0.620722	−	0.784031i	$-0.286840\pi$
$521$	336979.			1.24144			0.620722	+	0.784031i	$0.286840\pi$
$522$	−140933.	+	140933.i	−0.517217	+	0.517217i
$523$			82275.6i			0.300793i	0.988626	+	0.150396i	$0.0480550\pi$
$523$			82275.6i			0.300793i	−0.988626	+	0.150396i	$0.951945\pi$
$524$			58415.7i			0.212749i
$525$	449373.	+	240264.i	1.63038	+	0.871705i
$526$	39979.2	+	39979.2i	0.144498	+	0.144498i
$527$	−2766.61	−	2766.61i	−0.00996156	−	0.00996156i
$528$	−23574.9	−	23574.9i	−0.0845634	−	0.0845634i
$529$	456637.			1.63177
$530$	110265.	−	16349.6i	0.392543	−	0.0582044i
$531$	35988.5	−	35988.5i	0.127636	−	0.127636i
$532$	−60817.4			−0.214884
$533$	−52532.9	−	40157.5i	−0.184917	−	0.141355i
$534$	47429.4			0.166328
$535$	87433.4	+	64853.1i	0.305471	+	0.226581i
$536$	−282140.			−0.982052
$537$	448352.			1.55479
$538$	−47462.8	+	47462.8i	−0.163979	+	0.163979i
$539$	90527.8	+	90527.8i	0.311605	+	0.311605i
$540$	36031.6	−	48577.0i	0.123565	−	0.166588i
$541$	185136.	−	185136.i	0.632551	−	0.632551i	−0.316156	−	0.948707i	$-0.602392\pi$
$541$	185136.	−	185136.i	0.632551	−	0.632551i	0.948707	+	0.316156i	$0.102392\pi$
$542$		−	180031.i		−	0.612843i
$543$	−447878.			−1.51901
$544$	1860.52	−	1860.52i	0.00628688	−	0.00628688i
$545$	498591.	−	73928.6i	1.67861	−	0.248897i
$546$	−50612.7	−	379082.i	−0.169775	−	1.27159i
$547$		−	463547.i		−	1.54924i	−0.632426	−	0.774621i	$-0.717941\pi$
$547$		−	463547.i		−	1.54924i	0.632426	−	0.774621i	$-0.282059\pi$
$548$	127616.	−	127616.i	0.424956	−	0.424956i
$549$	291730.			0.967912
$550$	−86829.3	+	26328.1i	−0.287039	+	0.0870350i
$551$	−95298.1	−	95298.1i	−0.313892	−	0.313892i
$552$	479145.	−	479145.i	1.57249	−	1.57249i
$553$	−138461.	−	138461.i	−0.452770	−	0.452770i
$554$	180122.	−	180122.i	0.586876	−	0.586876i
$555$	34825.8	+	234873.i	0.113062	+	0.762514i
$556$			120141.i			0.388634i
$557$	−196769.	−	196769.i	−0.634228	−	0.634228i	0.314897	−	0.949126i	$-0.398030\pi$
$557$	−196769.	−	196769.i	−0.634228	−	0.634228i	−0.949126	+	0.314897i	$0.898030\pi$
$558$	−214822.			−0.689937
$559$	−559583.	+	74712.0i	−1.79077	+	0.239093i
$560$	−93748.1	+	13900.5i	−0.298942	+	0.0443256i
$561$	1227.95	+	1227.95i	0.00390172	+	0.00390172i
$562$		−	17995.2i		−	0.0569750i
$563$	−167590.			−0.528725			−0.264363	−	0.964423i	$-0.585162\pi$
$563$	−167590.			−0.528725			−0.264363	+	0.964423i	$0.585162\pi$
$564$	−33600.4	−	33600.4i	−0.105630	−	0.105630i
$565$	373990.	+	277404.i	1.17155	+	0.868993i
$566$	205841.	−	205841.i	0.642540	−	0.642540i
$567$	391840.	+	391840.i	1.21883	+	1.21883i
$568$		−	128151.i		−	0.397216i
$569$			212375.i			0.655962i	0.944684	+	0.327981i	$0.106368\pi$
$569$			212375.i			0.655962i	−0.944684	+	0.327981i	$0.893632\pi$
$570$	68700.8	+	50958.3i	0.211452	+	0.156843i
$571$			352407.i			1.08087i	0.841387	+	0.540433i	$0.181739\pi$
$571$			352407.i			1.08087i	−0.841387	+	0.540433i	$0.818261\pi$
$572$	−58258.0	−	44533.9i	−0.178059	−	0.136113i
$573$		−	683570.i		−	2.08197i
$574$	−53472.4	−	53472.4i	−0.162295	−	0.162295i
$575$	−155637.	−	513287.i	−0.470736	−	1.55248i
$576$		−	193326.i		−	0.582701i
$577$	−339319.	+	339319.i	−1.01919	+	1.01919i	−0.0193799	+	0.999812i	$0.506169\pi$
$577$	−339319.	+	339319.i	−1.01919	+	1.01919i	−0.999812	+	0.0193799i	$0.993831\pi$
$578$	−163907.	+	163907.i	−0.490617	+	0.490617i
$579$	−221302.	+	221302.i	−0.660129	+	0.660129i
$580$	213241.	+	158170.i	0.633890	+	0.470183i
$581$	−702963.			−2.08248
$582$	370754.			1.09456
$583$	59412.1	+	59412.1i	0.174798	+	0.174798i
$584$		−	112880.i		−	0.330972i
$585$	114758.	−	207360.i	0.335328	−	0.605917i
$586$	432570.			1.25968
$587$	−151834.	+	151834.i	−0.440649	+	0.440649i	−0.892230	−	0.451581i	$-0.850860\pi$
$587$	−151834.	+	151834.i	−0.440649	+	0.440649i	0.451581	+	0.892230i	$0.350860\pi$
$588$			237764.i			0.687688i
$589$		−	145261.i		−	0.418714i
$590$	50567.4	+	37508.0i	0.145267	+	0.107751i
$591$	−481951.	−	481951.i	−1.37984	−	1.37984i
$592$	−31226.3	−	31226.3i	−0.0891000	−	0.0891000i
$593$	91914.9	+	91914.9i	0.261383	+	0.261383i	0.825616	−	0.564233i	$-0.190828\pi$
$593$	91914.9	+	91914.9i	0.261383	+	0.261383i	−0.564233	+	0.825616i	$0.690828\pi$
$594$	−42335.1			−0.119985
$595$	4883.08	−	724.039i	0.0137930	−	0.00204516i
$596$	100777.	−	100777.i	0.283707	−	0.283707i
$597$	86315.1			0.242180
$598$	−244476.	+	319816.i	−0.683649	+	0.894331i
$599$	−90700.3			−0.252787			−0.126394	−	0.991980i	$-0.540340\pi$
$599$	−90700.3			−0.252787			−0.126394	+	0.991980i	$0.540340\pi$
$600$	−435196.	−	232684.i	−1.20888	−	0.646343i
$601$	125558.			0.347613			0.173806	−	0.984780i	$-0.444393\pi$
$601$	125558.			0.347613			0.173806	+	0.984780i	$0.444393\pi$
$602$	−645638.			−1.78154
$603$	165948.	−	165948.i	0.456391	−	0.456391i
$604$	−56092.8	−	56092.8i	−0.153756	−	0.153756i
$605$	239052.	+	177315.i	0.653103	+	0.484434i
$606$	−90410.3	+	90410.3i	−0.246191	+	0.246191i
$607$			247009.i			0.670403i	0.942147	+	0.335201i	$0.108804\pi$
$607$			247009.i			0.670403i	−0.942147	+	0.335201i	$0.891196\pi$
$608$	97686.1			0.264256
$609$	−738013.	+	738013.i	−1.98989	+	1.98989i
$610$	52930.9	+	356978.i	0.142249	+	0.959360i
$611$	65681.7	+	50208.8i	0.175939	+	0.134492i
$612$			1319.60i			0.00352323i
$613$	134125.	−	134125.i	0.356933	−	0.356933i	−0.505748	−	0.862681i	$-0.668783\pi$
$613$	134125.	−	134125.i	0.356933	−	0.356933i	0.862681	+	0.505748i	$0.168783\pi$
$614$	−341271.			−0.905237
$615$	−16798.3	−	113291.i	−0.0444134	−	0.299534i
$616$	−173668.	−	173668.i	−0.457677	−	0.457677i
$617$	−346776.	+	346776.i	−0.910916	+	0.910916i	−0.996344	−	0.0854281i	$-0.972774\pi$
$617$	−346776.	+	346776.i	−0.910916	+	0.910916i	0.0854281	+	0.996344i	$0.472774\pi$
$618$	358130.	+	358130.i	0.937699	+	0.937699i
$619$	524188.	−	524188.i	1.36806	−	1.36806i	0.504860	−	0.863201i	$-0.331544\pi$
$619$	524188.	−	524188.i	1.36806	−	1.36806i	0.863201	−	0.504860i	$-0.168456\pi$
$620$	41971.6	+	283066.i	0.109187	+	0.736384i
$621$		−	250262.i		−	0.648950i
$622$	191083.	+	191083.i	0.493903	+	0.493903i
$623$	101624.			0.261830
$624$	14256.5	+	106780.i	0.0366138	+	0.274233i
$625$	−324845.	+	216942.i	−0.831602	+	0.555372i
$626$	−85752.6	−	85752.6i	−0.218826	−	0.218826i
$627$			64473.5i			0.164001i
$628$	−101736.			−0.257963
$629$	1626.49	+	1626.49i	0.00411103	+	0.00411103i
$630$	161470.	−	217690.i	0.406828	−	0.548476i
$631$	222687.	−	222687.i	0.559288	−	0.559288i	−0.369817	−	0.929105i	$-0.620580\pi$
$631$	222687.	−	222687.i	0.559288	−	0.559288i	0.929105	+	0.369817i	$0.120580\pi$
$632$	134093.	+	134093.i	0.335716	+	0.335716i
$633$			244975.i			0.611385i
$634$			283566.i			0.705465i
$635$	309789.	−	417650.i	0.768279	−	1.03577i
$636$			156041.i			0.385767i
$637$	−54745.2	−	410034.i	−0.134917	−	1.01051i
$638$		−	185840.i		−	0.456561i
$639$	75375.6	+	75375.6i	0.184599	+	0.184599i
$640$	−130569.	+	19360.1i	−0.318772	+	0.0472659i
$641$			59224.2i			0.144140i	0.997400	+	0.0720698i	$0.0229604\pi$
$641$			59224.2i			0.144140i	−0.997400	+	0.0720698i	$0.977040\pi$
$642$	100065.	−	100065.i	0.242779	−	0.242779i
$643$	−314696.	+	314696.i	−0.761147	+	0.761147i	−0.976530	−	0.215383i	$-0.930900\pi$
$643$	−314696.	+	314696.i	−0.761147	+	0.761147i	0.215383	+	0.976530i	$0.430900\pi$
$644$	350548.	−	350548.i	0.845232	−	0.845232i
$645$	−785366.	−	582540.i	−1.88779	−	1.40025i
$646$	828.637			0.00198564
$647$	88056.1			0.210354			0.105177	−	0.994454i	$-0.466459\pi$
$647$	88056.1			0.210354			0.105177	+	0.994454i	$0.466459\pi$
$648$	−379478.	−	379478.i	−0.903725	−	0.903725i
$649$			47455.9i			0.112668i
$650$	274560.	+	102801.i	0.649845	+	0.243317i
$651$	−1.12494e6			−2.65440
$652$	17023.3	−	17023.3i	0.0400451	−	0.0400451i
$653$		−	261310.i		−	0.612815i	−0.951900	−	0.306407i	$-0.900873\pi$
$653$		−	261310.i		−	0.612815i	0.951900	−	0.306407i	$-0.0991270\pi$
$654$		−	655231.i		−	1.53193i
$655$	104873.	−	141387.i	0.244445	−	0.329555i
$656$	15062.0	+	15062.0i	0.0350007	+	0.0350007i
$657$	66393.3	+	66393.3i	0.153813	+	0.153813i
$658$	66856.3	+	66856.3i	0.154415	+	0.154415i
$659$	−805533.			−1.85487			−0.927433	−	0.373990i	$-0.877989\pi$
$659$	−805533.			−1.85487			−0.927433	+	0.373990i	$0.877989\pi$
$660$	−18629.0	−	125638.i	−0.0427662	−	0.288425i
$661$	209700.	−	209700.i	0.479949	−	0.479949i	−0.425167	−	0.905115i	$-0.639784\pi$
$661$	209700.	−	209700.i	0.479949	−	0.479949i	0.905115	+	0.425167i	$0.139784\pi$
$662$	−340591.			−0.777173
$663$	−742.584	−	5561.85i	−0.00168935	−	0.0126530i
$664$	680785.			1.54409
$665$	147200.	+	109185.i	0.332863	+	0.246899i
$666$	126294.			0.284730
$667$	1.09859e6			2.46935
$668$	174755.	−	174755.i	0.391630	−	0.391630i
$669$	402042.	+	402042.i	0.898296	+	0.898296i
$670$	233173.	+	172954.i	0.519432	+	0.385285i
$671$	−192343.	+	192343.i	−0.427200	+	0.427200i
$672$		−	756506.i		−	1.67523i
$673$	−583650.			−1.28861			−0.644306	−	0.764768i	$-0.722854\pi$
$673$	−583650.			−1.28861			−0.644306	+	0.764768i	$0.722854\pi$
$674$	7321.85	−	7321.85i	0.0161176	−	0.0161176i
$675$	−174420.	+	52886.9i	−0.382814	+	0.116075i
$676$	62161.7	+	228642.i	0.136028	+	0.500336i
$677$			313672.i			0.684382i	0.939630	+	0.342191i	$0.111169\pi$
$677$			313672.i			0.684382i	−0.939630	+	0.342191i	$0.888831\pi$
$678$	428020.	−	428020.i	0.931118	−	0.931118i
$679$	794390.			1.72304
$680$	−4729.02	+	701.196i	−0.0102271	+	0.00151643i
$681$	439117.	+	439117.i	0.946861	+	0.946861i
$682$	141636.	−	141636.i	0.304513	−	0.304513i
$683$	−224062.	−	224062.i	−0.480317	−	0.480317i	0.424916	−	0.905233i	$-0.360304\pi$
$683$	−224062.	−	224062.i	−0.480317	−	0.480317i	−0.905233	+	0.424916i	$0.860304\pi$
$684$	−34642.8	+	34642.8i	−0.0740458	+	0.0740458i
$685$	−537986.	+	79769.9i	−1.14654	+	0.170004i
$686$		−	9038.74i		−	0.0192070i
$687$	−59716.6	−	59716.6i	−0.126527	−	0.126527i
$688$	181863.			0.384208
$689$	−35928.4	−	269099.i	−0.0756833	−	0.566858i
$690$	−689709.	+	102267.i	−1.44866	+	0.214801i
$691$	162862.	+	162862.i	0.341086	+	0.341086i	0.856775	−	0.515690i	$-0.172464\pi$
$691$	162862.	+	162862.i	0.341086	+	0.341086i	−0.515690	+	0.856775i	$0.672464\pi$
$692$			51676.1i			0.107914i
$693$	204295.			0.425394
$694$	−68027.0	−	68027.0i	−0.141242	−	0.141242i
$695$	215688.	−	290785.i	0.446536	−	0.602009i
$696$	714729.	−	714729.i	1.47544	−	1.47544i
$697$	−784.540	−	784.540i	−0.00161492	−	0.00161492i
$698$			29096.3i			0.0597210i
$699$			714957.i			1.46327i
$700$	−318394.	−	170234.i	−0.649784	−	0.347416i
$701$			692713.i			1.40967i	0.709371	+	0.704835i	$0.248979\pi$
$701$			692713.i			1.40967i	−0.709371	+	0.704835i	$0.751021\pi$
$702$	108676.	+	83075.0i	0.220527	+	0.168576i
$703$			85398.8i			0.172799i
$704$	127464.	+	127464.i	0.257183	+	0.257183i
$705$	21002.8	+	141648.i	0.0422571	+	0.284991i
$706$			373648.i			0.749642i
$707$	−193716.	+	193716.i	−0.387549	+	0.387549i
$708$	−62319.5	+	62319.5i	−0.124325	+	0.124325i
$709$	383095.	−	383095.i	0.762103	−	0.762103i	−0.214599	−	0.976702i	$-0.568845\pi$
$709$	383095.	−	383095.i	0.762103	−	0.762103i	0.976702	+	0.214599i	$0.0688445\pi$
$710$	−78558.1	+	105910.i	−0.155838	+	0.210098i
$711$	−157741.			−0.312036
$712$	−98417.5			−0.194139
$713$	837275.	+	837275.i	1.64698	+	1.64698i
$714$		−	6417.18i		−	0.0125877i
$715$	61054.6	+	212379.i	0.119428	+	0.415431i
$716$	−317671.			−0.619657
$717$	−164542.	+	164542.i	−0.320065	+	0.320065i
$718$		−	293694.i		−	0.569699i
$719$		−	166519.i		−	0.322112i	−0.986945	−	0.161056i	$-0.948510\pi$
$719$		−	166519.i		−	0.322112i	0.986945	−	0.161056i	$-0.0514900\pi$
$720$	−45482.8	+	61318.8i	−0.0877368	+	0.118285i
$721$	767340.	+	767340.i	1.47610	+	1.47610i
$722$	−234021.	−	234021.i	−0.448933	−	0.448933i
$723$	−213359.	−	213359.i	−0.408164	−	0.408164i
$724$	317335.			0.605398
$725$	−232160.	−	765658.i	−0.441684	−	1.45666i
$726$	273588.	−	273588.i	0.519067	−	0.519067i
$727$	−552802.			−1.04593			−0.522963	−	0.852355i	$-0.675173\pi$
$727$	−552802.			−1.04593			−0.522963	+	0.852355i	$0.675173\pi$
$728$	105023.	+	786609.i	0.198163	+	1.48421i
$729$	169827.			0.319560
$730$	−69196.5	+	93289.1i	−0.129849	+	0.175059i
$731$	−9472.73			−0.0177272
$732$	−505174.			−0.942798
$733$	−340941.	+	340941.i	−0.634558	+	0.634558i	−0.949208	−	0.314650i	$-0.898113\pi$
$733$	−340941.	+	340941.i	−0.634558	+	0.634558i	0.314650	+	0.949208i	$0.398113\pi$
$734$	−152590.	−	152590.i	−0.283227	−	0.283227i
$735$	426856.	−	575477.i	0.790144	−	1.06525i
$736$	−563057.	+	563057.i	−1.03943	+	1.03943i
$737$			218825.i			0.402868i
$738$	−60917.8			−0.111849
$739$	−684691.	+	684691.i	−1.25373	+	1.25373i	−0.299701	+	0.954033i	$0.596887\pi$
$739$	−684691.	+	684691.i	−1.25373	+	1.25373i	−0.954033	+	0.299701i	$0.903113\pi$
$740$	−24675.1	−	166415.i	−0.0450605	−	0.303898i
$741$	126518.	−	165507.i	0.230417	−	0.301425i
$742$		−	310483.i		−	0.563936i
$743$	−86076.8	+	86076.8i	−0.155922	+	0.155922i	−0.780757	−	0.624835i	$-0.785166\pi$
$743$	−86076.8	+	86076.8i	−0.155922	+	0.155922i	0.624835	+	0.780757i	$0.285166\pi$
$744$	1.08945e6			1.96816
$745$	−424842.	+	62993.5i	−0.765447	+	0.113497i
$746$	448523.	+	448523.i	0.805947	+	0.805947i
$747$	−400422.	+	400422.i	−0.717590	+	0.717590i
$748$	−870.041	−	870.041i	−0.00155502	−	0.00155502i
$749$	214402.	−	214402.i	0.382178	−	0.382178i
$750$	217028.	+	459080.i	0.385828	+	0.816142i
$751$		−	142453.i		−	0.252575i	−0.991994	−	0.126288i	$-0.959694\pi$
$751$		−	142453.i		−	0.252575i	0.991994	−	0.126288i	$-0.0403062\pi$
$752$	−18832.0	−	18832.0i	−0.0333013	−	0.0333013i
$753$	1.37479e6			2.42464
$754$	−364678.	+	477062.i	−0.641456	+	0.839136i
$755$	35062.3	+	236468.i	0.0615101	+	0.414838i
$756$	−119119.	−	119119.i	−0.208420	−	0.208420i
$757$			564032.i			0.984266i	0.870520	+	0.492133i	$0.163783\pi$
$757$			564032.i			0.984266i	−0.870520	+	0.492133i	$0.836217\pi$
$758$	410494.			0.714445
$759$	−371622.	−	371622.i	−0.645086	−	0.645086i
$760$	−142556.	−	105740.i	−0.246808	−	0.183068i
$761$	−472994.	+	472994.i	−0.816744	+	0.816744i	−0.985635	−	0.168891i	$-0.945981\pi$
$761$	−472994.	+	472994.i	−0.816744	+	0.816744i	0.168891	+	0.985635i	$0.445981\pi$
$762$	−477988.	−	477988.i	−0.823204	−	0.823204i
$763$		−	1.40392e6i		−	2.41153i
$764$			484329.i			0.829763i
$765$	2369.07	−	3193.93i	0.00404814	−	0.00545760i
$766$		−	740604.i		−	1.26220i
$767$	93123.6	−	121822.i	0.158296	−	0.207078i
$768$			817250.i			1.38558i
$769$	−682483.	−	682483.i	−1.15409	−	1.15409i	−0.985725	−	0.168363i	$-0.946152\pi$
$769$	−682483.	−	682483.i	−1.15409	−	1.15409i	−0.168363	−	0.985725i	$-0.553848\pi$
$770$	37067.0	+	249988.i	0.0625181	+	0.421636i
$771$			775980.i			1.30539i
$772$	156799.	−	156799.i	0.263093	−	0.263093i
$773$	235511.	−	235511.i	0.394141	−	0.394141i	−0.482019	−	0.876161i	$-0.660097\pi$
$773$	235511.	−	235511.i	0.394141	−	0.394141i	0.876161	+	0.482019i	$0.160097\pi$
$774$	−367768.	+	367768.i	−0.613892	+	0.613892i
$775$	406599.	−	760475.i	0.676960	−	1.26614i
$776$	−769328.			−1.27758
$777$	661350.			1.09544
$778$	−37708.9	−	37708.9i	−0.0622995	−	0.0622995i
$779$		−	41192.2i		−	0.0678797i
$780$	−198720.	+	359075.i	−0.326628	+	0.590196i
$781$	−99393.3			−0.162950
$782$	−4776.22	+	4776.22i	−0.00781036	+	0.00781036i
$783$		−	373309.i		−	0.608899i
$784$			133260.i			0.216804i
$785$	246239.	+	182646.i	0.399593	+	0.296395i
$786$	−161814.	−	161814.i	−0.261921	−	0.261921i
$787$	499795.	+	499795.i	0.806942	+	0.806942i	0.984170	−	0.177227i	$-0.0567128\pi$
$787$	499795.	+	499795.i	0.806942	+	0.806942i	−0.177227	+	0.984170i	$0.556713\pi$
$788$	341476.	+	341476.i	0.549931	+	0.549931i
$789$	238506.			0.383130
$790$	−28620.2	−	193021.i	−0.0458583	−	0.309279i
$791$	917089.	−	917089.i	1.46575	−	1.46575i
$792$	−197850.			−0.315417
$793$	871194.	−	116316.i	1.38538	−	0.184967i
$794$	490482.			0.778005
$795$	280139.	−	377677.i	0.443241	−	0.597566i
$796$	−61156.8			−0.0965203
$797$	−446000.			−0.702131			−0.351065	−	0.936351i	$-0.614180\pi$
$797$	−446000.			−0.702131			−0.351065	+	0.936351i	$0.614180\pi$
$798$	168467.	−	168467.i	0.264550	−	0.264550i
$799$	980.909	+	980.909i	0.00153651	+	0.00153651i
$800$	511411.	+	273433.i	0.799079	+	0.427239i
$801$	57886.9	−	57886.9i	0.0902225	−	0.0902225i
$802$		−	232122.i		−	0.360885i
$803$	−87548.8			−0.135775
$804$	−287364.	+	287364.i	−0.444549	+	0.444549i
$805$	−1.47779e6	+	219120.i	−2.28045	+	0.338135i
$806$	−641523.	+	85652.1i	−0.987511	+	0.131846i
$807$			283151.i			0.434782i
$808$	187604.	−	187604.i	0.287356	−	0.287356i
$809$	235436.			0.359729			0.179865	−	0.983691i	$-0.442434\pi$
$809$	235436.			0.359729			0.179865	+	0.983691i	$0.442434\pi$
$810$	80994.0	+	546242.i	0.123448	+	0.832559i
$811$	−75024.6	−	75024.6i	−0.114068	−	0.114068i	0.647769	−	0.761837i	$-0.275702\pi$
$811$	−75024.6	−	75024.6i	−0.114068	−	0.114068i	−0.761837	+	0.647769i	$0.775702\pi$
$812$	522904.	−	522904.i	0.793067	−	0.793067i
$813$	−537011.	−	537011.i	−0.812460	−	0.812460i
$814$	−83267.9	+	83267.9i	−0.125669	+	0.125669i
$815$	−71764.6	+	10640.9i	−0.108043	+	0.0160200i
$816$			1807.59i			0.00271468i
$817$	−248682.	−	248682.i	−0.372563	−	0.372563i
$818$	298028.			0.445400
$819$	−524437.	−	400893.i	−0.781853	−	0.597668i
$820$	11902.1	+	80270.2i	0.0177009	+	0.119379i
$821$	−167606.	−	167606.i	−0.248659	−	0.248659i	0.571761	−	0.820420i	$-0.306260\pi$
$821$	−167606.	−	167606.i	−0.248659	−	0.248659i	−0.820420	+	0.571761i	$0.806260\pi$
$822$			707003.i			1.04635i
$823$	258606.			0.381803			0.190901	−	0.981609i	$-0.438859\pi$
$823$	258606.			0.381803			0.190901	+	0.981609i	$0.438859\pi$
$824$	−743131.	−	743131.i	−1.09449	−	1.09449i
$825$	−180468.	+	337534.i	−0.265150	+	0.495918i
$826$	124000.	−	124000.i	0.181745	−	0.181745i
$827$	−622523.	−	622523.i	−0.910216	−	0.910216i	0.0860730	−	0.996289i	$-0.472568\pi$
$827$	−622523.	−	622523.i	−0.910216	−	0.910216i	−0.996289	+	0.0860730i	$0.972568\pi$
$828$		−	399358.i		−	0.582508i
$829$			599629.i			0.872517i	0.899821	+	0.436258i	$0.143697\pi$
$829$			599629.i			0.872517i	−0.899821	+	0.436258i	$0.856303\pi$
$830$	−562632.	−	417328.i	−0.816710	−	0.605789i
$831$		−	1.07456e6i		−	1.55607i
$832$	−77081.6	−	577331.i	−0.111354	−	0.834024i
$833$		−	6941.14i		−	0.0100032i
$834$	−332795.	−	332795.i	−0.478459	−	0.478459i
$835$	−736706.	+	109235.i	−1.05663	+	0.156671i
$836$		−	45681.4i		−	0.0653622i
$837$	284513.	−	284513.i	0.406118	−	0.406118i
$838$	−226887.	+	226887.i	−0.323089	+	0.323089i
$839$	−706041.	+	706041.i	−1.00301	+	1.00301i	−0.00301619	+	0.999995i	$0.500960\pi$
$839$	−706041.	+	706041.i	−1.00301	+	1.00301i	−0.999995	+	0.00301619i	$0.999040\pi$
$840$	−818879.	+	1.10399e6i	−1.16054	+	1.56462i
$841$	931452.			1.31695
$842$	−214089.			−0.301974
$843$	−53677.5	−	53677.5i	−0.0755331	−	0.0755331i
$844$		−	173572.i		−	0.243666i
$845$	260024.	−	664996.i	0.364167	−	0.931334i
$846$	76165.4			0.106418
$847$	586198.	−	586198.i	0.817104	−	0.817104i
$848$			87456.5i			0.121619i
$849$		−	1.22800e6i		−	1.70366i
$850$	4338.12	+	2319.44i	0.00600432	+	0.00321030i
$851$	−492234.	−	492234.i	−0.679693	−	0.679693i
$852$	−130524.	−	130524.i	−0.179809	−	0.179809i
$853$	423516.	+	423516.i	0.582065	+	0.582065i	0.935470	−	0.353405i	$-0.114976\pi$
$853$	423516.	+	423516.i	0.582065	+	0.582065i	−0.353405	+	0.935470i	$0.614976\pi$
$854$	1.00517e6			1.37824
$855$	146042.	−	21654.4i	0.199777	−	0.0296220i
$856$	−207638.	+	207638.i	−0.283374	+	0.283374i
$857$	−881968.			−1.20086			−0.600428	−	0.799679i	$-0.705003\pi$
$857$	−881968.			−1.20086			−0.600428	+	0.799679i	$0.705003\pi$
$858$	284738.	−	38016.4i	0.386786	−	0.0516412i
$859$	−793616.			−1.07553			−0.537767	−	0.843093i	$-0.680732\pi$
$859$	−793616.			−1.07553			−0.537767	+	0.843093i	$0.680732\pi$
$860$	556455.	+	412747.i	0.752373	+	0.558067i
$861$	−319003.			−0.430317
$862$	529073.			0.712034
$863$	137937.	−	137937.i	0.185208	−	0.185208i	−0.608413	−	0.793621i	$-0.708193\pi$
$863$	137937.	−	137937.i	0.185208	−	0.185208i	0.793621	+	0.608413i	$0.208193\pi$
$864$	191332.	+	191332.i	0.256307	+	0.256307i
$865$	92773.7	−	125075.i	0.123992	−	0.167163i
$866$	83117.3	−	83117.3i	0.110830	−	0.110830i
$867$			977829.i			1.30084i
$868$	797050.			1.05790
$869$	104001.	−	104001.i	0.137721	−	0.137721i
$870$	−1.02882e6	+	152549.i	−1.35926	+	0.201544i
$871$	429405.	−	561736.i	0.566019	−	0.740451i
$872$			1.35963e6i			1.78808i
$873$	452500.	−	452500.i	0.593732	−	0.593732i
$874$	−250775.			−0.328293
$875$	465011.	+	983639.i	0.607362	+	1.28475i
$876$	−114970.	−	114970.i	−0.149822	−	0.149822i
$877$	−498804.	+	498804.i	−0.648531	+	0.648531i	−0.952638	−	0.304107i	$-0.901642\pi$
$877$	−498804.	+	498804.i	−0.648531	+	0.648531i	0.304107	+	0.952638i	$0.401642\pi$
$878$	−575953.	−	575953.i	−0.747133	−	0.747133i
$879$	1.29030e6	−	1.29030e6i	1.66999	−	1.66999i
$880$	−10441.0	−	70416.4i	−0.0134827	−	0.0909303i
$881$		−	702325.i		−	0.904870i	−0.891797	−	0.452435i	$-0.850556\pi$
$881$		−	702325.i		−	0.904870i	0.891797	−	0.452435i	$-0.149444\pi$
$882$	−269482.	−	269482.i	−0.346412	−	0.346412i
$883$	−42952.3			−0.0550890			−0.0275445	−	0.999621i	$-0.508769\pi$
$883$	−42952.3			−0.0550890			−0.0275445	+	0.999621i	$0.508769\pi$
$884$	526.143	+	3940.74i	0.000673285	+	0.00504282i
$885$	262718.	−	38954.5i	0.335431	−	0.0497361i
$886$	−470219.	−	470219.i	−0.599009	−	0.599009i
$887$		−	653556.i		−	0.830683i	−0.909666	−	0.415342i	$-0.863662\pi$
$887$		−	653556.i		−	0.830683i	0.909666	−	0.415342i	$-0.136338\pi$
$888$	−640485.			−0.812238
$889$	−1.02415e6	−	1.02415e6i	−1.29587	−	1.29587i
$890$	81336.8	+	60331.0i	0.102685	+	0.0761659i
$891$	−294320.	+	294320.i	−0.370736	+	0.370736i
$892$	−284859.	−	284859.i	−0.358014	−	0.358014i
$893$			51502.4i			0.0645840i
$894$			558314.i			0.698559i
$895$	768880.	+	570311.i	0.959870	+	0.711977i
$896$			367653.i			0.457954i
$897$	224732.	+	1.68321e6i	0.279306	+	2.09196i
$898$			768469.i			0.952958i
$899$	1.24894e6	+	1.24894e6i	1.54534	+	1.54534i
$900$	−278332.	+	84394.9i	−0.343620	+	0.104191i
$901$		−	4555.37i		−	0.00561143i
$902$	40164.3	−	40164.3i	0.0493660	−	0.0493660i
$903$	−1.92586e6	+	1.92586e6i	−2.36183	+	2.36183i
$904$	−888156.	+	888156.i	−1.08681	+	1.08681i
$905$	−768068.	−	569709.i	−0.937783	−	0.695594i
$906$	310758.			0.378588
$907$	906967.			1.10250			0.551248	−	0.834341i	$-0.314152\pi$
$907$	906967.			1.10250			0.551248	+	0.834341i	$0.314152\pi$
$908$	−311127.	−	311127.i	−0.377369	−	0.377369i
$909$			220689.i			0.267087i
$910$	395403.	−	714470.i	0.477483	−	0.862782i
$911$	722252.			0.870266			0.435133	−	0.900366i	$-0.356701\pi$
$911$	722252.			0.870266			0.435133	+	0.900366i	$0.356701\pi$
$912$	−47453.5	+	47453.5i	−0.0570530	+	0.0570530i
$913$		−	528012.i		−	0.633435i
$914$		−	345381.i		−	0.413433i
$915$	1.22271e6	+	906934.i	1.46043	+	1.08326i
$916$	42311.0	+	42311.0i	0.0504269	+	0.0504269i
$917$	−346707.	−	346707.i	−0.412310	−	0.412310i
$918$	1623.00	+	1623.00i	0.00192590	+	0.00192590i
$919$	494776.			0.585838			0.292919	−	0.956137i	$-0.405373\pi$
$919$	494776.			0.585838			0.292919	+	0.956137i	$0.405373\pi$
$920$	1.43117e6	−	212207.i	1.69089	−	0.250717i
$921$	−1.01797e6	+	1.01797e6i	−1.20009	+	1.20009i
$922$	220205.			0.259039
$923$	255148.	+	195041.i	0.299494	+	0.228941i
$924$	−353768.			−0.414357
$925$	−239040.	+	447084.i	−0.279375	+	0.522523i
$926$	85239.4			0.0994074
$927$	874184.			1.01729
$928$	−839899.	+	839899.i	−0.975284	+	0.975284i
$929$	−462963.	−	462963.i	−0.536432	−	0.536432i	0.386047	−	0.922479i	$-0.373840\pi$
$929$	−462963.	−	462963.i	−0.536432	−	0.536432i	−0.922479	+	0.386047i	$0.873840\pi$
$930$	−900367.	−	667841.i	−1.04101	−	0.772160i
$931$	182222.	−	182222.i	0.210233	−	0.210233i
$932$		−	506568.i		−	0.583185i
$933$	1.13996e6			1.30956
$934$	224893.	−	224893.i	0.257799	−	0.257799i
$935$	543.843	+	3667.80i	0.000622085	+	0.00419548i
$936$	507891.	+	388245.i	0.579721	+	0.443153i
$937$		−	337190.i		−	0.384057i	−0.981389	−	0.192029i	$-0.938493\pi$
$937$		−	337190.i		−	0.384057i	0.981389	−	0.192029i	$-0.0615066\pi$
$938$	571782.	−	571782.i	0.649867	−	0.649867i
$939$	−511579.			−0.580205
$940$	−14881.1	−	100362.i	−0.0168415	−	0.113583i
$941$	−192025.	−	192025.i	−0.216859	−	0.216859i	0.590314	−	0.807174i	$-0.299004\pi$
$941$	−192025.	−	192025.i	−0.216859	−	0.216859i	−0.807174	+	0.590314i	$0.799004\pi$
$942$	281814.	−	281814.i	0.317585	−	0.317585i
$943$	237429.	+	237429.i	0.267000	+	0.267000i
$944$	−34928.3	+	34928.3i	−0.0391952	+	0.0391952i
$945$	74458.8	+	502167.i	0.0833782	+	0.562321i
$946$		−	484954.i		−	0.541899i
$947$	−23050.0	−	23050.0i	−0.0257023	−	0.0257023i	0.694139	−	0.719841i	$-0.255785\pi$
$947$	−23050.0	−	23050.0i	−0.0257023	−	0.0257023i	−0.719841	+	0.694139i	$0.755785\pi$
$948$	273152.			0.303939
$949$	224742.	+	171799.i	0.249547	+	0.190760i
$950$	52995.3	+	174777.i	0.0587205	+	0.193659i
$951$	845842.	+	845842.i	0.935251	+	0.935251i
$952$			13315.9i			0.0146925i
$953$	1.32264e6			1.45632			0.728159	−	0.685409i	$-0.240376\pi$
$953$	1.32264e6			1.45632			0.728159	+	0.685409i	$0.240376\pi$
$954$	−176857.	−	176857.i	−0.194324	−	0.194324i
$955$	869512.	−	1.17226e6i	0.953387	−	1.28533i
$956$	116583.	−	116583.i	0.127561	−	0.127561i
$957$	−554339.	−	554339.i	−0.605273	−	0.605273i
$958$		−	1.01408e6i		−	1.10494i
$959$			1.51485e6i			1.64714i
$960$	601016.	−	810276.i	0.652144	−	0.879205i
$961$			980212.i			1.06139i
$962$	377151.	−	50354.9i	0.407536	−	0.0544116i
$963$		−	244255.i		−	0.263385i
$964$	151171.	+	151171.i	0.162673	+	0.162673i
$965$	−661013.	+	98011.7i	−0.709831	+	0.105250i
$966$			1.94206e6i			2.08118i
$967$	−367434.	+	367434.i	−0.392940	+	0.392940i	−0.875734	−	0.482794i	$-0.839622\pi$
$967$	−367434.	+	367434.i	−0.392940	+	0.392940i	0.482794	+	0.875734i	$0.339622\pi$
$968$	−567704.	+	567704.i	−0.605859	+	0.605859i
$969$	2471.72	−	2471.72i	0.00263240	−	0.00263240i
$970$	635808.	+	471606.i	0.675744	+	0.501228i
$971$	976368.			1.03556			0.517780	−	0.855514i	$-0.326759\pi$
$971$	976368.			1.03556			0.517780	+	0.855514i	$0.326759\pi$
$972$	−577049.			−0.610774
$973$	−713057.	−	713057.i	−0.753180	−	0.753180i
$974$		−	31338.8i		−	0.0330342i
$975$	1.12562e6	−	512334.i	1.18408	−	0.538944i
$976$	−283135.			−0.297231
$977$	326605.	−	326605.i	0.342164	−	0.342164i	−0.515016	−	0.857180i	$-0.672214\pi$
$977$	326605.	−	326605.i	0.342164	−	0.342164i	0.857180	+	0.515016i	$0.172214\pi$
$978$			94310.6i			0.0986014i
$979$			76331.9i			0.0796418i
$980$	−302440.	+	407742.i	−0.314910	+	0.424555i
$981$	−799700.	−	799700.i	−0.830977	−	0.830977i
$982$	33008.4	+	33008.4i	0.0342296	+	0.0342296i
$983$	−517424.	−	517424.i	−0.535476	−	0.535476i	0.386721	−	0.922197i	$-0.373608\pi$
$983$	−517424.	−	517424.i	−0.535476	−	0.535476i	−0.922197	+	0.386721i	$0.873608\pi$
$984$	308939.			0.319067
$985$	−213449.	−	1.43955e6i	−0.219999	−	1.48373i
$986$	−7124.57	+	7124.57i	−0.00732833	+	0.00732833i
$987$	398848.			0.409424
$988$	−89641.4	+	117266.i	−0.0918322	+	0.120132i
$989$	2.86678e6			2.93091
$990$	163512.	+	121284.i	0.166832	+	0.123747i
$991$	−1.03885e6			−1.05781			−0.528904	−	0.848681i	$-0.677397\pi$
$991$	−1.03885e6			−1.05781			−0.528904	+	0.848681i	$0.677397\pi$
$992$	−1.28024e6			−1.30097
$993$	−1.01594e6	+	1.01594e6i	−1.03032	+	1.03032i
$994$	259711.	+	259711.i	0.262855	+	0.262855i
$995$	148022.	+	109794.i	0.149513	+	0.110901i
$996$	693391.	−	693391.i	0.698971	−	0.698971i
$997$			1.68107e6i			1.69121i	0.533812	+	0.845603i	$0.320759\pi$
$997$			1.68107e6i			1.69121i	−0.533812	+	0.845603i	$0.679241\pi$
$998$	−1.10167e6			−1.10609
$999$	−167266.	+	167266.i	−0.167601	+	0.167601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.17	yes	52
5.4	even	2	inner	65.5.g.a.34.10	✓	52
13.5	odd	4	inner	65.5.g.a.44.10	yes	52
65.44	odd	4	inner	65.5.g.a.44.17	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.10	✓	52	5.4	even	2	inner
65.5.g.a.34.17	yes	52	1.1	even	1	trivial
65.5.g.a.44.10	yes	52	13.5	odd	4	inner
65.5.g.a.44.17	yes	52	65.44	odd	4	inner

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.96266 - 1.96266i) q^{2} -11.7087i q^{3} +8.29597i q^{4} +(14.8937 - 20.0793i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(-49.2380 - 49.2380i) q^{7} +(47.6846 + 47.6846i) q^{8} -56.0939 q^{9} +O(q^{10})\)	\(q+(1.96266 - 1.96266i) q^{2} -11.7087i q^{3} +8.29597i q^{4} +(14.8937 - 20.0793i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(-49.2380 - 49.2380i) q^{7} +(47.6846 + 47.6846i) q^{8} -56.0939 q^{9} +(-10.1776 - 68.6399i) q^{10} +(36.9838 - 36.9838i) q^{11} +97.1351 q^{12} +(-167.514 + 22.3654i) q^{13} -193.275 q^{14} +(-235.103 - 174.386i) q^{15} +54.4414 q^{16} -2.83570 q^{17} +(-110.093 + 110.093i) q^{18} +(-74.4440 - 74.4440i) q^{19} +(166.577 + 123.558i) q^{20} +(-576.514 + 576.514i) q^{21} -145.173i q^{22} +858.183 q^{23} +(558.325 - 558.325i) q^{24} +(-181.357 - 598.109i) q^{25} +(-284.876 + 372.667i) q^{26} -291.618i q^{27} +(408.477 - 408.477i) q^{28} +1280.13 q^{29} +(-803.685 + 119.166i) q^{30} +(975.637 + 975.637i) q^{31} +(-656.104 + 656.104i) q^{32} +(-433.033 - 433.033i) q^{33} +(-5.56551 + 5.56551i) q^{34} +(-1722.00 + 255.330i) q^{35} -465.353i q^{36} +(-573.577 - 573.577i) q^{37} -292.216 q^{38} +(261.869 + 1961.37i) q^{39} +(1667.67 - 247.274i) q^{40} +(276.665 + 276.665i) q^{41} +2263.00i q^{42} +3340.52 q^{43} +(306.817 + 306.817i) q^{44} +(-835.445 + 1126.33i) q^{45} +(1684.32 - 1684.32i) q^{46} +(-345.914 - 345.914i) q^{47} -637.439i q^{48} +2447.77i q^{49} +(-1529.82 - 817.942i) q^{50} +33.2024i q^{51} +(-185.542 - 1389.69i) q^{52} +1606.43i q^{53} +(-572.346 - 572.346i) q^{54} +(-191.784 - 1293.43i) q^{55} -4695.79i q^{56} +(-871.644 + 871.644i) q^{57} +(2512.45 - 2512.45i) q^{58} +(-641.576 + 641.576i) q^{59} +(1446.70 - 1950.40i) q^{60} -5200.73 q^{61} +3829.68 q^{62} +(2761.95 + 2761.95i) q^{63} +3446.47i q^{64} +(-2045.81 + 3696.66i) q^{65} -1699.79 q^{66} +(-2958.39 + 2958.39i) q^{67} -23.5249i q^{68} -10048.2i q^{69} +(-2878.57 + 3880.82i) q^{70} +(-1343.74 - 1343.74i) q^{71} +(-2674.82 - 2674.82i) q^{72} +(-1183.61 - 1183.61i) q^{73} -2251.47 q^{74} +(-7003.09 + 2123.45i) q^{75} +(617.585 - 617.585i) q^{76} -3642.02 q^{77} +(4363.45 + 3335.53i) q^{78} +2812.08 q^{79} +(810.833 - 1093.15i) q^{80} -7958.08 q^{81} +1086.00 q^{82} +(7138.41 - 7138.41i) q^{83} +(-4782.74 - 4782.74i) q^{84} +(-42.2340 + 56.9389i) q^{85} +(6556.29 - 6556.29i) q^{86} -14988.7i q^{87} +3527.12 q^{88} +(-1031.96 + 1031.96i) q^{89} +(570.901 + 3850.28i) q^{90} +(9349.26 + 7146.81i) q^{91} +7119.46i q^{92} +(11423.4 - 11423.4i) q^{93} -1357.82 q^{94} +(-2603.53 + 386.039i) q^{95} +(7682.13 + 7682.13i) q^{96} +(-8066.83 + 8066.83i) q^{97} +(4804.12 + 4804.12i) q^{98} +(-2074.57 + 2074.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more