LMFDB - Embedded newform 76.4.i.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

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, 16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	76.5
Dual form			76.4.i.a.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.267608 + 1.51768i) q^{3} +(-1.63306 - 1.37030i) q^{5} +(13.0616 + 22.6234i) q^{7} +(23.1400 + 8.42226i) q^{9} +O(q^{10})$	\(q+(-0.267608 + 1.51768i) q^{3} +(-1.63306 - 1.37030i) q^{5} +(13.0616 + 22.6234i) q^{7} +(23.1400 + 8.42226i) q^{9} +(-11.3825 + 19.7151i) q^{11} +(4.34945 + 24.6670i) q^{13} +(2.51669 - 2.11175i) q^{15} +(-30.9936 + 11.2808i) q^{17} +(70.1829 + 43.9699i) q^{19} +(-37.8305 + 13.7692i) q^{21} +(113.464 - 95.2074i) q^{23} +(-20.9169 - 118.625i) q^{25} +(-39.7794 + 68.9000i) q^{27} +(-205.716 - 74.8745i) q^{29} +(-38.0684 - 65.9364i) q^{31} +(-26.8752 - 22.5509i) q^{33} +(9.67043 - 54.8437i) q^{35} -76.6444 q^{37} -38.6005 q^{39} +(56.3556 - 319.609i) q^{41} +(4.61160 + 3.86960i) q^{43} +(-26.2479 - 45.4627i) q^{45} +(285.373 + 103.867i) q^{47} +(-169.713 + 293.952i) q^{49} +(-8.82643 - 50.0572i) q^{51} +(-76.7556 + 64.4056i) q^{53} +(45.6039 - 16.5985i) q^{55} +(-85.5137 + 94.7485i) q^{57} +(280.717 - 102.173i) q^{59} +(-16.1497 + 13.5512i) q^{61} +(111.706 + 633.514i) q^{63} +(26.6982 - 46.2426i) q^{65} +(658.575 + 239.702i) q^{67} +(114.130 + 197.680i) q^{69} +(-35.9923 - 30.2011i) q^{71} +(-58.8084 + 333.519i) q^{73} +185.633 q^{75} -594.698 q^{77} +(-135.559 + 768.792i) q^{79} +(415.402 + 348.563i) q^{81} +(-553.962 - 959.490i) q^{83} +(66.0724 + 24.0484i) q^{85} +(168.687 - 292.174i) q^{87} +(-183.254 - 1039.28i) q^{89} +(-501.241 + 420.591i) q^{91} +(110.258 - 40.1305i) q^{93} +(-54.3609 - 167.977i) q^{95} +(1681.92 - 612.170i) q^{97} +(-429.437 + 360.340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	−0.267608	+	1.51768i	−0.0515011	+	0.292077i	−0.999670	−	0.0256896i	$-0.991822\pi$
$3$	−0.267608	+	1.51768i	−0.0515011	+	0.292077i	0.948169	+	0.317767i	$0.102933\pi$
$4$		0			0
$5$	−1.63306	−	1.37030i	−0.146065	−	0.122563i	0.566827	−	0.823837i	$-0.308171\pi$
$5$	−1.63306	−	1.37030i	−0.146065	−	0.122563i	−0.712892	+	0.701274i	$0.752615\pi$
$6$		0			0
$7$	13.0616	+	22.6234i	0.705263	+	1.22155i	0.966597	+	0.256302i	$0.0825043\pi$
$7$	13.0616	+	22.6234i	0.705263	+	1.22155i	−0.261334	+	0.965248i	$0.584162\pi$
$8$		0			0
$9$	23.1400	+	8.42226i	0.857036	+	0.311936i
$10$		0			0
$11$	−11.3825	+	19.7151i	−0.311996	+	0.540394i	−0.978794	−	0.204845i	$-0.934331\pi$
$11$	−11.3825	+	19.7151i	−0.311996	+	0.540394i	0.666798	+	0.745238i	$0.267664\pi$
$12$		0			0
$13$	4.34945	+	24.6670i	0.0927940	+	0.526261i	0.995401	+	0.0957953i	$0.0305394\pi$
$13$	4.34945	+	24.6670i	0.0927940	+	0.526261i	−0.902607	+	0.430465i	$0.858349\pi$
$14$		0			0
$15$	2.51669	−	2.11175i	0.0433204	−	0.0363502i
$16$		0			0
$17$	−30.9936	+	11.2808i	−0.442180	+	0.160940i	−0.553509	−	0.832843i	$-0.686712\pi$
$17$	−30.9936	+	11.2808i	−0.442180	+	0.160940i	0.111329	+	0.993784i	$0.464489\pi$
$18$		0			0
$19$	70.1829	+	43.9699i	0.847425	+	0.530915i
$19$	70.1829	+	43.9699i	0.847425	+	0.530915i
$20$		0			0
$21$	−37.8305	+	13.7692i	−0.393109	+	0.143080i
$22$		0			0
$23$	113.464	−	95.2074i	1.02865	−	0.863136i	0.0379560	−	0.999279i	$-0.487915\pi$
$23$	113.464	−	95.2074i	1.02865	−	0.863136i	0.990689	+	0.136144i	$0.0434709\pi$
$24$		0			0
$25$	−20.9169	−	118.625i	−0.167335	−	0.949003i
$26$		0			0
$27$	−39.7794	+	68.9000i	−0.283539	+	0.491104i
$28$		0			0
$29$	−205.716	−	74.8745i	−1.31726	−	0.479443i	−0.414680	−	0.909967i	$-0.636106\pi$
$29$	−205.716	−	74.8745i	−1.31726	−	0.479443i	−0.902579	+	0.430524i	$0.858329\pi$
$30$		0			0
$31$	−38.0684	−	65.9364i	−0.220557	−	0.382017i	0.734420	−	0.678695i	$-0.237454\pi$
$31$	−38.0684	−	65.9364i	−0.220557	−	0.382017i	−0.954977	+	0.296679i	$0.904121\pi$
$32$		0			0
$33$	−26.8752	−	22.5509i	−0.141769	−	0.118958i
$34$		0			0
$35$	9.67043	−	54.8437i	0.0467029	−	0.264865i
$36$		0			0
$37$	−76.6444			−0.340548			−0.170274	−	0.985397i	$-0.554465\pi$
$37$	−76.6444			−0.340548			−0.170274	+	0.985397i	$0.554465\pi$
$38$		0			0
$39$	−38.6005			−0.158488
$40$		0			0
$41$	56.3556	−	319.609i	0.214665	−	1.21743i	−0.666822	−	0.745217i	$-0.732346\pi$
$41$	56.3556	−	319.609i	0.214665	−	1.21743i	0.881487	−	0.472209i	$-0.156543\pi$
$42$		0			0
$43$	4.61160	+	3.86960i	0.0163550	+	0.0137234i	0.650928	−	0.759139i	$-0.274380\pi$
$43$	4.61160	+	3.86960i	0.0163550	+	0.0137234i	−0.634574	+	0.772863i	$0.718824\pi$
$44$		0			0
$45$	−26.2479	−	45.4627i	−0.0869512	−	0.150604i
$46$		0			0
$47$	285.373	+	103.867i	0.885659	+	0.322353i	0.744491	−	0.667632i	$-0.232692\pi$
$47$	285.373	+	103.867i	0.885659	+	0.322353i	0.141168	+	0.989986i	$0.454914\pi$
$48$		0			0
$49$	−169.713	+	293.952i	−0.494791	+	0.857003i
$50$		0			0
$51$	−8.82643	−	50.0572i	−0.0242343	−	0.137439i
$52$		0			0
$53$	−76.7556	+	64.4056i	−0.198928	+	0.166921i	−0.736810	−	0.676099i	$-0.763669\pi$
$53$	−76.7556	+	64.4056i	−0.198928	+	0.166921i	0.537882	+	0.843020i	$0.319225\pi$
$54$		0			0
$55$	45.6039	−	16.5985i	0.111804	−	0.0406934i
$56$		0			0
$57$	−85.5137	+	94.7485i	−0.198712	+	0.220171i
$58$		0			0
$59$	280.717	−	102.173i	0.619427	−	0.225453i	−0.0131958	−	0.999913i	$-0.504200\pi$
$59$	280.717	−	102.173i	0.619427	−	0.225453i	0.632623	+	0.774460i	$0.281978\pi$
$60$		0			0
$61$	−16.1497	+	13.5512i	−0.0338978	+	0.0284436i	−0.659579	−	0.751635i	$-0.729265\pi$
$61$	−16.1497	+	13.5512i	−0.0338978	+	0.0284436i	0.625681	+	0.780079i	$0.284821\pi$
$62$		0			0
$63$	111.706	+	633.514i	0.223390	+	1.26691i
$64$		0			0
$65$	26.6982	−	46.2426i	0.0509462	−	0.0882414i
$66$		0			0
$67$	658.575	+	239.702i	1.20086	+	0.437078i	0.863525	−	0.504306i	$-0.168251\pi$
$67$	658.575	+	239.702i	1.20086	+	0.437078i	0.337337	+	0.941384i	$0.390474\pi$
$68$		0			0
$69$	114.130	+	197.680i	0.199126	+	0.344896i
$70$		0			0
$71$	−35.9923	−	30.2011i	−0.0601620	−	0.0504819i	0.612211	−	0.790695i	$-0.290280\pi$
$71$	−35.9923	−	30.2011i	−0.0601620	−	0.0504819i	−0.672373	+	0.740213i	$0.734725\pi$
$72$		0			0
$73$	−58.8084	+	333.519i	−0.0942877	+	0.534732i	0.900676	+	0.434492i	$0.143072\pi$
$73$	−58.8084	+	333.519i	−0.0942877	+	0.534732i	−0.994963	+	0.100240i	$0.968039\pi$
$74$		0			0
$75$	185.633			0.285800
$76$		0			0
$77$	−594.698			−0.880158
$78$		0			0
$79$	−135.559	+	768.792i	−0.193058	+	1.09488i	0.722100	+	0.691788i	$0.243177\pi$
$79$	−135.559	+	768.792i	−0.193058	+	1.09488i	−0.915158	+	0.403095i	$0.867934\pi$
$80$		0			0
$81$	415.402	+	348.563i	0.569824	+	0.478139i
$82$		0			0
$83$	−553.962	−	959.490i	−0.732593	−	1.26889i	−0.955771	−	0.294111i	$-0.904977\pi$
$83$	−553.962	−	959.490i	−0.732593	−	1.26889i	0.223178	−	0.974778i	$-0.428357\pi$
$84$		0			0
$85$	66.0724	+	24.0484i	0.0843124	+	0.0306872i
$86$		0			0
$87$	168.687	−	292.174i	0.207875	−	0.360050i
$88$		0			0
$89$	−183.254	−	1039.28i	−0.218257	−	1.23780i	−0.875164	−	0.483826i	$-0.839247\pi$
$89$	−183.254	−	1039.28i	−0.218257	−	1.23780i	0.656907	−	0.753971i	$-0.271864\pi$
$90$		0			0
$91$	−501.241	+	420.591i	−0.577410	+	0.484505i
$92$		0			0
$93$	110.258	−	40.1305i	0.122937	−	0.0447456i
$94$		0			0
$95$	−54.3609	−	167.977i	−0.0587085	−	0.181411i
$96$		0			0
$97$	1681.92	−	612.170i	1.76055	−	0.640789i	0.760588	−	0.649235i	$-0.224911\pi$
$97$	1681.92	−	612.170i	1.76055	−	0.640789i	0.999964	+	0.00844673i	$0.00268871\pi$
$98$		0			0
$99$	−429.437	+	360.340i	−0.435960	+	0.365814i
$100$		0			0
$101$	23.0248	+	130.580i	0.0226837	+	0.128646i	0.994047	−	0.108955i	$-0.0347503\pi$
$101$	23.0248	+	130.580i	0.0226837	+	0.128646i	−0.971363	+	0.237600i	$0.923639\pi$
$102$		0			0
$103$	−178.233	+	308.709i	−0.170503	+	0.295320i	−0.938596	−	0.345018i	$-0.887873\pi$
$103$	−178.233	+	308.709i	−0.170503	+	0.295320i	0.768093	+	0.640339i	$0.221206\pi$
$104$		0			0
$105$	80.6473	+	29.3532i	0.0749559	+	0.0272817i
$106$		0			0
$107$	−981.590	−	1700.16i	−0.886859	−	1.53608i	−0.843568	−	0.537022i	$-0.819549\pi$
$107$	−981.590	−	1700.16i	−0.886859	−	1.53608i	−0.0432905	−	0.999063i	$-0.513784\pi$
$108$		0			0
$109$	−1662.90	−	1395.34i	−1.46126	−	1.22614i	−0.923813	−	0.382845i	$-0.874944\pi$
$109$	−1662.90	−	1395.34i	−1.46126	−	1.22614i	−0.537447	−	0.843297i	$-0.680611\pi$
$110$		0			0
$111$	20.5106	−	116.322i	0.0175386	−	0.0994662i
$112$		0			0
$113$	313.929			0.261345			0.130673	−	0.991426i	$-0.458286\pi$
$113$	313.929			0.261345			0.130673	+	0.991426i	$0.458286\pi$
$114$		0			0
$115$	−315.755			−0.256038
$116$		0			0
$117$	−107.105	+	607.425i	−0.0846317	+	0.479970i
$118$		0			0
$119$	−660.038	−	553.837i	−0.508450	−	0.426640i
$120$		0			0
$121$	406.376	+	703.864i	0.305316	+	0.528824i
$122$		0			0
$123$	469.982	+	171.059i	0.344527	+	0.125398i
$124$		0			0
$125$	−261.632	+	453.159i	−0.187208	+	0.324254i
$126$		0			0
$127$	−293.637	−	1665.30i	−0.205166	−	1.16355i	−0.897179	−	0.441668i	$-0.854387\pi$
$127$	−293.637	−	1665.30i	−0.205166	−	1.16355i	0.692013	−	0.721885i	$-0.256724\pi$
$128$		0			0
$129$	−7.10690	+	5.96340i	−0.00485060	+	0.00407014i
$130$		0			0
$131$	584.622	−	212.785i	0.389913	−	0.141917i	−0.139622	−	0.990205i	$-0.544589\pi$
$131$	584.622	−	212.785i	0.389913	−	0.141917i	0.529535	+	0.848288i	$0.322366\pi$
$132$		0			0
$133$	−78.0460	+	2162.10i	−0.0508831	+	1.40961i
$134$		0			0
$135$	159.376	−	58.0080i	0.101606	−	0.0369817i
$136$		0			0
$137$	2114.97	−	1774.67i	1.31894	−	1.10672i	0.332408	−	0.943136i	$-0.392139\pi$
$137$	2114.97	−	1774.67i	1.31894	−	1.10672i	0.986529	−	0.163585i	$-0.0523057\pi$
$138$		0			0
$139$	347.163	+	1968.86i	0.211842	+	1.20141i	0.886303	+	0.463105i	$0.153265\pi$
$139$	347.163	+	1968.86i	0.211842	+	1.20141i	−0.674462	+	0.738310i	$0.735624\pi$
$140$		0			0
$141$	−234.005	+	405.309i	−0.139765	+	0.242079i
$142$		0			0
$143$	−535.820	−	195.023i	−0.313339	−	0.114046i
$144$		0			0
$145$	233.346	+	404.167i	0.133643	+	0.231477i
$146$		0			0
$147$	−400.708	−	336.234i	−0.224829	−	0.188654i
$148$		0			0
$149$	−124.233	+	704.558i	−0.0683055	+	0.387380i	0.931420	+	0.363947i	$0.118571\pi$
$149$	−124.233	+	704.558i	−0.0683055	+	0.387380i	−0.999725	+	0.0234335i	$0.992540\pi$
$150$		0			0
$151$	−1259.42			−0.678744			−0.339372	−	0.940652i	$-0.610214\pi$
$151$	−1259.42			−0.678744			−0.339372	+	0.940652i	$0.610214\pi$
$152$		0			0
$153$	−812.201			−0.429167
$154$		0			0
$155$	−28.1846	+	159.843i	−0.0146054	+	0.0828315i
$156$		0			0
$157$	1541.61	+	1293.57i	0.783657	+	0.657566i	0.944167	−	0.329468i	$-0.106869\pi$
$157$	1541.61	+	1293.57i	0.783657	+	0.657566i	−0.160510	+	0.987034i	$0.551314\pi$
$158$		0			0
$159$	−77.2066	−	133.726i	−0.0385087	−	0.0666990i
$160$		0			0
$161$	3635.94	+	1323.38i	1.77983	+	0.647805i
$162$		0			0
$163$	−710.994	+	1231.48i	−0.341653	+	0.591760i	−0.984740	−	0.174033i	$-0.944320\pi$
$163$	−710.994	+	1231.48i	−0.341653	+	0.591760i	0.643087	+	0.765793i	$0.277653\pi$
$164$		0			0
$165$	12.9872	+	73.6539i	0.00612758	+	0.0347512i
$166$		0			0
$167$	−747.800	+	627.479i	−0.346506	+	0.290753i	−0.799385	−	0.600819i	$-0.794841\pi$
$167$	−747.800	+	627.479i	−0.346506	+	0.290753i	0.452879	+	0.891572i	$0.350397\pi$
$168$		0			0
$169$	1474.96	−	536.842i	0.671353	−	0.244353i
$170$		0			0
$171$	1253.70	+	1608.56i	0.560662	+	0.719355i
$172$		0			0
$173$	1729.86	−	629.616i	0.760222	−	0.276698i	0.0673217	−	0.997731i	$-0.478555\pi$
$173$	1729.86	−	629.616i	0.760222	−	0.276698i	0.692901	+	0.721033i	$0.256332\pi$
$174$		0			0
$175$	2410.51	−	2022.65i	1.04124	−	0.873705i
$176$		0			0
$177$	79.9431	+	453.380i	0.0339485	+	0.192532i
$178$		0			0
$179$	−1729.27	+	2995.18i	−0.722076	+	1.25067i	0.238090	+	0.971243i	$0.423479\pi$
$179$	−1729.27	+	2995.18i	−0.722076	+	1.25067i	−0.960166	+	0.279429i	$0.909855\pi$
$180$		0			0
$181$	−3587.38	−	1305.70i	−1.47319	−	0.536198i	−0.524227	−	0.851578i	$-0.675646\pi$
$181$	−3587.38	−	1305.70i	−1.47319	−	0.536198i	−0.948965	+	0.315380i	$0.897868\pi$
$182$		0			0
$183$	−16.2446	−	28.1365i	−0.00656196	−	0.0113656i
$184$		0			0
$185$	125.165	+	105.026i	0.0497421	+	0.0417386i
$186$		0			0
$187$	130.384	−	739.447i	0.0509874	−	0.289164i
$188$		0			0
$189$	−2078.34			−0.799878
$190$		0			0
$191$	−4246.46			−1.60871			−0.804354	−	0.594151i	$-0.797488\pi$
$191$	−4246.46			−1.60871			−0.804354	+	0.594151i	$0.797488\pi$
$192$		0			0
$193$	51.0295	−	289.403i	0.0190320	−	0.107936i	−0.973812	−	0.227355i	$-0.926992\pi$
$193$	51.0295	−	289.403i	0.0190320	−	0.107936i	0.992844	+	0.119419i	$0.0381032\pi$
$194$		0			0
$195$	63.0368	+	52.8942i	0.0231495	+	0.0194248i
$196$		0			0
$197$	−598.715	−	1037.01i	−0.216532	−	0.375044i	0.737214	−	0.675660i	$-0.236141\pi$
$197$	−598.715	−	1037.01i	−0.216532	−	0.375044i	−0.953745	+	0.300616i	$0.902808\pi$
$198$		0			0
$199$	3091.89	+	1125.36i	1.10140	+	0.400877i	0.827832	−	0.560976i	$-0.189574\pi$
$199$	3091.89	+	1125.36i	1.10140	+	0.400877i	0.273568	+	0.961853i	$0.411796\pi$
$200$		0			0
$201$	−540.030	+	935.360i	−0.189506	+	0.328235i
$202$		0			0
$203$	−993.071	−	5631.99i	−0.343350	−	1.94723i
$204$		0			0
$205$	−529.991	+	444.715i	−0.180567	+	0.151513i
$206$		0			0
$207$	3427.41	−	1247.48i	1.15083	−	0.418867i
$208$		0			0
$209$	−1665.73	+	883.176i	−0.551297	+	0.292299i
$210$		0			0
$211$	1457.95	−	530.650i	0.475684	−	0.173135i	−0.0930414	−	0.995662i	$-0.529659\pi$
$211$	1457.95	−	530.650i	0.475684	−	0.173135i	0.568726	+	0.822527i	$0.307437\pi$
$212$		0			0
$213$	55.4674	−	46.5427i	0.0178430	−	0.0149721i
$214$		0			0
$215$	−2.22852	−	12.6385i	−0.000706900	−	0.00400903i
$216$		0			0
$217$	994.471	−	1722.48i	0.311102	−	0.538844i
$218$		0			0
$219$	−490.437	−	178.505i	−0.151327	−	0.0550786i
$220$		0			0
$221$	−413.068	−	715.454i	−0.125728	−	0.217768i
$222$		0			0
$223$	−906.611	−	760.737i	−0.272247	−	0.228443i	0.496434	−	0.868074i	$-0.334642\pi$
$223$	−906.611	−	760.737i	−0.272247	−	0.228443i	−0.768681	+	0.639632i	$0.779087\pi$
$224$		0			0
$225$	515.079	−	2921.16i	0.152616	−	0.865528i
$226$		0			0
$227$	2614.91			0.764570			0.382285	−	0.924044i	$-0.375137\pi$
$227$	2614.91			0.764570			0.382285	+	0.924044i	$0.375137\pi$
$228$		0			0
$229$	−5501.92			−1.58767			−0.793837	−	0.608131i	$-0.791920\pi$
$229$	−5501.92			−1.58767			−0.793837	+	0.608131i	$0.791920\pi$
$230$		0			0
$231$	159.146	−	902.561i	0.0453291	−	0.257074i
$232$		0			0
$233$	−1297.42	−	1088.66i	−0.364792	−	0.306097i	0.441905	−	0.897062i	$-0.354303\pi$
$233$	−1297.42	−	1088.66i	−0.364792	−	0.306097i	−0.806697	+	0.590965i	$0.798747\pi$
$234$		0			0
$235$	−323.702	−	560.668i	−0.0898552	−	0.155634i
$236$		0			0
$237$	−1130.50	−	411.469i	−0.309848	−	0.112775i
$238$		0			0
$239$	−2381.98	+	4125.71i	−0.644676	+	1.11661i	0.339701	+	0.940534i	$0.389674\pi$
$239$	−2381.98	+	4125.71i	−0.644676	+	1.11661i	−0.984376	+	0.176077i	$0.943659\pi$
$240$		0			0
$241$	−994.305	−	5638.98i	−0.265763	−	1.50721i	−0.766855	−	0.641821i	$-0.778179\pi$
$241$	−994.305	−	5638.98i	−0.265763	−	1.50721i	0.501092	−	0.865394i	$-0.332932\pi$
$242$		0			0
$243$	−2285.70	+	1917.93i	−0.603407	+	0.506319i
$244$		0			0
$245$	679.954	−	247.483i	0.177309	−	0.0645351i
$246$		0			0
$247$	−779.348	+	1922.45i	−0.200764	+	0.495232i
$248$		0			0
$249$	1604.44	−	583.969i	0.408343	−	0.148625i
$250$		0			0
$251$	3625.13	−	3041.85i	0.911619	−	0.764939i	−0.0608070	−	0.998150i	$-0.519367\pi$
$251$	3625.13	−	3041.85i	0.911619	−	0.764939i	0.972426	+	0.233210i	$0.0749230\pi$
$252$		0			0
$253$	585.521	+	3320.65i	0.145499	+	0.825169i
$254$		0			0
$255$	−54.1792	+	93.8411i	−0.0133052	+	0.0230453i
$256$		0			0
$257$	6840.93	+	2489.90i	1.66041	+	0.604340i	0.990427	−	0.138035i	$-0.0440788\pi$
$257$	6840.93	+	2489.90i	1.66041	+	0.604340i	0.669984	+	0.742376i	$0.266301\pi$
$258$		0			0
$259$	−1001.10	−	1733.96i	−0.240176	−	0.415996i
$260$		0			0
$261$	−4129.65	−	3465.19i	−0.979383	−	0.821800i
$262$		0			0
$263$	−1214.70	+	6888.92i	−0.284798	+	1.61517i	0.421210	+	0.906963i	$0.361605\pi$
$263$	−1214.70	+	6888.92i	−0.284798	+	1.61517i	−0.706008	+	0.708204i	$0.749506\pi$
$264$		0			0
$265$	213.601			0.0495148
$266$		0			0
$267$	1626.34			0.372773
$268$		0			0
$269$	−1327.89	+	7530.81i	−0.300976	+	1.70692i	0.340889	+	0.940103i	$0.389272\pi$
$269$	−1327.89	+	7530.81i	−0.300976	+	1.70692i	−0.641865	+	0.766817i	$0.721839\pi$
$270$		0			0
$271$	2637.32	+	2212.97i	0.591165	+	0.496046i	0.888592	−	0.458698i	$-0.151684\pi$
$271$	2637.32	+	2212.97i	0.591165	+	0.496046i	−0.297427	+	0.954745i	$0.596129\pi$
$272$		0			0
$273$	−504.186	−	873.276i	−0.111776	−	0.193601i
$274$		0			0
$275$	2576.80	+	937.879i	0.565043	+	0.205659i
$276$		0			0
$277$	2759.78	−	4780.08i	0.598625	−	1.03685i	−0.394400	−	0.918939i	$-0.629047\pi$
$277$	2759.78	−	4780.08i	0.598625	−	1.03685i	0.993024	−	0.117909i	$-0.0376193\pi$
$278$		0			0
$279$	−325.568	−	1846.39i	−0.0698611	−	0.396202i
$280$		0			0
$281$	−2825.84	+	2371.16i	−0.599912	+	0.503386i	−0.891417	−	0.453183i	$-0.850288\pi$
$281$	−2825.84	+	2371.16i	−0.599912	+	0.503386i	0.291506	+	0.956569i	$0.405844\pi$
$282$		0			0
$283$	767.067	−	279.190i	0.161122	−	0.0586434i	−0.260200	−	0.965555i	$-0.583789\pi$
$283$	767.067	−	279.190i	0.161122	−	0.0586434i	0.421322	+	0.906911i	$0.361566\pi$
$284$		0			0
$285$	269.482	−	37.5504i	0.0560097	−	0.00780454i
$286$		0			0
$287$	7966.74	−	2899.66i	1.63854	−	0.596381i
$288$		0			0
$289$	−2930.23	+	2458.75i	−0.596423	+	0.500458i
$290$		0			0
$291$	478.982	+	2716.44i	0.0964894	+	0.547219i
$292$		0			0
$293$	−4065.27	+	7041.25i	−0.810565	+	1.40394i	0.101905	+	0.994794i	$0.467506\pi$
$293$	−4065.27	+	7041.25i	−0.810565	+	1.40394i	−0.912469	+	0.409145i	$0.865827\pi$
$294$		0			0
$295$	−598.433	−	217.812i	−0.118109	−	0.0429881i
$296$		0			0
$297$	−905.581	−	1568.51i	−0.176926	−	0.306446i
$298$		0			0
$299$	2841.99	+	2384.71i	0.549687	+	0.461242i
$300$		0			0
$301$	−27.3084	+	154.874i	−0.00522934	+	0.0296570i
$302$		0			0
$303$	−204.340			−0.0387427
$304$		0			0
$305$	44.9427			0.00843742
$306$		0			0
$307$	−710.403	+	4028.90i	−0.132068	+	0.748994i	0.844789	+	0.535100i	$0.179726\pi$
$307$	−710.403	+	4028.90i	−0.132068	+	0.748994i	−0.976857	+	0.213895i	$0.931385\pi$
$308$		0			0
$309$	−420.824	−	353.113i	−0.0774752	−	0.0650094i
$310$		0			0
$311$	708.208	+	1226.65i	0.129128	+	0.223656i	0.923339	−	0.383986i	$-0.125449\pi$
$311$	708.208	+	1226.65i	0.129128	+	0.223656i	−0.794211	+	0.607642i	$0.792116\pi$
$312$		0			0
$313$	1029.24	+	374.612i	0.185866	+	0.0676496i	0.433276	−	0.901261i	$-0.357357\pi$
$313$	1029.24	+	374.612i	0.185866	+	0.0676496i	−0.247411	+	0.968911i	$0.579580\pi$
$314$		0			0
$315$	685.681	−	1187.63i	0.122647	−	0.212431i
$316$		0			0
$317$	−243.202	−	1379.27i	−0.0430901	−	0.244376i	0.955653	−	0.294495i	$-0.0951513\pi$
$317$	−243.202	−	1379.27i	−0.0430901	−	0.244376i	−0.998743	+	0.0501183i	$0.984040\pi$
$318$		0			0
$319$	3817.73	−	3203.45i	0.670068	−	0.562254i
$320$		0			0
$321$	2842.98	−	1034.76i	0.494330	−	0.179921i
$322$		0			0
$323$	−2671.24	−	571.071i	−0.460160	−	0.0983753i
$324$		0			0
$325$	2835.15	−	1031.91i	0.483896	−	0.176124i
$326$		0			0
$327$	2562.69	−	2150.35i	0.433385	−	0.363653i
$328$		0			0
$329$	1377.61	+	7812.80i	0.230851	+	1.30922i
$330$		0			0
$331$	−254.904	+	441.506i	−0.0423287	+	0.0733154i	−0.886414	−	0.462894i	$-0.846811\pi$
$331$	−254.904	+	441.506i	−0.0423287	+	0.0733154i	0.844085	+	0.536210i	$0.180144\pi$
$332$		0			0
$333$	−1773.55	−	645.519i	−0.291861	−	0.106229i
$334$		0			0
$335$	−747.028	−	1293.89i	−0.121834	−	0.211023i
$336$		0			0
$337$	−7504.69	−	6297.19i	−1.21308	−	1.01789i	−0.999157	−	0.0410405i	$-0.986933\pi$
$337$	−7504.69	−	6297.19i	−1.21308	−	1.01789i	−0.213919	−	0.976851i	$-0.568623\pi$
$338$		0			0
$339$	−84.0099	+	476.444i	−0.0134596	+	0.0763330i
$340$		0			0
$341$	1733.26			0.275253
$342$		0			0
$343$	93.3467			0.0146946
$344$		0			0
$345$	84.4986	−	479.215i	0.0131862	−	0.0747828i
$346$		0			0
$347$	−3217.28	−	2699.62i	−0.497731	−	0.417646i	0.359057	−	0.933316i	$-0.383099\pi$
$347$	−3217.28	−	2699.62i	−0.497731	−	0.417646i	−0.856787	+	0.515670i	$0.827543\pi$
$348$		0			0
$349$	−2759.33	−	4779.29i	−0.423219	−	0.733036i	0.573034	−	0.819532i	$-0.305766\pi$
$349$	−2759.33	−	4779.29i	−0.423219	−	0.733036i	−0.996252	+	0.0864957i	$0.972433\pi$
$350$		0			0
$351$	−1872.57	−	681.561i	−0.284760	−	0.103644i
$352$		0			0
$353$	−584.941	+	1013.15i	−0.0881963	+	0.152760i	−0.906749	−	0.421671i	$-0.861444\pi$
$353$	−584.941	+	1013.15i	−0.0881963	+	0.152760i	0.818552	+	0.574432i	$0.194777\pi$
$354$		0			0
$355$	17.3929	+	98.6403i	0.00260034	+	0.0147473i
$356$		0			0
$357$	1017.18	−	853.514i	0.150798	−	0.126534i
$358$		0			0
$359$	−12164.9	+	4427.67i	−1.78841	+	0.650928i	−0.789082	+	0.614288i	$0.789443\pi$
$359$	−12164.9	+	4427.67i	−1.78841	+	0.650928i	−0.999329	+	0.0366405i	$0.988334\pi$
$360$		0			0
$361$	2992.29	+	6171.88i	0.436258	+	0.899822i
$362$		0			0
$363$	−1176.99	+	428.389i	−0.170182	+	0.0619410i
$364$		0			0
$365$	553.058	−	464.071i	0.0793106	−	0.0665495i
$366$		0			0
$367$	−1065.47	−	6042.60i	−0.151546	−	0.859458i	−0.961876	−	0.273485i	$-0.911824\pi$
$367$	−1065.47	−	6042.60i	−0.151546	−	0.859458i	0.810331	−	0.585973i	$-0.199287\pi$
$368$		0			0
$369$	3995.89	−	6921.09i	0.563734	−	0.976416i
$370$		0			0
$371$	−2459.63	−	895.233i	−0.344199	−	0.125278i
$372$		0			0
$373$	−3446.91	−	5970.22i	−0.478483	−	0.828757i	0.521213	−	0.853427i	$-0.325480\pi$
$373$	−3446.91	−	5970.22i	−0.478483	−	0.828757i	−0.999696	+	0.0246701i	$0.992146\pi$
$374$		0			0
$375$	−617.735	−	518.341i	−0.0850659	−	0.0713788i
$376$		0			0
$377$	952.176	−	5400.06i	0.130078	−	0.737711i
$378$		0			0
$379$	−4738.31			−0.642192			−0.321096	−	0.947047i	$-0.604051\pi$
$379$	−4738.31			−0.642192			−0.321096	+	0.947047i	$0.604051\pi$
$380$		0			0
$381$	2605.96			0.350414
$382$		0			0
$383$	1767.08	−	10021.6i	0.235754	−	1.33703i	−0.605267	−	0.796022i	$-0.706934\pi$
$383$	1767.08	−	10021.6i	0.235754	−	1.33703i	0.841021	−	0.541003i	$-0.181955\pi$
$384$		0			0
$385$	971.176	+	814.914i	0.128560	+	0.107875i
$386$		0			0
$387$	74.1216	+	128.382i	0.00973595	+	0.0168632i
$388$		0			0
$389$	7036.59	+	2561.11i	0.917144	+	0.333813i	0.757102	−	0.653297i	$-0.226615\pi$
$389$	7036.59	+	2561.11i	0.917144	+	0.333813i	0.160043	+	0.987110i	$0.448837\pi$
$390$		0			0
$391$	−2442.64	+	4230.78i	−0.315933	+	0.547212i
$392$		0			0
$393$	166.490	+	944.211i	0.0213697	+	0.121194i
$394$		0			0
$395$	1274.85	−	1069.72i	0.162391	−	0.136263i
$396$		0			0
$397$	9576.26	−	3485.48i	1.21063	−	0.440632i	0.343706	−	0.939077i	$-0.388318\pi$
$397$	9576.26	−	3485.48i	1.21063	−	0.440632i	0.866921	+	0.498445i	$0.166095\pi$
$398$		0			0
$399$	−3260.49	−	697.043i	−0.409094	−	0.0874582i
$400$		0			0
$401$	−9605.55	+	3496.14i	−1.19621	+	0.435383i	−0.861898	−	0.507081i	$-0.830724\pi$
$401$	−9605.55	+	3496.14i	−1.19621	+	0.435383i	−0.334307	+	0.942464i	$0.608502\pi$
$402$		0			0
$403$	1460.87	−	1225.82i	0.180574	−	0.151520i
$404$		0			0
$405$	−200.739	−	1138.45i	−0.0246292	−	0.139679i
$406$		0			0
$407$	872.407	−	1511.05i	0.106250	−	0.184030i
$408$		0			0
$409$	−2549.54	−	927.955i	−0.308231	−	0.112187i	0.183273	−	0.983062i	$-0.441331\pi$
$409$	−2549.54	−	927.955i	−0.308231	−	0.112187i	−0.491504	+	0.870875i	$0.663553\pi$
$410$		0			0
$411$	2127.40	+	3684.77i	0.255321	+	0.442229i
$412$		0			0
$413$	5978.12	+	5016.24i	0.712261	+	0.597658i
$414$		0			0
$415$	−410.136	+	2326.00i	−0.0485127	+	0.275129i
$416$		0			0
$417$	−3081.00			−0.361816
$418$		0			0
$419$	−9715.75			−1.13280			−0.566402	−	0.824129i	$-0.691665\pi$
$419$	−9715.75			−1.13280			−0.566402	+	0.824129i	$0.691665\pi$
$420$		0			0
$421$	792.176	−	4492.65i	0.0917062	−	0.520091i	−0.904001	−	0.427531i	$-0.859384\pi$
$421$	792.176	−	4492.65i	0.0917062	−	0.520091i	0.995707	−	0.0925609i	$-0.0295053\pi$
$422$		0			0
$423$	5728.73	+	4806.97i	0.658488	+	0.552537i
$424$		0			0
$425$	1986.47	+	3440.67i	0.226725	+	0.392699i
$426$		0			0
$427$	−517.518	−	188.361i	−0.0586521	−	0.0213476i
$428$		0			0
$429$	439.371	−	761.013i	0.0494476	−	0.0856458i
$430$		0			0
$431$	564.188	+	3199.67i	0.0630534	+	0.357593i	0.999968	+	0.00803439i	$0.00255745\pi$
$431$	564.188	+	3199.67i	0.0630534	+	0.357593i	−0.936914	+	0.349559i	$0.886331\pi$
$432$		0			0
$433$	−6423.03	+	5389.57i	−0.712867	+	0.598166i	−0.925402	−	0.378987i	$-0.876272\pi$
$433$	−6423.03	+	5389.57i	−0.712867	+	0.598166i	0.212535	+	0.977153i	$0.431828\pi$
$434$		0			0
$435$	−675.840	+	245.986i	−0.0744921	+	0.0271129i
$436$		0			0
$437$	12149.5	−	1692.94i	1.32995	−	0.185319i
$438$		0			0
$439$	−411.251	+	149.683i	−0.0447105	+	0.0162733i	−0.364279	−	0.931290i	$-0.618684\pi$
$439$	−411.251	+	149.683i	−0.0447105	+	0.0162733i	0.319568	+	0.947563i	$0.396462\pi$
$440$		0			0
$441$	−6402.90	+	5372.67i	−0.691383	+	0.580140i
$442$		0			0
$443$	−1810.67	−	10268.8i	−0.194193	−	1.10132i	−0.913564	−	0.406695i	$-0.866681\pi$
$443$	−1810.67	−	10268.8i	−0.194193	−	1.10132i	0.719371	−	0.694626i	$-0.244430\pi$
$444$		0			0
$445$	−1124.87	+	1948.32i	−0.119829	+	0.207549i
$446$		0			0
$447$	−1036.05	−	377.090i	−0.109627	−	0.0399010i
$448$		0			0
$449$	6593.60	+	11420.5i	0.693032	+	1.20037i	0.970840	+	0.239729i	$0.0770587\pi$
$449$	6593.60	+	11420.5i	0.693032	+	1.20037i	−0.277808	+	0.960637i	$0.589608\pi$
$450$		0			0
$451$	5659.65	+	4749.01i	0.590915	+	0.495836i
$452$		0			0
$453$	337.031	−	1911.40i	0.0349561	−	0.198246i
$454$		0			0
$455$	1394.89			0.143722
$456$		0			0
$457$	8010.78			0.819974			0.409987	−	0.912091i	$-0.365533\pi$
$457$	8010.78			0.819974			0.409987	+	0.912091i	$0.365533\pi$
$458$		0			0
$459$	455.665	−	2584.20i	0.0463369	−	0.262789i
$460$		0			0
$461$	6625.35	+	5559.33i	0.669357	+	0.561657i	0.912875	−	0.408239i	$-0.133857\pi$
$461$	6625.35	+	5559.33i	0.669357	+	0.561657i	−0.243518	+	0.969896i	$0.578302\pi$
$462$		0			0
$463$	1698.73	+	2942.29i	0.170511	+	0.295334i	0.938599	−	0.345011i	$-0.112125\pi$
$463$	1698.73	+	2942.29i	0.170511	+	0.295334i	−0.768087	+	0.640345i	$0.778791\pi$
$464$		0			0
$465$	−235.048	−	85.5503i	−0.0234410	−	0.00853183i
$466$		0			0
$467$	−4802.34	+	8317.90i	−0.475859	+	0.824211i	−0.999618	−	0.0276553i	$-0.991196\pi$
$467$	−4802.34	+	8317.90i	−0.475859	+	0.824211i	0.523759	+	0.851867i	$0.324529\pi$
$468$		0			0
$469$	3179.20	+	18030.1i	0.313010	+	1.77517i
$470$		0			0
$471$	−2375.77	+	1993.51i	−0.232419	+	0.195023i
$472$		0			0
$473$	−128.781	+	46.8725i	−0.0125187	+	0.00455645i
$474$		0			0
$475$	3747.94	−	9245.19i	0.362037	−	0.893050i
$476$		0			0
$477$	−2318.56	+	843.888i	−0.222557	+	0.0810041i
$478$		0			0
$479$	2261.14	−	1897.32i	0.215687	−	0.180983i	−0.528543	−	0.848907i	$-0.677261\pi$
$479$	2261.14	−	1897.32i	0.215687	−	0.180983i	0.744230	+	0.667924i	$0.232817\pi$
$480$		0			0
$481$	−333.361	−	1890.59i	−0.0316008	−	0.179217i
$482$		0			0
$483$	−2981.46	+	5164.05i	−0.280872	+	0.486485i
$484$		0			0
$485$	−3585.53	−	1305.03i	−0.335692	−	0.122182i
$486$		0			0
$487$	2255.59	+	3906.80i	0.209878	+	0.363519i	0.951676	−	0.307104i	$-0.0993600\pi$
$487$	2255.59	+	3906.80i	0.209878	+	0.363519i	−0.741798	+	0.670623i	$0.766027\pi$
$488$		0			0
$489$	−1678.72	−	1408.61i	−0.155244	−	0.130265i
$490$		0			0
$491$	604.633	−	3429.04i	0.0555737	−	0.315174i	−0.944331	−	0.328998i	$-0.893289\pi$
$491$	604.633	−	3429.04i	0.0555737	−	0.315174i	0.999904	+	0.0138234i	$0.00440026\pi$
$492$		0			0
$493$	7220.53			0.659627
$494$		0			0
$495$	1195.07			0.108514
$496$		0			0
$497$	213.135	−	1208.75i	0.0192362	−	0.109094i
$498$		0			0
$499$	−10462.5	−	8779.07i	−0.938607	−	0.787585i	0.0387350	−	0.999250i	$-0.487667\pi$
$499$	−10462.5	−	8779.07i	−0.938607	−	0.787585i	−0.977342	+	0.211664i	$0.932112\pi$
$500$		0			0
$501$	−752.194	−	1302.84i	−0.0670770	−	0.116181i
$502$		0			0
$503$	−8681.93	−	3159.96i	−0.769599	−	0.280111i	−0.0727701	−	0.997349i	$-0.523184\pi$
$503$	−8681.93	−	3159.96i	−0.769599	−	0.280111i	−0.696829	+	0.717238i	$0.745406\pi$
$504$		0			0
$505$	141.333	−	244.796i	0.0124539	−	0.0215708i
$506$		0			0
$507$	420.043	+	2382.18i	0.0367944	+	0.208671i
$508$		0			0
$509$	9008.93	−	7559.39i	0.784507	−	0.658279i	−0.159873	−	0.987138i	$-0.551108\pi$
$509$	9008.93	−	7559.39i	0.784507	−	0.658279i	0.944379	+	0.328858i	$0.106664\pi$
$510$		0			0
$511$	−8313.48	+	3025.86i	−0.719700	+	0.261950i
$512$		0			0
$513$	−5821.37	+	3086.51i	−0.501013	+	0.265639i
$514$		0			0
$515$	714.088	−	259.907i	0.0610999	−	0.0222386i
$516$		0			0
$517$	−5296.02	+	4443.89i	−0.450520	+	0.378031i
$518$		0			0
$519$	492.632	+	2793.85i	0.0416650	+	0.236294i
$520$		0			0
$521$	10141.4	−	17565.4i	0.852790	−	1.47707i	−0.0258911	−	0.999665i	$-0.508242\pi$
$521$	10141.4	−	17565.4i	0.852790	−	1.47707i	0.878681	−	0.477410i	$-0.158424\pi$
$522$		0			0
$523$	13667.2	+	4974.46i	1.14269	+	0.415905i	0.842884	−	0.538096i	$-0.180856\pi$
$523$	13667.2	+	4974.46i	1.14269	+	0.415905i	0.299805	+	0.954001i	$0.403078\pi$
$524$		0			0
$525$	2424.67	+	4199.65i	0.201564	+	0.349120i
$526$		0			0
$527$	1923.69	+	1614.17i	0.159008	+	0.133424i
$528$		0			0
$529$	1696.80	−	9623.04i	0.139459	−	0.790913i
$530$		0			0
$531$	7356.30			0.601198
$532$		0			0
$533$	8128.89			0.660603
$534$		0			0
$535$	−726.738	+	4121.54i	−0.0587283	+	0.333065i
$536$		0			0
$537$	−4082.96	−	3426.01i	−0.328105	−	0.275313i
$538$		0			0
$539$	−3863.53	−	6691.84i	−0.308746	−	0.534764i
$540$		0			0
$541$	−19138.2	−	6965.74i	−1.52092	−	0.553568i	−0.559540	−	0.828804i	$-0.689022\pi$
$541$	−19138.2	−	6965.74i	−1.52092	−	0.553568i	−0.961377	+	0.275235i	$0.911244\pi$
$542$		0			0
$543$	2941.64	−	5095.07i	0.232482	−	0.402671i
$544$		0			0
$545$	803.583	+	4557.35i	0.0631591	+	0.358193i
$546$		0			0
$547$	−1575.78	+	1322.23i	−0.123173	+	0.103354i	−0.702293	−	0.711888i	$-0.747840\pi$
$547$	−1575.78	+	1322.23i	−0.123173	+	0.103354i	0.579121	+	0.815242i	$0.303396\pi$
$548$		0			0
$549$	−487.837	+	177.558i	−0.0379242	+	0.0138033i
$550$		0			0
$551$	−11145.5	−	14300.2i	−0.861734	−	1.10564i
$552$		0			0
$553$	−19163.3	+	6974.88i	−1.47361	+	0.536351i
$554$		0			0
$555$	−192.890	+	161.854i	−0.0147527	+	0.0123790i
$556$		0			0
$557$	−2314.71	−	13127.4i	−0.176082	−	0.998608i	−0.936888	−	0.349629i	$-0.886308\pi$
$557$	−2314.71	−	13127.4i	−0.176082	−	0.998608i	0.760807	−	0.648979i	$-0.224804\pi$
$558$		0			0
$559$	−75.3933	+	130.585i	−0.00570446	+	0.00988042i
$560$		0			0
$561$	1087.35	+	395.763i	0.0818324	+	0.0297846i
$562$		0			0
$563$	−5683.61	−	9844.29i	−0.425463	−	0.736923i	0.571001	−	0.820949i	$-0.306555\pi$
$563$	−5683.61	−	9844.29i	−0.425463	−	0.736923i	−0.996464	+	0.0840266i	$0.973222\pi$
$564$		0			0
$565$	−512.665	−	430.177i	−0.0381734	−	0.0320313i
$566$		0			0
$567$	−2459.87	+	13950.6i	−0.182196	+	1.03328i
$568$		0			0
$569$	−26606.1			−1.96026			−0.980129	−	0.198362i	$-0.936438\pi$
$569$	−26606.1			−1.96026			−0.980129	+	0.198362i	$0.936438\pi$
$570$		0			0
$571$	21163.7			1.55109			0.775545	−	0.631292i	$-0.217475\pi$
$571$	21163.7			1.55109			0.775545	+	0.631292i	$0.217475\pi$
$572$		0			0
$573$	1136.39	−	6444.76i	0.0828503	−	0.469867i
$574$		0			0
$575$	−13667.3	−	11468.3i	−0.991247	−	0.831755i
$576$		0			0
$577$	8084.37	+	14002.5i	0.583287	+	1.01028i	0.995087	+	0.0990082i	$0.0315670\pi$
$577$	8084.37	+	14002.5i	0.583287	+	1.01028i	−0.411800	+	0.911274i	$0.635100\pi$
$578$		0			0
$579$	425.564	+	154.893i	0.0305455	+	0.0111177i
$580$		0			0
$581$	14471.3	−	25065.0i	1.03334	−	1.78980i
$582$		0			0
$583$	−396.091	−	2246.34i	−0.0281379	−	0.159578i
$584$		0			0
$585$	1007.26	−	845.194i	0.0711884	−	0.0597341i
$586$		0			0
$587$	−12278.5	+	4469.00i	−0.863351	+	0.314234i	−0.735472	−	0.677556i	$-0.763039\pi$
$587$	−12278.5	+	4469.00i	−0.863351	+	0.314234i	−0.127880	+	0.991790i	$0.540817\pi$
$588$		0			0
$589$	227.466	−	6301.47i	0.0159127	−	0.440828i
$590$		0			0
$591$	1734.06	−	631.147i	0.120693	−	0.0439288i
$592$		0			0
$593$	−14656.3	+	12298.1i	−1.01495	+	0.851641i	−0.988984	−	0.148022i	$-0.952709\pi$
$593$	−14656.3	+	12298.1i	−1.01495	+	0.851641i	−0.0259618	+	0.999663i	$0.508265\pi$
$594$		0			0
$595$	318.957	+	1808.90i	0.0219764	+	0.124634i
$596$		0			0
$597$	−2535.34	+	4391.35i	−0.173810	+	0.301048i
$598$		0			0
$599$	8717.61	+	3172.95i	0.594644	+	0.216433i	0.621771	−	0.783199i	$-0.286414\pi$
$599$	8717.61	+	3172.95i	0.594644	+	0.216433i	−0.0271266	+	0.999632i	$0.508636\pi$
$600$		0			0
$601$	−3548.83	−	6146.75i	−0.240865	−	0.417190i	0.720096	−	0.693874i	$-0.244098\pi$
$601$	−3548.83	−	6146.75i	−0.240865	−	0.417190i	−0.960961	+	0.276684i	$0.910764\pi$
$602$		0			0
$603$	13220.6	+	11093.4i	0.892842	+	0.749183i
$604$		0			0
$605$	300.868	−	1706.31i	0.0202182	−	0.114663i
$606$		0			0
$607$	26734.0			1.78764			0.893822	−	0.448421i	$-0.148014\pi$
$607$	26734.0			1.78764			0.893822	+	0.448421i	$0.148014\pi$
$608$		0			0
$609$	8813.30			0.586425
$610$		0			0
$611$	−1320.88	+	7491.06i	−0.0874581	+	0.496000i
$612$		0			0
$613$	12504.3	+	10492.4i	0.823890	+	0.691325i	0.953879	−	0.300190i	$-0.0970500\pi$
$613$	12504.3	+	10492.4i	0.823890	+	0.691325i	−0.129990	+	0.991515i	$0.541494\pi$
$614$		0			0
$615$	−533.105	−	923.365i	−0.0349542	−	0.0605425i
$616$		0			0
$617$	−18643.0	−	6785.50i	−1.21643	−	0.442745i	−0.347502	−	0.937679i	$-0.612970\pi$
$617$	−18643.0	−	6785.50i	−1.21643	−	0.442745i	−0.868930	+	0.494934i	$0.835192\pi$
$618$		0			0
$619$	8978.10	−	15550.5i	0.582973	−	1.00974i	−0.412151	−	0.911115i	$-0.635223\pi$
$619$	8978.10	−	15550.5i	0.582973	−	1.00974i	0.995125	−	0.0986240i	$-0.0314441\pi$
$620$		0			0
$621$	2046.27	+	11605.0i	0.132228	+	0.749905i
$622$		0			0
$623$	21118.6	−	17720.6i	1.35810	−	1.13958i
$624$		0			0
$625$	−13100.7	+	4768.25i	−0.838442	+	0.305168i
$626$		0			0
$627$	−894.615	−	2764.39i	−0.0569816	−	0.176075i
$628$		0			0
$629$	2375.49	−	864.607i	0.150583	−	0.0548079i
$630$		0			0
$631$	−15164.7	+	12724.7i	−0.956732	+	0.802794i	−0.980418	−	0.196926i	$-0.936904\pi$
$631$	−15164.7	+	12724.7i	−0.956732	+	0.802794i	0.0236860	+	0.999719i	$0.492460\pi$
$632$		0			0
$633$	415.198	+	2354.70i	0.0260705	+	0.147853i
$634$		0			0
$635$	−1802.43	+	3121.89i	−0.112641	+	0.195100i
$636$		0			0
$637$	−7989.07	−	2907.78i	−0.496921	−	0.180864i
$638$		0			0
$639$	−578.499	−	1001.99i	−0.0358139	−	0.0620314i
$640$		0			0
$641$	−5732.25	−	4809.92i	−0.353214	−	0.296382i	0.448865	−	0.893599i	$-0.351828\pi$
$641$	−5732.25	−	4809.92i	−0.353214	−	0.296382i	−0.802079	+	0.597218i	$0.796273\pi$
$642$		0			0
$643$	−3550.28	+	20134.6i	−0.217744	+	1.23489i	0.658337	+	0.752723i	$0.271260\pi$
$643$	−3550.28	+	20134.6i	−0.217744	+	1.23489i	−0.876081	+	0.482164i	$0.839851\pi$
$644$		0			0
$645$	19.7776			0.00120735
$646$		0			0
$647$	7784.89			0.473038			0.236519	−	0.971627i	$-0.423993\pi$
$647$	7784.89			0.473038			0.236519	+	0.971627i	$0.423993\pi$
$648$		0			0
$649$	−1180.92	+	6697.34i	−0.0714257	+	0.405075i
$650$		0			0
$651$	2348.04	+	1970.24i	0.141362	+	0.118617i
$652$		0			0
$653$	−168.941	−	292.614i	−0.0101243	−	0.0175358i	0.860919	−	0.508742i	$-0.169889\pi$
$653$	−168.941	−	292.614i	−0.0101243	−	0.0175358i	−0.871043	+	0.491206i	$0.836556\pi$
$654$		0			0
$655$	−1246.30	−	453.616i	−0.0743465	−	0.0270599i
$656$		0			0
$657$	−4169.81	+	7222.32i	−0.247610	+	0.428873i
$658$		0			0
$659$	3543.67	+	20097.2i	0.209472	+	1.18797i	0.890246	+	0.455480i	$0.150532\pi$
$659$	3543.67	+	20097.2i	0.209472	+	1.18797i	−0.680774	+	0.732493i	$0.738356\pi$
$660$		0			0
$661$	9635.26	−	8084.94i	0.566972	−	0.475746i	−0.313668	−	0.949533i	$-0.601558\pi$
$661$	9635.26	−	8084.94i	0.566972	−	0.475746i	0.880639	+	0.473787i	$0.157113\pi$
$662$		0			0
$663$	1196.37	−	435.443i	0.0700802	−	0.0255071i
$664$		0			0
$665$	3090.17	−	3423.89i	0.180198	−	0.199658i
$666$		0			0
$667$	−30469.9	+	11090.1i	−1.76882	+	0.643796i
$668$		0			0
$669$	1397.17	−	1172.36i	0.0807439	−	0.0677522i
$670$		0			0
$671$	−83.3394	−	472.641i	−0.00479476	−	0.0271924i
$672$		0			0
$673$	10167.5	−	17610.6i	0.582360	−	1.00868i	−0.412839	−	0.910804i	$-0.635463\pi$
$673$	10167.5	−	17610.6i	0.582360	−	1.00868i	0.995199	−	0.0978730i	$-0.0312039\pi$
$674$		0			0
$675$	9005.35	+	3277.68i	0.513506	+	0.186901i
$676$		0			0
$677$	14100.1	+	24422.1i	0.800459	+	1.38644i	0.919314	+	0.393525i	$0.128744\pi$
$677$	14100.1	+	24422.1i	0.800459	+	1.38644i	−0.118855	+	0.992912i	$0.537922\pi$
$678$		0			0
$679$	35818.1	+	30055.0i	2.02441	+	1.69868i
$680$		0			0
$681$	−699.769	+	3968.59i	−0.0393762	+	0.223314i
$682$		0			0
$683$	14722.9			0.824827			0.412414	−	0.910997i	$-0.364686\pi$
$683$	14722.9			0.824827			0.412414	+	0.910997i	$0.364686\pi$
$684$		0			0
$685$	−5885.71			−0.328294
$686$		0			0
$687$	1472.36	−	8350.15i	0.0817670	−	0.463724i
$688$		0			0
$689$	−1922.54	−	1613.20i	−0.106303	−	0.0891989i
$690$		0			0
$691$	5943.50	+	10294.4i	0.327209	+	0.566742i	0.981957	−	0.189105i	$-0.0605586\pi$
$691$	5943.50	+	10294.4i	0.327209	+	0.566742i	−0.654748	+	0.755847i	$0.727225\pi$
$692$		0			0
$693$	−13761.3	−	5008.70i	−0.754327	−	0.274552i
$694$		0			0
$695$	2130.99	−	3690.98i	0.116306	−	0.201449i
$696$		0			0
$697$	1858.76	+	10541.6i	0.101012	+	0.572870i
$698$		0			0
$699$	1999.44	−	1677.73i	0.108191	−	0.0907832i
$700$		0			0
$701$	12821.2	−	4666.52i	0.690797	−	0.251430i	0.0273206	−	0.999627i	$-0.491302\pi$
$701$	12821.2	−	4666.52i	0.690797	−	0.251430i	0.663476	+	0.748197i	$0.269080\pi$
$702$		0			0
$703$	−5379.13	−	3370.05i	−0.288588	−	0.180802i
$704$		0			0
$705$	937.538	−	341.236i	0.0500847	−	0.0182293i
$706$		0			0
$707$	−2653.43	+	2226.49i	−0.141149	+	0.118438i
$708$		0			0
$709$	−2622.64	−	14873.7i	−0.138921	−	0.787863i	−0.972048	−	0.234781i	$-0.924563\pi$
$709$	−2622.64	−	14873.7i	−0.138921	−	0.787863i	0.833127	−	0.553082i	$-0.186548\pi$
$710$		0			0
$711$	−9611.78	+	16648.1i	−0.506990	+	0.878133i
$712$		0			0
$713$	−10597.0	−	3857.00i	−0.556608	−	0.202589i
$714$		0			0
$715$	607.786	+	1052.72i	0.0317901	+	0.0550620i
$716$		0			0
$717$	−5624.06	−	4719.15i	−0.292935	−	0.245802i
$718$		0			0
$719$	6245.24	−	35418.5i	0.323933	−	1.83712i	−0.193133	−	0.981173i	$-0.561865\pi$
$719$	6245.24	−	35418.5i	0.323933	−	1.83712i	0.517066	−	0.855945i	$-0.327024\pi$
$720$		0			0
$721$	−9312.07			−0.480998
$722$		0			0
$723$	8824.25			0.453910
$724$		0			0
$725$	−4579.09	+	25969.3i	−0.234570	+	1.33031i
$726$		0			0
$727$	−14785.6	−	12406.6i	−0.754290	−	0.632925i	0.182343	−	0.983235i	$-0.441632\pi$
$727$	−14785.6	−	12406.6i	−0.754290	−	0.632925i	−0.936634	+	0.350310i	$0.886076\pi$
$728$		0			0
$729$	5021.49	+	8697.48i	0.255118	+	0.441878i
$730$		0			0
$731$	−186.582	−	67.9104i	−0.00944049	−	0.00343606i
$732$		0			0
$733$	−5468.07	+	9470.97i	−0.275536	+	0.477242i	−0.970270	−	0.242024i	$-0.922189\pi$
$733$	−5468.07	+	9470.97i	−0.275536	+	0.477242i	0.694734	+	0.719266i	$0.255522\pi$
$734$		0			0
$735$	193.639	+	1098.18i	0.00971764	+	0.0551115i
$736$		0			0
$737$	−12222.0	+	10255.5i	−0.610859	+	0.512572i
$738$		0			0
$739$	−13389.5	+	4873.36i	−0.666494	+	0.242584i	−0.653038	−	0.757325i	$-0.726506\pi$
$739$	−13389.5	+	4873.36i	−0.666494	+	0.242584i	−0.0134565	+	0.999909i	$0.504283\pi$
$740$		0			0
$741$	−2709.10	−	1697.26i	−0.134307	−	0.0841436i
$742$		0			0
$743$	−26249.3	+	9553.95i	−1.29609	+	0.471737i	−0.895720	−	0.444618i	$-0.853339\pi$
$743$	−26249.3	+	9553.95i	−1.29609	+	0.471737i	−0.400366	+	0.916355i	$0.631117\pi$
$744$		0			0
$745$	1168.33	−	980.348i	0.0574556	−	0.0482109i
$746$		0			0
$747$	−4737.59	−	26868.2i	−0.232047	−	1.31600i
$748$		0			0
$749$	25642.4	−	44413.9i	1.25094	−	2.16669i
$750$		0			0
$751$	1804.35	+	656.731i	0.0876722	+	0.0319101i	0.385484	−	0.922715i	$-0.374035\pi$
$751$	1804.35	+	656.731i	0.0876722	+	0.0319101i	−0.297812	+	0.954625i	$0.596257\pi$
$752$		0			0
$753$	3646.43	+	6315.81i	0.176472	+	0.305659i
$754$		0			0
$755$	2056.71	+	1725.78i	0.0991407	+	0.0831889i
$756$		0			0
$757$	2007.34	−	11384.2i	0.0963778	−	0.546586i	−0.897939	−	0.440121i	$-0.854936\pi$
$757$	2007.34	−	11384.2i	0.0963778	−	0.546586i	0.994316	−	0.106465i	$-0.0339532\pi$
$758$		0			0
$759$	−5196.37			−0.248506
$760$		0			0
$761$	10081.5			0.480228			0.240114	−	0.970745i	$-0.422815\pi$
$761$	10081.5			0.480228			0.240114	+	0.970745i	$0.422815\pi$
$762$		0			0
$763$	9847.17	−	55846.1i	0.467223	−	2.64976i
$764$		0			0
$765$	1326.37	+	1112.96i	0.0626863	+	0.0526001i
$766$		0			0
$767$	3741.25	+	6480.04i	0.176126	+	0.305060i
$768$		0			0
$769$	3229.87	+	1175.58i	0.151459	+	0.0551266i	0.416637	−	0.909073i	$-0.363209\pi$
$769$	3229.87	+	1175.58i	0.151459	+	0.0551266i	−0.265178	+	0.964199i	$0.585431\pi$
$770$		0			0
$771$	−5609.55	+	9716.02i	−0.262027	+	0.453844i
$772$		0			0
$773$	3470.37	+	19681.5i	0.161476	+	0.915774i	0.952624	+	0.304150i	$0.0983723\pi$
$773$	3470.37	+	19681.5i	0.161476	+	0.915774i	−0.791149	+	0.611624i	$0.790517\pi$
$774$		0			0
$775$	−7025.46	+	5895.06i	−0.325628	+	0.273235i
$776$		0			0
$777$	2899.50	−	1055.33i	0.133872	−	0.0487256i
$778$		0			0
$779$	18008.4	−	19953.1i	0.828263	−	0.917708i
$780$		0			0
$781$	1005.10	−	365.827i	0.0460504	−	0.0167610i
$782$		0			0
$783$	13342.1	−	11195.4i	0.608951	−	0.510970i
$784$		0			0
$785$	−744.971	−	4224.94i	−0.0338715	−	0.192095i
$786$		0			0
$787$	−11063.9	+	19163.3i	−0.501126	+	0.867976i	0.498873	+	0.866675i	$0.333747\pi$
$787$	−11063.9	+	19163.3i	−0.501126	+	0.867976i	−0.999999	+	0.00130073i	$0.999586\pi$
$788$		0			0
$789$	−10130.1	−	3687.05i	−0.457086	−	0.166366i
$790$		0			0
$791$	4100.44	+	7102.16i	0.184317	+	0.319246i
$792$		0			0
$793$	−404.511	−	339.425i	−0.0181143	−	0.0151997i
$794$		0			0
$795$	−57.1613	+	324.178i	−0.00255007	+	0.0144621i
$796$		0			0
$797$	−38713.5			−1.72058			−0.860289	−	0.509806i	$-0.829717\pi$
$797$	−38713.5			−1.72058			−0.860289	+	0.509806i	$0.829717\pi$
$798$		0			0
$799$	−10016.5			−0.443500
$800$		0			0
$801$	4512.63	−	25592.4i	0.199059	−	1.12892i
$802$		0			0
$803$	−5905.98	−	4955.70i	−0.259549	−	0.217787i
$804$		0			0
$805$	−4124.29	−	7143.47i	−0.180574	−	0.312763i
$806$		0			0
$807$	−11074.0	−	4030.61i	−0.483052	−	0.175817i
$808$		0			0
$809$	9483.91	−	16426.6i	0.412159	−	0.713880i	−0.582967	−	0.812496i	$-0.698108\pi$
$809$	9483.91	−	16426.6i	0.412159	−	0.713880i	0.995126	+	0.0986157i	$0.0314415\pi$
$810$		0			0
$811$	−2428.30	−	13771.6i	−0.105141	−	0.596284i	−0.991164	−	0.132642i	$-0.957654\pi$
$811$	−2428.30	−	13771.6i	−0.105141	−	0.596284i	0.886023	−	0.463641i	$-0.153457\pi$
$812$		0			0
$813$	−4064.35	+	3410.39i	−0.175330	+	0.147119i
$814$		0			0
$815$	2848.59	−	1036.80i	0.122431	−	0.0445614i
$816$		0			0
$817$	153.510	+	474.352i	0.00657361	+	0.0203127i
$818$		0			0
$819$	−15141.0	+	5510.88i	−0.645995	+	0.235123i
$820$		0			0
$821$	−19809.0	+	16621.8i	−0.842071	+	0.706582i	−0.958029	−	0.286672i	$-0.907451\pi$
$821$	−19809.0	+	16621.8i	−0.842071	+	0.706582i	0.115957	+	0.993254i	$0.463006\pi$
$822$		0			0
$823$	−4375.10	−	24812.4i	−0.185305	−	1.05092i	−0.925562	−	0.378595i	$-0.876407\pi$
$823$	−4375.10	−	24812.4i	−0.185305	−	1.05092i	0.740257	−	0.672324i	$-0.234704\pi$
$824$		0			0
$825$	−2112.97	+	3659.77i	−0.0891687	+	0.154445i
$826$		0			0
$827$	−8325.15	−	3030.11i	−0.350053	−	0.127409i	0.161009	−	0.986953i	$-0.448525\pi$
$827$	−8325.15	−	3030.11i	−0.350053	−	0.127409i	−0.511061	+	0.859544i	$0.670748\pi$
$828$		0			0
$829$	13959.8	+	24179.2i	0.584856	+	1.01300i	0.994893	+	0.100932i	$0.0321823\pi$
$829$	13959.8	+	24179.2i	0.584856	+	1.01300i	−0.410037	+	0.912069i	$0.634484\pi$
$830$		0			0
$831$	6516.08	+	5467.64i	0.272010	+	0.228244i
$832$		0			0
$833$	1944.03	−	11025.1i	0.0808603	−	0.458582i
$834$		0			0
$835$	2081.03			0.0862481
$836$		0			0
$837$	6057.35			0.250147
$838$		0			0
$839$	−3193.91	+	18113.6i	−0.131426	+	0.745351i	0.845857	+	0.533410i	$0.179090\pi$
$839$	−3193.91	+	18113.6i	−0.131426	+	0.745351i	−0.977282	+	0.211941i	$0.932021\pi$
$840$		0			0
$841$	18029.8	+	15128.8i	0.739261	+	0.620313i
$842$		0			0
$843$	−2842.44	−	4923.25i	−0.116131	−	0.201146i
$844$		0			0
$845$	−3144.33	−	1144.44i	−0.128010	−	0.0465918i
$846$		0			0
$847$	−10615.9	+	18387.3i	−0.430657	+	0.745919i
$848$		0			0
$849$	218.447	+	1238.87i	0.00883048	+	0.0500802i
$850$		0			0
$851$	−8696.36	+	7297.12i	−0.350303	+	0.293939i
$852$		0			0
$853$	28473.0	−	10363.3i	1.14290	−	0.415982i	0.299942	−	0.953958i	$-0.403033\pi$
$853$	28473.0	−	10363.3i	1.14290	−	0.415982i	0.842961	+	0.537975i	$0.180811\pi$
$854$		0			0
$855$	156.837	−	4344.82i	0.00627333	−	0.173789i
$856$		0			0
$857$	1154.80	−	420.313i	0.0460295	−	0.0167534i	−0.318903	−	0.947787i	$-0.603314\pi$
$857$	1154.80	−	420.313i	0.0460295	−	0.0167534i	0.364932	+	0.931034i	$0.381092\pi$
$858$		0			0
$859$	19011.1	−	15952.2i	0.755123	−	0.633623i	−0.181729	−	0.983349i	$-0.558170\pi$
$859$	19011.1	−	15952.2i	0.755123	−	0.633623i	0.936852	+	0.349725i	$0.113725\pi$
$860$		0			0
$861$	2268.79	+	12866.9i	0.0898026	+	0.509296i
$862$		0			0
$863$	−4472.83	+	7747.16i	−0.176427	+	0.305581i	−0.940654	−	0.339366i	$-0.889787\pi$
$863$	−4472.83	+	7747.16i	−0.176427	+	0.305581i	0.764227	+	0.644947i	$0.223121\pi$
$864$		0			0
$865$	−3687.71	−	1342.22i	−0.144955	−	0.0527593i
$866$		0			0
$867$	−2947.44	−	5105.12i	−0.115456	−	0.199976i
$868$		0			0
$869$	−13613.8	−	11423.3i	−0.531435	−	0.445927i
$870$		0			0
$871$	−3048.28	+	17287.6i	−0.118584	+	0.672525i
$872$		0			0
$873$	44075.5			1.70874
$874$		0			0
$875$	−13669.4			−0.528124
$876$		0			0
$877$	−1049.03	+	5949.34i	−0.0403913	+	0.229070i	−0.998320	−	0.0579345i	$-0.981549\pi$
$877$	−1049.03	+	5949.34i	−0.0403913	+	0.229070i	0.957929	+	0.287005i	$0.0926596\pi$
$878$		0			0
$879$	−9598.45	−	8054.06i	−0.368314	−	0.309052i
$880$		0			0
$881$	8122.43	+	14068.5i	0.310615	+	0.538001i	0.978496	−	0.206268i	$-0.0661318\pi$
$881$	8122.43	+	14068.5i	0.310615	+	0.538001i	−0.667881	+	0.744268i	$0.732798\pi$
$882$		0			0
$883$	−7933.10	−	2887.41i	−0.302344	−	0.110044i	0.186393	−	0.982475i	$-0.440320\pi$
$883$	−7933.10	−	2887.41i	−0.302344	−	0.110044i	−0.488738	+	0.872431i	$0.662542\pi$
$884$		0			0
$885$	490.714	−	849.941i	0.0186386	−	0.0322830i
$886$		0			0
$887$	7396.96	+	41950.3i	0.280006	+	1.58800i	0.722596	+	0.691271i	$0.242949\pi$
$887$	7396.96	+	41950.3i	0.280006	+	1.58800i	−0.442589	+	0.896724i	$0.645940\pi$
$888$		0			0
$889$	33839.4	−	28394.6i	1.27664	−	1.07123i
$890$		0			0
$891$	−11600.3	+	4222.16i	−0.436166	+	0.158752i
$892$		0			0
$893$	15461.3	+	19837.6i	0.579387	+	0.743380i
$894$		0			0
$895$	6928.29	−	2521.69i	0.258756	−	0.0941797i
$896$		0			0
$897$	−4379.76	+	3675.05i	−0.163028	+	0.136797i
$898$		0			0
$899$	2894.32	+	16414.5i	0.107376	+	0.608960i
$900$		0			0
$901$	1652.39	−	2862.03i	0.0610978	−	0.105825i
$902$		0			0
$903$	−227.740	−	82.8908i	−0.00839283	−	0.00305474i
$904$		0			0
$905$	4069.20	+	7048.06i	0.149464	+	0.258879i
$906$		0			0
$907$	5510.93	+	4624.22i	0.201750	+	0.169288i	0.738065	−	0.674729i	$-0.235740\pi$
$907$	5510.93	+	4624.22i	0.201750	+	0.169288i	−0.536315	+	0.844018i	$0.680184\pi$
$908$		0			0
$909$	−566.986	+	3215.54i	−0.0206884	+	0.117330i
$910$		0			0
$911$	9425.93			0.342804			0.171402	−	0.985201i	$-0.445170\pi$
$911$	9425.93			0.342804			0.171402	+	0.985201i	$0.445170\pi$
$912$		0			0
$913$	25221.9			0.914266
$914$		0			0
$915$	−12.0270	+	68.2086i	−0.000434536	+	0.00246438i
$916$		0			0
$917$	12450.1	+	10446.8i	0.448350	+	0.376210i
$918$		0			0
$919$	−9106.34	−	15772.7i	−0.326867	−	0.566150i	0.655022	−	0.755610i	$-0.272660\pi$
$919$	−9106.34	−	15772.7i	−0.326867	−	0.566150i	−0.981888	+	0.189460i	$0.939326\pi$
$920$		0			0
$921$	−5924.46	−	2156.33i	−0.211963	−	0.0771481i
$922$		0			0
$923$	588.424	−	1019.18i	0.0209840	−	0.0363453i
$924$		0			0
$925$	1603.16	+	9091.97i	0.0569855	+	0.323181i
$926$		0			0
$927$	−6724.33	+	5642.38i	−0.238248	+	0.199914i
$928$		0			0
$929$	−15093.8	+	5493.70i	−0.533060	+	0.194018i	−0.594504	−	0.804093i	$-0.702652\pi$
$929$	−15093.8	+	5493.70i	−0.533060	+	0.194018i	0.0614444	+	0.998111i	$0.480429\pi$
$930$		0			0
$931$	−24836.0	+	13168.1i	−0.874295	+	0.463554i
$932$		0			0
$933$	−2051.18	+	746.570i	−0.0719751	+	0.0261968i
$934$		0			0
$935$	−1226.19	+	1028.89i	−0.0428883	+	0.0359876i
$936$		0			0
$937$	4399.66	+	24951.7i	0.153395	+	0.869944i	0.960239	+	0.279180i	$0.0900625\pi$
$937$	4399.66	+	24951.7i	0.153395	+	0.869944i	−0.806844	+	0.590764i	$0.798826\pi$
$938$		0			0
$939$	−843.973	+	1461.80i	−0.0293312	+	0.0508032i
$940$		0			0
$941$	15298.4	+	5568.15i	0.529981	+	0.192897i	0.593130	−	0.805107i	$-0.297892\pi$
$941$	15298.4	+	5568.15i	0.529981	+	0.192897i	−0.0631486	+	0.998004i	$0.520114\pi$
$942$		0			0
$943$	−24034.8	−	41629.5i	−0.829990	−	1.43758i
$944$		0			0
$945$	3394.05	+	2847.95i	0.116834	+	0.0980356i
$946$		0			0
$947$	−3063.37	+	17373.3i	−0.105117	+	0.596151i	0.886056	+	0.463579i	$0.153435\pi$
$947$	−3063.37	+	17373.3i	−0.105117	+	0.596151i	−0.991173	+	0.132572i	$0.957676\pi$
$948$		0			0
$949$	−8482.69			−0.290158
$950$		0			0
$951$	2158.37			0.0735960
$952$		0			0
$953$	−7643.82	+	43350.3i	−0.259819	+	1.47351i	0.523574	+	0.851980i	$0.324598\pi$
$953$	−7643.82	+	43350.3i	−0.259819	+	1.47351i	−0.783393	+	0.621527i	$0.786513\pi$
$954$		0			0
$955$	6934.71	+	5818.92i	0.234976	+	0.197168i
$956$		0			0
$957$	3840.16	+	6651.35i	0.129712	+	0.224668i
$958$		0			0
$959$	67774.3	+	24667.8i	2.28211	+	0.830621i
$960$		0			0
$961$	11997.1	−	20779.6i	0.402709	−	0.697512i
$962$		0			0
$963$	−8394.74	−	47608.9i	−0.280910	−	1.59312i
$964$		0			0
$965$	−479.902	+	402.686i	−0.0160089	+	0.0134331i
$966$		0			0
$967$	−34180.7	+	12440.8i	−1.13669	+	0.413721i	−0.840717	−	0.541475i	$-0.817866\pi$
$967$	−34180.7	+	12440.8i	−1.13669	+	0.413721i	−0.295973	+	0.955196i	$0.595644\pi$
$968$		0			0
$969$	1581.55	−	3901.26i	0.0524320	−	0.129336i
$970$		0			0
$971$	36463.0	−	13271.4i	1.20510	−	0.438621i	0.340098	−	0.940390i	$-0.389540\pi$
$971$	36463.0	−	13271.4i	1.20510	−	0.438621i	0.865001	+	0.501769i	$0.167317\pi$
$972$		0			0
$973$	−40007.9	+	33570.6i	−1.31819	+	1.10609i
$974$		0			0
$975$	807.401	+	4579.00i	0.0265205	+	0.150405i
$976$		0			0
$977$	13430.7	−	23262.6i	0.439800	−	0.761756i	−0.557873	−	0.829926i	$-0.688383\pi$
$977$	13430.7	−	23262.6i	0.439800	−	0.761756i	0.997674	+	0.0681696i	$0.0217159\pi$
$978$		0			0
$979$	22575.5	+	8216.81i	0.736993	+	0.268244i
$980$		0			0
$981$	−26727.6	−	46293.6i	−0.869874	−	1.50667i
$982$		0			0
$983$	−4736.00	−	3973.98i	−0.153667	−	0.128942i	0.562713	−	0.826653i	$-0.309758\pi$
$983$	−4736.00	−	3973.98i	−0.153667	−	0.128942i	−0.716380	+	0.697710i	$0.754202\pi$
$984$		0			0
$985$	−443.270	+	2513.91i	−0.0143388	+	0.0813195i
$986$		0			0
$987$	−12226.0			−0.394283
$988$		0			0
$989$	891.664			0.0286686
$990$		0			0
$991$	2958.63	−	16779.2i	0.0948374	−	0.537850i	−0.899960	−	0.435973i	$-0.856404\pi$
$991$	2958.63	−	16779.2i	0.0948374	−	0.537850i	0.994797	−	0.101877i	$-0.0324847\pi$
$992$		0			0
$993$	−601.851	−	505.013i	−0.0192338	−	0.0161391i
$994$		0			0
$995$	−3507.16	−	6074.59i	−0.111743	−	0.193545i
$996$		0			0
$997$	−25091.2	−	9132.45i	−0.797037	−	0.290098i	−0.0887791	−	0.996051i	$-0.528297\pi$
$997$	−25091.2	−	9132.45i	−0.797037	−	0.290098i	−0.708258	+	0.705953i	$0.750519\pi$
$998$		0			0
$999$	3048.87	−	5280.80i	0.0965586	−	0.167244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.5.3	✓	30
19.2	odd	18		1444.4.a.k.1.9		15
19.4	even	9	inner	76.4.i.a.61.3	yes	30
19.17	even	9		1444.4.a.j.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.5.3	✓	30	1.1	even	1	trivial
76.4.i.a.61.3	yes	30	19.4	even	9	inner
1444.4.a.j.1.7		15	19.17	even	9
1444.4.a.k.1.9		15	19.2	odd	18

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.267608 + 1.51768i) q^{3} +(-1.63306 - 1.37030i) q^{5} +(13.0616 + 22.6234i) q^{7} +(23.1400 + 8.42226i) q^{9} +O(q^{10})\)	\(q+(-0.267608 + 1.51768i) q^{3} +(-1.63306 - 1.37030i) q^{5} +(13.0616 + 22.6234i) q^{7} +(23.1400 + 8.42226i) q^{9} +(-11.3825 + 19.7151i) q^{11} +(4.34945 + 24.6670i) q^{13} +(2.51669 - 2.11175i) q^{15} +(-30.9936 + 11.2808i) q^{17} +(70.1829 + 43.9699i) q^{19} +(-37.8305 + 13.7692i) q^{21} +(113.464 - 95.2074i) q^{23} +(-20.9169 - 118.625i) q^{25} +(-39.7794 + 68.9000i) q^{27} +(-205.716 - 74.8745i) q^{29} +(-38.0684 - 65.9364i) q^{31} +(-26.8752 - 22.5509i) q^{33} +(9.67043 - 54.8437i) q^{35} -76.6444 q^{37} -38.6005 q^{39} +(56.3556 - 319.609i) q^{41} +(4.61160 + 3.86960i) q^{43} +(-26.2479 - 45.4627i) q^{45} +(285.373 + 103.867i) q^{47} +(-169.713 + 293.952i) q^{49} +(-8.82643 - 50.0572i) q^{51} +(-76.7556 + 64.4056i) q^{53} +(45.6039 - 16.5985i) q^{55} +(-85.5137 + 94.7485i) q^{57} +(280.717 - 102.173i) q^{59} +(-16.1497 + 13.5512i) q^{61} +(111.706 + 633.514i) q^{63} +(26.6982 - 46.2426i) q^{65} +(658.575 + 239.702i) q^{67} +(114.130 + 197.680i) q^{69} +(-35.9923 - 30.2011i) q^{71} +(-58.8084 + 333.519i) q^{73} +185.633 q^{75} -594.698 q^{77} +(-135.559 + 768.792i) q^{79} +(415.402 + 348.563i) q^{81} +(-553.962 - 959.490i) q^{83} +(66.0724 + 24.0484i) q^{85} +(168.687 - 292.174i) q^{87} +(-183.254 - 1039.28i) q^{89} +(-501.241 + 420.591i) q^{91} +(110.258 - 40.1305i) q^{93} +(-54.3609 - 167.977i) q^{95} +(1681.92 - 612.170i) q^{97} +(-429.437 + 360.340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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