LMFDB - Embedded newform 76.4.i.a.5.4

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			5.4
Character	$\chi$	$=$	76.5
Dual form			76.4.i.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.629037 - 3.56745i) q^{3} +(12.9592 + 10.8741i) q^{5} +(-4.22583 - 7.31935i) q^{7} +(13.0407 + 4.74643i) q^{9} +O(q^{10})$	\(q+(0.629037 - 3.56745i) q^{3} +(12.9592 + 10.8741i) q^{5} +(-4.22583 - 7.31935i) q^{7} +(13.0407 + 4.74643i) q^{9} +(29.3538 - 50.8423i) q^{11} +(-0.375178 - 2.12774i) q^{13} +(46.9445 - 39.3911i) q^{15} +(49.6354 - 18.0658i) q^{17} +(-33.2992 + 75.8299i) q^{19} +(-28.7696 + 10.4713i) q^{21} +(-103.460 + 86.8132i) q^{23} +(27.9897 + 158.738i) q^{25} +(74.0392 - 128.240i) q^{27} +(-121.431 - 44.1972i) q^{29} +(6.98090 + 12.0913i) q^{31} +(-162.913 - 136.700i) q^{33} +(24.8277 - 140.805i) q^{35} -319.286 q^{37} -7.82659 q^{39} +(-90.1832 + 511.454i) q^{41} +(105.887 + 88.8495i) q^{43} +(117.384 + 203.315i) q^{45} +(-314.151 - 114.341i) q^{47} +(135.785 - 235.186i) q^{49} +(-33.2263 - 188.436i) q^{51} +(-263.157 + 220.815i) q^{53} +(933.265 - 339.681i) q^{55} +(249.573 + 166.493i) q^{57} +(174.763 - 63.6086i) q^{59} +(261.981 - 219.828i) q^{61} +(-20.3670 - 115.507i) q^{63} +(18.2752 - 31.6535i) q^{65} +(-36.4792 - 13.2774i) q^{67} +(244.621 + 423.697i) q^{69} +(-440.912 - 369.969i) q^{71} +(63.6760 - 361.124i) q^{73} +583.894 q^{75} -496.177 q^{77} +(6.20502 - 35.1904i) q^{79} +(-123.881 - 103.949i) q^{81} +(250.594 + 434.042i) q^{83} +(839.683 + 305.620i) q^{85} +(-234.056 + 405.396i) q^{87} +(-237.161 - 1345.01i) q^{89} +(-13.9882 + 11.7375i) q^{91} +(47.5262 - 17.2981i) q^{93} +(-1256.11 + 620.598i) q^{95} +(-199.303 + 72.5404i) q^{97} +(624.114 - 523.694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.629037	−	3.56745i	0.121058	−	0.686556i	−0.862513	−	0.506035i	$-0.831111\pi$
$3$	0.629037	−	3.56745i	0.121058	−	0.686556i	0.983571	−	0.180521i	$-0.0577782\pi$
$4$		0			0
$5$	12.9592	+	10.8741i	1.15911	+	0.972606i	0.999893	−	0.0146382i	$-0.00465964\pi$
$5$	12.9592	+	10.8741i	1.15911	+	0.972606i	0.159214	+	0.987244i	$0.449104\pi$
$6$		0			0
$7$	−4.22583	−	7.31935i	−0.228173	−	0.395208i	0.729093	−	0.684414i	$-0.239942\pi$
$7$	−4.22583	−	7.31935i	−0.228173	−	0.395208i	−0.957267	+	0.289206i	$0.906609\pi$
$8$		0			0
$9$	13.0407	+	4.74643i	0.482989	+	0.175794i
$10$		0			0
$11$	29.3538	−	50.8423i	0.804592	−	1.39359i	−0.111974	−	0.993711i	$-0.535717\pi$
$11$	29.3538	−	50.8423i	0.804592	−	1.39359i	0.916566	−	0.399883i	$-0.130949\pi$
$12$		0			0
$13$	−0.375178	−	2.12774i	−0.00800427	−	0.0453945i	0.980544	−	0.196299i	$-0.0628924\pi$
$13$	−0.375178	−	2.12774i	−0.00800427	−	0.0453945i	−0.988548	+	0.150905i	$0.951781\pi$
$14$		0			0
$15$	46.9445	−	39.3911i	0.808068	−	0.678049i
$16$		0			0
$17$	49.6354	−	18.0658i	0.708138	−	0.257741i	0.0372564	−	0.999306i	$-0.488138\pi$
$17$	49.6354	−	18.0658i	0.708138	−	0.257741i	0.670881	+	0.741565i	$0.265916\pi$
$18$		0			0
$19$	−33.2992	+	75.8299i	−0.402071	+	0.915608i
$19$	−33.2992	+	75.8299i	−0.402071	+	0.915608i
$20$		0			0
$21$	−28.7696	+	10.4713i	−0.298954	+	0.108810i
$22$		0			0
$23$	−103.460	+	86.8132i	−0.937952	+	0.787035i	−0.977228	−	0.212193i	$-0.931939\pi$
$23$	−103.460	+	86.8132i	−0.937952	+	0.787035i	0.0392756	+	0.999228i	$0.487495\pi$
$24$		0			0
$25$	27.9897	+	158.738i	0.223918	+	1.26990i
$26$		0			0
$27$	74.0392	−	128.240i	0.527735	−	0.914064i
$28$		0			0
$29$	−121.431	−	44.1972i	−0.777557	−	0.283007i	−0.0774031	−	0.997000i	$-0.524663\pi$
$29$	−121.431	−	44.1972i	−0.777557	−	0.283007i	−0.700153	+	0.713992i	$0.746885\pi$
$30$		0			0
$31$	6.98090	+	12.0913i	0.0404454	+	0.0700535i	0.885539	−	0.464564i	$-0.153789\pi$
$31$	6.98090	+	12.0913i	0.0404454	+	0.0700535i	−0.845094	+	0.534618i	$0.820456\pi$
$32$		0			0
$33$	−162.913	−	136.700i	−0.859377	−	0.721103i
$34$		0			0
$35$	24.8277	−	140.805i	0.119904	−	0.680011i
$36$		0			0
$37$	−319.286			−1.41866			−0.709328	−	0.704878i	$-0.751002\pi$
$37$	−319.286			−1.41866			−0.709328	+	0.704878i	$0.751002\pi$
$38$		0			0
$39$	−7.82659			−0.0321348
$40$		0			0
$41$	−90.1832	+	511.454i	−0.343518	+	1.94819i	−0.0268930	+	0.999638i	$0.508561\pi$
$41$	−90.1832	+	511.454i	−0.343518	+	1.94819i	−0.316625	+	0.948551i	$0.602550\pi$
$42$		0			0
$43$	105.887	+	88.8495i	0.375525	+	0.315103i	0.810943	−	0.585126i	$-0.198955\pi$
$43$	105.887	+	88.8495i	0.375525	+	0.315103i	−0.435418	+	0.900229i	$0.643399\pi$
$44$		0			0
$45$	117.384	+	203.315i	0.388858	+	0.673522i
$46$		0			0
$47$	−314.151	−	114.341i	−0.974970	−	0.354860i	−0.195087	−	0.980786i	$-0.562499\pi$
$47$	−314.151	−	114.341i	−0.974970	−	0.354860i	−0.779883	+	0.625926i	$0.784721\pi$
$48$		0			0
$49$	135.785	−	235.186i	0.395874	−	0.685674i
$50$		0			0
$51$	−33.2263	−	188.436i	−0.0912276	−	0.517378i
$52$		0			0
$53$	−263.157	+	220.815i	−0.682026	+	0.572288i	−0.916598	−	0.399811i	$-0.869076\pi$
$53$	−263.157	+	220.815i	−0.682026	+	0.572288i	0.234571	+	0.972099i	$0.424631\pi$
$54$		0			0
$55$	933.265	−	339.681i	2.28803	−	0.832773i
$56$		0			0
$57$	249.573	+	166.493i	0.579942	+	0.386886i
$58$		0			0
$59$	174.763	−	63.6086i	0.385631	−	0.140358i	−0.141927	−	0.989877i	$-0.545330\pi$
$59$	174.763	−	63.6086i	0.385631	−	0.140358i	0.527558	+	0.849519i	$0.323108\pi$
$60$		0			0
$61$	261.981	−	219.828i	0.549888	−	0.461411i	−0.325015	−	0.945709i	$-0.605369\pi$
$61$	261.981	−	219.828i	0.549888	−	0.461411i	0.874903	+	0.484298i	$0.160925\pi$
$62$		0			0
$63$	−20.3670	−	115.507i	−0.0407302	−	0.230992i
$64$		0			0
$65$	18.2752	−	31.6535i	0.0348731	−	0.0604020i
$66$		0			0
$67$	−36.4792	−	13.2774i	−0.0665171	−	0.0242102i	0.308547	−	0.951209i	$-0.400157\pi$
$67$	−36.4792	−	13.2774i	−0.0665171	−	0.0242102i	−0.375064	+	0.926999i	$0.622379\pi$
$68$		0			0
$69$	244.621	+	423.697i	0.426797	+	0.739233i
$70$		0			0
$71$	−440.912	−	369.969i	−0.736995	−	0.618413i	0.195033	−	0.980797i	$-0.437518\pi$
$71$	−440.912	−	369.969i	−0.736995	−	0.618413i	−0.932029	+	0.362384i	$0.881963\pi$
$72$		0			0
$73$	63.6760	−	361.124i	0.102092	−	0.578992i	−0.890250	−	0.455472i	$-0.849471\pi$
$73$	63.6760	−	361.124i	0.102092	−	0.578992i	0.992342	−	0.123520i	$-0.0394184\pi$
$74$		0			0
$75$	583.894			0.898964
$76$		0			0
$77$	−496.177			−0.734346
$78$		0			0
$79$	6.20502	−	35.1904i	0.00883695	−	0.0501169i	−0.980070	−	0.198650i	$-0.936344\pi$
$79$	6.20502	−	35.1904i	0.00883695	−	0.0501169i	0.988907	+	0.148534i	$0.0474553\pi$
$80$		0			0
$81$	−123.881	−	103.949i	−0.169933	−	0.142591i
$82$		0			0
$83$	250.594	+	434.042i	0.331401	+	0.574004i	0.982787	−	0.184743i	$-0.0591453\pi$
$83$	250.594	+	434.042i	0.331401	+	0.574004i	−0.651386	+	0.758747i	$0.725812\pi$
$84$		0			0
$85$	839.683	+	305.620i	1.07149	+	0.389990i
$86$		0			0
$87$	−234.056	+	405.396i	−0.288430	+	0.499575i
$88$		0			0
$89$	−237.161	−	1345.01i	−0.282461	−	1.60192i	−0.714216	−	0.699926i	$-0.753217\pi$
$89$	−237.161	−	1345.01i	−0.282461	−	1.60192i	0.431755	−	0.901991i	$-0.357895\pi$
$90$		0			0
$91$	−13.9882	+	11.7375i	−0.0161139	+	0.0135212i
$92$		0			0
$93$	47.5262	−	17.2981i	0.0529918	−	0.0192875i
$94$		0			0
$95$	−1256.11	+	620.598i	−1.35657	+	0.670231i
$96$		0			0
$97$	−199.303	+	72.5404i	−0.208620	+	0.0759316i	−0.444217	−	0.895919i	$-0.646518\pi$
$97$	−199.303	+	72.5404i	−0.208620	+	0.0759316i	0.235596	+	0.971851i	$0.424296\pi$
$98$		0			0
$99$	624.114	−	523.694i	0.633594	−	0.531649i
$100$		0			0
$101$	80.9697	+	459.202i	0.0797702	+	0.452399i	0.998363	+	0.0571941i	$0.0182154\pi$
$101$	80.9697	+	459.202i	0.0797702	+	0.452399i	−0.918593	+	0.395205i	$0.870674\pi$
$102$		0			0
$103$	−761.885	+	1319.62i	−0.728842	+	1.26239i	0.228531	+	0.973537i	$0.426608\pi$
$103$	−761.885	+	1319.62i	−0.728842	+	1.26239i	−0.957373	+	0.288855i	$0.906726\pi$
$104$		0			0
$105$	−486.697	−	177.143i	−0.452350	−	0.164642i
$106$		0			0
$107$	−448.922	−	777.556i	−0.405598	−	0.702516i	0.588793	−	0.808284i	$-0.299603\pi$
$107$	−448.922	−	777.556i	−0.405598	−	0.702516i	−0.994391	+	0.105768i	$0.966270\pi$
$108$		0			0
$109$	1608.79	+	1349.94i	1.41371	+	1.18624i	0.954610	+	0.297857i	$0.0962720\pi$
$109$	1608.79	+	1349.94i	1.41371	+	1.18624i	0.459099	+	0.888385i	$0.348172\pi$
$110$		0			0
$111$	−200.843	+	1139.04i	−0.171740	+	0.973986i
$112$		0			0
$113$	−1547.81			−1.28855			−0.644274	−	0.764795i	$-0.722840\pi$
$113$	−1547.81			−1.28855			−0.644274	+	0.764795i	$0.722840\pi$
$114$		0			0
$115$	−2284.77			−1.85266
$116$		0			0
$117$	5.20657	−	29.5280i	0.00411409	−	0.0233321i
$118$		0			0
$119$	−341.980	−	286.956i	−0.263439	−	0.221052i
$120$		0			0
$121$	−1057.79	−	1832.15i	−0.794737	−	1.37652i
$122$		0			0
$123$	1767.86	+	643.448i	1.29595	+	0.471689i
$124$		0			0
$125$	−306.083	+	530.151i	−0.219015	+	0.379345i
$126$		0			0
$127$	−256.206	−	1453.02i	−0.179013	−	1.01523i	−0.933410	−	0.358813i	$-0.883182\pi$
$127$	−256.206	−	1453.02i	−0.179013	−	1.01523i	0.754397	−	0.656419i	$-0.227929\pi$
$128$		0			0
$129$	383.573	−	321.856i	0.261796	−	0.219673i
$130$		0			0
$131$	−1299.67	+	473.040i	−0.866813	+	0.315494i	−0.736876	−	0.676028i	$-0.763700\pi$
$131$	−1299.67	+	473.040i	−0.866813	+	0.315494i	−0.129937	+	0.991522i	$0.541478\pi$
$132$		0			0
$133$	695.742	−	76.7158i	0.453597	−	0.0500158i
$134$		0			0
$135$	2353.98	−	856.777i	1.50073	−	0.546220i
$136$		0			0
$137$	2228.16	−	1869.65i	1.38952	−	1.16595i	0.423992	−	0.905666i	$-0.360628\pi$
$137$	2228.16	−	1869.65i	1.38952	−	1.16595i	0.965532	−	0.260283i	$-0.0838160\pi$
$138$		0			0
$139$	319.210	+	1810.33i	0.194784	+	1.10468i	0.912726	+	0.408573i	$0.133973\pi$
$139$	319.210	+	1810.33i	0.194784	+	1.10468i	−0.717941	+	0.696103i	$0.754915\pi$
$140$		0			0
$141$	−605.520	+	1048.79i	−0.361659	+	0.626412i
$142$		0			0
$143$	−119.192	−	43.3823i	−0.0697017	−	0.0253693i
$144$		0			0
$145$	−1093.04	−	1893.21i	−0.626016	−	1.08429i
$146$		0			0
$147$	−753.600	−	632.346i	−0.422829	−	0.354796i
$148$		0			0
$149$	−392.617	+	2226.64i	−0.215869	+	1.22425i	0.663524	+	0.748155i	$0.269060\pi$
$149$	−392.617	+	2226.64i	−0.215869	+	1.22425i	−0.879393	+	0.476097i	$0.842051\pi$
$150$		0			0
$151$	3479.63			1.87529			0.937643	−	0.347599i	$-0.113003\pi$
$151$	3479.63			1.87529			0.937643	+	0.347599i	$0.113003\pi$
$152$		0			0
$153$	733.028			0.387332
$154$		0			0
$155$	−41.0144	+	232.604i	−0.0212539	+	0.120537i
$156$		0			0
$157$	200.295	+	168.068i	0.101817	+	0.0854348i	0.692275	−	0.721634i	$-0.256608\pi$
$157$	200.295	+	168.068i	0.101817	+	0.0854348i	−0.590458	+	0.807068i	$0.701053\pi$
$158$		0			0
$159$	622.210	+	1077.70i	0.310343	+	0.537529i
$160$		0			0
$161$	1072.62	+	390.402i	0.525058	+	0.191105i
$162$		0			0
$163$	−1231.85	+	2133.63i	−0.591939	+	1.02527i	0.402032	+	0.915626i	$0.368304\pi$
$163$	−1231.85	+	2133.63i	−0.591939	+	1.02527i	−0.993971	+	0.109643i	$0.965029\pi$
$164$		0			0
$165$	−624.735	−	3543.05i	−0.294761	−	1.67167i
$166$		0			0
$167$	−429.040	+	360.007i	−0.198803	+	0.166816i	−0.736755	−	0.676160i	$-0.763643\pi$
$167$	−429.040	+	360.007i	−0.198803	+	0.166816i	0.537952	+	0.842976i	$0.319198\pi$
$168$		0			0
$169$	2060.12	−	749.822i	0.937696	−	0.341293i
$170$		0			0
$171$	−794.165	+	830.823i	−0.355154	+	0.371547i
$172$		0			0
$173$	3355.24	−	1221.21i	1.47453	−	0.536686i	0.525206	−	0.850975i	$-0.323988\pi$
$173$	3355.24	−	1221.21i	1.47453	−	0.536686i	0.949327	+	0.314289i	$0.101766\pi$
$174$		0			0
$175$	1043.58	−	875.664i	0.450782	−	0.378251i
$176$		0			0
$177$	−116.988	−	663.471i	−0.0496799	−	0.281749i
$178$		0			0
$179$	−752.658	+	1303.64i	−0.314281	+	0.544351i	−0.979284	−	0.202490i	$-0.935097\pi$
$179$	−752.658	+	1303.64i	−0.314281	+	0.544351i	0.665003	+	0.746840i	$0.268430\pi$
$180$		0			0
$181$	3253.24	+	1184.08i	1.33598	+	0.486255i	0.908543	−	0.417792i	$-0.137196\pi$
$181$	3253.24	+	1184.08i	1.33598	+	0.486255i	0.427433	+	0.904047i	$0.359418\pi$
$182$		0			0
$183$	−619.429	−	1072.88i	−0.250216	−	0.433387i
$184$		0			0
$185$	−4137.69	−	3471.94i	−1.64437	−	1.37979i
$186$		0			0
$187$	538.481	−	3053.88i	0.210576	−	1.19423i
$188$		0			0
$189$	−1251.51			−0.481660
$190$		0			0
$191$	−2296.56			−0.870016			−0.435008	−	0.900427i	$-0.643254\pi$
$191$	−2296.56			−0.870016			−0.435008	+	0.900427i	$0.643254\pi$
$192$		0			0
$193$	−154.046	+	873.636i	−0.0574531	+	0.325833i	−0.999965	−	0.00833928i	$-0.997345\pi$
$193$	−154.046	+	873.636i	−0.0574531	+	0.325833i	0.942512	+	0.334172i	$0.108457\pi$
$194$		0			0
$195$	−101.426	−	85.1069i	−0.0372477	−	0.0312545i
$196$		0			0
$197$	−958.416	−	1660.03i	−0.346621	−	0.600365i	0.639026	−	0.769185i	$-0.279338\pi$
$197$	−958.416	−	1660.03i	−0.346621	−	0.600365i	−0.985647	+	0.168820i	$0.946004\pi$
$198$		0			0
$199$	2592.28	+	943.512i	0.923425	+	0.336099i	0.759600	−	0.650390i	$-0.225395\pi$
$199$	2592.28	+	943.512i	0.923425	+	0.336099i	0.163825	+	0.986489i	$0.447617\pi$
$200$		0			0
$201$	−70.3130	+	121.786i	−0.0246741	+	0.0427368i
$202$		0			0
$203$	189.651	+	1075.56i	0.0655709	+	0.371871i
$204$		0			0
$205$	−6730.29	+	5647.38i	−2.29299	+	1.92405i
$206$		0			0
$207$	−1761.24	+	641.040i	−0.591376	+	0.215243i
$208$		0			0
$209$	2877.91	+	3918.90i	0.952484	+	1.29702i
$210$		0			0
$211$	2742.63	−	998.234i	0.894835	−	0.325693i	0.146654	−	0.989188i	$-0.453150\pi$
$211$	2742.63	−	998.234i	0.894835	−	0.325693i	0.748181	+	0.663495i	$0.230927\pi$
$212$		0			0
$213$	−1597.20	+	1340.21i	−0.513794	+	0.431124i
$214$		0			0
$215$	406.053	+	2302.84i	0.128803	+	0.730476i
$216$		0			0
$217$	59.0002	−	102.191i	0.0184571	−	0.0319687i
$218$		0			0
$219$	−1248.24	−	454.322i	−0.385151	−	0.140184i
$220$		0			0
$221$	−57.0613	−	98.8331i	−0.0173681	−	0.0300825i
$222$		0			0
$223$	−4768.93	−	4001.60i	−1.43207	−	1.20165i	−0.944479	−	0.328573i	$-0.893432\pi$
$223$	−4768.93	−	4001.60i	−1.43207	−	1.20165i	−0.487588	−	0.873074i	$-0.662123\pi$
$224$		0			0
$225$	−388.431	+	2202.90i	−0.115091	+	0.652711i
$226$		0			0
$227$	−2053.82			−0.600516			−0.300258	−	0.953858i	$-0.597073\pi$
$227$	−2053.82			−0.600516			−0.300258	+	0.953858i	$0.597073\pi$
$228$		0			0
$229$	−2548.15			−0.735312			−0.367656	−	0.929962i	$-0.619840\pi$
$229$	−2548.15			−0.735312			−0.367656	+	0.929962i	$0.619840\pi$
$230$		0			0
$231$	−312.114	+	1770.09i	−0.0888986	+	0.504169i
$232$		0			0
$233$	4858.24	+	4076.55i	1.36598	+	1.14619i	0.974084	+	0.226186i	$0.0726258\pi$
$233$	4858.24	+	4076.55i	1.36598	+	1.14619i	0.391898	+	0.920009i	$0.371819\pi$
$234$		0			0
$235$	−2827.79	−	4897.87i	−0.784955	−	1.35958i
$236$		0			0
$237$	−121.637	−	44.2722i	−0.0333382	−	0.0121341i
$238$		0			0
$239$	−178.194	+	308.641i	−0.0482276	+	0.0835327i	−0.889131	−	0.457652i	$-0.848691\pi$
$239$	−178.194	+	308.641i	−0.0482276	+	0.0835327i	0.840904	+	0.541185i	$0.182024\pi$
$240$		0			0
$241$	−599.912	−	3402.27i	−0.160347	−	0.909375i	−0.953733	−	0.300656i	$-0.902795\pi$
$241$	−599.912	−	3402.27i	−0.160347	−	0.909375i	0.793385	−	0.608720i	$-0.208317\pi$
$242$		0			0
$243$	2613.98	−	2193.39i	0.690069	−	0.579037i
$244$		0			0
$245$	4317.09	−	1571.29i	1.12575	−	0.409740i
$246$		0			0
$247$	173.839	+	42.4022i	0.0447819	+	0.0109230i
$248$		0			0
$249$	1706.06	−	620.953i	0.434204	−	0.158037i
$250$		0			0
$251$	499.814	−	419.394i	0.125689	−	0.105466i	−0.577776	−	0.816195i	$-0.696079\pi$
$251$	499.814	−	419.394i	0.125689	−	0.105466i	0.703466	+	0.710729i	$0.251635\pi$
$252$		0			0
$253$	1376.84	+	7808.45i	0.342139	+	1.94037i
$254$		0			0
$255$	1618.47	−	2803.28i	0.397462	−	0.688424i
$256$		0			0
$257$	−5868.47	−	2135.95i	−1.42438	−	0.518431i	−0.489063	−	0.872249i	$-0.662661\pi$
$257$	−5868.47	−	2135.95i	−1.42438	−	0.518431i	−0.935314	+	0.353818i	$0.884883\pi$
$258$		0			0
$259$	1349.25	+	2336.97i	0.323699	+	0.560664i
$260$		0			0
$261$	−1373.76	−	1152.73i	−0.325800	−	0.273379i
$262$		0			0
$263$	758.990	−	4304.45i	0.177952	−	1.00922i	−0.756729	−	0.653728i	$-0.773204\pi$
$263$	758.990	−	4304.45i	0.177952	−	1.00922i	0.934681	−	0.355487i	$-0.115685\pi$
$264$		0			0
$265$	−5811.46			−1.34715
$266$		0			0
$267$	−4947.43			−1.13400
$268$		0			0
$269$	−32.8105	+	186.078i	−0.00743678	+	0.0421761i	−0.988300	−	0.152520i	$-0.951261\pi$
$269$	−32.8105	+	186.078i	−0.00743678	+	0.0421761i	0.980864	+	0.194696i	$0.0623722\pi$
$270$		0			0
$271$	197.740	+	165.924i	0.0443242	+	0.0371924i	0.664681	−	0.747128i	$-0.268568\pi$
$271$	197.740	+	165.924i	0.0443242	+	0.0371924i	−0.620356	+	0.784320i	$0.713012\pi$
$272$		0			0
$273$	33.0738	+	57.2856i	0.00733231	+	0.0126999i
$274$		0			0
$275$	8892.19	+	3236.49i	1.94989	+	0.709701i
$276$		0			0
$277$	−2280.12	+	3949.28i	−0.494582	+	0.856641i	−0.999980	−	0.00624514i	$-0.998012\pi$
$277$	−2280.12	+	3949.28i	−0.494582	+	0.856641i	0.505399	+	0.862886i	$0.331345\pi$
$278$		0			0
$279$	33.6455	+	190.813i	0.00721972	+	0.0409451i
$280$		0			0
$281$	4128.25	−	3464.01i	0.876408	−	0.735394i	−0.0890292	−	0.996029i	$-0.528376\pi$
$281$	4128.25	−	3464.01i	0.876408	−	0.735394i	0.965437	+	0.260635i	$0.0839320\pi$
$282$		0			0
$283$	6760.32	−	2460.56i	1.42000	−	0.516837i	0.485950	−	0.873986i	$-0.338474\pi$
$283$	6760.32	−	2460.56i	1.42000	−	0.516837i	0.934047	+	0.357149i	$0.116251\pi$
$284$		0			0
$285$	1423.81	+	4871.48i	0.295927	+	1.01250i
$286$		0			0
$287$	4124.61	−	1501.24i	0.848321	−	0.308764i
$288$		0			0
$289$	−1626.28	+	1364.61i	−0.331016	+	0.277755i
$290$		0			0
$291$	133.415	+	756.634i	0.0268760	+	0.152422i
$292$		0			0
$293$	2969.33	−	5143.03i	0.592048	−	1.02546i	−0.401909	−	0.915680i	$-0.631653\pi$
$293$	2969.33	−	5143.03i	0.592048	−	1.02546i	0.993956	−	0.109777i	$-0.0350136\pi$
$294$		0			0
$295$	2956.48	+	1076.07i	0.583501	+	0.212377i
$296$		0			0
$297$	−4346.67	−	7528.65i	−0.849223	−	1.47090i
$298$		0			0
$299$	223.532	+	187.565i	0.0432347	+	0.0362782i
$300$		0			0
$301$	202.862	−	1150.49i	0.0388463	−	0.220308i
$302$		0			0
$303$	1689.11			0.320254
$304$		0			0
$305$	5785.48			1.08615
$306$		0			0
$307$	1148.89	−	6515.65i	0.213584	−	1.21130i	−0.669762	−	0.742576i	$-0.733604\pi$
$307$	1148.89	−	6515.65i	0.213584	−	1.21130i	0.883346	−	0.468721i	$-0.155285\pi$
$308$		0			0
$309$	4228.43	+	3548.08i	0.778469	+	0.653213i
$310$		0			0
$311$	1240.70	+	2148.96i	0.226218	+	0.391821i	0.956684	−	0.291128i	$-0.0940305\pi$
$311$	1240.70	+	2148.96i	0.226218	+	0.391821i	−0.730466	+	0.682949i	$0.760697\pi$
$312$		0			0
$313$	−1914.41	−	696.789i	−0.345716	−	0.125830i	0.163326	−	0.986572i	$-0.447778\pi$
$313$	−1914.41	−	696.789i	−0.345716	−	0.125830i	−0.509042	+	0.860742i	$0.670000\pi$
$314$		0			0
$315$	992.091	−	1718.35i	0.177454	−	0.307359i
$316$		0			0
$317$	−388.571	−	2203.70i	−0.0688465	−	0.390448i	−0.999687	−	0.0250218i	$-0.992034\pi$
$317$	−388.571	−	2203.70i	−0.0688465	−	0.390448i	0.930840	−	0.365426i	$-0.119077\pi$
$318$		0			0
$319$	−5811.55	+	4876.47i	−1.02001	+	0.855893i
$320$		0			0
$321$	−3056.28	+	1112.40i	−0.531417	+	0.193420i
$322$		0			0
$323$	−282.889	+	4365.42i	−0.0487317	+	0.752007i
$324$		0			0
$325$	327.251	−	119.110i	0.0558542	−	0.0203293i
$326$		0			0
$327$	5827.82	−	4890.12i	0.985563	−	0.826985i
$328$		0			0
$329$	490.642	+	2782.57i	0.0822187	+	0.466285i
$330$		0			0
$331$	−4429.03	+	7671.31i	−0.735473	+	1.27388i	0.219043	+	0.975715i	$0.429707\pi$
$331$	−4429.03	+	7671.31i	−0.735473	+	1.27388i	−0.954516	+	0.298161i	$0.903627\pi$
$332$		0			0
$333$	−4163.71	−	1515.47i	−0.685195	−	0.249391i
$334$		0			0
$335$	−328.363	−	568.741i	−0.0535534	−	0.0927572i
$336$		0			0
$337$	−613.546	−	514.827i	−0.0991751	−	0.0832178i	0.591852	−	0.806047i	$-0.298397\pi$
$337$	−613.546	−	514.827i	−0.0991751	−	0.0832178i	−0.691027	+	0.722829i	$0.742841\pi$
$338$		0			0
$339$	−973.631	+	5521.74i	−0.155989	+	0.884659i
$340$		0			0
$341$	819.665			0.130168
$342$		0			0
$343$	−5194.13			−0.817658
$344$		0			0
$345$	−1437.21	+	8150.80i	−0.224280	+	1.27196i
$346$		0			0
$347$	−5681.57	−	4767.40i	−0.878970	−	0.737543i	0.0869974	−	0.996209i	$-0.472273\pi$
$347$	−5681.57	−	4767.40i	−0.878970	−	0.737543i	−0.965967	+	0.258666i	$0.916717\pi$
$348$		0			0
$349$	610.104	+	1056.73i	0.0935763	+	0.162079i	0.909014	−	0.416767i	$-0.136837\pi$
$349$	610.104	+	1056.73i	0.0935763	+	0.162079i	−0.815437	+	0.578845i	$0.803503\pi$
$350$		0			0
$351$	−300.638	−	109.423i	−0.0457176	−	0.0166399i
$352$		0			0
$353$	2469.61	−	4277.49i	0.372363	−	0.644951i	−0.617566	−	0.786519i	$-0.711881\pi$
$353$	2469.61	−	4277.49i	0.372363	−	0.644951i	0.989929	+	0.141568i	$0.0452144\pi$
$354$		0			0
$355$	−1690.80	−	9589.02i	−0.252785	−	1.43361i
$356$		0			0
$357$	−1238.82	+	1039.49i	−0.183656	+	0.154106i
$358$		0			0
$359$	−4993.79	+	1817.59i	−0.734156	+	0.267211i	−0.681923	−	0.731424i	$-0.738856\pi$
$359$	−4993.79	+	1817.59i	−0.734156	+	0.267211i	−0.0522331	+	0.998635i	$0.516634\pi$
$360$		0			0
$361$	−4641.33	−	5050.14i	−0.676678	−	0.736279i
$362$		0			0
$363$	−7201.51	+	2621.13i	−1.04127	+	0.378991i
$364$		0			0
$365$	4752.08	−	3987.47i	0.681467	−	0.571818i
$366$		0			0
$367$	−2388.30	−	13544.7i	−0.339696	−	1.92651i	−0.374754	−	0.927124i	$-0.622273\pi$
$367$	−2388.30	−	13544.7i	−0.339696	−	1.92651i	0.0350586	−	0.999385i	$-0.488838\pi$
$368$		0			0
$369$	−3603.63	+	6241.68i	−0.508395	+	0.880566i
$370$		0			0
$371$	2728.28	+	993.012i	0.381793	+	0.138961i
$372$		0			0
$373$	6272.90	+	10865.0i	0.870773	+	1.50822i	0.861198	+	0.508269i	$0.169714\pi$
$373$	6272.90	+	10865.0i	0.870773	+	1.50822i	0.00957454	+	0.999954i	$0.496952\pi$
$374$		0			0
$375$	1698.75	+	1425.42i	0.233928	+	0.196289i
$376$		0			0
$377$	−48.4819	+	274.955i	−0.00662320	+	0.0375620i
$378$		0			0
$379$	5850.13			0.792879			0.396440	−	0.918061i	$-0.370246\pi$
$379$	5850.13			0.792879			0.396440	+	0.918061i	$0.370246\pi$
$380$		0			0
$381$	−5344.72			−0.718684
$382$		0			0
$383$	−1448.01	+	8212.05i	−0.193184	+	1.09560i	0.721796	+	0.692106i	$0.243317\pi$
$383$	−1448.01	+	8212.05i	−0.193184	+	1.09560i	−0.914981	+	0.403498i	$0.867794\pi$
$384$		0			0
$385$	−6430.06	−	5395.46i	−0.851185	−	0.714229i
$386$		0			0
$387$	959.120	+	1661.24i	0.125981	+	0.218206i
$388$		0			0
$389$	−2711.71	−	986.981i	−0.353442	−	0.128643i	0.159196	−	0.987247i	$-0.449110\pi$
$389$	−2711.71	−	986.981i	−0.353442	−	0.128643i	−0.512639	+	0.858604i	$0.671332\pi$
$390$		0			0
$391$	−3566.92	+	6178.09i	−0.461348	+	0.799078i
$392$		0			0
$393$	870.007	+	4934.06i	0.111669	+	0.633308i
$394$		0			0
$395$	463.075	−	388.566i	0.0589869	−	0.0494959i
$396$		0			0
$397$	4524.85	−	1646.91i	0.572029	−	0.208202i	−0.0397781	−	0.999209i	$-0.512665\pi$
$397$	4524.85	−	1646.91i	0.572029	−	0.208202i	0.611807	+	0.791007i	$0.290443\pi$
$398$		0			0
$399$	163.968	−	2530.28i	0.0205731	−	0.317475i
$400$		0			0
$401$	5066.46	−	1844.04i	0.630940	−	0.229643i	−0.00670024	−	0.999978i	$-0.502133\pi$
$401$	5066.46	−	1844.04i	0.630940	−	0.229643i	0.637641	+	0.770334i	$0.279911\pi$
$402$		0			0
$403$	23.1080	−	19.3899i	0.00285630	−	0.00239672i
$404$		0			0
$405$	−475.057	−	2694.18i	−0.0582859	−	0.330556i
$406$		0			0
$407$	−9372.26	+	16233.2i	−1.14144	+	1.97703i
$408$		0			0
$409$	4143.91	+	1508.26i	0.500986	+	0.182344i	0.580137	−	0.814519i	$-0.302999\pi$
$409$	4143.91	+	1508.26i	0.500986	+	0.182344i	−0.0791517	+	0.996863i	$0.525221\pi$
$410$		0			0
$411$	−5268.28	−	9124.94i	−0.632276	−	1.09513i
$412$		0			0
$413$	−1204.09	−	1010.35i	−0.143461	−	0.120378i
$414$		0			0
$415$	−1472.30	+	8349.82i	−0.174150	+	0.987654i
$416$		0			0
$417$	6659.05			0.782002
$418$		0			0
$419$	6479.49			0.755475			0.377737	−	0.925913i	$-0.376702\pi$
$419$	6479.49			0.755475			0.377737	+	0.925913i	$0.376702\pi$
$420$		0			0
$421$	677.396	−	3841.70i	0.0784187	−	0.444734i	−0.920165	−	0.391531i	$-0.871946\pi$
$421$	677.396	−	3841.70i	0.0784187	−	0.444734i	0.998584	−	0.0532036i	$-0.0169432\pi$
$422$		0			0
$423$	−3554.03	−	2982.19i	−0.408518	−	0.342787i
$424$		0			0
$425$	4257.00	+	7373.34i	0.485870	+	0.841552i
$426$		0			0
$427$	−2716.08	−	988.573i	−0.307823	−	0.112038i
$428$		0			0
$429$	−229.740	+	397.922i	−0.0258554	+	0.0447829i
$430$		0			0
$431$	−846.707	−	4801.91i	−0.0946274	−	0.536659i	−0.994861	−	0.101251i	$-0.967715\pi$
$431$	−846.707	−	4801.91i	−0.0946274	−	0.536659i	0.900233	−	0.435408i	$-0.143396\pi$
$432$		0			0
$433$	4760.28	−	3994.35i	0.528324	−	0.443317i	−0.339198	−	0.940715i	$-0.610156\pi$
$433$	4760.28	−	3994.35i	0.528324	−	0.443317i	0.867522	+	0.497398i	$0.165711\pi$
$434$		0			0
$435$	−7441.48	+	2708.48i	−0.820211	+	0.298532i
$436$		0			0
$437$	−3137.91	−	10736.2i	−0.343493	−	1.17524i
$438$		0			0
$439$	977.701	−	355.854i	0.106294	−	0.0386879i	−0.288326	−	0.957532i	$-0.593099\pi$
$439$	977.701	−	355.854i	0.106294	−	0.0386879i	0.394620	+	0.918845i	$0.370876\pi$
$440$		0			0
$441$	2887.02	−	2422.50i	0.311740	−	0.261581i
$442$		0			0
$443$	1333.93	+	7565.09i	0.143063	+	0.811351i	0.968902	+	0.247445i	$0.0795909\pi$
$443$	1333.93	+	7565.09i	0.143063	+	0.811351i	−0.825839	+	0.563906i	$0.809298\pi$
$444$		0			0
$445$	11552.3	−	20009.1i	1.23063	−	2.13152i
$446$		0			0
$447$	7696.46	+	2801.28i	0.814385	+	0.296412i
$448$		0			0
$449$	−738.499	−	1279.12i	−0.0776212	−	0.134444i	0.824602	−	0.565713i	$-0.191399\pi$
$449$	−738.499	−	1279.12i	−0.0776212	−	0.134444i	−0.902223	+	0.431270i	$0.858066\pi$
$450$		0			0
$451$	23356.3	+	19598.3i	2.43859	+	2.04622i
$452$		0			0
$453$	2188.82	−	12413.4i	0.227019	−	1.28749i
$454$		0			0
$455$	−308.911			−0.0318285
$456$		0			0
$457$	−5451.45			−0.558004			−0.279002	−	0.960290i	$-0.590004\pi$
$457$	−5451.45			−0.558004			−0.279002	+	0.960290i	$0.590004\pi$
$458$		0			0
$459$	1358.21	−	7702.80i	0.138117	−	0.783303i
$460$		0			0
$461$	−6851.14	−	5748.79i	−0.692167	−	0.580797i	0.227366	−	0.973809i	$-0.426989\pi$
$461$	−6851.14	−	5748.79i	−0.692167	−	0.580797i	−0.919533	+	0.393012i	$0.871433\pi$
$462$		0			0
$463$	−1639.61	−	2839.89i	−0.164577	−	0.285056i	0.771928	−	0.635710i	$-0.219293\pi$
$463$	−1639.61	−	2839.89i	−0.164577	−	0.285056i	−0.936505	+	0.350654i	$0.885959\pi$
$464$		0			0
$465$	804.003	+	292.633i	0.0801823	+	0.0291840i
$466$		0			0
$467$	6530.97	−	11312.0i	0.647146	−	1.12089i	−0.336655	−	0.941628i	$-0.609296\pi$
$467$	6530.97	−	11312.0i	0.647146	−	1.12089i	0.983801	−	0.179262i	$-0.0573709\pi$
$468$		0			0
$469$	56.9734	+	323.112i	0.00560935	+	0.0318122i
$470$		0			0
$471$	725.566	−	608.822i	0.0709816	−	0.0595606i
$472$		0			0
$473$	7625.50	−	2775.45i	0.741270	−	0.269800i
$474$		0			0
$475$	−12969.1	−	3163.37i	−1.25276	−	0.305569i
$476$		0			0
$477$	−4479.84	+	1630.53i	−0.430016	+	0.156513i
$478$		0			0
$479$	1409.22	−	1182.47i	0.134423	−	0.112794i	−0.573097	−	0.819487i	$-0.694258\pi$
$479$	1409.22	−	1182.47i	0.134423	−	0.112794i	0.707520	+	0.706693i	$0.249814\pi$
$480$		0			0
$481$	119.789	+	679.357i	0.0113553	+	0.0643992i
$482$		0			0
$483$	2067.46	−	3580.94i	0.194767	−	0.337347i
$484$		0			0
$485$	−3371.62	−	1227.17i	−0.315665	−	0.114893i
$486$		0			0
$487$	7964.42	+	13794.8i	0.741073	+	1.28358i	0.952007	+	0.306075i	$0.0990159\pi$
$487$	7964.42	+	13794.8i	0.741073	+	1.28358i	−0.210935	+	0.977500i	$0.567651\pi$
$488$		0			0
$489$	6836.74	+	5736.70i	0.632245	+	0.530517i
$490$		0			0
$491$	−2425.75	+	13757.1i	−0.222959	+	1.26446i	0.643590	+	0.765370i	$0.277444\pi$
$491$	−2425.75	+	13757.1i	−0.222959	+	1.26446i	−0.866549	+	0.499092i	$0.833667\pi$
$492$		0			0
$493$	−6825.72			−0.623560
$494$		0			0
$495$	13782.7			1.25149
$496$		0			0
$497$	−844.715	+	4790.62i	−0.0762388	+	0.432372i
$498$		0			0
$499$	15675.4	+	13153.2i	1.40627	+	1.18000i	0.958235	+	0.285981i	$0.0923193\pi$
$499$	15675.4	+	13153.2i	1.40627	+	1.18000i	0.448032	+	0.894018i	$0.352125\pi$
$500$		0			0
$501$	1014.43	+	1757.04i	0.0904614	+	0.156684i
$502$		0			0
$503$	−9254.21	−	3368.26i	−0.820328	−	0.298575i	−0.102445	−	0.994739i	$-0.532667\pi$
$503$	−9254.21	−	3368.26i	−0.820328	−	0.298575i	−0.717883	+	0.696164i	$0.754889\pi$
$504$		0			0
$505$	−3944.09	+	6831.37i	−0.347544	+	0.601964i
$506$		0			0
$507$	−1379.06	−	7821.03i	−0.120801	−	0.685097i
$508$		0			0
$509$	9472.82	−	7948.64i	0.824903	−	0.692175i	−0.129212	−	0.991617i	$-0.541245\pi$
$509$	9472.82	−	7948.64i	0.824903	−	0.692175i	0.954115	+	0.299441i	$0.0968003\pi$
$510$		0			0
$511$	−2912.28	+	1059.98i	−0.252117	+	0.0917630i
$512$		0			0
$513$	7258.95	+	9884.66i	0.624738	+	0.850718i
$514$		0			0
$515$	−24223.1	+	8816.48i	−2.07261	+	0.754370i
$516$		0			0
$517$	−15034.9	+	12615.8i	−1.27898	+	1.07319i
$518$		0			0
$519$	−2246.02	−	12737.8i	−0.189960	−	1.07732i
$520$		0			0
$521$	267.382	−	463.120i	0.0224841	−	0.0389437i	−0.854564	−	0.519345i	$-0.826176\pi$
$521$	267.382	−	463.120i	0.0224841	−	0.0389437i	0.877049	+	0.480402i	$0.159509\pi$
$522$		0			0
$523$	−6916.26	−	2517.31i	−0.578255	−	0.210467i	0.0363011	−	0.999341i	$-0.488442\pi$
$523$	−6916.26	−	2517.31i	−0.578255	−	0.210467i	−0.614556	+	0.788873i	$0.710665\pi$
$524$		0			0
$525$	−2467.44	−	4273.73i	−0.205120	−	0.355278i
$526$		0			0
$527$	564.938	+	474.039i	0.0466965	+	0.0391831i
$528$		0			0
$529$	1054.65	−	5981.24i	0.0866815	−	0.491595i
$530$		0			0
$531$	2580.95			0.210930
$532$		0			0
$533$	1122.08			0.0911866
$534$		0			0
$535$	2637.52	−	14958.1i	0.213140	−	1.20878i
$536$		0			0
$537$	4177.22	+	3505.11i	0.335681	+	0.281670i
$538$		0			0
$539$	−7971.60	−	13807.2i	−0.637034	−	1.10338i
$540$		0			0
$541$	−11462.4	−	4171.97i	−0.910919	−	0.331547i	−0.156299	−	0.987710i	$-0.549956\pi$
$541$	−11462.4	−	4171.97i	−0.910919	−	0.331547i	−0.754620	+	0.656162i	$0.772179\pi$
$542$		0			0
$543$	6270.57	−	10860.9i	0.495572	−	0.858356i
$544$		0			0
$545$	6169.36	+	34988.2i	0.484893	+	2.74996i
$546$		0			0
$547$	1587.02	−	1331.67i	0.124051	−	0.104091i	−0.578652	−	0.815575i	$-0.696421\pi$
$547$	1587.02	−	1331.67i	0.124051	−	0.104091i	0.702703	+	0.711484i	$0.251976\pi$
$548$		0			0
$549$	4459.81	−	1623.24i	0.346703	−	0.126190i
$550$		0			0
$551$	7395.01	−	7736.35i	0.571757	−	0.598148i
$552$		0			0
$553$	−283.792	+	103.292i	−0.0218229	+	0.00794289i
$554$		0			0
$555$	−14988.7	+	12577.0i	−1.14637	+	0.961919i
$556$		0			0
$557$	685.651	+	3888.52i	0.0521579	+	0.295802i	0.999717	−	0.0237776i	$-0.00756937\pi$
$557$	685.651	+	3888.52i	0.0521579	+	0.295802i	−0.947559	+	0.319580i	$0.896458\pi$
$558$		0			0
$559$	149.322	−	258.634i	0.0112981	−	0.0195689i
$560$		0			0
$561$	−10555.8	−	3842.00i	−0.794416	−	0.289144i
$562$		0			0
$563$	1209.89	+	2095.59i	0.0905697	+	0.156871i	0.907751	−	0.419509i	$-0.137798\pi$
$563$	1209.89	+	2095.59i	0.0905697	+	0.156871i	−0.817181	+	0.576381i	$0.804465\pi$
$564$		0			0
$565$	−20058.4	−	16831.0i	−1.49356	−	1.25325i
$566$		0			0
$567$	−237.336	+	1346.00i	−0.0175788	+	0.0996943i
$568$		0			0
$569$	−13183.7			−0.971337			−0.485669	−	0.874143i	$-0.661424\pi$
$569$	−13183.7			−0.971337			−0.485669	+	0.874143i	$0.661424\pi$
$570$		0			0
$571$	6009.94			0.440470			0.220235	−	0.975447i	$-0.429318\pi$
$571$	6009.94			0.440470			0.220235	+	0.975447i	$0.429318\pi$
$572$		0			0
$573$	−1444.62	+	8192.85i	−0.105323	+	0.597314i
$574$		0			0
$575$	−16676.3	−	13993.1i	−1.20948	−	1.01487i
$576$		0			0
$577$	4702.49	+	8144.95i	0.339285	+	0.587658i	0.984298	−	0.176513i	$-0.0564817\pi$
$577$	4702.49	+	8144.95i	0.339285	+	0.587658i	−0.645014	+	0.764171i	$0.723148\pi$
$578$		0			0
$579$	3019.75	+	1099.10i	0.216747	+	0.0788895i
$580$		0			0
$581$	2117.94	−	3668.37i	0.151234	−	0.261945i
$582$		0			0
$583$	3502.08	+	19861.3i	0.248784	+	1.41093i
$584$		0			0
$585$	388.562	−	326.042i	0.0274616	−	0.0230431i
$586$		0			0
$587$	−22398.6	+	8152.41i	−1.57494	+	0.573230i	−0.974095	−	0.226138i	$-0.927390\pi$
$587$	−22398.6	+	8152.41i	−1.57494	+	0.573230i	−0.600841	+	0.799368i	$0.705168\pi$
$588$		0			0
$589$	−1149.34	+	126.731i	−0.0804034	+	0.00886567i
$590$		0			0
$591$	−6524.94	+	2374.88i	−0.454145	+	0.165295i
$592$		0			0
$593$	−15957.9	+	13390.3i	−1.10508	+	0.927271i	−0.997756	−	0.0669529i	$-0.978672\pi$
$593$	−15957.9	+	13390.3i	−1.10508	+	0.927271i	−0.107323	+	0.994224i	$0.534228\pi$
$594$		0			0
$595$	−1311.42	−	7437.43i	−0.0903580	−	0.512445i
$596$		0			0
$597$	4996.57	−	8654.31i	0.342539	−	0.593295i
$598$		0			0
$599$	3438.49	+	1251.51i	0.234546	+	0.0853676i	0.456619	−	0.889662i	$-0.349060\pi$
$599$	3438.49	+	1251.51i	0.234546	+	0.0853676i	−0.222073	+	0.975030i	$0.571282\pi$
$600$		0			0
$601$	11793.3	+	20426.5i	0.800428	+	1.38638i	0.919335	+	0.393477i	$0.128728\pi$
$601$	11793.3	+	20426.5i	0.800428	+	1.38638i	−0.118906	+	0.992905i	$0.537939\pi$
$602$		0			0
$603$	−412.695	−	346.292i	−0.0278710	−	0.0233866i
$604$		0			0
$605$	6214.78	−	35245.8i	0.417631	−	2.36850i
$606$		0			0
$607$	5045.17			0.337359			0.168680	−	0.985671i	$-0.446050\pi$
$607$	5045.17			0.337359			0.168680	+	0.985671i	$0.446050\pi$
$608$		0			0
$609$	3956.32			0.263248
$610$		0			0
$611$	−125.426	+	711.329i	−0.00830476	+	0.0470986i
$612$		0			0
$613$	12487.5	+	10478.2i	0.822781	+	0.690395i	0.953621	−	0.301008i	$-0.0973232\pi$
$613$	12487.5	+	10478.2i	0.822781	+	0.690395i	−0.130841	+	0.991403i	$0.541768\pi$
$614$		0			0
$615$	15913.1	+	27562.4i	1.04338	+	1.80719i
$616$		0			0
$617$	−6942.20	−	2526.76i	−0.452970	−	0.164868i	0.105452	−	0.994424i	$-0.466371\pi$
$617$	−6942.20	−	2526.76i	−0.452970	−	0.164868i	−0.558422	+	0.829557i	$0.688593\pi$
$618$		0			0
$619$	5650.59	−	9787.11i	0.366908	−	0.635504i	−0.622172	−	0.782881i	$-0.713750\pi$
$619$	5650.59	−	9787.11i	0.366908	−	0.635504i	0.989080	+	0.147376i	$0.0470829\pi$
$620$		0			0
$621$	3472.81	+	19695.3i	0.224410	+	1.27270i
$622$		0			0
$623$	−8842.38	+	7419.64i	−0.568640	+	0.477145i
$624$		0			0
$625$	9201.72	−	3349.15i	0.588910	−	0.214346i
$626$		0			0
$627$	15790.8	−	7801.65i	1.00578	−	0.496919i
$628$		0			0
$629$	−15847.9	+	5768.15i	−1.00460	+	0.365646i
$630$		0			0
$631$	20619.3	−	17301.6i	1.30086	−	1.09155i	0.310860	−	0.950456i	$-0.399383\pi$
$631$	20619.3	−	17301.6i	1.30086	−	1.09155i	0.989996	−	0.141092i	$-0.0450615\pi$
$632$		0			0
$633$	−1835.93	−	10412.1i	−0.115279	−	0.653782i
$634$		0			0
$635$	12480.0	−	21615.9i	0.779925	−	1.35087i
$636$		0			0
$637$	−551.358	−	200.678i	−0.0342945	−	0.0124822i
$638$		0			0
$639$	−3993.78	−	6917.42i	−0.247248	−	0.428246i
$640$		0			0
$641$	−8735.65	−	7330.08i	−0.538280	−	0.451670i	0.332669	−	0.943044i	$-0.392051\pi$
$641$	−8735.65	−	7330.08i	−0.538280	−	0.451670i	−0.870949	+	0.491373i	$0.836495\pi$
$642$		0			0
$643$	−102.254	+	579.909i	−0.00627137	+	0.0355667i	−0.987783	−	0.155837i	$-0.950193\pi$
$643$	−102.254	+	579.909i	−0.00627137	+	0.0355667i	0.981511	+	0.191403i	$0.0613038\pi$
$644$		0			0
$645$	8470.68			0.517105
$646$		0			0
$647$	24043.2			1.46095			0.730475	−	0.682939i	$-0.239299\pi$
$647$	24043.2			1.46095			0.730475	+	0.682939i	$0.239299\pi$
$648$		0			0
$649$	1895.96	−	10752.5i	0.114673	−	0.650344i
$650$		0			0
$651$	−327.449	−	274.762i	−0.0197139	−	0.0165419i
$652$		0			0
$653$	3045.34	+	5274.68i	0.182501	+	0.316102i	0.942732	−	0.333552i	$-0.108247\pi$
$653$	3045.34	+	5274.68i	0.182501	+	0.316102i	−0.760230	+	0.649654i	$0.774914\pi$
$654$		0			0
$655$	−21986.5	−	8002.44i	−1.31158	−	0.477376i
$656$		0			0
$657$	2544.43	−	4407.08i	0.151092	−	0.261700i
$658$		0			0
$659$	1816.83	+	10303.8i	0.107396	+	0.609070i	0.990236	+	0.139398i	$0.0445168\pi$
$659$	1816.83	+	10303.8i	0.107396	+	0.609070i	−0.882841	+	0.469672i	$0.844372\pi$
$660$		0			0
$661$	−2034.29	+	1706.97i	−0.119704	+	0.100444i	−0.700675	−	0.713481i	$-0.747118\pi$
$661$	−2034.29	+	1706.97i	−0.119704	+	0.100444i	0.580970	+	0.813925i	$0.302673\pi$
$662$		0			0
$663$	−388.476	+	141.394i	−0.0227559	+	0.00828246i
$664$		0			0
$665$	9850.47	+	6571.36i	0.574413	+	0.383198i
$666$		0			0
$667$	16400.1	−	5969.16i	0.952048	−	0.346517i
$668$		0			0
$669$	−17275.3	+	14495.7i	−0.998361	+	0.837724i
$670$		0			0
$671$	−3486.42	−	19772.5i	−0.200584	−	1.13757i
$672$		0			0
$673$	6785.86	−	11753.5i	0.388671	−	0.673199i	−0.603600	−	0.797287i	$-0.706267\pi$
$673$	6785.86	−	11753.5i	0.388671	−	0.673199i	0.992271	+	0.124089i	$0.0396008\pi$
$674$		0			0
$675$	22428.8	+	8163.41i	1.27894	+	0.465496i
$676$		0			0
$677$	178.870	+	309.811i	0.0101544	+	0.0175879i	0.871058	−	0.491180i	$-0.163434\pi$
$677$	178.870	+	309.811i	0.0101544	+	0.0175879i	−0.860904	+	0.508768i	$0.830101\pi$
$678$		0			0
$679$	1373.17	+	1152.23i	0.0776103	+	0.0651228i
$680$		0			0
$681$	−1291.93	+	7326.91i	−0.0726974	+	0.412287i
$682$		0			0
$683$	−26345.2			−1.47595			−0.737973	−	0.674831i	$-0.764217\pi$
$683$	−26345.2			−1.47595			−0.737973	+	0.674831i	$0.764217\pi$
$684$		0			0
$685$	49205.9			2.74462
$686$		0			0
$687$	−1602.88	+	9090.39i	−0.0890157	+	0.504833i
$688$		0			0
$689$	568.567	+	477.084i	0.0314378	+	0.0263795i
$690$		0			0
$691$	−14282.2	−	24737.6i	−0.786284	−	1.36188i	−0.928229	−	0.372009i	$-0.878669\pi$
$691$	−14282.2	−	24737.6i	−0.786284	−	1.36188i	0.141945	−	0.989875i	$-0.454664\pi$
$692$		0			0
$693$	−6470.50	−	2355.07i	−0.354681	−	0.129093i
$694$		0			0
$695$	−15548.9	+	26931.5i	−0.848639	+	1.46989i
$696$		0			0
$697$	4763.55	+	27015.4i	0.258870	+	1.46812i
$698$		0			0
$699$	17598.9	−	14767.2i	0.952290	−	0.799066i
$700$		0			0
$701$	−18220.4	+	6631.69i	−0.981705	+	0.357311i	−0.782503	−	0.622647i	$-0.786057\pi$
$701$	−18220.4	+	6631.69i	−0.981705	+	0.357311i	−0.199202	+	0.979958i	$0.563835\pi$
$702$		0			0
$703$	10631.9	−	24211.4i	0.570400	−	1.29893i
$704$		0			0
$705$	−19251.7	+	7007.04i	−1.02845	+	0.374327i
$706$		0			0
$707$	3018.90	−	2533.16i	0.160590	−	0.134751i
$708$		0			0
$709$	829.962	+	4706.95i	0.0439631	+	0.249327i	0.998867	−	0.0475876i	$-0.0151533\pi$
$709$	829.962	+	4706.95i	0.0439631	+	0.249327i	−0.954904	+	0.296915i	$0.904042\pi$
$710$		0			0
$711$	247.947	−	429.456i	0.0130784	−	0.0226524i
$712$		0			0
$713$	−1771.93	−	644.929i	−0.0930704	−	0.0338748i
$714$		0			0
$715$	−1072.89	−	1858.30i	−0.0561173	−	0.0971980i
$716$		0			0
$717$	988.969	+	829.844i	0.0515115	+	0.0432233i
$718$		0			0
$719$	−316.800	+	1796.66i	−0.0164320	+	0.0931907i	−0.991921	−	0.126858i	$-0.959511\pi$
$719$	−316.800	+	1796.66i	−0.0164320	+	0.0931907i	0.975489	+	0.220049i	$0.0706217\pi$
$720$		0			0
$721$	12878.4			0.665209
$722$		0			0
$723$	−12514.8			−0.643748
$724$		0			0
$725$	3616.94	−	20512.7i	0.185283	−	1.05079i
$726$		0			0
$727$	−1920.46	−	1611.45i	−0.0979722	−	0.0822085i	0.592486	−	0.805581i	$-0.298147\pi$
$727$	−1920.46	−	1611.45i	−0.0979722	−	0.0822085i	−0.690458	+	0.723372i	$0.742591\pi$
$728$		0			0
$729$	−8363.67	−	14486.3i	−0.424918	−	0.735980i
$730$		0			0
$731$	6860.86	+	2497.15i	0.347138	+	0.126348i
$732$		0			0
$733$	13288.5	−	23016.3i	0.669607	−	1.15979i	−0.308408	−	0.951254i	$-0.599796\pi$
$733$	13288.5	−	23016.3i	0.669607	−	1.15979i	0.978014	−	0.208538i	$-0.0668706\pi$
$734$		0			0
$735$	−2889.89	−	16389.4i	−0.145028	−	0.822493i
$736$		0			0
$737$	−1745.86	+	1464.95i	−0.0872584	+	0.0732185i
$738$		0			0
$739$	−15534.3	+	5654.03i	−0.773260	+	0.281444i	−0.698359	−	0.715747i	$-0.746086\pi$
$739$	−15534.3	+	5654.03i	−0.773260	+	0.281444i	−0.0749007	+	0.997191i	$0.523864\pi$
$740$		0			0
$741$	260.619	−	593.489i	0.0129205	−	0.0294229i
$742$		0			0
$743$	13834.1	−	5035.21i	0.683075	−	0.248619i	0.0229075	−	0.999738i	$-0.492708\pi$
$743$	13834.1	−	5035.21i	0.683075	−	0.248619i	0.660167	+	0.751119i	$0.270485\pi$
$744$		0			0
$745$	−29300.7	+	24586.2i	−1.44093	+	1.20908i
$746$		0			0
$747$	1207.78	+	6849.64i	0.0591570	+	0.335496i
$748$		0			0
$749$	−3794.14	+	6571.64i	−0.185093	+	0.320591i
$750$		0			0
$751$	−4779.15	−	1739.47i	−0.232215	−	0.0845194i	0.223292	−	0.974752i	$-0.428320\pi$
$751$	−4779.15	−	1739.47i	−0.232215	−	0.0845194i	−0.455507	+	0.890232i	$0.650542\pi$
$752$		0			0
$753$	−1181.76	−	2046.87i	−0.0571924	−	0.0990601i
$754$		0			0
$755$	45093.2	+	37837.7i	2.17366	+	1.82392i
$756$		0			0
$757$	−2965.89	+	16820.4i	−0.142400	+	0.807592i	0.827017	+	0.562176i	$0.190036\pi$
$757$	−2965.89	+	16820.4i	−0.142400	+	0.807592i	−0.969418	+	0.245416i	$0.921075\pi$
$758$		0			0
$759$	28722.3			1.37359
$760$		0			0
$761$	−19124.8			−0.911002			−0.455501	−	0.890235i	$-0.650540\pi$
$761$	−19124.8			−0.911002			−0.455501	+	0.890235i	$0.650540\pi$
$762$		0			0
$763$	3082.18	−	17479.9i	0.146242	−	0.829378i
$764$		0			0
$765$	9499.46	+	7970.99i	0.448959	+	0.376721i
$766$		0			0
$767$	−200.910	−	347.986i	−0.00945818	−	0.0163821i
$768$		0			0
$769$	−25358.3	−	9229.66i	−1.18913	−	0.432809i	−0.329713	−	0.944081i	$-0.606952\pi$
$769$	−25358.3	−	9229.66i	−1.18913	−	0.432809i	−0.859419	+	0.511272i	$0.829174\pi$
$770$		0			0
$771$	−11311.4	+	19591.9i	−0.528364	+	0.915154i
$772$		0			0
$773$	1495.94	+	8483.89i	0.0696057	+	0.394753i	0.999629	+	0.0272519i	$0.00867561\pi$
$773$	1495.94	+	8483.89i	0.0696057	+	0.394753i	−0.930023	+	0.367501i	$0.880213\pi$
$774$		0			0
$775$	−1723.95	+	1446.56i	−0.0799045	+	0.0670478i
$776$		0			0
$777$	9185.73	−	3343.33i	0.424113	−	0.154365i
$778$		0			0
$779$	−35780.5	−	23869.6i	−1.64566	−	1.09784i
$780$		0			0
$781$	−31752.6	+	11557.0i	−1.45480	+	0.529503i
$782$		0			0
$783$	−14658.5	+	12299.9i	−0.669031	+	0.561384i
$784$		0			0
$785$	768.089	+	4356.05i	0.0349227	+	0.198056i
$786$		0			0
$787$	−17346.9	+	30045.6i	−0.785703	+	1.36088i	0.142875	+	0.989741i	$0.454365\pi$
$787$	−17346.9	+	30045.6i	−0.785703	+	1.36088i	−0.928578	+	0.371137i	$0.878968\pi$
$788$		0			0
$789$	−14878.5	−	5415.32i	−0.671340	−	0.244348i
$790$		0			0
$791$	6540.78	+	11329.0i	0.294012	+	0.509244i
$792$		0			0
$793$	−566.025	−	474.952i	−0.0253470	−	0.0212686i
$794$		0			0
$795$	−3655.63	+	20732.1i	−0.163084	+	0.924895i
$796$		0			0
$797$	4419.90			0.196438			0.0982188	−	0.995165i	$-0.468686\pi$
$797$	4419.90			0.196438			0.0982188	+	0.995165i	$0.468686\pi$
$798$		0			0
$799$	−17658.6			−0.781875
$800$		0			0
$801$	3291.24	−	18665.5i	0.145181	−	0.823363i
$802$		0			0
$803$	−16491.3	−	13837.8i	−0.724738	−	0.608127i
$804$		0			0
$805$	9655.05	+	16723.0i	0.422728	+	0.732186i
$806$		0			0
$807$	643.184	+	234.100i	0.0280559	+	0.0102115i
$808$		0			0
$809$	10614.4	−	18384.6i	0.461288	−	0.798973i	−0.537738	−	0.843112i	$-0.680721\pi$
$809$	10614.4	−	18384.6i	0.461288	−	0.798973i	0.999025	+	0.0441387i	$0.0140543\pi$
$810$		0			0
$811$	3288.61	+	18650.6i	0.142390	+	0.807537i	0.969425	+	0.245386i	$0.0789147\pi$
$811$	3288.61	+	18650.6i	0.142390	+	0.807537i	−0.827035	+	0.562151i	$0.809974\pi$
$812$		0			0
$813$	716.310	−	601.055i	0.0309005	−	0.0259286i
$814$		0			0
$815$	−39165.1	+	14254.9i	−1.68330	+	0.612672i
$816$		0			0
$817$	−10263.4	+	5070.76i	−0.439499	+	0.217140i
$818$		0			0
$819$	−238.128	+	86.6713i	−0.0101598	+	0.00369785i
$820$		0			0
$821$	19184.3	−	16097.6i	0.815514	−	0.684298i	−0.136403	−	0.990653i	$-0.543554\pi$
$821$	19184.3	−	16097.6i	0.815514	−	0.684298i	0.951917	+	0.306356i	$0.0991097\pi$
$822$		0			0
$823$	−1686.62	−	9565.31i	−0.0714362	−	0.405135i	−0.999467	−	0.0326323i	$-0.989611\pi$
$823$	−1686.62	−	9565.31i	−0.0714362	−	0.405135i	0.928031	−	0.372502i	$-0.121500\pi$
$824$		0			0
$825$	17139.5	−	29686.5i	0.723299	−	1.25279i
$826$		0			0
$827$	15987.7	+	5819.06i	0.672246	+	0.244678i	0.655515	−	0.755182i	$-0.272452\pi$
$827$	15987.7	+	5819.06i	0.672246	+	0.244678i	0.0167317	+	0.999860i	$0.494674\pi$
$828$		0			0
$829$	−13959.8	−	24179.1i	−0.584855	−	1.01300i	−0.994894	−	0.100930i	$-0.967818\pi$
$829$	−13959.8	−	24179.1i	−0.584855	−	1.01300i	0.410039	−	0.912068i	$-0.365515\pi$
$830$		0			0
$831$	12654.6	+	10618.5i	0.528258	+	0.443261i
$832$		0			0
$833$	2490.90	−	14126.6i	0.103607	−	0.587584i
$834$		0			0
$835$	−9474.76			−0.392680
$836$		0			0
$837$	2067.44			0.0853778
$838$		0			0
$839$	2.88975	−	16.3886i	0.000118910	−	0.000674370i	−0.984748	−	0.173985i	$-0.944335\pi$
$839$	2.88975	−	16.3886i	0.000118910	−	0.000674370i	0.984867	+	0.173311i	$0.0554466\pi$
$840$		0			0
$841$	−5891.00	−	4943.14i	−0.241543	−	0.202679i
$842$		0			0
$843$	−9760.86	−	16906.3i	−0.398792	−	0.690728i
$844$		0			0
$845$	34851.1	+	12684.8i	1.41883	+	0.516413i
$846$		0			0
$847$	−8940.12	+	15484.7i	−0.362675	+	0.628172i
$848$		0			0
$849$	−4525.41	−	25664.9i	−0.182935	−	1.03747i
$850$		0			0
$851$	33033.3	−	27718.2i	1.33063	−	1.11653i
$852$		0			0
$853$	−18636.6	+	6783.18i	−0.748073	+	0.272276i	−0.687795	−	0.725905i	$-0.741421\pi$
$853$	−18636.6	+	6783.18i	−0.748073	+	0.272276i	−0.0602783	+	0.998182i	$0.519199\pi$
$854$		0			0
$855$	−19326.2	+	2131.00i	−0.773031	+	0.0852381i
$856$		0			0
$857$	17565.7	−	6393.39i	0.700155	−	0.254835i	0.0326777	−	0.999466i	$-0.489597\pi$
$857$	17565.7	−	6393.39i	0.700155	−	0.254835i	0.667477	+	0.744630i	$0.267374\pi$
$858$		0			0
$859$	12807.8	−	10747.1i	0.508729	−	0.426874i	−0.351953	−	0.936018i	$-0.614482\pi$
$859$	12807.8	−	10747.1i	0.508729	−	0.426874i	0.860682	+	0.509144i	$0.170038\pi$
$860$		0			0
$861$	−2761.05	−	15658.7i	−0.109287	−	0.619798i
$862$		0			0
$863$	−9659.52	+	16730.8i	−0.381013	+	0.659933i	−0.991207	−	0.132318i	$-0.957758\pi$
$863$	−9659.52	+	16730.8i	−0.381013	+	0.659933i	0.610195	+	0.792252i	$0.291091\pi$
$864$		0			0
$865$	56760.7	+	20659.2i	2.23113	+	0.812063i
$866$		0			0
$867$	3845.19	+	6660.06i	0.150622	+	0.260885i
$868$		0			0
$869$	−1607.02	−	1348.45i	−0.0627324	−	0.0526387i
$870$		0			0
$871$	−14.5645	+	82.5996i	−0.000566591	+	0.00321330i
$872$		0			0
$873$	−2943.36			−0.114110
$874$		0			0
$875$	5173.81			0.199893
$876$		0			0
$877$	−4134.42	+	23447.5i	−0.159190	+	0.902810i	0.795665	+	0.605737i	$0.207122\pi$
$877$	−4134.42	+	23447.5i	−0.159190	+	0.902810i	−0.954855	+	0.297073i	$0.903989\pi$
$878$		0			0
$879$	−16479.7	−	13828.1i	−0.632361	−	0.530614i
$880$		0			0
$881$	−15195.6	−	26319.5i	−0.581104	−	1.00650i	−0.995349	−	0.0963363i	$-0.969288\pi$
$881$	−15195.6	−	26319.5i	−0.581104	−	1.00650i	0.414245	−	0.910166i	$-0.364046\pi$
$882$		0			0
$883$	20114.6	+	7321.10i	0.766602	+	0.279020i	0.695574	−	0.718454i	$-0.255150\pi$
$883$	20114.6	+	7321.10i	0.766602	+	0.279020i	0.0710273	+	0.997474i	$0.477372\pi$
$884$		0			0
$885$	5698.55	−	9870.19i	0.216446	−	0.374896i
$886$		0			0
$887$	2941.22	+	16680.5i	0.111338	+	0.631426i	0.988499	+	0.151230i	$0.0483235\pi$
$887$	2941.22	+	16680.5i	0.111338	+	0.631426i	−0.877161	+	0.480196i	$0.840565\pi$
$888$		0			0
$889$	−9552.45	+	8015.46i	−0.360381	+	0.302396i
$890$		0			0
$891$	−8921.38	+	3247.12i	−0.335440	+	0.122090i
$892$		0			0
$893$	19131.4	−	20014.5i	0.716920	−	0.750012i
$894$		0			0
$895$	−23929.7	+	8709.71i	−0.893724	+	0.325289i
$896$		0			0
$897$	809.739	−	679.452i	0.0301409	−	0.0252912i
$898$		0			0
$899$	−313.296	−	1776.79i	−0.0116229	−	0.0659169i
$900$		0			0
$901$	−9072.69	+	15714.4i	−0.335466	+	0.581045i
$902$		0			0
$903$	−3976.69	−	1447.40i	−0.146551	−	0.0533403i
$904$		0			0
$905$	29283.6	+	50720.7i	1.07560	+	1.86300i
$906$		0			0
$907$	26731.4	+	22430.3i	0.978613	+	0.821154i	0.983880	−	0.178832i	$-0.0572320\pi$
$907$	26731.4	+	22430.3i	0.978613	+	0.821154i	−0.00526663	+	0.999986i	$0.501676\pi$
$908$		0			0
$909$	−1123.67	+	6372.64i	−0.0410008	+	0.232527i
$910$		0			0
$911$	32840.7			1.19436			0.597179	−	0.802108i	$-0.296288\pi$
$911$	32840.7			1.19436			0.597179	+	0.802108i	$0.296288\pi$
$912$		0			0
$913$	29423.6			1.06657
$914$		0			0
$915$	3639.28	−	20639.4i	0.131487	−	0.745703i
$916$		0			0
$917$	8954.52	+	7513.73i	0.322469	+	0.270584i
$918$		0			0
$919$	25033.2	+	43358.8i	0.898553	+	1.55634i	0.829345	+	0.558737i	$0.188714\pi$
$919$	25033.2	+	43358.8i	0.898553	+	1.55634i	0.0692078	+	0.997602i	$0.477953\pi$
$920$		0			0
$921$	−22521.6	−	8197.18i	−0.805766	−	0.293275i
$922$		0			0
$923$	−621.777	+	1076.95i	−0.0221734	+	0.0384055i
$924$		0			0
$925$	−8936.72	−	50682.7i	−0.317662	−	1.80155i
$926$		0			0
$927$	−16199.0	+	13592.6i	−0.573943	+	0.481595i
$928$		0			0
$929$	46208.8	−	16818.6i	1.63193	−	0.593974i	0.646328	−	0.763060i	$-0.276304\pi$
$929$	46208.8	−	16818.6i	1.63193	−	0.593974i	0.985601	+	0.169086i	$0.0540816\pi$
$930$		0			0
$931$	13312.6	+	18128.0i	0.468639	+	0.638155i
$932$		0			0
$933$	8446.75	−	3074.37i	0.296392	−	0.107878i
$934$		0			0
$935$	40186.3	−	33720.3i	1.40560	−	1.17944i
$936$		0			0
$937$	−3714.33	−	21065.0i	−0.129500	−	0.734433i	−0.978533	−	0.206092i	$-0.933925\pi$
$937$	−3714.33	−	21065.0i	−0.129500	−	0.734433i	0.849032	−	0.528341i	$-0.177186\pi$
$938$		0			0
$939$	−3690.00	+	6391.26i	−0.128241	+	0.222120i
$940$		0			0
$941$	−16476.6	−	5996.99i	−0.570799	−	0.207754i	0.0404646	−	0.999181i	$-0.487116\pi$
$941$	−16476.6	−	5996.99i	−0.570799	−	0.207754i	−0.611263	+	0.791427i	$0.709338\pi$
$942$		0			0
$943$	−35070.7	−	60744.2i	−1.21109	−	2.09767i
$944$		0			0
$945$	−16218.6	−	13609.0i	−0.558296	−	0.468466i
$946$		0			0
$947$	−3114.83	+	17665.1i	−0.106883	+	0.606165i	0.883568	+	0.468302i	$0.155134\pi$
$947$	−3114.83	+	17665.1i	−0.106883	+	0.606165i	−0.990451	+	0.137862i	$0.955977\pi$
$948$		0			0
$949$	−792.268			−0.0271002
$950$		0			0
$951$	−8106.00			−0.276399
$952$		0			0
$953$	−7312.88	+	41473.4i	−0.248570	+	1.40971i	0.563483	+	0.826128i	$0.309461\pi$
$953$	−7312.88	+	41473.4i	−0.248570	+	1.40971i	−0.812053	+	0.583584i	$0.801650\pi$
$954$		0			0
$955$	−29761.6	−	24972.9i	−1.00844	−	0.846183i
$956$		0			0
$957$	13740.9	+	23799.9i	0.464137	+	0.803909i
$958$		0			0
$959$	−23100.5	−	8407.88i	−0.777844	−	0.283112i
$960$		0			0
$961$	14798.0	−	25630.9i	0.496728	−	0.860359i
$962$		0			0
$963$	−2163.65	−	12270.7i	−0.0724015	−	0.410609i
$964$		0			0
$965$	−11496.3	+	9646.53i	−0.383501	+	0.321796i
$966$		0			0
$967$	37218.6	−	13546.5i	1.23771	−	0.450491i	0.361481	−	0.932380i	$-0.382271\pi$
$967$	37218.6	−	13546.5i	1.23771	−	0.450491i	0.876232	+	0.481889i	$0.160049\pi$
$968$		0			0
$969$	15395.4	+	3755.20i	0.510395	+	0.124494i
$970$		0			0
$971$	25423.6	−	9253.42i	0.840248	−	0.305825i	0.114190	−	0.993459i	$-0.463573\pi$
$971$	25423.6	−	9253.42i	0.840248	−	0.305825i	0.726058	+	0.687634i	$0.241350\pi$
$972$		0			0
$973$	11901.5	−	9986.54i	0.392132	−	0.329038i
$974$		0			0
$975$	−219.064	−	1242.37i	−0.00719555	−	0.0408080i
$976$		0			0
$977$	311.668	−	539.825i	0.0102059	−	0.0176771i	−0.860877	−	0.508813i	$-0.830085\pi$
$977$	311.668	−	539.825i	0.0102059	−	0.0176771i	0.871083	+	0.491135i	$0.163418\pi$
$978$		0			0
$979$	−75344.9	−	27423.3i	−2.45969	−	0.895253i
$980$		0			0
$981$	14572.4	+	25240.1i	0.474272	+	0.821463i
$982$		0			0
$983$	−3384.61	−	2840.02i	−0.109819	−	0.0921492i	0.586225	−	0.810149i	$-0.300614\pi$
$983$	−3384.61	−	2840.02i	−0.109819	−	0.0921492i	−0.696044	+	0.717999i	$0.745058\pi$
$984$		0			0
$985$	5630.91	−	31934.5i	0.182148	−	1.03301i
$986$		0			0
$987$	10235.3			0.330084
$988$		0			0
$989$	−18668.4			−0.600222
$990$		0			0
$991$	−3108.78	+	17630.8i	−0.0996506	+	0.565146i	0.893572	+	0.448920i	$0.148191\pi$
$991$	−3108.78	+	17630.8i	−0.0996506	+	0.565146i	−0.993223	+	0.116227i	$0.962920\pi$
$992$		0			0
$993$	24581.0	+	20625.9i	0.785552	+	0.659156i
$994$		0			0
$995$	23334.0	+	40415.8i	0.743456	+	1.28770i
$996$		0			0
$997$	−301.159	−	109.613i	−0.00956650	−	0.00348192i	0.337232	−	0.941421i	$-0.390509\pi$
$997$	−301.159	−	109.613i	−0.00956650	−	0.00348192i	−0.346799	+	0.937939i	$0.612731\pi$
$998$		0			0
$999$	−23639.7	+	40945.1i	−0.748675	+	1.29674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.5.4	✓	30
19.2	odd	18		1444.4.a.k.1.5		15
19.4	even	9	inner	76.4.i.a.61.4	yes	30
19.17	even	9		1444.4.a.j.1.11		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.5.4	✓	30	1.1	even	1	trivial
76.4.i.a.61.4	yes	30	19.4	even	9	inner
1444.4.a.j.1.11		15	19.17	even	9
1444.4.a.k.1.5		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)

\(f(q)\)	\(=\)	\(q+(0.629037 - 3.56745i) q^{3} +(12.9592 + 10.8741i) q^{5} +(-4.22583 - 7.31935i) q^{7} +(13.0407 + 4.74643i) q^{9} +O(q^{10})\)	\(q+(0.629037 - 3.56745i) q^{3} +(12.9592 + 10.8741i) q^{5} +(-4.22583 - 7.31935i) q^{7} +(13.0407 + 4.74643i) q^{9} +(29.3538 - 50.8423i) q^{11} +(-0.375178 - 2.12774i) q^{13} +(46.9445 - 39.3911i) q^{15} +(49.6354 - 18.0658i) q^{17} +(-33.2992 + 75.8299i) q^{19} +(-28.7696 + 10.4713i) q^{21} +(-103.460 + 86.8132i) q^{23} +(27.9897 + 158.738i) q^{25} +(74.0392 - 128.240i) q^{27} +(-121.431 - 44.1972i) q^{29} +(6.98090 + 12.0913i) q^{31} +(-162.913 - 136.700i) q^{33} +(24.8277 - 140.805i) q^{35} -319.286 q^{37} -7.82659 q^{39} +(-90.1832 + 511.454i) q^{41} +(105.887 + 88.8495i) q^{43} +(117.384 + 203.315i) q^{45} +(-314.151 - 114.341i) q^{47} +(135.785 - 235.186i) q^{49} +(-33.2263 - 188.436i) q^{51} +(-263.157 + 220.815i) q^{53} +(933.265 - 339.681i) q^{55} +(249.573 + 166.493i) q^{57} +(174.763 - 63.6086i) q^{59} +(261.981 - 219.828i) q^{61} +(-20.3670 - 115.507i) q^{63} +(18.2752 - 31.6535i) q^{65} +(-36.4792 - 13.2774i) q^{67} +(244.621 + 423.697i) q^{69} +(-440.912 - 369.969i) q^{71} +(63.6760 - 361.124i) q^{73} +583.894 q^{75} -496.177 q^{77} +(6.20502 - 35.1904i) q^{79} +(-123.881 - 103.949i) q^{81} +(250.594 + 434.042i) q^{83} +(839.683 + 305.620i) q^{85} +(-234.056 + 405.396i) q^{87} +(-237.161 - 1345.01i) q^{89} +(-13.9882 + 11.7375i) q^{91} +(47.5262 - 17.2981i) q^{93} +(-1256.11 + 620.598i) q^{95} +(-199.303 + 72.5404i) q^{97} +(624.114 - 523.694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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