LMFDB - Embedded newform 76.5.h.a.69.3

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			69.3
Root			$0.500000 - 4.44379i$ of defining polynomial
Character	$\chi$	$=$	76.69
Dual form			76.5.h.a.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.59843 + 2.65491i) q^{3} +(-1.89169 - 3.27650i) q^{5} +36.8385 q^{7} +(-26.4029 + 45.7312i) q^{9} +O(q^{10})$	\(q+(-4.59843 + 2.65491i) q^{3} +(-1.89169 - 3.27650i) q^{5} +36.8385 q^{7} +(-26.4029 + 45.7312i) q^{9} -226.922 q^{11} +(-177.578 - 102.525i) q^{13} +(17.3976 + 10.0445i) q^{15} +(15.7220 + 27.2313i) q^{17} +(-322.235 - 162.744i) q^{19} +(-169.400 + 97.8029i) q^{21} +(-439.921 + 761.966i) q^{23} +(305.343 - 528.870i) q^{25} -710.484i q^{27} +(203.329 + 117.392i) q^{29} +1652.02i q^{31} +(1043.49 - 602.458i) q^{33} +(-69.6871 - 120.702i) q^{35} -1067.59i q^{37} +1088.78 q^{39} +(70.5284 - 40.7196i) q^{41} +(617.894 + 1070.22i) q^{43} +199.785 q^{45} +(1149.90 - 1991.68i) q^{47} -1043.92 q^{49} +(-144.593 - 83.4808i) q^{51} +(2872.93 + 1658.69i) q^{53} +(429.267 + 743.512i) q^{55} +(1913.85 - 107.138i) q^{57} +(-1361.72 + 786.188i) q^{59} +(1686.52 - 2921.13i) q^{61} +(-972.645 + 1684.67i) q^{63} +775.782i q^{65} +(2803.02 + 1618.32i) q^{67} -4671.80i q^{69} +(-7883.38 + 4551.47i) q^{71} +(-3146.77 - 5450.36i) q^{73} +3242.63i q^{75} -8359.49 q^{77} +(-705.913 + 407.559i) q^{79} +(-252.367 - 437.113i) q^{81} -5757.37 q^{83} +(59.4823 - 103.026i) q^{85} -1246.66 q^{87} +(10151.8 + 5861.15i) q^{89} +(-6541.73 - 3776.87i) q^{91} +(-4385.97 - 7596.72i) q^{93} +(76.3383 + 1363.67i) q^{95} +(-8993.31 + 5192.29i) q^{97} +(5991.42 - 10377.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.59843	+	2.65491i	−0.510937	+	0.294990i	−0.733219	−	0.679993i	$-0.761983\pi$
$3$	−4.59843	+	2.65491i	−0.510937	+	0.294990i	0.222282	+	0.974983i	$0.428650\pi$
$4$		0			0
$5$	−1.89169	−	3.27650i	−0.0756676	−	0.131060i	0.825709	−	0.564097i	$-0.190775\pi$
$5$	−1.89169	−	3.27650i	−0.0756676	−	0.131060i	−0.901376	+	0.433036i	$0.857442\pi$
$6$		0			0
$7$	36.8385			0.751807			0.375903	−	0.926659i	$-0.377332\pi$
$7$	36.8385			0.751807			0.375903	+	0.926659i	$0.377332\pi$
$8$		0			0
$9$	−26.4029	+	45.7312i	−0.325962	+	0.564583i
$10$		0			0
$11$	−226.922			−1.87539			−0.937696	−	0.347457i	$-0.887045\pi$
$11$	−226.922			−1.87539			−0.937696	+	0.347457i	$0.887045\pi$
$12$		0			0
$13$	−177.578	−	102.525i	−1.05076	−	0.606657i	−0.127898	−	0.991787i	$-0.540823\pi$
$13$	−177.578	−	102.525i	−1.05076	−	0.606657i	−0.922862	+	0.385131i	$0.874156\pi$
$14$		0			0
$15$	17.3976	+	10.0445i	0.0773228	+	0.0446423i
$16$		0			0
$17$	15.7220	+	27.2313i	0.0544013	+	0.0942259i	0.891944	−	0.452147i	$-0.149342\pi$
$17$	15.7220	+	27.2313i	0.0544013	+	0.0942259i	−0.837542	+	0.546373i	$0.816008\pi$
$18$		0			0
$19$	−322.235	−	162.744i	−0.892618	−	0.450814i
$19$	−322.235	−	162.744i	−0.892618	−	0.450814i
$20$		0			0
$21$	−169.400	+	97.8029i	−0.384126	+	0.221775i
$22$		0			0
$23$	−439.921	+	761.966i	−0.831610	+	1.44039i	0.0651518	+	0.997875i	$0.479247\pi$
$23$	−439.921	+	761.966i	−0.831610	+	1.44039i	−0.896761	+	0.442515i	$0.854086\pi$
$24$		0			0
$25$	305.343	−	528.870i	0.488549	−	0.846191i
$26$		0			0
$27$		−	710.484i		−	0.974601i
$28$		0			0
$29$	203.329	+	117.392i	0.241770	+	0.139586i	0.615990	−	0.787754i	$-0.288756\pi$
$29$	203.329	+	117.392i	0.241770	+	0.139586i	−0.374220	+	0.927340i	$0.622089\pi$
$30$		0			0
$31$			1652.02i			1.71907i	0.511080	+	0.859533i	$0.329246\pi$
$31$			1652.02i			1.71907i	−0.511080	+	0.859533i	$0.670754\pi$
$32$		0			0
$33$	1043.49	−	602.458i	0.958208	−	0.553221i
$34$		0			0
$35$	−69.6871	−	120.702i	−0.0568874	−	0.0985319i
$36$		0			0
$37$		−	1067.59i		−	0.779829i	−0.920851	−	0.389914i	$-0.872505\pi$
$37$		−	1067.59i		−	0.779829i	0.920851	−	0.389914i	$-0.127495\pi$
$38$		0			0
$39$	1088.78			0.715830
$40$		0			0
$41$	70.5284	−	40.7196i	0.0419562	−	0.0242234i	−0.478875	−	0.877883i	$-0.658955\pi$
$41$	70.5284	−	40.7196i	0.0419562	−	0.0242234i	0.520831	+	0.853660i	$0.325622\pi$
$42$		0			0
$43$	617.894	+	1070.22i	0.334177	+	0.578812i	0.983326	−	0.181849i	$-0.0582082\pi$
$43$	617.894	+	1070.22i	0.334177	+	0.578812i	−0.649149	+	0.760661i	$0.724875\pi$
$44$		0			0
$45$	199.785			0.0986591
$46$		0			0
$47$	1149.90	−	1991.68i	0.520552	−	0.901622i	−0.479163	−	0.877726i	$-0.659060\pi$
$47$	1149.90	−	1991.68i	0.520552	−	0.901622i	0.999714	−	0.0238962i	$-0.00760711\pi$
$48$		0			0
$49$	−1043.92			−0.434787
$50$		0			0
$51$	−144.593	−	83.4808i	−0.0555913	−	0.0320957i
$52$		0			0
$53$	2872.93	+	1658.69i	1.02276	+	0.590491i	0.914902	−	0.403675i	$-0.132267\pi$
$53$	2872.93	+	1658.69i	1.02276	+	0.590491i	0.107858	+	0.994166i	$0.465601\pi$
$54$		0			0
$55$	429.267	+	743.512i	0.141906	+	0.245789i
$56$		0			0
$57$	1913.85	−	107.138i	0.589057	−	0.0329755i
$58$		0			0
$59$	−1361.72	+	786.188i	−0.391186	+	0.225851i	−0.682674	−	0.730723i	$-0.739183\pi$
$59$	−1361.72	+	786.188i	−0.391186	+	0.225851i	0.291488	+	0.956574i	$0.405850\pi$
$60$		0			0
$61$	1686.52	−	2921.13i	0.453243	−	0.785039i	−0.545343	−	0.838213i	$-0.683600\pi$
$61$	1686.52	−	2921.13i	0.453243	−	0.785039i	0.998585	+	0.0531739i	$0.0169338\pi$
$62$		0			0
$63$	−972.645	+	1684.67i	−0.245061	+	0.424457i
$64$		0			0
$65$			775.782i			0.183617i
$66$		0			0
$67$	2803.02	+	1618.32i	0.624420	+	0.360509i	0.778588	−	0.627536i	$-0.215936\pi$
$67$	2803.02	+	1618.32i	0.624420	+	0.360509i	−0.154168	+	0.988045i	$0.549270\pi$
$68$		0			0
$69$		−	4671.80i		−	0.981265i
$70$		0			0
$71$	−7883.38	+	4551.47i	−1.56385	+	0.902890i	−0.566990	+	0.823725i	$0.691892\pi$
$71$	−7883.38	+	4551.47i	−1.56385	+	0.902890i	−0.996861	+	0.0791654i	$0.974774\pi$
$72$		0			0
$73$	−3146.77	−	5450.36i	−0.590498	−	1.02277i	−0.994165	−	0.107867i	$-0.965598\pi$
$73$	−3146.77	−	5450.36i	−0.590498	−	1.02277i	0.403667	−	0.914906i	$-0.367735\pi$
$74$		0			0
$75$			3242.63i			0.576468i
$76$		0			0
$77$	−8359.49			−1.40993
$78$		0			0
$79$	−705.913	+	407.559i	−0.113109	+	0.0653035i	−0.555487	−	0.831525i	$-0.687468\pi$
$79$	−705.913	+	407.559i	−0.113109	+	0.0653035i	0.442378	+	0.896829i	$0.354135\pi$
$80$		0			0
$81$	−252.367	−	437.113i	−0.0384648	−	0.0666229i
$82$		0			0
$83$	−5757.37			−0.835734			−0.417867	−	0.908508i	$-0.637222\pi$
$83$	−5757.37			−0.835734			−0.417867	+	0.908508i	$0.637222\pi$
$84$		0			0
$85$	59.4823	−	103.026i	0.00823284	−	0.0142597i
$86$		0			0
$87$	−1246.66			−0.164706
$88$		0			0
$89$	10151.8	+	5861.15i	1.28163	+	0.739951i	0.977147	−	0.212566i	$-0.0681821\pi$
$89$	10151.8	+	5861.15i	1.28163	+	0.739951i	0.304486	+	0.952517i	$0.401515\pi$
$90$		0			0
$91$	−6541.73	−	3776.87i	−0.789968	−	0.456088i
$92$		0			0
$93$	−4385.97	−	7596.72i	−0.507107	−	0.878335i
$94$		0			0
$95$	76.3383	+	1363.67i	0.00845853	+	0.151099i
$96$		0			0
$97$	−8993.31	+	5192.29i	−0.955820	+	0.551843i	−0.894884	−	0.446299i	$-0.852742\pi$
$97$	−8993.31	+	5192.29i	−0.955820	+	0.551843i	−0.0609359	+	0.998142i	$0.519409\pi$
$98$		0			0
$99$	5991.42	−	10377.4i	0.611307	−	1.05881i
$100$		0			0
$101$	−2230.13	+	3862.70i	−0.218619	+	0.378659i	−0.954386	−	0.298576i	$-0.903488\pi$
$101$	−2230.13	+	3862.70i	−0.218619	+	0.378659i	0.735767	+	0.677235i	$0.236822\pi$
$102$		0			0
$103$			2027.86i			0.191145i	0.995422	+	0.0955724i	$0.0304681\pi$
$103$			2027.86i			0.191145i	−0.995422	+	0.0955724i	$0.969532\pi$
$104$		0			0
$105$	640.903	+	370.026i	0.0581318	+	0.0335624i
$106$		0			0
$107$			14889.6i			1.30052i	0.759712	+	0.650259i	$0.225340\pi$
$107$			14889.6i			1.30052i	−0.759712	+	0.650259i	$0.774660\pi$
$108$		0			0
$109$	11928.4	−	6886.87i	1.00399	−	0.579654i	0.0945635	−	0.995519i	$-0.469854\pi$
$109$	11928.4	−	6886.87i	1.00399	−	0.579654i	0.909426	+	0.415865i	$0.136521\pi$
$110$		0			0
$111$	2834.34	+	4909.22i	0.230041	+	0.398443i
$112$		0			0
$113$		−	3322.86i		−	0.260228i	−0.991499	−	0.130114i	$-0.958466\pi$
$113$		−	3322.86i		−	0.260228i	0.991499	−	0.130114i	$-0.0415344\pi$
$114$		0			0
$115$	3328.78			0.251704
$116$		0			0
$117$	9377.18	−	5413.92i	0.685016	−	0.395494i
$118$		0			0
$119$	579.175	+	1003.16i	0.0408993	+	0.0708396i
$120$		0			0
$121$	36852.8			2.51710
$122$		0			0
$123$	−216.214	+	374.493i	−0.0142913	+	0.0247533i
$124$		0			0
$125$	−4675.07			−0.299205
$126$		0			0
$127$	−826.038	−	476.913i	−0.0512145	−	0.0295687i	0.474174	−	0.880431i	$-0.342747\pi$
$127$	−826.038	−	476.913i	−0.0512145	−	0.0295687i	−0.525389	+	0.850862i	$0.676080\pi$
$128$		0			0
$129$	−5682.69	−	3280.90i	−0.341487	−	0.197158i
$130$		0			0
$131$	−4762.01	−	8248.04i	−0.277490	−	0.480627i	0.693270	−	0.720678i	$-0.256169\pi$
$131$	−4762.01	−	8248.04i	−0.277490	−	0.480627i	−0.970760	+	0.240051i	$0.922836\pi$
$132$		0			0
$133$	−11870.7	−	5995.24i	−0.671076	−	0.338925i
$134$		0			0
$135$	−2327.91	+	1344.02i	−0.127731	+	0.0737458i
$136$		0			0
$137$	−10584.3	+	18332.5i	−0.563924	+	0.976745i	0.433225	+	0.901286i	$0.357376\pi$
$137$	−10584.3	+	18332.5i	−0.563924	+	0.976745i	−0.997149	+	0.0754589i	$0.975958\pi$
$138$		0			0
$139$	11617.6	−	20122.4i	0.601296	−	1.04148i	−0.391329	−	0.920251i	$-0.627984\pi$
$139$	11617.6	−	20122.4i	0.601296	−	1.04148i	0.992625	−	0.121225i	$-0.0386822\pi$
$140$		0			0
$141$			12211.5i			0.614230i
$142$		0			0
$143$	40296.5	+	23265.2i	1.97059	+	1.13772i
$144$		0			0
$145$		−	888.277i		−	0.0422486i
$146$		0			0
$147$	4800.41	−	2771.52i	0.222149	−	0.128258i
$148$		0			0
$149$	−6852.38	−	11868.7i	−0.308652	−	0.534600i	0.669416	−	0.742888i	$-0.266544\pi$
$149$	−6852.38	−	11868.7i	−0.308652	−	0.534600i	−0.978068	+	0.208287i	$0.933211\pi$
$150$		0			0
$151$		−	40027.2i		−	1.75550i	−0.479118	−	0.877750i	$-0.659043\pi$
$151$		−	40027.2i		−	1.75550i	0.479118	−	0.877750i	$-0.340957\pi$
$152$		0			0
$153$	−1660.43			−0.0709311
$154$		0			0
$155$	5412.86	−	3125.12i	0.225301	−	0.130078i
$156$		0			0
$157$	12552.7	+	21741.8i	0.509256	+	0.882058i	0.999943	+	0.0107213i	$0.00341277\pi$
$157$	12552.7	+	21741.8i	0.509256	+	0.882058i	−0.490686	+	0.871336i	$0.663254\pi$
$158$		0			0
$159$	−17614.7			−0.696755
$160$		0			0
$161$	−16206.1	+	28069.7i	−0.625210	+	1.08289i
$162$		0			0
$163$	−23080.8			−0.868710			−0.434355	−	0.900742i	$-0.643024\pi$
$163$	−23080.8			−0.868710			−0.434355	+	0.900742i	$0.643024\pi$
$164$		0			0
$165$	−3947.91	−	2279.33i	−0.145011	−	0.0837219i
$166$		0			0
$167$	−5883.08	−	3396.60i	−0.210946	−	0.121790i	0.390805	−	0.920474i	$-0.372197\pi$
$167$	−5883.08	−	3396.60i	−0.210946	−	0.121790i	−0.601751	+	0.798684i	$0.705530\pi$
$168$		0			0
$169$	6742.24	+	11677.9i	0.236065	+	0.408876i
$170$		0			0
$171$	15950.4	−	10439.3i	0.545482	−	0.357009i
$172$		0			0
$173$	−32609.7	+	18827.2i	−1.08957	+	0.629063i	−0.933462	−	0.358677i	$-0.883228\pi$
$173$	−32609.7	+	18827.2i	−1.08957	+	0.629063i	−0.156107	+	0.987740i	$0.549895\pi$
$174$		0			0
$175$	11248.4	−	19482.8i	0.367294	−	0.636172i
$176$		0			0
$177$	4174.51	−	7230.47i	0.133248	−	0.230792i
$178$		0			0
$179$			14530.7i			0.453503i	0.973953	+	0.226752i	$0.0728106\pi$
$179$			14530.7i			0.453503i	−0.973953	+	0.226752i	$0.927189\pi$
$180$		0			0
$181$	−12435.8	−	7179.81i	−0.379591	−	0.219157i	0.298049	−	0.954551i	$-0.403664\pi$
$181$	−12435.8	−	7179.81i	−0.379591	−	0.219157i	−0.677641	+	0.735393i	$0.736997\pi$
$182$		0			0
$183$			17910.2i			0.534808i
$184$		0			0
$185$	−3497.95	+	2019.54i	−0.102204	+	0.0590078i
$186$		0			0
$187$	−3567.67	−	6179.39i	−0.102024	−	0.176710i
$188$		0			0
$189$		−	26173.2i		−	0.732712i
$190$		0			0
$191$	−41807.4			−1.14601			−0.573003	−	0.819554i	$-0.694221\pi$
$191$	−41807.4			−1.14601			−0.573003	+	0.819554i	$0.694221\pi$
$192$		0			0
$193$	−47304.7	+	27311.4i	−1.26996	+	0.733211i	−0.974980	−	0.222293i	$-0.928646\pi$
$193$	−47304.7	+	27311.4i	−1.26996	+	0.733211i	−0.294978	+	0.955504i	$0.595312\pi$
$194$		0			0
$195$	−2059.63	−	3567.38i	−0.0541651	−	0.0938168i
$196$		0			0
$197$	−56392.9			−1.45309			−0.726544	−	0.687120i	$-0.758875\pi$
$197$	−56392.9			−1.45309			−0.726544	+	0.687120i	$0.758875\pi$
$198$		0			0
$199$	17457.8	−	30237.8i	0.440842	−	0.763560i	−0.556910	−	0.830573i	$-0.688013\pi$
$199$	17457.8	−	30237.8i	0.440842	−	0.763560i	0.997752	+	0.0670122i	$0.0213466\pi$
$200$		0			0
$201$	−17186.0			−0.425386
$202$		0			0
$203$	7490.33	+	4324.55i	0.181765	+	0.104942i
$204$		0			0
$205$	−266.836	−	154.058i	−0.00634946	−	0.00366586i
$206$		0			0
$207$	−23230.4	−	40236.3i	−0.542146	−	0.939025i
$208$		0			0
$209$	73122.4	+	36930.2i	1.67401	+	0.845453i
$210$		0			0
$211$	−10853.9	+	6266.48i	−0.243792	+	0.140753i	−0.616918	−	0.787027i	$-0.711619\pi$
$211$	−10853.9	+	6266.48i	−0.243792	+	0.140753i	0.373126	+	0.927781i	$0.378286\pi$
$212$		0			0
$213$	24167.5	−	41859.3i	0.532687	−	0.922640i
$214$		0			0
$215$	2337.73	−	4049.07i	0.0505728	−	0.0875947i
$216$		0			0
$217$			60858.1i			1.29241i
$218$		0			0
$219$	28940.4	+	16708.7i	0.603415	+	0.348382i
$220$		0			0
$221$		−	6447.58i		−	0.132012i
$222$		0			0
$223$	26821.8	−	15485.6i	0.539359	−	0.311399i	−0.205460	−	0.978665i	$-0.565869\pi$
$223$	26821.8	−	15485.6i	0.539359	−	0.311399i	0.744819	+	0.667266i	$0.232536\pi$
$224$		0			0
$225$	16123.9	+	27927.4i	0.318497	+	0.551653i
$226$		0			0
$227$		−	3848.94i		−	0.0746946i	−0.999302	−	0.0373473i	$-0.988109\pi$
$227$		−	3848.94i		−	0.0746946i	0.999302	−	0.0373473i	$-0.0118908\pi$
$228$		0			0
$229$	−63827.1			−1.21712			−0.608561	−	0.793507i	$-0.708253\pi$
$229$	−63827.1			−1.21712			−0.608561	+	0.793507i	$0.708253\pi$
$230$		0			0
$231$	38440.6	−	22193.7i	0.720387	−	0.415916i
$232$		0			0
$233$	−20192.4	−	34974.2i	−0.371942	−	0.644223i	0.617922	−	0.786239i	$-0.287975\pi$
$233$	−20192.4	−	34974.2i	−0.371942	−	0.644223i	−0.989864	+	0.142016i	$0.954641\pi$
$234$		0			0
$235$	−8701.01			−0.157556
$236$		0			0
$237$	2164.06	−	3748.27i	0.0385277	−	0.0667320i
$238$		0			0
$239$	−31058.8			−0.543737			−0.271868	−	0.962334i	$-0.587642\pi$
$239$	−31058.8			−0.543737			−0.271868	+	0.962334i	$0.587642\pi$
$240$		0			0
$241$	71121.0	+	41061.7i	1.22451	+	0.706974i	0.965877	−	0.259001i	$-0.0833932\pi$
$241$	71121.0	+	41061.7i	1.22451	+	0.706974i	0.258637	+	0.965975i	$0.416727\pi$
$242$		0			0
$243$	52160.1	+	30114.6i	0.883336	+	0.509994i
$244$		0			0
$245$	1974.78	+	3420.42i	0.0328993	+	0.0569832i
$246$		0			0
$247$	40536.7	+	61936.9i	0.664438	+	1.01521i
$248$		0			0
$249$	26474.9	−	15285.3i	0.427007	−	0.246533i
$250$		0			0
$251$	−3685.23	+	6383.00i	−0.0584947	+	0.101316i	−0.893790	−	0.448486i	$-0.851963\pi$
$251$	−3685.23	+	6383.00i	−0.0584947	+	0.101316i	0.835295	+	0.549802i	$0.185297\pi$
$252$		0			0
$253$	99828.0	−	172907.i	1.55959	−	2.70130i
$254$		0			0
$255$			631.680i			0.00971441i
$256$		0			0
$257$	113757.	+	65677.8i	1.72232	+	0.994379i	0.914096	+	0.405498i	$0.132902\pi$
$257$	113757.	+	65677.8i	1.72232	+	0.994379i	0.808220	+	0.588881i	$0.200431\pi$
$258$		0			0
$259$		−	39328.3i		−	0.586280i
$260$		0			0
$261$	−10737.0	+	6198.98i	−0.157616	+	0.0909996i
$262$		0			0
$263$	11998.9	+	20782.6i	0.173472	+	0.300462i	0.939631	−	0.342189i	$-0.111168\pi$
$263$	11998.9	+	20782.6i	0.173472	+	0.300462i	−0.766160	+	0.642650i	$0.777835\pi$
$264$		0			0
$265$		−	12550.9i		−	0.178724i
$266$		0			0
$267$	−62243.2			−0.873111
$268$		0			0
$269$	26597.9	−	15356.3i	0.367572	−	0.212218i	−0.304825	−	0.952408i	$-0.598598\pi$
$269$	26597.9	−	15356.3i	0.367572	−	0.212218i	0.672397	+	0.740191i	$0.265265\pi$
$270$		0			0
$271$	40696.4	+	70488.3i	0.554138	+	0.959794i	0.997970	+	0.0636846i	$0.0202852\pi$
$271$	40696.4	+	70488.3i	0.554138	+	0.959794i	−0.443833	+	0.896110i	$0.646381\pi$
$272$		0			0
$273$	40108.9			0.538166
$274$		0			0
$275$	−69289.2	+	120012.i	−0.916221	+	1.58694i
$276$		0			0
$277$	−91978.7			−1.19875			−0.599374	−	0.800469i	$-0.704584\pi$
$277$	−91978.7			−1.19875			−0.599374	+	0.800469i	$0.704584\pi$
$278$		0			0
$279$	−75549.0	−	43618.2i	−0.970556	−	0.560351i
$280$		0			0
$281$	−125610.	−	72520.9i	−1.59078	−	0.918439i	−0.993173	−	0.116653i	$-0.962783\pi$
$281$	−125610.	−	72520.9i	−1.59078	−	0.918439i	−0.597611	−	0.801786i	$-0.703883\pi$
$282$		0			0
$283$	−31938.6	−	55319.4i	−0.398789	−	0.690723i	0.594787	−	0.803883i	$-0.297236\pi$
$283$	−31938.6	−	55319.4i	−0.398789	−	0.690723i	−0.993577	+	0.113160i	$0.963903\pi$
$284$		0			0
$285$	−3971.44	−	6068.06i	−0.0488943	−	0.0747068i
$286$		0			0
$287$	2598.16	−	1500.05i	0.0315430	−	0.0182113i
$288$		0			0
$289$	41266.1	−	71475.0i	0.494081	−	0.855773i
$290$		0			0
$291$	27570.1	−	47752.8i	0.325576	−	0.563914i
$292$		0			0
$293$			27420.6i			0.319405i	0.987165	+	0.159703i	$0.0510536\pi$
$293$			27420.6i			0.319405i	−0.987165	+	0.159703i	$0.948946\pi$
$294$		0			0
$295$	5151.90	+	2974.45i	0.0592002	+	0.0341793i
$296$		0			0
$297$			161225.i			1.82776i
$298$		0			0
$299$	156241.	−	90205.9i	1.74764	−	1.00900i
$300$		0			0
$301$	22762.3	+	39425.5i	0.251237	+	0.435155i
$302$		0			0
$303$		−	23683.2i		−	0.257961i
$304$		0			0
$305$	−12761.5			−0.137183
$306$		0			0
$307$	−137272.	+	79253.9i	−1.45648	+	0.840899i	−0.998836	−	0.0482361i	$-0.984640\pi$
$307$	−137272.	+	79253.9i	−1.45648	+	0.840899i	−0.457644	+	0.889135i	$0.651307\pi$
$308$		0			0
$309$	−5383.77	−	9324.96i	−0.0563858	−	0.0976630i
$310$		0			0
$311$	437.895			0.00452740			0.00226370	−	0.999997i	$-0.499279\pi$
$311$	437.895			0.00452740			0.00226370	+	0.999997i	$0.499279\pi$
$312$		0			0
$313$	−25325.9	+	43865.8i	−0.258509	+	0.447751i	−0.965843	−	0.259129i	$-0.916565\pi$
$313$	−25325.9	+	43865.8i	−0.258509	+	0.447751i	0.707333	+	0.706880i	$0.249898\pi$
$314$		0			0
$315$	7359.77			0.0741726
$316$		0			0
$317$	−82787.1	−	47797.1i	−0.823842	−	0.475645i	0.0278976	−	0.999611i	$-0.491119\pi$
$317$	−82787.1	−	47797.1i	−0.823842	−	0.475645i	−0.851740	+	0.523965i	$0.824452\pi$
$318$		0			0
$319$	−46139.9	−	26638.9i	−0.453414	−	0.261779i
$320$		0			0
$321$	−39530.6	−	68469.0i	−0.383640	−	0.664483i
$322$		0			0
$323$	−634.453	−	11333.5i	−0.00608127	−	0.108633i
$324$		0			0
$325$	−108445.	+	62610.6i	−1.02670	+	0.592763i
$326$		0			0
$327$	−36568.0	+	63337.6i	−0.341984	+	0.592333i
$328$		0			0
$329$	42360.6	−	73370.7i	0.391354	−	0.677846i
$330$		0			0
$331$			204896.i			1.87015i	0.354448	+	0.935076i	$0.384669\pi$
$331$			204896.i			1.87015i	−0.354448	+	0.935076i	$0.615331\pi$
$332$		0			0
$333$	48822.0	+	28187.4i	0.440278	+	0.254195i
$334$		0			0
$335$		−	12245.5i		−	0.109115i
$336$		0			0
$337$	1314.09	−	758.693i	0.0115709	−	0.00668046i	−0.494203	−	0.869346i	$-0.664540\pi$
$337$	1314.09	−	758.693i	0.0115709	−	0.00668046i	0.505774	+	0.862666i	$0.331207\pi$
$338$		0			0
$339$	8821.88	+	15279.9i	0.0767647	+	0.132960i
$340$		0			0
$341$		−	374881.i		−	3.22392i
$342$		0			0
$343$	−126906.			−1.07868
$344$		0			0
$345$	−15307.2	+	8837.61i	−0.128605	+	0.0742500i
$346$		0			0
$347$	40794.0	+	70657.3i	0.338796	+	0.586811i	0.984206	−	0.177024i	$-0.0566472\pi$
$347$	40794.0	+	70657.3i	0.338796	+	0.586811i	−0.645411	+	0.763836i	$0.723314\pi$
$348$		0			0
$349$	−6860.34			−0.0563242			−0.0281621	−	0.999603i	$-0.508965\pi$
$349$	−6860.34			−0.0563242			−0.0281621	+	0.999603i	$0.508965\pi$
$350$		0			0
$351$	−72842.4	+	126167.i	−0.591248	+	1.02407i
$352$		0			0
$353$	61160.0			0.490815			0.245408	−	0.969420i	$-0.421078\pi$
$353$	61160.0			0.490815			0.245408	+	0.969420i	$0.421078\pi$
$354$		0			0
$355$	29825.8	+	17219.9i	0.236666	+	0.136639i
$356$		0			0
$357$	−5326.59	−	3075.31i	−0.0417939	−	0.0241297i
$358$		0			0
$359$	−63108.8	−	109308.i	−0.489667	−	0.848128i	0.510262	−	0.860019i	$-0.329548\pi$
$359$	−63108.8	−	109308.i	−0.489667	−	0.848128i	−0.999929	+	0.0118907i	$0.996215\pi$
$360$		0			0
$361$	77349.9	+	104884.i	0.593534	+	0.804809i
$362$		0			0
$363$	−169465.	+	97840.8i	−1.28608	+	0.742517i
$364$		0			0
$365$	−11905.4	+	20620.8i	−0.0893632	+	0.154782i
$366$		0			0
$367$	42699.3	−	73957.4i	0.317022	−	0.549098i	−0.662844	−	0.748758i	$-0.730651\pi$
$367$	42699.3	−	73957.4i	0.317022	−	0.549098i	0.979865	+	0.199660i	$0.0639839\pi$
$368$		0			0
$369$			4300.47i			0.0315837i
$370$		0			0
$371$	105835.	+	61103.7i	0.768918	+	0.443935i
$372$		0			0
$373$		−	82472.8i		−	0.592779i	−0.955067	−	0.296390i	$-0.904217\pi$
$373$		−	82472.8i		−	0.592779i	0.955067	−	0.296390i	$-0.0957827\pi$
$374$		0			0
$375$	21498.0	−	12411.9i	0.152875	−	0.0882623i
$376$		0			0
$377$	−24071.2	−	41692.6i	−0.169362	−	0.293343i
$378$		0			0
$379$		−	62506.5i		−	0.435158i	−0.976043	−	0.217579i	$-0.930184\pi$
$379$		−	62506.5i		−	0.435158i	0.976043	−	0.217579i	$-0.0698159\pi$
$380$		0			0
$381$	5064.64			0.0348898
$382$		0			0
$383$	149781.	−	86476.0i	1.02108	−	0.589519i	0.106662	−	0.994295i	$-0.465984\pi$
$383$	149781.	−	86476.0i	1.02108	−	0.589519i	0.914416	+	0.404776i	$0.132650\pi$
$384$		0			0
$385$	15813.6	+	27389.9i	0.106686	+	0.184786i
$386$		0			0
$387$	−65256.9			−0.435717
$388$		0			0
$389$	9846.10	−	17053.9i	0.0650677	−	0.112700i	−0.831656	−	0.555291i	$-0.812607\pi$
$389$	9846.10	−	17053.9i	0.0650677	−	0.112700i	0.896724	+	0.442590i	$0.145940\pi$
$390$		0			0
$391$	−27665.7			−0.180963
$392$		0			0
$393$	43795.6	+	25285.4i	0.283560	+	0.163713i
$394$		0			0
$395$	2670.74	+	1541.95i	0.0171174	+	0.00988272i
$396$		0			0
$397$	89620.0	+	155226.i	0.568622	+	0.984883i	0.996703	+	0.0811421i	$0.0258568\pi$
$397$	89620.0	+	155226.i	0.568622	+	0.984883i	−0.428080	+	0.903741i	$0.640810\pi$
$398$		0			0
$399$	70503.3	−	3946.79i	0.442857	−	0.0247912i
$400$		0			0
$401$	114189.	−	65926.9i	0.710125	−	0.409991i	−0.100982	−	0.994888i	$-0.532199\pi$
$401$	114189.	−	65926.9i	0.710125	−	0.409991i	0.811107	+	0.584897i	$0.198865\pi$
$402$		0			0
$403$	169374.	−	293364.i	1.04288	−	1.80633i
$404$		0			0
$405$	−954.802	+	1653.77i	−0.00582107	+	0.0100824i
$406$		0			0
$407$			242259.i			1.46248i
$408$		0			0
$409$	110266.	+	63662.0i	0.659165	+	0.380569i	0.791959	−	0.610575i	$-0.209061\pi$
$409$	110266.	+	63662.0i	0.659165	+	0.380569i	−0.132794	+	0.991144i	$0.542395\pi$
$410$		0			0
$411$		−	112401.i		−	0.665407i
$412$		0			0
$413$	−50163.7	+	28962.0i	−0.294096	+	0.169796i
$414$		0			0
$415$	10891.2	+	18864.0i	0.0632380	+	0.109531i
$416$		0			0
$417$			123375.i			0.709505i
$418$		0			0
$419$	−90062.3			−0.512997			−0.256499	−	0.966545i	$-0.582569\pi$
$419$	−90062.3			−0.512997			−0.256499	+	0.966545i	$0.582569\pi$
$420$		0			0
$421$	78503.7	−	45324.1i	0.442920	−	0.255720i	−0.261915	−	0.965091i	$-0.584354\pi$
$421$	78503.7	−	45324.1i	0.442920	−	0.255720i	0.704836	+	0.709371i	$0.251021\pi$
$422$		0			0
$423$	60721.4	+	105173.i	0.339360	+	0.587789i
$424$		0			0
$425$	19202.4			0.106311
$426$		0			0
$427$	62128.8	−	107610.i	0.340751	−	0.590198i
$428$		0			0
$429$	−247068.			−1.34246
$430$		0			0
$431$	267527.	+	154457.i	1.44017	+	0.831482i	0.997860	−	0.0653808i	$-0.0208262\pi$
$431$	267527.	+	154457.i	1.44017	+	0.831482i	0.442309	+	0.896863i	$0.354160\pi$
$432$		0			0
$433$	74098.1	+	42780.5i	0.395213	+	0.228176i	0.684416	−	0.729091i	$-0.260057\pi$
$433$	74098.1	+	42780.5i	0.395213	+	0.228176i	−0.289203	+	0.957268i	$0.593390\pi$
$434$		0			0
$435$	2358.29	+	4084.68i	0.0124629	+	0.0215864i
$436$		0			0
$437$	265763.	−	173938.i	1.39166	−	0.910817i
$438$		0			0
$439$	−110978.	+	64073.3i	−0.575849	+	0.332467i	−0.759482	−	0.650528i	$-0.774548\pi$
$439$	−110978.	+	64073.3i	−0.575849	+	0.332467i	0.183633	+	0.982995i	$0.441214\pi$
$440$		0			0
$441$	27562.6	−	47739.9i	0.141724	−	0.245473i
$442$		0			0
$443$	102414.	−	177386.i	0.521858	−	0.903885i	−0.477819	−	0.878458i	$-0.658572\pi$
$443$	102414.	−	177386.i	0.521858	−	0.903885i	0.999677	−	0.0254261i	$-0.00809426\pi$
$444$		0			0
$445$		−	44349.9i		−	0.223961i
$446$		0			0
$447$	63020.4	+	36384.8i	0.315403	+	0.182098i
$448$		0			0
$449$			102243.i			0.507153i	0.967315	+	0.253577i	$0.0816070\pi$
$449$			102243.i			0.507153i	−0.967315	+	0.253577i	$0.918393\pi$
$450$		0			0
$451$	−16004.5	+	9240.19i	−0.0786844	+	0.0454284i
$452$		0			0
$453$	106268.	+	184062.i	0.517855	+	0.896951i
$454$		0			0
$455$			28578.7i			0.138045i
$456$		0			0
$457$	−243226.			−1.16460			−0.582301	−	0.812974i	$-0.697847\pi$
$457$	−243226.			−1.16460			−0.582301	+	0.812974i	$0.697847\pi$
$458$		0			0
$459$	19347.4	−	11170.2i	0.0918326	−	0.0530196i
$460$		0			0
$461$	−157859.	−	273420.i	−0.742794	−	1.28656i	−0.951218	−	0.308518i	$-0.900167\pi$
$461$	−157859.	−	273420.i	−0.742794	−	1.28656i	0.208425	−	0.978038i	$-0.433166\pi$
$462$		0			0
$463$	−152689.			−0.712273			−0.356136	−	0.934434i	$-0.615906\pi$
$463$	−152689.			−0.712273			−0.356136	+	0.934434i	$0.615906\pi$
$464$		0			0
$465$	−16593.8	+	28741.3i	−0.0767431	+	0.132923i
$466$		0			0
$467$	−249648.			−1.14470			−0.572352	−	0.820008i	$-0.693969\pi$
$467$	−249648.			−1.14470			−0.572352	+	0.820008i	$0.693969\pi$
$468$		0			0
$469$	103259.	+	59616.7i	0.469443	+	0.271033i
$470$		0			0
$471$	−115445.	−	66652.3i	−0.520396	−	0.300451i
$472$		0			0
$473$	−140214.	−	242858.i	−0.626714	−	1.08550i
$474$		0			0
$475$	−184462.	+	120728.i	−0.817562	+	0.535081i
$476$		0			0
$477$	−151708.	+	87588.5i	−0.666762	+	0.384955i
$478$		0			0
$479$	54598.1	−	94566.7i	0.237961	−	0.412161i	−0.722168	−	0.691718i	$-0.756854\pi$
$479$	54598.1	−	94566.7i	0.237961	−	0.412161i	0.960129	+	0.279557i	$0.0901875\pi$
$480$		0			0
$481$	−109454.	+	189580.i	−0.473088	+	0.819413i
$482$		0			0
$483$		−	172102.i		−	0.737722i
$484$		0			0
$485$	34025.1	+	19644.4i	0.144649	+	0.0835133i
$486$		0			0
$487$			311767.i			1.31454i	0.753657	+	0.657268i	$0.228288\pi$
$487$			311767.i			1.31454i	−0.753657	+	0.657268i	$0.771712\pi$
$488$		0			0
$489$	106135.	−	61277.3i	0.443856	−	0.256261i
$490$		0			0
$491$	−125216.	−	216880.i	−0.519393	−	0.899614i	−0.999746	−	0.0225393i	$-0.992825\pi$
$491$	−125216.	−	216880.i	−0.519393	−	0.899614i	0.480353	−	0.877075i	$-0.340508\pi$
$492$		0			0
$493$			7382.54i			0.0303747i
$494$		0			0
$495$	−45335.6			−0.185025
$496$		0			0
$497$	−290412.	+	167669.i	−1.17571	+	0.678799i
$498$		0			0
$499$	38005.5	+	65827.4i	0.152632	+	0.264366i	0.932194	−	0.361958i	$-0.117892\pi$
$499$	38005.5	+	65827.4i	0.152632	+	0.264366i	−0.779562	+	0.626325i	$0.784558\pi$
$500$		0			0
$501$	36070.6			0.143707
$502$		0			0
$503$	170103.	−	294628.i	0.672321	−	1.16449i	−0.304923	−	0.952377i	$-0.598631\pi$
$503$	170103.	−	294628.i	0.672321	−	1.16449i	0.977244	−	0.212117i	$-0.0680359\pi$
$504$		0			0
$505$	16874.9			0.0661695
$506$		0			0
$507$	−62007.5	−	35800.0i	−0.241228	−	0.139273i
$508$		0			0
$509$	96013.4	+	55433.3i	0.370592	+	0.213961i	0.673717	−	0.738989i	$-0.264697\pi$
$509$	96013.4	+	55433.3i	0.370592	+	0.213961i	−0.303125	+	0.952951i	$0.598030\pi$
$510$		0			0
$511$	−115922.	−	200783.i	−0.443941	−	0.768928i
$512$		0			0
$513$	−115627.	+	228943.i	−0.439364	+	0.869947i
$514$		0			0
$515$	6644.28	−	3836.07i	0.0250515	−	0.0144635i
$516$		0			0
$517$	−260938.	+	451958.i	−0.976239	+	1.69090i
$518$		0			0
$519$	99969.1	−	173151.i	0.371134	−	0.642823i
$520$		0			0
$521$			18134.4i			0.0668080i	0.999442	+	0.0334040i	$0.0106348\pi$
$521$			18134.4i			0.0668080i	−0.999442	+	0.0334040i	$0.989365\pi$
$522$		0			0
$523$	208824.	+	120565.i	0.763445	+	0.440775i	0.830531	−	0.556972i	$-0.188037\pi$
$523$	208824.	+	120565.i	0.763445	+	0.440775i	−0.0670861	+	0.997747i	$0.521370\pi$
$524$		0			0
$525$			119454.i			0.433392i
$526$		0			0
$527$	−44986.7	+	25973.1i	−0.161980	+	0.0935195i
$528$		0			0
$529$	−247141.	−	428061.i	−0.883149	−	1.52966i
$530$		0			0
$531$		−	83030.7i		−	0.294476i
$532$		0			0
$533$	−16699.1			−0.0587812
$534$		0			0
$535$	48786.0	−	28166.6i	0.170446	−	0.0984071i
$536$		0			0
$537$	−38577.7	−	66818.5i	−0.133779	−	0.231712i
$538$		0			0
$539$	236890.			0.815396
$540$		0			0
$541$	−184617.	+	319766.i	−0.630779	+	1.09254i	0.356614	+	0.934252i	$0.383931\pi$
$541$	−184617.	+	319766.i	−0.630779	+	1.09254i	−0.987393	+	0.158289i	$0.949402\pi$
$542$		0			0
$543$	76246.9			0.258597
$544$		0			0
$545$	−45129.7	−	26055.6i	−0.151939	−	0.0877221i
$546$		0			0
$547$	−136676.	−	78909.7i	−0.456790	−	0.263728i	0.253904	−	0.967230i	$-0.418285\pi$
$547$	−136676.	−	78909.7i	−0.456790	−	0.263728i	−0.710694	+	0.703502i	$0.751619\pi$
$548$		0			0
$549$	89057.9	+	154253.i	0.295480	+	0.511786i
$550$		0			0
$551$	−46414.9	−	70918.3i	−0.152881	−	0.233591i
$552$		0			0
$553$	−26004.8	+	15013.9i	−0.0850361	+	0.0490956i
$554$		0			0
$555$	10723.4	−	18573.5i	0.0348134	−	0.0602985i
$556$		0			0
$557$	−132160.	+	228908.i	−0.425980	+	0.737820i	−0.996511	−	0.0834563i	$-0.973404\pi$
$557$	−132160.	+	228908.i	−0.425980	+	0.737820i	0.570531	+	0.821276i	$0.306737\pi$
$558$		0			0
$559$		−	253398.i		−	0.810924i
$560$		0			0
$561$	32811.4	+	18943.7i	0.104256	+	0.0601920i
$562$		0			0
$563$			98927.9i			0.312106i	0.987749	+	0.156053i	$0.0498771\pi$
$563$			98927.9i			0.312106i	−0.987749	+	0.156053i	$0.950123\pi$
$564$		0			0
$565$	−10887.4	+	6285.82i	−0.0341056	+	0.0196909i
$566$		0			0
$567$	−9296.84	−	16102.6i	−0.0289181	−	0.0500876i
$568$		0			0
$569$		−	28178.2i		−	0.0870341i	−0.999053	−	0.0435171i	$-0.986144\pi$
$569$		−	28178.2i		−	0.0870341i	0.999053	−	0.0435171i	$-0.0138563\pi$
$570$		0			0
$571$	565936.			1.73578			0.867891	−	0.496755i	$-0.165475\pi$
$571$	565936.			1.73578			0.867891	+	0.496755i	$0.165475\pi$
$572$		0			0
$573$	192249.	−	110995.i	0.585537	−	0.338060i
$574$		0			0
$575$	268654.	+	465322.i	0.812564	+	1.40740i
$576$		0			0
$577$	454163.			1.36415			0.682073	−	0.731285i	$-0.261079\pi$
$577$	454163.			1.36415			0.682073	+	0.731285i	$0.261079\pi$
$578$		0			0
$579$	145018.	−	251179.i	0.432579	−	0.749249i
$580$		0			0
$581$	−212093.			−0.628310
$582$		0			0
$583$	−651933.	−	376394.i	−1.91808	−	1.10740i
$584$		0			0
$585$	−35477.5	−	20482.9i	−0.103667	−	0.0598522i
$586$		0			0
$587$	231313.	+	400646.i	0.671312	+	1.16275i	0.977532	+	0.210785i	$0.0676021\pi$
$587$	231313.	+	400646.i	0.671312	+	1.16275i	−0.306221	+	0.951961i	$0.599065\pi$
$588$		0			0
$589$	268856.	−	532340.i	0.774979	−	1.53447i
$590$		0			0
$591$	259319.	−	149718.i	0.742437	−	0.428646i
$592$		0			0
$593$	105805.	−	183260.i	0.300883	−	0.521145i	−0.675453	−	0.737403i	$-0.736052\pi$
$593$	105805.	−	183260.i	0.300883	−	0.521145i	0.976336	+	0.216258i	$0.0693853\pi$
$594$		0			0
$595$	2191.24	−	3795.34i	0.00618950	−	0.0107205i
$596$		0			0
$597$			185395.i			0.520175i
$598$		0			0
$599$	−202530.	−	116931.i	−0.564463	−	0.325893i	0.190472	−	0.981693i	$-0.438998\pi$
$599$	−202530.	−	116931.i	−0.564463	−	0.325893i	−0.754935	+	0.655800i	$0.772331\pi$
$600$		0			0
$601$			104860.i			0.290309i	0.989409	+	0.145155i	$0.0463680\pi$
$601$			104860.i			0.290309i	−0.989409	+	0.145155i	$0.953632\pi$
$602$		0			0
$603$	−148016.	+	85457.0i	−0.407074	+	0.235024i
$604$		0			0
$605$	−69714.1	−	120748.i	−0.190463	−	0.329891i
$606$		0			0
$607$		−	176193.i		−	0.478202i	−0.970995	−	0.239101i	$-0.923147\pi$
$607$		−	176193.i		−	0.478202i	0.970995	−	0.239101i	$-0.0768527\pi$
$608$		0			0
$609$	−45925.1			−0.123827
$610$		0			0
$611$	−408395.	+	235787.i	−1.09395	+	0.631593i
$612$		0			0
$613$	146841.	+	254336.i	0.390774	+	0.676841i	0.992552	−	0.121823i	$-0.0388739\pi$
$613$	146841.	+	254336.i	0.390774	+	0.676841i	−0.601778	+	0.798664i	$0.705541\pi$
$614$		0			0
$615$	1636.04			0.00432556
$616$		0			0
$617$	−92040.2	+	159418.i	−0.241773	+	0.418763i	−0.961219	−	0.275785i	$-0.911062\pi$
$617$	−92040.2	+	159418.i	−0.241773	+	0.418763i	0.719447	+	0.694548i	$0.244396\pi$
$618$		0			0
$619$	654259.			1.70753			0.853765	−	0.520658i	$-0.174313\pi$
$619$	654259.			1.70753			0.853765	+	0.520658i	$0.174313\pi$
$620$		0			0
$621$	541365.	+	312557.i	1.40381	+	0.810488i
$622$		0			0
$623$	373978.	+	215916.i	0.963540	+	0.556300i
$624$		0			0
$625$	−181996.	−	315226.i	−0.465909	−	0.806978i
$626$		0			0
$627$	−434295.	+	24311.9i	−1.10471	+	0.0618421i
$628$		0			0
$629$	29071.7	−	16784.6i	0.0734800	−	0.0424237i
$630$		0			0
$631$	55536.2	−	96191.5i	0.139482	−	0.241589i	−0.787819	−	0.615907i	$-0.788790\pi$
$631$	55536.2	−	96191.5i	0.139482	−	0.241589i	0.927301	+	0.374318i	$0.122123\pi$
$632$		0			0
$633$	33273.8	−	57632.0i	0.0830416	−	0.143832i
$634$		0			0
$635$			3608.69i			0.00894957i
$636$		0			0
$637$	185378.	+	107028.i	0.456857	+	0.263766i
$638$		0			0
$639$		−	480689.i		−	1.17723i
$640$		0			0
$641$	86653.1	−	50029.2i	0.210896	−	0.121761i	−0.390832	−	0.920462i	$-0.627813\pi$
$641$	86653.1	−	50029.2i	0.210896	−	0.121761i	0.601728	+	0.798701i	$0.294479\pi$
$642$		0			0
$643$	266450.	+	461505.i	0.644457	+	1.11623i	0.984427	+	0.175796i	$0.0562499\pi$
$643$	266450.	+	461505.i	0.644457	+	1.11623i	−0.339970	+	0.940436i	$0.610417\pi$
$644$		0			0
$645$			24825.8i			0.0596739i
$646$		0			0
$647$	176670.			0.422041			0.211020	−	0.977482i	$-0.432321\pi$
$647$	176670.			0.422041			0.211020	+	0.977482i	$0.432321\pi$
$648$		0			0
$649$	309004.	−	178404.i	0.733627	−	0.423560i
$650$		0			0
$651$	−161573.	−	279852.i	−0.381246	−	0.660338i
$652$		0			0
$653$	−164912.			−0.386746			−0.193373	−	0.981125i	$-0.561943\pi$
$653$	−164912.			−0.386746			−0.193373	+	0.981125i	$0.561943\pi$
$654$		0			0
$655$	−18016.5	+	31205.5i	−0.0419940	+	0.0727358i
$656$		0			0
$657$	332335.			0.769920
$658$		0			0
$659$	220485.	+	127297.i	0.507701	+	0.293121i	0.731888	−	0.681425i	$-0.238639\pi$
$659$	220485.	+	127297.i	0.507701	+	0.293121i	−0.224187	+	0.974546i	$0.571973\pi$
$660$		0			0
$661$	−143784.	−	83013.9i	−0.329085	−	0.189997i	0.326350	−	0.945249i	$-0.394181\pi$
$661$	−143784.	−	83013.9i	−0.329085	−	0.189997i	−0.655435	+	0.755252i	$0.727515\pi$
$662$		0			0
$663$	17117.7	+	29648.8i	0.0389421	+	0.0674497i
$664$		0			0
$665$	2812.19	+	50235.4i	0.00635918	+	0.113597i
$666$		0			0
$667$	−178897.	+	103286.i	−0.402117	+	0.232162i
$668$		0			0
$669$	−82225.5	+	142419.i	−0.183719	+	0.318211i
$670$		0			0
$671$	−382708.	+	662870.i	−0.850008	+	1.47226i
$672$		0			0
$673$		−	390456.i		−	0.862070i	−0.902335	−	0.431035i	$-0.858149\pi$
$673$		−	390456.i		−	0.862070i	0.902335	−	0.431035i	$-0.141851\pi$
$674$		0			0
$675$	−375754.	−	216941.i	−0.824699	−	0.476140i
$676$		0			0
$677$		−	515036.i		−	1.12372i	−0.827231	−	0.561862i	$-0.810085\pi$
$677$		−	515036.i		−	1.12372i	0.827231	−	0.561862i	$-0.189915\pi$
$678$		0			0
$679$	−331300.	+	191276.i	−0.718592	+	0.414879i
$680$		0			0
$681$	10218.6	+	17699.1i	0.0220341	+	0.0381643i
$682$		0			0
$683$			668370.i			1.43277i	0.697707	+	0.716383i	$0.254204\pi$
$683$			668370.i			1.43277i	−0.697707	+	0.716383i	$0.745796\pi$
$684$		0			0
$685$	80088.8			0.170683
$686$		0			0
$687$	293505.	−	169455.i	0.621873	−	0.359038i
$688$		0			0
$689$	−340114.	−	589095.i	−0.716451	−	1.24093i
$690$		0			0
$691$	−694627.			−1.45477			−0.727387	−	0.686227i	$-0.759266\pi$
$691$	−694627.			−1.45477			−0.727387	+	0.686227i	$0.759266\pi$
$692$		0			0
$693$	220715.	−	382290.i	0.459585	−	0.796024i
$694$		0			0
$695$	−87908.0			−0.181995
$696$		0			0
$697$	2217.69	+	1280.39i	0.00456495	+	0.00263557i
$698$		0			0
$699$	185707.	+	107218.i	0.380078	+	0.219438i
$700$		0			0
$701$	395358.	+	684780.i	0.804553	+	1.39353i	0.916592	+	0.399823i	$0.130928\pi$
$701$	395358.	+	684780.i	0.804553	+	1.39353i	−0.112040	+	0.993704i	$0.535738\pi$
$702$		0			0
$703$	−173743.	+	344013.i	−0.351558	+	0.696089i
$704$		0			0
$705$	40011.0	−	23100.4i	0.0805011	−	0.0464773i
$706$		0			0
$707$	−82154.8	+	142296.i	−0.164359	+	0.284678i
$708$		0			0
$709$	−294085.	+	509370.i	−0.585032	+	1.01331i	0.409839	+	0.912158i	$0.365585\pi$
$709$	−294085.	+	509370.i	−0.585032	+	1.01331i	−0.994871	+	0.101148i	$0.967748\pi$
$710$		0			0
$711$		−	43043.0i		−	0.0851459i
$712$		0			0
$713$	−1.25879e6	−	726760.i	−2.47613	−	1.42959i
$714$		0			0
$715$		−	176042.i		−	0.344354i
$716$		0			0
$717$	142822.	−	82458.2i	0.277815	−	0.160397i
$718$		0			0
$719$	187307.	+	324426.i	0.362324	+	0.627564i	0.988343	−	0.152244i	$-0.0486500\pi$
$719$	187307.	+	324426.i	0.362324	+	0.627564i	−0.626019	+	0.779808i	$0.715317\pi$
$720$		0			0
$721$			74703.2i			0.143704i
$722$		0			0
$723$	−436060.			−0.834200
$724$		0			0
$725$	124170.	−	71689.6i	0.236233	−	0.136389i
$726$		0			0
$727$	−410793.	−	711515.i	−0.777239	−	1.34622i	−0.933527	−	0.358506i	$-0.883286\pi$
$727$	−410793.	−	711515.i	−0.777239	−	1.34622i	0.156288	−	0.987711i	$-0.450047\pi$
$728$		0			0
$729$	−278923.			−0.524843
$730$		0			0
$731$	−19429.0	+	33652.1i	−0.0363594	+	0.0629763i
$732$		0			0
$733$	293019.			0.545366			0.272683	−	0.962104i	$-0.412089\pi$
$733$	293019.			0.545366			0.272683	+	0.962104i	$0.412089\pi$
$734$		0			0
$735$	−18161.8	−	10485.7i	−0.0336189	−	0.0194099i
$736$		0			0
$737$	−636068.	−	367234.i	−1.17103	−	0.676095i
$738$		0			0
$739$	−176057.	−	304940.i	−0.322377	−	0.558374i	0.658601	−	0.752493i	$-0.271149\pi$
$739$	−176057.	−	304940.i	−0.322377	−	0.558374i	−0.980978	+	0.194119i	$0.937815\pi$
$740$		0			0
$741$	−350842.	−	177192.i	−0.638963	−	0.322706i
$742$		0			0
$743$	−522289.	+	301544.i	−0.946092	+	0.546226i	−0.891865	−	0.452302i	$-0.850603\pi$
$743$	−522289.	+	301544.i	−0.946092	+	0.546226i	−0.0542270	+	0.998529i	$0.517269\pi$
$744$		0			0
$745$	−25925.1	+	44903.7i	−0.0467099	+	0.0809039i
$746$		0			0
$747$	152011.	−	263292.i	0.272418	−	0.471841i
$748$		0			0
$749$			548512.i			0.977738i
$750$		0			0
$751$	−209729.	−	121087.i	−0.371860	−	0.214693i	0.302411	−	0.953178i	$-0.402209\pi$
$751$	−209729.	−	121087.i	−0.371860	−	0.214693i	−0.674271	+	0.738484i	$0.735542\pi$
$752$		0			0
$753$		−	39135.7i		−	0.0690214i
$754$		0			0
$755$	−131149.	+	75719.0i	−0.230076	+	0.132835i
$756$		0			0
$757$	164381.	+	284716.i	0.286853	+	0.496844i	0.973057	−	0.230565i	$-0.0740575\pi$
$757$	164381.	+	284716.i	0.286853	+	0.496844i	−0.686204	+	0.727409i	$0.740724\pi$
$758$		0			0
$759$			1.06014e6i			1.84026i
$760$		0			0
$761$	812377.			1.40278			0.701388	−	0.712780i	$-0.252564\pi$
$761$	812377.			1.40278			0.701388	+	0.712780i	$0.252564\pi$
$762$		0			0
$763$	439425.	−	253702.i	0.754806	−	0.435788i
$764$		0			0
$765$	3141.01	+	5440.39i	0.00536719	+	0.00929624i
$766$		0			0
$767$	322416.			0.548057
$768$		0			0
$769$	20004.5	−	34648.8i	0.0338279	−	0.0585916i	−0.848616	−	0.529010i	$-0.822564\pi$
$769$	20004.5	−	34648.8i	0.0338279	−	0.0585916i	0.882444	+	0.470418i	$0.155897\pi$
$770$		0			0
$771$	−697473.			−1.17333
$772$		0			0
$773$	−411744.	−	237721.i	−0.689079	−	0.397840i	0.114188	−	0.993459i	$-0.463573\pi$
$773$	−411744.	−	237721.i	−0.689079	−	0.397840i	−0.803267	+	0.595619i	$0.796907\pi$
$774$		0			0
$775$	873705.	+	504434.i	1.45466	+	0.839848i
$776$		0			0
$777$	104413.	+	180849.i	0.172947	+	0.299552i
$778$		0			0
$779$	−29353.6	+	1643.22i	−0.0483711	+	0.00270783i
$780$		0			0
$781$	1.78891e6	−	1.03283e6i	2.93283	−	1.69327i
$782$		0			0
$783$	83405.1	−	144462.i	0.136041	−	0.235630i
$784$		0			0
$785$	47491.5	−	82257.7i	0.0770684	−	0.133486i
$786$		0			0
$787$		−	750343.i		−	1.21146i	−0.795669	−	0.605732i	$-0.792881\pi$
$787$		−	750343.i		−	1.21146i	0.795669	−	0.605732i	$-0.207119\pi$
$788$		0			0
$789$	−110352.	−	63711.7i	−0.177266	−	0.102345i
$790$		0			0
$791$		−	122409.i		−	0.195641i
$792$		0			0
$793$	−598978.	+	345820.i	−0.952499	+	0.549925i
$794$		0			0
$795$	33321.5	+	57714.5i	0.0527218	+	0.0913169i
$796$		0			0
$797$			451641.i			0.711011i	0.934674	+	0.355506i	$0.115691\pi$
$797$			451641.i			0.711011i	−0.934674	+	0.355506i	$0.884309\pi$
$798$		0			0
$799$	72314.8			0.113275
$800$		0			0
$801$	−536075.	+	309503.i	−0.835527	+	0.482392i
$802$		0			0
$803$	714072.	+	1.23681e6i	1.10742	+	1.91810i
$804$		0			0
$805$	122627.			0.189232
$806$		0			0
$807$	−81539.0	+	141230.i	−0.125204	+	0.216860i
$808$		0			0
$809$	722760.			1.10433			0.552163	−	0.833736i	$-0.313803\pi$
$809$	722760.			1.10433			0.552163	+	0.833736i	$0.313803\pi$
$810$		0			0
$811$	−600405.	−	346644.i	−0.912857	−	0.527038i	−0.0315076	−	0.999504i	$-0.510031\pi$
$811$	−600405.	−	346644.i	−0.912857	−	0.527038i	−0.881349	+	0.472465i	$0.843364\pi$
$812$		0			0
$813$	−374280.	−	216090.i	−0.566259	−	0.326930i
$814$		0			0
$815$	43661.7	+	75624.2i	0.0657332	+	0.113853i
$816$		0			0
$817$	−24934.8	−	445422.i	−0.0373562	−	0.667310i
$818$		0			0
$819$	345442.	−	199441.i	0.515000	−	0.297335i
$820$		0			0
$821$	−436911.	+	756751.i	−0.648196	+	1.12271i	0.335357	+	0.942091i	$0.391143\pi$
$821$	−436911.	+	756751.i	−0.648196	+	1.12271i	−0.983553	+	0.180617i	$0.942190\pi$
$822$		0			0
$823$	−165034.	+	285848.i	−0.243654	+	0.422022i	−0.961752	−	0.273920i	$-0.911680\pi$
$823$	−165034.	+	285848.i	−0.243654	+	0.422022i	0.718098	+	0.695942i	$0.245013\pi$
$824$		0			0
$825$		−	735825.i		−	1.08110i
$826$		0			0
$827$	−408375.	−	235776.i	−0.597102	−	0.344737i	0.170799	−	0.985306i	$-0.445365\pi$
$827$	−408375.	−	235776.i	−0.597102	−	0.344737i	−0.767901	+	0.640569i	$0.778699\pi$
$828$		0			0
$829$		−	299186.i		−	0.435344i	−0.976022	−	0.217672i	$-0.930154\pi$
$829$		−	299186.i		−	0.435344i	0.976022	−	0.217672i	$-0.0698463\pi$
$830$		0			0
$831$	422958.	−	244195.i	0.612485	−	0.353618i
$832$		0			0
$833$	−16412.5	−	28427.4i	−0.0236530	−	0.0409682i
$834$		0			0
$835$			25701.2i			0.0368622i
$836$		0			0
$837$	1.17374e6			1.67540
$838$		0			0
$839$	−331905.	+	191625.i	−0.471509	+	0.272226i	−0.716871	−	0.697206i	$-0.754426\pi$
$839$	−331905.	+	191625.i	−0.471509	+	0.272226i	0.245362	+	0.969431i	$0.421093\pi$
$840$		0			0
$841$	−326079.	−	564785.i	−0.461031	−	0.798530i
$842$		0			0
$843$	770145.			1.08372
$844$		0			0
$845$	25508.5	−	44181.9i	0.0357249	−	0.0618773i
$846$		0			0
$847$	1.35760e6			1.89237
$848$		0			0
$849$	293736.	+	169588.i	0.407513	+	0.235278i
$850$		0			0
$851$	813464.	+	469654.i	1.12326	+	0.648513i
$852$		0			0
$853$	546954.	+	947353.i	0.751715	+	1.30201i	0.946991	+	0.321260i	$0.104106\pi$
$853$	546954.	+	947353.i	0.751715	+	1.30201i	−0.195277	+	0.980748i	$0.562560\pi$
$854$		0			0
$855$	−64377.6	−	32513.7i	−0.0880649	−	0.0444769i
$856$		0			0
$857$	818169.	−	472370.i	1.11399	−	0.643162i	0.174130	−	0.984723i	$-0.444289\pi$
$857$	818169.	−	472370.i	1.11399	−	0.643162i	0.939860	+	0.341560i	$0.110955\pi$
$858$		0			0
$859$	−289902.	+	502125.i	−0.392885	+	0.680496i	−0.992829	−	0.119546i	$-0.961856\pi$
$859$	−289902.	+	502125.i	−0.392885	+	0.680496i	0.599944	+	0.800042i	$0.295190\pi$
$860$		0			0
$861$	−7964.99	+	13795.8i	−0.0107443	+	0.0186097i
$862$		0			0
$863$		−	1.18761e6i		−	1.59460i	−0.603582	−	0.797301i	$-0.706260\pi$
$863$		−	1.18761e6i		−	1.59460i	0.603582	−	0.797301i	$-0.293740\pi$
$864$		0			0
$865$	123375.	+	71230.6i	0.164890	+	0.0951994i
$866$		0			0
$867$			438231.i			0.582995i
$868$		0			0
$869$	160188.	−	92484.3i	0.212124	−	0.122470i
$870$		0			0
$871$	−331837.	−	574759.i	−0.437410	−	0.757616i
$872$		0			0
$873$		−	548367.i		−	0.719520i
$874$		0			0
$875$	−172223.			−0.224944
$876$		0			0
$877$	−991783.	+	572606.i	−1.28949	+	0.744487i	−0.978563	−	0.205948i	$-0.933972\pi$
$877$	−991783.	+	572606.i	−1.28949	+	0.744487i	−0.310926	+	0.950434i	$0.600639\pi$
$878$		0			0
$879$	−72799.2	−	126092.i	−0.0942213	−	0.163196i
$880$		0			0
$881$	−300648.			−0.387353			−0.193676	−	0.981065i	$-0.562041\pi$
$881$	−300648.			−0.387353			−0.193676	+	0.981065i	$0.562041\pi$
$882$		0			0
$883$	52445.8	−	90838.8i	0.0672650	−	0.116506i	−0.830431	−	0.557121i	$-0.811906\pi$
$883$	52445.8	−	90838.8i	0.0672650	−	0.116506i	0.897696	+	0.440614i	$0.145239\pi$
$884$		0			0
$885$	−31587.6			−0.0403301
$886$		0			0
$887$	−1.07659e6	−	621568.i	−1.36837	−	0.790026i	−0.377646	−	0.925950i	$-0.623266\pi$
$887$	−1.07659e6	−	621568.i	−1.36837	−	0.790026i	−0.990719	+	0.135924i	$0.956600\pi$
$888$		0			0
$889$	−30430.0	−	17568.8i	−0.0385034	−	0.0222299i
$890$		0			0
$891$	57267.8	+	99190.7i	0.0721365	+	0.124944i
$892$		0			0
$893$	−694672.	+	454651.i	−0.871118	+	0.570132i
$894$		0			0
$895$	47609.9	−	27487.6i	0.0594362	−	0.0343155i
$896$		0			0
$897$	−478976.	+	829612.i	−0.595291	+	1.03107i
$898$		0			0
$899$	−193934.	+	335904.i	−0.239958	+	0.415619i
$900$		0			0
$901$			104312.i			0.128494i
$902$		0			0
$903$	−209342.	−	120864.i	−0.256732	−	0.148225i
$904$		0			0
$905$			54327.9i			0.0663324i
$906$		0			0
$907$	277411.	−	160163.i	0.337216	−	0.194692i	−0.321824	−	0.946799i	$-0.604296\pi$
$907$	277411.	−	160163.i	0.337216	−	0.194692i	0.659040	+	0.752108i	$0.270963\pi$
$908$		0			0
$909$	−117764.	−	203973.i	−0.142523	−	0.246857i
$910$		0			0
$911$			53930.6i			0.0649828i	0.999472	+	0.0324914i	$0.0103441\pi$
$911$			53930.6i			0.0649828i	−0.999472	+	0.0324914i	$0.989656\pi$
$912$		0			0
$913$	1.30648e6			1.56733
$914$		0			0
$915$	58682.8	−	33880.5i	0.0700920	−	0.0404676i
$916$		0			0
$917$	−175425.	−	303846.i	−0.208619	−	0.361339i
$918$		0			0
$919$	−362715.			−0.429472			−0.214736	−	0.976672i	$-0.568889\pi$
$919$	−362715.			−0.429472			−0.214736	+	0.976672i	$0.568889\pi$
$920$		0			0
$921$	420824.	−	728888.i	0.496113	−	0.859293i
$922$		0			0
$923$	1.86656e6			2.19098
$924$		0			0
$925$	−564614.	−	325980.i	−0.659884	−	0.380984i
$926$		0			0
$927$	−92736.3	−	53541.3i	−0.107917	−	0.0623060i
$928$		0			0
$929$	54017.2	+	93560.6i	0.0625894	+	0.108408i	0.895622	−	0.444816i	$-0.146731\pi$
$929$	54017.2	+	93560.6i	0.0625894	+	0.108408i	−0.833033	+	0.553224i	$0.813397\pi$
$930$		0			0
$931$	336389.	+	169892.i	0.388098	+	0.196008i
$932$		0			0
$933$	−2013.63	+	1162.57i	−0.00231322	+	0.00133554i
$934$		0			0
$935$	−13497.9	+	23379.0i	−0.0154398	+	0.0267425i
$936$		0			0
$937$	−810490.	+	1.40381e6i	−0.923142	+	1.59893i	−0.128620	+	0.991694i	$0.541055\pi$
$937$	−810490.	+	1.40381e6i	−0.923142	+	1.59893i	−0.794522	+	0.607235i	$0.792279\pi$
$938$		0			0
$939$		−	268952.i		−	0.305031i
$940$		0			0
$941$	−172298.	−	99476.5i	−0.194582	−	0.112342i	0.399544	−	0.916714i	$-0.369168\pi$
$941$	−172298.	−	99476.5i	−0.194582	−	0.112342i	−0.594126	+	0.804372i	$0.702502\pi$
$942$		0			0
$943$			71653.7i			0.0805778i
$944$		0			0
$945$	−85756.6	+	49511.6i	−0.0960293	+	0.0554426i
$946$		0			0
$947$	−351057.	−	608049.i	−0.391452	−	0.678014i	0.601190	−	0.799106i	$-0.294694\pi$
$947$	−351057.	−	608049.i	−0.391452	−	0.678014i	−0.992641	+	0.121092i	$0.961360\pi$
$948$		0			0
$949$			1.29049e6i			1.43292i
$950$		0			0
$951$	507588.			0.561242
$952$		0			0
$953$	−308838.	+	178308.i	−0.340052	+	0.196329i	−0.660295	−	0.751006i	$-0.729569\pi$
$953$	−308838.	+	178308.i	−0.340052	+	0.196329i	0.320243	+	0.947335i	$0.396235\pi$
$954$		0			0
$955$	79086.7	+	136982.i	0.0867155	+	0.150196i
$956$		0			0
$957$	282895.			0.308888
$958$		0			0
$959$	−389909.	+	675343.i	−0.423962	+	0.734323i
$960$		0			0
$961$	−1.80566e6			−1.95519
$962$		0			0
$963$	−680921.	−	393130.i	−0.734251	−	0.423920i
$964$		0			0
$965$	178972.	+	103329.i	0.192189	+	0.110961i
$966$		0			0
$967$	−40946.5	−	70921.4i	−0.0437889	−	0.0758445i	0.843300	−	0.537443i	$-0.180610\pi$
$967$	−40946.5	−	70921.4i	−0.0437889	−	0.0758445i	−0.887089	+	0.461598i	$0.847276\pi$
$968$		0			0
$969$	33007.0	+	50432.1i	0.0351526	+	0.0537105i
$970$		0			0
$971$	−12481.8	+	7206.37i	−0.0132385	+	0.00764325i	−0.506605	−	0.862178i	$-0.669100\pi$
$971$	−12481.8	+	7206.37i	−0.0132385	+	0.00764325i	0.493366	+	0.869822i	$0.335766\pi$
$972$		0			0
$973$	427977.	−	741278.i	0.452059	−	0.782988i
$974$		0			0
$975$	332451.	−	575821.i	0.349718	−	0.605729i
$976$		0			0
$977$			414341.i			0.434079i	0.976163	+	0.217039i	$0.0696400\pi$
$977$			414341.i			0.434079i	−0.976163	+	0.217039i	$0.930360\pi$
$978$		0			0
$979$	−2.30367e6	−	1.33003e6i	−2.40356	−	1.38770i
$980$		0			0
$981$			727334.i			0.755781i
$982$		0			0
$983$	−1.14219e6	+	659446.i	−1.18204	+	0.682452i	−0.956486	−	0.291778i	$-0.905753\pi$
$983$	−1.14219e6	+	659446.i	−1.18204	+	0.682452i	−0.225556	+	0.974230i	$0.572420\pi$
$984$		0			0
$985$	106678.	+	184772.i	0.109952	+	0.190442i
$986$		0			0
$987$			449854.i			0.461782i
$988$		0			0
$989$	−1.08730e6			−1.11162
$990$		0			0
$991$	484272.	−	279595.i	0.493108	−	0.284696i	−0.232755	−	0.972535i	$-0.574774\pi$
$991$	484272.	−	279595.i	0.493108	−	0.284696i	0.725863	+	0.687839i	$0.241441\pi$
$992$		0			0
$993$	−543979.	−	942199.i	−0.551675	−	0.955530i
$994$		0			0
$995$	−132099.			−0.133430
$996$		0			0
$997$	583987.	−	1.01150e6i	0.587507	−	1.01759i	−0.407051	−	0.913405i	$-0.633443\pi$
$997$	583987.	−	1.01150e6i	0.587507	−	1.01759i	0.994558	−	0.104186i	$-0.0332238\pi$
$998$		0			0
$999$	−758503.			−0.760022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.h.a.69.3	yes	12
3.2	odd	2		684.5.y.c.145.3		12
4.3	odd	2		304.5.r.b.145.4		12
19.8	odd	6	inner	76.5.h.a.65.3	✓	12
57.8	even	6		684.5.y.c.217.3		12
76.27	even	6		304.5.r.b.65.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.3	✓	12	19.8	odd	6	inner
76.5.h.a.69.3	yes	12	1.1	even	1	trivial
304.5.r.b.65.4		12	76.27	even	6
304.5.r.b.145.4		12	4.3	odd	2
684.5.y.c.145.3		12	3.2	odd	2
684.5.y.c.217.3		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)

\(f(q)\)	\(=\)	\(q+(-4.59843 + 2.65491i) q^{3} +(-1.89169 - 3.27650i) q^{5} +36.8385 q^{7} +(-26.4029 + 45.7312i) q^{9} +O(q^{10})\)	\(q+(-4.59843 + 2.65491i) q^{3} +(-1.89169 - 3.27650i) q^{5} +36.8385 q^{7} +(-26.4029 + 45.7312i) q^{9} -226.922 q^{11} +(-177.578 - 102.525i) q^{13} +(17.3976 + 10.0445i) q^{15} +(15.7220 + 27.2313i) q^{17} +(-322.235 - 162.744i) q^{19} +(-169.400 + 97.8029i) q^{21} +(-439.921 + 761.966i) q^{23} +(305.343 - 528.870i) q^{25} -710.484i q^{27} +(203.329 + 117.392i) q^{29} +1652.02i q^{31} +(1043.49 - 602.458i) q^{33} +(-69.6871 - 120.702i) q^{35} -1067.59i q^{37} +1088.78 q^{39} +(70.5284 - 40.7196i) q^{41} +(617.894 + 1070.22i) q^{43} +199.785 q^{45} +(1149.90 - 1991.68i) q^{47} -1043.92 q^{49} +(-144.593 - 83.4808i) q^{51} +(2872.93 + 1658.69i) q^{53} +(429.267 + 743.512i) q^{55} +(1913.85 - 107.138i) q^{57} +(-1361.72 + 786.188i) q^{59} +(1686.52 - 2921.13i) q^{61} +(-972.645 + 1684.67i) q^{63} +775.782i q^{65} +(2803.02 + 1618.32i) q^{67} -4671.80i q^{69} +(-7883.38 + 4551.47i) q^{71} +(-3146.77 - 5450.36i) q^{73} +3242.63i q^{75} -8359.49 q^{77} +(-705.913 + 407.559i) q^{79} +(-252.367 - 437.113i) q^{81} -5757.37 q^{83} +(59.4823 - 103.026i) q^{85} -1246.66 q^{87} +(10151.8 + 5861.15i) q^{89} +(-6541.73 - 3776.87i) q^{91} +(-4385.97 - 7596.72i) q^{93} +(76.3383 + 1363.67i) q^{95} +(-8993.31 + 5192.29i) q^{97} +(5991.42 - 10377.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) \) 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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