LMFDB - Embedded newform 76.5.j.a.21.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.6
Character	$\chi$	$=$	76.21
Dual form			76.5.j.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +O(q^{10})$	\(q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +(-10.1615 + 17.6003i) q^{11} +(-101.104 - 120.492i) q^{13} +(162.181 - 445.589i) q^{15} +(-64.2649 + 364.464i) q^{17} +(-169.897 - 318.521i) q^{19} +(1116.86 + 196.933i) q^{21} +(-341.165 - 124.174i) q^{23} +(377.702 - 316.930i) q^{25} +(-480.325 - 277.316i) q^{27} +(-681.081 + 120.093i) q^{29} +(889.421 - 513.507i) q^{31} +(98.5730 + 270.827i) q^{33} +(2048.41 + 1718.82i) q^{35} +694.298i q^{37} -2230.59 q^{39} +(-1060.01 + 1263.27i) q^{41} +(-3223.73 + 1173.34i) q^{43} +(-2008.08 - 3478.10i) q^{45} +(-468.777 - 2658.57i) q^{47} +(-1997.17 + 3459.20i) q^{49} +(3373.56 + 4020.45i) q^{51} +(-767.791 + 2109.49i) q^{53} +(-118.003 + 669.226i) q^{55} +(-5008.98 - 1057.82i) q^{57} +(6503.10 + 1146.67i) q^{59} +(5819.67 + 2118.19i) q^{61} +(7358.09 - 6174.17i) q^{63} +(-4554.75 - 2629.69i) q^{65} +(6482.83 - 1143.10i) q^{67} +(-4458.88 + 2574.34i) q^{69} +(-1833.99 - 5038.85i) q^{71} +(-2417.99 - 2028.93i) q^{73} -6992.18i q^{75} -1625.26 q^{77} +(-1721.85 + 2052.02i) q^{79} +(1751.11 - 637.353i) q^{81} +(1760.24 + 3048.83i) q^{83} +(2148.85 + 12186.7i) q^{85} +(-4903.82 + 8493.66i) q^{87} +(-6598.36 - 7863.62i) q^{89} +(4302.16 - 11820.1i) q^{91} +(2529.09 - 14343.2i) q^{93} +(-8981.00 - 8065.22i) q^{95} +(11690.2 + 2061.29i) q^{97} +(2293.80 + 834.873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

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
$3$	9.11558	−	10.8635i	1.01284	−	1.20706i	0.0346409	−	0.999400i	$-0.488971\pi$
$3$	9.11558	−	10.8635i	1.01284	−	1.20706i	0.978201	−	0.207659i	$-0.0665843\pi$
$4$		0			0
$5$	31.4208	−	11.4362i	1.25683	−	0.457450i	0.374128	−	0.927377i	$-0.377942\pi$
$5$	31.4208	−	11.4362i	1.25683	−	0.457450i	0.882705	+	0.469927i	$0.155720\pi$
$6$		0			0
$7$	39.9854	+	69.2568i	0.816029	+	1.41340i	0.908586	+	0.417697i	$0.137163\pi$
$7$	39.9854	+	69.2568i	0.816029	+	1.41340i	−0.0925569	+	0.995707i	$0.529504\pi$
$8$		0			0
$9$	−20.8569	−	118.285i	−0.257492	−	1.46031i
$10$		0			0
$11$	−10.1615	+	17.6003i	−0.0839797	+	0.145457i	−0.904956	−	0.425505i	$-0.860096\pi$
$11$	−10.1615	+	17.6003i	−0.0839797	+	0.145457i	0.820976	+	0.570962i	$0.193430\pi$
$12$		0			0
$13$	−101.104	−	120.492i	−0.598251	−	0.712968i	0.378918	−	0.925430i	$-0.376296\pi$
$13$	−101.104	−	120.492i	−0.598251	−	0.712968i	−0.977169	+	0.212463i	$0.931852\pi$
$14$		0			0
$15$	162.181	−	445.589i	0.720805	−	1.98039i
$16$		0			0
$17$	−64.2649	+	364.464i	−0.222370	+	1.26112i	0.645280	+	0.763947i	$0.276741\pi$
$17$	−64.2649	+	364.464i	−0.222370	+	1.26112i	−0.867650	+	0.497176i	$0.834370\pi$
$18$		0			0
$19$	−169.897	−	318.521i	−0.470630	−	0.882331i
$19$	−169.897	−	318.521i	−0.470630	−	0.882331i
$20$		0			0
$21$	1116.86	+	196.933i	2.53257	+	0.446561i
$22$		0			0
$23$	−341.165	−	124.174i	−0.644924	−	0.234733i	−0.00121023	−	0.999999i	$-0.500385\pi$
$23$	−341.165	−	124.174i	−0.644924	−	0.234733i	−0.643714	+	0.765266i	$0.722607\pi$
$24$		0			0
$25$	377.702	−	316.930i	0.604324	−	0.507088i
$26$		0			0
$27$	−480.325	−	277.316i	−0.658882	−	0.380406i
$28$		0			0
$29$	−681.081	+	120.093i	−0.809847	+	0.142798i	−0.563214	−	0.826311i	$-0.690435\pi$
$29$	−681.081	+	120.093i	−0.809847	+	0.142798i	−0.246633	+	0.969109i	$0.579324\pi$
$30$		0			0
$31$	889.421	−	513.507i	0.925516	−	0.534347i	0.0401254	−	0.999195i	$-0.487224\pi$
$31$	889.421	−	513.507i	0.925516	−	0.534347i	0.885391	+	0.464848i	$0.153891\pi$
$32$		0			0
$33$	98.5730	+	270.827i	0.0905170	+	0.248693i
$34$		0			0
$35$	2048.41	+	1718.82i	1.67217	+	1.40312i
$36$		0			0
$37$			694.298i			0.507157i	0.967315	+	0.253578i	$0.0816076\pi$
$37$			694.298i			0.507157i	−0.967315	+	0.253578i	$0.918392\pi$
$38$		0			0
$39$	−2230.59			−1.46653
$40$		0			0
$41$	−1060.01	+	1263.27i	−0.630584	+	0.751501i	−0.982852	−	0.184399i	$-0.940966\pi$
$41$	−1060.01	+	1263.27i	−0.630584	+	0.751501i	0.352268	+	0.935899i	$0.385411\pi$
$42$		0			0
$43$	−3223.73	+	1173.34i	−1.74350	+	0.634581i	−0.999438	−	0.0335306i	$-0.989325\pi$
$43$	−3223.73	+	1173.34i	−1.74350	+	0.634581i	−0.744061	+	0.668112i	$0.767103\pi$
$44$		0			0
$45$	−2008.08	−	3478.10i	−0.991644	−	1.71758i
$46$		0			0
$47$	−468.777	−	2658.57i	−0.212212	−	1.20352i	−0.885679	−	0.464298i	$-0.846307\pi$
$47$	−468.777	−	2658.57i	−0.212212	−	1.20352i	0.673466	−	0.739218i	$-0.264805\pi$
$48$		0			0
$49$	−1997.17	+	3459.20i	−0.831808	+	1.44073i
$50$		0			0
$51$	3373.56	+	4020.45i	1.29702	+	1.54573i
$52$		0			0
$53$	−767.791	+	2109.49i	−0.273333	+	0.750975i	0.724746	+	0.689016i	$0.241957\pi$
$53$	−767.791	+	2109.49i	−0.273333	+	0.750975i	−0.998079	+	0.0619591i	$0.980265\pi$
$54$		0			0
$55$	−118.003	+	669.226i	−0.0390091	+	0.221232i
$56$		0			0
$57$	−5008.98	−	1057.82i	−1.54170	−	0.325584i
$58$		0			0
$59$	6503.10	+	1146.67i	1.86817	+	0.329409i	0.989096	−	0.147273i	$-0.0470497\pi$
$59$	6503.10	+	1146.67i	1.86817	+	0.329409i	0.879076	+	0.476683i	$0.158161\pi$
$60$		0			0
$61$	5819.67	+	2118.19i	1.56401	+	0.569252i	0.971650	−	0.236424i	$-0.0759754\pi$
$61$	5819.67	+	2118.19i	1.56401	+	0.569252i	0.592357	+	0.805676i	$0.298198\pi$
$62$		0			0
$63$	7358.09	−	6174.17i	1.85389	−	1.55560i
$64$		0			0
$65$	−4554.75	−	2629.69i	−1.07805	−	0.622411i
$66$		0			0
$67$	6482.83	−	1143.10i	1.44416	−	0.254644i	0.603999	−	0.796985i	$-0.293573\pi$
$67$	6482.83	−	1143.10i	1.44416	−	0.254644i	0.840159	+	0.542341i	$0.182462\pi$
$68$		0			0
$69$	−4458.88	+	2574.34i	−0.936544	+	0.540714i
$70$		0			0
$71$	−1833.99	−	5038.85i	−0.363815	−	0.999574i	−0.977668	−	0.210154i	$-0.932603\pi$
$71$	−1833.99	−	5038.85i	−0.363815	−	0.999574i	0.613853	−	0.789420i	$-0.289619\pi$
$72$		0			0
$73$	−2417.99	−	2028.93i	−0.453741	−	0.380734i	0.387081	−	0.922046i	$-0.373483\pi$
$73$	−2417.99	−	2028.93i	−0.453741	−	0.380734i	−0.840822	+	0.541312i	$0.817928\pi$
$74$		0			0
$75$		−	6992.18i		−	1.24305i
$76$		0			0
$77$	−1625.26			−0.274120
$78$		0			0
$79$	−1721.85	+	2052.02i	−0.275893	+	0.328796i	−0.886142	−	0.463413i	$-0.846625\pi$
$79$	−1721.85	+	2052.02i	−0.275893	+	0.328796i	0.610250	+	0.792209i	$0.291069\pi$
$80$		0			0
$81$	1751.11	−	637.353i	0.266897	−	0.0971427i
$82$		0			0
$83$	1760.24	+	3048.83i	0.255515	+	0.442564i	0.965035	−	0.262120i	$-0.0844218\pi$
$83$	1760.24	+	3048.83i	0.255515	+	0.442564i	−0.709521	+	0.704685i	$0.751088\pi$
$84$		0			0
$85$	2148.85	+	12186.7i	0.297418	+	1.68674i
$86$		0			0
$87$	−4903.82	+	8493.66i	−0.647882	+	1.12216i
$88$		0			0
$89$	−6598.36	−	7863.62i	−0.833021	−	0.992756i	−0.999977	−	0.00679184i	$-0.997838\pi$
$89$	−6598.36	−	7863.62i	−0.833021	−	0.992756i	0.166956	−	0.985964i	$-0.446606\pi$
$90$		0			0
$91$	4302.16	−	11820.1i	0.519521	−	1.42737i
$92$		0			0
$93$	2529.09	−	14343.2i	0.292414	−	1.65836i
$94$		0			0
$95$	−8981.00	−	8065.22i	−0.995125	−	0.893653i
$96$		0			0
$97$	11690.2	+	2061.29i	1.24245	+	0.219077i	0.755964	−	0.654613i	$-0.227168\pi$
$97$	11690.2	+	2061.29i	1.24245	+	0.219077i	0.486483	+	0.873690i	$0.338280\pi$
$98$		0			0
$99$	2293.80	+	834.873i	0.234037	+	0.0851824i
$100$		0			0
$101$	−11664.3	+	9787.51i	−1.14345	+	0.959466i	−0.999546	−	0.0301266i	$-0.990409\pi$
$101$	−11664.3	+	9787.51i	−1.14345	+	0.959466i	−0.143900	+	0.989592i	$0.545965\pi$
$102$		0			0
$103$	6416.27	+	3704.43i	0.604795	+	0.349178i	0.770925	−	0.636925i	$-0.219794\pi$
$103$	6416.27	+	3704.43i	0.604795	+	0.349178i	−0.166131	+	0.986104i	$0.553127\pi$
$104$		0			0
$105$	37344.9	−	6584.92i	3.38730	−	0.597272i
$106$		0			0
$107$	−1560.12	+	900.738i	−0.136267	+	0.0786739i	−0.566584	−	0.824004i	$-0.691735\pi$
$107$	−1560.12	+	900.738i	−0.136267	+	0.0786739i	0.430317	+	0.902678i	$0.358402\pi$
$108$		0			0
$109$	−404.983	−	1112.68i	−0.0340866	−	0.0936523i	0.921482	−	0.388421i	$-0.126979\pi$
$109$	−404.983	−	1112.68i	−0.0340866	−	0.0936523i	−0.955569	+	0.294769i	$0.904757\pi$
$110$		0			0
$111$	7542.52	+	6328.93i	0.612168	+	0.513670i
$112$		0			0
$113$		−	11311.2i		−	0.885831i	−0.896563	−	0.442915i	$-0.853944\pi$
$113$		−	11311.2i		−	0.885831i	0.896563	−	0.442915i	$-0.146056\pi$
$114$		0			0
$115$	−12139.8			−0.917941
$116$		0			0
$117$	−12143.6	+	14472.2i	−0.887110	+	1.05722i
$118$		0			0
$119$	−27811.3	+	10122.5i	−1.96394	+	0.714815i
$120$		0			0
$121$	7113.99	+	12321.8i	0.485895	+	0.841595i
$122$		0			0
$123$	4060.97	+	23030.9i	0.268423	+	1.52230i
$124$		0			0
$125$	−2205.94	+	3820.80i	−0.141180	+	0.244531i
$126$		0			0
$127$	−15879.3	−	18924.2i	−0.984516	−	1.17330i	−0.984869	−	0.173301i	$-0.944557\pi$
$127$	−15879.3	−	18924.2i	−0.984516	−	1.17330i	0.000352700	−	1.00000i	$-0.499888\pi$
$128$		0			0
$129$	−16639.5	+	45716.7i	−0.999912	+	2.74724i
$130$		0			0
$131$	2841.19	−	16113.2i	0.165561	−	0.938942i	−0.782924	−	0.622118i	$-0.786273\pi$
$131$	2841.19	−	16113.2i	0.165561	−	0.938942i	0.948484	−	0.316824i	$-0.102616\pi$
$132$		0			0
$133$	15266.4	−	24502.8i	0.863043	−	1.38520i
$134$		0			0
$135$	−18263.7	−	3220.38i	−1.00212	−	0.176701i
$136$		0			0
$137$	−1624.05	−	591.107i	−0.0865285	−	0.0314938i	0.298393	−	0.954443i	$-0.403549\pi$
$137$	−1624.05	−	591.107i	−0.0865285	−	0.0314938i	−0.384922	+	0.922949i	$0.625772\pi$
$138$		0			0
$139$	2634.82	−	2210.87i	0.136371	−	0.114429i	−0.572051	−	0.820218i	$-0.693852\pi$
$139$	2634.82	−	2210.87i	0.136371	−	0.114429i	0.708422	+	0.705790i	$0.249408\pi$
$140$		0			0
$141$	−33154.6	−	19141.8i	−1.66765	−	0.962819i
$142$		0			0
$143$	3148.06	−	555.089i	0.153947	−	0.0271450i
$144$		0			0
$145$	−20026.7	+	11562.4i	−0.952519	+	0.549937i
$146$		0			0
$147$	19373.8	+	53229.0i	0.896560	+	2.46328i
$148$		0			0
$149$	−10888.8	−	9136.81i	−0.490466	−	0.411550i	0.363727	−	0.931505i	$-0.381504\pi$
$149$	−10888.8	−	9136.81i	−0.490466	−	0.411550i	−0.854193	+	0.519956i	$0.825948\pi$
$150$		0			0
$151$		−	13297.5i		−	0.583199i	−0.956540	−	0.291600i	$-0.905813\pi$
$151$		−	13297.5i		−	0.583199i	0.956540	−	0.291600i	$-0.0941875\pi$
$152$		0			0
$153$	44451.1			1.89889
$154$		0			0
$155$	22073.7	−	26306.5i	0.918782	−	1.09496i
$156$		0			0
$157$	−3071.50	+	1117.94i	−0.124610	+	0.0453542i	−0.403572	−	0.914948i	$-0.632232\pi$
$157$	−3071.50	+	1117.94i	−0.124610	+	0.0453542i	0.278963	+	0.960302i	$0.410009\pi$
$158$		0			0
$159$	15917.6	+	27570.1i	0.629628	+	1.09055i
$160$		0			0
$161$	−5041.74	−	28593.2i	−0.194504	−	1.10309i
$162$		0			0
$163$	−1349.50	+	2337.40i	−0.0507923	+	0.0879749i	−0.890304	−	0.455367i	$-0.849508\pi$
$163$	−1349.50	+	2337.40i	−0.0507923	+	0.0879749i	0.839511	+	0.543342i	$0.182841\pi$
$164$		0			0
$165$	6194.49	+	7382.31i	0.227530	+	0.271159i
$166$		0			0
$167$	3277.80	−	9005.69i	0.117530	−	0.322912i	−0.866953	−	0.498390i	$-0.833925\pi$
$167$	3277.80	−	9005.69i	0.117530	−	0.322912i	0.984483	+	0.175478i	$0.0561470\pi$
$168$		0			0
$169$	663.458	−	3762.65i	0.0232295	−	0.131741i
$170$		0			0
$171$	−34132.9	+	26739.7i	−1.16729	+	0.914460i
$172$		0			0
$173$	−10425.9	−	1838.36i	−0.348354	−	0.0614241i	−0.00326608	−	0.999995i	$-0.501040\pi$
$173$	−10425.9	−	1838.36i	−0.348354	−	0.0614241i	−0.345087	+	0.938571i	$0.612151\pi$
$174$		0			0
$175$	37052.2	+	13485.9i	1.20987	+	0.440355i
$176$		0			0
$177$	71736.5	−	60194.1i	2.28978	−	1.92135i
$178$		0			0
$179$	−26213.8	−	15134.5i	−0.818132	−	0.472349i	0.0316398	−	0.999499i	$-0.489927\pi$
$179$	−26213.8	−	15134.5i	−0.818132	−	0.472349i	−0.849772	+	0.527150i	$0.823260\pi$
$180$		0			0
$181$	−22735.5	+	4008.87i	−0.693979	+	0.122367i	−0.509502	−	0.860469i	$-0.670170\pi$
$181$	−22735.5	+	4008.87i	−0.693979	+	0.122367i	−0.184477	+	0.982837i	$0.559059\pi$
$182$		0			0
$183$	76060.6	−	43913.6i	2.27121	−	1.31129i
$184$		0			0
$185$	7940.16	+	21815.4i	0.231999	+	0.637411i
$186$		0			0
$187$	−5761.66	−	4834.60i	−0.164765	−	0.138254i
$188$		0			0
$189$		−	44354.4i		−	1.24169i
$190$		0			0
$191$	−21072.9			−0.577641			−0.288821	−	0.957383i	$-0.593263\pi$
$191$	−21072.9			−0.577641			−0.288821	+	0.957383i	$0.593263\pi$
$192$		0			0
$193$	2698.18	−	3215.56i	0.0724362	−	0.0863261i	−0.728609	−	0.684929i	$-0.759833\pi$
$193$	2698.18	−	3215.56i	0.0724362	−	0.0863261i	0.801046	+	0.598603i	$0.204277\pi$
$194$		0			0
$195$	−70086.9	+	25509.5i	−1.84318	+	0.670862i
$196$		0			0
$197$	13290.6	+	23019.9i	0.342461	+	0.593159i	0.984889	−	0.173186i	$-0.0554063\pi$
$197$	13290.6	+	23019.9i	0.342461	+	0.593159i	−0.642428	+	0.766346i	$0.722073\pi$
$198$		0			0
$199$	−3824.40	−	21689.2i	−0.0965732	−	0.547694i	−0.994254	−	0.107047i	$-0.965860\pi$
$199$	−3824.40	−	21689.2i	−0.0965732	−	0.547694i	0.897681	−	0.440647i	$-0.145251\pi$
$200$		0			0
$201$	46676.7	−	80846.3i	1.15533	−	2.00110i
$202$		0			0
$203$	−35550.6	−	42367.6i	−0.862690	−	1.02811i
$204$		0			0
$205$	−18859.3	+	51815.6i	−0.448765	+	1.23297i
$206$		0			0
$207$	−7572.31	+	42944.7i	−0.176721	+	1.00223i
$208$		0			0
$209$	7332.49	+	246.424i	0.167865	+	0.00564145i
$210$		0			0
$211$	79876.0	+	14084.3i	1.79412	+	0.316352i	0.968713	−	0.248185i	$-0.0798342\pi$
$211$	79876.0	+	14084.3i	1.79412	+	0.316352i	0.825408	+	0.564537i	$0.190945\pi$
$212$		0			0
$213$	−71457.6	−	26008.5i	−1.57503	−	0.573265i
$214$		0			0
$215$	−87873.6	+	73734.7i	−1.90100	+	1.59513i
$216$		0			0
$217$	71127.8	+	41065.6i	1.51050	+	0.872086i
$218$		0			0
$219$	−44082.7	+	7772.97i	−0.919136	+	0.162069i
$220$		0			0
$221$	50412.3	−	29105.6i	1.03217	−	0.595925i
$222$		0			0
$223$	12288.9	+	33763.5i	0.247118	+	0.678950i	0.999789	+	0.0205533i	$0.00654279\pi$
$223$	12288.9	+	33763.5i	0.247118	+	0.678950i	−0.752671	+	0.658397i	$0.771235\pi$
$224$		0			0
$225$	−45365.8	−	38066.5i	−0.896115	−	0.751930i
$226$		0			0
$227$			12563.2i			0.243808i	0.992542	+	0.121904i	$0.0389000\pi$
$227$			12563.2i			0.243808i	−0.992542	+	0.121904i	$0.961100\pi$
$228$		0			0
$229$	35829.1			0.683228			0.341614	−	0.939840i	$-0.389027\pi$
$229$	35829.1			0.683228			0.341614	+	0.939840i	$0.389027\pi$
$230$		0			0
$231$	−14815.1	+	17656.0i	−0.277640	+	0.330878i
$232$		0			0
$233$	−50070.9	+	18224.3i	−0.922303	+	0.335691i	−0.759154	−	0.650911i	$-0.774387\pi$
$233$	−50070.9	+	18224.3i	−0.922303	+	0.335691i	−0.163149	+	0.986602i	$0.552165\pi$
$234$		0			0
$235$	−45133.4	−	78173.3i	−0.817264	−	1.41554i
$236$		0			0
$237$	6596.50	+	37410.6i	0.117440	+	0.666037i
$238$		0			0
$239$	50961.0	−	88267.0i	0.892158	−	1.54526i	0.0548758	−	0.998493i	$-0.482524\pi$
$239$	50961.0	−	88267.0i	0.892158	−	1.54526i	0.837283	−	0.546770i	$-0.184143\pi$
$240$		0			0
$241$	17732.2	+	21132.4i	0.305301	+	0.363843i	0.896780	−	0.442477i	$-0.145900\pi$
$241$	17732.2	+	21132.4i	0.305301	+	0.363843i	−0.591479	+	0.806320i	$0.701456\pi$
$242$		0			0
$243$	24403.8	−	67049.0i	0.413281	−	1.13548i
$244$		0			0
$245$	−23192.5	+	131531.i	−0.386380	+	2.19127i
$246$		0			0
$247$	−21201.8	+	52675.1i	−0.347519	+	0.863399i
$248$		0			0
$249$	49166.6	+	8669.40i	0.792997	+	0.139827i
$250$		0			0
$251$	18177.2	+	6615.95i	0.288522	+	0.105013i	0.482227	−	0.876046i	$-0.339828\pi$
$251$	18177.2	+	6615.95i	0.288522	+	0.105013i	−0.193705	+	0.981060i	$0.562050\pi$
$252$		0			0
$253$	5652.26	−	4742.81i	0.0883042	−	0.0740960i
$254$		0			0
$255$	151979.	+	87745.0i	2.33724	+	1.34940i
$256$		0			0
$257$	−8736.84	+	1540.54i	−0.132278	+	0.0233242i	−0.239395	−	0.970922i	$-0.576949\pi$
$257$	−8736.84	+	1540.54i	−0.132278	+	0.0233242i	0.107117	+	0.994246i	$0.465838\pi$
$258$		0			0
$259$	−48084.8	+	27761.8i	−0.716818	+	0.413855i
$260$		0			0
$261$	28410.5	+	78057.1i	0.417059	+	1.14586i
$262$		0			0
$263$	−64278.6	−	53936.1i	−0.929298	−	0.779773i	0.0463935	−	0.998923i	$-0.485227\pi$
$263$	−64278.6	−	53936.1i	−0.929298	−	0.779773i	−0.975691	+	0.219150i	$0.929672\pi$
$264$		0			0
$265$			75062.5i			1.06889i
$266$		0			0
$267$	−145575.			−2.04203
$268$		0			0
$269$	30336.6	−	36153.7i	0.419239	−	0.499630i	−0.514547	−	0.857462i	$-0.672040\pi$
$269$	30336.6	−	36153.7i	0.419239	−	0.499630i	0.933786	+	0.357833i	$0.116484\pi$
$270$		0			0
$271$	34101.1	−	12411.8i	0.464333	−	0.169003i	−0.0992505	−	0.995062i	$-0.531645\pi$
$271$	34101.1	−	12411.8i	0.464333	−	0.169003i	0.563584	+	0.826059i	$0.309422\pi$
$272$		0			0
$273$	−89191.0	−	154483.i	−1.19673	−	2.07280i
$274$		0			0
$275$	1740.03	+	9868.17i	0.0230086	+	0.130488i
$276$		0			0
$277$	1499.37	−	2596.99i	0.0195412	−	0.0338463i	−0.856089	−	0.516828i	$-0.827113\pi$
$277$	1499.37	−	2596.99i	0.0195412	−	0.0338463i	0.875631	+	0.482981i	$0.160446\pi$
$278$		0			0
$279$	−79290.9	−	94495.2i	−1.01863	−	1.21395i
$280$		0			0
$281$	−37837.4	+	103957.i	−0.479191	+	1.31657i	0.430991	+	0.902356i	$0.358164\pi$
$281$	−37837.4	+	103957.i	−0.479191	+	1.31657i	−0.910182	+	0.414209i	$0.864058\pi$
$282$		0			0
$283$	−21586.7	+	122424.i	−0.269534	+	1.52860i	0.486272	+	0.873807i	$0.338356\pi$
$283$	−21586.7	+	122424.i	−0.269534	+	1.52860i	−0.755806	+	0.654796i	$0.772755\pi$
$284$		0			0
$285$	−169484.	+	24046.2i	−2.08660	+	0.296044i
$286$		0			0
$287$	−129875.	−	22900.5i	−1.57675	−	0.278023i
$288$		0			0
$289$	−50220.3	−	18278.7i	−0.601290	−	0.218852i
$290$		0			0
$291$	128956.	−	108207.i	1.52284	−	1.27782i
$292$		0			0
$293$	−595.018	−	343.534i	−0.00693098	−	0.00400160i	0.496531	−	0.868019i	$-0.334607\pi$
$293$	−595.018	−	343.534i	−0.00693098	−	0.00400160i	−0.503461	+	0.864018i	$0.667940\pi$
$294$		0			0
$295$	217446.	−	38341.7i	2.49867	−	0.440582i
$296$		0			0
$297$	9761.69	−	5635.91i	0.110665	−	0.0638927i
$298$		0			0
$299$	19531.4	+	53662.0i	0.218469	+	0.600240i
$300$		0			0
$301$	−210164.	−	176349.i	−2.31967	−	1.94643i
$302$		0			0
$303$			215934.i			2.35199i
$304$		0			0
$305$	207083.			2.22610
$306$		0			0
$307$	3439.79	−	4099.38i	0.0364968	−	0.0434953i	−0.747487	−	0.664276i	$-0.768740\pi$
$307$	3439.79	−	4099.38i	0.0364968	−	0.0434953i	0.783984	+	0.620781i	$0.213184\pi$
$308$		0			0
$309$	98731.2	−	35935.2i	1.03404	−	0.376360i
$310$		0			0
$311$	66863.5	+	115811.i	0.691303	+	1.19737i	0.971411	+	0.237404i	$0.0762964\pi$
$311$	66863.5	+	115811.i	0.691303	+	1.19737i	−0.280108	+	0.959968i	$0.590370\pi$
$312$		0			0
$313$	44.4220	+	251.930i	0.000453430	+	0.00257153i	0.985034	−	0.172362i	$-0.0551400\pi$
$313$	44.4220	+	251.930i	0.000453430	+	0.00257153i	−0.984580	+	0.174934i	$0.944029\pi$
$314$		0			0
$315$	160588.	−	278146.i	1.61842	−	2.80319i
$316$		0			0
$317$	47164.2	+	56208.1i	0.469347	+	0.559346i	0.947840	−	0.318745i	$-0.103261\pi$
$317$	47164.2	+	56208.1i	0.469347	+	0.559346i	−0.478493	+	0.878091i	$0.658817\pi$
$318$		0			0
$319$	4807.16	−	13207.6i	0.0472397	−	0.129790i
$320$		0			0
$321$	−4436.25	+	25159.2i	−0.0430532	+	0.244167i
$322$		0			0
$323$	127008.	−	41451.8i	1.21738	−	0.397318i
$324$		0			0
$325$	−76374.7	−	13466.9i	−0.723074	−	0.127498i
$326$		0			0
$327$	−15779.3	−	5743.20i	−0.147568	−	0.0537104i
$328$		0			0
$329$	165380.	−	138770.i	1.52788	−	1.28205i
$330$		0			0
$331$	49342.1	+	28487.7i	0.450362	+	0.260016i	0.707983	−	0.706230i	$-0.249605\pi$
$331$	49342.1	+	28487.7i	0.450362	+	0.260016i	−0.257621	+	0.966246i	$0.582939\pi$
$332$		0			0
$333$	82125.2	−	14480.9i	0.740607	−	0.130589i
$334$		0			0
$335$	190623.	−	110056.i	1.69858	−	0.980675i
$336$		0			0
$337$	−32311.1	−	88774.1i	−0.284507	−	0.781675i	−0.996811	−	0.0798043i	$-0.974570\pi$
$337$	−32311.1	−	88774.1i	−0.284507	−	0.781675i	0.712304	−	0.701871i	$-0.247652\pi$
$338$		0			0
$339$	−122879.	−	103108.i	−1.06925	−	0.897207i
$340$		0			0
$341$			20872.1i			0.179497i
$342$		0			0
$343$	−127421.			−1.08306
$344$		0			0
$345$	−110661.	+	131881.i	−0.929729	+	1.10801i
$346$		0			0
$347$	38153.7	−	13886.8i	0.316867	−	0.115330i	−0.178690	−	0.983905i	$-0.557186\pi$
$347$	38153.7	−	13886.8i	0.316867	−	0.115330i	0.495557	+	0.868575i	$0.334964\pi$
$348$		0			0
$349$	−117786.	−	204011.i	−0.967036	−	1.67495i	−0.704043	−	0.710157i	$-0.748624\pi$
$349$	−117786.	−	204011.i	−0.967036	−	1.67495i	−0.262992	−	0.964798i	$-0.584709\pi$
$350$		0			0
$351$	15148.8	+	85913.0i	0.122960	+	0.697340i
$352$		0			0
$353$	−45139.8	+	78184.5i	−0.362252	+	0.627439i	−0.988331	−	0.152321i	$-0.951325\pi$
$353$	−45139.8	+	78184.5i	−0.362252	+	0.627439i	0.626079	+	0.779759i	$0.284659\pi$
$354$		0			0
$355$	−115251.	−	137351.i	−0.914510	−	1.08987i
$356$		0			0
$357$	−143550.	+	394401.i	−1.12634	+	3.09458i
$358$		0			0
$359$	31253.9	−	177250.i	0.242502	−	1.37530i	−0.583721	−	0.811954i	$-0.698404\pi$
$359$	31253.9	−	177250.i	0.242502	−	1.37530i	0.826223	−	0.563343i	$-0.190485\pi$
$360$		0			0
$361$	−72590.8	+	108232.i	−0.557015	+	0.830502i
$362$		0			0
$363$	198706.	+	35037.3i	1.50799	+	0.265899i
$364$		0			0
$365$	−99178.4	−	36098.0i	−0.744443	−	0.270955i
$366$		0			0
$367$	−16101.2	+	13510.5i	−0.119543	+	0.100309i	−0.700600	−	0.713555i	$-0.747084\pi$
$367$	−16101.2	+	13510.5i	−0.119543	+	0.100309i	0.581056	+	0.813863i	$0.302640\pi$
$368$		0			0
$369$	171535.	+	99035.8i	1.25980	+	0.727344i
$370$		0			0
$371$	−176797.	+	31174.1i	−1.28448	+	0.226488i
$372$		0			0
$373$	108749.	−	62786.3i	0.781642	−	0.451281i	−0.0553697	−	0.998466i	$-0.517634\pi$
$373$	108749.	−	62786.3i	0.781642	−	0.451281i	0.837012	+	0.547185i	$0.184300\pi$
$374$		0			0
$375$	21398.9	+	58793.0i	0.152170	+	0.418084i
$376$		0			0
$377$	83330.5	+	69922.6i	0.586302	+	0.491966i
$378$		0			0
$379$			67710.3i			0.471385i	0.971828	+	0.235693i	$0.0757359\pi$
$379$			67710.3i			0.471385i	−0.971828	+	0.235693i	$0.924264\pi$
$380$		0			0
$381$	−350332.			−2.41340
$382$		0			0
$383$	−70745.6	+	84311.4i	−0.482283	+	0.574763i	−0.951237	−	0.308460i	$-0.900186\pi$
$383$	−70745.6	+	84311.4i	−0.482283	+	0.574763i	0.468954	+	0.883223i	$0.344631\pi$
$384$		0			0
$385$	−51066.8	+	18586.8i	−0.344522	+	0.125396i
$386$		0			0
$387$	206026.	+	356847.i	1.37562	+	2.38265i
$388$		0			0
$389$	−35032.5	−	198679.i	−0.231511	−	1.31296i	−0.849838	−	0.527043i	$-0.823301\pi$
$389$	−35032.5	−	198679.i	−0.231511	−	1.31296i	0.618327	−	0.785921i	$-0.287811\pi$
$390$		0			0
$391$	67181.9	−	116363.i	0.439439	−	0.761131i
$392$		0			0
$393$	−149147.	−	177746.i	−0.965670	−	1.15084i
$394$		0			0
$395$	−30634.5	+	84167.5i	−0.196343	+	0.539449i
$396$		0			0
$397$	2992.49	−	16971.2i	0.0189868	−	0.107679i	−0.973842	−	0.227228i	$-0.927034\pi$
$397$	2992.49	−	16971.2i	0.0189868	−	0.107679i	0.992828	+	0.119549i	$0.0381448\pi$
$398$		0			0
$399$	−127025.	−	389203.i	−0.797889	−	2.44473i
$400$		0			0
$401$	−35490.2	−	6257.89i	−0.220709	−	0.0389170i	0.0622000	−	0.998064i	$-0.480188\pi$
$401$	−35490.2	−	6257.89i	−0.220709	−	0.0389170i	−0.282909	+	0.959147i	$0.591299\pi$
$402$		0			0
$403$	−151798.	−	55249.8i	−0.934663	−	0.340189i
$404$		0			0
$405$	47732.5	−	40052.3i	0.291007	−	0.244184i
$406$		0			0
$407$	−12219.9	−	7055.13i	−0.0737695	−	0.0425909i
$408$		0			0
$409$	164991.	−	29092.3i	0.986309	−	0.173913i	0.342847	−	0.939391i	$-0.388609\pi$
$409$	164991.	−	29092.3i	0.986309	−	0.173913i	0.643462	+	0.765478i	$0.277498\pi$
$410$		0			0
$411$	−21225.7	+	12254.7i	−0.125655	+	0.0725467i
$412$		0			0
$413$	180615.	+	496235.i	1.05889	+	2.90929i
$414$		0			0
$415$	90175.3	+	75666.1i	0.523590	+	0.439344i
$416$		0			0
$417$		−	48776.8i		−	0.280505i
$418$		0			0
$419$	287217.			1.63599			0.817997	−	0.575222i	$-0.195084\pi$
$419$	287217.			1.63599			0.817997	+	0.575222i	$0.195084\pi$
$420$		0			0
$421$	−1143.71	+	1363.01i	−0.00645283	+	0.00769018i	−0.769261	−	0.638934i	$-0.779376\pi$
$421$	−1143.71	+	1363.01i	−0.00645283	+	0.00769018i	0.762808	+	0.646625i	$0.223820\pi$
$422$		0			0
$423$	−304692.	+	110899.i	−1.70287	+	0.619793i
$424$		0			0
$425$	91236.7	+	158027.i	0.505117	+	0.874888i
$426$		0			0
$427$	86003.2	+	487748.i	0.471692	+	2.67510i
$428$		0			0
$429$	22666.2	−	39259.0i	0.123158	−	0.213317i
$430$		0			0
$431$	−180287.	−	214857.i	−0.970530	−	1.15663i	−0.987634	−	0.156779i	$-0.949889\pi$
$431$	−180287.	−	214857.i	−0.970530	−	1.15663i	0.0171038	−	0.999854i	$-0.494555\pi$
$432$		0			0
$433$	106300.	−	292057.i	0.566968	−	1.55773i	−0.242245	−	0.970215i	$-0.577884\pi$
$433$	106300.	−	292057.i	0.566968	−	1.55773i	0.809213	−	0.587516i	$-0.199894\pi$
$434$		0			0
$435$	−56946.4	+	322959.i	−0.300945	+	1.70675i
$436$		0			0
$437$	18411.0	+	129765.i	0.0964082	+	0.679509i
$438$		0			0
$439$	13886.1	+	2448.49i	0.0720528	+	0.0127049i	0.209558	−	0.977796i	$-0.432797\pi$
$439$	13886.1	+	2448.49i	0.0720528	+	0.0127049i	−0.137506	+	0.990501i	$0.543908\pi$
$440$		0			0
$441$	450827.	+	164088.i	2.31811	+	0.843721i
$442$		0			0
$443$	−121549.	+	101992.i	−0.619363	+	0.519708i	−0.897603	−	0.440804i	$-0.854693\pi$
$443$	−121549.	+	101992.i	−0.619363	+	0.519708i	0.278240	+	0.960512i	$0.410249\pi$
$444$		0			0
$445$	−297256.	−	171621.i	−1.50110	−	0.866663i
$446$		0			0
$447$	−198516.	+	35003.7i	−0.993529	+	0.175186i
$448$		0			0
$449$	−112147.	+	64748.0i	−0.556281	+	0.321169i	−0.751652	−	0.659560i	$-0.770742\pi$
$449$	−112147.	+	64748.0i	−0.556281	+	0.321169i	0.195370	+	0.980730i	$0.437409\pi$
$450$		0			0
$451$	−11462.6	−	31493.3i	−0.0563549	−	0.154834i
$452$		0			0
$453$	−144458.	−	121215.i	−0.703956	−	0.590689i
$454$		0			0
$455$		−	420597.i		−	2.03162i
$456$		0			0
$457$	150128.			0.718836			0.359418	−	0.933177i	$-0.382975\pi$
$457$	150128.			0.718836			0.359418	+	0.933177i	$0.382975\pi$
$458$		0			0
$459$	131940.	−	157240.i	0.626254	−	0.746341i
$460$		0			0
$461$	−344288.	+	125310.i	−1.62002	+	0.589638i	−0.983385	−	0.181531i	$-0.941895\pi$
$461$	−344288.	+	125310.i	−1.62002	+	0.589638i	−0.636631	+	0.771168i	$0.719673\pi$
$462$		0			0
$463$	−75550.3	−	130857.i	−0.352431	−	0.610428i	0.634244	−	0.773133i	$-0.281312\pi$
$463$	−75550.3	−	130857.i	−0.352431	−	0.610428i	−0.986675	+	0.162705i	$0.947978\pi$
$464$		0			0
$465$	−84565.9	−	479597.i	−0.391102	−	2.21805i
$466$		0			0
$467$	54139.2	−	93771.8i	0.248243	−	0.429970i	−0.714795	−	0.699334i	$-0.753480\pi$
$467$	54139.2	−	93771.8i	0.248243	−	0.429970i	0.963039	+	0.269364i	$0.0868134\pi$
$468$		0			0
$469$	338386.	+	403273.i	1.53839	+	1.83338i
$470$		0			0
$471$	−15853.8	+	43558.0i	−0.0714647	+	0.196348i
$472$		0			0
$473$	12106.9	−	68661.6i	0.0541141	−	0.306896i
$474$		0			0
$475$	−165120.	−	66460.8i	−0.731832	−	0.294563i
$476$		0			0
$477$	265535.	+	46821.0i	1.16704	+	0.205780i
$478$		0			0
$479$	3460.44	+	1259.50i	0.0150820	+	0.00548941i	0.349550	−	0.936918i	$-0.386334\pi$
$479$	3460.44	+	1259.50i	0.0150820	+	0.00548941i	−0.334468	+	0.942407i	$0.608557\pi$
$480$		0			0
$481$	83657.0	−	70196.5i	0.361586	−	0.303407i
$482$		0			0
$483$	−356581.	−	205872.i	−1.52849	−	0.882477i
$484$		0			0
$485$	390889.	−	68924.2i	1.66176	−	0.293014i
$486$		0			0
$487$	−226072.	+	130523.i	−0.953212	+	0.550337i	−0.894077	−	0.447913i	$-0.852168\pi$
$487$	−226072.	+	130523.i	−0.953212	+	0.550337i	−0.0591348	+	0.998250i	$0.518834\pi$
$488$		0			0
$489$	13091.0	+	35967.1i	0.0547462	+	0.150414i
$490$		0			0
$491$	186984.	+	156898.i	0.775607	+	0.650812i	0.942138	−	0.335224i	$-0.108812\pi$
$491$	186984.	+	156898.i	0.775607	+	0.650812i	−0.166531	+	0.986036i	$0.553257\pi$
$492$		0			0
$493$		−	255948.i		−	1.05307i
$494$		0			0
$495$	81620.7			0.333112
$496$		0			0
$497$	275642.	−	328497.i	1.11592	−	1.32990i
$498$		0			0
$499$	−273900.	+	99691.6i	−1.10000	+	0.400366i	−0.827315	−	0.561738i	$-0.810133\pi$
$499$	−273900.	+	99691.6i	−1.10000	+	0.400366i	−0.272682	+	0.962104i	$0.587911\pi$
$500$		0			0
$501$	−67954.5	−	117701.i	−0.270734	−	0.468925i
$502$		0			0
$503$	28729.7	+	162934.i	0.113552	+	0.643986i	0.987457	+	0.157889i	$0.0504689\pi$
$503$	28729.7	+	162934.i	0.113552	+	0.643986i	−0.873905	+	0.486097i	$0.838420\pi$
$504$		0			0
$505$	−254569.	+	440927.i	−0.998214	+	1.72896i
$506$		0			0
$507$	−34827.9	−	41506.3i	−0.135491	−	0.161472i
$508$		0			0
$509$	55300.2	−	151936.i	0.213448	−	0.586443i	−0.786049	−	0.618164i	$-0.787877\pi$
$509$	55300.2	−	151936.i	0.213448	−	0.586443i	0.999497	+	0.0317215i	$0.0100990\pi$
$510$		0			0
$511$	43833.1	−	248590.i	0.167865	−	0.952010i
$512$		0			0
$513$	−6725.09	+	200109.i	−0.0255543	+	0.760383i
$514$		0			0
$515$	243969.	+	43018.3i	0.919857	+	0.162196i
$516$		0			0
$517$	51555.1	+	18764.5i	0.192881	+	0.0702031i
$518$		0			0
$519$	−115009.	+	96504.0i	−0.426970	+	0.358270i
$520$		0			0
$521$	−92452.8	−	53377.6i	−0.340600	−	0.196645i	0.319937	−	0.947439i	$-0.396338\pi$
$521$	−92452.8	−	53377.6i	−0.340600	−	0.196645i	−0.660537	+	0.750793i	$0.729671\pi$
$522$		0			0
$523$	522060.	−	92053.2i	1.90861	−	0.336539i	0.911419	−	0.411478i	$-0.134987\pi$
$523$	522060.	−	92053.2i	1.90861	−	0.336539i	0.997188	+	0.0749394i	$0.0238763\pi$
$524$		0			0
$525$	484256.	−	279585.i	1.75694	−	1.01437i
$526$		0			0
$527$	129997.	+	357163.i	0.468070	+	1.28601i
$528$		0			0
$529$	−113396.	−	95150.7i	−0.405217	−	0.340017i
$530$		0			0
$531$		−	793137.i		−	2.81293i
$532$		0			0
$533$	259385.			0.913043
$534$		0			0
$535$	−38719.3	+	46143.9i	−0.135276	+	0.161215i
$536$		0			0
$537$	−403368.	+	146814.i	−1.39879	+	0.509118i
$538$		0			0
$539$	−40588.7	−	70301.7i	−0.139710	−	0.241985i
$540$		0			0
$541$	32808.2	+	186064.i	0.112095	+	0.635724i	0.988147	+	0.153508i	$0.0490570\pi$
$541$	32808.2	+	186064.i	0.112095	+	0.635724i	−0.876052	+	0.482216i	$0.839832\pi$
$542$		0			0
$543$	−163696.	+	283530.i	−0.555187	+	0.961612i
$544$		0			0
$545$	−25449.8	−	30329.9i	−0.0856824	−	0.102112i
$546$		0			0
$547$	−54831.0	+	150647.i	−0.183253	+	0.503484i	−0.996971	−	0.0777765i	$-0.975218\pi$
$547$	−54831.0	+	150647.i	−0.183253	+	0.503484i	0.813718	+	0.581260i	$0.197440\pi$
$548$		0			0
$549$	129170.	−	732560.i	0.428566	−	2.43052i
$550$		0			0
$551$	153966.	+	196536.i	0.507133	+	0.647348i
$552$		0			0
$553$	−210965.	−	37198.8i	−0.689858	−	0.121641i
$554$		0			0
$555$	309371.	+	112602.i	1.00437	+	0.365561i
$556$		0			0
$557$	107255.	−	89997.5i	0.345706	−	0.290082i	−0.453357	−	0.891329i	$-0.649774\pi$
$557$	107255.	−	89997.5i	0.345706	−	0.290082i	0.799063	+	0.601247i	$0.205329\pi$
$558$		0			0
$559$	467311.	+	269802.i	1.49549	+	0.863419i
$560$		0			0
$561$	−105042.	+	18521.7i	−0.333761	+	0.0588511i
$562$		0			0
$563$	−121704.	+	70266.1i	−0.383963	+	0.221681i	−0.679541	−	0.733637i	$-0.737821\pi$
$563$	−121704.	+	70266.1i	−0.383963	+	0.221681i	0.295578	+	0.955319i	$0.404488\pi$
$564$		0			0
$565$	−129357.	−	355406.i	−0.405223	−	1.11334i
$566$		0			0
$567$	114160.	+	95791.7i	0.355098	+	0.297963i
$568$		0			0
$569$		−	250293.i		−	0.773080i	−0.922273	−	0.386540i	$-0.873670\pi$
$569$		−	250293.i		−	0.773080i	0.922273	−	0.386540i	$-0.126330\pi$
$570$		0			0
$571$	199899.			0.613111			0.306555	−	0.951853i	$-0.400824\pi$
$571$	199899.			0.613111			0.306555	+	0.951853i	$0.400824\pi$
$572$		0			0
$573$	−192092.	+	228926.i	−0.585059	+	0.697247i
$574$		0			0
$575$	−168213.	+	61224.6i	−0.508774	+	0.185178i
$576$		0			0
$577$	−55103.4	−	95442.0i	−0.165511	−	0.286674i	0.771326	−	0.636441i	$-0.219594\pi$
$577$	−55103.4	−	95442.0i	−0.165511	−	0.286674i	−0.936837	+	0.349767i	$0.886261\pi$
$578$		0			0
$579$	−10336.9	−	58623.4i	−0.0308342	−	0.174869i
$580$		0			0
$581$	−140768.	+	243817.i	−0.417015	+	0.722291i
$582$		0			0
$583$	−29325.7	−	34949.0i	−0.0862803	−	0.102825i
$584$		0			0
$585$	−216055.	+	593607.i	−0.631325	+	1.73455i
$586$		0			0
$587$	−87834.7	+	498135.i	−0.254912	+	1.44568i	0.541387	+	0.840773i	$0.317899\pi$
$587$	−87834.7	+	498135.i	−0.254912	+	1.44568i	−0.796299	+	0.604903i	$0.793212\pi$
$588$		0			0
$589$	−314673.	−	196056.i	−0.907046	−	0.565132i
$590$		0			0
$591$	371229.	+	65457.6i	1.06284	+	0.187407i
$592$		0			0
$593$	−187637.	−	68294.1i	−0.533591	−	0.194211i	0.0611503	−	0.998129i	$-0.480523\pi$
$593$	−187637.	−	68294.1i	−0.533591	−	0.194211i	−0.594741	+	0.803917i	$0.702745\pi$
$594$		0			0
$595$	−758091.	+	636114.i	−2.14135	+	1.79680i
$596$		0			0
$597$	−270483.	−	156164.i	−0.758912	−	0.438158i
$598$		0			0
$599$	−641784.	+	113164.i	−1.78869	+	0.315395i	−0.967046	−	0.254604i	$-0.918055\pi$
$599$	−641784.	+	113164.i	−1.78869	+	0.315395i	−0.821646	+	0.569998i	$0.806944\pi$
$600$		0			0
$601$	−372533.	+	215082.i	−1.03137	+	0.595464i	−0.917378	−	0.398018i	$-0.869698\pi$
$601$	−372533.	+	215082.i	−1.03137	+	0.595464i	−0.113996	+	0.993481i	$0.536365\pi$
$602$		0			0
$603$	−270423.	−	742981.i	−0.743719	−	2.04335i
$604$		0			0
$605$	364442.	+	305803.i	0.995676	+	0.835471i
$606$		0			0
$607$		−	157443.i		−	0.427314i	−0.976909	−	0.213657i	$-0.931463\pi$
$607$		−	157443.i		−	0.427314i	0.976909	−	0.213657i	$-0.0685374\pi$
$608$		0			0
$609$	−784325.			−2.11476
$610$		0			0
$611$	−272939.	+	325276.i	−0.731112	+	0.871305i
$612$		0			0
$613$	410211.	−	149305.i	1.09166	−	0.397331i	0.267423	−	0.963579i	$-0.413828\pi$
$613$	410211.	−	149305.i	1.09166	−	0.397331i	0.824235	+	0.566248i	$0.191606\pi$
$614$		0			0
$615$	390986.	+	677208.i	1.03374	+	1.79049i
$616$		0			0
$617$	102238.	+	579819.i	0.268560	+	1.52308i	0.758703	+	0.651437i	$0.225833\pi$
$617$	102238.	+	579819.i	0.268560	+	1.52308i	−0.490143	+	0.871642i	$0.663056\pi$
$618$		0			0
$619$	205858.	−	356557.i	0.537263	−	0.930568i	−0.461787	−	0.886991i	$-0.652791\pi$
$619$	205858.	−	356557.i	0.537263	−	0.930568i	0.999050	−	0.0435765i	$-0.0138752\pi$
$620$		0			0
$621$	129435.	+	154254.i	0.335635	+	0.399995i
$622$		0			0
$623$	280771.	−	771412.i	0.723396	−	1.98751i
$624$		0			0
$625$	−79128.2	+	448758.i	−0.202568	+	1.14882i
$626$		0			0
$627$	69517.0	−	77410.4i	0.176830	−	0.196908i
$628$		0			0
$629$	−253047.	−	44619.0i	−0.639587	−	0.112776i
$630$		0			0
$631$	63143.6	+	22982.4i	0.158588	+	0.0577214i	0.420094	−	0.907480i	$-0.361997\pi$
$631$	63143.6	+	22982.4i	0.158588	+	0.0577214i	−0.261506	+	0.965202i	$0.584219\pi$
$632$		0			0
$633$	881122.	−	739349.i	2.19902	−	1.84519i
$634$		0			0
$635$	−715361.	−	413014.i	−1.77410	−	1.02428i
$636$		0			0
$637$	618727.	−	109098.i	1.52483	−	0.268868i
$638$		0			0
$639$	−557771.	+	322029.i	−1.36601	+	0.788667i
$640$		0			0
$641$	−7873.10	−	21631.2i	−0.0191615	−	0.0526458i	0.929743	−	0.368209i	$-0.120029\pi$
$641$	−7873.10	−	21631.2i	−0.0191615	−	0.0526458i	−0.948905	+	0.315563i	$0.897807\pi$
$642$		0			0
$643$	41981.6	+	35226.7i	0.101540	+	0.0852021i	0.692144	−	0.721759i	$-0.256666\pi$
$643$	41981.6	+	35226.7i	0.101540	+	0.0852021i	−0.590604	+	0.806961i	$0.701111\pi$
$644$		0			0
$645$			1.62675e6i			3.91022i
$646$		0			0
$647$	−485981.			−1.16094			−0.580471	−	0.814281i	$-0.697132\pi$
$647$	−485981.			−1.16094			−0.580471	+	0.814281i	$0.697132\pi$
$648$		0			0
$649$	−86263.4	+	102805.i	−0.204803	+	0.244075i
$650$		0			0
$651$	1.09449e6	−	398361.i	2.58255	−	0.939972i
$652$		0			0
$653$	243189.	+	421215.i	0.570318	+	0.987819i	0.996533	+	0.0831976i	$0.0265133\pi$
$653$	243189.	+	421215.i	0.570318	+	0.987819i	−0.426215	+	0.904622i	$0.640153\pi$
$654$		0			0
$655$	−95001.7	−	538782.i	−0.221436	−	1.25583i
$656$		0			0
$657$	−189561.	+	328329.i	−0.439155	+	0.760640i
$658$		0			0
$659$	−158420.	−	188797.i	−0.364786	−	0.434735i	0.552165	−	0.833735i	$-0.313802\pi$
$659$	−158420.	−	188797.i	−0.364786	−	0.434735i	−0.916951	+	0.399000i	$0.869357\pi$
$660$		0			0
$661$	239119.	−	656975.i	0.547283	−	1.50365i	−0.290082	−	0.957002i	$-0.593683\pi$
$661$	239119.	−	656975.i	0.547283	−	1.50365i	0.837365	−	0.546645i	$-0.184095\pi$
$662$		0			0
$663$	143349.	−	812970.i	0.326112	−	1.84947i
$664$		0			0
$665$	199462.	−	944487.i	0.451042	−	2.13576i
$666$		0			0
$667$	247274.	+	43601.0i	0.555810	+	0.0980042i
$668$		0			0
$669$	478811.	+	174273.i	1.06982	+	0.389384i
$670$		0			0
$671$	−96417.5	+	80903.9i	−0.214147	+	0.179690i
$672$		0			0
$673$	600361.	+	346618.i	1.32551	+	0.765282i	0.984601	−	0.174815i	$-0.0559328\pi$
$673$	600361.	+	346618.i	1.32551	+	0.765282i	0.340906	+	0.940097i	$0.389266\pi$
$674$		0			0
$675$	−269310.	+	47486.6i	−0.591078	+	0.104223i
$676$		0			0
$677$	205564.	−	118683.i	0.448508	−	0.258946i	−0.258692	−	0.965960i	$-0.583291\pi$
$677$	205564.	−	118683.i	0.448508	−	0.258946i	0.707200	+	0.707013i	$0.249958\pi$
$678$		0			0
$679$	324678.	+	892047.i	0.704229	+	1.93485i
$680$		0			0
$681$	136480.	+	114521.i	0.294290	+	0.246939i
$682$		0			0
$683$			561678.i			1.20405i	0.798476	+	0.602027i	$0.205640\pi$
$683$			561678.i			1.20405i	−0.798476	+	0.602027i	$0.794360\pi$
$684$		0			0
$685$	−57789.1			−0.123159
$686$		0			0
$687$	326603.	−	389231.i	0.692002	−	0.824696i
$688$		0			0
$689$	331803.	−	120766.i	0.698942	−	0.254394i
$690$		0			0
$691$	−145381.	−	251808.i	−0.304475	−	0.527367i	0.672669	−	0.739944i	$-0.265148\pi$
$691$	−145381.	−	251808.i	−0.304475	−	0.527367i	−0.977144	+	0.212577i	$0.931814\pi$
$692$		0			0
$693$	33897.8	+	192244.i	0.0705837	+	0.400300i
$694$		0			0
$695$	57504.0	−	99599.9i	0.119050	−	0.206200i
$696$		0			0
$697$	−392296.	−	467521.i	−0.807512	−	0.962355i
$698$		0			0
$699$	−258445.	+	710072.i	−0.528949	+	1.45328i
$700$		0			0
$701$	99320.0	−	563272.i	0.202116	−	1.14626i	−0.699798	−	0.714341i	$-0.746727\pi$
$701$	99320.0	−	563272.i	0.202116	−	1.14626i	0.901914	−	0.431916i	$-0.142162\pi$
$702$		0			0
$703$	221149.	−	117959.i	0.447480	−	0.238683i
$704$		0			0
$705$	−1.26065e6	−	222287.i	−2.53640	−	0.447236i
$706$		0			0
$707$	−1.14425e6	−	416474.i	−2.28920	−	0.833200i
$708$		0			0
$709$	−75386.6	+	63256.9i	−0.149969	+	0.125839i	−0.714685	−	0.699446i	$-0.753430\pi$
$709$	−75386.6	+	63256.9i	−0.149969	+	0.125839i	0.564716	+	0.825285i	$0.308986\pi$
$710$		0			0
$711$	278636.	+	160870.i	0.551185	+	0.318227i
$712$		0			0
$713$	−367204.	+	64747.9i	−0.722317	+	0.127364i
$714$		0			0
$715$	92566.6	−	53443.4i	0.181068	−	0.104540i
$716$		0			0
$717$	−494352.	−	1.35822e6i	−0.961608	−	2.64200i
$718$		0			0
$719$	−179686.	−	150775.i	−0.347582	−	0.291656i	0.452236	−	0.891898i	$-0.350626\pi$
$719$	−179686.	−	150775.i	−0.347582	−	0.291656i	−0.799818	+	0.600242i	$0.795071\pi$
$720$		0			0
$721$			592494.i			1.13976i
$722$		0			0
$723$	391211.			0.748402
$724$		0			0
$725$	−219185.	+	261214.i	−0.416999	+	0.496960i
$726$		0			0
$727$	378526.	−	137772.i	0.716188	−	0.260671i	0.0418813	−	0.999123i	$-0.486665\pi$
$727$	378526.	−	137772.i	0.716188	−	0.260671i	0.674307	+	0.738452i	$0.264443\pi$
$728$		0			0
$729$	−430462.	−	745581.i	−0.809989	−	1.40294i
$730$		0			0
$731$	−220469.	−	1.25034e6i	−0.412584	−	2.33988i
$732$		0			0
$733$	−13781.4	+	23870.1i	−0.0256499	+	0.0444269i	−0.878565	−	0.477622i	$-0.841499\pi$
$733$	−13781.4	+	23870.1i	−0.0256499	+	0.0444269i	0.852916	+	0.522049i	$0.174832\pi$
$734$		0			0
$735$	1.21748e6	+	1.45093e6i	2.25365	+	2.68580i
$736$		0			0
$737$	−45756.6	+	125715.i	−0.0842402	+	0.231448i
$738$		0			0
$739$	−50633.3	+	287155.i	−0.0927144	+	0.525809i	0.902709	+	0.430251i	$0.141575\pi$
$739$	−50633.3	+	287155.i	−0.0927144	+	0.525809i	−0.995424	+	0.0955586i	$0.969536\pi$
$740$		0			0
$741$	378971.	+	710490.i	0.690191	+	1.29396i
$742$		0			0
$743$	96689.8	+	17049.0i	0.175147	+	0.0308832i	0.260534	−	0.965465i	$-0.416101\pi$
$743$	96689.8	+	17049.0i	0.175147	+	0.0308832i	−0.0853867	+	0.996348i	$0.527213\pi$
$744$		0			0
$745$	−446627.	−	162559.i	−0.804697	−	0.292886i
$746$		0			0
$747$	323918.	−	271799.i	0.580489	−	0.487088i
$748$		0			0
$749$	−124764.	−	72032.8i	−0.222396	−	0.128401i
$750$		0			0
$751$	153713.	−	27103.8i	0.272541	−	0.0480563i	−0.0357074	−	0.999362i	$-0.511368\pi$
$751$	153713.	−	27103.8i	0.272541	−	0.0480563i	0.308248	+	0.951306i	$0.400257\pi$
$752$		0			0
$753$	237568.	−	137160.i	0.418984	−	0.241901i
$754$		0			0
$755$	−152074.	−	417819.i	−0.266784	−	0.732984i
$756$		0			0
$757$	208986.	+	175360.i	0.364690	+	0.306012i	0.806657	−	0.591020i	$-0.201275\pi$
$757$	208986.	+	175360.i	0.364690	+	0.306012i	−0.441966	+	0.897032i	$0.645719\pi$
$758$		0			0
$759$		−	104637.i		−	0.181636i
$760$		0			0
$761$	−51387.1			−0.0887330			−0.0443665	−	0.999015i	$-0.514127\pi$
$761$	−51387.1			−0.0887330			−0.0443665	+	0.999015i	$0.514127\pi$
$762$		0			0
$763$	60867.4	−	72539.0i	0.104553	−	0.124601i
$764$		0			0
$765$	1.39669e6	−	508354.i	2.38659	−	0.868647i
$766$		0			0
$767$	−519328.	−	899503.i	−0.882777	−	1.52901i
$768$		0			0
$769$	129377.	+	733731.i	0.218778	+	1.24075i	0.874229	+	0.485513i	$0.161367\pi$
$769$	129377.	+	733731.i	0.218778	+	1.24075i	−0.655452	+	0.755237i	$0.727522\pi$
$770$		0			0
$771$	−62905.7	+	108956.i	−0.105823	+	0.183291i
$772$		0			0
$773$	29794.7	+	35507.9i	0.0498632	+	0.0594246i	0.790400	−	0.612592i	$-0.209873\pi$
$773$	29794.7	+	35507.9i	0.0498632	+	0.0594246i	−0.740536	+	0.672016i	$0.765429\pi$
$774$		0			0
$775$	173191.	−	475837.i	0.288351	−	0.792237i
$776$		0			0
$777$	−136730.	+	775436.i	−0.226476	+	1.28441i
$778$		0			0
$779$	582472.	+	123010.i	0.959844	+	0.202705i
$780$		0			0
$781$	107322.	+	18923.7i	0.175948	+	0.0310244i
$782$		0			0
$783$	360444.	+	131191.i	0.587915	+	0.213984i
$784$		0			0
$785$	−83724.1	+	70252.9i	−0.135866	+	0.114005i
$786$		0			0
$787$	499855.	+	288591.i	0.807039	+	0.465944i	0.845927	−	0.533299i	$-0.179048\pi$
$787$	499855.	+	288591.i	0.807039	+	0.465944i	−0.0388875	+	0.999244i	$0.512381\pi$
$788$		0			0
$789$	−1.17187e6	+	206633.i	−1.88246	+	0.331929i
$790$		0			0
$791$	783376.	−	452282.i	1.25204	−	0.722864i
$792$		0			0
$793$	−333171.	−	915379.i	−0.529810	−	1.45564i
$794$		0			0
$795$	815444.	+	684238.i	1.29021	+	1.08261i
$796$		0			0
$797$			1.03925e6i			1.63607i	0.575168	+	0.818035i	$0.304937\pi$
$797$			1.03925e6i			1.63607i	−0.575168	+	0.818035i	$0.695063\pi$
$798$		0			0
$799$	999079.			1.56497
$800$		0			0
$801$	−792529.	+	944500.i	−1.23524	+	1.47210i
$802$		0			0
$803$	60280.3	−	21940.2i	0.0934855	−	0.0340259i
$804$		0			0
$805$	−485414.	−	840762.i	−0.749067	−	1.29742i
$806$		0			0
$807$	−116221.	−	659124.i	−0.178459	−	1.01209i
$808$		0			0
$809$	−251229.	+	435141.i	−0.383859	+	0.664864i	−0.991610	−	0.129264i	$-0.958739\pi$
$809$	−251229.	+	435141.i	−0.383859	+	0.664864i	0.607751	+	0.794128i	$0.292072\pi$
$810$		0			0
$811$	−185811.	−	221441.i	−0.282507	−	0.336679i	0.606065	−	0.795415i	$-0.292747\pi$
$811$	−185811.	−	221441.i	−0.282507	−	0.336679i	−0.888573	+	0.458736i	$0.848303\pi$
$812$		0			0
$813$	176015.	−	483598.i	0.266299	−	0.731651i
$814$		0			0
$815$	−15671.3	+	88876.4i	−0.0235934	+	0.133805i
$816$		0			0
$817$	921437.	+	827479.i	1.38045	+	1.23969i
$818$		0			0
$819$	−1.48787e6	−	262352.i	−2.21818	−	0.391125i
$820$		0			0
$821$	−895285.	−	325857.i	−1.32824	−	0.483438i	−0.422147	−	0.906527i	$-0.638723\pi$
$821$	−895285.	−	325857.i	−1.32824	−	0.483438i	−0.906088	+	0.423089i	$0.860946\pi$
$822$		0			0
$823$	−509070.	+	427160.i	−0.751585	+	0.630654i	−0.935921	−	0.352209i	$-0.885431\pi$
$823$	−509070.	+	427160.i	−0.751585	+	0.630654i	0.184337	+	0.982863i	$0.440986\pi$
$824$		0			0
$825$	123065.	+	71051.3i	0.180811	+	0.104391i
$826$		0			0
$827$	−269084.	+	47446.7i	−0.393438	+	0.0693737i	−0.366867	−	0.930273i	$-0.619570\pi$
$827$	−269084.	+	47446.7i	−0.393438	+	0.0693737i	−0.0265705	+	0.999647i	$0.508459\pi$
$828$		0			0
$829$	−1.08114e6	+	624199.i	−1.57317	+	0.908268i	−0.577388	+	0.816470i	$0.695928\pi$
$829$	−1.08114e6	+	624199.i	−1.57317	+	0.908268i	−0.995778	+	0.0917977i	$0.970739\pi$
$830$		0			0
$831$	−14544.8	−	39961.6i	−0.0210623	−	0.0578683i
$832$		0			0
$833$	−1.13241e6	−	950203.i	−1.63197	−	1.36939i
$834$		0			0
$835$		−	320452.i		−	0.459611i
$836$		0			0
$837$	−569615.			−0.813075
$838$		0			0
$839$	547779.	−	652817.i	0.778182	−	0.927401i	−0.220668	−	0.975349i	$-0.570824\pi$
$839$	547779.	−	652817.i	0.778182	−	0.927401i	0.998850	+	0.0479476i	$0.0152680\pi$
$840$		0			0
$841$	−215177.	+	78318.1i	−0.304232	+	0.110731i
$842$		0			0
$843$	784433.	+	1.35868e6i	1.10383	+	1.91188i
$844$		0			0
$845$	−22184.3	−	125813.i	−0.0310693	−	0.176203i
$846$		0			0
$847$	−568912.	+	985384.i	−0.793009	+	1.37353i
$848$		0			0
$849$	1.13318e6	+	1.35048e6i	1.57212	+	1.87358i
$850$		0			0
$851$	86213.7	−	236870.i	0.119047	−	0.327078i
$852$		0			0
$853$	−145652.	+	826034.i	−0.200179	+	1.13527i	0.704669	+	0.709536i	$0.251096\pi$
$853$	−145652.	+	826034.i	−0.200179	+	1.13527i	−0.904848	+	0.425735i	$0.860015\pi$
$854$		0			0
$855$	−766681.	+	1.23054e6i	−1.04877	+	1.68330i
$856$		0			0
$857$	874055.	+	154120.i	1.19008	+	0.209844i	0.733407	−	0.679789i	$-0.237929\pi$
$857$	874055.	+	154120.i	1.19008	+	0.209844i	0.456676	+	0.889633i	$0.349040\pi$
$858$		0			0
$859$	754617.	+	274658.i	1.02268	+	0.372225i	0.798290	−	0.602274i	$-0.205738\pi$
$859$	754617.	+	274658.i	1.02268	+	0.372225i	0.224391	+	0.974499i	$0.427961\pi$
$860$		0			0
$861$	−1.43267e6	+	1.20215e6i	−1.93259	+	1.62163i
$862$		0			0
$863$	786801.	+	454260.i	1.05644	+	0.609934i	0.924444	−	0.381317i	$-0.124529\pi$
$863$	786801.	+	454260.i	1.05644	+	0.609934i	0.131992	+	0.991251i	$0.457863\pi$
$864$		0			0
$865$	−348613.	+	61469.9i	−0.465921	+	0.0821544i
$866$		0			0
$867$	−656359.	+	378949.i	−0.873178	+	0.504130i
$868$		0			0
$869$	−18619.5	−	51156.7i	−0.0246563	−	0.0677427i
$870$		0			0
$871$	−793176.	−	665553.i	−1.04552	−	0.877297i
$872$		0			0
$873$		−	1.42577e6i		−	1.87077i
$874$		0			0
$875$	−352821.			−0.460828
$876$		0			0
$877$	877379.	−	1.04562e6i	1.14074	−	1.35948i	0.217138	−	0.976141i	$-0.430328\pi$
$877$	877379.	−	1.04562e6i	1.14074	−	1.35948i	0.923606	−	0.383344i	$-0.125228\pi$
$878$		0			0
$879$	−9155.92	+	3332.48i	−0.0118502	+	0.00431311i
$880$		0			0
$881$	97934.9	+	169628.i	0.126179	+	0.218548i	0.922193	−	0.386730i	$-0.126395\pi$
$881$	97934.9	+	169628.i	0.126179	+	0.218548i	−0.796014	+	0.605278i	$0.793062\pi$
$882$		0			0
$883$	39626.9	+	224735.i	0.0508240	+	0.288237i	0.999617	−	0.0276601i	$-0.00880560\pi$
$883$	39626.9	+	224735.i	0.0508240	+	0.288237i	−0.948793	+	0.315897i	$0.897694\pi$
$884$		0			0
$885$	1.56563e6	−	2.71174e6i	1.99895	−	3.46228i
$886$		0			0
$887$	−207235.	−	246973.i	−0.263400	−	0.313907i	0.618093	−	0.786105i	$-0.287905\pi$
$887$	−207235.	−	246973.i	−0.263400	−	0.313907i	−0.881493	+	0.472197i	$0.843461\pi$
$888$		0			0
$889$	675688.	−	1.85644e6i	0.854954	−	2.34897i
$890$		0			0
$891$	−6576.40	+	37296.6i	−0.00828386	+	0.0469801i
$892$		0			0
$893$	−767167.	+	600999.i	−0.962026	+	0.753652i
$894$		0			0
$895$	−996740.	−	175752.i	−1.24433	−	0.219409i
$896$		0			0
$897$	760999.	+	276981.i	0.945799	+	0.344243i
$898$		0			0
$899$	−544099.	+	456554.i	−0.673223	+	0.564901i
$900$		0			0
$901$	−719492.	−	415399.i	−0.886291	−	0.511700i
$902$		0			0
$903$	−3.83154e6	+	675603.i	−4.69891	+	0.828545i
$904$		0			0
$905$	−668520.	+	385970.i	−0.816239	+	0.471256i
$906$		0			0
$907$	125235.	+	344080.i	0.152234	+	0.418258i	0.992243	−	0.124314i	$-0.0396729\pi$
$907$	125235.	+	344080.i	0.152234	+	0.418258i	−0.840009	+	0.542572i	$0.817451\pi$
$908$		0			0
$909$	1.40100e6	+	1.17558e6i	1.69555	+	1.42273i
$910$		0			0
$911$			701763.i			0.845578i	0.906228	+	0.422789i	$0.138949\pi$
$911$			701763.i			0.845578i	−0.906228	+	0.422789i	$0.861051\pi$
$912$		0			0
$913$	−71547.0			−0.0858321
$914$		0			0
$915$	1.88768e6	−	2.24965e6i	2.25469	−	2.68703i
$916$		0			0
$917$	1.22955e6	−	447521.i	1.46221	−	0.532200i
$918$		0			0
$919$	−119074.	−	206242.i	−0.140989	−	0.244200i	0.786880	−	0.617106i	$-0.211695\pi$
$919$	−119074.	−	206242.i	−0.140989	−	0.244200i	−0.927869	+	0.372905i	$0.878362\pi$
$920$		0			0
$921$	−13178.1	−	74736.5i	−0.0155358	−	0.0881077i
$922$		0			0
$923$	−421714.	+	730431.i	−0.495011	+	0.857385i
$924$		0			0
$925$	220044.	+	262238.i	0.257173	+	0.306487i
$926$		0			0
$927$	304357.	−	836213.i	0.354179	−	0.973100i
$928$		0			0
$929$	−225387.	+	1.27823e6i	−0.261155	+	1.48108i	0.518611	+	0.855010i	$0.326449\pi$
$929$	−225387.	+	1.27823e6i	−0.261155	+	1.48108i	−0.779766	+	0.626071i	$0.784662\pi$
$930$		0			0
$931$	1.44114e6	+	48432.7i	1.66268	+	0.0558778i
$932$		0			0
$933$	1.86762e6	+	329311.i	2.14548	+	0.378306i
$934$		0			0
$935$	−236326.	−	86015.5i	−0.270326	−	0.0983906i
$936$		0			0
$937$	−246475.	+	206817.i	−0.280733	+	0.235563i	−0.772271	−	0.635293i	$-0.780879\pi$
$937$	−246475.	+	206817.i	−0.280733	+	0.235563i	0.491538	+	0.870856i	$0.336435\pi$
$938$		0			0
$939$	3141.78	+	1813.91i	0.00356324	+	0.00205724i
$940$		0			0
$941$	1.38888e6	−	244897.i	1.56850	−	0.276570i	0.679223	−	0.733932i	$-0.262317\pi$
$941$	1.38888e6	−	244897.i	1.56850	−	0.276570i	0.889281	+	0.457362i	$0.151206\pi$
$942$		0			0
$943$	518504.	−	299359.i	0.583081	−	0.336642i
$944$		0			0
$945$	−507248.	−	1.39365e6i	−0.568011	−	1.56060i
$946$		0			0
$947$	1.02630e6	+	861165.i	1.14439	+	0.960255i	0.999573	−	0.0292042i	$-0.00929730\pi$
$947$	1.02630e6	+	861165.i	1.14439	+	0.960255i	0.144814	+	0.989459i	$0.453742\pi$
$948$		0			0
$949$			496481.i			0.551277i
$950$		0			0
$951$	1.04055e6			1.15054
$952$		0			0
$953$	−781270.	+	931082.i	−0.860232	+	1.02518i	0.139159	+	0.990270i	$0.455560\pi$
$953$	−781270.	+	931082.i	−0.860232	+	1.02518i	−0.999390	+	0.0349142i	$0.988884\pi$
$954$		0			0
$955$	−662129.	+	240995.i	−0.725998	+	0.264242i
$956$		0			0
$957$	−99660.7	−	172617.i	−0.108818	−	0.188478i
$958$		0			0
$959$	−24000.3	−	136112.i	−0.0260963	−	0.148000i
$960$		0			0
$961$	65619.2	−	113656.i	0.0710532	−	0.123068i
$962$		0			0
$963$	139083.	+	165753.i	0.149976	+	0.178735i
$964$		0			0
$965$	48005.0	−	131893.i	0.0515503	−	0.141633i
$966$		0			0
$967$	107650.	−	610513.i	0.115123	−	0.652893i	−0.871567	−	0.490277i	$-0.836896\pi$
$967$	107650.	−	610513.i	0.115123	−	0.652893i	0.986689	−	0.162616i	$-0.0519932\pi$
$968$		0			0
$969$	707441.	−	1.75761e6i	0.753429	−	1.87187i
$970$		0			0
$971$	−1.30408e6	−	229944.i	−1.38314	−	0.243884i	−0.567941	−	0.823069i	$-0.692260\pi$
$971$	−1.30408e6	−	229944.i	−1.38314	−	0.243884i	−0.815196	+	0.579185i	$0.803371\pi$
$972$		0			0
$973$	258472.	+	94076.3i	0.273016	+	0.0993698i
$974$		0			0
$975$	−842498.	+	706940.i	−0.886257	+	0.743658i
$976$		0			0
$977$	423409.	+	244455.i	0.443579	+	0.256100i	0.705114	−	0.709094i	$-0.250896\pi$
$977$	423409.	+	244455.i	0.443579	+	0.256100i	−0.261536	+	0.965194i	$0.584229\pi$
$978$		0			0
$979$	205452.	−	36226.7i	0.214360	−	0.0377975i
$980$		0			0
$981$	−123167.	+	71110.7i	−0.127985	+	0.0738919i
$982$		0			0
$983$	−213047.	−	585343.i	−0.220480	−	0.605764i	0.779302	−	0.626649i	$-0.215574\pi$
$983$	−213047.	−	585343.i	−0.220480	−	0.605764i	−0.999782	+	0.0208850i	$0.993352\pi$
$984$		0			0
$985$	680862.	+	571311.i	0.701757	+	0.588844i
$986$		0			0
$987$		−	3.06158e6i		−	3.14276i
$988$		0			0
$989$	1.24552e6			1.27338
$990$		0			0
$991$	−204489.	+	243700.i	−0.208220	+	0.248147i	−0.860040	−	0.510227i	$-0.829561\pi$
$991$	−204489.	+	243700.i	−0.208220	+	0.248147i	0.651820	+	0.758374i	$0.274006\pi$
$992$		0			0
$993$	759258.	−	276347.i	0.770000	−	0.280257i
$994$		0			0
$995$	−368209.	−	637757.i	−0.371919	−	0.644182i
$996$		0			0
$997$	−311934.	−	1.76907e6i	−0.313814	−	1.77973i	−0.578792	−	0.815475i	$-0.696476\pi$
$997$	−311934.	−	1.76907e6i	−0.313814	−	1.77973i	0.264978	−	0.964255i	$-0.414635\pi$
$998$		0			0
$999$	192540.	−	333489.i	0.192925	−	0.334157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.21.6	✓	42
19.10	odd	18	inner	76.5.j.a.29.6	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.21.6	✓	42	1.1	even	1	trivial
76.5.j.a.29.6	yes	42	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +O(q^{10})\)	\(q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +(-10.1615 + 17.6003i) q^{11} +(-101.104 - 120.492i) q^{13} +(162.181 - 445.589i) q^{15} +(-64.2649 + 364.464i) q^{17} +(-169.897 - 318.521i) q^{19} +(1116.86 + 196.933i) q^{21} +(-341.165 - 124.174i) q^{23} +(377.702 - 316.930i) q^{25} +(-480.325 - 277.316i) q^{27} +(-681.081 + 120.093i) q^{29} +(889.421 - 513.507i) q^{31} +(98.5730 + 270.827i) q^{33} +(2048.41 + 1718.82i) q^{35} +694.298i q^{37} -2230.59 q^{39} +(-1060.01 + 1263.27i) q^{41} +(-3223.73 + 1173.34i) q^{43} +(-2008.08 - 3478.10i) q^{45} +(-468.777 - 2658.57i) q^{47} +(-1997.17 + 3459.20i) q^{49} +(3373.56 + 4020.45i) q^{51} +(-767.791 + 2109.49i) q^{53} +(-118.003 + 669.226i) q^{55} +(-5008.98 - 1057.82i) q^{57} +(6503.10 + 1146.67i) q^{59} +(5819.67 + 2118.19i) q^{61} +(7358.09 - 6174.17i) q^{63} +(-4554.75 - 2629.69i) q^{65} +(6482.83 - 1143.10i) q^{67} +(-4458.88 + 2574.34i) q^{69} +(-1833.99 - 5038.85i) q^{71} +(-2417.99 - 2028.93i) q^{73} -6992.18i q^{75} -1625.26 q^{77} +(-1721.85 + 2052.02i) q^{79} +(1751.11 - 637.353i) q^{81} +(1760.24 + 3048.83i) q^{83} +(2148.85 + 12186.7i) q^{85} +(-4903.82 + 8493.66i) q^{87} +(-6598.36 - 7863.62i) q^{89} +(4302.16 - 11820.1i) q^{91} +(2529.09 - 14343.2i) q^{93} +(-8981.00 - 8065.22i) q^{95} +(11690.2 + 2061.29i) q^{97} +(2293.80 + 834.873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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