LMFDB - Embedded newform 76.7.j.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	76.33
Dual form			76.7.j.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-37.6573 - 6.64000i) q^{3} +(174.066 + 146.059i) q^{5} +(-273.768 - 474.181i) q^{7} +(688.950 + 250.757i) q^{9} +O(q^{10})$	\(q+(-37.6573 - 6.64000i) q^{3} +(174.066 + 146.059i) q^{5} +(-273.768 - 474.181i) q^{7} +(688.950 + 250.757i) q^{9} +(77.7943 - 134.744i) q^{11} +(1475.53 - 260.176i) q^{13} +(-5585.03 - 6655.98i) q^{15} +(-353.760 + 128.758i) q^{17} +(-2387.07 + 6430.22i) q^{19} +(7160.82 + 19674.2i) q^{21} +(-14953.0 + 12547.1i) q^{23} +(6252.56 + 35460.0i) q^{25} +(-137.917 - 79.6266i) q^{27} +(-3350.10 + 9204.33i) q^{29} +(-41055.3 + 23703.3i) q^{31} +(-3824.23 + 4557.54i) q^{33} +(21604.4 - 122525. i) q^{35} -15960.4i q^{37} -57292.1 q^{39} +(-46188.1 - 8144.22i) q^{41} +(96887.8 + 81298.5i) q^{43} +(83297.4 + 144275. i) q^{45} +(33707.4 + 12268.5i) q^{47} +(-91073.7 + 157744. i) q^{49} +(14176.6 - 2499.72i) q^{51} +(-111310. - 132654. i) q^{53} +(33221.8 - 12091.8i) q^{55} +(132587. - 226295. i) q^{57} +(-62910.8 - 172846. i) q^{59} +(-232352. + 194967. i) q^{61} +(-69708.4 - 395336. i) q^{63} +(294840. + 170226. i) q^{65} +(-146670. + 402972. i) q^{67} +(646403. - 373201. i) q^{69} +(-93891.2 + 111895. i) q^{71} +(700.874 - 3974.85i) q^{73} -1.37685e6i q^{75} -85190.5 q^{77} +(759991. + 134007. i) q^{79} +(-404768. - 339641. i) q^{81} +(416361. + 721159. i) q^{83} +(-80383.8 - 29257.3i) q^{85} +(187273. - 324366. i) q^{87} +(-798173. + 140739. i) q^{89} +(-527324. - 628440. i) q^{91} +(1.70342e6 - 619995. i) q^{93} +(-1.35470e6 + 770631. i) q^{95} +(-318032. - 873784. i) q^{97} +(87384.3 - 73324.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−37.6573	−	6.64000i	−1.39472	−	0.245926i	−0.574746	−	0.818332i	$-0.694899\pi$
$3$	−37.6573	−	6.64000i	−1.39472	−	0.245926i	−0.819970	+	0.572406i	$0.806010\pi$
$4$		0			0
$5$	174.066	+	146.059i	1.39253	+	1.16847i	0.964305	+	0.264795i	$0.0853044\pi$
$5$	174.066	+	146.059i	1.39253	+	1.16847i	0.428222	+	0.903673i	$0.359140\pi$
$6$		0			0
$7$	−273.768	−	474.181i	−0.798158	−	1.38245i	−0.920814	−	0.390001i	$-0.872475\pi$
$7$	−273.768	−	474.181i	−0.798158	−	1.38245i	0.122656	−	0.992449i	$-0.460859\pi$
$8$		0			0
$9$	688.950	+	250.757i	0.945061	+	0.343974i
$10$		0			0
$11$	77.7943	−	134.744i	0.0584480	−	0.101235i	−0.835321	−	0.549763i	$-0.814718\pi$
$11$	77.7943	−	134.744i	0.0584480	−	0.101235i	0.893769	+	0.448528i	$0.148051\pi$
$12$		0			0
$13$	1475.53	−	260.176i	0.671612	−	0.118423i	0.172565	−	0.984998i	$-0.444795\pi$
$13$	1475.53	−	260.176i	0.671612	−	0.118423i	0.499047	+	0.866575i	$0.333684\pi$
$14$		0			0
$15$	−5585.03	−	6655.98i	−1.65482	−	1.97214i
$16$		0			0
$17$	−353.760	+	128.758i	−0.0720049	+	0.0262076i	−0.377771	−	0.925899i	$-0.623310\pi$
$17$	−353.760	+	128.758i	−0.0720049	+	0.0262076i	0.305767	+	0.952107i	$0.401087\pi$
$18$		0			0
$19$	−2387.07	+	6430.22i	−0.348020	+	0.937487i
$19$	−2387.07	+	6430.22i	−0.348020	+	0.937487i
$20$		0			0
$21$	7160.82	+	19674.2i	0.773224	+	2.12441i
$22$		0			0
$23$	−14953.0	+	12547.1i	−1.22898	+	1.03124i	−0.230677	+	0.973030i	$0.574094\pi$
$23$	−14953.0	+	12547.1i	−1.22898	+	1.03124i	−0.998305	+	0.0582075i	$0.981461\pi$
$24$		0			0
$25$	6252.56	+	35460.0i	0.400164	+	2.26944i
$26$		0			0
$27$	−137.917	−	79.6266i	−0.00700693	−	0.00404545i
$28$		0			0
$29$	−3350.10	+	9204.33i	−0.137361	+	0.377397i	−0.989232	−	0.146355i	$-0.953246\pi$
$29$	−3350.10	+	9204.33i	−0.137361	+	0.377397i	0.851871	+	0.523752i	$0.175468\pi$
$30$		0			0
$31$	−41055.3	+	23703.3i	−1.37811	+	0.795652i	−0.991932	−	0.126772i	$-0.959538\pi$
$31$	−41055.3	+	23703.3i	−1.37811	+	0.795652i	−0.386179	+	0.922424i	$0.626205\pi$
$32$		0			0
$33$	−3824.23	+	4557.54i	−0.106415	+	0.126820i
$34$		0			0
$35$	21604.4	−	122525.i	0.503894	−	2.85772i
$36$		0			0
$37$		−	15960.4i		−	0.315093i	−0.987512	−	0.157547i	$-0.949642\pi$
$37$		−	15960.4i		−	0.315093i	0.987512	−	0.157547i	$-0.0503585\pi$
$38$		0			0
$39$	−57292.1			−0.965831
$40$		0			0
$41$	−46188.1	−	8144.22i	−0.670161	−	0.118167i	−0.171793	−	0.985133i	$-0.554956\pi$
$41$	−46188.1	−	8144.22i	−0.670161	−	0.118167i	−0.498368	+	0.866966i	$0.666067\pi$
$42$		0			0
$43$	96887.8	+	81298.5i	1.21861	+	1.02253i	0.998896	+	0.0469679i	$0.0149558\pi$
$43$	96887.8	+	81298.5i	1.21861	+	1.02253i	0.219711	+	0.975565i	$0.429489\pi$
$44$		0			0
$45$	83297.4	+	144275.i	0.914100	+	1.58327i
$46$		0			0
$47$	33707.4	+	12268.5i	0.324662	+	0.118167i	0.499209	−	0.866481i	$-0.333624\pi$
$47$	33707.4	+	12268.5i	0.324662	+	0.118167i	−0.174547	+	0.984649i	$0.555846\pi$
$48$		0			0
$49$	−91073.7	+	157744.i	−0.774113	+	1.34080i
$50$		0			0
$51$	14176.6	−	2499.72i	0.106872	−	0.0188443i
$52$		0			0
$53$	−111310.	−	132654.i	−0.747664	−	0.891031i	0.249338	−	0.968417i	$-0.419787\pi$
$53$	−111310.	−	132654.i	−0.747664	−	0.891031i	−0.997001	+	0.0773858i	$0.975343\pi$
$54$		0			0
$55$	33221.8	−	12091.8i	0.199680	−	0.0726777i
$56$		0			0
$57$	132587.	−	226295.i	0.715941	−	1.22194i
$58$		0			0
$59$	−62910.8	−	172846.i	−0.306315	−	0.841595i	−0.993367	−	0.114986i	$-0.963318\pi$
$59$	−62910.8	−	172846.i	−0.306315	−	0.841595i	0.687052	−	0.726609i	$-0.258905\pi$
$60$		0			0
$61$	−232352.	+	194967.i	−1.02366	+	0.858957i	−0.990084	−	0.140479i	$-0.955136\pi$
$61$	−232352.	+	194967.i	−1.02366	+	0.858957i	−0.0335810	+	0.999436i	$0.510691\pi$
$62$		0			0
$63$	−69708.4	−	395336.i	−0.278781	−	1.58105i
$64$		0			0
$65$	294840.	+	170226.i	1.07361	+	0.619850i
$66$		0			0
$67$	−146670.	+	402972.i	−0.487659	+	1.33983i	0.415135	+	0.909760i	$0.363734\pi$
$67$	−146670.	+	402972.i	−0.487659	+	1.33983i	−0.902794	+	0.430073i	$0.858488\pi$
$68$		0			0
$69$	646403.	−	373201.i	1.96769	−	1.13605i
$70$		0			0
$71$	−93891.2	+	111895.i	−0.262331	+	0.312634i	−0.881092	−	0.472946i	$-0.843191\pi$
$71$	−93891.2	+	111895.i	−0.262331	+	0.312634i	0.618760	+	0.785580i	$0.287635\pi$
$72$		0			0
$73$	700.874	−	3974.85i	0.00180165	−	0.0102177i	−0.983894	−	0.178755i	$-0.942793\pi$
$73$	700.874	−	3974.85i	0.00180165	−	0.0102177i	0.985695	+	0.168537i	$0.0539043\pi$
$74$		0			0
$75$		−	1.37685e6i		−	3.26364i
$76$		0			0
$77$	−85190.5			−0.186603
$78$		0			0
$79$	759991.	+	134007.i	1.54144	+	0.271798i	0.878819	−	0.477156i	$-0.158332\pi$
$79$	759991.	+	134007.i	1.54144	+	0.271798i	0.662623	+	0.748953i	$0.269443\pi$
$80$		0			0
$81$	−404768.	−	339641.i	−0.761643	−	0.639094i
$82$		0			0
$83$	416361.	+	721159.i	0.728176	+	1.26124i	0.957653	+	0.287923i	$0.0929648\pi$
$83$	416361.	+	721159.i	0.728176	+	1.26124i	−0.229478	+	0.973314i	$0.573702\pi$
$84$		0			0
$85$	−80383.8	−	29257.3i	−0.130892	−	0.0476406i
$86$		0			0
$87$	187273.	−	324366.i	0.284392	−	0.492581i
$88$		0			0
$89$	−798173.	+	140739.i	−1.13221	+	0.199639i	−0.708196	−	0.706016i	$-0.750490\pi$
$89$	−798173.	+	140739.i	−1.13221	+	0.199639i	−0.424014	+	0.905656i	$0.639379\pi$
$90$		0			0
$91$	−527324.	−	628440.i	−0.699767	−	0.833950i
$92$		0			0
$93$	1.70342e6	−	619995.i	2.11774	−	0.770796i
$94$		0			0
$95$	−1.35470e6	+	770631.i	−1.58005	+	0.898826i
$96$		0			0
$97$	−318032.	−	873784.i	−0.348462	−	0.957390i	−0.982855	−	0.184380i	$-0.940972\pi$
$97$	−318032.	−	873784.i	−0.348462	−	0.957390i	0.634393	−	0.773010i	$-0.281250\pi$
$98$		0			0
$99$	87384.3	−	73324.2i	0.0900592	−	0.0755686i
$100$		0			0
$101$	245659.	+	1.39320e6i	0.238434	+	1.35223i	0.835260	+	0.549855i	$0.185317\pi$
$101$	245659.	+	1.39320e6i	0.238434	+	1.35223i	−0.596826	+	0.802371i	$0.703572\pi$
$102$		0			0
$103$	258071.	+	148998.i	0.236172	+	0.136354i	0.613416	−	0.789760i	$-0.289795\pi$
$103$	258071.	+	148998.i	0.236172	+	0.136354i	−0.377244	+	0.926114i	$0.623128\pi$
$104$		0			0
$105$	−1.62713e6	+	4.47051e6i	−1.40558	+	3.86179i
$106$		0			0
$107$	1.08122e6	−	624242.i	0.882596	−	0.509567i	0.0110827	−	0.999939i	$-0.496472\pi$
$107$	1.08122e6	−	624242.i	0.882596	−	0.509567i	0.871514	+	0.490371i	$0.163139\pi$
$108$		0			0
$109$	442626.	−	527501.i	0.341788	−	0.407327i	−0.567581	−	0.823318i	$-0.692121\pi$
$109$	442626.	−	527501.i	0.341788	−	0.407327i	0.909369	+	0.415990i	$0.136565\pi$
$110$		0			0
$111$	−105977.	+	601027.i	−0.0774897	+	0.439466i
$112$		0			0
$113$		−	382456.i		−	0.265061i	−0.991179	−	0.132530i	$-0.957690\pi$
$113$		−	382456.i		−	0.265061i	0.991179	−	0.132530i	$-0.0423102\pi$
$114$		0			0
$115$	−4.43542e6			−2.91636
$116$		0			0
$117$	1.08181e6	+	190752.i	0.675449	+	0.119100i
$118$		0			0
$119$	157903.	+	132496.i	0.0937021	+	0.0786254i
$120$		0			0
$121$	873677.	+	1.51325e6i	0.493168	+	0.854191i
$122$		0			0
$123$	1.68524e6	+	613379.i	0.905623	+	0.329620i
$124$		0			0
$125$	−2.31567e6	+	4.01086e6i	−1.18562	+	2.05356i
$126$		0			0
$127$	2.14090e6	−	377499.i	1.04517	−	0.184291i	0.375400	−	0.926863i	$-0.377505\pi$
$127$	2.14090e6	−	377499.i	1.04517	−	0.184291i	0.669767	+	0.742572i	$0.266394\pi$
$128$		0			0
$129$	−3.10871e6	−	3.70482e6i	−1.44814	−	1.72583i
$130$		0			0
$131$	−696222.	+	253404.i	−0.309695	+	0.112720i	−0.492192	−	0.870487i	$-0.663804\pi$
$131$	−696222.	+	253404.i	−0.309695	+	0.112720i	0.182497	+	0.983206i	$0.441582\pi$
$132$		0			0
$133$	3.70259e6	−	628490.i	1.57380	−	0.267143i
$134$		0			0
$135$	−12376.5	−	34004.3i	−0.00503035	−	0.0138208i
$136$		0			0
$137$	878291.	−	736974.i	0.341568	−	0.286609i	−0.455826	−	0.890069i	$-0.650656\pi$
$137$	878291.	−	736974.i	0.341568	−	0.286609i	0.797394	+	0.603460i	$0.206212\pi$
$138$		0			0
$139$	−492710.	−	2.79430e6i	−0.183462	−	1.04047i	−0.927915	−	0.372792i	$-0.878401\pi$
$139$	−492710.	−	2.79430e6i	−0.183462	−	1.04047i	0.744452	−	0.667675i	$-0.232711\pi$
$140$		0			0
$141$	−1.18787e6	−	685816.i	−0.423751	−	0.244653i
$142$		0			0
$143$	79730.9	−	219059.i	0.0272658	−	0.0749122i
$144$		0			0
$145$	−1.92751e6	+	1.11285e6i	−0.632255	+	0.365033i
$146$		0			0
$147$	4.47701e6	−	5.33550e6i	1.40941	−	1.67967i
$148$		0			0
$149$	−328943.	+	1.86553e6i	−0.0994403	+	0.563954i	0.893856	+	0.448355i	$0.147990\pi$
$149$	−328943.	+	1.86553e6i	−0.0994403	+	0.563954i	−0.993296	+	0.115599i	$0.963121\pi$
$150$		0			0
$151$		−	3.57213e6i		−	1.03752i	−0.854920	−	0.518760i	$-0.826394\pi$
$151$		−	3.57213e6i		−	1.03752i	0.854920	−	0.518760i	$-0.173606\pi$
$152$		0			0
$153$	−276010.			−0.0770638
$154$		0			0
$155$	−1.06084e7	−	1.87055e6i	−2.84875	−	0.502312i
$156$		0			0
$157$	2.99753e6	+	2.51523e6i	0.774577	+	0.649947i	0.941877	−	0.335959i	$-0.109060\pi$
$157$	2.99753e6	+	2.51523e6i	0.774577	+	0.649947i	−0.167300	+	0.985906i	$0.553505\pi$
$158$		0			0
$159$	3.31081e6	+	5.73449e6i	0.823651	+	1.42661i
$160$		0			0
$161$	1.00432e7	+	3.65544e6i	2.40656	+	0.875915i
$162$		0			0
$163$	−2.39003e6	+	4.13965e6i	−0.551874	+	0.955874i	0.446265	+	0.894901i	$0.352754\pi$
$163$	−2.39003e6	+	4.13965e6i	−0.551874	+	0.955874i	−0.998139	+	0.0609735i	$0.980579\pi$
$164$		0			0
$165$	−1.33133e6	+	234750.i	−0.296371	+	0.0522582i
$166$		0			0
$167$	−2.76299e6	−	3.29281e6i	−0.593240	−	0.706996i	0.382985	−	0.923754i	$-0.374896\pi$
$167$	−2.76299e6	−	3.29281e6i	−0.593240	−	0.706996i	−0.976225	+	0.216759i	$0.930452\pi$
$168$		0			0
$169$	−2.42622e6	+	883071.i	−0.502654	+	0.182951i
$170$		0			0
$171$	−3.25699e6	+	3.83153e6i	−0.651371	+	0.766273i
$172$		0			0
$173$	−1.03606e6	−	2.84654e6i	−0.200099	−	0.549767i	0.798539	−	0.601943i	$-0.205607\pi$
$173$	−1.03606e6	−	2.84654e6i	−0.200099	−	0.549767i	−0.998638	+	0.0521760i	$0.983384\pi$
$174$		0			0
$175$	1.51027e7	−	1.26727e7i	2.81800	−	2.36458i
$176$		0			0
$177$	1.22135e6	+	6.92664e6i	0.220253	+	1.24912i
$178$		0			0
$179$	−7.83470e6	−	4.52336e6i	−1.36604	−	0.788683i	−0.375619	−	0.926774i	$-0.622570\pi$
$179$	−7.83470e6	−	4.52336e6i	−1.36604	−	0.788683i	−0.990420	+	0.138091i	$0.955903\pi$
$180$		0			0
$181$	−1.13715e6	+	3.12431e6i	−0.191771	+	0.526887i	−0.997894	−	0.0648607i	$-0.979340\pi$
$181$	−1.13715e6	+	3.12431e6i	−0.191771	+	0.526887i	0.806123	+	0.591748i	$0.201562\pi$
$182$		0			0
$183$	1.00444e7	−	5.79911e6i	1.63896	−	0.946255i
$184$		0			0
$185$	2.33116e6	−	2.77817e6i	0.368177	−	0.438776i
$186$		0			0
$187$	−10171.2	+	57683.6i	−0.00155542	+	0.00882120i
$188$		0			0
$189$			87197.0i			0.0129156i
$190$		0			0
$191$	6.68314e6			0.959136			0.479568	−	0.877505i	$-0.340793\pi$
$191$	6.68314e6			0.959136			0.479568	+	0.877505i	$0.340793\pi$
$192$		0			0
$193$	−3.18616e6	−	561805.i	−0.443195	−	0.0781473i	−0.0524026	−	0.998626i	$-0.516688\pi$
$193$	−3.18616e6	−	561805.i	−0.443195	−	0.0781473i	−0.390793	+	0.920479i	$0.627799\pi$
$194$		0			0
$195$	−9.97260e6	−	8.36801e6i	−1.34495	−	1.12854i
$196$		0			0
$197$	−4.85764e6	−	8.41367e6i	−0.635369	−	1.10049i	−0.986437	−	0.164142i	$-0.947514\pi$
$197$	−4.85764e6	−	8.41367e6i	−0.635369	−	1.10049i	0.351067	−	0.936350i	$-0.385819\pi$
$198$		0			0
$199$	−1.25463e6	−	456646.i	−0.159204	−	0.0579456i	0.261189	−	0.965288i	$-0.415886\pi$
$199$	−1.25463e6	−	456646.i	−0.159204	−	0.0579456i	−0.420393	+	0.907342i	$0.638108\pi$
$200$		0			0
$201$	8.19893e6	−	1.42010e7i	1.00965	−	1.74876i
$202$		0			0
$203$	5.28166e6	−	931300.i	0.631368	−	0.111327i
$204$		0			0
$205$	−6.85025e6	−	8.16381e6i	−0.795142	−	0.947613i
$206$		0			0
$207$	−1.34481e7	+	4.89472e6i	−1.51618	+	0.551845i
$208$		0			0
$209$	680732.	+	821877.i	0.0745654	+	0.0900261i
$210$		0			0
$211$	−2.91196e6	−	8.00055e6i	−0.309983	−	0.851672i	−0.992659	−	0.120950i	$-0.961406\pi$
$211$	−2.91196e6	−	8.00055e6i	−0.309983	−	0.851672i	0.682675	−	0.730722i	$-0.260816\pi$
$212$		0			0
$213$	4.27868e6	−	3.59024e6i	0.442763	−	0.371522i
$214$		0			0
$215$	4.99051e6	+	2.83026e7i	0.502146	+	2.84781i
$216$		0			0
$217$	2.24793e7	+	1.29784e7i	2.19990	+	1.27011i
$218$		0			0
$219$	−52786.1	+	145029.i	−0.00502559	+	0.0138077i
$220$		0			0
$221$	−488484.	+	282026.i	−0.0452557	+	0.0261284i
$222$		0			0
$223$	−8.88915e6	+	1.05937e7i	−0.801578	+	0.955284i	−0.999690	−	0.0248958i	$-0.992075\pi$
$223$	−8.88915e6	+	1.05937e7i	−0.801578	+	0.955284i	0.198112	+	0.980179i	$0.436519\pi$
$224$		0			0
$225$	−4.58415e6	+	2.59980e7i	−0.402450	+	2.28241i
$226$		0			0
$227$			1.79264e7i			1.53256i	0.642510	+	0.766278i	$0.277893\pi$
$227$			1.79264e7i			1.53256i	−0.642510	+	0.766278i	$0.722107\pi$
$228$		0			0
$229$	−5.82294e6			−0.484882			−0.242441	−	0.970166i	$-0.577948\pi$
$229$	−5.82294e6			−0.484882			−0.242441	+	0.970166i	$0.577948\pi$
$230$		0			0
$231$	3.20805e6	+	565665.i	0.260258	+	0.0458906i
$232$		0			0
$233$	−6.06925e6	−	5.09271e6i	−0.479808	−	0.402607i	0.370549	−	0.928813i	$-0.379170\pi$
$233$	−6.06925e6	−	5.09271e6i	−0.479808	−	0.402607i	−0.850357	+	0.526206i	$0.823614\pi$
$234$		0			0
$235$	4.07539e6	+	7.05878e6i	0.314026	+	0.543909i
$236$		0			0
$237$	−2.77294e7	−	1.00927e7i	−2.08303	−	0.758161i
$238$		0			0
$239$	−6.94977e6	+	1.20374e7i	−0.509069	+	0.881734i	0.490876	+	0.871230i	$0.336677\pi$
$239$	−6.94977e6	+	1.20374e7i	−0.509069	+	0.881734i	−0.999945	+	0.0105042i	$0.996656\pi$
$240$		0			0
$241$	2.46798e7	−	4.35171e6i	1.76315	−	0.310891i	0.804179	−	0.594387i	$-0.202605\pi$
$241$	2.46798e7	−	4.35171e6i	1.76315	−	0.310891i	0.958973	+	0.283496i	$0.0914943\pi$
$242$		0			0
$243$	1.30619e7	+	1.55666e7i	0.910307	+	1.08486i
$244$		0			0
$245$	−3.88927e7	+	1.41558e7i	−2.64466	+	0.962578i
$246$		0			0
$247$	−1.84920e6	+	1.01091e7i	−0.122714	+	0.670841i
$248$		0			0
$249$	−1.08906e7	−	2.99216e7i	−0.705427	−	1.93815i
$250$		0			0
$251$	1.14375e7	−	9.59718e6i	0.723284	−	0.606907i	−0.205008	−	0.978760i	$-0.565722\pi$
$251$	1.14375e7	−	9.59718e6i	0.723284	−	0.606907i	0.928292	+	0.371853i	$0.121277\pi$
$252$		0			0
$253$	527379.	+	2.99092e6i	0.0325658	+	0.184690i
$254$		0			0
$255$	2.83277e6	+	1.63550e6i	0.170841	+	0.0986348i
$256$		0			0
$257$	6.22982e6	−	1.71163e7i	0.367008	−	1.00835i	−0.609485	−	0.792798i	$-0.708624\pi$
$257$	6.22982e6	−	1.71163e7i	0.367008	−	1.00835i	0.976493	−	0.215549i	$-0.0691541\pi$
$258$		0			0
$259$	−7.56812e6	+	4.36946e6i	−0.435601	+	0.251494i
$260$		0			0
$261$	−4.61610e6	+	5.50126e6i	−0.259629	+	0.309414i
$262$		0			0
$263$	209901.	−	1.19041e6i	0.0115384	−	0.0654378i	−0.978495	−	0.206271i	$-0.933867\pi$
$263$	209901.	−	1.19041e6i	0.0115384	−	0.0654378i	0.990033	+	0.140833i	$0.0449782\pi$
$264$		0			0
$265$		−	3.93483e7i		−	2.11441i
$266$		0			0
$267$	3.09916e7			1.62821
$268$		0			0
$269$	−3.44576e7	−	6.07581e6i	−1.77023	−	0.312138i	−0.808980	−	0.587836i	$-0.799980\pi$
$269$	−3.44576e7	−	6.07581e6i	−1.77023	−	0.312138i	−0.961245	+	0.275697i	$0.911091\pi$
$270$		0			0
$271$	−4.54189e6	−	3.81110e6i	−0.228207	−	0.191488i	0.521513	−	0.853243i	$-0.325368\pi$
$271$	−4.54189e6	−	3.81110e6i	−0.228207	−	0.191488i	−0.749721	+	0.661755i	$0.769812\pi$
$272$		0			0
$273$	1.56848e7	+	2.71668e7i	0.770886	+	1.33521i
$274$		0			0
$275$	5.26443e6	+	1.91609e6i	0.253136	+	0.0921338i
$276$		0			0
$277$	2.49176e6	−	4.31585e6i	0.117237	−	0.203061i	−0.801435	−	0.598083i	$-0.795929\pi$
$277$	2.49176e6	−	4.31585e6i	0.117237	−	0.203061i	0.918672	+	0.395021i	$0.129263\pi$
$278$		0			0
$279$	−3.42288e7	+	6.03546e6i	−1.57608	+	0.277906i
$280$		0			0
$281$	1.29985e7	+	1.54910e7i	0.585831	+	0.698167i	0.974799	−	0.223085i	$-0.0716126\pi$
$281$	1.29985e7	+	1.54910e7i	0.585831	+	0.698167i	−0.388968	+	0.921251i	$0.627168\pi$
$282$		0			0
$283$	2.35769e7	−	8.58129e6i	1.04023	−	0.378611i	0.235260	−	0.971933i	$-0.424406\pi$
$283$	2.35769e7	−	8.58129e6i	1.04023	−	0.378611i	0.804966	+	0.593322i	$0.202184\pi$
$284$		0			0
$285$	5.61313e7	−	2.00247e7i	2.42477	−	0.865031i
$286$		0			0
$287$	8.78302e6	+	2.41311e7i	0.371534	+	1.02078i
$288$		0			0
$289$	−1.83819e7	+	1.54242e7i	−0.761547	+	0.639013i
$290$		0			0
$291$	6.17429e6	+	3.50161e7i	0.250558	+	1.42098i
$292$		0			0
$293$	1.06882e7	+	6.17083e6i	0.424914	+	0.245324i	0.697178	−	0.716898i	$-0.254439\pi$
$293$	1.06882e7	+	6.17083e6i	0.424914	+	0.245324i	−0.272263	+	0.962223i	$0.587772\pi$
$294$		0			0
$295$	1.42950e7	−	3.92752e7i	0.556825	−	1.52986i
$296$		0			0
$297$	−21458.4	+	12389.0i	−0.000819082	+	0.000472897i
$298$		0			0
$299$	−1.87992e7	+	2.24040e7i	−0.703276	+	0.838131i
$300$		0			0
$301$	1.20254e7	−	6.81993e7i	0.440960	−	2.50081i
$302$		0			0
$303$		−	5.40954e7i		−	1.94461i
$304$		0			0
$305$	−6.89212e7			−2.42914
$306$		0			0
$307$	−4.27295e7	−	7.53437e6i	−1.47677	−	0.260394i	−0.623484	−	0.781836i	$-0.714283\pi$
$307$	−4.27295e7	−	7.53437e6i	−1.47677	−	0.260394i	−0.853287	+	0.521442i	$0.825394\pi$
$308$		0			0
$309$	−8.72893e6	−	7.32444e6i	−0.295860	−	0.248256i
$310$		0			0
$311$	−3.57015e6	−	6.18369e6i	−0.118688	−	0.205573i	0.800560	−	0.599252i	$-0.204535\pi$
$311$	−3.57015e6	−	6.18369e6i	−0.118688	−	0.205573i	−0.919248	+	0.393679i	$0.871202\pi$
$312$		0			0
$313$	3.52579e7	+	1.28328e7i	1.14980	+	0.418494i	0.845445	−	0.534063i	$-0.179335\pi$
$313$	3.52579e7	+	1.28328e7i	1.14980	+	0.418494i	0.304359	+	0.952557i	$0.401558\pi$
$314$		0			0
$315$	4.56083e7	−	7.89960e7i	1.45919	−	2.52740i
$316$		0			0
$317$	5.24585e7	−	9.24985e6i	1.64679	−	0.290373i	0.728134	−	0.685434i	$-0.240388\pi$
$317$	5.24585e7	−	9.24985e6i	1.64679	−	0.290373i	0.918655	+	0.395061i	$0.129277\pi$
$318$		0			0
$319$	979607.	+	1.16745e6i	0.0301772	+	0.0359638i
$320$		0			0
$321$	−4.48608e7	+	1.63280e7i	−1.35629	+	0.493648i
$322$		0			0
$323$	16505.5	−	2.58211e6i	0.000489802	−	0.0766244i
$324$		0			0
$325$	1.84517e7	+	5.06956e7i	0.537509	+	1.47679i
$326$		0			0
$327$	−2.01707e7	+	1.69252e7i	−0.576870	+	0.484051i
$328$		0			0
$329$	−3.41054e6	−	1.93421e7i	−0.0957713	−	0.543146i
$330$		0			0
$331$	2.66619e7	+	1.53932e7i	0.735202	+	0.424469i	0.820322	−	0.571902i	$-0.193794\pi$
$331$	2.66619e7	+	1.53932e7i	0.735202	+	0.424469i	−0.0851202	+	0.996371i	$0.527127\pi$
$332$		0			0
$333$	4.00219e6	−	1.09959e7i	0.108384	−	0.297782i
$334$		0			0
$335$	−8.43878e7	+	4.87213e7i	−2.24463	+	1.29594i
$336$		0			0
$337$	1.42076e6	−	1.69320e6i	0.0371221	−	0.0442404i	−0.747164	−	0.664640i	$-0.768585\pi$
$337$	1.42076e6	−	1.69320e6i	0.0371221	−	0.0442404i	0.784286	+	0.620399i	$0.213029\pi$
$338$		0			0
$339$	−2.53951e6	+	1.44023e7i	−0.0651854	+	0.369685i
$340$		0			0
$341$			7.37592e6i			0.186017i
$342$		0			0
$343$	3.53152e7			0.875143
$344$		0			0
$345$	1.67026e8	+	2.94512e7i	4.06749	+	0.717209i
$346$		0			0
$347$	−3.04345e7	−	2.55376e7i	−0.728412	−	0.611211i	0.201286	−	0.979533i	$-0.435488\pi$
$347$	−3.04345e7	−	2.55376e7i	−0.728412	−	0.611211i	−0.929698	+	0.368322i	$0.879932\pi$
$348$		0			0
$349$	−7.62860e6	−	1.32131e7i	−0.179460	−	0.310834i	0.762235	−	0.647300i	$-0.224102\pi$
$349$	−7.62860e6	−	1.32131e7i	−0.179460	−	0.310834i	−0.941696	+	0.336465i	$0.890768\pi$
$350$		0			0
$351$	−224218.	−	81608.8i	−0.00518501	−	0.00188719i
$352$		0			0
$353$	−1.96196e7	+	3.39821e7i	−0.446032	+	0.772550i	−0.998123	−	0.0612337i	$-0.980496\pi$
$353$	−1.96196e7	+	3.39821e7i	−0.446032	+	0.772550i	0.552092	+	0.833783i	$0.313830\pi$
$354$		0			0
$355$	−3.26865e7	+	5.76351e6i	−0.730607	+	0.128826i
$356$		0			0
$357$	−5.06643e6	−	6.03793e6i	−0.111352	−	0.132704i
$358$		0			0
$359$	2.75456e7	−	1.00258e7i	0.595346	−	0.216688i	−0.0267333	−	0.999643i	$-0.508510\pi$
$359$	2.75456e7	−	1.00258e7i	0.595346	−	0.216688i	0.622079	+	0.782954i	$0.286288\pi$
$360$		0			0
$361$	−3.56497e7	−	3.06988e7i	−0.757764	−	0.652528i
$362$		0			0
$363$	−2.28523e7	−	6.27863e7i	−0.477761	−	1.31264i
$364$		0			0
$365$	702560.	−	589518.i	0.0144479	−	0.0121232i
$366$		0			0
$367$	−385324.	−	2.18528e6i	−0.00779521	−	0.0442088i	0.980662	−	0.195709i	$-0.0627008\pi$
$367$	−385324.	−	2.18528e6i	−0.00779521	−	0.0442088i	−0.988457	+	0.151500i	$0.951590\pi$
$368$		0			0
$369$	−2.97791e7	−	1.71930e7i	−0.592696	−	0.342193i
$370$		0			0
$371$	−3.24288e7	+	8.90975e7i	−0.635052	+	1.74479i
$372$		0			0
$373$	−3.20879e7	+	1.85260e7i	−0.618322	+	0.356988i	−0.776215	−	0.630468i	$-0.782863\pi$
$373$	−3.20879e7	+	1.85260e7i	−0.618322	+	0.356988i	0.157893	+	0.987456i	$0.449530\pi$
$374$		0			0
$375$	1.13834e8	−	1.35662e8i	2.15863	−	2.57256i
$376$		0			0
$377$	−2.54843e6	+	1.44529e7i	−0.0475608	+	0.269731i
$378$		0			0
$379$		−	3.33486e7i		−	0.612576i	−0.951939	−	0.306288i	$-0.900913\pi$
$379$		−	3.33486e7i		−	0.612576i	0.951939	−	0.306288i	$-0.0990870\pi$
$380$		0			0
$381$	−8.31273e7			−1.50303
$382$		0			0
$383$	1.68618e7	+	2.97320e6i	0.300130	+	0.0529209i	0.321685	−	0.946847i	$-0.395751\pi$
$383$	1.68618e7	+	2.97320e6i	0.300130	+	0.0529209i	−0.0215556	+	0.999768i	$0.506862\pi$
$384$		0			0
$385$	−1.48288e7	−	1.24428e7i	−0.259850	−	0.218040i
$386$		0			0
$387$	4.63646e7	+	8.03059e7i	0.799933	+	1.38553i
$388$		0			0
$389$	−4.02626e7	−	1.46544e7i	−0.683995	−	0.248954i	−0.0234334	−	0.999725i	$-0.507460\pi$
$389$	−4.02626e7	−	1.46544e7i	−0.683995	−	0.248954i	−0.660562	+	0.750771i	$0.729682\pi$
$390$		0			0
$391$	3.67424e6	−	6.36398e6i	0.0614664	−	0.106463i
$392$		0			0
$393$	2.79005e7	−	4.91960e6i	0.459657	−	0.0810499i
$394$		0			0
$395$	1.12716e8	+	1.34329e8i	1.82891	+	2.17961i
$396$		0			0
$397$	759456.	−	276419.i	0.0121375	−	0.00441771i	−0.335944	−	0.941882i	$-0.609055\pi$
$397$	759456.	−	276419.i	0.0121375	−	0.00441771i	0.348082	+	0.937464i	$0.386833\pi$
$398$		0			0
$399$	−1.43603e8	−	917944.i	−2.26071	−	0.0144510i
$400$		0			0
$401$	3.63174e6	+	9.97813e6i	0.0563225	+	0.154745i	0.964663	−	0.263486i	$-0.0848724\pi$
$401$	3.63174e6	+	9.97813e6i	0.0563225	+	0.154745i	−0.908341	+	0.418231i	$0.862650\pi$
$402$		0			0
$403$	−5.44113e7	+	4.56565e7i	−0.831331	+	0.697570i
$404$		0			0
$405$	−2.08489e7	−	1.18240e8i	−0.313847	−	1.77991i
$406$		0			0
$407$	−2.15057e6	−	1.24163e6i	−0.0318985	−	0.0184166i
$408$		0			0
$409$	−1.30570e7	+	3.58737e7i	−0.190841	+	0.524332i	−0.997801	−	0.0662735i	$-0.978889\pi$
$409$	−1.30570e7	+	3.58737e7i	−0.190841	+	0.524332i	0.806960	+	0.590606i	$0.201111\pi$
$410$		0			0
$411$	−3.79676e7	+	2.19206e7i	−0.546875	+	0.315738i
$412$		0			0
$413$	−6.47372e7	+	7.71508e7i	−0.918975	+	1.09519i
$414$		0			0
$415$	−3.28572e7	+	1.86342e8i	−0.459712	+	2.60716i
$416$		0			0
$417$			1.08497e8i			1.49628i
$418$		0			0
$419$	4.82710e7			0.656212			0.328106	−	0.944641i	$-0.393590\pi$
$419$	4.82710e7			0.656212			0.328106	+	0.944641i	$0.393590\pi$
$420$		0			0
$421$	8.25443e7	+	1.45548e7i	1.10622	+	0.195056i	0.696782	−	0.717283i	$-0.254614\pi$
$421$	8.25443e7	+	1.45548e7i	1.10622	+	0.195056i	0.409436	+	0.912339i	$0.365726\pi$
$422$		0			0
$423$	2.01463e7	+	1.69047e7i	0.266179	+	0.223351i
$424$		0			0
$425$	−6.77767e6	−	1.17393e7i	−0.0882904	−	0.152923i
$426$		0			0
$427$	1.56060e8	+	5.68013e7i	2.00451	+	0.729583i
$428$		0			0
$429$	−4.45700e6	+	7.71976e6i	−0.0564509	+	0.0977759i
$430$		0			0
$431$	−7.94076e7	+	1.40017e7i	−0.991814	+	0.174884i	−0.645932	−	0.763395i	$-0.723531\pi$
$431$	−7.94076e7	+	1.40017e7i	−0.991814	+	0.174884i	−0.345881	+	0.938278i	$0.612420\pi$
$432$		0			0
$433$	−1.75196e7	−	2.08790e7i	−0.215804	−	0.257185i	0.647272	−	0.762259i	$-0.275910\pi$
$433$	−1.75196e7	−	2.08790e7i	−0.215804	−	0.257185i	−0.863076	+	0.505074i	$0.831465\pi$
$434$		0			0
$435$	7.99742e7	−	2.91082e7i	0.971588	−	0.353629i
$436$		0			0
$437$	−4.49866e7	−	1.26102e8i	−0.539062	−	1.51105i
$438$		0			0
$439$	−1.02320e7	−	2.81121e7i	−0.120939	−	0.332277i	0.864420	−	0.502771i	$-0.167686\pi$
$439$	−1.02320e7	−	2.81121e7i	−0.120939	−	0.332277i	−0.985359	+	0.170494i	$0.945464\pi$
$440$		0			0
$441$	−1.02301e8	+	8.58404e7i	−1.19279	+	1.00087i
$442$		0			0
$443$	−6.25839e6	−	3.54931e7i	−0.0719865	−	0.408256i	−0.999413	−	0.0342510i	$-0.989095\pi$
$443$	−6.25839e6	−	3.54931e7i	−0.0719865	−	0.408256i	0.927427	−	0.374005i	$-0.122016\pi$
$444$		0			0
$445$	−1.59491e8	−	9.20821e7i	−1.80990	−	1.04495i
$446$		0			0
$447$	2.47743e7	−	6.80667e7i	0.277382	−	0.762101i
$448$		0			0
$449$	−8.38894e7	+	4.84336e7i	−0.926762	+	0.535066i	−0.885786	−	0.464094i	$-0.846380\pi$
$449$	−8.38894e7	+	4.84336e7i	−0.926762	+	0.535066i	−0.0409761	+	0.999160i	$0.513047\pi$
$450$		0			0
$451$	−4.69056e6	+	5.58999e6i	−0.0511322	+	0.0609370i
$452$		0			0
$453$	−2.37189e7	+	1.34517e8i	−0.255153	+	1.44704i
$454$		0			0
$455$		−	1.86410e8i		−	1.97895i
$456$		0			0
$457$	9.44585e7			0.989674			0.494837	−	0.868986i	$-0.335228\pi$
$457$	9.44585e7			0.989674			0.494837	+	0.868986i	$0.335228\pi$
$458$		0			0
$459$	59042.2	+	10410.7i	0.000610555	+	0.000107657i
$460$		0			0
$461$	9.96676e7	+	8.36311e7i	1.01731	+	0.853621i	0.989287	−	0.145987i	$-0.0466357\pi$
$461$	9.96676e7	+	8.36311e7i	1.01731	+	0.853621i	0.0280190	+	0.999607i	$0.491080\pi$
$462$		0			0
$463$	−1.23541e7	−	2.13979e7i	−0.124471	−	0.215590i	0.797055	−	0.603906i	$-0.206390\pi$
$463$	−1.23541e7	−	2.13979e7i	−0.124471	−	0.215590i	−0.921526	+	0.388317i	$0.873057\pi$
$464$		0			0
$465$	3.87063e8	+	1.40880e8i	3.84967	+	1.40116i
$466$		0			0
$467$	9.86315e7	−	1.70835e8i	0.968423	−	1.67736i	0.268299	−	0.963336i	$-0.413539\pi$
$467$	9.86315e7	−	1.70835e8i	0.968423	−	1.67736i	0.700124	−	0.714021i	$-0.253128\pi$
$468$		0			0
$469$	2.31235e8	−	4.07730e7i	2.24148	−	0.395234i
$470$		0			0
$471$	−9.61779e7	−	1.14620e8i	−0.920476	−	1.09698i
$472$		0			0
$473$	1.84918e7	−	6.73046e6i	0.174741	−	0.0636006i
$474$		0			0
$475$	−2.42941e8	−	4.44401e7i	−2.26684	−	0.414662i
$476$		0			0
$477$	−4.34230e7	−	1.19304e8i	−0.400096	−	1.09926i
$478$		0			0
$479$	−3.01062e7	+	2.52621e7i	−0.273936	+	0.229860i	−0.769397	−	0.638770i	$-0.779443\pi$
$479$	−3.01062e7	+	2.52621e7i	−0.273936	+	0.229860i	0.495462	+	0.868630i	$0.334999\pi$
$480$		0			0
$481$	−4.15252e6	−	2.35501e7i	−0.0373144	−	0.211620i
$482$		0			0
$483$	−3.53930e8	−	2.04341e8i	−3.14105	−	1.81349i
$484$		0			0
$485$	7.22653e7	−	1.98547e8i	0.633439	−	1.74036i
$486$		0			0
$487$	3.22694e7	−	1.86307e7i	0.279386	−	0.161303i	−0.353760	−	0.935336i	$-0.615097\pi$
$487$	3.22694e7	−	1.86307e7i	0.279386	−	0.161303i	0.633145	+	0.774033i	$0.281764\pi$
$488$		0			0
$489$	1.17489e8	−	1.40018e8i	1.00478	−	1.19745i
$490$		0			0
$491$	3.90416e7	−	2.21416e8i	0.329825	−	1.87053i	−0.143512	−	0.989649i	$-0.545840\pi$
$491$	3.90416e7	−	2.21416e8i	0.329825	−	1.87053i	0.473337	−	0.880881i	$-0.343049\pi$
$492$		0			0
$493$		−	3.68748e6i		−	0.0307743i
$494$		0			0
$495$	2.59202e7			0.213709
$496$		0			0
$497$	7.87630e7	+	1.38880e7i	0.641583	+	0.113128i
$498$		0			0
$499$	5.94229e7	+	4.98617e7i	0.478247	+	0.401297i	0.849792	−	0.527118i	$-0.176727\pi$
$499$	5.94229e7	+	4.98617e7i	0.478247	+	0.401297i	−0.371545	+	0.928415i	$0.621172\pi$
$500$		0			0
$501$	8.21827e7	+	1.42345e8i	0.653533	+	1.13195i
$502$		0			0
$503$	−2.33626e6	−	850330.i	−0.0183577	−	0.00668165i	0.332825	−	0.942989i	$-0.391998\pi$
$503$	−2.33626e6	−	850330.i	−0.0183577	−	0.00668165i	−0.351183	+	0.936307i	$0.614220\pi$
$504$		0			0
$505$	−1.60728e8	+	2.78389e8i	−1.24801	+	2.16161i
$506$		0			0
$507$	9.72285e7	−	1.71440e7i	0.746053	−	0.131549i
$508$		0			0
$509$	2.89384e7	+	3.44875e7i	0.219443	+	0.261522i	0.864523	−	0.502593i	$-0.167620\pi$
$509$	2.89384e7	+	3.44875e7i	0.219443	+	0.261522i	−0.645080	+	0.764115i	$0.723176\pi$
$510$		0			0
$511$	−2.07668e6	+	755848.i	−0.0155634	+	0.00566463i
$512$		0			0
$513$	841235.	−	696765.i	0.00623111	−	0.00516101i
$514$		0			0
$515$	2.31590e7	+	6.36289e7i	0.169550	+	0.465836i
$516$		0			0
$517$	4.27535e6	−	3.58744e6i	0.0309385	−	0.0259605i
$518$		0			0
$519$	2.01141e7	+	1.14072e8i	0.143879	+	0.815978i
$520$		0			0
$521$	1.94033e8	+	1.12025e8i	1.37203	+	0.792141i	0.991183	−	0.132499i	$-0.0423000\pi$
$521$	1.94033e8	+	1.12025e8i	1.37203	+	0.792141i	0.380845	+	0.924639i	$0.375633\pi$
$522$		0			0
$523$	−3.48526e6	+	9.57567e6i	−0.0243629	+	0.0669366i	−0.951278	−	0.308335i	$-0.900228\pi$
$523$	−3.48526e6	+	9.57567e6i	−0.0243629	+	0.0669366i	0.926915	+	0.375271i	$0.122451\pi$
$524$		0			0
$525$	−6.52874e8	+	3.76937e8i	−4.51182	+	2.60490i
$526$		0			0
$527$	1.14717e7	−	1.36715e7i	0.0783785	−	0.0934079i
$528$		0			0
$529$	4.04576e7	−	2.29446e8i	0.273296	−	1.54994i
$530$		0			0
$531$		−	1.34857e8i		−	0.900723i
$532$		0			0
$533$	−7.02710e7			−0.464082
$534$		0			0
$535$	2.79379e8	+	4.92621e7i	1.82445	+	0.321700i
$536$		0			0
$537$	2.64999e8	+	2.22360e8i	1.71128	+	1.43593i
$538$		0			0
$539$	1.41700e7	+	2.45432e7i	0.0904908	+	0.156735i
$540$		0			0
$541$	−1.84994e8	−	6.73324e7i	−1.16833	−	0.425238i	−0.316265	−	0.948671i	$-0.602429\pi$
$541$	−1.84994e8	−	6.73324e7i	−1.16833	−	0.425238i	−0.852067	+	0.523433i	$0.824651\pi$
$542$		0			0
$543$	6.35676e7	−	1.10102e8i	0.397042	−	0.687697i
$544$		0			0
$545$	1.54092e8	−	2.71706e7i	0.951898	−	0.167845i
$546$		0			0
$547$	4.32149e7	+	5.15015e7i	0.264041	+	0.314672i	0.881733	−	0.471748i	$-0.156377\pi$
$547$	4.32149e7	+	5.15015e7i	0.264041	+	0.314672i	−0.617692	+	0.786420i	$0.711932\pi$
$548$		0			0
$549$	−2.08968e8	+	7.60583e7i	−1.26288	+	0.459652i
$550$		0			0
$551$	−5.11890e7	−	4.35133e7i	−0.306000	−	0.260116i
$552$		0			0
$553$	−1.44518e8	−	3.97060e8i	−0.854567	−	2.34790i
$554$		0			0
$555$	−1.06232e8	+	8.91394e7i	−0.621409	+	0.521424i
$556$		0			0
$557$	1.77161e7	+	1.00473e8i	0.102519	+	0.581412i	0.992182	+	0.124796i	$0.0398277\pi$
$557$	1.77161e7	+	1.00473e8i	0.102519	+	0.581412i	−0.889664	+	0.456616i	$0.849061\pi$
$558$		0			0
$559$	1.64113e8	+	9.47506e7i	0.939523	+	0.542434i
$560$		0			0
$561$	766039.	−	2.10467e6i	0.00433873	−	0.0119206i
$562$		0			0
$563$	1.33356e8	−	7.69930e7i	0.747286	−	0.431446i	−0.0774264	−	0.996998i	$-0.524670\pi$
$563$	1.33356e8	−	7.69930e7i	0.747286	−	0.431446i	0.824712	+	0.565552i	$0.191337\pi$
$564$		0			0
$565$	5.58609e7	−	6.65725e7i	0.309715	−	0.369104i
$566$		0			0
$567$	−5.02384e7	+	2.84916e8i	−0.275605	+	1.56303i
$568$		0			0
$569$			1.32358e8i			0.718478i	0.933246	+	0.359239i	$0.116964\pi$
$569$			1.32358e8i			0.718478i	−0.933246	+	0.359239i	$0.883036\pi$
$570$		0			0
$571$	−9.46637e6			−0.0508482			−0.0254241	−	0.999677i	$-0.508094\pi$
$571$	−9.46637e6			−0.0508482			−0.0254241	+	0.999677i	$0.508094\pi$
$572$		0			0
$573$	−2.51669e8	−	4.43761e7i	−1.33772	−	0.235877i
$574$		0			0
$575$	−5.38414e8	−	4.51783e8i	−2.83213	−	2.37644i
$576$		0			0
$577$	4.32510e7	+	7.49129e7i	0.225148	+	0.389968i	0.956364	−	0.292178i	$-0.0943800\pi$
$577$	4.32510e7	+	7.49129e7i	0.225148	+	0.389968i	−0.731216	+	0.682146i	$0.761047\pi$
$578$		0			0
$579$	1.16252e8	+	4.23122e7i	0.598913	+	0.217987i
$580$		0			0
$581$	2.27973e8	−	3.94861e8i	1.16240	−	2.01333i
$582$		0			0
$583$	−2.65336e7	+	4.67859e6i	−0.133903	+	0.0236107i
$584$		0			0
$585$	1.60445e8	+	1.91211e8i	0.801416	+	0.955090i
$586$		0			0
$587$	−1.72398e8	+	6.27479e7i	−0.852351	+	0.310231i	−0.730999	−	0.682379i	$-0.760945\pi$
$587$	−1.72398e8	+	6.27479e7i	−0.852351	+	0.310231i	−0.121353	+	0.992609i	$0.538723\pi$
$588$		0			0
$589$	−5.44157e7	−	3.20576e8i	−0.266304	−	1.56886i
$590$		0			0
$591$	1.27059e8	+	3.49091e8i	0.615520	+	1.69113i
$592$		0			0
$593$	−5.26603e6	+	4.41872e6i	−0.0252533	+	0.0211901i	−0.655327	−	0.755345i	$-0.727469\pi$
$593$	−5.26603e6	+	4.41872e6i	−0.0252533	+	0.0211901i	0.630074	+	0.776535i	$0.283025\pi$
$594$		0			0
$595$	8.13328e6	+	4.61261e7i	0.0386114	+	0.218976i
$596$		0			0
$597$	4.42137e7	+	2.55268e7i	0.207794	+	0.119970i
$598$		0			0
$599$	5.91758e7	−	1.62584e8i	0.275337	−	0.756481i	−0.722539	−	0.691330i	$-0.757025\pi$
$599$	5.91758e7	−	1.62584e8i	0.275337	−	0.756481i	0.997875	−	0.0651508i	$-0.0207528\pi$
$600$		0			0
$601$	−391665.	+	226128.i	−0.00180423	+	0.00104167i	−0.500902	−	0.865504i	$-0.666998\pi$
$601$	−391665.	+	226128.i	−0.00180423	+	0.00104167i	0.499098	+	0.866546i	$0.333665\pi$
$602$		0			0
$603$	−2.02096e8	+	2.40849e8i	−0.921736	+	1.09848i
$604$		0			0
$605$	−6.89462e7	+	3.91014e8i	−0.311347	+	1.76574i
$606$		0			0
$607$		−	5.54507e7i		−	0.247937i	−0.992286	−	0.123968i	$-0.960438\pi$
$607$		−	5.54507e7i		−	0.247937i	0.992286	−	0.123968i	$-0.0395621\pi$
$608$		0			0
$609$	−2.05077e8			−0.907958
$610$		0			0
$611$	5.29283e7	+	9.33269e6i	0.232041	+	0.0409151i
$612$		0			0
$613$	−5.94566e7	−	4.98900e7i	−0.258118	−	0.216587i	0.504540	−	0.863388i	$-0.331662\pi$
$613$	−5.94566e7	−	4.98900e7i	−0.258118	−	0.216587i	−0.762659	+	0.646801i	$0.776106\pi$
$614$		0			0
$615$	2.03754e8	+	3.52913e8i	0.875954	+	1.51720i
$616$		0			0
$617$	2.23509e8	+	8.13508e7i	0.951569	+	0.346343i	0.770724	−	0.637169i	$-0.219895\pi$
$617$	2.23509e8	+	8.13508e7i	0.951569	+	0.346343i	0.180845	+	0.983512i	$0.442117\pi$
$618$		0			0
$619$	1.19251e8	−	2.06549e8i	0.502794	−	0.870866i	−0.497200	−	0.867636i	$-0.665639\pi$
$619$	1.19251e8	−	2.06549e8i	0.502794	−	0.870866i	0.999995	−	0.00322982i	$-0.00102808\pi$
$620$		0			0
$621$	3.06136e6	−	539801.i	0.0127832	−	0.00225402i
$622$		0			0
$623$	2.85250e8	+	3.39948e8i	1.17967	+	1.40588i
$624$		0			0
$625$	−4.60220e8	+	1.67506e8i	−1.88506	+	0.686106i
$626$		0			0
$627$	−2.01773e7	−	3.54698e7i	−0.0818578	−	0.143898i
$628$		0			0
$629$	2.05503e6	+	5.64616e6i	0.00825785	+	0.0226883i
$630$		0			0
$631$	−1.31807e8	+	1.10599e8i	−0.524625	+	0.440213i	−0.866241	−	0.499627i	$-0.833470\pi$
$631$	−1.31807e8	+	1.10599e8i	−0.524625	+	0.440213i	0.341616	+	0.939840i	$0.389026\pi$
$632$		0			0
$633$	5.65331e7	+	3.20615e8i	0.222890	+	1.26407i
$634$		0			0
$635$	4.27795e8	+	2.46988e8i	1.67076	+	0.964615i
$636$		0			0
$637$	−9.33407e7	+	2.56452e8i	−0.361121	+	0.992172i
$638$		0			0
$639$	−9.27448e7	+	5.35463e7i	−0.355457	+	0.205223i
$640$		0			0
$641$	1.11011e8	−	1.32298e8i	0.421496	−	0.502320i	−0.512953	−	0.858417i	$-0.671448\pi$
$641$	1.11011e8	−	1.32298e8i	0.421496	−	0.502320i	0.934449	+	0.356097i	$0.115893\pi$
$642$		0			0
$643$	−7.39298e7	+	4.19277e8i	−0.278091	+	1.57713i	0.450878	+	0.892585i	$0.351111\pi$
$643$	−7.39298e7	+	4.19277e8i	−0.278091	+	1.57713i	−0.728969	+	0.684547i	$0.760000\pi$
$644$		0			0
$645$		−	1.09894e9i		−	4.09538i
$646$		0			0
$647$	8.19794e7			0.302686			0.151343	−	0.988481i	$-0.451640\pi$
$647$	8.19794e7			0.302686			0.151343	+	0.988481i	$0.451640\pi$
$648$		0			0
$649$	−2.81840e7	−	4.96960e6i	−0.103102	−	0.0181797i
$650$		0			0
$651$	−7.60333e8	−	6.37995e8i	−2.75588	−	2.31246i
$652$		0			0
$653$	−6.57302e7	−	1.13848e8i	−0.236062	−	0.408871i	0.723519	−	0.690305i	$-0.242523\pi$
$653$	−6.57302e7	−	1.13848e8i	−0.236062	−	0.408871i	−0.959581	+	0.281434i	$0.909190\pi$
$654$		0			0
$655$	−1.58200e8	−	5.75802e7i	−0.562968	−	0.204903i
$656$		0			0
$657$	1.47959e6	−	2.56272e6i	0.00521729	−	0.00903661i
$658$		0			0
$659$	−4.03247e8	+	7.11034e7i	−1.40901	+	0.248447i	−0.825842	−	0.563901i	$-0.809300\pi$
$659$	−4.03247e8	+	7.11034e7i	−1.40901	+	0.248447i	−0.583172	+	0.812349i	$0.698189\pi$
$660$		0			0
$661$	5.61743e7	+	6.69460e7i	0.194506	+	0.231804i	0.854479	−	0.519486i	$-0.173877\pi$
$661$	5.61743e7	+	6.69460e7i	0.194506	+	0.231804i	−0.659973	+	0.751290i	$0.729432\pi$
$662$		0			0
$663$	2.02677e7	−	7.37683e6i	0.0695446	−	0.0253122i
$664$		0			0
$665$	7.36291e8	+	4.31397e8i	2.50371	+	1.46694i
$666$		0			0
$667$	−6.53932e7	−	1.79666e8i	−0.220371	−	0.605466i
$668$		0			0
$669$	4.05084e8	−	3.39906e8i	1.35290	−	1.13522i
$670$		0			0
$671$	8.19486e6	+	4.64753e7i	0.0271253	+	0.153835i
$672$		0			0
$673$	−1.08350e8	−	6.25559e7i	−0.355454	−	0.205222i	0.311631	−	0.950203i	$-0.399125\pi$
$673$	−1.08350e8	−	6.25559e7i	−0.355454	−	0.205222i	−0.667085	+	0.744982i	$0.732458\pi$
$674$		0			0
$675$	1.96122e6	−	5.38842e6i	0.00637699	−	0.0175206i
$676$		0			0
$677$	−3.66045e8	+	2.11336e8i	−1.17969	+	0.681096i	−0.955943	−	0.293551i	$-0.905163\pi$
$677$	−3.66045e8	+	2.11336e8i	−1.17969	+	0.681096i	−0.223749	+	0.974647i	$0.571830\pi$
$678$		0			0
$679$	−3.27265e8	+	3.90019e8i	−1.04542	+	1.24588i
$680$		0			0
$681$	1.19032e8	−	6.75061e8i	0.376895	−	2.13748i
$682$		0			0
$683$		−	2.86637e8i		−	0.899643i	−0.893119	−	0.449821i	$-0.851488\pi$
$683$		−	2.86637e8i		−	0.899643i	0.893119	−	0.449821i	$-0.148512\pi$
$684$		0			0
$685$	2.60522e8			0.810536
$686$		0			0
$687$	2.19277e8	+	3.86644e7i	0.676273	+	0.119245i
$688$		0			0
$689$	−1.98755e8	−	1.66775e8i	−0.607658	−	0.509886i
$690$		0			0
$691$	2.93113e8	+	5.07686e8i	0.888384	+	1.53873i	0.841785	+	0.539812i	$0.181505\pi$
$691$	2.93113e8	+	5.07686e8i	0.888384	+	1.53873i	0.0465987	+	0.998914i	$0.485162\pi$
$692$		0			0
$693$	−5.86919e7	−	2.13621e7i	−0.176351	−	0.0641866i
$694$		0			0
$695$	3.22367e8	−	5.58357e8i	0.960277	−	1.66325i
$696$		0			0
$697$	1.73882e7	−	3.06600e6i	0.0513517	−	0.00905470i
$698$		0			0
$699$	1.94736e8	+	2.32078e8i	0.570185	+	0.679520i
$700$		0			0
$701$	−5.39660e8	+	1.96420e8i	−1.56663	+	0.570207i	−0.972243	−	0.233972i	$-0.924827\pi$
$701$	−5.39660e8	+	1.96420e8i	−1.56663	+	0.570207i	−0.594387	+	0.804179i	$0.702605\pi$
$702$		0			0
$703$	1.02629e8	+	3.80986e7i	0.295396	+	0.109659i
$704$		0			0
$705$	−1.06598e8	−	2.92876e8i	−0.304216	−	0.835826i
$706$		0			0
$707$	5.93375e8	−	4.97900e8i	1.67908	−	1.40891i
$708$		0			0
$709$	9.43513e7	+	5.35093e8i	0.264734	+	1.50138i	0.769792	+	0.638294i	$0.220360\pi$
$709$	9.43513e7	+	5.35093e8i	0.264734	+	1.50138i	−0.505059	+	0.863085i	$0.668529\pi$
$710$		0			0
$711$	4.89992e8	+	2.82897e8i	1.36326	+	0.787081i
$712$		0			0
$713$	3.16494e8	−	8.69559e8i	0.873165	−	2.39900i
$714$		0			0
$715$	4.58738e7	−	2.64853e7i	0.125501	−	0.0724580i
$716$		0			0
$717$	3.41638e8	−	4.07148e8i	0.926849	−	1.10458i
$718$		0			0
$719$	−3.82255e7	+	2.16788e8i	−0.102841	+	0.583241i	0.889219	+	0.457481i	$0.151248\pi$
$719$	−3.82255e7	+	2.16788e8i	−0.102841	+	0.583241i	−0.992061	+	0.125760i	$0.959863\pi$
$720$		0			0
$721$		−	1.63163e8i		−	0.435328i
$722$		0			0
$723$	−9.58269e8			−2.53555
$724$		0			0
$725$	−3.47332e8	−	6.12440e7i	−0.911446	−	0.160713i
$726$		0			0
$727$	3.79027e8	+	3.18041e8i	0.986431	+	0.827714i	0.985047	−	0.172285i	$-0.0551151\pi$
$727$	3.79027e8	+	3.18041e8i	0.986431	+	0.827714i	0.00138376	+	0.999999i	$0.499560\pi$
$728$		0			0
$729$	−1.95917e8	−	3.39339e8i	−0.505697	−	0.875892i
$730$		0			0
$731$	−4.47429e7	−	1.62851e7i	−0.114544	−	0.0416906i
$732$		0			0
$733$	−5.55655e7	+	9.62422e7i	−0.141089	+	0.244373i	−0.927907	−	0.372812i	$-0.878394\pi$
$733$	−5.55655e7	+	9.62422e7i	−0.141089	+	0.244373i	0.786818	+	0.617185i	$0.211727\pi$
$734$		0			0
$735$	1.55859e9	−	2.74822e8i	3.92527	−	0.692132i
$736$		0			0
$737$	4.28879e7	+	5.11118e7i	0.107135	+	0.127679i
$738$		0			0
$739$	−4.19094e8	+	1.52538e8i	−1.03843	+	0.377958i	−0.804285	−	0.594244i	$-0.797452\pi$
$739$	−4.19094e8	+	1.52538e8i	−1.03843	+	0.377958i	−0.234146	+	0.972201i	$0.575229\pi$
$740$		0			0
$741$	1.36760e8	−	3.68401e8i	0.336128	−	0.905454i
$742$		0			0
$743$	−1.19117e8	−	3.27272e8i	−0.290408	−	0.797889i	−0.996007	−	0.0892779i	$-0.971544\pi$
$743$	−1.19117e8	−	3.27272e8i	−0.290408	−	0.797889i	0.705599	−	0.708612i	$-0.250678\pi$
$744$		0			0
$745$	−3.29735e8	+	2.76680e8i	−0.797436	+	0.669128i
$746$		0			0
$747$	1.06016e8	+	6.01248e8i	0.254337	+	1.44242i
$748$		0			0
$749$	−5.92007e8	−	3.41795e8i	−1.40890	−	0.813431i
$750$		0			0
$751$	−1.39635e8	+	3.83644e8i	−0.329667	+	0.905752i	0.658529	+	0.752555i	$0.271179\pi$
$751$	−1.39635e8	+	3.83644e8i	−0.329667	+	0.905752i	−0.988196	+	0.153196i	$0.951043\pi$
$752$		0			0
$753$	−4.94430e8	+	2.85459e8i	−1.15803	+	0.668589i
$754$		0			0
$755$	5.21740e8	−	6.21785e8i	1.21231	−	1.44477i
$756$		0			0
$757$	1.40206e8	−	7.95148e8i	0.323206	−	1.83299i	−0.198789	−	0.980042i	$-0.563701\pi$
$757$	1.40206e8	−	7.95148e8i	0.323206	−	1.83299i	0.521995	−	0.852949i	$-0.325188\pi$
$758$		0			0
$759$		−	1.16132e8i		−	0.265599i
$760$		0			0
$761$	−2.32532e8			−0.527628			−0.263814	−	0.964574i	$-0.584981\pi$
$761$	−2.32532e8			−0.527628			−0.263814	+	0.964574i	$0.584981\pi$
$762$		0			0
$763$	−3.71307e8	−	6.54715e7i	−0.835911	−	0.147394i
$764$		0			0
$765$	−4.80439e7	−	4.03136e7i	−0.107313	−	0.0900466i
$766$		0			0
$767$	−1.37797e8	−	2.38672e8i	−0.305389	−	0.528950i
$768$		0			0
$769$	3.00541e8	+	1.09388e8i	0.660883	+	0.240542i	0.650617	−	0.759406i	$-0.274510\pi$
$769$	3.00541e8	+	1.09388e8i	0.660883	+	0.240542i	0.0102653	+	0.999947i	$0.496732\pi$
$770$		0			0
$771$	−3.48250e8	+	6.03187e8i	−0.759851	+	1.31610i
$772$		0			0
$773$	6.12066e8	−	1.07924e8i	1.32513	−	0.233657i	0.534096	−	0.845424i	$-0.320652\pi$
$773$	6.12066e8	−	1.07924e8i	1.32513	−	0.233657i	0.791038	+	0.611767i	$0.209541\pi$
$774$		0			0
$775$	−1.09722e9	−	1.30761e9i	−2.35716	−	2.80915i
$776$		0			0
$777$	3.14009e8	−	1.14290e8i	0.669389	−	0.243638i
$778$		0			0
$779$	1.62623e8	−	2.77559e8i	0.344010	−	0.587142i
$780$		0			0
$781$	7.77297e6	+	2.13561e7i	0.0163168	+	0.0448299i
$782$		0			0
$783$	1.19495e6	−	1.00268e6i	0.00248922	−	0.00208870i
$784$		0			0
$785$	1.54397e8	+	8.75630e8i	0.319176	+	1.81014i
$786$		0			0
$787$	4.08781e8	+	2.36010e8i	0.838623	+	0.484179i	0.856796	−	0.515656i	$-0.172452\pi$
$787$	4.08781e8	+	2.36010e8i	0.838623	+	0.484179i	−0.0181728	+	0.999835i	$0.505785\pi$
$788$		0			0
$789$	−1.58086e7	+	4.34338e7i	−0.0321857	+	0.0884295i
$790$		0			0
$791$	−1.81353e8	+	1.04704e8i	−0.366434	+	0.211561i
$792$		0			0
$793$	−2.92117e8	+	3.48132e8i	−0.585785	+	0.698111i
$794$		0			0
$795$	−2.61273e8	+	1.48175e9i	−0.519988	+	2.94900i
$796$		0			0
$797$			8.64643e8i			1.70790i	0.520356	+	0.853949i	$0.325799\pi$
$797$			8.64643e8i			1.70790i	−0.520356	+	0.853949i	$0.674201\pi$
$798$		0			0
$799$	−1.35040e7			−0.0264742
$800$		0			0
$801$	−5.85192e8	−	1.03185e8i	−1.13868	−	0.200780i
$802$		0			0
$803$	−481063.	−	403659.i	−0.000929084	−	0.000779594i
$804$		0			0
$805$	1.21428e9	+	2.10319e9i	2.32772	+	4.03172i
$806$		0			0
$807$	1.25724e9	+	4.57598e8i	2.39220	+	0.870689i
$808$		0			0
$809$	−1.70373e8	+	2.95095e8i	−0.321777	+	0.557335i	−0.980855	−	0.194740i	$-0.937614\pi$
$809$	−1.70373e8	+	2.95095e8i	−0.321777	+	0.557335i	0.659078	+	0.752075i	$0.270947\pi$
$810$		0			0
$811$	−5.01868e8	+	8.84928e7i	−0.940863	+	0.165900i	−0.622987	−	0.782232i	$-0.714081\pi$
$811$	−5.01868e8	+	8.84928e7i	−0.940863	+	0.165900i	−0.317877	+	0.948132i	$0.602970\pi$
$812$		0			0
$813$	1.45730e8	+	1.73674e8i	0.271192	+	0.323194i
$814$		0			0
$815$	−1.02065e9	+	3.71488e8i	−1.88541	+	0.686233i
$816$		0			0
$817$	−7.54046e8	+	4.28945e8i	−1.38271	+	0.786567i
$818$		0			0
$819$	−2.05714e8	−	5.65194e8i	−0.374465	−	1.02883i
$820$		0			0
$821$	5.25933e8	−	4.41310e8i	0.950388	−	0.797470i	−0.0289749	−	0.999580i	$-0.509224\pi$
$821$	5.25933e8	−	4.41310e8i	0.950388	−	0.797470i	0.979363	+	0.202110i	$0.0647798\pi$
$822$		0			0
$823$	2.18159e7	+	1.23724e8i	0.0391358	+	0.221950i	0.998103	−	0.0615670i	$-0.0196098\pi$
$823$	2.18159e7	+	1.23724e8i	0.0391358	+	0.221950i	−0.958967	+	0.283517i	$0.908499\pi$
$824$		0			0
$825$	−1.85521e8	−	1.07111e8i	−0.330394	−	0.190753i
$826$		0			0
$827$	−1.36159e8	+	3.74094e8i	−0.240730	+	0.661400i	0.759214	+	0.650841i	$0.225584\pi$
$827$	−1.36159e8	+	3.74094e8i	−0.240730	+	0.661400i	−0.999944	+	0.0105596i	$0.996639\pi$
$828$		0			0
$829$	6.40330e8	−	3.69695e8i	1.12393	−	0.648903i	0.181531	−	0.983385i	$-0.441895\pi$
$829$	6.40330e8	−	3.69695e8i	1.12393	−	0.648903i	0.942402	+	0.334482i	$0.108561\pi$
$830$		0			0
$831$	−1.22490e8	+	1.45978e8i	−0.213451	+	0.254381i
$832$		0			0
$833$	1.19074e7	−	6.75301e7i	0.0206007	−	0.116832i
$834$		0			0
$835$		−	9.76724e8i		−	1.67769i
$836$		0			0
$837$	7.54965e6			0.0128751
$838$		0			0
$839$	−4.17266e8	−	7.35752e7i	−0.706524	−	0.124579i	−0.191170	−	0.981557i	$-0.561228\pi$
$839$	−4.17266e8	−	7.35752e7i	−0.706524	−	0.124579i	−0.515354	+	0.856978i	$0.672339\pi$
$840$		0			0
$841$	3.82165e8	+	3.20674e8i	0.642484	+	0.539108i
$842$		0			0
$843$	−3.86627e8	−	6.69658e8i	−0.645371	−	1.11782i
$844$		0			0
$845$	−5.51302e8	−	2.00657e8i	−0.913733	−	0.332571i
$846$		0			0
$847$	4.78370e8	−	8.28561e8i	0.787252	−	1.36356i
$848$		0			0
$849$	−9.44823e8	+	1.66598e8i	−1.54393	+	0.272236i
$850$		0			0
$851$	2.00257e8	+	2.38657e8i	0.324936	+	0.387244i
$852$		0			0
$853$	8.48581e8	−	3.08858e8i	1.36725	−	0.497637i	0.448959	−	0.893553i	$-0.351795\pi$
$853$	8.48581e8	−	3.08858e8i	1.36725	−	0.497637i	0.918287	+	0.395916i	$0.129573\pi$
$854$		0			0
$855$	−1.12656e9	+	1.91226e8i	−1.80242	+	0.305949i
$856$		0			0
$857$	2.11218e8	+	5.80316e8i	0.335574	+	0.921981i	0.986634	+	0.162955i	$0.0521025\pi$
$857$	2.11218e8	+	5.80316e8i	0.335574	+	0.921981i	−0.651060	+	0.759026i	$0.725675\pi$
$858$		0			0
$859$	−2.03016e8	+	1.70350e8i	−0.320295	+	0.268759i	−0.788732	−	0.614738i	$-0.789262\pi$
$859$	−2.03016e8	+	1.70350e8i	−0.320295	+	0.268759i	0.468437	+	0.883497i	$0.344817\pi$
$860$		0			0
$861$	−1.70514e8	−	9.67034e8i	−0.267147	−	1.51507i
$862$		0			0
$863$	−5.62142e8	−	3.24553e8i	−0.874609	−	0.504956i	−0.00573168	−	0.999984i	$-0.501824\pi$
$863$	−5.62142e8	−	3.24553e8i	−0.874609	−	0.504956i	−0.868877	+	0.495028i	$0.835158\pi$
$864$		0			0
$865$	2.35420e8	−	6.46810e8i	0.363743	−	0.999375i
$866$		0			0
$867$	7.94630e8	−	4.58780e8i	1.21929	−	0.703958i
$868$		0			0
$869$	7.71796e7	−	9.19790e7i	0.117610	−	0.140162i
$870$		0			0
$871$	−1.11572e8	+	6.32758e8i	−0.168850	+	0.957598i
$872$		0			0
$873$		−	6.81742e8i		−	1.02465i
$874$		0			0
$875$	2.53583e9			3.78526
$876$		0			0
$877$	−4.59772e8	−	8.10703e7i	−0.681623	−	0.120188i	−0.177893	−	0.984050i	$-0.556928\pi$
$877$	−4.59772e8	−	8.10703e7i	−0.681623	−	0.120188i	−0.503730	+	0.863861i	$0.668039\pi$
$878$		0			0
$879$	−3.61514e8	−	3.03347e8i	−0.532303	−	0.446655i
$880$		0			0
$881$	2.91422e8	+	5.04758e8i	0.426182	+	0.738169i	0.996530	−	0.0832342i	$-0.0265249\pi$
$881$	2.91422e8	+	5.04758e8i	0.426182	+	0.738169i	−0.570348	+	0.821403i	$0.693192\pi$
$882$		0			0
$883$	3.85224e8	+	1.40210e8i	0.559540	+	0.203656i	0.606280	−	0.795251i	$-0.292661\pi$
$883$	3.85224e8	+	1.40210e8i	0.559540	+	0.203656i	−0.0467402	+	0.998907i	$0.514883\pi$
$884$		0			0
$885$	−7.99100e8	+	1.38408e9i	−1.15285	+	1.99679i
$886$		0			0
$887$	−2.83690e8	+	5.00222e7i	−0.406512	+	0.0716790i	−0.373165	−	0.927765i	$-0.621728\pi$
$887$	−2.83690e8	+	5.00222e7i	−0.406512	+	0.0716790i	−0.0333465	+	0.999444i	$0.510616\pi$
$888$		0			0
$889$	−7.65114e8	−	9.11827e8i	−1.08898	−	1.29780i
$890$		0			0
$891$	−7.72532e7	+	2.81179e7i	−0.109215	+	0.0397511i
$892$		0			0
$893$	−1.59351e8	+	1.87461e8i	−0.223769	+	0.263242i
$894$		0			0
$895$	−7.03077e8	−	1.93169e9i	−0.980694	−	2.69444i
$896$		0			0
$897$	8.56690e8	−	7.18849e8i	1.18699	−	0.996002i
$898$		0			0
$899$	−8.06334e7	−	4.57295e8i	−0.110978	−	0.629386i
$900$		0			0
$901$	5.64573e7	+	3.25956e7i	0.0771873	+	0.0445641i
$902$		0			0
$903$	−9.05687e8	+	2.48835e9i	−1.23003	+	3.37947i
$904$		0			0
$905$	−6.54271e8	+	3.77744e8i	−0.882698	+	0.509626i
$906$		0			0
$907$	2.07578e8	−	2.47382e8i	0.278202	−	0.331548i	−0.608792	−	0.793330i	$-0.708345\pi$
$907$	2.07578e8	−	2.47382e8i	0.278202	−	0.331548i	0.886993	+	0.461782i	$0.152790\pi$
$908$		0			0
$909$	−1.80108e8	+	1.02144e9i	−0.239796	+	1.35995i
$910$		0			0
$911$			1.32564e9i			1.75336i	0.481071	+	0.876682i	$0.340248\pi$
$911$			1.32564e9i			1.75336i	−0.481071	+	0.876682i	$0.659752\pi$
$912$		0			0
$913$	1.29562e8			0.170242
$914$		0			0
$915$	2.59539e9	+	4.57637e8i	3.38797	+	0.597390i
$916$		0			0
$917$	3.10763e8	+	2.60761e8i	0.403015	+	0.338169i
$918$		0			0
$919$	−5.76574e8	−	9.98656e8i	−0.742863	−	1.28668i	−0.951187	−	0.308617i	$-0.900134\pi$
$919$	−5.76574e8	−	9.98656e8i	−0.742863	−	1.28668i	0.208323	−	0.978060i	$-0.433199\pi$
$920$		0			0
$921$	1.55905e9	+	5.67449e8i	1.99564	+	0.726353i
$922$		0			0
$923$	−1.09427e8	+	1.89533e8i	−0.139162	+	0.241035i
$924$		0			0
$925$	5.65957e8	−	9.97935e7i	0.715086	−	0.126089i
$926$		0			0
$927$	1.40436e8	+	1.67365e8i	0.176295	+	0.210100i
$928$		0			0
$929$	−1.01591e9	+	3.69761e8i	−1.26709	+	0.461183i	−0.886142	−	0.463413i	$-0.846625\pi$
$929$	−1.01591e9	+	3.69761e8i	−1.26709	+	0.461183i	−0.380948	+	0.924596i	$0.624402\pi$
$930$		0			0
$931$	−7.96932e8	−	9.62170e8i	−0.987579	−	1.19235i
$932$		0			0
$933$	9.33828e7	+	2.56567e8i	0.114980	+	0.315905i
$934$		0			0
$935$	−1.01956e7	+	8.55516e6i	−0.0124733	+	0.0104663i
$936$		0			0
$937$	−3.61919e6	−	2.05255e7i	−0.00439939	−	0.0249502i	0.982529	−	0.186109i	$-0.0595879\pi$
$937$	−3.61919e6	−	2.05255e7i	−0.00439939	−	0.0249502i	−0.986928	+	0.161159i	$0.948477\pi$
$938$		0			0
$939$	−1.24251e9	−	7.17363e8i	−1.50073	−	0.866448i
$940$		0			0
$941$	2.42217e7	−	6.65485e7i	0.0290693	−	0.0798674i	−0.924309	−	0.381645i	$-0.875358\pi$
$941$	2.42217e7	−	6.65485e7i	0.0290693	−	0.0798674i	0.953378	+	0.301777i	$0.0975800\pi$
$942$		0			0
$943$	7.92838e8	−	4.57745e8i	0.945474	−	0.545870i
$944$		0			0
$945$	−1.27359e7	+	1.51780e7i	−0.0150915	+	0.0179854i
$946$		0			0
$947$	9.41752e6	−	5.34094e7i	0.0110889	−	0.0628880i	−0.978761	−	0.205004i	$-0.934279\pi$
$947$	9.41752e6	−	5.34094e7i	0.0110889	−	0.0628880i	0.989850	+	0.142116i	$0.0453905\pi$
$948$		0			0
$949$		−	6.04737e6i		−	0.00707567i
$950$		0			0
$951$	−2.03687e9			−2.36821
$952$		0			0
$953$	7.17246e8	+	1.26470e8i	0.828685	+	0.146120i	0.571873	−	0.820342i	$-0.306217\pi$
$953$	7.17246e8	+	1.26470e8i	0.828685	+	0.146120i	0.256812	+	0.966461i	$0.417328\pi$
$954$		0			0
$955$	1.16331e9	+	9.76130e8i	1.33562	+	1.12072i
$956$		0			0
$957$	−2.91375e7	−	5.04676e7i	−0.0332443	−	0.0575807i
$958$		0			0
$959$	−5.89907e8	−	2.14709e8i	−0.668848	−	0.243441i
$960$		0			0
$961$	6.79939e8	−	1.17769e9i	0.766126	−	1.32697i
$962$		0			0
$963$	9.01438e8	−	1.58948e8i	1.00939	−	0.177982i
$964$		0			0
$965$	−4.72544e8	−	5.63157e8i	−0.525849	−	0.626682i
$966$		0			0
$967$	9.85630e8	−	3.58740e8i	1.09002	−	0.396735i	0.266392	−	0.963865i	$-0.414168\pi$
$967$	9.85630e8	−	3.58740e8i	1.09002	−	0.396735i	0.823628	+	0.567130i	$0.191946\pi$
$968$		0			0
$969$	−1.77668e7	+	9.71258e7i	−0.0195271	+	0.106749i
$970$		0			0
$971$	9.02259e7	+	2.47894e8i	0.0985539	+	0.270775i	0.979165	−	0.203064i	$-0.0650901\pi$
$971$	9.02259e7	+	2.47894e8i	0.0985539	+	0.270775i	−0.880612	+	0.473839i	$0.842868\pi$
$972$		0			0
$973$	−1.19011e9	+	9.98624e8i	−1.29196	+	1.08409i
$974$		0			0
$975$	−3.58222e8	−	2.03158e9i	−0.386490	−	2.19190i
$976$		0			0
$977$	3.90483e8	+	2.25445e8i	0.418715	+	0.241745i	0.694527	−	0.719466i	$-0.255614\pi$
$977$	3.90483e8	+	2.25445e8i	0.418715	+	0.241745i	−0.275813	+	0.961211i	$0.588947\pi$
$978$		0			0
$979$	−4.31296e7	+	1.18498e8i	−0.0459650	+	0.126288i
$980$		0			0
$981$	4.37221e8	−	2.52430e8i	0.463121	−	0.267383i
$982$		0			0
$983$	8.53375e8	−	1.01701e9i	0.898420	−	1.07069i	−0.0987202	−	0.995115i	$-0.531475\pi$
$983$	8.53375e8	−	1.01701e9i	0.898420	−	1.07069i	0.997140	−	0.0755796i	$-0.0240807\pi$
$984$		0			0
$985$	3.83341e8	−	2.17403e9i	0.401122	−	2.27487i
$986$		0			0
$987$			7.51019e8i			0.781087i
$988$		0			0
$989$	−2.46882e9			−2.55212
$990$		0			0
$991$	5.16249e8	+	9.10287e7i	0.530443	+	0.0935314i	0.432454	−	0.901656i	$-0.357648\pi$
$991$	5.16249e8	+	9.10287e7i	0.530443	+	0.0935314i	0.0979891	+	0.995187i	$0.468759\pi$
$992$		0			0
$993$	−9.01804e8	−	7.56703e8i	−0.921010	−	0.772819i
$994$		0			0
$995$	−1.51690e8	−	2.62735e8i	−0.153989	−	0.266716i
$996$		0			0
$997$	3.56761e8	+	1.29850e8i	0.359991	+	0.131026i	0.515683	−	0.856780i	$-0.327538\pi$
$997$	3.56761e8	+	1.29850e8i	0.359991	+	0.131026i	−0.155692	+	0.987806i	$0.549761\pi$
$998$		0			0
$999$	−1.27087e6	+	2.20122e6i	−0.00127469	+	0.00220784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.33.2	✓	60
19.15	odd	18	inner	76.7.j.a.53.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.2	✓	60	1.1	even	1	trivial
76.7.j.a.53.2	yes	60	19.15	odd	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-37.6573 - 6.64000i) q^{3} +(174.066 + 146.059i) q^{5} +(-273.768 - 474.181i) q^{7} +(688.950 + 250.757i) q^{9} +O(q^{10})\)	\(q+(-37.6573 - 6.64000i) q^{3} +(174.066 + 146.059i) q^{5} +(-273.768 - 474.181i) q^{7} +(688.950 + 250.757i) q^{9} +(77.7943 - 134.744i) q^{11} +(1475.53 - 260.176i) q^{13} +(-5585.03 - 6655.98i) q^{15} +(-353.760 + 128.758i) q^{17} +(-2387.07 + 6430.22i) q^{19} +(7160.82 + 19674.2i) q^{21} +(-14953.0 + 12547.1i) q^{23} +(6252.56 + 35460.0i) q^{25} +(-137.917 - 79.6266i) q^{27} +(-3350.10 + 9204.33i) q^{29} +(-41055.3 + 23703.3i) q^{31} +(-3824.23 + 4557.54i) q^{33} +(21604.4 - 122525. i) q^{35} -15960.4i q^{37} -57292.1 q^{39} +(-46188.1 - 8144.22i) q^{41} +(96887.8 + 81298.5i) q^{43} +(83297.4 + 144275. i) q^{45} +(33707.4 + 12268.5i) q^{47} +(-91073.7 + 157744. i) q^{49} +(14176.6 - 2499.72i) q^{51} +(-111310. - 132654. i) q^{53} +(33221.8 - 12091.8i) q^{55} +(132587. - 226295. i) q^{57} +(-62910.8 - 172846. i) q^{59} +(-232352. + 194967. i) q^{61} +(-69708.4 - 395336. i) q^{63} +(294840. + 170226. i) q^{65} +(-146670. + 402972. i) q^{67} +(646403. - 373201. i) q^{69} +(-93891.2 + 111895. i) q^{71} +(700.874 - 3974.85i) q^{73} -1.37685e6i q^{75} -85190.5 q^{77} +(759991. + 134007. i) q^{79} +(-404768. - 339641. i) q^{81} +(416361. + 721159. i) q^{83} +(-80383.8 - 29257.3i) q^{85} +(187273. - 324366. i) q^{87} +(-798173. + 140739. i) q^{89} +(-527324. - 628440. i) q^{91} +(1.70342e6 - 619995. i) q^{93} +(-1.35470e6 + 770631. i) q^{95} +(-318032. - 873784. i) q^{97} +(87384.3 - 73324.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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