LMFDB - Embedded newform 76.7.j.a.33.9

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			33.9
Character	$\chi$	$=$	76.33
Dual form			76.7.j.a.53.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(31.1235 + 5.48792i) q^{3} +(-167.059 - 140.179i) q^{5} +(273.433 + 473.600i) q^{7} +(253.520 + 92.2739i) q^{9} +O(q^{10})$	\(q+(31.1235 + 5.48792i) q^{3} +(-167.059 - 140.179i) q^{5} +(273.433 + 473.600i) q^{7} +(253.520 + 92.2739i) q^{9} +(1163.27 - 2014.85i) q^{11} +(2461.73 - 434.069i) q^{13} +(-4430.17 - 5279.67i) q^{15} +(3134.71 - 1140.94i) q^{17} +(-32.2826 - 6858.92i) q^{19} +(5911.12 + 16240.7i) q^{21} +(1191.54 - 999.822i) q^{23} +(5545.25 + 31448.7i) q^{25} +(-12568.4 - 7256.35i) q^{27} +(12896.4 - 35432.7i) q^{29} +(3595.61 - 2075.93i) q^{31} +(47262.5 - 56325.2i) q^{33} +(20709.4 - 117449. i) q^{35} +30767.5i q^{37} +78999.8 q^{39} +(-48569.6 - 8564.13i) q^{41} +(50960.3 + 42760.7i) q^{43} +(-29418.0 - 50953.4i) q^{45} +(45459.6 + 16546.0i) q^{47} +(-90706.7 + 157109. i) q^{49} +(103825. - 18307.1i) q^{51} +(81092.6 + 96642.3i) q^{53} +(-476774. + 173532. i) q^{55} +(36636.5 - 213651. i) q^{57} +(32417.4 + 89066.1i) q^{59} +(16263.0 - 13646.3i) q^{61} +(25619.9 + 145298. i) q^{63} +(-472101. - 272568. i) q^{65} +(100234. - 275390. i) q^{67} +(42571.9 - 24578.9i) q^{69} +(-334328. + 398437. i) q^{71} +(-104527. + 592802. i) q^{73} +1.00923e6i q^{75} +1.27231e6 q^{77} +(-400036. - 70537.2i) q^{79} +(-502013. - 421239. i) q^{81} +(-386540. - 669506. i) q^{83} +(-683617. - 248816. i) q^{85} +(595834. - 1.03201e6i) q^{87} +(-110452. + 19475.7i) q^{89} +(878693. + 1.04719e6i) q^{91} +(123301. - 44877.7i) q^{93} +(-956084. + 1.15037e6i) q^{95} +(-297501. - 817379. i) q^{97} +(480831. - 403465. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	31.1235	+	5.48792i	1.15272	+	0.203256i	0.717164	−	0.696904i	$-0.245440\pi$
$3$	31.1235	+	5.48792i	1.15272	+	0.203256i	0.435559	+	0.900160i	$0.356551\pi$
$4$		0			0
$5$	−167.059	−	140.179i	−1.33647	−	1.12143i	−0.982518	−	0.186169i	$-0.940393\pi$
$5$	−167.059	−	140.179i	−1.33647	−	1.12143i	−0.353953	−	0.935263i	$-0.615163\pi$
$6$		0			0
$7$	273.433	+	473.600i	0.797181	+	1.38076i	0.921445	+	0.388508i	$0.127010\pi$
$7$	273.433	+	473.600i	0.797181	+	1.38076i	−0.124264	+	0.992249i	$0.539657\pi$
$8$		0			0
$9$	253.520	+	92.2739i	0.347765	+	0.126576i
$10$		0			0
$11$	1163.27	−	2014.85i	0.873984	−	1.51378i	0.0161431	−	0.999870i	$-0.494861\pi$
$11$	1163.27	−	2014.85i	0.873984	−	1.51378i	0.857841	−	0.513915i	$-0.171805\pi$
$12$		0			0
$13$	2461.73	−	434.069i	1.12050	−	0.197574i	0.417437	−	0.908706i	$-0.362928\pi$
$13$	2461.73	−	434.069i	1.12050	−	0.197574i	0.703059	+	0.711132i	$0.251817\pi$
$14$		0			0
$15$	−4430.17	−	5279.67i	−1.31264	−	1.56435i
$16$		0			0
$17$	3134.71	−	1140.94i	0.638044	−	0.232229i	−0.00268464	−	0.999996i	$-0.500855\pi$
$17$	3134.71	−	1140.94i	0.638044	−	0.232229i	0.640729	+	0.767767i	$0.278632\pi$
$18$		0			0
$19$	−32.2826	−	6858.92i	−0.00470661	−	0.999989i
$19$	−32.2826	−	6858.92i	−0.00470661	−	0.999989i
$20$		0			0
$21$	5911.12	+	16240.7i	0.638281	+	1.75366i
$22$		0			0
$23$	1191.54	−	999.822i	0.0979322	−	0.0821749i	−0.592507	−	0.805565i	$-0.701862\pi$
$23$	1191.54	−	999.822i	0.0979322	−	0.0821749i	0.690439	+	0.723390i	$0.257417\pi$
$24$		0			0
$25$	5545.25	+	31448.7i	0.354896	+	2.01272i
$26$		0			0
$27$	−12568.4	−	7256.35i	−0.638539	−	0.368661i
$28$		0			0
$29$	12896.4	−	35432.7i	0.528781	−	1.45281i	−0.331727	−	0.943375i	$-0.607631\pi$
$29$	12896.4	−	35432.7i	0.528781	−	1.45281i	0.860508	−	0.509437i	$-0.170146\pi$
$30$		0			0
$31$	3595.61	−	2075.93i	0.120695	−	0.0696830i	−0.438437	−	0.898762i	$-0.644468\pi$
$31$	3595.61	−	2075.93i	0.120695	−	0.0696830i	0.559132	+	0.829079i	$0.311135\pi$
$32$		0			0
$33$	47262.5	−	56325.2i	1.31515	−	1.56733i
$34$		0			0
$35$	20709.4	−	117449.i	0.483017	−	2.73933i
$36$		0			0
$37$			30767.5i			0.607417i	0.952765	+	0.303709i	$0.0982249\pi$
$37$			30767.5i			0.607417i	−0.952765	+	0.303709i	$0.901775\pi$
$38$		0			0
$39$	78999.8			1.33178
$40$		0			0
$41$	−48569.6	−	8564.13i	−0.704714	−	0.124260i	−0.190204	−	0.981745i	$-0.560915\pi$
$41$	−48569.6	−	8564.13i	−0.704714	−	0.124260i	−0.514510	+	0.857485i	$0.672026\pi$
$42$		0			0
$43$	50960.3	+	42760.7i	0.640953	+	0.537824i	0.904311	−	0.426875i	$-0.140385\pi$
$43$	50960.3	+	42760.7i	0.640953	+	0.537824i	−0.263358	+	0.964698i	$0.584830\pi$
$44$		0			0
$45$	−29418.0	−	50953.4i	−0.322831	−	0.559159i
$46$		0			0
$47$	45459.6	+	16546.0i	0.437857	+	0.159367i	0.551537	−	0.834150i	$-0.314042\pi$
$47$	45459.6	+	16546.0i	0.437857	+	0.159367i	−0.113680	+	0.993517i	$0.536264\pi$
$48$		0			0
$49$	−90706.7	+	157109.i	−0.770994	+	1.33540i
$50$		0			0
$51$	103825.	−	18307.1i	0.782690	−	0.138009i
$52$		0			0
$53$	81092.6	+	96642.3i	0.544695	+	0.649142i	0.966233	−	0.257668i	$-0.0829542\pi$
$53$	81092.6	+	96642.3i	0.544695	+	0.649142i	−0.421538	+	0.906811i	$0.638510\pi$
$54$		0			0
$55$	−476774.	+	173532.i	−2.86566	+	1.04302i
$56$		0			0
$57$	36636.5	−	213651.i	0.197828	−	1.15367i
$58$		0			0
$59$	32417.4	+	89066.1i	0.157842	+	0.433667i	0.993254	−	0.115957i	$-0.0369934\pi$
$59$	32417.4	+	89066.1i	0.157842	+	0.433667i	−0.835412	+	0.549624i	$0.814771\pi$
$60$		0			0
$61$	16263.0	−	13646.3i	0.0716493	−	0.0601209i	−0.606260	−	0.795267i	$-0.707331\pi$
$61$	16263.0	−	13646.3i	0.0716493	−	0.0601209i	0.677909	+	0.735146i	$0.262886\pi$
$62$		0			0
$63$	25619.9	+	145298.i	0.102461	+	0.581082i
$64$		0			0
$65$	−472101.	−	272568.i	−1.71908	−	0.992509i
$66$		0			0
$67$	100234.	−	275390.i	0.333264	−	0.915636i	−0.653992	−	0.756501i	$-0.726907\pi$
$67$	100234.	−	275390.i	0.333264	−	0.915636i	0.987257	−	0.159135i	$-0.0508706\pi$
$68$		0			0
$69$	42571.9	−	24578.9i	0.129591	−	0.0748196i
$70$		0			0
$71$	−334328.	+	398437.i	−0.934111	+	1.11323i	0.0592564	+	0.998243i	$0.481127\pi$
$71$	−334328.	+	398437.i	−0.934111	+	1.11323i	−0.993367	+	0.114987i	$0.963317\pi$
$72$		0			0
$73$	−104527.	+	592802.i	−0.268695	+	1.52385i	0.489606	+	0.871944i	$0.337140\pi$
$73$	−104527.	+	592802.i	−0.268695	+	1.52385i	−0.758302	+	0.651904i	$0.773971\pi$
$74$		0			0
$75$			1.00923e6i			2.39224i
$76$		0			0
$77$	1.27231e6			2.78689
$78$		0			0
$79$	−400036.	−	70537.2i	−0.811368	−	0.143066i	−0.247454	−	0.968900i	$-0.579594\pi$
$79$	−400036.	−	70537.2i	−0.811368	−	0.143066i	−0.563914	+	0.825833i	$0.690705\pi$
$80$		0			0
$81$	−502013.	−	421239.i	−0.944626	−	0.792635i
$82$		0			0
$83$	−386540.	−	669506.i	−0.676020	−	1.17090i	−0.976170	−	0.217009i	$-0.930370\pi$
$83$	−386540.	−	669506.i	−0.676020	−	1.17090i	0.300149	−	0.953892i	$-0.402963\pi$
$84$		0			0
$85$	−683617.	−	248816.i	−1.11316	−	0.405156i
$86$		0			0
$87$	595834.	−	1.03201e6i	0.904831	−	1.56721i
$88$		0			0
$89$	−110452.	+	19475.7i	−0.156677	+	0.0276263i	−0.251436	−	0.967874i	$-0.580903\pi$
$89$	−110452.	+	19475.7i	−0.156677	+	0.0276263i	0.0947595	+	0.995500i	$0.469792\pi$
$90$		0			0
$91$	878693.	+	1.04719e6i	1.16604	+	1.38963i
$92$		0			0
$93$	123301.	−	44877.7i	0.153291	−	0.0557933i
$94$		0			0
$95$	−956084.	+	1.15037e6i	−1.11513	+	1.34173i
$96$		0			0
$97$	−297501.	−	817379.i	−0.325967	−	0.895587i	−0.989121	−	0.147104i	$-0.953005\pi$
$97$	−297501.	−	817379.i	−0.325967	−	0.895587i	0.663154	−	0.748483i	$-0.269218\pi$
$98$		0			0
$99$	480831.	−	403465.i	0.495549	−	0.415815i
$100$		0			0
$101$	145595.	+	825711.i	0.141313	+	0.801427i	0.970254	+	0.242090i	$0.0778329\pi$
$101$	145595.	+	825711.i	0.141313	+	0.801427i	−0.828941	+	0.559337i	$0.811056\pi$
$102$		0			0
$103$	987618.	+	570201.i	0.903810	+	0.521815i	0.878434	−	0.477863i	$-0.158588\pi$
$103$	987618.	+	570201.i	0.903810	+	0.521815i	0.0253756	+	0.999678i	$0.491922\pi$
$104$		0			0
$105$	1.28910e6	−	3.54176e6i	1.11357	−	3.05951i
$106$		0			0
$107$	−1.20702e6	+	696875.i	−0.985290	+	0.568858i	−0.903863	−	0.427822i	$-0.859281\pi$
$107$	−1.20702e6	+	696875.i	−0.985290	+	0.568858i	−0.0814273	+	0.996679i	$0.525948\pi$
$108$		0			0
$109$	−41388.7	+	49325.1i	−0.0319597	+	0.0380881i	−0.781788	−	0.623545i	$-0.785692\pi$
$109$	−41388.7	+	49325.1i	−0.0319597	+	0.0380881i	0.749828	+	0.661633i	$0.230136\pi$
$110$		0			0
$111$	−168849.	+	957593.i	−0.123461	+	0.700184i
$112$		0			0
$113$			1.21088e6i			0.839202i	0.907709	+	0.419601i	$0.137830\pi$
$113$			1.21088e6i			0.839202i	−0.907709	+	0.419601i	$0.862170\pi$
$114$		0			0
$115$	−339212.			−0.223037
$116$		0			0
$117$	664152.	+	117108.i	0.414677	+	0.0731187i
$118$		0			0
$119$	1.39748e6	+	1.17263e6i	0.829289	+	0.695856i
$120$		0			0
$121$	−1.82063e6	−	3.15342e6i	−1.02770	−	1.78002i
$122$		0			0
$123$	−1.46466e6	−	533091.i	−0.787083	−	0.286475i
$124$		0			0
$125$	1.77831e6	−	3.08013e6i	0.910496	−	1.57703i
$126$		0			0
$127$	3.66121e6	−	645571.i	1.78737	−	0.315161i	0.820732	−	0.571314i	$-0.193566\pi$
$127$	3.66121e6	−	645571.i	1.78737	−	0.315161i	0.966636	+	0.256153i	$0.0824550\pi$
$128$		0			0
$129$	1.35140e6	+	1.61053e6i	0.629526	+	0.750239i
$130$		0			0
$131$	−1.43302e6	+	521577.i	−0.637439	+	0.232009i	−0.640466	−	0.767987i	$-0.721259\pi$
$131$	−1.43302e6	+	521577.i	−0.637439	+	0.232009i	0.00302685	+	0.999995i	$0.499037\pi$
$132$		0			0
$133$	3.23956e6	−	1.89075e6i	1.37699	−	0.803671i
$134$		0			0
$135$	1.08247e6	+	2.97406e6i	0.439961	+	1.20878i
$136$		0			0
$137$	195452.	−	164004.i	0.0760115	−	0.0637812i	−0.603990	−	0.796992i	$-0.706423\pi$
$137$	195452.	−	164004.i	0.0760115	−	0.0637812i	0.680002	+	0.733210i	$0.261979\pi$
$138$		0			0
$139$	−855935.	−	4.85425e6i	−0.318710	−	1.80750i	−0.550617	−	0.834758i	$-0.685607\pi$
$139$	−855935.	−	4.85425e6i	−0.318710	−	1.80750i	0.231906	−	0.972738i	$-0.425504\pi$
$140$		0			0
$141$	1.32406e6	+	764447.i	0.472336	+	0.272703i
$142$		0			0
$143$	1.98908e6	−	5.46495e6i	0.680212	−	1.86887i
$144$		0			0
$145$	−7.12138e6	+	4.11153e6i	−2.33593	+	1.34865i
$146$		0			0
$147$	−3.68531e6	+	4.39198e6i	−1.16017	+	1.38264i
$148$		0			0
$149$	841280.	−	4.77113e6i	0.254321	−	1.44232i	−0.543490	−	0.839416i	$-0.682897\pi$
$149$	841280.	−	4.77113e6i	0.254321	−	1.44232i	0.797811	−	0.602908i	$-0.205992\pi$
$150$		0			0
$151$			1.26472e6i			0.367336i	0.982988	+	0.183668i	$0.0587971\pi$
$151$			1.26472e6i			0.367336i	−0.982988	+	0.183668i	$0.941203\pi$
$152$		0			0
$153$	899992.			0.251284
$154$		0			0
$155$	−891680.	−	157227.i	−0.239450	−	0.0422214i
$156$		0			0
$157$	1.04577e6	+	877509.i	0.270233	+	0.226753i	0.767826	−	0.640658i	$-0.221338\pi$
$157$	1.04577e6	+	877509.i	0.270233	+	0.226753i	−0.497593	+	0.867411i	$0.665783\pi$
$158$		0			0
$159$	1.99352e6	+	3.45288e6i	0.495940	+	0.858994i
$160$		0			0
$161$	799322.	+	290930.i	0.191533	+	0.0697124i
$162$		0			0
$163$	−1.03372e6	+	1.79046e6i	−0.238693	+	0.413429i	−0.960340	−	0.278833i	$-0.910052\pi$
$163$	−1.03372e6	+	1.79046e6i	−0.238693	+	0.413429i	0.721646	+	0.692262i	$0.243386\pi$
$164$		0			0
$165$	−1.57912e7	+	2.78442e6i	−3.51531	+	0.619845i
$166$		0			0
$167$	4.75283e6	+	5.66421e6i	1.02048	+	1.21616i	0.976140	+	0.217140i	$0.0696729\pi$
$167$	4.75283e6	+	5.66421e6i	1.02048	+	1.21616i	0.0443364	+	0.999017i	$0.485883\pi$
$168$		0			0
$169$	1.33598e6	−	486257.i	0.276783	−	0.100741i
$170$		0			0
$171$	624715.	−	1.74186e6i	0.124938	−	0.348356i
$172$		0			0
$173$	2.59394e6	+	7.12678e6i	0.500980	+	1.37643i	0.890319	+	0.455338i	$0.150481\pi$
$173$	2.59394e6	+	7.12678e6i	0.500980	+	1.37643i	−0.389338	+	0.921095i	$0.627296\pi$
$174$		0			0
$175$	−1.33778e7	+	1.12253e7i	−2.49616	+	2.09452i
$176$		0			0
$177$	520156.	+	2.94995e6i	0.0938025	+	0.531980i
$178$		0			0
$179$	−3.06941e6	−	1.77213e6i	−0.535176	−	0.308984i	0.207946	−	0.978140i	$-0.433322\pi$
$179$	−3.06941e6	−	1.77213e6i	−0.535176	−	0.308984i	−0.743121	+	0.669157i	$0.766656\pi$
$180$		0			0
$181$	−1.50936e6	+	4.14693e6i	−0.254541	+	0.699345i	0.744940	+	0.667131i	$0.232478\pi$
$181$	−1.50936e6	+	4.14693e6i	−0.254541	+	0.699345i	−0.999481	+	0.0322136i	$0.989744\pi$
$182$		0			0
$183$	581052.	−	335471.i	0.0948117	−	0.0547395i
$184$		0			0
$185$	4.31296e6	−	5.13998e6i	0.681177	−	0.811795i
$186$		0			0
$187$	1.34770e6	−	7.64319e6i	0.206096	−	1.16883i
$188$		0			0
$189$		−	7.93650e6i		−	1.17556i
$190$		0			0
$191$	1.94902e6			0.279715			0.139858	−	0.990172i	$-0.455335\pi$
$191$	1.94902e6			0.279715			0.139858	+	0.990172i	$0.455335\pi$
$192$		0			0
$193$	1.05732e7	+	1.86434e6i	1.47074	+	0.259331i	0.850870	−	0.525376i	$-0.176075\pi$
$193$	1.05732e7	+	1.86434e6i	1.47074	+	0.259331i	0.619867	+	0.784707i	$0.287186\pi$
$194$		0			0
$195$	−1.31976e7	−	1.10741e7i	−1.77988	−	1.49350i
$196$		0			0
$197$	−520817.	−	902081.i	−0.0681218	−	0.117990i	0.829953	−	0.557834i	$-0.188367\pi$
$197$	−520817.	−	902081.i	−0.0681218	−	0.117990i	−0.898075	+	0.439843i	$0.855034\pi$
$198$		0			0
$199$	−2.21656e6	−	806763.i	−0.281269	−	0.102373i	0.197534	−	0.980296i	$-0.436707\pi$
$199$	−2.21656e6	−	806763.i	−0.281269	−	0.102373i	−0.478802	+	0.877923i	$0.658929\pi$
$200$		0			0
$201$	4.63094e6	−	8.02102e6i	0.570270	−	0.987737i
$202$		0			0
$203$	2.03072e7	−	3.58071e6i	2.42752	−	0.428037i
$204$		0			0
$205$	6.91347e6	+	8.23915e6i	0.802480	+	0.956358i
$206$		0			0
$207$	394337.	−	143527.i	0.0444587	−	0.0161817i
$208$		0			0
$209$	−1.38572e7	−	7.91376e6i	−1.51788	−	0.866850i
$210$		0			0
$211$	1.14389e6	+	3.14282e6i	0.121770	+	0.334559i	0.985568	−	0.169278i	$-0.0541435\pi$
$211$	1.14389e6	+	3.14282e6i	0.121770	+	0.334559i	−0.863799	+	0.503837i	$0.831921\pi$
$212$		0			0
$213$	−1.25921e7	+	1.05660e7i	−1.30304	+	1.09338i
$214$		0			0
$215$	−2.51921e6	−	1.42871e7i	−0.253483	−	1.43757i
$216$		0			0
$217$	1.96632e6	+	1.13525e6i	0.192431	+	0.111100i
$218$		0			0
$219$	−6.50650e6	+	1.78765e7i	−0.619463	+	1.70196i
$220$		0			0
$221$	7.22156e6	−	4.16937e6i	0.669044	−	0.386272i
$222$		0			0
$223$	−419388.	+	499808.i	−0.0378183	+	0.0450701i	−0.784622	−	0.619974i	$-0.787143\pi$
$223$	−419388.	+	499808.i	−0.0378183	+	0.0450701i	0.746804	+	0.665044i	$0.231587\pi$
$224$		0			0
$225$	−1.49606e6	+	8.48456e6i	−0.131341	+	0.744872i
$226$		0			0
$227$			3.78345e6i			0.323452i	0.986836	+	0.161726i	$0.0517061\pi$
$227$			3.78345e6i			0.323452i	−0.986836	+	0.161726i	$0.948294\pi$
$228$		0			0
$229$	−5.24557e6			−0.436804			−0.218402	−	0.975859i	$-0.570084\pi$
$229$	−5.24557e6			−0.436804			−0.218402	+	0.975859i	$0.570084\pi$
$230$		0			0
$231$	3.95987e7	+	6.98232e6i	3.21252	+	0.566453i
$232$		0			0
$233$	1.45764e7	+	1.22310e7i	1.15234	+	0.966931i	0.999772	−	0.0213618i	$-0.00680019\pi$
$233$	1.45764e7	+	1.22310e7i	1.15234	+	0.966931i	0.152571	+	0.988292i	$0.451245\pi$
$234$		0			0
$235$	−5.27504e6	−	9.13664e6i	−0.406464	−	0.704016i
$236$		0			0
$237$	−1.20634e7	−	4.39073e6i	−0.906204	−	0.329831i
$238$		0			0
$239$	−4.31435e6	+	7.47267e6i	−0.316025	+	0.547372i	−0.979655	−	0.200690i	$-0.935682\pi$
$239$	−4.31435e6	+	7.47267e6i	−0.316025	+	0.547372i	0.663630	+	0.748061i	$0.269015\pi$
$240$		0			0
$241$	−1.00187e7	+	1.76657e6i	−0.715751	+	0.126206i	−0.519652	−	0.854378i	$-0.673938\pi$
$241$	−1.00187e7	+	1.76657e6i	−0.715751	+	0.126206i	−0.196099	+	0.980584i	$0.562827\pi$
$242$		0			0
$243$	−6.51215e6	−	7.76088e6i	−0.453843	−	0.540869i
$244$		0			0
$245$	3.71767e7	−	1.35312e7i	2.52797	−	0.920107i
$246$		0			0
$247$	−3.05672e6	−	1.68708e7i	−0.202845	−	1.11955i
$248$		0			0
$249$	−8.35628e6	−	2.29587e7i	−0.541271	−	1.48713i
$250$		0			0
$251$	5.60972e6	−	4.70711e6i	0.354748	−	0.297669i	−0.447945	−	0.894061i	$-0.647844\pi$
$251$	5.60972e6	−	4.70711e6i	0.354748	−	0.297669i	0.802693	+	0.596392i	$0.203400\pi$
$252$		0			0
$253$	−628401.	−	3.56384e6i	−0.0388039	−	0.220068i
$254$		0			0
$255$	−1.99111e7	−	1.14957e7i	−1.20081	−	0.693288i
$256$		0			0
$257$	3.81404e6	−	1.04790e7i	0.224691	−	0.617334i	−0.775206	−	0.631709i	$-0.782354\pi$
$257$	3.81404e6	−	1.04790e7i	0.224691	−	0.617334i	0.999897	+	0.0143753i	$0.00457597\pi$
$258$		0			0
$259$	−1.45715e7	+	8.41285e6i	−0.838696	+	0.484221i
$260$		0			0
$261$	6.53901e6	−	7.79289e6i	0.367782	−	0.438306i
$262$		0			0
$263$	−222743.	+	1.26324e6i	−0.0122444	+	0.0694414i	−0.990318	−	0.138820i	$-0.955669\pi$
$263$	−222743.	+	1.26324e6i	−0.0122444	+	0.0694414i	0.978073	+	0.208261i	$0.0667803\pi$
$264$		0			0
$265$		−	2.75124e7i		−	1.47840i
$266$		0			0
$267$	−3.54454e6			−0.186220
$268$		0			0
$269$	−5.10232e6	−	899676.i	−0.262126	−	0.0462200i	0.0410403	−	0.999157i	$-0.486933\pi$
$269$	−5.10232e6	−	899676.i	−0.262126	−	0.0462200i	−0.303167	+	0.952938i	$0.598044\pi$
$270$		0			0
$271$	1.44675e7	+	1.21397e7i	0.726918	+	0.609956i	0.929289	−	0.369352i	$-0.120420\pi$
$271$	1.44675e7	+	1.21397e7i	0.726918	+	0.609956i	−0.202372	+	0.979309i	$0.564865\pi$
$272$		0			0
$273$	2.16012e7	+	3.74143e7i	1.06167	+	1.83886i
$274$		0			0
$275$	6.98149e7	+	2.54106e7i	3.35699	+	1.22184i
$276$		0			0
$277$	−1.04069e7	+	1.80253e7i	−0.489646	+	0.848092i	−0.999929	−	0.0119144i	$-0.996207\pi$
$277$	−1.04069e7	+	1.80253e7i	−0.489646	+	0.848092i	0.510283	+	0.860007i	$0.329541\pi$
$278$		0			0
$279$	1.10311e6	−	194509.i	0.0507935	−	0.00895626i
$280$		0			0
$281$	1.10139e6	+	1.31258e6i	0.0496387	+	0.0591571i	0.790293	−	0.612730i	$-0.209929\pi$
$281$	1.10139e6	+	1.31258e6i	0.0496387	+	0.0591571i	−0.740654	+	0.671887i	$0.765484\pi$
$282$		0			0
$283$	1.41912e6	−	516518.i	0.0626124	−	0.0227891i	−0.310524	−	0.950566i	$-0.600505\pi$
$283$	1.41912e6	−	516518.i	0.0626124	−	0.0227891i	0.373137	+	0.927776i	$0.378282\pi$
$284$		0			0
$285$	−3.60698e7	+	3.05566e7i	−1.55815	+	1.31999i
$286$		0			0
$287$	−9.22455e6	−	2.53443e7i	−0.390211	−	1.07210i
$288$		0			0
$289$	−9.96579e6	+	8.36229e6i	−0.412875	+	0.346443i
$290$		0			0
$291$	−4.77359e6	−	2.70724e7i	−0.193716	−	1.09862i
$292$		0			0
$293$	−2.76601e7	−	1.59695e7i	−1.09964	−	0.634877i	−0.163513	−	0.986541i	$-0.552283\pi$
$293$	−2.76601e7	−	1.59695e7i	−1.09964	−	0.634877i	−0.936126	+	0.351664i	$0.885616\pi$
$294$		0			0
$295$	7.06958e6	−	1.94235e7i	0.275377	−	0.756592i
$296$		0			0
$297$	−2.92409e7	+	1.68822e7i	−1.11615	+	0.644407i
$298$		0			0
$299$	2.49926e6	−	2.97850e6i	0.0934971	−	0.111425i
$300$		0			0
$301$	−6.31726e6	+	3.58270e7i	−0.231648	+	1.31374i
$302$		0			0
$303$			2.64980e7i			0.952546i
$304$		0			0
$305$	−4.62981e6			−0.163179
$306$		0			0
$307$	−5.35619e7	−	9.44441e6i	−1.85115	−	0.326407i	−0.866259	−	0.499595i	$-0.833482\pi$
$307$	−5.35619e7	−	9.44441e6i	−1.85115	−	0.326407i	−0.984889	+	0.173187i	$0.944593\pi$
$308$		0			0
$309$	2.76089e7	+	2.31666e7i	0.935780	+	0.785213i
$310$		0			0
$311$	−5.92197e6	−	1.02572e7i	−0.196873	−	0.340993i	0.750640	−	0.660711i	$-0.229745\pi$
$311$	−5.92197e6	−	1.02572e7i	−0.196873	−	0.340993i	−0.947513	+	0.319718i	$0.896412\pi$
$312$		0			0
$313$	4.42021e7	+	1.60882e7i	1.44148	+	0.524657i	0.940199	−	0.340626i	$-0.110639\pi$
$313$	4.42021e7	+	1.60882e7i	1.44148	+	0.524657i	0.501284	+	0.865283i	$0.332861\pi$
$314$		0			0
$315$	1.60877e7	−	2.78647e7i	0.514709	−	0.891502i
$316$		0			0
$317$	−1.19266e6	+	210298.i	−0.0374402	+	0.00660172i	−0.192337	−	0.981329i	$-0.561607\pi$
$317$	−1.19266e6	+	210298.i	−0.0374402	+	0.00660172i	0.154897	+	0.987931i	$0.450496\pi$
$318$		0			0
$319$	−5.63893e7	−	6.72022e7i	−1.73710	−	2.07020i
$320$		0			0
$321$	−4.13912e7	+	1.50652e7i	−1.25139	+	0.455469i
$322$		0			0
$323$	−7.92683e6	−	2.14639e7i	−0.235230	−	0.636944i
$324$		0			0
$325$	2.73018e7	+	7.50111e7i	0.795319	+	2.18512i
$326$		0			0
$327$	−1.55885e6	+	1.30803e6i	−0.0445823	+	0.0374090i
$328$		0			0
$329$	4.59400e6	+	2.60539e7i	0.129004	+	0.731619i
$330$		0			0
$331$	2.20775e7	+	1.27465e7i	0.608789	+	0.351484i	0.772491	−	0.635025i	$-0.219010\pi$
$331$	2.20775e7	+	1.27465e7i	0.608789	+	0.351484i	−0.163702	+	0.986510i	$0.552344\pi$
$332$		0			0
$333$	−2.83904e6	+	7.80019e6i	−0.0768844	+	0.211238i
$334$		0			0
$335$	−5.53488e7	+	3.19556e7i	−1.47222	+	0.849988i
$336$		0			0
$337$	3.10780e6	−	3.70374e6i	0.0812015	−	0.0967722i	−0.723914	−	0.689890i	$-0.757659\pi$
$337$	3.10780e6	−	3.70374e6i	0.0812015	−	0.0967722i	0.805116	+	0.593118i	$0.202103\pi$
$338$		0			0
$339$	−6.64522e6	+	3.76869e7i	−0.170573	+	0.967367i
$340$		0			0
$341$		−	9.65948e6i		−	0.243607i
$342$		0			0
$343$	−3.48706e7			−0.864126
$344$		0			0
$345$	−1.05575e7	−	1.86156e6i	−0.257100	−	0.0453337i
$346$		0			0
$347$	2.35449e7	+	1.97565e7i	0.563518	+	0.472848i	0.879488	−	0.475921i	$-0.157885\pi$
$347$	2.35449e7	+	1.97565e7i	0.563518	+	0.472848i	−0.315970	+	0.948769i	$0.602330\pi$
$348$		0			0
$349$	1.18414e7	+	2.05099e7i	0.278565	+	0.482489i	0.971028	−	0.238964i	$-0.0768078\pi$
$349$	1.18414e7	+	2.05099e7i	0.278565	+	0.482489i	−0.692463	+	0.721453i	$0.743474\pi$
$350$		0			0
$351$	−3.40897e7	−	1.24076e7i	−0.788318	−	0.286924i
$352$		0			0
$353$	−1.44141e6	+	2.49659e6i	−0.0327689	+	0.0567574i	−0.881945	−	0.471353i	$-0.843766\pi$
$353$	−1.44141e6	+	2.49659e6i	−0.0327689	+	0.0567574i	0.849176	+	0.528110i	$0.177099\pi$
$354$		0			0
$355$	1.11705e8	−	1.96966e7i	2.49682	−	0.440257i
$356$		0			0
$357$	3.70593e7	+	4.41656e7i	0.814503	+	0.970687i
$358$		0			0
$359$	−4.46284e7	+	1.62434e7i	−0.964558	+	0.351070i	−0.775818	−	0.630957i	$-0.782662\pi$
$359$	−4.46284e7	+	1.62434e7i	−0.964558	+	0.351070i	−0.188740	+	0.982027i	$0.560440\pi$
$360$		0			0
$361$	−4.70438e7	+	442848.i	−0.999956	+	0.00941312i
$362$		0			0
$363$	−3.93586e7	−	1.08137e8i	−0.822849	−	2.26076i
$364$		0			0
$365$	1.00561e8	−	8.43804e7i	2.06799	−	1.73525i
$366$		0			0
$367$	5.51455e6	+	3.12746e7i	0.111561	+	0.632693i	0.988396	+	0.151901i	$0.0485396\pi$
$367$	5.51455e6	+	3.12746e7i	0.111561	+	0.632693i	−0.876835	+	0.480792i	$0.840349\pi$
$368$		0			0
$369$	−1.15231e7	−	6.65288e6i	−0.229346	−	0.132413i
$370$		0			0
$371$	−2.35964e7	+	6.48306e7i	−0.462088	+	1.26958i
$372$		0			0
$373$	2.51159e7	−	1.45006e7i	0.483973	−	0.279422i	−0.238097	−	0.971241i	$-0.576524\pi$
$373$	2.51159e7	−	1.45006e7i	0.483973	−	0.279422i	0.722071	+	0.691819i	$0.243190\pi$
$374$		0			0
$375$	7.22508e7	−	8.61052e7i	1.37009	−	1.63281i
$376$		0			0
$377$	1.63673e7	−	9.28236e7i	0.305459	−	1.73234i
$378$		0			0
$379$			3.18400e7i			0.584864i	0.956286	+	0.292432i	$0.0944645\pi$
$379$			3.18400e7i			0.584864i	−0.956286	+	0.292432i	$0.905535\pi$
$380$		0			0
$381$	1.17493e8			2.12440
$382$		0			0
$383$	8.40837e7	+	1.48262e7i	1.49663	+	0.263897i	0.861203	−	0.508261i	$-0.169712\pi$
$383$	8.40837e7	+	1.48262e7i	1.49663	+	0.263897i	0.635430	+	0.772158i	$0.280823\pi$
$384$		0			0
$385$	−2.12550e8	−	1.78351e8i	−3.72460	−	3.12531i
$386$		0			0
$387$	8.97377e6	+	1.55430e7i	0.154825	+	0.268165i
$388$		0			0
$389$	1.88102e7	+	6.84636e6i	0.319555	+	0.116308i	0.496817	−	0.867855i	$-0.334502\pi$
$389$	1.88102e7	+	6.84636e6i	0.319555	+	0.116308i	−0.177262	+	0.984164i	$0.556724\pi$
$390$		0			0
$391$	2.59440e6	−	4.49363e6i	0.0434017	−	0.0751739i
$392$		0			0
$393$	−4.74630e7	+	8.36901e6i	−0.781948	+	0.137879i
$394$		0			0
$395$	5.69418e7	+	6.78605e7i	0.923931	+	1.10110i
$396$		0			0
$397$	−6.36991e7	+	2.31846e7i	−1.01803	+	0.370533i	−0.796512	−	0.604622i	$-0.793324\pi$
$397$	−6.36991e7	+	2.31846e7i	−1.01803	+	0.370533i	−0.221520	+	0.975156i	$0.571102\pi$
$398$		0			0
$399$	1.11203e8	−	4.10682e7i	1.75064	−	0.646528i
$400$		0			0
$401$	−3.29881e7	−	9.06342e7i	−0.511593	−	1.40559i	−0.879576	−	0.475758i	$-0.842174\pi$
$401$	−3.29881e7	−	9.06342e7i	−0.511593	−	1.40559i	0.367983	−	0.929832i	$-0.380048\pi$
$402$		0			0
$403$	7.95033e6	−	6.67112e6i	0.121470	−	0.101926i
$404$		0			0
$405$	2.48169e7	+	1.40743e8i	0.373578	+	2.11867i
$406$		0			0
$407$	6.19918e7	+	3.57910e7i	0.919499	+	0.530873i
$408$		0			0
$409$	3.16645e7	−	8.69975e7i	0.462810	−	1.27156i	−0.460553	−	0.887632i	$-0.652349\pi$
$409$	3.16645e7	−	8.69975e7i	0.462810	−	1.27156i	0.923363	−	0.383928i	$-0.125429\pi$
$410$		0			0
$411$	6.98321e6	−	4.03176e6i	0.100584	−	0.0580723i
$412$		0			0
$413$	−3.33177e7	+	3.97065e7i	−0.472960	+	0.563652i
$414$		0			0
$415$	−2.92759e7	+	1.66032e8i	−0.409605	+	2.32299i
$416$		0			0
$417$		−	1.55779e8i		−	2.14832i
$418$		0			0
$419$	−7.83994e7			−1.06579			−0.532894	−	0.846182i	$-0.678895\pi$
$419$	−7.83994e7			−1.06579			−0.532894	+	0.846182i	$0.678895\pi$
$420$		0			0
$421$	−3.13392e7	−	5.52594e6i	−0.419992	−	0.0740560i	−0.0403417	−	0.999186i	$-0.512845\pi$
$421$	−3.13392e7	−	5.52594e6i	−0.419992	−	0.0740560i	−0.379651	+	0.925130i	$0.623956\pi$
$422$		0			0
$423$	9.99818e6	+	8.38947e6i	0.132099	+	0.110844i
$424$		0			0
$425$	5.32638e7	+	9.22557e7i	0.693850	+	1.20178i
$426$		0			0
$427$	1.09097e7	+	3.97082e6i	0.140130	+	0.0510031i
$428$		0			0
$429$	9.18984e7	−	1.59173e8i	1.16395	−	2.01603i
$430$		0			0
$431$	−4.42527e6	+	780295.i	−0.0552724	+	0.00974601i	−0.201216	−	0.979547i	$-0.564489\pi$
$431$	−4.42527e6	+	780295.i	−0.0552724	+	0.00974601i	0.145944	+	0.989293i	$0.453378\pi$
$432$		0			0
$433$	4.82769e7	+	5.75342e7i	0.594670	+	0.708700i	0.976496	−	0.215534i	$-0.0691493\pi$
$433$	4.82769e7	+	5.75342e7i	0.594670	+	0.708700i	−0.381827	+	0.924234i	$0.624705\pi$
$434$		0			0
$435$	−2.44206e8	+	8.88837e7i	−2.96680	+	1.07983i
$436$		0			0
$437$	−6.89617e6	−	8.14042e6i	−0.0826349	−	0.0975444i
$438$		0			0
$439$	3.18975e7	+	8.76377e7i	0.377019	+	1.03585i	0.972586	+	0.232546i	$0.0747055\pi$
$439$	3.18975e7	+	8.76377e7i	0.377019	+	1.03585i	−0.595566	+	0.803306i	$0.703072\pi$
$440$		0			0
$441$	−3.74930e7	+	3.14604e7i	−0.437154	+	0.366816i
$442$		0			0
$443$	2.63948e7	+	1.49693e8i	0.303604	+	1.72183i	0.630002	+	0.776593i	$0.283054\pi$
$443$	2.63948e7	+	1.49693e8i	0.303604	+	1.72183i	−0.326398	+	0.945232i	$0.605835\pi$
$444$		0			0
$445$	2.11821e7	+	1.22295e7i	0.240375	+	0.138781i
$446$		0			0
$447$	5.23672e7	−	1.43878e8i	0.586322	−	1.61091i
$448$		0			0
$449$	8.23379e7	−	4.75378e7i	0.909622	−	0.525170i	0.0293123	−	0.999570i	$-0.490668\pi$
$449$	8.23379e7	−	4.75378e7i	0.909622	−	0.525170i	0.880309	+	0.474400i	$0.157335\pi$
$450$		0			0
$451$	−7.37551e7	+	8.78979e7i	−0.804011	+	0.958184i
$452$		0			0
$453$	−6.94068e6	+	3.93625e7i	−0.0746633	+	0.423437i
$454$		0			0
$455$		−	2.98116e8i		−	3.16484i
$456$		0			0
$457$	−3.68196e7			−0.385771			−0.192886	−	0.981221i	$-0.561785\pi$
$457$	−3.68196e7			−0.385771			−0.192886	+	0.981221i	$0.561785\pi$
$458$		0			0
$459$	−4.76772e7	−	8.40678e6i	−0.493030	−	0.0869344i
$460$		0			0
$461$	−1.21665e8	−	1.02089e8i	−1.24183	−	1.04202i	−0.997379	−	0.0723543i	$-0.976949\pi$
$461$	−1.21665e8	−	1.02089e8i	−1.24183	−	1.04202i	−0.244448	−	0.969662i	$-0.578607\pi$
$462$		0			0
$463$	−2.22736e7	−	3.85790e7i	−0.224412	−	0.388694i	0.731731	−	0.681594i	$-0.238713\pi$
$463$	−2.22736e7	−	3.85790e7i	−0.224412	−	0.388694i	−0.956143	+	0.292900i	$0.905380\pi$
$464$		0			0
$465$	−2.68894e7	−	9.78693e6i	−0.267437	−	0.0973392i
$466$		0			0
$467$	−4.99152e7	+	8.64556e7i	−0.490097	+	0.848873i	−0.999935	−	0.0113975i	$-0.996372\pi$
$467$	−4.99152e7	+	8.64556e7i	−0.490097	+	0.848873i	0.509838	+	0.860270i	$0.329705\pi$
$468$		0			0
$469$	1.57832e8	−	2.78300e7i	1.52994	−	0.269770i
$470$		0			0
$471$	2.77325e7	+	3.30503e7i	0.265415	+	0.316310i
$472$		0			0
$473$	1.45437e8	−	5.29348e7i	1.37433	−	0.500216i
$474$		0			0
$475$	2.15525e8	−	3.90497e7i	2.01102	−	0.364365i
$476$		0			0
$477$	1.16410e7	+	3.19835e7i	0.107260	+	0.294694i
$478$		0			0
$479$	−7.02413e7	+	5.89394e7i	−0.639125	+	0.536290i	−0.903749	−	0.428062i	$-0.859196\pi$
$479$	−7.02413e7	+	5.89394e7i	−0.639125	+	0.536290i	0.264624	+	0.964352i	$0.414752\pi$
$480$		0			0
$481$	1.33552e7	+	7.57413e7i	0.120010	+	0.680609i
$482$		0			0
$483$	2.32811e7	+	1.34414e7i	0.206615	+	0.119289i
$484$		0			0
$485$	−6.48791e7	+	1.78254e8i	−0.568695	+	1.56248i
$486$		0			0
$487$	−1.95041e8	+	1.12607e8i	−1.68865	+	0.974941i	−0.733092	+	0.680129i	$0.761924\pi$
$487$	−1.95041e8	+	1.12607e8i	−1.68865	+	0.974941i	−0.955555	+	0.294812i	$0.904743\pi$
$488$		0			0
$489$	−4.19989e7	+	5.00523e7i	−0.359179	+	0.428053i
$490$		0			0
$491$	2.60638e7	−	1.47815e8i	0.220188	−	1.24875i	−0.651485	−	0.758661i	$-0.725854\pi$
$491$	2.60638e7	−	1.47815e8i	0.220188	−	1.24875i	0.871673	−	0.490087i	$-0.163035\pi$
$492$		0			0
$493$		−	1.25785e8i		−	1.04976i
$494$		0			0
$495$	−1.36884e8			−1.12860
$496$		0			0
$497$	−2.80116e8	−	4.93920e7i	−2.28176	−	0.402335i
$498$		0			0
$499$	6.58061e7	+	5.52179e7i	0.529620	+	0.444404i	0.867970	−	0.496616i	$-0.165424\pi$
$499$	6.58061e7	+	5.52179e7i	0.529620	+	0.444404i	−0.338350	+	0.941020i	$0.609869\pi$
$500$		0			0
$501$	1.16840e8	+	2.02373e8i	0.929136	+	1.60931i
$502$		0			0
$503$	−2.80908e7	−	1.02242e7i	−0.220730	−	0.0803390i	0.229288	−	0.973359i	$-0.426360\pi$
$503$	−2.80908e7	−	1.02242e7i	−0.220730	−	0.0803390i	−0.450018	+	0.893020i	$0.648582\pi$
$504$		0			0
$505$	9.14244e7	−	1.58352e8i	0.709885	−	1.22956i
$506$		0			0
$507$	4.42489e7	−	7.80228e6i	0.339531	−	0.0598684i
$508$		0			0
$509$	1.47195e6	+	1.75420e6i	0.0111619	+	0.0133023i	0.771597	−	0.636112i	$-0.219458\pi$
$509$	1.47195e6	+	1.75420e6i	0.0111619	+	0.0133023i	−0.760435	+	0.649415i	$0.775014\pi$
$510$		0			0
$511$	−3.09332e8	+	1.12588e8i	−2.31826	+	0.843779i
$512$		0			0
$513$	−4.93650e7	+	8.64397e7i	−0.365651	+	0.640267i
$514$		0			0
$515$	−8.50600e7	−	2.33700e8i	−0.622736	−	1.71095i
$516$		0			0
$517$	8.62195e7	−	7.23468e7i	0.623927	−	0.523537i
$518$		0			0
$519$	4.16212e7	+	2.36046e8i	0.297723	+	1.68847i
$520$		0			0
$521$	2.03535e8	+	1.17511e8i	1.43922	+	0.830932i	0.997795	−	0.0663672i	$-0.0211409\pi$
$521$	2.03535e8	+	1.17511e8i	1.43922	+	0.830932i	0.441422	+	0.897300i	$0.354474\pi$
$522$		0			0
$523$	4.82967e7	−	1.32694e8i	0.337608	−	0.927570i	−0.648463	−	0.761246i	$-0.724588\pi$
$523$	4.82967e7	−	1.32694e8i	0.337608	−	0.927570i	0.986071	−	0.166324i	$-0.0531897\pi$
$524$		0			0
$525$	−4.77969e8	+	2.75955e8i	−3.30310	+	1.90705i
$526$		0			0
$527$	8.90269e6	−	1.06098e7i	0.0608260	−	0.0724896i
$528$		0			0
$529$	−2.52860e7	+	1.43404e8i	−0.170810	+	0.968713i
$530$		0			0
$531$			2.55713e7i			0.170793i
$532$		0			0
$533$	−1.23283e8			−0.814179
$534$		0			0
$535$	2.99331e8	+	5.27802e7i	1.95475	+	0.344675i
$536$		0			0
$537$	−8.58057e7	−	7.19995e7i	−0.554106	−	0.464950i
$538$		0			0
$539$	2.11033e8	+	3.65520e8i	1.34767	+	2.33424i
$540$		0			0
$541$	1.68756e8	+	6.14221e7i	1.06578	+	0.387912i	0.814596	−	0.580028i	$-0.196958\pi$
$541$	1.68756e8	+	6.14221e7i	1.06578	+	0.387912i	0.251182	+	0.967940i	$0.419181\pi$
$542$		0			0
$543$	−6.97346e7	+	1.20784e8i	−0.435561	+	0.754414i
$544$		0			0
$545$	1.38287e7	−	2.43837e6i	0.0854263	−	0.0150630i
$546$		0			0
$547$	−5.70970e7	−	6.80456e7i	−0.348860	−	0.415755i	0.562870	−	0.826546i	$-0.309697\pi$
$547$	−5.70970e7	−	6.80456e7i	−0.348860	−	0.415755i	−0.911730	+	0.410790i	$0.865253\pi$
$548$		0			0
$549$	5.38220e6	−	1.95896e6i	0.0325269	−	0.0118388i
$550$		0			0
$551$	−2.43446e8	−	8.73118e7i	−1.45529	−	0.521937i
$552$		0			0
$553$	−7.59767e7	−	2.08744e8i	−0.449268	−	1.23435i
$554$		0			0
$555$	1.62442e8	−	1.36305e8i	0.950211	−	0.797322i
$556$		0			0
$557$	−1.41897e7	−	8.04736e7i	−0.0821120	−	0.465680i	−0.997942	−	0.0641153i	$-0.979577\pi$
$557$	−1.41897e7	−	8.04736e7i	−0.0821120	−	0.465680i	0.915830	−	0.401565i	$-0.131534\pi$
$558$		0			0
$559$	1.44012e8	+	8.31451e7i	0.824445	+	0.475994i
$560$		0			0
$561$	8.38904e7	−	2.30487e8i	0.475142	−	1.30544i
$562$		0			0
$563$	−8.00068e7	+	4.61920e7i	−0.448334	+	0.258846i	−0.707126	−	0.707087i	$-0.750009\pi$
$563$	−8.00068e7	+	4.61920e7i	−0.448334	+	0.258846i	0.258792	+	0.965933i	$0.416676\pi$
$564$		0			0
$565$	1.69740e8	−	2.02289e8i	0.941108	−	1.12157i
$566$		0			0
$567$	6.22318e7	−	3.52934e8i	0.341400	−	1.93617i
$568$		0			0
$569$		−	2.75438e7i		−	0.149516i	−0.997202	−	0.0747580i	$-0.976182\pi$
$569$		−	2.75438e7i		−	0.149516i	0.997202	−	0.0747580i	$-0.0238184\pi$
$570$		0			0
$571$	−1.80669e8			−0.970454			−0.485227	−	0.874388i	$-0.661263\pi$
$571$	−1.80669e8			−0.970454			−0.485227	+	0.874388i	$0.661263\pi$
$572$		0			0
$573$	6.06604e7	+	1.06961e7i	0.322434	+	0.0568539i
$574$		0			0
$575$	3.80505e7	+	3.19281e7i	0.200150	+	0.167946i
$576$		0			0
$577$	−1.57071e8	−	2.72055e8i	−0.817652	−	1.41621i	−0.907408	−	0.420251i	$-0.861942\pi$
$577$	−1.57071e8	−	2.72055e8i	−0.817652	−	1.41621i	0.0897559	−	0.995964i	$-0.471391\pi$
$578$		0			0
$579$	3.18844e8	+	1.16050e8i	1.64264	+	0.597873i
$580$		0			0
$581$	2.11385e8	−	3.66130e8i	1.07782	−	1.86684i
$582$		0			0
$583$	2.89052e8	−	5.09677e7i	1.45872	−	0.257211i
$584$		0			0
$585$	−9.45364e7	−	1.12664e8i	−0.472206	−	0.562753i
$586$		0			0
$587$	5.71732e7	−	2.08094e7i	0.282669	−	0.102883i	−0.196795	−	0.980445i	$-0.563053\pi$
$587$	5.71732e7	−	2.08094e7i	0.282669	−	0.102883i	0.479464	+	0.877562i	$0.340831\pi$
$588$		0			0
$589$	−1.43547e7	−	2.45950e7i	−0.0702503	−	0.120365i
$590$		0			0
$591$	−1.12591e7	−	3.09341e7i	−0.0545433	−	0.149857i
$592$		0			0
$593$	−2.56412e8	+	2.15156e8i	−1.22963	+	1.03178i	−0.231369	+	0.972866i	$0.574320\pi$
$593$	−2.56412e8	+	2.15156e8i	−1.22963	+	1.03178i	−0.998263	+	0.0589172i	$0.981235\pi$
$594$		0			0
$595$	−6.90841e7	−	3.91796e8i	−0.327965	−	1.85998i
$596$		0			0
$597$	−6.45598e7	−	3.72736e7i	−0.303417	−	0.175178i
$598$		0			0
$599$	−1.04773e8	+	2.87862e8i	−0.487494	+	1.33938i	0.415447	+	0.909617i	$0.363625\pi$
$599$	−1.04773e8	+	2.87862e8i	−0.487494	+	1.33938i	−0.902942	+	0.429763i	$0.858597\pi$
$600$		0			0
$601$	2.74557e8	−	1.58515e8i	1.26476	−	0.730210i	0.290769	−	0.956793i	$-0.406089\pi$
$601$	2.74557e8	−	1.58515e8i	1.26476	−	0.730210i	0.973992	+	0.226583i	$0.0727556\pi$
$602$		0			0
$603$	5.08225e7	−	6.05679e7i	0.231795	−	0.276243i
$604$		0			0
$605$	−1.37891e8	+	7.82020e8i	−0.622688	+	3.53144i
$606$		0			0
$607$		−	1.73592e7i		−	0.0776182i	−0.999247	−	0.0388091i	$-0.987644\pi$
$607$		−	1.73592e7i		−	0.0776182i	0.999247	−	0.0388091i	$-0.0123564\pi$
$608$		0			0
$609$	6.51682e8			2.88525
$610$		0			0
$611$	1.19091e8	+	2.09990e7i	0.522104	+	0.0920610i
$612$		0			0
$613$	−8.16837e7	−	6.85408e7i	−0.354612	−	0.297555i	0.448027	−	0.894020i	$-0.352127\pi$
$613$	−8.16837e7	−	6.85408e7i	−0.354612	−	0.297555i	−0.802639	+	0.596465i	$0.796571\pi$
$614$		0			0
$615$	1.69956e8	+	2.94372e8i	0.730651	+	1.26553i
$616$		0			0
$617$	3.31870e8	+	1.20791e8i	1.41290	+	0.514254i	0.931980	−	0.362509i	$-0.118080\pi$
$617$	3.31870e8	+	1.20791e8i	1.41290	+	0.514254i	0.480922	+	0.876763i	$0.340302\pi$
$618$		0			0
$619$	1.07370e8	−	1.85971e8i	0.452702	−	0.784103i	−0.545851	−	0.837882i	$-0.683794\pi$
$619$	1.07370e8	−	1.85971e8i	0.452702	−	0.784103i	0.998553	+	0.0537796i	$0.0171269\pi$
$620$		0			0
$621$	−2.22308e7	+	3.91989e6i	−0.0928282	+	0.0163681i
$622$		0			0
$623$	−3.94250e7	−	4.69849e7i	−0.163045	−	0.194309i
$624$		0			0
$625$	−2.59978e8	+	9.46241e7i	−1.06487	+	0.387580i
$626$		0			0
$627$	−3.87856e8	−	3.22351e8i	−1.57350	−	1.30776i
$628$		0			0
$629$	3.51039e7	+	9.64472e7i	0.141060	+	0.387559i
$630$		0			0
$631$	2.12157e8	−	1.78021e8i	0.844440	−	0.708569i	−0.114118	−	0.993467i	$-0.536404\pi$
$631$	2.12157e8	−	1.78021e8i	0.844440	−	0.708569i	0.958558	+	0.284898i	$0.0919597\pi$
$632$		0			0
$633$	1.83545e7	+	1.04093e8i	0.0723653	+	0.410404i
$634$		0			0
$635$	−7.02134e8	−	4.05377e8i	−2.74220	−	1.58321i
$636$		0			0
$637$	−1.55099e8	+	4.26132e8i	−0.600056	+	1.64864i
$638$		0			0
$639$	−1.21524e8	+	7.01621e7i	−0.465759	+	0.268906i
$640$		0			0
$641$	1.59144e8	−	1.89661e8i	0.604251	−	0.720118i	−0.374026	−	0.927418i	$-0.622023\pi$
$641$	1.59144e8	−	1.89661e8i	0.604251	−	0.720118i	0.978277	+	0.207300i	$0.0664675\pi$
$642$		0			0
$643$	−7.27695e7	+	4.12696e8i	−0.273726	+	1.55238i	0.469253	+	0.883064i	$0.344523\pi$
$643$	−7.27695e7	+	4.12696e8i	−0.273726	+	1.55238i	−0.742979	+	0.669315i	$0.766588\pi$
$644$		0			0
$645$		−	4.58491e8i		−	1.70864i
$646$		0			0
$647$	−9.11540e7			−0.336560			−0.168280	−	0.985739i	$-0.553821\pi$
$647$	−9.11540e7			−0.336560			−0.168280	+	0.985739i	$0.553821\pi$
$648$		0			0
$649$	2.17165e8	+	3.82920e7i	0.794430	+	0.140079i
$650$		0			0
$651$	5.49685e7	+	4.61241e7i	0.199238	+	0.167180i
$652$		0			0
$653$	1.31309e6	+	2.27433e6i	0.00471578	+	0.00816797i	0.868374	−	0.495910i	$-0.165166\pi$
$653$	1.31309e6	+	2.27433e6i	0.00471578	+	0.00816797i	−0.863658	+	0.504078i	$0.831832\pi$
$654$		0			0
$655$	3.12513e8	+	1.13745e8i	1.11210	+	0.404772i
$656$		0			0
$657$	−8.11999e7	+	1.40642e8i	−0.286325	+	0.495930i
$658$		0			0
$659$	−1.44867e8	+	2.55440e7i	−0.506189	+	0.0892549i	−0.420910	−	0.907102i	$-0.638289\pi$
$659$	−1.44867e8	+	2.55440e7i	−0.506189	+	0.0892549i	−0.0852791	+	0.996357i	$0.527178\pi$
$660$		0			0
$661$	2.97878e8	+	3.54997e8i	1.03142	+	1.22919i	0.972977	+	0.230902i	$0.0741675\pi$
$661$	2.97878e8	+	3.54997e8i	1.03142	+	1.22919i	0.0584379	+	0.998291i	$0.481388\pi$
$662$		0			0
$663$	2.47642e8	−	9.01342e7i	0.849734	−	0.309278i
$664$		0			0
$665$	−8.06240e8	−	1.38252e8i	−2.74157	−	0.470119i
$666$		0			0
$667$	−2.00597e7	−	5.51136e7i	−0.0676001	−	0.185730i
$668$		0			0
$669$	−1.57957e7	+	1.32542e7i	−0.0527548	+	0.0442665i
$670$		0			0
$671$	−8.57687e6	−	4.86419e7i	−0.0283897	−	0.161006i
$672$		0			0
$673$	−4.06675e8	−	2.34794e8i	−1.33414	−	0.770268i	−0.348211	−	0.937416i	$-0.613211\pi$
$673$	−4.06675e8	−	2.34794e8i	−1.33414	−	0.770268i	−0.985932	+	0.167148i	$0.946544\pi$
$674$		0			0
$675$	1.58508e8	−	4.35496e8i	0.515394	−	1.41603i
$676$		0			0
$677$	−8.84097e7	+	5.10434e7i	−0.284927	+	0.164503i	−0.635652	−	0.771976i	$-0.719269\pi$
$677$	−8.84097e7	+	5.10434e7i	−0.284927	+	0.164503i	0.350725	+	0.936479i	$0.385935\pi$
$678$		0			0
$679$	3.05764e8	−	3.64395e8i	0.976734	−	1.16403i
$680$		0			0
$681$	−2.07632e7	+	1.17754e8i	−0.0657436	+	0.372851i
$682$		0			0
$683$		−	1.08162e8i		−	0.339479i	−0.985489	−	0.169739i	$-0.945707\pi$
$683$		−	1.08162e8i		−	0.339479i	0.985489	−	0.169739i	$-0.0542926\pi$
$684$		0			0
$685$	−5.56420e7			−0.173113
$686$		0			0
$687$	−1.63261e8	−	2.87873e7i	−0.503514	−	0.0887831i
$688$		0			0
$689$	2.41577e8	+	2.02708e8i	0.738582	+	0.619744i
$690$		0			0
$691$	−3.88618e7	−	6.73107e7i	−0.117785	−	0.204009i	0.801105	−	0.598524i	$-0.204246\pi$
$691$	−3.88618e7	−	6.73107e7i	−0.117785	−	0.204009i	−0.918890	+	0.394515i	$0.870913\pi$
$692$		0			0
$693$	3.22556e8	+	1.17401e8i	0.969183	+	0.352754i
$694$		0			0
$695$	−5.37472e8	+	9.30929e8i	−1.60104	+	2.77308i
$696$		0			0
$697$	−1.62023e8	+	2.85690e7i	−0.478495	+	0.0843716i
$698$		0			0
$699$	3.86545e8	+	4.60667e8i	1.13180	+	1.34882i
$700$		0			0
$701$	−2.08952e8	+	7.60523e7i	−0.606586	+	0.220779i	−0.627009	−	0.779012i	$-0.715721\pi$
$701$	−2.08952e8	+	7.60523e7i	−0.606586	+	0.220779i	0.0204227	+	0.999791i	$0.493499\pi$
$702$		0			0
$703$	2.11032e8	−	993257.i	0.607410	−	0.00285888i
$704$		0			0
$705$	−1.14037e8	−	3.13313e8i	−0.325445	−	0.894152i
$706$		0			0
$707$	−3.51246e8	+	2.94730e8i	−0.993924	+	0.834001i
$708$		0			0
$709$	8.13524e7	+	4.61372e8i	0.228261	+	1.29453i	0.856352	+	0.516392i	$0.172725\pi$
$709$	8.13524e7	+	4.61372e8i	0.228261	+	1.29453i	−0.628091	+	0.778140i	$0.716164\pi$
$710$		0			0
$711$	−9.49086e7	−	5.47955e7i	−0.264056	−	0.152453i
$712$		0			0
$713$	2.20876e6	−	6.06852e6i	0.00609369	−	0.0167423i
$714$		0			0
$715$	−1.09836e9	+	6.34141e8i	−3.00489	+	1.73487i
$716$		0			0
$717$	−1.75287e8	+	2.08899e8i	−0.475546	+	0.566734i
$718$		0			0
$719$	9.02484e7	−	5.11824e8i	0.242802	−	1.37700i	−0.582739	−	0.812659i	$-0.698019\pi$
$719$	9.02484e7	−	5.11824e8i	0.242802	−	1.37700i	0.825541	−	0.564341i	$-0.190870\pi$
$720$		0			0
$721$			6.23647e8i			1.66392i
$722$		0			0
$723$	−3.21513e8			−0.850715
$724$		0			0
$725$	1.18582e9	+	2.09093e8i	3.11176	+	0.548687i
$726$		0			0
$727$	−2.88207e8	−	2.41835e8i	−0.750070	−	0.629384i	0.185451	−	0.982653i	$-0.440625\pi$
$727$	−2.88207e8	−	2.41835e8i	−0.750070	−	0.629384i	−0.935521	+	0.353270i	$0.885070\pi$
$728$		0			0
$729$	7.87782e7	+	1.36448e8i	0.203340	+	0.352196i
$730$		0			0
$731$	2.08533e8	+	7.58999e7i	0.533855	+	0.194307i
$732$		0			0
$733$	1.74211e8	−	3.01742e8i	0.442347	−	0.766167i	−0.555516	−	0.831506i	$-0.687479\pi$
$733$	1.74211e8	−	3.01742e8i	0.442347	−	0.766167i	0.997863	+	0.0653386i	$0.0208127\pi$
$734$		0			0
$735$	1.23133e9	−	2.17116e8i	3.10107	−	0.546802i
$736$		0			0
$737$	−4.38269e8	−	5.22309e8i	−1.09481	−	1.30474i
$738$		0			0
$739$	5.82888e8	−	2.12154e8i	1.44428	−	0.525676i	0.503294	−	0.864115i	$-0.332121\pi$
$739$	5.82888e8	−	2.12154e8i	1.44428	−	0.525676i	0.940988	+	0.338440i	$0.109899\pi$
$740$		0			0
$741$	−2.55032e6	−	5.41854e8i	−0.00626817	−	1.33176i
$742$		0			0
$743$	−1.91049e8	−	5.24902e8i	−0.465777	−	1.27971i	−0.921080	−	0.389374i	$-0.872691\pi$
$743$	−1.91049e8	−	5.24902e8i	−0.465777	−	1.27971i	0.455303	−	0.890336i	$-0.349531\pi$
$744$		0			0
$745$	−8.09356e8	+	6.79130e8i	−1.95736	+	1.64242i
$746$		0			0
$747$	−3.62177e7	−	2.05401e8i	−0.0868879	−	0.492766i
$748$		0			0
$749$	−6.60080e8	−	3.81097e8i	−1.57091	−	0.906965i
$750$		0			0
$751$	6.99570e7	−	1.92205e8i	0.165162	−	0.453780i	−0.829309	−	0.558791i	$-0.811266\pi$
$751$	6.99570e7	−	1.92205e8i	0.165162	−	0.453780i	0.994471	+	0.105011i	$0.0334877\pi$
$752$		0			0
$753$	2.00426e8	−	1.15716e8i	0.469429	−	0.271025i
$754$		0			0
$755$	1.77287e8	−	2.11283e8i	0.411942	−	0.490934i
$756$		0			0
$757$	−4.02773e7	+	2.28424e8i	−0.0928480	+	0.526567i	0.902538	+	0.430611i	$0.141702\pi$
$757$	−4.02773e7	+	2.28424e8i	−0.0928480	+	0.526567i	−0.995386	+	0.0959562i	$0.969409\pi$
$758$		0			0
$759$		−	1.14368e8i		−	0.261564i
$760$		0			0
$761$	−3.75624e8			−0.852314			−0.426157	−	0.904649i	$-0.640133\pi$
$761$	−3.75624e8			−0.852314			−0.426157	+	0.904649i	$0.640133\pi$
$762$		0			0
$763$	−3.46774e7	−	6.11456e6i	−0.0780680	−	0.0137655i
$764$		0			0
$765$	−1.50352e8	−	1.26160e8i	−0.335833	−	0.281798i
$766$		0			0
$767$	1.18464e8	+	2.05185e8i	0.262542	+	0.454737i
$768$		0			0
$769$	−1.23010e8	−	4.47720e7i	−0.270497	−	0.0984528i	0.203211	−	0.979135i	$-0.434862\pi$
$769$	−1.23010e8	−	4.47720e7i	−0.270497	−	0.0984528i	−0.473707	+	0.880682i	$0.657085\pi$
$770$		0			0
$771$	1.76214e8	−	3.05212e8i	0.384483	−	0.665945i
$772$		0			0
$773$	2.58130e8	−	4.55152e7i	0.558856	−	0.0985413i	0.112916	−	0.993605i	$-0.463981\pi$
$773$	2.58130e8	−	4.55152e7i	0.558856	−	0.0985413i	0.445939	+	0.895063i	$0.352870\pi$
$774$		0			0
$775$	8.52237e7	+	1.01566e8i	0.183086	+	0.218194i
$776$		0			0
$777$	−4.99685e8	+	1.81870e8i	−1.06521	+	0.387703i
$778$		0			0
$779$	−5.71727e7	+	3.33411e8i	−0.120942	+	0.705291i
$780$		0			0
$781$	4.13875e8	+	1.13711e9i	0.868792	+	2.38699i
$782$		0			0
$783$	−4.19199e8	+	3.51749e8i	−0.873242	+	0.732737i
$784$		0			0
$785$	−5.16975e7	−	2.93191e8i	−0.106871	−	0.606097i
$786$		0			0
$787$	−1.14104e6	−	658782.i	−0.00234088	−	0.00135150i	0.498829	−	0.866700i	$-0.333764\pi$
$787$	−1.14104e6	−	658782.i	−0.00234088	−	0.00135150i	−0.501170	+	0.865349i	$0.667097\pi$
$788$		0			0
$789$	−1.38651e7	+	3.80940e7i	−0.0282288	+	0.0775579i
$790$		0			0
$791$	−5.73473e8	+	3.31095e8i	−1.15873	+	0.668995i
$792$		0			0
$793$	3.41117e7	−	4.06528e7i	0.0684044	−	0.0815212i
$794$		0			0
$795$	1.50986e8	−	8.56284e8i	0.300494	−	1.70418i
$796$		0			0
$797$		−	2.59597e8i		−	0.512773i	−0.966574	−	0.256386i	$-0.917468\pi$
$797$		−	2.59597e8i		−	0.512773i	0.966574	−	0.256386i	$-0.0825319\pi$
$798$		0			0
$799$	1.61381e8			0.316382
$800$		0			0
$801$	−2.97990e7	−	5.25437e6i	−0.0579835	−	0.0102240i
$802$		0			0
$803$	1.07281e9	+	9.00197e8i	2.07194	+	1.73857i
$804$		0			0
$805$	−9.27517e7	−	1.60651e8i	−0.177801	−	0.307960i
$806$		0			0
$807$	−1.53865e8	−	5.60022e7i	−0.292765	−	0.106558i
$808$		0			0
$809$	2.69163e8	−	4.66204e8i	0.508358	−	0.880501i	−0.491595	−	0.870824i	$-0.663586\pi$
$809$	2.69163e8	−	4.66204e8i	0.508358	−	0.880501i	0.999953	−	0.00967768i	$-0.00308055\pi$
$810$		0			0
$811$	−8.57443e8	+	1.51190e8i	−1.60747	+	0.283440i	−0.904080	−	0.427364i	$-0.859442\pi$
$811$	−8.57443e8	+	1.51190e8i	−1.60747	+	0.283440i	−0.703390	+	0.710804i	$0.748331\pi$
$812$		0			0
$813$	3.83658e8	+	4.57225e8i	0.713957	+	0.850861i
$814$		0			0
$815$	4.23676e8	−	1.54206e8i	0.782639	−	0.284857i
$816$		0			0
$817$	2.91648e8	−	3.50913e8i	0.534801	−	0.643477i
$818$		0			0
$819$	1.26139e8	+	3.46563e8i	0.229613	+	0.630857i
$820$		0			0
$821$	3.90661e8	−	3.27804e8i	0.705945	−	0.592358i	−0.217513	−	0.976057i	$-0.569795\pi$
$821$	3.90661e8	−	3.27804e8i	0.705945	−	0.592358i	0.923458	+	0.383699i	$0.125350\pi$
$822$		0			0
$823$	9.14391e6	+	5.18577e7i	0.0164033	+	0.0930280i	0.991910	−	0.126940i	$-0.0405157\pi$
$823$	9.14391e6	+	5.18577e7i	0.0164033	+	0.0930280i	−0.975507	+	0.219968i	$0.929405\pi$
$824$		0			0
$825$	2.03344e9	+	1.17400e9i	3.62133	+	2.09078i
$826$		0			0
$827$	8.17283e7	−	2.24547e8i	0.144496	−	0.397000i	−0.846240	−	0.532802i	$-0.821139\pi$
$827$	8.17283e7	−	2.24547e8i	0.144496	−	0.397000i	0.990736	+	0.135802i	$0.0433613\pi$
$828$		0			0
$829$	−4.58059e8	+	2.64460e8i	−0.804003	+	0.464191i	−0.844869	−	0.534973i	$-0.820322\pi$
$829$	−4.58059e8	+	2.64460e8i	−0.804003	+	0.464191i	0.0408662	+	0.999165i	$0.486988\pi$
$830$		0			0
$831$	−4.22821e8	+	5.03898e8i	−0.736807	+	0.878092i
$832$		0			0
$833$	−1.05088e8	+	5.95981e8i	−0.181809	+	1.03109i
$834$		0			0
$835$		−	1.61250e9i		−	2.76975i
$836$		0			0
$837$	−6.02546e7			−0.102758
$838$		0			0
$839$	−6.19073e8	−	1.09159e8i	−1.04823	−	0.184831i	−0.377100	−	0.926172i	$-0.623079\pi$
$839$	−6.19073e8	−	1.09159e8i	−1.04823	−	0.184831i	−0.671128	+	0.741342i	$0.734190\pi$
$840$		0			0
$841$	−6.33494e8	−	5.31564e8i	−1.06501	−	0.893651i
$842$		0			0
$843$	2.70757e7	+	4.68964e7i	0.0451956	+	0.0782811i
$844$		0			0
$845$	−2.91350e8	−	1.06043e8i	−0.482887	−	0.175756i
$846$		0			0
$847$	9.95639e8	−	1.72450e9i	1.63852	−	2.83800i
$848$		0			0
$849$	4.70027e7	−	8.28785e6i	0.0768068	−	0.0135431i
$850$		0			0
$851$	3.07620e7	+	3.66608e7i	0.0499144	+	0.0594857i
$852$		0			0
$853$	3.36215e8	−	1.22372e8i	0.541714	−	0.197168i	−0.0566470	−	0.998394i	$-0.518041\pi$
$853$	3.36215e8	−	1.22372e8i	0.541714	−	0.197168i	0.598361	+	0.801226i	$0.295819\pi$
$854$		0			0
$855$	−3.48536e8	+	2.03420e8i	−0.557634	+	0.325459i
$856$		0			0
$857$	−4.28889e8	−	1.17836e9i	−0.681401	−	1.87213i	−0.423167	−	0.906052i	$-0.639082\pi$
$857$	−4.28889e8	−	1.17836e9i	−0.681401	−	1.87213i	−0.258234	−	0.966082i	$-0.583141\pi$
$858$		0			0
$859$	2.26472e8	−	1.90033e8i	0.357302	−	0.299812i	−0.446412	−	0.894827i	$-0.647299\pi$
$859$	2.26472e8	−	1.90033e8i	0.357302	−	0.299812i	0.803714	+	0.595016i	$0.202854\pi$
$860$		0			0
$861$	−1.48013e8	−	8.39426e8i	−0.231895	−	1.31514i
$862$		0			0
$863$	7.80849e7	+	4.50823e7i	0.121488	+	0.0701413i	0.559513	−	0.828822i	$-0.310988\pi$
$863$	7.80849e7	+	4.50823e7i	0.121488	+	0.0701413i	−0.438024	+	0.898963i	$0.644322\pi$
$864$		0			0
$865$	5.65685e8	−	1.55421e9i	0.874030	−	2.40138i
$866$		0			0
$867$	−3.56062e8	+	2.05572e8i	−0.546347	+	0.315433i
$868$		0			0
$869$	−6.07473e8	+	7.23958e8i	−0.925694	+	1.10320i
$870$		0			0
$871$	1.27210e8	−	7.21443e8i	0.192516	−	1.09181i
$872$		0			0
$873$		−	2.34674e8i		−	0.352713i
$874$		0			0
$875$	1.94500e9			2.90332
$876$		0			0
$877$	5.83231e8	+	1.02839e8i	0.864653	+	0.152462i	0.588348	−	0.808608i	$-0.299779\pi$
$877$	5.83231e8	+	1.02839e8i	0.864653	+	0.152462i	0.276306	+	0.961070i	$0.410890\pi$
$878$		0			0
$879$	−7.73239e8	−	6.48825e8i	−1.13854	−	0.955346i
$880$		0			0
$881$	5.91613e8	+	1.02470e9i	0.865187	+	1.49855i	0.866861	+	0.498550i	$0.166134\pi$
$881$	5.91613e8	+	1.02470e9i	0.865187	+	1.49855i	−0.00167375	+	0.999999i	$0.500533\pi$
$882$		0			0
$883$	4.90638e8	+	1.78577e8i	0.712654	+	0.259385i	0.672804	−	0.739821i	$-0.265090\pi$
$883$	4.90638e8	+	1.78577e8i	0.712654	+	0.259385i	0.0398500	+	0.999206i	$0.487312\pi$
$884$		0			0
$885$	3.26625e8	−	5.65731e8i	0.471215	−	0.816169i
$886$		0			0
$887$	−6.07248e8	+	1.07074e8i	−0.870152	+	0.153431i	−0.590859	−	0.806775i	$-0.701211\pi$
$887$	−6.07248e8	+	1.07074e8i	−0.870152	+	0.153431i	−0.279293	+	0.960206i	$0.590100\pi$
$888$		0			0
$889$	1.30684e9	+	1.55743e9i	1.86002	+	2.21668i
$890$		0			0
$891$	−1.43271e9	+	5.21464e8i	−2.02547	+	0.737210i
$892$		0			0
$893$	1.12020e8	−	3.12338e8i	0.157304	−	0.438602i
$894$		0			0
$895$	2.64358e8	+	7.26317e8i	0.368742	+	1.01311i
$896$		0			0
$897$	9.41316e7	−	7.89858e7i	0.130424	−	0.109439i
$898$		0			0
$899$	−2.71851e7	−	1.54174e8i	−0.0374155	−	0.212194i
$900$		0			0
$901$	3.64465e8	+	2.10424e8i	0.498289	+	0.287687i
$902$		0			0
$903$	−3.93231e8	+	1.08039e9i	−0.534053	+	1.46730i
$904$		0			0
$905$	8.33465e8	−	4.81201e8i	1.12445	−	0.649204i
$906$		0			0
$907$	8.20687e7	−	9.78057e7i	0.109991	−	0.131082i	−0.708240	−	0.705972i	$-0.750511\pi$
$907$	8.20687e7	−	9.78057e7i	0.109991	−	0.131082i	0.818231	+	0.574890i	$0.194955\pi$
$908$		0			0
$909$	−3.92802e7	+	2.22769e8i	−0.0522976	+	0.296595i
$910$		0			0
$911$			6.17273e8i			0.816436i	0.912885	+	0.408218i	$0.133850\pi$
$911$			6.17273e8i			0.816436i	−0.912885	+	0.408218i	$0.866150\pi$
$912$		0			0
$913$	−1.79860e9			−2.36332
$914$		0			0
$915$	−1.44096e8	−	2.54080e7i	−0.188100	−	0.0331671i
$916$		0			0
$917$	−6.38854e8	−	5.36062e8i	−0.828502	−	0.695196i
$918$		0			0
$919$	−5.17183e7	−	8.95786e7i	−0.0666342	−	0.115414i	0.830784	−	0.556596i	$-0.187893\pi$
$919$	−5.17183e7	−	8.95786e7i	−0.0666342	−	0.115414i	−0.897418	+	0.441182i	$0.854559\pi$
$920$		0			0
$921$	−1.61521e9	−	5.87887e8i	−2.06752	−	0.752514i
$922$		0			0
$923$	−6.50077e8	+	1.12597e9i	−0.826722	+	1.43193i
$924$		0			0
$925$	−9.67597e8	+	1.70613e8i	−1.22256	+	0.215570i
$926$		0			0
$927$	1.97766e8	+	2.35689e8i	0.248264	+	0.295869i
$928$		0			0
$929$	−3.21389e8	+	1.16976e8i	−0.400852	+	0.145898i	−0.534576	−	0.845120i	$-0.679529\pi$
$929$	−3.21389e8	+	1.16976e8i	−0.400852	+	0.145898i	0.133724	+	0.991019i	$0.457306\pi$
$930$		0			0
$931$	1.08052e9	+	6.17079e8i	1.33902	+	0.764701i
$932$		0			0
$933$	−1.28022e8	−	3.51738e8i	−0.157631	−	0.433086i
$934$		0			0
$935$	−1.29656e9	+	1.08794e9i	−1.58620	+	1.33098i
$936$		0			0
$937$	2.28025e7	+	1.29319e8i	0.0277181	+	0.157197i	0.995525	−	0.0944958i	$-0.0301239\pi$
$937$	2.28025e7	+	1.29319e8i	0.0277181	+	0.157197i	−0.967807	+	0.251693i	$0.919013\pi$
$938$		0			0
$939$	1.28743e9	+	7.43300e8i	1.55499	+	0.897775i
$940$		0			0
$941$	2.62363e8	−	7.20835e8i	0.314871	−	0.865102i	−0.676784	−	0.736182i	$-0.736627\pi$
$941$	2.62363e8	−	7.20835e8i	0.314871	−	0.865102i	0.991655	−	0.128920i	$-0.0411510\pi$
$942$		0			0
$943$	−6.64353e7	+	3.83564e7i	−0.0792252	+	0.0457407i
$944$		0			0
$945$	−1.11253e9	+	1.32586e9i	−1.31831	+	1.57110i
$946$		0			0
$947$	−1.52816e8	+	8.66663e8i	−0.179937	+	1.02047i	0.752354	+	0.658759i	$0.228918\pi$
$947$	−1.52816e8	+	8.66663e8i	−0.179937	+	1.02047i	−0.932290	+	0.361711i	$0.882193\pi$
$948$		0			0
$949$			1.50469e9i			1.76055i
$950$		0			0
$951$	−3.82738e7			−0.0445000
$952$		0			0
$953$	1.34473e9	+	2.37112e8i	1.55366	+	0.273952i	0.883560	−	0.468318i	$-0.155140\pi$
$953$	1.34473e9	+	2.37112e8i	1.55366	+	0.273952i	0.670100	+	0.742271i	$0.266251\pi$
$954$		0			0
$955$	−3.25601e8	−	2.73212e8i	−0.373831	−	0.313682i
$956$		0			0
$957$	−1.38623e9	−	2.40103e9i	−1.58162	−	2.73944i
$958$		0			0
$959$	1.31115e8	+	4.77221e7i	0.148661	+	0.0541083i
$960$		0			0
$961$	−4.35133e8	+	7.53672e8i	−0.490289	+	0.849205i
$962$		0			0
$963$	−3.70308e8	+	6.52953e7i	−0.414653	+	0.0731145i
$964$		0			0
$965$	−1.50501e9	−	1.79360e9i	−1.67478	−	1.99592i
$966$		0			0
$967$	−3.69746e8	+	1.34577e8i	−0.408907	+	0.148830i	−0.538280	−	0.842766i	$-0.680926\pi$
$967$	−3.69746e8	+	1.34577e8i	−0.408907	+	0.148830i	0.129373	+	0.991596i	$0.458703\pi$
$968$		0			0
$969$	−1.28919e8	−	7.11534e8i	−0.141692	−	0.782032i
$970$		0			0
$971$	1.83897e8	+	5.05252e8i	0.200871	+	0.551887i	0.998699	−	0.0509975i	$-0.0162401\pi$
$971$	1.83897e8	+	5.05252e8i	0.200871	+	0.551887i	−0.797828	+	0.602885i	$0.794018\pi$
$972$		0			0
$973$	2.06493e9	−	1.73268e9i	2.24164	−	1.88096i
$974$		0			0
$975$	4.38074e8	+	2.48444e9i	0.472643	+	2.68049i
$976$		0			0
$977$	6.96132e8	+	4.01912e8i	0.746462	+	0.430970i	0.824414	−	0.565987i	$-0.191505\pi$
$977$	6.96132e8	+	4.01912e8i	0.746462	+	0.430970i	−0.0779519	+	0.996957i	$0.524838\pi$
$978$		0			0
$979$	−8.92455e7	+	2.45200e8i	−0.0951127	+	0.261320i
$980$		0			0
$981$	−1.50443e7	+	8.68583e6i	−0.0159355	+	0.00920035i
$982$		0			0
$983$	7.96841e8	−	9.49638e8i	0.838902	−	0.999764i	−0.161016	−	0.986952i	$-0.551477\pi$
$983$	7.96841e8	−	9.49638e8i	0.838902	−	0.999764i	0.999918	−	0.0128122i	$-0.00407836\pi$
$984$		0			0
$985$	−3.94458e7	+	2.23708e8i	−0.0412755	+	0.234085i
$986$		0			0
$987$			8.36100e8i			0.869575i
$988$		0			0
$989$	1.03474e8			0.106966
$990$		0			0
$991$	−1.87081e9	−	3.29874e8i	−1.92224	−	0.338943i	−0.923266	−	0.384161i	$-0.874491\pi$
$991$	−1.87081e9	−	3.29874e8i	−1.92224	−	0.338943i	−0.998977	+	0.0452177i	$0.985602\pi$
$992$		0			0
$993$	6.17179e8	+	5.17875e8i	0.630323	+	0.528904i
$994$		0			0
$995$	2.57205e8	+	4.45493e8i	0.261102	+	0.452243i
$996$		0			0
$997$	−1.38954e9	−	5.05750e8i	−1.40212	−	0.510330i	−0.473312	−	0.880895i	$-0.656942\pi$
$997$	−1.38954e9	−	5.05750e8i	−1.40212	−	0.510330i	−0.928807	+	0.370565i	$0.879164\pi$
$998$		0			0
$999$	2.23260e8	−	3.86697e8i	0.223931	−	0.387859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.33.9	✓	60
19.15	odd	18	inner	76.7.j.a.53.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.9	✓	60	1.1	even	1	trivial
76.7.j.a.53.9	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)

\(f(q)\)	\(=\)	\(q+(31.1235 + 5.48792i) q^{3} +(-167.059 - 140.179i) q^{5} +(273.433 + 473.600i) q^{7} +(253.520 + 92.2739i) q^{9} +O(q^{10})\)	\(q+(31.1235 + 5.48792i) q^{3} +(-167.059 - 140.179i) q^{5} +(273.433 + 473.600i) q^{7} +(253.520 + 92.2739i) q^{9} +(1163.27 - 2014.85i) q^{11} +(2461.73 - 434.069i) q^{13} +(-4430.17 - 5279.67i) q^{15} +(3134.71 - 1140.94i) q^{17} +(-32.2826 - 6858.92i) q^{19} +(5911.12 + 16240.7i) q^{21} +(1191.54 - 999.822i) q^{23} +(5545.25 + 31448.7i) q^{25} +(-12568.4 - 7256.35i) q^{27} +(12896.4 - 35432.7i) q^{29} +(3595.61 - 2075.93i) q^{31} +(47262.5 - 56325.2i) q^{33} +(20709.4 - 117449. i) q^{35} +30767.5i q^{37} +78999.8 q^{39} +(-48569.6 - 8564.13i) q^{41} +(50960.3 + 42760.7i) q^{43} +(-29418.0 - 50953.4i) q^{45} +(45459.6 + 16546.0i) q^{47} +(-90706.7 + 157109. i) q^{49} +(103825. - 18307.1i) q^{51} +(81092.6 + 96642.3i) q^{53} +(-476774. + 173532. i) q^{55} +(36636.5 - 213651. i) q^{57} +(32417.4 + 89066.1i) q^{59} +(16263.0 - 13646.3i) q^{61} +(25619.9 + 145298. i) q^{63} +(-472101. - 272568. i) q^{65} +(100234. - 275390. i) q^{67} +(42571.9 - 24578.9i) q^{69} +(-334328. + 398437. i) q^{71} +(-104527. + 592802. i) q^{73} +1.00923e6i q^{75} +1.27231e6 q^{77} +(-400036. - 70537.2i) q^{79} +(-502013. - 421239. i) q^{81} +(-386540. - 669506. i) q^{83} +(-683617. - 248816. i) q^{85} +(595834. - 1.03201e6i) q^{87} +(-110452. + 19475.7i) q^{89} +(878693. + 1.04719e6i) q^{91} +(123301. - 44877.7i) q^{93} +(-956084. + 1.15037e6i) q^{95} +(-297501. - 817379. i) q^{97} +(480831. - 403465. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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