LMFDB - Embedded newform 35.5.g.a.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.3
Character	$\chi$	$=$	35.22
Dual form			35.5.g.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +O(q^{10})$	\(q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +(-80.1039 + 100.519i) q^{10} -220.093 q^{11} +(31.2333 + 31.2333i) q^{12} +(176.455 - 176.455i) q^{13} +95.2184i q^{14} +(-82.7738 - 65.9628i) q^{15} +314.080 q^{16} +(-101.380 - 101.380i) q^{17} +(229.310 - 229.310i) q^{18} -152.947i q^{19} +(259.177 - 29.2937i) q^{20} -78.4091 q^{21} +(800.137 + 800.137i) q^{22} +(596.607 - 596.607i) q^{23} +121.173i q^{24} +(-609.233 + 139.500i) q^{25} -1282.99 q^{26} +(431.316 + 431.316i) q^{27} +(136.630 - 136.630i) q^{28} -801.994i q^{29} +(61.1159 + 540.726i) q^{30} -175.829 q^{31} +(-818.013 - 818.013i) q^{32} +(-658.885 + 658.885i) q^{33} +737.127i q^{34} +(-288.554 + 362.094i) q^{35} -658.077 q^{36} +(423.393 + 423.393i) q^{37} +(-556.032 + 556.032i) q^{38} -1056.50i q^{39} +(559.579 + 445.930i) q^{40} +919.754 q^{41} +(285.053 + 285.053i) q^{42} +(628.316 - 628.316i) q^{43} -2296.25i q^{44} +(1566.92 - 177.102i) q^{45} -4337.88 q^{46} +(-2208.69 - 2208.69i) q^{47} +(940.253 - 940.253i) q^{48} +343.000i q^{49} +(2721.99 + 1707.69i) q^{50} -606.999 q^{51} +(1840.97 + 1840.97i) q^{52} +(554.147 - 554.147i) q^{53} -3136.06i q^{54} +(617.968 + 5467.50i) q^{55} +530.072 q^{56} +(-457.873 - 457.873i) q^{57} +(-2915.61 + 2915.61i) q^{58} +3164.90i q^{59} +(688.196 - 863.588i) q^{60} +5297.88 q^{61} +(639.219 + 639.219i) q^{62} +(826.029 - 826.029i) q^{63} +922.421i q^{64} +(-4878.91 - 3888.02i) q^{65} +4790.70 q^{66} +(-1090.73 - 1090.73i) q^{67} +(1057.71 - 1057.71i) q^{68} -3572.09i q^{69} +(2365.40 - 267.351i) q^{70} -1622.41 q^{71} +(-1276.54 - 1276.54i) q^{72} +(1908.39 - 1908.39i) q^{73} -3078.45i q^{74} +(-1406.23 + 2241.46i) q^{75} +1595.71 q^{76} +(2882.29 + 2882.29i) q^{77} +(-3840.85 + 3840.85i) q^{78} +5038.95i q^{79} +(-881.863 - 7802.32i) q^{80} -2526.71 q^{81} +(-3343.73 - 3343.73i) q^{82} +(-2986.51 + 2986.51i) q^{83} -818.050i q^{84} +(-2233.82 + 2803.12i) q^{85} -4568.43 q^{86} +(-2400.91 - 2400.91i) q^{87} +(4454.28 - 4454.28i) q^{88} +9634.86i q^{89} +(-6340.32 - 5052.62i) q^{90} -4621.64 q^{91} +(6224.45 + 6224.45i) q^{92} +(-526.374 + 526.374i) q^{93} +16059.2i q^{94} +(-3799.48 + 429.439i) q^{95} -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} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−3.63546	−	3.63546i	−0.908864	−	0.908864i	0.0873163	−	0.996181i	$-0.472171\pi$
$2$	−3.63546	−	3.63546i	−0.908864	−	0.908864i	−0.996181	+	0.0873163i	$0.972171\pi$
$3$	2.99367	−	2.99367i	0.332630	−	0.332630i	−0.520954	−	0.853585i	$-0.674424\pi$
$3$	2.99367	−	2.99367i	0.332630	−	0.332630i	0.853585	+	0.520954i	$0.174424\pi$
$4$			10.4331i			0.652069i
$5$	−2.80777	−	24.8418i	−0.112311	−	0.993673i
$5$	−2.80777	−	24.8418i	−0.112311	−	0.993673i
$6$	−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
$10$	−80.1039	+	100.519i	−0.801039	+	1.00519i
$11$	−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	0.0451321	−	0.998981i	$-0.485629\pi$
$13$	176.455	−	176.455i	1.04411	−	1.04411i	0.998981	−	0.0451321i	$-0.0143709\pi$
$14$			95.2184i			0.485808i
$15$	−82.7738	−	65.9628i	−0.367884	−	0.293168i
$16$	314.080			1.22688
$17$	−101.380	−	101.380i	−0.350797	−	0.350797i	0.509609	−	0.860406i	$-0.329790\pi$
$17$	−101.380	−	101.380i	−0.350797	−	0.350797i	−0.860406	+	0.509609i	$0.829790\pi$
$18$	229.310	−	229.310i	0.707746	−	0.707746i
$19$		−	152.947i		−	0.423676i	−0.977305	−	0.211838i	$-0.932055\pi$
$19$		−	152.947i		−	0.423676i	0.977305	−	0.211838i	$-0.0679449\pi$
$20$	259.177	−	29.2937i	0.647943	−	0.0732343i
$21$	−78.4091			−0.177798
$22$	800.137	+	800.137i	1.65318	+	1.65318i
$23$	596.607	−	596.607i	1.12780	−	1.12780i	0.137266	−	0.990534i	$-0.456168\pi$
$23$	596.607	−	596.607i	1.12780	−	1.12780i	0.990534	−	0.137266i	$-0.0438317\pi$
$24$			121.173i			0.210370i
$25$	−609.233	+	139.500i	−0.974773	+	0.223200i
$26$	−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	$-0.841793\pi$
$29$		−	801.994i		−	0.953619i	0.879007	−	0.476810i	$-0.158207\pi$
$30$	61.1159	+	540.726i	0.0679066	+	0.600806i
$31$	−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
$35$	−288.554	+	362.094i	−0.235554	+	0.295587i
$36$	−658.077			−0.507775
$37$	423.393	+	423.393i	0.309271	+	0.309271i	0.844627	−	0.535355i	$-0.179822\pi$
$37$	423.393	+	423.393i	0.309271	+	0.309271i	−0.535355	+	0.844627i	$0.679822\pi$
$38$	−556.032	+	556.032i	−0.385064	+	0.385064i
$39$		−	1056.50i		−	0.694607i
$40$	559.579	+	445.930i	0.349737	+	0.278707i
$41$	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	$-0.672759\pi$
$43$	628.316	−	628.316i	0.339814	−	0.339814i	0.856297	+	0.516483i	$0.172759\pi$
$44$		−	2296.25i		−	1.18608i
$45$	1566.92	−	177.102i	0.773787	−	0.0874579i
$46$	−4337.88			−2.05004
$47$	−2208.69	−	2208.69i	−0.999857	−	0.999857i	0.000142581	−	1.00000i	$-0.499955\pi$
$47$	−2208.69	−	2208.69i	−0.999857	−	0.999857i	−1.00000		0.000142581i	$0.999955\pi$
$48$	940.253	−	940.253i	0.408096	−	0.408096i
$49$			343.000i			0.142857i
$50$	2721.99	+	1707.69i	1.08879	+	0.683077i
$51$	−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	$-0.705452\pi$
$53$	554.147	−	554.147i	0.197275	−	0.197275i	0.798831	+	0.601556i	$0.205452\pi$
$54$		−	3136.06i		−	1.07547i
$55$	617.968	+	5467.50i	0.204287	+	1.80744i
$56$	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	$0.150216\pi$
$59$			3164.90i			0.909192i	−0.890698	+	0.454596i	$0.849784\pi$
$60$	688.196	−	863.588i	0.191166	−	0.239885i
$61$	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
$65$	−4878.91	−	3888.02i	−1.15477	−	0.920242i
$66$	4790.70			1.09979
$67$	−1090.73	−	1090.73i	−0.242979	−	0.242979i	0.575102	−	0.818081i	$-0.304962\pi$
$67$	−1090.73	−	1090.73i	−0.242979	−	0.242979i	−0.818081	+	0.575102i	$0.804962\pi$
$68$	1057.71	−	1057.71i	0.228744	−	0.228744i
$69$		−	3572.09i		−	0.750281i
$70$	2365.40	−	267.351i	0.482735	−	0.0545615i
$71$	−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	$-0.668509\pi$
$73$	1908.39	−	1908.39i	0.358114	−	0.358114i	0.863117	+	0.505003i	$0.168509\pi$
$74$		−	3078.45i		−	0.562171i
$75$	−1406.23	+	2241.46i	−0.249996	+	0.398482i
$76$	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	$0.132275\pi$
$79$			5038.95i			0.807395i	−0.914893	+	0.403697i	$0.867725\pi$
$80$	−881.863	−	7802.32i	−0.137791	−	1.21911i
$81$	−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	$-0.849173\pi$
$83$	−2986.51	+	2986.51i	−0.433519	+	0.433519i	0.456305	+	0.889824i	$0.349173\pi$
$84$		−	818.050i		−	0.115937i
$85$	−2233.82	+	2803.12i	−0.309179	+	0.387975i
$86$	−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	$0.208102\pi$
$89$			9634.86i			1.21637i	−0.793796	+	0.608185i	$0.791898\pi$
$90$	−6340.32	−	5052.62i	−0.782755	−	0.623780i
$91$	−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
$95$	−3799.48	+	429.439i	−0.420995	+	0.0475833i
$96$	−4897.73			−0.531437
$97$	−2618.19	−	2618.19i	−0.278265	−	0.278265i	0.554151	−	0.832416i	$-0.313043\pi$
$97$	−2618.19	−	2618.19i	−0.278265	−	0.278265i	−0.832416	+	0.554151i	$0.813043\pi$
$98$	1246.96	−	1246.96i	0.129838	−	0.129838i
$99$		−	13882.5i		−	1.41644i
$100$	−1455.42	−	6356.19i	−0.145542	−	0.635619i
$101$	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	$-0.899603\pi$
$103$	−6794.71	+	6794.71i	−0.640466	+	0.640466i	0.310204	+	0.950670i	$0.399603\pi$
$104$			7142.28i			0.660344i
$105$	220.154	+	1947.82i	0.0199686	+	0.176673i
$106$	−4029.15			−0.358593
$107$	6174.02	+	6174.02i	0.539263	+	0.539263i	0.923313	−	0.384049i	$-0.125471\pi$
$107$	6174.02	+	6174.02i	0.539263	+	0.539263i	−0.384049	+	0.923313i	$0.625471\pi$
$108$	−4499.96	+	4499.96i	−0.385799	+	0.385799i
$109$			4665.43i			0.392680i	0.980536	+	0.196340i	$0.0629056\pi$
$109$			4665.43i			0.392680i	−0.980536	+	0.196340i	$0.937094\pi$
$110$	17630.3	−	22123.5i	1.45705	−	1.82839i
$111$	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	$-0.554838\pi$
$113$	10391.0	−	10391.0i	0.813769	−	0.813769i	0.985197	+	0.171427i	$0.0548379\pi$
$114$			3329.16i			0.256168i
$115$	−16495.9	−	13145.7i	−1.24733	−	0.994001i
$116$	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
$120$	3010.17	−	340.226i	0.209039	−	0.0236268i
$121$	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
$125$	5176.02	+	14742.8i	0.331265	+	0.943538i
$126$	−6005.98			−0.378306
$127$	−4261.99	−	4261.99i	−0.264244	−	0.264244i	0.562532	−	0.826776i	$-0.309827\pi$
$127$	−4261.99	−	4261.99i	−0.264244	−	0.264244i	−0.826776	+	0.562532i	$0.809827\pi$
$128$	−9734.78	+	9734.78i	−0.594164	+	0.594164i
$129$		−	3761.95i		−	0.226065i
$130$	3602.34	+	31871.8i	0.213156	+	1.88591i
$131$	−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
$135$	9503.64	−	11925.7i	0.521462	−	0.654360i
$136$	4103.51			0.221860
$137$	−180.184	−	180.184i	−0.00960008	−	0.00960008i	0.702290	−	0.711891i	$-0.252161\pi$
$137$	−180.184	−	180.184i	−0.00960008	−	0.00960008i	−0.711891	+	0.702290i	$0.752161\pi$
$138$	−12986.2	+	12986.2i	−0.681904	+	0.681904i
$139$		−	23370.3i		−	1.20958i	−0.796384	−	0.604791i	$-0.793257\pi$
$139$		−	23370.3i		−	1.20958i	0.796384	−	0.604791i	$-0.206743\pi$
$140$	−3777.76	−	3010.51i	−0.192743	−	0.153597i
$141$	−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
$145$	−19923.0	+	2251.81i	−0.947586	+	0.107102i
$146$	−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	$-0.800040\pi$
$149$		−	26094.3i		−	1.17537i	0.809091	−	0.587684i	$-0.199960\pi$
$150$	13261.0	−	3036.46i	0.589378	−	0.134954i
$151$	−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
$155$	493.687	+	4367.91i	0.0205489	+	0.181807i
$156$	11022.5			0.452932
$157$	−25099.1	−	25099.1i	−1.01826	−	1.01826i	−0.999830	−	0.0184285i	$-0.994134\pi$
$157$	−25099.1	−	25099.1i	−1.01826	−	1.01826i	−0.0184285	−	0.999830i	$-0.505866\pi$
$158$	18318.9	−	18318.9i	0.733812	−	0.733812i
$159$		−	3317.87i		−	0.131240i
$160$	−18024.1	+	22617.7i	−0.704068	+	0.883505i
$161$	−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	$-0.763473\pi$
$163$	−1589.95	+	1589.95i	−0.0598424	+	0.0598424i	0.676552	+	0.736395i	$0.263473\pi$
$164$			9595.88i			0.356777i
$165$	18217.9	+	14517.9i	0.669161	+	0.533257i
$166$	21714.7			0.788020
$167$	−11320.6	−	11320.6i	−0.405917	−	0.405917i	0.474395	−	0.880312i	$-0.342667\pi$
$167$	−11320.6	−	11320.6i	−0.405917	−	0.405917i	−0.880312	+	0.474395i	$0.842667\pi$
$168$	1586.86	−	1586.86i	0.0562238	−	0.0562238i
$169$		−	33711.8i		−	1.18034i
$170$	18311.6	−	2069.68i	0.633619	−	0.0716152i
$171$	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	$-0.673978\pi$
$173$	10012.9	−	10012.9i	0.334555	−	0.334555i	0.854313	+	0.519758i	$0.173978\pi$
$174$			17456.8i			0.576588i
$175$	9805.26	+	6151.53i	0.320172	+	0.200866i
$176$	−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	$-0.898065\pi$
$179$		−	20172.5i		−	0.629584i	0.949161	−	0.314792i	$-0.101935\pi$
$180$	1847.73	+	16347.8i	0.0570286	+	0.504563i
$181$	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
$185$	9329.06	−	11706.6i	0.272580	−	0.342049i
$186$	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
$190$	15374.1	+	12251.6i	0.425874	+	0.339381i
$191$	−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	$-0.797134\pi$
$193$	−7771.80	+	7771.80i	−0.208645	+	0.208645i	0.595047	+	0.803691i	$0.297134\pi$
$194$			19036.7i			0.505810i
$195$	−26245.3	+	2966.40i	−0.690213	+	0.0780118i
$196$	−3578.55			−0.0931527
$197$	37777.3	+	37777.3i	0.973416	+	0.973416i	0.999656	−	0.0262392i	$-0.00835317\pi$
$197$	37777.3	+	37777.3i	0.973416	+	0.973416i	−0.0262392	+	0.999656i	$0.508353\pi$
$198$	−50469.3	+	50469.3i	−1.28735	+	1.28735i
$199$			20867.2i			0.526937i	0.964668	+	0.263469i	$0.0848666\pi$
$199$			20867.2i			0.526937i	−0.964668	+	0.263469i	$0.915133\pi$
$200$	9506.56	−	15153.0i	0.237664	−	0.378826i
$201$	−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
$205$	−2582.45	−	22848.4i	−0.0614504	−	0.543685i
$206$	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
$210$	6280.87	−	7881.60i	0.142423	−	0.178721i
$211$	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
$215$	−17372.7	−	13844.4i	−0.375829	−	0.299499i
$216$	−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
$220$	−57043.0	+	6447.32i	−1.17857	+	0.133209i
$221$	−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	$-0.502316\pi$
$223$	49365.9	−	49365.9i	0.992698	−	0.992698i	0.999974	+	0.00727547i	$0.00231588\pi$
$224$			21425.1i			0.426998i
$225$	−8799.09	−	38427.9i	−0.173809	−	0.759069i
$226$	−75552.2			−1.47921
$227$	60511.8	+	60511.8i	1.17433	+	1.17433i	0.981168	+	0.193158i	$0.0618729\pi$
$227$	60511.8	+	60511.8i	1.17433	+	1.17433i	0.193158	+	0.981168i	$0.438127\pi$
$228$	4777.03	−	4777.03i	0.0918943	−	0.0918943i
$229$			83.0802i			0.00158426i	1.00000		0.000792130i	$0.000252143\pi$
$229$			83.0802i			0.00158426i	−1.00000		0.000792130i	$0.999748\pi$
$230$	12179.7	+	107761.i	0.230241	+	2.03707i
$231$	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	$-0.635895\pi$
$233$	26936.3	−	26936.3i	0.496166	−	0.496166i	0.910242	+	0.414076i	$0.135895\pi$
$234$		−	80925.7i		−	1.47793i
$235$	−48666.3	+	61069.2i	−0.881237	+	1.10583i
$236$	−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	$0.00826032\pi$
$239$			2964.31i			0.0518953i	−0.999663	+	0.0259476i	$0.991740\pi$
$240$	−25997.6	−	20717.6i	−0.451347	−	0.359680i
$241$	−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
$245$	8520.75	−	963.064i	0.141953	−	0.0160444i
$246$	−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
$250$	34779.5	−	72413.9i	0.556472	−	1.15862i
$251$	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
$255$	1704.31	+	15079.0i	0.0262101	+	0.231895i
$256$	85539.5			1.30523
$257$	7872.26	+	7872.26i	0.119188	+	0.119188i	0.764185	−	0.644997i	$-0.223141\pi$
$257$	7872.26	+	7872.26i	0.119188	+	0.119188i	−0.644997	+	0.764185i	$0.723141\pi$
$258$	−13676.4	+	13676.4i	−0.205462	+	0.205462i
$259$		−	11089.3i		−	0.165313i
$260$	40564.1	−	50902.2i	0.600061	−	0.752991i
$261$	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	$-0.589501\pi$
$263$	47259.4	−	47259.4i	0.683246	−	0.683246i	0.960730	+	0.277484i	$0.0895007\pi$
$264$		−	26669.3i		−	0.382652i
$265$	−15321.9	−	12210.1i	−0.218183	−	0.173871i
$266$	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	$0.354620\pi$
$269$			129888.i			1.79500i	−0.441010	+	0.897502i	$0.645380\pi$
$270$	−77905.5	+	8805.33i	−1.06866	+	0.120786i
$271$	−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
$275$	134088.	−	30702.9i	1.77306	−	0.405989i
$276$	37268.0			0.489235
$277$	−73039.6	−	73039.6i	−0.951916	−	0.951916i	0.0469796	−	0.998896i	$-0.485040\pi$
$277$	−73039.6	−	73039.6i	−0.951916	−	0.951916i	−0.998896	+	0.0469796i	$0.985040\pi$
$278$	−84961.9	+	84961.9i	−1.09935	+	1.09935i
$279$		−	11090.6i		−	0.142477i
$280$	−1488.32	−	13167.9i	−0.0189836	−	0.167959i
$281$	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	$-0.704450\pi$
$283$	16152.8	−	16152.8i	0.201685	−	0.201685i	0.800722	+	0.599037i	$0.204450\pi$
$284$		−	16926.7i		−	0.209863i
$285$	−10088.8	+	12660.0i	−0.124208	+	0.155863i
$286$	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
$290$	80615.6	+	64242.8i	0.958568	+	0.763886i
$291$	−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	$-0.763924\pi$
$293$	−5309.17	+	5309.17i	−0.0618431	+	0.0618431i	0.675509	+	0.737352i	$0.263924\pi$
$294$		−	7465.99i		−	0.0863759i
$295$	78621.8	−	8886.29i	0.903439	−	0.102112i
$296$	−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
$300$	−23385.4	−	14671.3i	−0.259838	−	0.163014i
$301$	−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
$305$	−14875.2	−	131609.i	−0.159906	−	1.41477i
$306$	−46494.9			−0.496550
$307$	−41603.9	−	41603.9i	−0.441425	−	0.441425i	0.451065	−	0.892491i	$-0.351044\pi$
$307$	−41603.9	−	41603.9i	−0.441425	−	0.441425i	−0.892491	+	0.451065i	$0.851044\pi$
$308$	−30071.2	+	30071.2i	−0.316993	+	0.316993i
$309$			40682.3i			0.426077i
$310$	14084.6	−	17674.1i	0.146562	−	0.183914i
$311$	−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	$-0.890744\pi$
$313$	−59284.2	+	59284.2i	−0.605133	+	0.605133i	0.336537	+	0.941670i	$0.390744\pi$
$314$			182493.i			1.85092i
$315$	−22839.4	−	18200.8i	−0.230177	−	0.183429i
$316$	−52571.9			−0.526477
$317$	12194.9	+	12194.9i	0.121355	+	0.121355i	0.765176	−	0.643821i	$-0.222652\pi$
$317$	12194.9	+	12194.9i	0.121355	+	0.121355i	−0.643821	+	0.765176i	$0.722652\pi$
$318$	−12062.0	+	12062.0i	−0.119279	+	0.119279i
$319$			176513.i			1.73458i
$320$	22914.6	−	2589.94i	0.223776	−	0.0252924i
$321$	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
$325$	−82886.8	+	132118.i	−0.784727	+	1.25082i
$326$	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
$330$	−13451.2	−	119010.i	−0.123518	−	1.09283i
$331$	−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
$335$	−24033.3	+	30158.3i	−0.214153	+	0.268731i
$336$	−24626.7			−0.218136
$337$	−39492.6	−	39492.6i	−0.347741	−	0.347741i	0.511527	−	0.859267i	$-0.329080\pi$
$337$	−39492.6	−	39492.6i	−0.347741	−	0.347741i	−0.859267	+	0.511527i	$0.829080\pi$
$338$	−122558.	+	122558.i	−1.07277	+	1.07277i
$339$		−	62214.6i		−	0.541369i
$340$	−29245.3	−	23305.7i	−0.252987	−	0.201606i
$341$	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
$345$	−88737.2	+	10029.6i	−0.745534	+	0.0842646i
$346$	−72802.9			−0.608130
$347$	−93020.1	−	93020.1i	−0.772534	−	0.772534i	0.206015	−	0.978549i	$-0.433951\pi$
$347$	−93020.1	−	93020.1i	−0.772534	−	0.772534i	−0.978549	+	0.206015i	$0.933951\pi$
$348$	25048.9	−	25048.9i	0.206838	−	0.206838i
$349$		−	158624.i		−	1.30232i	−0.758939	−	0.651162i	$-0.774282\pi$
$349$		−	158624.i		−	1.30232i	0.758939	−	0.651162i	$-0.225718\pi$
$350$	−13283.0	−	58010.2i	−0.108433	−	0.473553i
$351$	152216.			1.23551
$352$	180039.	+	180039.i	1.45305	+	1.45305i
$353$	153311.	−	153311.i	1.23034	−	1.23034i	0.266502	−	0.963834i	$-0.414132\pi$
$353$	153311.	−	153311.i	1.23034	−	1.23034i	0.963834	−	0.266502i	$-0.0858678\pi$
$354$		−	68889.5i		−	0.549726i
$355$	4555.34	+	40303.5i	0.0361463	+	0.319806i
$356$	−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	$0.0221024\pi$
$359$			17883.8i			0.138762i	−0.997590	+	0.0693811i	$0.977898\pi$
$360$	−28127.4	+	35295.9i	−0.217033	+	0.272345i
$361$	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
$365$	−52766.2	−	42049.6i	−0.396069	−	0.315628i
$366$	−115318.			−0.860862
$367$	157754.	+	157754.i	1.17125	+	1.17125i	0.981912	+	0.189337i	$0.0606337\pi$
$367$	157754.	+	157754.i	1.17125	+	1.17125i	0.189337	+	0.981912i	$0.439366\pi$
$368$	187382.	−	187382.i	1.38367	−	1.38367i
$369$			58014.2i			0.426071i
$370$	−76474.3	+	8643.57i	−0.558615	+	0.0631378i
$371$	−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	$-0.670506\pi$
$373$	48628.6	−	48628.6i	0.349522	−	0.349522i	0.859931	+	0.510410i	$0.170506\pi$
$374$		−	162236.i		−	1.15986i
$375$	59630.4	+	28639.7i	0.424038	+	0.203660i
$376$	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	$0.183962\pi$
$379$			156941.i			1.09259i	−0.837593	+	0.546295i	$0.816038\pi$
$380$	−4480.38	−	39640.4i	−0.0310276	−	0.274518i
$381$	−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	$-0.618194\pi$
$383$	83467.3	−	83467.3i	0.569009	−	0.569009i	0.931851	+	0.362842i	$0.118194\pi$
$384$			58285.5i			0.395274i
$385$	63508.5	−	79694.1i	0.428460	−	0.537656i
$386$	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	$0.281163\pi$
$389$			233893.i			1.54567i	−0.634605	+	0.772837i	$0.718837\pi$
$390$	106198.	+	84629.6i	0.698212	+	0.556407i
$391$	−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
$395$	125177.	−	14148.2i	0.802286	−	0.0906790i
$396$	144838.			0.923616
$397$	66916.0	+	66916.0i	0.424570	+	0.424570i	0.886774	−	0.462204i	$-0.152941\pi$
$397$	66916.0	+	66916.0i	0.424570	+	0.424570i	−0.462204	+	0.886774i	$0.652941\pi$
$398$	75862.0	−	75862.0i	0.478915	−	0.478915i
$399$			11992.4i			0.0753289i
$400$	−191348.	+	43814.2i	−1.19592	+	0.273839i
$401$	−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
$405$	7094.40	+	62768.0i	0.0432519	+	0.382673i
$406$	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	$0.00892015\pi$
$409$			9374.36i			0.0560396i	−0.999607	+	0.0280198i	$0.991080\pi$
$410$	−73675.9	+	92452.6i	−0.438286	+	0.549986i
$411$	−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
$415$	82575.8	+	65805.0i	0.479465	+	0.382087i
$416$	−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	$0.273366\pi$
$419$			265821.i			1.51412i	−0.653343	+	0.757062i	$0.726634\pi$
$420$	−20321.9	+	2296.89i	−0.115203	+	0.0130209i
$421$	−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
$425$	75906.7	+	47621.6i	0.420245	+	0.263649i
$426$	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
$430$	12827.1	+	113488.i	0.0693731	+	0.613782i
$431$	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	−0.00241596	+	0.999997i	$0.500769\pi$
$433$	−187941.	+	187941.i	−1.00241	+	1.00241i	−0.999997	+	0.00241596i	$0.999231\pi$
$434$		−	16742.2i		−	0.0888858i
$435$	−52901.7	+	66384.1i	−0.279571	+	0.350821i
$436$	−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	$-0.722424\pi$
$439$		−	295109.i		−	1.53128i	0.643272	−	0.765638i	$-0.277576\pi$
$440$	−123159.	−	98146.0i	−0.636153	−	0.506952i
$441$	−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	$-0.758694\pi$
$443$	−7579.35	+	7579.35i	−0.0386211	+	0.0386211i	0.687533	+	0.726154i	$0.258694\pi$
$444$			26447.9i			0.134161i
$445$	239348.	−	27052.4i	1.20867	−	0.136611i
$446$	−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	$-0.722589\pi$
$449$		−	308572.i		−	1.53061i	0.643669	−	0.765304i	$-0.277411\pi$
$450$	−107714.	+	171692.i	−0.531922	+	0.847860i
$451$	−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
$455$	12976.5	+	114810.i	0.0626808	+	0.554571i
$456$	18533.1			0.0891288
$457$	−47861.1	−	47861.1i	−0.229166	−	0.229166i	0.583178	−	0.812344i	$-0.301809\pi$
$457$	−47861.1	−	47861.1i	−0.229166	−	0.229166i	−0.812344	+	0.583178i	$0.801809\pi$
$458$	302.034	−	302.034i	0.00143988	−	0.00143988i
$459$		−	87453.8i		−	0.415101i
$460$	137150.	−	172104.i	0.648157	−	0.813344i
$461$	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	$-0.821558\pi$
$463$	−67580.4	+	67580.4i	−0.315252	+	0.315252i	0.531688	+	0.846940i	$0.321558\pi$
$464$		−	251890.i		−	1.16997i
$465$	14554.0	+	11598.2i	0.0673097	+	0.0536393i
$466$	−195852.			−0.901895
$467$	172621.	+	172621.i	0.791517	+	0.791517i	0.981741	−	0.190223i	$-0.0609213\pi$
$467$	172621.	+	172621.i	0.791517	+	0.791517i	−0.190223	+	0.981741i	$0.560921\pi$
$468$	−116121.	+	116121.i	−0.530175	+	0.530175i
$469$			28568.1i			0.129878i
$470$	398939.	−	45090.4i	1.80597	−	0.204121i
$471$	−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
$475$	21336.1	+	93180.3i	0.0945645	+	0.412988i
$476$	−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	$-0.958971\pi$
$479$		−	58984.8i		−	0.257080i	0.991704	−	0.128540i	$-0.0410291\pi$
$480$	13751.7	+	121668.i	0.0596861	+	0.528075i
$481$	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
$485$	−57689.5	+	72392.0i	−0.245252	+	0.307756i
$486$	309019.			1.30832
$487$	−145300.	−	145300.i	−0.612645	−	0.612645i	0.330989	−	0.943635i	$-0.392618\pi$
$487$	−145300.	−	145300.i	−0.612645	−	0.612645i	−0.943635	+	0.330989i	$0.892618\pi$
$488$	−107220.	+	107220.i	−0.450231	+	0.450231i
$489$			9519.60i			0.0398108i
$490$	−34478.0	−	27475.6i	−0.143598	−	0.114434i
$491$	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
$495$	−344867.	+	38978.9i	−1.40748	+	0.159081i
$496$	−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	$0.0681859\pi$
$499$			105864.i			0.425155i	−0.977144	+	0.212578i	$0.931814\pi$
$500$	−153813.	+	54001.9i	−0.615251	+	0.216008i
$501$	−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	$-0.774078\pi$
$503$	−27040.0	+	27040.0i	−0.106874	+	0.106874i	0.651648	+	0.758522i	$0.274078\pi$
$504$			33434.7i			0.131624i
$505$	−48884.6	−	432508.i	−0.191685	−	1.69595i
$506$	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	$0.264559\pi$
$509$			382765.i			1.47740i	−0.674037	+	0.738698i	$0.735441\pi$
$510$	48622.9	−	61014.8i	0.186939	−	0.234582i
$511$	−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
$515$	187871.	+	149715.i	0.708345	+	0.564483i
$516$	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
$520$	177427.	−	20053.8i	0.656166	−	0.0741636i
$521$	−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	$-0.748730\pi$
$523$	1542.91	−	1542.91i	0.00564075	−	0.00564075i	0.709922	+	0.704281i	$0.248730\pi$
$524$		−	46444.4i		−	0.169149i
$525$	47769.4	−	10938.1i	0.173313	−	0.0396846i
$526$	−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
$530$	11312.9	+	100092.i	0.0402738	+	0.356324i
$531$	−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
$535$	136039.	−	170709.i	0.475286	−	0.596416i
$536$	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
$540$	124422.	+	99152.4i	0.426688	+	0.340029i
$541$	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
$545$	115898.	−	13099.4i	0.390196	−	0.0441021i
$546$	100598.			0.337446
$547$	239848.	+	239848.i	0.801607	+	0.801607i	0.983347	−	0.181740i	$-0.0581729\pi$
$547$	239848.	+	239848.i	0.801607	+	0.801607i	−0.181740	+	0.983347i	$0.558173\pi$
$548$	1879.88	−	1879.88i	0.00625991	−	0.00625991i
$549$			334168.i			1.10872i
$550$	−599089.	−	375851.i	−1.98046	−	1.24248i
$551$	−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
$555$	−7117.68	−	62974.0i	−0.0231075	−	0.204444i
$556$	243825.			0.788731
$557$	28293.7	+	28293.7i	0.0911967	+	0.0911967i	0.751233	−	0.660037i	$-0.229459\pi$
$557$	28293.7	+	28293.7i	0.0911967	+	0.0911967i	−0.660037	+	0.751233i	$0.729459\pi$
$558$	−40319.3	+	40319.3i	−0.129492	+	0.129492i
$559$		−	221739.i		−	0.709608i
$560$	−90629.0	+	113726.i	−0.288995	+	0.362648i
$561$	133596.			0.424490
$562$	−316165.	−	316165.i	−1.00102	−	1.00102i
$563$	174942.	−	174942.i	0.551920	−	0.551920i	−0.375074	−	0.926995i	$-0.622383\pi$
$563$	174942.	−	174942.i	0.551920	−	0.551920i	0.926995	+	0.375074i	$0.122383\pi$
$564$		−	137969.i		−	0.433734i
$565$	−287308.	−	228956.i	−0.900016	−	0.717226i
$566$	−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	$0.298589\pi$
$569$			522164.i			1.61281i	−0.591367	+	0.806403i	$0.701411\pi$
$570$	82702.3	−	9347.49i	0.254547	−	0.0287704i
$571$	−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
$575$	−280246.	+	446699.i	−0.847624	+	1.35107i
$576$	−58182.5			−0.175367
$577$	−203594.	−	203594.i	−0.611524	−	0.611524i	0.331819	−	0.943343i	$-0.392338\pi$
$577$	−203594.	−	203594.i	−0.611524	−	0.611524i	−0.943343	+	0.331819i	$0.892338\pi$
$578$	−228907.	+	228907.i	−0.685178	+	0.685178i
$579$			46532.5i			0.138803i
$580$	−23493.4	−	207859.i	−0.0698376	−	0.617891i
$581$	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
$585$	245240.	−	307742.i	0.716606	−	0.899237i
$586$	38602.5			0.112414
$587$	−148674.	−	148674.i	−0.431477	−	0.431477i	0.457654	−	0.889131i	$-0.348690\pi$
$587$	−148674.	−	148674.i	−0.431477	−	0.431477i	−0.889131	+	0.457654i	$0.848690\pi$
$588$	−10713.0	+	10713.0i	−0.0309854	+	0.0309854i
$589$			26892.5i			0.0775177i
$590$	−318132.	−	253521.i	−0.913910	−	0.728298i
$591$	226186.			0.647576
$592$	132979.	+	132979.i	0.379437	+	0.379437i
$593$	184484.	−	184484.i	0.524626	−	0.524626i	−0.394339	−	0.918965i	$-0.629026\pi$
$593$	184484.	−	184484.i	0.524626	−	0.524626i	0.918965	+	0.394339i	$0.129026\pi$
$594$			690224.i			1.95622i
$595$	65962.8	−	7455.49i	0.186322	−	0.0210592i
$596$	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	$-0.971658\pi$
$599$		−	63809.1i		−	0.177840i	0.996039	−	0.0889199i	$-0.0283415\pi$
$600$	−16903.7	−	73822.7i	−0.0469547	−	0.205063i
$601$	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
$605$	−94901.7	−	839647.i	−0.259277	−	2.29396i
$606$	−378970.			−1.03195
$607$	−55070.6	−	55070.6i	−0.149466	−	0.149466i	0.628413	−	0.777880i	$-0.283705\pi$
$607$	−55070.6	−	55070.6i	−0.149466	−	0.149466i	−0.777880	+	0.628413i	$0.783705\pi$
$608$	−125113.	+	125113.i	−0.338449	+	0.338449i
$609$			62883.6i			0.169552i
$610$	−424381.	+	532537.i	−1.14050	+	1.43117i
$611$	−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	$-0.758619\pi$
$613$	−14387.2	+	14387.2i	−0.0382873	+	0.0382873i	0.687704	+	0.725991i	$0.258619\pi$
$614$			302498.i			0.802392i
$615$	−76131.5	−	60669.5i	−0.201286	−	0.160406i
$616$	−116665.			−0.307453
$617$	−267377.	−	267377.i	−0.702350	−	0.702350i	0.262564	−	0.964915i	$-0.415432\pi$
$617$	−267377.	−	267377.i	−0.702350	−	0.702350i	−0.964915	+	0.262564i	$0.915432\pi$
$618$	147899.	−	147899.i	0.387246	−	0.387246i
$619$			256622.i			0.669749i	0.942263	+	0.334874i	$0.108694\pi$
$619$			256622.i			0.669749i	−0.942263	+	0.334874i	$0.891306\pi$
$620$	−45570.9	+	5150.68i	−0.118551	+	0.0133993i
$621$	514652.			1.33454
$622$	407249.	+	407249.i	1.05264	+	1.05264i
$623$	126176.	−	126176.i	0.325088	−	0.325088i
$624$		−	331825.i		−	0.852196i
$625$	351704.	−	169976.i	0.900363	−	0.435139i
$626$	431051.			1.09997
$627$	100774.	+	100774.i	0.256339	+	0.256339i
$628$	261861.	−	261861.i	0.663975	−	0.663975i
$629$		−	85847.3i		−	0.216983i
$630$	16863.4	+	149200.i	0.0424878	+	0.375912i
$631$	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
$635$	−93908.9	+	117842.i	−0.232894	+	0.292249i
$636$	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
$640$	269163.	+	214497.i	0.657136	+	0.523674i
$641$	−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	$-0.829987\pi$
$643$	−145387.	+	145387.i	−0.351645	+	0.351645i	0.509076	+	0.860721i	$0.329987\pi$
$644$		−	163028.i		−	0.393090i
$645$	−93453.6	+	10562.7i	−0.224635	+	0.0253895i
$646$	112741.			0.270158
$647$	520127.	+	520127.i	1.24251	+	1.24251i	0.958955	+	0.283557i	$0.0915145\pi$
$647$	520127.	+	520127.i	1.24251	+	1.24251i	0.283557	+	0.958955i	$0.408485\pi$
$648$	51136.1	−	51136.1i	0.121780	−	0.121780i
$649$		−	696570.i		−	1.65377i
$650$	781640.	−	178977.i	1.85003	−	0.423615i
$651$	13786.6			0.0325308
$652$	−16588.1	−	16588.1i	−0.0390214	−	0.0390214i
$653$	−515377.	+	515377.i	−1.20864	+	1.20864i	−0.237179	+	0.971466i	$0.576223\pi$
$653$	−515377.	+	515377.i	−1.20864	+	1.20864i	−0.971466	+	0.237179i	$0.923777\pi$
$654$		−	101551.i		−	0.237427i
$655$	12499.2	+	110587.i	0.0291339	+	0.257763i
$656$	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	$-0.712016\pi$
$659$		−	682913.i		−	1.57251i	0.617899	−	0.786257i	$-0.287984\pi$
$660$	−151467.	+	190069.i	−0.347720	+	0.436339i
$661$	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
$665$	55381.1	+	44133.4i	0.125233	+	0.0997985i
$666$	194176.			0.437771
$667$	−478475.	−	478475.i	−1.07549	−	1.07549i
$668$	118109.	−	118109.i	0.264686	−	0.264686i
$669$		−	295571.i		−	0.660403i
$670$	197011.	−	22267.3i	0.438876	−	0.0496043i
$671$	−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	$-0.925056\pi$
$673$	−334777.	+	334777.i	−0.739137	+	0.739137i	0.233274	+	0.972411i	$0.425056\pi$
$674$			287147.i			0.632098i
$675$	−322940.	−	202603.i	−0.708786	−	0.444671i
$676$	351719.			0.769666
$677$	456455.	+	456455.i	0.995911	+	0.995911i	0.999992	−	0.00408059i	$-0.00129890\pi$
$677$	456455.	+	456455.i	0.995911	+	0.995911i	−0.00408059	+	0.999992i	$0.501299\pi$
$678$	−226179.	+	226179.i	−0.492031	+	0.492031i
$679$			68574.7i			0.148739i
$680$	−11521.7	−	101939.i	−0.0249172	−	0.220456i
$681$	362305.			0.781232
$682$	−140687.	−	140687.i	−0.302473	−	0.302473i
$683$	365344.	−	365344.i	0.783179	−	0.783179i	−0.197187	−	0.980366i	$-0.563181\pi$
$683$	365344.	−	365344.i	0.783179	−	0.783179i	0.980366	+	0.197187i	$0.0631807\pi$
$684$			100651.i			0.215132i
$685$	−3970.18	+	4982.01i	−0.00846115	+	0.0106175i
$686$	−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
$690$	359063.	+	286138.i	0.754175	+	0.601005i
$691$	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
$695$	−580562.	+	65618.5i	−1.20193	+	0.135849i
$696$	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
$700$	−64179.5	+	102299.i	−0.130979	+	0.208774i
$701$	−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
$705$	37130.3	+	328512.i	0.0747052	+	0.660957i
$706$	−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	$0.251964\pi$
$709$			715270.i			1.42291i	−0.702731	+	0.711455i	$0.748036\pi$
$710$	129961.	−	163082.i	0.257808	−	0.323512i
$711$	−317836.			−0.628730
$712$	−194993.	−	194993.i	−0.384643	−	0.384643i
$713$	−104901.	+	104901.i	−0.206348	+	0.206348i
$714$		−	57797.5i		−	0.113374i
$715$	1.07381e6	+	855725.i	2.10047	+	1.67387i
$716$	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	$-0.734911\pi$
$719$		−	764914.i		−	1.47964i	0.672807	−	0.739818i	$-0.265089\pi$
$720$	492138.	−	55624.3i	0.949340	−	0.107300i
$721$	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
$725$	111878.	+	488601.i	0.212848	+	0.929562i
$726$	−735710.			−1.39583
$727$	535539.	+	535539.i	1.01326	+	1.01326i	0.999911	+	0.0133519i	$0.00425016\pi$
$727$	535539.	+	535539.i	1.01326	+	1.01326i	0.0133519	+	0.999911i	$0.495750\pi$
$728$	93533.9	−	93533.9i	0.176484	−	0.176484i
$729$			49803.3i			0.0937136i
$730$	38959.9	+	344699.i	0.0731091	+	0.646836i
$731$	−127398.			−0.238411
$732$	165470.	+	165470.i	0.308815	+	0.308815i
$733$	−137194.	+	137194.i	−0.255345	+	0.255345i	−0.823158	−	0.567813i	$-0.807790\pi$
$733$	−137194.	+	137194.i	−0.255345	+	0.255345i	0.567813	+	0.823158i	$0.307790\pi$
$734$		−	1.14702e6i		−	2.12901i
$735$	22625.2	−	28391.4i	0.0418811	−	0.0525548i
$736$	−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	$-0.971180\pi$
$739$		−	98757.6i		−	0.180835i	0.995904	−	0.0904173i	$-0.0288201\pi$
$740$	122136.	+	97331.0i	0.223040	+	0.177741i
$741$	−161588.			−0.294288
$742$	52765.0	+	52765.0i	0.0958381	+	0.0958381i
$743$	−154662.	+	154662.i	−0.280160	+	0.280160i	−0.833173	−	0.553013i	$-0.813478\pi$
$743$	−154662.	+	154662.i	−0.280160	+	0.280160i	0.553013	+	0.833173i	$0.313478\pi$
$744$		−	21305.8i		−	0.0384903i
$745$	−648231.	+	73266.8i	−1.16793	+	0.132006i
$746$	−353574.			−0.635335
$747$	−188377.	−	188377.i	−0.337587	−	0.337587i
$748$	−232794.	+	232794.i	−0.416072	+	0.416072i
$749$		−	161708.i		−	0.288248i
$750$	−112665.	−	320902.i	−0.200293	−	0.570493i
$751$	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
$755$	2141.02	+	18942.7i	0.00375601	+	0.0332314i
$756$	117861.			0.206218
$757$	−524986.	−	524986.i	−0.916128	−	0.916128i	0.0806176	−	0.996745i	$-0.474311\pi$
$757$	−524986.	−	524986.i	−0.916128	−	0.916128i	−0.996745	+	0.0806176i	$0.974311\pi$
$758$	570551.	−	570551.i	0.993015	−	0.993015i
$759$			786190.i			1.36472i
$760$	68203.7	−	85585.9i	0.118081	−	0.148175i
$761$	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
$765$	−176809.	−	140900.i	−0.302122	−	0.240762i
$766$	−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	$-0.908593\pi$
$769$		−	334985.i		−	0.566465i	0.959051	−	0.283233i	$-0.0914068\pi$
$770$	−520607.	+	58842.0i	−0.878069	+	0.0992444i
$771$	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	$-0.810847\pi$
$773$	−160551.	+	160551.i	−0.268691	+	0.268691i	0.559881	+	0.828573i	$0.310847\pi$
$774$		−	288158.i		−	0.481004i
$775$	107121.	−	24528.2i	0.178349	−	0.0408377i
$776$	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
$780$	−30948.7	−	273820.i	−0.0508690	−	0.450066i
$781$	357079.			0.585413
$782$	439775.	+	439775.i	0.719146	+	0.719146i
$783$	345913.	−	345913.i	0.564213	−	0.564213i
$784$			107729.i			0.175268i
$785$	−553034.	+	693979.i	−0.897455	+	1.12618i
$786$	96897.6			0.156844
$787$	−137724.	−	137724.i	−0.222362	−	0.222362i	0.587130	−	0.809492i	$-0.300258\pi$
$787$	−137724.	−	137724.i	−0.222362	−	0.222362i	−0.809492	+	0.587130i	$0.800258\pi$
$788$	−394135.	+	394135.i	−0.634734	+	0.634734i
$789$		−	282958.i		−	0.454536i
$790$	−506510.	−	403639.i	−0.811584	−	0.646754i
$791$	−272158.			−0.434978
$792$	280958.	+	280958.i	0.447910	+	0.447910i
$793$	934839.	−	934839.i	1.48659	−	1.48659i
$794$		−	486541.i		−	0.771753i
$795$	−82421.9	+	9315.80i	−0.130409	+	0.0147396i
$796$	−217710.			−0.343599
$797$	−220496.	−	220496.i	−0.347124	−	0.347124i	0.511913	−	0.859037i	$-0.328937\pi$
$797$	−220496.	−	220496.i	−0.347124	−	0.347124i	−0.859037	+	0.511913i	$0.828937\pi$
$798$	43598.0	−	43598.0i	0.0684637	−	0.0684637i
$799$			447834.i			0.701493i
$800$	612473.	+	384247.i	0.956989	+	0.600387i
$801$	−607727.			−0.947204
$802$	858054.	+	858054.i	1.33403	+	1.33403i
$803$	−420023.	+	420023.i	−0.651391	+	0.651391i
$804$		−	68134.4i		−	0.105403i
$805$	43874.4	+	388180.i	0.0677048	+	0.599021i
$806$	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	$0.360060\pi$
$809$			1.18449e6i			1.80982i	−0.425608	+	0.904908i	$0.639940\pi$
$810$	202399.	−	253982.i	0.308488	−	0.387108i
$811$	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
$815$	43961.6	+	35033.1i	0.0661847	+	0.0527429i
$816$	−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
$820$	238379.	−	26943.0i	0.354520	−	0.0400699i
$821$	−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	$-0.892331\pi$
$823$	−414184.	+	414184.i	−0.611497	+	0.611497i	0.331839	+	0.943336i	$0.392331\pi$
$824$		−	275026.i		−	0.405060i
$825$	309500.	−	493329.i	0.454729	−	0.724817i
$826$	−301357.			−0.441693
$827$	832331.	+	832331.i	1.21698	+	1.21698i	0.968683	+	0.248301i	$0.0798722\pi$
$827$	832331.	+	832331.i	1.21698	+	1.21698i	0.248301	+	0.968683i	$0.420128\pi$
$828$	−392613.	+	392613.i	−0.572669	+	0.572669i
$829$		−	265850.i		−	0.386837i	−0.981116	−	0.193419i	$-0.938042\pi$
$829$		−	265850.i		−	0.386837i	0.981116	−	0.193419i	$-0.0619575\pi$
$830$	−60969.7	−	539432.i	−0.0885030	−	0.783034i
$831$	−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
$835$	−249439.	+	313010.i	−0.357760	+	0.448937i
$836$	−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	$-0.837601\pi$
$839$		−	687513.i		−	0.976691i	0.872650	−	0.488345i	$-0.162399\pi$
$840$	−43876.1	−	34965.0i	−0.0621826	−	0.0495536i
$841$	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
$845$	−837463.	+	94654.9i	−1.17288	+	0.132565i
$846$	−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
$850$	−102829.	−	449082.i	−0.142324	−	0.621567i
$851$	505197.			0.697593
$852$	−50673.0	−	50673.0i	−0.0698068	−	0.0698068i
$853$	−266208.	+	266208.i	−0.365866	+	0.365866i	−0.865967	−	0.500101i	$-0.833296\pi$
$853$	−266208.	+	266208.i	−0.365866	+	0.365866i	0.500101	+	0.865967i	$0.333296\pi$
$854$			504456.i			0.691684i
$855$	−27087.2	−	239656.i	−0.0370538	−	0.327835i
$856$	−249903.			−0.341054
$857$	882590.	+	882590.i	1.20170	+	1.20170i	0.973648	+	0.228056i	$0.0732368\pi$
$857$	882590.	+	882590.i	1.20170	+	1.20170i	0.228056	+	0.973648i	$0.426763\pi$
$858$	845343.	−	845343.i	1.14831	−	1.14831i
$859$			558403.i			0.756765i	0.925649	+	0.378383i	$0.123520\pi$
$859$			558403.i			0.756765i	−0.925649	+	0.378383i	$0.876480\pi$
$860$	144440.	−	181251.i	0.195294	−	0.245066i
$861$	−72117.0			−0.0972818
$862$	−942732.	−	942732.i	−1.26874	−	1.26874i
$863$	795231.	−	795231.i	1.06776	−	1.06776i	0.0702242	−	0.997531i	$-0.477629\pi$
$863$	795231.	−	795231.i	1.06776	−	1.06776i	0.997531	−	0.0702242i	$-0.0223715\pi$
$864$		−	705644.i		−	0.945275i
$865$	−276852.	−	220625.i	−0.370012	−	0.294864i
$866$	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
$870$	433659.	−	49014.6i	0.572940	−	0.0647570i
$871$	−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
$875$	125284.	−	260853.i	0.163637	−	0.340705i
$876$	119211.			0.155348
$877$	−835839.	−	835839.i	−1.08673	−	1.08673i	−0.995863	−	0.0908715i	$-0.971035\pi$
$877$	−835839.	−	835839.i	−1.08673	−	1.08673i	−0.0908715	−	0.995863i	$-0.528965\pi$
$878$	−1.07286e6	+	1.07286e6i	−1.39172	+	1.39172i
$879$			31787.8i			0.0411418i
$880$	194092.	+	1.71723e6i	0.250635	+	2.21750i
$881$	−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	$-0.748697\pi$
$883$	4513.98	−	4513.98i	0.00578946	−	0.00578946i	0.709996	+	0.704206i	$0.248697\pi$
$884$		−	373277.i		−	0.477668i
$885$	208765.	−	261971.i	0.266546	−	0.334477i
$886$	55108.8			0.0702027
$887$	−706482.	−	706482.i	−0.897953	−	0.897953i	0.0973016	−	0.995255i	$-0.468979\pi$
$887$	−706482.	−	706482.i	−0.897953	−	0.897953i	−0.995255	+	0.0973016i	$0.968979\pi$
$888$	−51303.9	+	51303.9i	−0.0650615	+	0.0650615i
$889$			111628.i			0.141244i
$890$	−968486.	−	771790.i	−1.22268	−	0.974359i
$891$	556109.			0.700494
$892$	515039.	+	515039.i	0.647307	+	0.647307i
$893$	−337812.	+	337812.i	−0.423615	+	0.423615i
$894$			567989.i			0.710665i
$895$	−501121.	+	56639.6i	−0.625600	+	0.0707089i
$896$	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
$900$	400922.	−	91801.7i	0.494965	−	0.113335i
$901$	−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
$905$	−49421.4	−	437258.i	−0.0603418	−	0.533877i
$906$	16597.9			0.0202207
$907$	−80791.0	−	80791.0i	−0.0982084	−	0.0982084i	0.656296	−	0.754504i	$-0.272122\pi$
$907$	−80791.0	−	80791.0i	−0.0982084	−	0.0982084i	−0.754504	+	0.656296i	$0.772122\pi$
$908$	−631326.	+	631326.i	−0.765741	+	0.765741i
$909$			1.09818e6i			1.32907i
$910$	370212.	−	464562.i	0.447061	−	0.560998i
$911$	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
$915$	−438526.	−	349463.i	−0.523785	−	0.417406i
$916$	−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	$-0.985009\pi$
$919$		−	79518.7i		−	0.0941539i	0.998891	−	0.0470769i	$-0.0149906\pi$
$920$	599893.	−	67803.4i	0.708759	−	0.0801080i
$921$	−249097.			−0.293663
$922$	−914434.	−	914434.i	−1.07570	−	1.07570i
$923$	−286282.	+	286282.i	−0.336039	+	0.336039i
$924$			180047.i			0.210883i
$925$	−317008.	−	198881.i	−0.370499	−	0.232440i
$926$	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	$0.134600\pi$
$929$			708329.i			0.820736i	−0.911920	+	0.410368i	$0.865400\pi$
$930$	−10745.9	−	95075.2i	−0.0124245	−	0.109926i
$931$	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
$935$	491647.	−	616946.i	0.562380	−	0.705707i
$936$	−450505.			−0.514219
$937$	−440943.	−	440943.i	−0.502231	−	0.502231i	0.409899	−	0.912131i	$-0.365564\pi$
$937$	−440943.	−	440943.i	−0.502231	−	0.502231i	−0.912131	+	0.409899i	$0.865564\pi$
$938$	103858.	−	103858.i	0.118041	−	0.118041i
$939$			354955.i			0.402571i
$940$	−637141.	−	507740.i	−0.721075	−	0.574627i
$941$	−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
$945$	−280635.	+	31718.9i	−0.314252	+	0.0355185i
$946$	1.00548e6			1.12354
$947$	−564803.	−	564803.i	−0.629792	−	0.629792i	0.318224	−	0.948016i	$-0.396914\pi$
$947$	−564803.	−	564803.i	−0.629792	−	0.629792i	−0.948016	+	0.318224i	$0.896914\pi$
$948$	−157383.	+	157383.i	−0.175122	+	0.175122i
$949$		−	673491.i		−	0.747824i
$950$	261187.	−	416320.i	0.289403	−	0.461296i
$951$	73015.0			0.0807330
$952$	−53738.8	−	53738.8i	−0.0592945	−	0.0592945i
$953$	−922850.	+	922850.i	−1.01612	+	1.01612i	−0.0162533	+	0.999868i	$0.505174\pi$
$953$	−922850.	+	922850.i	−1.01612	+	1.01612i	−0.999868	+	0.0162533i	$0.994826\pi$
$954$		−	254142.i		−	0.279242i
$955$	184886.	+	1.63579e6i	0.202721	+	1.79358i
$956$	−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
$960$	60845.4	−	76352.3i	0.0660215	−	0.0828476i
$961$	−892605.			−0.966524
$962$	−543208.	−	543208.i	−0.586971	−	0.586971i
$963$	−389432.	+	389432.i	−0.419932	+	0.419932i
$964$		−	51963.7i		−	0.0559173i
$965$	214887.	+	171244.i	0.230758	+	0.183892i
$966$	340129.			0.364493
$967$	621553.	+	621553.i	0.664700	+	0.664700i	0.956484	−	0.291784i	$-0.0942490\pi$
$967$	621553.	+	621553.i	0.664700	+	0.664700i	−0.291784	+	0.956484i	$0.594249\pi$
$968$	−684046.	+	684046.i	−0.730020	+	0.730020i
$969$			92838.6i			0.0988737i
$970$	472906.	−	53450.5i	0.502610	−	0.0568079i
$971$	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
$975$	147382.	+	643653.i	0.155036	+	0.677084i
$976$	1.66396e6			1.74680
$977$	−655904.	−	655904.i	−0.687150	−	0.687150i	0.274451	−	0.961601i	$-0.411504\pi$
$977$	−655904.	−	655904.i	−0.687150	−	0.687150i	−0.961601	+	0.274451i	$0.911504\pi$
$978$	34608.1	−	34608.1i	0.0361826	−	0.0361826i
$979$		−	2.12056e6i		−	2.21251i
$980$	10047.7	+	88897.8i	0.0104620	+	0.0925633i
$981$	−294276.			−0.305785
$982$	−513341.	−	513341.i	−0.532333	−	0.532333i
$983$	831878.	−	831878.i	0.860900	−	0.860900i	−0.130543	−	0.991443i	$-0.541672\pi$
$983$	831878.	−	831878.i	0.860900	−	0.860900i	0.991443	+	0.130543i	$0.0416720\pi$
$984$			111450.i			0.115103i
$985$	832388.	−	1.04453e6i	0.857933	−	1.07658i
$986$	591171.			0.608079
$987$	173181.	+	173181.i	0.177773	+	0.177773i
$988$	281571.	−	281571.i	0.288453	−	0.288453i
$989$		−	749715.i		−	0.766485i
$990$	1.39546e6	+	1.11204e6i	1.42379	+	1.13462i
$991$	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
$995$	518381.	−	58590.3i	0.523603	−	0.0591807i
$996$	−186557.			−0.188059
$997$	225364.	+	225364.i	0.226722	+	0.226722i	0.811322	−	0.584600i	$-0.198748\pi$
$997$	225364.	+	225364.i	0.226722	+	0.226722i	−0.584600	+	0.811322i	$0.698748\pi$
$998$	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	35.5.g.a.22.3	yes	24
5.2	odd	4		175.5.g.c.43.10		24
5.3	odd	4	inner	35.5.g.a.8.3	✓	24
5.4	even	2		175.5.g.c.57.10		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +O(q^{10})\)	\(q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +(-80.1039 + 100.519i) q^{10} -220.093 q^{11} +(31.2333 + 31.2333i) q^{12} +(176.455 - 176.455i) q^{13} +95.2184i q^{14} +(-82.7738 - 65.9628i) q^{15} +314.080 q^{16} +(-101.380 - 101.380i) q^{17} +(229.310 - 229.310i) q^{18} -152.947i q^{19} +(259.177 - 29.2937i) q^{20} -78.4091 q^{21} +(800.137 + 800.137i) q^{22} +(596.607 - 596.607i) q^{23} +121.173i q^{24} +(-609.233 + 139.500i) q^{25} -1282.99 q^{26} +(431.316 + 431.316i) q^{27} +(136.630 - 136.630i) q^{28} -801.994i q^{29} +(61.1159 + 540.726i) q^{30} -175.829 q^{31} +(-818.013 - 818.013i) q^{32} +(-658.885 + 658.885i) q^{33} +737.127i q^{34} +(-288.554 + 362.094i) q^{35} -658.077 q^{36} +(423.393 + 423.393i) q^{37} +(-556.032 + 556.032i) q^{38} -1056.50i q^{39} +(559.579 + 445.930i) q^{40} +919.754 q^{41} +(285.053 + 285.053i) q^{42} +(628.316 - 628.316i) q^{43} -2296.25i q^{44} +(1566.92 - 177.102i) q^{45} -4337.88 q^{46} +(-2208.69 - 2208.69i) q^{47} +(940.253 - 940.253i) q^{48} +343.000i q^{49} +(2721.99 + 1707.69i) q^{50} -606.999 q^{51} +(1840.97 + 1840.97i) q^{52} +(554.147 - 554.147i) q^{53} -3136.06i q^{54} +(617.968 + 5467.50i) q^{55} +530.072 q^{56} +(-457.873 - 457.873i) q^{57} +(-2915.61 + 2915.61i) q^{58} +3164.90i q^{59} +(688.196 - 863.588i) q^{60} +5297.88 q^{61} +(639.219 + 639.219i) q^{62} +(826.029 - 826.029i) q^{63} +922.421i q^{64} +(-4878.91 - 3888.02i) q^{65} +4790.70 q^{66} +(-1090.73 - 1090.73i) q^{67} +(1057.71 - 1057.71i) q^{68} -3572.09i q^{69} +(2365.40 - 267.351i) q^{70} -1622.41 q^{71} +(-1276.54 - 1276.54i) q^{72} +(1908.39 - 1908.39i) q^{73} -3078.45i q^{74} +(-1406.23 + 2241.46i) q^{75} +1595.71 q^{76} +(2882.29 + 2882.29i) q^{77} +(-3840.85 + 3840.85i) q^{78} +5038.95i q^{79} +(-881.863 - 7802.32i) q^{80} -2526.71 q^{81} +(-3343.73 - 3343.73i) q^{82} +(-2986.51 + 2986.51i) q^{83} -818.050i q^{84} +(-2233.82 + 2803.12i) q^{85} -4568.43 q^{86} +(-2400.91 - 2400.91i) q^{87} +(4454.28 - 4454.28i) q^{88} +9634.86i q^{89} +(-6340.32 - 5052.62i) q^{90} -4621.64 q^{91} +(6224.45 + 6224.45i) q^{92} +(-526.374 + 526.374i) q^{93} +16059.2i q^{94} +(-3799.48 + 429.439i) q^{95} -4897.73 q^{96} +(-2618.19 - 2618.19i) q^{97} +(1246.96 - 1246.96i) q^{98} -13882.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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