LMFDB - Embedded newform 92.6.e.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,6,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$14.7553114228$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	92.13
Dual form			92.6.e.a.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.41459 + 5.40773i) q^{3} +(36.4994 - 79.9225i) q^{5} +(-123.792 - 36.3487i) q^{7} +(-59.3840 - 130.033i) q^{9} +(-98.0288 + 113.131i) q^{11} +(-1019.12 + 299.240i) q^{13} +(739.326 - 475.136i) q^{15} +(-111.465 - 775.255i) q^{17} +(-167.632 + 1165.90i) q^{19} +(-845.098 - 975.295i) q^{21} +(1844.57 - 1741.81i) q^{23} +(-3008.96 - 3472.52i) q^{25} +(549.400 - 3821.16i) q^{27} +(-612.434 - 4259.58i) q^{29} +(-1625.42 + 1044.60i) q^{31} +(-1436.66 + 421.840i) q^{33} +(-7423.42 + 8567.08i) q^{35} +(3045.92 + 6669.63i) q^{37} +(-10193.7 - 2993.13i) q^{39} +(6641.80 - 14543.5i) q^{41} +(-10665.7 - 6854.40i) q^{43} -12560.0 q^{45} +20511.6 q^{47} +(-135.641 - 87.1712i) q^{49} +(3254.44 - 7126.23i) q^{51} +(15531.6 + 4560.49i) q^{53} +(5463.74 + 11963.9i) q^{55} +(-7715.45 + 8904.10i) q^{57} +(28387.3 - 8335.26i) q^{59} +(13570.4 - 8721.16i) q^{61} +(2624.76 + 18255.6i) q^{63} +(-13281.1 + 92372.4i) q^{65} +(-8306.54 - 9586.26i) q^{67} +(24940.5 - 4681.70i) q^{69} +(31765.8 + 36659.6i) q^{71} +(-8935.58 + 62148.3i) q^{73} +(-6540.69 - 45491.5i) q^{75} +(16247.4 - 10441.6i) q^{77} +(2693.96 - 791.017i) q^{79} +(2538.83 - 2929.96i) q^{81} +(-10240.8 - 22424.3i) q^{83} +(-66028.7 - 19387.8i) q^{85} +(17881.3 - 39154.5i) q^{87} +(-90334.1 - 58054.2i) q^{89} +137036. q^{91} -19326.2 q^{93} +(87063.5 + 55952.3i) q^{95} +(-54135.6 + 118540. i) q^{97} +(20532.1 + 6028.78i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{3} - 86 q^{5} - 118 q^{7} - 368 q^{9} - 242 q^{11} + 322 q^{13} - 3717 q^{15} + 2953 q^{17} - 259 q^{19} - 12349 q^{21} - 6038 q^{23} - 1324 q^{25} + 23933 q^{27} + 12677 q^{29} - 4401 q^{31}+ \cdots + 26799 q^{99}+O(q^{100}) $ 100 * q + 2 * q^3 - 86 * q^5 - 118 * q^7 - 368 * q^9 - 242 * q^11 + 322 * q^13 - 3717 * q^15 + 2953 * q^17 - 259 * q^19 - 12349 * q^21 - 6038 * q^23 - 1324 * q^25 + 23933 * q^27 + 12677 * q^29 - 4401 * q^31 - 43115 * q^33 + 10774 * q^35 - 72670 * q^37 - 61242 * q^39 - 30296 * q^41 + 69436 * q^43 + 125954 * q^45 + 79010 * q^47 + 27788 * q^49 - 65954 * q^51 - 60934 * q^53 - 234558 * q^55 + 37333 * q^57 + 392206 * q^59 + 153404 * q^61 + 7889 * q^63 - 178529 * q^65 - 52012 * q^67 - 280729 * q^69 - 166585 * q^71 + 42932 * q^73 + 484227 * q^75 + 434675 * q^77 + 150490 * q^79 - 132170 * q^81 - 236441 * q^83 - 399844 * q^85 + 121816 * q^87 + 151010 * q^89 + 240938 * q^91 - 54450 * q^93 - 281447 * q^95 - 76051 * q^97 + 26799 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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
$3$	8.41459	+	5.40773i	0.539796	+	0.346906i	0.781959	−	0.623329i	$-0.214220\pi$
$3$	8.41459	+	5.40773i	0.539796	+	0.346906i	−0.242163	+	0.970236i	$0.577857\pi$
$4$		0			0
$5$	36.4994	−	79.9225i	0.652920	−	1.42970i	−0.236054	−	0.971740i	$-0.575854\pi$
$5$	36.4994	−	79.9225i	0.652920	−	1.42970i	0.888975	−	0.457956i	$-0.151418\pi$
$6$		0			0
$7$	−123.792	−	36.3487i	−0.954879	−	0.280378i	−0.233062	−	0.972462i	$-0.574875\pi$
$7$	−123.792	−	36.3487i	−0.954879	−	0.280378i	−0.721817	+	0.692084i	$0.756693\pi$
$8$		0			0
$9$	−59.3840	−	130.033i	−0.244379	−	0.535115i
$10$		0			0
$11$	−98.0288	+	113.131i	−0.244271	+	0.281904i	−0.864625	−	0.502418i	$-0.832444\pi$
$11$	−98.0288	+	113.131i	−0.244271	+	0.281904i	0.620353	+	0.784322i	$0.286989\pi$
$12$		0			0
$13$	−1019.12	+	299.240i	−1.67250	+	0.491090i	−0.974383	−	0.224896i	$-0.927796\pi$
$13$	−1019.12	+	299.240i	−1.67250	+	0.491090i	−0.698115	+	0.715986i	$0.745978\pi$
$14$		0			0
$15$	739.326	−	475.136i	0.848415	−	0.545243i
$16$		0			0
$17$	−111.465	−	775.255i	−0.0935439	−	0.650612i	−0.981610	−	0.190897i	$-0.938860\pi$
$17$	−111.465	−	775.255i	−0.0935439	−	0.650612i	0.888066	−	0.459716i	$-0.152049\pi$
$18$		0			0
$19$	−167.632	+	1165.90i	−0.106530	+	0.740933i	0.864614	+	0.502437i	$0.167563\pi$
$19$	−167.632	+	1165.90i	−0.106530	+	0.740933i	−0.971144	+	0.238495i	$0.923346\pi$
$20$		0			0
$21$	−845.098	−	975.295i	−0.418176	−	0.482601i
$22$		0			0
$23$	1844.57	−	1741.81i	0.727069	−	0.686565i
$23$	1844.57	−	1741.81i	0.727069	−	0.686565i
$24$		0			0
$25$	−3008.96	−	3472.52i	−0.962866	−	1.11121i
$26$		0			0
$27$	549.400	−	3821.16i	0.145037	−	1.00876i
$28$		0			0
$29$	−612.434	−	4259.58i	−0.135227	−	0.940527i	−0.938589	−	0.345036i	$-0.887867\pi$
$29$	−612.434	−	4259.58i	−0.135227	−	0.940527i	0.803362	−	0.595491i	$-0.203042\pi$
$30$		0			0
$31$	−1625.42	+	1044.60i	−0.303782	+	0.195229i	−0.683646	−	0.729813i	$-0.739607\pi$
$31$	−1625.42	+	1044.60i	−0.303782	+	0.195229i	0.379865	+	0.925042i	$0.375971\pi$
$32$		0			0
$33$	−1436.66	+	421.840i	−0.229651	+	0.0674316i
$34$		0			0
$35$	−7423.42	+	8567.08i	−1.02432	+	1.18212i
$36$		0			0
$37$	3045.92	+	6669.63i	0.365775	+	0.800936i	0.999622	+	0.0274775i	$0.00874746\pi$
$37$	3045.92	+	6669.63i	0.365775	+	0.800936i	−0.633847	+	0.773458i	$0.718525\pi$
$38$		0			0
$39$	−10193.7	−	2993.13i	−1.07317	−	0.315111i
$40$		0			0
$41$	6641.80	−	14543.5i	0.617058	−	1.35117i	−0.300581	−	0.953756i	$-0.597181\pi$
$41$	6641.80	−	14543.5i	0.617058	−	1.35117i	0.917640	−	0.397413i	$-0.130092\pi$
$42$		0			0
$43$	−10665.7	−	6854.40i	−0.879664	−	0.565325i	0.0210307	−	0.999779i	$-0.493305\pi$
$43$	−10665.7	−	6854.40i	−0.879664	−	0.565325i	−0.900694	+	0.434453i	$0.856942\pi$
$44$		0			0
$45$	−12560.0			−0.924611
$46$		0			0
$47$	20511.6			1.35442			0.677212	−	0.735788i	$-0.263188\pi$
$47$	20511.6			1.35442			0.677212	+	0.735788i	$0.263188\pi$
$48$		0			0
$49$	−135.641	−	87.1712i	−0.00807051	−	0.00518660i
$50$		0			0
$51$	3254.44	−	7126.23i	0.175207	−	0.383649i
$52$		0			0
$53$	15531.6	+	4560.49i	0.759498	+	0.223009i	0.638477	−	0.769641i	$-0.279565\pi$
$53$	15531.6	+	4560.49i	0.759498	+	0.223009i	0.121022	+	0.992650i	$0.461383\pi$
$54$		0			0
$55$	5463.74	+	11963.9i	0.243547	+	0.533294i
$56$		0			0
$57$	−7715.45	+	8904.10i	−0.314539	+	0.362997i
$58$		0			0
$59$	28387.3	−	8335.26i	1.06168	−	0.311738i	0.296153	−	0.955140i	$-0.404296\pi$
$59$	28387.3	−	8335.26i	1.06168	−	0.311738i	0.765528	+	0.643403i	$0.222478\pi$
$60$		0			0
$61$	13570.4	−	8721.16i	0.466947	−	0.300089i	−0.285929	−	0.958251i	$-0.592302\pi$
$61$	13570.4	−	8721.16i	0.466947	−	0.300089i	0.752876	+	0.658162i	$0.228666\pi$
$62$		0			0
$63$	2624.76	+	18255.6i	0.0833178	+	0.579488i
$64$		0			0
$65$	−13281.1	+	92372.4i	−0.389899	+	2.71181i
$66$		0			0
$67$	−8306.54	−	9586.26i	−0.226065	−	0.260893i	0.631374	−	0.775478i	$-0.282491\pi$
$67$	−8306.54	−	9586.26i	−0.226065	−	0.260893i	−0.857439	+	0.514586i	$0.827946\pi$
$68$		0			0
$69$	24940.5	−	4681.70i	0.630643	−	0.118381i
$70$		0			0
$71$	31765.8	+	36659.6i	0.747848	+	0.863063i	0.994358	−	0.106078i	$-0.0338292\pi$
$71$	31765.8	+	36659.6i	0.747848	+	0.863063i	−0.246510	+	0.969140i	$0.579284\pi$
$72$		0			0
$73$	−8935.58	+	62148.3i	−0.196253	+	1.36497i	0.618785	+	0.785560i	$0.287625\pi$
$73$	−8935.58	+	62148.3i	−0.196253	+	1.36497i	−0.815038	+	0.579407i	$0.803284\pi$
$74$		0			0
$75$	−6540.69	−	45491.5i	−0.134267	−	0.933849i
$76$		0			0
$77$	16247.4	−	10441.6i	0.312289	−	0.200696i
$78$		0			0
$79$	2693.96	−	791.017i	0.0485649	−	0.0142600i	−0.257360	−	0.966316i	$-0.582853\pi$
$79$	2693.96	−	791.017i	0.0485649	−	0.0142600i	0.305925	+	0.952056i	$0.401034\pi$
$80$		0			0
$81$	2538.83	−	2929.96i	0.0429952	−	0.0496191i
$82$		0			0
$83$	−10240.8	−	22424.3i	−0.163170	−	0.357292i	0.810332	−	0.585971i	$-0.199287\pi$
$83$	−10240.8	−	22424.3i	−0.163170	−	0.357292i	−0.973502	+	0.228679i	$0.926559\pi$
$84$		0			0
$85$	−66028.7	−	19387.8i	−0.991255	−	0.291059i
$86$		0			0
$87$	17881.3	−	39154.5i	0.253279	−	0.554604i
$88$		0			0
$89$	−90334.1	−	58054.2i	−1.20886	−	0.776888i	−0.228394	−	0.973569i	$-0.573348\pi$
$89$	−90334.1	−	58054.2i	−1.20886	−	0.776888i	−0.980468	+	0.196680i	$0.936984\pi$
$90$		0			0
$91$	137036.			1.73472
$92$		0			0
$93$	−19326.2			−0.231707
$94$		0			0
$95$	87063.5	+	55952.3i	0.989753	+	0.636076i
$96$		0			0
$97$	−54135.6	+	118540.i	−0.584189	+	1.27920i	0.354702	+	0.934980i	$0.384582\pi$
$97$	−54135.6	+	118540.i	−0.584189	+	1.27920i	−0.938891	+	0.344216i	$0.888145\pi$
$98$		0			0
$99$	20532.1	+	6028.78i	0.210546	+	0.0618217i
$100$		0			0
$101$	−14177.9	−	31045.2i	−0.138295	−	0.302825i	0.827794	−	0.561032i	$-0.189596\pi$
$101$	−14177.9	−	31045.2i	−0.138295	−	0.302825i	−0.966090	+	0.258207i	$0.916868\pi$
$102$		0			0
$103$	125885.	−	145279.i	1.16918	−	1.34930i	0.243994	−	0.969777i	$-0.421542\pi$
$103$	125885.	−	145279.i	1.16918	−	1.34930i	0.925182	−	0.379524i	$-0.123912\pi$
$104$		0			0
$105$	−108794.	+	31944.7i	−0.963008	+	0.282765i
$106$		0			0
$107$	−173913.	+	111767.i	−1.46849	+	0.943743i	−0.470372	+	0.882468i	$0.655880\pi$
$107$	−173913.	+	111767.i	−1.46849	+	0.943743i	−0.998121	+	0.0612754i	$0.980483\pi$
$108$		0			0
$109$	−19488.5	−	135546.i	−0.157113	−	1.09275i	−0.903919	−	0.427704i	$-0.859323\pi$
$109$	−19488.5	−	135546.i	−0.157113	−	1.09275i	0.746806	−	0.665042i	$-0.231586\pi$
$110$		0			0
$111$	−10437.4	+	72593.8i	−0.0804054	+	0.559232i
$112$		0			0
$113$	−121367.	−	140065.i	−0.894140	−	1.03189i	−0.999299	−	0.0374373i	$-0.988081\pi$
$113$	−121367.	−	140065.i	−0.894140	−	1.03189i	0.105159	−	0.994455i	$-0.466465\pi$
$114$		0			0
$115$	−71884.3	−	210998.i	−0.506861	−	1.48776i
$116$		0			0
$117$	99430.2	+	114749.i	0.671512	+	0.774966i
$118$		0			0
$119$	−14381.0	+	100022.i	−0.0930941	+	0.647484i
$120$		0			0
$121$	19730.9	+	137231.i	0.122513	+	0.852100i
$122$		0			0
$123$	134535.	−	86460.7i	0.801815	−	0.515295i
$124$		0			0
$125$	−123909.	+	36383.0i	−0.709298	+	0.208269i
$126$		0			0
$127$	158380.	−	182780.i	0.871348	−	1.00559i	−0.128556	−	0.991702i	$-0.541034\pi$
$127$	158380.	−	182780.i	0.871348	−	1.00559i	0.999904	−	0.0138864i	$-0.00442033\pi$
$128$		0			0
$129$	−52680.4	−	115354.i	−0.278724	−	0.610321i
$130$		0			0
$131$	−240469.	−	70608.0i	−1.22428	−	0.359481i	−0.395191	−	0.918599i	$-0.629322\pi$
$131$	−240469.	−	70608.0i	−1.22428	−	0.359481i	−0.829088	+	0.559118i	$0.811140\pi$
$132$		0			0
$133$	63130.6	−	138237.i	0.309465	−	0.677633i
$134$		0			0
$135$	−285344.	−	183379.i	−1.34752	−	0.865996i
$136$		0			0
$137$	151539.			0.689800			0.344900	−	0.938639i	$-0.387913\pi$
$137$	151539.			0.689800			0.344900	+	0.938639i	$0.387913\pi$
$138$		0			0
$139$	309472.			1.35858			0.679288	−	0.733872i	$-0.262289\pi$
$139$	309472.			1.35858			0.679288	+	0.733872i	$0.262289\pi$
$140$		0			0
$141$	172597.	+	110921.i	0.731114	+	0.469858i
$142$		0			0
$143$	66049.4	−	144628.i	0.270103	−	0.591443i
$144$		0			0
$145$	−362789.	−	106525.i	−1.43296	−	0.420755i
$146$		0			0
$147$	−669.966	−	1467.02i	−0.00255717	−	0.00559942i
$148$		0			0
$149$	−73254.0	+	84539.6i	−0.270312	+	0.311957i	−0.874634	−	0.484783i	$-0.838898\pi$
$149$	−73254.0	+	84539.6i	−0.270312	+	0.311957i	0.604322	+	0.796740i	$0.293444\pi$
$150$		0			0
$151$	−226329.	+	66456.3i	−0.807790	+	0.237189i	−0.659451	−	0.751748i	$-0.729211\pi$
$151$	−226329.	+	66456.3i	−0.807790	+	0.237189i	−0.148340	+	0.988936i	$0.547393\pi$
$152$		0			0
$153$	−94189.4	+	60531.8i	−0.325292	+	0.209052i
$154$		0			0
$155$	24159.8	+	168035.i	0.0807725	+	0.561785i
$156$		0			0
$157$	−69988.2	+	486779.i	−0.226608	+	1.57609i	0.485635	+	0.874162i	$0.338588\pi$
$157$	−69988.2	+	486779.i	−0.226608	+	1.57609i	−0.712243	+	0.701933i	$0.752321\pi$
$158$		0			0
$159$	106030.	+	122365.i	0.332611	+	0.383854i
$160$		0			0
$161$	−291656.	+	148575.i	−0.886760	+	0.451733i
$162$		0			0
$163$	32323.7	+	37303.5i	0.0952910	+	0.109972i	0.801392	−	0.598139i	$-0.204093\pi$
$163$	32323.7	+	37303.5i	0.0952910	+	0.109972i	−0.706101	+	0.708111i	$0.749548\pi$
$164$		0			0
$165$	−18722.5	+	130218.i	−0.0535371	+	0.372358i
$166$		0			0
$167$	−20526.8	−	142767.i	−0.0569547	−	0.396128i	−0.998280	−	0.0586276i	$-0.981328\pi$
$167$	−20526.8	−	142767.i	−0.0569547	−	0.396128i	0.941325	−	0.337501i	$-0.109582\pi$
$168$		0			0
$169$	636703.	−	409184.i	1.71483	−	1.10205i
$170$		0			0
$171$	161560.	−	47438.4i	0.422518	−	0.124062i
$172$		0			0
$173$	−69246.4	+	79914.6i	−0.175907	+	0.203007i	−0.836855	−	0.547424i	$-0.815609\pi$
$173$	−69246.4	+	79914.6i	−0.175907	+	0.203007i	0.660949	+	0.750431i	$0.270154\pi$
$174$		0			0
$175$	246264.	+	539243.i	0.607863	+	1.33103i
$176$		0			0
$177$	283942.	+	83373.0i	0.681235	+	0.200029i
$178$		0			0
$179$	36576.3	−	80091.0i	0.0853233	−	0.186832i	−0.862161	−	0.506635i	$-0.830889\pi$
$179$	36576.3	−	80091.0i	0.0853233	−	0.186832i	0.947484	+	0.319803i	$0.103617\pi$
$180$		0			0
$181$	72077.4	+	46321.3i	0.163532	+	0.105096i	0.619847	−	0.784723i	$-0.287195\pi$
$181$	72077.4	+	46321.3i	0.163532	+	0.105096i	−0.456315	+	0.889818i	$0.650831\pi$
$182$		0			0
$183$	161351.			0.356159
$184$		0			0
$185$	644228.			1.38392
$186$		0			0
$187$	98632.3	+	63387.2i	0.206260	+	0.132555i
$188$		0			0
$189$	−206906.	+	453060.i	−0.421326	+	0.922575i
$190$		0			0
$191$	747298.	+	219427.i	1.48221	+	0.435217i	0.920047	−	0.391808i	$-0.128150\pi$
$191$	747298.	+	219427.i	1.48221	+	0.435217i	0.562166	+	0.827025i	$0.309968\pi$
$192$		0			0
$193$	−212772.	−	465907.i	−0.411171	−	0.900338i	−0.996014	−	0.0891920i	$-0.971572\pi$
$193$	−212772.	−	465907.i	−0.411171	−	0.900338i	0.584844	−	0.811146i	$-0.301156\pi$
$194$		0			0
$195$	−611280.	+	705455.i	−1.15121	+	1.32857i
$196$		0			0
$197$	647860.	−	190229.i	1.18937	−	0.349229i	0.373588	−	0.927595i	$-0.378127\pi$
$197$	647860.	−	190229.i	1.18937	−	0.349229i	0.815778	+	0.578365i	$0.196309\pi$
$198$		0			0
$199$	210414.	−	135225.i	0.376654	−	0.242061i	−0.338592	−	0.940933i	$-0.609951\pi$
$199$	210414.	−	135225.i	0.376654	−	0.242061i	0.715247	+	0.698872i	$0.246314\pi$
$200$		0			0
$201$	−18056.2	−	125584.i	−0.0315237	−	0.219252i
$202$		0			0
$203$	−79015.4	+	549564.i	−0.134577	+	0.936005i
$204$		0			0
$205$	−919932.	−	1.06166e6i	−1.52887	−	1.76441i
$206$		0			0
$207$	−336031.	−	136419.i	−0.545071	−	0.221283i
$208$		0			0
$209$	−115467.	−	133257.i	−0.182850	−	0.211020i
$210$		0			0
$211$	105194.	−	731643.i	0.162662	−	1.13134i	−0.730927	−	0.682455i	$-0.760912\pi$
$211$	105194.	−	731643.i	0.162662	−	1.13134i	0.893589	−	0.448885i	$-0.148179\pi$
$212$		0			0
$213$	69050.5	+	480257.i	0.104284	+	0.725311i
$214$		0			0
$215$	−937111.	+	602244.i	−1.38259	+	0.888539i
$216$		0			0
$217$	239184.	−	70230.9i	0.344813	−	0.101246i
$218$		0			0
$219$	−411271.	+	474632.i	−0.579452	+	0.668723i
$220$		0			0
$221$	345583.	+	756720.i	0.475961	+	1.04221i
$222$		0			0
$223$	438273.	+	128689.i	0.590178	+	0.173292i	0.563167	−	0.826343i	$-0.309583\pi$
$223$	438273.	+	128689.i	0.590178	+	0.173292i	0.0270109	+	0.999635i	$0.491401\pi$
$224$		0			0
$225$	−272858.	+	597475.i	−0.359319	+	0.786799i
$226$		0			0
$227$	123016.	+	79057.4i	0.158451	+	0.101830i	0.617464	−	0.786599i	$-0.288160\pi$
$227$	123016.	+	79057.4i	0.158451	+	0.101830i	−0.459012	+	0.888430i	$0.651797\pi$
$228$		0			0
$229$	−550947.			−0.694258			−0.347129	−	0.937817i	$-0.612843\pi$
$229$	−550947.			−0.694258			−0.347129	+	0.937817i	$0.612843\pi$
$230$		0			0
$231$	193180.			0.238195
$232$		0			0
$233$	−796049.	−	511590.i	−0.960617	−	0.617351i	−0.0364481	−	0.999336i	$-0.511604\pi$
$233$	−796049.	−	511590.i	−0.960617	−	0.617351i	−0.924169	+	0.381985i	$0.875241\pi$
$234$		0			0
$235$	748660.	−	1.63934e6i	0.884331	−	1.93642i
$236$		0			0
$237$	26946.2	+	7912.11i	0.0311621	+	0.00915000i
$238$		0			0
$239$	5361.70	+	11740.5i	0.00607167	+	0.0132951i	0.912644	−	0.408756i	$-0.134037\pi$
$239$	5361.70	+	11740.5i	0.00607167	+	0.0132951i	−0.906572	+	0.422051i	$0.861310\pi$
$240$		0			0
$241$	738573.	−	852358.i	0.819126	−	0.945322i	−0.180140	−	0.983641i	$-0.557655\pi$
$241$	738573.	−	852358.i	0.819126	−	0.945322i	0.999266	+	0.0383195i	$0.0122004\pi$
$242$		0			0
$243$	−862884.	+	253366.i	−0.937425	+	0.275253i
$244$		0			0
$245$	−11917.7	+	7659.07i	−0.0126847	+	0.00815194i
$246$		0			0
$247$	−178048.	−	1.23835e6i	−0.185693	−	1.29152i
$248$		0			0
$249$	35092.1	−	244071.i	0.0358683	−	0.249470i
$250$		0			0
$251$	−340563.	−	393031.i	−0.341204	−	0.393770i	0.559051	−	0.829133i	$-0.311165\pi$
$251$	−340563.	−	393031.i	−0.341204	−	0.393770i	−0.900255	+	0.435363i	$0.856620\pi$
$252$		0			0
$253$	16232.4	+	379426.i	0.0159435	+	0.372671i
$254$		0			0
$255$	−450761.	−	520205.i	−0.434106	−	0.500985i
$256$		0			0
$257$	76655.7	−	533152.i	0.0723955	−	0.503522i	−0.921071	−	0.389395i	$-0.872684\pi$
$257$	76655.7	−	533152.i	0.0723955	−	0.503522i	0.993466	−	0.114126i	$-0.0364069\pi$
$258$		0			0
$259$	−134629.	−	936364.i	−0.124706	−	0.867352i
$260$		0			0
$261$	−517516.	+	332587.i	−0.470243	+	0.302207i
$262$		0			0
$263$	−583335.	+	171283.i	−0.520030	+	0.152695i	−0.531206	−	0.847243i	$-0.678261\pi$
$263$	−583335.	+	171283.i	−0.520030	+	0.152695i	0.0111755	+	0.999938i	$0.496443\pi$
$264$		0			0
$265$	931380.	−	1.07487e6i	0.814727	−	0.940245i
$266$		0			0
$267$	−446183.	−	977005.i	−0.383032	−	0.838723i
$268$		0			0
$269$	505960.	+	148563.i	0.426320	+	0.125179i	0.487852	−	0.872926i	$-0.337781\pi$
$269$	505960.	+	148563.i	0.426320	+	0.125179i	−0.0615324	+	0.998105i	$0.519599\pi$
$270$		0			0
$271$	−797478.	+	1.74623e6i	−0.659623	+	1.44437i	0.223251	+	0.974761i	$0.428333\pi$
$271$	−797478.	+	1.74623e6i	−0.659623	+	1.44437i	−0.882873	+	0.469611i	$0.844394\pi$
$272$		0			0
$273$	1.15310e6	+	741053.i	0.936398	+	0.601786i
$274$		0			0
$275$	687815.			0.548454
$276$		0			0
$277$	−680305.			−0.532727			−0.266363	−	0.963873i	$-0.585822\pi$
$277$	−680305.			−0.532727			−0.266363	+	0.963873i	$0.585822\pi$
$278$		0			0
$279$	232356.	+	149326.i	0.178708	+	0.114848i
$280$		0			0
$281$	229509.	−	502554.i	0.173394	−	0.379679i	−0.802905	−	0.596107i	$-0.796713\pi$
$281$	229509.	−	502554.i	0.173394	−	0.379679i	0.976299	+	0.216428i	$0.0694406\pi$
$282$		0			0
$283$	−465499.	−	136683.i	−0.345504	−	0.101449i	0.104377	−	0.994538i	$-0.466715\pi$
$283$	−465499.	−	136683.i	−0.345504	−	0.101449i	−0.449881	+	0.893089i	$0.648533\pi$
$284$		0			0
$285$	430029.	+	941632.i	0.313607	+	0.686703i
$286$		0			0
$287$	−1.35084e6	+	1.55895e6i	−0.968054	+	1.11719i
$288$		0			0
$289$	773747.	−	227193.i	0.544947	−	0.160011i
$290$		0			0
$291$	−1.09656e6	+	704718.i	−0.759104	+	0.487846i
$292$		0			0
$293$	−102341.	−	711801.i	−0.0696438	−	0.484384i	−0.994556	−	0.104203i	$-0.966771\pi$
$293$	−102341.	−	711801.i	−0.0696438	−	0.484384i	0.924912	−	0.380181i	$-0.124138\pi$
$294$		0			0
$295$	369944.	−	2.57301e6i	0.247503	−	1.72142i
$296$		0			0
$297$	378436.	+	436738.i	0.248944	+	0.287296i
$298$		0			0
$299$	−1.35861e6	+	2.32708e6i	−0.878856	+	1.50533i
$300$		0			0
$301$	1.07118e6	+	1.23621e6i	0.681468	+	0.786456i
$302$		0			0
$303$	48583.1	−	337903.i	0.0304004	−	0.211439i
$304$		0			0
$305$	−201706.	−	1.40290e6i	−0.124156	−	0.863527i
$306$		0			0
$307$	−2.13774e6	+	1.37384e6i	−1.29452	+	0.831936i	−0.992604	−	0.121399i	$-0.961262\pi$
$307$	−2.13774e6	+	1.37384e6i	−1.29452	+	0.831936i	−0.301914	+	0.953335i	$0.597626\pi$
$308$		0			0
$309$	1.84490e6	−	541710.i	1.09920	−	0.322754i
$310$		0			0
$311$	−319828.	+	369101.i	−0.187506	+	0.216394i	−0.841718	−	0.539918i	$-0.818455\pi$
$311$	−319828.	+	369101.i	−0.187506	+	0.216394i	0.654211	+	0.756312i	$0.273001\pi$
$312$		0			0
$313$	−1.12563e6	−	2.46478e6i	−0.649433	−	1.42206i	−0.892050	−	0.451937i	$-0.850733\pi$
$313$	−1.12563e6	−	2.46478e6i	−0.649433	−	1.42206i	0.242617	−	0.970122i	$-0.421994\pi$
$314$		0			0
$315$	1.55483e6	+	456541.i	0.882892	+	0.259241i
$316$		0			0
$317$	194075.	−	424965.i	0.108473	−	0.237523i	−0.847609	−	0.530621i	$-0.821959\pi$
$317$	194075.	−	424965.i	0.108473	−	0.237523i	0.956082	+	0.293098i	$0.0946862\pi$
$318$		0			0
$319$	541928.	+	348276.i	0.298170	+	0.191622i
$320$		0			0
$321$	−2.06781e6			−1.12008
$322$		0			0
$323$	922558.			0.492025
$324$		0			0
$325$	4.10559e6	+	2.63850e6i	2.15609	+	1.38564i
$326$		0			0
$327$	569006.	−	1.24595e6i	0.294271	−	0.644364i
$328$		0			0
$329$	−2.53918e6	−	745570.i	−1.29331	−	0.379751i
$330$		0			0
$331$	818444.	+	1.79214e6i	0.410600	+	0.899089i	0.996085	+	0.0884052i	$0.0281770\pi$
$331$	818444.	+	1.79214e6i	0.410600	+	0.899089i	−0.585485	+	0.810684i	$0.699096\pi$
$332$		0			0
$333$	686392.	−	792139.i	0.339205	−	0.391463i
$334$		0			0
$335$	−1.06934e6	+	313987.i	−0.520600	+	0.152862i
$336$		0			0
$337$	741642.	−	476624.i	0.355729	−	0.228613i	−0.350554	−	0.936542i	$-0.614007\pi$
$337$	741642.	−	476624.i	0.355729	−	0.228613i	0.706284	+	0.707929i	$0.250370\pi$
$338$		0			0
$339$	−263821.	−	1.83491e6i	−0.124684	−	0.867195i
$340$		0			0
$341$	41161.8	−	286287.i	0.0191694	−	0.133326i
$342$		0			0
$343$	1.43363e6	+	1.65450e6i	0.657964	+	0.759331i
$344$		0			0
$345$	536141.	−	2.16419e6i	0.242511	−	0.978921i
$346$		0			0
$347$	2.03648e6	+	2.35022e6i	0.907938	+	1.04782i	0.998650	+	0.0519397i	$0.0165403\pi$
$347$	2.03648e6	+	2.35022e6i	0.907938	+	1.04782i	−0.0907118	+	0.995877i	$0.528914\pi$
$348$		0			0
$349$	−87529.7	+	608783.i	−0.0384673	+	0.267546i	−0.999974	−	0.00723609i	$-0.997697\pi$
$349$	−87529.7	+	608783.i	−0.0384673	+	0.267546i	0.961506	+	0.274782i	$0.0886058\pi$
$350$		0			0
$351$	583540.	+	4.05861e6i	0.252815	+	1.75837i
$352$		0			0
$353$	−3.24429e6	+	2.08498e6i	−1.38574	+	0.890563i	−0.999493	−	0.0318319i	$-0.989866\pi$
$353$	−3.24429e6	+	2.08498e6i	−1.38574	+	0.890563i	−0.386249	+	0.922394i	$0.626230\pi$
$354$		0			0
$355$	4.08936e6	−	1.20074e6i	1.72220	−	0.505684i
$356$		0			0
$357$	−661904.	+	763877.i	−0.274868	+	0.317215i
$358$		0			0
$359$	134868.	+	295320.i	0.0552298	+	0.120936i	0.935235	−	0.354028i	$-0.115188\pi$
$359$	134868.	+	295320.i	0.0552298	+	0.120936i	−0.880005	+	0.474964i	$0.842461\pi$
$360$		0			0
$361$	1.04457e6	+	306713.i	0.421860	+	0.123869i
$362$		0			0
$363$	−576083.	+	1.26145e6i	−0.229466	+	0.502461i
$364$		0			0
$365$	4.64090e6	+	2.98253e6i	1.82335	+	1.17180i
$366$		0			0
$367$	−2.04589e6			−0.792896			−0.396448	−	0.918057i	$-0.629757\pi$
$367$	−2.04589e6			−0.792896			−0.396448	+	0.918057i	$0.629757\pi$
$368$		0			0
$369$	−2.28555e6			−0.873826
$370$		0			0
$371$	−1.75693e6	−	1.12911e6i	−0.662703	−	0.425893i
$372$		0			0
$373$	−1.26934e6	+	2.77947e6i	−0.472396	+	1.03440i	0.512088	+	0.858933i	$0.328872\pi$
$373$	−1.26934e6	+	2.77947e6i	−0.472396	+	1.03440i	−0.984485	+	0.175471i	$0.943855\pi$
$374$		0			0
$375$	−1.23940e6	−	363920.i	−0.455126	−	0.133637i
$376$		0			0
$377$	1.89878e6	+	4.15774e6i	0.688051	+	1.50662i
$378$		0			0
$379$	704046.	−	812513.i	0.251770	−	0.290558i	−0.615770	−	0.787926i	$-0.711155\pi$
$379$	704046.	−	812513.i	0.251770	−	0.290558i	0.867539	+	0.497369i	$0.165700\pi$
$380$		0			0
$381$	2.32113e6	−	681546.i	0.819195	−	0.240537i
$382$		0			0
$383$	2.79355e6	−	1.79531e6i	0.973105	−	0.625377i	0.0455099	−	0.998964i	$-0.485509\pi$
$383$	2.79355e6	−	1.79531e6i	0.973105	−	0.625377i	0.927595	+	0.373587i	$0.121872\pi$
$384$		0			0
$385$	−241496.	−	1.67964e6i	−0.0830344	−	0.577517i
$386$		0			0
$387$	−257928.	+	1.79393e6i	−0.0875429	+	0.608874i
$388$		0			0
$389$	−2.59346e6	−	2.99301e6i	−0.868972	−	1.00285i	−0.999934	−	0.0114599i	$-0.996352\pi$
$389$	−2.59346e6	−	2.99301e6i	−0.868972	−	1.00285i	0.130962	−	0.991387i	$-0.458193\pi$
$390$		0			0
$391$	−1.55595e6	−	1.23586e6i	−0.514700	−	0.408816i
$392$		0			0
$393$	−1.64162e6	−	1.89453e6i	−0.536155	−	0.618756i
$394$		0			0
$395$	35107.7	−	244179.i	0.0113216	−	0.0787437i
$396$		0			0
$397$	−743844.	−	5.17355e6i	−0.236868	−	1.64745i	−0.667271	−	0.744815i	$-0.732538\pi$
$397$	−743844.	−	5.17355e6i	−0.236868	−	1.64745i	0.430404	−	0.902637i	$-0.358371\pi$
$398$		0			0
$399$	1.27877e6	−	821813.i	0.402123	−	0.258429i
$400$		0			0
$401$	−3.63045e6	+	1.06600e6i	−1.12746	+	0.331051i	−0.791708	−	0.610900i	$-0.790808\pi$
$401$	−3.63045e6	+	1.06600e6i	−1.12746	+	0.331051i	−0.335749	+	0.941951i	$0.608989\pi$
$402$		0			0
$403$	1.34391e6	−	1.55096e6i	0.412200	−	0.475704i
$404$		0			0
$405$	−141504.	−	309851.i	−0.0428678	−	0.0938675i
$406$		0			0
$407$	−1.05313e6	−	309227.i	−0.315135	−	0.0925320i
$408$		0			0
$409$	2.39873e6	−	5.25249e6i	0.709044	−	1.55259i	−0.119604	−	0.992822i	$-0.538163\pi$
$409$	2.39873e6	−	5.25249e6i	0.709044	−	1.55259i	0.828649	−	0.559769i	$-0.189110\pi$
$410$		0			0
$411$	1.27514e6	+	819483.i	0.372352	+	0.239296i
$412$		0			0
$413$	−3.81711e6			−1.10118
$414$		0			0
$415$	−2.16599e6			−0.617356
$416$		0			0
$417$	2.60408e6	+	1.67354e6i	0.733354	+	0.471298i
$418$		0			0
$419$	1.47501e6	−	3.22981e6i	0.410449	−	0.898757i	−0.585655	−	0.810561i	$-0.699162\pi$
$419$	1.47501e6	−	3.22981e6i	0.410449	−	0.898757i	0.996103	−	0.0881963i	$-0.0281103\pi$
$420$		0			0
$421$	1.84126e6	+	540644.i	0.506303	+	0.148664i	0.524902	−	0.851163i	$-0.324102\pi$
$421$	1.84126e6	+	540644.i	0.506303	+	0.148664i	−0.0185982	+	0.999827i	$0.505920\pi$
$422$		0			0
$423$	−1.21806e6	−	2.66718e6i	−0.330992	−	0.724772i
$424$		0			0
$425$	−2.35670e6	+	2.71977e6i	−0.632894	+	0.730399i
$426$		0			0
$427$	−1.99691e6	+	586347.i	−0.530017	+	0.155627i
$428$		0			0
$429$	1.33789e6	−	859809.i	0.350976	−	0.225558i
$430$		0			0
$431$	−516342.	−	3.59124e6i	−0.133889	−	0.931216i	−0.940418	−	0.340022i	$-0.889566\pi$
$431$	−516342.	−	3.59124e6i	−0.133889	−	0.931216i	0.806529	−	0.591195i	$-0.201344\pi$
$432$		0			0
$433$	−988348.	+	6.87411e6i	−0.253332	+	1.76196i	0.324574	+	0.945860i	$0.394779\pi$
$433$	−988348.	+	6.87411e6i	−0.253332	+	1.76196i	−0.577906	+	0.816103i	$0.696130\pi$
$434$		0			0
$435$	−2.47667e6	−	2.85823e6i	−0.627545	−	0.724225i
$436$		0			0
$437$	1.72158e6	+	2.44257e6i	0.431244	+	0.611849i
$438$		0			0
$439$	−4.62592e6	−	5.33860e6i	−1.14561	−	1.32210i	−0.939094	−	0.343661i	$-0.888333\pi$
$439$	−4.62592e6	−	5.33860e6i	−1.14561	−	1.32210i	−0.206516	−	0.978443i	$-0.566213\pi$
$440$		0			0
$441$	−3280.21	+	22814.4i	−0.000803166	+	0.00558614i
$442$		0			0
$443$	735215.	+	5.11353e6i	0.177994	+	1.23797i	0.861397	+	0.507933i	$0.169590\pi$
$443$	735215.	+	5.11353e6i	0.177994	+	1.23797i	−0.683403	+	0.730041i	$0.739501\pi$
$444$		0			0
$445$	−7.93697e6	+	5.10078e6i	−1.90001	+	1.22106i
$446$		0			0
$447$	−1.07357e6	+	315228.i	−0.254133	+	0.0746202i
$448$		0			0
$449$	3.34331e6	−	3.85839e6i	0.782639	−	0.903213i	−0.214658	−	0.976689i	$-0.568864\pi$
$449$	3.34331e6	−	3.85839e6i	0.782639	−	0.903213i	0.997297	+	0.0734759i	$0.0234092\pi$
$450$		0			0
$451$	994239.	+	2.17708e6i	0.230170	+	0.504003i
$452$		0			0
$453$	−2.26385e6	−	664726.i	−0.518325	−	0.152194i
$454$		0			0
$455$	5.00172e6	−	1.09522e7i	1.13264	−	2.48013i
$456$		0			0
$457$	−6.14564e6	−	3.94956e6i	−1.37650	−	0.884624i	−0.377360	−	0.926067i	$-0.623168\pi$
$457$	−6.14564e6	−	3.94956e6i	−1.37650	−	0.884624i	−0.999141	+	0.0414429i	$0.986805\pi$
$458$		0			0
$459$	−3.02361e6			−0.669876
$460$		0			0
$461$	335873.			0.0736076			0.0368038	−	0.999323i	$-0.488282\pi$
$461$	335873.			0.0736076			0.0368038	+	0.999323i	$0.488282\pi$
$462$		0			0
$463$	4.07121e6	+	2.61641e6i	0.882615	+	0.567222i	0.901587	−	0.432598i	$-0.142403\pi$
$463$	4.07121e6	+	2.61641e6i	0.882615	+	0.567222i	−0.0189721	+	0.999820i	$0.506039\pi$
$464$		0			0
$465$	−705393.	+	1.54459e6i	−0.151286	+	0.331270i
$466$		0			0
$467$	4.16794e6	+	1.22382e6i	0.884360	+	0.259671i	0.692212	−	0.721695i	$-0.256636\pi$
$467$	4.16794e6	+	1.22382e6i	0.884360	+	0.259671i	0.192148	+	0.981366i	$0.438455\pi$
$468$		0			0
$469$	679837.	+	1.48864e6i	0.142716	+	0.312505i
$470$		0			0
$471$	−3.22129e6	+	3.71757e6i	−0.669079	+	0.772159i
$472$		0			0
$473$	1.82099e6	−	534691.i	0.374244	−	0.109888i
$474$		0			0
$475$	4.55302e6	−	2.92605e6i	0.925903	−	0.595042i
$476$		0			0
$477$	−329316.	−	2.29044e6i	−0.0662699	−	0.460917i
$478$		0			0
$479$	339460.	−	2.36099e6i	0.0676004	−	0.470171i	−0.927699	−	0.373328i	$-0.878217\pi$
$479$	339460.	−	2.36099e6i	0.0676004	−	0.470171i	0.995300	−	0.0968428i	$-0.0308744\pi$
$480$		0			0
$481$	−5.09997e6	−	5.88567e6i	−1.00509	−	1.15993i
$482$		0			0
$483$	−3.25762e6	−	326998.i	−0.635379	−	0.0637789i
$484$		0			0
$485$	7.49812e6	+	8.65330e6i	1.44743	+	1.67043i
$486$		0			0
$487$	−1.06807e6	+	7.42859e6i	−0.204069	+	1.41933i	0.587980	+	0.808875i	$0.299923\pi$
$487$	−1.06807e6	+	7.42859e6i	−0.204069	+	1.41933i	−0.792050	+	0.610457i	$0.790986\pi$
$488$		0			0
$489$	70263.3	+	488692.i	0.0132879	+	0.0924194i
$490$		0			0
$491$	1.38292e6	−	888751.i	0.258878	−	0.166371i	−0.404764	−	0.914421i	$-0.632646\pi$
$491$	1.38292e6	−	888751.i	0.258878	−	0.166371i	0.663642	+	0.748051i	$0.269010\pi$
$492$		0			0
$493$	−3.23399e6	+	949586.i	−0.599269	+	0.175961i
$494$		0			0
$495$	1.23124e6	−	1.42093e6i	0.225856	−	0.260651i
$496$		0			0
$497$	−2.59983e6	−	5.69282e6i	−0.472121	−	1.03380i
$498$		0			0
$499$	4.19479e6	+	1.23170e6i	0.754153	+	0.221439i	0.636141	−	0.771573i	$-0.280530\pi$
$499$	4.19479e6	+	1.23170e6i	0.754153	+	0.221439i	0.118012	+	0.993012i	$0.462348\pi$
$500$		0			0
$501$	599320.	−	1.31233e6i	0.106675	−	0.233587i
$502$		0			0
$503$	5.25949e6	+	3.38007e6i	0.926880	+	0.595670i	0.914646	−	0.404256i	$-0.132469\pi$
$503$	5.25949e6	+	3.38007e6i	0.926880	+	0.595670i	0.0122340	+	0.999925i	$0.496106\pi$
$504$		0			0
$505$	−2.99869e6			−0.523243
$506$		0			0
$507$	7.57035e6			1.30797
$508$		0			0
$509$	6.49937e6	+	4.17689e6i	1.11193	+	0.714593i	0.961712	−	0.274061i	$-0.0883669\pi$
$509$	6.49937e6	+	4.17689e6i	1.11193	+	0.714593i	0.150216	+	0.988653i	$0.452003\pi$
$510$		0			0
$511$	3.36517e6	−	7.36869e6i	0.570104	−	1.24835i
$512$		0			0
$513$	4.36301e6	+	1.28110e6i	0.731969	+	0.214926i
$514$		0			0
$515$	−7.01632e6	−	1.53636e7i	−1.16571	−	2.55255i
$516$		0			0
$517$	−2.01073e6	+	2.32050e6i	−0.330847	+	0.381818i
$518$		0			0
$519$	−1.01484e6	+	297983.i	−0.165378	+	0.0485594i
$520$		0			0
$521$	−2.48448e6	+	1.59668e6i	−0.400996	+	0.257705i	−0.725560	−	0.688159i	$-0.758419\pi$
$521$	−2.48448e6	+	1.59668e6i	−0.400996	+	0.257705i	0.324563	+	0.945864i	$0.394783\pi$
$522$		0			0
$523$	1.05205e6	+	7.31718e6i	0.168183	+	1.16974i	0.882636	+	0.470057i	$0.155766\pi$
$523$	1.05205e6	+	7.31718e6i	0.168183	+	1.16974i	−0.714453	+	0.699683i	$0.753324\pi$
$524$		0			0
$525$	−843869.	+	5.86924e6i	−0.133622	+	0.929359i
$526$		0			0
$527$	991005.	+	1.14368e6i	0.155435	+	0.179382i
$528$		0			0
$529$	368528.	−	6.42578e6i	0.0572574	−	0.998359i
$530$		0			0
$531$	−2.76961e6	−	3.19630e6i	−0.426268	−	0.491939i
$532$		0			0
$533$	−2.41677e6	+	1.68090e7i	−0.368483	+	2.56286i
$534$		0			0
$535$	2.58498e6	+	1.79790e7i	0.390457	+	2.71569i
$536$		0			0
$537$	740886.	−	476138.i	0.110870	−	0.0712520i
$538$		0			0
$539$	23158.5	−	6799.95i	0.00343351	−	0.00100817i
$540$		0			0
$541$	2.49051e6	−	2.87421e6i	0.365844	−	0.422207i	−0.542745	−	0.839897i	$-0.682615\pi$
$541$	2.49051e6	−	2.87421e6i	0.365844	−	0.422207i	0.908589	+	0.417691i	$0.137161\pi$
$542$		0			0
$543$	356009.	+	779551.i	0.0518157	+	0.113461i
$544$		0			0
$545$	−1.15445e7	−	3.38976e6i	−1.66488	−	0.488852i
$546$		0			0
$547$	−390501.	+	855079.i	−0.0558026	+	0.122191i	−0.935479	−	0.353382i	$-0.885032\pi$
$547$	−390501.	+	855079.i	−0.0558026	+	0.122191i	0.879677	+	0.475572i	$0.157759\pi$
$548$		0			0
$549$	−1.93990e6	−	1.24670e6i	−0.274694	−	0.176535i
$550$		0			0
$551$	5.06892e6			0.711273
$552$		0			0
$553$	−362244.			−0.0503718
$554$		0			0
$555$	5.42091e6	+	3.48381e6i	0.747033	+	0.480089i
$556$		0			0
$557$	136535.	−	298969.i	0.0186468	−	0.0408309i	−0.900079	−	0.435726i	$-0.856492\pi$
$557$	136535.	−	298969.i	0.0186468	−	0.0408309i	0.918726	+	0.394895i	$0.129219\pi$
$558$		0			0
$559$	1.29207e7	+	3.79385e6i	1.74886	+	0.513512i
$560$		0			0
$561$	487170.	+	1.06675e6i	0.0653542	+	0.143106i
$562$		0			0
$563$	−4.97918e6	+	5.74628e6i	−0.662044	+	0.764039i	−0.983110	−	0.183018i	$-0.941413\pi$
$563$	−4.97918e6	+	5.74628e6i	−0.662044	+	0.764039i	0.321066	+	0.947057i	$0.395959\pi$
$564$		0			0
$565$	−1.56242e7	+	4.58768e6i	−2.05910	+	0.604605i
$566$		0			0
$567$	−420787.	+	270424.i	−0.0549674	+	0.0353254i
$568$		0			0
$569$	−2.09885e6	−	1.45978e7i	−0.271769	−	1.89020i	−0.430052	−	0.902804i	$-0.641505\pi$
$569$	−2.09885e6	−	1.45978e7i	−0.271769	−	1.89020i	0.158283	−	0.987394i	$-0.449404\pi$
$570$		0			0
$571$	−789496.	+	5.49106e6i	−0.101335	+	0.704800i	0.874298	+	0.485390i	$0.161322\pi$
$571$	−789496.	+	5.49106e6i	−0.101335	+	0.704800i	−0.975633	+	0.219410i	$0.929587\pi$
$572$		0			0
$573$	5.10161e6	+	5.88757e6i	0.649114	+	0.749117i
$574$		0			0
$575$	−1.15987e7	−	1.16427e6i	−1.46298	−	0.146853i
$576$		0			0
$577$	1.49683e6	+	1.72743e6i	0.187168	+	0.216004i	0.841577	−	0.540138i	$-0.181628\pi$
$577$	1.49683e6	+	1.72743e6i	0.187168	+	0.216004i	−0.654409	+	0.756141i	$0.727082\pi$
$578$		0			0
$579$	729104.	−	5.07103e6i	0.0903843	−	0.628637i
$580$		0			0
$581$	452642.	+	3.14819e6i	0.0556307	+	0.386920i
$582$		0			0
$583$	−2.03848e6	+	1.31005e6i	−0.248391	+	0.159631i
$584$		0			0
$585$	1.28001e7	−	3.75846e6i	1.54641	−	0.454067i
$586$		0			0
$587$	8.34473e6	−	9.63033e6i	0.999578	−	1.15357i	0.0114514	−	0.999934i	$-0.496355\pi$
$587$	8.34473e6	−	9.63033e6i	0.999578	−	1.15357i	0.988127	−	0.153640i	$-0.0490997\pi$
$588$		0			0
$589$	−945426.	−	2.07019e6i	−0.112290	−	0.245880i
$590$		0			0
$591$	6.48019e6	+	1.90275e6i	0.763166	+	0.224086i
$592$		0			0
$593$	5.98347e6	−	1.31020e7i	0.698741	−	1.53003i	−0.142750	−	0.989759i	$-0.545595\pi$
$593$	5.98347e6	−	1.31020e7i	0.698741	−	1.53003i	0.841491	−	0.540271i	$-0.181678\pi$
$594$		0			0
$595$	7.46912e6	+	4.80011e6i	0.864922	+	0.555852i
$596$		0			0
$597$	2.50181e6			0.287289
$598$		0			0
$599$	689542.			0.0785224			0.0392612	−	0.999229i	$-0.487500\pi$
$599$	689542.			0.0785224			0.0392612	+	0.999229i	$0.487500\pi$
$600$		0			0
$601$	1.25530e7	+	8.06732e6i	1.41762	+	0.911052i	0.999997	+	0.00243344i	$0.000774589\pi$
$601$	1.25530e7	+	8.06732e6i	1.41762	+	0.911052i	0.417627	+	0.908618i	$0.362862\pi$
$602$		0			0
$603$	−753253.	+	1.64939e6i	−0.0843621	+	0.184727i
$604$		0			0
$605$	1.16880e7	+	3.43192e6i	1.29824	+	0.381196i
$606$		0			0
$607$	1.26521e6	+	2.77043e6i	0.139377	+	0.305194i	0.966430	−	0.256931i	$-0.0827113\pi$
$607$	1.26521e6	+	2.77043e6i	0.139377	+	0.305194i	−0.827052	+	0.562125i	$0.809984\pi$
$608$		0			0
$609$	−3.63678e6	+	4.19706e6i	−0.397350	+	0.458566i
$610$		0			0
$611$	−2.09037e7	+	6.13788e6i	−2.26527	+	0.665144i
$612$		0			0
$613$	−3.25290e6	+	2.09051e6i	−0.349639	+	0.224699i	−0.703658	−	0.710539i	$-0.748451\pi$
$613$	−3.25290e6	+	2.09051e6i	−0.349639	+	0.224699i	0.354019	+	0.935238i	$0.384815\pi$
$614$		0			0
$615$	−1.99969e6	−	1.39082e7i	−0.213194	−	1.48280i
$616$		0			0
$617$	229098.	−	1.59341e6i	0.0242274	−	0.168506i	−0.974115	−	0.226051i	$-0.927418\pi$
$617$	229098.	−	1.59341e6i	0.0242274	−	0.168506i	0.998343	+	0.0575456i	$0.0183274\pi$
$618$		0			0
$619$	−6.61893e6	−	7.63865e6i	−0.694322	−	0.801290i	0.293652	−	0.955913i	$-0.405129\pi$
$619$	−6.61893e6	−	7.63865e6i	−0.694322	−	0.801290i	−0.987974	+	0.154622i	$0.950584\pi$
$620$		0			0
$621$	−5.64234e6	−	8.00535e6i	−0.587124	−	0.833012i
$622$		0			0
$623$	9.07247e6	+	1.04702e7i	0.936495	+	1.08077i
$624$		0			0
$625$	428677.	−	2.98151e6i	0.0438965	−	0.305307i
$626$		0			0
$627$	−250996.	−	1.74572e6i	−0.0254975	−	0.177339i
$628$		0			0
$629$	4.83115e6	−	3.10479e6i	0.486882	−	0.312900i
$630$		0			0
$631$	−1.10052e7	+	3.23141e6i	−1.10033	+	0.323087i	−0.780984	−	0.624551i	$-0.785282\pi$
$631$	−1.10052e7	+	3.23141e6i	−1.10033	+	0.323087i	−0.319348	+	0.947638i	$0.603464\pi$
$632$		0			0
$633$	4.84170e6	−	5.58762e6i	0.480273	−	0.554265i
$634$		0			0
$635$	−8.82749e6	−	1.93295e7i	−0.868766	−	1.90233i
$636$		0			0
$637$	164319.	+	48248.4i	0.0160450	+	0.00471123i
$638$		0			0
$639$	2.88058e6	−	6.30759e6i	0.279079	−	0.611098i
$640$		0			0
$641$	5.11229e6	+	3.28547e6i	0.491440	+	0.315829i	0.762784	−	0.646653i	$-0.223832\pi$
$641$	5.11229e6	+	3.28547e6i	0.491440	+	0.315829i	−0.271344	+	0.962482i	$0.587468\pi$
$642$		0			0
$643$	−1.29122e7			−1.23161			−0.615803	−	0.787900i	$-0.711168\pi$
$643$	−1.29122e7			−1.23161			−0.615803	+	0.787900i	$0.711168\pi$
$644$		0			0
$645$	−1.11422e7			−1.05456
$646$		0			0
$647$	−1.05383e7	−	6.77254e6i	−0.989712	−	0.636049i	−0.0576455	−	0.998337i	$-0.518359\pi$
$647$	−1.05383e7	−	6.77254e6i	−0.989712	−	0.636049i	−0.932066	+	0.362288i	$0.881996\pi$
$648$		0			0
$649$	−1.83979e6	+	4.02859e6i	−0.171458	+	0.375440i
$650$		0			0
$651$	2.39243e6	+	702481.i	0.221252	+	0.0649654i
$652$		0			0
$653$	1.68597e6	+	3.69176e6i	0.154728	+	0.338806i	0.971082	−	0.238745i	$-0.0767359\pi$
$653$	1.68597e6	+	3.69176e6i	0.154728	+	0.338806i	−0.816355	+	0.577551i	$0.804009\pi$
$654$		0			0
$655$	−1.44201e7	+	1.66417e7i	−1.31330	+	1.51563i
$656$		0			0
$657$	8.61196e6	−	2.52870e6i	0.778374	−	0.228551i
$658$		0			0
$659$	−6.41709e6	+	4.12402e6i	−0.575605	+	0.369919i	−0.795821	−	0.605532i	$-0.792960\pi$
$659$	−6.41709e6	+	4.12402e6i	−0.575605	+	0.369919i	0.220215	+	0.975451i	$0.429324\pi$
$660$		0			0
$661$	19195.9	+	133510.i	0.00170885	+	0.0118853i	0.990658	−	0.136370i	$-0.0435435\pi$
$661$	19195.9	+	133510.i	0.00170885	+	0.0118853i	−0.988949	+	0.148255i	$0.952634\pi$
$662$		0			0
$663$	−1.18420e6	+	8.23631e6i	−0.104627	+	0.727694i
$664$		0			0
$665$	−8.74399e6	−	1.00911e7i	−0.766753	−	0.884881i
$666$		0			0
$667$	−8.54906e6	−	6.79034e6i	−0.744052	−	0.590985i
$668$		0			0
$669$	2.99198e6	+	3.45293e6i	0.258460	+	0.298278i
$670$		0			0
$671$	−343653.	+	2.39016e6i	−0.0294655	+	0.204937i
$672$		0			0
$673$	659431.	+	4.58644e6i	0.0561218	+	0.390336i	0.998451	+	0.0556469i	$0.0177221\pi$
$673$	659431.	+	4.58644e6i	0.0561218	+	0.390336i	−0.942329	+	0.334689i	$0.891369\pi$
$674$		0			0
$675$	−1.49222e7	+	9.58990e6i	−1.26059	+	0.810130i
$676$		0			0
$677$	7.63852e6	−	2.24287e6i	0.640527	−	0.188076i	0.0546883	−	0.998503i	$-0.482583\pi$
$677$	7.63852e6	−	2.24287e6i	0.640527	−	0.188076i	0.585838	+	0.810428i	$0.300765\pi$
$678$		0			0
$679$	1.10104e7	−	1.27066e7i	0.916488	−	1.05768i
$680$		0			0
$681$	607606.	+	1.33047e6i	0.0502059	+	0.109935i
$682$		0			0
$683$	1.27106e7	+	3.73216e6i	1.04259	+	0.306132i	0.757820	−	0.652464i	$-0.226265\pi$
$683$	1.27106e7	+	3.73216e6i	1.04259	+	0.306132i	0.284770	+	0.958596i	$0.408083\pi$
$684$		0			0
$685$	5.53108e6	−	1.21114e7i	0.450385	−	0.986205i
$686$		0			0
$687$	−4.63599e6	−	2.97937e6i	−0.374758	−	0.240842i
$688$		0			0
$689$	−1.71932e7			−1.37978
$690$		0			0
$691$	1.61556e7			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$691$	1.61556e7			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$692$		0			0
$693$	−2.32258e6	−	1.49263e6i	−0.183712	−	0.118065i
$694$		0			0
$695$	1.12955e7	−	2.47337e7i	0.887042	−	1.94235i
$696$		0			0
$697$	−1.20153e7	−	3.52800e6i	−0.936809	−	0.275072i
$698$		0			0
$699$	−3.93189e6	−	8.60964e6i	−0.304375	−	0.666488i
$700$		0			0
$701$	3.23992e6	−	3.73907e6i	0.249023	−	0.287388i	−0.617452	−	0.786609i	$-0.711835\pi$
$701$	3.23992e6	−	3.73907e6i	0.249023	−	0.287388i	0.866475	+	0.499221i	$0.166380\pi$
$702$		0			0
$703$	−8.28674e6	+	2.43321e6i	−0.632405	+	0.185691i
$704$		0			0
$705$	1.51648e7	−	9.74580e6i	1.14911	−	0.738490i
$706$		0			0
$707$	626659.	+	4.35851e6i	0.0471501	+	0.327936i
$708$		0			0
$709$	1.99900e6	−	1.39034e7i	0.149348	−	1.03874i	−0.767943	−	0.640518i	$-0.778720\pi$
$709$	1.99900e6	−	1.39034e7i	0.149348	−	1.03874i	0.917291	−	0.398218i	$-0.130371\pi$
$710$		0			0
$711$	−262836.	−	303329.i	−0.0194989	−	0.0225030i
$712$		0			0
$713$	−1.17872e6	+	4.75801e6i	−0.0868331	+	0.350511i
$714$		0			0
$715$	−9.14827e6	−	1.05577e7i	−0.669228	−	0.772330i
$716$		0			0
$717$	−18372.9	+	127786.i	−0.00133469	+	0.00928295i
$718$		0			0
$719$	−2.15081e6	−	1.49592e7i	−0.155160	−	1.07916i	−0.907399	−	0.420270i	$-0.861936\pi$
$719$	−2.15081e6	−	1.49592e7i	−0.155160	−	1.07916i	0.752240	−	0.658890i	$-0.228974\pi$
$720$		0			0
$721$	−2.08642e7	+	1.34086e7i	−1.49474	+	0.960608i
$722$		0			0
$723$	1.08241e7	−	3.17825e6i	0.770099	−	0.226121i
$724$		0			0
$725$	−1.29487e7	+	1.49436e7i	−0.914914	+	1.05587i
$726$		0			0
$727$	8.49542e6	+	1.86024e7i	0.596141	+	1.30537i	0.931659	+	0.363333i	$0.118361\pi$
$727$	8.49542e6	+	1.86024e7i	0.596141	+	1.30537i	−0.335519	+	0.942034i	$0.608912\pi$
$728$		0			0
$729$	−9.53487e6	−	2.79969e6i	−0.664502	−	0.195115i
$730$		0			0
$731$	−4.12506e6	+	9.03263e6i	−0.285520	+	0.625203i
$732$		0			0
$733$	1.08355e7	+	6.96357e6i	0.744886	+	0.478709i	0.857213	−	0.514962i	$-0.172194\pi$
$733$	1.08355e7	+	6.96357e6i	0.744886	+	0.478709i	−0.112327	+	0.993671i	$0.535830\pi$
$734$		0			0
$735$	−141701.			−0.00967509
$736$		0			0
$737$	1.89879e6			0.128768
$738$		0			0
$739$	1.87886e7	+	1.20747e7i	1.26556	+	0.813327i	0.989035	−	0.147679i	$-0.0471802\pi$
$739$	1.87886e7	+	1.20747e7i	1.26556	+	0.813327i	0.276527	+	0.961006i	$0.410817\pi$
$740$		0			0
$741$	5.19848e6	−	1.13831e7i	0.347801	−	0.761578i
$742$		0			0
$743$	6.13804e6	+	1.80229e6i	0.407904	+	0.119771i	0.479246	−	0.877681i	$-0.340910\pi$
$743$	6.13804e6	+	1.80229e6i	0.407904	+	0.119771i	−0.0713425	+	0.997452i	$0.522728\pi$
$744$		0			0
$745$	4.08289e6	+	8.94028e6i	0.269511	+	0.590147i
$746$		0			0
$747$	−2.30775e6	+	2.66329e6i	−0.151317	+	0.174629i
$748$		0			0
$749$	2.55916e7	−	7.51438e6i	1.66684	−	0.489428i
$750$		0			0
$751$	4.55374e6	−	2.92651e6i	0.294624	−	0.189343i	−0.384975	−	0.922927i	$-0.625790\pi$
$751$	4.55374e6	−	2.92651e6i	0.294624	−	0.189343i	0.679599	+	0.733584i	$0.262154\pi$
$752$		0			0
$753$	−740296.	−	5.14887e6i	−0.0475793	−	0.330921i
$754$		0			0
$755$	−2.94953e6	+	2.05144e7i	−0.188315	+	1.30976i
$756$		0			0
$757$	−1.20476e7	−	1.39037e7i	−0.764118	−	0.881839i	0.231739	−	0.972778i	$-0.425559\pi$
$757$	−1.20476e7	−	1.39037e7i	−0.764118	−	0.881839i	−0.995856	+	0.0909391i	$0.971013\pi$
$758$		0			0
$759$	−1.91525e6	+	3.28050e6i	−0.120676	+	0.206698i
$760$		0			0
$761$	2.38502e6	+	2.75246e6i	0.149290	+	0.172290i	0.825469	−	0.564448i	$-0.190911\pi$
$761$	2.38502e6	+	2.75246e6i	0.149290	+	0.172290i	−0.676179	+	0.736737i	$0.736365\pi$
$762$		0			0
$763$	−2.51438e6	+	1.74879e7i	−0.156358	+	1.08749i
$764$		0			0
$765$	1.40000e6	+	9.73722e6i	0.0864917	+	0.601563i
$766$		0			0
$767$	−2.64357e7	+	1.69892e7i	−1.62257	+	1.04276i
$768$		0			0
$769$	9.04304e6	−	2.65528e6i	0.551440	−	0.161917i	0.00587032	−	0.999983i	$-0.498131\pi$
$769$	9.04304e6	−	2.65528e6i	0.551440	−	0.161917i	0.545570	+	0.838065i	$0.316313\pi$
$770$		0			0
$771$	3.52817e6	−	4.07172e6i	0.213754	−	0.246685i
$772$		0			0
$773$	794575.	+	1.73988e6i	0.0478284	+	0.104730i	0.932038	−	0.362361i	$-0.118029\pi$
$773$	794575.	+	1.73988e6i	0.0478284	+	0.104730i	−0.884209	+	0.467091i	$0.845302\pi$
$774$		0			0
$775$	8.51820e6	+	2.50117e6i	0.509441	+	0.149585i
$776$		0			0
$777$	3.93076e6	−	8.60716e6i	0.233574	−	0.511455i
$778$		0			0
$779$	1.58430e7	+	1.01817e7i	0.935390	+	0.601139i
$780$		0			0
$781$	−7.26131e6			−0.425978
$782$		0			0
$783$	−1.66130e7			−0.968375
$784$		0			0
$785$	3.63500e7	+	2.33607e7i	2.10538	+	1.35305i
$786$		0			0
$787$	−2.06010e6	+	4.51100e6i	−0.118564	+	0.259619i	−0.959604	−	0.281354i	$-0.909216\pi$
$787$	−2.06010e6	+	4.51100e6i	−0.118564	+	0.259619i	0.841040	+	0.540973i	$0.181944\pi$
$788$		0			0
$789$	−5.83478e6	−	1.71324e6i	−0.333681	−	0.0979776i
$790$		0			0
$791$	9.93315e6	+	2.17506e7i	0.564476	+	1.23603i
$792$		0			0
$793$	−1.12201e7	+	1.29487e7i	−0.633598	+	0.731211i
$794$		0			0
$795$	1.36498e7	−	4.00794e6i	0.765963	−	0.224907i
$796$		0			0
$797$	2.14810e7	−	1.38050e7i	1.19787	−	0.769824i	0.219283	−	0.975661i	$-0.429628\pi$
$797$	2.14810e7	−	1.38050e7i	1.19787	−	0.769824i	0.978586	+	0.205838i	$0.0659918\pi$
$798$		0			0
$799$	−2.28632e6	−	1.59017e7i	−0.126698	−	0.881205i
$800$		0			0
$801$	−2.18455e6	+	1.51939e7i	−0.120304	+	0.836735i
$802$		0			0
$803$	−6.15498e6	−	7.10322e6i	−0.336851	−	0.388747i
$804$		0			0
$805$	1.22923e6	+	2.87328e7i	0.0668566	+	1.56274i
$806$		0			0
$807$	3.45406e6	+	3.98619e6i	0.186701	+	0.215464i
$808$		0			0
$809$	3.39447e6	−	2.36091e7i	0.182348	−	1.26826i	−0.668843	−	0.743403i	$-0.733210\pi$
$809$	3.39447e6	−	2.36091e7i	0.182348	−	1.26826i	0.851191	−	0.524855i	$-0.175881\pi$
$810$		0			0
$811$	−1.67796e6	−	1.16705e7i	−0.0895838	−	0.623069i	−0.984309	−	0.176452i	$-0.943538\pi$
$811$	−1.67796e6	−	1.16705e7i	−0.0895838	−	0.623069i	0.894725	−	0.446617i	$-0.147371\pi$
$812$		0			0
$813$	−1.61536e7	+	1.03813e7i	−0.857123	+	0.550840i
$814$		0			0
$815$	4.16118e6	−	1.22183e6i	0.219444	−	0.0644345i
$816$		0			0
$817$	9.77948e6	−	1.12861e7i	0.512579	−	0.591547i
$818$		0			0
$819$	−8.13773e6	−	1.78192e7i	−0.423930	−	0.928276i
$820$		0			0
$821$	2.28685e7	+	6.71479e6i	1.18408	+	0.347676i	0.813744	−	0.581223i	$-0.197426\pi$
$821$	2.28685e7	+	6.71479e6i	1.18408	+	0.347676i	0.370332	+	0.928900i	$0.379244\pi$
$822$		0			0
$823$	−1.09426e7	+	2.39610e7i	−0.563147	+	1.23312i	0.387220	+	0.921987i	$0.373435\pi$
$823$	−1.09426e7	+	2.39610e7i	−0.563147	+	1.23312i	−0.950367	+	0.311132i	$0.899292\pi$
$824$		0			0
$825$	5.78768e6	+	3.71952e6i	0.296053	+	0.190262i
$826$		0			0
$827$	−2.75664e7			−1.40157			−0.700786	−	0.713371i	$-0.747167\pi$
$827$	−2.75664e7			−1.40157			−0.700786	+	0.713371i	$0.747167\pi$
$828$		0			0
$829$	4.57539e6			0.231229			0.115614	−	0.993294i	$-0.463116\pi$
$829$	4.57539e6			0.231229			0.115614	+	0.993294i	$0.463116\pi$
$830$		0			0
$831$	−5.72449e6	−	3.67891e6i	−0.287564	−	0.184806i
$832$		0			0
$833$	−52460.7	+	114873.i	−0.00261952	+	0.00573594i
$834$		0			0
$835$	−1.21595e7	−	3.57035e6i	−0.603530	−	0.177212i
$836$		0			0
$837$	3.09856e6	+	6.78490e6i	0.152878	+	0.334757i
$838$		0			0
$839$	1.18424e7	−	1.36669e7i	0.580812	−	0.670292i	−0.386967	−	0.922093i	$-0.626477\pi$
$839$	1.18424e7	−	1.36669e7i	0.580812	−	0.670292i	0.967779	+	0.251801i	$0.0810229\pi$
$840$		0			0
$841$	1.91140e6	−	561236.i	0.0931881	−	0.0273625i
$842$		0			0
$843$	4.64890e6	−	2.98767e6i	0.225310	−	0.144798i
$844$		0			0
$845$	−9.46375e6	−	6.58218e7i	−0.455954	−	3.17123i
$846$		0			0
$847$	2.54565e6	−	1.77054e7i	0.121924	−	0.848002i
$848$		0			0
$849$	−3.17784e6	−	3.66743e6i	−0.151308	−	0.174619i
$850$		0			0
$851$	1.72357e7	+	6.99718e6i	0.815838	+	0.331207i
$852$		0			0
$853$	−1.56634e7	−	1.80765e7i	−0.737079	−	0.850634i	0.256171	−	0.966632i	$-0.417539\pi$
$853$	−1.56634e7	−	1.80765e7i	−0.737079	−	0.850634i	−0.993250	+	0.115997i	$0.962994\pi$
$854$		0			0
$855$	2.10546e6	−	1.46438e7i	0.0984989	−	0.685075i
$856$		0			0
$857$	4.15755e6	+	2.89164e7i	0.193369	+	1.34491i	0.823012	+	0.568024i	$0.192292\pi$
$857$	4.15755e6	+	2.89164e7i	0.193369	+	1.34491i	−0.629644	+	0.776884i	$0.716799\pi$
$858$		0			0
$859$	−1.69699e7	+	1.09059e7i	−0.784685	+	0.504286i	−0.870585	−	0.492018i	$-0.836260\pi$
$859$	−1.69699e7	+	1.09059e7i	−0.784685	+	0.504286i	0.0859007	+	0.996304i	$0.472623\pi$
$860$		0			0
$861$	−1.97972e7	+	5.81298e6i	−0.910114	+	0.267234i
$862$		0			0
$863$	−2.58523e7	+	2.98352e7i	−1.18161	+	1.36365i	−0.264805	+	0.964302i	$0.585308\pi$
$863$	−2.58523e7	+	2.98352e7i	−1.18161	+	1.36365i	−0.916801	+	0.399344i	$0.869238\pi$
$864$		0			0
$865$	3.85952e6	+	8.45118e6i	0.175385	+	0.384040i
$866$		0			0
$867$	7.73937e6	+	2.27248e6i	0.349669	+	0.102672i
$868$		0			0
$869$	−174597.	+	382313.i	−0.00784308	+	0.0171739i
$870$		0			0
$871$	1.13339e7	+	7.28387e6i	0.506215	+	0.325324i
$872$		0			0
$873$	1.86289e7			0.827279
$874$		0			0
$875$	1.66615e7			0.735688
$876$		0			0
$877$	2.82224e7	+	1.81374e7i	1.23907	+	0.796300i	0.985278	−	0.170960i	$-0.0546868\pi$
$877$	2.82224e7	+	1.81374e7i	1.23907	+	0.796300i	0.253789	+	0.967260i	$0.418323\pi$
$878$		0			0
$879$	2.98806e6	−	6.54295e6i	0.130442	−	0.285628i
$880$		0			0
$881$	−2.46523e7	−	7.23855e6i	−1.07008	−	0.314204i	−0.301177	−	0.953568i	$-0.597380\pi$
$881$	−2.46523e7	−	7.23855e6i	−1.07008	−	0.314204i	−0.768904	+	0.639364i	$0.779198\pi$
$882$		0			0
$883$	1.22452e7	+	2.68133e7i	0.528524	+	1.15731i	0.966110	+	0.258129i	$0.0831061\pi$
$883$	1.22452e7	+	2.68133e7i	0.528524	+	1.15731i	−0.437587	+	0.899176i	$0.644167\pi$
$884$		0			0
$885$	1.70271e7	−	1.96503e7i	0.730773	−	0.843357i
$886$		0			0
$887$	1.29826e6	−	381202.i	0.0554053	−	0.0162685i	−0.253912	−	0.967227i	$-0.581718\pi$
$887$	1.29826e6	−	381202.i	0.0554053	−	0.0162685i	0.309318	+	0.950959i	$0.399899\pi$
$888$		0			0
$889$	−2.62501e7	+	1.68699e7i	−1.11398	+	0.715909i
$890$		0			0
$891$	82592.2	+	574441.i	0.00348534	+	0.0242410i
$892$		0			0
$893$	−3.43839e6	+	2.39146e7i	−0.144287	+	1.00354i
$894$		0			0
$895$	−5.06606e6	−	5.84654e6i	−0.211404	−	0.243973i
$896$		0			0
$897$	−2.40164e7	+	1.22344e7i	−0.996613	+	0.507694i
$898$		0			0
$899$	5.44500e6	+	6.28386e6i	0.224698	+	0.259315i
$900$		0			0
$901$	1.80432e6	−	1.25493e7i	0.0740458	−	0.515000i
$902$		0			0
$903$	2.32846e6	+	1.61948e7i	0.0950276	+	0.660932i
$904$		0			0
$905$	6.33290e6	−	4.06991e6i	0.257028	−	0.165182i
$906$		0			0
$907$	−2.45934e6	+	722127.i	−0.0992659	+	0.0291471i	−0.330988	−	0.943635i	$-0.607382\pi$
$907$	−2.45934e6	+	722127.i	−0.0992659	+	0.0291471i	0.231722	+	0.972782i	$0.425564\pi$
$908$		0			0
$909$	−3.19496e6	+	3.68718e6i	−0.128249	+	0.148008i
$910$		0			0
$911$	−1.74151e7	−	3.81337e7i	−0.695232	−	1.52234i	−0.845659	−	0.533724i	$-0.820792\pi$
$911$	−1.74151e7	−	3.81337e7i	−0.695232	−	1.52234i	0.150427	−	0.988621i	$-0.451935\pi$
$912$		0			0
$913$	3.54078e6	+	1.03967e6i	0.140580	+	0.0412779i
$914$		0			0
$915$	5.88921e6	−	1.28956e7i	0.232544	−	0.509200i
$916$		0			0
$917$	2.72017e7	+	1.74814e7i	1.06825	+	0.686521i
$918$		0			0
$919$	−4.67691e6			−0.182671			−0.0913356	−	0.995820i	$-0.529114\pi$
$919$	−4.67691e6			−0.182671			−0.0913356	+	0.995820i	$0.529114\pi$
$920$		0			0
$921$	−2.54175e7			−0.987380
$922$		0			0
$923$	−4.33430e7	−	2.78549e7i	−1.67461	−	1.07621i
$924$		0			0
$925$	1.39954e7	−	3.06456e7i	0.537813	−	1.17765i
$926$		0			0
$927$	−2.63665e7	−	7.74191e6i	−1.00775	−	0.295903i
$928$		0			0
$929$	−1.31815e7	−	2.88634e7i	−0.501100	−	1.09726i	−0.976110	−	0.217275i	$-0.930283\pi$
$929$	−1.31815e7	−	2.88634e7i	−0.501100	−	1.09726i	0.475011	−	0.879980i	$-0.342444\pi$
$930$		0			0
$931$	124371.	−	143532.i	0.00470267	−	0.00542717i
$932$		0			0
$933$	−4.68722e6	+	1.37629e6i	−0.176283	+	0.0517615i
$934$		0			0
$935$	8.66608e6	−	5.56935e6i	0.324185	−	0.208341i
$936$		0			0
$937$	996070.	+	6.92782e6i	0.0370630	+	0.257779i	0.999925	−	0.0122136i	$-0.00388780\pi$
$937$	996070.	+	6.92782e6i	0.0370630	+	0.257779i	−0.962862	+	0.269993i	$0.912979\pi$
$938$		0			0
$939$	3.85717e6	−	2.68272e7i	0.142760	−	0.992915i
$940$		0			0
$941$	−1.17670e7	−	1.35799e7i	−0.433204	−	0.499944i	0.496610	−	0.867974i	$-0.334578\pi$
$941$	−1.17670e7	−	1.35799e7i	−0.433204	−	0.499944i	−0.929814	+	0.368030i	$0.880032\pi$
$942$		0			0
$943$	−1.30808e7	−	3.83953e7i	−0.479022	−	1.40604i
$944$		0			0
$945$	2.86578e7	+	3.30728e7i	1.04391	+	1.20474i
$946$		0			0
$947$	−4.70936e6	+	3.27543e7i	−0.170642	+	1.18684i	0.706889	+	0.707325i	$0.250098\pi$
$947$	−4.70936e6	+	3.27543e7i	−0.170642	+	1.18684i	−0.877531	+	0.479519i	$0.840811\pi$
$948$		0			0
$949$	−9.49085e6	−	6.60103e7i	−0.342089	−	2.37928i
$950$		0			0
$951$	3.93116e6	−	2.52640e6i	0.140951	−	0.0905839i
$952$		0			0
$953$	2.39056e7	−	7.01931e6i	0.852642	−	0.250358i	0.173926	−	0.984759i	$-0.444355\pi$
$953$	2.39056e7	−	7.01931e6i	0.852642	−	0.250358i	0.678716	+	0.734400i	$0.262537\pi$
$954$		0			0
$955$	4.48130e7	−	5.17170e7i	1.59000	−	1.83495i
$956$		0			0
$957$	2.67672e6	+	5.86120e6i	0.0944763	+	0.206874i
$958$		0			0
$959$	−1.87594e7	−	5.50825e6i	−0.658676	−	0.193405i
$960$		0			0
$961$	−1.03422e7	+	2.26462e7i	−0.361246	+	0.791018i
$962$		0			0
$963$	2.48610e7	+	1.59772e7i	0.863879	+	0.555182i
$964$		0			0
$965$	−4.50024e7			−1.55567
$966$		0			0
$967$	3.88647e7			1.33656			0.668282	−	0.743908i	$-0.267030\pi$
$967$	3.88647e7			1.33656			0.668282	+	0.743908i	$0.267030\pi$
$968$		0			0
$969$	7.76295e6	+	4.98894e6i	0.265593	+	0.170687i
$970$		0			0
$971$	−1.82452e7	+	3.99515e7i	−0.621014	+	1.35983i	0.293766	+	0.955877i	$0.405091\pi$
$971$	−1.82452e7	+	3.99515e7i	−0.621014	+	1.35983i	−0.914780	+	0.403953i	$0.867636\pi$
$972$		0			0
$973$	−3.83102e7	−	1.12489e7i	−1.29728	−	0.380915i
$974$		0			0
$975$	2.02786e7	+	4.44039e7i	0.683165	+	1.49592i
$976$		0			0
$977$	−1.78652e7	+	2.06175e7i	−0.598785	+	0.691035i	−0.971535	−	0.236897i	$-0.923870\pi$
$977$	−1.78652e7	+	2.06175e7i	−0.598785	+	0.691035i	0.372749	+	0.927932i	$0.378415\pi$
$978$		0			0
$979$	1.54231e7	−	4.52863e6i	0.514298	−	0.151011i
$980$		0			0
$981$	−1.64681e7	+	1.05834e7i	−0.546349	+	0.351117i
$982$		0			0
$983$	−6.67089e6	−	4.63971e7i	−0.220191	−	1.53146i	−0.737313	−	0.675551i	$-0.763906\pi$
$983$	−6.67089e6	−	4.63971e7i	−0.220191	−	1.53146i	0.517122	−	0.855912i	$-0.327003\pi$
$984$		0			0
$985$	8.44292e6	−	5.87218e7i	0.277270	−	1.92845i
$986$		0			0
$987$	−1.73343e7	−	2.00049e7i	−0.566387	−	0.653646i
$988$		0			0
$989$	−3.16126e7	+	5.93415e6i	−1.02771	+	0.192916i
$990$		0			0
$991$	1.38894e7	+	1.60292e7i	0.449261	+	0.518475i	0.934527	−	0.355892i	$-0.115823\pi$
$991$	1.38894e7	+	1.60292e7i	0.449261	+	0.518475i	−0.485266	+	0.874366i	$0.661277\pi$
$992$		0			0
$993$	−2.80455e6	+	1.95061e7i	−0.0902589	+	0.627765i
$994$		0			0
$995$	−3.12753e6	−	2.17525e7i	−0.100148	−	0.696548i
$996$		0			0
$997$	7.57856e6	−	4.87044e6i	0.241462	−	0.155178i	−0.414313	−	0.910134i	$-0.635978\pi$
$997$	7.57856e6	−	4.87044e6i	0.241462	−	0.155178i	0.655775	+	0.754956i	$0.272342\pi$
$998$		0			0
$999$	2.71592e7	−	7.97465e6i	0.860999	−	0.252812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.6.e.a.13.7	✓	100
23.16	even	11	inner	92.6.e.a.85.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.6.e.a.13.7	✓	100	1.1	even	1	trivial
92.6.e.a.85.7	yes	100	23.16	even	11	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(8.41459 + 5.40773i) q^{3} +(36.4994 - 79.9225i) q^{5} +(-123.792 - 36.3487i) q^{7} +(-59.3840 - 130.033i) q^{9} +(-98.0288 + 113.131i) q^{11} +(-1019.12 + 299.240i) q^{13} +(739.326 - 475.136i) q^{15} +(-111.465 - 775.255i) q^{17} +(-167.632 + 1165.90i) q^{19} +(-845.098 - 975.295i) q^{21} +(1844.57 - 1741.81i) q^{23} +(-3008.96 - 3472.52i) q^{25} +(549.400 - 3821.16i) q^{27} +(-612.434 - 4259.58i) q^{29} +(-1625.42 + 1044.60i) q^{31} +(-1436.66 + 421.840i) q^{33} +(-7423.42 + 8567.08i) q^{35} +(3045.92 + 6669.63i) q^{37} +(-10193.7 - 2993.13i) q^{39} +(6641.80 - 14543.5i) q^{41} +(-10665.7 - 6854.40i) q^{43} -12560.0 q^{45} +20511.6 q^{47} +(-135.641 - 87.1712i) q^{49} +(3254.44 - 7126.23i) q^{51} +(15531.6 + 4560.49i) q^{53} +(5463.74 + 11963.9i) q^{55} +(-7715.45 + 8904.10i) q^{57} +(28387.3 - 8335.26i) q^{59} +(13570.4 - 8721.16i) q^{61} +(2624.76 + 18255.6i) q^{63} +(-13281.1 + 92372.4i) q^{65} +(-8306.54 - 9586.26i) q^{67} +(24940.5 - 4681.70i) q^{69} +(31765.8 + 36659.6i) q^{71} +(-8935.58 + 62148.3i) q^{73} +(-6540.69 - 45491.5i) q^{75} +(16247.4 - 10441.6i) q^{77} +(2693.96 - 791.017i) q^{79} +(2538.83 - 2929.96i) q^{81} +(-10240.8 - 22424.3i) q^{83} +(-66028.7 - 19387.8i) q^{85} +(17881.3 - 39154.5i) q^{87} +(-90334.1 - 58054.2i) q^{89} +137036. q^{91} -19326.2 q^{93} +(87063.5 + 55952.3i) q^{95} +(-54135.6 + 118540. i) q^{97} +(20532.1 + 6028.78i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{3} - 86 q^{5} - 118 q^{7} - 368 q^{9} - 242 q^{11} + 322 q^{13} - 3717 q^{15} + 2953 q^{17} - 259 q^{19} - 12349 q^{21} - 6038 q^{23} - 1324 q^{25} + 23933 q^{27} + 12677 q^{29} - 4401 q^{31}+ \cdots + 26799 q^{99}+O(q^{100}) \) 100 * q + 2 * q^3 - 86 * q^5 - 118 * q^7 - 368 * q^9 - 242 * q^11 + 322 * q^13 - 3717 * q^15 + 2953 * q^17 - 259 * q^19 - 12349 * q^21 - 6038 * q^23 - 1324 * q^25 + 23933 * q^27 + 12677 * q^29 - 4401 * q^31 - 43115 * q^33 + 10774 * q^35 - 72670 * q^37 - 61242 * q^39 - 30296 * q^41 + 69436 * q^43 + 125954 * q^45 + 79010 * q^47 + 27788 * q^49 - 65954 * q^51 - 60934 * q^53 - 234558 * q^55 + 37333 * q^57 + 392206 * q^59 + 153404 * q^61 + 7889 * q^63 - 178529 * q^65 - 52012 * q^67 - 280729 * q^69 - 166585 * q^71 + 42932 * q^73 + 484227 * q^75 + 434675 * q^77 + 150490 * q^79 - 132170 * q^81 - 236441 * q^83 - 399844 * q^85 + 121816 * q^87 + 151010 * q^89 + 240938 * q^91 - 54450 * q^93 - 281447 * q^95 - 76051 * q^97 + 26799 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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