LMFDB - Embedded newform 76.5.h.a.69.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.h (of order $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 $ x^12 - 6x^11 + 631x^10 - 3100x^9 + 142264x^8 - 550522x^7 + 14083117x^6 - 40335478x^5 + 638031136x^4 - 1209472584x^3 + 12784623475x^2 - 12186518934*x + 90728724573
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.5
Root			$0.500000 + 6.42649i$ of defining polynomial
Character	$\chi$	$=$	76.69
Dual form			76.5.h.a.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.81550 - 2.78023i) q^{3} +(-13.2594 - 22.9660i) q^{5} -84.4930 q^{7} +(-25.0406 + 43.3717i) q^{9} +O(q^{10})$	\(q+(4.81550 - 2.78023i) q^{3} +(-13.2594 - 22.9660i) q^{5} -84.4930 q^{7} +(-25.0406 + 43.3717i) q^{9} +33.3991 q^{11} +(-32.2160 - 18.5999i) q^{13} +(-127.701 - 73.7284i) q^{15} +(-62.9369 - 109.010i) q^{17} +(-354.290 - 69.2806i) q^{19} +(-406.876 + 234.910i) q^{21} +(199.345 - 345.275i) q^{23} +(-39.1233 + 67.7635i) q^{25} +728.872i q^{27} +(-480.756 - 277.565i) q^{29} -1323.28i q^{31} +(160.833 - 92.8571i) q^{33} +(1120.33 + 1940.46i) q^{35} -630.480i q^{37} -206.848 q^{39} +(2615.46 - 1510.04i) q^{41} +(953.243 + 1651.07i) q^{43} +1328.10 q^{45} +(-1710.41 + 2962.52i) q^{47} +4738.07 q^{49} +(-606.145 - 349.958i) q^{51} +(-527.826 - 304.741i) q^{53} +(-442.852 - 767.041i) q^{55} +(-1898.70 + 651.386i) q^{57} +(-4229.93 + 2442.15i) q^{59} +(2120.39 - 3672.62i) q^{61} +(2115.76 - 3664.60i) q^{63} +986.495i q^{65} +(-3198.52 - 1846.67i) q^{67} -2216.90i q^{69} +(588.629 - 339.845i) q^{71} +(2278.44 + 3946.38i) q^{73} +435.087i q^{75} -2821.99 q^{77} +(-6779.56 + 3914.18i) q^{79} +(-1.85929 - 3.22038i) q^{81} -3820.26 q^{83} +(-1669.01 + 2890.81i) q^{85} -3086.77 q^{87} +(-12667.5 - 7313.61i) q^{89} +(2722.03 + 1571.56i) q^{91} +(-3679.03 - 6372.26i) q^{93} +(3106.57 + 9055.22i) q^{95} +(8157.18 - 4709.55i) q^{97} +(-836.334 + 1448.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	4.81550	−	2.78023i	0.535056	−	0.308914i	−0.208017	−	0.978125i	$-0.566701\pi$
$3$	4.81550	−	2.78023i	0.535056	−	0.308914i	0.743073	+	0.669211i	$0.233368\pi$
$4$		0			0
$5$	−13.2594	−	22.9660i	−0.530376	−	0.918638i	−0.999372	−	0.0354377i	$-0.988717\pi$
$5$	−13.2594	−	22.9660i	−0.530376	−	0.918638i	0.468996	−	0.883200i	$-0.344616\pi$
$6$		0			0
$7$	−84.4930			−1.72435			−0.862174	−	0.506613i	$-0.830897\pi$
$7$	−84.4930			−1.72435			−0.862174	+	0.506613i	$0.830897\pi$
$8$		0			0
$9$	−25.0406	+	43.3717i	−0.309144	+	0.535453i
$10$		0			0
$11$	33.3991			0.276025			0.138013	−	0.990430i	$-0.455929\pi$
$11$	33.3991			0.276025			0.138013	+	0.990430i	$0.455929\pi$
$12$		0			0
$13$	−32.2160	−	18.5999i	−0.190627	−	0.110059i	0.401649	−	0.915794i	$-0.368437\pi$
$13$	−32.2160	−	18.5999i	−0.190627	−	0.110059i	−0.592276	+	0.805735i	$0.701771\pi$
$14$		0			0
$15$	−127.701	−	73.7284i	−0.567561	−	0.327682i
$16$		0			0
$17$	−62.9369	−	109.010i	−0.217775	−	0.377197i	0.736353	−	0.676598i	$-0.236546\pi$
$17$	−62.9369	−	109.010i	−0.217775	−	0.377197i	−0.954127	+	0.299401i	$0.903213\pi$
$18$		0			0
$19$	−354.290	−	69.2806i	−0.981412	−	0.191913i
$19$	−354.290	−	69.2806i	−0.981412	−	0.191913i
$20$		0			0
$21$	−406.876	+	234.910i	−0.922622	+	0.532676i
$22$		0			0
$23$	199.345	−	345.275i	0.376833	−	0.652695i	−0.613766	−	0.789488i	$-0.710346\pi$
$23$	199.345	−	345.275i	0.376833	−	0.652695i	0.990600	+	0.136793i	$0.0436796\pi$
$24$		0			0
$25$	−39.1233	+	67.7635i	−0.0625972	+	0.108422i
$26$		0			0
$27$			728.872i			0.999825i
$28$		0			0
$29$	−480.756	−	277.565i	−0.571648	−	0.330041i	0.186159	−	0.982520i	$-0.440396\pi$
$29$	−480.756	−	277.565i	−0.571648	−	0.330041i	−0.757807	+	0.652478i	$0.773729\pi$
$30$		0			0
$31$		−	1323.28i		−	1.37698i	−0.725244	−	0.688492i	$-0.758273\pi$
$31$		−	1323.28i		−	1.37698i	0.725244	−	0.688492i	$-0.241727\pi$
$32$		0			0
$33$	160.833	−	92.8571i	0.147689	−	0.0852682i
$34$		0			0
$35$	1120.33	+	1940.46i	0.914552	+	1.58405i
$36$		0			0
$37$		−	630.480i		−	0.460541i	−0.973127	−	0.230270i	$-0.926039\pi$
$37$		−	630.480i		−	0.460541i	0.973127	−	0.230270i	$-0.0739610\pi$
$38$		0			0
$39$	−206.848			−0.135995
$40$		0			0
$41$	2615.46	−	1510.04i	1.55589	−	0.898296i	0.558251	−	0.829672i	$-0.311473\pi$
$41$	2615.46	−	1510.04i	1.55589	−	0.898296i	0.997643	−	0.0686238i	$-0.0218608\pi$
$42$		0			0
$43$	953.243	+	1651.07i	0.515545	+	0.892950i	0.999837	+	0.0180440i	$0.00574389\pi$
$43$	953.243	+	1651.07i	0.515545	+	0.892950i	−0.484292	+	0.874906i	$0.660923\pi$
$44$		0			0
$45$	1328.10			0.655850
$46$		0			0
$47$	−1710.41	+	2962.52i	−0.774292	+	1.34111i	0.160900	+	0.986971i	$0.448560\pi$
$47$	−1710.41	+	2962.52i	−0.774292	+	1.34111i	−0.935192	+	0.354142i	$0.884773\pi$
$48$		0			0
$49$	4738.07			1.97337
$50$		0			0
$51$	−606.145	−	349.958i	−0.233043	−	0.134547i
$52$		0			0
$53$	−527.826	−	304.741i	−0.187905	−	0.108487i	0.403096	−	0.915158i	$-0.367934\pi$
$53$	−527.826	−	304.741i	−0.187905	−	0.108487i	−0.591002	+	0.806670i	$0.701267\pi$
$54$		0			0
$55$	−442.852	−	767.041i	−0.146397	−	0.253567i
$56$		0			0
$57$	−1898.70	+	651.386i	−0.584395	+	0.200488i
$58$		0			0
$59$	−4229.93	+	2442.15i	−1.21515	+	0.701566i	−0.963876	−	0.266351i	$-0.914182\pi$
$59$	−4229.93	+	2442.15i	−1.21515	+	0.701566i	−0.251271	+	0.967917i	$0.580849\pi$
$60$		0			0
$61$	2120.39	−	3672.62i	0.569844	−	0.986998i	−0.426737	−	0.904376i	$-0.640337\pi$
$61$	2120.39	−	3672.62i	0.569844	−	0.986998i	0.996581	−	0.0826224i	$-0.0263295\pi$
$62$		0			0
$63$	2115.76	−	3664.60i	0.533071	−	0.923306i
$64$		0			0
$65$			986.495i			0.233490i
$66$		0			0
$67$	−3198.52	−	1846.67i	−0.712524	−	0.411376i	0.0994711	−	0.995040i	$-0.468285\pi$
$67$	−3198.52	−	1846.67i	−0.712524	−	0.411376i	−0.811995	+	0.583665i	$0.801618\pi$
$68$		0			0
$69$		−	2216.90i		−	0.465637i
$70$		0			0
$71$	588.629	−	339.845i	0.116768	−	0.0674162i	−0.440478	−	0.897763i	$-0.645191\pi$
$71$	588.629	−	339.845i	0.116768	−	0.0674162i	0.557247	+	0.830347i	$0.311858\pi$
$72$		0			0
$73$	2278.44	+	3946.38i	0.427555	+	0.740548i	0.996655	−	0.0817208i	$-0.0260416\pi$
$73$	2278.44	+	3946.38i	0.427555	+	0.740548i	−0.569100	+	0.822268i	$0.692708\pi$
$74$		0			0
$75$			435.087i			0.0773487i
$76$		0			0
$77$	−2821.99			−0.475964
$78$		0			0
$79$	−6779.56	+	3914.18i	−1.08629	+	0.627172i	−0.932587	−	0.360944i	$-0.882455\pi$
$79$	−6779.56	+	3914.18i	−1.08629	+	0.627172i	−0.153707	+	0.988116i	$0.549121\pi$
$80$		0			0
$81$	−1.85929	−	3.22038i	−0.000283384	−	0.000490836i
$82$		0			0
$83$	−3820.26			−0.554545			−0.277272	−	0.960791i	$-0.589430\pi$
$83$	−3820.26			−0.554545			−0.277272	+	0.960791i	$0.589430\pi$
$84$		0			0
$85$	−1669.01	+	2890.81i	−0.231005	+	0.400112i
$86$		0			0
$87$	−3086.77			−0.407818
$88$		0			0
$89$	−12667.5	−	7313.61i	−1.59924	−	0.923319i	−0.991635	−	0.129077i	$-0.958799\pi$
$89$	−12667.5	−	7313.61i	−1.59924	−	0.923319i	−0.607601	−	0.794242i	$-0.707868\pi$
$90$		0			0
$91$	2722.03	+	1571.56i	0.328707	+	0.189779i
$92$		0			0
$93$	−3679.03	−	6372.26i	−0.425370	−	0.736763i
$94$		0			0
$95$	3106.57	+	9055.22i	0.344219	+	1.00335i
$96$		0			0
$97$	8157.18	−	4709.55i	0.866955	−	0.500536i	0.000619586	−	1.00000i	$-0.499803\pi$
$97$	8157.18	−	4709.55i	0.866955	−	0.500536i	0.866335	+	0.499463i	$0.166469\pi$
$98$		0			0
$99$	−836.334	+	1448.57i	−0.0853315	+	0.147799i
$100$		0			0
$101$	5659.50	−	9802.55i	0.554799	−	0.960940i	−0.443120	−	0.896462i	$-0.646129\pi$
$101$	5659.50	−	9802.55i	0.554799	−	0.960940i	0.997919	−	0.0644777i	$-0.0205381\pi$
$102$		0			0
$103$		−	6757.10i		−	0.636922i	−0.947936	−	0.318461i	$-0.896834\pi$
$103$		−	6757.10i		−	0.636922i	0.947936	−	0.318461i	$-0.103166\pi$
$104$		0			0
$105$	10789.9	+	6229.53i	0.978673	+	0.565037i
$106$		0			0
$107$			7055.61i			0.616264i	0.951344	+	0.308132i	$0.0997039\pi$
$107$			7055.61i			0.616264i	−0.951344	+	0.308132i	$0.900296\pi$
$108$		0			0
$109$	2141.22	−	1236.23i	0.180222	−	0.104051i	−0.407175	−	0.913350i	$-0.633486\pi$
$109$	2141.22	−	1236.23i	0.180222	−	0.104051i	0.587397	+	0.809299i	$0.300153\pi$
$110$		0			0
$111$	−1752.88	−	3036.08i	−0.142268	−	0.246415i
$112$		0			0
$113$			4623.82i			0.362113i	0.983473	+	0.181056i	$0.0579516\pi$
$113$			4623.82i			0.362113i	−0.983473	+	0.181056i	$0.942048\pi$
$114$		0			0
$115$	−10572.8			−0.799454
$116$		0			0
$117$	1613.42	−	931.507i	0.117862	−	0.0680479i
$118$		0			0
$119$	5317.73	+	9210.57i	0.375519	+	0.650418i
$120$		0			0
$121$	−13525.5			−0.923810
$122$		0			0
$123$	8396.49	−	14543.1i	0.554993	−	0.961276i
$124$		0			0
$125$	−14499.2			−0.927952
$126$		0			0
$127$	14711.8	+	8493.88i	0.912136	+	0.526622i	0.881118	−	0.472897i	$-0.156792\pi$
$127$	14711.8	+	8493.88i	0.912136	+	0.526622i	0.0310181	+	0.999519i	$0.490125\pi$
$128$		0			0
$129$	9180.68	+	5300.47i	0.551691	+	0.318519i
$130$		0			0
$131$	9571.65	+	16578.6i	0.557756	+	0.966062i	0.997683	+	0.0680283i	$0.0216708\pi$
$131$	9571.65	+	16578.6i	0.557756	+	0.966062i	−0.439927	+	0.898033i	$0.644996\pi$
$132$		0			0
$133$	29935.0	+	5853.73i	1.69230	+	0.330925i
$134$		0			0
$135$	16739.2	−	9664.41i	0.918477	−	0.530283i
$136$		0			0
$137$	−6048.91	+	10477.0i	−0.322282	+	0.558208i	−0.980958	−	0.194218i	$-0.937783\pi$
$137$	−6048.91	+	10477.0i	−0.322282	+	0.558208i	0.658677	+	0.752426i	$0.271117\pi$
$138$		0			0
$139$	14680.6	−	25427.5i	0.759826	−	1.31606i	−0.183114	−	0.983092i	$-0.558618\pi$
$139$	14680.6	−	25427.5i	0.759826	−	1.31606i	0.942939	−	0.332965i	$-0.108049\pi$
$140$		0			0
$141$			19021.3i			0.956759i
$142$		0			0
$143$	−1075.98	−	621.220i	−0.0526179	−	0.0303790i
$144$		0			0
$145$			14721.4i			0.700184i
$146$		0			0
$147$	22816.2	−	13172.9i	1.05586	−	0.609604i
$148$		0			0
$149$	2080.34	+	3603.26i	0.0937049	+	0.162302i	0.909067	−	0.416649i	$-0.136796\pi$
$149$	2080.34	+	3603.26i	0.0937049	+	0.162302i	−0.815362	+	0.578951i	$0.803462\pi$
$150$		0			0
$151$		−	23274.8i		−	1.02078i	−0.859943	−	0.510390i	$-0.829501\pi$
$151$		−	23274.8i		−	1.02078i	0.859943	−	0.510390i	$-0.170499\pi$
$152$		0			0
$153$	6303.92			0.269295
$154$		0			0
$155$	−30390.4	+	17545.9i	−1.26495	+	0.730319i
$156$		0			0
$157$	−20323.4	−	35201.2i	−0.824513	−	1.42810i	−0.902291	−	0.431127i	$-0.858116\pi$
$157$	−20323.4	−	35201.2i	−0.824513	−	1.42810i	0.0777786	−	0.996971i	$-0.475217\pi$
$158$		0			0
$159$	−3388.99			−0.134053
$160$		0			0
$161$	−16843.3	+	29173.4i	−0.649792	+	1.12547i
$162$		0			0
$163$	−25586.5			−0.963023			−0.481511	−	0.876440i	$-0.659912\pi$
$163$	−25586.5			−0.963023			−0.481511	+	0.876440i	$0.659912\pi$
$164$		0			0
$165$	−4265.10	−	2462.46i	−0.156661	−	0.0904484i
$166$		0			0
$167$	−16030.7	−	9255.32i	−0.574803	−	0.331863i	0.184262	−	0.982877i	$-0.441010\pi$
$167$	−16030.7	−	9255.32i	−0.574803	−	0.331863i	−0.759065	+	0.651014i	$0.774344\pi$
$168$		0			0
$169$	−13588.6	−	23536.1i	−0.475774	−	0.824065i
$170$		0			0
$171$	11876.5	−	13631.3i	0.406158	−	0.466171i
$172$		0			0
$173$	−30408.0	+	17556.0i	−1.01600	+	0.586590i	−0.912944	−	0.408086i	$-0.866196\pi$
$173$	−30408.0	+	17556.0i	−1.01600	+	0.586590i	−0.103059	+	0.994675i	$0.532863\pi$
$174$		0			0
$175$	3305.64	−	5725.54i	0.107939	−	0.186956i
$176$		0			0
$177$	−13579.5	+	23520.4i	−0.433448	+	0.750753i
$178$		0			0
$179$			20859.6i			0.651028i	0.945537	+	0.325514i	$0.105537\pi$
$179$			20859.6i			0.651028i	−0.945537	+	0.325514i	$0.894463\pi$
$180$		0			0
$181$	41594.9	+	24014.8i	1.26965	+	0.733030i	0.974921	−	0.222552i	$-0.0714387\pi$
$181$	41594.9	+	24014.8i	1.26965	+	0.733030i	0.294725	+	0.955582i	$0.404772\pi$
$182$		0			0
$183$		−	23580.7i		−	0.704132i
$184$		0			0
$185$	−14479.6	+	8359.79i	−0.423070	+	0.244260i
$186$		0			0
$187$	−2102.03	−	3640.83i	−0.0601113	−	0.104116i
$188$		0			0
$189$		−	61584.6i		−	1.72405i
$190$		0			0
$191$	−52465.4			−1.43816			−0.719079	−	0.694929i	$-0.755436\pi$
$191$	−52465.4			−1.43816			−0.719079	+	0.694929i	$0.755436\pi$
$192$		0			0
$193$	46145.2	−	26642.0i	1.23883	−	0.715240i	0.269976	−	0.962867i	$-0.412984\pi$
$193$	46145.2	−	26642.0i	1.23883	−	0.715240i	0.968855	+	0.247627i	$0.0796508\pi$
$194$		0			0
$195$	2742.68	+	4750.46i	0.0721284	+	0.124930i
$196$		0			0
$197$	−10872.8			−0.280161			−0.140081	−	0.990140i	$-0.544736\pi$
$197$	−10872.8			−0.280161			−0.140081	+	0.990140i	$0.544736\pi$
$198$		0			0
$199$	−10950.4	+	18966.6i	−0.276517	+	0.478942i	−0.970517	−	0.241033i	$-0.922514\pi$
$199$	−10950.4	+	18966.6i	−0.276517	+	0.478942i	0.694000	+	0.719975i	$0.255847\pi$
$200$		0			0
$201$	−20536.6			−0.508320
$202$		0			0
$203$	40620.5	+	23452.3i	0.985720	+	0.569106i
$204$		0			0
$205$	−69358.8	−	40044.3i	−1.65042	−	0.952869i
$206$		0			0
$207$	9983.45	+	17291.8i	0.232991	+	0.403553i
$208$		0			0
$209$	−11832.9	−	2313.91i	−0.270895	−	0.0529729i
$210$		0			0
$211$	−19016.9	+	10979.4i	−0.427143	+	0.246611i	−0.698129	−	0.715972i	$-0.745984\pi$
$211$	−19016.9	+	10979.4i	−0.427143	+	0.246611i	0.270985	+	0.962583i	$0.412650\pi$
$212$		0			0
$213$	1889.70	−	3273.05i	0.0416517	−	0.0721429i
$214$		0			0
$215$	25278.9	−	43784.3i	0.546865	−	0.947199i
$216$		0			0
$217$			111808.i			2.37440i
$218$		0			0
$219$	21943.7	+	12669.2i	0.457532	+	0.264156i
$220$		0			0
$221$			4682.48i			0.0958719i
$222$		0			0
$223$	36180.1	−	20888.6i	0.727545	−	0.420048i	−0.0899783	−	0.995944i	$-0.528680\pi$
$223$	36180.1	−	20888.6i	0.727545	−	0.420048i	0.817523	+	0.575895i	$0.195346\pi$
$224$		0			0
$225$	−1959.34	−	3393.68i	−0.0387031	−	0.0670357i
$226$		0			0
$227$		−	51321.1i		−	0.995966i	−0.867187	−	0.497983i	$-0.834074\pi$
$227$		−	51321.1i		−	0.995966i	0.867187	−	0.497983i	$-0.165926\pi$
$228$		0			0
$229$	9344.76			0.178196			0.0890978	−	0.996023i	$-0.471602\pi$
$229$	9344.76			0.178196			0.0890978	+	0.996023i	$0.471602\pi$
$230$		0			0
$231$	−13589.3	+	7845.78i	−0.254667	+	0.147032i
$232$		0			0
$233$	37637.2	+	65189.6i	0.693275	+	1.20079i	0.970759	+	0.240057i	$0.0771662\pi$
$233$	37637.2	+	65189.6i	0.693275	+	1.20079i	−0.277484	+	0.960730i	$0.589500\pi$
$234$		0			0
$235$	90716.0			1.64266
$236$		0			0
$237$	−21764.7	+	37697.5i	−0.387485	+	0.671144i
$238$		0			0
$239$	32265.1			0.564855			0.282427	−	0.959289i	$-0.408860\pi$
$239$	32265.1			0.564855			0.282427	+	0.959289i	$0.408860\pi$
$240$		0			0
$241$	13807.1	+	7971.52i	0.237721	+	0.137248i	0.614129	−	0.789206i	$-0.289507\pi$
$241$	13807.1	+	7971.52i	0.237721	+	0.137248i	−0.376408	+	0.926454i	$0.622841\pi$
$242$		0			0
$243$	−51146.9	−	29529.7i	−0.866177	−	0.500087i
$244$		0			0
$245$	−62824.0	−	108814.i	−1.04663	−	1.81282i
$246$		0			0
$247$	10125.2	+	8821.70i	0.165962	+	0.144597i
$248$		0			0
$249$	−18396.5	+	10621.2i	−0.296712	+	0.171307i
$250$		0			0
$251$	58283.1	−	100949.i	0.925114	−	1.60234i	0.133736	−	0.991017i	$-0.457303\pi$
$251$	58283.1	−	100949.i	0.925114	−	1.60234i	0.791378	−	0.611327i	$-0.209364\pi$
$252$		0			0
$253$	6657.93	−	11531.9i	0.104016	−	0.180160i
$254$		0			0
$255$			18560.9i			0.285443i
$256$		0			0
$257$	86480.5	+	49929.6i	1.30934	+	0.755947i	0.981986	−	0.188955i	$-0.0605100\pi$
$257$	86480.5	+	49929.6i	1.30934	+	0.755947i	0.327353	+	0.944902i	$0.393843\pi$
$258$		0			0
$259$			53271.2i			0.794132i
$260$		0			0
$261$	24076.9	−	13900.8i	0.353443	−	0.204060i
$262$		0			0
$263$	27926.3	+	48369.8i	0.403740	+	0.699299i	0.994174	−	0.107788i	$-0.0343766\pi$
$263$	27926.3	+	48369.8i	0.403740	+	0.699299i	−0.590434	+	0.807086i	$0.701043\pi$
$264$		0			0
$265$			16162.7i			0.230156i
$266$		0			0
$267$	−81334.1			−1.14091
$268$		0			0
$269$	82433.0	−	47592.7i	1.13919	−	0.657712i	0.192961	−	0.981207i	$-0.438191\pi$
$269$	82433.0	−	47592.7i	1.13919	−	0.657712i	0.946230	+	0.323495i	$0.104858\pi$
$270$		0			0
$271$	19687.4	+	34099.6i	0.268071	+	0.464313i	0.968364	−	0.249543i	$-0.0802804\pi$
$271$	19687.4	+	34099.6i	0.268071	+	0.464313i	−0.700293	+	0.713856i	$0.746947\pi$
$272$		0			0
$273$	17477.2			0.234502
$274$		0			0
$275$	−1306.68	+	2263.24i	−0.0172784	+	0.0299271i
$276$		0			0
$277$	−52790.5			−0.688013			−0.344006	−	0.938967i	$-0.611784\pi$
$277$	−52790.5			−0.688013			−0.344006	+	0.938967i	$0.611784\pi$
$278$		0			0
$279$	57392.9	+	33135.8i	0.737310	+	0.425686i
$280$		0			0
$281$	112961.	+	65217.8i	1.43059	+	0.825950i	0.997165	−	0.0752419i	$-0.0239729\pi$
$281$	112961.	+	65217.8i	1.43059	+	0.825950i	0.433421	+	0.901191i	$0.357306\pi$
$282$		0			0
$283$	−37625.8	−	65169.8i	−0.469800	−	0.813718i	0.529604	−	0.848245i	$-0.322341\pi$
$283$	−37625.8	−	65169.8i	−0.469800	−	0.813718i	−0.999404	+	0.0345275i	$0.989007\pi$
$284$		0			0
$285$	40135.3	+	34968.4i	0.494125	+	0.430513i
$286$		0			0
$287$	−220988.	+	127587.i	−2.68290	+	1.54897i
$288$		0			0
$289$	33838.4	−	58609.8i	0.405148	−	0.701738i
$290$		0			0
$291$	26187.3	−	45357.7i	0.309246	−	0.535630i
$292$		0			0
$293$		−	26421.2i		−	0.307763i	−0.988089	−	0.153882i	$-0.950823\pi$
$293$		−	26421.2i		−	0.307763i	0.988089	−	0.153882i	$-0.0491775\pi$
$294$		0			0
$295$	112173.	+	64762.9i	1.28897	+	0.744187i
$296$		0			0
$297$			24343.7i			0.275977i
$298$		0			0
$299$	−12844.2	+	7415.60i	−0.143669	+	0.0829476i
$300$		0			0
$301$	−80542.4	−	139503.i	−0.888979	−	1.53976i
$302$		0			0
$303$		−	62938.9i		−	0.685542i
$304$		0			0
$305$	−112460.			−1.20893
$306$		0			0
$307$	−113735.	+	65665.0i	−1.20675	+	0.696718i	−0.962048	−	0.272880i	$-0.912024\pi$
$307$	−113735.	+	65665.0i	−1.20675	+	0.696718i	−0.244703	+	0.969598i	$0.578690\pi$
$308$		0			0
$309$	−18786.3	−	32538.8i	−0.196754	−	0.340789i
$310$		0			0
$311$	−66871.7			−0.691388			−0.345694	−	0.938347i	$-0.612356\pi$
$311$	−66871.7			−0.691388			−0.345694	+	0.938347i	$0.612356\pi$
$312$		0			0
$313$	12163.3	−	21067.4i	0.124154	−	0.215042i	−0.797248	−	0.603652i	$-0.793712\pi$
$313$	12163.3	−	21067.4i	0.124154	−	0.215042i	0.921402	+	0.388611i	$0.127045\pi$
$314$		0			0
$315$	−112215.			−1.13091
$316$		0			0
$317$	−74607.7	−	43074.8i	−0.742447	−	0.428652i	0.0805116	−	0.996754i	$-0.474345\pi$
$317$	−74607.7	−	43074.8i	−0.742447	−	0.428652i	−0.822958	+	0.568102i	$0.807678\pi$
$318$		0			0
$319$	−16056.8	−	9270.40i	−0.157789	−	0.0910998i
$320$		0			0
$321$	19616.2	+	33976.3i	0.190373	+	0.329736i
$322$		0			0
$323$	14745.6	+	42981.4i	0.141338	+	0.411979i
$324$		0			0
$325$	2520.79	−	1455.38i	0.0238655	−	0.0137787i
$326$		0			0
$327$	6874.03	−	11906.2i	0.0642859	−	0.111346i
$328$		0			0
$329$	144518.	−	250312.i	1.33515	−	2.31254i
$330$		0			0
$331$		−	101411.i		−	0.925616i	−0.886459	−	0.462808i	$-0.846842\pi$
$331$		−	101411.i		−	0.925616i	0.886459	−	0.462808i	$-0.153158\pi$
$332$		0			0
$333$	27345.0	+	15787.6i	0.246598	+	0.142373i
$334$		0			0
$335$			97942.7i			0.872735i
$336$		0			0
$337$	−30062.6	+	17356.6i	−0.264708	+	0.152829i	−0.626480	−	0.779437i	$-0.715505\pi$
$337$	−30062.6	+	17356.6i	−0.264708	+	0.152829i	0.361773	+	0.932266i	$0.382172\pi$
$338$		0			0
$339$	12855.3	+	22266.0i	0.111862	+	0.193750i
$340$		0			0
$341$		−	44196.4i		−	0.380082i
$342$		0			0
$343$	−197466.			−1.67843
$344$		0			0
$345$	−50913.2	+	29394.7i	−0.427752	+	0.246963i
$346$		0			0
$347$	107740.	+	186612.i	0.894786	+	1.54981i	0.834069	+	0.551660i	$0.186005\pi$
$347$	107740.	+	186612.i	0.894786	+	1.54981i	0.0607169	+	0.998155i	$0.480661\pi$
$348$		0			0
$349$	−61536.9			−0.505225			−0.252612	−	0.967568i	$-0.581290\pi$
$349$	−61536.9			−0.505225			−0.252612	+	0.967568i	$0.581290\pi$
$350$		0			0
$351$	13557.0	−	23481.3i	0.110039	−	0.190594i
$352$		0			0
$353$	−184748.			−1.48262			−0.741311	−	0.671162i	$-0.765796\pi$
$353$	−184748.			−1.48262			−0.741311	+	0.671162i	$0.765796\pi$
$354$		0			0
$355$	−15609.7	−	9012.29i	−0.123862	−	0.0715119i
$356$		0			0
$357$	51215.0	+	29569.0i	0.401847	+	0.232007i
$358$		0			0
$359$	−40117.9	−	69486.2i	−0.311279	−	0.539150i	0.667361	−	0.744734i	$-0.267424\pi$
$359$	−40117.9	−	69486.2i	−0.311279	−	0.539150i	−0.978639	+	0.205584i	$0.934091\pi$
$360$		0			0
$361$	120721.	+	49090.8i	0.926339	+	0.376692i
$362$		0			0
$363$	−65132.1	+	37604.0i	−0.494290	+	0.285378i
$364$		0			0
$365$	60421.6	−	104653.i	0.453530	−	0.785537i
$366$		0			0
$367$	10611.8	−	18380.2i	0.0787877	−	0.136464i	−0.823939	−	0.566678i	$-0.808228\pi$
$367$	10611.8	−	18380.2i	0.0787877	−	0.136464i	0.902727	+	0.430214i	$0.141562\pi$
$368$		0			0
$369$			151249.i			1.11081i
$370$		0			0
$371$	44597.6	+	25748.4i	0.324014	+	0.187070i
$372$		0			0
$373$			136406.i			0.980428i	0.871602	+	0.490214i	$0.163081\pi$
$373$			136406.i			0.980428i	−0.871602	+	0.490214i	$0.836919\pi$
$374$		0			0
$375$	−69821.1	+	40311.2i	−0.496506	+	0.286658i
$376$		0			0
$377$	10325.4	+	17884.0i	0.0726478	+	0.125830i
$378$		0			0
$379$		−	120694.i		−	0.840244i	−0.907468	−	0.420122i	$-0.861987\pi$
$379$		−	120694.i		−	0.840244i	0.907468	−	0.420122i	$-0.138013\pi$
$380$		0			0
$381$	94459.8			0.650724
$382$		0			0
$383$	199020.	−	114904.i	1.35675	−	0.783320i	0.367566	−	0.929998i	$-0.380191\pi$
$383$	199020.	−	114904.i	1.35675	−	0.783320i	0.989184	+	0.146677i	$0.0468579\pi$
$384$		0			0
$385$	37417.9	+	64809.6i	0.252440	+	0.437238i
$386$		0			0
$387$	−95479.3			−0.637510
$388$		0			0
$389$	125565.	−	217485.i	0.829793	−	1.43724i	−0.0684079	−	0.997657i	$-0.521792\pi$
$389$	125565.	−	217485.i	0.829793	−	1.43724i	0.898201	−	0.439586i	$-0.144875\pi$
$390$		0			0
$391$	−50184.6			−0.328259
$392$		0			0
$393$	92184.6	+	53222.8i	0.596861	+	0.344598i
$394$		0			0
$395$	179786.	+	103799.i	1.15229	+	0.665274i
$396$		0			0
$397$	−37440.2	−	64848.4i	−0.237551	−	0.411451i	0.722460	−	0.691413i	$-0.243012\pi$
$397$	−37440.2	−	64848.4i	−0.237551	−	0.411451i	−0.960011	+	0.279962i	$0.909678\pi$
$398$		0			0
$399$	160427.	−	55037.6i	1.00770	−	0.345711i
$400$		0			0
$401$	−102868.	+	59390.9i	−0.639723	+	0.369344i	−0.784508	−	0.620119i	$-0.787084\pi$
$401$	−102868.	+	59390.9i	−0.639723	+	0.369344i	0.144785	+	0.989463i	$0.453751\pi$
$402$		0			0
$403$	−24612.9	+	42630.8i	−0.151549	+	0.262491i
$404$		0			0
$405$	−49.3060	+	85.4005i	−0.000300601	+	0.000520655i
$406$		0			0
$407$		−	21057.4i		−	0.127121i
$408$		0			0
$409$	282457.	+	163076.i	1.68852	+	0.974865i	0.955655	+	0.294487i	$0.0951488\pi$
$409$	282457.	+	163076.i	1.68852	+	0.974865i	0.732861	+	0.680378i	$0.238185\pi$
$410$		0			0
$411$			67269.4i			0.398230i
$412$		0			0
$413$	357399.	−	206345.i	2.09534	−	1.20974i
$414$		0			0
$415$	50654.3	+	87735.9i	0.294117	+	0.509426i
$416$		0			0
$417$		−	163262.i		−	0.938884i
$418$		0			0
$419$	10223.8			0.0582350			0.0291175	−	0.999576i	$-0.490730\pi$
$419$	10223.8			0.0582350			0.0291175	+	0.999576i	$0.490730\pi$
$420$		0			0
$421$	−221712.	+	128006.i	−1.25091	+	0.722213i	−0.971290	−	0.237898i	$-0.923541\pi$
$421$	−221712.	+	128006.i	−1.25091	+	0.722213i	−0.279619	+	0.960111i	$0.590208\pi$
$422$		0			0
$423$	−85659.5	−	148367.i	−0.478735	−	0.829193i
$424$		0			0
$425$	9849.18			0.0545283
$426$		0			0
$427$	−179158.	+	310311.i	−0.982608	+	1.70193i
$428$		0			0
$429$	−6908.54			−0.0375380
$430$		0			0
$431$	−75203.7	−	43418.8i	−0.404841	−	0.233735i	0.283730	−	0.958904i	$-0.408428\pi$
$431$	−75203.7	−	43418.8i	−0.404841	−	0.233735i	−0.688571	+	0.725169i	$0.741761\pi$
$432$		0			0
$433$	−282022.	−	162825.i	−1.50420	−	0.868453i	−0.999988	−	0.00487606i	$-0.998448\pi$
$433$	−282022.	−	162825.i	−1.50420	−	0.868453i	−0.504217	−	0.863577i	$-0.668219\pi$
$434$		0			0
$435$	40928.8	+	70890.7i	0.216297	+	0.374637i
$436$		0			0
$437$	−94546.8	+	108517.i	−0.495090	+	0.568243i
$438$		0			0
$439$	200497.	−	115757.i	1.04035	−	0.600647i	0.120418	−	0.992723i	$-0.461576\pi$
$439$	200497.	−	115757.i	1.04035	−	0.600647i	0.919933	+	0.392076i	$0.128243\pi$
$440$		0			0
$441$	−118644.	+	205498.i	−0.610056	+	1.05665i
$442$		0			0
$443$	103566.	−	179381.i	0.527726	−	0.914048i	−0.471752	−	0.881731i	$-0.656378\pi$
$443$	103566.	−	179381.i	0.527726	−	0.914048i	0.999478	−	0.0323166i	$-0.0102885\pi$
$444$		0			0
$445$			387896.i			1.95882i
$446$		0			0
$447$	20035.8	+	11567.7i	0.100275	+	0.0578936i
$448$		0			0
$449$		−	320126.i		−	1.58792i	−0.607971	−	0.793959i	$-0.708016\pi$
$449$		−	320126.i		−	1.58792i	0.607971	−	0.793959i	$-0.291984\pi$
$450$		0			0
$451$	87353.8	−	50433.8i	0.429466	−	0.247952i
$452$		0			0
$453$	−64709.4	−	112080.i	−0.315334	−	0.546174i
$454$		0			0
$455$		−	83351.9i		−	0.402618i
$456$		0			0
$457$	−186438.			−0.892695			−0.446347	−	0.894860i	$-0.647275\pi$
$457$	−186438.			−0.892695			−0.446347	+	0.894860i	$0.647275\pi$
$458$		0			0
$459$	79454.3	−	45872.9i	0.377131	−	0.217736i
$460$		0			0
$461$	8745.73	+	15148.0i	0.0411523	+	0.0712779i	0.885868	−	0.463938i	$-0.153564\pi$
$461$	8745.73	+	15148.0i	0.0411523	+	0.0712779i	−0.844716	+	0.535215i	$0.820230\pi$
$462$		0			0
$463$	168691.			0.786920			0.393460	−	0.919342i	$-0.371278\pi$
$463$	168691.			0.786920			0.393460	+	0.919342i	$0.371278\pi$
$464$		0			0
$465$	−97563.4	+	168985.i	−0.451212	+	0.781522i
$466$		0			0
$467$	183184.			0.839950			0.419975	−	0.907536i	$-0.362039\pi$
$467$	183184.			0.839950			0.419975	+	0.907536i	$0.362039\pi$
$468$		0			0
$469$	270253.	+	156030.i	1.22864	+	0.709355i
$470$		0			0
$471$	−195735.	−	113008.i	−0.882320	−	0.509408i
$472$		0			0
$473$	31837.4	+	55144.0i	0.142304	+	0.246477i
$474$		0			0
$475$	18555.7	−	21297.4i	0.0822412	−	0.0943930i
$476$		0			0
$477$	26434.2	−	15261.8i	0.116179	−	0.0670763i
$478$		0			0
$479$	159926.	−	276999.i	0.697022	−	1.20728i	−0.272472	−	0.962164i	$-0.587841\pi$
$479$	159926.	−	276999.i	0.697022	−	1.20728i	0.969494	−	0.245114i	$-0.0788255\pi$
$480$		0			0
$481$	−11726.9	+	20311.5i	−0.0506865	+	0.0877916i
$482$		0			0
$483$			187312.i			0.802920i
$484$		0			0
$485$	−216318.	−	124892.i	−0.919624	−	0.530945i
$486$		0			0
$487$		−	22667.1i		−	0.0955736i	−0.998858	−	0.0477868i	$-0.984783\pi$
$487$		−	22667.1i		−	0.0955736i	0.998858	−	0.0477868i	$-0.0152168\pi$
$488$		0			0
$489$	−123212.	+	71136.5i	−0.515271	+	0.297492i
$490$		0			0
$491$	102131.	+	176895.i	0.423636	+	0.733759i	0.996292	−	0.0860370i	$-0.0274203\pi$
$491$	102131.	+	176895.i	0.423636	+	0.733759i	−0.572656	+	0.819796i	$0.694087\pi$
$492$		0			0
$493$			69876.2i			0.287498i
$494$		0			0
$495$	44357.1			0.181031
$496$		0			0
$497$	−49735.1	+	28714.6i	−0.201349	+	0.116249i
$498$		0			0
$499$	−207921.	−	360129.i	−0.835020	−	1.44630i	−0.894015	−	0.448038i	$-0.852123\pi$
$499$	−207921.	−	360129.i	−0.835020	−	1.44630i	0.0589950	−	0.998258i	$-0.481210\pi$
$500$		0			0
$501$	−102928.			−0.410069
$502$		0			0
$503$	−217012.	+	375875.i	−0.857724	+	1.48562i	0.0163716	+	0.999866i	$0.494789\pi$
$503$	−217012.	+	375875.i	−0.857724	+	1.48562i	−0.874095	+	0.485755i	$0.838545\pi$
$504$		0			0
$505$	−300166.			−1.17701
$506$		0			0
$507$	−130872.	−	75558.8i	−0.509131	−	0.293947i
$508$		0			0
$509$	−315207.	−	181985.i	−1.21663	−	0.702424i	−0.252437	−	0.967613i	$-0.581232\pi$
$509$	−315207.	−	181985.i	−1.21663	−	0.702424i	−0.964196	+	0.265189i	$0.914566\pi$
$510$		0			0
$511$	−192513.	−	333441.i	−0.737254	−	1.27696i
$512$		0			0
$513$	50496.7	−	258232.i	0.191880	−	0.981240i
$514$		0			0
$515$	−155183.	+	89595.1i	−0.585101	+	0.337808i
$516$		0			0
$517$	−57126.1	+	98945.3i	−0.213724	+	0.370181i
$518$		0			0
$519$	−97619.7	+	169082.i	−0.362412	+	0.627716i
$520$		0			0
$521$			100484.i			0.370187i	0.982721	+	0.185094i	$0.0592589\pi$
$521$			100484.i			0.370187i	−0.982721	+	0.185094i	$0.940741\pi$
$522$		0			0
$523$	5151.62	+	2974.29i	0.0188339	+	0.0108738i	0.509387	−	0.860537i	$-0.329872\pi$
$523$	5151.62	+	2974.29i	0.0188339	+	0.0108738i	−0.490553	+	0.871411i	$0.663205\pi$
$524$		0			0
$525$		−	36761.8i		−	0.133376i
$526$		0			0
$527$	−144251.	+	83283.2i	−0.519394	+	0.299872i
$528$		0			0
$529$	60443.7	+	104692.i	0.215993	+	0.374111i
$530$		0			0
$531$		−	244612.i		−	0.867539i
$532$		0			0
$533$	−112346.			−0.395461
$534$		0			0
$535$	162039.	−	93553.1i	0.566124	−	0.326852i
$536$		0			0
$537$	57994.5	+	100449.i	0.201112	+	0.348336i
$538$		0			0
$539$	158247.			0.544701
$540$		0			0
$541$	−25692.0	+	44499.9i	−0.0877817	+	0.152042i	−0.906573	−	0.422049i	$-0.861311\pi$
$541$	−25692.0	+	44499.9i	−0.0877817	+	0.152042i	0.818791	+	0.574091i	$0.194644\pi$
$542$		0			0
$543$	267067.			0.905775
$544$		0			0
$545$	−56782.5	−	32783.4i	−0.191171	−	0.110373i
$546$		0			0
$547$	−253560.	−	146393.i	−0.847434	−	0.489266i	0.0123501	−	0.999924i	$-0.496069\pi$
$547$	−253560.	−	146393.i	−0.847434	−	0.489266i	−0.859784	+	0.510657i	$0.829402\pi$
$548$		0			0
$549$	106192.	+	183929.i	0.352327	+	0.610248i
$550$		0			0
$551$	151097.	+	131645.i	0.497683	+	0.433613i
$552$		0			0
$553$	572826.	−	330721.i	1.87315	−	1.08146i
$554$		0			0
$555$	−46484.3	+	80513.1i	−0.150911	+	0.261385i
$556$		0			0
$557$	−52344.2	+	90662.9i	−0.168717	+	0.292226i	−0.937969	−	0.346719i	$-0.887296\pi$
$557$	−52344.2	+	90662.9i	−0.168717	+	0.292226i	0.769252	+	0.638945i	$0.220629\pi$
$558$		0			0
$559$		−	70920.9i		−	0.226961i
$560$		0			0
$561$	−20244.7	−	11688.3i	−0.0643258	−	0.0371385i
$562$		0			0
$563$		−	3123.45i		−	0.00985411i	−0.999988	−	0.00492706i	$-0.998432\pi$
$563$		−	3123.45i		−	0.00985411i	0.999988	−	0.00492706i	$-0.00156834\pi$
$564$		0			0
$565$	106190.	−	61309.0i	0.332650	−	0.192056i
$566$		0			0
$567$	157.097	+	272.099i	0.000488653	+	0.000846372i
$568$		0			0
$569$		−	35963.3i		−	0.111080i	−0.998456	−	0.0555399i	$-0.982312\pi$
$569$		−	35963.3i		−	0.111080i	0.998456	−	0.0555399i	$-0.0176880\pi$
$570$		0			0
$571$	62530.8			0.191788			0.0958941	−	0.995392i	$-0.469429\pi$
$571$	62530.8			0.191788			0.0958941	+	0.995392i	$0.469429\pi$
$572$		0			0
$573$	−252647.	+	145866.i	−0.769494	+	0.444268i
$574$		0			0
$575$	15598.0	+	27016.6i	0.0471774	+	0.0817137i
$576$		0			0
$577$	242182.			0.727429			0.363715	−	0.931510i	$-0.381508\pi$
$577$	242182.			0.727429			0.363715	+	0.931510i	$0.381508\pi$
$578$		0			0
$579$	148142.	−	256589.i	0.441896	−	0.765386i
$580$		0			0
$581$	322785.			0.956228
$582$		0			0
$583$	−17628.9	−	10178.0i	−0.0518666	−	0.0299452i
$584$		0			0
$585$	−42785.9	−	24702.5i	−0.125023	−	0.0721819i
$586$		0			0
$587$	10340.3	+	17910.0i	0.0300095	+	0.0519779i	0.880640	−	0.473786i	$-0.157113\pi$
$587$	10340.3	+	17910.0i	0.0300095	+	0.0519779i	−0.850631	+	0.525764i	$0.823780\pi$
$588$		0			0
$589$	−91677.8	+	468825.i	−0.264261	+	1.35139i
$590$		0			0
$591$	−52357.9	+	30228.8i	−0.149902	+	0.0865459i
$592$		0			0
$593$	−73184.7	+	126760.i	−0.208118	+	0.360472i	−0.951122	−	0.308816i	$-0.900067\pi$
$593$	−73184.7	+	126760.i	−0.208118	+	0.360472i	0.743003	+	0.669288i	$0.233401\pi$
$594$		0			0
$595$	141020.	−	244253.i	0.398333	−	0.689932i
$596$		0			0
$597$			121778.i			0.341681i
$598$		0			0
$599$	−28855.0	−	16659.4i	−0.0804206	−	0.0464308i	0.459250	−	0.888307i	$-0.348118\pi$
$599$	−28855.0	−	16659.4i	−0.0804206	−	0.0464308i	−0.539671	+	0.841876i	$0.681451\pi$
$600$		0			0
$601$		−	301579.i		−	0.834933i	−0.908692	−	0.417467i	$-0.862918\pi$
$601$		−	301579.i		−	0.834933i	0.908692	−	0.417467i	$-0.137082\pi$
$602$		0			0
$603$	160186.	−	92483.4i	0.440544	−	0.254348i
$604$		0			0
$605$	179340.	+	310626.i	0.489967	+	0.848647i
$606$		0			0
$607$			671101.i			1.82142i	0.413045	+	0.910711i	$0.364465\pi$
$607$			671101.i			1.82142i	−0.413045	+	0.910711i	$0.635535\pi$
$608$		0			0
$609$	260811.			0.703220
$610$		0			0
$611$	110205.	−	63627.0i	0.295202	−	0.170435i
$612$		0			0
$613$	−116030.	−	200969.i	−0.308779	−	0.534822i	0.669316	−	0.742978i	$-0.266587\pi$
$613$	−116030.	−	200969.i	−0.308779	−	0.534822i	−0.978096	+	0.208156i	$0.933254\pi$
$614$		0			0
$615$	−445330.			−1.17742
$616$		0			0
$617$	61529.0	−	106571.i	0.161625	−	0.279943i	−0.773826	−	0.633398i	$-0.781660\pi$
$617$	61529.0	−	106571.i	0.161625	−	0.279943i	0.935452	+	0.353455i	$0.114993\pi$
$618$		0			0
$619$	159886.			0.417283			0.208641	−	0.977992i	$-0.433096\pi$
$619$	159886.			0.417283			0.208641	+	0.977992i	$0.433096\pi$
$620$		0			0
$621$	251662.	+	145297.i	0.652580	+	0.376767i
$622$		0			0
$623$	1.07032e6	+	617949.i	2.75764	+	1.59212i
$624$		0			0
$625$	216703.	+	375341.i	0.554760	+	0.960873i
$626$		0			0
$627$	−63414.7	+	21755.7i	−0.161308	+	0.0553398i
$628$		0			0
$629$	−68728.5	+	39680.4i	−0.173714	+	0.100294i
$630$		0			0
$631$	92668.8	−	160507.i	0.232742	−	0.403121i	−0.725872	−	0.687830i	$-0.758564\pi$
$631$	92668.8	−	160507.i	0.232742	−	0.403121i	0.958614	+	0.284709i	$0.0918969\pi$
$632$		0			0
$633$	−61050.4	+	105742.i	−0.152364	+	0.263902i
$634$		0			0
$635$		−	450495.i		−	1.11723i
$636$		0			0
$637$	−152642.	−	88127.7i	−0.376179	−	0.217187i
$638$		0			0
$639$			34039.8i			0.0833652i
$640$		0			0
$641$	142059.	−	82017.6i	0.345742	−	0.199614i	−0.317066	−	0.948403i	$-0.602698\pi$
$641$	142059.	−	82017.6i	0.345742	−	0.199614i	0.662808	+	0.748789i	$0.269364\pi$
$642$		0			0
$643$	−252661.	−	437622.i	−0.611106	−	1.05847i	−0.991054	−	0.133459i	$-0.957391\pi$
$643$	−252661.	−	437622.i	−0.611106	−	1.05847i	0.379948	−	0.925008i	$-0.375942\pi$
$644$		0			0
$645$		−	281124.i		−	0.675739i
$646$		0			0
$647$	95116.5			0.227220			0.113610	−	0.993525i	$-0.463759\pi$
$647$	95116.5			0.227220			0.113610	+	0.993525i	$0.463759\pi$
$648$		0			0
$649$	−141276.	+	81565.6i	−0.335412	+	0.193650i
$650$		0			0
$651$	310852.	+	538412.i	0.733486	+	1.27043i
$652$		0			0
$653$	−586580.			−1.37563			−0.687813	−	0.725888i	$-0.741429\pi$
$653$	−586580.			−1.37563			−0.687813	+	0.725888i	$0.741429\pi$
$654$		0			0
$655$	253829.	−	439644.i	0.591641	−	1.02475i
$656$		0			0
$657$	−228215.			−0.528704
$658$		0			0
$659$	−619966.	−	357938.i	−1.42757	−	0.824207i	−0.430640	−	0.902524i	$-0.641712\pi$
$659$	−619966.	−	357938.i	−1.42757	−	0.824207i	−0.996929	+	0.0783166i	$0.975046\pi$
$660$		0			0
$661$	316498.	+	182730.i	0.724383	+	0.418223i	0.816364	−	0.577538i	$-0.195987\pi$
$661$	316498.	+	182730.i	0.724383	+	0.418223i	−0.0919808	+	0.995761i	$0.529320\pi$
$662$		0			0
$663$	13018.4	+	22548.5i	0.0296162	+	0.0512968i
$664$		0			0
$665$	−262484.	−	765103.i	−0.593552	−	1.73012i
$666$		0			0
$667$	−191673.	+	110662.i	−0.430832	+	0.248741i
$668$		0			0
$669$	116150.	−	201178.i	0.259518	−	0.449498i
$670$		0			0
$671$	70819.0	−	122662.i	0.157291	−	0.272436i
$672$		0			0
$673$		−	769776.i		−	1.69955i	−0.527144	−	0.849776i	$-0.676737\pi$
$673$		−	769776.i		−	1.69955i	0.527144	−	0.849776i	$-0.323263\pi$
$674$		0			0
$675$	−49390.9	−	28515.9i	−0.108403	−	0.0625862i
$676$		0			0
$677$			789698.i			1.72299i	0.507762	+	0.861497i	$0.330473\pi$
$677$			789698.i			1.72299i	−0.507762	+	0.861497i	$0.669527\pi$
$678$		0			0
$679$	−689224.	+	397924.i	−1.49493	+	0.863099i
$680$		0			0
$681$	−142685.	−	247137.i	−0.307668	−	0.532897i
$682$		0			0
$683$			644105.i			1.38075i	0.723451	+	0.690376i	$0.242555\pi$
$683$			644105.i			1.38075i	−0.723451	+	0.690376i	$0.757445\pi$
$684$		0			0
$685$	320819.			0.683722
$686$		0			0
$687$	44999.7	−	25980.6i	0.0953445	−	0.0550472i
$688$		0			0
$689$	11336.3	+	19635.0i	0.0238799	+	0.0413612i
$690$		0			0
$691$	338350.			0.708616			0.354308	−	0.935129i	$-0.384717\pi$
$691$	338350.			0.708616			0.354308	+	0.935129i	$0.384717\pi$
$692$		0			0
$693$	70664.4	−	122394.i	0.147141	−	0.254856i
$694$		0			0
$695$	−778623.			−1.61197
$696$		0			0
$697$	−329217.	−	190074.i	−0.677668	−	0.391252i
$698$		0			0
$699$	362484.	+	209280.i	0.741881	+	0.428325i
$700$		0			0
$701$	−150371.	−	260451.i	−0.306006	−	0.530017i	0.671479	−	0.741023i	$-0.265659\pi$
$701$	−150371.	−	260451.i	−0.306006	−	0.530017i	−0.977485	+	0.211006i	$0.932326\pi$
$702$		0			0
$703$	−43680.1	+	223373.i	−0.0883838	+	0.451980i
$704$		0			0
$705$	436843.	−	252211.i	0.878916	−	0.507442i
$706$		0			0
$707$	−478189.	+	828247.i	−0.956666	+	1.65699i
$708$		0			0
$709$	−207160.	+	358811.i	−0.412110	+	0.713795i	−0.995120	−	0.0986695i	$-0.968541\pi$
$709$	−207160.	+	358811.i	−0.412110	+	0.713795i	0.583010	+	0.812465i	$0.301875\pi$
$710$		0			0
$711$		−	392055.i		−	0.775546i
$712$		0			0
$713$	−456897.	−	263789.i	−0.898750	−	0.518894i
$714$		0			0
$715$			32948.0i			0.0644491i
$716$		0			0
$717$	155372.	−	89704.3i	0.302229	−	0.174492i
$718$		0			0
$719$	135419.	+	234553.i	0.261952	+	0.453715i	0.966761	−	0.255683i	$-0.0823003\pi$
$719$	135419.	+	234553.i	0.261952	+	0.453715i	−0.704808	+	0.709398i	$0.748967\pi$
$720$		0			0
$721$			570928.i			1.09827i
$722$		0			0
$723$	88650.7			0.169592
$724$		0			0
$725$	37617.5	−	21718.5i	0.0715672	−	0.0413193i
$726$		0			0
$727$	4386.18	+	7597.09i	0.00829885	+	0.0143740i	0.870145	−	0.492796i	$-0.164025\pi$
$727$	4386.18	+	7597.09i	0.00829885	+	0.0143740i	−0.861846	+	0.507170i	$0.830692\pi$
$728$		0			0
$729$	−328096.			−0.617370
$730$		0			0
$731$	119988.	−	207826.i	0.224545	−	0.388924i
$732$		0			0
$733$	653473.			1.21624			0.608121	−	0.793844i	$-0.291924\pi$
$733$	653473.			1.21624			0.608121	+	0.793844i	$0.291924\pi$
$734$		0			0
$735$	−605058.	−	349330.i	−1.12001	−	0.646638i
$736$		0			0
$737$	−106828.	−	61676.9i	−0.196675	−	0.113550i
$738$		0			0
$739$	189565.	+	328336.i	0.347112	+	0.601215i	0.985735	−	0.168304i	$-0.0538292\pi$
$739$	189565.	+	328336.i	0.347112	+	0.601215i	−0.638623	+	0.769519i	$0.720496\pi$
$740$		0			0
$741$	73284.2	+	14330.6i	0.133467	+	0.0260992i
$742$		0			0
$743$	−643576.	+	371569.i	−1.16580	+	0.673072i	−0.952686	−	0.303956i	$-0.901692\pi$
$743$	−643576.	+	371569.i	−1.16580	+	0.673072i	−0.213109	+	0.977028i	$0.568359\pi$
$744$		0			0
$745$	55168.2	−	95554.1i	0.0993977	−	0.172162i
$746$		0			0
$747$	95661.7	−	165691.i	0.171434	−	0.296933i
$748$		0			0
$749$		−	596150.i		−	1.06265i
$750$		0			0
$751$	−832933.	−	480894.i	−1.47683	−	0.852648i	−0.477172	−	0.878810i	$-0.658338\pi$
$751$	−832933.	−	480894.i	−1.47683	−	0.852648i	−0.999658	+	0.0261621i	$0.991671\pi$
$752$		0			0
$753$		−	648162.i		−	1.14312i
$754$		0			0
$755$	−534528.	+	308610.i	−0.937728	+	0.541398i
$756$		0			0
$757$	−68686.5	−	118968.i	−0.119861	−	0.207606i	0.799851	−	0.600198i	$-0.204912\pi$
$757$	−68686.5	−	118968.i	−0.119861	−	0.207606i	−0.919713	+	0.392592i	$0.871578\pi$
$758$		0			0
$759$		−	74042.4i		−	0.128528i
$760$		0			0
$761$	−275441.			−0.475619			−0.237809	−	0.971312i	$-0.576429\pi$
$761$	−275441.			−0.475619			−0.237809	+	0.971312i	$0.576429\pi$
$762$		0			0
$763$	−180918.	+	104453.i	−0.310766	+	0.179421i
$764$		0			0
$765$	−83586.2	−	144775.i	−0.142827	−	0.247384i
$766$		0			0
$767$	181695.			0.308854
$768$		0			0
$769$	303928.	−	526419.i	0.513947	−	0.890182i	−0.485922	−	0.874002i	$-0.661516\pi$
$769$	303928.	−	526419.i	0.513947	−	0.890182i	0.999869	−	0.0161801i	$-0.00515050\pi$
$770$		0			0
$771$	555263.			0.934092
$772$		0			0
$773$	955688.	+	551767.i	1.59940	+	0.923414i	0.991603	+	0.129321i	$0.0412799\pi$
$773$	955688.	+	551767.i	1.59940	+	0.923414i	0.607797	+	0.794092i	$0.292053\pi$
$774$		0			0
$775$	89670.1	+	51771.1i	0.149295	+	0.0861953i
$776$		0			0
$777$	148106.	+	256527.i	0.245319	+	0.424905i
$778$		0			0
$779$	−1.03125e6	+	353789.i	−1.69937	+	0.583002i
$780$		0			0
$781$	19659.7	−	11350.5i	0.0322310	−	0.0186086i
$782$		0			0
$783$	202309.	−	350410.i	0.329983	−	0.571548i
$784$		0			0
$785$	−538952.	+	933493.i	−0.874603	+	1.51486i
$786$		0			0
$787$		−	619317.i		−	0.999916i	−0.866050	−	0.499958i	$-0.833349\pi$
$787$		−	619317.i		−	0.999916i	0.866050	−	0.499958i	$-0.166651\pi$
$788$		0			0
$789$	268958.	+	155283.i	0.432047	+	0.249442i
$790$		0			0
$791$		−	390680.i		−	0.624408i
$792$		0			0
$793$	−136621.	+	78878.1i	−0.217255	+	0.125432i
$794$		0			0
$795$	44936.0	+	77831.5i	0.0710985	+	0.123146i
$796$		0			0
$797$		−	22197.8i		−	0.0349457i	−0.999847	−	0.0174728i	$-0.994438\pi$
$797$		−	22197.8i		−	0.0349457i	0.999847	−	0.0174728i	$-0.00556206\pi$
$798$		0			0
$799$	430591.			0.674484
$800$		0			0
$801$	634407.	−	366275.i	0.988787	−	0.570877i
$802$		0			0
$803$	76097.9	+	131805.i	0.118016	+	0.204410i
$804$		0			0
$805$	893326.			1.37854
$806$		0			0
$807$	264637.	−	458365.i	0.406353	−	0.703825i
$808$		0			0
$809$	110260.			0.168469			0.0842345	−	0.996446i	$-0.473156\pi$
$809$	110260.			0.168469			0.0842345	+	0.996446i	$0.473156\pi$
$810$		0			0
$811$	274722.	+	158611.i	0.417688	+	0.241152i	0.694088	−	0.719890i	$-0.255808\pi$
$811$	274722.	+	158611.i	0.417688	+	0.241152i	−0.276399	+	0.961043i	$0.589141\pi$
$812$		0			0
$813$	189609.	+	109471.i	0.286866	+	0.165622i
$814$		0			0
$815$	339262.	+	587619.i	0.510764	+	0.884669i
$816$		0			0
$817$	−223337.	−	650997.i	−0.334593	−	0.975292i
$818$		0			0
$819$	−136323.	+	78705.9i	−0.203236	+	0.117338i
$820$		0			0
$821$	−423971.	+	734339.i	−0.628999	+	1.08946i	0.358754	+	0.933432i	$0.383202\pi$
$821$	−423971.	+	734339.i	−0.628999	+	1.08946i	−0.987753	+	0.156026i	$0.950132\pi$
$822$		0			0
$823$	−295443.	+	511723.i	−0.436189	+	0.755502i	−0.997392	−	0.0721768i	$-0.977005\pi$
$823$	−295443.	+	511723.i	−0.436189	+	0.755502i	0.561203	+	0.827678i	$0.310339\pi$
$824$		0			0
$825$			14531.5i			0.0213502i
$826$		0			0
$827$	−615143.	−	355153.i	−0.899425	−	0.519283i	−0.0224113	−	0.999749i	$-0.507134\pi$
$827$	−615143.	−	355153.i	−0.899425	−	0.519283i	−0.877014	+	0.480466i	$0.840468\pi$
$828$		0			0
$829$			986161.i			1.43496i	0.696581	+	0.717479i	$0.254704\pi$
$829$			986161.i			1.43496i	−0.696581	+	0.717479i	$0.745296\pi$
$830$		0			0
$831$	−254213.	+	146770.i	−0.368125	+	0.212537i
$832$		0			0
$833$	−298199.	−	516496.i	−0.429751	−	0.744350i
$834$		0			0
$835$			490880.i			0.704048i
$836$		0			0
$837$	964503.			1.37674
$838$		0			0
$839$	296225.	−	171026.i	0.420822	−	0.242962i	−0.274607	−	0.961557i	$-0.588548\pi$
$839$	296225.	−	171026.i	0.420822	−	0.242962i	0.695429	+	0.718595i	$0.255214\pi$
$840$		0			0
$841$	−199556.	−	345641.i	−0.282146	−	0.488690i
$842$		0			0
$843$	725282.			1.02059
$844$		0			0
$845$	−360353.	+	624150.i	−0.504678	+	0.874129i
$846$		0			0
$847$	1.14281e6			1.59297
$848$		0			0
$849$	−362374.	−	209217.i	−0.502738	−	0.290256i
$850$		0			0
$851$	−217689.	−	125683.i	−0.300592	−	0.173547i
$852$		0			0
$853$	−478069.	−	828040.i	−0.657041	−	1.13803i	−0.981378	−	0.192087i	$-0.938474\pi$
$853$	−478069.	−	828040.i	−0.657041	−	1.13803i	0.324337	−	0.945942i	$-0.394859\pi$
$854$		0			0
$855$	−470530.	−	92011.3i	−0.643659	−	0.125866i
$856$		0			0
$857$	1.22953e6	−	709870.i	1.67409	−	0.966535i	0.708776	−	0.705434i	$-0.249248\pi$
$857$	1.22953e6	−	709870.i	1.67409	−	0.966535i	0.965312	−	0.261101i	$-0.0840855\pi$
$858$		0			0
$859$	557394.	−	965435.i	0.755399	−	1.30839i	−0.189777	−	0.981827i	$-0.560777\pi$
$859$	557394.	−	965435.i	0.755399	−	1.30839i	0.945176	−	0.326562i	$-0.105890\pi$
$860$		0			0
$861$	−709445.	+	1.22879e6i	−0.957001	+	1.65757i
$862$		0			0
$863$			1.04519e6i			1.40338i	0.712483	+	0.701690i	$0.247571\pi$
$863$			1.04519e6i			1.40338i	−0.712483	+	0.701690i	$0.752429\pi$
$864$		0			0
$865$	806382.	+	465565.i	1.07773	+	0.622226i
$866$		0			0
$867$		−	376314.i		−	0.500625i
$868$		0			0
$869$	−226431.	+	130730.i	−0.299845	+	0.173116i
$870$		0			0
$871$	68695.6	+	118984.i	0.0905509	+	0.156839i
$872$		0			0
$873$			471720.i			0.618951i
$874$		0			0
$875$	1.22508e6			1.60011
$876$		0			0
$877$	121311.	−	70038.7i	0.157725	−	0.0910624i	−0.419060	−	0.907958i	$-0.637640\pi$
$877$	121311.	−	70038.7i	0.157725	−	0.0910624i	0.576785	+	0.816896i	$0.304307\pi$
$878$		0			0
$879$	−73457.0	−	127231.i	−0.0950726	−	0.164670i
$880$		0			0
$881$	517628.			0.666908			0.333454	−	0.942766i	$-0.391786\pi$
$881$	517628.			0.666908			0.333454	+	0.942766i	$0.391786\pi$
$882$		0			0
$883$	−199591.	+	345702.i	−0.255988	+	0.443384i	−0.965163	−	0.261648i	$-0.915734\pi$
$883$	−199591.	+	345702.i	−0.255988	+	0.443384i	0.709176	+	0.705032i	$0.249067\pi$
$884$		0			0
$885$	720223.			0.919561
$886$		0			0
$887$	902167.	+	520867.i	1.14667	+	0.662032i	0.948074	−	0.318048i	$-0.103027\pi$
$887$	902167.	+	520867.i	1.14667	+	0.662032i	0.198599	+	0.980081i	$0.436361\pi$
$888$		0			0
$889$	−1.24305e6	−	717674.i	−1.57284	−	0.908079i
$890$		0			0
$891$	−62.0984	−	107.558i	−7.82213e−5	−	0.000135483i
$892$		0			0
$893$	811226.	−	931091.i	1.01728	−	1.16759i
$894$		0			0
$895$	479061.	−	276586.i	0.598059	−	0.345290i
$896$		0			0
$897$	−41234.1	+	71419.6i	−0.0512474	+	0.0887631i
$898$		0			0
$899$	−367296.	+	636176.i	−0.454461	+	0.787150i
$900$		0			0
$901$			76717.7i			0.0945030i
$902$		0			0
$903$	−775704.	−	447853.i	−0.951306	−	0.549237i
$904$		0			0
$905$		−	1.27369e6i		−	1.55513i
$906$		0			0
$907$	694514.	−	400978.i	0.844241	−	0.487422i	−0.0144629	−	0.999895i	$-0.504604\pi$
$907$	694514.	−	400978.i	0.844241	−	0.487422i	0.858703	+	0.512473i	$0.171271\pi$
$908$		0			0
$909$	283435.	+	490924.i	0.343025	+	0.594137i
$910$		0			0
$911$			1.38700e6i			1.67125i	0.549301	+	0.835625i	$0.314894\pi$
$911$			1.38700e6i			1.67125i	−0.549301	+	0.835625i	$0.685106\pi$
$912$		0			0
$913$	−127593.			−0.153068
$914$		0			0
$915$	−541552.	+	312665.i	−0.646842	+	0.373454i
$916$		0			0
$917$	−808738.	−	1.40077e6i	−0.961765	−	1.66583i
$918$		0			0
$919$	−751701.			−0.890049			−0.445025	−	0.895518i	$-0.646805\pi$
$919$	−751701.			−0.890049			−0.445025	+	0.895518i	$0.646805\pi$
$920$		0			0
$921$	−365127.	+	632419.i	−0.430453	+	0.745566i
$922$		0			0
$923$	−25284.4			−0.0296790
$924$		0			0
$925$	42723.5	+	24666.4i	0.0499325	+	0.0288286i
$926$		0			0
$927$	293067.	+	169202.i	0.341041	+	0.196900i
$928$		0			0
$929$	570771.	+	988605.i	0.661349	+	1.14549i	0.980261	+	0.197706i	$0.0633492\pi$
$929$	570771.	+	988605.i	0.661349	+	1.14549i	−0.318912	+	0.947784i	$0.603317\pi$
$930$		0			0
$931$	−1.67865e6	−	328257.i	−1.93669	−	0.378716i
$932$		0			0
$933$	−322021.	+	185919.i	−0.369931	+	0.213580i
$934$		0			0
$935$	−55743.4	+	96550.4i	−0.0637632	+	0.110441i
$936$		0			0
$937$	−281582.	+	487714.i	−0.320719	+	0.555502i	−0.980637	−	0.195836i	$-0.937258\pi$
$937$	−281582.	+	487714.i	−0.320719	+	0.555502i	0.659917	+	0.751338i	$0.270591\pi$
$938$		0			0
$939$		−	135267.i		−	0.153412i
$940$		0			0
$941$	−927824.	−	535679.i	−1.04782	−	0.604959i	−0.125781	−	0.992058i	$-0.540144\pi$
$941$	−927824.	−	535679.i	−1.04782	−	0.604959i	−0.922038	+	0.387100i	$0.873477\pi$
$942$		0			0
$943$		−	1.20407e6i		−	1.35403i
$944$		0			0
$945$	−1.41435e6	+	816575.i	−1.58377	+	0.914392i
$946$		0			0
$947$	−721456.	−	1.24960e6i	−0.804470	−	1.39338i	−0.916648	−	0.399695i	$-0.869116\pi$
$947$	−721456.	−	1.24960e6i	−0.804470	−	1.39338i	0.112178	−	0.993688i	$-0.464217\pi$
$948$		0			0
$949$		−	169515.i		−	0.188225i
$950$		0			0
$951$	−479031.			−0.529667
$952$		0			0
$953$	239343.	−	138185.i	0.263533	−	0.152151i	−0.362412	−	0.932018i	$-0.618047\pi$
$953$	239343.	−	138185.i	0.263533	−	0.152151i	0.625945	+	0.779867i	$0.284713\pi$
$954$		0			0
$955$	695660.	+	1.20492e6i	0.762764	+	1.32115i
$956$		0			0
$957$	−103095.			−0.112568
$958$		0			0
$959$	511090.	−	885234.i	0.555726	−	0.962545i
$960$		0			0
$961$	−827553.			−0.896084
$962$		0			0
$963$	−306013.	−	176677.i	−0.329980	−	0.190514i
$964$		0			0
$965$	−1.22372e6	−	706513.i	−1.31409	−	0.758692i
$966$		0			0
$967$	−43685.9	−	75666.3i	−0.0467185	−	0.0809188i	0.841721	−	0.539913i	$-0.181543\pi$
$967$	−43685.9	−	75666.3i	−0.0467185	−	0.0809188i	−0.888439	+	0.458995i	$0.848210\pi$
$968$		0			0
$969$	190506.	+	165981.i	0.202890	+	0.176771i
$970$		0			0
$971$	483492.	−	279144.i	0.512803	−	0.296067i	−0.221182	−	0.975233i	$-0.570992\pi$
$971$	483492.	−	279144.i	0.512803	−	0.296067i	0.733985	+	0.679166i	$0.237658\pi$
$972$		0			0
$973$	−1.24041e6	+	2.14845e6i	−1.31020	+	2.26934i
$974$		0			0
$975$	8092.57	−	14016.7i	0.00851290	−	0.0147448i
$976$		0			0
$977$		−	36446.8i		−	0.0381830i	−0.999818	−	0.0190915i	$-0.993923\pi$
$977$		−	36446.8i		−	0.0381830i	0.999818	−	0.0190915i	$-0.00607738\pi$
$978$		0			0
$979$	−423084.	−	244268.i	−0.441430	−	0.254859i
$980$		0			0
$981$			123824.i			0.128667i
$982$		0			0
$983$	819884.	−	473360.i	0.848487	−	0.489874i	−0.0116529	−	0.999932i	$-0.503709\pi$
$983$	819884.	−	473360.i	0.848487	−	0.489874i	0.860140	+	0.510058i	$0.170376\pi$
$984$		0			0
$985$	144167.	+	249704.i	0.148591	+	0.257367i
$986$		0			0
$987$		−	1.60717e6i		−	1.64979i
$988$		0			0
$989$	760097.			0.777099
$990$		0			0
$991$	361483.	−	208702.i	0.368078	−	0.212510i	−0.304540	−	0.952499i	$-0.598503\pi$
$991$	361483.	−	208702.i	0.368078	−	0.212510i	0.672619	+	0.739989i	$0.265169\pi$
$992$		0			0
$993$	−281947.	−	488347.i	−0.285936	−	0.495256i
$994$		0			0
$995$	580781.			0.586632
$996$		0			0
$997$	247061.	−	427922.i	0.248550	−	0.430501i	−0.714574	−	0.699560i	$-0.753379\pi$
$997$	247061.	−	427922.i	0.248550	−	0.430501i	0.963124	+	0.269059i	$0.0867126\pi$
$998$		0			0
$999$	459539.			0.460460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.h.a.69.5	yes	12
3.2	odd	2		684.5.y.c.145.6		12
4.3	odd	2		304.5.r.b.145.2		12
19.8	odd	6	inner	76.5.h.a.65.5	✓	12
57.8	even	6		684.5.y.c.217.6		12
76.27	even	6		304.5.r.b.65.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.5	✓	12	19.8	odd	6	inner
76.5.h.a.69.5	yes	12	1.1	even	1	trivial
304.5.r.b.65.2		12	76.27	even	6
304.5.r.b.145.2		12	4.3	odd	2
684.5.y.c.145.6		12	3.2	odd	2
684.5.y.c.217.6		12	57.8	even	6

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.81550 - 2.78023i) q^{3} +(-13.2594 - 22.9660i) q^{5} -84.4930 q^{7} +(-25.0406 + 43.3717i) q^{9} +O(q^{10})\)	\(q+(4.81550 - 2.78023i) q^{3} +(-13.2594 - 22.9660i) q^{5} -84.4930 q^{7} +(-25.0406 + 43.3717i) q^{9} +33.3991 q^{11} +(-32.2160 - 18.5999i) q^{13} +(-127.701 - 73.7284i) q^{15} +(-62.9369 - 109.010i) q^{17} +(-354.290 - 69.2806i) q^{19} +(-406.876 + 234.910i) q^{21} +(199.345 - 345.275i) q^{23} +(-39.1233 + 67.7635i) q^{25} +728.872i q^{27} +(-480.756 - 277.565i) q^{29} -1323.28i q^{31} +(160.833 - 92.8571i) q^{33} +(1120.33 + 1940.46i) q^{35} -630.480i q^{37} -206.848 q^{39} +(2615.46 - 1510.04i) q^{41} +(953.243 + 1651.07i) q^{43} +1328.10 q^{45} +(-1710.41 + 2962.52i) q^{47} +4738.07 q^{49} +(-606.145 - 349.958i) q^{51} +(-527.826 - 304.741i) q^{53} +(-442.852 - 767.041i) q^{55} +(-1898.70 + 651.386i) q^{57} +(-4229.93 + 2442.15i) q^{59} +(2120.39 - 3672.62i) q^{61} +(2115.76 - 3664.60i) q^{63} +986.495i q^{65} +(-3198.52 - 1846.67i) q^{67} -2216.90i q^{69} +(588.629 - 339.845i) q^{71} +(2278.44 + 3946.38i) q^{73} +435.087i q^{75} -2821.99 q^{77} +(-6779.56 + 3914.18i) q^{79} +(-1.85929 - 3.22038i) q^{81} -3820.26 q^{83} +(-1669.01 + 2890.81i) q^{85} -3086.77 q^{87} +(-12667.5 - 7313.61i) q^{89} +(2722.03 + 1571.56i) q^{91} +(-3679.03 - 6372.26i) q^{93} +(3106.57 + 9055.22i) q^{95} +(8157.18 - 4709.55i) q^{97} +(-836.334 + 1448.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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