LMFDB - Embedded newform 115.7.c.c.114.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.c (of order $2$, degree $1$, 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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.10
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.4471i q^{2} +3.70784i q^{3} -144.720 q^{4} +(95.5216 + 80.6265i) q^{5} -53.5677 q^{6} +454.114 q^{7} -1166.17i q^{8} +715.252 q^{9} +O(q^{10})$	\(q+14.4471i q^{2} +3.70784i q^{3} -144.720 q^{4} +(95.5216 + 80.6265i) q^{5} -53.5677 q^{6} +454.114 q^{7} -1166.17i q^{8} +715.252 q^{9} +(-1164.82 + 1380.01i) q^{10} +1344.78i q^{11} -536.598i q^{12} +3188.96i q^{13} +6560.65i q^{14} +(-298.950 + 354.179i) q^{15} +7585.76 q^{16} +2309.58 q^{17} +10333.3i q^{18} -2898.81i q^{19} +(-13823.9 - 11668.3i) q^{20} +1683.78i q^{21} -19428.3 q^{22} +(5950.46 - 10612.6i) q^{23} +4323.97 q^{24} +(2623.74 + 15403.1i) q^{25} -46071.4 q^{26} +5355.05i q^{27} -65719.3 q^{28} +40194.1 q^{29} +(-5116.87 - 4318.97i) q^{30} +5774.59 q^{31} +34957.6i q^{32} -4986.24 q^{33} +33366.9i q^{34} +(43377.7 + 36613.6i) q^{35} -103511. q^{36} -100068. q^{37} +41879.5 q^{38} -11824.2 q^{39} +(94024.2 - 111394. i) q^{40} -65360.8 q^{41} -24325.8 q^{42} +87522.8 q^{43} -194617. i q^{44} +(68322.0 + 57668.2i) q^{45} +(153322. + 85967.1i) q^{46} -167340. i q^{47} +28126.8i q^{48} +88570.6 q^{49} +(-222531. + 37905.5i) q^{50} +8563.56i q^{51} -461506. i q^{52} -83815.9 q^{53} -77365.2 q^{54} +(-108425. + 128456. i) q^{55} -529575. i q^{56} +10748.3 q^{57} +580689. i q^{58} -33392.8 q^{59} +(43264.0 - 51256.7i) q^{60} -229407. i q^{61} +83426.3i q^{62} +324806. q^{63} -19548.9 q^{64} +(-257115. + 304615. i) q^{65} -72036.9i q^{66} -441802. q^{67} -334242. q^{68} +(39349.9 + 22063.4i) q^{69} +(-528962. + 626684. i) q^{70} +73472.2 q^{71} -834106. i q^{72} -242444. i q^{73} -1.44570e6i q^{74} +(-57112.4 + 9728.41i) q^{75} +419515. i q^{76} +610685. i q^{77} -170825. i q^{78} +547549. i q^{79} +(724604. + 611613. i) q^{80} +501563. q^{81} -944277. i q^{82} -640953. q^{83} -243677. i q^{84} +(220615. + 186213. i) q^{85} +1.26445e6i q^{86} +149033. i q^{87} +1.56825e6 q^{88} +504452. i q^{89} +(-833141. + 987057. i) q^{90} +1.44815e6i q^{91} +(-861150. + 1.53586e6i) q^{92} +21411.3i q^{93} +2.41758e6 q^{94} +(233721. - 276899. i) q^{95} -129617. q^{96} -100060. q^{97} +1.27959e6i q^{98} +961859. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$			14.4471i			1.80589i	0.429754	+	0.902946i	$0.358600\pi$
$2$			14.4471i			1.80589i	−0.429754	+	0.902946i	$0.641400\pi$
$3$			3.70784i			0.137327i	0.997640	+	0.0686637i	$0.0218735\pi$
$3$			3.70784i			0.137327i	−0.997640	+	0.0686637i	$0.978126\pi$
$4$	−144.720			−2.26125
$5$	95.5216	+	80.6265i	0.764173	+	0.645012i
$5$	95.5216	+	80.6265i	0.764173	+	0.645012i
$6$	−53.5677			−0.247998
$7$	454.114			1.32395			0.661974	−	0.749527i	$-0.269719\pi$
$7$	454.114			1.32395			0.661974	+	0.749527i	$0.269719\pi$
$8$		−	1166.17i		−	2.27768i
$9$	715.252			0.981141
$10$	−1164.82	+	1380.01i	−1.16482	+	1.38001i
$11$			1344.78i			1.01036i	0.863015	+	0.505178i	$0.168573\pi$
$11$			1344.78i			1.01036i	−0.863015	+	0.505178i	$0.831427\pi$
$12$		−	536.598i		−	0.310531i
$13$			3188.96i			1.45151i	0.687954	+	0.725754i	$0.258509\pi$
$13$			3188.96i			1.45151i	−0.687954	+	0.725754i	$0.741491\pi$
$14$			6560.65i			2.39091i
$15$	−298.950	+	354.179i	−0.0885778	+	0.104942i
$16$	7585.76			1.85199
$17$	2309.58			0.470096			0.235048	−	0.971984i	$-0.424475\pi$
$17$	2309.58			0.470096			0.235048	+	0.971984i	$0.424475\pi$
$18$			10333.3i			1.77184i
$19$		−	2898.81i		−	0.422629i	−0.977418	−	0.211314i	$-0.932226\pi$
$19$		−	2898.81i		−	0.422629i	0.977418	−	0.211314i	$-0.0677743\pi$
$20$	−13823.9	−	11668.3i	−1.72798	−	1.45853i
$21$			1683.78i			0.181814i
$22$	−19428.3			−1.82459
$23$	5950.46	−	10612.6i	0.489066	−	0.872247i
$23$	5950.46	−	10612.6i	0.489066	−	0.872247i
$24$	4323.97			0.312787
$25$	2623.74	+	15403.1i	0.167919	+	0.985801i
$26$	−46071.4			−2.62127
$27$			5355.05i			0.272065i
$28$	−65719.3			−2.99377
$29$	40194.1			1.64804			0.824020	−	0.566561i	$-0.191726\pi$
$29$	40194.1			1.64804			0.824020	+	0.566561i	$0.191726\pi$
$30$	−5116.87	−	4318.97i	−0.189514	−	0.159962i
$31$	5774.59			0.193837			0.0969184	−	0.995292i	$-0.469101\pi$
$31$	5774.59			0.193837			0.0969184	+	0.995292i	$0.469101\pi$
$32$			34957.6i			1.06682i
$33$	−4986.24			−0.138749
$34$			33366.9i			0.848943i
$35$	43377.7	+	36613.6i	1.01172	+	0.853962i
$36$	−103511.			−2.21860
$37$	−100068.			−1.97556			−0.987781	−	0.155849i	$-0.950189\pi$
$37$	−100068.			−1.97556			−0.987781	+	0.155849i	$0.950189\pi$
$38$	41879.5			0.763222
$39$	−11824.2			−0.199332
$40$	94024.2	−	111394.i	1.46913	−	1.74054i
$41$	−65360.8			−0.948344			−0.474172	−	0.880432i	$-0.657253\pi$
$41$	−65360.8			−0.948344			−0.474172	+	0.880432i	$0.657253\pi$
$42$	−24325.8			−0.328337
$43$	87522.8			1.10082			0.550409	−	0.834895i	$-0.314472\pi$
$43$	87522.8			1.10082			0.550409	+	0.834895i	$0.314472\pi$
$44$		−	194617.i		−	2.28466i
$45$	68322.0	+	57668.2i	0.749761	+	0.632848i
$46$	153322.	+	85967.1i	1.57518	+	0.883200i
$47$		−	167340.i		−	1.61178i	−0.592064	−	0.805891i	$-0.701687\pi$
$47$		−	167340.i		−	1.61178i	0.592064	−	0.805891i	$-0.298313\pi$
$48$			28126.8i			0.254329i
$49$	88570.6			0.752838
$50$	−222531.	+	37905.5i	−1.78025	+	0.303244i
$51$			8563.56i			0.0645571i
$52$		−	461506.i		−	3.28222i
$53$	−83815.9			−0.562988			−0.281494	−	0.959563i	$-0.590830\pi$
$53$	−83815.9			−0.562988			−0.281494	+	0.959563i	$0.590830\pi$
$54$	−77365.2			−0.491320
$55$	−108425.	+	128456.i	−0.651691	+	0.772086i
$56$		−	529575.i		−	3.01553i
$57$	10748.3			0.0580385
$58$			580689.i			2.97618i
$59$	−33392.8			−0.162591			−0.0812956	−	0.996690i	$-0.525906\pi$
$59$	−33392.8			−0.162591			−0.0812956	+	0.996690i	$0.525906\pi$
$60$	43264.0	−	51256.7i	0.200296	−	0.237299i
$61$		−	229407.i		−	1.01069i	−0.862918	−	0.505345i	$-0.831365\pi$
$61$		−	229407.i		−	1.01069i	0.862918	−	0.505345i	$-0.168635\pi$
$62$			83426.3i			0.350048i
$63$	324806.			1.29898
$64$	−19548.9			−0.0745730
$65$	−257115.	+	304615.i	−0.936240	+	1.10920i
$66$		−	72036.9i		−	0.250567i
$67$	−441802.			−1.46894			−0.734469	−	0.678642i	$-0.762569\pi$
$67$	−441802.			−1.46894			−0.734469	+	0.678642i	$0.762569\pi$
$68$	−334242.			−1.06300
$69$	39349.9	+	22063.4i	0.119783	+	0.0671621i
$70$	−528962.	+	626684.i	−1.54216	+	1.82707i
$71$	73472.2			0.205281			0.102640	−	0.994719i	$-0.467271\pi$
$71$	73472.2			0.205281			0.102640	+	0.994719i	$0.467271\pi$
$72$		−	834106.i		−	2.23472i
$73$		−	242444.i		−	0.623223i	−0.950210	−	0.311612i	$-0.899131\pi$
$73$		−	242444.i		−	0.623223i	0.950210	−	0.311612i	$-0.100869\pi$
$74$		−	1.44570e6i		−	3.56765i
$75$	−57112.4	+	9728.41i	−0.135377	+	0.0230599i
$76$			419515.i			0.955668i
$77$			610685.i			1.33766i
$78$		−	170825.i		−	0.359972i
$79$			547549.i			1.11056i	0.831663	+	0.555280i	$0.187389\pi$
$79$			547549.i			1.11056i	−0.831663	+	0.555280i	$0.812611\pi$
$80$	724604.	+	611613.i	1.41524	+	1.19456i
$81$	501563.			0.943779
$82$		−	944277.i		−	1.71261i
$83$	−640953.			−1.12096			−0.560482	−	0.828167i	$-0.689384\pi$
$83$	−640953.			−1.12096			−0.560482	+	0.828167i	$0.689384\pi$
$84$		−	243677.i		−	0.411127i
$85$	220615.	+	186213.i	0.359235	+	0.303218i
$86$			1.26445e6i			1.98796i
$87$			149033.i			0.226321i
$88$	1.56825e6			2.30126
$89$			504452.i			0.715566i	0.933805	+	0.357783i	$0.116467\pi$
$89$			504452.i			0.715566i	−0.933805	+	0.357783i	$0.883533\pi$
$90$	−833141.	+	987057.i	−1.14285	+	1.35399i
$91$			1.44815e6i			1.92172i
$92$	−861150.	+	1.53586e6i	−1.10590	+	1.97237i
$93$			21411.3i			0.0266191i
$94$	2.41758e6			2.91070
$95$	233721.	−	276899.i	0.272600	−	0.322961i
$96$	−129617.			−0.146504
$97$	−100060.			−0.109634			−0.0548168	−	0.998496i	$-0.517457\pi$
$97$	−100060.			−0.109634			−0.0548168	+	0.998496i	$0.517457\pi$
$98$			1.27959e6i			1.35954i
$99$			961859.i			0.991301i
$100$	−379707.	−	2.22914e6i	−0.379707	−	2.22914i
$101$	−511425.			−0.496384			−0.248192	−	0.968711i	$-0.579836\pi$
$101$	−511425.			−0.496384			−0.248192	+	0.968711i	$0.579836\pi$
$102$	−123719.			−0.116583
$103$	866738.			0.793188			0.396594	−	0.917994i	$-0.370192\pi$
$103$	866738.			0.793188			0.396594	+	0.917994i	$0.370192\pi$
$104$	3.71887e6			3.30607
$105$	−135757.	+	160838.i	−0.117272	+	0.138937i
$106$		−	1.21090e6i		−	1.01670i
$107$	−809076.			−0.660447			−0.330223	−	0.943903i	$-0.607124\pi$
$107$	−809076.			−0.660447			−0.330223	+	0.943903i	$0.607124\pi$
$108$		−	774983.i		−	0.615206i
$109$		−	1.57882e6i		−	1.21914i	−0.792733	−	0.609569i	$-0.791342\pi$
$109$		−	1.57882e6i		−	1.21914i	0.792733	−	0.609569i	$-0.208658\pi$
$110$	−1.85582e6	−	1.56643e6i	−1.39430	−	1.17688i
$111$		−	371037.i		−	0.271299i
$112$	3.44480e6			2.45194
$113$	−1.32022e6			−0.914982			−0.457491	−	0.889214i	$-0.651252\pi$
$113$	−1.32022e6			−0.914982			−0.457491	+	0.889214i	$0.651252\pi$
$114$			155282.i			0.104811i
$115$	1.42406e6	−	533970.i	0.936340	−	0.351094i
$116$	−5.81688e6			−3.72663
$117$			2.28091e6i			1.42413i
$118$		−	482431.i		−	0.293622i
$119$	1.04881e6			0.622383
$120$	413033.	+	348627.i	0.239024	+	0.201752i
$121$	−36880.9			−0.0208183
$122$	3.31428e6			1.82520
$123$		−	242347.i		−	0.130234i
$124$	−835698.			−0.438313
$125$	−991277.	+	1.68287e6i	−0.507534	+	0.861632i
$126$			4.69252e6i			2.34582i
$127$		−	2.80478e6i		−	1.36926i	−0.728889	−	0.684632i	$-0.759963\pi$
$127$		−	2.80478e6i		−	1.36926i	0.728889	−	0.684632i	$-0.240037\pi$
$128$			1.95486e6i			0.932151i
$129$			324521.i			0.151173i
$130$	−4.40081e6	−	3.71457e6i	−2.00310	−	1.69075i
$131$	−490972.			−0.218395			−0.109198	−	0.994020i	$-0.534828\pi$
$131$	−490972.			−0.218395			−0.109198	+	0.994020i	$0.534828\pi$
$132$	721608.			0.313747
$133$		−	1.31639e6i		−	0.559538i
$134$		−	6.38278e6i		−	2.65274i
$135$	−431759.	+	511523.i	−0.175485	+	0.207905i
$136$		−	2.69337e6i		−	1.07073i
$137$	1.65858e6			0.645022			0.322511	−	0.946566i	$-0.395473\pi$
$137$	1.65858e6			0.645022			0.322511	+	0.946566i	$0.395473\pi$
$138$	−318752.	+	568494.i	−0.121288	+	0.216316i
$139$	4.55698e6			1.69681			0.848405	−	0.529348i	$-0.177563\pi$
$139$	4.55698e6			1.69681			0.848405	+	0.529348i	$0.177563\pi$
$140$	−6.27761e6	−	5.29872e6i	−2.28776	−	1.93102i
$141$	620470.			0.221342
$142$			1.06146e6i			0.370715i
$143$	−4.28846e6			−1.46654
$144$	5.42573e6			1.81707
$145$	3.83940e6	+	3.24071e6i	1.25939	+	1.06301i
$146$	3.50263e6			1.12547
$147$			328406.i			0.103385i
$148$	1.44818e7			4.46723
$149$			3.48875e6i			1.05466i	0.849662	+	0.527328i	$0.176806\pi$
$149$			3.48875e6i			1.05466i	−0.849662	+	0.527328i	$0.823194\pi$
$150$	−140548.	−	825110.i	−0.0416437	−	0.244477i
$151$	−914162.			−0.265517			−0.132759	−	0.991148i	$-0.542383\pi$
$151$	−914162.			−0.265517			−0.132759	+	0.991148i	$0.542383\pi$
$152$	−3.38051e6			−0.962611
$153$	1.65193e6			0.461231
$154$	−8.82265e6			−2.41567
$155$	551598.	+	465585.i	0.148125	+	0.125027i
$156$	1.71119e6			0.450738
$157$	5.72267e6			1.47877			0.739383	−	0.673285i	$-0.235117\pi$
$157$	5.72267e6			1.47877			0.739383	+	0.673285i	$0.235117\pi$
$158$	−7.91052e6			−2.00555
$159$		−	310776.i		−	0.0773136i
$160$	−2.81851e6	+	3.33921e6i	−0.688113	+	0.815236i
$161$	2.70219e6	−	4.81934e6i	0.647497	−	1.15481i
$162$			7.24615e6i			1.70436i
$163$			27407.0i			0.00632847i	0.999995	+	0.00316423i	$0.00100721\pi$
$163$			27407.0i			0.00632847i	−0.999995	+	0.00316423i	$0.998993\pi$
$164$	9.45901e6			2.14444
$165$	−476294.	−	402023.i	−0.106029	−	0.0894951i
$166$		−	9.25993e6i		−	2.02434i
$167$			243555.i			0.0522936i	0.999658	+	0.0261468i	$0.00832373\pi$
$167$			243555.i			0.0522936i	−0.999658	+	0.0261468i	$0.991676\pi$
$168$	1.96358e6			0.414114
$169$	−5.34267e6			−1.10688
$170$	−2.69025e6	+	3.18725e6i	−0.547578	+	0.648739i
$171$		−	2.07338e6i		−	0.414658i
$172$	−1.26663e7			−2.48922
$173$		−	496614.i		−	0.0959137i	−0.998849	−	0.0479569i	$-0.984729\pi$
$173$		−	496614.i		−	0.0959137i	0.998849	−	0.0479569i	$-0.0152710\pi$
$174$	−2.15310e6			−0.408712
$175$	1.19148e6	+	6.99478e6i	0.222316	+	1.30515i
$176$			1.02012e7i			1.87117i
$177$		−	123815.i		−	0.0223282i
$178$	−7.28789e6			−1.29224
$179$	6.20825e6			1.08246			0.541228	−	0.840876i	$-0.317960\pi$
$179$	6.20825e6			1.08246			0.541228	+	0.840876i	$0.317960\pi$
$180$	−9.88755e6	−	8.34574e6i	−1.69540	−	1.43103i
$181$			5.95741e6i			1.00467i	0.864674	+	0.502333i	$0.167525\pi$
$181$			5.95741e6i			1.00467i	−0.864674	+	0.502333i	$0.832475\pi$
$182$	−2.09217e7			−3.47042
$183$	850605.			0.138795
$184$	−1.23761e7	−	6.93925e6i	−1.98670	−	1.11393i
$185$	−9.55867e6	−	8.06814e6i	−1.50967	−	1.27426i
$186$	−309331.			−0.0480712
$187$			3.10589e6i			0.474964i
$188$			2.42174e7i			3.64464i
$189$			2.43181e6i			0.360200i
$190$	4.00040e6	+	3.37660e6i	0.583233	+	0.492287i
$191$		−	1.83210e6i		−	0.262936i	−0.991320	−	0.131468i	$-0.958031\pi$
$191$		−	1.83210e6i		−	0.262936i	0.991320	−	0.131468i	$-0.0419690\pi$
$192$		−	72484.1i		−	0.0102409i
$193$			5.97069e6i			0.830524i	0.909702	+	0.415262i	$0.136310\pi$
$193$			5.97069e6i			0.830524i	−0.909702	+	0.415262i	$0.863690\pi$
$194$		−	1.44558e6i		−	0.197987i
$195$	−1.12946e6	−	953341.i	−0.152324	−	0.128571i
$196$	−1.28179e7			−1.70235
$197$		−	1.28195e7i		−	1.67677i	−0.545077	−	0.838386i	$-0.683500\pi$
$197$		−	1.28195e7i		−	1.67677i	0.545077	−	0.838386i	$-0.316500\pi$
$198$	−1.38961e7			−1.79018
$199$		−	1.04999e7i		−	1.33237i	−0.745787	−	0.666184i	$-0.767926\pi$
$199$		−	1.04999e7i		−	1.33237i	0.745787	−	0.666184i	$-0.232074\pi$
$200$	1.79627e7	−	3.05973e6i	2.24534	−	0.382466i
$201$		−	1.63813e6i		−	0.201725i
$202$		−	7.38863e6i		−	0.896417i
$203$	1.82527e7			2.18192
$204$		−	1.23932e6i		−	0.145980i
$205$	−6.24337e6	−	5.26981e6i	−0.724698	−	0.611693i
$206$			1.25219e7i			1.43241i
$207$	4.25608e6	−	7.59070e6i	0.479842	−	0.855797i
$208$			2.41907e7i			2.68818i
$209$	3.89827e6			0.427005
$210$	−2.32364e6	−	1.96131e6i	−0.250906	−	0.211781i
$211$	−1.45098e6			−0.154459			−0.0772295	−	0.997013i	$-0.524607\pi$
$211$	−1.45098e6			−0.154459			−0.0772295	+	0.997013i	$0.524607\pi$
$212$	1.21298e7			1.27305
$213$			272423.i			0.0281907i
$214$		−	1.16888e7i		−	1.19270i
$215$	8.36032e6	+	7.05666e6i	0.841216	+	0.710041i
$216$	6.24491e6			0.619676
$217$	2.62232e6			0.256630
$218$	2.28094e7			2.20163
$219$	898945.			0.0855856
$220$	1.56913e7	−	1.85901e7i	1.47364	−	1.74588i
$221$			7.36517e6i			0.682348i
$222$	5.36042e6			0.489936
$223$		−	9.39033e6i		−	0.846771i	−0.905950	−	0.423386i	$-0.860842\pi$
$223$		−	9.39033e6i		−	0.846771i	0.905950	−	0.423386i	$-0.139158\pi$
$224$			1.58747e7i			1.41242i
$225$	1.87664e6	+	1.10171e7i	0.164753	+	0.967210i
$226$		−	1.90735e7i		−	1.65236i
$227$	2.01506e6			0.172270			0.0861350	−	0.996283i	$-0.472548\pi$
$227$	2.01506e6			0.172270			0.0861350	+	0.996283i	$0.472548\pi$
$228$	−1.55549e6			−0.131239
$229$			1.84118e7i			1.53317i	0.642142	+	0.766586i	$0.278046\pi$
$229$			1.84118e7i			1.53317i	−0.642142	+	0.766586i	$0.721954\pi$
$230$	7.71434e6	+	2.05735e7i	0.634038	+	1.69093i
$231$	−2.26432e6			−0.183697
$232$		−	4.68731e7i		−	3.75370i
$233$		−	1.63387e7i		−	1.29167i	−0.763478	−	0.645833i	$-0.776510\pi$
$233$		−	1.63387e7i		−	1.29167i	0.763478	−	0.645833i	$-0.223490\pi$
$234$	−3.29526e7			−2.57183
$235$	1.34920e7	−	1.59846e7i	1.03962	−	1.23168i
$236$	4.83260e6			0.367659
$237$	−2.03023e6			−0.152510
$238$			1.51524e7i			1.12396i
$239$	−4.95176e6			−0.362715			−0.181358	−	0.983417i	$-0.558049\pi$
$239$	−4.95176e6			−0.362715			−0.181358	+	0.983417i	$0.558049\pi$
$240$	−2.26776e6	+	2.68671e6i	−0.164045	+	0.194351i
$241$		−	2.54349e7i		−	1.81710i	−0.417777	−	0.908550i	$-0.637191\pi$
$241$		−	2.54349e7i		−	1.81710i	0.417777	−	0.908550i	$-0.362809\pi$
$242$		−	532823.i		−	0.0375956i
$243$			5.76355e6i			0.401672i
$244$			3.31998e7i			2.28542i
$245$	8.46040e6	+	7.14114e6i	0.575298	+	0.485589i
$246$	3.50123e6			0.235188
$247$	9.24419e6			0.613449
$248$		−	6.73416e6i		−	0.441498i
$249$		−	2.37655e6i		−	0.153939i
$250$	−2.43127e7	−	1.43211e7i	−1.55601	−	0.916551i
$251$			2.34408e7i			1.48235i	0.671309	+	0.741177i	$0.265732\pi$
$251$			2.34408e7i			1.48235i	−0.671309	+	0.741177i	$0.734268\pi$
$252$	−4.70059e7			−2.93731
$253$	1.42717e7	+	8.00208e6i	0.881280	+	0.494130i
$254$	4.05210e7			2.47274
$255$	−690450.	+	818005.i	−0.0416401	+	0.0493327i
$256$	−2.94933e7			−1.75794
$257$		−	9.81416e6i		−	0.578168i	−0.957304	−	0.289084i	$-0.906649\pi$
$257$		−	9.81416e6i		−	0.578168i	0.957304	−	0.289084i	$-0.0933506\pi$
$258$	−4.68839e6			−0.273001
$259$	−4.54424e7			−2.61554
$260$	3.72096e7	−	4.40838e7i	2.11707	−	2.50818i
$261$	2.87489e7			1.61696
$262$		−	7.09314e6i		−	0.394398i
$263$	1.56511e7			0.860357			0.430178	−	0.902744i	$-0.358451\pi$
$263$	1.56511e7			0.860357			0.430178	+	0.902744i	$0.358451\pi$
$264$			5.81481e6i			0.316027i
$265$	−8.00623e6	−	6.75778e6i	−0.430220	−	0.363134i
$266$	1.90181e7			1.01047
$267$	−1.87043e6			−0.0982668
$268$	6.39375e7			3.32163
$269$	−2.42990e7			−1.24834			−0.624169	−	0.781289i	$-0.714562\pi$
$269$	−2.42990e7			−1.24834			−0.624169	+	0.781289i	$0.714562\pi$
$270$	−7.39005e6	−	6.23769e6i	−0.375453	−	0.316907i
$271$	1.90357e7			0.956449			0.478224	−	0.878238i	$-0.341281\pi$
$271$	1.90357e7			0.956449			0.478224	+	0.878238i	$0.341281\pi$
$272$	1.75199e7			0.870614
$273$	−5.36952e6			−0.263905
$274$			2.39617e7i			1.16484i
$275$	−2.07139e7	+	3.52836e6i	−0.996009	+	0.169658i
$276$	−5.69471e6	−	3.19301e6i	−0.270860	−	0.151870i
$277$			1.57122e6i			0.0739263i	0.999317	+	0.0369632i	$0.0117684\pi$
$277$			1.57122e6i			0.0739263i	−0.999317	+	0.0369632i	$0.988232\pi$
$278$			6.58354e7i			3.06426i
$279$	4.13029e6			0.190181
$280$	4.26977e7	−	5.05858e7i	1.94505	−	2.30438i
$281$		−	1.42810e7i		−	0.643637i	−0.946801	−	0.321819i	$-0.895706\pi$
$281$		−	1.42810e7i		−	0.643637i	0.946801	−	0.321819i	$-0.104294\pi$
$282$			8.96402e6i			0.399719i
$283$	8.38454e6			0.369930			0.184965	−	0.982745i	$-0.440783\pi$
$283$	8.38454e6			0.369930			0.184965	+	0.982745i	$0.440783\pi$
$284$	−1.06329e7			−0.464190
$285$	1.02670e6	+	866599.i	0.0443514	+	0.0374355i
$286$		−	6.19560e7i		−	2.64841i
$287$	−2.96813e7			−1.25556
$288$			2.50035e7i			1.04670i
$289$	−1.88034e7			−0.779010
$290$	−4.68189e7	+	5.54683e7i	−1.91967	+	2.27432i
$291$		−	371005.i		−	0.0150557i
$292$			3.50865e7i			1.40926i
$293$	−2.43170e7			−0.966733			−0.483367	−	0.875418i	$-0.660586\pi$
$293$	−2.43170e7			−0.966733			−0.483367	+	0.875418i	$0.660586\pi$
$294$	−4.74452e6			−0.186703
$295$	−3.18973e6	−	2.69234e6i	−0.124248	−	0.104873i
$296$			1.16697e8i			4.49969i
$297$	−7.20139e6			−0.274882
$298$	−5.04024e7			−1.90460
$299$	3.38433e7	+	1.89758e7i	1.26607	+	0.709883i
$300$	8.26529e6	−	1.40789e6i	0.306122	−	0.0521442i
$301$	3.97453e7			1.45743
$302$		−	1.32070e7i		−	0.479495i
$303$		−	1.89628e6i		−	0.0681672i
$304$		−	2.19897e7i		−	0.782705i
$305$	1.84963e7	−	2.19133e7i	0.651907	−	0.772341i
$306$			2.38657e7i			0.832933i
$307$		−	1.78458e6i		−	0.0616765i	−0.999524	−	0.0308383i	$-0.990182\pi$
$307$		−	1.78458e6i		−	0.0616765i	0.999524	−	0.0308383i	$-0.00981768\pi$
$308$		−	8.83782e7i		−	3.02478i
$309$			3.21373e6i			0.108926i
$310$	−6.72637e6	+	7.96901e6i	−0.225785	+	0.267497i
$311$	2.38789e7			0.793839			0.396920	−	0.917853i	$-0.370079\pi$
$311$	2.38789e7			0.793839			0.396920	+	0.917853i	$0.370079\pi$
$312$			1.37890e7i			0.454013i
$313$	1.08463e7			0.353711			0.176856	−	0.984237i	$-0.443407\pi$
$313$	1.08463e7			0.353711			0.176856	+	0.984237i	$0.443407\pi$
$314$			8.26762e7i			2.67049i
$315$	3.10260e7	+	2.61880e7i	0.992645	+	0.837857i
$316$		−	7.92413e7i		−	2.51125i
$317$			2.02018e7i			0.634178i	0.948396	+	0.317089i	$0.102705\pi$
$317$			2.02018e7i			0.634178i	−0.948396	+	0.317089i	$0.897295\pi$
$318$	4.48982e6			0.139620
$319$			5.40523e7i			1.66511i
$320$	−1.86734e6	−	1.57616e6i	−0.0569867	−	0.0481005i
$321$		−	2.99992e6i		−	0.0906974i
$322$	6.96257e7	+	3.90389e7i	2.08546	+	1.16931i
$323$		−	6.69504e6i		−	0.198676i
$324$	−7.25861e7			−2.13412
$325$	−4.91200e7	+	8.36701e6i	−1.43090	+	0.243736i
$326$	−395953.			−0.0114285
$327$	5.85401e6			0.167421
$328$			7.62219e7i			2.16002i
$329$		−	7.59915e7i		−	2.13391i
$330$	5.80808e6	−	6.88108e6i	0.161618	−	0.191476i
$331$	1.56904e7			0.432664			0.216332	−	0.976320i	$-0.430591\pi$
$331$	1.56904e7			0.432664			0.216332	+	0.976320i	$0.430591\pi$
$332$	9.27585e7			2.53478
$333$	−7.15739e7			−1.93831
$334$	−3.51868e6			−0.0944365
$335$	−4.22016e7	−	3.56210e7i	−1.12252	−	0.947483i
$336$			1.27728e7i			0.336719i
$337$	6.50165e6			0.169877			0.0849384	−	0.996386i	$-0.472931\pi$
$337$	6.50165e6			0.169877			0.0849384	+	0.996386i	$0.472931\pi$
$338$		−	7.71864e7i		−	1.99890i
$339$		−	4.89518e6i		−	0.125652i
$340$	−3.19274e7	−	2.69488e7i	−0.812318	−	0.685650i
$341$			7.76557e6i			0.195844i
$342$	2.99544e7			0.748828
$343$	−1.32049e7			−0.327230
$344$		−	1.02067e8i		−	2.50731i
$345$	1.97988e6	+	5.28017e6i	0.0482148	+	0.128585i
$346$	7.17465e6			0.173210
$347$			5.93954e7i			1.42156i	0.703416	+	0.710779i	$0.251657\pi$
$347$			5.93954e7i			1.42156i	−0.703416	+	0.710779i	$0.748343\pi$
$348$		−	2.15680e7i		−	0.511768i
$349$	6.08567e6			0.143163			0.0715817	−	0.997435i	$-0.477195\pi$
$349$	6.08567e6			0.143163			0.0715817	+	0.997435i	$0.477195\pi$
$350$	−1.01055e8	+	1.72134e7i	−2.35696	+	0.401480i
$351$	−1.70771e7			−0.394904
$352$	−4.70104e7			−1.07787
$353$			4.52737e7i			1.02925i	0.857415	+	0.514626i	$0.172069\pi$
$353$			4.52737e7i			1.02925i	−0.857415	+	0.514626i	$0.827931\pi$
$354$	1.78878e6			0.0403224
$355$	7.01818e6	+	5.92381e6i	0.156870	+	0.132408i
$356$		−	7.30042e7i		−	1.61807i
$357$			3.88883e6i			0.0854702i
$358$			8.96915e7i			1.95480i
$359$			7.47898e7i			1.61644i	0.588881	+	0.808219i	$0.299568\pi$
$359$			7.47898e7i			1.61644i	−0.588881	+	0.808219i	$0.700432\pi$
$360$	6.72510e7	−	7.96751e7i	1.44142	−	1.70771i
$361$	3.86428e7			0.821385
$362$	−8.60676e7			−1.81432
$363$		−	136748.i		−	0.00285892i
$364$		−	2.09576e8i		−	4.34549i
$365$	1.95474e7	−	2.31587e7i	0.401986	−	0.476250i
$366$			1.22888e7i			0.250649i
$367$	−7.56972e7			−1.53137			−0.765687	−	0.643213i	$-0.777601\pi$
$367$	−7.56972e7			−1.53137			−0.765687	+	0.643213i	$0.777601\pi$
$368$	4.51388e7	−	8.05049e7i	0.905746	−	1.61539i
$369$	−4.67494e7			−0.930459
$370$	1.16562e8	−	1.38095e8i	2.30118	−	2.72630i
$371$	−3.80620e7			−0.745366
$372$		−	3.09863e6i		−	0.0601924i
$373$	1.58831e7			0.306062			0.153031	−	0.988221i	$-0.451097\pi$
$373$	1.58831e7			0.306062			0.153031	+	0.988221i	$0.451097\pi$
$374$	−4.48712e7			−0.857734
$375$	−6.23983e6	−	3.67550e6i	−0.118326	−	0.0696983i
$376$	−1.95147e8			−3.67112
$377$			1.28177e8i			2.39214i
$378$	−3.51326e7			−0.650482
$379$			2.29476e7i			0.421521i	0.977538	+	0.210760i	$0.0675940\pi$
$379$			2.29476e7i			0.421521i	−0.977538	+	0.210760i	$0.932406\pi$
$380$	−3.38240e7	+	4.00727e7i	−0.616417	+	0.730295i
$381$	1.03997e7			0.188037
$382$	2.64686e7			0.474834
$383$	−3.12689e7			−0.556565			−0.278282	−	0.960499i	$-0.589765\pi$
$383$	−3.12689e7			−0.556565			−0.278282	+	0.960499i	$0.589765\pi$
$384$	−7.24832e6			−0.128010
$385$	−4.92374e7	+	5.83336e7i	−0.862805	+	1.02220i
$386$	−8.62593e7			−1.49984
$387$	6.26009e7			1.08006
$388$	1.44806e7			0.247909
$389$		−	9.23294e7i		−	1.56852i	−0.620430	−	0.784262i	$-0.713042\pi$
$389$		−	9.23294e7i		−	1.56852i	0.620430	−	0.784262i	$-0.286958\pi$
$390$	1.37730e7	−	1.63175e7i	0.232186	−	0.275081i
$391$	1.37431e7	−	2.45107e7i	0.229908	−	0.410040i
$392$		−	1.03288e8i		−	1.71472i
$393$		−	1.82045e6i		−	0.0299916i
$394$	1.85206e8			3.02807
$395$	−4.41470e7	+	5.23028e7i	−0.716324	+	0.848660i
$396$		−	1.39200e8i		−	2.24158i
$397$		−	3.93714e7i		−	0.629230i	−0.949219	−	0.314615i	$-0.898125\pi$
$397$		−	3.93714e7i		−	0.629230i	0.949219	−	0.314615i	$-0.101875\pi$
$398$	1.51693e8			2.40611
$399$	4.88096e6			0.0768399
$400$	1.99031e7	+	1.16845e8i	0.310985	+	1.82570i
$401$		−	3.14689e7i		−	0.488032i	−0.969771	−	0.244016i	$-0.921535\pi$
$401$		−	3.14689e7i		−	0.488032i	0.969771	−	0.244016i	$-0.0784650\pi$
$402$	2.36663e7			0.364294
$403$			1.84150e7i			0.281356i
$404$	7.40134e7			1.12245
$405$	4.79101e7	+	4.04393e7i	0.721210	+	0.608749i
$406$			2.63699e8i			3.94031i
$407$		−	1.34570e8i		−	1.99602i
$408$	9.98657e6			0.147040
$409$	6.18938e7			0.904643			0.452321	−	0.891855i	$-0.350596\pi$
$409$	6.18938e7			0.904643			0.452321	+	0.891855i	$0.350596\pi$
$410$	7.61337e7	−	9.01988e7i	1.10465	−	1.30873i
$411$			6.14975e6i			0.0885792i
$412$	−1.25434e8			−1.79359
$413$	−1.51641e7			−0.215262
$414$	1.09664e8	+	6.14882e7i	1.54548	+	0.866544i
$415$	−6.12248e7	−	5.16778e7i	−0.856610	−	0.723035i
$416$	−1.11479e8			−1.54850
$417$			1.68966e7i			0.233018i
$418$			5.63188e7i			0.771125i
$419$		−	2.52204e7i		−	0.342854i	−0.985197	−	0.171427i	$-0.945162\pi$
$419$		−	2.52204e7i		−	0.342854i	0.985197	−	0.171427i	$-0.0548378\pi$
$420$	1.96468e7	−	2.32764e7i	0.265182	−	0.314172i
$421$			5.51391e7i			0.738948i	0.929241	+	0.369474i	$0.120462\pi$
$421$			5.51391e7i			0.738948i	−0.929241	+	0.369474i	$0.879538\pi$
$422$		−	2.09625e7i		−	0.278936i
$423$		−	1.19690e8i		−	1.58139i
$424$			9.77437e7i			1.28230i
$425$	6.05974e6	+	3.55748e7i	0.0789382	+	0.463421i
$426$	−3.93574e6			−0.0509093
$427$		−	1.04177e8i		−	1.33810i
$428$	1.17089e8			1.49343
$429$		−	1.59009e7i		−	0.201396i
$430$	−1.01948e8	+	1.20783e8i	−1.28226	+	1.51914i
$431$		−	3.63184e7i		−	0.453623i	−0.973939	−	0.226812i	$-0.927170\pi$
$431$		−	3.63184e7i		−	0.453623i	0.973939	−	0.226812i	$-0.0728302\pi$
$432$			4.06222e7i			0.503862i
$433$	−1.41519e8			−1.74322			−0.871609	−	0.490203i	$-0.836923\pi$
$433$	−1.41519e8			−1.74322			−0.871609	+	0.490203i	$0.836923\pi$
$434$			3.78851e7i			0.463446i
$435$	−1.20160e7	+	1.42359e7i	−0.145980	+	0.172948i
$436$			2.28486e8i			2.75677i
$437$	−3.07640e7	−	1.72493e7i	−0.368636	−	0.206693i
$438$			1.29872e7i			0.154558i
$439$	2.37952e7			0.281252			0.140626	−	0.990063i	$-0.455089\pi$
$439$	2.37952e7			0.281252			0.140626	+	0.990063i	$0.455089\pi$
$440$	1.49801e8	+	1.26442e8i	1.75856	+	1.48434i
$441$	6.33503e7			0.738640
$442$	−1.06406e8			−1.23225
$443$			5.76395e7i			0.662993i	0.943456	+	0.331497i	$0.107554\pi$
$443$			5.76395e7i			0.662993i	−0.943456	+	0.331497i	$0.892446\pi$
$444$			5.36964e7i			0.613474i
$445$	−4.06722e7	+	4.81860e7i	−0.461549	+	0.546816i
$446$	1.35663e8			1.52918
$447$	−1.29357e7			−0.144833
$448$	−8.87742e6			−0.0987308
$449$	8.94417e7			0.988101			0.494050	−	0.869433i	$-0.335516\pi$
$449$	8.94417e7			0.988101			0.494050	+	0.869433i	$0.335516\pi$
$450$	−1.59166e8	+	2.71120e7i	−1.74668	+	0.297525i
$451$		−	8.78961e7i		−	0.958165i
$452$	1.91063e8			2.06900
$453$		−	3.38957e6i		−	0.0364628i
$454$			2.91118e7i			0.311101i
$455$	−1.16759e8	+	1.38330e8i	−1.23953	+	1.46853i
$456$		−	1.25344e7i		−	0.132193i
$457$	−4.30619e7			−0.451175			−0.225587	−	0.974223i	$-0.572430\pi$
$457$	−4.30619e7			−0.451175			−0.225587	+	0.974223i	$0.572430\pi$
$458$	−2.65998e8			−2.76874
$459$			1.23679e7i			0.127897i
$460$	−2.06089e8	+	7.72761e7i	−2.11730	+	0.793911i
$461$	3.20062e7			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$461$	3.20062e7			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$462$		−	3.27130e7i		−	0.331737i
$463$			7.62354e7i			0.768092i	0.923314	+	0.384046i	$0.125470\pi$
$463$			7.62354e7i			0.768092i	−0.923314	+	0.384046i	$0.874530\pi$
$464$	3.04902e8			3.05216
$465$	−1.72631e6	+	2.04524e6i	−0.0171696	+	0.0203416i
$466$	2.36048e8			2.33261
$467$	−1.14370e8			−1.12296			−0.561479	−	0.827491i	$-0.689767\pi$
$467$	−1.14370e8			−1.12296			−0.561479	+	0.827491i	$0.689767\pi$
$468$		−	3.30093e8i		−	3.22032i
$469$	−2.00629e8			−1.94480
$470$	2.30931e8	+	1.94921e8i	2.22428	+	1.87744i
$471$			2.12187e7i			0.203075i
$472$			3.89417e7i			0.370330i
$473$			1.17699e8i			1.11222i
$474$		−	2.93310e7i		−	0.275417i
$475$	4.46508e7	−	7.60572e6i	0.416628	−	0.0709675i
$476$	−1.51784e8			−1.40736
$477$	−5.99495e7			−0.552371
$478$		−	7.15388e7i		−	0.655025i
$479$		−	4.61367e7i		−	0.419798i	−0.977723	−	0.209899i	$-0.932687\pi$
$479$		−	4.61367e7i		−	0.419798i	0.977723	−	0.209899i	$-0.0673135\pi$
$480$	−1.23812e7	−	1.04506e7i	−0.111954	−	0.0944967i
$481$		−	3.19114e8i		−	2.86754i
$482$	3.67461e8			3.28149
$483$	1.78694e7	+	1.00193e7i	0.158587	+	0.0889191i
$484$	5.33740e6			0.0470753
$485$	−9.55786e6	−	8.06746e6i	−0.0837790	−	0.0707150i
$486$	−8.32668e7			−0.725376
$487$		−	1.13979e8i		−	0.986824i	−0.869796	−	0.493412i	$-0.835750\pi$
$487$		−	1.13979e8i		−	0.986824i	0.869796	−	0.493412i	$-0.164250\pi$
$488$	−2.67528e8			−2.30202
$489$	−101621.			−0.000869072
$490$	−1.03169e8	+	1.22229e8i	−0.876922	+	1.03893i
$491$	1.62610e8			1.37373			0.686866	−	0.726784i	$-0.258986\pi$
$491$	1.62610e8			1.37373			0.686866	+	0.726784i	$0.258986\pi$
$492$			3.50725e7i			0.294490i
$493$	9.28315e7			0.774737
$494$			1.33552e8i			1.10782i
$495$	−7.75513e7	+	9.18783e7i	−0.639401	+	0.757525i
$496$	4.38047e7			0.358984
$497$	3.33648e7			0.271781
$498$	3.43343e7			0.277997
$499$	1.23715e8			0.995679			0.497839	−	0.867269i	$-0.334127\pi$
$499$	1.23715e8			0.995679			0.497839	+	0.867269i	$0.334127\pi$
$500$	1.43457e8	−	2.43545e8i	1.14766	−	1.94836i
$501$	−903064.			−0.00718134
$502$	−3.38653e8			−2.67697
$503$	2.02011e8			1.58735			0.793673	−	0.608344i	$-0.208166\pi$
$503$	2.02011e8			1.58735			0.793673	+	0.608344i	$0.208166\pi$
$504$		−	3.78779e8i		−	2.95866i
$505$	−4.88521e7	−	4.12344e7i	−0.379323	−	0.320174i
$506$	−1.15607e8	+	2.06185e8i	−0.892346	+	1.59150i
$507$		−	1.98098e7i		−	0.152004i
$508$			4.05907e8i			3.09624i
$509$	−2.49247e8			−1.89007			−0.945033	−	0.326976i	$-0.893970\pi$
$509$	−2.49247e8			−1.89007			−0.945033	+	0.326976i	$0.893970\pi$
$510$	−1.18178e7	−	9.97502e6i	−0.0890896	−	0.0751975i
$511$		−	1.10097e8i		−	0.825115i
$512$		−	3.00983e8i		−	2.24249i
$513$	1.55233e7			0.114982
$514$	1.41787e8			1.04411
$515$	8.27922e7	+	6.98821e7i	0.606133	+	0.511616i
$516$		−	4.69646e7i		−	0.341839i
$517$	2.25036e8			1.62847
$518$		−	6.56512e8i		−	4.72339i
$519$	1.84137e6			0.0131716
$520$	3.55233e8	+	2.99840e8i	2.52640	+	2.13245i
$521$			4.86877e6i			0.0344276i	0.999852	+	0.0172138i	$0.00547959\pi$
$521$			4.86877e6i			0.0344276i	−0.999852	+	0.0172138i	$0.994520\pi$
$522$			4.15339e8i			2.92006i
$523$	2.56582e8			1.79358			0.896790	−	0.442457i	$-0.145893\pi$
$523$	2.56582e8			1.79358			0.896790	+	0.442457i	$0.145893\pi$
$524$	7.10534e7			0.493845
$525$	−2.59355e7	+	4.41781e6i	−0.179233	+	0.0305301i
$526$			2.26114e8i			1.55371i
$527$	1.33369e7			0.0911219
$528$	−3.78244e7			−0.256963
$529$	−7.72199e7	−	1.26300e8i	−0.521630	−	0.853172i
$530$	9.76306e7	−	1.15667e8i	0.655781	−	0.776931i
$531$	−2.38843e7			−0.159525
$532$			1.90508e8i			1.26525i
$533$		−	2.08433e8i		−	1.37653i
$534$		−	2.70223e7i		−	0.177459i
$535$	−7.72842e7	−	6.52329e7i	−0.504695	−	0.425996i
$536$			5.15217e8i			3.34577i
$537$			2.30192e7i			0.148651i
$538$		−	3.51052e8i		−	2.25437i
$539$			1.19108e8i			0.760634i
$540$	6.24841e7	−	7.40276e7i	0.396815	−	0.470124i
$541$	9.49861e7			0.599886			0.299943	−	0.953957i	$-0.403032\pi$
$541$	9.49861e7			0.599886			0.299943	+	0.953957i	$0.403032\pi$
$542$			2.75012e8i			1.72724i
$543$	−2.20891e7			−0.137968
$544$			8.07375e7i			0.501509i
$545$	1.27295e8	−	1.50811e8i	0.786359	−	0.931632i
$546$		−	7.75742e7i		−	0.476584i
$547$		−	9.47033e7i		−	0.578633i	−0.957234	−	0.289316i	$-0.906572\pi$
$547$		−	9.47033e7i		−	0.578633i	0.957234	−	0.289316i	$-0.0934279\pi$
$548$	−2.40029e8			−1.45855
$549$		−	1.64084e8i		−	0.991629i
$550$	−5.09747e7	−	2.99256e8i	−0.306385	−	1.79869i
$551$		−	1.16515e8i		−	0.696509i
$552$	2.57296e7	−	4.58887e7i	0.152974	−	0.272828i
$553$			2.48650e8i			1.47032i
$554$	−2.26997e7			−0.133503
$555$	2.99154e7	−	3.54420e7i	0.174991	−	0.207319i
$556$	−6.59486e8			−3.83691
$557$	−1.75817e8			−1.01741			−0.508703	−	0.860942i	$-0.669875\pi$
$557$	−1.75817e8			−1.01741			−0.508703	+	0.860942i	$0.669875\pi$
$558$			5.96708e7i			0.343447i
$559$			2.79107e8i			1.59785i
$560$	3.29053e8	+	2.77742e8i	1.87371	+	1.58153i
$561$	−1.15161e7			−0.0652256
$562$	2.06320e8			1.16234
$563$	1.56046e7			0.0874433			0.0437217	−	0.999044i	$-0.486079\pi$
$563$	1.56046e7			0.0874433			0.0437217	+	0.999044i	$0.486079\pi$
$564$	−8.97943e7			−0.500509
$565$	−1.26110e8	−	1.06445e8i	−0.699204	−	0.590174i
$566$			1.21133e8i			0.668055i
$567$	2.27767e8			1.24951
$568$		−	8.56811e7i		−	0.467563i
$569$			3.44560e7i			0.187037i	0.995618	+	0.0935186i	$0.0298115\pi$
$569$			3.44560e7i			0.187037i	−0.995618	+	0.0935186i	$0.970189\pi$
$570$	−1.25199e7	+	1.48328e7i	−0.0676045	+	0.0800939i
$571$		−	2.36637e8i		−	1.27108i	−0.772066	−	0.635542i	$-0.780777\pi$
$571$		−	2.36637e8i		−	1.27108i	0.772066	−	0.635542i	$-0.219223\pi$
$572$	6.20626e8			3.31621
$573$	6.79314e6			0.0361083
$574$		−	4.28809e8i		−	2.26740i
$575$	1.79080e8	+	6.38110e7i	0.941985	+	0.335654i
$576$	−1.39824e7			−0.0731667
$577$		−	1.63773e8i		−	0.852542i	−0.904596	−	0.426271i	$-0.859827\pi$
$577$		−	1.63773e8i		−	0.852542i	0.904596	−	0.426271i	$-0.140173\pi$
$578$		−	2.71655e8i		−	1.40681i
$579$	−2.21383e7			−0.114054
$580$	−5.55637e8	−	4.68994e8i	−2.84779	−	2.40372i
$581$	−2.91066e8			−1.48410
$582$	5.35996e6			0.0271890
$583$		−	1.12714e8i		−	0.568818i
$584$	−2.82732e8			−1.41950
$585$	−1.83902e8	+	2.17876e8i	−0.918583	+	1.08828i
$586$		−	3.51311e8i		−	1.74582i
$587$			2.66853e8i			1.31935i	0.751553	+	0.659673i	$0.229305\pi$
$587$			2.66853e8i			1.31935i	−0.751553	+	0.659673i	$0.770695\pi$
$588$		−	4.75268e7i		−	0.233780i
$589$		−	1.67394e7i		−	0.0819209i
$590$	3.88967e7	−	4.60825e7i	0.189390	−	0.224378i
$591$	4.75328e7			0.230267
$592$	−7.59093e8			−3.65873
$593$		−	2.52270e8i		−	1.20976i	−0.796315	−	0.604882i	$-0.793220\pi$
$593$		−	2.52270e8i		−	1.20976i	0.796315	−	0.604882i	$-0.206780\pi$
$594$		−	1.04039e8i		−	0.496408i
$595$	1.00184e8	+	8.45622e7i	0.475608	+	0.401444i
$596$		−	5.04891e8i		−	2.38484i
$597$	3.89318e7			0.182971
$598$	−2.74146e8	+	4.88939e8i	−1.28197	+	2.28639i
$599$	−1.04813e8			−0.487680			−0.243840	−	0.969815i	$-0.578407\pi$
$599$	−1.04813e8			−0.487680			−0.243840	+	0.969815i	$0.578407\pi$
$600$	1.13450e7	+	6.66028e7i	0.0525231	+	0.308346i
$601$	−1.37629e8			−0.633998			−0.316999	−	0.948426i	$-0.602675\pi$
$601$	−1.37629e8			−0.633998			−0.316999	+	0.948426i	$0.602675\pi$
$602$			5.74206e8i			2.63196i
$603$	−3.16000e8			−1.44124
$604$	1.32297e8			0.600400
$605$	−3.52292e6	−	2.97358e6i	−0.0159088	−	0.0134281i
$606$	2.73959e7			0.123103
$607$		−	2.47318e7i		−	0.110583i	−0.998470	−	0.0552917i	$-0.982391\pi$
$607$		−	2.47318e7i		−	0.110583i	0.998470	−	0.0552917i	$-0.0176089\pi$
$608$	1.01335e8			0.450869
$609$			6.76780e7i			0.299637i
$610$	3.16585e8	+	2.67219e8i	1.39476	+	1.17727i
$611$	5.33641e8			2.33951
$612$	−2.39067e8			−1.04296
$613$	−3.84237e7			−0.166808			−0.0834042	−	0.996516i	$-0.526579\pi$
$613$	−3.84237e7			−0.166808			−0.0834042	+	0.996516i	$0.526579\pi$
$614$	2.57820e7			0.111381
$615$	1.95396e7	−	2.31494e7i	0.0840022	−	0.0995209i
$616$	7.12163e8			3.04675
$617$	−2.42571e8			−1.03272			−0.516360	−	0.856372i	$-0.672713\pi$
$617$	−2.42571e8			−1.03272			−0.516360	+	0.856372i	$0.672713\pi$
$618$	−4.64292e7			−0.196709
$619$			1.37558e8i			0.579980i	0.957030	+	0.289990i	$0.0936519\pi$
$619$			1.37558e8i			0.579980i	−0.957030	+	0.289990i	$0.906348\pi$
$620$	−7.98272e7	−	6.73794e7i	−0.334947	−	0.282717i
$621$	5.68312e7	+	3.18650e7i	0.237308	+	0.133058i
$622$			3.44981e8i			1.43359i
$623$			2.29079e8i			0.947372i
$624$	−8.96953e7			−0.369161
$625$	−2.30373e8	+	8.08277e7i	−0.943606	+	0.331070i
$626$			1.56698e8i			0.638764i
$627$			1.44542e7i			0.0586395i
$628$	−8.28184e8			−3.34386
$629$	−2.31116e8			−0.928704
$630$	−3.78341e8	+	4.48237e8i	−1.51308	+	1.79261i
$631$			4.40692e8i			1.75407i	0.480427	+	0.877035i	$0.340482\pi$
$631$			4.40692e8i			1.75407i	−0.480427	+	0.877035i	$0.659518\pi$
$632$	6.38536e8			2.52950
$633$		−	5.37999e6i		−	0.0212115i
$634$	−2.91858e8			−1.14526
$635$	2.26139e8	−	2.67917e8i	0.883191	−	1.04635i
$636$			4.49755e7i			0.174825i
$637$			2.82448e8i			1.09275i
$638$	−7.80901e8			−3.00700
$639$	5.25511e7			0.201409
$640$	−1.57614e8	+	1.86731e8i	−0.601248	+	0.712324i
$641$			1.28432e8i			0.487639i	0.969821	+	0.243820i	$0.0784005\pi$
$641$			1.28432e8i			0.487639i	−0.969821	+	0.243820i	$0.921600\pi$
$642$	4.33403e7			0.163790
$643$	2.80441e8			1.05489			0.527447	−	0.849588i	$-0.323149\pi$
$643$	2.80441e8			1.05489			0.527447	+	0.849588i	$0.323149\pi$
$644$	−3.91060e8	+	6.97455e8i	−1.46415	+	2.61131i
$645$	−2.61649e7	+	3.09987e7i	−0.0975081	+	0.115522i
$646$	9.67241e7			0.358788
$647$		−	2.37356e8i		−	0.876369i	−0.898885	−	0.438184i	$-0.855622\pi$
$647$		−	2.37356e8i		−	0.876369i	0.898885	−	0.438184i	$-0.144378\pi$
$648$		−	5.84908e8i		−	2.14962i
$649$		−	4.49061e7i		−	0.164275i
$650$	−1.20879e8	−	7.09644e8i	−0.440161	−	2.58405i
$651$			9.72315e6i			0.0352423i
$652$		−	3.96633e6i		−	0.0143102i
$653$		−	3.05149e8i		−	1.09590i	−0.836510	−	0.547951i	$-0.815408\pi$
$653$		−	3.05149e8i		−	1.09590i	0.836510	−	0.547951i	$-0.184592\pi$
$654$			8.45737e7i			0.302344i
$655$	−4.68984e7	−	3.95854e7i	−0.166892	−	0.140867i
$656$	−4.95811e8			−1.75633
$657$		−	1.73409e8i		−	0.611470i
$658$	1.09786e9			3.85362
$659$			4.53455e8i			1.58445i	0.610232	+	0.792223i	$0.291076\pi$
$659$			4.53455e8i			1.58445i	−0.610232	+	0.792223i	$0.708924\pi$
$660$	6.89291e7	+	5.81807e7i	0.239757	+	0.202370i
$661$		−	1.68737e8i		−	0.584258i	−0.956379	−	0.292129i	$-0.905636\pi$
$661$		−	1.68737e8i		−	0.584258i	0.956379	−	0.292129i	$-0.0943637\pi$
$662$			2.26682e8i			0.781345i
$663$	−2.73089e7			−0.0937051
$664$			7.47460e8i			2.55319i
$665$	1.06136e8	−	1.25744e8i	0.360909	−	0.427584i
$666$		−	1.03404e9i		−	3.50037i
$667$	2.39173e8	−	4.26565e8i	0.806000	−	1.43750i
$668$		−	3.52473e7i		−	0.118249i
$669$	3.48178e7			0.116285
$670$	5.14621e8	−	6.09693e8i	1.71105	−	2.02715i
$671$	3.08503e8			1.02116
$672$	−5.88610e7			−0.193963
$673$			5.50540e8i			1.80611i	0.429525	+	0.903055i	$0.358681\pi$
$673$			5.50540e8i			1.80611i	−0.429525	+	0.903055i	$0.641319\pi$
$674$			9.39302e7i			0.306779i
$675$	−8.24846e7	+	1.40503e7i	−0.268202	+	0.0456850i
$676$	7.73191e8			2.50292
$677$	−5.21033e8			−1.67919			−0.839593	−	0.543215i	$-0.817207\pi$
$677$	−5.21033e8			−1.67919			−0.839593	+	0.543215i	$0.817207\pi$
$678$	7.07214e7			0.226914
$679$	−4.54385e7			−0.145149
$680$	2.17157e8	−	2.57275e8i	0.690632	−	0.818220i
$681$			7.47150e6i			0.0236574i
$682$	−1.12190e8			−0.353673
$683$			4.43281e7i			0.139129i	0.997577	+	0.0695644i	$0.0221609\pi$
$683$			4.43281e7i			0.139129i	−0.997577	+	0.0695644i	$0.977839\pi$
$684$			3.00059e8i			0.937645i
$685$	1.58430e8	+	1.33725e8i	0.492908	+	0.416047i
$686$		−	1.90773e8i		−	0.590942i
$687$	−6.82682e7			−0.210546
$688$	6.63927e8			2.03871
$689$		−	2.67286e8i		−	0.817181i
$690$	−7.62834e7	+	2.86035e7i	−0.232211	+	0.0870708i
$691$	4.02116e8			1.21876			0.609378	−	0.792880i	$-0.291419\pi$
$691$	4.02116e8			1.21876			0.609378	+	0.792880i	$0.291419\pi$
$692$			7.18699e7i			0.216885i
$693$			4.36794e8i			1.31243i
$694$	−8.58093e8			−2.56718
$695$	4.35290e8	+	3.67414e8i	1.29666	+	1.09446i
$696$	1.73798e8			0.515486
$697$	−1.50956e8			−0.445813
$698$			8.79205e7i			0.258538i
$699$	6.05814e7			0.177381
$700$	−1.72430e8	−	1.01228e9i	−0.502713	−	2.95126i
$701$			8.41138e7i			0.244182i	0.992519	+	0.122091i	$0.0389599\pi$
$701$			8.41138e7i			0.244182i	−0.992519	+	0.122091i	$0.961040\pi$
$702$		−	2.46715e8i		−	0.713155i
$703$			2.90078e8i			0.834929i
$704$		−	2.62890e7i		−	0.0753453i
$705$	5.92683e7	+	5.00263e7i	0.169143	+	0.142768i
$706$	−6.54075e8			−1.85872
$707$	−2.32245e8			−0.657187
$708$			1.79185e7i			0.0504896i
$709$			7.87448e7i			0.220945i	0.993879	+	0.110472i	$0.0352363\pi$
$709$			7.87448e7i			0.220945i	−0.993879	+	0.110472i	$0.964764\pi$
$710$	−8.55821e7	+	1.01393e8i	−0.239115	+	0.283290i
$711$			3.91636e8i			1.08962i
$712$	5.88277e8			1.62983
$713$	3.43615e7	−	6.12836e7i	0.0947989	−	0.169074i
$714$	−5.61825e7			−0.154350
$715$	−4.09641e8	−	3.45764e8i	−1.12069	−	0.945935i
$716$	−8.98457e8			−2.44770
$717$		−	1.83603e7i		−	0.0498108i
$718$	−1.08050e9			−2.91911
$719$	5.20406e8			1.40009			0.700045	−	0.714099i	$-0.253163\pi$
$719$	5.20406e8			1.40009			0.700045	+	0.714099i	$0.253163\pi$
$720$	5.18274e8	+	4.37458e8i	1.38855	+	1.17203i
$721$	3.93598e8			1.05014
$722$			5.58278e8i			1.48333i
$723$	9.43085e7			0.249538
$724$		−	8.62156e8i		−	2.27180i
$725$	1.05459e8	+	6.19115e8i	0.276738	+	1.62464i
$726$	1.97562e6			0.00516291
$727$	5.88183e8			1.53077			0.765383	−	0.643575i	$-0.222549\pi$
$727$	5.88183e8			1.53077			0.765383	+	0.643575i	$0.222549\pi$
$728$	1.68879e9			4.37706
$729$	3.44269e8			0.888619
$730$	3.34577e8	+	2.82405e8i	0.860056	+	0.725944i
$731$	2.02141e8			0.517491
$732$	−1.23099e8			−0.313851
$733$	−1.34273e8			−0.340939			−0.170469	−	0.985363i	$-0.554528\pi$
$733$	−1.34273e8			−0.340939			−0.170469	+	0.985363i	$0.554528\pi$
$734$		−	1.09361e9i		−	2.76550i
$735$	−2.64782e7	+	3.13698e7i	−0.0666847	+	0.0790042i
$736$	3.70992e8	+	2.08014e8i	0.930532	+	0.521746i
$737$		−	5.94128e8i		−	1.48415i
$738$		−	6.75396e8i		−	1.68031i
$739$	2.24429e8			0.556090			0.278045	−	0.960568i	$-0.410314\pi$
$739$	2.24429e8			0.556090			0.278045	+	0.960568i	$0.410314\pi$
$740$	1.38333e9	+	1.16762e9i	3.41374	+	2.88142i
$741$			3.42760e7i			0.0842433i
$742$		−	5.49887e8i		−	1.34605i
$743$	−2.96463e8			−0.722776			−0.361388	−	0.932416i	$-0.617697\pi$
$743$	−2.96463e8			−0.722776			−0.361388	+	0.932416i	$0.617697\pi$
$744$	2.49692e7			0.0606297
$745$	−2.81286e8	+	3.33251e8i	−0.680266	+	0.805939i
$746$			2.29466e8i			0.552715i
$747$	−4.58443e8			−1.09982
$748$		−	4.49483e8i		−	1.07401i
$749$	−3.67413e8			−0.874397
$750$	5.31004e7	−	9.01477e7i	0.125868	−	0.213683i
$751$			2.54254e8i			0.600272i	0.953896	+	0.300136i	$0.0970321\pi$
$751$			2.54254e8i			0.600272i	−0.953896	+	0.300136i	$0.902968\pi$
$752$		−	1.26940e9i		−	2.98501i
$753$	−8.69149e7			−0.203568
$754$	−1.85180e9			−4.31995
$755$	−8.73222e7	−	7.37057e7i	−0.202901	−	0.171262i
$756$		−	3.51931e8i		−	0.814501i
$757$	−1.64432e8			−0.379052			−0.189526	−	0.981876i	$-0.560695\pi$
$757$	−1.64432e8			−0.379052			−0.189526	+	0.981876i	$0.560695\pi$
$758$	−3.31527e8			−0.761221
$759$	−2.96704e7	+	5.29171e7i	−0.0678576	+	0.121024i
$760$	−3.22911e8	−	2.72558e8i	−0.735601	−	0.620896i
$761$	−5.23690e8			−1.18828			−0.594142	−	0.804360i	$-0.702508\pi$
$761$	−5.23690e8			−1.18828			−0.594142	+	0.804360i	$0.702508\pi$
$762$			1.50245e8i			0.339575i
$763$		−	7.16964e8i		−	1.61408i
$764$			2.65141e8i			0.594563i
$765$	1.57795e8	+	1.33190e8i	0.352460	+	0.297499i
$766$		−	4.51746e8i		−	1.00510i
$767$		−	1.06488e8i		−	0.236002i
$768$		−	1.09356e8i		−	0.241413i
$769$		−	5.01267e8i		−	1.10228i	−0.834414	−	0.551138i	$-0.814194\pi$
$769$		−	5.01267e8i		−	1.10228i	0.834414	−	0.551138i	$-0.185806\pi$
$770$	−8.42754e8	−	7.11339e8i	−1.84599	−	1.55813i
$771$	3.63893e7			0.0793983
$772$		−	8.64077e8i		−	1.87802i
$773$	−5.04958e8			−1.09324			−0.546622	−	0.837380i	$-0.684086\pi$
$773$	−5.04958e8			−1.09324			−0.546622	+	0.837380i	$0.684086\pi$
$774$			9.04403e8i			1.95047i
$775$	1.51510e7	+	8.89468e7i	0.0325489	+	0.191084i
$776$			1.16687e8i			0.249710i
$777$		−	1.68493e8i		−	0.359185i
$778$	1.33390e9			2.83259
$779$			1.89469e8i			0.400797i
$780$	1.63456e8	+	1.37967e8i	0.344442	+	0.290732i
$781$			9.88042e7i			0.207406i
$782$	3.54110e8	+	1.98548e8i	0.740488	+	0.415189i
$783$			2.15241e8i			0.448374i
$784$	6.71875e8			1.39425
$785$	5.46638e8	+	4.61399e8i	1.13003	+	0.953822i
$786$	2.63002e7			0.0541617
$787$	2.32789e8			0.477572			0.238786	−	0.971072i	$-0.423251\pi$
$787$	2.32789e8			0.477572			0.238786	+	0.971072i	$0.423251\pi$
$788$			1.85524e9i			3.79159i
$789$			5.80319e7i			0.118151i
$790$	−7.55626e8	−	6.37798e8i	−1.53259	−	1.29360i
$791$	−5.99533e8			−1.21139
$792$	1.12169e9			2.25786
$793$	7.31571e8			1.46702
$794$	5.68804e8			1.13632
$795$	2.50568e7	−	2.96858e7i	0.0498682	−	0.0590810i
$796$			1.51954e9i			3.01282i
$797$	−3.58693e7			−0.0708513			−0.0354257	−	0.999372i	$-0.511279\pi$
$797$	−3.58693e7			−0.0708513			−0.0354257	+	0.999372i	$0.511279\pi$
$798$			7.05160e7i			0.138765i
$799$		−	3.86486e8i		−	0.757692i
$800$	−5.38457e8	+	9.17197e7i	−1.05167	+	0.179140i
$801$			3.60810e8i			0.702071i
$802$	4.54636e8			0.881334
$803$	3.26035e8			0.629677
$804$			2.37070e8i			0.456151i
$805$	6.46684e8	−	2.42483e8i	1.23967	−	0.464830i
$806$	−2.66043e8			−0.508098
$807$		−	9.00970e7i		−	0.171431i
$808$			5.96409e8i			1.13060i
$809$	7.27782e8			1.37453			0.687267	−	0.726405i	$-0.258810\pi$
$809$	7.27782e8			1.37453			0.687267	+	0.726405i	$0.258810\pi$
$810$	−5.84232e8	+	6.92164e8i	−1.09933	+	1.30243i
$811$	−3.64238e8			−0.682845			−0.341423	−	0.939910i	$-0.610909\pi$
$811$	−3.64238e8			−0.682845			−0.341423	+	0.939910i	$0.610909\pi$
$812$	−2.64153e9			−4.93386
$813$			7.05814e7i			0.131347i
$814$	1.94415e9			3.60460
$815$	−2.20973e6	+	2.61796e6i	−0.00408194	+	0.00483604i
$816$			6.49611e7i			0.119559i
$817$		−	2.53712e8i		−	0.465237i
$818$			8.94188e8i			1.63369i
$819$			1.03579e9i			1.88548i
$820$	9.03539e8	+	7.62646e8i	1.63872	+	1.38319i
$821$	−5.66091e8			−1.02296			−0.511478	−	0.859296i	$-0.670902\pi$
$821$	−5.66091e8			−1.02296			−0.511478	+	0.859296i	$0.670902\pi$
$822$	−8.88462e7			−0.159964
$823$		−	2.92339e8i		−	0.524430i	−0.965009	−	0.262215i	$-0.915547\pi$
$823$		−	2.92339e8i		−	0.524430i	0.965009	−	0.262215i	$-0.0844530\pi$
$824$		−	1.01076e9i		−	1.80663i
$825$	−1.30826e7	−	7.68037e7i	−0.0232987	−	0.136779i
$826$		−	2.19079e8i		−	0.388740i
$827$	−4.03764e8			−0.713856			−0.356928	−	0.934132i	$-0.616176\pi$
$827$	−4.03764e8			−0.713856			−0.356928	+	0.934132i	$0.616176\pi$
$828$	−6.15939e8	+	1.09853e9i	−1.08504	+	1.93517i
$829$	8.52671e7			0.149664			0.0748321	−	0.997196i	$-0.476158\pi$
$829$	8.52671e7			0.149664			0.0748321	+	0.997196i	$0.476158\pi$
$830$	7.46596e8	−	8.84523e8i	1.30572	−	1.54695i
$831$	−5.82585e6			−0.0101521
$832$		−	6.23406e7i		−	0.108243i
$833$	2.04561e8			0.353906
$834$	−2.44107e8			−0.420806
$835$	−1.96370e7	+	2.32648e7i	−0.0337300	+	0.0399613i
$836$	−5.64157e8			−0.965564
$837$			3.09233e7i			0.0527362i
$838$	3.64362e8			0.619158
$839$			1.26265e8i			0.213795i	0.994270	+	0.106897i	$0.0340916\pi$
$839$			1.26265e8i			0.213795i	−0.994270	+	0.106897i	$0.965908\pi$
$840$	1.87564e8	+	1.58316e8i	0.316455	+	0.267109i
$841$	1.02074e9			1.71604
$842$	−7.96603e8			−1.33446
$843$	5.29518e7			0.0883890
$844$	2.09985e8			0.349270
$845$	−5.10341e8	−	4.30761e8i	−0.845844	−	0.713948i
$846$	1.72918e9			2.85581
$847$	−1.67481e7			−0.0275623
$848$	−6.35808e8			−1.04265
$849$			3.10885e7i			0.0508016i
$850$	−5.13954e8	+	8.75460e7i	−0.836889	+	0.142554i
$851$	−5.95452e8	+	1.06199e9i	−0.966179	+	1.72318i
$852$		−	3.94250e7i		−	0.0637461i
$853$			4.78036e8i			0.770218i	0.922871	+	0.385109i	$0.125836\pi$
$853$			4.78036e8i			0.770218i	−0.922871	+	0.385109i	$0.874164\pi$
$854$	1.50506e9			2.41646
$855$	1.67169e8	−	1.98052e8i	0.267459	−	0.316870i
$856$			9.43520e8i			1.50428i
$857$			7.02998e8i			1.11689i	0.829540	+	0.558447i	$0.188603\pi$
$857$			7.02998e8i			1.11689i	−0.829540	+	0.558447i	$0.811397\pi$
$858$	2.29723e8			0.363699
$859$	−8.88962e8			−1.40250			−0.701251	−	0.712914i	$-0.747375\pi$
$859$	−8.88962e8			−1.40250			−0.701251	+	0.712914i	$0.747375\pi$
$860$	−1.20990e9	−	1.02124e9i	−1.90220	−	1.60558i
$861$		−	1.10053e8i		−	0.172423i
$862$	5.24697e8			0.819195
$863$		−	5.56119e8i		−	0.865237i	−0.901577	−	0.432619i	$-0.857590\pi$
$863$		−	5.56119e8i		−	0.865237i	0.901577	−	0.432619i	$-0.142410\pi$
$864$	−1.87200e8			−0.290245
$865$	4.00402e7	−	4.74374e7i	0.0618655	−	0.0732946i
$866$		−	2.04455e9i		−	3.14806i
$867$		−	6.97200e7i		−	0.106979i
$868$	−3.79502e8			−0.580303
$869$	−7.36335e8			−1.12206
$870$	−2.05668e8	−	1.73597e8i	−0.312326	−	0.263624i
$871$		−	1.40889e9i		−	2.13218i
$872$	−1.84117e9			−2.77680
$873$	−7.15679e7			−0.107566
$874$	2.49202e8	−	4.44452e8i	0.373265	−	0.665718i
$875$	−4.50153e8	+	7.64217e8i	−0.671948	+	1.14076i
$876$	−1.30095e8			−0.193530
$877$		−	8.31734e8i		−	1.23306i	−0.787330	−	0.616532i	$-0.788537\pi$
$877$		−	8.31734e8i		−	1.23306i	0.787330	−	0.616532i	$-0.211463\pi$
$878$			3.43772e8i			0.507910i
$879$		−	9.01634e7i		−	0.132759i
$880$	−8.22487e8	+	9.74435e8i	−1.20693	+	1.42990i
$881$		−	3.75024e8i		−	0.548443i	−0.961667	−	0.274221i	$-0.911580\pi$
$881$		−	3.75024e8i		−	0.548443i	0.961667	−	0.274221i	$-0.0884201\pi$
$882$			9.15231e8i			1.33390i
$883$		−	6.76061e8i		−	0.981982i	−0.871165	−	0.490991i	$-0.836635\pi$
$883$		−	6.76061e8i		−	0.981982i	0.871165	−	0.490991i	$-0.163365\pi$
$884$		−	1.06589e9i		−	1.54296i
$885$	9.98278e6	−	1.18270e7i	0.0144020	−	0.0170626i
$886$	−8.32726e8			−1.19729
$887$			6.52558e8i			0.935079i	0.883972	+	0.467539i	$0.154859\pi$
$887$			6.52558e8i			0.935079i	−0.883972	+	0.467539i	$0.845141\pi$
$888$	−4.32692e8			−0.617931
$889$		−	1.27369e9i		−	1.81283i
$890$	−6.96150e8	−	5.87597e8i	−0.987491	−	0.833507i
$891$			6.74493e8i			0.953553i
$892$			1.35897e9i			1.91476i
$893$	−4.85087e8			−0.681185
$894$		−	1.86884e8i		−	0.261553i
$895$	5.93022e8	+	5.00550e8i	0.827183	+	0.698197i
$896$			8.87730e8i			1.23412i
$897$	−7.03592e7	+	1.25485e8i	−0.0974863	+	0.173867i
$898$			1.29218e9i			1.78440i
$899$	2.32104e8			0.319451
$900$	−2.71586e8	−	1.59440e9i	−0.372546	−	2.18710i
$901$	−1.93580e8			−0.264658
$902$	1.26985e9			1.73034
$903$			1.47369e8i			0.200145i
$904$			1.53961e9i			2.08403i
$905$	−4.80325e8	+	5.69061e8i	−0.648022	+	0.767739i
$906$	4.89696e7			0.0658478
$907$	9.61845e8			1.28909			0.644545	−	0.764566i	$-0.277047\pi$
$907$	9.61845e8			1.28909			0.644545	+	0.764566i	$0.277047\pi$
$908$	−2.91619e8			−0.389545
$909$	−3.65798e8			−0.487023
$910$	−1.99847e9	−	1.68684e9i	−2.65200	−	2.23846i
$911$			3.13110e8i			0.414134i	0.978327	+	0.207067i	$0.0663919\pi$
$911$			3.13110e8i			0.414134i	−0.978327	+	0.207067i	$0.933608\pi$
$912$	8.15342e7			0.107487
$913$		−	8.61942e8i		−	1.13257i
$914$		−	6.22122e8i		−	0.814773i
$915$	8.12512e7	+	6.85813e7i	0.106064	+	0.0895246i
$916$		−	2.66456e9i		−	3.46688i
$917$	−2.22957e8			−0.289144
$918$	−1.78681e8			−0.230968
$919$			2.11882e8i			0.272990i	0.990641	+	0.136495i	$0.0435838\pi$
$919$			2.11882e8i			0.272990i	−0.990641	+	0.136495i	$0.956416\pi$
$920$	−6.22700e8	−	1.66069e9i	−0.799679	−	2.13268i
$921$	6.61692e6			0.00846988
$922$			4.62398e8i			0.589960i
$923$			2.34300e8i			0.297967i
$924$	3.27692e8			0.415385
$925$	−2.62553e8	−	1.54136e9i	−0.331735	−	1.94751i
$926$	−1.10138e9			−1.38709
$927$	6.19936e8			0.778230
$928$			1.40509e9i			1.75817i
$929$	4.27927e8			0.533732			0.266866	−	0.963734i	$-0.414012\pi$
$929$	4.27927e8			0.533732			0.266866	+	0.963734i	$0.414012\pi$
$930$	−2.95478e7	−	2.49403e7i	−0.0367347	−	0.0310065i
$931$		−	2.56749e8i		−	0.318171i
$932$			2.36454e9i			2.92078i
$933$			8.85390e7i			0.109016i
$934$		−	1.65233e9i		−	2.02794i
$935$	−2.50417e8	+	2.96679e8i	−0.306358	+	0.362955i
$936$	2.65993e9			3.24372
$937$	1.94631e8			0.236588			0.118294	−	0.992979i	$-0.462257\pi$
$937$	1.94631e8			0.236588			0.118294	+	0.992979i	$0.462257\pi$
$938$		−	2.89851e9i		−	3.51209i
$939$			4.02163e7i			0.0485742i
$940$	−1.95257e9	+	2.31329e9i	−2.35083	+	2.78513i
$941$		−	6.86546e7i		−	0.0823949i	−0.999151	−	0.0411975i	$-0.986883\pi$
$941$		−	6.86546e7i		−	0.0823949i	0.999151	−	0.0411975i	$-0.0131173\pi$
$942$	−3.06550e8			−0.366732
$943$	−3.88927e8	+	6.93650e8i	−0.463802	+	0.827190i
$944$	−2.53310e8			−0.301118
$945$	−1.96068e8	+	2.32290e8i	−0.232333	+	0.275255i
$946$	−1.70042e9			−2.00855
$947$		−	4.61667e8i		−	0.543600i	−0.962354	−	0.271800i	$-0.912381\pi$
$947$		−	4.61667e8i		−	0.543600i	0.962354	−	0.271800i	$-0.0876189\pi$
$948$	2.93814e8			0.344864
$949$	7.73146e8			0.904613
$950$	1.09881e8	+	6.45076e8i	0.128160	+	0.752384i
$951$	−7.49049e7			−0.0870901
$952$		−	1.22310e9i		−	1.41759i
$953$	1.53760e9			1.77650			0.888248	−	0.459365i	$-0.151923\pi$
$953$	1.53760e9			1.77650			0.888248	+	0.459365i	$0.151923\pi$
$954$		−	8.66099e8i		−	0.997522i
$955$	1.47716e8	−	1.75005e8i	0.169597	−	0.200928i
$956$	7.16618e8			0.820189
$957$	−2.00417e8			−0.228665
$958$	6.66544e8			0.758110
$959$	7.53184e8			0.853975
$960$	5.84414e6	−	6.92379e6i	0.00660551	−	0.00782583i
$961$	−8.54158e8			−0.962427
$962$	4.61028e9			5.17848
$963$	−5.78693e8			−0.647991
$964$			3.68093e9i			4.10891i
$965$	−4.81395e8	+	5.70329e8i	−0.535698	+	0.634664i
$966$	−1.44750e8	+	2.58161e8i	−0.160578	+	0.286391i
$967$		−	1.67835e9i		−	1.85610i	−0.372452	−	0.928051i	$-0.621483\pi$
$967$		−	1.67835e9i		−	1.85610i	0.372452	−	0.928051i	$-0.378517\pi$
$968$			4.30094e7i			0.0474174i
$969$	2.48241e7			0.0272837
$970$	1.16552e8	−	1.38084e8i	0.127704	−	0.151296i
$971$			2.64977e8i			0.289435i	0.989473	+	0.144717i	$0.0462273\pi$
$971$			2.64977e8i			0.289435i	−0.989473	+	0.144717i	$0.953773\pi$
$972$		−	8.34100e8i		−	0.908279i
$973$	2.06939e9			2.24649
$974$	1.64668e9			1.78210
$975$	−3.10235e7	−	1.82129e8i	−0.0334717	−	0.196501i
$976$		−	1.74023e9i		−	1.87179i
$977$	−2.69731e8			−0.289233			−0.144616	−	0.989488i	$-0.546195\pi$
$977$	−2.69731e8			−0.289233			−0.144616	+	0.989488i	$0.546195\pi$
$978$		−	1.46813e6i		−	0.00156945i
$979$	−6.78379e8			−0.722976
$980$	−1.22439e9	−	1.03346e9i	−1.30089	−	1.09804i
$981$		−	1.12925e9i		−	1.19615i
$982$			2.34924e9i			2.48081i
$983$	5.21470e8			0.548995			0.274498	−	0.961588i	$-0.411488\pi$
$983$	5.21470e8			0.548995			0.274498	+	0.961588i	$0.411488\pi$
$984$	−2.82618e8			−0.296630
$985$	1.03359e9	−	1.22454e9i	1.08154	−	1.28134i
$986$			1.34115e9i			1.39909i
$987$	2.81764e8			0.293045
$988$	−1.33782e9			−1.38716
$989$	5.20801e8	−	9.28847e8i	0.538373	−	0.960186i
$990$	−1.32738e9	−	1.12039e9i	−1.36801	−	1.15469i
$991$	−7.80432e7			−0.0801889			−0.0400944	−	0.999196i	$-0.512766\pi$
$991$	−7.80432e7			−0.0801889			−0.0400944	+	0.999196i	$0.512766\pi$
$992$			2.01866e8i			0.206789i
$993$			5.81776e7i			0.0594166i
$994$			4.82025e8i			0.490807i
$995$	8.46567e8	−	1.00296e9i	0.859394	−	1.01816i
$996$			3.43934e8i			0.348094i
$997$		−	5.05761e8i		−	0.510340i	−0.966896	−	0.255170i	$-0.917869\pi$
$997$		−	5.05761e8i		−	0.510340i	0.966896	−	0.255170i	$-0.0821315\pi$
$998$			1.78732e9i			1.79809i
$999$		−	5.35870e8i		−	0.537481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.10	yes	68
5.4	even	2	inner	115.7.c.c.114.59	yes	68
23.22	odd	2	inner	115.7.c.c.114.60	yes	68
115.114	odd	2	inner	115.7.c.c.114.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.9	✓	68	115.114	odd	2	inner
115.7.c.c.114.10	yes	68	1.1	even	1	trivial
115.7.c.c.114.59	yes	68	5.4	even	2	inner
115.7.c.c.114.60	yes	68	23.22	odd	2	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+14.4471i q^{2} +3.70784i q^{3} -144.720 q^{4} +(95.5216 + 80.6265i) q^{5} -53.5677 q^{6} +454.114 q^{7} -1166.17i q^{8} +715.252 q^{9} +O(q^{10})\)	\(q+14.4471i q^{2} +3.70784i q^{3} -144.720 q^{4} +(95.5216 + 80.6265i) q^{5} -53.5677 q^{6} +454.114 q^{7} -1166.17i q^{8} +715.252 q^{9} +(-1164.82 + 1380.01i) q^{10} +1344.78i q^{11} -536.598i q^{12} +3188.96i q^{13} +6560.65i q^{14} +(-298.950 + 354.179i) q^{15} +7585.76 q^{16} +2309.58 q^{17} +10333.3i q^{18} -2898.81i q^{19} +(-13823.9 - 11668.3i) q^{20} +1683.78i q^{21} -19428.3 q^{22} +(5950.46 - 10612.6i) q^{23} +4323.97 q^{24} +(2623.74 + 15403.1i) q^{25} -46071.4 q^{26} +5355.05i q^{27} -65719.3 q^{28} +40194.1 q^{29} +(-5116.87 - 4318.97i) q^{30} +5774.59 q^{31} +34957.6i q^{32} -4986.24 q^{33} +33366.9i q^{34} +(43377.7 + 36613.6i) q^{35} -103511. q^{36} -100068. q^{37} +41879.5 q^{38} -11824.2 q^{39} +(94024.2 - 111394. i) q^{40} -65360.8 q^{41} -24325.8 q^{42} +87522.8 q^{43} -194617. i q^{44} +(68322.0 + 57668.2i) q^{45} +(153322. + 85967.1i) q^{46} -167340. i q^{47} +28126.8i q^{48} +88570.6 q^{49} +(-222531. + 37905.5i) q^{50} +8563.56i q^{51} -461506. i q^{52} -83815.9 q^{53} -77365.2 q^{54} +(-108425. + 128456. i) q^{55} -529575. i q^{56} +10748.3 q^{57} +580689. i q^{58} -33392.8 q^{59} +(43264.0 - 51256.7i) q^{60} -229407. i q^{61} +83426.3i q^{62} +324806. q^{63} -19548.9 q^{64} +(-257115. + 304615. i) q^{65} -72036.9i q^{66} -441802. q^{67} -334242. q^{68} +(39349.9 + 22063.4i) q^{69} +(-528962. + 626684. i) q^{70} +73472.2 q^{71} -834106. i q^{72} -242444. i q^{73} -1.44570e6i q^{74} +(-57112.4 + 9728.41i) q^{75} +419515. i q^{76} +610685. i q^{77} -170825. i q^{78} +547549. i q^{79} +(724604. + 611613. i) q^{80} +501563. q^{81} -944277. i q^{82} -640953. q^{83} -243677. i q^{84} +(220615. + 186213. i) q^{85} +1.26445e6i q^{86} +149033. i q^{87} +1.56825e6 q^{88} +504452. i q^{89} +(-833141. + 987057. i) q^{90} +1.44815e6i q^{91} +(-861150. + 1.53586e6i) q^{92} +21411.3i q^{93} +2.41758e6 q^{94} +(233721. - 276899. i) q^{95} -129617. q^{96} -100060. q^{97} +1.27959e6i q^{98} +961859. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

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