LMFDB - Embedded newform 76.5.j.a.29.6

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			29.6
Character	$\chi$	$=$	76.29
Dual form			76.5.j.a.21.6

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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	0.978201	+	0.207659i	$0.0665843\pi$
$3$	9.11558	+	10.8635i	1.01284	+	1.20706i	0.0346409	+	0.999400i	$0.488971\pi$
$4$		0			0
$5$	31.4208	+	11.4362i	1.25683	+	0.457450i	0.882705	−	0.469927i	$-0.155720\pi$
$5$	31.4208	+	11.4362i	1.25683	+	0.457450i	0.374128	+	0.927377i	$0.377942\pi$
$6$		0			0
$7$	39.9854	−	69.2568i	0.816029	−	1.41340i	−0.0925569	−	0.995707i	$-0.529504\pi$
$7$	39.9854	−	69.2568i	0.816029	−	1.41340i	0.908586	−	0.417697i	$-0.137163\pi$
$8$		0			0
$9$	−20.8569	+	118.285i	−0.257492	+	1.46031i
$10$		0			0
$11$	−10.1615	−	17.6003i	−0.0839797	−	0.145457i	0.820976	−	0.570962i	$-0.193430\pi$
$11$	−10.1615	−	17.6003i	−0.0839797	−	0.145457i	−0.904956	+	0.425505i	$0.860096\pi$
$12$		0			0
$13$	−101.104	+	120.492i	−0.598251	+	0.712968i	−0.977169	−	0.212463i	$-0.931852\pi$
$13$	−101.104	+	120.492i	−0.598251	+	0.712968i	0.378918	+	0.925430i	$0.376296\pi$
$14$		0			0
$15$	162.181	+	445.589i	0.720805	+	1.98039i
$16$		0			0
$17$	−64.2649	−	364.464i	−0.222370	−	1.26112i	−0.867650	−	0.497176i	$-0.834370\pi$
$17$	−64.2649	−	364.464i	−0.222370	−	1.26112i	0.645280	−	0.763947i	$-0.276741\pi$
$18$		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	−0.643714	−	0.765266i	$-0.722607\pi$
$23$	−341.165	+	124.174i	−0.644924	+	0.234733i	−0.00121023	+	0.999999i	$0.500385\pi$
$24$		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	−0.246633	−	0.969109i	$-0.579324\pi$
$29$	−681.081	−	120.093i	−0.809847	−	0.142798i	−0.563214	+	0.826311i	$0.690435\pi$
$30$		0			0
$31$	889.421	+	513.507i	0.925516	+	0.534347i	0.885391	−	0.464848i	$-0.153891\pi$
$31$	889.421	+	513.507i	0.925516	+	0.534347i	0.0401254	+	0.999195i	$0.487224\pi$
$32$		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	$-0.918392\pi$
$37$		−	694.298i		−	0.507157i	0.967315	−	0.253578i	$-0.0816076\pi$
$38$		0			0
$39$	−2230.59			−1.46653
$40$		0			0
$41$	−1060.01	−	1263.27i	−0.630584	−	0.751501i	0.352268	−	0.935899i	$-0.385411\pi$
$41$	−1060.01	−	1263.27i	−0.630584	−	0.751501i	−0.982852	+	0.184399i	$0.940966\pi$
$42$		0			0
$43$	−3223.73	−	1173.34i	−1.74350	−	0.634581i	−0.744061	−	0.668112i	$-0.767103\pi$
$43$	−3223.73	−	1173.34i	−1.74350	−	0.634581i	−0.999438	+	0.0335306i	$0.989325\pi$
$44$		0			0
$45$	−2008.08	+	3478.10i	−0.991644	+	1.71758i
$46$		0			0
$47$	−468.777	+	2658.57i	−0.212212	+	1.20352i	0.673466	+	0.739218i	$0.264805\pi$
$47$	−468.777	+	2658.57i	−0.212212	+	1.20352i	−0.885679	+	0.464298i	$0.846307\pi$
$48$		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	−0.998079	−	0.0619591i	$-0.980265\pi$
$53$	−767.791	−	2109.49i	−0.273333	−	0.750975i	0.724746	−	0.689016i	$-0.241957\pi$
$54$		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	0.879076	−	0.476683i	$-0.158161\pi$
$59$	6503.10	−	1146.67i	1.86817	−	0.329409i	0.989096	+	0.147273i	$0.0470497\pi$
$60$		0			0
$61$	5819.67	−	2118.19i	1.56401	−	0.569252i	0.592357	−	0.805676i	$-0.298198\pi$
$61$	5819.67	−	2118.19i	1.56401	−	0.569252i	0.971650	+	0.236424i	$0.0759754\pi$
$62$		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	0.840159	−	0.542341i	$-0.182462\pi$
$67$	6482.83	+	1143.10i	1.44416	+	0.254644i	0.603999	+	0.796985i	$0.293573\pi$
$68$		0			0
$69$	−4458.88	−	2574.34i	−0.936544	−	0.540714i
$70$		0			0
$71$	−1833.99	+	5038.85i	−0.363815	+	0.999574i	0.613853	+	0.789420i	$0.289619\pi$
$71$	−1833.99	+	5038.85i	−0.363815	+	0.999574i	−0.977668	+	0.210154i	$0.932603\pi$
$72$		0			0
$73$	−2417.99	+	2028.93i	−0.453741	+	0.380734i	−0.840822	−	0.541312i	$-0.817928\pi$
$73$	−2417.99	+	2028.93i	−0.453741	+	0.380734i	0.387081	+	0.922046i	$0.373483\pi$
$74$		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	0.610250	−	0.792209i	$-0.291069\pi$
$79$	−1721.85	−	2052.02i	−0.275893	−	0.328796i	−0.886142	+	0.463413i	$0.846625\pi$
$80$		0			0
$81$	1751.11	+	637.353i	0.266897	+	0.0971427i
$82$		0			0
$83$	1760.24	−	3048.83i	0.255515	−	0.442564i	−0.709521	−	0.704685i	$-0.751088\pi$
$83$	1760.24	−	3048.83i	0.255515	−	0.442564i	0.965035	+	0.262120i	$0.0844218\pi$
$84$		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	0.166956	+	0.985964i	$0.446606\pi$
$89$	−6598.36	+	7863.62i	−0.833021	+	0.992756i	−0.999977	+	0.00679184i	$0.997838\pi$
$90$		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	0.486483	−	0.873690i	$-0.338280\pi$
$97$	11690.2	−	2061.29i	1.24245	−	0.219077i	0.755964	+	0.654613i	$0.227168\pi$
$98$		0			0
$99$	2293.80	−	834.873i	0.234037	−	0.0851824i
$100$		0			0
$101$	−11664.3	−	9787.51i	−1.14345	−	0.959466i	−0.143900	−	0.989592i	$-0.545965\pi$
$101$	−11664.3	−	9787.51i	−1.14345	−	0.959466i	−0.999546	+	0.0301266i	$0.990409\pi$
$102$		0			0
$103$	6416.27	−	3704.43i	0.604795	−	0.349178i	−0.166131	−	0.986104i	$-0.553127\pi$
$103$	6416.27	−	3704.43i	0.604795	−	0.349178i	0.770925	+	0.636925i	$0.219794\pi$
$104$		0			0
$105$	37344.9	+	6584.92i	3.38730	+	0.597272i
$106$		0			0
$107$	−1560.12	−	900.738i	−0.136267	−	0.0786739i	0.430317	−	0.902678i	$-0.358402\pi$
$107$	−1560.12	−	900.738i	−0.136267	−	0.0786739i	−0.566584	+	0.824004i	$0.691735\pi$
$108$		0			0
$109$	−404.983	+	1112.68i	−0.0340866	+	0.0936523i	−0.955569	−	0.294769i	$-0.904757\pi$
$109$	−404.983	+	1112.68i	−0.0340866	+	0.0936523i	0.921482	+	0.388421i	$0.126979\pi$
$110$		0			0
$111$	7542.52	−	6328.93i	0.612168	−	0.513670i
$112$		0			0
$113$			11311.2i			0.885831i	0.896563	+	0.442915i	$0.146056\pi$
$113$			11311.2i			0.885831i	−0.896563	+	0.442915i	$0.853944\pi$
$114$		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	0.000352700		1.00000i	$0.499888\pi$
$127$	−15879.3	+	18924.2i	−0.984516	+	1.17330i	−0.984869	+	0.173301i	$0.944557\pi$
$128$		0			0
$129$	−16639.5	−	45716.7i	−0.999912	−	2.74724i
$130$		0			0
$131$	2841.19	+	16113.2i	0.165561	+	0.938942i	0.948484	+	0.316824i	$0.102616\pi$
$131$	2841.19	+	16113.2i	0.165561	+	0.938942i	−0.782924	+	0.622118i	$0.786273\pi$
$132$		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	−0.384922	−	0.922949i	$-0.625772\pi$
$137$	−1624.05	+	591.107i	−0.0865285	+	0.0314938i	0.298393	+	0.954443i	$0.403549\pi$
$138$		0			0
$139$	2634.82	+	2210.87i	0.136371	+	0.114429i	0.708422	−	0.705790i	$-0.249408\pi$
$139$	2634.82	+	2210.87i	0.136371	+	0.114429i	−0.572051	+	0.820218i	$0.693852\pi$
$140$		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	−0.854193	−	0.519956i	$-0.825948\pi$
$149$	−10888.8	+	9136.81i	−0.490466	+	0.411550i	0.363727	+	0.931505i	$0.381504\pi$
$150$		0			0
$151$			13297.5i			0.583199i	0.956540	+	0.291600i	$0.0941875\pi$
$151$			13297.5i			0.583199i	−0.956540	+	0.291600i	$0.905813\pi$
$152$		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	0.278963	−	0.960302i	$-0.410009\pi$
$157$	−3071.50	−	1117.94i	−0.124610	−	0.0453542i	−0.403572	+	0.914948i	$0.632232\pi$
$158$		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	0.839511	−	0.543342i	$-0.182841\pi$
$163$	−1349.50	−	2337.40i	−0.0507923	−	0.0879749i	−0.890304	+	0.455367i	$0.849508\pi$
$164$		0			0
$165$	6194.49	−	7382.31i	0.227530	−	0.271159i
$166$		0			0
$167$	3277.80	+	9005.69i	0.117530	+	0.322912i	0.984483	−	0.175478i	$-0.0561470\pi$
$167$	3277.80	+	9005.69i	0.117530	+	0.322912i	−0.866953	+	0.498390i	$0.833925\pi$
$168$		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	−0.345087	−	0.938571i	$-0.612151\pi$
$173$	−10425.9	+	1838.36i	−0.348354	+	0.0614241i	−0.00326608	+	0.999995i	$0.501040\pi$
$174$		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	−0.849772	−	0.527150i	$-0.823260\pi$
$179$	−26213.8	+	15134.5i	−0.818132	+	0.472349i	0.0316398	+	0.999499i	$0.489927\pi$
$180$		0			0
$181$	−22735.5	−	4008.87i	−0.693979	−	0.122367i	−0.184477	−	0.982837i	$-0.559059\pi$
$181$	−22735.5	−	4008.87i	−0.693979	−	0.122367i	−0.509502	+	0.860469i	$0.670170\pi$
$182$		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	0.801046	−	0.598603i	$-0.204277\pi$
$193$	2698.18	+	3215.56i	0.0724362	+	0.0863261i	−0.728609	+	0.684929i	$0.759833\pi$
$194$		0			0
$195$	−70086.9	−	25509.5i	−1.84318	−	0.670862i
$196$		0			0
$197$	13290.6	−	23019.9i	0.342461	−	0.593159i	−0.642428	−	0.766346i	$-0.722073\pi$
$197$	13290.6	−	23019.9i	0.342461	−	0.593159i	0.984889	+	0.173186i	$0.0554063\pi$
$198$		0			0
$199$	−3824.40	+	21689.2i	−0.0965732	+	0.547694i	0.897681	+	0.440647i	$0.145251\pi$
$199$	−3824.40	+	21689.2i	−0.0965732	+	0.547694i	−0.994254	+	0.107047i	$0.965860\pi$
$200$		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	0.825408	−	0.564537i	$-0.190945\pi$
$211$	79876.0	−	14084.3i	1.79412	−	0.316352i	0.968713	+	0.248185i	$0.0798342\pi$
$212$		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	−0.752671	−	0.658397i	$-0.771235\pi$
$223$	12288.9	−	33763.5i	0.247118	−	0.678950i	0.999789	−	0.0205533i	$-0.00654279\pi$
$224$		0			0
$225$	−45365.8	+	38066.5i	−0.896115	+	0.751930i
$226$		0			0
$227$		−	12563.2i		−	0.243808i	−0.992542	−	0.121904i	$-0.961100\pi$
$227$		−	12563.2i		−	0.243808i	0.992542	−	0.121904i	$-0.0389000\pi$
$228$		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	−0.163149	−	0.986602i	$-0.552165\pi$
$233$	−50070.9	−	18224.3i	−0.922303	−	0.335691i	−0.759154	+	0.650911i	$0.774387\pi$
$234$		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	0.837283	+	0.546770i	$0.184143\pi$
$239$	50961.0	+	88267.0i	0.892158	+	1.54526i	0.0548758	+	0.998493i	$0.482524\pi$
$240$		0			0
$241$	17732.2	−	21132.4i	0.305301	−	0.363843i	−0.591479	−	0.806320i	$-0.701456\pi$
$241$	17732.2	−	21132.4i	0.305301	−	0.363843i	0.896780	+	0.442477i	$0.145900\pi$
$242$		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	−0.193705	−	0.981060i	$-0.562050\pi$
$251$	18177.2	−	6615.95i	0.288522	−	0.105013i	0.482227	+	0.876046i	$0.339828\pi$
$252$		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	0.107117	−	0.994246i	$-0.465838\pi$
$257$	−8736.84	−	1540.54i	−0.132278	−	0.0233242i	−0.239395	+	0.970922i	$0.576949\pi$
$258$		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	−0.975691	−	0.219150i	$-0.929672\pi$
$263$	−64278.6	+	53936.1i	−0.929298	+	0.779773i	0.0463935	+	0.998923i	$0.485227\pi$
$264$		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	0.933786	−	0.357833i	$-0.116484\pi$
$269$	30336.6	+	36153.7i	0.419239	+	0.499630i	−0.514547	+	0.857462i	$0.672040\pi$
$270$		0			0
$271$	34101.1	+	12411.8i	0.464333	+	0.169003i	0.563584	−	0.826059i	$-0.309422\pi$
$271$	34101.1	+	12411.8i	0.464333	+	0.169003i	−0.0992505	+	0.995062i	$0.531645\pi$
$272$		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	0.875631	−	0.482981i	$-0.160446\pi$
$277$	1499.37	+	2596.99i	0.0195412	+	0.0338463i	−0.856089	+	0.516828i	$0.827113\pi$
$278$		0			0
$279$	−79290.9	+	94495.2i	−1.01863	+	1.21395i
$280$		0			0
$281$	−37837.4	−	103957.i	−0.479191	−	1.31657i	−0.910182	−	0.414209i	$-0.864058\pi$
$281$	−37837.4	−	103957.i	−0.479191	−	1.31657i	0.430991	−	0.902356i	$-0.358164\pi$
$282$		0			0
$283$	−21586.7	−	122424.i	−0.269534	−	1.52860i	−0.755806	−	0.654796i	$-0.772755\pi$
$283$	−21586.7	−	122424.i	−0.269534	−	1.52860i	0.486272	−	0.873807i	$-0.338356\pi$
$284$		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	−0.503461	−	0.864018i	$-0.667940\pi$
$293$	−595.018	+	343.534i	−0.00693098	+	0.00400160i	0.496531	+	0.868019i	$0.334607\pi$
$294$		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	0.783984	−	0.620781i	$-0.213184\pi$
$307$	3439.79	+	4099.38i	0.0364968	+	0.0434953i	−0.747487	+	0.664276i	$0.768740\pi$
$308$		0			0
$309$	98731.2	+	35935.2i	1.03404	+	0.376360i
$310$		0			0
$311$	66863.5	−	115811.i	0.691303	−	1.19737i	−0.280108	−	0.959968i	$-0.590370\pi$
$311$	66863.5	−	115811.i	0.691303	−	1.19737i	0.971411	−	0.237404i	$-0.0762964\pi$
$312$		0			0
$313$	44.4220	−	251.930i	0.000453430	−	0.00257153i	−0.984580	−	0.174934i	$-0.944029\pi$
$313$	44.4220	−	251.930i	0.000453430	−	0.00257153i	0.985034	+	0.172362i	$0.0551400\pi$
$314$		0			0
$315$	160588.	+	278146.i	1.61842	+	2.80319i
$316$		0			0
$317$	47164.2	−	56208.1i	0.469347	−	0.559346i	−0.478493	−	0.878091i	$-0.658817\pi$
$317$	47164.2	−	56208.1i	0.469347	−	0.559346i	0.947840	+	0.318745i	$0.103261\pi$
$318$		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	−0.257621	−	0.966246i	$-0.582939\pi$
$331$	49342.1	−	28487.7i	0.450362	−	0.260016i	0.707983	+	0.706230i	$0.249605\pi$
$332$		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	0.712304	+	0.701871i	$0.247652\pi$
$337$	−32311.1	+	88774.1i	−0.284507	+	0.781675i	−0.996811	+	0.0798043i	$0.974570\pi$
$338$		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	0.495557	−	0.868575i	$-0.334964\pi$
$347$	38153.7	+	13886.8i	0.316867	+	0.115330i	−0.178690	+	0.983905i	$0.557186\pi$
$348$		0			0
$349$	−117786.	+	204011.i	−0.967036	+	1.67495i	−0.262992	+	0.964798i	$0.584709\pi$
$349$	−117786.	+	204011.i	−0.967036	+	1.67495i	−0.704043	+	0.710157i	$0.748624\pi$
$350$		0			0
$351$	15148.8	−	85913.0i	0.122960	−	0.697340i
$352$		0			0
$353$	−45139.8	−	78184.5i	−0.362252	−	0.627439i	0.626079	−	0.779759i	$-0.284659\pi$
$353$	−45139.8	−	78184.5i	−0.362252	−	0.627439i	−0.988331	+	0.152321i	$0.951325\pi$
$354$		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	0.826223	+	0.563343i	$0.190485\pi$
$359$	31253.9	+	177250.i	0.242502	+	1.37530i	−0.583721	+	0.811954i	$0.698404\pi$
$360$		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	0.581056	−	0.813863i	$-0.302640\pi$
$367$	−16101.2	−	13510.5i	−0.119543	−	0.100309i	−0.700600	+	0.713555i	$0.747084\pi$
$368$		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	0.837012	−	0.547185i	$-0.184300\pi$
$373$	108749.	+	62786.3i	0.781642	+	0.451281i	−0.0553697	+	0.998466i	$0.517634\pi$
$374$		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	$-0.924264\pi$
$379$		−	67710.3i		−	0.471385i	0.971828	−	0.235693i	$-0.0757359\pi$
$380$		0			0
$381$	−350332.			−2.41340
$382$		0			0
$383$	−70745.6	−	84311.4i	−0.482283	−	0.574763i	0.468954	−	0.883223i	$-0.344631\pi$
$383$	−70745.6	−	84311.4i	−0.482283	−	0.574763i	−0.951237	+	0.308460i	$0.900186\pi$
$384$		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	0.618327	+	0.785921i	$0.287811\pi$
$389$	−35032.5	+	198679.i	−0.231511	+	1.31296i	−0.849838	+	0.527043i	$0.823301\pi$
$390$		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	0.992828	−	0.119549i	$-0.0381448\pi$
$397$	2992.49	+	16971.2i	0.0189868	+	0.107679i	−0.973842	+	0.227228i	$0.927034\pi$
$398$		0			0
$399$	−127025.	+	389203.i	−0.797889	+	2.44473i
$400$		0			0
$401$	−35490.2	+	6257.89i	−0.220709	+	0.0389170i	−0.282909	−	0.959147i	$-0.591299\pi$
$401$	−35490.2	+	6257.89i	−0.220709	+	0.0389170i	0.0622000	+	0.998064i	$0.480188\pi$
$402$		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	0.643462	−	0.765478i	$-0.277498\pi$
$409$	164991.	+	29092.3i	0.986309	+	0.173913i	0.342847	+	0.939391i	$0.388609\pi$
$410$		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	0.762808	−	0.646625i	$-0.223820\pi$
$421$	−1143.71	−	1363.01i	−0.00645283	−	0.00769018i	−0.769261	+	0.638934i	$0.779376\pi$
$422$		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	0.0171038	+	0.999854i	$0.494555\pi$
$431$	−180287.	+	214857.i	−0.970530	+	1.15663i	−0.987634	+	0.156779i	$0.949889\pi$
$432$		0			0
$433$	106300.	+	292057.i	0.566968	+	1.55773i	0.809213	+	0.587516i	$0.199894\pi$
$433$	106300.	+	292057.i	0.566968	+	1.55773i	−0.242245	+	0.970215i	$0.577884\pi$
$434$		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	−0.137506	−	0.990501i	$-0.543908\pi$
$439$	13886.1	−	2448.49i	0.0720528	−	0.0127049i	0.209558	+	0.977796i	$0.432797\pi$
$440$		0			0
$441$	450827.	−	164088.i	2.31811	−	0.843721i
$442$		0			0
$443$	−121549.	−	101992.i	−0.619363	−	0.519708i	0.278240	−	0.960512i	$-0.410249\pi$
$443$	−121549.	−	101992.i	−0.619363	−	0.519708i	−0.897603	+	0.440804i	$0.854693\pi$
$444$		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	0.195370	−	0.980730i	$-0.437409\pi$
$449$	−112147.	−	64748.0i	−0.556281	−	0.321169i	−0.751652	+	0.659560i	$0.770742\pi$
$450$		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	−0.636631	−	0.771168i	$-0.719673\pi$
$461$	−344288.	−	125310.i	−1.62002	−	0.589638i	−0.983385	+	0.181531i	$0.941895\pi$
$462$		0			0
$463$	−75550.3	+	130857.i	−0.352431	+	0.610428i	−0.986675	−	0.162705i	$-0.947978\pi$
$463$	−75550.3	+	130857.i	−0.352431	+	0.610428i	0.634244	+	0.773133i	$0.281312\pi$
$464$		0			0
$465$	−84565.9	+	479597.i	−0.391102	+	2.21805i
$466$		0			0
$467$	54139.2	+	93771.8i	0.248243	+	0.429970i	0.963039	−	0.269364i	$-0.0868134\pi$
$467$	54139.2	+	93771.8i	0.248243	+	0.429970i	−0.714795	+	0.699334i	$0.753480\pi$
$468$		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	−0.334468	−	0.942407i	$-0.608557\pi$
$479$	3460.44	−	1259.50i	0.0150820	−	0.00548941i	0.349550	+	0.936918i	$0.386334\pi$
$480$		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	−0.0591348	−	0.998250i	$-0.518834\pi$
$487$	−226072.	−	130523.i	−0.953212	−	0.550337i	−0.894077	+	0.447913i	$0.852168\pi$
$488$		0			0
$489$	13091.0	−	35967.1i	0.0547462	−	0.150414i
$490$		0			0
$491$	186984.	−	156898.i	0.775607	−	0.650812i	−0.166531	−	0.986036i	$-0.553257\pi$
$491$	186984.	−	156898.i	0.775607	−	0.650812i	0.942138	+	0.335224i	$0.108812\pi$
$492$		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	−0.272682	−	0.962104i	$-0.587911\pi$
$499$	−273900.	−	99691.6i	−1.10000	−	0.400366i	−0.827315	+	0.561738i	$0.810133\pi$
$500$		0			0
$501$	−67954.5	+	117701.i	−0.270734	+	0.468925i
$502$		0			0
$503$	28729.7	−	162934.i	0.113552	−	0.643986i	−0.873905	−	0.486097i	$-0.838420\pi$
$503$	28729.7	−	162934.i	0.113552	−	0.643986i	0.987457	−	0.157889i	$-0.0504689\pi$
$504$		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	0.999497	−	0.0317215i	$-0.0100990\pi$
$509$	55300.2	+	151936.i	0.213448	+	0.586443i	−0.786049	+	0.618164i	$0.787877\pi$
$510$		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	−0.660537	−	0.750793i	$-0.729671\pi$
$521$	−92452.8	+	53377.6i	−0.340600	+	0.196645i	0.319937	+	0.947439i	$0.396338\pi$
$522$		0			0
$523$	522060.	+	92053.2i	1.90861	+	0.336539i	0.997188	−	0.0749394i	$-0.0238763\pi$
$523$	522060.	+	92053.2i	1.90861	+	0.336539i	0.911419	+	0.411478i	$0.134987\pi$
$524$		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	−0.876052	−	0.482216i	$-0.839832\pi$
$541$	32808.2	−	186064.i	0.112095	−	0.635724i	0.988147	−	0.153508i	$-0.0490570\pi$
$542$		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	0.813718	−	0.581260i	$-0.197440\pi$
$547$	−54831.0	−	150647.i	−0.183253	−	0.503484i	−0.996971	+	0.0777765i	$0.975218\pi$
$548$		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	0.799063	−	0.601247i	$-0.205329\pi$
$557$	107255.	+	89997.5i	0.345706	+	0.290082i	−0.453357	+	0.891329i	$0.649774\pi$
$558$		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	0.295578	−	0.955319i	$-0.404488\pi$
$563$	−121704.	−	70266.1i	−0.383963	−	0.221681i	−0.679541	+	0.733637i	$0.737821\pi$
$564$		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	$0.126330\pi$
$569$			250293.i			0.773080i	−0.922273	+	0.386540i	$0.873670\pi$
$570$		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	−0.936837	−	0.349767i	$-0.886261\pi$
$577$	−55103.4	+	95442.0i	−0.165511	+	0.286674i	0.771326	+	0.636441i	$0.219594\pi$
$578$		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	−0.796299	−	0.604903i	$-0.793212\pi$
$587$	−87834.7	−	498135.i	−0.254912	−	1.44568i	0.541387	−	0.840773i	$-0.317899\pi$
$588$		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	−0.594741	−	0.803917i	$-0.702745\pi$
$593$	−187637.	+	68294.1i	−0.533591	+	0.194211i	0.0611503	+	0.998129i	$0.480523\pi$
$594$		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	−0.821646	−	0.569998i	$-0.806944\pi$
$599$	−641784.	−	113164.i	−1.78869	−	0.315395i	−0.967046	+	0.254604i	$0.918055\pi$
$600$		0			0
$601$	−372533.	−	215082.i	−1.03137	−	0.595464i	−0.113996	−	0.993481i	$-0.536365\pi$
$601$	−372533.	−	215082.i	−1.03137	−	0.595464i	−0.917378	+	0.398018i	$0.869698\pi$
$602$		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	$0.0685374\pi$
$607$			157443.i			0.427314i	−0.976909	+	0.213657i	$0.931463\pi$
$608$		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	0.824235	−	0.566248i	$-0.191606\pi$
$613$	410211.	+	149305.i	1.09166	+	0.397331i	0.267423	+	0.963579i	$0.413828\pi$
$614$		0			0
$615$	390986.	−	677208.i	1.03374	−	1.79049i
$616$		0			0
$617$	102238.	−	579819.i	0.268560	−	1.52308i	−0.490143	−	0.871642i	$-0.663056\pi$
$617$	102238.	−	579819.i	0.268560	−	1.52308i	0.758703	−	0.651437i	$-0.225833\pi$
$618$		0			0
$619$	205858.	+	356557.i	0.537263	+	0.930568i	0.999050	+	0.0435765i	$0.0138752\pi$
$619$	205858.	+	356557.i	0.537263	+	0.930568i	−0.461787	+	0.886991i	$0.652791\pi$
$620$		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	−0.261506	−	0.965202i	$-0.584219\pi$
$631$	63143.6	−	22982.4i	0.158588	−	0.0577214i	0.420094	+	0.907480i	$0.361997\pi$
$632$		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	−0.948905	−	0.315563i	$-0.897807\pi$
$641$	−7873.10	+	21631.2i	−0.0191615	+	0.0526458i	0.929743	+	0.368209i	$0.120029\pi$
$642$		0			0
$643$	41981.6	−	35226.7i	0.101540	−	0.0852021i	−0.590604	−	0.806961i	$-0.701111\pi$
$643$	41981.6	−	35226.7i	0.101540	−	0.0852021i	0.692144	+	0.721759i	$0.256666\pi$
$644$		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	−0.426215	−	0.904622i	$-0.640153\pi$
$653$	243189.	−	421215.i	0.570318	−	0.987819i	0.996533	−	0.0831976i	$-0.0265133\pi$
$654$		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	−0.916951	−	0.399000i	$-0.869357\pi$
$659$	−158420.	+	188797.i	−0.364786	+	0.434735i	0.552165	+	0.833735i	$0.313802\pi$
$660$		0			0
$661$	239119.	+	656975.i	0.547283	+	1.50365i	0.837365	+	0.546645i	$0.184095\pi$
$661$	239119.	+	656975.i	0.547283	+	1.50365i	−0.290082	+	0.957002i	$0.593683\pi$
$662$		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	0.340906	−	0.940097i	$-0.389266\pi$
$673$	600361.	−	346618.i	1.32551	−	0.765282i	0.984601	+	0.174815i	$0.0559328\pi$
$674$		0			0
$675$	−269310.	−	47486.6i	−0.591078	−	0.104223i
$676$		0			0
$677$	205564.	+	118683.i	0.448508	+	0.258946i	0.707200	−	0.707013i	$-0.249958\pi$
$677$	205564.	+	118683.i	0.448508	+	0.258946i	−0.258692	+	0.965960i	$0.583291\pi$
$678$		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	$-0.794360\pi$
$683$		−	561678.i		−	1.20405i	0.798476	−	0.602027i	$-0.205640\pi$
$684$		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	−0.977144	−	0.212577i	$-0.931814\pi$
$691$	−145381.	+	251808.i	−0.304475	+	0.527367i	0.672669	+	0.739944i	$0.265148\pi$
$692$		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	0.901914	+	0.431916i	$0.142162\pi$
$701$	99320.0	+	563272.i	0.202116	+	1.14626i	−0.699798	+	0.714341i	$0.746727\pi$
$702$		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	0.564716	−	0.825285i	$-0.308986\pi$
$709$	−75386.6	−	63256.9i	−0.149969	−	0.125839i	−0.714685	+	0.699446i	$0.753430\pi$
$710$		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	−0.799818	−	0.600242i	$-0.795071\pi$
$719$	−179686.	+	150775.i	−0.347582	+	0.291656i	0.452236	+	0.891898i	$0.350626\pi$
$720$		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	0.674307	−	0.738452i	$-0.264443\pi$
$727$	378526.	+	137772.i	0.716188	+	0.260671i	0.0418813	+	0.999123i	$0.486665\pi$
$728$		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	0.852916	−	0.522049i	$-0.174832\pi$
$733$	−13781.4	−	23870.1i	−0.0256499	−	0.0444269i	−0.878565	+	0.477622i	$0.841499\pi$
$734$		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	−0.995424	−	0.0955586i	$-0.969536\pi$
$739$	−50633.3	−	287155.i	−0.0927144	−	0.525809i	0.902709	−	0.430251i	$-0.141575\pi$
$740$		0			0
$741$	378971.	−	710490.i	0.690191	−	1.29396i
$742$		0			0
$743$	96689.8	−	17049.0i	0.175147	−	0.0308832i	−0.0853867	−	0.996348i	$-0.527213\pi$
$743$	96689.8	−	17049.0i	0.175147	−	0.0308832i	0.260534	+	0.965465i	$0.416101\pi$
$744$		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	0.308248	−	0.951306i	$-0.400257\pi$
$751$	153713.	+	27103.8i	0.272541	+	0.0480563i	−0.0357074	+	0.999362i	$0.511368\pi$
$752$		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	−0.441966	−	0.897032i	$-0.645719\pi$
$757$	208986.	−	175360.i	0.364690	−	0.306012i	0.806657	+	0.591020i	$0.201275\pi$
$758$		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	−0.655452	−	0.755237i	$-0.727522\pi$
$769$	129377.	−	733731.i	0.218778	−	1.24075i	0.874229	−	0.485513i	$-0.161367\pi$
$770$		0			0
$771$	−62905.7	−	108956.i	−0.105823	−	0.183291i
$772$		0			0
$773$	29794.7	−	35507.9i	0.0498632	−	0.0594246i	−0.740536	−	0.672016i	$-0.765429\pi$
$773$	29794.7	−	35507.9i	0.0498632	−	0.0594246i	0.790400	+	0.612592i	$0.209873\pi$
$774$		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	−0.0388875	−	0.999244i	$-0.512381\pi$
$787$	499855.	−	288591.i	0.807039	−	0.465944i	0.845927	+	0.533299i	$0.179048\pi$
$788$		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	$-0.695063\pi$
$797$		−	1.03925e6i		−	1.63607i	0.575168	−	0.818035i	$-0.304937\pi$
$798$		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	0.607751	−	0.794128i	$-0.292072\pi$
$809$	−251229.	−	435141.i	−0.383859	−	0.664864i	−0.991610	+	0.129264i	$0.958739\pi$
$810$		0			0
$811$	−185811.	+	221441.i	−0.282507	+	0.336679i	−0.888573	−	0.458736i	$-0.848303\pi$
$811$	−185811.	+	221441.i	−0.282507	+	0.336679i	0.606065	+	0.795415i	$0.292747\pi$
$812$		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	−0.906088	−	0.423089i	$-0.860946\pi$
$821$	−895285.	+	325857.i	−1.32824	+	0.483438i	−0.422147	+	0.906527i	$0.638723\pi$
$822$		0			0
$823$	−509070.	−	427160.i	−0.751585	−	0.630654i	0.184337	−	0.982863i	$-0.440986\pi$
$823$	−509070.	−	427160.i	−0.751585	−	0.630654i	−0.935921	+	0.352209i	$0.885431\pi$
$824$		0			0
$825$	123065.	−	71051.3i	0.180811	−	0.104391i
$826$		0			0
$827$	−269084.	−	47446.7i	−0.393438	−	0.0693737i	−0.0265705	−	0.999647i	$-0.508459\pi$
$827$	−269084.	−	47446.7i	−0.393438	−	0.0693737i	−0.366867	+	0.930273i	$0.619570\pi$
$828$		0			0
$829$	−1.08114e6	−	624199.i	−1.57317	−	0.908268i	−0.995778	−	0.0917977i	$-0.970739\pi$
$829$	−1.08114e6	−	624199.i	−1.57317	−	0.908268i	−0.577388	−	0.816470i	$-0.695928\pi$
$830$		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	0.998850	−	0.0479476i	$-0.0152680\pi$
$839$	547779.	+	652817.i	0.778182	+	0.927401i	−0.220668	+	0.975349i	$0.570824\pi$
$840$		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	−0.904848	−	0.425735i	$-0.860015\pi$
$853$	−145652.	−	826034.i	−0.200179	−	1.13527i	0.704669	−	0.709536i	$-0.251096\pi$
$854$		0			0
$855$	−766681.	−	1.23054e6i	−1.04877	−	1.68330i
$856$		0			0
$857$	874055.	−	154120.i	1.19008	−	0.209844i	0.456676	−	0.889633i	$-0.349040\pi$
$857$	874055.	−	154120.i	1.19008	−	0.209844i	0.733407	+	0.679789i	$0.237929\pi$
$858$		0			0
$859$	754617.	−	274658.i	1.02268	−	0.372225i	0.224391	−	0.974499i	$-0.427961\pi$
$859$	754617.	−	274658.i	1.02268	−	0.372225i	0.798290	+	0.602274i	$0.205738\pi$
$860$		0			0
$861$	−1.43267e6	−	1.20215e6i	−1.93259	−	1.62163i
$862$		0			0
$863$	786801.	−	454260.i	1.05644	−	0.609934i	0.131992	−	0.991251i	$-0.457863\pi$
$863$	786801.	−	454260.i	1.05644	−	0.609934i	0.924444	+	0.381317i	$0.124529\pi$
$864$		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	0.923606	+	0.383344i	$0.125228\pi$
$877$	877379.	+	1.04562e6i	1.14074	+	1.35948i	0.217138	+	0.976141i	$0.430328\pi$
$878$		0			0
$879$	−9155.92	−	3332.48i	−0.0118502	−	0.00431311i
$880$		0			0
$881$	97934.9	−	169628.i	0.126179	−	0.218548i	−0.796014	−	0.605278i	$-0.793062\pi$
$881$	97934.9	−	169628.i	0.126179	−	0.218548i	0.922193	+	0.386730i	$0.126395\pi$
$882$		0			0
$883$	39626.9	−	224735.i	0.0508240	−	0.288237i	−0.948793	−	0.315897i	$-0.897694\pi$
$883$	39626.9	−	224735.i	0.0508240	−	0.288237i	0.999617	+	0.0276601i	$0.00880560\pi$
$884$		0			0
$885$	1.56563e6	+	2.71174e6i	1.99895	+	3.46228i
$886$		0			0
$887$	−207235.	+	246973.i	−0.263400	+	0.313907i	−0.881493	−	0.472197i	$-0.843461\pi$
$887$	−207235.	+	246973.i	−0.263400	+	0.313907i	0.618093	+	0.786105i	$0.287905\pi$
$888$		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	−0.840009	−	0.542572i	$-0.817451\pi$
$907$	125235.	−	344080.i	0.152234	−	0.418258i	0.992243	+	0.124314i	$0.0396729\pi$
$908$		0			0
$909$	1.40100e6	−	1.17558e6i	1.69555	−	1.42273i
$910$		0			0
$911$		−	701763.i		−	0.845578i	−0.906228	−	0.422789i	$-0.861051\pi$
$911$		−	701763.i		−	0.845578i	0.906228	−	0.422789i	$-0.138949\pi$
$912$		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	−0.927869	−	0.372905i	$-0.878362\pi$
$919$	−119074.	+	206242.i	−0.140989	+	0.244200i	0.786880	+	0.617106i	$0.211695\pi$
$920$		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	−0.779766	−	0.626071i	$-0.784662\pi$
$929$	−225387.	−	1.27823e6i	−0.261155	−	1.48108i	0.518611	−	0.855010i	$-0.326449\pi$
$930$		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	0.491538	−	0.870856i	$-0.336435\pi$
$937$	−246475.	−	206817.i	−0.280733	−	0.235563i	−0.772271	+	0.635293i	$0.780879\pi$
$938$		0			0
$939$	3141.78	−	1813.91i	0.00356324	−	0.00205724i
$940$		0			0
$941$	1.38888e6	+	244897.i	1.56850	+	0.276570i	0.889281	−	0.457362i	$-0.151206\pi$
$941$	1.38888e6	+	244897.i	1.56850	+	0.276570i	0.679223	+	0.733932i	$0.262317\pi$
$942$		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	0.144814	−	0.989459i	$-0.453742\pi$
$947$	1.02630e6	−	861165.i	1.14439	−	0.960255i	0.999573	+	0.0292042i	$0.00929730\pi$
$948$		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	−0.999390	−	0.0349142i	$-0.988884\pi$
$953$	−781270.	−	931082.i	−0.860232	−	1.02518i	0.139159	−	0.990270i	$-0.455560\pi$
$954$		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	0.986689	+	0.162616i	$0.0519932\pi$
$967$	107650.	+	610513.i	0.115123	+	0.652893i	−0.871567	+	0.490277i	$0.836896\pi$
$968$		0			0
$969$	707441.	+	1.75761e6i	0.753429	+	1.87187i
$970$		0			0
$971$	−1.30408e6	+	229944.i	−1.38314	+	0.243884i	−0.815196	−	0.579185i	$-0.803371\pi$
$971$	−1.30408e6	+	229944.i	−1.38314	+	0.243884i	−0.567941	+	0.823069i	$0.692260\pi$
$972$		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	−0.261536	−	0.965194i	$-0.584229\pi$
$977$	423409.	−	244455.i	0.443579	−	0.256100i	0.705114	+	0.709094i	$0.250896\pi$
$978$		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	−0.999782	−	0.0208850i	$-0.993352\pi$
$983$	−213047.	+	585343.i	−0.220480	+	0.605764i	0.779302	+	0.626649i	$0.215574\pi$
$984$		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	0.651820	−	0.758374i	$-0.274006\pi$
$991$	−204489.	−	243700.i	−0.208220	−	0.248147i	−0.860040	+	0.510227i	$0.829561\pi$
$992$		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	0.264978	+	0.964255i	$0.414635\pi$
$997$	−311934.	+	1.76907e6i	−0.313814	+	1.77973i	−0.578792	+	0.815475i	$0.696476\pi$
$998$		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.29.6	yes	42
19.2	odd	18	inner	76.5.j.a.21.6	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.21.6	✓	42	19.2	odd	18	inner
76.5.j.a.29.6	yes	42	1.1	even	1	trivial

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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