LMFDB - Embedded newform 350.2.o.c.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.4
Root			$0.587308 - 2.01725i$ of defining polynomial
Character	$\chi$	$=$	350.157
Dual form			350.2.o.c.243.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(2.80762 - 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} -2.90667i q^{6} +(-0.559876 - 2.58583i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(2.80762 - 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} -2.90667i q^{6} +(-0.559876 - 2.58583i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +(-1.83557 + 3.17930i) q^{11} +(-2.80762 - 0.752300i) q^{12} +(-0.830578 - 0.830578i) q^{13} +(-2.64263 - 0.128464i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.204036 + 0.761471i) q^{17} +(-1.41023 - 5.26305i) q^{18} +(1.09461 + 1.89593i) q^{19} +(-3.51725 - 6.83885i) q^{21} +(2.59589 + 2.59589i) q^{22} +(4.54529 + 1.21791i) q^{23} +(-1.45333 + 2.51725i) q^{24} +(-1.01725 + 0.587308i) q^{26} +(5.03288 - 5.03288i) q^{27} +(-0.808050 + 2.51934i) q^{28} +2.62236i q^{29} +(0.0359651 + 0.0207644i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.76180 + 10.3072i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(-0.0664979 + 0.248174i) q^{37} +(2.11463 - 0.566614i) q^{38} +(-2.95680 - 1.70711i) q^{39} +8.98026i q^{41} +(-7.51616 + 1.62737i) q^{42} +(0.474569 - 0.474569i) q^{43} +(3.17930 - 1.83557i) q^{44} +(2.35282 - 4.07520i) q^{46} +(-6.18205 - 1.65648i) q^{47} +(2.05532 + 2.05532i) q^{48} +(-6.37308 + 2.89549i) q^{49} +(1.14571 + 1.98443i) q^{51} +(0.304013 + 1.13459i) q^{52} +(-2.04824 - 7.64413i) q^{53} +(-3.55879 - 6.16400i) q^{54} +(2.22435 + 1.43257i) q^{56} +(4.49957 + 4.49957i) q^{57} +(2.53301 + 0.678717i) q^{58} +(5.35616 - 9.27713i) q^{59} +(1.72539 - 0.996157i) q^{61} +(0.0293654 - 0.0293654i) q^{62} +(-9.68662 - 10.6765i) q^{63} -1.00000i q^{64} +(9.24117 + 5.33539i) q^{66} +(-6.39671 + 1.71399i) q^{67} +(0.204036 - 0.761471i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(-1.41023 + 5.26305i) q^{72} +(-9.52910 + 2.55331i) q^{73} +(0.222506 + 0.128464i) q^{74} -2.18923i q^{76} +(9.24884 + 2.96647i) q^{77} +(-2.41421 + 2.41421i) q^{78} +(-11.6145 + 6.70563i) q^{79} +(2.17114 - 3.76053i) q^{81} +(8.67427 + 2.32426i) q^{82} +(9.73033 + 9.73033i) q^{83} +(-0.373402 + 7.68124i) q^{84} +(-0.335571 - 0.581226i) q^{86} +(1.97280 + 7.36260i) q^{87} +(-0.950161 - 3.54605i) q^{88} +(0.715130 + 1.23864i) q^{89} +(-1.68272 + 2.61276i) q^{91} +(-3.32739 - 3.32739i) q^{92} +(0.116597 + 0.0312422i) q^{93} +(-3.20007 + 5.54268i) q^{94} +(2.51725 - 1.45333i) q^{96} +(3.16693 - 3.16693i) q^{97} +(1.14736 + 6.90533i) q^{98} +20.0030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	2.80762	−	0.752300i	1.62098	−	0.434341i	0.669692	−	0.742639i	$-0.266426\pi$
$3$	2.80762	−	0.752300i	1.62098	−	0.434341i	0.951290	+	0.308298i	$0.0997593\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	2.90667i		−	1.18664i
$7$	−0.559876	−	2.58583i	−0.211613	−	0.977353i
$7$	−0.559876	−	2.58583i	−0.211613	−	0.977353i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	4.71872	−	2.72435i	1.57291	−	0.908118i
$10$		0			0
$11$	−1.83557	+	3.17930i	−0.553445	+	0.958596i	0.444577	+	0.895741i	$0.353354\pi$
$11$	−1.83557	+	3.17930i	−0.553445	+	0.958596i	−0.998023	+	0.0628551i	$0.979979\pi$
$12$	−2.80762	−	0.752300i	−0.810491	−	0.217170i
$13$	−0.830578	−	0.830578i	−0.230361	−	0.230361i	0.582482	−	0.812843i	$-0.302082\pi$
$13$	−0.830578	−	0.830578i	−0.230361	−	0.230361i	−0.812843	+	0.582482i	$0.802082\pi$
$14$	−2.64263	−	0.128464i	−0.706273	−	0.0343335i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.204036	+	0.761471i	0.0494859	+	0.184684i	0.986245	−	0.165292i	$-0.0528565\pi$
$17$	0.204036	+	0.761471i	0.0494859	+	0.184684i	−0.936759	+	0.349976i	$0.886190\pi$
$18$	−1.41023	−	5.26305i	−0.332394	−	1.24051i
$19$	1.09461	+	1.89593i	0.251122	+	0.434955i	0.963835	−	0.266500i	$-0.0858673\pi$
$19$	1.09461	+	1.89593i	0.251122	+	0.434955i	−0.712713	+	0.701455i	$0.752534\pi$
$20$		0			0
$21$	−3.51725	−	6.83885i	−0.767526	−	1.49236i
$22$	2.59589	+	2.59589i	0.553445	+	0.553445i
$23$	4.54529	+	1.21791i	0.947759	+	0.253951i	0.699411	−	0.714719i	$-0.253446\pi$
$23$	4.54529	+	1.21791i	0.947759	+	0.253951i	0.248348	+	0.968671i	$0.420112\pi$
$24$	−1.45333	+	2.51725i	−0.296660	+	0.513831i
$25$		0			0
$26$	−1.01725	+	0.587308i	−0.199498	+	0.115180i
$27$	5.03288	−	5.03288i	0.968579	−	0.968579i
$28$	−0.808050	+	2.51934i	−0.152707	+	0.476110i
$29$			2.62236i			0.486960i	0.969906	+	0.243480i	$0.0782891\pi$
$29$			2.62236i			0.486960i	−0.969906	+	0.243480i	$0.921711\pi$
$30$		0			0
$31$	0.0359651	+	0.0207644i	0.00645952	+	0.00372940i	0.503226	−	0.864155i	$-0.332146\pi$
$31$	0.0359651	+	0.0207644i	0.00645952	+	0.00372940i	−0.496767	+	0.867884i	$0.665480\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−2.76180	+	10.3072i	−0.480768	+	1.79425i
$34$	0.788333			0.135198
$35$		0			0
$36$	−5.44871			−0.908118
$37$	−0.0664979	+	0.248174i	−0.0109322	+	0.0407995i	−0.971176	−	0.238362i	$-0.923390\pi$
$37$	−0.0664979	+	0.248174i	−0.0109322	+	0.0407995i	0.960244	+	0.279161i	$0.0900563\pi$
$38$	2.11463	−	0.566614i	0.343038	−	0.0919169i
$39$	−2.95680	−	1.70711i	−0.473466	−	0.273356i
$40$		0			0
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$	−7.51616	+	1.62737i	−1.15977	+	0.251109i
$43$	0.474569	−	0.474569i	0.0723711	−	0.0723711i	−0.669995	−	0.742366i	$-0.733704\pi$
$43$	0.474569	−	0.474569i	0.0723711	−	0.0723711i	0.742366	+	0.669995i	$0.233704\pi$
$44$	3.17930	−	1.83557i	0.479298	−	0.276723i
$45$		0			0
$46$	2.35282	−	4.07520i	0.346904	−	0.600855i
$47$	−6.18205	−	1.65648i	−0.901745	−	0.241622i	−0.221980	−	0.975051i	$-0.571252\pi$
$47$	−6.18205	−	1.65648i	−0.901745	−	0.241622i	−0.679766	+	0.733429i	$0.737919\pi$
$48$	2.05532	+	2.05532i	0.296660	+	0.296660i
$49$	−6.37308	+	2.89549i	−0.910440	+	0.413642i
$50$		0			0
$51$	1.14571	+	1.98443i	0.160432	+	0.277876i
$52$	0.304013	+	1.13459i	0.0421590	+	0.157339i
$53$	−2.04824	−	7.64413i	−0.281347	−	1.05000i	−0.951468	−	0.307749i	$-0.900424\pi$
$53$	−2.04824	−	7.64413i	−0.281347	−	1.05000i	0.670120	−	0.742252i	$-0.266242\pi$
$54$	−3.55879	−	6.16400i	−0.484289	−	0.838814i
$55$		0			0
$56$	2.22435	+	1.43257i	0.297242	+	0.191435i
$57$	4.49957	+	4.49957i	0.595982	+	0.595982i
$58$	2.53301	+	0.678717i	0.332600	+	0.0891199i
$59$	5.35616	−	9.27713i	0.697312	−	1.20778i	−0.272083	−	0.962274i	$-0.587713\pi$
$59$	5.35616	−	9.27713i	0.697312	−	1.20778i	0.969395	−	0.245506i	$-0.0789541\pi$
$60$		0			0
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	−0.385459	−	0.922725i	$-0.625957\pi$
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	0.606373	+	0.795180i	$0.292624\pi$
$62$	0.0293654	−	0.0293654i	0.00372940	−	0.00372940i
$63$	−9.68662	−	10.6765i	−1.22040	−	1.34512i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	9.24117	+	5.33539i	1.13751	+	0.656741i
$67$	−6.39671	+	1.71399i	−0.781482	+	0.209398i	−0.627438	−	0.778666i	$-0.715897\pi$
$67$	−6.39671	+	1.71399i	−0.781482	+	0.209398i	−0.154044	+	0.988064i	$0.549230\pi$
$68$	0.204036	−	0.761471i	0.0247430	−	0.0923420i
$69$	13.6777			1.64660
$70$		0			0
$71$	8.11777			0.963402			0.481701	−	0.876336i	$-0.340019\pi$
$71$	8.11777			0.963402			0.481701	+	0.876336i	$0.340019\pi$
$72$	−1.41023	+	5.26305i	−0.166197	+	0.620256i
$73$	−9.52910	+	2.55331i	−1.11530	+	0.298843i	−0.768979	−	0.639274i	$-0.779235\pi$
$73$	−9.52910	+	2.55331i	−1.11530	+	0.298843i	−0.346318	+	0.938117i	$0.612568\pi$
$74$	0.222506	+	0.128464i	0.0258658	+	0.0149336i
$75$		0			0
$76$		−	2.18923i		−	0.251122i
$77$	9.24884	+	2.96647i	1.05400	+	0.338060i
$78$	−2.41421	+	2.41421i	−0.273356	+	0.273356i
$79$	−11.6145	+	6.70563i	−1.30673	+	0.754443i	−0.981550	−	0.191208i	$-0.938760\pi$
$79$	−11.6145	+	6.70563i	−1.30673	+	0.754443i	−0.325184	+	0.945651i	$0.605426\pi$
$80$		0			0
$81$	2.17114	−	3.76053i	0.241238	−	0.417836i
$82$	8.67427	+	2.32426i	0.957912	+	0.256672i
$83$	9.73033	+	9.73033i	1.06804	+	1.06804i	0.997509	+	0.0705331i	$0.0224700\pi$
$83$	9.73033	+	9.73033i	1.06804	+	1.06804i	0.0705331	+	0.997509i	$0.477530\pi$
$84$	−0.373402	+	7.68124i	−0.0407415	+	0.838092i
$85$		0			0
$86$	−0.335571	−	0.581226i	−0.0361855	−	0.0626752i
$87$	1.97280	+	7.36260i	0.211507	+	0.789354i
$88$	−0.950161	−	3.54605i	−0.101288	−	0.378010i
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	0.901435	−	0.432914i	$-0.142514\pi$
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	−0.825632	+	0.564209i	$0.809181\pi$
$90$		0			0
$91$	−1.68272	+	2.61276i	−0.176397	+	0.273892i
$92$	−3.32739	−	3.32739i	−0.346904	−	0.346904i
$93$	0.116597	+	0.0312422i	0.0120906	+	0.00323967i
$94$	−3.20007	+	5.54268i	−0.330062	+	0.571684i
$95$		0			0
$96$	2.51725	−	1.45333i	0.256915	−	0.148330i
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	−0.527810	−	0.849363i	$-0.676987\pi$
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	0.849363	+	0.527810i	$0.176987\pi$
$98$	1.14736	+	6.90533i	0.115901	+	0.697544i
$99$			20.0030i			2.01037i
$100$		0			0
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	0.496899	−	0.867809i	$-0.334472\pi$
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	−0.503095	+	0.864231i	$0.667805\pi$
$102$	2.21334	−	0.593063i	0.219154	−	0.0587220i
$103$	4.29116	−	16.0148i	0.422820	−	1.57799i	−0.345817	−	0.938302i	$-0.612398\pi$
$103$	4.29116	−	16.0148i	0.422820	−	1.57799i	0.768638	−	0.639685i	$-0.220935\pi$
$104$	1.17462			0.115180
$105$		0			0
$106$	−7.91378			−0.768654
$107$	−1.18265	+	4.41372i	−0.114331	+	0.426690i	−0.999236	−	0.0390819i	$-0.987557\pi$
$107$	−1.18265	+	4.41372i	−0.114331	+	0.426690i	0.884905	+	0.465772i	$0.154223\pi$
$108$	−6.87505	+	1.84216i	−0.661552	+	0.177262i
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.999998	−	0.00186842i	$-0.999405\pi$
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.501617	−	0.865090i	$-0.667261\pi$
$110$		0			0
$111$			0.746804i			0.0708835i
$112$	1.95946	−	1.77778i	0.185152	−	0.167985i
$113$	−1.52064	+	1.52064i	−0.143049	+	0.143049i	−0.775005	−	0.631955i	$-0.782253\pi$
$113$	−1.52064	+	1.52064i	−0.143049	+	0.143049i	0.631955	+	0.775005i	$0.282253\pi$
$114$	5.51082	−	3.18168i	0.516136	−	0.297991i
$115$		0			0
$116$	1.31118	−	2.27103i	0.121740	−	0.210860i
$117$	−6.18205	−	1.65648i	−0.571531	−	0.153141i
$118$	−7.57475	−	7.57475i	−0.697312	−	0.697312i
$119$	1.85480	−	0.953932i	0.170030	−	0.0874468i
$120$		0			0
$121$	−1.23864	−	2.14539i	−0.112604	−	0.195035i
$122$	−0.515649	−	1.92443i	−0.0466846	−	0.174229i
$123$	6.75585	+	25.2132i	0.609155	+	2.27340i
$124$	−0.0207644	−	0.0359651i	−0.00186470	−	0.00322976i
$125$		0			0
$126$	−12.8198	+	6.59327i	−1.14208	+	0.587376i
$127$	13.2527	+	13.2527i	1.17599	+	1.17599i	0.980757	+	0.195234i	$0.0625467\pi$
$127$	13.2527	+	13.2527i	1.17599	+	1.17599i	0.195234	+	0.980757i	$0.437453\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	0.975392	−	1.68943i	0.0858785	−	0.148746i
$130$		0			0
$131$	12.2929	−	7.09731i	1.07404	−	0.620095i	0.144755	−	0.989468i	$-0.453761\pi$
$131$	12.2929	−	7.09731i	1.07404	−	0.620095i	0.929281	+	0.369372i	$0.120427\pi$
$132$	7.54538	−	7.54538i	0.656741	−	0.656741i
$133$	4.28970	−	3.89197i	0.371964	−	0.337477i
$134$			6.62236i			0.572085i
$135$		0			0
$136$	−0.682717	−	0.394167i	−0.0585425	−	0.0337995i
$137$	−18.3201	+	4.90887i	−1.56519	+	0.419393i	−0.934303	−	0.356479i	$-0.883977\pi$
$137$	−18.3201	+	4.90887i	−1.56519	+	0.419393i	−0.630891	+	0.775871i	$0.717311\pi$
$138$	3.54005	−	13.2117i	0.301349	−	1.12465i
$139$	8.23706			0.698658			0.349329	−	0.937000i	$-0.386409\pi$
$139$	8.23706			0.698658			0.349329	+	0.937000i	$0.386409\pi$
$140$		0			0
$141$	−18.6030			−1.56666
$142$	2.10103	−	7.84116i	0.176315	−	0.658016i
$143$	4.16524	−	1.11607i	0.348315	−	0.0933308i
$144$	4.71872	+	2.72435i	0.393227	+	0.227029i
$145$		0			0
$146$			9.86525i			0.816454i
$147$	−15.7149	+	12.9239i	−1.29614	+	1.06595i
$148$	0.181676	−	0.181676i	0.0149336	−	0.0149336i
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	−0.318309	−	0.947987i	$-0.603115\pi$
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	0.661826	+	0.749657i	$0.269782\pi$
$150$		0			0
$151$	−5.02292	+	8.69995i	−0.408759	+	0.707992i	−0.994751	−	0.102325i	$-0.967372\pi$
$151$	−5.02292	+	8.69995i	−0.408759	+	0.707992i	0.585992	+	0.810317i	$0.300705\pi$
$152$	−2.11463	−	0.566614i	−0.171519	−	0.0459584i
$153$	3.03730	+	3.03730i	0.245551	+	0.245551i
$154$	5.25916	−	8.16592i	0.423795	−	0.658028i
$155$		0			0
$156$	1.70711	+	2.95680i	0.136678	+	0.236733i
$157$	−6.33762	−	23.6523i	−0.505797	−	1.88766i	−0.458320	−	0.888788i	$-0.651548\pi$
$157$	−6.33762	−	23.6523i	−0.505797	−	1.88766i	−0.0474774	−	0.998872i	$-0.515118\pi$
$158$	3.47109	+	12.9543i	0.276145	+	1.03059i
$159$	−11.5014	−	19.9209i	−0.912117	−	1.57983i
$160$		0			0
$161$	0.604505	−	12.4353i	0.0476417	−	0.980035i
$162$	−3.07046	−	3.07046i	−0.241238	−	0.241238i
$163$	−21.2171	−	5.68510i	−1.66185	−	0.445291i	−0.698954	−	0.715166i	$-0.746351\pi$
$163$	−21.2171	−	5.68510i	−1.66185	−	0.445291i	−0.962895	+	0.269875i	$0.913018\pi$
$164$	4.49013	−	7.77713i	0.350620	−	0.607292i
$165$		0			0
$166$	11.9172	−	6.88038i	0.924952	−	0.534021i
$167$	3.14616	−	3.14616i	0.243457	−	0.243457i	−0.574821	−	0.818279i	$-0.694928\pi$
$167$	3.14616	−	3.14616i	0.243457	−	0.243457i	0.818279	+	0.574821i	$0.194928\pi$
$168$	7.32287	+	2.34873i	0.564972	+	0.181209i
$169$		−	11.6203i		−	0.893868i
$170$		0			0
$171$	10.3303	+	5.96423i	0.789981	+	0.456096i
$172$	−0.648273	+	0.173704i	−0.0494304	+	0.0132448i
$173$	1.35273	−	5.04844i	0.102846	−	0.383826i	−0.895246	−	0.445572i	$-0.853000\pi$
$173$	1.35273	−	5.04844i	0.102846	−	0.383826i	0.998092	+	0.0617463i	$0.0196670\pi$
$174$	7.62233			0.577847
$175$		0			0
$176$	−3.67114			−0.276723
$177$	8.05888	−	30.0761i	0.605742	−	2.26066i
$178$	1.38152	−	0.370178i	0.103550	−	0.0277460i
$179$	10.8847	+	6.28428i	0.813560	+	0.469709i	0.848191	−	0.529691i	$-0.177692\pi$
$179$	10.8847	+	6.28428i	0.813560	+	0.469709i	−0.0346308	+	0.999400i	$0.511026\pi$
$180$		0			0
$181$		−	11.6742i		−	0.867740i	−0.900976	−	0.433870i	$-0.857148\pi$
$181$		−	11.6742i		−	0.867740i	0.900976	−	0.433870i	$-0.142852\pi$
$182$	2.08821	+	2.30161i	0.154789	+	0.170607i
$183$	4.09485	−	4.09485i	0.302700	−	0.302700i
$184$	−4.07520	+	2.35282i	−0.300428	+	0.173452i
$185$		0			0
$186$	0.0603553	−	0.104538i	0.00442546	−	0.00766513i
$187$	−2.79547	−	0.749044i	−0.204425	−	0.0547755i
$188$	4.52558	+	4.52558i	0.330062	+	0.330062i
$189$	−15.8320	−	10.1964i	−1.15161	−	0.741680i
$190$		0			0
$191$	−7.75170	−	13.4263i	−0.560894	−	0.971496i	−0.997419	−	0.0718040i	$-0.977124\pi$
$191$	−7.75170	−	13.4263i	−0.560894	−	0.971496i	0.436525	−	0.899692i	$-0.356209\pi$
$192$	−0.752300	−	2.80762i	−0.0542926	−	0.202623i
$193$	−2.32883	−	8.69132i	−0.167633	−	0.625615i	−0.997690	−	0.0679359i	$-0.978359\pi$
$193$	−2.32883	−	8.69132i	−0.167633	−	0.625615i	0.830057	−	0.557679i	$-0.188308\pi$
$194$	−2.23936	−	3.87868i	−0.160776	−	0.278473i
$195$		0			0
$196$	6.96699	+	0.678966i	0.497642	+	0.0484976i
$197$	−12.1951	−	12.1951i	−0.868865	−	0.868865i	0.123482	−	0.992347i	$-0.460594\pi$
$197$	−12.1951	−	12.1951i	−0.868865	−	0.868865i	−0.992347	+	0.123482i	$0.960594\pi$
$198$	19.3214	+	5.17715i	1.37311	+	0.367924i
$199$	4.36557	−	7.56140i	0.309467	−	0.536013i	−0.668779	−	0.743462i	$-0.733183\pi$
$199$	4.36557	−	7.56140i	0.309467	−	0.536013i	0.978246	+	0.207448i	$0.0665159\pi$
$200$		0			0
$201$	−16.6701	+	9.62450i	−1.17582	+	0.678860i
$202$	−0.0508460	+	0.0508460i	−0.00357751	+	0.00357751i
$203$	6.78099	−	1.46820i	0.475932	−	0.103047i
$204$		−	2.29142i		−	0.160432i
$205$		0			0
$206$	−14.3585	−	8.28988i	−1.00040	−	0.577583i
$207$	24.7660	−	6.63602i	1.72135	−	0.461235i
$208$	0.304013	−	1.13459i	0.0210795	−	0.0786697i
$209$	−8.03696			−0.555928
$210$		0			0
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	−2.04824	+	7.64413i	−0.140674	+	0.525001i
$213$	22.7916	−	6.10700i	1.56166	−	0.418445i
$214$	3.95723	+	2.28471i	0.270511	+	0.156179i
$215$		0			0
$216$			7.11757i			0.484289i
$217$	0.0335574	−	0.104625i	0.00227803	−	0.00710242i
$218$	−12.8005	+	12.8005i	−0.866958	+	0.866958i
$219$	−24.8333	+	14.3375i	−1.67808	+	0.968838i
$220$		0			0
$221$	0.462994	−	0.801929i	0.0311443	−	0.0539436i
$222$	0.721358	+	0.193287i	0.0484143	+	0.0129726i
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	0.681660	−	0.731669i	$-0.261258\pi$
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	−0.731669	+	0.681660i	$0.761258\pi$
$224$	−1.21006	−	2.35282i	−0.0808507	−	0.157204i
$225$		0			0
$226$	1.07525	+	1.86239i	0.0715247	+	0.123884i
$227$	0.807609	+	3.01404i	0.0536029	+	0.200049i	0.987534	−	0.157403i	$-0.0503122\pi$
$227$	0.807609	+	3.01404i	0.0536029	+	0.200049i	−0.933932	+	0.357452i	$0.883646\pi$
$228$	−1.64696	−	6.14653i	−0.109072	−	0.407064i
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	0.970954	−	0.239268i	$-0.0769075\pi$
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	−0.692689	+	0.721236i	$0.743574\pi$
$230$		0			0
$231$	28.1989	+	1.37081i	1.85535	+	0.0901928i
$232$	−1.85429	−	1.85429i	−0.121740	−	0.121740i
$233$	−22.0201	−	5.90027i	−1.44259	−	0.386540i	−0.549148	−	0.835725i	$-0.685048\pi$
$233$	−22.0201	−	5.90027i	−1.44259	−	0.386540i	−0.893439	+	0.449186i	$0.851714\pi$
$234$	−3.20007	+	5.54268i	−0.209195	+	0.362336i
$235$		0			0
$236$	−9.27713	+	5.35616i	−0.603890	+	0.348656i
$237$	−27.5645	+	27.5645i	−1.79051	+	1.79051i
$238$	−0.441369	−	2.03850i	−0.0286097	−	0.132136i
$239$			23.9971i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$239$			23.9971i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$240$		0			0
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.390295	−	0.920690i	$-0.627627\pi$
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.992488	+	0.122340i	$0.960960\pi$
$242$	−2.39287	+	0.641168i	−0.153820	+	0.0412158i
$243$	−2.25979	+	8.43364i	−0.144965	+	0.541018i
$244$	−1.99231			−0.127545
$245$		0			0
$246$	26.1026			1.66424
$247$	0.665553	−	2.48388i	0.0423481	−	0.158045i
$248$	−0.0401138	+	0.0107485i	−0.00254723	+	0.000682528i
$249$	34.6392	+	19.9990i	2.19517	+	1.26738i
$250$		0			0
$251$			11.1158i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$251$			11.1158i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$252$	3.05060	+	14.0895i	0.192170	+	0.887552i
$253$	−12.2153	+	12.2153i	−0.767970	+	0.767970i
$254$	16.2312	−	9.37110i	1.01844	−	0.587995i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	24.4314	+	6.54637i	1.52399	+	0.408351i	0.921052	−	0.389439i	$-0.127331\pi$
$257$	24.4314	+	6.54637i	1.52399	+	0.408351i	0.602935	+	0.797790i	$0.293998\pi$
$258$	−1.37941	−	1.37941i	−0.0858785	−	0.0858785i
$259$	0.678966	+	0.0330060i	0.0421889	+	0.00205090i
$260$		0			0
$261$	7.14424	+	12.3742i	0.442217	+	0.765943i
$262$	−3.67384	−	13.7110i	−0.226971	−	0.847066i
$263$	−2.93659	−	10.9595i	−0.181078	−	0.675792i	−0.995436	−	0.0954297i	$-0.969577\pi$
$263$	−2.93659	−	10.9595i	−0.181078	−	0.675792i	0.814358	−	0.580363i	$-0.197089\pi$
$264$	−5.33539	−	9.24117i	−0.328371	−	0.568755i
$265$		0			0
$266$	−2.64910	−	5.15085i	−0.162427	−	0.315819i
$267$	2.93964	+	2.93964i	0.179903	+	0.179903i
$268$	6.39671	+	1.71399i	0.390741	+	0.104699i
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	−0.962391	−	0.271668i	$-0.912425\pi$
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	0.716467	+	0.697621i	$0.245758\pi$
$270$		0			0
$271$	7.27419	−	4.19976i	0.441876	−	0.255117i	−0.262517	−	0.964927i	$-0.584553\pi$
$271$	7.27419	−	4.19976i	0.441876	−	0.255117i	0.704393	+	0.709810i	$0.251219\pi$
$272$	−0.557436	+	0.557436i	−0.0337995	+	0.0337995i
$273$	−2.75885	+	8.60155i	−0.166974	+	0.520590i
$274$			18.9664i			1.14580i
$275$		0			0
$276$	−11.8452	−	6.83885i	−0.713000	−	0.411651i
$277$	5.48646	−	1.47009i	0.329650	−	0.0883293i	−0.0901983	−	0.995924i	$-0.528750\pi$
$277$	5.48646	−	1.47009i	0.329650	−	0.0883293i	0.419848	+	0.907594i	$0.362083\pi$
$278$	2.13191	−	7.95639i	0.127863	−	0.477193i
$279$	0.226279			0.0135470
$280$		0			0
$281$	7.27627			0.434066			0.217033	−	0.976164i	$-0.430362\pi$
$281$	7.27627			0.434066			0.217033	+	0.976164i	$0.430362\pi$
$282$	−4.81482	+	17.9692i	−0.286719	+	1.07005i
$283$	7.44729	−	1.99550i	0.442696	−	0.118620i	−0.0305840	−	0.999532i	$-0.509737\pi$
$283$	7.44729	−	1.99550i	0.442696	−	0.118620i	0.473280	+	0.880912i	$0.343070\pi$
$284$	−7.03019	−	4.05888i	−0.417165	−	0.240850i
$285$		0			0
$286$		−	4.31218i		−	0.254984i
$287$	23.2215	−	5.02784i	1.37072	−	0.296784i
$288$	3.85282	−	3.85282i	0.227029	−	0.227029i
$289$	14.1842	−	8.18927i	0.834366	−	0.481721i
$290$		0			0
$291$	6.50906	−	11.2740i	0.381568	−	0.660895i
$292$	9.52910	+	2.55331i	0.557648	+	0.149421i
$293$	−3.35198	−	3.35198i	−0.195824	−	0.195824i	0.602383	−	0.798207i	$-0.294218\pi$
$293$	−3.35198	−	3.35198i	−0.195824	−	0.195824i	−0.798207	+	0.602383i	$0.794218\pi$
$294$	8.41624	+	18.5244i	0.490845	+	1.08037i
$295$		0			0
$296$	−0.128464	−	0.222506i	−0.00746682	−	0.0129329i
$297$	6.76284	+	25.2393i	0.392420	+	1.46453i
$298$	−1.25316	−	4.67687i	−0.0725938	−	0.270924i
$299$	−2.76365	−	4.78679i	−0.159826	−	0.276827i
$300$		0			0
$301$	−1.49286	−	0.961456i	−0.0860468	−	0.0554174i
$302$	7.10348	+	7.10348i	0.408759	+	0.408759i
$303$	−0.201888	−	0.0540958i	−0.0115982	−	0.00310772i
$304$	−1.09461	+	1.89593i	−0.0627804	+	0.108739i
$305$		0			0
$306$	3.71992	−	2.14770i	0.212654	−	0.122776i
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	−0.676048	−	0.736857i	$-0.736309\pi$
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	0.736857	+	0.676048i	$0.236309\pi$
$308$	−6.52650	−	7.19345i	−0.371882	−	0.409885i
$309$		−	48.1918i		−	2.74154i
$310$		0			0
$311$	11.9584	+	6.90417i	0.678097	+	0.391500i	0.799138	−	0.601148i	$-0.205290\pi$
$311$	11.9584	+	6.90417i	0.678097	+	0.391500i	−0.121040	+	0.992648i	$0.538623\pi$
$312$	3.29788	−	0.883663i	0.186706	−	0.0500276i
$313$	−6.04266	+	22.5515i	−0.341551	+	1.27469i	0.555038	+	0.831825i	$0.312704\pi$
$313$	−6.04266	+	22.5515i	−0.341551	+	1.27469i	−0.896590	+	0.442863i	$0.853963\pi$
$314$	−24.4867			−1.38186
$315$		0			0
$316$	13.4113			0.754443
$317$	−3.41352	+	12.7394i	−0.191722	+	0.715518i	0.801369	+	0.598171i	$0.204106\pi$
$317$	−3.41352	+	12.7394i	−0.191722	+	0.715518i	−0.993091	+	0.117347i	$0.962561\pi$
$318$	−22.2189	+	5.95354i	−1.24598	+	0.333858i
$319$	−8.33728	−	4.81353i	−0.466798	−	0.269506i
$320$		0			0
$321$			13.2818i			0.741316i
$322$	−11.8551	−	3.80239i	−0.660658	−	0.211899i
$323$	−1.22035	+	1.22035i	−0.0679023	+	0.0679023i
$324$	−3.76053	+	2.17114i	−0.208918	+	0.120619i
$325$		0			0
$326$	−10.9828	+	19.0227i	−0.608279	+	1.05357i
$327$	−50.8253	−	13.6186i	−2.81065	−	0.753111i
$328$	−6.35000	−	6.35000i	−0.350620	−	0.350620i
$329$	−0.822187	+	16.9132i	−0.0453286	+	0.932454i
$330$		0			0
$331$	9.54799	+	16.5376i	0.524805	+	0.908989i	0.999583	+	0.0288830i	$0.00919501\pi$
$331$	9.54799	+	16.5376i	0.524805	+	0.908989i	−0.474778	+	0.880106i	$0.657472\pi$
$332$	−3.56155	−	13.2919i	−0.195465	−	0.729487i
$333$	0.362328	+	1.35222i	0.0198554	+	0.0741015i
$334$	−2.22467	−	3.85325i	−0.121729	−	0.210840i
$335$		0			0
$336$	4.16400	−	6.46545i	0.227165	−	0.352719i
$337$	−0.488226	−	0.488226i	−0.0265953	−	0.0265953i	0.693684	−	0.720279i	$-0.255986\pi$
$337$	−0.488226	−	0.488226i	−0.0265953	−	0.0265953i	−0.720279	+	0.693684i	$0.755986\pi$
$338$	−11.2243	−	3.00755i	−0.610523	−	0.163589i
$339$	−3.12540	+	5.41335i	−0.169748	+	0.294013i
$340$		0			0
$341$	−0.132033	+	0.0762292i	−0.00714998	+	0.00412804i
$342$	8.43469	−	8.43469i	0.456096	−	0.456096i
$343$	11.0554	+	14.8586i	0.596936	+	0.802289i
$344$			0.671142i			0.0361855i
$345$		0			0
$346$	−4.52631	−	2.61327i	−0.243336	−	0.140490i
$347$	3.68015	−	0.986094i	0.197561	−	0.0529363i	−0.158682	−	0.987330i	$-0.550724\pi$
$347$	3.68015	−	0.986094i	0.197561	−	0.0529363i	0.356243	+	0.934393i	$0.384058\pi$
$348$	1.97280	−	7.36260i	0.105753	−	0.394677i
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$		0			0
$351$	−8.36041			−0.446246
$352$	−0.950161	+	3.54605i	−0.0506438	+	0.189005i
$353$	24.9004	−	6.67203i	1.32531	−	0.355116i	0.474347	−	0.880338i	$-0.342684\pi$
$353$	24.9004	−	6.67203i	1.32531	−	0.355116i	0.850965	+	0.525222i	$0.176018\pi$
$354$	−26.9655	−	15.5686i	−1.43320	−	0.827459i
$355$		0			0
$356$		−	1.43026i		−	0.0758036i
$357$	4.48995	−	4.07365i	0.237633	−	0.215601i
$358$	8.88731	−	8.88731i	0.469709	−	0.469709i
$359$	8.99497	−	5.19325i	0.474737	−	0.274089i	−0.243484	−	0.969905i	$-0.578290\pi$
$359$	8.99497	−	5.19325i	0.474737	−	0.274089i	0.718220	+	0.695816i	$0.244957\pi$
$360$		0			0
$361$	7.10364	−	12.3039i	0.373876	−	0.647572i
$362$	−11.2765	−	3.02152i	−0.592677	−	0.158807i
$363$	−5.09161	−	5.09161i	−0.267240	−	0.267240i
$364$	2.76365	−	1.42136i	0.144855	−	0.0744994i
$365$		0			0
$366$	−2.89549	−	5.01514i	−0.151350	−	0.262146i
$367$	2.24811	+	8.39004i	0.117350	+	0.437957i	0.999452	−	0.0331020i	$-0.0105386\pi$
$367$	2.24811	+	8.39004i	0.117350	+	0.437957i	−0.882102	+	0.471059i	$0.843872\pi$
$368$	1.21791	+	4.54529i	0.0634878	+	0.236940i
$369$	24.4654	+	42.3753i	1.27362	+	2.20597i
$370$		0			0
$371$	−18.6197	+	9.57617i	−0.966686	+	0.497170i
$372$	−0.0853553	−	0.0853553i	−0.00442546	−	0.00442546i
$373$	12.8560	+	3.44476i	0.665660	+	0.178363i	0.575799	−	0.817591i	$-0.304691\pi$
$373$	12.8560	+	3.44476i	0.665660	+	0.178363i	0.0898611	+	0.995954i	$0.471358\pi$
$374$	−1.44704	+	2.50635i	−0.0748247	+	0.129600i
$375$		0			0
$376$	5.54268	−	3.20007i	0.285842	−	0.165031i
$377$	2.17808	−	2.17808i	0.112177	−	0.112177i
$378$	−13.9466	+	12.6535i	−0.717336	+	0.650826i
$379$		−	25.3453i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$379$		−	25.3453i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$380$		0			0
$381$	47.1788	+	27.2387i	2.41704	+	1.39548i
$382$	−14.9751	+	4.01258i	−0.766195	+	0.205301i
$383$	−4.76251	+	17.7739i	−0.243353	+	0.908205i	0.730851	+	0.682537i	$0.239123\pi$
$383$	−4.76251	+	17.7739i	−0.243353	+	0.908205i	−0.974204	+	0.225668i	$0.927543\pi$
$384$	−2.90667			−0.148330
$385$		0			0
$386$	−8.99792			−0.457982
$387$	0.946464	−	3.53225i	0.0481114	−	0.179554i
$388$	−4.32611	+	1.15918i	−0.219625	+	0.0588483i
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.0789164	−	0.996881i	$-0.525146\pi$
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.902783	+	0.430097i	$0.858479\pi$
$390$		0			0
$391$			3.70961i			0.187603i
$392$	2.45902	−	6.55387i	0.124199	−	0.331020i
$393$	29.1745	−	29.1745i	1.47166	−	1.47166i
$394$	−14.9359	+	8.62324i	−0.752459	+	0.434432i
$395$		0			0
$396$	10.0015	−	17.3231i	0.502594	−	0.870518i
$397$	15.2461	+	4.08518i	0.765181	+	0.205029i	0.620241	−	0.784411i	$-0.287035\pi$
$397$	15.2461	+	4.08518i	0.765181	+	0.205029i	0.144939	+	0.989441i	$0.453701\pi$
$398$	−6.17385	−	6.17385i	−0.309467	−	0.309467i
$399$	9.11594	−	14.1543i	0.456368	−	0.708603i
$400$		0			0
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$	4.98201	+	18.5931i	0.248480	+	0.927339i
$403$	−0.0126253	−	0.0471183i	−0.000628911	−	0.00234713i
$404$	0.0359536	+	0.0622734i	0.00178876	+	0.00309822i
$405$		0			0
$406$	0.336879	−	6.92993i	0.0167190	−	0.343927i
$407$	−0.666957	−	0.666957i	−0.0330598	−	0.0330598i
$408$	−2.21334	−	0.593063i	−0.109577	−	0.0293610i
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	−0.869873	−	0.493276i	$-0.835799\pi$
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	0.862126	+	0.506694i	$0.169133\pi$
$410$		0			0
$411$	−47.7431	+	27.5645i	−2.35499	+	1.35966i
$412$	−11.7237	+	11.7237i	−0.577583	+	0.577583i
$413$	−26.9879	−	8.65608i	−1.32799	−	0.425938i
$414$		−	25.6396i		−	1.26012i
$415$		0			0
$416$	−1.01725	−	0.587308i	−0.0498746	−	0.0287951i
$417$	23.1266	−	6.19675i	1.13251	−	0.303456i
$418$	−2.08012	+	7.76311i	−0.101742	+	0.379706i
$419$	31.6254			1.54500			0.772501	−	0.635014i	$-0.219006\pi$
$419$	31.6254			1.54500			0.772501	+	0.635014i	$0.219006\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	−2.89219	+	10.7938i	−0.140789	+	0.525433i
$423$	−33.6842	+	9.02565i	−1.63778	+	0.438842i
$424$	6.85354	+	3.95689i	0.332837	+	0.192164i
$425$		0			0
$426$		−	23.5956i		−	1.14321i
$427$	−3.54190	−	3.90386i	−0.171405	−	0.188921i
$428$	3.23107	−	3.23107i	0.156179	−	0.156179i
$429$	10.8548	−	6.26703i	0.524075	−	0.302575i
$430$		0			0
$431$	−0.779037	+	1.34933i	−0.0375249	+	0.0649950i	−0.884178	−	0.467150i	$-0.845281\pi$
$431$	−0.779037	+	1.34933i	−0.0375249	+	0.0649950i	0.846653	+	0.532145i	$0.178614\pi$
$432$	6.87505	+	1.84216i	0.330776	+	0.0886311i
$433$	−6.28166	−	6.28166i	−0.301877	−	0.301877i	0.539871	−	0.841748i	$-0.318473\pi$
$433$	−6.28166	−	6.28166i	−0.301877	−	0.301877i	−0.841748	+	0.539871i	$0.818473\pi$
$434$	−0.0923749	−	0.0594930i	−0.00443414	−	0.00285575i
$435$		0			0
$436$	9.05131	+	15.6773i	0.433479	+	0.750808i
$437$	2.66628	+	9.95068i	0.127545	+	0.476006i
$438$	7.42163	+	27.6979i	0.354619	+	1.32346i
$439$	11.9571	+	20.7103i	0.570681	+	0.988449i	0.996496	+	0.0836389i	$0.0266542\pi$
$439$	11.9571	+	20.7103i	0.570681	+	0.988449i	−0.425815	+	0.904810i	$0.640012\pi$
$440$		0			0
$441$	−22.1844	+	31.0255i	−1.05640	+	1.47741i
$442$	−0.654772	−	0.654772i	−0.0311443	−	0.0311443i
$443$	12.4238	+	3.32895i	0.590272	+	0.158163i	0.541578	−	0.840651i	$-0.317827\pi$
$443$	12.4238	+	3.32895i	0.590272	+	0.158163i	0.0486946	+	0.998814i	$0.484494\pi$
$444$	0.373402	−	0.646751i	0.0177209	−	0.0306935i
$445$		0			0
$446$	−0.914645	+	0.528070i	−0.0433097	+	0.0250049i
$447$	9.95157	−	9.95157i	0.470693	−	0.470693i
$448$	−2.58583	+	0.559876i	−0.122169	+	0.0264517i
$449$			17.8932i			0.844435i	0.906495	+	0.422217i	$0.138748\pi$
$449$			17.8932i			0.844435i	−0.906495	+	0.422217i	$0.861252\pi$
$450$		0			0
$451$	−28.5510	−	16.4839i	−1.34441	−	0.776197i
$452$	2.07723	−	0.556592i	0.0977046	−	0.0261799i
$453$	−7.55749	+	28.2049i	−0.355082	+	1.32518i
$454$	3.12036			0.146446
$455$		0			0
$456$	−6.36335			−0.297991
$457$	−8.85449	+	33.0454i	−0.414196	+	1.54580i	0.372246	+	0.928134i	$0.378588\pi$
$457$	−8.85449	+	33.0454i	−0.414196	+	1.54580i	−0.786442	+	0.617665i	$0.788079\pi$
$458$	8.13485	−	2.17973i	0.380116	−	0.101852i
$459$	4.85928	+	2.80551i	0.226812	+	0.130950i
$460$		0			0
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$	8.62252	−	26.8833i	0.401156	−	1.25072i
$463$	−3.98510	+	3.98510i	−0.185203	+	0.185203i	−0.793619	−	0.608415i	$-0.791805\pi$
$463$	−3.98510	+	3.98510i	−0.185203	+	0.185203i	0.608415	+	0.793619i	$0.291805\pi$
$464$	−2.27103	+	1.31118i	−0.105430	+	0.0608700i
$465$		0			0
$466$	−11.3985	+	19.7427i	−0.528023	+	0.914563i
$467$	4.71932	+	1.26454i	0.218384	+	0.0585159i	0.366352	−	0.930476i	$-0.380607\pi$
$467$	4.71932	+	1.26454i	0.218384	+	0.0585159i	−0.147968	+	0.988992i	$0.547273\pi$
$468$	4.52558	+	4.52558i	0.209195	+	0.209195i
$469$	8.01347	+	15.5812i	0.370028	+	0.719473i
$470$		0			0
$471$	−35.5873	−	61.6390i	−1.63978	−	2.84017i
$472$	2.77255	+	10.3473i	0.127617	+	0.476273i
$473$	0.637693	+	2.37990i	0.0293212	+	0.109428i
$474$	19.4910	+	33.7595i	0.895253	+	1.55062i
$475$		0			0
$476$	−2.08327	−	0.101272i	−0.0954867	−	0.00464182i
$477$	−30.4904	−	30.4904i	−1.39606	−	1.39606i
$478$	23.1794	+	6.21090i	1.06020	+	0.284080i
$479$	−8.55572	+	14.8189i	−0.390921	+	0.677094i	−0.992571	−	0.121665i	$-0.961177\pi$
$479$	−8.55572	+	14.8189i	−0.390921	+	0.677094i	0.601651	+	0.798759i	$0.294510\pi$
$480$		0			0
$481$	0.261359	−	0.150896i	0.0119170	−	0.00688026i
$482$	−17.5274	+	17.5274i	−0.798350	+	0.798350i
$483$	−7.65783	−	35.3683i	−0.348443	−	1.60931i
$484$			2.47728i			0.112604i
$485$		0			0
$486$	7.56140	+	4.36557i	0.342992	+	0.198026i
$487$	0.125860	−	0.0337240i	0.00570325	−	0.00152818i	−0.255966	−	0.966686i	$-0.582394\pi$
$487$	0.125860	−	0.0337240i	0.00570325	−	0.00152818i	0.261670	+	0.965158i	$0.415727\pi$
$488$	−0.515649	+	1.92443i	−0.0233423	+	0.0871147i
$489$	−63.8465			−2.88724
$490$		0			0
$491$	26.9895			1.21802			0.609011	−	0.793162i	$-0.291567\pi$
$491$	26.9895			1.21802			0.609011	+	0.793162i	$0.291567\pi$
$492$	6.75585	−	25.2132i	0.304577	−	1.13670i
$493$	−1.99685	+	0.535055i	−0.0899337	+	0.0240977i
$494$	−2.22698	−	1.28575i	−0.100197	−	0.0578486i
$495$		0			0
$496$			0.0415289i			0.00186470i
$497$	−4.54495	−	20.9912i	−0.203869	−	0.941584i
$498$	28.2828	−	28.2828i	1.26738	−	1.26738i
$499$	−0.0833977	+	0.0481497i	−0.00373339	+	0.00215548i	−0.501866	−	0.864946i	$-0.667353\pi$
$499$	−0.0833977	+	0.0481497i	−0.00373339	+	0.00215548i	0.498132	+	0.867101i	$0.334019\pi$
$500$		0			0
$501$	6.46638	−	11.2001i	0.288897	−	0.500384i
$502$	10.7370	+	2.87698i	0.479217	+	0.128406i
$503$	13.6334	+	13.6334i	0.607883	+	0.607883i	0.942392	−	0.334509i	$-0.108571\pi$
$503$	13.6334	+	13.6334i	0.607883	+	0.607883i	−0.334509	+	0.942392i	$0.608571\pi$
$504$	14.3989	+	0.699963i	0.641379	+	0.0311788i
$505$		0			0
$506$	8.63753	+	14.9606i	0.383985	+	0.665081i
$507$	−8.74194	−	32.6254i	−0.388243	−	1.44894i
$508$	−4.85084	−	18.1036i	−0.215221	−	0.803217i
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	0.696480	−	0.717576i	$-0.254749\pi$
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	−0.969679	+	0.244381i	$0.921415\pi$
$510$		0			0
$511$	11.9376	+	23.2111i	0.528087	+	1.02680i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	15.0510	+	4.03291i	0.664520	+	0.178057i
$514$	12.6466	−	21.9046i	0.557818	−	0.966169i
$515$		0			0
$516$	−1.68943	+	0.975392i	−0.0743730	+	0.0429393i
$517$	16.6140	−	16.6140i	0.730684	−	0.730684i
$518$	0.207611	−	0.647288i	0.00912189	−	0.0284402i
$519$		−	15.1918i		−	0.666845i
$520$		0			0
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	0.776694	−	0.629878i	$-0.216895\pi$
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	−0.157143	+	0.987576i	$0.550228\pi$
$522$	13.8016	−	3.69813i	0.604080	−	0.161863i
$523$	7.09270	−	26.4703i	0.310142	−	1.15747i	−0.618286	−	0.785953i	$-0.712173\pi$
$523$	7.09270	−	26.4703i	0.310142	−	1.15747i	0.928428	−	0.371512i	$-0.121161\pi$
$524$	−14.1946			−0.620095
$525$		0			0
$526$	−11.3461			−0.494714
$527$	−0.00847337	+	0.0316231i	−0.000369106	+	0.00137752i
$528$	−10.3072	+	2.76180i	−0.448563	+	0.120192i
$529$	−0.742186	−	0.428501i	−0.0322689	−	0.0186305i
$530$		0			0
$531$		−	58.3682i		−	2.53297i
$532$	−5.66098	+	1.22570i	−0.245435	+	0.0531407i
$533$	7.45881	−	7.45881i	0.323077	−	0.323077i
$534$	3.60031	−	2.07864i	0.155801	−	0.0899517i
$535$		0			0
$536$	3.31118	−	5.73513i	0.143021	−	0.247720i
$537$	35.2878	+	9.45533i	1.52278	+	0.408028i
$538$	5.70417	+	5.70417i	0.245924	+	0.245924i
$539$	2.49258	−	25.5768i	0.107363	−	1.10167i
$540$		0			0
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.846069	+	0.533073i	$0.178963\pi$
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.0386200	+	0.999254i	$0.487704\pi$
$542$	−2.17395	−	8.11330i	−0.0933793	−	0.348496i
$543$	−8.78254	−	32.7769i	−0.376895	−	1.40659i
$544$	0.394167	+	0.682717i	0.0168998	+	0.0292712i
$545$		0			0
$546$	7.59442	+	4.89109i	0.325011	+	0.209320i
$547$	−8.06541	−	8.06541i	−0.344852	−	0.344852i	0.513336	−	0.858188i	$-0.328410\pi$
$547$	−8.06541	−	8.06541i	−0.344852	−	0.344852i	−0.858188	+	0.513336i	$0.828410\pi$
$548$	18.3201	+	4.90887i	0.782597	+	0.209696i
$549$	5.42777	−	9.40117i	0.231651	−	0.401232i
$550$		0			0
$551$	−4.97180	+	2.87047i	−0.211806	+	0.122286i
$552$	−9.67160	+	9.67160i	−0.411651	+	0.411651i
$553$	23.8423	+	26.2788i	1.01388	+	1.11749i
$554$		−	5.68000i		−	0.241320i
$555$		0			0
$556$	−7.13350	−	4.11853i	−0.302528	−	0.174665i
$557$	−24.7826	+	6.64049i	−1.05007	+	0.281367i	−0.742282	−	0.670087i	$-0.766257\pi$
$557$	−24.7826	+	6.64049i	−1.05007	+	0.281367i	−0.307792	+	0.951454i	$0.599590\pi$
$558$	0.0585652	−	0.218568i	0.00247926	−	0.00925274i
$559$	−0.788333			−0.0333429
$560$		0			0
$561$	−8.41213			−0.355160
$562$	1.88324	−	7.02834i	0.0794396	−	0.296473i
$563$	12.3749	−	3.31584i	0.521539	−	0.139746i	0.0115606	−	0.999933i	$-0.496320\pi$
$563$	12.3749	−	3.31584i	0.521539	−	0.139746i	0.509978	+	0.860187i	$0.329653\pi$
$564$	16.1107	+	9.30152i	0.678383	+	0.391665i
$565$		0			0
$566$		−	7.71000i		−	0.324076i
$567$	−10.9397	−	3.50878i	−0.459423	−	0.147355i
$568$	−5.74013	+	5.74013i	−0.240850	+	0.240850i
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.971209	−	0.238229i	$-0.923433\pi$
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.279292	+	0.960206i	$0.590100\pi$
$570$		0			0
$571$	4.11985	−	7.13579i	0.172410	−	0.298623i	−0.766852	−	0.641824i	$-0.778178\pi$
$571$	4.11985	−	7.13579i	0.172410	−	0.298623i	0.939262	+	0.343201i	$0.111511\pi$
$572$	−4.16524	−	1.11607i	−0.174158	−	0.0466654i
$573$	−31.8645	−	31.8645i	−1.33116	−	1.33116i
$574$	1.15364	−	23.7315i	0.0481520	−	0.990534i
$575$		0			0
$576$	−2.72435	−	4.71872i	−0.113515	−	0.196613i
$577$	0.910086	+	3.39649i	0.0378874	+	0.141398i	0.982279	−	0.187426i	$-0.0600145\pi$
$577$	0.910086	+	3.39649i	0.0378874	+	0.141398i	−0.944391	+	0.328824i	$0.893348\pi$
$578$	−4.23908	−	15.8204i	−0.176322	−	0.658044i
$579$	−13.0770	−	22.6500i	−0.543460	−	0.941301i
$580$		0			0
$581$	19.7132	−	30.6088i	0.817843	−	1.26987i
$582$	−9.20520	−	9.20520i	−0.381568	−	0.381568i
$583$	28.0627	+	7.51937i	1.16224	+	0.311421i
$584$	4.93262	−	8.54355i	0.204113	−	0.353535i
$585$		0			0
$586$	−4.10531	+	2.37020i	−0.169589	+	0.0979122i
$587$	5.37485	−	5.37485i	0.221844	−	0.221844i	−0.587431	−	0.809275i	$-0.699861\pi$
$587$	5.37485	−	5.37485i	0.221844	−	0.221844i	0.809275	+	0.587431i	$0.199861\pi$
$588$	20.0715	−	3.33499i	0.827734	−	0.137533i
$589$			0.0909162i			0.00374613i
$590$		0			0
$591$	−43.4136	−	25.0649i	−1.78580	−	1.03103i
$592$	−0.248174	+	0.0664979i	−0.0101999	+	0.00273305i
$593$	−0.190155	+	0.709668i	−0.00780872	+	0.0291426i	−0.969720	−	0.244218i	$-0.921469\pi$
$593$	−0.190155	+	0.709668i	−0.00780872	+	0.0291426i	0.961912	+	0.273361i	$0.0881353\pi$
$594$	26.1296			1.07211
$595$		0			0
$596$	−4.84185			−0.198330
$597$	6.56845	−	24.5138i	0.268829	−	1.00328i
$598$	−5.33897	+	1.43057i	−0.218327	+	0.0585005i
$599$	7.23778	+	4.17873i	0.295727	+	0.170738i	0.640522	−	0.767940i	$-0.278718\pi$
$599$	7.23778	+	4.17873i	0.295727	+	0.170738i	−0.344794	+	0.938678i	$0.612051\pi$
$600$		0			0
$601$			39.9236i			1.62852i	0.580501	+	0.814259i	$0.302857\pi$
$601$			39.9236i			1.62852i	−0.580501	+	0.814259i	$0.697143\pi$
$602$	−1.31508	+	1.19315i	−0.0535985	+	0.0486290i
$603$	−25.5147	+	25.5147i	−1.03904	+	1.03904i
$604$	8.69995	−	5.02292i	0.353996	−	0.204380i
$605$		0			0
$606$	−0.104505	+	0.181008i	−0.00424523	+	0.00735295i
$607$	−33.2758	−	8.91623i	−1.35062	−	0.361899i	−0.490259	−	0.871577i	$-0.663098\pi$
$607$	−33.2758	−	8.91623i	−1.35062	−	0.361899i	−0.860365	+	0.509678i	$0.829765\pi$
$608$	1.54802	+	1.54802i	0.0627804	+	0.0627804i
$609$	17.9339	−	9.22349i	0.726720	−	0.373755i
$610$		0			0
$611$	3.75885	+	6.51051i	0.152067	+	0.263387i
$612$	−1.11173	−	4.14903i	−0.0449390	−	0.167715i
$613$	8.46832	+	31.6042i	0.342032	+	1.27648i	0.896041	+	0.443971i	$0.146431\pi$
$613$	8.46832	+	31.6042i	0.342032	+	1.27648i	−0.554009	+	0.832510i	$0.686903\pi$
$614$	−0.753393	−	1.30491i	−0.0304044	−	0.0526620i
$615$		0			0
$616$	−8.63753	+	4.44231i	−0.348016	+	0.178986i
$617$	15.5005	+	15.5005i	0.624025	+	0.624025i	0.946558	−	0.322533i	$-0.104534\pi$
$617$	15.5005	+	15.5005i	0.624025	+	0.624025i	−0.322533	+	0.946558i	$0.604534\pi$
$618$	−46.5497	−	12.4730i	−1.87250	−	0.501736i
$619$	4.31138	−	7.46752i	0.173289	−	0.300145i	−0.766279	−	0.642508i	$-0.777894\pi$
$619$	4.31138	−	7.46752i	0.173289	−	0.300145i	0.939568	+	0.342363i	$0.111227\pi$
$620$		0			0
$621$	29.0055	−	16.7463i	1.16395	−	0.672008i
$622$	9.76397	−	9.76397i	0.391500	−	0.391500i
$623$	2.80254	−	2.54269i	0.112281	−	0.101871i
$624$		−	3.41421i		−	0.136678i
$625$		0			0
$626$	20.2191	+	11.6735i	0.808119	+	0.466568i
$627$	−22.5648	+	6.04621i	−0.901150	+	0.241462i
$628$	−6.33762	+	23.6523i	−0.252898	+	0.943830i
$629$	−0.202545			−0.00807600
$630$		0			0
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	3.47109	−	12.9543i	0.138073	−	0.515294i
$633$	−31.3739	+	8.40662i	−1.24700	+	0.334133i
$634$	11.4219	+	6.59442i	0.453620	+	0.261898i
$635$		0			0
$636$			23.0027i			0.912117i
$637$	7.69827	+	2.88840i	0.305017	+	0.114443i
$638$	−6.80736	+	6.80736i	−0.269506	+	0.269506i
$639$	38.3055	−	22.1157i	1.51534	−	0.874882i
$640$		0			0
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	−0.953086	−	0.302701i	$-0.902112\pi$
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	0.738690	+	0.674046i	$0.235445\pi$
$642$	12.8292	+	3.43757i	0.506328	+	0.135670i
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	0.847978	−	0.530032i	$-0.177820\pi$
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	−0.530032	+	0.847978i	$0.677820\pi$
$644$	−6.74114	+	10.4670i	−0.265638	+	0.412457i
$645$		0			0
$646$	0.862920	+	1.49462i	0.0339511	+	0.0588051i
$647$	2.69865	+	10.0715i	0.106095	+	0.395951i	0.998467	−	0.0553490i	$-0.0176271\pi$
$647$	2.69865	+	10.0715i	0.106095	+	0.395951i	−0.892372	+	0.451300i	$0.850960\pi$
$648$	1.12387	+	4.19432i	0.0441496	+	0.164769i
$649$	19.6632	+	34.0577i	0.771848	+	1.33688i
$650$		0			0
$651$	0.0155070	−	0.318994i	0.000607766	−	0.0125023i
$652$	15.5320	+	15.5320i	0.608279	+	0.608279i
$653$	−6.41946	−	1.72009i	−0.251213	−	0.0673123i	0.131015	−	0.991380i	$-0.458176\pi$
$653$	−6.41946	−	1.72009i	−0.251213	−	0.0673123i	−0.382228	+	0.924068i	$0.624843\pi$
$654$	−26.3091	+	45.5687i	−1.02877	+	1.78188i
$655$		0			0
$656$	−7.77713	+	4.49013i	−0.303646	+	0.175310i
$657$	−38.0090	+	38.0090i	−1.48287	+	1.48287i
$658$	16.1241	+	5.17163i	0.628582	+	0.201611i
$659$		−	22.0345i		−	0.858343i	−0.903223	−	0.429172i	$-0.858806\pi$
$659$		−	22.0345i		−	0.858343i	0.903223	−	0.429172i	$-0.141194\pi$
$660$		0			0
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	0.294013	−	0.955802i	$-0.405009\pi$
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	−0.680742	+	0.732523i	$0.738343\pi$
$662$	18.4453	−	4.94240i	0.716897	−	0.192092i
$663$	0.696621	−	2.59983i	0.0270545	−	0.100969i
$664$	−13.7608			−0.534021
$665$		0			0
$666$	1.39993			0.0542460
$667$	−3.19379	+	11.9194i	−0.123664	+	0.461521i
$668$	−4.29774	+	1.15158i	−0.166285	+	0.0445558i
$669$	−2.65857	−	1.53492i	−0.102786	−	0.0593436i
$670$		0			0
$671$			7.31407i			0.282356i
$672$	−5.16742	−	5.69550i	−0.199338	−	0.219708i
$673$	15.2073	−	15.2073i	0.586198	−	0.586198i	−0.350402	−	0.936600i	$-0.613955\pi$
$673$	15.2073	−	15.2073i	0.586198	−	0.586198i	0.936600	+	0.350402i	$0.113955\pi$
$674$	−0.597952	+	0.345228i	−0.0230322	+	0.0132977i
$675$		0			0
$676$	−5.81014	+	10.0635i	−0.223467	+	0.387056i
$677$	5.54296	+	1.48523i	0.213033	+	0.0570821i	0.363757	−	0.931494i	$-0.381494\pi$
$677$	5.54296	+	1.48523i	0.213033	+	0.0570821i	−0.150724	+	0.988576i	$0.548160\pi$
$678$	4.41998	+	4.41998i	0.169748	+	0.169748i
$679$	−9.96224	−	6.41606i	−0.382316	−	0.246226i
$680$		0			0
$681$	4.53492	+	7.85472i	0.173779	+	0.300993i
$682$	0.0394591	+	0.147264i	0.00151097	+	0.00563901i
$683$	−5.02900	−	18.7685i	−0.192430	−	0.718157i	−0.992917	−	0.118808i	$-0.962093\pi$
$683$	−5.02900	−	18.7685i	−0.192430	−	0.718157i	0.800488	−	0.599349i	$-0.204574\pi$
$684$	−5.96423	−	10.3303i	−0.228048	−	0.394991i
$685$		0			0
$686$	17.2137	−	6.83301i	0.657220	−	0.260886i
$687$	17.3095	+	17.3095i	0.660400	+	0.660400i
$688$	0.648273	+	0.173704i	0.0247152	+	0.00662241i
$689$	−4.64782	+	8.05027i	−0.177068	+	0.306691i
$690$		0			0
$691$	19.0914	−	11.0224i	0.726270	−	0.419312i	−0.0907861	−	0.995870i	$-0.528938\pi$
$691$	19.0914	−	11.0224i	0.726270	−	0.419312i	0.817056	+	0.576558i	$0.195605\pi$
$692$	−3.69572	+	3.69572i	−0.140490	+	0.140490i
$693$	51.7244	−	11.1992i	1.96485	−	0.425422i
$694$		−	3.80998i		−	0.144625i
$695$		0			0
$696$	−6.60113	−	3.81116i	−0.250215	−	0.144462i
$697$	−6.83821	+	1.83229i	−0.259016	+	0.0694031i
$698$	−2.04804	+	7.64340i	−0.0775196	+	0.289307i
$699$	−66.2630			−2.50630
$700$		0			0
$701$	−18.0270			−0.680870			−0.340435	−	0.940268i	$-0.610574\pi$
$701$	−18.0270			−0.680870			−0.340435	+	0.940268i	$0.610574\pi$
$702$	−2.16383	+	8.07553i	−0.0816686	+	0.304791i
$703$	−0.543308	+	0.145579i	−0.0204913	+	0.00549062i
$704$	3.17930	+	1.83557i	0.119824	+	0.0691807i
$705$		0			0
$706$		−	25.7787i		−	0.970196i
$707$	−0.0581046	+	0.181158i	−0.00218525	+	0.00681316i
$708$	−22.0173	+	22.0173i	−0.827459	+	0.827459i
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.993522	−	0.113637i	$-0.963750\pi$
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.398349	+	0.917234i	$0.630417\pi$
$710$		0			0
$711$	−36.5370	+	63.2840i	−1.37025	+	2.37334i
$712$	−1.38152	−	0.370178i	−0.0517748	−	0.0138730i
$713$	0.138183	+	0.138183i	0.00517498	+	0.00517498i
$714$	−2.77276	−	5.39130i	−0.103768	−	0.201764i
$715$		0			0
$716$	−6.28428	−	10.8847i	−0.234854	−	0.406780i
$717$	18.0530	+	67.3747i	0.674202	+	2.51615i
$718$	−2.68822	−	10.0326i	−0.100324	−	0.374413i
$719$	−2.72691	−	4.72315i	−0.101697	−	0.176144i	0.810687	−	0.585480i	$-0.199094\pi$
$719$	−2.72691	−	4.72315i	−0.101697	−	0.176144i	−0.912384	+	0.409336i	$0.865760\pi$
$720$		0			0
$721$	−43.8142	−	2.12990i	−1.63172	−	0.0793217i
$722$	−10.0461	−	10.0461i	−0.373876	−	0.373876i
$723$	−69.5938	−	18.6476i	−2.58822	−	0.693512i
$724$	−5.83712	+	10.1102i	−0.216935	+	0.375742i
$725$		0			0
$726$	−6.23593	+	3.60031i	−0.231437	+	0.133620i
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	−0.945161	−	0.326606i	$-0.894095\pi$
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	0.326606	+	0.945161i	$0.394095\pi$
$728$	−0.657639	−	3.03736i	−0.0243737	−	0.112572i
$729$			38.4054i			1.42242i
$730$		0			0
$731$	0.458200	+	0.264542i	0.0169471	+	0.00978443i
$732$	−5.59367	+	1.49882i	−0.206748	+	0.0553979i
$733$	8.79960	−	32.8405i	0.325021	−	1.21299i	−0.589271	−	0.807936i	$-0.700585\pi$
$733$	8.79960	−	32.8405i	0.325021	−	1.21299i	0.914291	−	0.405057i	$-0.132748\pi$
$734$	8.68601			0.320607
$735$		0			0
$736$	4.70563			0.173452
$737$	6.29231	−	23.4832i	0.231780	−	0.865016i
$738$	47.2635	−	12.6642i	1.73979	−	0.466177i
$739$	25.0733	+	14.4761i	0.922335	+	0.532510i	0.884379	−	0.466769i	$-0.154582\pi$
$739$	25.0733	+	14.4761i	0.922335	+	0.532510i	0.0379557	+	0.999279i	$0.487915\pi$
$740$		0			0
$741$		−	7.47449i		−	0.274582i
$742$	4.43074	+	20.4637i	0.162658	+	0.751247i
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.292300	+	0.956327i	$0.594421\pi$
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.956327	+	0.292300i	$0.905579\pi$
$744$	−0.104538	+	0.0603553i	−0.00383257	+	0.00221273i
$745$		0			0
$746$	6.65477	−	11.5264i	0.243649	−	0.422012i
$747$	72.4235	+	19.4058i	2.64984	+	0.710022i
$748$	2.04643	+	2.04643i	0.0748247	+	0.0748247i
$749$	12.0753	+	0.587006i	0.441221	+	0.0214487i
$750$		0			0
$751$	9.30569	+	16.1179i	0.339569	+	0.588151i	0.984352	−	0.176215i	$-0.0563853\pi$
$751$	9.30569	+	16.1179i	0.339569	+	0.588151i	−0.644782	+	0.764366i	$0.723052\pi$
$752$	−1.65648	−	6.18205i	−0.0604055	−	0.225436i
$753$	8.36242	+	31.2090i	0.304743	+	1.13732i
$754$	−1.54013	−	2.66759i	−0.0560883	−	0.0971478i
$755$		0			0
$756$	8.61270	+	16.7463i	0.313241	+	0.609059i
$757$	−29.7422	−	29.7422i	−1.08100	−	1.08100i	−0.996416	−	0.0845825i	$-0.973044\pi$
$757$	−29.7422	−	29.7422i	−1.08100	−	1.08100i	−0.0845825	−	0.996416i	$-0.526956\pi$
$758$	−24.4816	−	6.55984i	−0.889213	−	0.238264i
$759$	−25.1064	+	43.4856i	−0.911305	+	1.57843i
$760$		0			0
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	−0.144788	−	0.989463i	$-0.546250\pi$
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	0.784506	+	0.620122i	$0.212917\pi$
$762$	38.5213	−	38.5213i	1.39548	−	1.39548i
$763$	−14.6278	+	45.6066i	−0.529563	+	1.65107i
$764$			15.5034i			0.560894i
$765$		0			0
$766$	15.9357	+	9.20046i	0.575779	+	0.332426i
$767$	−12.1541	+	3.25668i	−0.438859	+	0.117592i
$768$	−0.752300	+	2.80762i	−0.0271463	+	0.101311i
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$		0			0
$771$	73.5189			2.64772
$772$	−2.32883	+	8.69132i	−0.0838165	+	0.312808i
$773$	−23.8577	+	6.39265i	−0.858101	+	0.229928i	−0.660936	−	0.750443i	$-0.729840\pi$
$773$	−23.8577	+	6.39265i	−0.858101	+	0.229928i	−0.197166	+	0.980370i	$0.563174\pi$
$774$	−3.16693	−	1.82843i	−0.113833	−	0.0657215i
$775$		0			0
$776$			4.47871i			0.160776i
$777$	1.93111	−	0.418118i	0.0692783	−	0.0149999i
$778$	−15.8091	+	15.8091i	−0.566784	+	0.566784i
$779$	−17.0259	+	9.82991i	−0.610017	+	0.352193i
$780$		0			0
$781$	−14.9007	+	25.8088i	−0.533190	+	0.923513i
$782$	3.58321	+	0.960117i	0.128135	+	0.0343337i
$783$	13.1980	+	13.1980i	0.471659	+	0.471659i
$784$	−5.69411	−	4.07150i	−0.203361	−	0.145411i
$785$		0			0
$786$	−20.6295	−	35.7314i	−0.735831	−	1.27450i
$787$	−2.12442	−	7.92843i	−0.0757273	−	0.282618i	0.917670	−	0.397343i	$-0.130068\pi$
$787$	−2.12442	−	7.92843i	−0.0757273	−	0.282618i	−0.993397	+	0.114725i	$0.963401\pi$
$788$	4.46372	+	16.6588i	0.159013	+	0.593446i
$789$	−16.4897	−	28.5610i	−0.587048	−	1.01680i
$790$		0			0
$791$	4.78348	+	3.08075i	0.170081	+	0.109539i
$792$	−14.1442	−	14.1442i	−0.502594	−	0.502594i
$793$	−2.26046	−	0.605689i	−0.0802713	−	0.0215086i
$794$	7.89197	−	13.6693i	0.280076	−	0.485105i
$795$		0			0
$796$	−7.56140	+	4.36557i	−0.268007	+	0.154734i
$797$	−11.7928	+	11.7928i	−0.417722	+	0.417722i	−0.884418	−	0.466696i	$-0.845444\pi$
$797$	−11.7928	+	11.7928i	−0.417722	+	0.417722i	0.466696	+	0.884418i	$0.345444\pi$
$798$	−11.3127	−	12.4687i	−0.400464	−	0.441388i
$799$		−	5.04544i		−	0.178495i
$800$		0			0
$801$	6.74899	+	3.89653i	0.238464	+	0.137677i
$802$	−13.4945	+	3.61585i	−0.476508	+	0.127680i
$803$	9.37358	−	34.9827i	0.330786	−	1.23451i
$804$	19.2490			0.678860
$805$		0			0
$806$	−0.0487805			−0.00171822
$807$	−6.06875	+	22.6489i	−0.213630	+	0.797278i
$808$	0.0694570	−	0.0186109i	0.00244349	−	0.000654730i
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.101855	−	0.994799i	$-0.532478\pi$
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.912449	+	0.409191i	$0.865811\pi$
$810$		0			0
$811$		−	55.2368i		−	1.93963i	−0.243850	−	0.969813i	$-0.578410\pi$
$811$		−	55.2368i		−	1.93963i	0.243850	−	0.969813i	$-0.421590\pi$
$812$	−6.60661	−	2.11900i	−0.231847	−	0.0743623i
$813$	17.2637	−	17.2637i	0.605465	−	0.605465i
$814$	−0.816852	+	0.471610i	−0.0286307	+	0.0165299i
$815$		0			0
$816$	−1.14571	+	1.98443i	−0.0401079	+	0.0694689i
$817$	1.41922	+	0.380278i	0.0496521	+	0.0133042i
$818$	0.221580	+	0.221580i	0.00774737	+	0.00774737i
$819$	−0.822187	+	16.9132i	−0.0287295	+	0.590995i
$820$		0			0
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	0.656448	−	0.754371i	$-0.272058\pi$
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	−0.981529	+	0.191315i	$0.938725\pi$
$822$	14.2684	+	53.2505i	0.497669	+	1.85732i
$823$	4.37130	+	16.3139i	0.152374	+	0.568668i	0.999316	+	0.0369821i	$0.0117745\pi$
$823$	4.37130	+	16.3139i	0.152374	+	0.568668i	−0.846942	+	0.531685i	$0.821559\pi$
$824$	8.28988	+	14.3585i	0.288792	+	0.500202i
$825$		0			0
$826$	−15.3461	+	23.8280i	−0.533960	+	0.829081i
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	0.798143	−	0.602468i	$-0.205816\pi$
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	−0.602468	+	0.798143i	$0.705816\pi$
$828$	−24.7660	−	6.63602i	−0.860677	−	0.230618i
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	−0.803062	−	0.595895i	$-0.796797\pi$
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	0.917591	+	0.397525i	$0.130131\pi$
$830$		0			0
$831$	14.2980	−	8.25494i	0.495991	−	0.286361i
$832$	−0.830578	+	0.830578i	−0.0287951	+	0.0287951i
$833$	−3.50517	−	4.26213i	−0.121447	−	0.147674i
$834$		−	23.9424i		−	0.829057i
$835$		0			0
$836$	6.96021	+	4.01848i	0.240724	+	0.138982i
$837$	0.285513	−	0.0765030i	0.00986877	−	0.00264433i
$838$	8.18525	−	30.5478i	0.282755	−	1.05526i
$839$	46.0930			1.59131			0.795654	−	0.605752i	$-0.207128\pi$
$839$	46.0930			1.59131			0.795654	+	0.605752i	$0.207128\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$	6.26698	−	23.3887i	0.215974	−	0.806027i
$843$	20.4290	−	5.47394i	0.703613	−	0.188533i
$844$	9.67744	+	5.58727i	0.333111	+	0.192322i
$845$		0			0
$846$			34.8724i			1.19894i
$847$	−4.85413	+	4.40407i	−0.166790	+	0.151326i
$848$	5.59589	−	5.59589i	0.192164	−	0.192164i
$849$	19.4080	−	11.2052i	0.666080	−	0.384562i
$850$		0			0
$851$	−0.604505	+	1.04703i	−0.0207222	+	0.0358918i
$852$	−22.7916	−	6.10700i	−0.780828	−	0.209222i
$853$	−14.9594	−	14.9594i	−0.512200	−	0.512200i	0.403000	−	0.915200i	$-0.367968\pi$
$853$	−14.9594	−	14.9594i	−0.512200	−	0.512200i	−0.915200	+	0.403000i	$0.867968\pi$
$854$	−4.68755	+	2.41082i	−0.160405	+	0.0824967i
$855$		0			0
$856$	−2.28471	−	3.95723i	−0.0780897	−	0.135255i
$857$	−3.12136	−	11.6491i	−0.106623	−	0.397924i	0.891901	−	0.452231i	$-0.149372\pi$
$857$	−3.12136	−	11.6491i	−0.106623	−	0.397924i	−0.998524	+	0.0543068i	$0.982705\pi$
$858$	−3.24405	−	12.1070i	−0.110750	−	0.413325i
$859$	−2.90061	−	5.02401i	−0.0989677	−	0.171417i	0.812290	−	0.583254i	$-0.198221\pi$
$859$	−2.90061	−	5.02401i	−0.0989677	−	0.171417i	−0.911258	+	0.411837i	$0.864887\pi$
$860$		0			0
$861$	61.4147	−	31.5858i	2.09301	−	1.07644i
$862$	1.10172	+	1.10172i	0.0375249	+	0.0375249i
$863$	−2.90586	−	0.778623i	−0.0989167	−	0.0265046i	0.209021	−	0.977911i	$-0.432972\pi$
$863$	−2.90586	−	0.778623i	−0.0989167	−	0.0265046i	−0.307938	+	0.951406i	$0.599639\pi$
$864$	3.55879	−	6.16400i	0.121072	−	0.209703i
$865$		0			0
$866$	−7.69343	+	4.44180i	−0.261433	+	0.150939i
$867$	33.6632	−	33.6632i	1.14326	−	1.14326i
$868$	−0.0813742	+	0.0738294i	−0.00276202	+	0.00250593i
$869$		−	49.2347i		−	1.67017i
$870$		0			0
$871$	6.73657	+	3.88936i	0.228260	+	0.131786i
$872$	17.4858	−	4.68530i	0.592143	−	0.158664i
$873$	6.31601	−	23.5717i	0.213765	−	0.797780i
$874$	10.3017			0.348460
$875$		0			0
$876$	28.6750			0.968838
$877$	−9.07228	+	33.8582i	−0.306349	+	1.14331i	0.625428	+	0.780282i	$0.284924\pi$
$877$	−9.07228	+	33.8582i	−0.306349	+	1.14331i	−0.931778	+	0.363030i	$0.881742\pi$
$878$	23.0994	−	6.18945i	0.779565	−	0.208884i
$879$	−11.9328	−	6.88939i	−0.402483	−	0.232373i
$880$		0			0
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$	24.2266	+	29.4585i	0.815753	+	0.991919i
$883$	7.95370	−	7.95370i	0.267663	−	0.267663i	−0.560495	−	0.828158i	$-0.689389\pi$
$883$	7.95370	−	7.95370i	0.267663	−	0.267663i	0.828158	+	0.560495i	$0.189389\pi$
$884$	−0.801929	+	0.462994i	−0.0269718	+	0.0155722i
$885$		0			0
$886$	6.43103	−	11.1389i	0.216055	−	0.374218i
$887$	19.6954	+	5.27738i	0.661308	+	0.177197i	0.573836	−	0.818970i	$-0.305455\pi$
$887$	19.6954	+	5.27738i	0.661308	+	0.177197i	0.0874718	+	0.996167i	$0.472121\pi$
$888$	−0.528070	−	0.528070i	−0.0177209	−	0.0177209i
$889$	26.8495	−	41.6893i	0.900503	−	1.39821i
$890$		0			0
$891$	7.97057	+	13.8054i	0.267024	+	0.462499i
$892$	0.273349	+	1.02015i	0.00915241	+	0.0341573i
$893$	−3.62640	−	13.5339i	−0.121353	−	0.452895i
$894$	−7.03682	−	12.1881i	−0.235347	−	0.407632i
$895$		0			0
$896$	−0.128464	+	2.64263i	−0.00429168	+	0.0882841i
$897$	−11.3604	−	11.3604i	−0.379313	−	0.379313i
$898$	17.2836	+	4.63111i	0.576760	+	0.154542i
$899$	−0.0544519	+	0.0943134i	−0.00181607	+	0.00314553i
$900$		0			0
$901$	5.40287	−	3.11935i	0.179996	−	0.103921i
$902$	−23.3118	+	23.3118i	−0.776197	+	0.776197i
$903$	−4.91468	−	1.57633i	−0.163550	−	0.0524570i
$904$		−	2.15051i		−	0.0715247i
$905$		0			0
$906$	25.2878	+	14.5999i	0.840132	+	0.485051i
$907$	−6.29276	+	1.68614i	−0.208948	+	0.0559874i	−0.361775	−	0.932266i	$-0.617829\pi$
$907$	−6.29276	+	1.68614i	−0.208948	+	0.0559874i	0.152827	+	0.988253i	$0.451162\pi$
$908$	0.807609	−	3.01404i	0.0268014	−	0.100024i
$909$	−0.391801			−0.0129952
$910$		0			0
$911$	−24.2528			−0.803531			−0.401765	−	0.915743i	$-0.631603\pi$
$911$	−24.2528			−0.803531			−0.401765	+	0.915743i	$0.631603\pi$
$912$	−1.64696	+	6.14653i	−0.0545362	+	0.203532i
$913$	−48.7964	+	13.0749i	−1.61492	+	0.432718i
$914$	29.6277	+	17.1056i	0.979997	+	0.565802i
$915$		0			0
$916$		−	8.42181i		−	0.278264i
$917$	−25.2350	−	27.8138i	−0.833333	−	0.918493i
$918$	3.96759	−	3.96759i	0.130950	−	0.130950i
$919$	−31.2542	+	18.0446i	−1.03098	+	0.595236i	−0.917265	−	0.398277i	$-0.869608\pi$
$919$	−31.2542	+	18.0446i	−1.03098	+	0.595236i	−0.113714	+	0.993513i	$0.536275\pi$
$920$		0			0
$921$	2.18986	−	3.79295i	0.0721583	−	0.124982i
$922$	−22.5515	−	6.04266i	−0.742695	−	0.199004i
$923$	−6.74244	−	6.74244i	−0.221930	−	0.221930i
$924$	−23.7356	−	15.2866i	−0.780844	−	0.502893i
$925$		0			0
$926$	2.81789	+	4.88073i	0.0926017	+	0.160391i
$927$	−23.3813	−	87.2600i	−0.767941	−	2.86600i
$928$	0.678717	+	2.53301i	0.0222800	+	0.0831500i
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	−0.969949	−	0.243307i	$-0.921768\pi$
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	0.274264	−	0.961654i	$-0.411566\pi$
$930$		0			0
$931$	−12.4657	−	8.91344i	−0.408547	−	0.292126i
$932$	16.1198	+	16.1198i	0.528023	+	0.528023i
$933$	38.7686	+	10.3880i	1.26923	+	0.340089i
$934$	2.44290	−	4.23123i	0.0799342	−	0.138450i
$935$		0			0
$936$	5.54268	−	3.20007i	0.181168	−	0.104597i
$937$	−4.06709	+	4.06709i	−0.132866	+	0.132866i	−0.770412	−	0.637546i	$-0.779950\pi$
$937$	−4.06709	+	4.06709i	−0.132866	+	0.132866i	0.637546	+	0.770412i	$0.279950\pi$
$938$	17.1243	−	3.70770i	0.559129	−	0.121061i
$939$			67.8621i			2.21460i
$940$		0			0
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	0.188677	−	0.982039i	$-0.439580\pi$
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	−0.756132	+	0.654419i	$0.772913\pi$
$942$	−68.7494	+	18.4213i	−2.23998	+	0.600200i
$943$	−10.9371	+	40.8179i	−0.356162	+	1.32921i
$944$	10.7123			0.348656
$945$		0			0
$946$	2.46386			0.0801069
$947$	15.2583	−	56.9449i	0.495830	−	1.85046i	−0.0295030	−	0.999565i	$-0.509392\pi$
$947$	15.2583	−	56.9449i	0.495830	−	1.85046i	0.525333	−	0.850897i	$-0.323941\pi$
$948$	37.6538	−	10.0893i	1.22294	−	0.327685i
$949$	10.0354	+	5.79393i	0.325762	+	0.188079i
$950$		0			0
$951$			38.3355i			1.24311i
$952$	−0.637013	+	1.98608i	−0.0206457	+	0.0643691i
$953$	31.1044	−	31.1044i	1.00757	−	1.00757i	0.00759828	−	0.999971i	$-0.497581\pi$
$953$	31.1044	−	31.1044i	1.00757	−	1.00757i	0.999971	−	0.00759828i	$-0.00241863\pi$
$954$	−37.3429	+	21.5599i	−1.20902	+	0.698029i
$955$		0			0
$956$	11.9985	−	20.7821i	0.388060	−	0.672140i
$957$	−27.0292	−	7.24244i	−0.873729	−	0.234115i
$958$	12.0996	+	12.0996i	0.390921	+	0.390921i
$959$	22.9505	+	44.6245i	0.741111	+	1.44100i
$960$		0			0
$961$	−15.4991	−	26.8453i	−0.499972	−	0.865977i
$962$	−0.0781094	−	0.291508i	−0.00251835	−	0.00939861i
$963$	6.44392	+	24.0491i	0.207653	+	0.774970i
$964$	12.3937	+	21.4666i	0.399175	+	0.691391i
$965$		0			0
$966$	−36.1451	−	1.75709i	−1.16295	−	0.0565336i
$967$	21.5036	+	21.5036i	0.691510	+	0.691510i	0.962564	−	0.271054i	$-0.0873721\pi$
$967$	21.5036	+	21.5036i	0.691510	+	0.691510i	−0.271054	+	0.962564i	$0.587372\pi$
$968$	2.39287	+	0.641168i	0.0769098	+	0.0206079i
$969$	−2.50822	+	4.34437i	−0.0805756	+	0.139561i
$970$		0			0
$971$	−45.3034	+	26.1559i	−1.45385	+	0.839384i	−0.998697	−	0.0510273i	$-0.983750\pi$
$971$	−45.3034	+	26.1559i	−1.45385	+	0.839384i	−0.455158	+	0.890411i	$0.650417\pi$
$972$	6.17385	−	6.17385i	0.198026	−	0.198026i
$973$	−4.61174	−	21.2997i	−0.147845	−	0.682836i
$974$		−	0.130300i		−	0.00417507i
$975$		0			0
$976$	1.72539	+	0.996157i	0.0552285	+	0.0318862i
$977$	54.6658	−	14.6477i	1.74891	−	0.468620i	0.764520	−	0.644599i	$-0.222976\pi$
$977$	54.6658	−	14.6477i	1.74891	−	0.468620i	0.984394	+	0.175979i	$0.0563092\pi$
$978$	−16.5247	+	61.6710i	−0.528401	+	1.97202i
$979$	−5.25068			−0.167813
$980$		0			0
$981$	−98.6358			−3.14920
$982$	6.98541	−	26.0699i	0.222913	−	0.831924i
$983$	−14.9514	+	4.00621i	−0.476875	+	0.127778i	−0.489247	−	0.872145i	$-0.662728\pi$
$983$	−14.9514	+	4.00621i	−0.476875	+	0.127778i	0.0123723	+	0.999923i	$0.496062\pi$
$984$	−22.6055	−	13.0513i	−0.720638	−	0.416061i
$985$		0			0
$986$			2.06729i			0.0658361i
$987$	10.4154	+	48.1044i	0.331526	+	1.53118i
$988$	−1.81832	+	1.81832i	−0.0578486	+	0.0578486i
$989$	2.73504	−	1.57907i	0.0869691	−	0.0502116i
$990$		0			0
$991$	26.8648	−	46.5311i	0.853388	−	1.47811i	−0.0247453	−	0.999694i	$-0.507877\pi$
$991$	26.8648	−	46.5311i	0.853388	−	1.47811i	0.878133	−	0.478417i	$-0.158789\pi$
$992$	0.0401138	+	0.0107485i	0.00127362	+	0.000341264i
$993$	39.2484	+	39.2484i	1.24551	+	1.24551i
$994$	−21.4523	−	1.04284i	−0.680424	−	0.0330769i
$995$		0			0
$996$	−19.9990	−	34.6392i	−0.633692	−	1.09759i
$997$	−9.97217	−	37.2167i	−0.315822	−	1.17866i	−0.923222	−	0.384267i	$-0.874454\pi$
$997$	−9.97217	−	37.2167i	−0.315822	−	1.17866i	0.607400	−	0.794396i	$-0.292213\pi$
$998$	0.0249241	+	0.0930180i	0.000788959	+	0.00294443i
$999$	0.914352	+	1.58370i	0.0289288	+	0.0501062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.c.157.4		16
5.2	odd	4		70.2.k.a.3.3	✓	16
5.3	odd	4	inner	350.2.o.c.143.2		16
5.4	even	2		70.2.k.a.17.1	yes	16
7.5	odd	6	inner	350.2.o.c.257.2		16
15.2	even	4		630.2.bv.c.73.1		16
15.14	odd	2		630.2.bv.c.577.4		16
20.7	even	4		560.2.ci.c.353.4		16
20.19	odd	2		560.2.ci.c.17.4		16
35.2	odd	12		490.2.l.c.313.2		16
35.4	even	6		490.2.g.c.97.4		16
35.9	even	6		490.2.l.c.117.4		16
35.12	even	12		70.2.k.a.33.1	yes	16
35.17	even	12		490.2.g.c.293.4		16
35.19	odd	6		70.2.k.a.47.3	yes	16
35.24	odd	6		490.2.g.c.97.1		16
35.27	even	4		490.2.l.c.423.4		16
35.32	odd	12		490.2.g.c.293.1		16
35.33	even	12	inner	350.2.o.c.243.4		16
35.34	odd	2		490.2.l.c.227.2		16
105.47	odd	12		630.2.bv.c.523.4		16
105.89	even	6		630.2.bv.c.397.1		16
140.19	even	6		560.2.ci.c.257.4		16
140.47	odd	12		560.2.ci.c.33.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	5.2	odd	4
70.2.k.a.17.1	yes	16	5.4	even	2
70.2.k.a.33.1	yes	16	35.12	even	12
70.2.k.a.47.3	yes	16	35.19	odd	6
350.2.o.c.143.2		16	5.3	odd	4	inner
350.2.o.c.157.4		16	1.1	even	1	trivial
350.2.o.c.243.4		16	35.33	even	12	inner
350.2.o.c.257.2		16	7.5	odd	6	inner
490.2.g.c.97.1		16	35.24	odd	6
490.2.g.c.97.4		16	35.4	even	6
490.2.g.c.293.1		16	35.32	odd	12
490.2.g.c.293.4		16	35.17	even	12
490.2.l.c.117.4		16	35.9	even	6
490.2.l.c.227.2		16	35.34	odd	2
490.2.l.c.313.2		16	35.2	odd	12
490.2.l.c.423.4		16	35.27	even	4
560.2.ci.c.17.4		16	20.19	odd	2
560.2.ci.c.33.4		16	140.47	odd	12
560.2.ci.c.257.4		16	140.19	even	6
560.2.ci.c.353.4		16	20.7	even	4
630.2.bv.c.73.1		16	15.2	even	4
630.2.bv.c.397.1		16	105.89	even	6
630.2.bv.c.523.4		16	105.47	odd	12
630.2.bv.c.577.4		16	15.14	odd	2

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(2.80762 - 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} -2.90667i q^{6} +(-0.559876 - 2.58583i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(2.80762 - 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} -2.90667i q^{6} +(-0.559876 - 2.58583i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +(-1.83557 + 3.17930i) q^{11} +(-2.80762 - 0.752300i) q^{12} +(-0.830578 - 0.830578i) q^{13} +(-2.64263 - 0.128464i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.204036 + 0.761471i) q^{17} +(-1.41023 - 5.26305i) q^{18} +(1.09461 + 1.89593i) q^{19} +(-3.51725 - 6.83885i) q^{21} +(2.59589 + 2.59589i) q^{22} +(4.54529 + 1.21791i) q^{23} +(-1.45333 + 2.51725i) q^{24} +(-1.01725 + 0.587308i) q^{26} +(5.03288 - 5.03288i) q^{27} +(-0.808050 + 2.51934i) q^{28} +2.62236i q^{29} +(0.0359651 + 0.0207644i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.76180 + 10.3072i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(-0.0664979 + 0.248174i) q^{37} +(2.11463 - 0.566614i) q^{38} +(-2.95680 - 1.70711i) q^{39} +8.98026i q^{41} +(-7.51616 + 1.62737i) q^{42} +(0.474569 - 0.474569i) q^{43} +(3.17930 - 1.83557i) q^{44} +(2.35282 - 4.07520i) q^{46} +(-6.18205 - 1.65648i) q^{47} +(2.05532 + 2.05532i) q^{48} +(-6.37308 + 2.89549i) q^{49} +(1.14571 + 1.98443i) q^{51} +(0.304013 + 1.13459i) q^{52} +(-2.04824 - 7.64413i) q^{53} +(-3.55879 - 6.16400i) q^{54} +(2.22435 + 1.43257i) q^{56} +(4.49957 + 4.49957i) q^{57} +(2.53301 + 0.678717i) q^{58} +(5.35616 - 9.27713i) q^{59} +(1.72539 - 0.996157i) q^{61} +(0.0293654 - 0.0293654i) q^{62} +(-9.68662 - 10.6765i) q^{63} -1.00000i q^{64} +(9.24117 + 5.33539i) q^{66} +(-6.39671 + 1.71399i) q^{67} +(0.204036 - 0.761471i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(-1.41023 + 5.26305i) q^{72} +(-9.52910 + 2.55331i) q^{73} +(0.222506 + 0.128464i) q^{74} -2.18923i q^{76} +(9.24884 + 2.96647i) q^{77} +(-2.41421 + 2.41421i) q^{78} +(-11.6145 + 6.70563i) q^{79} +(2.17114 - 3.76053i) q^{81} +(8.67427 + 2.32426i) q^{82} +(9.73033 + 9.73033i) q^{83} +(-0.373402 + 7.68124i) q^{84} +(-0.335571 - 0.581226i) q^{86} +(1.97280 + 7.36260i) q^{87} +(-0.950161 - 3.54605i) q^{88} +(0.715130 + 1.23864i) q^{89} +(-1.68272 + 2.61276i) q^{91} +(-3.32739 - 3.32739i) q^{92} +(0.116597 + 0.0312422i) q^{93} +(-3.20007 + 5.54268i) q^{94} +(2.51725 - 1.45333i) q^{96} +(3.16693 - 3.16693i) q^{97} +(1.14736 + 6.90533i) q^{98} +20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more