LMFDB - Embedded newform 76.7.j.a.13.8

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			13.8
Character	$\chi$	$=$	76.13
Dual form			76.7.j.a.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.61067 - 26.4051i) q^{3} +(26.4812 + 150.182i) q^{5} +(197.423 - 341.946i) q^{7} +(-46.4181 - 38.9494i) q^{9} +O(q^{10})$	\(q+(9.61067 - 26.4051i) q^{3} +(26.4812 + 150.182i) q^{5} +(197.423 - 341.946i) q^{7} +(-46.4181 - 38.9494i) q^{9} +(403.111 + 698.209i) q^{11} +(674.923 + 1854.34i) q^{13} +(4220.07 + 744.113i) q^{15} +(-722.165 + 605.969i) q^{17} +(6573.76 - 1957.42i) q^{19} +(-7131.76 - 8499.30i) q^{21} +(3876.04 - 21982.1i) q^{23} +(-7170.71 + 2609.92i) q^{25} +(16265.7 - 9391.00i) q^{27} +(6965.80 - 8301.52i) q^{29} +(19159.1 + 11061.5i) q^{31} +(22310.5 - 3933.93i) q^{33} +(56582.2 + 20594.2i) q^{35} +63273.4i q^{37} +55450.4 q^{39} +(24822.9 - 68200.3i) q^{41} +(2093.79 + 11874.4i) q^{43} +(4620.30 - 8002.59i) q^{45} +(-110893. - 93050.5i) q^{47} +(-19127.0 - 33129.0i) q^{49} +(9060.17 + 24892.6i) q^{51} +(23048.9 + 4064.15i) q^{53} +(-94183.6 + 79029.5i) q^{55} +(11492.4 - 192393. i) q^{57} +(-35824.8 - 42694.4i) q^{59} +(-67722.4 + 384073. i) q^{61} +(-22482.6 + 8183.00i) q^{63} +(-260615. + 150466. i) q^{65} +(-142739. + 170110. i) q^{67} +(-543188. - 313610. i) q^{69} +(100843. - 17781.3i) q^{71} +(122731. + 44670.3i) q^{73} +214426. i q^{75} +318333. q^{77} +(-44636.7 + 122638. i) q^{79} +(-99316.8 - 563254. i) q^{81} +(-490002. + 848709. i) q^{83} +(-110129. - 92409.6i) q^{85} +(-152256. - 263716. i) q^{87} +(219248. + 602378. i) q^{89} +(767328. + 135301. i) q^{91} +(476213. - 399590. i) q^{93} +(468050. + 935427. i) q^{95} +(-1.02042e6 - 1.21609e6i) q^{97} +(8483.18 - 48110.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	9.61067	−	26.4051i	0.355951	−	0.977967i	−0.624469	−	0.781049i	$-0.714685\pi$
$3$	9.61067	−	26.4051i	0.355951	−	0.977967i	0.980420	−	0.196917i	$-0.0630931\pi$
$4$		0			0
$5$	26.4812	+	150.182i	0.211849	+	1.20146i	0.886291	+	0.463129i	$0.153273\pi$
$5$	26.4812	+	150.182i	0.211849	+	1.20146i	−0.674442	+	0.738328i	$0.735616\pi$
$6$		0			0
$7$	197.423	−	341.946i	0.575577	−	0.996928i	−0.420402	−	0.907338i	$-0.638111\pi$
$7$	197.423	−	341.946i	0.575577	−	0.996928i	0.995979	−	0.0895901i	$-0.0285557\pi$
$8$		0			0
$9$	−46.4181	−	38.9494i	−0.0636737	−	0.0534286i
$10$		0			0
$11$	403.111	+	698.209i	0.302863	+	0.524575i	0.976783	−	0.214230i	$-0.0687241\pi$
$11$	403.111	+	698.209i	0.302863	+	0.524575i	−0.673920	+	0.738804i	$0.735391\pi$
$12$		0			0
$13$	674.923	+	1854.34i	0.307202	+	0.844031i	0.993199	+	0.116427i	$0.0371440\pi$
$13$	674.923	+	1854.34i	0.307202	+	0.844031i	−0.685997	+	0.727604i	$0.740634\pi$
$14$		0			0
$15$	4220.07	+	744.113i	1.25039	+	0.220478i
$16$		0			0
$17$	−722.165	+	605.969i	−0.146991	+	0.123340i	−0.713318	−	0.700841i	$-0.752808\pi$
$17$	−722.165	+	605.969i	−0.146991	+	0.123340i	0.566327	+	0.824181i	$0.308364\pi$
$18$		0			0
$19$	6573.76	−	1957.42i	0.958414	−	0.285380i
$19$	6573.76	−	1957.42i	0.958414	−	0.285380i
$20$		0			0
$21$	−7131.76	−	8499.30i	−0.770086	−	0.917752i
$22$		0			0
$23$	3876.04	−	21982.1i	0.318570	−	1.80670i	−0.232898	−	0.972501i	$-0.574821\pi$
$23$	3876.04	−	21982.1i	0.318570	−	1.80670i	0.551467	−	0.834196i	$-0.314068\pi$
$24$		0			0
$25$	−7170.71	+	2609.92i	−0.458925	+	0.167035i
$26$		0			0
$27$	16265.7	−	9391.00i	0.826383	−	0.477112i
$28$		0			0
$29$	6965.80	−	8301.52i	0.285612	−	0.340380i	−0.604094	−	0.796913i	$-0.706465\pi$
$29$	6965.80	−	8301.52i	0.285612	−	0.340380i	0.889706	+	0.456534i	$0.150909\pi$
$30$		0			0
$31$	19159.1	+	11061.5i	0.643119	+	0.371305i	0.785815	−	0.618462i	$-0.212244\pi$
$31$	19159.1	+	11061.5i	0.643119	+	0.371305i	−0.142696	+	0.989767i	$0.545577\pi$
$32$		0			0
$33$	22310.5	−	3933.93i	0.620821	−	0.109468i
$34$		0			0
$35$	56582.2	+	20594.2i	1.31970	+	0.480332i
$36$		0			0
$37$			63273.4i			1.24915i	0.780963	+	0.624577i	$0.214729\pi$
$37$			63273.4i			1.24915i	−0.780963	+	0.624577i	$0.785271\pi$
$38$		0			0
$39$	55450.4			0.934783
$40$		0			0
$41$	24822.9	−	68200.3i	0.360164	−	0.989543i	−0.618807	−	0.785543i	$-0.712384\pi$
$41$	24822.9	−	68200.3i	0.360164	−	0.989543i	0.978971	−	0.204000i	$-0.0653942\pi$
$42$		0			0
$43$	2093.79	+	11874.4i	0.0263346	+	0.149351i	0.995140	−	0.0984728i	$-0.0313957\pi$
$43$	2093.79	+	11874.4i	0.0263346	+	0.149351i	−0.968805	+	0.247824i	$0.920285\pi$
$44$		0			0
$45$	4620.30	−	8002.59i	0.0507029	−	0.0878200i
$46$		0			0
$47$	−110893.	−	93050.5i	−1.06810	−	0.896242i	−0.0732206	−	0.997316i	$-0.523328\pi$
$47$	−110893.	−	93050.5i	−1.06810	−	0.896242i	−0.994879	+	0.101074i	$0.967772\pi$
$48$		0			0
$49$	−19127.0	−	33129.0i	−0.162577	−	0.281592i
$50$		0			0
$51$	9060.17	+	24892.6i	0.0683008	+	0.187655i
$52$		0			0
$53$	23048.9	+	4064.15i	0.154819	+	0.0272987i	0.250520	−	0.968111i	$-0.419398\pi$
$53$	23048.9	+	4064.15i	0.154819	+	0.0272987i	−0.0957016	+	0.995410i	$0.530509\pi$
$54$		0			0
$55$	−94183.6	+	79029.5i	−0.566092	+	0.475008i
$56$		0			0
$57$	11492.4	−	192393.i	0.0620562	−	1.03888i
$58$		0			0
$59$	−35824.8	−	42694.4i	−0.174433	−	0.207881i	0.671744	−	0.740784i	$-0.265546\pi$
$59$	−35824.8	−	42694.4i	−0.174433	−	0.207881i	−0.846176	+	0.532903i	$0.821101\pi$
$60$		0			0
$61$	−67722.4	+	384073.i	−0.298362	+	1.69209i	0.354855	+	0.934921i	$0.384530\pi$
$61$	−67722.4	+	384073.i	−0.298362	+	1.69209i	−0.653216	+	0.757171i	$0.726581\pi$
$62$		0			0
$63$	−22482.6	+	8183.00i	−0.0899135	+	0.0327258i
$64$		0			0
$65$	−260615.	+	150466.i	−0.948986	+	0.547897i
$66$		0			0
$67$	−142739.	+	170110.i	−0.474591	+	0.565595i	−0.949229	−	0.314586i	$-0.898134\pi$
$67$	−142739.	+	170110.i	−0.474591	+	0.565595i	0.474638	+	0.880181i	$0.342579\pi$
$68$		0			0
$69$	−543188.	−	313610.i	−1.65350	−	0.954646i
$70$		0			0
$71$	100843.	−	17781.3i	0.281753	−	0.0496807i	−0.0309857	−	0.999520i	$-0.509865\pi$
$71$	100843.	−	17781.3i	0.281753	−	0.0496807i	0.312739	+	0.949839i	$0.398754\pi$
$72$		0			0
$73$	122731.	+	44670.3i	0.315489	+	0.114829i	0.494911	−	0.868944i	$-0.335201\pi$
$73$	122731.	+	44670.3i	0.315489	+	0.114829i	−0.179422	+	0.983772i	$0.557423\pi$
$74$		0			0
$75$			214426.i			0.508270i
$76$		0			0
$77$	318333.			0.697284
$78$		0			0
$79$	−44636.7	+	122638.i	−0.0905337	+	0.248739i	−0.976693	−	0.214642i	$-0.931142\pi$
$79$	−44636.7	+	122638.i	−0.0905337	+	0.248739i	0.886159	+	0.463381i	$0.153364\pi$
$80$		0			0
$81$	−99316.8	−	563254.i	−0.186882	−	1.05986i
$82$		0			0
$83$	−490002.	+	848709.i	−0.856967	+	1.48431i	0.0178420	+	0.999841i	$0.494320\pi$
$83$	−490002.	+	848709.i	−0.856967	+	1.48431i	−0.874809	+	0.484469i	$0.839013\pi$
$84$		0			0
$85$	−110129.	−	92409.6i	−0.179327	−	0.150474i
$86$		0			0
$87$	−152256.	−	263716.i	−0.231216	−	0.400478i
$88$		0			0
$89$	219248.	+	602378.i	0.311003	+	0.854475i	0.992455	+	0.122611i	$0.0391269\pi$
$89$	219248.	+	602378.i	0.311003	+	0.854475i	−0.681451	+	0.731863i	$0.738651\pi$
$90$		0			0
$91$	767328.	+	135301.i	1.01826	+	0.179546i
$92$		0			0
$93$	476213.	−	399590.i	0.592042	−	0.496782i
$94$		0			0
$95$	468050.	+	935427.i	0.545911	+	1.09104i
$96$		0			0
$97$	−1.02042e6	−	1.21609e6i	−1.11806	−	1.33245i	−0.937142	−	0.348948i	$-0.886539\pi$
$97$	−1.02042e6	−	1.21609e6i	−1.11806	−	1.33245i	−0.180913	−	0.983499i	$-0.557905\pi$
$98$		0			0
$99$	8483.18	−	48110.5i	0.00874285	−	0.0495832i
$100$		0			0
$101$	76505.6	−	27845.7i	0.0742555	−	0.0270268i	−0.304625	−	0.952472i	$-0.598531\pi$
$101$	76505.6	−	27845.7i	0.0742555	−	0.0270268i	0.378881	+	0.925445i	$0.376309\pi$
$102$		0			0
$103$	−1.21817e6	+	703313.i	−1.11480	+	0.643631i	−0.940069	−	0.340984i	$-0.889240\pi$
$103$	−1.21817e6	+	703313.i	−1.11480	+	0.643631i	−0.174733	+	0.984616i	$0.555906\pi$
$104$		0			0
$105$	1.08759e6	−	1.29613e6i	0.939497	−	1.11965i
$106$		0			0
$107$	−1.71778e6	−	991759.i	−1.40222	−	0.809571i	−0.407598	−	0.913162i	$-0.633633\pi$
$107$	−1.71778e6	−	991759.i	−1.40222	−	0.809571i	−0.994620	+	0.103591i	$0.966967\pi$
$108$		0			0
$109$	365117.	−	64380.0i	0.281937	−	0.0497131i	−0.0308913	−	0.999523i	$-0.509835\pi$
$109$	365117.	−	64380.0i	0.281937	−	0.0497131i	0.312829	+	0.949810i	$0.398723\pi$
$110$		0			0
$111$	1.67074e6	+	608100.i	1.22163	+	0.444638i
$112$		0			0
$113$		−	1.51843e6i		−	1.05235i	−0.850377	−	0.526174i	$-0.823626\pi$
$113$		−	1.51843e6i		−	1.05235i	0.850377	−	0.526174i	$-0.176374\pi$
$114$		0			0
$115$	3.40396e6			2.23816
$116$		0			0
$117$	40896.6	−	112363.i	0.0255347	−	0.0701559i
$118$		0			0
$119$	64636.9	+	366574.i	0.0383565	+	0.217531i
$120$		0			0
$121$	560783.	−	971305.i	0.316548	−	0.548276i
$122$		0			0
$123$	−1.56227e6	−	1.31090e6i	−0.839539	−	0.704457i
$124$		0			0
$125$	609545.	+	1.05576e6i	0.312087	+	0.540551i
$126$		0			0
$127$	944399.	+	2.59472e6i	0.461046	+	1.26671i	0.924700	+	0.380697i	$0.124316\pi$
$127$	944399.	+	2.59472e6i	0.461046	+	1.26671i	−0.463654	+	0.886017i	$0.653462\pi$
$128$		0			0
$129$	333669.	+	58834.8i	0.155434	+	0.0274072i
$130$		0			0
$131$	1.29984e6	−	1.09069e6i	0.578197	−	0.485165i	−0.306158	−	0.951981i	$-0.599043\pi$
$131$	1.29984e6	−	1.09069e6i	0.578197	−	0.485165i	0.884354	+	0.466816i	$0.154599\pi$
$132$		0			0
$133$	628478.	−	2.63431e6i	0.267138	−	1.11973i
$134$		0			0
$135$	1.84109e6	+	2.19413e6i	0.748299	+	0.891787i
$136$		0			0
$137$	11429.8	−	64821.8i	0.00444506	−	0.0252092i	−0.982505	−	0.186239i	$-0.940370\pi$
$137$	11429.8	−	64821.8i	0.00444506	−	0.0252092i	0.986950	+	0.161029i	$0.0514814\pi$
$138$		0			0
$139$	1.00228e6	−	364798.i	0.373201	−	0.135834i	−0.148609	−	0.988896i	$-0.547479\pi$
$139$	1.00228e6	−	364798.i	0.373201	−	0.135834i	0.521809	+	0.853062i	$0.325257\pi$
$140$		0			0
$141$	−3.52277e6	+	2.03387e6i	−1.25669	+	0.725548i
$142$		0			0
$143$	−1.02264e6	+	1.21874e6i	−0.349717	+	0.416776i
$144$		0			0
$145$	1.43120e6	+	826305.i	0.469458	+	0.271042i
$146$		0			0
$147$	−1.05860e6	+	186659.i	−0.333257	+	0.0587622i
$148$		0			0
$149$	680757.	+	247775.i	0.205794	+	0.0749030i	0.442861	−	0.896590i	$-0.353964\pi$
$149$	680757.	+	247775.i	0.205794	+	0.0749030i	−0.237066	+	0.971493i	$0.576186\pi$
$150$		0			0
$151$			58611.7i			0.0170237i	0.999964	+	0.00851185i	$0.00270944\pi$
$151$			58611.7i			0.0170237i	−0.999964	+	0.00851185i	$0.997291\pi$
$152$		0			0
$153$	57123.7			0.0159493
$154$		0			0
$155$	−1.15389e6	+	3.17028e6i	−0.309862	+	0.851340i
$156$		0			0
$157$	202162.	+	1.14652e6i	0.0522396	+	0.296265i	0.999723	−	0.0235398i	$-0.00749366\pi$
$157$	202162.	+	1.14652e6i	0.0522396	+	0.296265i	−0.947483	+	0.319805i	$0.896383\pi$
$158$		0			0
$159$	328830.	−	569550.i	0.0818050	−	0.141690i
$160$		0			0
$161$	−6.75148e6	−	5.66516e6i	−1.61779	−	1.35748i
$162$		0			0
$163$	−3.90764e6	−	6.76822e6i	−0.902301	−	1.56283i	−0.824500	−	0.565862i	$-0.808544\pi$
$163$	−3.90764e6	−	6.76822e6i	−0.902301	−	1.56283i	−0.0778007	−	0.996969i	$-0.524790\pi$
$164$		0			0
$165$	1.18161e6	+	3.24645e6i	0.263041	+	0.722699i
$166$		0			0
$167$	−2.69691e6	−	475538.i	−0.579051	−	0.102102i	−0.123551	−	0.992338i	$-0.539428\pi$
$167$	−2.69691e6	−	475538.i	−0.579051	−	0.102102i	−0.455500	+	0.890236i	$0.650539\pi$
$168$		0			0
$169$	714511.	−	599546.i	0.148030	−	0.124212i
$170$		0			0
$171$	−381382.	−	165185.i	−0.0762732	−	0.0330355i
$172$		0			0
$173$	−4.92508e6	−	5.86948e6i	−0.951207	−	1.13360i	−0.990928	−	0.134394i	$-0.957091\pi$
$173$	−4.92508e6	−	5.86948e6i	−0.951207	−	1.13360i	0.0397206	−	0.999211i	$-0.487353\pi$
$174$		0			0
$175$	−523207.	+	2.96726e6i	−0.0976247	+	0.553657i
$176$		0			0
$177$	−1.47165e6	+	535637.i	−0.265390	+	0.0965941i
$178$		0			0
$179$	−5.15677e6	+	2.97726e6i	−0.899123	+	0.519109i	−0.876915	−	0.480645i	$-0.840403\pi$
$179$	−5.15677e6	+	2.97726e6i	−0.899123	+	0.519109i	−0.0222073	+	0.999753i	$0.507069\pi$
$180$		0			0
$181$	−3.04070e6	+	3.62376e6i	−0.512787	+	0.611116i	−0.958860	−	0.283881i	$-0.908378\pi$
$181$	−3.04070e6	+	3.62376e6i	−0.512787	+	0.611116i	0.446072	+	0.894997i	$0.352822\pi$
$182$		0			0
$183$	9.49063e6	+	5.47942e6i	1.54861	+	0.894090i
$184$		0			0
$185$	−9.50254e6	+	1.67555e6i	−1.50081	+	0.264632i
$186$		0			0
$187$	−714206.	−	259950.i	−0.109219	−	0.0397525i
$188$		0			0
$189$		−	7.41599e6i		−	1.09846i
$190$		0			0
$191$	5.83569e6			0.837514			0.418757	−	0.908098i	$-0.362466\pi$
$191$	5.83569e6			0.837514			0.418757	+	0.908098i	$0.362466\pi$
$192$		0			0
$193$	−4.84465e6	+	1.33106e7i	−0.673893	+	1.85150i	−0.175686	+	0.984446i	$0.556214\pi$
$193$	−4.84465e6	+	1.33106e7i	−0.673893	+	1.85150i	−0.498207	+	0.867058i	$0.666008\pi$
$194$		0			0
$195$	1.46839e6	+	8.32765e6i	0.198033	+	1.12310i
$196$		0			0
$197$	4.72438e6	−	8.18286e6i	0.617940	−	1.07030i	−0.371921	−	0.928264i	$-0.621301\pi$
$197$	4.72438e6	−	8.18286e6i	0.617940	−	1.07030i	0.989861	−	0.142039i	$-0.0453657\pi$
$198$		0			0
$199$	5.54781e6	+	4.65516e6i	0.703983	+	0.590712i	0.922904	−	0.385031i	$-0.125809\pi$
$199$	5.54781e6	+	4.65516e6i	0.703983	+	0.590712i	−0.218921	+	0.975743i	$0.570254\pi$
$200$		0			0
$201$	3.11995e6	+	5.40392e6i	0.384202	+	0.665458i
$202$		0			0
$203$	−1.46347e6	−	4.02084e6i	−0.174942	−	0.480650i
$204$		0			0
$205$	1.08998e7	+	1.92193e6i	1.26519	+	0.223088i
$206$		0			0
$207$	−1.03611e6	+	869398.i	−0.116814	+	0.0980184i
$208$		0			0
$209$	4.01665e6	+	3.80080e6i	0.439972	+	0.416329i
$210$		0			0
$211$	−7.68456e6	−	9.15810e6i	−0.818034	−	0.974895i	0.181930	−	0.983311i	$-0.441765\pi$
$211$	−7.68456e6	−	9.15810e6i	−0.818034	−	0.974895i	−0.999965	+	0.00841610i	$0.997321\pi$
$212$		0			0
$213$	499649.	−	2.83365e6i	0.0517042	−	0.293229i
$214$		0			0
$215$	−1.72788e6	+	628898.i	−0.173860	+	0.0632798i
$216$		0			0
$217$	7.56490e6	−	4.36760e6i	0.740328	−	0.427429i
$218$		0			0
$219$	2.35905e6	−	2.81140e6i	0.224597	−	0.267664i
$220$		0			0
$221$	−1.61108e6	−	930155.i	−0.149259	−	0.0861744i
$222$		0			0
$223$	−1.42826e7	+	2.51841e6i	−1.28793	+	0.227097i	−0.775345	−	0.631538i	$-0.782424\pi$
$223$	−1.42826e7	+	2.51841e6i	−1.28793	+	0.227097i	−0.512587	+	0.858635i	$0.671313\pi$
$224$		0			0
$225$	434506.	+	158147.i	0.0381459	+	0.0138840i
$226$		0			0
$227$		−	1.61867e7i		−	1.38383i	−0.721980	−	0.691914i	$-0.756768\pi$
$227$		−	1.61867e7i		−	1.38383i	0.721980	−	0.691914i	$-0.243232\pi$
$228$		0			0
$229$	4.21678e6			0.351135			0.175568	−	0.984467i	$-0.443824\pi$
$229$	4.21678e6			0.351135			0.175568	+	0.984467i	$0.443824\pi$
$230$		0			0
$231$	3.05940e6	−	8.40563e6i	0.248199	−	0.681921i
$232$		0			0
$233$	−644840.	−	3.65707e6i	−0.0509782	−	0.289112i	0.948652	−	0.316323i	$-0.102448\pi$
$233$	−644840.	−	3.65707e6i	−0.0509782	−	0.289112i	−0.999630	+	0.0272114i	$0.991337\pi$
$234$		0			0
$235$	1.10379e7	−	1.91183e7i	0.850520	−	1.47314i
$236$		0			0
$237$	2.80929e6	+	2.35727e6i	0.211033	+	0.177078i
$238$		0			0
$239$	−2.49683e6	−	4.32464e6i	−0.182892	−	0.316779i	0.759972	−	0.649956i	$-0.225213\pi$
$239$	−2.49683e6	−	4.32464e6i	−0.182892	−	0.316779i	−0.942864	+	0.333177i	$0.891879\pi$
$240$		0			0
$241$	−2.75072e6	−	7.55753e6i	−0.196515	−	0.539919i	0.801823	−	0.597562i	$-0.203864\pi$
$241$	−2.75072e6	−	7.55753e6i	−0.196515	−	0.539919i	−0.998337	+	0.0576427i	$0.981642\pi$
$242$		0			0
$243$	−2.34320e6	−	413170.i	−0.163302	−	0.0287945i
$244$		0			0
$245$	4.46887e6	−	3.74983e6i	0.303878	−	0.254984i
$246$		0			0
$247$	8.06650e6	+	1.08689e7i	0.535296	+	0.721262i
$248$		0			0
$249$	1.77010e7	+	2.10952e7i	1.14657	+	1.36643i
$250$		0			0
$251$	−3.79221e6	+	2.15067e7i	−0.239812	+	1.36004i	0.592427	+	0.805624i	$0.298170\pi$
$251$	−3.79221e6	+	2.15067e7i	−0.239812	+	1.36004i	−0.832239	+	0.554417i	$0.812941\pi$
$252$		0			0
$253$	1.69106e7	−	6.15494e6i	1.04423	−	0.380069i
$254$		0			0
$255$	−3.49850e6	+	2.01986e6i	−0.210990	+	0.121815i
$256$		0			0
$257$	−8.92917e6	+	1.06414e7i	−0.526031	+	0.626900i	−0.961996	−	0.273064i	$-0.911963\pi$
$257$	−8.92917e6	+	1.06414e7i	−0.526031	+	0.626900i	0.435965	+	0.899964i	$0.356407\pi$
$258$		0			0
$259$	2.16361e7	+	1.24916e7i	1.24532	+	0.718984i
$260$		0			0
$261$	−646679.	+	114027.i	−0.0363720	+	0.00641336i
$262$		0			0
$263$	−2.44268e7	−	8.89064e6i	−1.34277	−	0.488727i	−0.432083	−	0.901834i	$-0.642221\pi$
$263$	−2.44268e7	−	8.89064e6i	−1.34277	−	0.488727i	−0.910682	+	0.413107i	$0.864443\pi$
$264$		0			0
$265$			3.56916e6i			0.191791i
$266$		0			0
$267$	1.80130e7			0.946350
$268$		0			0
$269$	2.76324e6	−	7.59193e6i	0.141958	−	0.390028i	−0.848255	−	0.529588i	$-0.822347\pi$
$269$	2.76324e6	−	7.59193e6i	0.141958	−	0.390028i	0.990214	+	0.139560i	$0.0445688\pi$
$270$		0			0
$271$	−6.07065e6	−	3.44283e7i	−0.305019	−	1.72985i	−0.623415	−	0.781891i	$-0.714255\pi$
$271$	−6.07065e6	−	3.44283e7i	−0.305019	−	1.72985i	0.318395	−	0.947958i	$-0.396856\pi$
$272$		0			0
$273$	1.09472e7	−	1.89611e7i	0.538039	−	0.931911i
$274$		0			0
$275$	−4.71286e6	−	3.95456e6i	−0.226614	−	0.190152i
$276$		0			0
$277$	1.40991e7	+	2.44203e7i	0.663364	+	1.14898i	0.979726	+	0.200341i	$0.0642051\pi$
$277$	1.40991e7	+	2.44203e7i	0.663364	+	1.14898i	−0.316362	+	0.948638i	$0.602462\pi$
$278$		0			0
$279$	−458491.	−	1.25969e6i	−0.0211115	−	0.0580032i
$280$		0			0
$281$	−1.54569e7	−	2.72546e6i	−0.696630	−	0.122835i	−0.185891	−	0.982570i	$-0.559517\pi$
$281$	−1.54569e7	−	2.72546e6i	−0.696630	−	0.122835i	−0.510739	+	0.859736i	$0.670628\pi$
$282$		0			0
$283$	−1.54762e7	+	1.29861e7i	−0.682818	+	0.572952i	−0.916828	−	0.399282i	$-0.869260\pi$
$283$	−1.54762e7	+	1.29861e7i	−0.682818	+	0.572952i	0.234010	+	0.972234i	$0.424815\pi$
$284$		0			0
$285$	2.91983e7	−	3.36884e6i	1.26131	−	0.145528i
$286$		0			0
$287$	−1.84202e7	−	2.19524e7i	−0.779201	−	0.928616i
$288$		0			0
$289$	−4.03712e6	+	2.28956e7i	−0.167255	+	0.948548i
$290$		0			0
$291$	−4.19178e7	+	1.52568e7i	−1.70106	+	0.619136i
$292$		0			0
$293$	−3.77132e7	+	2.17737e7i	−1.49931	+	0.865625i	−1.00000		0.000800815i	$-0.999745\pi$
$293$	−3.77132e7	+	2.17737e7i	−1.49931	+	0.865625i	−0.499306	+	0.866426i	$0.666412\pi$
$294$		0			0
$295$	5.46324e6	−	6.51084e6i	0.212806	−	0.253613i
$296$		0			0
$297$	1.31138e7	+	7.57124e6i	0.500562	+	0.289000i
$298$		0			0
$299$	4.33782e7	−	7.64875e6i	1.62277	−	0.286139i
$300$		0			0
$301$	4.47378e6	+	1.62832e6i	0.164050	+	0.0597092i
$302$		0			0
$303$		−	2.28775e6i		−	0.0822397i
$304$		0			0
$305$	−5.94742e7			−2.09618
$306$		0			0
$307$	5.34301e6	−	1.46798e7i	0.184659	−	0.507347i	−0.812475	−	0.582996i	$-0.801880\pi$
$307$	5.34301e6	−	1.46798e7i	0.184659	−	0.507347i	0.997135	+	0.0756485i	$0.0241027\pi$
$308$		0			0
$309$	6.86359e6	+	3.89253e7i	0.232635	+	1.31934i
$310$		0			0
$311$	−187666.	+	325047.i	−0.00623885	+	0.0108060i	−0.869128	−	0.494587i	$-0.835319\pi$
$311$	−187666.	+	325047.i	−0.00623885	+	0.0108060i	0.862889	+	0.505393i	$0.168653\pi$
$312$		0			0
$313$	−269242.	−	225921.i	−0.00878032	−	0.00736756i	0.638387	−	0.769716i	$-0.279602\pi$
$313$	−269242.	−	225921.i	−0.00878032	−	0.00736756i	−0.647167	+	0.762348i	$0.724046\pi$
$314$		0			0
$315$	−1.82431e6	−	3.15979e6i	−0.0583668	−	0.101094i
$316$		0			0
$317$	−5.78808e6	−	1.59026e7i	−0.181701	−	0.499219i	0.815084	−	0.579343i	$-0.196691\pi$
$317$	−5.78808e6	−	1.59026e7i	−0.181701	−	0.499219i	−0.996785	+	0.0801237i	$0.974468\pi$
$318$		0			0
$319$	8.60419e6	+	1.51715e6i	0.265056	+	0.0467366i
$320$		0			0
$321$	−4.26965e7	+	3.58266e7i	−1.29085	+	1.08315i
$322$		0			0
$323$	−3.56121e6	+	5.39708e6i	−0.105679	+	0.160159i
$324$		0			0
$325$	−9.67935e6	−	1.15354e7i	−0.281966	−	0.336033i
$326$		0			0
$327$	1.80906e6	−	1.02597e7i	0.0517380	−	0.293421i
$328$		0			0
$329$	−5.37111e7	+	1.95493e7i	−1.50826	+	0.548962i
$330$		0			0
$331$	1.66583e7	−	9.61765e6i	0.459352	−	0.265207i	−0.252420	−	0.967618i	$-0.581226\pi$
$331$	1.66583e7	−	9.61765e6i	0.459352	−	0.265207i	0.711772	+	0.702411i	$0.247893\pi$
$332$		0			0
$333$	2.46446e6	−	2.93703e6i	0.0667406	−	0.0795383i
$334$		0			0
$335$	−2.93274e7	−	1.69322e7i	−0.780080	−	0.450379i
$336$		0			0
$337$	−3.42452e7	+	6.03835e6i	−0.894766	+	0.157771i	−0.602079	−	0.798437i	$-0.705661\pi$
$337$	−3.42452e7	+	6.03835e6i	−0.894766	+	0.157771i	−0.292687	+	0.956208i	$0.594550\pi$
$338$		0			0
$339$	−4.00943e7	−	1.45931e7i	−1.02916	−	0.374584i
$340$		0			0
$341$			1.78361e7i			0.449818i
$342$		0			0
$343$	3.13487e7			0.776851
$344$		0			0
$345$	3.27143e7	−	8.98819e7i	0.796674	−	2.18884i
$346$		0			0
$347$	1.54383e6	+	8.75552e6i	0.0369498	+	0.209553i	0.997693	−	0.0678862i	$-0.0216255\pi$
$347$	1.54383e6	+	8.75552e6i	0.0369498	+	0.209553i	−0.960743	+	0.277439i	$0.910514\pi$
$348$		0			0
$349$	−2.45519e7	+	4.25251e7i	−0.577575	+	1.00039i	0.418181	+	0.908363i	$0.362668\pi$
$349$	−2.45519e7	+	4.25251e7i	−0.577575	+	1.00039i	−0.995757	+	0.0920259i	$0.970666\pi$
$350$		0			0
$351$	2.83922e7	+	2.38239e7i	0.656564	+	0.550923i
$352$		0			0
$353$	9.50131e6	+	1.64567e7i	0.216003	+	0.374128i	0.953582	−	0.301132i	$-0.0973646\pi$
$353$	9.50131e6	+	1.64567e7i	0.216003	+	0.374128i	−0.737580	+	0.675260i	$0.764031\pi$
$354$		0			0
$355$	5.34086e6	+	1.46739e7i	0.119378	+	0.327990i
$356$		0			0
$357$	1.03006e7	+	1.81628e6i	0.226391	+	0.0399188i
$358$		0			0
$359$	4.94956e7	−	4.15317e7i	1.06975	−	0.897628i	0.0747220	−	0.997204i	$-0.476193\pi$
$359$	4.94956e7	−	4.15317e7i	1.06975	−	0.897628i	0.995030	+	0.0995759i	$0.0317486\pi$
$360$		0			0
$361$	3.93829e7	−	2.57353e7i	0.837117	−	0.547025i
$362$		0			0
$363$	−2.02579e7	−	2.41424e7i	−0.423521	−	0.504732i
$364$		0			0
$365$	−3.45863e6	+	1.96149e7i	−0.0711255	+	0.403373i
$366$		0			0
$367$	2.93940e6	−	1.06985e6i	0.0594649	−	0.0216434i	−0.312116	−	0.950044i	$-0.601038\pi$
$367$	2.93940e6	−	1.06985e6i	0.0594649	−	0.0216434i	0.371581	+	0.928400i	$0.378816\pi$
$368$		0			0
$369$	−3.80859e6	+	2.19889e6i	−0.0758028	+	0.0437648i
$370$		0			0
$371$	5.94010e6	−	7.07914e6i	0.116325	−	0.138630i
$372$		0			0
$373$	9.02387e6	+	5.20994e6i	0.173887	+	0.100394i	0.584417	−	0.811453i	$-0.301323\pi$
$373$	9.02387e6	+	5.20994e6i	0.173887	+	0.100394i	−0.410531	+	0.911847i	$0.634656\pi$
$374$		0			0
$375$	3.37357e7	−	5.94851e6i	0.639728	−	0.112801i
$376$		0			0
$377$	2.00952e7	+	7.31405e6i	0.375032	+	0.136500i
$378$		0			0
$379$			7.68127e7i			1.41096i	0.708729	+	0.705481i	$0.249269\pi$
$379$			7.68127e7i			1.41096i	−0.708729	+	0.705481i	$0.750731\pi$
$380$		0			0
$381$	7.75900e7			1.40291
$382$		0			0
$383$	−4.51356e6	+	1.24009e7i	−0.0803384	+	0.220728i	−0.973358	−	0.229289i	$-0.926360\pi$
$383$	−4.51356e6	+	1.24009e7i	−0.0803384	+	0.220728i	0.893020	+	0.450017i	$0.148582\pi$
$384$		0			0
$385$	8.42983e6	+	4.78080e7i	0.147719	+	0.837757i
$386$		0			0
$387$	365313.	−	632741.i	0.00630279	−	0.0109167i
$388$		0			0
$389$	5.02447e7	+	4.21603e7i	0.853575	+	0.716234i	0.960574	−	0.278025i	$-0.0896797\pi$
$389$	5.02447e7	+	4.21603e7i	0.853575	+	0.716234i	−0.106999	+	0.994259i	$0.534124\pi$
$390$		0			0
$391$	1.05213e7	+	1.82235e7i	0.176011	+	0.304860i
$392$		0			0
$393$	−1.63076e7	−	4.48047e7i	−0.268665	−	0.738152i
$394$		0			0
$395$	−1.96001e7	−	3.45602e6i	−0.318029	−	0.0560771i
$396$		0			0
$397$	9.25176e7	−	7.76315e7i	1.47861	−	1.24070i	0.570951	−	0.820984i	$-0.306575\pi$
$397$	9.25176e7	−	7.76315e7i	1.47861	−	1.24070i	0.907656	−	0.419714i	$-0.137870\pi$
$398$		0			0
$399$	−6.35192e7	−	4.19126e7i	−0.999969	−	0.659820i
$400$		0			0
$401$	−4.13892e7	−	4.93257e7i	−0.641880	−	0.764963i	0.342786	−	0.939414i	$-0.388630\pi$
$401$	−4.13892e7	−	4.93257e7i	−0.641880	−	0.764963i	−0.984666	+	0.174450i	$0.944185\pi$
$402$		0			0
$403$	−7.58086e6	+	4.29932e7i	−0.115825	+	0.656877i
$404$		0			0
$405$	8.19606e7	−	2.98312e7i	1.23379	−	0.449061i
$406$		0			0
$407$	−4.41781e7	+	2.55062e7i	−0.655275	+	0.378323i
$408$		0			0
$409$	5.82871e7	−	6.94639e7i	0.851928	−	1.01529i	−0.147727	−	0.989028i	$-0.547196\pi$
$409$	5.82871e7	−	6.94639e7i	0.851928	−	1.01529i	0.999655	−	0.0262600i	$-0.00835978\pi$
$410$		0			0
$411$	−1.60178e6	−	924787.i	−0.0230715	−	0.0133204i
$412$		0			0
$413$	−2.16718e7	+	3.82133e6i	−0.307642	+	0.0542455i
$414$		0			0
$415$	−1.40437e8	−	5.11148e7i	−1.96488	−	0.715158i
$416$		0			0
$417$		−	2.99711e7i		−	0.413328i
$418$		0			0
$419$	−1.67979e7			−0.228356			−0.114178	−	0.993460i	$-0.536423\pi$
$419$	−1.67979e7			−0.228356			−0.114178	+	0.993460i	$0.536423\pi$
$420$		0			0
$421$	4.37748e7	−	1.20270e8i	0.586648	−	1.61180i	−0.189941	−	0.981796i	$-0.560830\pi$
$421$	4.37748e7	−	1.20270e8i	0.586648	−	1.61180i	0.776589	−	0.630008i	$-0.216948\pi$
$422$		0			0
$423$	1.52319e6	+	8.63846e6i	0.0201249	+	0.114134i
$424$		0			0
$425$	3.59690e6	−	6.23002e6i	0.0468557	−	0.0811564i
$426$		0			0
$427$	1.17962e8	+	9.89822e7i	1.51516	+	1.27137i
$428$		0			0
$429$	2.23527e7	+	3.87160e7i	0.283112	+	0.490364i
$430$		0			0
$431$	3.72172e7	+	1.02254e8i	0.464850	+	1.27716i	0.921798	+	0.387670i	$0.126720\pi$
$431$	3.72172e7	+	1.02254e8i	0.464850	+	1.27716i	−0.456948	+	0.889493i	$0.651058\pi$
$432$		0			0
$433$	−7.88860e7	−	1.39097e7i	−0.971709	−	0.171339i	−0.334810	−	0.942286i	$-0.608672\pi$
$433$	−7.88860e7	−	1.39097e7i	−0.971709	−	0.171339i	−0.636899	+	0.770947i	$0.719783\pi$
$434$		0			0
$435$	3.55735e7	−	2.98497e7i	0.432174	−	0.362637i
$436$		0			0
$437$	−1.75481e7	−	1.52092e8i	−0.210274	−	1.82248i
$438$		0			0
$439$	−2.92893e7	−	3.49056e7i	−0.346190	−	0.412574i	0.564651	−	0.825330i	$-0.309011\pi$
$439$	−2.92893e7	−	3.49056e7i	−0.346190	−	0.412574i	−0.910842	+	0.412756i	$0.864566\pi$
$440$		0			0
$441$	−402514.	+	2.28277e6i	−0.00469316	+	0.0266162i
$442$		0			0
$443$	1.16177e8	−	4.22851e7i	1.33632	−	0.486381i	0.427669	−	0.903936i	$-0.359335\pi$
$443$	1.16177e8	−	4.22851e7i	1.33632	−	0.486381i	0.908652	+	0.417555i	$0.137113\pi$
$444$		0			0
$445$	−8.46605e7	+	4.88788e7i	−0.960729	+	0.554677i
$446$		0			0
$447$	1.30851e7	−	1.55942e7i	0.146505	−	0.174598i
$448$		0			0
$449$	−6.62254e7	−	3.82353e7i	−0.731620	−	0.422401i	0.0873946	−	0.996174i	$-0.472146\pi$
$449$	−6.62254e7	−	3.82353e7i	−0.731620	−	0.422401i	−0.819015	+	0.573773i	$0.805479\pi$
$450$		0			0
$451$	5.76244e7	−	1.01607e7i	0.628170	−	0.110763i
$452$		0			0
$453$	1.54765e6	+	563298.i	0.0166486	+	0.00605960i
$454$		0			0
$455$			1.18822e8i			1.26143i
$456$		0			0
$457$	−1.66101e8			−1.74030			−0.870150	−	0.492788i	$-0.835978\pi$
$457$	−1.66101e8			−1.74030			−0.870150	+	0.492788i	$0.835978\pi$
$458$		0			0
$459$	−6.05587e6	+	1.66384e7i	−0.0626237	+	0.172057i
$460$		0			0
$461$	2.86876e7	+	1.62695e8i	0.292813	+	1.66063i	0.675959	+	0.736939i	$0.263729\pi$
$461$	2.86876e7	+	1.62695e8i	0.292813	+	1.66063i	−0.383146	+	0.923688i	$0.625159\pi$
$462$		0			0
$463$	−4.22060e7	+	7.31030e7i	−0.425238	+	0.736533i	−0.996443	−	0.0842743i	$-0.973143\pi$
$463$	−4.22060e7	+	7.31030e7i	−0.425238	+	0.736533i	0.571205	+	0.820807i	$0.306476\pi$
$464$		0			0
$465$	7.26220e7	+	6.09371e7i	0.722286	+	0.606070i
$466$		0			0
$467$	−2.35463e7	−	4.07834e7i	−0.231192	−	0.400436i	0.726967	−	0.686672i	$-0.240929\pi$
$467$	−2.35463e7	−	4.07834e7i	−0.231192	−	0.400436i	−0.958159	+	0.286236i	$0.907596\pi$
$468$		0			0
$469$	2.99885e7	+	8.23928e7i	0.290694	+	0.798676i
$470$		0			0
$471$	3.22168e7	+	5.68068e6i	0.308332	+	0.0543673i
$472$		0			0
$473$	−7.44682e6	+	6.24862e6i	−0.0703700	+	0.0590474i
$474$		0			0
$475$	−4.20298e7	+	3.11931e7i	−0.392172	+	0.291057i
$476$		0			0
$477$	−911591.	−	1.08639e6i	−0.00839934	−	0.0100099i
$478$		0			0
$479$	2.15066e7	−	1.21970e8i	0.195689	−	1.10981i	−0.715745	−	0.698361i	$-0.753913\pi$
$479$	2.15066e7	−	1.21970e8i	0.195689	−	1.10981i	0.911434	−	0.411446i	$-0.134976\pi$
$480$		0			0
$481$	−1.17330e8	+	4.27047e7i	−1.05433	+	0.383743i
$482$		0			0
$483$	−2.14475e8	+	1.23827e8i	−1.90343	+	1.09894i
$484$		0			0
$485$	1.55613e8	−	1.85452e8i	1.36402	−	1.62557i
$486$		0			0
$487$	1.42317e8	+	8.21666e7i	1.23217	+	0.711391i	0.967481	−	0.252944i	$-0.0813989\pi$
$487$	1.42317e8	+	8.21666e7i	1.23217	+	0.711391i	0.264684	+	0.964335i	$0.414732\pi$
$488$		0			0
$489$	−2.16271e8	+	3.81344e7i	−1.84957	+	0.326129i
$490$		0			0
$491$	1.55454e6	+	565806.i	0.0131328	+	0.00477995i	0.348578	−	0.937280i	$-0.386665\pi$
$491$	1.55454e6	+	565806.i	0.0131328	+	0.00477995i	−0.335445	+	0.942060i	$0.608887\pi$
$492$		0			0
$493$			1.02161e7i			0.0852601i
$494$		0			0
$495$	7.44998e6			0.0614242
$496$		0			0
$497$	1.38284e7	−	3.79932e7i	0.112643	−	0.309483i
$498$		0			0
$499$	1.76476e7	+	1.00085e8i	0.142032	+	0.805501i	0.969703	+	0.244288i	$0.0785542\pi$
$499$	1.76476e7	+	1.00085e8i	0.142032	+	0.805501i	−0.827671	+	0.561213i	$0.810335\pi$
$500$		0			0
$501$	−3.84757e7	+	6.66419e7i	−0.305966	+	0.529949i
$502$		0			0
$503$	1.47556e8	+	1.23814e8i	1.15946	+	0.972898i	0.999898	−	0.0142904i	$-0.00454893\pi$
$503$	1.47556e8	+	1.23814e8i	1.15946	+	0.972898i	0.159557	+	0.987189i	$0.448993\pi$
$504$		0			0
$505$	6.20789e6	+	1.07524e7i	0.0482025	+	0.0834892i
$506$		0			0
$507$	−8.96414e6	−	2.46288e7i	−0.0687836	−	0.188981i
$508$		0			0
$509$	−2.53662e8	−	4.47275e7i	−1.92355	−	0.339173i	−0.924436	−	0.381338i	$-0.875463\pi$
$509$	−2.53662e8	−	4.47275e7i	−1.92355	−	0.339173i	−0.999111	+	0.0421649i	$0.986575\pi$
$510$		0			0
$511$	3.95047e7	−	3.31483e7i	0.296064	−	0.248427i
$512$		0			0
$513$	8.85447e7	−	9.35731e7i	0.655859	−	0.693105i
$514$		0			0
$515$	−1.37884e8	−	1.64323e8i	−1.00947	−	1.20303i
$516$		0			0
$517$	2.02664e7	−	1.14936e8i	0.146658	−	0.831737i
$518$		0			0
$519$	−2.02318e8	+	7.36376e7i	−1.44721	+	0.526742i
$520$		0			0
$521$	−6.46169e7	+	3.73066e7i	−0.456912	+	0.263798i	−0.710745	−	0.703450i	$-0.751642\pi$
$521$	−6.46169e7	+	3.73066e7i	−0.456912	+	0.263798i	0.253833	+	0.967248i	$0.418309\pi$
$522$		0			0
$523$	1.91069e7	−	2.27707e7i	0.133562	−	0.159174i	−0.695118	−	0.718896i	$-0.744648\pi$
$523$	1.91069e7	−	2.27707e7i	0.133562	−	0.159174i	0.828680	+	0.559722i	$0.189092\pi$
$524$		0			0
$525$	7.33223e7	+	4.23327e7i	0.506709	+	0.292548i
$526$		0			0
$527$	−2.05390e7	+	3.62158e6i	−0.140329	+	0.0247438i
$528$		0			0
$529$	−3.29080e8	−	1.19775e8i	−2.22298	−	0.809097i
$530$		0			0
$531$			3.37715e6i			0.0225562i
$532$		0			0
$533$	1.43220e8			0.945848
$534$		0			0
$535$	1.03456e8	−	2.84242e8i	0.675605	−	1.85621i
$536$		0			0
$537$	2.90549e7	+	1.64779e8i	0.187628	+	1.06409i
$538$		0			0
$539$	1.54206e7	−	2.67093e7i	0.0984773	−	0.170568i
$540$		0			0
$541$	−1.88357e8	−	1.58050e8i	−1.18957	−	0.998168i	−0.999867	−	0.0163264i	$-0.994803\pi$
$541$	−1.88357e8	−	1.58050e8i	−1.18957	−	0.998168i	−0.189703	−	0.981841i	$-0.560753\pi$
$542$		0			0
$543$	6.64626e7	+	1.15117e8i	0.415124	+	0.719016i
$544$		0			0
$545$	1.93374e7	+	5.31291e7i	0.119456	+	0.328204i
$546$		0			0
$547$	3.53339e7	+	6.23032e6i	0.215889	+	0.0380670i	0.280546	−	0.959841i	$-0.409484\pi$
$547$	3.53339e7	+	6.23032e6i	0.215889	+	0.0380670i	−0.0646575	+	0.997908i	$0.520596\pi$
$548$		0			0
$549$	1.81030e7	−	1.51902e7i	0.109404	−	0.0918007i
$550$		0			0
$551$	2.95420e7	−	6.82073e7i	0.176598	−	0.407733i
$552$		0			0
$553$	3.31234e7	+	3.94749e7i	0.195866	+	0.233424i
$554$		0			0
$555$	−4.70826e7	+	2.67019e8i	−0.275411	+	1.56193i
$556$		0			0
$557$	1.51561e8	−	5.51638e7i	0.877047	−	0.319219i	0.136029	−	0.990705i	$-0.456566\pi$
$557$	1.51561e8	−	5.51638e7i	0.877047	−	0.319219i	0.741017	+	0.671486i	$0.234344\pi$
$558$		0			0
$559$	−2.06061e7	+	1.18969e7i	−0.117967	+	0.0681081i
$560$		0			0
$561$	−1.37280e7	+	1.63604e7i	−0.0777533	+	0.0926627i
$562$		0			0
$563$	−1.11851e7	−	6.45775e6i	−0.0626782	−	0.0361873i	0.468333	−	0.883552i	$-0.344855\pi$
$563$	−1.11851e7	−	6.45775e6i	−0.0626782	−	0.0361873i	−0.531012	+	0.847365i	$0.678188\pi$
$564$		0			0
$565$	2.28041e8	−	4.02097e7i	1.26435	−	0.222939i
$566$		0			0
$567$	−2.12210e8	−	7.72381e7i	−1.16417	−	0.423723i
$568$		0			0
$569$			1.45400e8i			0.789274i	0.918837	+	0.394637i	$0.129130\pi$
$569$			1.45400e8i			0.789274i	−0.918837	+	0.394637i	$0.870870\pi$
$570$		0			0
$571$	3.58822e6			0.0192740			0.00963699	−	0.999954i	$-0.496932\pi$
$571$	3.58822e6			0.0192740			0.00963699	+	0.999954i	$0.496932\pi$
$572$		0			0
$573$	5.60849e7	−	1.54092e8i	0.298114	−	0.819061i
$574$		0			0
$575$	2.95777e7	+	1.67743e8i	0.155582	+	0.882351i
$576$		0			0
$577$	1.41871e8	−	2.45728e8i	0.738528	−	1.27917i	−0.214629	−	0.976696i	$-0.568854\pi$
$577$	1.41871e8	−	2.45728e8i	0.738528	−	1.27917i	0.953158	−	0.302473i	$-0.0978123\pi$
$578$		0			0
$579$	3.04907e8	+	2.55847e8i	1.57084	+	1.31809i
$580$		0			0
$581$	1.93475e8	+	3.35109e8i	0.986500	+	1.70867i
$582$		0			0
$583$	6.45365e6	+	1.77313e7i	0.0325687	+	0.0894817i
$584$		0			0
$585$	1.79578e7	+	3.16645e6i	0.0896988	+	0.0158163i
$586$		0			0
$587$	3.02834e8	−	2.54108e8i	1.49724	−	1.25633i	0.612292	−	0.790632i	$-0.290248\pi$
$587$	3.02834e8	−	2.54108e8i	1.49724	−	1.25633i	0.884944	−	0.465698i	$-0.154197\pi$
$588$		0			0
$589$	1.47600e8	+	3.52134e7i	0.722337	+	0.172331i
$590$		0			0
$591$	−1.70665e8	−	2.03391e8i	−0.826765	−	0.985300i
$592$		0			0
$593$	−3.67942e7	+	2.08670e8i	−0.176447	+	1.00068i	0.760013	+	0.649908i	$0.225193\pi$
$593$	−3.67942e7	+	2.08670e8i	−0.176447	+	1.00068i	−0.936460	+	0.350774i	$0.885918\pi$
$594$		0			0
$595$	−5.33412e7	+	1.94146e7i	−0.253228	+	0.0921674i
$596$		0			0
$597$	1.76238e8	−	1.01751e8i	0.828280	−	0.478207i
$598$		0			0
$599$	−1.23827e8	+	1.47571e8i	−0.576149	+	0.686628i	−0.972881	−	0.231307i	$-0.925700\pi$
$599$	−1.23827e8	+	1.47571e8i	−0.576149	+	0.686628i	0.396732	+	0.917935i	$0.370144\pi$
$600$		0			0
$601$	1.31929e8	+	7.61690e7i	0.607737	+	0.350877i	0.772079	−	0.635526i	$-0.219217\pi$
$601$	1.31929e8	+	7.61690e7i	0.607737	+	0.350877i	−0.164343	+	0.986403i	$0.552550\pi$
$602$		0			0
$603$	1.32514e7	−	2.33658e6i	0.0604379	−	0.0106568i
$604$		0			0
$605$	1.60723e8	+	5.84983e7i	0.725791	+	0.264166i
$606$		0			0
$607$		−	2.68257e8i		−	1.19946i	−0.800204	−	0.599728i	$-0.795275\pi$
$607$		−	2.68257e8i		−	1.19946i	0.800204	−	0.599728i	$-0.204725\pi$
$608$		0			0
$609$	−1.20236e8			−0.532330
$610$		0			0
$611$	9.77025e7	−	2.68435e8i	0.428333	−	1.17684i
$612$		0			0
$613$	−3.12482e7	−	1.77217e8i	−0.135657	−	0.769351i	−0.974400	−	0.224823i	$-0.927820\pi$
$613$	−3.12482e7	−	1.77217e8i	−0.135657	−	0.769351i	0.838742	−	0.544528i	$-0.183291\pi$
$614$		0			0
$615$	1.55503e8	−	2.69339e8i	0.668519	−	1.15791i
$616$		0			0
$617$	4.87601e7	+	4.09146e7i	0.207591	+	0.174190i	0.740656	−	0.671885i	$-0.234515\pi$
$617$	4.87601e7	+	4.09146e7i	0.207591	+	0.174190i	−0.533064	+	0.846075i	$0.678960\pi$
$618$		0			0
$619$	−1.18613e8	−	2.05444e8i	−0.500105	−	0.866207i	−1.00000		0.000121168i	$-0.999961\pi$
$619$	−1.18613e8	−	2.05444e8i	−0.500105	−	0.866207i	0.499895	−	0.866086i	$-0.333372\pi$
$620$		0			0
$621$	−1.43387e8	−	3.93954e8i	−0.598737	−	1.64502i
$622$		0			0
$623$	2.49266e8	+	4.39522e7i	1.03086	+	0.181768i
$624$		0			0
$625$	−2.33753e8	+	1.96142e8i	−0.957452	+	0.803398i
$626$		0			0
$627$	1.38963e8	−	6.95317e7i	0.563764	−	0.282085i
$628$		0			0
$629$	−3.83417e7	−	4.56939e7i	−0.154071	−	0.183614i
$630$		0			0
$631$	−7.70815e7	+	4.37151e8i	−0.306805	+	1.73998i	0.308081	+	0.951360i	$0.400313\pi$
$631$	−7.70815e7	+	4.37151e8i	−0.306805	+	1.73998i	−0.614886	+	0.788616i	$0.710798\pi$
$632$		0			0
$633$	−3.15674e8	+	1.14896e8i	−1.24460	+	0.452996i
$634$		0			0
$635$	−3.64671e8	+	2.10543e8i	−1.42423	+	0.822279i
$636$		0			0
$637$	4.85230e7	−	5.78274e7i	0.187728	−	0.223726i
$638$		0			0
$639$	−5.37349e6	−	3.10239e6i	−0.0205946	−	0.0118903i
$640$		0			0
$641$	1.11928e8	−	1.97359e7i	0.424975	−	0.0749346i	0.0429296	−	0.999078i	$-0.486331\pi$
$641$	1.11928e8	−	1.97359e7i	0.424975	−	0.0749346i	0.382045	+	0.924144i	$0.375220\pi$
$642$		0			0
$643$	−2.31162e8	−	8.41362e7i	−0.869529	−	0.316483i	−0.131553	−	0.991309i	$-0.541996\pi$
$643$	−2.31162e8	−	8.41362e7i	−0.869529	−	0.316483i	−0.737976	+	0.674826i	$0.764218\pi$
$644$		0			0
$645$			5.16691e7i			0.192554i
$646$		0			0
$647$	4.86637e8			1.79677			0.898385	−	0.439208i	$-0.144741\pi$
$647$	4.86637e8			1.79677			0.898385	+	0.439208i	$0.144741\pi$
$648$		0			0
$649$	1.53682e7	−	4.22238e7i	0.0562198	−	0.154463i
$650$		0			0
$651$	−4.26231e7	−	2.41728e8i	−0.154491	−	0.876160i
$652$		0			0
$653$	−4.51687e7	+	7.82345e7i	−0.162218	+	0.280969i	−0.935664	−	0.352893i	$-0.885198\pi$
$653$	−4.51687e7	+	7.82345e7i	−0.162218	+	0.280969i	0.773446	+	0.633862i	$0.218531\pi$
$654$		0			0
$655$	1.98224e8	+	1.66330e8i	0.705395	+	0.591897i
$656$		0			0
$657$	−3.95704e6	−	6.85380e6i	−0.0139532	−	0.0241677i
$658$		0			0
$659$	−5.80641e7	−	1.59530e8i	−0.202886	−	0.557424i	0.795966	−	0.605342i	$-0.206964\pi$
$659$	−5.80641e7	−	1.59530e8i	−0.202886	−	0.557424i	−0.998851	+	0.0479180i	$0.984741\pi$
$660$		0			0
$661$	9.84249e7	+	1.73550e7i	0.340801	+	0.0600924i	0.341429	−	0.939907i	$-0.389089\pi$
$661$	9.84249e7	+	1.73550e7i	0.340801	+	0.0600924i	−0.000628625		1.00000i	$0.500200\pi$
$662$		0			0
$663$	−4.00444e7	+	3.36012e7i	−0.137404	+	0.115296i
$664$		0			0
$665$	4.12270e8	+	2.46265e7i	1.40190	+	0.0837408i
$666$		0			0
$667$	−1.55485e8	−	1.85300e8i	−0.523976	−	0.624450i
$668$		0			0
$669$	−7.07666e7	+	4.01337e8i	−0.236347	+	1.34039i
$670$		0			0
$671$	−2.95463e8	+	1.07540e8i	−0.977992	+	0.355960i
$672$		0			0
$673$	−3.64893e8	+	2.10671e8i	−1.19707	+	0.691130i	−0.959901	−	0.280338i	$-0.909553\pi$
$673$	−3.64893e8	+	2.10671e8i	−1.19707	+	0.691130i	−0.237171	+	0.971468i	$0.576220\pi$
$674$		0			0
$675$	−9.21267e7	+	1.09792e8i	−0.299553	+	0.356994i
$676$		0			0
$677$	5.08379e8	+	2.93513e8i	1.63841	+	0.945934i	0.981383	+	0.192063i	$0.0615178\pi$
$677$	5.08379e8	+	2.93513e8i	1.63841	+	0.945934i	0.657023	+	0.753871i	$0.271816\pi$
$678$		0			0
$679$	−6.17291e8	+	1.08845e8i	−1.97188	+	0.347696i
$680$		0			0
$681$	−4.27413e8	−	1.55566e8i	−1.35334	−	0.492575i
$682$		0			0
$683$		−	3.41997e8i		−	1.07340i	−0.843775	−	0.536698i	$-0.819672\pi$
$683$		−	3.41997e8i		−	1.07340i	0.843775	−	0.536698i	$-0.180328\pi$
$684$		0			0
$685$	1.00377e7			0.0312295
$686$		0			0
$687$	4.05261e7	−	1.11345e8i	0.124987	−	0.343399i
$688$		0			0
$689$	8.01995e6	+	4.54834e7i	0.0245196	+	0.139058i
$690$		0			0
$691$	1.86643e8	−	3.23275e8i	0.565689	−	0.979802i	−0.431296	−	0.902210i	$-0.641944\pi$
$691$	1.86643e8	−	3.23275e8i	0.565689	−	0.979802i	0.996985	−	0.0775919i	$-0.0247231\pi$
$692$		0			0
$693$	−1.47764e7	−	1.23989e7i	−0.0443987	−	0.0372549i
$694$		0			0
$695$	8.13276e7	+	1.40863e8i	0.242261	+	0.419608i
$696$		0			0
$697$	2.34010e7	+	6.42938e7i	0.0691093	+	0.189876i
$698$		0			0
$699$	−1.02763e8	−	1.81198e7i	−0.300887	−	0.0530546i
$700$		0			0
$701$	−3.64738e8	+	3.06052e8i	−1.05883	+	0.888466i	−0.993995	−	0.109430i	$-0.965097\pi$
$701$	−3.64738e8	+	3.06052e8i	−1.05883	+	0.888466i	−0.0648379	+	0.997896i	$0.520653\pi$
$702$		0			0
$703$	1.23853e8	+	4.15945e8i	0.356484	+	1.19721i
$704$		0			0
$705$	−3.98738e8	−	4.75197e8i	−1.13794	−	1.35615i
$706$		0			0
$707$	5.58219e6	−	3.16582e7i	0.0157960	−	0.0895834i
$708$		0			0
$709$	−3.68509e7	+	1.34126e7i	−0.103397	+	0.0376336i	−0.393201	−	0.919453i	$-0.628632\pi$
$709$	−3.68509e7	+	1.34126e7i	−0.103397	+	0.0376336i	0.289803	+	0.957086i	$0.406410\pi$
$710$		0			0
$711$	6.84864e6	−	3.95406e6i	0.0190544	−	0.0110011i
$712$		0			0
$713$	3.17417e8	−	3.78283e8i	0.875713	−	1.04363i
$714$		0			0
$715$	−2.10114e8	−	1.21309e8i	−0.574826	−	0.331876i
$716$		0			0
$717$	−1.38189e8	+	2.43664e7i	−0.374900	+	0.0661049i
$718$		0			0
$719$	8.06321e7	+	2.93477e7i	0.216931	+	0.0789564i	0.448200	−	0.893934i	$-0.352065\pi$
$719$	8.06321e7	+	2.93477e7i	0.216931	+	0.0789564i	−0.231269	+	0.972890i	$0.574288\pi$
$720$		0			0
$721$			5.55400e8i			1.48184i
$722$		0			0
$723$	−2.25994e8			−0.597973
$724$		0			0
$725$	−2.82834e7	+	7.77080e7i	−0.0742194	+	0.203916i
$726$		0			0
$727$	4.32733e7	+	2.45415e8i	0.112620	+	0.638702i	0.987901	+	0.155087i	$0.0495657\pi$
$727$	4.32733e7	+	2.45415e8i	0.112620	+	0.638702i	−0.875280	+	0.483616i	$0.839323\pi$
$728$		0			0
$729$	1.75044e8	−	3.03184e8i	0.451818	−	0.782572i
$730$		0			0
$731$	−8.70760e6	−	7.30655e6i	−0.0222919	−	0.0187051i
$732$		0			0
$733$	2.03466e8	+	3.52413e8i	0.516630	+	0.894830i	0.999814	+	0.0193107i	$0.00614716\pi$
$733$	2.03466e8	+	3.52413e8i	0.516630	+	0.894830i	−0.483183	+	0.875519i	$0.660520\pi$
$734$		0			0
$735$	−5.60658e7	−	1.54039e8i	−0.141200	−	0.387945i
$736$		0			0
$737$	−1.76312e8	−	3.10886e7i	−0.440433	−	0.0776602i
$738$		0			0
$739$	−4.67822e8	+	3.92550e8i	−1.15917	+	0.972661i	−0.999894	−	0.0145732i	$-0.995361\pi$
$739$	−4.67822e8	+	3.92550e8i	−1.15917	+	0.972661i	−0.159278	+	0.987234i	$0.550917\pi$
$740$		0			0
$741$	3.64518e8	−	1.08540e8i	0.895909	−	0.266768i
$742$		0			0
$743$	−1.12282e7	−	1.33812e7i	−0.0273743	−	0.0326234i	0.752184	−	0.658954i	$-0.229001\pi$
$743$	−1.12282e7	−	1.33812e7i	−0.0273743	−	0.0326234i	−0.779558	+	0.626330i	$0.784556\pi$
$744$		0			0
$745$	−1.91842e7	+	1.08799e8i	−0.0463953	+	0.263121i
$746$		0			0
$747$	5.58017e7	−	2.03102e7i	0.133871	−	0.0487250i
$748$		0			0
$749$	−6.78257e8	+	3.91592e8i	−1.61417	+	0.931940i
$750$		0			0
$751$	−8.87795e7	+	1.05803e8i	−0.209601	+	0.249792i	−0.860595	−	0.509291i	$-0.829908\pi$
$751$	−8.87795e7	+	1.05803e8i	−0.209601	+	0.249792i	0.650994	+	0.759083i	$0.274352\pi$
$752$		0			0
$753$	5.31440e8	+	3.06827e8i	1.24471	+	0.718636i
$754$		0			0
$755$	−8.80243e6	+	1.55211e6i	−0.0204532	+	0.00360646i
$756$		0			0
$757$	−1.16441e8	−	4.23810e7i	−0.268422	−	0.0976975i	0.204303	−	0.978908i	$-0.434507\pi$
$757$	−1.16441e8	−	4.23810e7i	−0.268422	−	0.0976975i	−0.472725	+	0.881210i	$0.656729\pi$
$758$		0			0
$759$		−	5.05678e8i		−	1.15651i
$760$		0			0
$761$	5.97285e8			1.35528			0.677638	−	0.735396i	$-0.263004\pi$
$761$	5.97285e8			1.35528			0.677638	+	0.735396i	$0.263004\pi$
$762$		0			0
$763$	5.00679e7	−	1.37560e8i	0.112716	−	0.309685i
$764$		0			0
$765$	1.51270e6	+	8.57895e6i	0.00337885	+	0.0191624i
$766$		0			0
$767$	5.49907e7	−	9.52466e7i	0.121872	−	0.211088i
$768$		0			0
$769$	−2.60060e8	−	2.18216e8i	−0.571866	−	0.479853i	0.310398	−	0.950607i	$-0.399538\pi$
$769$	−2.60060e8	−	2.18216e8i	−0.571866	−	0.479853i	−0.882265	+	0.470754i	$0.843982\pi$
$770$		0			0
$771$	1.95171e8	+	3.38046e8i	0.425846	+	0.737586i
$772$		0			0
$773$	2.72755e8	+	7.49390e8i	0.590521	+	1.62244i	0.769542	+	0.638597i	$0.220485\pi$
$773$	2.72755e8	+	7.49390e8i	0.590521	+	1.62244i	−0.179021	+	0.983845i	$0.557293\pi$
$774$		0			0
$775$	−1.66254e8	−	2.93151e7i	−0.357164	−	0.0629777i
$776$		0			0
$777$	5.37780e8	−	4.51251e8i	1.14641	−	0.961956i
$778$		0			0
$779$	2.96830e7	−	4.96921e8i	0.0627908	−	1.05118i
$780$		0			0
$781$	5.30658e7	+	6.32414e7i	0.111394	+	0.132754i
$782$		0			0
$783$	3.53440e7	−	2.00446e8i	0.0736259	−	0.417553i
$784$		0			0
$785$	−1.66833e8	+	6.07221e7i	−0.344883	+	0.125527i
$786$		0			0
$787$	1.50568e8	−	8.69306e7i	0.308894	−	0.178340i	−0.337538	−	0.941312i	$-0.609594\pi$
$787$	1.50568e8	−	8.69306e7i	0.308894	−	0.178340i	0.646431	+	0.762972i	$0.276261\pi$
$788$		0			0
$789$	−4.69517e8	+	5.59548e8i	−0.955917	+	1.13922i
$790$		0			0
$791$	−5.19221e8	−	2.99772e8i	−1.04911	−	0.605707i
$792$		0			0
$793$	−7.57907e8	+	1.33640e8i	−1.51984	+	0.267988i
$794$		0			0
$795$	9.42440e7	+	3.43020e7i	0.187565	+	0.0682681i
$796$		0			0
$797$		−	3.01357e8i		−	0.595259i	−0.954681	−	0.297630i	$-0.903804\pi$
$797$		−	3.01357e8i		−	0.595259i	0.954681	−	0.297630i	$-0.0961960\pi$
$798$		0			0
$799$	1.36469e8			0.267543
$800$		0			0
$801$	1.32852e7	−	3.65008e7i	0.0258506	−	0.0710240i
$802$		0			0
$803$	1.82849e7	+	1.03699e8i	0.0353139	+	0.200275i
$804$		0			0
$805$	6.72019e8	−	1.16397e9i	1.28823	−	2.23128i
$806$		0			0
$807$	−1.73909e8	−	1.45927e8i	−0.330904	−	0.277661i
$808$		0			0
$809$	−3.33002e8	−	5.76777e8i	−0.628929	−	1.08934i	−0.987767	−	0.155937i	$-0.950160\pi$
$809$	−3.33002e8	−	5.76777e8i	−0.628929	−	1.08934i	0.358838	−	0.933400i	$-0.383173\pi$
$810$		0			0
$811$	8.06082e6	+	2.21469e7i	0.0151118	+	0.0415193i	0.947019	−	0.321177i	$-0.104078\pi$
$811$	8.06082e6	+	2.21469e7i	0.0151118	+	0.0415193i	−0.931907	+	0.362696i	$0.881856\pi$
$812$		0			0
$813$	−9.67427e8	−	1.70583e8i	−1.80031	−	0.317443i
$814$		0			0
$815$	9.12987e8	−	7.66087e8i	1.68652	−	1.41516i
$816$		0			0
$817$	3.70073e7	+	7.39614e7i	0.0678612	+	0.135625i
$818$		0			0
$819$	−3.03481e7	−	3.61674e7i	−0.0552432	−	0.0658363i
$820$		0			0
$821$	−7.71094e6	+	4.37309e7i	−0.0139341	+	0.0790240i	−0.990982	−	0.133996i	$-0.957219\pi$
$821$	−7.71094e6	+	4.37309e7i	−0.0139341	+	0.0790240i	0.977048	+	0.213020i	$0.0683301\pi$
$822$		0			0
$823$	9.13893e8	−	3.32630e8i	1.63944	−	0.596708i	0.652500	−	0.757789i	$-0.273720\pi$
$823$	9.13893e8	−	3.32630e8i	1.63944	−	0.596708i	0.986941	+	0.161082i	$0.0514982\pi$
$824$		0			0
$825$	−1.49714e8	+	8.64377e7i	−0.266626	+	0.153936i
$826$		0			0
$827$	1.37395e8	−	1.63741e8i	0.242915	−	0.289495i	−0.630787	−	0.775956i	$-0.717268\pi$
$827$	1.37395e8	−	1.63741e8i	0.242915	−	0.289495i	0.873702	+	0.486461i	$0.161712\pi$
$828$		0			0
$829$	9.24510e8	+	5.33766e8i	1.62274	+	0.936887i	0.986184	+	0.165654i	$0.0529736\pi$
$829$	9.24510e8	+	5.33766e8i	1.62274	+	0.936887i	0.636553	+	0.771233i	$0.280360\pi$
$830$		0			0
$831$	7.80323e8	−	1.37592e8i	1.35979	−	0.239767i
$832$		0			0
$833$	3.38880e7	+	1.23342e7i	0.0586288	+	0.0213391i
$834$		0			0
$835$		−	4.17620e8i		−	0.717335i
$836$		0			0
$837$	4.15516e8			0.708616
$838$		0			0
$839$	−2.34263e8	+	6.43632e8i	−0.396659	+	1.08981i	0.567242	+	0.823551i	$0.308010\pi$
$839$	−2.34263e8	+	6.43632e8i	−0.396659	+	1.08981i	−0.963901	+	0.266261i	$0.914212\pi$
$840$		0			0
$841$	8.28972e7	+	4.70133e8i	0.139364	+	0.790374i
$842$		0			0
$843$	−2.20517e8	+	3.81946e8i	−0.368094	+	0.637558i
$844$		0			0
$845$	1.08962e8	+	9.14300e7i	0.180595	+	0.151537i
$846$		0			0
$847$	−2.21423e8	−	3.83516e8i	−0.364395	−	0.631150i
$848$		0			0
$849$	1.94162e8	+	5.33456e8i	0.317279	+	0.871716i
$850$		0			0
$851$	1.39088e9	+	2.45250e8i	2.25685	+	0.397943i
$852$		0			0
$853$	2.49397e8	−	2.09269e8i	0.401831	−	0.337176i	−0.419370	−	0.907816i	$-0.637749\pi$
$853$	2.49397e8	−	2.09269e8i	0.401831	−	0.337176i	0.821201	+	0.570639i	$0.193304\pi$
$854$		0			0
$855$	1.47083e7	−	6.16510e7i	0.0235323	−	0.0986375i
$856$		0			0
$857$	8.08265e7	+	9.63252e7i	0.128414	+	0.153037i	0.826420	−	0.563054i	$-0.190374\pi$
$857$	8.08265e7	+	9.63252e7i	0.128414	+	0.153037i	−0.698006	+	0.716092i	$0.745929\pi$
$858$		0			0
$859$	−1.62744e8	+	9.22968e8i	−0.256759	+	1.45615i	0.534757	+	0.845006i	$0.320403\pi$
$859$	−1.62744e8	+	9.22968e8i	−0.256759	+	1.45615i	−0.791517	+	0.611148i	$0.790708\pi$
$860$		0			0
$861$	−7.56686e8	+	2.75411e8i	−1.18551	+	0.431491i
$862$		0			0
$863$	−7.69158e8	+	4.44074e8i	−1.19669	+	0.690912i	−0.959817	−	0.280627i	$-0.909457\pi$
$863$	−7.69158e8	+	4.44074e8i	−1.19669	+	0.690912i	−0.236878	+	0.971539i	$0.576124\pi$
$864$		0			0
$865$	7.51070e8	−	8.95090e8i	1.16046	−	1.38299i
$866$		0			0
$867$	5.65762e8	+	3.26643e8i	0.868114	+	0.501206i
$868$		0			0
$869$	−1.03621e8	+	1.82711e7i	−0.157902	+	0.0278423i
$870$		0			0
$871$	−4.11779e8	−	1.49875e8i	−0.623175	−	0.226817i
$872$		0			0
$873$			9.61932e7i			0.144578i
$874$		0			0
$875$	4.81352e8			0.718520
$876$		0			0
$877$	3.70849e8	−	1.01890e9i	0.549792	−	1.51054i	−0.284200	−	0.958765i	$-0.591728\pi$
$877$	3.70849e8	−	1.01890e9i	0.549792	−	1.51054i	0.833992	−	0.551777i	$-0.186050\pi$
$878$		0			0
$879$	2.12488e8	+	1.20508e9i	0.312873	+	1.77439i
$880$		0			0
$881$	−5.14430e8	+	8.91019e8i	−0.752313	+	1.30304i	0.194386	+	0.980925i	$0.437729\pi$
$881$	−5.14430e8	+	8.91019e8i	−0.752313	+	1.30304i	−0.946699	+	0.322120i	$0.895605\pi$
$882$		0			0
$883$	3.04914e8	+	2.55853e8i	0.442889	+	0.371628i	0.836789	−	0.547525i	$-0.184430\pi$
$883$	3.04914e8	+	2.55853e8i	0.442889	+	0.371628i	−0.393900	+	0.919153i	$0.628874\pi$
$884$		0			0
$885$	−1.19414e8	−	2.06831e8i	−0.172276	−	0.298391i
$886$		0			0
$887$	8.87811e6	+	2.43924e7i	0.0127218	+	0.0349529i	0.945891	−	0.324485i	$-0.105191\pi$
$887$	8.87811e6	+	2.43924e7i	0.0127218	+	0.0349529i	−0.933169	+	0.359437i	$0.882969\pi$
$888$		0			0
$889$	1.07370e9	+	1.89322e8i	1.52819	+	0.269461i
$890$		0			0
$891$	3.53233e8	−	2.96398e8i	0.499377	−	0.419027i
$892$		0			0
$893$	−9.11126e8	−	3.94627e8i	−1.27945	−	0.554157i
$894$		0			0
$895$	−5.83689e8	−	6.95614e8i	−0.814165	−	0.970284i
$896$		0			0
$897$	2.14928e8	−	1.21892e9i	0.297793	−	1.68887i
$898$		0			0
$899$	2.25286e8	−	8.19976e7i	0.310067	−	0.112855i
$900$		0			0
$901$	−1.91079e7	+	1.10319e7i	−0.0261239	+	0.0150826i
$902$		0			0
$903$	8.59921e7	−	1.02481e8i	0.116787	−	0.139182i
$904$		0			0
$905$	−6.24745e8	−	3.60697e8i	−0.842863	−	0.486627i
$906$		0			0
$907$	−9.54701e8	+	1.68340e8i	−1.27952	+	0.225613i	−0.771775	−	0.635896i	$-0.780631\pi$
$907$	−9.54701e8	+	1.68340e8i	−1.27952	+	0.225613i	−0.507742	+	0.861509i	$0.669519\pi$
$908$		0			0
$909$	−4.63582e6	−	1.68730e6i	−0.00617213	−	0.00224647i
$910$		0			0
$911$		−	4.88876e8i		−	0.646612i	−0.946294	−	0.323306i	$-0.895206\pi$
$911$		−	4.88876e8i		−	0.646612i	0.946294	−	0.323306i	$-0.104794\pi$
$912$		0			0
$913$	−7.90102e8			−1.03818
$914$		0			0
$915$	−5.71587e8	+	1.57042e9i	−0.746138	+	2.05000i
$916$		0			0
$917$	−1.16341e8	−	6.59803e8i	−0.150878	−	0.855670i
$918$		0			0
$919$	−4.98571e8	+	8.63551e8i	−0.642363	+	1.11261i	0.342541	+	0.939503i	$0.388713\pi$
$919$	−4.98571e8	+	8.63551e8i	−0.642363	+	1.11261i	−0.984904	+	0.173103i	$0.944621\pi$
$920$		0			0
$921$	−3.36272e8	−	2.82166e8i	−0.430439	−	0.361181i
$922$		0			0
$923$	1.01033e8	+	1.74995e8i	0.128487	+	0.222546i
$924$		0			0
$925$	−1.65139e8	−	4.53715e8i	−0.208653	−	0.573269i
$926$		0			0
$927$	8.39390e7	+	1.48007e7i	0.105372	+	0.0185799i
$928$		0			0
$929$	−1.62920e8	+	1.36706e8i	−0.203201	+	0.170506i	−0.738710	−	0.674024i	$-0.764564\pi$
$929$	−1.62920e8	+	1.36706e8i	−0.203201	+	0.170506i	0.535508	+	0.844530i	$0.320120\pi$
$930$		0			0
$931$	−1.90584e8	−	1.80342e8i	−0.236177	−	0.223485i
$932$		0			0
$933$	6.77931e6	+	8.07927e6i	0.00834719	+	0.00994780i
$934$		0			0
$935$	2.01268e7	−	1.14145e8i	0.0246229	−	0.139644i
$936$		0			0
$937$	6.42179e8	−	2.33734e8i	0.780616	−	0.284121i	0.0791862	−	0.996860i	$-0.474768\pi$
$937$	6.42179e8	−	2.33734e8i	0.780616	−	0.284121i	0.701429	+	0.712739i	$0.252546\pi$
$938$		0			0
$939$	−8.55307e6	+	4.93812e6i	−0.0103306	+	0.00596437i
$940$		0			0
$941$	−3.00500e8	+	3.58122e8i	−0.360641	+	0.429796i	−0.915605	−	0.402079i	$-0.868288\pi$
$941$	−3.00500e8	+	3.58122e8i	−0.360641	+	0.429796i	0.554964	+	0.831875i	$0.312732\pi$
$942$		0			0
$943$	−1.40297e9	−	8.10005e8i	−1.67307	−	0.965946i
$944$		0			0
$945$	1.11375e9	−	1.96384e8i	1.31975	−	0.232708i
$946$		0			0
$947$	−4.30602e6	−	1.56726e6i	−0.00507022	−	0.00184541i	0.339484	−	0.940612i	$-0.389748\pi$
$947$	−4.30602e6	−	1.56726e6i	−0.00507022	−	0.00184541i	−0.344554	+	0.938766i	$0.611970\pi$
$948$		0			0
$949$			2.57733e8i			0.301558i
$950$		0			0
$951$	−4.75538e8			−0.552896
$952$		0			0
$953$	−1.12984e8	+	3.10421e8i	−0.130538	+	0.358651i	−0.987692	−	0.156409i	$-0.950008\pi$
$953$	−1.12984e8	+	3.10421e8i	−0.130538	+	0.358651i	0.857154	+	0.515060i	$0.172230\pi$
$954$		0			0
$955$	1.54536e8	+	8.76416e8i	0.177427	+	1.00624i
$956$		0			0
$957$	1.22753e8	−	2.12614e8i	0.140054	−	0.242580i
$958$		0			0
$959$	−1.99091e7	−	1.67057e7i	−0.0225733	−	0.0189412i
$960$		0			0
$961$	−1.99037e8	−	3.44741e8i	−0.224266	−	0.388439i
$962$		0			0
$963$	4.11075e7	+	1.12942e8i	0.0460302	+	0.126467i
$964$		0			0
$965$	−2.12730e9	−	3.75101e8i	−2.36727	−	0.417413i
$966$		0			0
$967$	3.84061e8	−	3.22265e8i	0.424737	−	0.356397i	−0.405224	−	0.914217i	$-0.632807\pi$
$967$	3.84061e8	−	3.22265e8i	0.424737	−	0.356397i	0.829962	+	0.557820i	$0.188362\pi$
$968$		0			0
$969$	1.08285e8	+	1.45904e8i	0.119013	+	0.160360i
$970$		0			0
$971$	−1.49281e8	−	1.77906e8i	−0.163059	−	0.194327i	0.678328	−	0.734759i	$-0.262705\pi$
$971$	−1.49281e8	−	1.77906e8i	−0.163059	−	0.194327i	−0.841387	+	0.540433i	$0.818260\pi$
$972$		0			0
$973$	7.31305e7	−	4.14744e8i	0.0793890	−	0.450237i
$974$		0			0
$975$	−3.97618e8	+	1.44721e8i	−0.428995	+	0.156142i
$976$		0			0
$977$	−1.80735e8	+	1.04347e8i	−0.193802	+	0.111892i	−0.593761	−	0.804641i	$-0.702358\pi$
$977$	−1.80735e8	+	1.04347e8i	−0.193802	+	0.111892i	0.399959	+	0.916533i	$0.369024\pi$
$978$		0			0
$979$	−3.32205e8	+	3.95906e8i	−0.354044	+	0.421934i
$980$		0			0
$981$	−1.94556e7	−	1.12327e7i	−0.0206081	−	0.0118981i
$982$		0			0
$983$	−1.06226e9	+	1.87305e8i	−1.11833	+	0.197192i	−0.702108	−	0.712070i	$-0.747758\pi$
$983$	−1.06226e9	+	1.87305e8i	−1.11833	+	0.197192i	−0.416223	+	0.909262i	$0.636647\pi$
$984$		0			0
$985$	1.35403e9	+	4.92825e8i	1.41683	+	0.515685i
$986$		0			0
$987$			1.60613e9i			1.67043i
$988$		0			0
$989$	2.69141e8			0.278221
$990$		0			0
$991$	2.26899e8	−	6.23400e8i	0.233137	−	0.640539i	−0.766862	−	0.641812i	$-0.778183\pi$
$991$	2.26899e8	−	6.23400e8i	0.233137	−	0.640539i	0.999999	+	0.00127277i	$0.000405134\pi$
$992$		0			0
$993$	−9.38580e7	−	5.32295e8i	−0.0958570	−	0.543632i
$994$		0			0
$995$	−5.52210e8	+	9.56455e8i	−0.560576	+	0.970946i
$996$		0			0
$997$	2.78322e8	+	2.33540e8i	0.280842	+	0.235655i	0.772317	−	0.635237i	$-0.219098\pi$
$997$	2.78322e8	+	2.33540e8i	0.280842	+	0.235655i	−0.491475	+	0.870892i	$0.663542\pi$
$998$		0			0
$999$	5.94201e8	+	1.02919e9i	0.595987	+	1.03228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.13.8	✓	60
19.3	odd	18	inner	76.7.j.a.41.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.13.8	✓	60	1.1	even	1	trivial
76.7.j.a.41.8	yes	60	19.3	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)

\(f(q)\)	\(=\)	\(q+(9.61067 - 26.4051i) q^{3} +(26.4812 + 150.182i) q^{5} +(197.423 - 341.946i) q^{7} +(-46.4181 - 38.9494i) q^{9} +O(q^{10})\)	\(q+(9.61067 - 26.4051i) q^{3} +(26.4812 + 150.182i) q^{5} +(197.423 - 341.946i) q^{7} +(-46.4181 - 38.9494i) q^{9} +(403.111 + 698.209i) q^{11} +(674.923 + 1854.34i) q^{13} +(4220.07 + 744.113i) q^{15} +(-722.165 + 605.969i) q^{17} +(6573.76 - 1957.42i) q^{19} +(-7131.76 - 8499.30i) q^{21} +(3876.04 - 21982.1i) q^{23} +(-7170.71 + 2609.92i) q^{25} +(16265.7 - 9391.00i) q^{27} +(6965.80 - 8301.52i) q^{29} +(19159.1 + 11061.5i) q^{31} +(22310.5 - 3933.93i) q^{33} +(56582.2 + 20594.2i) q^{35} +63273.4i q^{37} +55450.4 q^{39} +(24822.9 - 68200.3i) q^{41} +(2093.79 + 11874.4i) q^{43} +(4620.30 - 8002.59i) q^{45} +(-110893. - 93050.5i) q^{47} +(-19127.0 - 33129.0i) q^{49} +(9060.17 + 24892.6i) q^{51} +(23048.9 + 4064.15i) q^{53} +(-94183.6 + 79029.5i) q^{55} +(11492.4 - 192393. i) q^{57} +(-35824.8 - 42694.4i) q^{59} +(-67722.4 + 384073. i) q^{61} +(-22482.6 + 8183.00i) q^{63} +(-260615. + 150466. i) q^{65} +(-142739. + 170110. i) q^{67} +(-543188. - 313610. i) q^{69} +(100843. - 17781.3i) q^{71} +(122731. + 44670.3i) q^{73} +214426. i q^{75} +318333. q^{77} +(-44636.7 + 122638. i) q^{79} +(-99316.8 - 563254. i) q^{81} +(-490002. + 848709. i) q^{83} +(-110129. - 92409.6i) q^{85} +(-152256. - 263716. i) q^{87} +(219248. + 602378. i) q^{89} +(767328. + 135301. i) q^{91} +(476213. - 399590. i) q^{93} +(468050. + 935427. i) q^{95} +(-1.02042e6 - 1.21609e6i) q^{97} +(8483.18 - 48110.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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