LMFDB - Embedded newform 76.5.j.a.29.3

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			29.3
Character	$\chi$	$=$	76.29
Dual form			76.5.j.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.504186 - 0.600866i) q^{3} +(-8.75235 - 3.18559i) q^{5} +(-3.87876 + 6.71820i) q^{7} +(13.9587 - 79.1635i) q^{9} +O(q^{10})$	\(q+(-0.504186 - 0.600866i) q^{3} +(-8.75235 - 3.18559i) q^{5} +(-3.87876 + 6.71820i) q^{7} +(13.9587 - 79.1635i) q^{9} +(-94.7123 - 164.047i) q^{11} +(-152.490 + 181.730i) q^{13} +(2.49870 + 6.86512i) q^{15} +(-73.3453 - 415.962i) q^{17} +(171.374 - 317.729i) q^{19} +(5.99236 - 1.05661i) q^{21} +(-669.617 + 243.721i) q^{23} +(-412.322 - 345.979i) q^{25} +(-109.627 + 63.2931i) q^{27} +(1556.26 + 274.410i) q^{29} +(-389.047 - 224.616i) q^{31} +(-50.8173 + 139.619i) q^{33} +(55.3497 - 46.4439i) q^{35} +923.124i q^{37} +186.079 q^{39} +(1592.45 + 1897.81i) q^{41} +(374.881 + 136.446i) q^{43} +(-374.354 + 648.400i) q^{45} +(189.007 - 1071.91i) q^{47} +(1170.41 + 2027.21i) q^{49} +(-212.957 + 253.793i) q^{51} +(-293.848 - 807.340i) q^{53} +(306.370 + 1737.51i) q^{55} +(-277.317 + 57.2217i) q^{57} +(-2307.63 + 406.897i) q^{59} +(5176.31 - 1884.02i) q^{61} +(477.695 + 400.833i) q^{63} +(1913.56 - 1104.80i) q^{65} +(-6476.74 - 1142.02i) q^{67} +(484.055 + 279.469i) q^{69} +(877.159 - 2409.97i) q^{71} +(-3639.17 + 3053.62i) q^{73} +422.188i q^{75} +1469.46 q^{77} +(-7424.75 - 8848.48i) q^{79} +(-6025.19 - 2192.99i) q^{81} +(5155.43 - 8929.47i) q^{83} +(-683.142 + 3874.29i) q^{85} +(-619.759 - 1073.45i) q^{87} +(1402.20 - 1671.08i) q^{89} +(-629.430 - 1729.35i) q^{91} +(61.1878 + 347.013i) q^{93} +(-2512.09 + 2234.95i) q^{95} +(6417.59 - 1131.59i) q^{97} +(-14308.6 + 5207.89i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.504186	−	0.600866i	−0.0560207	−	0.0667629i	0.737306	−	0.675558i	$-0.236097\pi$
$3$	−0.504186	−	0.600866i	−0.0560207	−	0.0667629i	−0.793327	+	0.608796i	$0.791653\pi$
$4$		0			0
$5$	−8.75235	−	3.18559i	−0.350094	−	0.127424i	0.160987	−	0.986957i	$-0.448532\pi$
$5$	−8.75235	−	3.18559i	−0.350094	−	0.127424i	−0.511081	+	0.859533i	$0.670755\pi$
$6$		0			0
$7$	−3.87876	+	6.71820i	−0.0791583	+	0.137106i	−0.902887	−	0.429878i	$-0.858557\pi$
$7$	−3.87876	+	6.71820i	−0.0791583	+	0.137106i	0.823729	+	0.566984i	$0.191890\pi$
$8$		0			0
$9$	13.9587	−	79.1635i	0.172329	−	0.977328i
$10$		0			0
$11$	−94.7123	−	164.047i	−0.782746	−	1.35576i	−0.930336	−	0.366708i	$-0.880485\pi$
$11$	−94.7123	−	164.047i	−0.782746	−	1.35576i	0.147590	−	0.989049i	$-0.452849\pi$
$12$		0			0
$13$	−152.490	+	181.730i	−0.902307	+	1.07533i	0.0945038	+	0.995524i	$0.469874\pi$
$13$	−152.490	+	181.730i	−0.902307	+	1.07533i	−0.996811	+	0.0798029i	$0.974571\pi$
$14$		0			0
$15$	2.49870	+	6.86512i	0.0111053	+	0.0305117i
$16$		0			0
$17$	−73.3453	−	415.962i	−0.253790	−	1.43931i	−0.799160	−	0.601118i	$-0.794722\pi$
$17$	−73.3453	−	415.962i	−0.253790	−	1.43931i	0.545370	−	0.838195i	$-0.316389\pi$
$18$		0			0
$19$	171.374	−	317.729i	0.474721	−	0.880136i
$19$	171.374	−	317.729i	0.474721	−	0.880136i
$20$		0			0
$21$	5.99236	−	1.05661i	0.0135881	−	0.00239595i
$22$		0			0
$23$	−669.617	+	243.721i	−1.26582	+	0.460720i	−0.885717	−	0.464226i	$-0.846333\pi$
$23$	−669.617	+	243.721i	−1.26582	+	0.460720i	−0.380100	+	0.924945i	$0.624110\pi$
$24$		0			0
$25$	−412.322	−	345.979i	−0.659715	−	0.553567i
$26$		0			0
$27$	−109.627	+	63.2931i	−0.150380	+	0.0868217i
$28$		0			0
$29$	1556.26	+	274.410i	1.85048	+	0.326290i	0.984717	−	0.174160i	$-0.0557211\pi$
$29$	1556.26	+	274.410i	1.85048	+	0.326290i	0.865765	+	0.500450i	$0.166832\pi$
$30$		0			0
$31$	−389.047	−	224.616i	−0.404835	−	0.233732i	0.283733	−	0.958903i	$-0.408427\pi$
$31$	−389.047	−	224.616i	−0.404835	−	0.233732i	−0.688568	+	0.725172i	$0.741760\pi$
$32$		0			0
$33$	−50.8173	+	139.619i	−0.0466642	+	0.128209i
$34$		0			0
$35$	55.3497	−	46.4439i	0.0451834	−	0.0379134i
$36$		0			0
$37$			923.124i			0.674305i	0.941450	+	0.337153i	$0.109464\pi$
$37$			923.124i			0.674305i	−0.941450	+	0.337153i	$0.890536\pi$
$38$		0			0
$39$	186.079			0.122340
$40$		0			0
$41$	1592.45	+	1897.81i	0.947322	+	1.12897i	0.991520	+	0.129952i	$0.0414822\pi$
$41$	1592.45	+	1897.81i	0.947322	+	1.12897i	−0.0441984	+	0.999023i	$0.514073\pi$
$42$		0			0
$43$	374.881	+	136.446i	0.202748	+	0.0737942i	0.441398	−	0.897311i	$-0.354483\pi$
$43$	374.881	+	136.446i	0.202748	+	0.0737942i	−0.238650	+	0.971106i	$0.576705\pi$
$44$		0			0
$45$	−374.354	+	648.400i	−0.184866	+	0.320198i
$46$		0			0
$47$	189.007	−	1071.91i	0.0855623	−	0.485248i	−0.911672	−	0.410920i	$-0.865208\pi$
$47$	189.007	−	1071.91i	0.0855623	−	0.485248i	0.997234	−	0.0743281i	$-0.0236812\pi$
$48$		0			0
$49$	1170.41	+	2027.21i	0.487468	+	0.844319i
$50$		0			0
$51$	−212.957	+	253.793i	−0.0818752	+	0.0975751i
$52$		0			0
$53$	−293.848	−	807.340i	−0.104609	−	0.287412i	0.876335	−	0.481703i	$-0.159982\pi$
$53$	−293.848	−	807.340i	−0.104609	−	0.287412i	−0.980944	+	0.194291i	$0.937759\pi$
$54$		0			0
$55$	306.370	+	1737.51i	0.101279	+	0.574383i
$56$		0			0
$57$	−277.317	+	57.2217i	−0.0853546	+	0.0176121i
$58$		0			0
$59$	−2307.63	+	406.897i	−0.662921	+	0.116891i	−0.494978	−	0.868906i	$-0.664824\pi$
$59$	−2307.63	+	406.897i	−0.662921	+	0.116891i	−0.167944	+	0.985797i	$0.553713\pi$
$60$		0			0
$61$	5176.31	−	1884.02i	1.39111	−	0.506321i	0.465580	−	0.885006i	$-0.345846\pi$
$61$	5176.31	−	1884.02i	1.39111	−	0.506321i	0.925526	+	0.378684i	$0.123623\pi$
$62$		0			0
$63$	477.695	+	400.833i	0.120356	+	0.100991i
$64$		0			0
$65$	1913.56	−	1104.80i	0.452915	−	0.261490i
$66$		0			0
$67$	−6476.74	−	1142.02i	−1.44280	−	0.254405i	−0.603193	−	0.797596i	$-0.706105\pi$
$67$	−6476.74	−	1142.02i	−1.44280	−	0.254405i	−0.839609	+	0.543191i	$0.817216\pi$
$68$		0			0
$69$	484.055	+	279.469i	0.101671	+	0.0586997i
$70$		0			0
$71$	877.159	−	2409.97i	0.174005	−	0.478075i	−0.821779	−	0.569807i	$-0.807018\pi$
$71$	877.159	−	2409.97i	0.174005	−	0.478075i	0.995784	+	0.0917320i	$0.0292403\pi$
$72$		0			0
$73$	−3639.17	+	3053.62i	−0.682898	+	0.573020i	−0.916852	−	0.399228i	$-0.869278\pi$
$73$	−3639.17	+	3053.62i	−0.682898	+	0.573020i	0.233953	+	0.972248i	$0.424834\pi$
$74$		0			0
$75$			422.188i			0.0750557i
$76$		0			0
$77$	1469.46			0.247844
$78$		0			0
$79$	−7424.75	−	8848.48i	−1.18967	−	1.41780i	−0.885158	−	0.465291i	$-0.845950\pi$
$79$	−7424.75	−	8848.48i	−1.18967	−	1.41780i	−0.304516	−	0.952507i	$-0.598495\pi$
$80$		0			0
$81$	−6025.19	−	2192.99i	−0.918334	−	0.334246i
$82$		0			0
$83$	5155.43	−	8929.47i	0.748357	−	1.29619i	−0.200253	−	0.979744i	$-0.564176\pi$
$83$	5155.43	−	8929.47i	0.748357	−	1.29619i	0.948610	−	0.316448i	$-0.102490\pi$
$84$		0			0
$85$	−683.142	+	3874.29i	−0.0945525	+	0.536234i
$86$		0			0
$87$	−619.759	−	1073.45i	−0.0818813	−	0.141823i
$88$		0			0
$89$	1402.20	−	1671.08i	0.177023	−	0.210968i	−0.670236	−	0.742148i	$-0.733807\pi$
$89$	1402.20	−	1671.08i	0.177023	−	0.210968i	0.847259	+	0.531181i	$0.178251\pi$
$90$		0			0
$91$	−629.430	−	1729.35i	−0.0760090	−	0.208833i
$92$		0			0
$93$	61.1878	+	347.013i	0.00707455	+	0.0401218i
$94$		0			0
$95$	−2512.09	+	2234.95i	−0.278347	+	0.247640i
$96$		0			0
$97$	6417.59	−	1131.59i	0.682070	−	0.120267i	0.178131	−	0.984007i	$-0.442995\pi$
$97$	6417.59	−	1131.59i	0.682070	−	0.120267i	0.503939	+	0.863739i	$0.331884\pi$
$98$		0			0
$99$	−14308.6	+	5207.89i	−1.45991	+	0.531363i
$100$		0			0
$101$	826.363	+	693.401i	0.0810081	+	0.0679738i	0.682393	−	0.730986i	$-0.260940\pi$
$101$	826.363	+	693.401i	0.0810081	+	0.0679738i	−0.601384	+	0.798960i	$0.705384\pi$
$102$		0			0
$103$	−3188.70	+	1841.00i	−0.300566	+	0.173532i	−0.642697	−	0.766120i	$-0.722185\pi$
$103$	−3188.70	+	1841.00i	−0.300566	+	0.173532i	0.342131	+	0.939652i	$0.388851\pi$
$104$		0			0
$105$	−55.8131	−	9.84136i	−0.00506242	−	0.000892641i
$106$		0			0
$107$	13571.7	+	7835.61i	1.18540	+	0.684393i	0.957258	−	0.289234i	$-0.0934007\pi$
$107$	13571.7	+	7835.61i	1.18540	+	0.684393i	0.228145	+	0.973627i	$0.426734\pi$
$108$		0			0
$109$	4348.57	−	11947.6i	0.366010	−	1.00561i	−0.610853	−	0.791744i	$-0.709174\pi$
$109$	4348.57	−	11947.6i	0.366010	−	1.00561i	0.976864	−	0.213862i	$-0.0686042\pi$
$110$		0			0
$111$	554.673	−	465.426i	0.0450185	−	0.0377750i
$112$		0			0
$113$		−	9061.84i		−	0.709675i	−0.934928	−	0.354837i	$-0.884536\pi$
$113$		−	9061.84i		−	0.709675i	0.934928	−	0.354837i	$-0.115464\pi$
$114$		0			0
$115$	6637.12			0.501862
$116$		0			0
$117$	12257.9	+	14608.3i	0.895453	+	1.06716i
$118$		0			0
$119$	3079.00	+	1120.67i	0.217428	+	0.0791375i
$120$		0			0
$121$	−10620.3	+	18395.0i	−0.725384	+	1.25640i
$122$		0			0
$123$	337.436	−	1913.70i	0.0223039	−	0.126492i
$124$		0			0
$125$	5417.28	+	9383.00i	0.346706	+	0.600512i
$126$		0			0
$127$	−14942.6	+	17807.9i	−0.926444	+	1.10409i	0.0678790	+	0.997694i	$0.478377\pi$
$127$	−14942.6	+	17807.9i	−0.926444	+	1.10409i	−0.994323	+	0.106400i	$0.966068\pi$
$128$		0			0
$129$	−107.024	−	294.047i	−0.00643137	−	0.0176700i
$130$		0			0
$131$	−2940.86	−	16678.4i	−0.171369	−	0.971880i	−0.942252	−	0.334904i	$-0.891296\pi$
$131$	−2940.86	−	16678.4i	−0.171369	−	0.971880i	0.770884	−	0.636976i	$-0.219815\pi$
$132$		0			0
$133$	1469.85	+	2383.72i	0.0830940	+	0.134757i
$134$		0			0
$135$	1161.12	−	204.736i	0.0637102	−	0.0112338i
$136$		0			0
$137$	9299.62	−	3384.78i	0.495478	−	0.180339i	−0.0821812	−	0.996617i	$-0.526189\pi$
$137$	9299.62	−	3384.78i	0.495478	−	0.180339i	0.577659	+	0.816278i	$0.303966\pi$
$138$		0			0
$139$	15521.6	+	13024.2i	0.803356	+	0.674096i	0.949012	−	0.315240i	$-0.102085\pi$
$139$	15521.6	+	13024.2i	0.803356	+	0.674096i	−0.145656	+	0.989335i	$0.546529\pi$
$140$		0			0
$141$	−739.370	+	426.876i	−0.0371898	+	0.0214715i
$142$		0			0
$143$	44254.9	+	7803.33i	2.16416	+	0.381600i
$144$		0			0
$145$	−12746.7	−	7359.33i	−0.606266	−	0.350028i
$146$		0			0
$147$	627.977	−	1725.35i	0.0290609	−	0.0798441i
$148$		0			0
$149$	2762.13	−	2317.70i	0.124415	−	0.104396i	−0.578457	−	0.815713i	$-0.696345\pi$
$149$	2762.13	−	2317.70i	0.124415	−	0.104396i	0.702872	+	0.711316i	$0.251901\pi$
$150$		0			0
$151$			17076.6i			0.748940i	0.927239	+	0.374470i	$0.122175\pi$
$151$			17076.6i			0.748940i	−0.927239	+	0.374470i	$0.877825\pi$
$152$		0			0
$153$	−33952.8			−1.45042
$154$		0			0
$155$	2689.54	+	3205.26i	0.111947	+	0.133414i
$156$		0			0
$157$	−23631.5	−	8601.16i	−0.958720	−	0.348945i	−0.185188	−	0.982703i	$-0.559289\pi$
$157$	−23631.5	−	8601.16i	−0.958720	−	0.348945i	−0.773532	+	0.633758i	$0.781512\pi$
$158$		0			0
$159$	−336.949	+	583.613i	−0.0133282	+	0.0230850i
$160$		0			0
$161$	959.917	−	5443.96i	0.0370324	−	0.210021i
$162$		0			0
$163$	11840.5	+	20508.4i	0.445651	+	0.771891i	0.998097	−	0.0616580i	$-0.0196388\pi$
$163$	11840.5	+	20508.4i	0.445651	+	0.771891i	−0.552446	+	0.833549i	$0.686305\pi$
$164$		0			0
$165$	889.542	−	1060.11i	0.0326737	−	0.0389390i
$166$		0			0
$167$	−13247.0	−	36395.9i	−0.474991	−	1.30503i	−0.913697	−	0.406397i	$-0.866785\pi$
$167$	−13247.0	−	36395.9i	−0.474991	−	1.30503i	0.438706	−	0.898631i	$-0.355437\pi$
$168$		0			0
$169$	−4813.19	−	27297.0i	−0.168523	−	0.955743i
$170$		0			0
$171$	−22760.4	−	18001.7i	−0.778373	−	0.615631i
$172$		0			0
$173$	4285.42	−	755.635i	0.143186	−	0.0252476i	−0.101596	−	0.994826i	$-0.532395\pi$
$173$	4285.42	−	755.635i	0.143186	−	0.0252476i	0.244782	+	0.969578i	$0.421284\pi$
$174$		0			0
$175$	3923.66	−	1428.09i	0.128119	−	0.0466317i
$176$		0			0
$177$	1407.97	+	1181.42i	0.0449413	+	0.0377102i
$178$		0			0
$179$	37315.9	−	21544.3i	1.16463	−	0.672399i	0.212220	−	0.977222i	$-0.431931\pi$
$179$	37315.9	−	21544.3i	1.16463	−	0.672399i	0.952409	+	0.304823i	$0.0985975\pi$
$180$		0			0
$181$	−10363.9	−	1827.44i	−0.316349	−	0.0557808i	0.0132194	−	0.999913i	$-0.495792\pi$
$181$	−10363.9	−	1827.44i	−0.316349	−	0.0557808i	−0.329568	+	0.944132i	$0.606903\pi$
$182$		0			0
$183$	−3741.87	−	2160.37i	−0.111734	−	0.0645098i
$184$		0			0
$185$	2940.70	−	8079.50i	0.0859225	−	0.236070i
$186$		0			0
$187$	−61290.4	+	51428.7i	−1.75271	+	1.47070i
$188$		0			0
$189$		−	981.994i		−	0.0274907i
$190$		0			0
$191$	10198.0			0.279543			0.139772	−	0.990184i	$-0.455363\pi$
$191$	10198.0			0.279543			0.139772	+	0.990184i	$0.455363\pi$
$192$		0			0
$193$	−32382.4	−	38591.8i	−0.869349	−	1.03605i	−0.999010	−	0.0444917i	$-0.985833\pi$
$193$	−32382.4	−	38591.8i	−0.869349	−	1.03605i	0.129660	−	0.991558i	$-0.458611\pi$
$194$		0			0
$195$	−1628.63	−	592.772i	−0.0428304	−	0.0155890i
$196$		0			0
$197$	11238.5	−	19465.7i	0.289585	−	0.501576i	−0.684126	−	0.729364i	$-0.739816\pi$
$197$	11238.5	−	19465.7i	0.289585	−	0.501576i	0.973711	+	0.227788i	$0.0731493\pi$
$198$		0			0
$199$	8018.46	−	45475.0i	0.202481	−	1.14833i	−0.698873	−	0.715246i	$-0.746315\pi$
$199$	8018.46	−	45475.0i	0.202481	−	1.14833i	0.901354	−	0.433083i	$-0.142574\pi$
$200$		0			0
$201$	2579.28	+	4467.44i	0.0638420	+	0.110578i
$202$		0			0
$203$	−7879.88	+	9390.88i	−0.191217	+	0.227884i
$204$		0			0
$205$	−7892.02	−	21683.2i	−0.187794	−	0.515958i
$206$		0			0
$207$	9946.83	+	56411.3i	0.232137	+	1.31651i
$208$		0			0
$209$	−68353.6	+	1979.49i	−1.56484	+	0.0453169i
$210$		0			0
$211$	47835.1	−	8434.62i	1.07444	−	0.189453i	0.391684	−	0.920100i	$-0.371893\pi$
$211$	47835.1	−	8434.62i	1.07444	−	0.189453i	0.682755	+	0.730647i	$0.260782\pi$
$212$		0			0
$213$	−1890.32	+	688.021i	−0.0416655	+	0.0151650i
$214$		0			0
$215$	−2846.43	−	2388.44i	−0.0615777	−	0.0516698i
$216$		0			0
$217$	3018.03	−	1742.46i	0.0640921	−	0.0370036i
$218$		0			0
$219$	3669.63	+	647.056i	0.0765129	+	0.0134913i
$220$		0			0
$221$	86777.3	+	50100.9i	1.77673	+	1.02580i
$222$		0			0
$223$	16111.5	−	44266.0i	0.323986	−	0.890145i	−0.665613	−	0.746297i	$-0.731830\pi$
$223$	16111.5	−	44266.0i	0.323986	−	0.890145i	0.989600	−	0.143848i	$-0.0459478\pi$
$224$		0			0
$225$	−33144.4	+	27811.5i	−0.654705	+	0.549362i
$226$		0			0
$227$		−	11619.6i		−	0.225497i	−0.993624	−	0.112748i	$-0.964035\pi$
$227$		−	11619.6i		−	0.225497i	0.993624	−	0.112748i	$-0.0359654\pi$
$228$		0			0
$229$	38184.6			0.728145			0.364072	−	0.931371i	$-0.381386\pi$
$229$	38184.6			0.728145			0.364072	+	0.931371i	$0.381386\pi$
$230$		0			0
$231$	−740.884	−	882.951i	−0.0138844	−	0.0165467i
$232$		0			0
$233$	−62685.9	−	22815.8i	−1.15467	−	0.420266i	−0.307480	−	0.951554i	$-0.599486\pi$
$233$	−62685.9	−	22815.8i	−1.15467	−	0.420266i	−0.847191	+	0.531289i	$0.821708\pi$
$234$		0			0
$235$	−5068.93	+	8779.65i	−0.0917870	+	0.158980i
$236$		0			0
$237$	−1573.29	+	8922.56i	−0.0280099	+	0.158852i
$238$		0			0
$239$	25095.4	+	43466.4i	0.439337	+	0.760954i	0.997638	−	0.0686844i	$-0.0218801\pi$
$239$	25095.4	+	43466.4i	0.439337	+	0.760954i	−0.558302	+	0.829638i	$0.688547\pi$
$240$		0			0
$241$	−45715.6	+	54481.7i	−0.787100	+	0.938030i	−0.999231	−	0.0392116i	$-0.987515\pi$
$241$	−45715.6	+	54481.7i	−0.787100	+	0.938030i	0.212131	+	0.977241i	$0.431960\pi$
$242$		0			0
$243$	5227.02	+	14361.1i	0.0885201	+	0.243207i
$244$		0			0
$245$	−3785.97	−	21471.3i	−0.0630732	−	0.357706i
$246$		0			0
$247$	31608.2	+	79594.4i	0.518090	+	1.30463i
$248$		0			0
$249$	−7964.71	+	1404.39i	−0.128461	+	0.0226511i
$250$		0			0
$251$	32866.8	−	11962.5i	0.521687	−	0.189878i	−0.0677358	−	0.997703i	$-0.521578\pi$
$251$	32866.8	−	11962.5i	0.521687	−	0.189878i	0.589423	+	0.807825i	$0.299355\pi$
$252$		0			0
$253$	103403.	+	86765.0i	1.61544	+	1.35551i
$254$		0			0
$255$	2672.36	−	1542.89i	0.0410974	−	0.0237276i
$256$		0			0
$257$	89242.7	+	15735.9i	1.35116	+	0.238246i	0.801926	−	0.597423i	$-0.203809\pi$
$257$	89242.7	+	15735.9i	1.35116	+	0.238246i	0.549233	+	0.835669i	$0.314920\pi$
$258$		0			0
$259$	−6201.73	−	3580.57i	−0.0924514	−	0.0533769i
$260$		0			0
$261$	43446.5	−	119368.i	0.637784	−	1.75230i
$262$		0			0
$263$	−15528.7	+	13030.1i	−0.224504	+	0.188381i	−0.748101	−	0.663585i	$-0.769034\pi$
$263$	−15528.7	+	13030.1i	−0.224504	+	0.188381i	0.523597	+	0.851966i	$0.324590\pi$
$264$		0			0
$265$			8002.20i			0.113951i
$266$		0			0
$267$	−1711.06			−0.0240018
$268$		0			0
$269$	−13981.4	−	16662.4i	−0.193218	−	0.230268i	0.660734	−	0.750620i	$-0.270245\pi$
$269$	−13981.4	−	16662.4i	−0.193218	−	0.230268i	−0.853952	+	0.520352i	$0.825801\pi$
$270$		0			0
$271$	−104267.	−	37950.1i	−1.41974	−	0.516743i	−0.485766	−	0.874089i	$-0.661459\pi$
$271$	−104267.	−	37950.1i	−1.41974	−	0.516743i	−0.933972	+	0.357346i	$0.883682\pi$
$272$		0			0
$273$	−721.755	+	1250.12i	−0.00968421	+	0.0167735i
$274$		0			0
$275$	−17704.7	+	100409.i	−0.234112	+	1.32772i
$276$		0			0
$277$	56652.4	+	98124.8i	0.738344	+	1.27885i	0.953241	+	0.302212i	$0.0977250\pi$
$277$	56652.4	+	98124.8i	0.738344	+	1.27885i	−0.214897	+	0.976637i	$0.568942\pi$
$278$		0			0
$279$	−23212.0	+	27663.0i	−0.298197	+	0.355378i
$280$		0			0
$281$	−12444.0	−	34189.7i	−0.157597	−	0.432995i	0.835614	−	0.549317i	$-0.185112\pi$
$281$	−12444.0	−	34189.7i	−0.157597	−	0.432995i	−0.993212	+	0.116321i	$0.962890\pi$
$282$		0			0
$283$	−20132.3	−	114176.i	−0.251374	−	1.42562i	−0.805210	−	0.592990i	$-0.797948\pi$
$283$	−20132.3	−	114176.i	−0.251374	−	1.42562i	0.553836	−	0.832626i	$-0.313164\pi$
$284$		0			0
$285$	2609.46	+	382.596i	0.0321263	+	0.00471033i
$286$		0			0
$287$	−18926.6	+	3337.26i	−0.229778	+	0.0405160i
$288$		0			0
$289$	−89160.5	+	32451.8i	−1.06752	+	0.388546i
$290$		0			0
$291$	−3915.60	−	3285.58i	−0.0462394	−	0.0387995i
$292$		0			0
$293$	1781.50	−	1028.55i	0.0207515	−	0.0119809i	−0.489588	−	0.871954i	$-0.662853\pi$
$293$	1781.50	−	1028.55i	0.0207515	−	0.0119809i	0.510340	+	0.859973i	$0.329520\pi$
$294$		0			0
$295$	21493.4	+	3789.86i	0.246979	+	0.0435491i
$296$		0			0
$297$	20766.0	+	11989.3i	0.235418	+	0.135919i
$298$		0			0
$299$	57818.4	−	158855.i	0.646731	−	1.77688i
$300$		0			0
$301$	−2370.74	+	1989.29i	−0.0261668	+	0.0219566i
$302$		0			0
$303$		−	846.137i		−	0.00921627i
$304$		0			0
$305$	−51306.6			−0.551535
$306$		0			0
$307$	72507.7	+	86411.3i	0.769321	+	0.916841i	0.998399	−	0.0565673i	$-0.0180156\pi$
$307$	72507.7	+	86411.3i	0.769321	+	0.916841i	−0.229078	+	0.973408i	$0.573571\pi$
$308$		0			0
$309$	2713.89	+	987.776i	0.0284234	+	0.0103453i
$310$		0			0
$311$	−8320.72	+	14411.9i	−0.0860281	+	0.149005i	−0.905829	−	0.423644i	$-0.860751\pi$
$311$	−8320.72	+	14411.9i	−0.0860281	+	0.149005i	0.819801	+	0.572649i	$0.194084\pi$
$312$		0			0
$313$	27818.3	−	157766.i	0.283950	−	1.61036i	−0.425060	−	0.905165i	$-0.639747\pi$
$313$	27818.3	−	157766.i	0.283950	−	1.61036i	0.709011	−	0.705198i	$-0.249142\pi$
$314$		0			0
$315$	−2904.06	−	5029.97i	−0.0292674	−	0.0506926i
$316$		0			0
$317$	−101170.	+	120569.i	−1.00677	+	1.19982i	−0.0270146	+	0.999635i	$0.508600\pi$
$317$	−101170.	+	120569.i	−1.00677	+	1.19982i	−0.979757	+	0.200189i	$0.935844\pi$
$318$		0			0
$319$	−102381.	−	281288.i	−1.00609	−	2.76421i
$320$		0			0
$321$	−2134.50	−	12105.4i	−0.0207151	−	0.117481i
$322$		0			0
$323$	−144733.	−	47981.3i	−1.38727	−	0.459903i
$324$		0			0
$325$	125750.	−	22173.1i	1.19053	−	0.209923i
$326$		0			0
$327$	−9371.39	+	3410.91i	−0.0876413	+	0.0318988i
$328$		0			0
$329$	6468.21	+	5427.48i	0.0597575	+	0.0501425i
$330$		0			0
$331$	−95092.2	+	54901.5i	−0.867939	+	0.501105i	−0.866663	−	0.498895i	$-0.833739\pi$
$331$	−95092.2	+	54901.5i	−0.867939	+	0.501105i	−0.00127600	+	0.999999i	$0.500406\pi$
$332$		0			0
$333$	73077.7	+	12885.6i	0.659017	+	0.116202i
$334$		0			0
$335$	53048.7	+	30627.7i	0.472699	+	0.272913i
$336$		0			0
$337$	−12804.4	+	35179.9i	−0.112746	+	0.309767i	−0.983213	−	0.182459i	$-0.941594\pi$
$337$	−12804.4	+	35179.9i	−0.112746	+	0.309767i	0.870468	+	0.492226i	$0.163817\pi$
$338$		0			0
$339$	−5444.95	+	4568.85i	−0.0473799	+	0.0397565i
$340$		0			0
$341$			85095.7i			0.731811i
$342$		0			0
$343$	−36784.7			−0.312665
$344$		0			0
$345$	−3346.34	−	3988.02i	−0.0281146	−	0.0335057i
$346$		0			0
$347$	−169961.	−	61860.6i	−1.41153	−	0.513754i	−0.479950	−	0.877296i	$-0.659345\pi$
$347$	−169961.	−	61860.6i	−1.41153	−	0.513754i	−0.931578	+	0.363542i	$0.881567\pi$
$348$		0			0
$349$	66787.2	−	115679.i	0.548330	−	0.949736i	−0.450059	−	0.892999i	$-0.648597\pi$
$349$	66787.2	−	115679.i	0.548330	−	0.949736i	0.998389	−	0.0567371i	$-0.0180697\pi$
$350$		0			0
$351$	5214.70	−	29574.1i	0.0423268	−	0.240047i
$352$		0			0
$353$	19867.3	+	34411.1i	0.159437	+	0.276153i	0.934666	−	0.355528i	$-0.115699\pi$
$353$	19867.3	+	34411.1i	0.159437	+	0.276153i	−0.775229	+	0.631680i	$0.782366\pi$
$354$		0			0
$355$	−15354.4	+	18298.7i	−0.121836	+	0.145199i
$356$		0			0
$357$	−879.022	−	2415.09i	−0.00689705	−	0.0189495i
$358$		0			0
$359$	−12869.3	−	72985.6i	−0.0998543	−	0.566302i	−0.993151	−	0.116835i	$-0.962725\pi$
$359$	−12869.3	−	72985.6i	−0.0998543	−	0.566302i	0.893297	−	0.449467i	$-0.148386\pi$
$360$		0			0
$361$	−71582.6	−	108901.i	−0.549279	−	0.835639i
$362$		0			0
$363$	16407.6	−	2893.09i	0.124518	−	0.0219558i
$364$		0			0
$365$	41578.9	−	15133.5i	0.312095	−	0.113593i
$366$		0			0
$367$	46243.9	+	38803.3i	0.343339	+	0.288095i	0.798109	−	0.602514i	$-0.205834\pi$
$367$	46243.9	+	38803.3i	0.343339	+	0.288095i	−0.454770	+	0.890609i	$0.650279\pi$
$368$		0			0
$369$	172465.	−	99573.0i	1.26663	−	0.731289i
$370$		0			0
$371$	6563.64	+	1157.35i	0.0476867	+	0.00840845i
$372$		0			0
$373$	122597.	+	70781.6i	0.881178	+	0.508748i	0.871046	−	0.491201i	$-0.163442\pi$
$373$	122597.	+	70781.6i	0.881178	+	0.508748i	0.0101310	+	0.999949i	$0.496775\pi$
$374$		0			0
$375$	2906.61	−	7985.84i	0.0206692	−	0.0567882i
$376$		0			0
$377$	−287182.	+	240974.i	−2.02057	+	1.69546i
$378$		0			0
$379$			121623.i			0.846715i	0.905963	+	0.423358i	$0.139149\pi$
$379$			121623.i			0.846715i	−0.905963	+	0.423358i	$0.860851\pi$
$380$		0			0
$381$	18234.0			0.125613
$382$		0			0
$383$	−51324.3	−	61165.9i	−0.349885	−	0.416977i	0.562185	−	0.827012i	$-0.309961\pi$
$383$	−51324.3	−	61165.9i	−0.349885	−	0.416977i	−0.912070	+	0.410035i	$0.865517\pi$
$384$		0			0
$385$	−12861.3	−	4681.12i	−0.0867685	−	0.0315812i
$386$		0			0
$387$	16034.3	−	27772.3i	0.107061	−	0.185434i
$388$		0			0
$389$	5919.35	−	33570.3i	0.0391178	−	0.221848i	−0.958982	−	0.283467i	$-0.908515\pi$
$389$	5919.35	−	33570.3i	0.0391178	−	0.221848i	0.998100	+	0.0616190i	$0.0196264\pi$
$390$		0			0
$391$	150492.	+	260659.i	0.984372	+	1.70498i
$392$		0			0
$393$	−8538.76	+	10176.1i	−0.0552853	+	0.0658865i
$394$		0			0
$395$	36796.4	+	101097.i	0.235836	+	0.647955i
$396$		0			0
$397$	16108.0	+	91352.8i	0.102202	+	0.579617i	0.992301	+	0.123849i	$0.0395240\pi$
$397$	16108.0	+	91352.8i	0.102202	+	0.579617i	−0.890099	+	0.455767i	$0.849365\pi$
$398$		0			0
$399$	691.219	−	2085.02i	0.00434180	−	0.0130968i
$400$		0			0
$401$	20240.3	−	3568.92i	0.125872	−	0.0221946i	−0.110357	−	0.993892i	$-0.535199\pi$
$401$	20240.3	−	3568.92i	0.125872	−	0.0221946i	0.236229	+	0.971697i	$0.424088\pi$
$402$		0			0
$403$	100145.	−	36449.9i	0.616624	−	0.224433i
$404$		0			0
$405$	45748.6	+	38387.6i	0.278912	+	0.234035i
$406$		0			0
$407$	151435.	−	87431.2i	0.914194	−	0.527810i
$408$		0			0
$409$	192872.	+	34008.5i	1.15298	+	0.203302i	0.717277	−	0.696788i	$-0.245388\pi$
$409$	192872.	+	34008.5i	1.15298	+	0.203302i	0.435704	+	0.900090i	$0.356499\pi$
$410$		0			0
$411$	−6722.54	−	3881.26i	−0.0397970	−	0.0229768i
$412$		0			0
$413$	6217.11	−	17081.4i	0.0364493	−	0.100144i
$414$		0			0
$415$	−73567.8	+	61730.7i	−0.427161	+	0.358431i
$416$		0			0
$417$		−	15893.0i		−	0.0913977i
$418$		0			0
$419$	71668.6			0.408226			0.204113	−	0.978947i	$-0.434569\pi$
$419$	71668.6			0.408226			0.204113	+	0.978947i	$0.434569\pi$
$420$		0			0
$421$	−78684.7	−	93772.7i	−0.443942	−	0.529069i	0.496949	−	0.867780i	$-0.334454\pi$
$421$	−78684.7	−	93772.7i	−0.443942	−	0.529069i	−0.940891	+	0.338711i	$0.890009\pi$
$422$		0			0
$423$	−82218.1	−	29924.9i	−0.459501	−	0.167245i
$424$		0			0
$425$	−113672.	+	196886.i	−0.629328	+	1.09003i
$426$		0			0
$427$	−7420.39	+	42083.1i	−0.0406978	+	0.230809i
$428$		0			0
$429$	−17624.0	−	30525.6i	−0.0957611	−	0.165863i
$430$		0			0
$431$	−63488.9	+	75663.1i	−0.341777	+	0.407314i	−0.909365	−	0.415998i	$-0.863432\pi$
$431$	−63488.9	+	75663.1i	−0.341777	+	0.407314i	0.567588	+	0.823313i	$0.307877\pi$
$432$		0			0
$433$	−6334.35	−	17403.5i	−0.0337852	−	0.0928240i	0.921653	−	0.388015i	$-0.126839\pi$
$433$	−6334.35	−	17403.5i	−0.0337852	−	0.0928240i	−0.955438	+	0.295191i	$0.904617\pi$
$434$		0			0
$435$	2004.76	+	11369.6i	0.0105946	+	0.0600848i
$436$		0			0
$437$	−37318.1	+	254524.i	−0.195414	+	1.33280i
$438$		0			0
$439$	47901.5	−	8446.33i	0.248554	−	0.0438267i	−0.0479832	−	0.998848i	$-0.515279\pi$
$439$	47901.5	−	8446.33i	0.248554	−	0.0438267i	0.296537	+	0.955021i	$0.404168\pi$
$440$		0			0
$441$	176819.	−	64356.7i	0.909181	−	0.330915i
$442$		0			0
$443$	133793.	+	112265.i	0.681749	+	0.572055i	0.916517	−	0.399996i	$-0.130989\pi$
$443$	133793.	+	112265.i	0.681749	+	0.572055i	−0.234768	+	0.972051i	$0.575433\pi$
$444$		0			0
$445$	−17595.9	+	10159.0i	−0.0888570	+	0.0513016i
$446$		0			0
$447$	−2785.26	−	491.116i	−0.0139396	−	0.00245793i
$448$		0			0
$449$	−180265.	−	104076.i	−0.894165	−	0.516247i	−0.0188626	−	0.999822i	$-0.506005\pi$
$449$	−180265.	−	104076.i	−0.894165	−	0.516247i	−0.875303	+	0.483576i	$0.839338\pi$
$450$		0			0
$451$	160504.	−	440981.i	0.789102	−	2.16804i
$452$		0			0
$453$	10260.7	−	8609.78i	0.0500014	−	0.0419562i
$454$		0			0
$455$			17141.0i			0.0827965i
$456$		0			0
$457$	78903.9			0.377804			0.188902	−	0.981996i	$-0.439507\pi$
$457$	78903.9			0.377804			0.188902	+	0.981996i	$0.439507\pi$
$458$		0			0
$459$	34368.1	+	40958.3i	0.163129	+	0.194409i
$460$		0			0
$461$	−74686.5	−	27183.7i	−0.351431	−	0.127910i	0.160272	−	0.987073i	$-0.448763\pi$
$461$	−74686.5	−	27183.7i	−0.351431	−	0.127910i	−0.511703	+	0.859162i	$0.670985\pi$
$462$		0			0
$463$	−70223.0	+	121630.i	−0.327580	+	0.567385i	−0.982031	−	0.188719i	$-0.939566\pi$
$463$	−70223.0	+	121630.i	−0.327580	+	0.567385i	0.654451	+	0.756104i	$0.272900\pi$
$464$		0			0
$465$	569.906	−	3232.10i	0.00263571	−	0.0149479i
$466$		0			0
$467$	−18527.0	−	32089.7i	−0.0849514	−	0.147140i	0.820419	−	0.571763i	$-0.193740\pi$
$467$	−18527.0	−	32089.7i	−0.0849514	−	0.147140i	−0.905371	+	0.424622i	$0.860407\pi$
$468$		0			0
$469$	32794.0	−	39082.4i	0.149090	−	0.177679i
$470$		0			0
$471$	6746.53	+	18535.9i	0.0304116	+	0.0835551i
$472$		0			0
$473$	−13122.4	−	74421.0i	−0.0586532	−	0.332639i
$474$		0			0
$475$	−180589.	+	71714.8i	−0.800395	+	0.317849i
$476$		0			0
$477$	−68013.6	+	11992.6i	−0.298923	+	0.0527082i
$478$		0			0
$479$	−329391.	+	119889.i	−1.43563	+	0.522525i	−0.938538	−	0.345176i	$-0.887819\pi$
$479$	−329391.	+	119889.i	−1.43563	+	0.522525i	−0.497087	+	0.867701i	$0.665597\pi$
$480$		0			0
$481$	−167760.	−	140767.i	−0.725099	−	0.608430i
$482$		0			0
$483$	−3755.07	+	2167.99i	−0.0160962	+	0.00929314i
$484$		0			0
$485$	−59773.8	−	10539.7i	−0.254113	−	0.0448071i
$486$		0			0
$487$	262839.	+	151750.i	1.10823	+	0.639839i	0.938371	−	0.345629i	$-0.112334\pi$
$487$	262839.	+	151750.i	1.10823	+	0.639839i	0.169862	+	0.985468i	$0.445668\pi$
$488$		0			0
$489$	6352.95	−	17454.6i	0.0265679	−	0.0729948i
$490$		0			0
$491$	−37420.5	+	31399.5i	−0.155220	+	0.130245i	−0.717090	−	0.696980i	$-0.754526\pi$
$491$	−37420.5	+	31399.5i	−0.155220	+	0.130245i	0.561870	+	0.827225i	$0.310082\pi$
$492$		0			0
$493$		−	667470.i		−	2.74623i
$494$		0			0
$495$	141824.			0.578814
$496$		0			0
$497$	12788.4	+	15240.6i	0.0517731	+	0.0617007i
$498$		0			0
$499$	−32724.7	−	11910.8i	−0.131424	−	0.0478345i	0.275471	−	0.961309i	$-0.411166\pi$
$499$	−32724.7	−	11910.8i	−0.131424	−	0.0478345i	−0.406895	+	0.913475i	$0.633388\pi$
$500$		0			0
$501$	−15190.1	+	26310.0i	−0.0605180	+	0.104820i
$502$		0			0
$503$	46195.2	−	261986.i	0.182583	−	1.03548i	−0.746438	−	0.665455i	$-0.768238\pi$
$503$	46195.2	−	261986.i	0.182583	−	1.03548i	0.929021	−	0.370026i	$-0.120651\pi$
$504$		0			0
$505$	−5023.73	−	8701.35i	−0.0196990	−	0.0341196i
$506$		0			0
$507$	−13975.1	+	16654.8i	−0.0543673	+	0.0647925i
$508$		0			0
$509$	−127751.	−	350992.i	−0.493091	−	1.35476i	−0.897837	−	0.440327i	$-0.854862\pi$
$509$	−127751.	−	350992.i	−0.493091	−	1.35476i	0.404746	−	0.914429i	$-0.367360\pi$
$510$		0			0
$511$	−6399.42	−	36292.9i	−0.0245075	−	0.138989i
$512$		0			0
$513$	1322.82	+	45678.4i	0.00502652	+	0.173571i
$514$		0			0
$515$	33773.3	−	5955.15i	0.127338	−	0.0224532i
$516$		0			0
$517$	−193745.	+	70517.4i	−0.724852	+	0.263824i
$518$		0			0
$519$	−2614.68	−	2193.98i	−0.00970699	−	0.00814513i
$520$		0			0
$521$	−164152.	+	94773.2i	−0.604743	+	0.349149i	−0.770905	−	0.636950i	$-0.780196\pi$
$521$	−164152.	+	94773.2i	−0.604743	+	0.349149i	0.166162	+	0.986098i	$0.446862\pi$
$522$		0			0
$523$	83466.4	+	14717.4i	0.305147	+	0.0538056i	0.324125	−	0.946014i	$-0.394930\pi$
$523$	83466.4	+	14717.4i	0.305147	+	0.0538056i	−0.0189782	+	0.999820i	$0.506041\pi$
$524$		0			0
$525$	−2836.35	−	1637.57i	−0.0102906	−	0.00594128i
$526$		0			0
$527$	−64897.0	+	178303.i	−0.233670	+	0.642004i
$528$		0			0
$529$	174617.	−	146521.i	0.623985	−	0.523586i
$530$		0			0
$531$			188360.i			0.668035i
$532$		0			0
$533$	−587721.			−2.06879
$534$		0			0
$535$	−93823.0	−	111814.i	−0.327795	−	0.390650i
$536$		0			0
$537$	−31759.4	−	11559.5i	−0.110135	−	0.0400857i
$538$		0			0
$539$	221705.	−	384004.i	0.763128	−	1.32178i
$540$		0			0
$541$	−82338.9	+	466967.i	−0.281326	+	1.59548i	0.436794	+	0.899562i	$0.356114\pi$
$541$	−82338.9	+	466967.i	−0.281326	+	1.59548i	−0.718120	+	0.695919i	$0.754997\pi$
$542$		0			0
$543$	4127.29	+	7148.68i	0.0139980	+	0.0242452i
$544$		0			0
$545$	−76120.4	+	90716.8i	−0.256276	+	0.305418i
$546$		0			0
$547$	67687.8	+	185971.i	0.226223	+	0.621541i	0.999928	−	0.0120041i	$-0.00382113\pi$
$547$	67687.8	+	185971.i	0.226223	+	0.621541i	−0.773705	+	0.633546i	$0.781599\pi$
$548$		0			0
$549$	−76891.4	−	436073.i	−0.255113	−	1.44682i
$550$		0			0
$551$	353890.	−	447441.i	1.16564	−	1.47378i
$552$		0			0
$553$	88244.7	−	15559.9i	0.288561	−	0.0508812i
$554$		0			0
$555$	−6337.36	+	2306.61i	−0.0205742	+	0.00748838i
$556$		0			0
$557$	414735.	+	348004.i	1.33678	+	1.12169i	0.982440	+	0.186576i	$0.0597391\pi$
$557$	414735.	+	348004.i	1.33678	+	1.12169i	0.354341	+	0.935116i	$0.384705\pi$
$558$		0			0
$559$	−81961.8	+	47320.7i	−0.262294	+	0.151435i
$560$		0			0
$561$	61803.5	+	10897.6i	0.196376	+	0.0346263i
$562$		0			0
$563$	69780.4	+	40287.7i	0.220149	+	0.127103i	0.606019	−	0.795450i	$-0.292765\pi$
$563$	69780.4	+	40287.7i	0.220149	+	0.127103i	−0.385870	+	0.922553i	$0.626099\pi$
$564$		0			0
$565$	−28867.3	+	79312.4i	−0.0904295	+	0.248453i
$566$		0			0
$567$	38103.2	−	31972.4i	0.118521	−	0.0994510i
$568$		0			0
$569$			219752.i			0.678749i	0.940651	+	0.339374i	$0.110215\pi$
$569$			219752.i			0.678749i	−0.940651	+	0.339374i	$0.889785\pi$
$570$		0			0
$571$	−71941.6			−0.220652			−0.110326	−	0.993895i	$-0.535190\pi$
$571$	−71941.6			−0.220652			−0.110326	+	0.993895i	$0.535190\pi$
$572$		0			0
$573$	−5141.70	−	6127.64i	−0.0156602	−	0.0186631i
$574$		0			0
$575$	360420.	+	131182.i	1.09012	+	0.396771i
$576$		0			0
$577$	48217.9	−	83515.8i	0.144829	−	0.250852i	−0.784480	−	0.620154i	$-0.787070\pi$
$577$	48217.9	−	83515.8i	0.144829	−	0.250852i	0.929309	+	0.369303i	$0.120403\pi$
$578$		0			0
$579$	−6861.76	+	38914.9i	−0.0204681	+	0.116081i
$580$		0			0
$581$	39993.3	+	69270.5i	0.118477	+	0.205209i
$582$		0			0
$583$	−104610.	+	124670.i	−0.307778	+	0.366796i
$584$		0			0
$585$	−60748.8	−	166906.i	−0.177511	−	0.487708i
$586$		0			0
$587$	67100.9	+	380548.i	0.194739	+	1.10442i	0.912790	+	0.408428i	$0.133923\pi$
$587$	67100.9	+	380548.i	0.194739	+	1.10442i	−0.718052	+	0.695990i	$0.754966\pi$
$588$		0			0
$589$	−138040.	+	85118.0i	−0.397900	+	0.245353i
$590$		0			0
$591$	−17362.6	+	3061.49i	−0.0497094	+	0.00876511i
$592$		0			0
$593$	109933.	−	40012.2i	0.312620	−	0.113784i	−0.180945	−	0.983493i	$-0.557916\pi$
$593$	109933.	−	40012.2i	0.312620	−	0.113784i	0.493565	+	0.869709i	$0.335693\pi$
$594$		0			0
$595$	−23378.5	−	19616.9i	−0.0660364	−	0.0554111i
$596$		0			0
$597$	−31367.1	+	18109.8i	−0.0880089	+	0.0508119i
$598$		0			0
$599$	−127777.	−	22530.6i	−0.356123	−	0.0627940i	−0.00727514	−	0.999974i	$-0.502316\pi$
$599$	−127777.	−	22530.6i	−0.356123	−	0.0627940i	−0.348847	+	0.937180i	$0.613427\pi$
$600$		0			0
$601$	30321.7	+	17506.3i	0.0839470	+	0.0484668i	0.541386	−	0.840774i	$-0.317900\pi$
$601$	30321.7	+	17506.3i	0.0839470	+	0.0484668i	−0.457439	+	0.889241i	$0.651233\pi$
$602$		0			0
$603$	−180813.	+	496780.i	−0.497274	+	1.36625i
$604$		0			0
$605$	151552.	−	127167.i	0.414048	−	0.347428i
$606$		0			0
$607$			469725.i			1.27487i	0.770504	+	0.637435i	$0.220005\pi$
$607$			469725.i			1.27487i	−0.770504	+	0.637435i	$0.779995\pi$
$608$		0			0
$609$	9615.58			0.0259263
$610$		0			0
$611$	165977.	+	197804.i	0.444597	+	0.529850i
$612$		0			0
$613$	224865.	+	81844.2i	0.598413	+	0.217805i	0.623426	−	0.781883i	$-0.285740\pi$
$613$	224865.	+	81844.2i	0.598413	+	0.217805i	−0.0250126	+	0.999687i	$0.507963\pi$
$614$		0			0
$615$	−9049.62	+	15674.4i	−0.0239265	+	0.0414420i
$616$		0			0
$617$	49410.0	−	280218.i	0.129791	−	0.736081i	−0.848555	−	0.529107i	$-0.822527\pi$
$617$	49410.0	−	280218.i	0.129791	−	0.736081i	0.978346	−	0.206974i	$-0.0663617\pi$
$618$		0			0
$619$	−176197.	−	305181.i	−0.459850	−	0.796484i	0.539103	−	0.842240i	$-0.318763\pi$
$619$	−176197.	−	305181.i	−0.459850	−	0.796484i	−0.998953	+	0.0457565i	$0.985430\pi$
$620$		0			0
$621$	57982.1	−	69100.4i	0.150353	−	0.179183i
$622$		0			0
$623$	5787.84	+	15902.0i	0.0149122	+	0.0409708i
$624$		0			0
$625$	40892.7	+	231914.i	0.104685	+	0.593699i
$626$		0			0
$627$	35652.4	+	40073.3i	0.0906887	+	0.101934i
$628$		0			0
$629$	383984.	−	67706.8i	0.970537	−	0.171132i
$630$		0			0
$631$	402796.	−	146606.i	1.01164	−	0.368207i	0.217578	−	0.976043i	$-0.430184\pi$
$631$	402796.	−	146606.i	1.01164	−	0.368207i	0.794062	+	0.607836i	$0.207962\pi$
$632$		0			0
$633$	−29185.9	−	24489.8i	−0.0728392	−	0.0611193i
$634$		0			0
$635$	187512.	−	108260.i	0.465030	−	0.268485i
$636$		0			0
$637$	−546881.	−	96429.9i	−1.34777	−	0.237647i
$638$		0			0
$639$	−178538.	−	103079.i	−0.437249	−	0.252446i
$640$		0			0
$641$	11509.8	−	31622.9i	0.0280125	−	0.0769637i	−0.924898	−	0.380215i	$-0.875850\pi$
$641$	11509.8	−	31622.9i	0.0280125	−	0.0769637i	0.952911	+	0.303251i	$0.0980722\pi$
$642$		0			0
$643$	−15196.8	+	12751.6i	−0.0367562	+	0.0308421i	−0.660981	−	0.750403i	$-0.729859\pi$
$643$	−15196.8	+	12751.6i	−0.0367562	+	0.0308421i	0.624225	+	0.781245i	$0.285415\pi$
$644$		0			0
$645$			2914.54i			0.00700568i
$646$		0			0
$647$	609119.			1.45510			0.727551	−	0.686053i	$-0.240658\pi$
$647$	609119.			1.45510			0.727551	+	0.686053i	$0.240658\pi$
$648$		0			0
$649$	285311.	+	340020.i	0.677375	+	0.807264i
$650$		0			0
$651$	−2568.64	−	934.908i	−0.00606095	−	0.00220601i
$652$		0			0
$653$	−318930.	+	552403.i	−0.747944	+	1.29548i	0.200863	+	0.979619i	$0.435626\pi$
$653$	−318930.	+	552403.i	−0.747944	+	1.29548i	−0.948807	+	0.315858i	$0.897708\pi$
$654$		0			0
$655$	−27391.3	+	155344.i	−0.0638455	+	0.362086i
$656$		0			0
$657$	190938.	+	330714.i	0.442345	+	0.766163i
$658$		0			0
$659$	201555.	−	240204.i	0.464111	−	0.553106i	−0.482327	−	0.875991i	$-0.660208\pi$
$659$	201555.	−	240204.i	0.464111	−	0.553106i	0.946438	+	0.322885i	$0.104653\pi$
$660$		0			0
$661$	160266.	+	440328.i	0.366808	+	1.00780i	0.976568	+	0.215211i	$0.0690440\pi$
$661$	160266.	+	440328.i	0.366808	+	1.00780i	−0.609759	+	0.792587i	$0.708734\pi$
$662$		0			0
$663$	−13648.0	−	77401.7i	−0.0310486	−	0.176085i
$664$		0			0
$665$	−5271.07	−	25545.5i	−0.0119194	−	0.0577659i
$666$		0			0
$667$	−1.10897e6	+	195542.i	−2.49270	+	0.439530i
$668$		0			0
$669$	−34721.1	+	12637.5i	−0.0775786	+	0.0282363i
$670$		0			0
$671$	−799327.	−	670715.i	−1.77533	−	1.48968i
$672$		0			0
$673$	418973.	−	241894.i	0.925031	−	0.534067i	0.0397942	−	0.999208i	$-0.487330\pi$
$673$	418973.	−	241894.i	0.925031	−	0.534067i	0.885237	+	0.465141i	$0.153996\pi$
$674$		0			0
$675$	67099.6	+	11831.5i	0.147269	+	0.0259676i
$676$		0			0
$677$	−439608.	−	253808.i	−0.959154	−	0.553768i	−0.0632415	−	0.997998i	$-0.520144\pi$
$677$	−439608.	−	253808.i	−0.959154	−	0.553768i	−0.895913	+	0.444230i	$0.853477\pi$
$678$		0			0
$679$	−17290.0	+	47503.9i	−0.0375021	+	0.103036i
$680$		0			0
$681$	−6981.83	+	5858.45i	−0.0150548	+	0.0126325i
$682$		0			0
$683$		−	560367.i		−	1.20124i	−0.799533	−	0.600622i	$-0.794920\pi$
$683$		−	560367.i		−	1.20124i	0.799533	−	0.600622i	$-0.205080\pi$
$684$		0			0
$685$	−92176.1			−0.196443
$686$		0			0
$687$	−19252.2	−	22943.8i	−0.0407912	−	0.0486130i
$688$		0			0
$689$	191527.	+	69710.1i	0.403452	+	0.146844i
$690$		0			0
$691$	197689.	−	342407.i	0.414024	−	0.717111i	−0.581301	−	0.813689i	$-0.697456\pi$
$691$	197689.	−	342407.i	0.414024	−	0.717111i	0.995325	+	0.0965773i	$0.0307895\pi$
$692$		0			0
$693$	20511.8	−	116328.i	0.0427107	−	0.242224i
$694$		0			0
$695$	−94361.0	−	163438.i	−0.195354	−	0.338364i
$696$		0			0
$697$	672616.	−	801593.i	1.38453	−	1.65002i
$698$		0			0
$699$	17896.1	+	49169.3i	0.0366273	+	0.100633i
$700$		0			0
$701$	47480.8	+	269277.i	0.0966233	+	0.547978i	0.994238	+	0.107197i	$0.0341874\pi$
$701$	47480.8	+	269277.i	0.0966233	+	0.547978i	−0.897615	+	0.440781i	$0.854701\pi$
$702$		0			0
$703$	293303.	+	158200.i	0.593480	+	0.320107i
$704$		0			0
$705$	7831.08	−	1380.83i	0.0157559	−	0.00277819i
$706$		0			0
$707$	−7863.67	+	2862.14i	−0.0157321	+	0.00572602i
$708$		0			0
$709$	−223386.	−	187443.i	−0.444389	−	0.372886i	0.392960	−	0.919556i	$-0.371451\pi$
$709$	−223386.	−	187443.i	−0.444389	−	0.372886i	−0.837349	+	0.546669i	$0.815895\pi$
$710$		0			0
$711$	−804116.	+	464257.i	−1.59067	+	0.918373i
$712$		0			0
$713$	315256.	+	55588.1i	0.620132	+	0.109346i
$714$		0			0
$715$	−362476.	−	209276.i	−0.709034	−	0.409361i
$716$		0			0
$717$	13464.8	−	36994.1i	0.0261915	−	0.0719605i
$718$		0			0
$719$	59480.3	−	49909.9i	0.115058	−	0.0965448i	−0.583444	−	0.812154i	$-0.698295\pi$
$719$	59480.3	−	49909.9i	0.115058	−	0.0965448i	0.698501	+	0.715609i	$0.253851\pi$
$720$		0			0
$721$		−	28563.1i		−	0.0549459i
$722$		0			0
$723$	55785.4			0.106719
$724$		0			0
$725$	−546739.	−	651578.i	−1.04017	−	1.23962i
$726$		0			0
$727$	−727130.	−	264654.i	−1.37576	−	0.500737i	−0.454872	−	0.890557i	$-0.650315\pi$
$727$	−727130.	−	264654.i	−1.37576	−	0.500737i	−0.920891	+	0.389821i	$0.872537\pi$
$728$		0			0
$729$	−253687.	+	439399.i	−0.477357	+	0.826807i
$730$		0			0
$731$	29260.4	−	165944.i	0.0547577	−	0.310546i
$732$		0			0
$733$	−521382.	−	903059.i	−0.970393	−	1.68077i	−0.694368	−	0.719620i	$-0.744316\pi$
$733$	−521382.	−	903059.i	−0.970393	−	1.68077i	−0.276025	−	0.961150i	$-0.589017\pi$
$734$		0			0
$735$	−10992.5	+	13100.4i	−0.0203481	+	0.0242499i
$736$		0			0
$737$	426082.	+	1.17065e6i	0.784437	+	2.15522i
$738$		0			0
$739$	56940.7	+	322926.i	0.104264	+	0.591309i	0.991512	+	0.130017i	$0.0415031\pi$
$739$	56940.7	+	322926.i	0.104264	+	0.591309i	−0.887248	+	0.461293i	$0.847386\pi$
$740$		0			0
$741$	31889.1	−	59122.7i	0.0580773	−	0.107676i
$742$		0			0
$743$	336541.	−	59341.2i	0.609621	−	0.107493i	0.139689	−	0.990195i	$-0.455390\pi$
$743$	336541.	−	59341.2i	0.609621	−	0.107493i	0.469932	+	0.882703i	$0.344278\pi$
$744$		0			0
$745$	−31558.4	+	11486.3i	−0.0568594	+	0.0206951i
$746$		0			0
$747$	−634925.	−	532766.i	−1.13784	−	0.954762i
$748$		0			0
$749$	−105283.	+	60784.9i	−0.187669	+	0.108351i
$750$		0			0
$751$	−577391.	−	101810.i	−1.02374	−	0.180513i	−0.363522	−	0.931586i	$-0.618426\pi$
$751$	−577391.	−	101810.i	−1.02374	−	0.180513i	−0.660220	+	0.751073i	$0.729537\pi$
$752$		0			0
$753$	−23758.9	−	13717.2i	−0.0419021	−	0.0241922i
$754$		0			0
$755$	54399.1	−	149460.i	0.0954328	−	0.262200i
$756$		0			0
$757$	342910.	−	287735.i	0.598395	−	0.502113i	−0.292534	−	0.956255i	$-0.594499\pi$
$757$	342910.	−	287735.i	0.598395	−	0.502113i	0.890929	+	0.454142i	$0.150054\pi$
$758$		0			0
$759$		−	105877.i		−	0.183788i
$760$		0			0
$761$	741840.			1.28098			0.640488	−	0.767968i	$-0.278732\pi$
$761$	741840.			1.28098			0.640488	+	0.767968i	$0.278732\pi$
$762$		0			0
$763$	63399.4	+	75556.4i	0.108902	+	0.129784i
$764$		0			0
$765$	297167.	+	108160.i	0.507782	+	0.184818i
$766$		0			0
$767$	277944.	−	481414.i	0.472462	−	0.818329i
$768$		0			0
$769$	−75631.6	+	428928.i	−0.127894	+	0.725323i	0.851653	+	0.524107i	$0.175601\pi$
$769$	−75631.6	+	428928.i	−0.127894	+	0.725323i	−0.979547	+	0.201217i	$0.935510\pi$
$770$		0			0
$771$	−35539.8	−	61556.7i	−0.0597869	−	0.103554i
$772$		0			0
$773$	260878.	−	310902.i	0.436595	−	0.520313i	−0.502218	−	0.864741i	$-0.667483\pi$
$773$	260878.	−	310902.i	0.436595	−	0.520313i	0.938813	+	0.344428i	$0.111927\pi$
$774$		0			0
$775$	82700.0	+	227216.i	0.137690	+	0.378300i
$776$		0			0
$777$	975.385	+	5531.69i	0.00161560	+	0.00916253i
$778$		0			0
$779$	875893.	−	180732.i	1.44337	−	0.297824i
$780$		0			0
$781$	−478426.	+	84359.4i	−0.784355	+	0.138303i
$782$		0			0
$783$	−187976.	+	68417.5i	−0.306604	+	0.111595i
$784$		0			0
$785$	179431.	+	150561.i	0.291178	+	0.244327i
$786$		0			0
$787$	334739.	−	193261.i	0.540451	−	0.312030i	−0.204811	−	0.978802i	$-0.565658\pi$
$787$	334739.	−	193261.i	0.540451	−	0.312030i	0.745262	+	0.666772i	$0.232325\pi$
$788$		0			0
$789$	15658.7	+	2761.06i	0.0251537	+	0.00443528i
$790$		0			0
$791$	60879.3	+	35148.7i	0.0973008	+	0.0561767i
$792$		0			0
$793$	−446950.	+	1.22799e6i	−0.710743	+	1.95275i
$794$		0			0
$795$	4808.25	−	4034.60i	0.00760769	−	0.00638361i
$796$		0			0
$797$			390632.i			0.614966i	0.951554	+	0.307483i	$0.0994868\pi$
$797$			390632.i			0.614966i	−0.951554	+	0.307483i	$0.900513\pi$
$798$		0			0
$799$	−459737.			−0.720139
$800$		0			0
$801$	−112715.	−	134329.i	−0.175678	−	0.209365i
$802$		0			0
$803$	845610.	+	307777.i	1.31141	+	0.477315i
$804$		0			0
$805$	−25743.8	+	44589.5i	−0.0397265	+	0.0688083i
$806$		0			0
$807$	−2962.63	+	16801.9i	−0.00454915	+	0.0257995i
$808$		0			0
$809$	−446878.	−	774016.i	−0.682798	−	1.18264i	−0.974123	−	0.226017i	$-0.927430\pi$
$809$	−446878.	−	774016.i	−0.682798	−	1.18264i	0.291326	−	0.956624i	$-0.405904\pi$
$810$		0			0
$811$	−590057.	+	703202.i	−0.897123	+	1.06915i	0.100122	+	0.994975i	$0.468077\pi$
$811$	−590057.	+	703202.i	−0.897123	+	1.06915i	−0.997245	+	0.0741749i	$0.976368\pi$
$812$		0			0
$813$	29767.1	+	81784.4i	0.0450355	+	0.123734i
$814$		0			0
$815$	−38300.9	−	217215.i	−0.0576626	−	0.327021i
$816$		0			0
$817$	107598.	−	95727.3i	0.161198	−	0.143414i
$818$		0			0
$819$	−145687.	+	25688.6i	−0.217197	+	0.0382977i
$820$		0			0
$821$	−218235.	+	79431.0i	−0.323771	+	0.117843i	−0.498792	−	0.866722i	$-0.666223\pi$
$821$	−218235.	+	79431.0i	−0.323771	+	0.117843i	0.175021	+	0.984565i	$0.444001\pi$
$822$		0			0
$823$	712295.	+	597687.i	1.05162	+	0.882417i	0.993263	−	0.115878i	$-0.0369683\pi$
$823$	712295.	+	597687.i	1.05162	+	0.882417i	0.0583605	+	0.998296i	$0.481413\pi$
$824$		0			0
$825$	69258.5	−	39986.4i	0.101757	−	0.0587496i
$826$		0			0
$827$	−1.07287e6	−	189177.i	−1.56869	−	0.276603i	−0.679340	−	0.733824i	$-0.737734\pi$
$827$	−1.07287e6	−	189177.i	−1.56869	−	0.276603i	−0.889353	+	0.457221i	$0.848845\pi$
$828$		0			0
$829$	51152.8	+	29533.1i	0.0744322	+	0.0429734i	0.536754	−	0.843739i	$-0.319650\pi$
$829$	51152.8	+	29533.1i	0.0744322	+	0.0429734i	−0.462322	+	0.886712i	$0.652984\pi$
$830$		0			0
$831$	30396.5	−	83513.6i	0.0440171	−	0.120936i
$832$		0			0
$833$	757398.	−	635532.i	1.09153	−	0.915899i
$834$		0			0
$835$			360749.i			0.517408i
$836$		0			0
$837$	56866.6			0.0811720
$838$		0			0
$839$	841547.	+	1.00292e6i	1.19551	+	1.42476i	0.879431	+	0.476027i	$0.157923\pi$
$839$	841547.	+	1.00292e6i	1.19551	+	1.42476i	0.316083	+	0.948732i	$0.397632\pi$
$840$		0			0
$841$	1.68200e6	+	612200.i	2.37813	+	0.865568i
$842$		0			0
$843$	−14269.3	+	24715.2i	−0.0200793	+	0.0347784i
$844$		0			0
$845$	−44830.3	+	254246.i	−0.0627854	+	0.356074i
$846$		0			0
$847$	−82387.5	−	142699.i	−0.114840	−	0.198909i
$848$		0			0
$849$	−58454.1	+	69662.9i	−0.0810960	+	0.0966465i
$850$		0			0
$851$	−224984.	−	618139.i	−0.310666	−	0.853547i
$852$		0			0
$853$	−11939.6	−	67712.7i	−0.0164093	−	0.0930620i	0.975503	−	0.219985i	$-0.0706009\pi$
$853$	−11939.6	−	67712.7i	−0.0164093	−	0.0930620i	−0.991913	+	0.126923i	$0.959490\pi$
$854$		0			0
$855$	141861.	+	230062.i	0.194058	+	0.314712i
$856$		0			0
$857$	590017.	−	104036.i	0.803347	−	0.141652i	0.243126	−	0.969995i	$-0.421827\pi$
$857$	590017.	−	104036.i	0.803347	−	0.141652i	0.560221	+	0.828343i	$0.310716\pi$
$858$		0			0
$859$	93942.4	−	34192.3i	0.127314	−	0.0463384i	−0.277578	−	0.960703i	$-0.589532\pi$
$859$	93942.4	−	34192.3i	0.127314	−	0.0463384i	0.404891	+	0.914365i	$0.367309\pi$
$860$		0			0
$861$	11547.8	+	9689.72i	0.0155773	+	0.0130709i
$862$		0			0
$863$	−1.10332e6	+	637004.i	−1.48143	+	0.855304i	−0.999778	−	0.0210585i	$-0.993296\pi$
$863$	−1.10332e6	+	637004.i	−1.48143	+	0.855304i	−0.481652	+	0.876363i	$0.659963\pi$
$864$		0			0
$865$	−39914.6	−	7038.02i	−0.0533457	−	0.00940629i
$866$		0			0
$867$	64452.7	+	37211.8i	0.0857438	+	0.0495042i
$868$		0			0
$869$	−748346.	+	2.05607e6i	−0.990976	+	2.72268i
$870$		0			0
$871$	1.19518e6	−	1.00287e6i	1.57542	−	1.32193i
$872$		0			0
$873$		−	523835.i		−	0.687331i
$874$		0			0
$875$	−84049.3			−0.109779
$876$		0			0
$877$	57433.7	+	68446.9i	0.0746737	+	0.0889927i	0.802088	−	0.597206i	$-0.203723\pi$
$877$	57433.7	+	68446.9i	0.0746737	+	0.0889927i	−0.727414	+	0.686199i	$0.759278\pi$
$878$		0			0
$879$	−1516.23	−	551.862i	−0.00196240	−	0.000714254i
$880$		0			0
$881$	337422.	−	584431.i	0.434732	−	0.752977i	−0.562542	−	0.826769i	$-0.690177\pi$
$881$	337422.	−	584431.i	0.434732	−	0.752977i	0.997274	+	0.0737915i	$0.0235099\pi$
$882$		0			0
$883$	−133261.	+	755759.i	−0.170915	+	0.969308i	0.771839	+	0.635818i	$0.219337\pi$
$883$	−133261.	+	755759.i	−0.170915	+	0.969308i	−0.942754	+	0.333489i	$0.891774\pi$
$884$		0			0
$885$	−8559.47	−	14825.4i	−0.0109285	−	0.0189287i
$886$		0			0
$887$	903796.	−	1.07710e6i	1.14874	−	1.36902i	0.230468	−	0.973080i	$-0.425974\pi$
$887$	903796.	−	1.07710e6i	1.14874	−	1.36902i	0.918276	−	0.395940i	$-0.129581\pi$
$888$		0			0
$889$	−61678.5	−	169460.i	−0.0780423	−	0.214419i
$890$		0			0
$891$	210907.	+	1.19612e6i	0.265666	+	1.50667i
$892$		0			0
$893$	−308187.	−	243751.i	−0.386466	−	0.305664i
$894$		0			0
$895$	−395233.	+	69690.2i	−0.493409	+	0.0870013i
$896$		0			0
$897$	−124602.	+	45351.3i	−0.154860	+	0.0563644i
$898$		0			0
$899$	−543819.	−	456318.i	−0.672876	−	0.564610i
$900$		0			0
$901$	−314270.	+	181444.i	−0.387127	+	0.223508i
$902$		0			0
$903$	2390.59	+	421.526i	0.00293177	+	0.000516950i
$904$		0			0
$905$	84887.0	+	49009.6i	0.103644	+	0.0598389i
$906$		0			0
$907$	132260.	−	363381.i	0.160773	−	0.441721i	−0.832982	−	0.553300i	$-0.813368\pi$
$907$	132260.	−	363381.i	0.160773	−	0.441721i	0.993756	+	0.111579i	$0.0355907\pi$
$908$		0			0
$909$	66427.0	−	55738.9i	0.0803928	−	0.0674575i
$910$		0			0
$911$			260514.i			0.313902i	0.987606	+	0.156951i	$0.0501665\pi$
$911$			260514.i			0.313902i	−0.987606	+	0.156951i	$0.949834\pi$
$912$		0			0
$913$	−1.95313e6			−2.34310
$914$		0			0
$915$	25868.1	+	30828.4i	0.0308974	+	0.0368221i
$916$		0			0
$917$	123456.	+	44934.3i	0.146816	+	0.0534367i
$918$		0			0
$919$	24980.7	−	43267.9i	0.0295783	−	0.0512312i	−0.850857	−	0.525397i	$-0.823917\pi$
$919$	24980.7	−	43267.9i	0.0295783	−	0.0512312i	0.880436	+	0.474166i	$0.157250\pi$
$920$		0			0
$921$	15364.2	−	87134.8i	0.0181130	−	0.102724i
$922$		0			0
$923$	304208.	+	526903.i	0.357081	+	0.618482i
$924$		0			0
$925$	319382.	−	380624.i	0.373273	−	0.444850i
$926$		0			0
$927$	101230.	+	278127.i	0.117801	+	0.323656i
$928$		0			0
$929$	−27203.8	−	154280.i	−0.0315208	−	0.178764i	0.964983	−	0.262313i	$-0.0844854\pi$
$929$	−27203.8	−	154280.i	−0.0315208	−	0.178764i	−0.996504	+	0.0835497i	$0.973374\pi$
$930$		0			0
$931$	844682.	−	24461.6i	0.974527	−	0.0282218i
$932$		0			0
$933$	12854.8	−	2266.65i	0.0147674	−	0.00260388i
$934$		0			0
$935$	700266.	−	254876.i	0.801014	−	0.291545i
$936$		0			0
$937$	−128884.	−	108146.i	−0.146798	−	0.123178i	0.566431	−	0.824109i	$-0.308324\pi$
$937$	−128884.	−	108146.i	−0.146798	−	0.123178i	−0.713229	+	0.700931i	$0.752768\pi$
$938$		0			0
$939$	−108822.	+	62828.2i	−0.123420	+	0.0712563i
$940$		0			0
$941$	95914.7	+	16912.3i	0.108319	+	0.0190996i	0.227545	−	0.973768i	$-0.426930\pi$
$941$	95914.7	+	16912.3i	0.108319	+	0.0190996i	−0.119226	+	0.992867i	$0.538041\pi$
$942$		0			0
$943$	−1.52887e6	−	882691.i	−1.71928	−	0.992625i
$944$		0			0
$945$	−3128.23	+	8594.75i	−0.00350296	+	0.00962431i
$946$		0			0
$947$	442250.	−	371092.i	0.493138	−	0.413792i	−0.362011	−	0.932174i	$-0.617910\pi$
$947$	442250.	−	371092.i	0.493138	−	0.413792i	0.855149	+	0.518382i	$0.173465\pi$
$948$		0			0
$949$		−	1.12699e6i		−	1.25138i
$950$		0			0
$951$	123454.			0.136504
$952$		0			0
$953$	−776882.	−	925852.i	−0.855400	−	1.01943i	−0.999554	−	0.0298712i	$-0.990490\pi$
$953$	−776882.	−	925852.i	−0.855400	−	1.01943i	0.144153	−	0.989555i	$-0.453954\pi$
$954$		0			0
$955$	−89256.6	−	32486.7i	−0.0978664	−	0.0356205i
$956$		0			0
$957$	−117398.	+	203339.i	−0.128185	+	0.222022i
$958$		0			0
$959$	−13331.3	+	75605.5i	−0.0144956	+	0.0822084i
$960$		0			0
$961$	−360856.	−	625020.i	−0.390739	−	0.676780i
$962$		0			0
$963$	809738.	−	965008.i	0.873156	−	1.04059i
$964$		0			0
$965$	160484.	+	440926.i	0.172337	+	0.473491i
$966$		0			0
$967$	−45497.4	−	258029.i	−0.0486557	−	0.275940i	0.950767	−	0.309906i	$-0.100297\pi$
$967$	−45497.4	−	258029.i	−0.0486557	−	0.275940i	−0.999423	+	0.0339655i	$0.989186\pi$
$968$		0			0
$969$	44141.9	+	111156.i	0.0470115	+	0.118382i
$970$		0			0
$971$	−1.41989e6	+	250365.i	−1.50597	+	0.265543i	−0.864901	−	0.501943i	$-0.832619\pi$
$971$	−1.41989e6	+	250365.i	−1.50597	+	0.265543i	−0.641067	+	0.767485i	$0.721508\pi$
$972$		0			0
$973$	−147704.	+	53759.8i	−0.156015	+	0.0567848i
$974$		0			0
$975$	−76724.4	−	64379.4i	−0.0807095	−	0.0677233i
$976$		0			0
$977$	169383.	−	97793.1i	0.177451	−	0.102452i	−0.408643	−	0.912694i	$-0.633998\pi$
$977$	169383.	−	97793.1i	0.177451	−	0.102452i	0.586095	+	0.810243i	$0.300665\pi$
$978$		0			0
$979$	−406940.	−	71754.5i	−0.424585	−	0.0748658i
$980$		0			0
$981$	−885114.	−	511021.i	−0.919732	−	0.531007i
$982$		0			0
$983$	−219280.	+	602467.i	−0.226930	+	0.623485i	−0.999941	−	0.0109081i	$-0.996528\pi$
$983$	−219280.	+	602467.i	−0.226930	+	0.623485i	0.773010	+	0.634393i	$0.218750\pi$
$984$		0			0
$985$	−160373.	+	134569.i	−0.165295	+	0.138699i
$986$		0			0
$987$		−	6622.99i		−	0.00679860i
$988$		0			0
$989$	−284281.			−0.290640
$990$		0			0
$991$	400726.	+	477567.i	0.408038	+	0.486281i	0.930453	−	0.366411i	$-0.119413\pi$
$991$	400726.	+	477567.i	0.408038	+	0.486281i	−0.522415	+	0.852691i	$0.674969\pi$
$992$		0			0
$993$	80932.6	+	29457.1i	0.0820777	+	0.0298738i
$994$		0			0
$995$	−215045.	+	372469.i	−0.217212	+	0.376222i
$996$		0			0
$997$	178904.	−	1.01461e6i	0.179982	−	1.02073i	−0.752253	−	0.658875i	$-0.771033\pi$
$997$	178904.	−	1.01461e6i	0.179982	−	1.02073i	0.932235	−	0.361854i	$-0.117856\pi$
$998$		0			0
$999$	−58427.3	−	101199.i	−0.0585443	−	0.101402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.29.3	yes	42
19.2	odd	18	inner	76.5.j.a.21.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.21.3	✓	42	19.2	odd	18	inner
76.5.j.a.29.3	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)

\(f(q)\)	\(=\)	\(q+(-0.504186 - 0.600866i) q^{3} +(-8.75235 - 3.18559i) q^{5} +(-3.87876 + 6.71820i) q^{7} +(13.9587 - 79.1635i) q^{9} +O(q^{10})\)	\(q+(-0.504186 - 0.600866i) q^{3} +(-8.75235 - 3.18559i) q^{5} +(-3.87876 + 6.71820i) q^{7} +(13.9587 - 79.1635i) q^{9} +(-94.7123 - 164.047i) q^{11} +(-152.490 + 181.730i) q^{13} +(2.49870 + 6.86512i) q^{15} +(-73.3453 - 415.962i) q^{17} +(171.374 - 317.729i) q^{19} +(5.99236 - 1.05661i) q^{21} +(-669.617 + 243.721i) q^{23} +(-412.322 - 345.979i) q^{25} +(-109.627 + 63.2931i) q^{27} +(1556.26 + 274.410i) q^{29} +(-389.047 - 224.616i) q^{31} +(-50.8173 + 139.619i) q^{33} +(55.3497 - 46.4439i) q^{35} +923.124i q^{37} +186.079 q^{39} +(1592.45 + 1897.81i) q^{41} +(374.881 + 136.446i) q^{43} +(-374.354 + 648.400i) q^{45} +(189.007 - 1071.91i) q^{47} +(1170.41 + 2027.21i) q^{49} +(-212.957 + 253.793i) q^{51} +(-293.848 - 807.340i) q^{53} +(306.370 + 1737.51i) q^{55} +(-277.317 + 57.2217i) q^{57} +(-2307.63 + 406.897i) q^{59} +(5176.31 - 1884.02i) q^{61} +(477.695 + 400.833i) q^{63} +(1913.56 - 1104.80i) q^{65} +(-6476.74 - 1142.02i) q^{67} +(484.055 + 279.469i) q^{69} +(877.159 - 2409.97i) q^{71} +(-3639.17 + 3053.62i) q^{73} +422.188i q^{75} +1469.46 q^{77} +(-7424.75 - 8848.48i) q^{79} +(-6025.19 - 2192.99i) q^{81} +(5155.43 - 8929.47i) q^{83} +(-683.142 + 3874.29i) q^{85} +(-619.759 - 1073.45i) q^{87} +(1402.20 - 1671.08i) q^{89} +(-629.430 - 1729.35i) q^{91} +(61.1878 + 347.013i) q^{93} +(-2512.09 + 2234.95i) q^{95} +(6417.59 - 1131.59i) q^{97} +(-14308.6 + 5207.89i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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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