LMFDB - Embedded newform 175.5.g.c.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(43,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("175.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.63546 - 3.63546i) q^{2} +(-2.99367 - 2.99367i) q^{3} -10.4331i q^{4} -21.7667 q^{6} +(13.0958 - 13.0958i) q^{7} +(20.2382 + 20.2382i) q^{8} -63.0758i q^{9} +O(q^{10})$	\(q+(3.63546 - 3.63546i) q^{2} +(-2.99367 - 2.99367i) q^{3} -10.4331i q^{4} -21.7667 q^{6} +(13.0958 - 13.0958i) q^{7} +(20.2382 + 20.2382i) q^{8} -63.0758i q^{9} -220.093 q^{11} +(-31.2333 + 31.2333i) q^{12} +(-176.455 - 176.455i) q^{13} -95.2184i q^{14} +314.080 q^{16} +(101.380 - 101.380i) q^{17} +(-229.310 - 229.310i) q^{18} +152.947i q^{19} -78.4091 q^{21} +(-800.137 + 800.137i) q^{22} +(-596.607 - 596.607i) q^{23} -121.173i q^{24} -1282.99 q^{26} +(-431.316 + 431.316i) q^{27} +(-136.630 - 136.630i) q^{28} +801.994i q^{29} -175.829 q^{31} +(818.013 - 818.013i) q^{32} +(658.885 + 658.885i) q^{33} -737.127i q^{34} -658.077 q^{36} +(-423.393 + 423.393i) q^{37} +(556.032 + 556.032i) q^{38} +1056.50i q^{39} +919.754 q^{41} +(-285.053 + 285.053i) q^{42} +(-628.316 - 628.316i) q^{43} +2296.25i q^{44} -4337.88 q^{46} +(2208.69 - 2208.69i) q^{47} +(-940.253 - 940.253i) q^{48} -343.000i q^{49} -606.999 q^{51} +(-1840.97 + 1840.97i) q^{52} +(-554.147 - 554.147i) q^{53} +3136.06i q^{54} +530.072 q^{56} +(457.873 - 457.873i) q^{57} +(2915.61 + 2915.61i) q^{58} -3164.90i q^{59} +5297.88 q^{61} +(-639.219 + 639.219i) q^{62} +(-826.029 - 826.029i) q^{63} -922.421i q^{64} +4790.70 q^{66} +(1090.73 - 1090.73i) q^{67} +(-1057.71 - 1057.71i) q^{68} +3572.09i q^{69} -1622.41 q^{71} +(1276.54 - 1276.54i) q^{72} +(-1908.39 - 1908.39i) q^{73} +3078.45i q^{74} +1595.71 q^{76} +(-2882.29 + 2882.29i) q^{77} +(3840.85 + 3840.85i) q^{78} -5038.95i q^{79} -2526.71 q^{81} +(3343.73 - 3343.73i) q^{82} +(2986.51 + 2986.51i) q^{83} +818.050i q^{84} -4568.43 q^{86} +(2400.91 - 2400.91i) q^{87} +(-4454.28 - 4454.28i) q^{88} -9634.86i q^{89} -4621.64 q^{91} +(-6224.45 + 6224.45i) q^{92} +(526.374 + 526.374i) q^{93} -16059.2i q^{94} -4897.73 q^{96} +(2618.19 - 2618.19i) q^{97} +(-1246.96 - 1246.96i) q^{98} +13882.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) $ 24 * q - 20 * q^3 + 72 * q^6	$ 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) $ 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	3.63546	−	3.63546i	0.908864	−	0.908864i	−0.0873163	−	0.996181i	$-0.527829\pi$
$2$	3.63546	−	3.63546i	0.908864	−	0.908864i	0.996181	+	0.0873163i	$0.0278291\pi$
$3$	−2.99367	−	2.99367i	−0.332630	−	0.332630i	0.520954	−	0.853585i	$-0.325576\pi$
$3$	−2.99367	−	2.99367i	−0.332630	−	0.332630i	−0.853585	+	0.520954i	$0.825576\pi$
$4$		−	10.4331i		−	0.652069i
$5$		0			0
$5$		0			0
$6$	−21.7667			−0.604632
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	20.2382	+	20.2382i	0.316222	+	0.316222i
$9$		−	63.0758i		−	0.778714i
$10$		0			0
$11$	−220.093			−1.81895			−0.909473	−	0.415763i	$-0.863515\pi$
$11$	−220.093			−1.81895			−0.909473	+	0.415763i	$0.863515\pi$
$12$	−31.2333	+	31.2333i	−0.216898	+	0.216898i
$13$	−176.455	−	176.455i	−1.04411	−	1.04411i	−0.998981	−	0.0451321i	$-0.985629\pi$
$13$	−176.455	−	176.455i	−1.04411	−	1.04411i	−0.0451321	−	0.998981i	$-0.514371\pi$
$14$		−	95.2184i		−	0.485808i
$15$		0			0
$16$	314.080			1.22688
$17$	101.380	−	101.380i	0.350797	−	0.350797i	−0.509609	−	0.860406i	$-0.670210\pi$
$17$	101.380	−	101.380i	0.350797	−	0.350797i	0.860406	+	0.509609i	$0.170210\pi$
$18$	−229.310	−	229.310i	−0.707746	−	0.707746i
$19$			152.947i			0.423676i	0.977305	+	0.211838i	$0.0679449\pi$
$19$			152.947i			0.423676i	−0.977305	+	0.211838i	$0.932055\pi$
$20$		0			0
$21$	−78.4091			−0.177798
$22$	−800.137	+	800.137i	−1.65318	+	1.65318i
$23$	−596.607	−	596.607i	−1.12780	−	1.12780i	−0.990534	−	0.137266i	$-0.956168\pi$
$23$	−596.607	−	596.607i	−1.12780	−	1.12780i	−0.137266	−	0.990534i	$-0.543832\pi$
$24$		−	121.173i		−	0.210370i
$25$		0			0
$26$	−1282.99			−1.89791
$27$	−431.316	+	431.316i	−0.591654	+	0.591654i
$28$	−136.630	−	136.630i	−0.174273	−	0.174273i
$29$			801.994i			0.953619i	0.879007	+	0.476810i	$0.158207\pi$
$29$			801.994i			0.953619i	−0.879007	+	0.476810i	$0.841793\pi$
$30$		0			0
$31$	−175.829			−0.182965			−0.0914823	−	0.995807i	$-0.529160\pi$
$31$	−175.829			−0.182965			−0.0914823	+	0.995807i	$0.529160\pi$
$32$	818.013	−	818.013i	0.798841	−	0.798841i
$33$	658.885	+	658.885i	0.605037	+	0.605037i
$34$		−	737.127i		−	0.637653i
$35$		0			0
$36$	−658.077			−0.507775
$37$	−423.393	+	423.393i	−0.309271	+	0.309271i	−0.844627	−	0.535355i	$-0.820178\pi$
$37$	−423.393	+	423.393i	−0.309271	+	0.309271i	0.535355	+	0.844627i	$0.320178\pi$
$38$	556.032	+	556.032i	0.385064	+	0.385064i
$39$			1056.50i			0.694607i
$40$		0			0
$41$	919.754			0.547147			0.273573	−	0.961851i	$-0.411794\pi$
$41$	919.754			0.547147			0.273573	+	0.961851i	$0.411794\pi$
$42$	−285.053	+	285.053i	−0.161595	+	0.161595i
$43$	−628.316	−	628.316i	−0.339814	−	0.339814i	0.516483	−	0.856297i	$-0.327241\pi$
$43$	−628.316	−	628.316i	−0.339814	−	0.339814i	−0.856297	+	0.516483i	$0.827241\pi$
$44$			2296.25i			1.18608i
$45$		0			0
$46$	−4337.88			−2.05004
$47$	2208.69	−	2208.69i	0.999857	−	0.999857i	−0.000142581	−	1.00000i	$-0.500045\pi$
$47$	2208.69	−	2208.69i	0.999857	−	0.999857i	1.00000		0.000142581i	$4.53849e-5\pi$
$48$	−940.253	−	940.253i	−0.408096	−	0.408096i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	−606.999			−0.233371
$52$	−1840.97	+	1840.97i	−0.680833	+	0.680833i
$53$	−554.147	−	554.147i	−0.197275	−	0.197275i	0.601556	−	0.798831i	$-0.294548\pi$
$53$	−554.147	−	554.147i	−0.197275	−	0.197275i	−0.798831	+	0.601556i	$0.794548\pi$
$54$			3136.06i			1.07547i
$55$		0			0
$56$	530.072			0.169028
$57$	457.873	−	457.873i	0.140927	−	0.140927i
$58$	2915.61	+	2915.61i	0.866711	+	0.866711i
$59$		−	3164.90i		−	0.909192i	−0.890698	−	0.454596i	$-0.849784\pi$
$59$		−	3164.90i		−	0.909192i	0.890698	−	0.454596i	$-0.150216\pi$
$60$		0			0
$61$	5297.88			1.42378			0.711890	−	0.702291i	$-0.247840\pi$
$61$	5297.88			1.42378			0.711890	+	0.702291i	$0.247840\pi$
$62$	−639.219	+	639.219i	−0.166290	+	0.166290i
$63$	−826.029	−	826.029i	−0.208120	−	0.208120i
$64$		−	922.421i		−	0.225200i
$65$		0			0
$66$	4790.70			1.09979
$67$	1090.73	−	1090.73i	0.242979	−	0.242979i	−0.575102	−	0.818081i	$-0.695038\pi$
$67$	1090.73	−	1090.73i	0.242979	−	0.242979i	0.818081	+	0.575102i	$0.195038\pi$
$68$	−1057.71	−	1057.71i	−0.228744	−	0.228744i
$69$			3572.09i			0.750281i
$70$		0			0
$71$	−1622.41			−0.321842			−0.160921	−	0.986967i	$-0.551446\pi$
$71$	−1622.41			−0.321842			−0.160921	+	0.986967i	$0.551446\pi$
$72$	1276.54	−	1276.54i	0.246247	−	0.246247i
$73$	−1908.39	−	1908.39i	−0.358114	−	0.358114i	0.505003	−	0.863117i	$-0.331491\pi$
$73$	−1908.39	−	1908.39i	−0.358114	−	0.358114i	−0.863117	+	0.505003i	$0.831491\pi$
$74$			3078.45i			0.562171i
$75$		0			0
$76$	1595.71			0.276266
$77$	−2882.29	+	2882.29i	−0.486134	+	0.486134i
$78$	3840.85	+	3840.85i	0.631304	+	0.631304i
$79$		−	5038.95i		−	0.807395i	−0.914893	−	0.403697i	$-0.867725\pi$
$79$		−	5038.95i		−	0.807395i	0.914893	−	0.403697i	$-0.132275\pi$
$80$		0			0
$81$	−2526.71			−0.385110
$82$	3343.73	−	3343.73i	0.497282	−	0.497282i
$83$	2986.51	+	2986.51i	0.433519	+	0.433519i	0.889824	−	0.456305i	$-0.150827\pi$
$83$	2986.51	+	2986.51i	0.433519	+	0.433519i	−0.456305	+	0.889824i	$0.650827\pi$
$84$			818.050i			0.115937i
$85$		0			0
$86$	−4568.43			−0.617690
$87$	2400.91	−	2400.91i	0.317203	−	0.317203i
$88$	−4454.28	−	4454.28i	−0.575192	−	0.575192i
$89$		−	9634.86i		−	1.21637i	−0.793796	−	0.608185i	$-0.791898\pi$
$89$		−	9634.86i		−	1.21637i	0.793796	−	0.608185i	$-0.208102\pi$
$90$		0			0
$91$	−4621.64			−0.558102
$92$	−6224.45	+	6224.45i	−0.735403	+	0.735403i
$93$	526.374	+	526.374i	0.0608596	+	0.0608596i
$94$		−	16059.2i		−	1.81747i
$95$		0			0
$96$	−4897.73			−0.531437
$97$	2618.19	−	2618.19i	0.278265	−	0.278265i	−0.554151	−	0.832416i	$-0.686957\pi$
$97$	2618.19	−	2618.19i	0.278265	−	0.278265i	0.832416	+	0.554151i	$0.186957\pi$
$98$	−1246.96	−	1246.96i	−0.129838	−	0.129838i
$99$			13882.5i			1.41644i
$100$		0			0
$101$	17410.5			1.70674			0.853372	−	0.521303i	$-0.174554\pi$
$101$	17410.5			1.70674			0.853372	+	0.521303i	$0.174554\pi$
$102$	−2206.72	+	2206.72i	−0.212103	+	0.212103i
$103$	6794.71	+	6794.71i	0.640466	+	0.640466i	0.950670	−	0.310204i	$-0.100397\pi$
$103$	6794.71	+	6794.71i	0.640466	+	0.640466i	−0.310204	+	0.950670i	$0.600397\pi$
$104$		−	7142.28i		−	0.660344i
$105$		0			0
$106$	−4029.15			−0.358593
$107$	−6174.02	+	6174.02i	−0.539263	+	0.539263i	−0.923313	−	0.384049i	$-0.874529\pi$
$107$	−6174.02	+	6174.02i	−0.539263	+	0.539263i	0.384049	+	0.923313i	$0.374529\pi$
$108$	4499.96	+	4499.96i	0.385799	+	0.385799i
$109$		−	4665.43i		−	0.392680i	−0.980536	−	0.196340i	$-0.937094\pi$
$109$		−	4665.43i		−	0.392680i	0.980536	−	0.196340i	$-0.0629056\pi$
$110$		0			0
$111$	2535.00			0.205746
$112$	4113.13	−	4113.13i	0.327896	−	0.327896i
$113$	−10391.0	−	10391.0i	−0.813769	−	0.813769i	0.171427	−	0.985197i	$-0.445162\pi$
$113$	−10391.0	−	10391.0i	−0.813769	−	0.813769i	−0.985197	+	0.171427i	$0.945162\pi$
$114$		−	3329.16i		−	0.256168i
$115$		0			0
$116$	8367.28			0.621825
$117$	−11130.1	+	11130.1i	−0.813066	+	0.813066i
$118$	−11505.8	−	11505.8i	−0.826332	−	0.826332i
$119$		−	2655.31i		−	0.187509i
$120$		0			0
$121$	33799.7			2.30857
$122$	19260.2	−	19260.2i	1.29402	−	1.29402i
$123$	−2753.44	−	2753.44i	−0.181998	−	0.181998i
$124$			1834.44i			0.119306i
$125$		0			0
$126$	−6005.98			−0.378306
$127$	4261.99	−	4261.99i	0.264244	−	0.264244i	−0.562532	−	0.826776i	$-0.690173\pi$
$127$	4261.99	−	4261.99i	0.264244	−	0.264244i	0.826776	+	0.562532i	$0.190173\pi$
$128$	9734.78	+	9734.78i	0.594164	+	0.594164i
$129$			3761.95i			0.226065i
$130$		0			0
$131$	−4451.64			−0.259404			−0.129702	−	0.991553i	$-0.541402\pi$
$131$	−4451.64			−0.259404			−0.129702	+	0.991553i	$0.541402\pi$
$132$	6874.21	−	6874.21i	0.394525	−	0.394525i
$133$	2002.96	+	2002.96i	0.113232	+	0.113232i
$134$		−	7930.63i		−	0.441670i
$135$		0			0
$136$	4103.51			0.221860
$137$	180.184	−	180.184i	0.00960008	−	0.00960008i	−0.702290	−	0.711891i	$-0.747839\pi$
$137$	180.184	−	180.184i	0.00960008	−	0.00960008i	0.711891	+	0.702290i	$0.247839\pi$
$138$	12986.2	+	12986.2i	0.681904	+	0.681904i
$139$			23370.3i			1.20958i	0.796384	+	0.604791i	$0.206743\pi$
$139$			23370.3i			1.20958i	−0.796384	+	0.604791i	$0.793257\pi$
$140$		0			0
$141$	−13224.2			−0.665166
$142$	−5898.19	+	5898.19i	−0.292511	+	0.292511i
$143$	38836.5	+	38836.5i	1.89919	+	1.89919i
$144$		−	19810.9i		−	0.955385i
$145$		0			0
$146$	−13875.7			−0.650955
$147$	−1026.83	+	1026.83i	−0.0475186	+	0.0475186i
$148$	4417.30	+	4417.30i	0.201666	+	0.201666i
$149$			26094.3i			1.17537i	0.809091	+	0.587684i	$0.199960\pi$
$149$			26094.3i			1.17537i	−0.809091	+	0.587684i	$0.800040\pi$
$150$		0			0
$151$	−762.534			−0.0334430			−0.0167215	−	0.999860i	$-0.505323\pi$
$151$	−762.534			−0.0334430			−0.0167215	+	0.999860i	$0.505323\pi$
$152$	−3095.38	+	3095.38i	−0.133976	+	0.133976i
$153$	−6394.65	−	6394.65i	−0.273170	−	0.273170i
$154$			20956.9i			0.883659i
$155$		0			0
$156$	11022.5			0.452932
$157$	25099.1	−	25099.1i	1.01826	−	1.01826i	0.0184285	−	0.999830i	$-0.494134\pi$
$157$	25099.1	−	25099.1i	1.01826	−	1.01826i	0.999830	−	0.0184285i	$-0.00586630\pi$
$158$	−18318.9	−	18318.9i	−0.733812	−	0.733812i
$159$			3317.87i			0.131240i
$160$		0			0
$161$	−15626.1			−0.602835
$162$	−9185.73	+	9185.73i	−0.350013	+	0.350013i
$163$	1589.95	+	1589.95i	0.0598424	+	0.0598424i	0.736395	−	0.676552i	$-0.236527\pi$
$163$	1589.95	+	1589.95i	0.0598424	+	0.0598424i	−0.676552	+	0.736395i	$0.736527\pi$
$164$		−	9595.88i		−	0.356777i
$165$		0			0
$166$	21714.7			0.788020
$167$	11320.6	−	11320.6i	0.405917	−	0.405917i	−0.474395	−	0.880312i	$-0.657333\pi$
$167$	11320.6	−	11320.6i	0.405917	−	0.405917i	0.880312	+	0.474395i	$0.157333\pi$
$168$	−1586.86	−	1586.86i	−0.0562238	−	0.0562238i
$169$			33711.8i			1.18034i
$170$		0			0
$171$	9647.26			0.329922
$172$	−6555.28	+	6555.28i	−0.221582	+	0.221582i
$173$	−10012.9	−	10012.9i	−0.334555	−	0.334555i	0.519758	−	0.854313i	$-0.326022\pi$
$173$	−10012.9	−	10012.9i	−0.334555	−	0.334555i	−0.854313	+	0.519758i	$0.826022\pi$
$174$		−	17456.8i		−	0.576588i
$175$		0			0
$176$	−69126.7			−2.23162
$177$	−9474.66	+	9474.66i	−0.302425	+	0.302425i
$178$	−35027.1	−	35027.1i	−1.10551	−	1.10551i
$179$			20172.5i			0.629584i	0.949161	+	0.314792i	$0.101935\pi$
$179$			20172.5i			0.629584i	−0.949161	+	0.314792i	$0.898065\pi$
$180$		0			0
$181$	17601.7			0.537276			0.268638	−	0.963241i	$-0.413427\pi$
$181$	17601.7			0.537276			0.268638	+	0.963241i	$0.413427\pi$
$182$	−16801.8	+	16801.8i	−0.507239	+	0.507239i
$183$	−15860.1	−	15860.1i	−0.473592	−	0.473592i
$184$		−	24148.5i		−	0.713272i
$185$		0			0
$186$	3827.22			0.110626
$187$	−22313.0	+	22313.0i	−0.638080	+	0.638080i
$188$	−23043.4	−	23043.4i	−0.651976	−	0.651976i
$189$			11296.9i			0.316252i
$190$		0			0
$191$	−65848.1			−1.80500			−0.902499	−	0.430692i	$-0.858270\pi$
$191$	−65848.1			−1.80500			−0.902499	+	0.430692i	$0.858270\pi$
$192$	−2761.43	+	2761.43i	−0.0749085	+	0.0749085i
$193$	7771.80	+	7771.80i	0.208645	+	0.208645i	0.803691	−	0.595047i	$-0.202866\pi$
$193$	7771.80	+	7771.80i	0.208645	+	0.208645i	−0.595047	+	0.803691i	$0.702866\pi$
$194$		−	19036.7i		−	0.505810i
$195$		0			0
$196$	−3578.55			−0.0931527
$197$	−37777.3	+	37777.3i	−0.973416	+	0.973416i	−0.999656	−	0.0262392i	$-0.991647\pi$
$197$	−37777.3	+	37777.3i	−0.973416	+	0.973416i	0.0262392	+	0.999656i	$0.491647\pi$
$198$	50469.3	+	50469.3i	1.28735	+	1.28735i
$199$		−	20867.2i		−	0.526937i	−0.964668	−	0.263469i	$-0.915133\pi$
$199$		−	20867.2i		−	0.526937i	0.964668	−	0.263469i	$-0.0848666\pi$
$200$		0			0
$201$	−6530.60			−0.161644
$202$	63295.1	−	63295.1i	1.55120	−	1.55120i
$203$	10502.8	+	10502.8i	0.254866	+	0.254866i
$204$			6332.88i			0.152174i
$205$		0			0
$206$	49403.7			1.16419
$207$	−37631.5	+	37631.5i	−0.878234	+	0.878234i
$208$	−55421.0	−	55421.0i	−1.28100	−	1.28100i
$209$		−	33662.5i		−	0.770643i
$210$		0			0
$211$	6527.71			0.146621			0.0733104	−	0.997309i	$-0.476644\pi$
$211$	6527.71			0.146621			0.0733104	+	0.997309i	$0.476644\pi$
$212$	−5781.47	+	5781.47i	−0.128637	+	0.128637i
$213$	4856.95	+	4856.95i	0.107054	+	0.107054i
$214$			44890.8i			0.980234i
$215$		0			0
$216$	−17458.1			−0.374189
$217$	−2302.62	+	2302.62i	−0.0488994	+	0.0488994i
$218$	−16961.0	−	16961.0i	−0.356893	−	0.356893i
$219$			11426.2i			0.238239i
$220$		0			0
$221$	−35778.1			−0.732543
$222$	9215.87	−	9215.87i	0.186995	−	0.186995i
$223$	−49365.9	−	49365.9i	−0.992698	−	0.992698i	0.00727547	−	0.999974i	$-0.497684\pi$
$223$	−49365.9	−	49365.9i	−0.992698	−	0.992698i	−0.999974	+	0.00727547i	$0.997684\pi$
$224$		−	21425.1i		−	0.426998i
$225$		0			0
$226$	−75552.2			−1.47921
$227$	−60511.8	+	60511.8i	−1.17433	+	1.17433i	−0.193158	+	0.981168i	$0.561873\pi$
$227$	−60511.8	+	60511.8i	−1.17433	+	1.17433i	−0.981168	+	0.193158i	$0.938127\pi$
$228$	−4777.03	−	4777.03i	−0.0918943	−	0.0918943i
$229$		−	83.0802i		−	0.00158426i	−1.00000		0.000792130i	$-0.999748\pi$
$229$		−	83.0802i		−	0.00158426i	1.00000		0.000792130i	$-0.000252143\pi$
$230$		0			0
$231$	17257.3			0.323406
$232$	−16230.9	+	16230.9i	−0.301556	+	0.301556i
$233$	−26936.3	−	26936.3i	−0.496166	−	0.496166i	0.414076	−	0.910242i	$-0.364105\pi$
$233$	−26936.3	−	26936.3i	−0.496166	−	0.496166i	−0.910242	+	0.414076i	$0.864105\pi$
$234$			80925.7i			1.47793i
$235$		0			0
$236$	−33019.7			−0.592855
$237$	−15085.0	+	15085.0i	−0.268564	+	0.268564i
$238$	−9653.27	−	9653.27i	−0.170420	−	0.170420i
$239$		−	2964.31i		−	0.0518953i	−0.999663	−	0.0259476i	$-0.991740\pi$
$239$		−	2964.31i		−	0.0518953i	0.999663	−	0.0259476i	$-0.00826032\pi$
$240$		0			0
$241$	−4980.66			−0.0857537			−0.0428769	−	0.999080i	$-0.513652\pi$
$241$	−4980.66			−0.0857537			−0.0428769	+	0.999080i	$0.513652\pi$
$242$	122877.	−	122877.i	2.09817	−	2.09817i
$243$	42500.7	+	42500.7i	0.719753	+	0.719753i
$244$		−	55273.3i		−	0.928402i
$245$		0			0
$246$	−20020.0			−0.330822
$247$	26988.3	−	26988.3i	0.442365	−	0.442365i
$248$	−3558.47	−	3558.47i	−0.0578575	−	0.0578575i
$249$		−	17881.3i		−	0.288403i
$250$		0			0
$251$	51772.6			0.821775			0.410887	−	0.911686i	$-0.365219\pi$
$251$	51772.6			0.821775			0.410887	+	0.911686i	$0.365219\pi$
$252$	−8618.04	+	8618.04i	−0.135709	+	0.135709i
$253$	131309.	+	131309.i	2.05141	+	2.05141i
$254$		−	30988.5i		−	0.480323i
$255$		0			0
$256$	85539.5			1.30523
$257$	−7872.26	+	7872.26i	−0.119188	+	0.119188i	−0.764185	−	0.644997i	$-0.776859\pi$
$257$	−7872.26	+	7872.26i	−0.119188	+	0.119188i	0.644997	+	0.764185i	$0.276859\pi$
$258$	13676.4	+	13676.4i	0.205462	+	0.205462i
$259$			11089.3i			0.165313i
$260$		0			0
$261$	50586.4			0.742597
$262$	−16183.7	+	16183.7i	−0.235763	+	0.235763i
$263$	−47259.4	−	47259.4i	−0.683246	−	0.683246i	0.277484	−	0.960730i	$-0.410499\pi$
$263$	−47259.4	−	47259.4i	−0.683246	−	0.683246i	−0.960730	+	0.277484i	$0.910499\pi$
$264$			26669.3i			0.382652i
$265$		0			0
$266$	14563.4			0.205825
$267$	−28843.6	+	28843.6i	−0.404601	+	0.404601i
$268$	−11379.7	−	11379.7i	−0.158439	−	0.158439i
$269$		−	129888.i		−	1.79500i	−0.441010	−	0.897502i	$-0.645380\pi$
$269$		−	129888.i		−	1.79500i	0.441010	−	0.897502i	$-0.354620\pi$
$270$		0			0
$271$	−55592.0			−0.756962			−0.378481	−	0.925609i	$-0.623553\pi$
$271$	−55592.0			−0.756962			−0.378481	+	0.925609i	$0.623553\pi$
$272$	31841.5	−	31841.5i	0.430384	−	0.430384i
$273$	13835.7	+	13835.7i	0.185642	+	0.185642i
$274$		−	1310.10i		−	0.0174503i
$275$		0			0
$276$	37268.0			0.489235
$277$	73039.6	−	73039.6i	0.951916	−	0.951916i	−0.0469796	−	0.998896i	$-0.514960\pi$
$277$	73039.6	−	73039.6i	0.951916	−	0.951916i	0.998896	+	0.0469796i	$0.0149596\pi$
$278$	84961.9	+	84961.9i	1.09935	+	1.09935i
$279$			11090.6i			0.142477i
$280$		0			0
$281$	86967.1			1.10139			0.550696	−	0.834706i	$-0.314362\pi$
$281$	86967.1			1.10139			0.550696	+	0.834706i	$0.314362\pi$
$282$	−48075.9	+	48075.9i	−0.604545	+	0.604545i
$283$	−16152.8	−	16152.8i	−0.201685	−	0.201685i	0.599037	−	0.800722i	$-0.295550\pi$
$283$	−16152.8	−	16152.8i	−0.201685	−	0.201685i	−0.800722	+	0.599037i	$0.795550\pi$
$284$			16926.7i			0.209863i
$285$		0			0
$286$	282377.			3.45220
$287$	12044.9	−	12044.9i	0.146231	−	0.146231i
$288$	−51596.9	−	51596.9i	−0.622069	−	0.622069i
$289$			62965.1i			0.753883i
$290$		0			0
$291$	−15676.0			−0.185119
$292$	−19910.4	+	19910.4i	−0.233515	+	0.233515i
$293$	5309.17	+	5309.17i	0.0618431	+	0.0618431i	0.737352	−	0.675509i	$-0.236076\pi$
$293$	5309.17	+	5309.17i	0.0618431	+	0.0618431i	−0.675509	+	0.737352i	$0.736076\pi$
$294$			7465.99i			0.0863759i
$295$		0			0
$296$	−17137.4			−0.195597
$297$	94929.4	−	94929.4i	1.07619	−	1.07619i
$298$	94864.9	+	94864.9i	1.06825	+	1.06825i
$299$			210549.i			2.35510i
$300$		0			0
$301$	−16456.6			−0.181638
$302$	−2772.16	+	2772.16i	−0.0303952	+	0.0303952i
$303$	−52121.3	−	52121.3i	−0.567715	−	0.567715i
$304$			48037.6i			0.519797i
$305$		0			0
$306$	−46494.9			−0.496550
$307$	41603.9	−	41603.9i	0.441425	−	0.441425i	−0.451065	−	0.892491i	$-0.648956\pi$
$307$	41603.9	−	41603.9i	0.441425	−	0.441425i	0.892491	+	0.451065i	$0.148956\pi$
$308$	30071.2	+	30071.2i	0.316993	+	0.316993i
$309$		−	40682.3i		−	0.426077i
$310$		0			0
$311$	−112022.			−1.15819			−0.579096	−	0.815259i	$-0.696594\pi$
$311$	−112022.			−1.15819			−0.579096	+	0.815259i	$0.696594\pi$
$312$	−21381.6	+	21381.6i	−0.219650	+	0.219650i
$313$	59284.2	+	59284.2i	0.605133	+	0.605133i	0.941670	−	0.336537i	$-0.109256\pi$
$313$	59284.2	+	59284.2i	0.605133	+	0.605133i	−0.336537	+	0.941670i	$0.609256\pi$
$314$		−	182493.i		−	1.85092i
$315$		0			0
$316$	−52571.9			−0.526477
$317$	−12194.9	+	12194.9i	−0.121355	+	0.121355i	−0.765176	−	0.643821i	$-0.777348\pi$
$317$	−12194.9	+	12194.9i	−0.121355	+	0.121355i	0.643821	+	0.765176i	$0.277348\pi$
$318$	12062.0	+	12062.0i	0.119279	+	0.119279i
$319$		−	176513.i		−	1.73458i
$320$		0			0
$321$	36966.0			0.358751
$322$	−56807.9	+	56807.9i	−0.547895	+	0.547895i
$323$	15505.8	+	15505.8i	0.148624	+	0.148624i
$324$			26361.4i			0.251118i
$325$		0			0
$326$	11560.4			0.108777
$327$	−13966.8	+	13966.8i	−0.130617	+	0.130617i
$328$	18614.2	+	18614.2i	0.173020	+	0.173020i
$329$		−	57849.0i		−	0.534446i
$330$		0			0
$331$	−31443.4			−0.286995			−0.143497	−	0.989651i	$-0.545835\pi$
$331$	−31443.4			−0.286995			−0.143497	+	0.989651i	$0.545835\pi$
$332$	31158.6	−	31158.6i	0.282684	−	0.282684i
$333$	26705.8	+	26705.8i	0.240834	+	0.240834i
$334$		−	82311.2i		−	0.737846i
$335$		0			0
$336$	−24626.7			−0.218136
$337$	39492.6	−	39492.6i	0.347741	−	0.347741i	−0.511527	−	0.859267i	$-0.670920\pi$
$337$	39492.6	−	39492.6i	0.347741	−	0.347741i	0.859267	+	0.511527i	$0.170920\pi$
$338$	122558.	+	122558.i	1.07277	+	1.07277i
$339$			62214.6i			0.541369i
$340$		0			0
$341$	38698.6			0.332803
$342$	35072.2	−	35072.2i	0.299855	−	0.299855i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$		−	25432.0i		−	0.214914i
$345$		0			0
$346$	−72802.9			−0.608130
$347$	93020.1	−	93020.1i	0.772534	−	0.772534i	−0.206015	−	0.978549i	$-0.566049\pi$
$347$	93020.1	−	93020.1i	0.772534	−	0.772534i	0.978549	+	0.206015i	$0.0660494\pi$
$348$	−25048.9	−	25048.9i	−0.206838	−	0.206838i
$349$			158624.i			1.30232i	0.758939	+	0.651162i	$0.225718\pi$
$349$			158624.i			1.30232i	−0.758939	+	0.651162i	$0.774282\pi$
$350$		0			0
$351$	152216.			1.23551
$352$	−180039.	+	180039.i	−1.45305	+	1.45305i
$353$	−153311.	−	153311.i	−1.23034	−	1.23034i	−0.963834	−	0.266502i	$-0.914132\pi$
$353$	−153311.	−	153311.i	−1.23034	−	1.23034i	−0.266502	−	0.963834i	$-0.585868\pi$
$354$			68889.5i			0.549726i
$355$		0			0
$356$	−100521.			−0.793156
$357$	−7949.13	+	7949.13i	−0.0623711	+	0.0623711i
$358$	73336.2	+	73336.2i	0.572206	+	0.572206i
$359$		−	17883.8i		−	0.138762i	−0.997590	−	0.0693811i	$-0.977898\pi$
$359$		−	17883.8i		−	0.138762i	0.997590	−	0.0693811i	$-0.0221024\pi$
$360$		0			0
$361$	106928.			0.820499
$362$	63990.2	−	63990.2i	0.488311	−	0.488311i
$363$	−101185.	−	101185.i	−0.767899	−	0.767899i
$364$			48218.0i			0.363921i
$365$		0			0
$366$	−115318.			−0.860862
$367$	−157754.	+	157754.i	−1.17125	+	1.17125i	−0.189337	+	0.981912i	$0.560634\pi$
$367$	−157754.	+	157754.i	−1.17125	+	1.17125i	−0.981912	+	0.189337i	$0.939366\pi$
$368$	−187382.	−	187382.i	−1.38367	−	1.38367i
$369$		−	58014.2i		−	0.426071i
$370$		0			0
$371$	−14514.0			−0.105448
$372$	5491.72	−	5491.72i	0.0396846	−	0.0396846i
$373$	−48628.6	−	48628.6i	−0.349522	−	0.349522i	0.510410	−	0.859931i	$-0.329494\pi$
$373$	−48628.6	−	48628.6i	−0.349522	−	0.349522i	−0.859931	+	0.510410i	$0.829494\pi$
$374$			162236.i			1.15986i
$375$		0			0
$376$	89399.8			0.632355
$377$	141516.	−	141516.i	0.995687	−	0.995687i
$378$	41069.2	+	41069.2i	0.287431	+	0.287431i
$379$		−	156941.i		−	1.09259i	−0.837593	−	0.546295i	$-0.816038\pi$
$379$		−	156941.i		−	1.09259i	0.837593	−	0.546295i	$-0.183962\pi$
$380$		0			0
$381$	−25518.0			−0.175791
$382$	−239388.	+	239388.i	−1.64050	+	1.64050i
$383$	−83467.3	−	83467.3i	−0.569009	−	0.569009i	0.362842	−	0.931851i	$-0.381806\pi$
$383$	−83467.3	−	83467.3i	−0.569009	−	0.569009i	−0.931851	+	0.362842i	$0.881806\pi$
$384$		−	58285.5i		−	0.395274i
$385$		0			0
$386$	56508.1			0.379259
$387$	−39631.6	+	39631.6i	−0.264618	+	0.264618i
$388$	−27315.9	−	27315.9i	−0.181448	−	0.181448i
$389$		−	233893.i		−	1.54567i	−0.634605	−	0.772837i	$-0.718837\pi$
$389$		−	233893.i		−	1.54567i	0.634605	−	0.772837i	$-0.281163\pi$
$390$		0			0
$391$	−120968.			−0.791258
$392$	6941.71	−	6941.71i	0.0451746	−	0.0451746i
$393$	13326.7	+	13326.7i	0.0862857	+	0.0862857i
$394$			274676.i			1.76941i
$395$		0			0
$396$	144838.			0.923616
$397$	−66916.0	+	66916.0i	−0.424570	+	0.424570i	−0.886774	−	0.462204i	$-0.847059\pi$
$397$	−66916.0	+	66916.0i	−0.424570	+	0.424570i	0.462204	+	0.886774i	$0.347059\pi$
$398$	−75862.0	−	75862.0i	−0.478915	−	0.478915i
$399$		−	11992.4i		−	0.0753289i
$400$		0			0
$401$	−236024.			−1.46780			−0.733900	−	0.679257i	$-0.762302\pi$
$401$	−236024.			−1.46780			−0.733900	+	0.679257i	$0.762302\pi$
$402$	−23741.7	+	23741.7i	−0.146913	+	0.146913i
$403$	31025.9	+	31025.9i	0.191036	+	0.191036i
$404$		−	181645.i		−	1.11291i
$405$		0			0
$406$	76364.6			0.463276
$407$	93185.5	−	93185.5i	0.562548	−	0.562548i
$408$	−12284.6	−	12284.6i	−0.0737972	−	0.0737972i
$409$		−	9374.36i		−	0.0560396i	−0.999607	−	0.0280198i	$-0.991080\pi$
$409$		−	9374.36i		−	0.0560396i	0.999607	−	0.0280198i	$-0.00892015\pi$
$410$		0			0
$411$	−1078.82			−0.00638656
$412$	70889.9	−	70889.9i	0.417628	−	0.417628i
$413$	−41446.9	−	41446.9i	−0.242992	−	0.242992i
$414$			273615.i			1.59639i
$415$		0			0
$416$	−288685.			−1.66816
$417$	69963.2	−	69963.2i	0.402344	−	0.402344i
$418$	−122378.	−	122378.i	−0.700410	−	0.700410i
$419$		−	265821.i		−	1.51412i	−0.653343	−	0.757062i	$-0.726634\pi$
$419$		−	265821.i		−	1.51412i	0.653343	−	0.757062i	$-0.273366\pi$
$420$		0			0
$421$	−222521.			−1.25547			−0.627737	−	0.778425i	$-0.716019\pi$
$421$	−222521.			−1.25547			−0.627737	+	0.778425i	$0.716019\pi$
$422$	23731.2	−	23731.2i	0.133258	−	0.133258i
$423$	−139315.	−	139315.i	−0.778603	−	0.778603i
$424$		−	22429.9i		−	0.124766i
$425$		0			0
$426$	35314.5			0.194596
$427$	69380.0	−	69380.0i	0.380521	−	0.380521i
$428$	64414.2	+	64414.2i	0.351637	+	0.351637i
$429$		−	232527.i		−	1.26345i
$430$		0			0
$431$	259316.			1.39597			0.697983	−	0.716115i	$-0.254081\pi$
$431$	259316.			1.39597			0.697983	+	0.716115i	$0.254081\pi$
$432$	−135468.	+	135468.i	−0.725886	+	0.725886i
$433$	187941.	+	187941.i	1.00241	+	1.00241i	0.999997	+	0.00241596i	$0.000769026\pi$
$433$	187941.	+	187941.i	1.00241	+	1.00241i	0.00241596	+	0.999997i	$0.499231\pi$
$434$			16742.2i			0.0888858i
$435$		0			0
$436$	−48674.9			−0.256054
$437$	91249.1	−	91249.1i	0.477822	−	0.477822i
$438$	41539.4	+	41539.4i	0.216527	+	0.216527i
$439$			295109.i			1.53128i	0.643272	+	0.765638i	$0.277576\pi$
$439$			295109.i			1.53128i	−0.643272	+	0.765638i	$0.722424\pi$
$440$		0			0
$441$	−21635.0			−0.111245
$442$	−130070.	+	130070.i	−0.665782	+	0.665782i
$443$	7579.35	+	7579.35i	0.0386211	+	0.0386211i	0.726154	−	0.687533i	$-0.241306\pi$
$443$	7579.35	+	7579.35i	0.0386211	+	0.0386211i	−0.687533	+	0.726154i	$0.741306\pi$
$444$		−	26447.9i		−	0.134161i
$445$		0			0
$446$	−358935.			−1.80446
$447$	78117.9	−	78117.9i	0.390963	−	0.390963i
$448$	−12079.8	−	12079.8i	−0.0601873	−	0.0601873i
$449$			308572.i			1.53061i	0.643669	+	0.765304i	$0.277411\pi$
$449$			308572.i			1.53061i	−0.643669	+	0.765304i	$0.722589\pi$
$450$		0			0
$451$	−202431.			−0.995231
$452$	−108411.	+	108411.i	−0.530634	+	0.530634i
$453$	2282.78	+	2282.78i	0.0111242	+	0.0111242i
$454$			439976.i			2.13460i
$455$		0			0
$456$	18533.1			0.0891288
$457$	47861.1	−	47861.1i	0.229166	−	0.229166i	−0.583178	−	0.812344i	$-0.698191\pi$
$457$	47861.1	−	47861.1i	0.229166	−	0.229166i	0.812344	+	0.583178i	$0.198191\pi$
$458$	−302.034	−	302.034i	−0.00143988	−	0.00143988i
$459$			87453.8i			0.415101i
$460$		0			0
$461$	251532.			1.18356			0.591782	−	0.806098i	$-0.298425\pi$
$461$	251532.			1.18356			0.591782	+	0.806098i	$0.298425\pi$
$462$	62738.0	−	62738.0i	0.293932	−	0.293932i
$463$	67580.4	+	67580.4i	0.315252	+	0.315252i	0.846940	−	0.531688i	$-0.178442\pi$
$463$	67580.4	+	67580.4i	0.315252	+	0.315252i	−0.531688	+	0.846940i	$0.678442\pi$
$464$			251890.i			1.16997i
$465$		0			0
$466$	−195852.			−0.901895
$467$	−172621.	+	172621.i	−0.791517	+	0.791517i	−0.981741	−	0.190223i	$-0.939079\pi$
$467$	−172621.	+	172621.i	−0.791517	+	0.791517i	0.190223	+	0.981741i	$0.439079\pi$
$468$	116121.	+	116121.i	0.530175	+	0.530175i
$469$		−	28568.1i		−	0.129878i
$470$		0			0
$471$	−150277.			−0.677407
$472$	64051.9	−	64051.9i	0.287507	−	0.287507i
$473$	138288.	+	138288.i	0.618103	+	0.618103i
$474$			109681.i			0.488176i
$475$		0			0
$476$	−27703.1			−0.122269
$477$	−34953.3	+	34953.3i	−0.153621	+	0.153621i
$478$	−10776.6	−	10776.6i	−0.0471658	−	0.0471658i
$479$			58984.8i			0.257080i	0.991704	+	0.128540i	$0.0410291\pi$
$479$			58984.8i			0.257080i	−0.991704	+	0.128540i	$0.958971\pi$
$480$		0			0
$481$	149420.			0.645829
$482$	−18107.0	+	18107.0i	−0.0779385	+	0.0779385i
$483$	46779.4	+	46779.4i	0.200521	+	0.200521i
$484$		−	352636.i		−	1.50534i
$485$		0			0
$486$	309019.			1.30832
$487$	145300.	−	145300.i	0.612645	−	0.612645i	−0.330989	−	0.943635i	$-0.607382\pi$
$487$	145300.	−	145300.i	0.612645	−	0.612645i	0.943635	+	0.330989i	$0.107382\pi$
$488$	107220.	+	107220.i	0.450231	+	0.450231i
$489$		−	9519.60i		−	0.0398108i
$490$		0			0
$491$	141204.			0.585712			0.292856	−	0.956157i	$-0.405394\pi$
$491$	141204.			0.585712			0.292856	+	0.956157i	$0.405394\pi$
$492$	−28726.9	+	28726.9i	−0.118675	+	0.118675i
$493$	81306.3	+	81306.3i	0.334527	+	0.334527i
$494$		−	196229.i		−	0.804100i
$495$		0			0
$496$	−55224.4			−0.224475
$497$	−21246.7	+	21246.7i	−0.0860159	+	0.0860159i
$498$	−65006.6	−	65006.6i	−0.262119	−	0.262119i
$499$		−	105864.i		−	0.425155i	−0.977144	−	0.212578i	$-0.931814\pi$
$499$		−	105864.i		−	0.425155i	0.977144	−	0.212578i	$-0.0681859\pi$
$500$		0			0
$501$	−67780.4			−0.270040
$502$	188217.	−	188217.i	0.746882	−	0.746882i
$503$	27040.0	+	27040.0i	0.106874	+	0.106874i	0.758522	−	0.651648i	$-0.225922\pi$
$503$	27040.0	+	27040.0i	0.106874	+	0.106874i	−0.651648	+	0.758522i	$0.725922\pi$
$504$		−	33434.7i		−	0.131624i
$505$		0			0
$506$	954734.			3.72890
$507$	100922.	−	100922.i	0.392618	−	0.392618i
$508$	−44465.7	−	44465.7i	−0.172305	−	0.172305i
$509$		−	382765.i		−	1.47740i	−0.674037	−	0.738698i	$-0.735441\pi$
$509$		−	382765.i		−	1.47740i	0.674037	−	0.738698i	$-0.264559\pi$
$510$		0			0
$511$	−49983.8			−0.191420
$512$	155219.	−	155219.i	0.592112	−	0.592112i
$513$	−65968.4	−	65968.4i	−0.250670	−	0.250670i
$514$			57238.5i			0.216652i
$515$		0			0
$516$	39248.7			0.147410
$517$	−486115.	+	486115.i	−1.81869	+	1.81869i
$518$	40314.8	+	40314.8i	0.150247	+	0.150247i
$519$			59950.7i			0.222566i
$520$		0			0
$521$	−126422.			−0.465743			−0.232871	−	0.972508i	$-0.574812\pi$
$521$	−126422.			−0.465743			−0.232871	+	0.972508i	$0.574812\pi$
$522$	183905.	−	183905.i	0.674920	−	0.674920i
$523$	−1542.91	−	1542.91i	−0.00564075	−	0.00564075i	0.704281	−	0.709922i	$-0.251270\pi$
$523$	−1542.91	−	1542.91i	−0.00564075	−	0.00564075i	−0.709922	+	0.704281i	$0.751270\pi$
$524$			46444.4i			0.169149i
$525$		0			0
$526$	−343619.			−1.24196
$527$	−17825.6	+	17825.6i	−0.0641834	+	0.0641834i
$528$	206943.	+	206943.i	0.742304	+	0.742304i
$529$			432038.i			1.54387i
$530$		0			0
$531$	−199629.			−0.708000
$532$	20897.1	−	20897.1i	0.0738351	−	0.0738351i
$533$	−162295.	−	162295.i	−0.571283	−	0.571283i
$534$			209719.i			0.735455i
$535$		0			0
$536$	44149.0			0.153671
$537$	60389.8	−	60389.8i	0.209419	−	0.209419i
$538$	−472203.	−	472203.i	−1.63142	−	1.63142i
$539$			75491.7i			0.259849i
$540$		0			0
$541$	270804.			0.925252			0.462626	−	0.886554i	$-0.346907\pi$
$541$	270804.			0.925252			0.462626	+	0.886554i	$0.346907\pi$
$542$	−202102.	+	202102.i	−0.687976	+	0.687976i
$543$	−52693.7	−	52693.7i	−0.178714	−	0.178714i
$544$		−	165861.i		−	0.560461i
$545$		0			0
$546$	100598.			0.337446
$547$	−239848.	+	239848.i	−0.801607	+	0.801607i	−0.983347	−	0.181740i	$-0.941827\pi$
$547$	−239848.	+	239848.i	−0.801607	+	0.801607i	0.181740	+	0.983347i	$0.441827\pi$
$548$	−1879.88	−	1879.88i	−0.00625991	−	0.00625991i
$549$		−	334168.i		−	1.10872i
$550$		0			0
$551$	−122663.			−0.404025
$552$	−72292.8	+	72292.8i	−0.237256	+	0.237256i
$553$	−65989.1	−	65989.1i	−0.215785	−	0.215785i
$554$		−	531065.i		−	1.73033i
$555$		0			0
$556$	243825.			0.788731
$557$	−28293.7	+	28293.7i	−0.0911967	+	0.0911967i	−0.751233	−	0.660037i	$-0.770541\pi$
$557$	−28293.7	+	28293.7i	−0.0911967	+	0.0911967i	0.660037	+	0.751233i	$0.270541\pi$
$558$	40319.3	+	40319.3i	0.129492	+	0.129492i
$559$			221739.i			0.709608i
$560$		0			0
$561$	133596.			0.424490
$562$	316165.	−	316165.i	1.00102	−	1.00102i
$563$	−174942.	−	174942.i	−0.551920	−	0.551920i	0.375074	−	0.926995i	$-0.377617\pi$
$563$	−174942.	−	174942.i	−0.551920	−	0.551920i	−0.926995	+	0.375074i	$0.877617\pi$
$564$			137969.i			0.433734i
$565$		0			0
$566$	−117445.			−0.366609
$567$	−33089.2	+	33089.2i	−0.102925	+	0.102925i
$568$	−32834.6	−	32834.6i	−0.101774	−	0.101774i
$569$		−	522164.i		−	1.61281i	−0.591367	−	0.806403i	$-0.701411\pi$
$569$		−	522164.i		−	1.61281i	0.591367	−	0.806403i	$-0.298589\pi$
$570$		0			0
$571$	−447593.			−1.37281			−0.686406	−	0.727219i	$-0.740813\pi$
$571$	−447593.			−1.37281			−0.686406	+	0.727219i	$0.740813\pi$
$572$	405185.	−	405185.i	1.23840	−	1.23840i
$573$	197128.	+	197128.i	0.600397	+	0.600397i
$574$		−	87577.5i		−	0.265808i
$575$		0			0
$576$	−58182.5			−0.175367
$577$	203594.	−	203594.i	0.611524	−	0.611524i	−0.331819	−	0.943343i	$-0.607662\pi$
$577$	203594.	−	203594.i	0.611524	−	0.611524i	0.943343	+	0.331819i	$0.107662\pi$
$578$	228907.	+	228907.i	0.685178	+	0.685178i
$579$		−	46532.5i		−	0.138803i
$580$		0			0
$581$	78221.5			0.231726
$582$	−56989.6	+	56989.6i	−0.168248	+	0.168248i
$583$	121964.	+	121964.i	0.358833	+	0.358833i
$584$		−	77244.9i		−	0.226487i
$585$		0			0
$586$	38602.5			0.112414
$587$	148674.	−	148674.i	0.431477	−	0.431477i	−0.457654	−	0.889131i	$-0.651310\pi$
$587$	148674.	−	148674.i	0.431477	−	0.431477i	0.889131	+	0.457654i	$0.151310\pi$
$588$	10713.0	+	10713.0i	0.0309854	+	0.0309854i
$589$		−	26892.5i		−	0.0775177i
$590$		0			0
$591$	226186.			0.647576
$592$	−132979.	+	132979.i	−0.379437	+	0.379437i
$593$	−184484.	−	184484.i	−0.524626	−	0.524626i	0.394339	−	0.918965i	$-0.370974\pi$
$593$	−184484.	−	184484.i	−0.524626	−	0.524626i	−0.918965	+	0.394339i	$0.870974\pi$
$594$		−	690224.i		−	1.95622i
$595$		0			0
$596$	272245.			0.766421
$597$	−62469.7	+	62469.7i	−0.175275	+	0.175275i
$598$	765440.	+	765440.i	2.14047	+	2.14047i
$599$			63809.1i			0.177840i	0.996039	+	0.0889199i	$0.0283415\pi$
$599$			63809.1i			0.177840i	−0.996039	+	0.0889199i	$0.971658\pi$
$600$		0			0
$601$	364460.			1.00902			0.504511	−	0.863405i	$-0.331673\pi$
$601$	364460.			1.00902			0.504511	+	0.863405i	$0.331673\pi$
$602$	−59827.3	+	59827.3i	−0.165084	+	0.165084i
$603$	−68798.9	−	68798.9i	−0.189211	−	0.189211i
$604$			7955.59i			0.0218071i
$605$		0			0
$606$	−378970.			−1.03195
$607$	55070.6	−	55070.6i	0.149466	−	0.149466i	−0.628413	−	0.777880i	$-0.716295\pi$
$607$	55070.6	−	55070.6i	0.149466	−	0.149466i	0.777880	+	0.628413i	$0.216295\pi$
$608$	125113.	+	125113.i	0.338449	+	0.338449i
$609$		−	62883.6i		−	0.169552i
$610$		0			0
$611$	−779468.			−2.08793
$612$	−66716.0	+	66716.0i	−0.178126	+	0.178126i
$613$	14387.2	+	14387.2i	0.0382873	+	0.0382873i	0.725991	−	0.687704i	$-0.241381\pi$
$613$	14387.2	+	14387.2i	0.0382873	+	0.0382873i	−0.687704	+	0.725991i	$0.741381\pi$
$614$		−	302498.i		−	0.802392i
$615$		0			0
$616$	−116665.			−0.307453
$617$	267377.	−	267377.i	0.702350	−	0.702350i	−0.262564	−	0.964915i	$-0.584568\pi$
$617$	267377.	−	267377.i	0.702350	−	0.702350i	0.964915	+	0.262564i	$0.0845682\pi$
$618$	−147899.	−	147899.i	−0.387246	−	0.387246i
$619$		−	256622.i		−	0.669749i	−0.942263	−	0.334874i	$-0.891306\pi$
$619$		−	256622.i		−	0.669749i	0.942263	−	0.334874i	$-0.108694\pi$
$620$		0			0
$621$	514652.			1.33454
$622$	−407249.	+	407249.i	−1.05264	+	1.05264i
$623$	−126176.	−	126176.i	−0.325088	−	0.325088i
$624$			331825.i			0.852196i
$625$		0			0
$626$	431051.			1.09997
$627$	−100774.	+	100774.i	−0.256339	+	0.256339i
$628$	−261861.	−	261861.i	−0.663975	−	0.663975i
$629$			85847.3i			0.216983i
$630$		0			0
$631$	115571.			0.290263			0.145132	−	0.989412i	$-0.453639\pi$
$631$	115571.			0.290263			0.145132	+	0.989412i	$0.453639\pi$
$632$	101979.	−	101979.i	0.255316	−	0.255316i
$633$	−19541.8	−	19541.8i	−0.0487705	−	0.0487705i
$634$			88668.0i			0.220591i
$635$		0			0
$636$	34615.6			0.0855772
$637$	−60524.1	+	60524.1i	−0.149159	+	0.149159i
$638$	−641705.	−	641705.i	−1.57650	−	1.57650i
$639$			102335.i			0.250623i
$640$		0			0
$641$	−393645.			−0.958050			−0.479025	−	0.877801i	$-0.659010\pi$
$641$	−393645.			−0.958050			−0.479025	+	0.877801i	$0.659010\pi$
$642$	134388.	−	134388.i	0.326056	−	0.326056i
$643$	145387.	+	145387.i	0.351645	+	0.351645i	0.860721	−	0.509076i	$-0.170013\pi$
$643$	145387.	+	145387.i	0.351645	+	0.351645i	−0.509076	+	0.860721i	$0.670013\pi$
$644$			163028.i			0.393090i
$645$		0			0
$646$	112741.			0.270158
$647$	−520127.	+	520127.i	−1.24251	+	1.24251i	−0.283557	+	0.958955i	$0.591515\pi$
$647$	−520127.	+	520127.i	−1.24251	+	1.24251i	−0.958955	+	0.283557i	$0.908485\pi$
$648$	−51136.1	−	51136.1i	−0.121780	−	0.121780i
$649$			696570.i			1.65377i
$650$		0			0
$651$	13786.6			0.0325308
$652$	16588.1	−	16588.1i	0.0390214	−	0.0390214i
$653$	515377.	+	515377.i	1.20864	+	1.20864i	0.971466	+	0.237179i	$0.0762228\pi$
$653$	515377.	+	515377.i	1.20864	+	1.20864i	0.237179	+	0.971466i	$0.423777\pi$
$654$			101551.i			0.237427i
$655$		0			0
$656$	288876.			0.671281
$657$	−120373.	+	120373.i	−0.278869	+	0.278869i
$658$	−210308.	−	210308.i	−0.485739	−	0.485739i
$659$			682913.i			1.57251i	0.617899	+	0.786257i	$0.287984\pi$
$659$			682913.i			1.57251i	−0.617899	+	0.786257i	$0.712016\pi$
$660$		0			0
$661$	833390.			1.90742			0.953708	−	0.300734i	$-0.0972315\pi$
$661$	833390.			1.90742			0.953708	+	0.300734i	$0.0972315\pi$
$662$	−114311.	+	114311.i	−0.260839	+	0.260839i
$663$	107108.	+	107108.i	0.243666	+	0.243666i
$664$			120883.i			0.274177i
$665$		0			0
$666$	194176.			0.437771
$667$	478475.	−	478475.i	1.07549	−	1.07549i
$668$	−118109.	−	118109.i	−0.264686	−	0.264686i
$669$			295571.i			0.660403i
$670$		0			0
$671$	−1.16602e6			−2.58978
$672$	−64139.6	+	64139.6i	−0.142033	+	0.142033i
$673$	334777.	+	334777.i	0.739137	+	0.739137i	0.972411	−	0.233274i	$-0.0749439\pi$
$673$	334777.	+	334777.i	0.739137	+	0.739137i	−0.233274	+	0.972411i	$0.574944\pi$
$674$		−	287147.i		−	0.632098i
$675$		0			0
$676$	351719.			0.769666
$677$	−456455.	+	456455.i	−0.995911	+	0.995911i	−0.999992	−	0.00408059i	$-0.998701\pi$
$677$	−456455.	+	456455.i	−0.995911	+	0.995911i	0.00408059	+	0.999992i	$0.498701\pi$
$678$	226179.	+	226179.i	0.492031	+	0.492031i
$679$		−	68574.7i		−	0.148739i
$680$		0			0
$681$	362305.			0.781232
$682$	140687.	−	140687.i	0.302473	−	0.302473i
$683$	−365344.	−	365344.i	−0.783179	−	0.783179i	0.197187	−	0.980366i	$-0.436819\pi$
$683$	−365344.	−	365344.i	−0.783179	−	0.783179i	−0.980366	+	0.197187i	$0.936819\pi$
$684$		−	100651.i		−	0.215132i
$685$		0			0
$686$	−32659.9			−0.0694012
$687$	−248.715	+	248.715i	−0.000526973	+	0.000526973i
$688$	−197342.	−	197342.i	−0.416909	−	0.416909i
$689$			195564.i			0.411956i
$690$		0			0
$691$	183959.			0.385269			0.192634	−	0.981271i	$-0.438297\pi$
$691$	183959.			0.385269			0.192634	+	0.981271i	$0.438297\pi$
$692$	−104466.	+	104466.i	−0.218153	+	0.218153i
$693$	181803.	+	181803.i	0.378559	+	0.378559i
$694$		−	676341.i		−	1.40426i
$695$		0			0
$696$	97180.2			0.200613
$697$	93244.9	−	93244.9i	0.191937	−	0.191937i
$698$	576672.	+	576672.i	1.18364	+	1.18364i
$699$			161277.i			0.330079i
$700$		0			0
$701$	−176822.			−0.359833			−0.179916	−	0.983682i	$-0.557583\pi$
$701$	−176822.			−0.359833			−0.179916	+	0.983682i	$0.557583\pi$
$702$	553374.	−	553374.i	1.12291	−	1.12291i
$703$	−64756.6	−	64756.6i	−0.131031	−	0.131031i
$704$			203018.i			0.409627i
$705$		0			0
$706$	−1.11471e6			−2.23642
$707$	228004.	−	228004.i	0.456146	−	0.456146i
$708$	98850.1	+	98850.1i	0.197202	+	0.197202i
$709$		−	715270.i		−	1.42291i	−0.702731	−	0.711455i	$-0.748036\pi$
$709$		−	715270.i		−	1.42291i	0.702731	−	0.711455i	$-0.251964\pi$
$710$		0			0
$711$	−317836.			−0.628730
$712$	194993.	−	194993.i	0.384643	−	0.384643i
$713$	104901.	+	104901.i	0.206348	+	0.206348i
$714$			57797.5i			0.113374i
$715$		0			0
$716$	210462.			0.410532
$717$	−8874.18	+	8874.18i	−0.0172619	+	0.0172619i
$718$	−65015.8	−	65015.8i	−0.126116	−	0.126116i
$719$			764914.i			1.47964i	0.672807	+	0.739818i	$0.265089\pi$
$719$			764914.i			1.47964i	−0.672807	+	0.739818i	$0.734911\pi$
$720$		0			0
$721$	177964.			0.342344
$722$	388733.	−	388733.i	0.745722	−	0.745722i
$723$	14910.5	+	14910.5i	0.0285243	+	0.0285243i
$724$		−	183640.i		−	0.350341i
$725$		0			0
$726$	−735710.			−1.39583
$727$	−535539.	+	535539.i	−1.01326	+	1.01326i	−0.0133519	+	0.999911i	$0.504250\pi$
$727$	−535539.	+	535539.i	−1.01326	+	1.01326i	−0.999911	+	0.0133519i	$0.995750\pi$
$728$	−93533.9	−	93533.9i	−0.176484	−	0.176484i
$729$		−	49803.3i		−	0.0937136i
$730$		0			0
$731$	−127398.			−0.238411
$732$	−165470.	+	165470.i	−0.308815	+	0.308815i
$733$	137194.	+	137194.i	0.255345	+	0.255345i	0.823158	−	0.567813i	$-0.192210\pi$
$733$	137194.	+	137194.i	0.255345	+	0.255345i	−0.567813	+	0.823158i	$0.692210\pi$
$734$			1.14702e6i			2.12901i
$735$		0			0
$736$	−976064.			−1.80187
$737$	−240062.	+	240062.i	−0.441966	+	0.441966i
$738$	−210908.	−	210908.i	−0.387241	−	0.387241i
$739$			98757.6i			0.180835i	0.995904	+	0.0904173i	$0.0288201\pi$
$739$			98757.6i			0.180835i	−0.995904	+	0.0904173i	$0.971180\pi$
$740$		0			0
$741$	−161588.			−0.294288
$742$	−52765.0	+	52765.0i	−0.0958381	+	0.0958381i
$743$	154662.	+	154662.i	0.280160	+	0.280160i	0.833173	−	0.553013i	$-0.186522\pi$
$743$	154662.	+	154662.i	0.280160	+	0.280160i	−0.553013	+	0.833173i	$0.686522\pi$
$744$			21305.8i			0.0384903i
$745$		0			0
$746$	−353574.			−0.635335
$747$	188377.	−	188377.i	0.337587	−	0.337587i
$748$	232794.	+	232794.i	0.416072	+	0.416072i
$749$			161708.i			0.288248i
$750$		0			0
$751$	649137.			1.15095			0.575475	−	0.817819i	$-0.304817\pi$
$751$	649137.			1.15095			0.575475	+	0.817819i	$0.304817\pi$
$752$	693704.	−	693704.i	1.22670	−	1.22670i
$753$	−154990.	−	154990.i	−0.273347	−	0.273347i
$754$		−	1.02895e6i		−	1.80989i
$755$		0			0
$756$	117861.			0.206218
$757$	524986.	−	524986.i	0.916128	−	0.916128i	−0.0806176	−	0.996745i	$-0.525689\pi$
$757$	524986.	−	524986.i	0.916128	−	0.916128i	0.996745	+	0.0806176i	$0.0256892\pi$
$758$	−570551.	−	570551.i	−0.993015	−	0.993015i
$759$		−	786190.i		−	1.36472i
$760$		0			0
$761$	804359.			1.38893			0.694465	−	0.719526i	$-0.255641\pi$
$761$	804359.			1.38893			0.694465	+	0.719526i	$0.255641\pi$
$762$	−92769.5	+	92769.5i	−0.159770	+	0.159770i
$763$	−61097.5	−	61097.5i	−0.104948	−	0.104948i
$764$			687000.i			1.17698i
$765$		0			0
$766$	−606884.			−1.03430
$767$	−558462.	+	558462.i	−0.949299	+	0.949299i
$768$	−256077.	−	256077.i	−0.434159	−	0.434159i
$769$			334985.i			0.566465i	0.959051	+	0.283233i	$0.0914068\pi$
$769$			334985.i			0.566465i	−0.959051	+	0.283233i	$0.908593\pi$
$770$		0			0
$771$	47133.9			0.0792912
$772$	81084.0	−	81084.0i	0.136051	−	0.136051i
$773$	160551.	+	160551.i	0.268691	+	0.268691i	0.828573	−	0.559881i	$-0.189153\pi$
$773$	160551.	+	160551.i	0.268691	+	0.268691i	−0.559881	+	0.828573i	$0.689153\pi$
$774$			288158.i			0.481004i
$775$		0			0
$776$	105975.			0.175987
$777$	33197.8	−	33197.8i	0.0549879	−	0.0549879i
$778$	−850307.	−	850307.i	−1.40481	−	1.40481i
$779$			140674.i			0.231813i
$780$		0			0
$781$	357079.			0.585413
$782$	−439775.	+	439775.i	−0.719146	+	0.719146i
$783$	−345913.	−	345913.i	−0.564213	−	0.564213i
$784$		−	107729.i		−	0.175268i
$785$		0			0
$786$	96897.6			0.156844
$787$	137724.	−	137724.i	0.222362	−	0.222362i	−0.587130	−	0.809492i	$-0.699742\pi$
$787$	137724.	−	137724.i	0.222362	−	0.222362i	0.809492	+	0.587130i	$0.199742\pi$
$788$	394135.	+	394135.i	0.634734	+	0.634734i
$789$			282958.i			0.454536i
$790$		0			0
$791$	−272158.			−0.434978
$792$	−280958.	+	280958.i	−0.447910	+	0.447910i
$793$	−934839.	−	934839.i	−1.48659	−	1.48659i
$794$			486541.i			0.771753i
$795$		0			0
$796$	−217710.			−0.343599
$797$	220496.	−	220496.i	0.347124	−	0.347124i	−0.511913	−	0.859037i	$-0.671063\pi$
$797$	220496.	−	220496.i	0.347124	−	0.347124i	0.859037	+	0.511913i	$0.171063\pi$
$798$	−43598.0	−	43598.0i	−0.0684637	−	0.0684637i
$799$		−	447834.i		−	0.701493i
$800$		0			0
$801$	−607727.			−0.947204
$802$	−858054.	+	858054.i	−1.33403	+	1.33403i
$803$	420023.	+	420023.i	0.651391	+	0.651391i
$804$			68134.4i			0.105403i
$805$		0			0
$806$	225587.			0.347251
$807$	−388843.	+	388843.i	−0.597073	+	0.597073i
$808$	352358.	+	352358.i	0.539710	+	0.539710i
$809$		−	1.18449e6i		−	1.80982i	−0.425608	−	0.904908i	$-0.639940\pi$
$809$		−	1.18449e6i		−	1.80982i	0.425608	−	0.904908i	$-0.360060\pi$
$810$		0			0
$811$	969549.			1.47410			0.737052	−	0.675836i	$-0.236217\pi$
$811$	969549.			1.47410			0.737052	+	0.675836i	$0.236217\pi$
$812$	109576.	−	109576.i	0.166190	−	0.166190i
$813$	166424.	+	166424.i	0.251788	+	0.251788i
$814$		−	677544.i		−	1.02256i
$815$		0			0
$816$	−190646.			−0.286317
$817$	96099.0	−	96099.0i	0.143971	−	0.143971i
$818$	−34080.1	−	34080.1i	−0.0509324	−	0.0509324i
$819$			291514.i			0.434602i
$820$		0			0
$821$	−8559.25			−0.0126984			−0.00634920	−	0.999980i	$-0.502021\pi$
$821$	−8559.25			−0.0126984			−0.00634920	+	0.999980i	$0.502021\pi$
$822$	−3922.02	+	3922.02i	−0.00580451	+	0.00580451i
$823$	414184.	+	414184.i	0.611497	+	0.611497i	0.943336	−	0.331839i	$-0.107669\pi$
$823$	414184.	+	414184.i	0.611497	+	0.611497i	−0.331839	+	0.943336i	$0.607669\pi$
$824$			275026.i			0.405060i
$825$		0			0
$826$	−301357.			−0.441693
$827$	−832331.	+	832331.i	−1.21698	+	1.21698i	−0.248301	+	0.968683i	$0.579872\pi$
$827$	−832331.	+	832331.i	−1.21698	+	1.21698i	−0.968683	+	0.248301i	$0.920128\pi$
$828$	392613.	+	392613.i	0.572669	+	0.572669i
$829$			265850.i			0.386837i	0.981116	+	0.193419i	$0.0619575\pi$
$829$			265850.i			0.386837i	−0.981116	+	0.193419i	$0.938042\pi$
$830$		0			0
$831$	−437313.			−0.633272
$832$	−162766.	+	162766.i	−0.235135	+	0.235135i
$833$	−34773.4	−	34773.4i	−0.0501138	−	0.0501138i
$834$		−	508696.i		−	0.731352i
$835$		0			0
$836$	−351204.			−0.502512
$837$	75837.8	−	75837.8i	0.108252	−	0.108252i
$838$	−966381.	−	966381.i	−1.37613	−	1.37613i
$839$			687513.i			0.976691i	0.872650	+	0.488345i	$0.162399\pi$
$839$			687513.i			0.976691i	−0.872650	+	0.488345i	$0.837601\pi$
$840$		0			0
$841$	64086.7			0.0906100
$842$	−808967.	+	808967.i	−1.14106	+	1.14106i
$843$	−260351.	−	260351.i	−0.366357	−	0.366357i
$844$		−	68104.2i		−	0.0956069i
$845$		0			0
$846$	−1.01295e6			−1.41529
$847$	442634.	−	442634.i	0.616990	−	0.616990i
$848$	−174046.	−	174046.i	−0.242032	−	0.242032i
$849$			96712.2i			0.134173i
$850$		0			0
$851$	505197.			0.697593
$852$	50673.0	−	50673.0i	0.0698068	−	0.0698068i
$853$	266208.	+	266208.i	0.365866	+	0.365866i	0.865967	−	0.500101i	$-0.166704\pi$
$853$	266208.	+	266208.i	0.365866	+	0.365866i	−0.500101	+	0.865967i	$0.666704\pi$
$854$		−	504456.i		−	0.691684i
$855$		0			0
$856$	−249903.			−0.341054
$857$	−882590.	+	882590.i	−1.20170	+	1.20170i	−0.228056	+	0.973648i	$0.573237\pi$
$857$	−882590.	+	882590.i	−1.20170	+	1.20170i	−0.973648	+	0.228056i	$0.926763\pi$
$858$	−845343.	−	845343.i	−1.14831	−	1.14831i
$859$		−	558403.i		−	0.756765i	−0.925649	−	0.378383i	$-0.876480\pi$
$859$		−	558403.i		−	0.756765i	0.925649	−	0.378383i	$-0.123520\pi$
$860$		0			0
$861$	−72117.0			−0.0972818
$862$	942732.	−	942732.i	1.26874	−	1.26874i
$863$	−795231.	−	795231.i	−1.06776	−	1.06776i	−0.997531	−	0.0702242i	$-0.977629\pi$
$863$	−795231.	−	795231.i	−1.06776	−	1.06776i	−0.0702242	−	0.997531i	$-0.522371\pi$
$864$			705644.i			0.945275i
$865$		0			0
$866$	1.36651e6			1.82211
$867$	188497.	−	188497.i	0.250764	−	0.250764i
$868$	24023.5	+	24023.5i	0.0318857	+	0.0318857i
$869$			1.10904e6i			1.46861i
$870$		0			0
$871$	−384931.			−0.507395
$872$	94420.1	−	94420.1i	0.124174	−	0.124174i
$873$	−165145.	−	165145.i	−0.216689	−	0.216689i
$874$		−	663465.i		−	0.868550i
$875$		0			0
$876$	119211.			0.155348
$877$	835839.	−	835839.i	1.08673	−	1.08673i	0.0908715	−	0.995863i	$-0.471035\pi$
$877$	835839.	−	835839.i	1.08673	−	1.08673i	0.995863	−	0.0908715i	$-0.0289653\pi$
$878$	1.07286e6	+	1.07286e6i	1.39172	+	1.39172i
$879$		−	31787.8i		−	0.0411418i
$880$		0			0
$881$	−185915.			−0.239531			−0.119765	−	0.992802i	$-0.538214\pi$
$881$	−185915.			−0.239531			−0.119765	+	0.992802i	$0.538214\pi$
$882$	−78653.2	+	78653.2i	−0.101107	+	0.101107i
$883$	−4513.98	−	4513.98i	−0.00578946	−	0.00578946i	0.704206	−	0.709996i	$-0.251303\pi$
$883$	−4513.98	−	4513.98i	−0.00578946	−	0.00578946i	−0.709996	+	0.704206i	$0.751303\pi$
$884$			373277.i			0.477668i
$885$		0			0
$886$	55108.8			0.0702027
$887$	706482.	−	706482.i	0.897953	−	0.897953i	−0.0973016	−	0.995255i	$-0.531021\pi$
$887$	706482.	−	706482.i	0.897953	−	0.897953i	0.995255	+	0.0973016i	$0.0310211\pi$
$888$	51303.9	+	51303.9i	0.0650615	+	0.0650615i
$889$		−	111628.i		−	0.141244i
$890$		0			0
$891$	556109.			0.700494
$892$	−515039.	+	515039.i	−0.647307	+	0.647307i
$893$	337812.	+	337812.i	0.423615	+	0.423615i
$894$		−	567989.i		−	0.710665i
$895$		0			0
$896$	254970.			0.317594
$897$	630313.	−	630313.i	0.783379	−	0.783379i
$898$	1.12180e6	+	1.12180e6i	1.39112	+	1.39112i
$899$		−	141014.i		−	0.174479i
$900$		0			0
$901$	−112359.			−0.138407
$902$	−735929.	+	735929.i	−0.904530	+	0.904530i
$903$	49265.7	+	49265.7i	0.0604184	+	0.0604184i
$904$		−	420592.i		−	0.514664i
$905$		0			0
$906$	16597.9			0.0202207
$907$	80791.0	−	80791.0i	0.0982084	−	0.0982084i	−0.656296	−	0.754504i	$-0.727878\pi$
$907$	80791.0	−	80791.0i	0.0982084	−	0.0982084i	0.754504	+	0.656296i	$0.227878\pi$
$908$	631326.	+	631326.i	0.765741	+	0.765741i
$909$		−	1.09818e6i		−	1.32907i
$910$		0			0
$911$	951125.			1.14604			0.573022	−	0.819540i	$-0.305771\pi$
$911$	951125.			1.14604			0.573022	+	0.819540i	$0.305771\pi$
$912$	143809.	−	143809.i	0.172900	−	0.172900i
$913$	−657309.	−	657309.i	−0.788548	−	0.788548i
$914$		−	347994.i		−	0.416562i
$915$		0			0
$916$	−866.784			−0.00103305
$917$	−58297.7	+	58297.7i	−0.0693287	+	0.0693287i
$918$	317935.	+	317935.i	0.377270	+	0.377270i
$919$			79518.7i			0.0941539i	0.998891	+	0.0470769i	$0.0149906\pi$
$919$			79518.7i			0.0941539i	−0.998891	+	0.0470769i	$0.985009\pi$
$920$		0			0
$921$	−249097.			−0.293663
$922$	914434.	−	914434.i	1.07570	−	1.07570i
$923$	286282.	+	286282.i	0.336039	+	0.336039i
$924$		−	180047.i		−	0.210883i
$925$		0			0
$926$	491371.			0.573043
$927$	428582.	−	428582.i	0.498740	−	0.498740i
$928$	656041.	+	656041.i	0.761790	+	0.761790i
$929$		−	708329.i		−	0.820736i	−0.911920	−	0.410368i	$-0.865400\pi$
$929$		−	708329.i		−	0.820736i	0.911920	−	0.410368i	$-0.134600\pi$
$930$		0			0
$931$	52460.8			0.0605251
$932$	−281029.	+	281029.i	−0.323534	+	0.323534i
$933$	335356.	+	335356.i	0.385250	+	0.385250i
$934$			1.25511e6i			1.43876i
$935$		0			0
$936$	−450505.			−0.514219
$937$	440943.	−	440943.i	0.502231	−	0.502231i	−0.409899	−	0.912131i	$-0.634436\pi$
$937$	440943.	−	440943.i	0.502231	−	0.502231i	0.912131	+	0.409899i	$0.134436\pi$
$938$	−103858.	−	103858.i	−0.118041	−	0.118041i
$939$		−	354955.i		−	0.402571i
$940$		0			0
$941$	−605919.			−0.684282			−0.342141	−	0.939649i	$-0.611152\pi$
$941$	−605919.			−0.684282			−0.342141	+	0.939649i	$0.611152\pi$
$942$	−546325.	+	546325.i	−0.615671	+	0.615671i
$943$	−548731.	−	548731.i	−0.617072	−	0.617072i
$944$		−	994031.i		−	1.11546i
$945$		0			0
$946$	1.00548e6			1.12354
$947$	564803.	−	564803.i	0.629792	−	0.629792i	−0.318224	−	0.948016i	$-0.603086\pi$
$947$	564803.	−	564803.i	0.629792	−	0.629792i	0.948016	+	0.318224i	$0.103086\pi$
$948$	157383.	+	157383.i	0.175122	+	0.175122i
$949$			673491.i			0.747824i
$950$		0			0
$951$	73015.0			0.0807330
$952$	53738.8	−	53738.8i	0.0592945	−	0.0592945i
$953$	922850.	+	922850.i	1.01612	+	1.01612i	0.999868	+	0.0162533i	$0.00517381\pi$
$953$	922850.	+	922850.i	1.01612	+	1.01612i	0.0162533	+	0.999868i	$0.494826\pi$
$954$			254142.i			0.279242i
$955$		0			0
$956$	−30926.9			−0.0338393
$957$	−528422.	+	528422.i	−0.576975	+	0.576975i
$958$	214437.	+	214437.i	0.233651	+	0.233651i
$959$		−	4719.31i		−	0.00513146i
$960$		0			0
$961$	−892605.			−0.966524
$962$	543208.	−	543208.i	0.586971	−	0.586971i
$963$	389432.	+	389432.i	0.419932	+	0.419932i
$964$			51963.7i			0.0559173i
$965$		0			0
$966$	340129.			0.364493
$967$	−621553.	+	621553.i	−0.664700	+	0.664700i	−0.956484	−	0.291784i	$-0.905751\pi$
$967$	−621553.	+	621553.i	−0.664700	+	0.664700i	0.291784	+	0.956484i	$0.405751\pi$
$968$	684046.	+	684046.i	0.730020	+	0.730020i
$969$		−	92838.6i		−	0.0988737i
$970$		0			0
$971$	240374.			0.254947			0.127473	−	0.991842i	$-0.459313\pi$
$971$	240374.			0.254947			0.127473	+	0.991842i	$0.459313\pi$
$972$	443414.	−	443414.i	0.469329	−	0.469329i
$973$	306053.	+	306053.i	0.323274	+	0.323274i
$974$		−	1.05647e6i		−	1.11362i
$975$		0			0
$976$	1.66396e6			1.74680
$977$	655904.	−	655904.i	0.687150	−	0.687150i	−0.274451	−	0.961601i	$-0.588496\pi$
$977$	655904.	−	655904.i	0.687150	−	0.687150i	0.961601	+	0.274451i	$0.0884962\pi$
$978$	−34608.1	−	34608.1i	−0.0361826	−	0.0361826i
$979$			2.12056e6i			2.21251i
$980$		0			0
$981$	−294276.			−0.305785
$982$	513341.	−	513341.i	0.532333	−	0.532333i
$983$	−831878.	−	831878.i	−0.860900	−	0.860900i	0.130543	−	0.991443i	$-0.458328\pi$
$983$	−831878.	−	831878.i	−0.860900	−	0.860900i	−0.991443	+	0.130543i	$0.958328\pi$
$984$		−	111450.i		−	0.115103i
$985$		0			0
$986$	591171.			0.608079
$987$	−173181.	+	173181.i	−0.177773	+	0.177773i
$988$	−281571.	−	281571.i	−0.288453	−	0.288453i
$989$			749715.i			0.766485i
$990$		0			0
$991$	1.42684e6			1.45288			0.726438	−	0.687232i	$-0.241174\pi$
$991$	1.42684e6			1.45288			0.726438	+	0.687232i	$0.241174\pi$
$992$	−143830.	+	143830.i	−0.146160	+	0.146160i
$993$	94131.3	+	94131.3i	0.0954632	+	0.0954632i
$994$			154483.i			0.156354i
$995$		0			0
$996$	−186557.			−0.188059
$997$	−225364.	+	225364.i	−0.226722	+	0.226722i	−0.811322	−	0.584600i	$-0.801252\pi$
$997$	−225364.	+	225364.i	−0.226722	+	0.226722i	0.584600	+	0.811322i	$0.301252\pi$
$998$	−384865.	−	384865.i	−0.386409	−	0.386409i
$999$		−	365232.i		−	0.365963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.10		24
5.2	odd	4	inner	175.5.g.c.57.10		24
5.3	odd	4		35.5.g.a.22.3	yes	24
5.4	even	2		35.5.g.a.8.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.3	✓	24	5.4	even	2
35.5.g.a.22.3	yes	24	5.3	odd	4
175.5.g.c.43.10		24	1.1	even	1	trivial
175.5.g.c.57.10		24	5.2	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.63546 - 3.63546i) q^{2} +(-2.99367 - 2.99367i) q^{3} -10.4331i q^{4} -21.7667 q^{6} +(13.0958 - 13.0958i) q^{7} +(20.2382 + 20.2382i) q^{8} -63.0758i q^{9} +O(q^{10})\)	\(q+(3.63546 - 3.63546i) q^{2} +(-2.99367 - 2.99367i) q^{3} -10.4331i q^{4} -21.7667 q^{6} +(13.0958 - 13.0958i) q^{7} +(20.2382 + 20.2382i) q^{8} -63.0758i q^{9} -220.093 q^{11} +(-31.2333 + 31.2333i) q^{12} +(-176.455 - 176.455i) q^{13} -95.2184i q^{14} +314.080 q^{16} +(101.380 - 101.380i) q^{17} +(-229.310 - 229.310i) q^{18} +152.947i q^{19} -78.4091 q^{21} +(-800.137 + 800.137i) q^{22} +(-596.607 - 596.607i) q^{23} -121.173i q^{24} -1282.99 q^{26} +(-431.316 + 431.316i) q^{27} +(-136.630 - 136.630i) q^{28} +801.994i q^{29} -175.829 q^{31} +(818.013 - 818.013i) q^{32} +(658.885 + 658.885i) q^{33} -737.127i q^{34} -658.077 q^{36} +(-423.393 + 423.393i) q^{37} +(556.032 + 556.032i) q^{38} +1056.50i q^{39} +919.754 q^{41} +(-285.053 + 285.053i) q^{42} +(-628.316 - 628.316i) q^{43} +2296.25i q^{44} -4337.88 q^{46} +(2208.69 - 2208.69i) q^{47} +(-940.253 - 940.253i) q^{48} -343.000i q^{49} -606.999 q^{51} +(-1840.97 + 1840.97i) q^{52} +(-554.147 - 554.147i) q^{53} +3136.06i q^{54} +530.072 q^{56} +(457.873 - 457.873i) q^{57} +(2915.61 + 2915.61i) q^{58} -3164.90i q^{59} +5297.88 q^{61} +(-639.219 + 639.219i) q^{62} +(-826.029 - 826.029i) q^{63} -922.421i q^{64} +4790.70 q^{66} +(1090.73 - 1090.73i) q^{67} +(-1057.71 - 1057.71i) q^{68} +3572.09i q^{69} -1622.41 q^{71} +(1276.54 - 1276.54i) q^{72} +(-1908.39 - 1908.39i) q^{73} +3078.45i q^{74} +1595.71 q^{76} +(-2882.29 + 2882.29i) q^{77} +(3840.85 + 3840.85i) q^{78} -5038.95i q^{79} -2526.71 q^{81} +(3343.73 - 3343.73i) q^{82} +(2986.51 + 2986.51i) q^{83} +818.050i q^{84} -4568.43 q^{86} +(2400.91 - 2400.91i) q^{87} +(-4454.28 - 4454.28i) q^{88} -9634.86i q^{89} -4621.64 q^{91} +(-6224.45 + 6224.45i) q^{92} +(526.374 + 526.374i) q^{93} -16059.2i q^{94} -4897.73 q^{96} +(2618.19 - 2618.19i) q^{97} +(-1246.96 - 1246.96i) q^{98} +13882.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 24 * q - 20 * q^3 + 72 * q^6	\( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more