LMFDB - Embedded newform 308.3.r.a.57.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.5
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.376205 + 0.273329i) q^{3} +(-1.04910 - 3.22879i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.71433 + 8.35385i) q^{9} +O(q^{10})$	\(q+(-0.376205 + 0.273329i) q^{3} +(-1.04910 - 3.22879i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.71433 + 8.35385i) q^{9} +(10.8336 - 1.90598i) q^{11} +(10.0945 + 3.27990i) q^{13} +(1.27720 + 0.927938i) q^{15} +(17.6380 - 5.73095i) q^{17} +(-4.04333 - 5.56517i) q^{19} -1.23031i q^{21} +36.4379 q^{23} +(10.9009 - 7.91999i) q^{25} +(-2.55548 - 7.86496i) q^{27} +(-14.6247 + 20.1292i) q^{29} +(2.67256 - 8.22529i) q^{31} +(-3.55470 + 3.67818i) q^{33} +(8.54258 + 2.77565i) q^{35} +(16.9821 + 12.3382i) q^{37} +(-4.69409 + 1.52520i) q^{39} +(31.3414 + 43.1377i) q^{41} +3.76280i q^{43} +29.8205 q^{45} +(21.6879 - 15.7571i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-5.06908 + 6.97700i) q^{51} +(-22.8543 + 70.3384i) q^{53} +(-17.5195 - 32.9799i) q^{55} +(3.04224 + 0.988484i) q^{57} +(-62.9548 - 45.7393i) q^{59} +(53.8673 - 17.5025i) q^{61} +(-13.6599 - 18.8013i) q^{63} -36.0340i q^{65} -71.4835 q^{67} +(-13.7081 + 9.95951i) q^{69} +(5.05978 + 15.5724i) q^{71} +(49.5595 - 68.2128i) q^{73} +(-1.93622 + 5.95908i) q^{75} +(-12.7681 + 26.1529i) q^{77} +(5.40325 + 1.75562i) q^{79} +(-60.8448 - 44.2063i) q^{81} +(-80.1975 + 26.0578i) q^{83} +(-37.0081 - 50.9373i) q^{85} -11.5700i q^{87} -11.6437 q^{89} +(-22.7188 + 16.5062i) q^{91} +(1.24278 + 3.82488i) q^{93} +(-13.7269 + 18.8935i) q^{95} +(-35.4575 + 109.127i) q^{97} +(-13.4838 + 95.6759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	−0.376205	+	0.273329i	−0.125402	+	0.0911096i	−0.648718	−	0.761029i	$-0.724695\pi$
$3$	−0.376205	+	0.273329i	−0.125402	+	0.0911096i	0.523316	+	0.852138i	$0.324695\pi$
$4$		0			0
$5$	−1.04910	−	3.22879i	−0.209820	−	0.645758i	−0.999481	−	0.0322154i	$-0.989744\pi$
$5$	−1.04910	−	3.22879i	−0.209820	−	0.645758i	0.789661	−	0.613543i	$-0.210256\pi$
$6$		0			0
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$8$		0			0
$9$	−2.71433	+	8.35385i	−0.301592	+	0.928206i
$10$		0			0
$11$	10.8336	−	1.90598i	0.984874	−	0.173270i
$11$	10.8336	−	1.90598i	0.984874	−	0.173270i
$12$		0			0
$13$	10.0945	+	3.27990i	0.776500	+	0.252300i	0.670345	−	0.742050i	$-0.266146\pi$
$13$	10.0945	+	3.27990i	0.776500	+	0.252300i	0.106155	+	0.994350i	$0.466146\pi$
$14$		0			0
$15$	1.27720	+	0.927938i	0.0851465	+	0.0618626i
$16$		0			0
$17$	17.6380	−	5.73095i	1.03753	−	0.337115i	0.259768	−	0.965671i	$-0.416354\pi$
$17$	17.6380	−	5.73095i	1.03753	−	0.337115i	0.777764	+	0.628556i	$0.216354\pi$
$18$		0			0
$19$	−4.04333	−	5.56517i	−0.212807	−	0.292903i	0.689247	−	0.724526i	$-0.257941\pi$
$19$	−4.04333	−	5.56517i	−0.212807	−	0.292903i	−0.902054	+	0.431622i	$0.857941\pi$
$20$		0			0
$21$		−	1.23031i		−	0.0585863i
$22$		0			0
$23$	36.4379			1.58425			0.792127	−	0.610356i	$-0.208974\pi$
$23$	36.4379			1.58425			0.792127	+	0.610356i	$0.208974\pi$
$24$		0			0
$25$	10.9009	−	7.91999i	0.436037	−	0.316800i
$26$		0			0
$27$	−2.55548	−	7.86496i	−0.0946475	−	0.291295i
$28$		0			0
$29$	−14.6247	+	20.1292i	−0.504300	+	0.694109i	−0.982945	−	0.183899i	$-0.941128\pi$
$29$	−14.6247	+	20.1292i	−0.504300	+	0.694109i	0.478645	+	0.878008i	$0.341128\pi$
$30$		0			0
$31$	2.67256	−	8.22529i	0.0862116	−	0.265332i	−0.898652	−	0.438662i	$-0.855453\pi$
$31$	2.67256	−	8.22529i	0.0862116	−	0.265332i	0.984864	+	0.173330i	$0.0554526\pi$
$32$		0			0
$33$	−3.55470	+	3.67818i	−0.107718	+	0.111460i
$34$		0			0
$35$	8.54258	+	2.77565i	0.244074	+	0.0793044i
$36$		0			0
$37$	16.9821	+	12.3382i	0.458976	+	0.333465i	0.793129	−	0.609053i	$-0.208450\pi$
$37$	16.9821	+	12.3382i	0.458976	+	0.333465i	−0.334154	+	0.942519i	$0.608450\pi$
$38$		0			0
$39$	−4.69409	+	1.52520i	−0.120361	+	0.0391077i
$40$		0			0
$41$	31.3414	+	43.1377i	0.764424	+	1.05214i	0.996833	+	0.0795214i	$0.0253392\pi$
$41$	31.3414	+	43.1377i	0.764424	+	1.05214i	−0.232409	+	0.972618i	$0.574661\pi$
$42$		0			0
$43$			3.76280i			0.0875069i	0.999042	+	0.0437535i	$0.0139316\pi$
$43$			3.76280i			0.0875069i	−0.999042	+	0.0437535i	$0.986068\pi$
$44$		0			0
$45$	29.8205			0.662677
$46$		0			0
$47$	21.6879	−	15.7571i	0.461444	−	0.335259i	−0.332654	−	0.943049i	$-0.607944\pi$
$47$	21.6879	−	15.7571i	0.461444	−	0.335259i	0.794097	+	0.607791i	$0.207944\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−5.06908	+	6.97700i	−0.0993938	+	0.136804i
$52$		0			0
$53$	−22.8543	+	70.3384i	−0.431214	+	1.32714i	0.465704	+	0.884941i	$0.345801\pi$
$53$	−22.8543	+	70.3384i	−0.431214	+	1.32714i	−0.896917	+	0.442198i	$0.854199\pi$
$54$		0			0
$55$	−17.5195	−	32.9799i	−0.318537	−	0.599635i
$56$		0			0
$57$	3.04224	+	0.988484i	0.0533726	+	0.0173418i
$58$		0			0
$59$	−62.9548	−	45.7393i	−1.06703	−	0.775243i	−0.0916545	−	0.995791i	$-0.529216\pi$
$59$	−62.9548	−	45.7393i	−1.06703	−	0.775243i	−0.975376	+	0.220548i	$0.929216\pi$
$60$		0			0
$61$	53.8673	−	17.5025i	0.883070	−	0.286927i	0.167839	−	0.985814i	$-0.446321\pi$
$61$	53.8673	−	17.5025i	0.883070	−	0.286927i	0.715232	+	0.698887i	$0.246321\pi$
$62$		0			0
$63$	−13.6599	−	18.8013i	−0.216824	−	0.298433i
$64$		0			0
$65$		−	36.0340i		−	0.554369i
$66$		0			0
$67$	−71.4835			−1.06692			−0.533459	−	0.845826i	$-0.679108\pi$
$67$	−71.4835			−1.06692			−0.533459	+	0.845826i	$0.679108\pi$
$68$		0			0
$69$	−13.7081	+	9.95951i	−0.198668	+	0.144341i
$70$		0			0
$71$	5.05978	+	15.5724i	0.0712645	+	0.219330i	0.980345	−	0.197291i	$-0.0632144\pi$
$71$	5.05978	+	15.5724i	0.0712645	+	0.219330i	−0.909080	+	0.416621i	$0.863214\pi$
$72$		0			0
$73$	49.5595	−	68.2128i	0.678897	−	0.934422i	−0.321023	−	0.947072i	$-0.604027\pi$
$73$	49.5595	−	68.2128i	0.678897	−	0.934422i	0.999920	+	0.0126494i	$0.00402655\pi$
$74$		0			0
$75$	−1.93622	+	5.95908i	−0.0258163	+	0.0794544i
$76$		0			0
$77$	−12.7681	+	26.1529i	−0.165819	+	0.339649i
$78$		0			0
$79$	5.40325	+	1.75562i	0.0683956	+	0.0222231i	0.343015	−	0.939330i	$-0.388552\pi$
$79$	5.40325	+	1.75562i	0.0683956	+	0.0222231i	−0.274619	+	0.961553i	$0.588552\pi$
$80$		0			0
$81$	−60.8448	−	44.2063i	−0.751170	−	0.545757i
$82$		0			0
$83$	−80.1975	+	26.0578i	−0.966235	+	0.313949i	−0.749295	−	0.662236i	$-0.769608\pi$
$83$	−80.1975	+	26.0578i	−0.966235	+	0.313949i	−0.216940	+	0.976185i	$0.569608\pi$
$84$		0			0
$85$	−37.0081	−	50.9373i	−0.435389	−	0.599262i
$86$		0			0
$87$		−	11.5700i		−	0.132989i
$88$		0			0
$89$	−11.6437			−0.130829			−0.0654143	−	0.997858i	$-0.520837\pi$
$89$	−11.6437			−0.130829			−0.0654143	+	0.997858i	$0.520837\pi$
$90$		0			0
$91$	−22.7188	+	16.5062i	−0.249657	+	0.181386i
$92$		0			0
$93$	1.24278	+	3.82488i	0.0133632	+	0.0411278i
$94$		0			0
$95$	−13.7269	+	18.8935i	−0.144494	+	0.198879i
$96$		0			0
$97$	−35.4575	+	109.127i	−0.365541	+	1.12502i	0.584101	+	0.811681i	$0.301447\pi$
$97$	−35.4575	+	109.127i	−0.365541	+	1.12502i	−0.949642	+	0.313338i	$0.898553\pi$
$98$		0			0
$99$	−13.4838	+	95.6759i	−0.136200	+	0.966423i
$100$		0			0
$101$	109.637	+	35.6232i	1.08551	+	0.352705i	0.796512	−	0.604623i	$-0.206676\pi$
$101$	109.637	+	35.6232i	1.08551	+	0.352705i	0.289003	+	0.957328i	$0.406676\pi$
$102$		0			0
$103$	−10.2123	−	7.41966i	−0.0991484	−	0.0720355i	0.537106	−	0.843514i	$-0.319517\pi$
$103$	−10.2123	−	7.41966i	−0.0991484	−	0.0720355i	−0.636255	+	0.771479i	$0.719517\pi$
$104$		0			0
$105$	−3.97243	+	1.29072i	−0.0378326	+	0.0122926i
$106$		0			0
$107$	−115.642	−	159.167i	−1.08076	−	1.48754i	−0.858679	−	0.512513i	$-0.828715\pi$
$107$	−115.642	−	159.167i	−1.08076	−	1.48754i	−0.222083	−	0.975028i	$-0.571285\pi$
$108$		0			0
$109$		−	34.8079i		−	0.319339i	−0.987171	−	0.159669i	$-0.948957\pi$
$109$		−	34.8079i		−	0.319339i	0.987171	−	0.159669i	$-0.0510428\pi$
$110$		0			0
$111$	−9.76114			−0.0879382
$112$		0			0
$113$	−81.7735	+	59.4120i	−0.723660	+	0.525770i	−0.887551	−	0.460709i	$-0.847595\pi$
$113$	−81.7735	+	59.4120i	−0.723660	+	0.525770i	0.163892	+	0.986478i	$0.447595\pi$
$114$		0			0
$115$	−38.2269	−	117.650i	−0.332408	−	1.02305i
$116$		0			0
$117$	−54.7996	+	75.4252i	−0.468373	+	0.644660i
$118$		0			0
$119$	−15.1627	+	46.6659i	−0.127417	+	0.392150i
$120$		0			0
$121$	113.735	−	41.2972i	0.939955	−	0.341299i
$122$		0			0
$123$	−23.5816	−	7.66211i	−0.191720	−	0.0622936i
$124$		0			0
$125$	−105.673	−	76.7756i	−0.845380	−	0.614205i
$126$		0			0
$127$	−193.881	+	62.9958i	−1.52662	+	0.496030i	−0.947649	−	0.319315i	$-0.896547\pi$
$127$	−193.881	+	62.9958i	−1.52662	+	0.496030i	−0.578975	+	0.815345i	$0.696547\pi$
$128$		0			0
$129$	−1.02848	−	1.41558i	−0.00797272	−	0.0109735i
$130$		0			0
$131$		−	72.6453i		−	0.554544i	−0.960791	−	0.277272i	$-0.910570\pi$
$131$		−	72.6453i		−	0.554544i	0.960791	−	0.277272i	$-0.0894304\pi$
$132$		0			0
$133$	18.1999			0.136842
$134$		0			0
$135$	−22.7134	+	16.5022i	−0.168247	+	0.122239i
$136$		0			0
$137$	72.9595	+	224.546i	0.532551	+	1.63902i	0.748881	+	0.662704i	$0.230591\pi$
$137$	72.9595	+	224.546i	0.532551	+	1.63902i	−0.216330	+	0.976320i	$0.569409\pi$
$138$		0			0
$139$	148.066	−	203.796i	1.06522	−	1.46616i	0.190406	−	0.981706i	$-0.439020\pi$
$139$	148.066	−	203.796i	1.06522	−	1.46616i	0.874819	−	0.484450i	$-0.160980\pi$
$140$		0			0
$141$	−3.85219	+	11.8558i	−0.0273205	+	0.0840839i
$142$		0			0
$143$	115.611	+	16.2933i	0.808471	+	0.113939i
$144$		0			0
$145$	80.3357	+	26.1026i	0.554039	+	0.180018i
$146$		0			0
$147$	2.63343	+	1.91330i	0.0179145	+	0.0130157i
$148$		0			0
$149$	−3.63778	+	1.18199i	−0.0244146	+	0.00793280i	−0.321199	−	0.947012i	$-0.604086\pi$
$149$	−3.63778	+	1.18199i	−0.0244146	+	0.00793280i	0.296784	+	0.954945i	$0.404086\pi$
$150$		0			0
$151$	−12.9931	−	17.8835i	−0.0860471	−	0.118434i	0.763823	−	0.645425i	$-0.223320\pi$
$151$	−12.9931	−	17.8835i	−0.0860471	−	0.118434i	−0.849870	+	0.526992i	$0.823320\pi$
$152$		0			0
$153$			162.901i			1.06471i
$154$		0			0
$155$	−29.3615			−0.189429
$156$		0			0
$157$	171.967	−	124.941i	1.09533	−	0.795805i	0.115040	−	0.993361i	$-0.463300\pi$
$157$	171.967	−	124.941i	1.09533	−	0.795805i	0.980292	+	0.197555i	$0.0633003\pi$
$158$		0			0
$159$	−10.6276	−	32.7084i	−0.0668402	−	0.205713i
$160$		0			0
$161$	−56.6657	+	77.9937i	−0.351961	+	0.484433i
$162$		0			0
$163$	42.0324	−	129.362i	0.257867	−	0.793634i	−0.735384	−	0.677651i	$-0.762998\pi$
$163$	42.0324	−	129.362i	0.257867	−	0.793634i	0.993251	−	0.115983i	$-0.0370020\pi$
$164$		0			0
$165$	15.6053	+	7.61862i	0.0945776	+	0.0461735i
$166$		0			0
$167$	−25.5876	−	8.31392i	−0.153219	−	0.0497839i	0.231403	−	0.972858i	$-0.425668\pi$
$167$	−25.5876	−	8.31392i	−0.153219	−	0.0497839i	−0.384622	+	0.923074i	$0.625668\pi$
$168$		0			0
$169$	−45.5828	−	33.1178i	−0.269721	−	0.195963i
$170$		0			0
$171$	57.4655	−	18.6717i	0.336056	−	0.109191i
$172$		0			0
$173$	−70.8921	−	97.5746i	−0.409781	−	0.564015i	0.553384	−	0.832926i	$-0.313336\pi$
$173$	−70.8921	−	97.5746i	−0.409781	−	0.564015i	−0.963165	+	0.268911i	$0.913336\pi$
$174$		0			0
$175$			35.6496i			0.203712i
$176$		0			0
$177$	36.1858			0.204439
$178$		0			0
$179$	−114.538	+	83.2167i	−0.639877	+	0.464898i	−0.859808	−	0.510617i	$-0.829417\pi$
$179$	−114.538	+	83.2167i	−0.639877	+	0.464898i	0.219931	+	0.975515i	$0.429417\pi$
$180$		0			0
$181$	17.5726	+	54.0829i	0.0970861	+	0.298800i	0.987792	−	0.155780i	$-0.0497892\pi$
$181$	17.5726	+	54.0829i	0.0970861	+	0.298800i	−0.890706	+	0.454581i	$0.849789\pi$
$182$		0			0
$183$	−15.4812	+	21.3080i	−0.0845967	+	0.116437i
$184$		0			0
$185$	22.0217	−	67.7757i	0.119036	−	0.366355i
$186$		0			0
$187$	180.161	−	95.7046i	0.963427	−	0.511789i
$188$		0			0
$189$	20.8087	+	6.76117i	0.110099	+	0.0357734i
$190$		0			0
$191$	148.914	+	108.192i	0.779654	+	0.566452i	0.904875	−	0.425677i	$-0.139964\pi$
$191$	148.914	+	108.192i	0.779654	+	0.566452i	−0.125221	+	0.992129i	$0.539964\pi$
$192$		0			0
$193$	−43.2554	+	14.0545i	−0.224121	+	0.0728214i	−0.418925	−	0.908021i	$-0.637593\pi$
$193$	−43.2554	+	14.0545i	−0.224121	+	0.0728214i	0.194804	+	0.980842i	$0.437593\pi$
$194$		0			0
$195$	9.84912	+	13.5562i	0.0505083	+	0.0695187i
$196$		0			0
$197$			40.9397i			0.207816i	0.994587	+	0.103908i	$0.0331347\pi$
$197$			40.9397i			0.207816i	−0.994587	+	0.103908i	$0.966865\pi$
$198$		0			0
$199$	371.775			1.86822			0.934109	−	0.356989i	$-0.116196\pi$
$199$	371.775			1.86822			0.934109	+	0.356989i	$0.116196\pi$
$200$		0			0
$201$	26.8924	−	19.5385i	0.133793	−	0.0972064i
$202$		0			0
$203$	−20.3423	−	62.6071i	−0.100208	−	0.308409i
$204$		0			0
$205$	106.403	−	146.451i	0.519037	−	0.714393i
$206$		0			0
$207$	−98.9044	+	304.396i	−0.477799	+	1.47051i
$208$		0			0
$209$	−54.4110	−	52.5844i	−0.260340	−	0.251600i
$210$		0			0
$211$	141.523	+	45.9837i	0.670726	+	0.217932i	0.624531	−	0.781000i	$-0.285290\pi$
$211$	141.523	+	45.9837i	0.670726	+	0.217932i	0.0461954	+	0.998932i	$0.485290\pi$
$212$		0			0
$213$	−6.15990	−	4.47543i	−0.0289197	−	0.0210114i
$214$		0			0
$215$	12.1493	−	3.94754i	0.0565083	−	0.0183607i
$216$		0			0
$217$	13.4497	+	18.5119i	0.0619802	+	0.0853084i
$218$		0			0
$219$			39.2080i			0.179032i
$220$		0			0
$221$	196.844			0.890697
$222$		0			0
$223$	−309.492	+	224.859i	−1.38786	+	1.00834i	−0.391762	+	0.920067i	$0.628134\pi$
$223$	−309.492	+	224.859i	−1.38786	+	1.00834i	−0.996096	+	0.0882715i	$0.971866\pi$
$224$		0			0
$225$	36.5737	+	112.562i	0.162550	+	0.500277i
$226$		0			0
$227$	143.715	−	197.806i	0.633104	−	0.871392i	−0.365121	−	0.930960i	$-0.618972\pi$
$227$	143.715	−	197.806i	0.633104	−	0.871392i	0.998224	+	0.0595679i	$0.0189723\pi$
$228$		0			0
$229$	−112.815	+	347.209i	−0.492643	+	1.51620i	0.327956	+	0.944693i	$0.393640\pi$
$229$	−112.815	+	347.209i	−0.492643	+	1.51620i	−0.820599	+	0.571505i	$0.806360\pi$
$230$		0			0
$231$	−2.34495	−	13.3287i	−0.0101513	−	0.0577002i
$232$		0			0
$233$	271.400	+	88.1832i	1.16481	+	0.378469i	0.826702	−	0.562640i	$-0.190214\pi$
$233$	271.400	+	88.1832i	1.16481	+	0.378469i	0.338104	+	0.941109i	$0.390214\pi$
$234$		0			0
$235$	−73.6293	−	53.4948i	−0.313316	−	0.227637i
$236$		0			0
$237$	−2.51259	+	0.816390i	−0.0106016	+	0.00344468i
$238$		0			0
$239$	22.4209	+	30.8597i	0.0938113	+	0.129120i	0.853343	−	0.521351i	$-0.174572\pi$
$239$	22.4209	+	30.8597i	0.0938113	+	0.129120i	−0.759531	+	0.650471i	$0.774572\pi$
$240$		0			0
$241$		−	437.194i		−	1.81408i	−0.421040	−	0.907042i	$-0.638335\pi$
$241$		−	437.194i		−	1.81408i	0.421040	−	0.907042i	$-0.361665\pi$
$242$		0			0
$243$	109.400			0.450207
$244$		0			0
$245$	−19.2260	+	13.9685i	−0.0784736	+	0.0570144i
$246$		0			0
$247$	−22.5622	−	69.4393i	−0.0913449	−	0.281131i
$248$		0			0
$249$	23.0484	−	31.7234i	0.0925637	−	0.127403i
$250$		0			0
$251$	−88.9240	+	273.680i	−0.354279	+	1.09036i	0.602148	+	0.798385i	$0.294312\pi$
$251$	−88.9240	+	273.680i	−0.354279	+	1.09036i	−0.956426	+	0.291973i	$0.905688\pi$
$252$		0			0
$253$	394.754	−	69.4496i	1.56029	−	0.274505i
$254$		0			0
$255$	27.8452	+	9.04747i	0.109197	+	0.0354803i
$256$		0			0
$257$	−88.3055	−	64.1577i	−0.343601	−	0.249641i	0.402579	−	0.915385i	$-0.368114\pi$
$257$	−88.3055	−	64.1577i	−0.343601	−	0.249641i	−0.746180	+	0.665745i	$0.768114\pi$
$258$		0			0
$259$	−52.8189	+	17.1619i	−0.203934	+	0.0662621i
$260$		0			0
$261$	−128.460	−	176.810i	−0.492183	−	0.677432i
$262$		0			0
$263$		−	104.497i		−	0.397327i	−0.980068	−	0.198663i	$-0.936340\pi$
$263$		−	104.497i		−	0.397327i	0.980068	−	0.198663i	$-0.0636601\pi$
$264$		0			0
$265$	251.084			0.947488
$266$		0			0
$267$	4.38043	−	3.18257i	0.0164061	−	0.0119197i
$268$		0			0
$269$	58.8361	+	181.079i	0.218721	+	0.673155i	0.998868	+	0.0475590i	$0.0151442\pi$
$269$	58.8361	+	181.079i	0.218721	+	0.673155i	−0.780147	+	0.625596i	$0.784856\pi$
$270$		0			0
$271$	185.893	−	255.860i	0.685954	−	0.944134i	−0.314032	−	0.949412i	$-0.601680\pi$
$271$	185.893	−	255.860i	0.685954	−	0.944134i	0.999986	+	0.00527811i	$0.00168008\pi$
$272$		0			0
$273$	4.03531	−	12.4194i	0.0147813	−	0.0454923i
$274$		0			0
$275$	103.001	−	106.579i	0.374550	−	0.387560i
$276$		0			0
$277$	−191.986	−	62.3799i	−0.693089	−	0.225198i	−0.0587721	−	0.998271i	$-0.518719\pi$
$277$	−191.986	−	62.3799i	−0.693089	−	0.225198i	−0.634317	+	0.773073i	$0.718719\pi$
$278$		0			0
$279$	61.4587	+	44.6523i	0.220282	+	0.160044i
$280$		0			0
$281$	−498.804	+	162.071i	−1.77510	+	0.576766i	−0.998578	−	0.0533185i	$-0.983020\pi$
$281$	−498.804	+	162.071i	−1.77510	+	0.576766i	−0.776526	+	0.630085i	$0.783020\pi$
$282$		0			0
$283$	−97.6001	−	134.335i	−0.344877	−	0.474682i	0.600981	−	0.799263i	$-0.294777\pi$
$283$	−97.6001	−	134.335i	−0.344877	−	0.474682i	−0.945858	+	0.324581i	$0.894777\pi$
$284$		0			0
$285$		−	10.8598i		−	0.0381045i
$286$		0			0
$287$	−141.075			−0.491549
$288$		0			0
$289$	44.4510	−	32.2955i	0.153810	−	0.111749i
$290$		0			0
$291$	−16.4882	−	50.7456i	−0.0566606	−	0.174383i
$292$		0			0
$293$	−12.4027	+	17.0708i	−0.0423299	+	0.0582621i	−0.829657	−	0.558273i	$-0.811464\pi$
$293$	−12.4027	+	17.0708i	−0.0423299	+	0.0582621i	0.787327	+	0.616535i	$0.211464\pi$
$294$		0			0
$295$	−81.6371	+	251.253i	−0.276736	+	0.851705i
$296$		0			0
$297$	−42.6755	−	80.3353i	−0.143689	−	0.270489i
$298$		0			0
$299$	367.822	+	119.513i	1.23017	+	0.399707i
$300$		0			0
$301$	−8.05411	−	5.85165i	−0.0267578	−	0.0194407i
$302$		0			0
$303$	−50.9828	+	16.5653i	−0.168260	+	0.0546710i
$304$		0			0
$305$	−113.024	−	155.564i	−0.370571	−	0.510047i
$306$		0			0
$307$		−	144.521i		−	0.470753i	−0.971904	−	0.235377i	$-0.924368\pi$
$307$		−	144.521i		−	0.470753i	0.971904	−	0.235377i	$-0.0756324\pi$
$308$		0			0
$309$	5.86992			0.0189965
$310$		0			0
$311$	−176.091	+	127.938i	−0.566209	+	0.411375i	−0.833726	−	0.552178i	$-0.813797\pi$
$311$	−176.091	+	127.938i	−0.566209	+	0.411375i	0.267517	+	0.963553i	$0.413797\pi$
$312$		0			0
$313$	−120.125	−	369.708i	−0.383787	−	1.18118i	−0.937356	−	0.348372i	$-0.886734\pi$
$313$	−120.125	−	369.708i	−0.383787	−	1.18118i	0.553569	−	0.832803i	$-0.313266\pi$
$314$		0			0
$315$	−46.3748	+	63.8294i	−0.147222	+	0.202633i
$316$		0			0
$317$	−143.510	+	441.679i	−0.452714	+	1.39331i	0.421084	+	0.907022i	$0.361650\pi$
$317$	−143.510	+	441.679i	−0.452714	+	1.39331i	−0.873798	+	0.486289i	$0.838350\pi$
$318$		0			0
$319$	−120.073	+	245.946i	−0.376403	+	0.770991i
$320$		0			0
$321$	87.0098	+	28.2712i	0.271059	+	0.0880723i
$322$		0			0
$323$	−103.210	−	74.9865i	−0.319536	−	0.232156i
$324$		0			0
$325$	136.016	−	44.1943i	0.418511	−	0.135983i
$326$		0			0
$327$	9.51401	+	13.0949i	0.0290948	+	0.0400456i
$328$		0			0
$329$			70.9264i			0.215582i
$330$		0			0
$331$	−123.537			−0.373222			−0.186611	−	0.982434i	$-0.559750\pi$
$331$	−123.537			−0.373222			−0.186611	+	0.982434i	$0.559750\pi$
$332$		0			0
$333$	−149.167	+	108.376i	−0.447948	+	0.325453i
$334$		0			0
$335$	74.9932	+	230.805i	0.223860	+	0.688971i
$336$		0			0
$337$	−201.095	+	276.783i	−0.596720	+	0.821314i	−0.995403	−	0.0957744i	$-0.969467\pi$
$337$	−201.095	+	276.783i	−0.596720	+	0.821314i	0.398683	+	0.917089i	$0.369467\pi$
$338$		0			0
$339$	14.5246	−	44.7021i	0.0428454	−	0.131865i
$340$		0			0
$341$	13.2763	−	94.2035i	0.0389334	−	0.276257i
$342$		0			0
$343$	17.6138	+	5.72307i	0.0513522	+	0.0166853i
$344$		0			0
$345$	46.5383	+	33.8121i	0.134894	+	0.0980060i
$346$		0			0
$347$	−157.493	+	51.1724i	−0.453869	+	0.147471i	−0.527025	−	0.849849i	$-0.676693\pi$
$347$	−157.493	+	51.1724i	−0.453869	+	0.147471i	0.0731564	+	0.997320i	$0.476693\pi$
$348$		0			0
$349$	−376.991	−	518.884i	−1.08020	−	1.48677i	−0.859297	−	0.511477i	$-0.829098\pi$
$349$	−376.991	−	518.884i	−1.08020	−	1.48677i	−0.220906	−	0.975295i	$-0.570902\pi$
$350$		0			0
$351$		−	87.7746i		−	0.250070i
$352$		0			0
$353$	−36.3938			−0.103099			−0.0515493	−	0.998670i	$-0.516416\pi$
$353$	−36.3938			−0.103099			−0.0515493	+	0.998670i	$0.516416\pi$
$354$		0			0
$355$	44.9719	−	32.6740i	0.126681	−	0.0920393i
$356$		0			0
$357$	−7.05086	−	21.7003i	−0.0197503	−	0.0607852i
$358$		0			0
$359$	−86.1217	+	118.536i	−0.239893	+	0.330185i	−0.911940	−	0.410324i	$-0.865416\pi$
$359$	−86.1217	+	118.536i	−0.239893	+	0.330185i	0.672046	+	0.740509i	$0.265416\pi$
$360$		0			0
$361$	96.9326	−	298.328i	0.268511	−	0.826393i
$362$		0			0
$363$	−31.4998	+	46.6231i	−0.0867762	+	0.128438i
$364$		0			0
$365$	−272.238	−	88.4554i	−0.745857	−	0.242344i
$366$		0			0
$367$	−303.674	−	220.632i	−0.827449	−	0.601177i	0.0913878	−	0.995815i	$-0.470870\pi$
$367$	−303.674	−	220.632i	−0.827449	−	0.601177i	−0.918836	+	0.394639i	$0.870870\pi$
$368$		0			0
$369$	−445.437	+	144.731i	−1.20715	+	0.392226i
$370$		0			0
$371$	−115.015	−	158.304i	−0.310013	−	0.426696i
$372$		0			0
$373$		−	136.431i		−	0.365768i	−0.983135	−	0.182884i	$-0.941457\pi$
$373$		−	136.431i		−	0.365768i	0.983135	−	0.182884i	$-0.0585433\pi$
$374$		0			0
$375$	60.7395			0.161972
$376$		0			0
$377$	−213.651	+	155.226i	−0.566713	+	0.411741i
$378$		0			0
$379$	−81.1060	−	249.619i	−0.214000	−	0.658625i	−0.999223	−	0.0394115i	$-0.987452\pi$
$379$	−81.1060	−	249.619i	−0.214000	−	0.658625i	0.785223	−	0.619213i	$-0.212548\pi$
$380$		0			0
$381$	55.7205	−	76.6927i	0.146248	−	0.201293i
$382$		0			0
$383$	−87.0695	+	267.972i	−0.227336	+	0.699667i	0.770711	+	0.637185i	$0.219901\pi$
$383$	−87.0695	+	267.972i	−0.227336	+	0.699667i	−0.998046	+	0.0624815i	$0.980099\pi$
$384$		0			0
$385$	97.8374	+	13.7884i	0.254123	+	0.0358141i
$386$		0			0
$387$	−31.4339	−	10.2135i	−0.0812244	−	0.0263914i
$388$		0			0
$389$	−60.2323	−	43.7613i	−0.154839	−	0.112497i	0.507668	−	0.861553i	$-0.330508\pi$
$389$	−60.2323	−	43.7613i	−0.154839	−	0.112497i	−0.662507	+	0.749056i	$0.730508\pi$
$390$		0			0
$391$	642.692	−	208.823i	1.64371	−	0.534075i
$392$		0			0
$393$	19.8561	+	27.3295i	0.0505243	+	0.0695407i
$394$		0			0
$395$		−	19.2878i		−	0.0488299i
$396$		0			0
$397$	−751.743			−1.89356			−0.946780	−	0.321881i	$-0.895685\pi$
$397$	−751.743			−1.89356			−0.946780	+	0.321881i	$0.895685\pi$
$398$		0			0
$399$	−6.84690	+	4.97456i	−0.0171601	+	0.0124676i
$400$		0			0
$401$	−112.644	−	346.683i	−0.280908	−	0.864546i	−0.987595	−	0.157020i	$-0.949811\pi$
$401$	−112.644	−	346.683i	−0.280908	−	0.864546i	0.706688	−	0.707526i	$-0.250189\pi$
$402$		0			0
$403$	53.9563	−	74.2644i	0.133887	−	0.184279i
$404$		0			0
$405$	−78.9009	+	242.832i	−0.194817	+	0.599585i
$406$		0			0
$407$	207.494	+	101.300i	0.509813	+	0.248895i
$408$		0			0
$409$	100.739	+	32.7322i	0.246306	+	0.0800297i	0.429568	−	0.903034i	$-0.358666\pi$
$409$	100.739	+	32.7322i	0.246306	+	0.0800297i	−0.183262	+	0.983064i	$0.558666\pi$
$410$		0			0
$411$	−88.8227	−	64.5335i	−0.216114	−	0.157016i
$412$		0			0
$413$	195.806	−	63.6213i	0.474107	−	0.154047i
$414$		0			0
$415$	168.270	+	231.604i	0.405470	+	0.558082i
$416$		0			0
$417$			117.140i			0.280910i
$418$		0			0
$419$	−77.2048			−0.184260			−0.0921299	−	0.995747i	$-0.529367\pi$
$419$	−77.2048			−0.184260			−0.0921299	+	0.995747i	$0.529367\pi$
$420$		0			0
$421$	191.283	−	138.976i	0.454355	−	0.330108i	−0.336958	−	0.941520i	$-0.609398\pi$
$421$	191.283	−	138.976i	0.454355	−	0.330108i	0.791313	+	0.611412i	$0.209398\pi$
$422$		0			0
$423$	72.7649	+	223.947i	0.172021	+	0.529426i
$424$		0			0
$425$	146.882	−	202.166i	0.345605	−	0.475684i
$426$		0			0
$427$	−46.3074	+	142.519i	−0.108448	+	0.333769i
$428$		0			0
$429$	−47.9470	+	25.4703i	−0.111764	+	0.0593713i
$430$		0			0
$431$	751.788	+	244.271i	1.74429	+	0.566753i	0.995388	−	0.0959315i	$-0.0305830\pi$
$431$	751.788	+	244.271i	1.74429	+	0.566753i	0.748899	+	0.662685i	$0.230583\pi$
$432$		0			0
$433$	−478.778	−	347.852i	−1.10572	−	0.803354i	−0.123738	−	0.992315i	$-0.539488\pi$
$433$	−478.778	−	347.852i	−1.10572	−	0.803354i	−0.981985	+	0.188961i	$0.939488\pi$
$434$		0			0
$435$	−37.3573	+	12.1381i	−0.0858788	+	0.0279037i
$436$		0			0
$437$	−147.330	−	202.783i	−0.337140	−	0.464034i
$438$		0			0
$439$			366.223i			0.834220i	0.908856	+	0.417110i	$0.136957\pi$
$439$			366.223i			0.834220i	−0.908856	+	0.417110i	$0.863043\pi$
$440$		0			0
$441$	61.4863			0.139425
$442$		0			0
$443$	−112.725	+	81.8993i	−0.254458	+	0.184874i	−0.707700	−	0.706513i	$-0.750267\pi$
$443$	−112.725	+	81.8993i	−0.254458	+	0.184874i	0.453242	+	0.891387i	$0.350267\pi$
$444$		0			0
$445$	12.2154	+	37.5952i	0.0274504	+	0.0844836i
$446$		0			0
$447$	1.04548	−	1.43898i	0.00233888	−	0.00321919i
$448$		0			0
$449$	−4.93621	+	15.1921i	−0.0109938	+	0.0338354i	−0.956403	−	0.292050i	$-0.905662\pi$
$449$	−4.93621	+	15.1921i	−0.0109938	+	0.0338354i	0.945409	+	0.325886i	$0.105662\pi$
$450$		0			0
$451$	421.760	+	407.602i	0.935166	+	0.903773i
$452$		0			0
$453$	9.77615	+	3.17646i	0.0215809	+	0.00701206i
$454$		0			0
$455$	77.1292	+	56.0376i	0.169515	+	0.123160i
$456$		0			0
$457$	150.104	−	48.7716i	0.328454	−	0.106721i	−0.140148	−	0.990131i	$-0.544758\pi$
$457$	150.104	−	48.7716i	0.328454	−	0.106721i	0.468602	+	0.883409i	$0.344758\pi$
$458$		0			0
$459$	−90.1474	−	124.077i	−0.196400	−	0.270321i
$460$		0			0
$461$		−	46.1569i		−	0.100123i	−0.998746	−	0.0500617i	$-0.984058\pi$
$461$		−	46.1569i		−	0.100123i	0.998746	−	0.0500617i	$-0.0159418\pi$
$462$		0			0
$463$	330.251			0.713284			0.356642	−	0.934241i	$-0.383922\pi$
$463$	330.251			0.713284			0.356642	+	0.934241i	$0.383922\pi$
$464$		0			0
$465$	11.0460	−	8.02535i	0.0237547	−	0.0172588i
$466$		0			0
$467$	−7.54377	−	23.2173i	−0.0161537	−	0.0497159i	0.942655	−	0.333769i	$-0.108321\pi$
$467$	−7.54377	−	23.2173i	−0.0161537	−	0.0497159i	−0.958808	+	0.284053i	$0.908321\pi$
$468$		0			0
$469$	111.166	−	153.007i	0.237028	−	0.326242i
$470$		0			0
$471$	−30.5448	+	94.0071i	−0.0648509	+	0.199591i
$472$		0			0
$473$	7.17180	+	40.7647i	0.0151624	+	0.0861833i
$474$		0			0
$475$	−88.1521	−	28.6424i	−0.185583	−	0.0602997i
$476$		0			0
$477$	−525.562	−	381.843i	−1.10181	−	0.800510i
$478$		0			0
$479$	−536.950	+	174.466i	−1.12098	+	0.364229i	−0.810142	−	0.586234i	$-0.800610\pi$
$479$	−536.950	+	174.466i	−1.12098	+	0.364229i	−0.310839	+	0.950463i	$0.600610\pi$
$480$		0			0
$481$	130.958	+	180.248i	0.272261	+	0.374735i
$482$		0			0
$483$		−	44.8300i		−	0.0928157i
$484$		0			0
$485$	389.546			0.803188
$486$		0			0
$487$	−501.274	+	364.197i	−1.02931	+	0.747837i	−0.968170	−	0.250292i	$-0.919473\pi$
$487$	−501.274	+	364.197i	−1.02931	+	0.747837i	−0.0611392	+	0.998129i	$0.519473\pi$
$488$		0			0
$489$	19.5457	+	60.1554i	0.0399707	+	0.123017i
$490$		0			0
$491$	409.812	−	564.058i	0.834648	−	1.14879i	−0.152392	−	0.988320i	$-0.548698\pi$
$491$	409.812	−	564.058i	0.834648	−	1.14879i	0.987040	−	0.160474i	$-0.0513024\pi$
$492$		0			0
$493$	−142.592	+	438.853i	−0.289233	+	0.890168i
$494$		0			0
$495$	323.063	−	56.8371i	0.652653	−	0.114822i
$496$		0			0
$497$	−41.2007	−	13.3869i	−0.0828988	−	0.0269355i
$498$		0			0
$499$	−525.902	−	382.090i	−1.05391	−	0.765712i	−0.0809597	−	0.996717i	$-0.525799\pi$
$499$	−525.902	−	382.090i	−1.05391	−	0.765712i	−0.972952	+	0.231005i	$0.925799\pi$
$500$		0			0
$501$	11.8986	−	3.86609i	0.0237497	−	0.00771675i
$502$		0			0
$503$	237.340	+	326.671i	0.471849	+	0.649445i	0.976913	−	0.213637i	$-0.0685311\pi$
$503$	237.340	+	326.671i	0.471849	+	0.649445i	−0.505064	+	0.863082i	$0.668531\pi$
$504$		0			0
$505$		−	391.367i		−	0.774985i
$506$		0			0
$507$	26.2005			0.0516775
$508$		0			0
$509$	100.381	−	72.9311i	0.197212	−	0.143283i	−0.484797	−	0.874627i	$-0.661106\pi$
$509$	100.381	−	72.9311i	0.197212	−	0.143283i	0.682009	+	0.731344i	$0.261106\pi$
$510$		0			0
$511$	68.9350	+	212.160i	0.134902	+	0.415186i
$512$		0			0
$513$	−33.4372	+	46.0223i	−0.0651797	+	0.0897121i
$514$		0			0
$515$	−13.2428	+	40.7573i	−0.0257143	+	0.0791404i
$516$		0			0
$517$	204.925	−	212.043i	0.396374	−	0.410142i
$518$		0			0
$519$	53.3399	+	17.3312i	0.102774	+	0.0333934i
$520$		0			0
$521$	358.169	+	260.225i	0.687464	+	0.499472i	0.875825	−	0.482628i	$-0.160318\pi$
$521$	358.169	+	260.225i	0.687464	+	0.499472i	−0.188362	+	0.982100i	$0.560318\pi$
$522$		0			0
$523$	623.678	−	202.645i	1.19250	−	0.387467i	0.355504	−	0.934675i	$-0.384309\pi$
$523$	623.678	−	202.645i	1.19250	−	0.387467i	0.836997	+	0.547208i	$0.184309\pi$
$524$		0			0
$525$	−9.74407	−	13.4116i	−0.0185601	−	0.0255458i
$526$		0			0
$527$		−	160.394i		−	0.304354i
$528$		0			0
$529$	798.717			1.50986
$530$		0			0
$531$	552.980	−	401.764i	1.04139	−	0.756617i
$532$		0			0
$533$	174.888	+	538.250i	0.328120	+	1.00985i
$534$		0			0
$535$	−392.598	+	540.364i	−0.733827	+	1.01003i
$536$		0			0
$537$	20.3442	−	62.6131i	0.0378850	−	0.116598i
$538$		0			0
$539$	−36.1232	−	68.0008i	−0.0670190	−	0.126161i
$540$		0			0
$541$	547.177	+	177.789i	1.01142	+	0.328629i	0.767419	−	0.641146i	$-0.221541\pi$
$541$	547.177	+	177.789i	1.01142	+	0.328629i	0.243999	+	0.969776i	$0.421541\pi$
$542$		0			0
$543$	−21.3933	−	15.5431i	−0.0393983	−	0.0286246i
$544$		0			0
$545$	−112.388	+	36.5169i	−0.206216	+	0.0670035i
$546$		0			0
$547$	368.849	+	507.678i	0.674313	+	0.928113i	0.999848	−	0.0174172i	$-0.00554435\pi$
$547$	368.849	+	507.678i	0.674313	+	0.928113i	−0.325535	+	0.945530i	$0.605544\pi$
$548$		0			0
$549$			497.507i			0.906206i
$550$		0			0
$551$	171.155			0.310626
$552$		0			0
$553$	−12.1606	+	8.83520i	−0.0219903	+	0.0159769i
$554$		0			0
$555$	10.2404	+	31.5167i	0.0184512	+	0.0567868i
$556$		0			0
$557$	176.102	−	242.384i	0.316162	−	0.435159i	−0.621129	−	0.783709i	$-0.713326\pi$
$557$	176.102	−	242.384i	0.316162	−	0.435159i	0.937290	+	0.348549i	$0.113326\pi$
$558$		0			0
$559$	−12.3416	+	37.9835i	−0.0220780	+	0.0679491i
$560$		0			0
$561$	−41.6185	+	85.2477i	−0.0741863	+	0.151957i
$562$		0			0
$563$	−619.738	−	201.365i	−1.10078	−	0.357665i	−0.298376	−	0.954448i	$-0.596445\pi$
$563$	−619.738	−	201.365i	−1.10078	−	0.357665i	−0.802402	+	0.596784i	$0.796445\pi$
$564$		0			0
$565$	277.617	+	201.701i	0.491358	+	0.356993i
$566$		0			0
$567$	189.244	−	61.4890i	0.333763	−	0.108446i
$568$		0			0
$569$	−596.022	−	820.354i	−1.04749	−	1.44175i	−0.890964	−	0.454073i	$-0.849970\pi$
$569$	−596.022	−	820.354i	−1.04749	−	1.44175i	−0.156526	−	0.987674i	$-0.550030\pi$
$570$		0			0
$571$		−	1024.22i		−	1.79373i	−0.442304	−	0.896865i	$-0.645839\pi$
$571$		−	1024.22i		−	1.79373i	0.442304	−	0.896865i	$-0.354161\pi$
$572$		0			0
$573$	−85.5942			−0.149379
$574$		0			0
$575$	397.207	−	288.587i	0.690794	−	0.501891i
$576$		0			0
$577$	114.691	+	352.984i	0.198772	+	0.611758i	0.999912	+	0.0132802i	$0.00422736\pi$
$577$	114.691	+	352.984i	0.198772	+	0.611758i	−0.801140	+	0.598477i	$0.795773\pi$
$578$		0			0
$579$	12.4314	−	17.1103i	0.0214704	−	0.0295515i
$580$		0			0
$581$	68.9423	−	212.183i	0.118662	−	0.365203i
$582$		0			0
$583$	−113.532	+	805.579i	−0.194737	+	1.38178i
$584$		0			0
$585$	301.022	+	97.8081i	0.514568	+	0.167193i
$586$		0			0
$587$	317.242	+	230.490i	0.540447	+	0.392658i	0.824251	−	0.566225i	$-0.191597\pi$
$587$	317.242	+	230.490i	0.540447	+	0.392658i	−0.283804	+	0.958882i	$0.591597\pi$
$588$		0			0
$589$	−56.5812	+	18.3843i	−0.0960631	+	0.0312128i
$590$		0			0
$591$	−11.1900	−	15.4017i	−0.0189340	−	0.0260604i
$592$		0			0
$593$			682.486i			1.15090i	0.817836	+	0.575452i	$0.195174\pi$
$593$			682.486i			1.15090i	−0.817836	+	0.575452i	$0.804826\pi$
$594$		0			0
$595$	166.582			0.279969
$596$		0			0
$597$	−139.864	+	101.617i	−0.234277	+	0.170213i
$598$		0			0
$599$	−49.5291	−	152.435i	−0.0826863	−	0.254482i	0.901163	−	0.433480i	$-0.142715\pi$
$599$	−49.5291	−	152.435i	−0.0826863	−	0.254482i	−0.983849	+	0.178998i	$0.942715\pi$
$600$		0			0
$601$	80.8957	−	111.343i	0.134602	−	0.185263i	−0.736395	−	0.676551i	$-0.763474\pi$
$601$	80.8957	−	111.343i	0.134602	−	0.185263i	0.870997	+	0.491288i	$0.163474\pi$
$602$		0			0
$603$	194.030	−	597.162i	0.321774	−	0.990319i
$604$		0			0
$605$	−252.659	−	323.900i	−0.417618	−	0.535372i
$606$		0			0
$607$	205.593	+	66.8012i	0.338703	+	0.110051i	0.473430	−	0.880831i	$-0.343016\pi$
$607$	205.593	+	66.8012i	0.338703	+	0.110051i	−0.134727	+	0.990883i	$0.543016\pi$
$608$		0			0
$609$	24.7652	+	17.9930i	0.0406653	+	0.0295451i
$610$		0			0
$611$	270.610	−	87.9265i	0.442897	−	0.143906i
$612$		0			0
$613$	−143.792	−	197.912i	−0.234570	−	0.322858i	0.675463	−	0.737394i	$-0.263944\pi$
$613$	−143.792	−	197.912i	−0.234570	−	0.322858i	−0.910033	+	0.414536i	$0.863944\pi$
$614$		0			0
$615$			84.1783i			0.136875i
$616$		0			0
$617$	−128.561			−0.208365			−0.104182	−	0.994558i	$-0.533223\pi$
$617$	−128.561			−0.208365			−0.104182	+	0.994558i	$0.533223\pi$
$618$		0			0
$619$	−670.328	+	487.022i	−1.08292	+	0.786788i	−0.978190	−	0.207712i	$-0.933398\pi$
$619$	−670.328	+	487.022i	−1.08292	+	0.786788i	−0.104731	+	0.994501i	$0.533398\pi$
$620$		0			0
$621$	−93.1162	−	286.582i	−0.149946	−	0.461485i
$622$		0			0
$623$	18.1076	−	24.9229i	0.0290651	−	0.0400047i
$624$		0			0
$625$	−32.9369	+	101.369i	−0.0526990	+	0.162191i
$626$		0			0
$627$	34.8425	+	4.91042i	0.0555702	+	0.00783161i
$628$		0			0
$629$	370.241	+	120.299i	0.588618	+	0.191254i
$630$		0			0
$631$	506.843	+	368.243i	0.803238	+	0.583586i	0.911862	−	0.410497i	$-0.134645\pi$
$631$	506.843	+	368.243i	0.803238	+	0.583586i	−0.108625	+	0.994083i	$0.534645\pi$
$632$		0			0
$633$	−65.8104	+	21.3831i	−0.103966	+	0.0337805i
$634$		0			0
$635$	406.801	+	559.913i	0.640631	+	0.881754i
$636$		0			0
$637$		−	74.2979i		−	0.116637i
$638$		0			0
$639$	−143.824			−0.225076
$640$		0			0
$641$	884.912	−	642.926i	1.38052	−	1.00301i	0.383686	−	0.923463i	$-0.374654\pi$
$641$	884.912	−	642.926i	1.38052	−	1.00301i	0.996832	−	0.0795416i	$-0.0253457\pi$
$642$		0			0
$643$	−333.297	−	1025.78i	−0.518347	−	1.59531i	−0.777109	−	0.629367i	$-0.783314\pi$
$643$	−333.297	−	1025.78i	−0.518347	−	1.59531i	0.258762	−	0.965941i	$-0.416686\pi$
$644$		0			0
$645$	−3.49164	+	4.80584i	−0.00541340	+	0.00745091i
$646$		0			0
$647$	27.2876	−	83.9826i	0.0421756	−	0.129803i	−0.927752	−	0.373198i	$-0.878261\pi$
$647$	27.2876	−	83.9826i	0.0421756	−	0.129803i	0.969927	+	0.243395i	$0.0782612\pi$
$648$		0			0
$649$	−769.206	−	375.532i	−1.18522	−	0.578632i
$650$		0			0
$651$	−10.1197	−	3.28809i	−0.0155448	−	0.00505082i
$652$		0			0
$653$	30.6327	+	22.2559i	0.0469107	+	0.0340826i	0.610994	−	0.791636i	$-0.290770\pi$
$653$	30.6327	+	22.2559i	0.0469107	+	0.0340826i	−0.564083	+	0.825718i	$0.690770\pi$
$654$		0			0
$655$	−234.557	+	76.2120i	−0.358102	+	0.116354i
$656$		0			0
$657$	435.319	+	599.165i	0.662586	+	0.911971i
$658$		0			0
$659$		−	384.158i		−	0.582940i	−0.956580	−	0.291470i	$-0.905856\pi$
$659$		−	384.158i		−	0.582940i	0.956580	−	0.291470i	$-0.0941444\pi$
$660$		0			0
$661$	22.2454			0.0336542			0.0168271	−	0.999858i	$-0.494644\pi$
$661$	22.2454			0.0336542			0.0168271	+	0.999858i	$0.494644\pi$
$662$		0			0
$663$	−74.0537	+	53.8032i	−0.111695	+	0.0811511i
$664$		0			0
$665$	−19.0935	−	58.7638i	−0.0287120	−	0.0883666i
$666$		0			0
$667$	−532.893	+	733.464i	−0.798939	+	1.09965i
$668$		0			0
$669$	54.9720	−	169.186i	0.0821704	−	0.252894i
$670$		0			0
$671$	550.218	−	292.286i	0.819997	−	0.435597i
$672$		0			0
$673$	−71.6594	−	23.2835i	−0.106478	−	0.0345966i	0.255294	−	0.966864i	$-0.417828\pi$
$673$	−71.6594	−	23.2835i	−0.106478	−	0.0345966i	−0.361771	+	0.932267i	$0.617828\pi$
$674$		0			0
$675$	−90.1476	−	65.4960i	−0.133552	−	0.0970312i
$676$		0			0
$677$	−1202.82	+	390.819i	−1.77669	+	0.577281i	−0.998699	−	0.0509978i	$-0.983760\pi$
$677$	−1202.82	+	390.819i	−1.77669	+	0.577281i	−0.777989	+	0.628278i	$0.783760\pi$
$678$		0			0
$679$	−178.440	−	245.602i	−0.262799	−	0.361711i
$680$		0			0
$681$			113.697i			0.166956i
$682$		0			0
$683$	−290.752			−0.425698			−0.212849	−	0.977085i	$-0.568274\pi$
$683$	−290.752			−0.425698			−0.212849	+	0.977085i	$0.568274\pi$
$684$		0			0
$685$	648.472	−	471.142i	0.946674	−	0.687799i
$686$		0			0
$687$	−52.4607	−	161.457i	−0.0763620	−	0.235018i
$688$		0			0
$689$	−461.406	+	635.071i	−0.669675	+	0.921728i
$690$		0			0
$691$	−160.951	+	495.356i	−0.232925	+	0.716869i	0.764465	+	0.644665i	$0.223003\pi$
$691$	−160.951	+	495.356i	−0.232925	+	0.716869i	−0.997390	+	0.0722037i	$0.976997\pi$
$692$		0			0
$693$	−183.821	−	177.650i	−0.265254	−	0.256350i
$694$		0			0
$695$	−813.350	−	264.273i	−1.17029	−	0.380249i
$696$		0			0
$697$	800.021	+	581.249i	1.14781	+	0.833930i
$698$		0			0
$699$	−126.205	+	41.0065i	−0.180551	+	0.0586645i
$700$		0			0
$701$	37.9406	+	52.2208i	0.0541235	+	0.0744947i	0.835221	−	0.549915i	$-0.185340\pi$
$701$	37.9406	+	52.2208i	0.0541235	+	0.0744947i	−0.781097	+	0.624409i	$0.785340\pi$
$702$		0			0
$703$		−	144.396i		−	0.205399i
$704$		0			0
$705$	42.3213			0.0600303
$706$		0			0
$707$	−246.750	+	179.274i	−0.349010	+	0.253571i
$708$		0			0
$709$	368.142	+	1133.02i	0.519241	+	1.59806i	0.775431	+	0.631432i	$0.217533\pi$
$709$	368.142	+	1133.02i	0.519241	+	1.59806i	−0.256190	+	0.966626i	$0.582467\pi$
$710$		0			0
$711$	−29.3324	+	40.3726i	−0.0412552	+	0.0567829i
$712$		0			0
$713$	97.3823	−	299.712i	0.136581	−	0.420353i
$714$		0			0
$715$	−68.6798	−	390.378i	−0.0960557	−	0.545984i
$716$		0			0
$717$	−16.8697	−	5.48130i	−0.0235282	−	0.00764477i
$718$		0			0
$719$	208.003	+	151.123i	0.289295	+	0.210185i	0.722962	−	0.690888i	$-0.242780\pi$
$719$	208.003	+	151.123i	0.289295	+	0.210185i	−0.433666	+	0.901074i	$0.642780\pi$
$720$		0			0
$721$	31.7629	−	10.3204i	0.0440540	−	0.0143140i
$722$		0			0
$723$	119.498	+	164.475i	0.165281	+	0.227489i
$724$		0			0
$725$			335.254i			0.462420i
$726$		0			0
$727$	−1255.72			−1.72727			−0.863633	−	0.504121i	$-0.831817\pi$
$727$	−1255.72			−1.72727			−0.863633	+	0.504121i	$0.831817\pi$
$728$		0			0
$729$	506.446	−	367.955i	0.694714	−	0.504739i
$730$		0			0
$731$	21.5644	+	66.3684i	0.0294999	+	0.0907912i
$732$		0			0
$733$	−46.9853	+	64.6698i	−0.0641001	+	0.0882262i	−0.839863	−	0.542798i	$-0.817365\pi$
$733$	−46.9853	+	64.6698i	−0.0641001	+	0.0882262i	0.775763	+	0.631024i	$0.217365\pi$
$734$		0			0
$735$	3.41492	−	10.5101i	0.00464615	−	0.0142994i
$736$		0			0
$737$	−774.424	+	136.246i	−1.05078	+	0.184865i
$738$		0			0
$739$	−844.628	−	274.436i	−1.14293	−	0.371362i	−0.324456	−	0.945901i	$-0.605181\pi$
$739$	−844.628	−	274.436i	−1.14293	−	0.371362i	−0.818477	+	0.574539i	$0.805181\pi$
$740$		0			0
$741$	27.4678	+	19.9565i	0.0370685	+	0.0269318i
$742$		0			0
$743$	434.698	−	141.242i	0.585058	−	0.190097i	−0.00150738	−	0.999999i	$-0.500480\pi$
$743$	434.698	−	141.242i	0.585058	−	0.190097i	0.586565	+	0.809902i	$0.300480\pi$
$744$		0			0
$745$	7.63278	+	10.5056i	0.0102453	+	0.0141015i
$746$		0			0
$747$		−	740.688i		−	0.991550i
$748$		0			0
$749$	520.528			0.694964
$750$		0			0
$751$	−1000.46	+	726.874i	−1.33217	+	0.967875i	−0.332472	+	0.943113i	$0.607883\pi$
$751$	−1000.46	+	726.874i	−1.33217	+	0.967875i	−0.999693	+	0.0247620i	$0.992117\pi$
$752$		0			0
$753$	−41.3510	−	127.265i	−0.0549150	−	0.169011i
$754$		0			0
$755$	−44.1110	+	60.7136i	−0.0584252	+	0.0804154i
$756$		0			0
$757$	20.4577	−	62.9623i	0.0270247	−	0.0831735i	−0.936635	−	0.350308i	$-0.886077\pi$
$757$	20.4577	−	62.9623i	0.0270247	−	0.0831735i	0.963659	+	0.267135i	$0.0860769\pi$
$758$		0			0
$759$	−129.526	+	134.025i	−0.170653	+	0.176581i
$760$		0			0
$761$	−1207.43	−	392.318i	−1.58664	−	0.515530i	−0.622882	−	0.782316i	$-0.714038\pi$
$761$	−1207.43	−	392.318i	−1.58664	−	0.515530i	−0.963756	+	0.266786i	$0.914038\pi$
$762$		0			0
$763$	74.5049	+	54.1310i	0.0976473	+	0.0709449i
$764$		0			0
$765$	525.975	−	170.899i	0.687548	−	0.223398i
$766$		0			0
$767$	−485.477	−	668.201i	−0.632955	−	0.871188i
$768$		0			0
$769$			675.170i			0.877985i	0.898491	+	0.438992i	$0.144664\pi$
$769$			675.170i			0.877985i	−0.898491	+	0.438992i	$0.855336\pi$
$770$		0			0
$771$	50.7571			0.0658328
$772$		0			0
$773$	−572.476	+	415.928i	−0.740590	+	0.538070i	−0.892896	−	0.450264i	$-0.851330\pi$
$773$	−572.476	+	415.928i	−0.740590	+	0.538070i	0.152306	+	0.988333i	$0.451330\pi$
$774$		0			0
$775$	−36.0108	−	110.830i	−0.0464656	−	0.143006i
$776$		0			0
$777$	15.1799	−	20.8933i	0.0195365	−	0.0268897i
$778$		0			0
$779$	113.345	−	348.840i	0.145501	−	0.447805i
$780$		0			0
$781$	84.4963	+	159.062i	0.108190	+	0.203664i
$782$		0			0
$783$	195.688	+	63.5830i	0.249921	+	0.0812043i
$784$		0			0
$785$	−583.820	−	424.170i	−0.743720	−	0.540344i
$786$		0			0
$787$	−1111.40	+	361.115i	−1.41220	+	0.458850i	−0.913114	−	0.407704i	$-0.866329\pi$
$787$	−1111.40	+	361.115i	−1.41220	+	0.458850i	−0.499082	+	0.866555i	$0.666329\pi$
$788$		0			0
$789$	28.5620	+	39.3123i	0.0362003	+	0.0498254i
$790$		0			0
$791$		−	267.426i		−	0.338086i
$792$		0			0
$793$	601.170			0.758096
$794$		0			0
$795$	−94.4592	+	68.6286i	−0.118817	+	0.0863253i
$796$		0			0
$797$	−236.546	−	728.014i	−0.296796	−	0.913443i	−0.982612	−	0.185669i	$-0.940555\pi$
$797$	−236.546	−	728.014i	−0.296796	−	0.913443i	0.685817	−	0.727774i	$-0.259445\pi$
$798$		0			0
$799$	292.228	−	402.217i	0.365742	−	0.503401i
$800$		0			0
$801$	31.6050	−	97.2701i	0.0394569	−	0.121436i
$802$		0			0
$803$	406.897	−	833.451i	0.506721	−	1.03792i
$804$		0			0
$805$	311.273	+	101.139i	0.386675	+	0.125638i
$806$		0			0
$807$	−71.6284	−	52.0411i	−0.0887589	−	0.0644871i
$808$		0			0
$809$	497.378	−	161.608i	0.614806	−	0.199763i	0.0149733	−	0.999888i	$-0.495234\pi$
$809$	497.378	−	161.608i	0.614806	−	0.199763i	0.599833	+	0.800125i	$0.295234\pi$
$810$		0			0
$811$	−185.145	−	254.831i	−0.228293	−	0.314218i	0.679469	−	0.733704i	$-0.262210\pi$
$811$	−185.145	−	254.831i	−0.228293	−	0.314218i	−0.907762	+	0.419486i	$0.862210\pi$
$812$		0			0
$813$			147.066i			0.180893i
$814$		0			0
$815$	−461.780			−0.566602
$816$		0			0
$817$	20.9406	−	15.2142i	0.0256311	−	0.0186221i
$818$		0			0
$819$	−76.2237	−	234.593i	−0.0930693	−	0.286438i
$820$		0			0
$821$	272.596	−	375.196i	0.332029	−	0.456999i	−0.610063	−	0.792353i	$-0.708856\pi$
$821$	272.596	−	375.196i	0.332029	−	0.456999i	0.942092	+	0.335354i	$0.108856\pi$
$822$		0			0
$823$	286.053	−	880.380i	0.347573	−	1.06972i	−0.612619	−	0.790379i	$-0.709884\pi$
$823$	286.053	−	880.380i	0.347573	−	1.06972i	0.960192	−	0.279342i	$-0.0901162\pi$
$824$		0			0
$825$	−9.61843	+	68.2488i	−0.0116587	+	0.0827258i
$826$		0			0
$827$	102.339	+	33.2520i	0.123748	+	0.0402080i	0.370236	−	0.928938i	$-0.379277\pi$
$827$	102.339	+	33.2520i	0.123748	+	0.0402080i	−0.246489	+	0.969146i	$0.579277\pi$
$828$		0			0
$829$	−304.407	−	221.164i	−0.367197	−	0.266785i	0.388850	−	0.921301i	$-0.372872\pi$
$829$	−304.407	−	221.164i	−0.367197	−	0.266785i	−0.756048	+	0.654516i	$0.772872\pi$
$830$		0			0
$831$	89.2762	−	29.0076i	0.107432	−	0.0349068i
$832$		0			0
$833$	−76.3064	−	105.027i	−0.0916043	−	0.126082i
$834$		0			0
$835$			91.3392i			0.109388i
$836$		0			0
$837$	−71.5213			−0.0854496
$838$		0			0
$839$	274.748	−	199.616i	0.327471	−	0.237921i	−0.411886	−	0.911235i	$-0.635130\pi$
$839$	274.748	−	199.616i	0.327471	−	0.237921i	0.739357	+	0.673314i	$0.235130\pi$
$840$		0			0
$841$	68.5816	+	211.072i	0.0815477	+	0.250978i
$842$		0			0
$843$	143.354	−	197.310i	0.170052	−	0.234056i
$844$		0			0
$845$	−59.1098	+	181.921i	−0.0699524	+	0.215291i
$846$		0			0
$847$	−88.4774	+	307.667i	−0.104460	+	0.363243i
$848$		0			0
$849$	73.4352	+	23.8605i	0.0864961	+	0.0281043i
$850$		0			0
$851$	618.791	+	449.578i	0.727134	+	0.528294i
$852$		0			0
$853$	−967.134	+	314.241i	−1.13380	+	0.368395i	−0.815020	−	0.579433i	$-0.803274\pi$
$853$	−967.134	+	314.241i	−1.13380	+	0.368395i	−0.318783	+	0.947828i	$0.603274\pi$
$854$		0			0
$855$	−120.574	−	165.956i	−0.141022	−	0.194100i
$856$		0			0
$857$			1406.18i			1.64082i	0.571774	+	0.820411i	$0.306255\pi$
$857$			1406.18i			1.64082i	−0.571774	+	0.820411i	$0.693745\pi$
$858$		0			0
$859$	−1603.23			−1.86640			−0.933198	−	0.359362i	$-0.882995\pi$
$859$	−1603.23			−1.86640			−0.933198	+	0.359362i	$0.882995\pi$
$860$		0			0
$861$	53.0729	−	38.5597i	0.0616410	−	0.0447848i
$862$		0			0
$863$	210.969	+	649.295i	0.244460	+	0.752370i	0.995725	+	0.0923693i	$0.0294440\pi$
$863$	210.969	+	649.295i	0.244460	+	0.752370i	−0.751265	+	0.660001i	$0.770556\pi$
$864$		0			0
$865$	−240.675	+	331.261i	−0.278237	+	0.382961i
$866$		0			0
$867$	−7.89537	+	24.2995i	−0.00910654	+	0.0280271i
$868$		0			0
$869$	61.8829	+	8.72128i	0.0712116	+	0.0100360i
$870$		0			0
$871$	−721.589	−	234.459i	−0.828461	−	0.269183i
$872$		0			0
$873$	−815.386	−	592.413i	−0.934005	−	0.678594i
$874$		0			0
$875$	328.670	−	106.791i	0.375623	−	0.122047i
$876$		0			0
$877$	265.254	+	365.091i	0.302456	+	0.416295i	0.933010	−	0.359850i	$-0.117172\pi$
$877$	265.254	+	365.091i	0.302456	+	0.416295i	−0.630554	+	0.776145i	$0.717172\pi$
$878$		0			0
$879$		−	9.81212i		−	0.0111628i
$880$		0			0
$881$	345.919			0.392644			0.196322	−	0.980540i	$-0.437100\pi$
$881$	345.919			0.392644			0.196322	+	0.980540i	$0.437100\pi$
$882$		0			0
$883$	−787.403	+	572.082i	−0.891736	+	0.647884i	−0.936330	−	0.351121i	$-0.885801\pi$
$883$	−787.403	+	572.082i	−0.891736	+	0.647884i	0.0445942	+	0.999005i	$0.485801\pi$
$884$		0			0
$885$	−37.9624	−	116.836i	−0.0428954	−	0.132019i
$886$		0			0
$887$	614.009	−	845.110i	0.692231	−	0.952774i	−0.307768	−	0.951461i	$-0.599582\pi$
$887$	614.009	−	845.110i	0.692231	−	0.952774i	0.999999	−	0.00131255i	$-0.000417797\pi$
$888$		0			0
$889$	166.671	−	512.962i	0.187482	−	0.577010i
$890$		0			0
$891$	−743.425	−	362.946i	−0.834372	−	0.407347i
$892$		0			0
$893$	−175.382	−	56.9852i	−0.196397	−	0.0638132i
$894$		0			0
$895$	388.851	+	282.517i	0.434471	+	0.315661i
$896$		0			0
$897$	−171.043	+	55.5751i	−0.190683	+	0.0619566i
$898$		0			0
$899$	126.483	+	174.089i	0.140693	+	0.193647i
$900$		0			0
$901$			1371.61i			1.52232i
$902$		0			0
$903$	4.62942			0.00512671
$904$		0			0
$905$	156.187	−	113.476i	0.172582	−	0.125388i
$906$		0			0
$907$	151.283	+	465.601i	0.166795	+	0.513342i	0.999164	−	0.0408798i	$-0.0130161\pi$
$907$	151.283	+	465.601i	0.166795	+	0.513342i	−0.832369	+	0.554221i	$0.813016\pi$
$908$		0			0
$909$	−595.182	+	819.198i	−0.654766	+	0.901208i
$910$		0			0
$911$	284.532	−	875.699i	0.312329	−	0.961250i	−0.664511	−	0.747279i	$-0.731360\pi$
$911$	284.532	−	875.699i	0.312329	−	0.961250i	0.976840	−	0.213971i	$-0.0686400\pi$
$912$		0			0
$913$	−819.164	+	435.154i	−0.897222	+	0.476620i
$914$		0			0
$915$	85.0405	+	27.6313i	0.0929404	+	0.0301982i
$916$		0			0
$917$	155.494	+	112.973i	0.169568	+	0.123199i
$918$		0			0
$919$	631.846	−	205.299i	0.687537	−	0.223394i	0.0556446	−	0.998451i	$-0.482279\pi$
$919$	631.846	−	205.299i	0.687537	−	0.223394i	0.631892	+	0.775056i	$0.282279\pi$
$920$		0			0
$921$	39.5018	+	54.3696i	0.0428901	+	0.0590332i
$922$		0			0
$923$			173.791i			0.188289i
$924$		0			0
$925$	282.839			0.305772
$926$		0			0
$927$	89.7023	−	65.1725i	0.0967662	−	0.0703048i
$928$		0			0
$929$	203.753	+	627.086i	0.219325	+	0.675012i	0.998818	+	0.0486016i	$0.0154765\pi$
$929$	203.753	+	627.086i	0.219325	+	0.675012i	−0.779494	+	0.626410i	$0.784524\pi$
$930$		0			0
$931$	−28.3033	+	38.9562i	−0.0304010	+	0.0418434i
$932$		0			0
$933$	31.2773	−	96.2615i	0.0335233	−	0.103174i
$934$		0			0
$935$	−498.017	−	481.298i	−0.532638	−	0.514757i
$936$		0			0
$937$	−42.9628	−	13.9595i	−0.0458514	−	0.0148980i	0.286001	−	0.958229i	$-0.407674\pi$
$937$	−42.9628	−	13.9595i	−0.0458514	−	0.0148980i	−0.331853	+	0.943331i	$0.607674\pi$
$938$		0			0
$939$	146.244	+	106.252i	0.155744	+	0.113155i
$940$		0			0
$941$	1363.28	−	442.958i	1.44876	−	0.470731i	0.524144	−	0.851630i	$-0.324385\pi$
$941$	1363.28	−	442.958i	1.44876	−	0.470731i	0.924617	+	0.380899i	$0.124385\pi$
$942$		0			0
$943$	1142.01	+	1571.85i	1.21104	+	1.66686i
$944$		0			0
$945$		−	74.2802i		−	0.0786034i
$946$		0			0
$947$	−270.183			−0.285304			−0.142652	−	0.989773i	$-0.545563\pi$
$947$	−270.183			−0.285304			−0.142652	+	0.989773i	$0.545563\pi$
$948$		0			0
$949$	724.010	−	526.024i	0.762918	−	0.554293i
$950$		0			0
$951$	−66.7344	−	205.387i	−0.0701729	−	0.215970i
$952$		0			0
$953$	500.358	−	688.684i	0.525035	−	0.722649i	−0.461329	−	0.887229i	$-0.652627\pi$
$953$	500.358	−	688.684i	0.525035	−	0.722649i	0.986364	+	0.164581i	$0.0526271\pi$
$954$		0			0
$955$	193.105	−	594.317i	0.202204	−	0.622321i
$956$		0			0
$957$	−22.0522	−	125.345i	−0.0230431	−	0.130977i
$958$		0			0
$959$	−594.094	−	193.033i	−0.619493	−	0.201285i
$960$		0			0
$961$	716.952	+	520.896i	0.746048	+	0.542036i
$962$		0			0
$963$	1643.55	−	534.021i	1.70669	−	0.554539i
$964$		0			0
$965$	90.7583	+	124.918i	0.0940500	+	0.129449i
$966$		0			0
$967$			1528.89i			1.58106i	0.612420	+	0.790532i	$0.290196\pi$
$967$			1528.89i			1.58106i	−0.612420	+	0.790532i	$0.709804\pi$
$968$		0			0
$969$	59.3241			0.0612220
$970$		0			0
$971$	1263.21	−	917.779i	1.30094	−	0.945190i	0.300977	−	0.953631i	$-0.402687\pi$
$971$	1263.21	−	917.779i	1.30094	−	0.945190i	0.999964	+	0.00844174i	$0.00268712\pi$
$972$		0			0
$973$	205.953	+	633.859i	0.211668	+	0.651448i
$974$		0			0
$975$	−39.0904	+	53.8033i	−0.0400927	+	0.0551828i
$976$		0			0
$977$	292.977	−	901.691i	0.299874	−	0.922918i	−0.681666	−	0.731663i	$-0.738744\pi$
$977$	292.977	−	901.691i	0.299874	−	0.922918i	0.981540	−	0.191254i	$-0.0612556\pi$
$978$		0			0
$979$	−126.144	+	22.1927i	−0.128850	+	0.0226687i
$980$		0			0
$981$	290.780	+	94.4802i	0.296412	+	0.0963101i
$982$		0			0
$983$	1241.80	+	902.223i	1.26328	+	0.917826i	0.998914	−	0.0465971i	$-0.0148377\pi$
$983$	1241.80	+	902.223i	1.26328	+	0.917826i	0.264365	+	0.964423i	$0.414838\pi$
$984$		0			0
$985$	132.186	−	42.9497i	0.134199	−	0.0436038i
$986$		0			0
$987$	−19.3862	−	26.6829i	−0.0196416	−	0.0270343i
$988$		0			0
$989$			137.108i			0.138633i
$990$		0			0
$991$	−926.071			−0.934481			−0.467241	−	0.884130i	$-0.654752\pi$
$991$	−926.071			−0.934481			−0.467241	+	0.884130i	$0.654752\pi$
$992$		0			0
$993$	46.4750	−	33.7661i	0.0468027	−	0.0340041i
$994$		0			0
$995$	−390.029	−	1200.39i	−0.391989	−	1.20642i
$996$		0			0
$997$	−425.735	+	585.974i	−0.427016	+	0.587737i	−0.967265	−	0.253768i	$-0.918330\pi$
$997$	−425.735	+	585.974i	−0.427016	+	0.587737i	0.540249	+	0.841505i	$0.318330\pi$
$998$		0			0
$999$	53.6422	−	165.094i	0.0536959	−	0.165259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.5	✓	48
11.6	odd	10	inner	308.3.r.a.281.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.5	✓	48	1.1	even	1	trivial
308.3.r.a.281.5	yes	48	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376205 + 0.273329i) q^{3} +(-1.04910 - 3.22879i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.71433 + 8.35385i) q^{9} +O(q^{10})\)	\(q+(-0.376205 + 0.273329i) q^{3} +(-1.04910 - 3.22879i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.71433 + 8.35385i) q^{9} +(10.8336 - 1.90598i) q^{11} +(10.0945 + 3.27990i) q^{13} +(1.27720 + 0.927938i) q^{15} +(17.6380 - 5.73095i) q^{17} +(-4.04333 - 5.56517i) q^{19} -1.23031i q^{21} +36.4379 q^{23} +(10.9009 - 7.91999i) q^{25} +(-2.55548 - 7.86496i) q^{27} +(-14.6247 + 20.1292i) q^{29} +(2.67256 - 8.22529i) q^{31} +(-3.55470 + 3.67818i) q^{33} +(8.54258 + 2.77565i) q^{35} +(16.9821 + 12.3382i) q^{37} +(-4.69409 + 1.52520i) q^{39} +(31.3414 + 43.1377i) q^{41} +3.76280i q^{43} +29.8205 q^{45} +(21.6879 - 15.7571i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-5.06908 + 6.97700i) q^{51} +(-22.8543 + 70.3384i) q^{53} +(-17.5195 - 32.9799i) q^{55} +(3.04224 + 0.988484i) q^{57} +(-62.9548 - 45.7393i) q^{59} +(53.8673 - 17.5025i) q^{61} +(-13.6599 - 18.8013i) q^{63} -36.0340i q^{65} -71.4835 q^{67} +(-13.7081 + 9.95951i) q^{69} +(5.05978 + 15.5724i) q^{71} +(49.5595 - 68.2128i) q^{73} +(-1.93622 + 5.95908i) q^{75} +(-12.7681 + 26.1529i) q^{77} +(5.40325 + 1.75562i) q^{79} +(-60.8448 - 44.2063i) q^{81} +(-80.1975 + 26.0578i) q^{83} +(-37.0081 - 50.9373i) q^{85} -11.5700i q^{87} -11.6437 q^{89} +(-22.7188 + 16.5062i) q^{91} +(1.24278 + 3.82488i) q^{93} +(-13.7269 + 18.8935i) q^{95} +(-35.4575 + 109.127i) q^{97} +(-13.4838 + 95.6759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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